LMFDB - Embedded newform 2020.1.cd.a.1227.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2020,1,Mod(7,2020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2020, base_ring=CyclotomicField(100))

chi = DirichletCharacter(H, H._module([50, 25, 9]))

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

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

chi := DirichletCharacter("2020.7");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2020 = 2^{2} \cdot 5 \cdot 101 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2020.cd (of order $100$, degree $40$, 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:	$1.00811132552$
Analytic rank:	$0$
Dimension:	$40$
Coefficient field:	$\Q(\zeta_{100})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{30} + x^{20} - x^{10} + 1 $ x^40 - x^30 + x^20 - x^10 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{100}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{100} - \cdots)$

Embedding invariants

Embedding label			1227.1
Root			$-0.998027 + 0.0627905i$ of defining polynomial
Character	$\chi$	$=$	2020.1227
Dual form			2020.1.cd.a.1643.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.844328 - 0.535827i) q^{2} +(0.425779 + 0.904827i) q^{4} +(0.248690 - 0.968583i) q^{5} +(0.125333 - 0.992115i) q^{8} +(0.876307 - 0.481754i) q^{9} +O(q^{10})$	\(q+(-0.844328 - 0.535827i) q^{2} +(0.425779 + 0.904827i) q^{4} +(0.248690 - 0.968583i) q^{5} +(0.125333 - 0.992115i) q^{8} +(0.876307 - 0.481754i) q^{9} +(-0.728969 + 0.684547i) q^{10} +(-1.57990 - 0.683684i) q^{13} +(-0.637424 + 0.770513i) q^{16} +(-1.76007 - 0.896802i) q^{17} +(-0.998027 - 0.0627905i) q^{18} +(0.982287 - 0.187381i) q^{20} +(-0.876307 - 0.481754i) q^{25} +(0.967618 + 1.42381i) q^{26} +(-1.63545 - 0.707723i) q^{29} +(0.951057 - 0.309017i) q^{32} +(1.00555 + 1.70029i) q^{34} +(0.809017 + 0.587785i) q^{36} +(0.957895 + 1.61971i) q^{37} +(-0.929776 - 0.368125i) q^{40} +(1.77410 - 0.903951i) q^{41} +(-0.248690 - 0.968583i) q^{45} +(-0.728969 - 0.684547i) q^{49} +(0.481754 + 0.876307i) q^{50} +(-0.0540731 - 1.72063i) q^{52} +(0.666178 + 0.313480i) q^{53} +(1.00164 + 1.47387i) q^{58} +(-0.415230 + 1.15334i) q^{61} +(-0.968583 - 0.248690i) q^{64} +(-1.05511 + 1.36024i) q^{65} +(0.0620481 - 1.97440i) q^{68} +(-0.368125 - 0.929776i) q^{72} +(0.0235315 + 0.374023i) q^{73} +(0.0591076 - 1.88083i) q^{74} +(0.587785 + 0.809017i) q^{80} +(0.535827 - 0.844328i) q^{81} +(-1.98229 - 0.187381i) q^{82} +(-1.30634 + 1.48175i) q^{85} +(-0.555506 - 0.0525108i) q^{89} +(-0.309017 + 0.951057i) q^{90} +(0.621757 - 1.72700i) q^{97} +(0.248690 + 0.968583i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 10 q^{17} + 10 q^{36} + 10 q^{74} - 40 q^{82} + 10 q^{90}+O(q^{100}) $ 40 * q - 10 * q^17 + 10 * q^36 + 10 * q^74 - 40 * q^82 + 10 * q^90

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2020\mathbb{Z}\right)^\times$.

$n$	$1011$	$1617$	$1921$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{93}{100}\right)$

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 $

$2$	−0.844328	−	0.535827i	−0.844328	−	0.535827i
$2$	−0.844328	−	0.535827i	−0.844328	−	0.535827i
$3$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$3$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$4$	0.425779	+	0.904827i	0.425779	+	0.904827i
$5$	0.248690	−	0.968583i	0.248690	−	0.968583i
$5$	0.248690	−	0.968583i	0.248690	−	0.968583i
$6$		0			0
$7$		0			0		0.368125	−	0.929776i	$-0.380000\pi$
$7$		0			0		−0.368125	+	0.929776i	$0.620000\pi$
$8$	0.125333	−	0.992115i	0.125333	−	0.992115i
$9$	0.876307	−	0.481754i	0.876307	−	0.481754i
$10$	−0.728969	+	0.684547i	−0.728969	+	0.684547i
$11$		0			0		−0.960294	−	0.278991i	$-0.910000\pi$
$11$		0			0		0.960294	+	0.278991i	$0.0900000\pi$
$12$		0			0
$13$	−1.57990	−	0.683684i	−1.57990	−	0.683684i	−0.587785	−	0.809017i	$-0.700000\pi$
$13$	−1.57990	−	0.683684i	−1.57990	−	0.683684i	−0.992115	+	0.125333i	$0.960000\pi$
$14$		0			0
$15$		0			0
$16$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$17$	−1.76007	−	0.896802i	−1.76007	−	0.896802i	−0.951057	−	0.309017i	$-0.900000\pi$
$17$	−1.76007	−	0.896802i	−1.76007	−	0.896802i	−0.809017	−	0.587785i	$-0.800000\pi$
$18$	−0.998027	−	0.0627905i	−0.998027	−	0.0627905i
$19$		0			0		0.770513	−	0.637424i	$-0.220000\pi$
$19$		0			0		−0.770513	+	0.637424i	$0.780000\pi$
$20$	0.982287	−	0.187381i	0.982287	−	0.187381i
$21$		0			0
$22$		0			0
$23$		0			0		0.661312	−	0.750111i	$-0.270000\pi$
$23$		0			0		−0.661312	+	0.750111i	$0.730000\pi$
$24$		0			0
$25$	−0.876307	−	0.481754i	−0.876307	−	0.481754i
$26$	0.967618	+	1.42381i	0.967618	+	1.42381i
$27$		0			0
$28$		0			0
$29$	−1.63545	−	0.707723i	−1.63545	−	0.707723i	−0.637424	−	0.770513i	$-0.720000\pi$
$29$	−1.63545	−	0.707723i	−1.63545	−	0.707723i	−0.998027	+	0.0627905i	$0.980000\pi$
$30$		0			0
$31$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$31$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$32$	0.951057	−	0.309017i	0.951057	−	0.309017i
$33$		0			0
$34$	1.00555	+	1.70029i	1.00555	+	1.70029i
$35$		0			0
$36$	0.809017	+	0.587785i	0.809017	+	0.587785i
$37$	0.957895	+	1.61971i	0.957895	+	1.61971i	0.770513	+	0.637424i	$0.220000\pi$
$37$	0.957895	+	1.61971i	0.957895	+	1.61971i	0.187381	+	0.982287i	$0.440000\pi$
$38$		0			0
$39$		0			0
$40$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$41$	1.77410	−	0.903951i	1.77410	−	0.903951i	0.844328	−	0.535827i	$-0.180000\pi$
$41$	1.77410	−	0.903951i	1.77410	−	0.903951i	0.929776	−	0.368125i	$-0.120000\pi$
$42$		0			0
$43$		0			0		0.827081	−	0.562083i	$-0.190000\pi$
$43$		0			0		−0.827081	+	0.562083i	$0.810000\pi$
$44$		0			0
$45$	−0.248690	−	0.968583i	−0.248690	−	0.968583i
$46$		0			0
$47$		0			0		−0.827081	−	0.562083i	$-0.810000\pi$
$47$		0			0		0.827081	+	0.562083i	$0.190000\pi$
$48$		0			0
