LMFDB - Embedded newform 1939.1.by.a.62.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1939,1,Mod(34,1939)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1939, base_ring=CyclotomicField(138))

chi = DirichletCharacter(H, H._module([69, 125]))

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

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

chi := DirichletCharacter("1939.34");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1939 = 7 \cdot 277 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1939.by (of order $138$, degree $44$, 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:	$0.967687059495$
Analytic rank:	$0$
Dimension:	$44$
Coefficient field:	$\Q(\zeta_{69})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{44} - x^{43} + x^{41} - x^{40} + x^{38} - x^{37} + x^{35} - x^{34} + x^{32} - x^{31} + x^{29} + \cdots + 1 $ x^44 - x^43 + x^41 - x^40 + x^38 - x^37 + x^35 - x^34 + x^32 - x^31 + x^29 - x^28 + x^26 - x^25 + x^23 - x^22 + x^21 - x^19 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{138}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{138} - \cdots)$

Embedding invariants

Embedding label			62.1
Root			$-0.877183 - 0.480157i$ of defining polynomial
Character	$\chi$	$=$	1939.62
Dual form			1939.1.by.a.1595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00676 + 1.65554i) q^{2} +(-1.26719 + 2.44556i) q^{4} +(0.113580 + 0.993529i) q^{7} +(-3.39137 + 0.231976i) q^{8} +(0.613267 + 0.789876i) q^{9} +O(q^{10})$	\(q+(1.00676 + 1.65554i) q^{2} +(-1.26719 + 2.44556i) q^{4} +(0.113580 + 0.993529i) q^{7} +(-3.39137 + 0.231976i) q^{8} +(0.613267 + 0.789876i) q^{9} +(1.89709 - 0.485249i) q^{11} +(-1.53048 + 1.18828i) q^{14} +(-2.20993 - 3.13076i) q^{16} +(-0.690261 + 1.81050i) q^{18} +(2.71326 + 2.65218i) q^{22} +(-1.50182 - 1.11217i) q^{23} +(-0.291646 - 0.956526i) q^{25} +(-2.57366 - 0.981220i) q^{28} +(0.919177 + 0.0418794i) q^{29} +(1.60395 - 3.69267i) q^{32} +(-2.70881 + 0.498860i) q^{36} +(-1.61223 - 0.835390i) q^{37} +(-0.0873260 + 0.159533i) q^{43} +(-1.21726 + 5.25435i) q^{44} +(0.329275 - 3.60600i) q^{46} +(-0.974199 + 0.225690i) q^{49} +(1.28995 - 1.44582i) q^{50} +(0.993991 + 0.303069i) q^{53} +(-0.615667 - 3.34307i) q^{56} +(0.856053 + 1.56389i) q^{58} +(-0.715110 + 0.699012i) q^{63} +(3.93168 - 0.540397i) q^{64} +(0.514134 - 1.11358i) q^{67} +(-0.337690 + 0.227030i) q^{71} +(-2.26304 - 2.53650i) q^{72} +(-0.240100 - 3.51014i) q^{74} +(0.697581 + 1.82970i) q^{77} +(0.215721 - 1.88699i) q^{79} +(-0.247808 + 0.968809i) q^{81} +(-0.352029 + 0.0160391i) q^{86} +(-6.32116 + 2.08574i) q^{88} +(4.62295 - 2.26346i) q^{92} +(-1.35442 - 1.38561i) q^{98} +(1.54671 + 1.20088i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{4} + q^{7} + q^{9}+O(q^{10}) $ 44 * q + 4 * q^4 + q^7 + q^9	$ 44 q + 4 q^{4} + q^{7} + q^{9} - 3 q^{14} - 2 q^{16} - 3 q^{18} + q^{23} - q^{25} - 2 q^{28} + 21 q^{29} - 2 q^{36} - 3 q^{43} - 23 q^{44} - 26 q^{46} + q^{49} - 3 q^{50} + 3 q^{56} - 6 q^{58} + q^{63} - 2 q^{64} + q^{67} + 2 q^{71} + 3 q^{72} + 6 q^{74} + q^{79} + q^{81} - 3 q^{86} - 2 q^{92} - 20 q^{98}+O(q^{100}) $ 44 * q + 4 * q^4 + q^7 + q^9 - 3 * q^14 - 2 * q^16 - 3 * q^18 + q^23 - q^25 - 2 * q^28 + 21 * q^29 - 2 * q^36 - 3 * q^43 - 23 * q^44 - 26 * q^46 + q^49 - 3 * q^50 + 3 * q^56 - 6 * q^58 + q^63 - 2 * q^64 + q^67 + 2 * q^71 + 3 * q^72 + 6 * q^74 + q^79 + q^81 - 3 * q^86 - 2 * q^92 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1939\mathbb{Z}\right)^\times$.

$n$	$1109$	$1667$
$\chi(n)$	$-1$	$e\left(\frac{97}{138}\right)$

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 $

$2$	1.00676	+	1.65554i	1.00676	+	1.65554i	0.715110	+	0.699012i	$0.246377\pi$
$2$	1.00676	+	1.65554i	1.00676	+	1.65554i	0.291646	+	0.956526i	$0.405797\pi$
$3$		0			0		−0.898128	−	0.439735i	$-0.855072\pi$
$3$		0			0		0.898128	+	0.439735i	$0.144928\pi$
$4$	−1.26719	+	2.44556i	−1.26719	+	2.44556i
$5$		0			0		0.595128	−	0.803631i	$-0.297101\pi$
$5$		0			0		−0.595128	+	0.803631i	$0.702899\pi$
$6$		0			0
$7$	0.113580	+	0.993529i	0.113580	+	0.993529i
$7$	0.113580	+	0.993529i	0.113580	+	0.993529i
$8$	−3.39137	+	0.231976i	−3.39137	+	0.231976i
$9$	0.613267	+	0.789876i	0.613267	+	0.789876i
$10$		0			0
$11$	1.89709	−	0.485249i	1.89709	−	0.485249i	0.898128	−	0.439735i	$-0.144928\pi$
$11$	1.89709	−	0.485249i	1.89709	−	0.485249i	0.998964	−	0.0455146i	$-0.0144928\pi$
$12$		0			0
$13$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$13$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$14$	−1.53048	+	1.18828i	−1.53048	+	1.18828i
$15$		0			0
$16$	−2.20993	−	3.13076i	−2.20993	−	3.13076i
$17$		0			0		−0.313344	−	0.949640i	$-0.601449\pi$
$17$		0			0		0.313344	+	0.949640i	$0.398551\pi$
$18$	−0.690261	+	1.81050i	−0.690261	+	1.81050i
$19$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$19$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$20$		0			0
$21$		0			0
$22$	2.71326	+	2.65218i	2.71326	+	2.65218i
$23$	−1.50182	−	1.11217i	−1.50182	−	1.11217i	−0.962917	−	0.269797i	$-0.913043\pi$
$23$	−1.50182	−	1.11217i	−1.50182	−	1.11217i	−0.538899	−	0.842371i	$-0.681159\pi$
$24$		0			0
$25$	−0.291646	−	0.956526i	−0.291646	−	0.956526i
$26$		0			0
$27$		0			0
$28$	−2.57366	−	0.981220i	−2.57366	−	0.981220i
$29$	0.919177	+	0.0418794i	0.919177	+	0.0418794i	0.500000	−	0.866025i	$-0.333333\pi$
$29$	0.919177	+	0.0418794i	0.919177	+	0.0418794i	0.419177	+	0.907905i	$0.362319\pi$
$30$		0			0
$31$		0			0		−0.993529	−	0.113580i	$-0.963768\pi$
$31$		0			0		0.993529	+	0.113580i	$0.0362319\pi$
$32$	1.60395	−	3.69267i	1.60395	−	3.69267i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−2.70881	+	0.498860i	−2.70881	+	0.498860i
$37$	−1.61223	−	0.835390i	−1.61223	−	0.835390i	−0.998964	−	0.0455146i	$-0.985507\pi$
