LMFDB - Embedded newform 1939.1.by.a.1238.1

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			1238.1
Root			$0.746184 + 0.665740i$ of defining polynomial
Character	$\chi$	$=$	1939.1238
Dual form			1939.1.by.a.1336.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.697581 + 0.144959i) q^{2} +(-0.451605 - 0.196160i) q^{4} +(0.0227632 + 0.999741i) q^{7} +(-0.868673 - 0.613177i) q^{8} +(0.983462 + 0.181116i) q^{9} +O(q^{10})$	\(q+(0.697581 + 0.144959i) q^{2} +(-0.451605 - 0.196160i) q^{4} +(0.0227632 + 0.999741i) q^{7} +(-0.868673 - 0.613177i) q^{8} +(0.983462 + 0.181116i) q^{9} +(0.192226 + 0.504193i) q^{11} +(-0.129042 + 0.700700i) q^{14} +(-0.181018 - 0.193823i) q^{16} +(0.659790 + 0.268905i) q^{18} +(0.0610057 + 0.379580i) q^{22} +(0.662131 - 0.362441i) q^{23} +(-0.538899 + 0.842371i) q^{25} +(0.185829 - 0.455953i) q^{28} +(1.47420 + 1.09172i) q^{29} +(0.454289 + 0.747046i) q^{32} +(-0.408608 - 0.274709i) q^{36} +(-0.179831 + 0.414012i) q^{37} +(1.27360 - 1.42749i) q^{43} +(0.0120922 - 0.265403i) q^{44} +(0.514429 - 0.156850i) q^{46} +(-0.998964 + 0.0455146i) q^{49} +(-0.498035 + 0.509504i) q^{50} +(-1.64950 + 1.05525i) q^{53} +(0.593244 - 0.882406i) q^{56} +(0.870119 + 0.975259i) q^{58} +(-0.158683 + 0.987330i) q^{63} +(0.297425 + 0.836872i) q^{64} +(1.91617 - 0.443916i) q^{67} +(-0.807265 - 1.74847i) q^{71} +(-0.743251 - 0.760367i) q^{72} +(-0.185461 + 0.262739i) q^{74} +(-0.499687 + 0.203653i) q^{77} +(0.0112818 - 0.495487i) q^{79} +(0.934394 + 0.356242i) q^{81} +(1.09536 - 0.811170i) q^{86} +(0.142178 - 0.555847i) q^{88} +(-0.370118 + 0.0337967i) q^{92} +(-0.703456 - 0.113059i) q^{98} +(0.0977291 + 0.530670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1939\mathbb{Z}\right)^\times$.

$n$	$1109$	$1667$
$\chi(n)$	$-1$	$e\left(\frac{47}{138}\right)$

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 $

$2$	0.697581	+	0.144959i	0.697581	+	0.144959i	0.538899	−	0.842371i	$-0.318841\pi$
$2$	0.697581	+	0.144959i	0.697581	+	0.144959i	0.158683	+	0.987330i	$0.449275\pi$
$3$		0			0		−0.995857	−	0.0909349i	$-0.971014\pi$
$3$		0			0		0.995857	+	0.0909349i	$0.0289855\pi$
$4$	−0.451605	−	0.196160i	−0.451605	−	0.196160i
$5$		0			0		−0.480157	−	0.877183i	$-0.659420\pi$
$5$		0			0		0.480157	+	0.877183i	$0.340580\pi$
$6$		0			0
$7$	0.0227632	+	0.999741i	0.0227632	+	0.999741i
$7$	0.0227632	+	0.999741i	0.0227632	+	0.999741i
$8$	−0.868673	−	0.613177i	−0.868673	−	0.613177i
$9$	0.983462	+	0.181116i	0.983462	+	0.181116i
$10$		0			0
$11$	0.192226	+	0.504193i	0.192226	+	0.504193i	0.995857	−	0.0909349i	$-0.0289855\pi$
$11$	0.192226	+	0.504193i	0.192226	+	0.504193i	−0.803631	+	0.595128i	$0.797101\pi$
$12$		0			0
$13$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$13$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$14$	−0.129042	+	0.700700i	−0.129042	+	0.700700i
$15$		0			0
$16$	−0.181018	−	0.193823i	−0.181018	−	0.193823i
$17$		0			0		−0.968809	−	0.247808i	$-0.920290\pi$
$17$		0			0		0.968809	+	0.247808i	$0.0797101\pi$
$18$	0.659790	+	0.268905i	0.659790	+	0.268905i
$19$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$19$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$20$		0			0
$21$		0			0
$22$	0.0610057	+	0.379580i	0.0610057	+	0.379580i
$23$	0.662131	−	0.362441i	0.662131	−	0.362441i	−0.113580	−	0.993529i	$-0.536232\pi$
$23$	0.662131	−	0.362441i	0.662131	−	0.362441i	0.775711	+	0.631088i	$0.217391\pi$
$24$		0			0
$25$	−0.538899	+	0.842371i	−0.538899	+	0.842371i
$26$		0			0
$27$		0			0
$28$	0.185829	−	0.455953i	0.185829	−	0.455953i
$29$	1.47420	+	1.09172i	1.47420	+	1.09172i	0.974199	+	0.225690i	$0.0724638\pi$
$29$	1.47420	+	1.09172i	1.47420	+	1.09172i	0.500000	+	0.866025i	$0.333333\pi$
$30$		0			0
$31$		0			0		−0.999741	−	0.0227632i	$-0.992754\pi$
$31$		0			0		0.999741	+	0.0227632i	$0.00724638\pi$
$32$	0.454289	+	0.747046i	0.454289	+	0.747046i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.408608	−	0.274709i	−0.408608	−	0.274709i
$37$	−0.179831	+	0.414012i	−0.179831	+	0.414012i	−0.983462	−	0.181116i	$-0.942029\pi$
$37$	−0.179831	+	0.414012i	−0.179831	+	0.414012i	0.803631	+	0.595128i	$0.202899\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$41$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$42$		0			0
$43$	1.27360	−	1.42749i	1.27360	−	1.42749i	0.419177	−	0.907905i	$-0.362319\pi$
$43$	1.27360	−	1.42749i	1.27360	−	1.42749i	0.854419	−	0.519584i	$-0.173913\pi$
$44$	0.0120922	−	0.265403i	0.0120922	−	0.265403i
$45$		0			0
$46$	0.514429	−	0.156850i	0.514429	−	0.156850i
$47$		0			0		−0.715110	−	0.699012i	$-0.753623\pi$
$47$		0			0		0.715110	+	0.699012i	$0.246377\pi$
$48$		0			0
$49$	−0.998964	+	0.0455146i	−0.998964	+	0.0455146i
$50$	−0.498035	+	0.509504i	−0.498035	+	0.509504i
$51$		0			0
$52$		0			0
$53$	−1.64950	+	1.05525i	−1.64950	+	1.05525i	−0.715110	+	0.699012i	$0.753623\pi$
$53$	−1.64950	+	1.05525i	−1.64950	+	1.05525i	−0.934394	+	0.356242i	$0.884058\pi$
$54$		0			0
$55$		0			0
$56$	0.593244	−	0.882406i	0.593244	−	0.882406i
$57$		0			0
$58$	0.870119	+	0.975259i	0.870119	+	0.975259i
$59$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$59$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$60$		0			0
$61$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$61$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$62$		0			0
$63$	−0.158683	+	0.987330i	−0.158683	+	0.987330i
$64$	0.297425	+	0.836872i	0.297425	+	0.836872i
$65$		0			0
$66$		0			0
$67$	1.91617	−	0.443916i	1.91617	−	0.443916i	0.917211	−	0.398401i	$-0.130435\pi$