$49$	−0.728969	−	0.684547i	−0.728969	−	0.684547i
$50$	0.481754	+	0.876307i	0.481754	+	0.876307i
$51$		0			0
$52$	−0.0540731	−	1.72063i	−0.0540731	−	1.72063i
$53$	0.666178	+	0.313480i	0.666178	+	0.313480i	0.728969	−	0.684547i	$-0.240000\pi$
$53$	0.666178	+	0.313480i	0.666178	+	0.313480i	−0.0627905	+	0.998027i	$0.520000\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	1.00164	+	1.47387i	1.00164	+	1.47387i
$59$		0			0		−0.0941083	−	0.995562i	$-0.530000\pi$
$59$		0			0		0.0941083	+	0.995562i	$0.470000\pi$
$60$		0			0
$61$	−0.415230	+	1.15334i	−0.415230	+	1.15334i	0.535827	+	0.844328i	$0.320000\pi$
$61$	−0.415230	+	1.15334i	−0.415230	+	1.15334i	−0.951057	+	0.309017i	$0.900000\pi$
$62$		0			0
$63$		0			0
$64$	−0.968583	−	0.248690i	−0.968583	−	0.248690i
$65$	−1.05511	+	1.36024i	−1.05511	+	1.36024i
$66$		0			0
$67$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$67$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$68$	0.0620481	−	1.97440i	0.0620481	−	1.97440i
$69$		0			0
$70$		0			0
$71$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$71$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$72$	−0.368125	−	0.929776i	−0.368125	−	0.929776i
$73$	0.0235315	+	0.374023i	0.0235315	+	0.374023i	0.992115	+	0.125333i	$0.0400000\pi$
$73$	0.0235315	+	0.374023i	0.0235315	+	0.374023i	−0.968583	+	0.248690i	$0.920000\pi$
$74$	0.0591076	−	1.88083i	0.0591076	−	1.88083i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.998027	−	0.0627905i	$-0.980000\pi$
$79$		0			0		0.998027	+	0.0627905i	$0.0200000\pi$
$80$	0.587785	+	0.809017i	0.587785	+	0.809017i
$81$	0.535827	−	0.844328i	0.535827	−	0.844328i
$82$	−1.98229	−	0.187381i	−1.98229	−	0.187381i
$83$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$83$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$84$		0			0
$85$	−1.30634	+	1.48175i	−1.30634	+	1.48175i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.555506	−	0.0525108i	−0.555506	−	0.0525108i	−0.187381	−	0.982287i	$-0.560000\pi$
$89$	−0.555506	−	0.0525108i	−0.555506	−	0.0525108i	−0.368125	+	0.929776i	$0.620000\pi$
$90$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.621757	−	1.72700i	0.621757	−	1.72700i	−0.0627905	−	0.998027i	$-0.520000\pi$
$97$	0.621757	−	1.72700i	0.621757	−	1.72700i	0.684547	−	0.728969i	$-0.260000\pi$
$98$	0.248690	+	0.968583i	0.248690	+	0.968583i
$99$		0			0
$100$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$101$	0.904827	−	0.425779i	0.904827	−	0.425779i
$101$	0.904827	−	0.425779i	0.904827	−	0.425779i
$102$		0			0
$103$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$103$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$104$	−0.876307	+	1.48175i	−0.876307	+	1.48175i
$105$		0			0
$106$	−0.394502	−	0.621636i	−0.394502	−	0.621636i
$107$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$107$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$108$		0			0
$109$	−1.19629	−	1.54225i	−1.19629	−	1.54225i	−0.770513	−	0.637424i	$-0.780000\pi$
$109$	−1.19629	−	1.54225i	−1.19629	−	1.54225i	−0.425779	−	0.904827i	$-0.640000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.30113	−	1.07639i	1.30113	−	1.07639i	0.309017	−	0.951057i	$-0.400000\pi$
$113$	1.30113	−	1.07639i	1.30113	−	1.07639i	0.992115	−	0.125333i	$-0.0400000\pi$
$114$		0			0
$115$		0			0
$116$	−0.0559744	−	1.78113i	−0.0559744	−	1.78113i
$117$	−1.71384	+	0.162006i	−1.71384	+	0.162006i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.844328	+	0.535827i	0.844328	+	0.535827i
$122$	0.968583	−	0.751310i	0.968583	−	0.751310i
$123$		0			0
$124$		0			0
$125$	−0.684547	+	0.728969i	−0.684547	+	0.728969i
$126$		0			0
$127$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$127$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$128$	0.684547	+	0.728969i	0.684547	+	0.728969i
$129$		0			0
$130$	1.61971	−	0.583132i	1.61971	−	0.583132i
$131$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$131$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−1.11033	+	1.63380i	−1.11033	+	1.63380i
$137$	−0.258768	−	1.63380i	−0.258768	−	1.63380i	−0.684547	−	0.728969i	$-0.740000\pi$
$137$	−0.258768	−	1.63380i	−0.258768	−	1.63380i	0.425779	−	0.904827i	$-0.360000\pi$
$138$		0			0
$139$		0			0		0.612907	−	0.790155i	$-0.290000\pi$
$139$		0			0		−0.612907	+	0.790155i	$0.710000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$145$	−1.09221	+	1.40807i	−1.09221	+	1.40807i
$146$	0.180543	−	0.328407i	0.180543	−	0.328407i
$147$		0			0
$148$	−1.05771	+	1.55637i	−1.05771	+	1.55637i
$149$	0.380798	+	1.05771i	0.380798	+	1.05771i	0.968583	+	0.248690i	$0.0800000\pi$
$149$	0.380798	+	1.05771i	0.380798	+	1.05771i	−0.587785	+	0.809017i	$0.700000\pi$
$150$		0			0
$151$		0			0		0.218143	−	0.975917i	$-0.430000\pi$
$151$		0			0		−0.218143	+	0.975917i	$0.570000\pi$
$152$		0			0
$153$	−1.97440	+	0.0620481i	−1.97440	+	0.0620481i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.121720	+	0.418963i	0.121720	+	0.418963i	0.998027	−	0.0627905i	$-0.0200000\pi$
$157$	0.121720	+	0.418963i	0.121720	+	0.418963i	−0.876307	+	0.481754i	$0.840000\pi$
$158$		0			0
$159$		0			0
$160$	−0.0627905	−	0.998027i	−0.0627905	−	0.998027i
$161$		0			0
$162$	−0.904827	+	0.425779i	−0.904827	+	0.425779i
$163$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$163$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$164$	1.57330	+	1.22037i	1.57330	+	1.22037i
$165$		0			0
$166$		0			0
$167$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$167$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$168$		0			0
$169$	1.34411	+	1.43134i	1.34411	+	1.43134i
$170$	1.89694	−	0.551113i	1.89694	−	0.551113i
$171$		0			0
$172$		0			0
$173$	0.791759	−	0.313480i	0.791759	−	0.313480i	0.0627905	−	0.998027i	$-0.480000\pi$
$173$	0.791759	−	0.313480i	0.791759	−	0.313480i	0.728969	+	0.684547i	$0.240000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.440892	+	0.341991i	0.440892	+	0.341991i
