LMFDB - Embedded newform 1939.1.by.a.867.1

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			867.1
Root			$-0.998964 - 0.0455146i$ of defining polynomial
Character	$\chi$	$=$	1939.867
Dual form			1939.1.by.a.454.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.77531 - 0.919892i) q^{2} +(1.72885 - 2.44922i) q^{4} +(0.291646 + 0.956526i) q^{7} +(0.543961 - 3.95761i) q^{8} +(-0.715110 + 0.699012i) q^{9} +O(q^{10})$	\(q+(1.77531 - 0.919892i) q^{2} +(1.72885 - 2.44922i) q^{4} +(0.291646 + 0.956526i) q^{7} +(0.543961 - 3.95761i) q^{8} +(-0.715110 + 0.699012i) q^{9} +(0.796596 - 0.0181378i) q^{11} +(1.39766 + 1.42985i) q^{14} +(-1.67093 - 4.70154i) q^{16} +(-0.626526 + 1.89879i) q^{18} +(1.39752 - 0.764982i) q^{22} +(-1.85028 + 0.428649i) q^{23} +(-0.898128 + 0.439735i) q^{25} +(2.84695 + 0.939382i) q^{28} +(-0.483462 + 1.04714i) q^{29} +(-4.37177 - 4.08295i) q^{32} +(0.475719 + 2.95994i) q^{36} +(0.295933 + 0.208892i) q^{37} +(0.0692864 - 1.52071i) q^{43} +(1.33277 - 1.98239i) q^{44} +(-2.89050 + 2.46304i) q^{46} +(-0.829885 + 0.557934i) q^{49} +(-1.18995 + 1.60685i) q^{50} +(0.780868 - 1.59487i) q^{53} +(3.94420 - 0.633908i) q^{56} +(0.104962 + 2.30373i) q^{58} +(-0.877183 - 0.480157i) q^{63} +(-6.71251 - 1.88076i) q^{64} +(1.40657 + 0.259036i) q^{67} +(-1.12499 + 1.44897i) q^{71} +(2.37743 + 3.21036i) q^{72} +(0.717531 + 0.0986224i) q^{74} +(0.249673 + 0.756675i) q^{77} +(-0.0662504 + 0.217285i) q^{79} +(0.0227632 - 0.999741i) q^{81} +(-1.27589 - 2.76347i) q^{86} +(0.361535 - 3.16248i) q^{88} +(-2.14899 + 5.27280i) q^{92} +(-0.960065 + 1.75391i) q^{98} +(-0.556975 + 0.569801i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1939\mathbb{Z}\right)^\times$.