$67$	1.91617	−	0.443916i	1.91617	−	0.443916i	0.998964	−	0.0455146i	$-0.0144928\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.807265	−	1.74847i	−0.807265	−	1.74847i	−0.648582	−	0.761145i	$-0.724638\pi$
$71$	−0.807265	−	1.74847i	−0.807265	−	1.74847i	−0.158683	−	0.987330i	$-0.550725\pi$
$72$	−0.743251	−	0.760367i	−0.743251	−	0.760367i
$73$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$73$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$74$	−0.185461	+	0.262739i	−0.185461	+	0.262739i
$75$		0			0
$76$		0			0
$77$	−0.499687	+	0.203653i	−0.499687	+	0.203653i
$78$		0			0
$79$	0.0112818	−	0.495487i	0.0112818	−	0.495487i	−0.962917	−	0.269797i	$-0.913043\pi$
$79$	0.0112818	−	0.495487i	0.0112818	−	0.495487i	0.974199	−	0.225690i	$-0.0724638\pi$
$80$		0			0
$81$	0.934394	+	0.356242i	0.934394	+	0.356242i
$82$		0			0
$83$		0			0		0.291646	−	0.956526i	$-0.405797\pi$
$83$		0			0		−0.291646	+	0.956526i	$0.594203\pi$
$84$		0			0
$85$		0			0
$86$	1.09536	−	0.811170i	1.09536	−	0.811170i
$87$		0			0
$88$	0.142178	−	0.555847i	0.142178	−	0.555847i
$89$		0			0		−0.377419	−	0.926043i	$-0.623188\pi$
$89$		0			0		0.377419	+	0.926043i	$0.376812\pi$
$90$		0			0
$91$		0			0
$92$	−0.370118	+	0.0337967i	−0.370118	+	0.0337967i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.0909349	−	0.995857i	$-0.471014\pi$
$97$		0			0		−0.0909349	+	0.995857i	$0.528986\pi$
$98$	−0.703456	−	0.113059i	−0.703456	−	0.113059i
$99$	0.0977291	+	0.530670i	0.0977291	+	0.530670i
$100$	0.408608	−	0.274709i	0.408608	−	0.274709i
$101$		0			0		0.439735	−	0.898128i	$-0.355072\pi$
$101$		0			0		−0.439735	+	0.898128i	$0.644928\pi$
$102$		0			0
$103$		0			0		−0.595128	−	0.803631i	$-0.702899\pi$
$103$		0			0		0.595128	+	0.803631i	$0.297101\pi$
$104$		0			0
$105$		0			0
$106$	−1.30363	+	0.497015i	−1.30363	+	0.497015i
$107$	−0.0692864	−	1.52071i	−0.0692864	−	1.52071i	−0.682553	−	0.730836i	$-0.739130\pi$
$107$	−0.0692864	−	1.52071i	−0.0692864	−	1.52071i	0.613267	−	0.789876i	$-0.289855\pi$
$108$		0			0
$109$	−1.16883	+	1.43668i	−1.16883	+	1.43668i	−0.291646	+	0.956526i	$0.594203\pi$
$109$	−1.16883	+	1.43668i	−1.16883	+	1.43668i	−0.877183	+	0.480157i	$0.840580\pi$
$110$		0			0
$111$		0			0
$112$	0.189652	−	0.185383i	0.189652	−	0.185383i
$113$	−1.85138	−	0.254467i	−1.85138	−	0.254467i	−0.877183	−	0.480157i	$-0.840580\pi$
$113$	−1.85138	−	0.254467i	−1.85138	−	0.254467i	−0.974199	+	0.225690i	$0.927536\pi$
$114$		0			0
$115$		0			0
$116$	−0.451605	−	0.782203i	−0.451605	−	0.782203i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.528924	−	0.471902i	0.528924	−	0.471902i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.253816	+	0.665740i	−0.253816	+	0.665740i
$127$	−1.38209	+	1.17770i	−1.38209	+	1.17770i	−0.419177	+	0.907905i	$0.637681\pi$
$127$	−1.38209	+	1.17770i	−1.38209	+	1.17770i	−0.962917	+	0.269797i	$0.913043\pi$
$128$	−0.0328892	−	0.239287i	−0.0328892	−	0.239287i
$129$		0			0
$130$		0			0
$131$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$131$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$132$		0			0
$133$		0			0
$134$	1.40104	−	0.0319004i	1.40104	−	0.0319004i
$135$		0			0
$136$		0			0
$137$	−0.954100	+	0.109073i	−0.954100	+	0.109073i	−0.576680	−	0.816970i	$-0.695652\pi$
$137$	−0.954100	+	0.109073i	−0.954100	+	0.109073i	−0.377419	+	0.926043i	$0.623188\pi$
$138$		0			0
$139$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$139$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$140$		0			0
$141$		0			0
$142$	−0.309675	−	1.33672i	−0.309675	−	1.33672i
$143$		0			0
$144$	−0.142920	−	0.223403i	−0.142920	−	0.223403i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.162425	−	0.151694i	0.162425	−	0.151694i
$149$	−0.181303	−	1.31908i	−0.181303	−	1.31908i	−0.829885	−	0.557934i	$-0.811594\pi$
$149$	−0.181303	−	1.31908i	−0.181303	−	1.31908i	0.648582	−	0.761145i	$-0.275362\pi$
$150$		0			0
$151$	0.703456	−	1.84511i	0.703456	−	1.84511i	0.203456	−	0.979084i	$-0.434783\pi$
$151$	0.703456	−	1.84511i	0.703456	−	1.84511i	0.500000	−	0.866025i	$-0.333333\pi$
$152$		0			0
$153$		0			0
$154$	−0.378093	+	0.0696304i	−0.378093	+	0.0696304i
$155$		0			0
$156$		0			0
$157$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$157$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$158$	0.0796953	−	0.344007i	0.0796953	−	0.344007i
$159$		0			0
$160$		0			0
$161$	0.377419	+	0.653709i	0.377419	+	0.653709i
$162$	0.600175	+	0.383956i	0.600175	+	0.383956i
$163$	−1.08106	+	0.276521i	−1.08106	+	0.276521i	−0.746184	−	0.665740i	$-0.768116\pi$
$163$	−1.08106	+	0.276521i	−1.08106	+	0.276521i	−0.334880	+	0.942261i	$0.608696\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.789876	−	0.613267i	$-0.210145\pi$
$167$		0			0		−0.789876	+	0.613267i	$0.789855\pi$
$168$		0			0
$169$	−0.775711	−	0.631088i	−0.775711	−	0.631088i
$170$		0			0
$171$		0			0
$172$	−0.855178	+	0.394833i	−0.855178	+	0.394833i
$173$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$173$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$174$		0			0
$175$	−0.854419	−	0.519584i	−0.854419	−	0.519584i
$176$	0.0629278	−	0.128526i	0.0629278	−	0.128526i
$177$		0			0
$178$		0			0
$179$	−1.97006	−	0.316625i	−1.97006	−	0.316625i	−0.995857	−	0.0909349i	$-0.971014\pi$
$179$	−1.97006	−	0.316625i	−1.97006	−	0.316625i	−0.974199	−	0.225690i	$-0.927536\pi$
$180$		0			0
$181$		0			0		−0.439735	−	0.898128i	$-0.644928\pi$
$181$		0			0		0.439735	+	0.898128i	$0.355072\pi$
$182$		0			0
$183$		0			0
$184$	−0.797416	−	0.0911606i	−0.797416	−	0.0911606i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.60560	−	1.18902i	1.60560	−	1.18902i	0.775711	−	0.631088i	$-0.217391\pi$