$179$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$179$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$180$	0.770513	−	0.637424i	0.770513	−	0.637424i
$181$	−0.248690	−	0.0314168i	−0.248690	−	0.0314168i		−	1.00000i	$-0.5\pi$
$181$	−0.248690	−	0.0314168i	−0.248690	−	0.0314168i	−0.248690	+	0.968583i	$0.580000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.80704	−	0.524995i	1.80704	−	0.524995i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.278991	−	0.960294i	$-0.410000\pi$
$191$		0			0		−0.278991	+	0.960294i	$0.590000\pi$
$192$		0			0
$193$	−0.0525108	+	0.180743i	−0.0525108	+	0.180743i	−0.982287	−	0.187381i	$-0.940000\pi$
$193$	−0.0525108	+	0.180743i	−0.0525108	+	0.180743i	0.929776	+	0.368125i	$0.120000\pi$
$194$	−1.45034	+	1.12500i	−1.45034	+	1.12500i
$195$		0			0
$196$	0.309017	−	0.951057i	0.309017	−	0.951057i
$197$	0.886114	+	0.198070i	0.886114	+	0.198070i	0.637424	−	0.770513i	$-0.280000\pi$
$197$	0.886114	+	0.198070i	0.886114	+	0.198070i	0.248690	+	0.968583i	$0.420000\pi$
$198$		0			0
$199$		0			0		−0.860742	−	0.509041i	$-0.830000\pi$
$199$		0			0		0.860742	+	0.509041i	$0.170000\pi$
$200$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$201$		0			0
$202$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$203$		0			0
$204$		0			0
$205$	−0.434350	−	1.94317i	−0.434350	−	1.94317i
$206$		0			0
$207$		0			0
$208$	1.53385	−	0.781537i	1.53385	−	0.781537i
$209$		0			0
$210$		0			0
$211$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$211$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$212$			0.736249i			0.736249i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.183684	+	1.94317i	0.183684	+	1.94317i
$219$		0			0
$220$		0			0
$221$	2.16761	+	2.62019i	2.16761	+	2.62019i
$222$		0			0
$223$		0			0		−0.612907	−	0.790155i	$-0.710000\pi$
$223$		0			0		0.612907	+	0.790155i	$0.290000\pi$
$224$		0			0
$225$	−1.00000			−1.00000
$226$	−1.67534	+	0.211645i	−1.67534	+	0.211645i
$227$		0			0		0.940881	−	0.338738i	$-0.110000\pi$
$227$		0			0		−0.940881	+	0.338738i	$0.890000\pi$
$228$		0			0
$229$	−0.793904	−	0.0249494i	−0.793904	−	0.0249494i	−0.368125	−	0.929776i	$-0.620000\pi$
$229$	−0.793904	−	0.0249494i	−0.793904	−	0.0249494i	−0.425779	+	0.904827i	$0.640000\pi$
$230$		0			0
$231$		0			0
$232$	−0.907118	+	1.53385i	−0.907118	+	1.53385i
$233$	−1.45034	+	0.627617i	−1.45034	+	0.627617i	−0.968583	−	0.248690i	$-0.920000\pi$
$233$	−1.45034	+	0.627617i	−1.45034	+	0.627617i	−0.481754	+	0.876307i	$0.660000\pi$
$234$	1.53385	+	0.781537i	1.53385	+	0.781537i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$239$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$240$		0			0
$241$	0.234686	−	1.48175i	0.234686	−	1.48175i	−0.535827	−	0.844328i	$-0.680000\pi$
$241$	0.234686	−	1.48175i	0.234686	−	1.48175i	0.770513	−	0.637424i	$-0.220000\pi$
$242$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$243$		0			0
$244$	−1.22037	+	0.115359i	−1.22037	+	0.115359i
$245$	−0.844328	+	0.535827i	−0.844328	+	0.535827i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.968583	−	0.248690i	0.968583	−	0.248690i
$251$		0			0		0.684547	−	0.728969i	$-0.260000\pi$
$251$		0			0		−0.684547	+	0.728969i	$0.740000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$257$	0.955910	−	1.73879i	0.955910	−	1.73879i	0.368125	−	0.929776i	$-0.380000\pi$
$257$	0.955910	−	1.73879i	0.955910	−	1.73879i	0.587785	−	0.809017i	$-0.300000\pi$
$258$		0			0
$259$		0			0
$260$	−1.68003	−	0.375530i	−1.68003	−	0.375530i
$261$	−1.77410	+	0.167702i	−1.77410	+	0.167702i
$262$		0			0
$263$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$263$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$264$		0			0
$265$	0.469303	−	0.567290i	0.469303	−	0.567290i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.13844	−	0.673270i	1.13844	−	0.673270i	0.187381	−	0.982287i	$-0.440000\pi$
$269$	1.13844	−	0.673270i	1.13844	−	0.673270i	0.951057	+	0.309017i	$0.100000\pi$
$270$		0			0
$271$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$271$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$272$	1.81291	−	0.784517i	1.81291	−	0.784517i
$273$		0			0
$274$	−0.656947	+	1.51811i	−0.656947	+	1.51811i
$275$		0			0
$276$		0			0
$277$	1.25227	+	0.238883i	1.25227	+	0.238883i	0.770513	−	0.637424i	$-0.220000\pi$
$277$	1.25227	+	0.238883i	1.25227	+	0.238883i	0.481754	+	0.876307i	$0.340000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.113629	+	1.80608i	−0.113629	+	1.80608i	0.368125	+	0.929776i	$0.380000\pi$
$281$	−0.113629	+	1.80608i	−0.113629	+	1.80608i	−0.481754	+	0.876307i	$0.660000\pi$
$282$		0			0
$283$		0			0		−0.218143	−	0.975917i	$-0.570000\pi$
$283$		0			0		0.218143	+	0.975917i	$0.430000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.684547	−	0.728969i	0.684547	−	0.728969i
$289$	1.70582	+	2.34786i	1.70582	+	2.34786i
$290$	1.67666	−	0.603635i	1.67666	−	0.603635i
$291$		0			0
$292$	−0.328407	+	0.180543i	−0.328407	+	0.180543i
$293$		−	1.75261i		−	1.75261i	−0.481754	−	0.876307i	$-0.660000\pi$
$293$		−	1.75261i		−	1.75261i	0.481754	−	0.876307i	$-0.340000\pi$
$294$		0			0
$295$		0			0
$296$	1.72700	−	0.747338i	1.72700	−	0.747338i
$297$		0			0
$298$	0.245229	−	1.09709i	0.245229	−	1.09709i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.01385	+	0.689010i	1.01385	+	0.689010i
$306$	1.70029	+	1.00555i	1.70029	+	1.00555i
$307$		0			0		−0.940881	−	0.338738i	$-0.890000\pi$
$307$		0			0		0.940881	+	0.338738i	$0.110000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.790155	−	0.612907i	$-0.210000\pi$
$311$		0			0		−0.790155	+	0.612907i	$0.790000\pi$
$312$		0			0
$313$	1.17557			1.17557			0.587785	−	0.809017i	$-0.300000\pi$
$313$	1.17557			1.17557			0.587785	+	0.809017i	$0.300000\pi$