$37$	−1.61223	−	0.835390i	−1.61223	−	0.835390i	−0.613267	−	0.789876i	$-0.710145\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$41$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$42$		0			0
$43$	−0.0873260	+	0.159533i	−0.0873260	+	0.159533i	−0.917211	−	0.398401i	$-0.869565\pi$
$43$	−0.0873260	+	0.159533i	−0.0873260	+	0.159533i	0.829885	+	0.557934i	$0.188406\pi$
$44$	−1.21726	+	5.25435i	−1.21726	+	5.25435i
$45$		0			0
$46$	0.329275	−	3.60600i	0.329275	−	3.60600i
$47$		0			0		−0.746184	−	0.665740i	$-0.768116\pi$
$47$		0			0		0.746184	+	0.665740i	$0.231884\pi$
$48$		0			0
$49$	−0.974199	+	0.225690i	−0.974199	+	0.225690i
$50$	1.28995	−	1.44582i	1.28995	−	1.44582i
$51$		0			0
$52$		0			0
$53$	0.993991	+	0.303069i	0.993991	+	0.303069i	0.746184	−	0.665740i	$-0.231884\pi$
$53$	0.993991	+	0.303069i	0.993991	+	0.303069i	0.247808	+	0.968809i	$0.420290\pi$
$54$		0			0
$55$		0			0
$56$	−0.615667	−	3.34307i	−0.615667	−	3.34307i
$57$		0			0
$58$	0.856053	+	1.56389i	0.856053	+	1.56389i
$59$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$59$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$60$		0			0
$61$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$61$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$62$		0			0
$63$	−0.715110	+	0.699012i	−0.715110	+	0.699012i
$64$	3.93168	−	0.540397i	3.93168	−	0.540397i
$65$		0			0
$66$		0			0
$67$	0.514134	−	1.11358i	0.514134	−	1.11358i	−0.460065	−	0.887885i	$-0.652174\pi$
$67$	0.514134	−	1.11358i	0.514134	−	1.11358i	0.974199	−	0.225690i	$-0.0724638\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.337690	+	0.227030i	−0.337690	+	0.227030i	−0.715110	−	0.699012i	$-0.753623\pi$
$71$	−0.337690	+	0.227030i	−0.337690	+	0.227030i	0.377419	+	0.926043i	$0.376812\pi$
$72$	−2.26304	−	2.53650i	−2.26304	−	2.53650i
$73$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$73$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$74$	−0.240100	−	3.51014i	−0.240100	−	3.51014i
$75$		0			0
$76$		0			0
$77$	0.697581	+	1.82970i	0.697581	+	1.82970i
$78$		0			0
$79$	0.215721	−	1.88699i	0.215721	−	1.88699i	−0.203456	−	0.979084i	$-0.565217\pi$
$79$	0.215721	−	1.88699i	0.215721	−	1.88699i	0.419177	−	0.907905i	$-0.362319\pi$
$80$		0			0
$81$	−0.247808	+	0.968809i	−0.247808	+	0.968809i
$82$		0			0
$83$		0			0		0.995857	−	0.0909349i	$-0.0289855\pi$
$83$		0			0		−0.995857	+	0.0909349i	$0.971014\pi$
$84$		0			0
$85$		0			0
$86$	−0.352029	+	0.0160391i	−0.352029	+	0.0160391i
$87$		0			0
$88$	−6.32116	+	2.08574i	−6.32116	+	2.08574i
$89$		0			0		0.934394	−	0.356242i	$-0.115942\pi$
$89$		0			0		−0.934394	+	0.356242i	$0.884058\pi$
$90$		0			0
$91$		0			0
$92$	4.62295	−	2.26346i	4.62295	−	2.26346i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.439735	−	0.898128i	$-0.355072\pi$
$97$		0			0		−0.439735	+	0.898128i	$0.644928\pi$
$98$	−1.35442	−	1.38561i	−1.35442	−	1.38561i
$99$	1.54671	+	1.20088i	1.54671	+	1.20088i
$100$	2.70881	+	0.498860i	2.70881	+	0.498860i
$101$		0			0		−0.761145	−	0.648582i	$-0.775362\pi$
$101$		0			0		0.761145	+	0.648582i	$0.224638\pi$
$102$		0			0
$103$		0			0		−0.0455146	−	0.998964i	$-0.514493\pi$
$103$		0			0		0.0455146	+	0.998964i	$0.485507\pi$
$104$		0			0
$105$		0			0
$106$	0.498964	+	1.95071i	0.498964	+	1.95071i
$107$	0.417998	+	1.80430i	0.417998	+	1.80430i	0.576680	+	0.816970i	$0.304348\pi$
$107$	0.417998	+	1.80430i	0.417998	+	1.80430i	−0.158683	+	0.987330i	$0.550725\pi$
$108$		0			0
$109$	−0.192226	+	0.686063i	−0.192226	+	0.686063i	0.803631	+	0.595128i	$0.202899\pi$
$109$	−0.192226	+	0.686063i	−0.192226	+	0.686063i	−0.995857	+	0.0909349i	$0.971014\pi$
$110$		0			0
$111$		0			0
$112$	2.85950	−	2.55122i	2.85950	−	2.55122i
$113$	0.384455	+	0.312777i	0.384455	+	0.312777i	0.803631	−	0.595128i	$-0.202899\pi$
$113$	0.384455	+	0.312777i	0.384455	+	0.312777i	−0.419177	+	0.907905i	$0.637681\pi$
$114$		0			0
$115$		0			0
$116$	−1.26719	+	2.19483i	−1.26719	+	2.19483i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.48631	−	1.36097i	2.48631	−	1.36097i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.87718	−	0.480157i	−1.87718	−	0.480157i
$127$	−1.03334	+	0.421150i	−1.03334	+	0.421150i	−0.829885	−	0.557934i	$-0.811594\pi$
$127$	−1.03334	+	0.421150i	−1.03334	+	0.421150i	−0.203456	+	0.979084i	$0.565217\pi$
$128$	2.31215	+	2.84201i	2.31215	+	2.84201i
$129$		0			0
$130$		0			0
$131$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$131$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$132$		0			0
$133$		0			0
$134$	2.36117	−	0.269929i	2.36117	−	0.269929i
$135$		0			0
$136$		0			0
$137$	−1.00264	+	0.641427i	−1.00264	+	0.641427i	−0.934394	−	0.356242i	$-0.884058\pi$
$137$	−1.00264	+	0.641427i	−1.00264	+	0.641427i	−0.0682424	+	0.997669i	$0.521739\pi$
$138$		0			0
$139$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$139$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$140$		0			0
$141$		0			0
$142$	−0.715829	−	0.330496i	−0.715829	−	0.330496i
$143$		0			0
$144$	1.11763	−	3.66556i	1.11763	−	3.66556i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	4.08600	−	2.88421i	4.08600	−	2.88421i
$149$	0.606043	+	0.744926i	0.606043	+	0.744926i	0.983462	−	0.181116i	$-0.0579710\pi$
$149$	0.606043	+	0.744926i	0.606043	+	0.744926i	−0.377419	+	0.926043i	$0.623188\pi$
$150$		0			0
$151$	1.35442	+	0.346441i	1.35442	+	0.346441i	0.854419	−	0.519584i	$-0.173913\pi$
$151$	1.35442	+	0.346441i	1.35442	+	0.346441i	0.500000	+	0.866025i	$0.333333\pi$
$152$		0			0
$153$		0			0
$154$	−2.32685	+	2.99693i	−2.32685	+	2.99693i
$155$		0			0
$156$		0			0
$157$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$157$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$158$	3.34116	−	1.54260i	3.34116	−	1.54260i
$159$		0			0
$160$		0			0
$161$	0.934394	−	1.61842i	0.934394	−	1.61842i
$162$	−1.85338	+	0.565099i	−1.85338	+	0.565099i