$191$	1.60560	−	1.18902i	1.60560	−	1.18902i	0.829885	−	0.557934i	$-0.188406\pi$
$192$		0			0
$193$	0.146009	−	0.281784i	0.146009	−	0.281784i	−0.803631	−	0.595128i	$-0.797101\pi$
$193$	0.146009	−	0.281784i	0.146009	−	0.281784i	0.949640	+	0.313344i	$0.101449\pi$
$194$		0			0
$195$		0			0
$196$	0.460065	+	0.175402i	0.460065	+	0.175402i
$197$	−0.249673	+	0.756675i	−0.249673	+	0.756675i	0.746184	+	0.665740i	$0.231884\pi$
$197$	−0.249673	+	0.756675i	−0.249673	+	0.756675i	−0.995857	+	0.0909349i	$0.971014\pi$
$198$	−0.00875134	+	0.384352i	−0.00875134	+	0.384352i
$199$		0			0		0.595128	−	0.803631i	$-0.297101\pi$
$199$		0			0		−0.595128	+	0.803631i	$0.702899\pi$
$200$	0.984649	−	0.401305i	0.984649	−	0.401305i
$201$		0			0
$202$		0			0
$203$	−1.05788	+	1.49867i	−1.05788	+	1.49867i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.716825	−	0.236524i	0.716825	−	0.236524i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.129611	+	1.89485i	0.129611	+	1.89485i	0.377419	+	0.926043i	$0.376812\pi$
$211$	0.129611	+	1.89485i	0.129611	+	1.89485i	−0.247808	+	0.968809i	$0.579710\pi$
$212$	0.951922	−	0.152992i	0.951922	−	0.152992i
$213$		0			0
$214$	0.172108	−	1.07086i	0.172108	−	1.07086i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.02361	+	0.832771i	−1.02361	+	0.832771i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$223$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$224$	−0.736511	+	0.471176i	−0.736511	+	0.471176i
$225$	−0.682553	+	0.730836i	−0.682553	+	0.730836i
$226$	−1.25460	−	0.445886i	−1.25460	−	0.445886i
$227$		0			0		0.699012	−	0.715110i	$-0.253623\pi$
$227$		0			0		−0.699012	+	0.715110i	$0.746377\pi$
$228$		0			0
$229$		0			0		−0.613267	−	0.789876i	$-0.710145\pi$
$229$		0			0		0.613267	+	0.789876i	$0.289855\pi$
$230$		0			0
$231$		0			0
$232$	−0.611183	−	1.85229i	−0.611183	−	1.85229i
$233$	0.0857733	−	1.88257i	0.0857733	−	1.88257i	−0.291646	−	0.956526i	$-0.594203\pi$
$233$	0.0857733	−	1.88257i	0.0857733	−	1.88257i	0.377419	−	0.926043i	$-0.376812\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.590504	−	0.209865i	0.590504	−	0.209865i	−0.0227632	−	0.999741i	$-0.507246\pi$
$239$	0.590504	−	0.209865i	0.590504	−	0.209865i	0.613267	+	0.789876i	$0.289855\pi$
$240$		0			0
$241$		0			0		−0.829885	−	0.557934i	$-0.811594\pi$
$241$		0			0		0.829885	+	0.557934i	$0.188406\pi$
$242$	0.437374	−	0.252518i	0.437374	−	0.252518i
$243$		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		0.519584	−	0.854419i	$-0.326087\pi$
$251$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$252$	0.265336	−	0.414756i	0.265336	−	0.414756i
$253$	0.310019	+	0.264171i	0.310019	+	0.264171i
$254$	−1.13484	+	0.621195i	−1.13484	+	0.621195i
$255$		0			0
$256$	0.0723536	−	1.05777i	0.0723536	−	1.05777i
$257$		0			0		−0.0909349	−	0.995857i	$-0.528986\pi$
$257$		0			0		0.0909349	+	0.995857i	$0.471014\pi$
$258$		0			0
$259$	−0.417998	−	0.170360i	−0.417998	−	0.170360i
$260$		0			0
$261$	1.25209	+	1.34066i	1.25209	+	1.34066i
$262$		0			0
$263$	0.0493240	−	0.267829i	0.0493240	−	0.267829i	−0.949640	−	0.313344i	$-0.898551\pi$
$263$	0.0493240	−	0.267829i	0.0493240	−	0.267829i	0.998964	+	0.0455146i	$0.0144928\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.952432	−	0.175402i	−0.952432	−	0.175402i
$269$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$269$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$270$		0			0
$271$		0			0		−0.956526	−	0.291646i	$-0.905797\pi$
$271$		0			0		0.956526	+	0.291646i	$0.0942029\pi$
$272$		0			0
$273$		0			0
$274$	−0.681373	−	0.0622183i	−0.681373	−	0.0622183i
$275$	−0.528307	−	0.109784i	−0.528307	−	0.109784i
$276$		0			0
$277$	−0.829885	+	0.557934i	−0.829885	+	0.557934i
$277$	−0.829885	+	0.557934i	−0.829885	+	0.557934i
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.42298	+	0.618088i	1.42298	+	0.618088i	0.962917	−	0.269797i	$-0.0869565\pi$
$281$	1.42298	+	0.618088i	1.42298	+	0.618088i	0.460065	+	0.887885i	$0.347826\pi$
$282$		0			0
$283$		0			0		−0.956526	−	0.291646i	$-0.905797\pi$
$283$		0			0		0.956526	+	0.291646i	$0.0942029\pi$
$284$	0.0215845	+	0.947972i	0.0215845	+	0.947972i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.311473	+	0.816970i	0.311473	+	0.816970i
$289$	0.877183	+	0.480157i	0.877183	+	0.480157i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$293$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$294$		0			0
$295$		0			0
$296$	0.410076	−	0.249373i	0.410076	−	0.249373i
$297$		0			0
$298$	0.0647387	−	0.946446i	0.0647387	−	0.946446i
$299$		0			0
$300$		0			0
$301$	1.45611	+	1.24077i	1.45611	+	1.24077i
$302$	0.758183	−	1.18514i	0.758183	−	1.18514i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$307$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$308$	0.265609	+	0.00604769i	0.265609	+	0.00604769i
$309$		0			0
$310$		0			0
$311$		0			0		−0.898128	−	0.439735i	$-0.855072\pi$
$311$		0			0		0.898128	+	0.439735i	$0.144928\pi$
$312$		0			0
$313$		0			0		−0.829885	−	0.557934i	$-0.811594\pi$
$313$		0			0		0.829885	+	0.557934i	$0.188406\pi$
$314$		0			0
$315$		0			0
$316$	−0.102290	+	0.221551i	−0.102290	+	0.221551i
$317$	0.176211	−	1.54138i	0.176211	−	1.54138i	−0.538899	−	0.842371i	$-0.681159\pi$
$317$	0.176211	−	1.54138i	0.176211	−	1.54138i	0.715110	−	0.699012i	$-0.246377\pi$
$318$		0			0
$319$	−0.267056	+	0.953137i	−0.267056	+	0.953137i
$320$		0			0
$321$		0			0
$322$	0.168519	+	0.510726i	0.168519	+	0.510726i
$323$		0			0
$324$	−0.352097	−	0.344171i	−0.352097	−	0.344171i
$325$		0			0