$314$	0.121720	−	0.418963i	0.121720	−	0.418963i
$315$		0			0
$316$		0			0
$317$	−0.300446	+	1.89694i	−0.300446	+	1.89694i	0.125333	+	0.992115i	$0.460000\pi$
$317$	−0.300446	+	1.89694i	−0.300446	+	1.89694i	−0.425779	+	0.904827i	$0.640000\pi$
$318$		0			0
$319$		0			0
$320$	−0.481754	+	0.876307i	−0.481754	+	0.876307i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.992115	+	0.125333i	0.992115	+	0.125333i
$325$	1.05511	+	1.36024i	1.05511	+	1.36024i
$326$		0			0
$327$		0			0
$328$	−0.674469	−	1.87341i	−0.674469	−	1.87341i
$329$		0			0
$330$		0			0
$331$		0			0		−0.750111	−	0.661312i	$-0.770000\pi$
$331$		0			0		0.750111	+	0.661312i	$0.230000\pi$
$332$		0			0
$333$	1.61971	+	0.957895i	1.61971	+	0.957895i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.90285	+	0.488570i	1.90285	+	0.488570i	0.998027	+	0.0627905i	$0.0200000\pi$
$337$	1.90285	+	0.488570i	1.90285	+	0.488570i	0.904827	+	0.425779i	$0.140000\pi$
$338$	−0.367925	−	1.92873i	−0.367925	−	1.92873i
$339$		0			0
$340$	−1.89694	−	0.551113i	−1.89694	−	0.551113i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.836475	−	0.159566i	−0.836475	−	0.159566i
$347$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$347$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$348$		0			0
$349$	−0.189010	−	0.650576i	−0.189010	−	0.650576i	−0.998027	−	0.0627905i	$-0.980000\pi$
$349$	−0.189010	−	0.650576i	−0.189010	−	0.650576i	0.809017	−	0.587785i	$-0.200000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.331159	+	0.521823i	0.331159	+	0.521823i	0.968583	−	0.248690i	$-0.0800000\pi$
$353$	0.331159	+	0.521823i	0.331159	+	0.521823i	−0.637424	+	0.770513i	$0.720000\pi$
$354$		0			0
$355$		0			0
$356$	−0.189010	−	0.524995i	−0.189010	−	0.524995i
$357$		0			0
$358$		0			0
$359$		0			0		0.481754	−	0.876307i	$-0.340000\pi$
$359$		0			0		−0.481754	+	0.876307i	$0.660000\pi$
$360$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$361$	0.187381	−	0.982287i	0.187381	−	0.982287i
$362$	0.193142	+	0.159781i	0.193142	+	0.159781i
$363$		0			0
$364$		0			0
$365$	0.368125	+	0.0702235i	0.368125	+	0.0702235i
$366$		0			0
$367$		0			0		0.860742	−	0.509041i	$-0.170000\pi$
$367$		0			0		−0.860742	+	0.509041i	$0.830000\pi$
$368$		0			0
$369$	1.11918	−	1.64682i	1.11918	−	1.64682i
$370$	−1.80704	−	0.524995i	−1.80704	−	0.524995i
$371$		0			0
$372$		0			0
$373$	0.269058	+	0.621757i	0.269058	+	0.621757i	0.998027	−	0.0627905i	$-0.0200000\pi$
$373$	0.269058	+	0.621757i	0.269058	+	0.621757i	−0.728969	+	0.684547i	$0.760000\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.09999	+	2.23626i	2.09999	+	2.23626i
$378$		0			0
$379$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$379$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.790155	−	0.612907i	$-0.210000\pi$
$383$		0			0		−0.790155	+	0.612907i	$0.790000\pi$
$384$		0			0
$385$		0			0
$386$	0.141183	−	0.124470i	0.141183	−	0.124470i
$387$		0			0
$388$	1.82736	−	0.172737i	1.82736	−	0.172737i
$389$	−0.00982745	−	0.312715i	−0.00982745	−	0.312715i	−0.992115	−	0.125333i	$-0.960000\pi$
$389$	−0.00982745	−	0.312715i	−0.00982745	−	0.312715i	0.982287	−	0.187381i	$-0.0600000\pi$
$390$		0			0
$391$		0			0
$392$	−0.770513	+	0.637424i	−0.770513	+	0.637424i
$393$		0			0
$394$	−0.642040	−	0.642040i	−0.642040	−	0.642040i
$395$		0			0
$396$		0			0
$397$	−0.462452	−	0.183098i	−0.462452	−	0.183098i	0.125333	−	0.992115i	$-0.460000\pi$
$397$	−0.462452	−	0.183098i	−0.462452	−	0.183098i	−0.587785	+	0.809017i	$0.700000\pi$
$398$		0			0
$399$		0			0
$400$	0.929776	−	0.368125i	0.929776	−	0.368125i
$401$	−0.518246	+	0.876307i	−0.518246	+	0.876307i	0.481754	+	0.876307i	$0.340000\pi$
$401$	−0.518246	+	0.876307i	−0.518246	+	0.876307i	−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	0.770513	+	0.637424i	0.770513	+	0.637424i
$405$	−0.684547	−	0.728969i	−0.684547	−	0.728969i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.904827	−	0.574221i	0.904827	−	0.574221i		−	1.00000i	$-0.5\pi$
$409$	0.904827	−	0.574221i	0.904827	−	0.574221i	0.904827	+	0.425779i	$0.140000\pi$
$410$	−0.674469	+	1.87341i	−0.674469	+	1.87341i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−1.71384	−	0.162006i	−1.71384	−	0.162006i
$417$		0			0
$418$		0			0
$419$		0			0		0.999507	−	0.0314108i	$-0.0100000\pi$
$419$		0			0		−0.999507	+	0.0314108i	$0.990000\pi$
$420$		0			0
$421$	−0.119435	+	0.0388067i	−0.119435	+	0.0388067i	−0.368125	−	0.929776i	$-0.620000\pi$
$421$	−0.119435	+	0.0388067i	−0.119435	+	0.0388067i	0.248690	+	0.968583i	$0.420000\pi$
$422$		0			0
$423$		0			0
$424$	0.394502	−	0.621636i	0.394502	−	0.621636i
$425$	1.11033	+	1.63380i	1.11033	+	1.63380i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.0314108	−	0.999507i	$-0.490000\pi$
$431$		0			0		−0.0314108	+	0.999507i	$0.510000\pi$
$432$		0			0
$433$	0.0462295	+	0.116762i	0.0462295	+	0.116762i	0.951057	−	0.309017i	$-0.100000\pi$
$433$	0.0462295	+	0.116762i	0.0462295	+	0.116762i	−0.904827	+	0.425779i	$0.860000\pi$
$434$		0			0
$435$		0			0
$436$	0.886114	−	1.73910i	0.886114	−	1.73910i
$437$		0			0
$438$		0			0
$439$		0			0		−0.827081	−	0.562083i	$-0.810000\pi$
$439$		0			0		0.827081	+	0.562083i	$0.190000\pi$
$440$		0			0
$441$	−0.968583	−	0.248690i	−0.968583	−	0.248690i
$442$	−0.426206	−	3.37376i	−0.426206	−	3.37376i
$443$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$443$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$444$		0			0
$445$	−0.189010	+	0.524995i	−0.189010	+	0.524995i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.74915	−	0.961606i	−1.74915	−	0.961606i	−0.904827	−	0.425779i	$-0.860000\pi$
$449$	−1.74915	−	0.961606i	−1.74915	−	0.961606i	−0.844328	−	0.535827i	$-0.820000\pi$
$450$	0.844328	+	0.535827i	0.844328	+	0.535827i
$451$		0			0
$452$	1.52794	+	0.718995i	1.52794	+	0.718995i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.824805	+	1.75280i	−0.824805	+	1.75280i	−0.187381	+	0.982287i	$0.560000\pi$