$163$	−0.113503	+	0.343990i	−0.113503	+	0.343990i	−0.990686	−	0.136167i	$-0.956522\pi$
$163$	−0.113503	+	0.343990i	−0.113503	+	0.343990i	0.877183	+	0.480157i	$0.159420\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.987330	−	0.158683i	$-0.0507246\pi$
$167$		0			0		−0.987330	+	0.158683i	$0.949275\pi$
$168$		0			0
$169$	0.962917	+	0.269797i	0.962917	+	0.269797i
$170$		0			0
$171$		0			0
$172$	−0.279489	−	0.415719i	−0.279489	−	0.415719i
$173$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$173$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$174$		0			0
$175$	0.917211	−	0.398401i	0.917211	−	0.398401i
$176$	−5.71164	−	4.86697i	−5.71164	−	4.86697i
$177$		0			0
$178$		0			0
$179$	−1.31730	−	1.34764i	−1.31730	−	1.34764i	−0.898128	−	0.439735i	$-0.855072\pi$
$179$	−1.31730	−	1.34764i	−1.31730	−	1.34764i	−0.419177	−	0.907905i	$-0.637681\pi$
$180$		0			0
$181$		0			0		0.761145	−	0.648582i	$-0.224638\pi$
$181$		0			0		−0.761145	+	0.648582i	$0.775362\pi$
$182$		0			0
$183$		0			0
$184$	5.35120	+	3.42338i	5.35120	+	3.42338i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.94638	+	0.0886806i	−1.94638	+	0.0886806i	−0.983462	−	0.181116i	$-0.942029\pi$
$191$	−1.94638	+	0.0886806i	−1.94638	+	0.0886806i	−0.962917	+	0.269797i	$0.913043\pi$
$192$		0			0
$193$	0.976200	+	1.04526i	0.976200	+	1.04526i	0.998964	+	0.0455146i	$0.0144928\pi$
$193$	0.976200	+	1.04526i	0.976200	+	1.04526i	−0.0227632	+	0.999741i	$0.507246\pi$
$194$		0			0
$195$		0			0
$196$	0.682553	−	2.66845i	0.682553	−	2.66845i
$197$	−1.77531	−	0.0404222i	−1.77531	−	0.0404222i	−0.877183	−	0.480157i	$-0.840580\pi$
$197$	−1.77531	−	0.0404222i	−1.77531	−	0.0404222i	−0.898128	+	0.439735i	$0.855072\pi$
$198$	−0.430944	+	3.76963i	−0.430944	+	3.76963i
$199$		0			0		0.0455146	−	0.998964i	$-0.485507\pi$
$199$		0			0		−0.0455146	+	0.998964i	$0.514493\pi$
$200$	1.21097	+	3.17628i	1.21097	+	3.17628i
$201$		0			0
$202$		0			0
$203$	0.0627919	+	0.917985i	0.0627919	+	0.917985i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.0425396	−	1.86830i	−0.0425396	−	1.86830i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.0152459	−	0.0428977i	−0.0152459	−	0.0428977i	0.934394	−	0.356242i	$-0.115942\pi$
$211$	−0.0152459	−	0.0428977i	−0.0152459	−	0.0428977i	−0.949640	+	0.313344i	$0.898551\pi$
$212$	−2.00075	+	2.04682i	−2.00075	+	2.04682i
$213$		0			0
$214$	−2.56627	+	2.50850i	−2.56627	+	2.50850i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.32933	+	0.372460i	−1.32933	+	0.372460i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$223$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$224$	3.85095	+	1.17416i	3.85095	+	1.17416i
$225$	0.576680	−	0.816970i	0.576680	−	0.816970i
$226$	−0.130763	+	0.951369i	−0.130763	+	0.951369i
$227$		0			0		0.665740	−	0.746184i	$-0.268116\pi$
$227$		0			0		−0.665740	+	0.746184i	$0.731884\pi$
$228$		0			0
$229$		0			0		−0.158683	−	0.987330i	$-0.550725\pi$
$229$		0			0		0.158683	+	0.987330i	$0.449275\pi$
$230$		0			0
$231$		0			0
$232$	−3.12698	+	0.0711985i	−3.12698	+	0.0711985i
$233$	−0.0614630	+	0.265307i	−0.0614630	+	0.265307i	−0.995857	−	0.0909349i	$-0.971014\pi$
$233$	−0.0614630	+	0.265307i	−0.0614630	+	0.265307i	0.934394	+	0.356242i	$0.115942\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.272263	−	1.98086i	−0.272263	−	1.98086i	−0.158683	−	0.987330i	$-0.550725\pi$
$239$	−0.272263	−	1.98086i	−0.272263	−	1.98086i	−0.113580	−	0.993529i	$-0.536232\pi$
$240$		0			0
$241$		0			0		0.983462	−	0.181116i	$-0.0579710\pi$
$241$		0			0		−0.983462	+	0.181116i	$0.942029\pi$
$242$	4.75624	+	2.74601i	4.75624	+	2.74601i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$251$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$252$	−0.803299	−	2.63462i	−0.803299	−	2.63462i
$253$	−3.38876	−	1.38113i	−3.38876	−	1.38113i
$254$	−1.73755	−	1.28674i	−1.73755	−	1.28674i
$255$		0			0
$256$	−1.04827	+	2.94955i	−1.04827	+	2.94955i
$257$		0			0		−0.439735	−	0.898128i	$-0.644928\pi$
$257$		0			0		0.439735	+	0.898128i	$0.355072\pi$
$258$		0			0
$259$	0.646867	−	1.69668i	0.646867	−	1.69668i
$260$		0			0
$261$	0.530621	+	0.751719i	0.530621	+	0.751719i
$262$		0			0
$263$	0.996962	−	0.774051i	0.996962	−	0.774051i	0.0227632	−	0.999741i	$-0.492754\pi$
$263$	0.996962	−	0.774051i	0.996962	−	0.774051i	0.974199	+	0.225690i	$0.0724638\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	2.07181	+	2.66845i	2.07181	+	2.66845i
$269$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$269$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$270$		0			0
$271$		0			0		−0.0909349	−	0.995857i	$-0.528986\pi$
$271$		0			0		0.0909349	+	0.995857i	$0.471014\pi$
$272$		0			0
$273$		0			0
$274$	−2.07132	−	1.01414i	−2.07132	−	1.01414i
$275$	−1.01743	−	1.67310i	−1.01743	−	1.67310i
$276$		0			0
$277$	0.983462	+	0.181116i	0.983462	+	0.181116i
$277$	0.983462	+	0.181116i	0.983462	+	0.181116i
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.886009	−	1.70992i	0.886009	−	1.70992i	0.203456	−	0.979084i	$-0.434783\pi$
$281$	0.886009	−	1.70992i	0.886009	−	1.70992i	0.682553	−	0.730836i	$-0.260870\pi$
$282$		0			0
$283$		0			0		−0.0909349	−	0.995857i	$-0.528986\pi$
$283$		0			0		0.0909349	+	0.995857i	$0.471014\pi$
$284$	−0.127299	−	1.11353i	−0.127299	−	1.11353i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	3.90040	−	0.997669i	3.90040	−	0.997669i
$289$	−0.803631	+	0.595128i	−0.803631	+	0.595128i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$293$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$294$		0			0
$295$		0			0
$296$	5.66145	+	2.45912i	5.66145	+	2.45912i
$297$		0			0
$298$	−0.623118	+	1.75329i	−0.623118	+	1.75329i
$299$		0			0
$300$		0			0
$301$	−0.168419	−	0.0686411i	−0.168419	−	0.0686411i