$326$	−0.794214	+	0.0361858i	−0.794214	+	0.0361858i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.24129	+	0.643182i	1.24129	+	0.643182i	0.949640	−	0.313344i	$-0.101449\pi$
$331$	1.24129	+	0.643182i	1.24129	+	0.643182i	0.291646	+	0.956526i	$0.405797\pi$
$332$		0			0
$333$	−0.251841	+	0.374594i	−0.251841	+	0.374594i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	1.88452i		−	1.88452i	−0.334880	−	0.942261i	$-0.608696\pi$
$337$		−	1.88452i		−	1.88452i	0.334880	−	0.942261i	$-0.391304\pi$
$338$	−0.449640	−	0.552681i	−0.449640	−	0.552681i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.0682424	−	0.997669i	−0.0682424	−	0.997669i
$344$	−1.98164	+	0.459082i	−1.98164	+	0.459082i
$345$		0			0
$346$		0			0
$347$	0.553917	−	0.182771i	0.553917	−	0.182771i	−0.0227632	−	0.999741i	$-0.507246\pi$
$347$	0.553917	−	0.182771i	0.553917	−	0.182771i	0.576680	+	0.816970i	$0.304348\pi$
$348$		0			0
$349$		0			0		−0.699012	−	0.715110i	$-0.746377\pi$
$349$		0			0		0.699012	+	0.715110i	$0.253623\pi$
$350$	−0.520709	−	0.486308i	−0.520709	−	0.486308i
$351$		0			0
$352$	−0.289329	+	0.372650i	−0.289329	+	0.372650i
$353$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$353$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.32838	−	0.506449i	−1.32838	−	0.506449i
$359$	−0.625227	+	0.0427667i	−0.625227	+	0.0427667i	−0.377419	−	0.926043i	$-0.623188\pi$
$359$	−0.625227	+	0.0427667i	−0.625227	+	0.0427667i	−0.247808	+	0.968809i	$0.579710\pi$
$360$		0			0
$361$	0.460065	−	0.887885i	0.460065	−	0.887885i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.113580	−	0.993529i	$-0.536232\pi$
$367$		0			0		0.113580	+	0.993529i	$0.463768\pi$
$368$	−0.190107	−	0.0627278i	−0.190107	−	0.0627278i
$369$		0			0
$370$		0			0
$371$	−1.09253	−	1.62505i	−1.09253	−	1.62505i
$372$		0			0
$373$	0.761643	+	1.55560i	0.761643	+	1.55560i	0.829885	+	0.557934i	$0.188406\pi$
$373$	0.761643	+	1.55560i	0.761643	+	1.55560i	−0.0682424	+	0.997669i	$0.521739\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.716305	+	0.435595i	0.716305	+	0.435595i	0.829885	−	0.557934i	$-0.188406\pi$
$379$	0.716305	+	0.435595i	0.716305	+	0.435595i	−0.113580	+	0.993529i	$0.536232\pi$
$380$		0			0
$381$		0			0
$382$	1.29239	−	0.596694i	1.29239	−	0.596694i
$383$		0			0		0.934394	−	0.356242i	$-0.115942\pi$
$383$		0			0		−0.934394	+	0.356242i	$0.884058\pi$
$384$		0			0
$385$		0			0
$386$	0.142700	−	0.175402i	0.142700	−	0.175402i
$387$	1.51107	−	1.17321i	1.51107	−	1.17321i
$388$		0			0
$389$	0.715110	−	0.699012i	0.715110	−	0.699012i	−0.247808	−	0.968809i	$-0.579710\pi$
$389$	0.715110	−	0.699012i	0.715110	−	0.699012i	0.962917	+	0.269797i	$0.0869565\pi$
$390$		0			0
$391$		0			0
$392$	0.895682	+	0.573004i	0.895682	+	0.573004i
$393$		0			0
$394$	−0.283854	+	0.491650i	−0.283854	+	0.491650i
$395$		0			0
$396$	0.0599610	−	0.258824i	0.0599610	−	0.258824i
$397$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$397$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$398$		0			0
$399$		0			0
$400$	0.260821	−	0.0480333i	0.260821	−	0.0480333i
$401$	0.723420	+	0.334001i	0.723420	+	0.334001i	0.746184	−	0.665740i	$-0.231884\pi$
$401$	0.723420	+	0.334001i	0.723420	+	0.334001i	−0.0227632	+	0.999741i	$0.507246\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.955199	+	0.892094i	−0.955199	+	0.892094i
$407$	−0.243310	−	0.0110856i	−0.243310	−	0.0110856i
$408$		0			0
$409$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$409$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.534330	−	0.0610845i	0.534330	−	0.0610845i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.225690	−	0.974199i	$-0.572464\pi$
$419$		0			0		0.225690	+	0.974199i	$0.427536\pi$
$420$		0			0
$421$	1.04999	+	1.64127i	1.04999	+	1.64127i	0.715110	+	0.699012i	$0.246377\pi$
$421$	1.04999	+	1.64127i	1.04999	+	1.64127i	0.334880	+	0.942261i	$0.391304\pi$
$422$	−0.184261	+	1.34060i	−0.184261	+	1.34060i
$423$		0			0
$424$	2.07994	+	0.0947657i	2.07994	+	0.0947657i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.267012	+	0.700352i	−0.267012	+	0.700352i
$429$		0			0
$430$		0			0
$431$	−0.573645	+	0.105644i	−0.573645	+	0.105644i	−0.460065	−	0.887885i	$-0.652174\pi$
$431$	−0.573645	+	0.105644i	−0.573645	+	0.105644i	−0.113580	+	0.993529i	$0.536232\pi$
$432$		0			0
$433$		0			0		0.746184	−	0.665740i	$-0.231884\pi$
$433$		0			0		−0.746184	+	0.665740i	$0.768116\pi$
$434$		0			0
$435$		0			0
$436$	0.809668	−	0.419536i	0.809668	−	0.419536i
$437$		0			0
$438$		0			0
$439$		0			0		−0.842371	−	0.538899i	$-0.818841\pi$
$439$		0			0		0.842371	+	0.538899i	$0.181159\pi$
$440$		0			0
$441$	−0.990686	−	0.136167i	−0.990686	−	0.136167i
$442$		0			0
$443$	0.0437083	−	0.0798492i	0.0437083	−	0.0798492i	−0.854419	−	0.519584i	$-0.826087\pi$
$443$	0.0437083	−	0.0798492i	0.0437083	−	0.0798492i	0.898128	+	0.439735i	$0.144928\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.829885	+	0.316397i	−0.829885	+	0.316397i
$449$	1.32706	−	0.612699i	1.32706	−	0.612699i	0.377419	−	0.926043i	$-0.376812\pi$
$449$	1.32706	−	0.612699i	1.32706	−	0.612699i	0.949640	+	0.313344i	$0.101449\pi$
$450$	−0.582078	+	0.410875i	−0.582078	+	0.410875i
$451$		0			0
$452$	0.786177	+	0.478085i	0.786177	+	0.478085i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.153202	+	1.67776i	−0.153202	+	1.67776i	0.460065	+	0.887885i	$0.347826\pi$
$457$	−0.153202	+	1.67776i	−0.153202	+	1.67776i	−0.613267	+	0.789876i	$0.710145\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.993529	−	0.113580i	$-0.963768\pi$
$461$		0			0		0.993529	+	0.113580i	$0.0362319\pi$
$462$		0			0
$463$	−0.386420	−	0.127503i	−0.386420	−	0.127503i	0.113580	−	0.993529i	$-0.463768\pi$