$457$	−0.824805	+	1.75280i	−0.824805	+	1.75280i	−0.637424	+	0.770513i	$0.720000\pi$
$458$	0.656947	+	0.446460i	0.656947	+	0.446460i
$459$		0			0
$460$		0			0
$461$	−0.300446	−	1.89694i	−0.300446	−	1.89694i	−0.425779	−	0.904827i	$-0.640000\pi$
$461$	−0.300446	−	1.89694i	−0.300446	−	1.89694i	0.125333	−	0.992115i	$-0.460000\pi$
$462$		0			0
$463$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$463$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$464$	1.58779	−	0.809017i	1.58779	−	0.809017i
$465$		0			0
$466$	1.56085	+	0.247215i	1.56085	+	0.247215i
$467$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$467$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$468$	−0.876307	−	1.48175i	−0.876307	−	1.48175i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.734796	−	0.0462295i	0.734796	−	0.0462295i
$478$		0			0
$479$		0			0		−0.562083	−	0.827081i	$-0.690000\pi$
$479$		0			0		0.562083	+	0.827081i	$0.310000\pi$
$480$		0			0
$481$	−0.406007	−	3.21388i	−0.406007	−	3.21388i
$482$	−0.992115	+	1.12533i	−0.992115	+	1.12533i
$483$		0			0
$484$	−0.125333	+	0.992115i	−0.125333	+	0.992115i
$485$	−1.51811	−	1.03171i	−1.51811	−	1.03171i
$486$		0			0
$487$		0			0		−0.998027	−	0.0627905i	$-0.980000\pi$
$487$		0			0		0.998027	+	0.0627905i	$0.0200000\pi$
$488$	1.09221	+	0.556508i	1.09221	+	0.556508i
$489$		0			0
$490$	1.00000			1.00000
$491$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$491$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$492$		0			0
$493$	2.24383	+	2.71232i	2.24383	+	2.71232i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$499$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$500$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$501$		0			0
$502$		0			0
$503$		0			0		−0.844328	−	0.535827i	$-0.820000\pi$
$503$		0			0		0.844328	+	0.535827i	$0.180000\pi$
$504$		0			0
$505$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.263146	+	0.559214i	0.263146	+	0.559214i	0.992115	−	0.125333i	$-0.0400000\pi$
$509$	0.263146	+	0.559214i	0.263146	+	0.559214i	−0.728969	+	0.684547i	$0.760000\pi$
$510$		0			0
$511$		0			0
$512$	−0.368125	+	0.929776i	−0.368125	+	0.929776i
$513$		0			0
$514$	−1.73879	+	0.955910i	−1.73879	+	0.955910i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	1.21727	+	1.21727i	1.21727	+	1.21727i
$521$	−1.26480	+	1.52888i	−1.26480	+	1.52888i	−0.535827	+	0.844328i	$0.680000\pi$
$521$	−1.26480	+	1.52888i	−1.26480	+	1.52888i	−0.728969	+	0.684547i	$0.760000\pi$
$522$	1.58779	+	0.809017i	1.58779	+	0.809017i
$523$		0			0		−0.998027	−	0.0627905i	$-0.980000\pi$
$523$		0			0		0.998027	+	0.0627905i	$0.0200000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.125333	−	0.992115i	−0.125333	−	0.992115i
$530$	−0.700215	+	0.227513i	−0.700215	+	0.227513i
$531$		0			0
$532$		0			0
$533$	−3.42092	+	0.215226i	−3.42092	+	0.215226i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.32197	−	0.0415446i	−1.32197	−	0.0415446i
$539$		0			0
$540$		0			0
$541$	1.41789	+	1.03016i	1.41789	+	1.03016i	0.992115	+	0.125333i	$0.0400000\pi$
$541$	1.41789	+	1.03016i	1.41789	+	1.03016i	0.425779	+	0.904827i	$0.360000\pi$
$542$		0			0
$543$		0			0
$544$	−1.95106	−	0.309017i	−1.95106	−	0.309017i
$545$	−1.79130	+	0.775167i	−1.79130	+	0.775167i
$546$		0			0
$547$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$547$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$548$	1.36812	−	0.929776i	1.36812	−	0.929776i
$549$	0.191760	+	1.21072i	0.191760	+	1.21072i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−0.929324	−	0.872693i	−0.929324	−	0.872693i
$555$		0			0
$556$		0			0
$557$	−0.0249494	−	0.793904i	−0.0249494	−	0.793904i	−0.929776	−	0.368125i	$-0.880000\pi$
$557$	−0.0249494	−	0.793904i	−0.0249494	−	0.793904i	0.904827	−	0.425779i	$-0.140000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.06369	−	1.46404i	1.06369	−	1.46404i
$563$		0			0		−0.562083	−	0.827081i	$-0.690000\pi$
$563$		0			0		0.562083	+	0.827081i	$0.310000\pi$
$564$		0			0
$565$	−0.718995	−	1.52794i	−0.718995	−	1.52794i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.598617	+	0.153699i	0.598617	+	0.153699i	0.535827	−	0.844328i	$-0.320000\pi$
$569$	0.598617	+	0.153699i	0.598617	+	0.153699i	0.0627905	+	0.998027i	$0.480000\pi$
$570$		0			0
$571$		0			0		−0.827081	−	0.562083i	$-0.810000\pi$
$571$		0			0		0.827081	+	0.562083i	$0.190000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.968583	+	0.248690i	−0.968583	+	0.248690i
$577$	0.567290	+	1.43281i	0.567290	+	1.43281i	0.876307	+	0.481754i	$0.160000\pi$
$577$	0.567290	+	1.43281i	0.567290	+	1.43281i	−0.309017	+	0.951057i	$0.600000\pi$
$578$	−0.182225	−	2.89639i	−0.182225	−	2.89639i
$579$		0			0
$580$	−1.73910	−	0.388734i	−1.73910	−	0.388734i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.374023	+	0.0235315i	0.374023	+	0.0235315i
$585$	−0.269299	+	1.70029i	−0.269299	+	1.70029i
$586$	−0.939097	+	1.47978i	−0.939097	+	1.47978i
$587$		0			0		−0.995562	−	0.0941083i	$-0.970000\pi$
$587$		0			0		0.995562	+	0.0941083i	$0.0300000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.85859	−	0.294372i	−1.85859	−	0.294372i
$593$	−0.525277	+	1.21384i	−0.525277	+	1.21384i	0.425779	+	0.904827i	$0.360000\pi$
$593$	−0.525277	+	1.21384i	−0.525277	+	1.21384i	−0.951057	+	0.309017i	$0.900000\pi$
$594$		0			0
$595$		0			0
$596$	−0.794906	+	0.794906i	−0.794906	+	0.794906i
$597$		0			0
$598$		0			0
$599$		0			0		−0.397148	−	0.917755i	$-0.630000\pi$
$599$		0			0		0.397148	+	0.917755i	$0.370000\pi$
$600$		0			0
$601$	−1.36615	+	0.866986i	−1.36615	+	0.866986i	−0.998027	−	0.0627905i	$-0.980000\pi$
$601$	−1.36615	+	0.866986i	−1.36615	+	0.866986i	−0.368125	+	0.929776i	$0.620000\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.728969	−	0.684547i	0.728969	−	0.684547i