$302$	0.790022	+	2.59108i	0.790022	+	2.59108i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$307$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$308$	−5.35861	−	0.612596i	−5.35861	−	0.612596i
$309$		0			0
$310$		0			0
$311$		0			0		0.648582	−	0.761145i	$-0.275362\pi$
$311$		0			0		−0.648582	+	0.761145i	$0.724638\pi$
$312$		0			0
$313$		0			0		0.983462	−	0.181116i	$-0.0579710\pi$
$313$		0			0		−0.983462	+	0.181116i	$0.942029\pi$
$314$		0			0
$315$		0			0
$316$	4.34139	+	2.91873i	4.34139	+	2.91873i
$317$	−1.03783	+	1.62227i	−1.03783	+	1.62227i	−0.291646	+	0.956526i	$0.594203\pi$
$317$	−1.03783	+	1.62227i	−1.03783	+	1.62227i	−0.746184	+	0.665740i	$0.768116\pi$
$318$		0			0
$319$	1.76408	−	0.366581i	1.76408	−	0.366581i
$320$		0			0
$321$		0			0
$322$	3.62006	−	0.0824255i	3.62006	−	0.0824255i
$323$		0			0
$324$	−2.05526	−	1.83369i	−2.05526	−	1.83369i
$325$		0			0
$326$	−0.683759	+	0.158405i	−0.683759	+	0.158405i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.973094	−	0.908806i	0.973094	−	0.908806i	−0.0227632	−	0.999741i	$-0.507246\pi$
$331$	0.973094	−	0.908806i	0.973094	−	0.908806i	0.995857	+	0.0909349i	$0.0289855\pi$
$332$		0			0
$333$	−0.328873	−	1.78578i	−0.328873	−	1.78578i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			0.272333i			0.272333i	0.990686	+	0.136167i	$0.0434783\pi$
$337$			0.272333i			0.272333i	−0.990686	+	0.136167i	$0.956522\pi$
$338$	0.522763	+	1.86577i	0.522763	+	1.86577i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.334880	−	0.942261i	−0.334880	−	0.942261i
$344$	0.259147	−	0.561292i	0.259147	−	0.561292i
$345$		0			0
$346$		0			0
$347$	−0.0453378	−	1.99120i	−0.0453378	−	1.99120i	−0.113580	−	0.993529i	$-0.536232\pi$
$347$	−0.0453378	−	1.99120i	−0.0453378	−	1.99120i	0.0682424	−	0.997669i	$-0.478261\pi$
$348$		0			0
$349$		0			0		−0.665740	−	0.746184i	$-0.731884\pi$
$349$		0			0		0.665740	+	0.746184i	$0.268116\pi$
$350$	1.58298	+	1.11739i	1.58298	+	1.11739i
$351$		0			0
$352$	1.25098	−	7.78366i	1.25098	−	7.78366i
$353$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$353$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.904866	−	3.53759i	0.904866	−	3.53759i
$359$	−1.88403	+	0.669586i	−1.88403	+	0.669586i	−0.934394	+	0.356242i	$0.884058\pi$
$359$	−1.88403	+	0.669586i	−1.88403	+	0.669586i	−0.949640	+	0.313344i	$0.898551\pi$
$360$		0			0
$361$	0.682553	+	0.730836i	0.682553	+	0.730836i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.538899	−	0.842371i	$-0.681159\pi$
$367$		0			0		0.538899	+	0.842371i	$0.318841\pi$
$368$	−0.163019	+	7.15964i	−0.163019	+	7.15964i
$369$		0			0
$370$		0			0
$371$	−0.188210	+	1.02198i	−0.188210	+	1.02198i
$372$		0			0
$373$	−1.31834	+	1.12338i	−1.31834	+	1.12338i	−0.334880	+	0.942261i	$0.608696\pi$
$373$	−1.31834	+	1.12338i	−1.31834	+	1.12338i	−0.983462	+	0.181116i	$0.942029\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.52236	+	0.661254i	−1.52236	+	0.661254i	−0.983462	−	0.181116i	$-0.942029\pi$
$379$	−1.52236	+	0.661254i	−1.52236	+	0.661254i	−0.538899	+	0.842371i	$0.681159\pi$
$380$		0			0
$381$		0			0
$382$	−2.10634	−	3.13303i	−2.10634	−	3.13303i
$383$		0			0		−0.247808	−	0.968809i	$-0.579710\pi$
$383$		0			0		0.247808	+	0.968809i	$0.420290\pi$
$384$		0			0
$385$		0			0
$386$	−0.747666	+	2.66845i	−0.747666	+	2.66845i
$387$	−0.179565	+	0.0288596i	−0.179565	+	0.0288596i
$388$		0			0
$389$	−0.746184	+	0.665740i	−0.746184	+	0.665740i	−0.949640	−	0.313344i	$-0.898551\pi$
$389$	−0.746184	+	0.665740i	−0.746184	+	0.665740i	0.203456	+	0.979084i	$0.434783\pi$
$390$		0			0
$391$		0			0
$392$	3.25151	−	0.991389i	3.25151	−	0.991389i
$393$		0			0
$394$	−1.72038	−	2.97979i	−1.72038	−	2.97979i
$395$		0			0
$396$	−4.89679	+	2.26083i	−4.89679	+	2.26083i
$397$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$397$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$398$		0			0
$399$		0			0
$400$	−2.35014	+	3.02693i	−2.35014	+	3.02693i
$401$	−0.990763	+	1.47369i	−0.990763	+	1.47369i	−0.113580	+	0.993529i	$0.536232\pi$
$401$	−0.990763	+	1.47369i	−0.990763	+	1.47369i	−0.877183	+	0.480157i	$0.840580\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−1.45654	+	1.02814i	−1.45654	+	1.02814i
$407$	−3.46392	−	0.802478i	−3.46392	−	0.802478i
$408$		0			0
$409$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$409$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	3.05022	−	1.95135i	3.05022	−	1.95135i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.907905	−	0.419177i	$-0.862319\pi$
$419$		0			0		0.907905	+	0.419177i	$0.137681\pi$
$420$		0			0
$421$	0.244502	−	0.801907i	0.244502	−	0.801907i	−0.746184	−	0.665740i	$-0.768116\pi$
$421$	0.244502	−	0.801907i	0.244502	−	0.801907i	0.990686	−	0.136167i	$-0.0434783\pi$
$422$	0.0556700	−	0.0684277i	0.0556700	−	0.0684277i
$423$		0			0
$424$	−3.44129	−	0.797236i	−3.44129	−	0.797236i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−4.94220	−	1.26415i	−4.94220	−	1.26415i
$429$		0			0
$430$		0			0
$431$	−1.22145	+	1.57321i	−1.22145	+	1.57321i	−0.538899	+	0.842371i	$0.681159\pi$
$431$	−1.22145	+	1.57321i	−1.22145	+	1.57321i	−0.682553	+	0.730836i	$0.739130\pi$
$432$		0			0
$433$		0			0		0.877183	−	0.480157i	$-0.159420\pi$
$433$		0			0		−0.877183	+	0.480157i	$0.840580\pi$
$434$		0			0
$435$		0			0
$436$	−1.43422	−	1.33947i	−1.43422	−	1.33947i
$437$		0			0
$438$		0			0
$439$		0			0		0.956526	−	0.291646i	$-0.0942029\pi$
$439$		0			0		−0.956526	+	0.291646i	$0.905797\pi$
$440$		0			0
$441$	−0.775711	−	0.631088i	−0.775711	−	0.631088i
$442$		0			0
$443$	0.268629	+	0.362744i	0.268629	+	0.362744i	0.917211	−	0.398401i	$-0.130435\pi$
$443$	0.268629	+	0.362744i	0.268629	+	0.362744i	−0.648582	+	0.761145i	$0.724638\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.983462	+	3.84486i	0.983462	+	3.84486i
$449$	0.911631	+	1.35598i	0.911631	+	1.35598i	0.934394	+	0.356242i	$0.115942\pi$