$463$	−0.386420	−	0.127503i	−0.386420	−	0.127503i	−0.500000	+	0.866025i	$0.666667\pi$
$464$	−0.0552570	−	0.483353i	−0.0552570	−	0.483353i
$465$		0			0
$466$	0.332729	−	1.30081i	0.332729	−	1.30081i
$467$		0			0		−0.746184	−	0.665740i	$-0.768116\pi$
$467$		0			0		0.746184	+	0.665740i	$0.231884\pi$
$468$		0			0
$469$	0.487419	+	1.90557i	0.487419	+	1.90557i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.964548	+	0.367738i	0.964548	+	0.367738i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.81335	+	0.739050i	−1.81335	+	0.739050i
$478$	0.442346	−	0.0607991i	0.442346	−	0.0607991i
$479$		0			0		0.613267	−	0.789876i	$-0.289855\pi$
$479$		0			0		−0.613267	+	0.789876i	$0.710145\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.331433	+	0.109360i	−0.331433	+	0.109360i
$485$		0			0
$486$		0			0
$487$	−1.74991	+	0.405398i	−1.74991	+	0.405398i	−0.974199	−	0.225690i	$-0.927536\pi$
$487$	−1.74991	+	0.405398i	−1.74991	+	0.405398i	−0.775711	+	0.631088i	$0.782609\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.263377	−	1.63874i	0.263377	−	1.63874i	−0.419177	−	0.907905i	$-0.637681\pi$
$491$	0.263377	−	1.63874i	0.263377	−	1.63874i	0.682553	−	0.730836i	$-0.260870\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.72965	−	0.846856i	1.72965	−	0.846856i
$498$		0			0
$499$	−0.841317	+	0.987330i	−0.841317	+	0.987330i	0.158683	+	0.987330i	$0.449275\pi$
$499$	−0.841317	+	0.987330i	−0.841317	+	0.987330i	−1.00000			$\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$503$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$504$	0.743251	−	0.760367i	0.743251	−	0.760367i
$505$		0			0
$506$	0.177969	+	0.229221i	0.177969	+	0.229221i
$507$		0			0
$508$	0.855178	−	0.260745i	0.855178	−	0.260745i
$509$		0			0		−0.313344	−	0.949640i	$-0.601449\pi$
$509$		0			0		0.313344	+	0.949640i	$0.398551\pi$
$510$		0			0
$511$		0			0
$512$	0.138640	−	0.494814i	0.138640	−	0.494814i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.266892	−	0.179432i	−0.266892	−	0.179432i
$519$		0			0
$520$		0			0
$521$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$521$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$522$	0.679094	+	1.11672i	0.679094	+	1.11672i
$523$		0			0		−0.999741	−	0.0227632i	$-0.992754\pi$
$523$		0			0		0.999741	+	0.0227632i	$0.00724638\pi$
$524$		0			0
$525$		0			0
$526$	0.0732318	−	0.179683i	0.0732318	−	0.179683i
$527$		0			0
$528$		0			0
$529$	−0.231844	+	0.362404i	−0.231844	+	0.362404i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−1.93673	−	0.789336i	−1.93673	−	0.789336i
$537$		0			0
$538$		0			0
$539$	−0.214975	−	0.494921i	−0.214975	−	0.494921i
$540$		0			0
$541$	−0.410741	+	1.15571i	−0.410741	+	1.15571i	0.538899	+	0.842371i	$0.318841\pi$
$541$	−0.410741	+	1.15571i	−0.410741	+	1.15571i	−0.949640	+	0.313344i	$0.898551\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.0209451	−	0.919892i	−0.0209451	−	0.919892i	−0.898128	−	0.439735i	$-0.855072\pi$
$547$	−0.0209451	−	0.919892i	−0.0209451	−	0.919892i	0.877183	−	0.480157i	$-0.159420\pi$
$548$	0.452272	+	0.137898i	0.452272	+	0.137898i
$549$		0			0
$550$	−0.352623	−	0.153166i	−0.352623	−	0.153166i
$551$		0			0
$552$		0			0
$553$	0.495616			0.495616
$554$	−0.659790	+	0.268905i	−0.659790	+	0.268905i
$555$		0			0
$556$		0			0
$557$	−1.14858	−	0.104881i	−1.14858	−	0.104881i	−0.500000	−	0.866025i	$-0.666667\pi$
$557$	−1.14858	−	0.104881i	−1.14858	−	0.104881i	−0.648582	+	0.761145i	$0.724638\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.903048	+	0.637441i	0.903048	+	0.637441i
$563$		0			0		−0.983462	−	0.181116i	$-0.942029\pi$
$563$		0			0		0.983462	+	0.181116i	$0.0579710\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.334880	+	0.942261i	−0.334880	+	0.942261i
$568$	−0.370874	+	2.01385i	−0.370874	+	2.01385i
$569$	−0.629375	−	1.44897i	−0.629375	−	1.44897i	−0.877183	−	0.480157i	$-0.840580\pi$
$569$	−0.629375	−	1.44897i	−0.629375	−	1.44897i	0.247808	−	0.968809i	$-0.420290\pi$
$570$		0			0
$571$	−0.350934	−	0.0897640i	−0.350934	−	0.0897640i	0.0682424	−	0.997669i	$-0.478261\pi$
$571$	−0.350934	−	0.0897640i	−0.350934	−	0.0897640i	−0.419177	+	0.907905i	$0.637681\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.0515120	+	0.753079i	−0.0515120	+	0.753079i
$576$	0.140934	+	0.876900i	0.140934	+	0.876900i
$577$		0			0		0.877183	−	0.480157i	$-0.159420\pi$
$577$		0			0		−0.877183	+	0.480157i	$0.840580\pi$
$578$	0.542303	+	0.462104i	0.542303	+	0.462104i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.849129	−	0.628821i	−0.849129	−	0.628821i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$587$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.112797	−	0.0400882i	0.112797	−	0.0400882i
$593$		0			0		0.419177	−	0.907905i	$-0.362319\pi$
$593$		0			0		−0.419177	+	0.907905i	$0.637681\pi$
$594$		0			0
$595$		0			0
$596$	−0.176873	+	0.631267i	−0.176873	+	0.631267i
$597$		0			0
$598$		0			0
$599$	0.625227	+	1.89485i	0.625227	+	1.89485i	0.377419	+	0.926043i	$0.376812\pi$
$599$	0.625227	+	1.89485i	0.625227	+	1.89485i	0.247808	+	0.968809i	$0.420290\pi$
$600$		0			0
$601$		0			0		−0.715110	−	0.699012i	$-0.753623\pi$
$601$		0			0		0.715110	+	0.699012i	$0.246377\pi$
$602$	0.835894	+	1.07662i	0.835894	+	1.07662i
$603$	1.96489	−	0.0895237i	1.96489	−	0.0895237i
$604$	−0.679620	+	0.695271i	−0.679620	+	0.695271i
$605$		0			0
$606$		0			0
$607$		0			0		0.842371	−	0.538899i	$-0.181159\pi$
$607$		0			0		−0.842371	+	0.538899i	$0.818841\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.775711	+	0.631088i	−0.775711	+	0.631088i	−0.934394	−	0.356242i	$-0.884058\pi$