$606$		0			0
$607$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$607$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$608$		0			0
$609$		0			0
$610$	−0.486829	−	1.12500i	−0.486829	−	1.12500i
$611$		0			0
$612$	−0.896802	−	1.76007i	−0.896802	−	1.76007i
$613$	0.116762	+	0.0462295i	0.116762	+	0.0462295i	0.425779	−	0.904827i	$-0.360000\pi$
$613$	0.116762	+	0.0462295i	0.116762	+	0.0462295i	−0.309017	+	0.951057i	$0.600000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.895846	−	1.62954i	−0.895846	−	1.62954i	−0.770513	−	0.637424i	$-0.780000\pi$
$617$	−0.895846	−	1.62954i	−0.895846	−	1.62954i	−0.125333	−	0.992115i	$-0.540000\pi$
$618$		0			0
$619$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$619$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.535827	+	0.844328i	0.535827	+	0.844328i
$626$	−0.992567	−	0.629902i	−0.992567	−	0.629902i
$627$		0			0
$628$	−0.327263	+	0.288521i	−0.327263	+	0.288521i
$629$	−0.233404	−	3.70985i	−0.233404	−	3.70985i
$630$		0			0
$631$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$631$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$632$		0			0
$633$		0			0
$634$	1.27011	−	1.44065i	1.27011	−	1.44065i
$635$		0			0
$636$		0			0
$637$	0.683684	+	1.57990i	0.683684	+	1.57990i
$638$		0			0
$639$		0			0
$640$	0.876307	−	0.481754i	0.876307	−	0.481754i
$641$	0.888266	−	1.30704i	0.888266	−	1.30704i	−0.0627905	−	0.998027i	$-0.520000\pi$
$641$	0.888266	−	1.30704i	0.888266	−	1.30704i	0.951057	−	0.309017i	$-0.100000\pi$
$642$		0			0
$643$		0			0		0.860742	−	0.509041i	$-0.170000\pi$
$643$		0			0		−0.860742	+	0.509041i	$0.830000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$647$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$648$	−0.770513	−	0.637424i	−0.770513	−	0.637424i
$649$		0			0
$650$	−0.162006	−	1.71384i	−0.162006	−	1.71384i
$651$		0			0
$652$		0			0
$653$	0.175858	−	0.258768i	0.175858	−	0.258768i	−0.728969	−	0.684547i	$-0.760000\pi$
$653$	0.175858	−	0.258768i	0.175858	−	0.258768i	0.904827	+	0.425779i	$0.140000\pi$
$654$		0			0
$655$		0			0
$656$	−0.434350	+	1.94317i	−0.434350	+	1.94317i
$657$	0.200808	+	0.316423i	0.200808	+	0.316423i
$658$		0			0
$659$		0			0		0.940881	−	0.338738i	$-0.110000\pi$
$659$		0			0		−0.940881	+	0.338738i	$0.890000\pi$
$660$		0			0
$661$	0.0525108	+	0.180743i	0.0525108	+	0.180743i	0.982287	−	0.187381i	$-0.0600000\pi$
$661$	0.0525108	+	0.180743i	0.0525108	+	0.180743i	−0.929776	+	0.368125i	$0.880000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.854302	−	1.67666i	−0.854302	−	1.67666i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.75280	+	0.450043i	1.75280	+	0.450043i	0.982287	−	0.187381i	$-0.0600000\pi$
$673$	1.75280	+	0.450043i	1.75280	+	0.450043i	0.770513	+	0.637424i	$0.220000\pi$
$674$	−1.34484	−	1.43211i	−1.34484	−	1.43211i
$675$		0			0
$676$	−0.722815	+	1.82562i	−0.722815	+	1.82562i
$677$	−1.29130	−	0.763675i	−1.29130	−	0.763675i	−0.309017	−	0.951057i	$-0.600000\pi$
$677$	−1.29130	−	0.763675i	−1.29130	−	0.763675i	−0.982287	+	0.187381i	$0.940000\pi$
$678$		0			0
$679$		0			0
$680$	1.30634	+	1.48175i	1.30634	+	1.48175i
$681$		0			0
$682$		0			0
$683$		0			0		−0.790155	−	0.612907i	$-0.790000\pi$
$683$		0			0		0.790155	+	0.612907i	$0.210000\pi$
$684$		0			0
$685$	−1.64682	−	0.155670i	−1.64682	−	0.155670i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.838174	−	0.950722i	−0.838174	−	0.950722i
$690$		0			0
$691$		0			0		−0.770513	−	0.637424i	$-0.780000\pi$
$691$		0			0		0.770513	+	0.637424i	$0.220000\pi$
$692$	0.620759	+	0.582932i	0.620759	+	0.582932i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−3.93322			−3.93322
$698$	−0.189010	+	0.650576i	−0.189010	+	0.650576i
$699$		0			0
$700$		0			0
$701$	−0.331159	+	1.01920i	−0.331159	+	1.01920i	0.637424	+	0.770513i	$0.280000\pi$
$701$	−0.331159	+	1.01920i	−0.331159	+	1.01920i	−0.968583	+	0.248690i	$0.920000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		−	0.618034i		−	0.618034i
$707$		0			0
$708$		0			0
$709$	0.418963	+	1.87433i	0.418963	+	1.87433i	0.481754	+	0.876307i	$0.340000\pi$
$709$	0.418963	+	1.87433i	0.418963	+	1.87433i	−0.0627905	+	0.998027i	$0.520000\pi$
$710$		0			0
$711$		0			0
$712$	−0.121720	+	0.544544i	−0.121720	+	0.544544i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.0941083	−	0.995562i	$-0.470000\pi$
$719$		0			0		−0.0941083	+	0.995562i	$0.530000\pi$
$720$	0.904827	+	0.425779i	0.904827	+	0.425779i
$721$		0			0
$722$	−0.684547	+	0.728969i	−0.684547	+	0.728969i
$723$		0			0
$724$	−0.0774602	−	0.238398i	−0.0774602	−	0.238398i
$725$	1.09221	+	1.40807i	1.09221	+	1.40807i
$726$		0			0
$727$		0			0		−0.218143	−	0.975917i	$-0.570000\pi$
$727$		0			0		0.218143	+	0.975917i	$0.430000\pi$
$728$		0			0
$729$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$730$	−0.273190	−	0.256543i	−0.273190	−	0.256543i
$731$		0			0
$732$		0			0
$733$	−1.05267	−	0.200808i	−1.05267	−	0.200808i	−0.368125	−	0.929776i	$-0.620000\pi$
$733$	−1.05267	−	0.200808i	−1.05267	−	0.200808i	−0.684547	+	0.728969i	$0.740000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−1.82736	+	0.790771i	−1.82736	+	0.790771i
$739$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$739$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$740$	1.24443	+	1.41153i	1.24443	+	1.41153i
$741$		0			0
$742$		0			0
$743$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$743$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$744$		0			0
$745$	1.11918	−	0.105793i	1.11918	−	0.105793i
$746$	0.105981	−	0.669135i	0.105981	−	0.669135i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$751$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$752$		0			0
$753$		0			0
$754$	−0.574831	−	3.01337i	−0.574831	−	3.01337i
$755$		0			0
$756$		0			0
$757$	−0.813516	+	0.516273i	−0.813516	+	0.516273i	−0.876307	−	0.481754i	$-0.840000\pi$