$449$	0.911631	+	1.35598i	0.911631	+	1.35598i	−0.0227632	+	0.999741i	$0.507246\pi$
$450$	1.93310	+	0.132228i	1.93310	+	0.132228i
$451$		0			0
$452$	−1.25209	+	0.543860i	−1.25209	+	0.543860i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.841236	−	1.71817i	0.841236	−	1.71817i	0.158683	−	0.987330i	$-0.449275\pi$
$457$	0.841236	−	1.71817i	0.841236	−	1.71817i	0.682553	−	0.730836i	$-0.260870\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.842371	−	0.538899i	$-0.818841\pi$
$461$		0			0		0.842371	+	0.538899i	$0.181159\pi$
$462$		0			0
$463$	0.0388986	−	1.70840i	0.0388986	−	1.70840i	−0.500000	−	0.866025i	$-0.666667\pi$
$463$	0.0388986	−	1.70840i	0.0388986	−	1.70840i	0.538899	−	0.842371i	$-0.318841\pi$
$464$	−1.90020	−	2.97027i	−1.90020	−	2.97027i
$465$		0			0
$466$	−0.501104	+	0.165345i	−0.501104	+	0.165345i
$467$		0			0		−0.877183	−	0.480157i	$-0.840580\pi$
$467$		0			0		0.877183	+	0.480157i	$0.159420\pi$
$468$		0			0
$469$	1.16476	+	0.384327i	1.16476	+	0.384327i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.0882522	+	0.345023i	−0.0882522	+	0.345023i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.370195	+	0.970992i	0.370195	+	0.970992i
$478$	3.00529	−	2.44498i	3.00529	−	2.44498i
$479$		0			0		0.158683	−	0.987330i	$-0.449275\pi$
$479$		0			0		−0.158683	+	0.987330i	$0.550725\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.177713	+	7.80501i	0.177713	+	7.80501i
$485$		0			0
$486$		0			0
$487$	0.543741	−	1.17770i	0.543741	−	1.17770i	−0.419177	−	0.907905i	$-0.637681\pi$
$487$	0.543741	−	1.17770i	0.543741	−	1.17770i	0.962917	−	0.269797i	$-0.0869565\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.40657	+	1.37490i	−1.40657	+	1.37490i	−0.576680	+	0.816970i	$0.695652\pi$
$491$	−1.40657	+	1.37490i	−1.40657	+	1.37490i	−0.829885	+	0.557934i	$0.811594\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.263916	−	0.309719i	−0.263916	−	0.309719i
$498$		0			0
$499$	−0.284890	+	0.699012i	−0.284890	+	0.699012i	0.715110	+	0.699012i	$0.246377\pi$
$499$	−0.284890	+	0.699012i	−0.284890	+	0.699012i	−1.00000			$\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$503$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$504$	2.26304	−	2.53650i	2.26304	−	2.53650i
$505$		0			0
$506$	−1.12514	−	7.00068i	−1.12514	−	7.00068i
$507$		0			0
$508$	0.279489	−	3.06077i	0.279489	−	3.06077i
$509$		0			0		0.999741	−	0.0227632i	$-0.00724638\pi$
$509$		0			0		−0.999741	+	0.0227632i	$0.992754\pi$
$510$		0			0
$511$		0			0
$512$	−2.35134	+	0.488614i	−2.35134	+	0.488614i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	3.46016	−	0.637229i	3.46016	−	0.637229i
$519$		0			0
$520$		0			0
$521$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$521$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$522$	−0.710294	+	1.63526i	−0.710294	+	1.63526i
$523$		0			0		−0.993529	−	0.113580i	$-0.963768\pi$
$523$		0			0		0.993529	+	0.113580i	$0.0362319\pi$
$524$		0			0
$525$		0			0
$526$	2.28517	+	0.871230i	2.28517	+	0.871230i
$527$		0			0
$528$		0			0
$529$	0.726889	+	2.38402i	0.726889	+	2.38402i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−1.48529	+	3.89581i	−1.48529	+	3.89581i
$537$		0			0
$538$		0			0
$539$	−1.73863	+	0.900885i	−1.73863	+	0.900885i
$540$		0			0
$541$	0.314409	+	0.0432145i	0.314409	+	0.0432145i	0.291646	−	0.956526i	$-0.405797\pi$
$541$	0.314409	+	0.0432145i	0.314409	+	0.0432145i	0.0227632	+	0.999741i	$0.492754\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.155049	−	1.35627i	−0.155049	−	1.35627i	−0.803631	−	0.595128i	$-0.797101\pi$
$547$	−0.155049	−	1.35627i	−0.155049	−	1.35627i	0.648582	−	0.761145i	$-0.275362\pi$
$548$	−0.298121	−	3.26482i	−0.298121	−	3.26482i
$549$		0			0
$550$	1.74557	−	3.36880i	1.74557	−	3.36880i
$551$		0			0
$552$		0			0
$553$	1.89928			1.89928
$554$	0.690261	+	1.81050i	0.690261	+	1.81050i
$555$		0			0
$556$		0			0
$557$	−0.122581	−	0.0600171i	−0.122581	−	0.0600171i	0.377419	−	0.926043i	$-0.376812\pi$
$557$	−0.122581	−	0.0600171i	−0.122581	−	0.0600171i	−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	3.72283	−	0.254649i	3.72283	−	0.254649i
$563$		0			0		−0.613267	−	0.789876i	$-0.710145\pi$
$563$		0			0		0.613267	+	0.789876i	$0.289855\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.990686	−	0.136167i	−0.990686	−	0.136167i
$568$	1.09257	−	0.848278i	1.09257	−	0.848278i
$569$	1.75327	−	0.908472i	1.75327	−	0.908472i	0.803631	−	0.595128i	$-0.202899\pi$
$569$	1.75327	−	0.908472i	1.75327	−	0.908472i	0.949640	−	0.313344i	$-0.101449\pi$
$570$		0			0
$571$	−0.495006	−	1.50019i	−0.495006	−	1.50019i	−0.829885	−	0.557934i	$-0.811594\pi$
$571$	−0.495006	−	1.50019i	−0.495006	−	1.50019i	0.334880	−	0.942261i	$-0.391304\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.625819	+	1.76089i	−0.625819	+	1.76089i
$576$	2.83802	+	2.77413i	2.83802	+	2.77413i
$577$		0			0		−0.803631	−	0.595128i	$-0.797101\pi$
$577$		0			0		0.803631	+	0.595128i	$0.202899\pi$
$578$	−1.79432	−	0.731294i	−1.79432	−	0.731294i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	2.03276	+	0.0926161i	2.03276	+	0.0926161i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$587$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.947513	+	6.89367i	0.947513	+	6.89367i
$593$		0			0		−0.829885	−	0.557934i	$-0.811594\pi$
$593$		0			0		0.829885	+	0.557934i	$0.188406\pi$
$594$		0			0
$595$		0			0
$596$	−2.58973	+	0.538152i	−2.58973	+	0.538152i
$597$		0			0
$598$		0			0
$599$	1.88403	−	0.0428977i	1.88403	−	0.0428977i	0.934394	−	0.356242i	$-0.115942\pi$
$599$	1.88403	−	0.0428977i	1.88403	−	0.0428977i	0.949640	+	0.313344i	$0.101449\pi$
$600$		0			0
$601$		0			0		−0.746184	−	0.665740i	$-0.768116\pi$
$601$		0			0		0.746184	+	0.665740i	$0.231884\pi$
$602$	−0.0559188	−	0.347929i	−0.0559188	−	0.347929i
$603$	1.19489	−	0.276817i	1.19489	−	0.276817i