$613$	−0.775711	+	0.631088i	−0.775711	+	0.631088i	0.158683	+	0.987330i	$0.449275\pi$
$614$		0			0
$615$		0			0
$616$	0.558940	+	0.129488i	0.558940	+	0.129488i
$617$	0.314409	−	1.95627i	0.314409	−	1.95627i	0.0227632	−	0.999741i	$-0.492754\pi$
$617$	0.314409	−	1.95627i	0.314409	−	1.95627i	0.291646	−	0.956526i	$-0.405797\pi$
$618$		0			0
$619$		0			0		0.987330	−	0.158683i	$-0.0507246\pi$
$619$		0			0		−0.987330	+	0.158683i	$0.949275\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.419177	−	0.907905i	−0.419177	−	0.907905i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.85161	−	0.754643i	1.85161	−	0.754643i	0.917211	−	0.398401i	$-0.130435\pi$
$631$	1.85161	−	0.754643i	1.85161	−	0.754643i	0.934394	−	0.356242i	$-0.115942\pi$
$632$	−0.313621	+	0.423499i	−0.313621	+	0.423499i
$633$		0			0
$634$	0.346359	−	1.04970i	0.346359	−	1.04970i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.324459	+	0.626178i	−0.324459	+	0.626178i
$639$	−0.477237	−	1.86577i	−0.477237	−	1.86577i
$640$		0			0
$641$	−0.967923	−	0.863574i	−0.967923	−	0.863574i	0.0227632	−	0.999741i	$-0.492754\pi$
$641$	−0.967923	−	0.863574i	−0.967923	−	0.863574i	−0.990686	+	0.136167i	$0.956522\pi$
$642$		0			0
$643$		0			0		−0.377419	−	0.926043i	$-0.623188\pi$
$643$		0			0		0.377419	+	0.926043i	$0.376812\pi$
$644$	−0.0422130	−	0.369253i	−0.0422130	−	0.369253i
$645$		0			0
$646$		0			0
$647$		0			0		−0.993529	−	0.113580i	$-0.963768\pi$
$647$		0			0		0.993529	+	0.113580i	$0.0362319\pi$
$648$	−0.593244	−	0.882406i	−0.593244	−	0.882406i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.542456	+	0.0871829i	0.542456	+	0.0871829i
$653$	−0.215575	−	1.17057i	−0.215575	−	1.17057i	−0.898128	−	0.439735i	$-0.855072\pi$
$653$	−0.215575	−	1.17057i	−0.215575	−	1.17057i	0.682553	−	0.730836i	$-0.260870\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.75917	+	0.812204i	−1.75917	+	0.812204i	−0.775711	+	0.631088i	$0.782609\pi$
$659$	−1.75917	+	0.812204i	−1.75917	+	0.812204i	−0.983462	+	0.181116i	$0.942029\pi$
$660$		0			0
$661$		0			0		−0.0455146	−	0.998964i	$-0.514493\pi$
$661$		0			0		0.0455146	+	0.998964i	$0.485507\pi$
$662$	0.772662	+	0.628607i	0.772662	+	0.628607i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.229980	+	0.224803i	−0.229980	+	0.224803i
$667$	1.37180	+	0.188549i	1.37180	+	0.188549i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.300502	−	1.29713i	0.300502	−	1.29713i	−0.576680	−	0.816970i	$-0.695652\pi$
$673$	0.300502	−	1.29713i	0.300502	−	1.29713i	0.877183	−	0.480157i	$-0.159420\pi$
$674$	0.273178	−	1.31461i	0.273178	−	1.31461i
$675$		0			0
$676$	0.226521	+	0.437166i	0.226521	+	0.437166i
$677$		0			0		0.983462	−	0.181116i	$-0.0579710\pi$
$677$		0			0		−0.983462	+	0.181116i	$0.942029\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.922444	+	0.861502i	−0.922444	+	0.861502i	−0.990686	−	0.136167i	$-0.956522\pi$
$683$	−0.922444	+	0.861502i	−0.922444	+	0.861502i	0.0682424	+	0.997669i	$0.478261\pi$
$684$		0			0
$685$		0			0
$686$	0.0970165	−	0.705847i	0.0970165	−	0.705847i
$687$		0			0
$688$	−0.507223	+	0.0115490i	−0.507223	+	0.0115490i
$689$		0			0
$690$		0			0
$691$		0			0		0.993529	−	0.113580i	$-0.0362319\pi$
$691$		0			0		−0.993529	+	0.113580i	$0.963768\pi$
$692$		0			0
$693$	−0.528307	+	0.109784i	−0.528307	+	0.109784i
$694$	0.412896	−	0.0472023i	0.412896	−	0.0472023i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.283939	+	0.402249i	0.283939	+	0.402249i
$701$	−1.70707	−	0.0777771i	−1.70707	−	0.0777771i	−0.829885	−	0.557934i	$-0.811594\pi$
$701$	−1.70707	−	0.0777771i	−1.70707	−	0.0777771i	−0.877183	+	0.480157i	$0.840580\pi$
$702$		0			0
$703$		0			0
$704$	−0.364772	+	0.310828i	−0.364772	+	0.310828i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.859764	+	1.65927i	0.859764	+	1.65927i	0.746184	+	0.665740i	$0.231884\pi$
$709$	0.859764	+	1.65927i	0.859764	+	1.65927i	0.113580	+	0.993529i	$0.463768\pi$
$710$		0			0
$711$	0.100836	−	0.485249i	0.100836	−	0.485249i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.827578	+	0.529435i	0.827578	+	0.529435i
$717$		0			0
$718$	−0.442346	−	0.0607991i	−0.442346	−	0.0607991i
$719$		0			0		0.715110	−	0.699012i	$-0.246377\pi$
$719$		0			0		−0.715110	+	0.699012i	$0.753623\pi$
$720$		0			0
$721$		0			0
$722$	0.449640	−	0.552681i	0.449640	−	0.552681i
$723$		0			0
$724$		0			0
$725$	−1.71407	+	0.653498i	−1.71407	+	0.653498i
$726$		0			0
$727$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$727$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$728$		0			0
$729$	0.854419	+	0.519584i	0.854419	+	0.519584i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.987330	−	0.158683i	$-0.949275\pi$
$733$		0			0		0.987330	+	0.158683i	$0.0507246\pi$
$734$		0			0
$735$		0			0
$736$	0.571559	+	0.329989i	0.571559	+	0.329989i
$737$	0.592157	+	0.880790i	0.592157	+	0.880790i
$738$		0			0
$739$	0.666984	−	0.0609045i	0.666984	−	0.0609045i	0.247808	−	0.968809i	$-0.420290\pi$
$739$	0.666984	−	0.0609045i	0.666984	−	0.0609045i	0.419177	+	0.907905i	$0.362319\pi$
$740$		0			0
$741$		0			0
$742$	−0.526561	−	1.29198i	−0.526561	−	1.29198i
$743$	−0.482828	+	1.88763i	−0.482828	+	1.88763i	−0.0227632	+	0.999741i	$0.507246\pi$
$743$	−0.482828	+	1.88763i	−0.482828	+	1.88763i	−0.460065	+	0.887885i	$0.652174\pi$
$744$		0			0
$745$		0			0
$746$	0.305809	+	1.19557i	0.305809	+	1.19557i
$747$		0			0
$748$		0			0
$749$	1.51874	−	0.103885i	1.51874	−	0.103885i
$750$		0			0
$751$	−0.275576	+	0.835179i	−0.275576	+	0.835179i	0.715110	+	0.699012i	$0.246377\pi$