$757$	−0.813516	+	0.516273i	−0.813516	+	0.516273i	0.0627905	+	0.998027i	$0.480000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.159566	+	0.836475i	0.159566	+	0.836475i	0.968583	+	0.248690i	$0.0800000\pi$
$761$	0.159566	+	0.836475i	0.159566	+	0.836475i	−0.809017	+	0.587785i	$0.800000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.430915	+	1.92780i	−0.430915	+	1.92780i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.142040	−	0.896802i	0.142040	−	0.896802i	−0.809017	−	0.587785i	$-0.800000\pi$
$769$	0.142040	−	0.896802i	0.142040	−	0.896802i	0.951057	−	0.309017i	$-0.100000\pi$
$770$		0			0
$771$		0			0
$772$	−0.185899	+	0.0294436i	−0.185899	+	0.0294436i
$773$	−1.92978	+	0.368125i	−1.92978	+	0.368125i	−0.929776	+	0.368125i	$0.880000\pi$
$773$	−1.92978	+	0.368125i	−1.92978	+	0.368125i	−1.00000			$1.00000\pi$
$774$		0			0
$775$		0			0
$776$	−1.63545	−	0.833304i	−1.63545	−	0.833304i
$777$		0			0
$778$	−0.159263	+	0.269299i	−0.159263	+	0.269299i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.992115	−	0.125333i	0.992115	−	0.125333i
$785$	0.436071	−	0.0137041i	0.436071	−	0.0137041i
$786$		0			0
$787$		0			0		−0.612907	−	0.790155i	$-0.710000\pi$
$787$		0			0		0.612907	+	0.790155i	$0.290000\pi$
$788$	0.198070	+	0.886114i	0.198070	+	0.886114i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.44454	−	1.53828i	1.44454	−	1.53828i
$794$	0.292352	+	0.402389i	0.292352	+	0.402389i
$795$		0			0
$796$		0			0
$797$	−0.219661	+	0.120759i	−0.219661	+	0.120759i	−0.587785	−	0.809017i	$-0.700000\pi$
$797$	−0.219661	+	0.120759i	−0.219661	+	0.120759i	0.368125	+	0.929776i	$0.380000\pi$
$798$		0			0
$799$		0			0
$800$	−0.982287	−	0.187381i	−0.982287	−	0.187381i
$801$	−0.512091	+	0.221601i	−0.512091	+	0.221601i
$802$	0.907118	−	0.462200i	0.907118	−	0.462200i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$809$			1.98423i			1.98423i	0.125333	+	0.992115i	$0.460000\pi$
$809$			1.98423i			1.98423i	−0.125333	+	0.992115i	$0.540000\pi$
$810$	0.187381	+	0.982287i	0.187381	+	0.982287i
$811$		0			0		−0.860742	−	0.509041i	$-0.830000\pi$
$811$		0			0		0.860742	+	0.509041i	$0.170000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−1.07165			−1.07165
$819$		0			0
$820$	1.57330	−	1.22037i	1.57330	−	1.22037i
$821$	−0.469303	−	1.18532i	−0.469303	−	1.18532i	−0.951057	−	0.309017i	$-0.900000\pi$
$821$	−0.469303	−	1.18532i	−0.469303	−	1.18532i	0.481754	−	0.876307i	$-0.340000\pi$
$822$		0			0
$823$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$823$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.0941083	−	0.995562i	$-0.470000\pi$
$827$		0			0		−0.0941083	+	0.995562i	$0.530000\pi$
$828$		0			0
$829$	−1.92189	−	0.242791i	−1.92189	−	0.242791i	−0.929776	−	0.368125i	$-0.880000\pi$
$829$	−1.92189	−	0.242791i	−1.92189	−	0.242791i	−0.992115	+	0.125333i	$0.960000\pi$
$830$		0			0
$831$		0			0
$832$	1.36024	+	1.05511i	1.36024	+	1.05511i
$833$	0.669135	+	1.85859i	0.669135	+	1.85859i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.368125	−	0.929776i	$-0.380000\pi$
$839$		0			0		−0.368125	+	0.929776i	$0.620000\pi$
$840$		0			0
$841$	1.48928	+	1.58592i	1.48928	+	1.58592i
$842$	0.121636	+	0.0312307i	0.121636	+	0.0312307i
$843$		0			0
$844$		0			0
$845$	1.72063	−	0.945927i	1.72063	−	0.945927i
$846$		0			0
$847$		0			0
$848$	−0.666178	+	0.313480i	−0.666178	+	0.313480i
$849$		0			0
$850$	−0.0620481	−	1.97440i	−0.0620481	−	1.97440i
$851$		0			0
$852$		0			0
$853$	0.535827	+	1.84433i	0.535827	+	1.84433i	0.535827	+	0.844328i	$0.320000\pi$
$853$	0.535827	+	1.84433i	0.535827	+	1.84433i			1.00000i	$0.500000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.12361	−	0.0353109i	1.12361	−	0.0353109i	0.535827	−	0.844328i	$-0.320000\pi$
$857$	1.12361	−	0.0353109i	1.12361	−	0.0353109i	0.587785	+	0.809017i	$0.300000\pi$
$858$		0			0
$859$		0			0		0.218143	−	0.975917i	$-0.430000\pi$
$859$		0			0		−0.218143	+	0.975917i	$0.570000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$863$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$864$		0			0
$865$	−0.106729	−	0.844844i	−0.106729	−	0.844844i
$866$	0.0235315	−	0.123357i	0.0235315	−	0.123357i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−1.68003	+	0.993564i	−1.68003	+	0.993564i
$873$	−0.287137	−	1.81291i	−0.287137	−	1.81291i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.541587	−	1.66683i	−0.541587	−	1.66683i	−0.728969	−	0.684547i	$-0.760000\pi$
$877$	−0.541587	−	1.66683i	−0.541587	−	1.66683i	0.187381	−	0.982287i	$-0.440000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.288521	+	0.327263i	−0.288521	+	0.327263i	−0.876307	−	0.481754i	$-0.840000\pi$
$881$	−0.288521	+	0.327263i	−0.288521	+	0.327263i	0.587785	+	0.809017i	$0.300000\pi$
$882$	0.684547	+	0.728969i	0.684547	+	0.728969i
$883$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$883$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$884$	−1.44790	+	3.07694i	−1.44790	+	3.07694i
$885$		0			0
$886$		0			0
$887$		0			0		0.750111	−	0.661312i	$-0.230000\pi$
$887$		0			0		−0.750111	+	0.661312i	$0.770000\pi$
$888$		0			0
$889$		0			0
$890$	0.440892	−	0.341991i	0.440892	−	0.341991i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.961606	+	1.74915i	0.961606	+	1.74915i
$899$		0			0
$900$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$901$	−0.891393	−	1.14918i	−0.891393	−	1.14918i
$902$		0			0
$903$		0			0
$904$	−0.904827	−	1.42578i	−0.904827	−	1.42578i
$905$	−0.0922765	+	0.233064i	−0.0922765	+	0.233064i
$906$		0			0
$907$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$907$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$908$		0			0
$909$	0.587785	−	0.809017i	0.587785	−	0.809017i
$910$		0			0
$911$		0			0		0.975917	−	0.218143i	$-0.0700000\pi$
$911$		0			0		−0.975917	+	0.218143i	$0.930000\pi$
$912$		0			0