$604$	−2.56355	+	2.87331i	−2.56355	+	2.87331i
$605$		0			0
$606$		0			0
$607$		0			0		−0.956526	−	0.291646i	$-0.905797\pi$
$607$		0			0		0.956526	+	0.291646i	$0.0942029\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.962917	−	0.269797i	0.962917	−	0.269797i	0.247808	−	0.968809i	$-0.420290\pi$
$613$	0.962917	−	0.269797i	0.962917	−	0.269797i	0.715110	+	0.699012i	$0.246377\pi$
$614$		0			0
$615$		0			0
$616$	−2.79020	−	6.04336i	−2.79020	−	6.04336i
$617$	1.10944	−	1.08446i	1.10944	−	1.08446i	0.113580	−	0.993529i	$-0.463768\pi$
$617$	1.10944	−	1.08446i	1.10944	−	1.08446i	0.995857	−	0.0909349i	$-0.0289855\pi$
$618$		0			0
$619$		0			0		0.699012	−	0.715110i	$-0.253623\pi$
$619$		0			0		−0.699012	+	0.715110i	$0.746377\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.829885	+	0.557934i	−0.829885	+	0.557934i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.707873	−	1.85669i	−0.707873	−	1.85669i	−0.460065	−	0.887885i	$-0.652174\pi$
$631$	−0.707873	−	1.85669i	−0.707873	−	1.85669i	−0.247808	−	0.968809i	$-0.579710\pi$
$632$	−0.293851	+	6.44951i	−0.293851	+	6.44951i
$633$		0			0
$634$	−3.73057	−	0.0849416i	−3.73057	−	0.0849416i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	2.38289	+	2.55145i	2.38289	+	2.55145i
$639$	−0.386420	−	0.127503i	−0.386420	−	0.127503i
$640$		0			0
$641$	−0.662131	−	0.362441i	−0.662131	−	0.362441i	0.113580	−	0.993529i	$-0.463768\pi$
$641$	−0.662131	−	0.362441i	−0.662131	−	0.362441i	−0.775711	+	0.631088i	$0.782609\pi$
$642$		0			0
$643$		0			0		0.934394	−	0.356242i	$-0.115942\pi$
$643$		0			0		−0.934394	+	0.356242i	$0.884058\pi$
$644$	2.77389	+	4.33595i	2.77389	+	4.33595i
$645$		0			0
$646$		0			0
$647$		0			0		−0.842371	−	0.538899i	$-0.818841\pi$
$647$		0			0		0.842371	+	0.538899i	$0.181159\pi$
$648$	0.615667	−	3.34307i	0.615667	−	3.34307i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.697419	−	0.713479i	−0.697419	−	0.713479i
$653$	0.0719018	+	0.0558252i	0.0719018	+	0.0558252i	0.648582	−	0.761145i	$-0.275362\pi$
$653$	0.0719018	+	0.0558252i	0.0719018	+	0.0558252i	−0.576680	+	0.816970i	$0.695652\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.349651	+	0.520079i	0.349651	+	0.520079i	0.962917	−	0.269797i	$-0.0869565\pi$
$659$	0.349651	+	0.520079i	0.349651	+	0.520079i	−0.613267	+	0.789876i	$0.710145\pi$
$660$		0			0
$661$		0			0		−0.225690	−	0.974199i	$-0.572464\pi$
$661$		0			0		0.225690	+	0.974199i	$0.427536\pi$
$662$	2.48423	+	0.696049i	2.48423	+	0.696049i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	2.62533	−	2.34230i	2.62533	−	2.34230i
$667$	−1.33386	−	1.08517i	−1.33386	−	1.08517i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.871874	+	0.402541i	−0.871874	+	0.402541i	−0.803631	−	0.595128i	$-0.797101\pi$
$673$	−0.871874	+	0.402541i	−0.871874	+	0.402541i	−0.0682424	+	0.997669i	$0.521739\pi$
$674$	−0.450858	+	0.274173i	−0.450858	+	0.274173i
$675$		0			0
$676$	−1.88000	+	2.01299i	−1.88000	+	2.01299i
$677$		0			0		0.613267	−	0.789876i	$-0.289855\pi$
$677$		0			0		−0.613267	+	0.789876i	$0.710145\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.440832	+	0.311173i	−0.440832	+	0.311173i	−0.775711	−	0.631088i	$-0.782609\pi$
$683$	−0.440832	+	0.311173i	−0.440832	+	0.311173i	0.334880	+	0.942261i	$0.391304\pi$
$684$		0			0
$685$		0			0
$686$	1.22281	−	1.50303i	1.22281	−	1.50303i
$687$		0			0
$688$	0.692444	−	0.0791602i	0.692444	−	0.0791602i
$689$		0			0
$690$		0			0
$691$		0			0		0.842371	−	0.538899i	$-0.181159\pi$
$691$		0			0		−0.842371	+	0.538899i	$0.818841\pi$
$692$		0			0
$693$	−1.01743	+	1.67310i	−1.01743	+	1.67310i
$694$	3.25086	−	2.07971i	3.25086	−	2.07971i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.187965	+	2.74794i	−0.187965	+	2.74794i
$701$	1.78709	+	0.414012i	1.78709	+	0.414012i	0.983462	−	0.181116i	$-0.0579710\pi$
$701$	1.78709	+	0.414012i	1.78709	+	0.414012i	0.803631	+	0.595128i	$0.202899\pi$
$702$		0			0
$703$		0			0
$704$	7.19653	−	2.93303i	7.19653	−	2.93303i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.338284	+	0.362214i	−0.338284	+	0.362214i	−0.877183	−	0.480157i	$-0.840580\pi$
$709$	−0.338284	+	0.362214i	−0.338284	+	0.362214i	0.538899	+	0.842371i	$0.318841\pi$
$710$		0			0
$711$	1.62278	−	0.986835i	1.62278	−	0.986835i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	4.96500	−	1.51384i	4.96500	−	1.51384i
$717$		0			0
$718$	−3.00529	−	2.44498i	−3.00529	−	2.44498i
$719$		0			0		0.746184	−	0.665740i	$-0.231884\pi$
$719$		0			0		−0.746184	+	0.665740i	$0.768116\pi$
$720$		0			0
$721$		0			0
$722$	−0.522763	+	1.86577i	−0.522763	+	1.86577i
$723$		0			0
$724$		0			0
$725$	−0.228015	−	0.891430i	−0.228015	−	0.891430i
$726$		0			0
$727$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$727$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$728$		0			0
$729$	−0.917211	+	0.398401i	−0.917211	+	0.398401i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.699012	−	0.715110i	$-0.746377\pi$
$733$		0			0		0.699012	+	0.715110i	$0.253623\pi$
$734$		0			0
$735$		0			0
$736$	−6.51571	+	3.76185i	−6.51571	+	3.76185i
$737$	0.434997	−	2.36204i	0.434997	−	2.36204i
$738$		0			0
$739$	1.77952	−	0.871278i	1.77952	−	0.871278i	0.829885	−	0.557934i	$-0.188406\pi$
$739$	1.77952	−	0.871278i	1.77952	−	0.871278i	0.949640	−	0.313344i	$-0.101449\pi$
$740$		0			0
$741$		0			0
$742$	−1.88141	+	0.717297i	−1.88141	+	0.717297i
$743$	−0.796133	+	0.262693i	−0.796133	+	0.262693i	−0.682553	−	0.730836i	$-0.739130\pi$
$743$	−0.796133	+	0.262693i	−0.796133	+	0.262693i	−0.113580	+	0.993529i	$0.536232\pi$
$744$		0			0
$745$		0			0
$746$	−3.18704	−	1.05160i	−3.18704	−	1.05160i
$747$		0			0
$748$		0			0
$749$	−1.74515	+	0.620226i	−1.74515	+	0.620226i
$750$		0			0
$751$	−1.52189	−	0.0346522i	−1.52189	−	0.0346522i	−0.746184	−	0.665740i	$-0.768116\pi$