$751$	−0.275576	+	0.835179i	−0.275576	+	0.835179i	−0.990686	+	0.136167i	$0.956522\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.01171	−	1.43326i	1.01171	−	1.43326i	0.113580	−	0.993529i	$-0.463768\pi$
$757$	1.01171	−	1.43326i	1.01171	−	1.43326i	0.898128	−	0.439735i	$-0.144928\pi$
$758$	0.436538	+	0.407698i	0.436538	+	0.407698i
$759$		0			0
$760$		0			0
$761$		0			0		0.949640	−	0.313344i	$-0.101449\pi$
$761$		0			0		−0.949640	+	0.313344i	$0.898551\pi$
$762$		0			0
$763$	−1.46292	−	1.13582i	−1.46292	−	1.13582i
$764$	−0.958334	+	0.222015i	−0.958334	+	0.222015i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.974199	−	0.225690i	$-0.927536\pi$
$769$		0			0		0.974199	+	0.225690i	$0.0724638\pi$
$770$		0			0
$771$		0			0
$772$	−0.121213	+	0.0986139i	−0.121213	+	0.0986139i
$773$		0			0		−0.665740	−	0.746184i	$-0.731884\pi$
$773$		0			0		0.665740	+	0.746184i	$0.268116\pi$
$774$	1.22416	−	0.599366i	1.22416	−	0.599366i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.600175	−	0.383956i	0.600175	−	0.383956i
$779$		0			0
$780$		0			0
$781$	0.726391	−	0.743119i	0.726391	−	0.743119i
$782$		0			0
$783$		0			0
$784$	0.189652	+	0.185383i	0.189652	+	0.185383i
$785$		0			0
$786$		0			0
$787$		0			0		0.0455146	−	0.998964i	$-0.485507\pi$
$787$		0			0		−0.0455146	+	0.998964i	$0.514493\pi$
$788$	0.261183	−	0.292742i	0.261183	−	0.292742i
$789$		0			0
$790$		0			0
$791$	0.212257	−	1.85669i	0.212257	−	1.85669i
$792$	0.240500	−	0.520904i	0.240500	−	0.520904i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.898128	−	0.439735i	$-0.855072\pi$
$797$		0			0		0.898128	+	0.439735i	$0.144928\pi$
$798$		0			0
$799$		0			0
$800$	−0.874105	−	0.0199026i	−0.874105	−	0.0199026i
$801$		0			0
$802$	0.456228	+	0.337859i	0.456228	+	0.337859i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.226951	−	1.41210i	−0.226951	−	1.41210i	−0.803631	−	0.595128i	$-0.797101\pi$
$809$	−0.226951	−	1.41210i	−0.226951	−	1.41210i	0.576680	−	0.816970i	$-0.304348\pi$
$810$		0			0
$811$		0			0		−0.0909349	−	0.995857i	$-0.528986\pi$
$811$		0			0		0.0909349	+	0.995857i	$0.471014\pi$
$812$	0.771720	−	0.469293i	0.771720	−	0.469293i
$813$		0			0
$814$	−0.168121	−	0.0430031i	−0.168121	−	0.0430031i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.568242	+	1.86369i	0.568242	+	1.86369i	0.500000	+	0.866025i	$0.333333\pi$
$821$	0.568242	+	1.86369i	0.568242	+	1.86369i	0.0682424	+	0.997669i	$0.478261\pi$
$822$		0			0
$823$	1.41503	+	0.998840i	1.41503	+	0.998840i	0.995857	+	0.0909349i	$0.0289855\pi$
$823$	1.41503	+	0.998840i	1.41503	+	0.998840i	0.419177	+	0.907905i	$0.362319\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.25209	−	0.543860i	−1.25209	−	0.543860i	−0.334880	−	0.942261i	$-0.608696\pi$
$827$	−1.25209	−	0.543860i	−1.25209	−	0.543860i	−0.917211	+	0.398401i	$0.869565\pi$
$828$	−0.370118	−	0.0337967i	−0.370118	−	0.0337967i
$829$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$829$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$830$		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		−0.816970	−	0.576680i	$-0.804348\pi$
$839$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$840$		0			0
$841$	0.689774	+	2.26229i	0.689774	+	2.26229i
$842$	0.494535	+	1.29713i	0.494535	+	1.29713i
$843$		0			0
$844$	0.313160	−	0.881149i	0.313160	−	0.881149i
$845$		0			0
$846$		0			0
$847$	0.483820	+	0.518045i	0.483820	+	0.518045i
$848$	0.503122	+	0.128692i	0.503122	+	0.128692i
$849$		0			0
$850$		0			0
$851$	0.0309833	+	0.339308i	0.0309833	+	0.339308i
$852$		0			0
$853$		0			0		−0.158683	−	0.987330i	$-0.550725\pi$
$853$		0			0		0.158683	+	0.987330i	$0.449275\pi$
$854$		0			0
$855$		0			0
$856$	−0.872278	+	1.36349i	−0.872278	+	1.36349i
$857$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$857$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$858$		0			0
$859$		0			0		0.377419	−	0.926043i	$-0.376812\pi$
$859$		0			0		−0.377419	+	0.926043i	$0.623188\pi$
$860$		0			0
$861$		0			0
$862$	−0.415478	−	0.00946006i	−0.415478	−	0.00946006i
$863$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$863$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.251990	−	0.0895572i	0.251990	−	0.0895572i
$870$		0			0
$871$		0			0
$872$	1.89627	−	0.531310i	1.89627	−	0.531310i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.90067	+	0.579517i	−1.90067	+	0.579517i	−0.917211	+	0.398401i	$0.869565\pi$
$877$	−1.90067	+	0.579517i	−1.90067	+	0.579517i	−0.983462	+	0.181116i	$0.942029\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.699012	−	0.715110i	$-0.253623\pi$
$881$		0			0		−0.699012	+	0.715110i	$0.746377\pi$
$882$	−0.671345	−	0.238596i	−0.671345	−	0.238596i
$883$	0.885383	−	0.948014i	0.885383	−	0.948014i	−0.113580	−	0.993529i	$-0.536232\pi$
$883$	0.885383	−	0.948014i	0.885383	−	0.948014i	0.998964	+	0.0455146i	$0.0144928\pi$
$884$		0			0
$885$		0			0
$886$	0.0420650	−	0.0493654i	0.0420650	−	0.0493654i
$887$		0			0		0.557934	−	0.829885i	$-0.311594\pi$
$887$		0			0		−0.557934	+	0.829885i	$0.688406\pi$
$888$		0			0
$889$	−1.20886	−	1.35493i	−1.20886	−	1.35493i
$890$		0			0
$891$			0.539594i			0.539594i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.238476	−	0.0383277i	0.238476	−	0.0383277i
$897$		0			0
$898$	1.01455	−	0.235038i	1.01455	−	0.235038i
$899$		0			0
$900$	0.451605	−	0.196160i	0.451605	−	0.196160i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	1.45221	+	1.35627i	1.45221	+	1.35627i
$905$		0			0
$906$		0			0
$907$	1.59229	−	0.218856i	1.59229	−	0.218856i	0.715110	−	0.699012i	$-0.246377\pi$
$907$	1.59229	−	0.218856i	1.59229	−	0.218856i	0.877183	+	0.480157i	$0.159420\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.511985	+	1.55165i	−0.511985	+	1.55165i	0.291646	+	0.956526i	$0.405797\pi$