$913$		0			0
$914$	1.63560	−	1.03799i	1.63560	−	1.03799i
$915$		0			0
$916$	−0.315453	−	0.728969i	−0.315453	−	0.728969i
$917$		0			0
$918$		0			0
$919$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$919$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$920$		0			0
$921$		0			0
$922$	−0.762757	+	1.76263i	−0.762757	+	1.76263i
$923$		0			0
$924$		0			0
$925$	−0.0591076	−	1.88083i	−0.0591076	−	1.88083i
$926$		0			0
$927$		0			0
$928$	−1.77410	−	0.167702i	−1.77410	−	0.167702i
$929$	−1.01920	+	1.60601i	−1.01920	+	1.60601i	−0.248690	+	0.968583i	$0.580000\pi$
$929$	−1.01920	+	1.60601i	−1.01920	+	1.60601i	−0.770513	+	0.637424i	$0.780000\pi$
$930$		0			0
$931$		0			0
$932$	−1.18541	−	1.04508i	−1.18541	−	1.04508i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.0540731	+	1.72063i	−0.0540731	+	1.72063i
$937$	0.0312307	+	0.496398i	0.0312307	+	0.496398i	0.982287	+	0.187381i	$0.0600000\pi$
$937$	0.0312307	+	0.496398i	0.0312307	+	0.496398i	−0.951057	+	0.309017i	$0.900000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.750973	−	1.47387i	0.750973	−	1.47387i	−0.125333	−	0.992115i	$-0.540000\pi$
$941$	0.750973	−	1.47387i	0.750973	−	1.47387i	0.876307	−	0.481754i	$-0.160000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.125333	−	0.992115i	$-0.540000\pi$
$947$		0			0		0.125333	+	0.992115i	$0.460000\pi$
$948$		0			0
$949$	0.218536	−	0.607007i	0.218536	−	0.607007i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.690983	−	0.951057i	0.690983	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$953$	0.690983	−	0.951057i	0.690983	−	0.951057i	1.00000			$0$
$954$	−0.645180	−	0.354691i	−0.645180	−	0.354691i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.728969	+	0.684547i	0.728969	+	0.684547i
$962$	−1.37928	+	2.93112i	−1.37928	+	2.93112i
$963$		0			0
$964$	1.44065	−	0.418549i	1.44065	−	0.418549i
$965$	0.162006	+	0.0958101i	0.162006	+	0.0958101i
$966$		0			0
$967$		0			0		0.827081	−	0.562083i	$-0.190000\pi$
$967$		0			0		−0.827081	+	0.562083i	$0.810000\pi$
$968$	0.637424	−	0.770513i	0.637424	−	0.770513i
$969$		0			0
$970$	0.728969	+	1.68455i	0.728969	+	1.68455i
$971$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$971$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.623990	−	1.05511i	−0.623990	−	1.05511i
$977$	−1.01758	−	0.0319788i	−1.01758	−	0.0319788i	−0.481754	−	0.876307i	$-0.660000\pi$
$977$	−1.01758	−	0.0319788i	−1.01758	−	0.0319788i	−0.535827	+	0.844328i	$0.680000\pi$
$978$		0			0
$979$		0			0
$980$	−0.844328	−	0.535827i	−0.844328	−	0.535827i
$981$	−1.79130	−	0.775167i	−1.79130	−	0.775167i
$982$		0			0
$983$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$983$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$984$		0			0
$985$	0.412215	−	0.809017i	0.412215	−	0.809017i
$986$	−0.441191	−	3.49239i	−0.441191	−	3.49239i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.770513	−	0.637424i	$-0.220000\pi$
$991$		0			0		−0.770513	+	0.637424i	$0.780000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.728969	+	0.315453i	0.728969	+	0.315453i	0.728969	−	0.684547i	$-0.240000\pi$
$997$	0.728969	+	0.315453i	0.728969	+	0.315453i			1.00000i	$0.5\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2020.1.cd.a.1227.1	yes	40
4.3	odd	2	CM	2020.1.cd.a.1227.1	yes	40
5.3	odd	4		2020.1.ca.a.823.1	yes	40
20.3	even	4		2020.1.ca.a.823.1	yes	40
101.27	odd	100		2020.1.ca.a.27.1	✓	40
404.27	even	100		2020.1.ca.a.27.1	✓	40
505.128	even	100	inner	2020.1.cd.a.1643.1	yes	40
2020.1643	odd	100	inner	2020.1.cd.a.1643.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2020.1.ca.a.27.1	✓	40	101.27	odd	100
2020.1.ca.a.27.1	✓	40	404.27	even	100
2020.1.ca.a.823.1	yes	40	5.3	odd	4
2020.1.ca.a.823.1	yes	40	20.3	even	4
2020.1.cd.a.1227.1	yes	40	1.1	even	1	trivial
2020.1.cd.a.1227.1	yes	40	4.3	odd	2	CM
2020.1.cd.a.1643.1	yes	40	505.128	even	100	inner
2020.1.cd.a.1643.1	yes	40	2020.1643	odd	100	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:	\( N \)	\(=\)	\( 2020 = 2^{2} \cdot 5 \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2020.cd (of order \(100\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.844328 - 0.535827i) q^{2} +(0.425779 + 0.904827i) q^{4} +(0.248690 - 0.968583i) q^{5} +(0.125333 - 0.992115i) q^{8} +(0.876307 - 0.481754i) q^{9} +O(q^{10})\)	\(q+(-0.844328 - 0.535827i) q^{2} +(0.425779 + 0.904827i) q^{4} +(0.248690 - 0.968583i) q^{5} +(0.125333 - 0.992115i) q^{8} +(0.876307 - 0.481754i) q^{9} +(-0.728969 + 0.684547i) q^{10} +(-1.57990 - 0.683684i) q^{13} +(-0.637424 + 0.770513i) q^{16} +(-1.76007 - 0.896802i) q^{17} +(-0.998027 - 0.0627905i) q^{18} +(0.982287 - 0.187381i) q^{20} +(-0.876307 - 0.481754i) q^{25} +(0.967618 + 1.42381i) q^{26} +(-1.63545 - 0.707723i) q^{29} +(0.951057 - 0.309017i) q^{32} +(1.00555 + 1.70029i) q^{34} +(0.809017 + 0.587785i) q^{36} +(0.957895 + 1.61971i) q^{37} +(-0.929776 - 0.368125i) q^{40} +(1.77410 - 0.903951i) q^{41} +(-0.248690 - 0.968583i) q^{45} +(-0.728969 - 0.684547i) q^{49} +(0.481754 + 0.876307i) q^{50} +(-0.0540731 - 1.72063i) q^{52} +(0.666178 + 0.313480i) q^{53} +(1.00164 + 1.47387i) q^{58} +(-0.415230 + 1.15334i) q^{61} +(-0.968583 - 0.248690i) q^{64} +(-1.05511 + 1.36024i) q^{65} +(0.0620481 - 1.97440i) q^{68} +(-0.368125 - 0.929776i) q^{72} +(0.0235315 + 0.374023i) q^{73} +(0.0591076 - 1.88083i) q^{74} +(0.587785 + 0.809017i) q^{80} +(0.535827 - 0.844328i) q^{81} +(-1.98229 - 0.187381i) q^{82} +(-1.30634 + 1.48175i) q^{85} +(-0.555506 - 0.0525108i) q^{89} +(-0.309017 + 0.951057i) q^{90} +(0.621757 - 1.72700i) q^{97} +(0.248690 + 0.968583i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 10 q^{17} + 10 q^{36} + 10 q^{74} - 40 q^{82} + 10 q^{90}+O(q^{100}) \) 40 * q - 10 * q^17 + 10 * q^36 + 10 * q^74 - 40 * q^82 + 10 * q^90

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