$751$	−1.52189	−	0.0346522i	−1.52189	−	0.0346522i	−0.775711	+	0.631088i	$0.782609\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.109683	−	1.60352i	−0.109683	−	1.60352i	−0.648582	−	0.761145i	$-0.724638\pi$
$757$	−0.109683	−	1.60352i	−0.109683	−	1.60352i	0.538899	−	0.842371i	$-0.318841\pi$
$758$	−2.62738	−	1.85461i	−2.62738	−	1.85461i
$759$		0			0
$760$		0			0
$761$		0			0		−0.0227632	−	0.999741i	$-0.507246\pi$
$761$		0			0		0.0227632	+	0.999741i	$0.492754\pi$
$762$		0			0
$763$	−0.703456	−	0.113059i	−0.703456	−	0.113059i
$764$	2.24955	−	4.87236i	2.24955	−	4.87236i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.419177	−	0.907905i	$-0.637681\pi$
$769$		0			0		0.419177	+	0.907905i	$0.362319\pi$
$770$		0			0
$771$		0			0
$772$	−3.79326	+	1.06282i	−3.79326	+	1.06282i
$773$		0			0		−0.480157	−	0.877183i	$-0.659420\pi$
$773$		0			0		0.480157	+	0.877183i	$0.340580\pi$
$774$	−0.228557	−	0.268223i	−0.228557	−	0.268223i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.85338	−	0.565099i	−1.85338	−	0.565099i
$779$		0			0
$780$		0			0
$781$	−0.530463	+	0.594561i	−0.530463	+	0.594561i
$782$		0			0
$783$		0			0
$784$	2.85950	+	2.55122i	2.85950	+	2.55122i
$785$		0			0
$786$		0			0
$787$		0			0		0.225690	−	0.974199i	$-0.427536\pi$
$787$		0			0		−0.225690	+	0.974199i	$0.572464\pi$
$788$	2.34851	−	4.29041i	2.34851	−	4.29041i
$789$		0			0
$790$		0			0
$791$	−0.267087	+	0.417492i	−0.267087	+	0.417492i
$792$	−5.52403	−	3.71382i	−5.52403	−	3.71382i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.648582	−	0.761145i	$-0.275362\pi$
$797$		0			0		−0.648582	+	0.761145i	$0.724638\pi$
$798$		0			0
$799$		0			0
$800$	−3.99993	−	0.457271i	−3.99993	−	0.457271i
$801$		0			0
$802$	−3.43720	−	0.156605i	−3.43720	−	0.156605i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.06721	+	1.04318i	1.06721	+	1.04318i	0.998964	+	0.0455146i	$0.0144928\pi$
$809$	1.06721	+	1.04318i	1.06721	+	1.04318i	0.0682424	+	0.997669i	$0.478261\pi$
$810$		0			0
$811$		0			0		−0.439735	−	0.898128i	$-0.644928\pi$
$811$		0			0		0.439735	+	0.898128i	$0.355072\pi$
$812$	−2.32456	−	1.00970i	−2.32456	−	1.00970i
$813$		0			0
$814$	−2.15879	−	6.54256i	−2.15879	−	6.54256i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.834880	+	0.0762355i	0.834880	+	0.0762355i	0.500000	−	0.866025i	$-0.333333\pi$
$821$	0.834880	+	0.0762355i	0.834880	+	0.0762355i	0.334880	+	0.942261i	$0.391304\pi$
$822$		0			0
$823$	1.72801	−	0.118199i	1.72801	−	0.118199i	0.829885	−	0.557934i	$-0.188406\pi$
$823$	1.72801	−	0.118199i	1.72801	−	0.118199i	0.898128	+	0.439735i	$0.144928\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.530621	+	1.02405i	−0.530621	+	1.02405i	0.460065	+	0.887885i	$0.347826\pi$
$827$	−0.530621	+	1.02405i	−0.530621	+	1.02405i	−0.990686	+	0.136167i	$0.956522\pi$
$828$	4.62295	+	2.26346i	4.62295	+	2.26346i
$829$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$829$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$839$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$840$		0			0
$841$	−0.152725	−	0.0139458i	−0.152725	−	0.0139458i
$842$	1.57374	−	0.402541i	1.57374	−	0.402541i
$843$		0			0
$844$	0.124228	+	0.0170748i	0.124228	+	0.0170748i
$845$		0			0
$846$		0			0
$847$	1.63456	+	2.31564i	1.63456	+	2.31564i
$848$	−1.24782	−	3.78171i	−1.24782	−	3.78171i
$849$		0			0
$850$		0			0
$851$	1.49218	+	3.04767i	1.49218	+	3.04767i
$852$		0			0
$853$		0			0		−0.715110	−	0.699012i	$-0.753623\pi$
$853$		0			0		0.715110	+	0.699012i	$0.246377\pi$
$854$		0			0
$855$		0			0
$856$	−1.83614	−	6.02207i	−1.83614	−	6.02207i
$857$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$857$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$858$		0			0
$859$		0			0		−0.934394	−	0.356242i	$-0.884058\pi$
$859$		0			0		0.934394	+	0.356242i	$0.115942\pi$
$860$		0			0
$861$		0			0
$862$	−3.83421	−	0.438327i	−3.83421	−	0.438327i
$863$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$863$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.506419	−	3.68447i	−0.506419	−	3.68447i
$870$		0			0
$871$		0			0
$872$	0.492758	−	2.37128i	0.492758	−	2.37128i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.153202	+	1.67776i	−0.153202	+	1.67776i	0.460065	+	0.887885i	$0.347826\pi$
$877$	−0.153202	+	1.67776i	−0.153202	+	1.67776i	−0.613267	+	0.789876i	$0.710145\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.665740	−	0.746184i	$-0.268116\pi$
$881$		0			0		−0.665740	+	0.746184i	$0.731884\pi$
$882$	0.263839	−	1.91957i	0.263839	−	1.91957i
$883$	0.435300	−	0.616680i	0.435300	−	0.616680i	−0.538899	−	0.842371i	$-0.681159\pi$
$883$	0.435300	−	0.616680i	0.435300	−	0.616680i	0.974199	+	0.225690i	$0.0724638\pi$
$884$		0			0
$885$		0			0
$886$	−0.330092	+	0.809920i	−0.330092	+	0.809920i
$887$		0			0		−0.181116	−	0.983462i	$-0.557971\pi$
$887$		0			0		0.181116	+	0.983462i	$0.442029\pi$
$888$		0			0
$889$	−0.535792	−	0.978820i	−0.535792	−	0.978820i
$890$		0			0
$891$			1.95817i			1.95817i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−2.56100	+	2.61998i	−2.56100	+	2.61998i
$897$		0			0
$898$	−1.32709	+	2.87438i	−1.32709	+	2.87438i
$899$		0			0
$900$	1.26719	+	2.44556i	1.26719	+	2.44556i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−1.37638	−	0.971557i	−1.37638	−	0.971557i
$905$		0			0
$906$		0			0
$907$	−1.54981	+	1.26087i	−1.54981	+	1.26087i	−0.746184	+	0.665740i	$0.768116\pi$
$907$	−1.54981	+	1.26087i	−1.54981	+	1.26087i	−0.803631	+	0.595128i	$0.797101\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.99482	+	0.0454203i	1.99482	+	0.0454203i	0.998964	−	0.0455146i	$-0.0144928\pi$
$911$	1.99482	+	0.0454203i	1.99482	+	0.0454203i	0.995857	+	0.0909349i	$0.0289855\pi$
$912$		0			0
$913$		0			0
$914$	3.69141	−	0.337074i	3.69141	−	0.337074i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.949640	−	0.313344i	0.949640	−	0.313344i	0.203456	−	0.979084i	$-0.434783\pi$