$911$	−0.511985	+	1.55165i	−0.511985	+	1.55165i	−0.803631	+	0.595128i	$0.797101\pi$
$912$		0			0
$913$		0			0
$914$	−0.350077	+	1.14817i	−0.350077	+	1.14817i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.247808	−	0.968809i	0.247808	−	0.968809i	−0.715110	−	0.699012i	$-0.753623\pi$
$919$	0.247808	−	0.968809i	0.247808	−	0.968809i	0.962917	−	0.269797i	$-0.0869565\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.251841	−	0.374594i	−0.251841	−	0.374594i
$926$	−0.251076	−	0.144959i	−0.251076	−	0.144959i
$927$		0			0
$928$	−0.145850	+	1.59725i	−0.145850	+	1.59725i
$929$		0			0		−0.987330	−	0.158683i	$-0.949275\pi$
$929$		0			0		0.987330	+	0.158683i	$0.0507246\pi$
$930$		0			0
$931$		0			0
$932$	−0.408020	+	0.833352i	−0.408020	+	0.833352i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.934394	−	0.356242i	$-0.115942\pi$
$937$		0			0		−0.934394	+	0.356242i	$0.884058\pi$
$938$	0.0637842	+	1.39995i	0.0637842	+	1.39995i
$939$		0			0
$940$		0			0
$941$		0			0		0.789876	−	0.613267i	$-0.210145\pi$
$941$		0			0		−0.789876	+	0.613267i	$0.789855\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.619543	+	0.396347i	0.619543	+	0.396347i
$947$	0.877183	+	1.51932i	0.877183	+	1.51932i	0.854419	+	0.519584i	$0.173913\pi$
$947$	0.877183	+	1.51932i	0.877183	+	1.51932i	0.0227632	+	0.999741i	$0.492754\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.423320	−	0.816970i	−0.423320	−	0.816970i	0.576680	−	0.816970i	$-0.304348\pi$
$953$	−0.423320	−	0.816970i	−0.423320	−	0.816970i	−1.00000			$\pi$
$954$	−1.37209	+	0.252687i	−1.37209	+	0.252687i
$955$		0			0
$956$	−0.307841	−	0.0210569i	−0.307841	−	0.0210569i
$957$		0			0
$958$		0			0
$959$	−0.130763	−	0.951369i	−0.130763	−	0.951369i
$960$		0			0
$961$	0.998964	+	0.0455146i	0.998964	+	0.0455146i
$962$		0			0
$963$	0.207285	−	1.50811i	0.207285	−	1.50811i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.28508	−	1.50811i	−1.28508	−	1.50811i	−0.746184	−	0.665740i	$-0.768116\pi$
$967$	−1.28508	−	1.50811i	−1.28508	−	1.50811i	−0.538899	−	0.842371i	$-0.681159\pi$
$968$	−0.748822	+	0.0856053i	−0.748822	+	0.0856053i
$969$		0			0
$970$		0			0
$971$		0			0		0.993529	−	0.113580i	$-0.0362319\pi$
$971$		0			0		−0.993529	+	0.113580i	$0.963768\pi$
$972$		0			0
$973$		0			0
$974$	−1.27947	+	0.0291324i	−1.27947	+	0.0291324i
$975$		0			0
$976$		0			0
$977$	0.386237	+	0.547173i	0.386237	+	0.547173i	0.962917	−	0.269797i	$-0.0869565\pi$
$977$	0.386237	+	0.547173i	0.386237	+	0.547173i	−0.576680	+	0.816970i	$0.695652\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.40970	+	1.20123i	−1.40970	+	1.20123i
$982$	0.421277	−	1.10498i	0.421277	−	1.10498i
$983$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$983$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.325907	−	1.40679i	0.325907	−	1.40679i
$990$		0			0
$991$	0.576680	−	0.998840i	0.576680	−	0.998840i	−0.419177	−	0.907905i	$-0.637681\pi$
$991$	0.576680	−	0.998840i	0.576680	−	0.998840i	0.995857	−	0.0909349i	$-0.0289855\pi$
$992$		0			0
$993$		0			0
$994$	1.32933	−	0.340023i	1.32933	−	0.340023i
$995$		0			0
$996$		0			0
$997$		0			0		0.480157	−	0.877183i	$-0.340580\pi$
$997$		0			0		−0.480157	+	0.877183i	$0.659420\pi$
$998$	−0.730010	+	0.566786i	−0.730010	+	0.566786i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1939.1.by.a.1238.1	✓	44
7.6	odd	2	CM	1939.1.by.a.1238.1	✓	44
277.228	even	138	inner	1939.1.by.a.1336.1	yes	44
1939.1336	odd	138	inner	1939.1.by.a.1336.1	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1939.1.by.a.1238.1	✓	44	1.1	even	1	trivial
1939.1.by.a.1238.1	✓	44	7.6	odd	2	CM
1939.1.by.a.1336.1	yes	44	277.228	even	138	inner
1939.1.by.a.1336.1	yes	44	1939.1336	odd	138	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:	\( N \)	\(=\)	\( 1939 = 7 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1939.by (of order \(138\), degree \(44\), minimal)

\(f(q)\)	\(=\)	\(q+(0.697581 + 0.144959i) q^{2} +(-0.451605 - 0.196160i) q^{4} +(0.0227632 + 0.999741i) q^{7} +(-0.868673 - 0.613177i) q^{8} +(0.983462 + 0.181116i) q^{9} +O(q^{10})\)	\(q+(0.697581 + 0.144959i) q^{2} +(-0.451605 - 0.196160i) q^{4} +(0.0227632 + 0.999741i) q^{7} +(-0.868673 - 0.613177i) q^{8} +(0.983462 + 0.181116i) q^{9} +(0.192226 + 0.504193i) q^{11} +(-0.129042 + 0.700700i) q^{14} +(-0.181018 - 0.193823i) q^{16} +(0.659790 + 0.268905i) q^{18} +(0.0610057 + 0.379580i) q^{22} +(0.662131 - 0.362441i) q^{23} +(-0.538899 + 0.842371i) q^{25} +(0.185829 - 0.455953i) q^{28} +(1.47420 + 1.09172i) q^{29} +(0.454289 + 0.747046i) q^{32} +(-0.408608 - 0.274709i) q^{36} +(-0.179831 + 0.414012i) q^{37} +(1.27360 - 1.42749i) q^{43} +(0.0120922 - 0.265403i) q^{44} +(0.514429 - 0.156850i) q^{46} +(-0.998964 + 0.0455146i) q^{49} +(-0.498035 + 0.509504i) q^{50} +(-1.64950 + 1.05525i) q^{53} +(0.593244 - 0.882406i) q^{56} +(0.870119 + 0.975259i) q^{58} +(-0.158683 + 0.987330i) q^{63} +(0.297425 + 0.836872i) q^{64} +(1.91617 - 0.443916i) q^{67} +(-0.807265 - 1.74847i) q^{71} +(-0.743251 - 0.760367i) q^{72} +(-0.185461 + 0.262739i) q^{74} +(-0.499687 + 0.203653i) q^{77} +(0.0112818 - 0.495487i) q^{79} +(0.934394 + 0.356242i) q^{81} +(1.09536 - 0.811170i) q^{86} +(0.142178 - 0.555847i) q^{88} +(-0.370118 + 0.0337967i) q^{92} +(-0.703456 - 0.113059i) q^{98} +(0.0977291 + 0.530670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{4} + q^{7} + q^{9}+O(q^{10}) \) 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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