$919$	0.949640	−	0.313344i	0.949640	−	0.313344i	0.746184	+	0.665740i	$0.231884\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.328873	+	1.78578i	−0.328873	+	1.78578i
$926$	2.86748	−	1.65554i	2.86748	−	1.65554i
$927$		0			0
$928$	1.62896	−	3.32705i	1.62896	−	3.32705i
$929$		0			0		−0.699012	−	0.715110i	$-0.746377\pi$
$929$		0			0		0.699012	+	0.715110i	$0.253623\pi$
$930$		0			0
$931$		0			0
$932$	−0.570939	−	0.486505i	−0.570939	−	0.486505i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.247808	−	0.968809i	$-0.579710\pi$
$937$		0			0		0.247808	+	0.968809i	$0.420290\pi$
$938$	0.536365	+	2.31524i	0.536365	+	2.31524i
$939$		0			0
$940$		0			0
$941$		0			0		0.987330	−	0.158683i	$-0.0507246\pi$
$941$		0			0		−0.987330	+	0.158683i	$0.949275\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.660048	+	0.201249i	−0.660048	+	0.201249i
$947$	−0.803631	+	1.39193i	−0.803631	+	1.39193i	0.113580	+	0.993529i	$0.463768\pi$
$947$	−0.803631	+	1.39193i	−0.803631	+	1.39193i	−0.917211	+	0.398401i	$0.869565\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.931758	+	0.997669i	−0.931758	+	0.997669i	0.0682424	+	0.997669i	$0.478261\pi$
$953$	−0.931758	+	0.997669i	−0.931758	+	0.997669i	−1.00000			$1.00000\pi$
$954$	−1.23482	+	1.59042i	−1.23482	+	1.59042i
$955$		0			0
$956$	5.18932	+	1.84428i	5.18932	+	1.84428i
$957$		0			0
$958$		0			0
$959$	−0.751156	−	0.923295i	−0.751156	−	0.923295i
$960$		0			0
$961$	0.974199	+	0.225690i	0.974199	+	0.225690i
$962$		0			0
$963$	−1.16883	+	1.43668i	−1.16883	+	1.43668i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.585537	+	1.43668i	0.585537	+	1.43668i	0.877183	+	0.480157i	$0.159420\pi$
$967$	0.585537	+	1.43668i	0.585537	+	1.43668i	−0.291646	+	0.956526i	$0.594203\pi$
$968$	−8.11626	+	5.19230i	−8.11626	+	5.19230i
$969$		0			0
$970$		0			0
$971$		0			0		0.842371	−	0.538899i	$-0.181159\pi$
$971$		0			0		−0.842371	+	0.538899i	$0.818841\pi$
$972$		0			0
$973$		0			0
$974$	2.49714	−	0.285473i	2.49714	−	0.285473i
$975$		0			0
$976$		0			0
$977$	0.135214	−	1.97675i	0.135214	−	1.97675i	−0.0682424	−	0.997669i	$-0.521739\pi$
$977$	0.135214	−	1.97675i	0.135214	−	1.97675i	0.203456	−	0.979084i	$-0.434783\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.659790	+	0.268905i	−0.659790	+	0.268905i
$982$	−3.69227	−	0.944432i	−3.69227	−	0.944432i
$983$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$983$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.308575	−	0.142468i	0.308575	−	0.142468i
$990$		0			0
$991$	0.0682424	+	0.118199i	0.0682424	+	0.118199i	0.898128	−	0.439735i	$-0.144928\pi$
$991$	0.0682424	+	0.118199i	0.0682424	+	0.118199i	−0.829885	+	0.557934i	$0.811594\pi$
$992$		0			0
$993$		0			0
$994$	0.247053	−	0.748734i	0.247053	−	0.748734i
$995$		0			0
$996$		0			0
$997$		0			0		−0.595128	−	0.803631i	$-0.702899\pi$
$997$		0			0		0.595128	+	0.803631i	$0.297101\pi$
$998$	−1.44406	+	0.232087i	−1.44406	+	0.232087i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1939.1.by.a.62.1	✓	44
7.6	odd	2	CM	1939.1.by.a.62.1	✓	44
277.210	even	138	inner	1939.1.by.a.1595.1	yes	44
1939.1595	odd	138	inner	1939.1.by.a.1595.1	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1939.1.by.a.62.1	✓	44	1.1	even	1	trivial
1939.1.by.a.62.1	✓	44	7.6	odd	2	CM
1939.1.by.a.1595.1	yes	44	277.210	even	138	inner
1939.1.by.a.1595.1	yes	44	1939.1595	odd	138	inner

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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:	\( N \)	\(=\)	\( 1939 = 7 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1939.by (of order \(138\), degree \(44\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00676 + 1.65554i) q^{2} +(-1.26719 + 2.44556i) q^{4} +(0.113580 + 0.993529i) q^{7} +(-3.39137 + 0.231976i) q^{8} +(0.613267 + 0.789876i) q^{9} +O(q^{10})\)	\(q+(1.00676 + 1.65554i) q^{2} +(-1.26719 + 2.44556i) q^{4} +(0.113580 + 0.993529i) q^{7} +(-3.39137 + 0.231976i) q^{8} +(0.613267 + 0.789876i) q^{9} +(1.89709 - 0.485249i) q^{11} +(-1.53048 + 1.18828i) q^{14} +(-2.20993 - 3.13076i) q^{16} +(-0.690261 + 1.81050i) q^{18} +(2.71326 + 2.65218i) q^{22} +(-1.50182 - 1.11217i) q^{23} +(-0.291646 - 0.956526i) q^{25} +(-2.57366 - 0.981220i) q^{28} +(0.919177 + 0.0418794i) q^{29} +(1.60395 - 3.69267i) q^{32} +(-2.70881 + 0.498860i) q^{36} +(-1.61223 - 0.835390i) q^{37} +(-0.0873260 + 0.159533i) q^{43} +(-1.21726 + 5.25435i) q^{44} +(0.329275 - 3.60600i) q^{46} +(-0.974199 + 0.225690i) q^{49} +(1.28995 - 1.44582i) q^{50} +(0.993991 + 0.303069i) q^{53} +(-0.615667 - 3.34307i) q^{56} +(0.856053 + 1.56389i) q^{58} +(-0.715110 + 0.699012i) q^{63} +(3.93168 - 0.540397i) q^{64} +(0.514134 - 1.11358i) q^{67} +(-0.337690 + 0.227030i) q^{71} +(-2.26304 - 2.53650i) q^{72} +(-0.240100 - 3.51014i) q^{74} +(0.697581 + 1.82970i) q^{77} +(0.215721 - 1.88699i) q^{79} +(-0.247808 + 0.968809i) q^{81} +(-0.352029 + 0.0160391i) q^{86} +(-6.32116 + 2.08574i) q^{88} +(4.62295 - 2.26346i) q^{92} +(-1.35442 - 1.38561i) q^{98} +(1.54671 + 1.20088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{4} + q^{7} + q^{9}+O(q^{10}) \) 44 * q + 4 * q^4 + q^7 + q^9	\( 44 q + 4 q^{4} + q^{7} + q^{9} - 3 q^{14} - 2 q^{16} - 3 q^{18} + q^{23} - q^{25} - 2 q^{28} + 21 q^{29} - 2 q^{36} - 3 q^{43} - 23 q^{44} - 26 q^{46} + q^{49} - 3 q^{50} + 3 q^{56} - 6 q^{58} + q^{63} - 2 q^{64} + q^{67} + 2 q^{71} + 3 q^{72} + 6 q^{74} + q^{79} + q^{81} - 3 q^{86} - 2 q^{92} - 20 q^{98}+O(q^{100}) \) 44 * q + 4 * q^4 + q^7 + q^9 - 3 * q^14 - 2 * q^16 - 3 * q^18 + q^23 - q^25 - 2 * q^28 + 21 * q^29 - 2 * q^36 - 3 * q^43 - 23 * q^44 - 26 * q^46 + q^49 - 3 * q^50 + 3 * q^56 - 6 * q^58 + q^63 - 2 * q^64 + q^67 + 2 * q^71 + 3 * q^72 + 6 * q^74 + q^79 + q^81 - 3 * q^86 - 2 * q^92 - 20 * q^98

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