$n$	$1109$	$1667$
$\chi(n)$	$-1$	$e\left(\frac{59}{138}\right)$

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 $

$2$	1.77531	−	0.919892i	1.77531	−	0.919892i	0.877183	−	0.480157i	$-0.159420\pi$
$2$	1.77531	−	0.919892i	1.77531	−	0.919892i	0.898128	−	0.439735i	$-0.144928\pi$
$3$		0			0		−0.377419	−	0.926043i	$-0.623188\pi$
$3$		0			0		0.377419	+	0.926043i	$0.376812\pi$
$4$	1.72885	−	2.44922i	1.72885	−	2.44922i
$5$		0			0		−0.225690	−	0.974199i	$-0.572464\pi$
$5$		0			0		0.225690	+	0.974199i	$0.427536\pi$
$6$		0			0
$7$	0.291646	+	0.956526i	0.291646	+	0.956526i
$7$	0.291646	+	0.956526i	0.291646	+	0.956526i
$8$	0.543961	−	3.95761i	0.543961	−	3.95761i
$9$	−0.715110	+	0.699012i	−0.715110	+	0.699012i
$10$		0			0
$11$	0.796596	−	0.0181378i	0.796596	−	0.0181378i	0.377419	−	0.926043i	$-0.376812\pi$
$11$	0.796596	−	0.0181378i	0.796596	−	0.0181378i	0.419177	+	0.907905i	$0.362319\pi$
$12$		0			0
$13$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$13$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$14$	1.39766	+	1.42985i	1.39766	+	1.42985i
$15$		0			0
$16$	−1.67093	−	4.70154i	−1.67093	−	4.70154i
$17$		0			0		−0.993529	−	0.113580i	$-0.963768\pi$
$17$		0			0		0.993529	+	0.113580i	$0.0362319\pi$
$18$	−0.626526	+	1.89879i	−0.626526	+	1.89879i
$19$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$19$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$20$		0			0
$21$		0			0
$22$	1.39752	−	0.764982i	1.39752	−	0.764982i
$23$	−1.85028	+	0.428649i	−1.85028	+	0.428649i	−0.995857	−	0.0909349i	$-0.971014\pi$
$23$	−1.85028	+	0.428649i	−1.85028	+	0.428649i	−0.854419	+	0.519584i	$0.826087\pi$
$24$		0			0
$25$	−0.898128	+	0.439735i	−0.898128	+	0.439735i
$26$		0			0
$27$		0			0
$28$	2.84695	+	0.939382i	2.84695	+	0.939382i
$29$	−0.483462	+	1.04714i	−0.483462	+	1.04714i	0.500000	+	0.866025i	$0.333333\pi$
$29$	−0.483462	+	1.04714i	−0.483462	+	1.04714i	−0.983462	+	0.181116i	$0.942029\pi$
$30$		0			0
$31$		0			0		−0.956526	−	0.291646i	$-0.905797\pi$
$31$		0			0		0.956526	+	0.291646i	$0.0942029\pi$
$32$	−4.37177	−	4.08295i	−4.37177	−	4.08295i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.475719	+	2.95994i	0.475719	+	2.95994i
$37$	0.295933	+	0.208892i	0.295933	+	0.208892i	0.715110	−	0.699012i	$-0.246377\pi$
$37$	0.295933	+	0.208892i	0.295933	+	0.208892i	−0.419177	+	0.907905i	$0.637681\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$41$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$42$		0			0
$43$	0.0692864	−	1.52071i	0.0692864	−	1.52071i	−0.613267	−	0.789876i	$-0.710145\pi$
$43$	0.0692864	−	1.52071i	0.0692864	−	1.52071i	0.682553	−	0.730836i	$-0.260870\pi$
$44$	1.33277	−	1.98239i	1.33277	−	1.98239i
$45$		0			0
$46$	−2.89050	+	2.46304i	−2.89050	+	2.46304i
$47$		0			0		−0.803631	−	0.595128i	$-0.797101\pi$
$47$		0			0		0.803631	+	0.595128i	$0.202899\pi$
$48$		0			0
$49$	−0.829885	+	0.557934i	−0.829885	+	0.557934i
$50$	−1.18995	+	1.60685i	−1.18995	+	1.60685i
$51$		0			0
$52$		0			0
$53$	0.780868	−	1.59487i	0.780868	−	1.59487i	−0.0227632	−	0.999741i	$-0.507246\pi$
$53$	0.780868	−	1.59487i	0.780868	−	1.59487i	0.803631	−	0.595128i	$-0.202899\pi$
$54$		0			0
$55$		0			0
$56$	3.94420	−	0.633908i	3.94420	−	0.633908i
$57$		0			0
$58$	0.104962	+	2.30373i	0.104962	+	2.30373i
$59$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$59$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$60$		0			0
$61$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$61$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$62$		0			0
$63$	−0.877183	−	0.480157i	−0.877183	−	0.480157i
$64$	−6.71251	−	1.88076i	−6.71251	−	1.88076i
$65$		0			0
$66$		0			0
$67$	1.40657	+	0.259036i	1.40657	+	0.259036i	0.829885	−	0.557934i	$-0.188406\pi$
$67$	1.40657	+	0.259036i	1.40657	+	0.259036i	0.576680	+	0.816970i	$0.304348\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.12499	+	1.44897i	−1.12499	+	1.44897i	−0.247808	+	0.968809i	$0.579710\pi$
$71$	−1.12499	+	1.44897i	−1.12499	+	1.44897i	−0.877183	+	0.480157i	$0.840580\pi$
$72$	2.37743	+	3.21036i	2.37743	+	3.21036i
$73$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$73$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$74$	0.717531	+	0.0986224i	0.717531	+	0.0986224i
$75$		0			0
$76$		0			0
$77$	0.249673	+	0.756675i	0.249673	+	0.756675i
$78$		0			0
$79$	−0.0662504	+	0.217285i	−0.0662504	+	0.217285i	−0.983462	−	0.181116i	$-0.942029\pi$
$79$	−0.0662504	+	0.217285i	−0.0662504	+	0.217285i	0.917211	+	0.398401i	$0.130435\pi$
$80$		0			0
$81$	0.0227632	−	0.999741i	0.0227632	−	0.999741i
$82$		0			0
$83$		0			0		0.648582	−	0.761145i	$-0.275362\pi$
$83$		0			0		−0.648582	+	0.761145i	$0.724638\pi$
$84$		0			0
$85$		0			0
$86$	−1.27589	−	2.76347i	−1.27589	−	2.76347i
$87$		0			0
$88$	0.361535	−	3.16248i	0.361535	−	3.16248i
$89$		0			0		0.949640	−	0.313344i	$-0.101449\pi$
$89$		0			0		−0.949640	+	0.313344i	$0.898551\pi$
$90$		0			0
$91$		0			0
$92$	−2.14899	+	5.27280i	−2.14899	+	5.27280i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.926043	−	0.377419i	$-0.123188\pi$
$97$		0			0		−0.926043	+	0.377419i	$0.876812\pi$
$98$	−0.960065	+	1.75391i	−0.960065	+	1.75391i
$99$	−0.556975	+	0.569801i	−0.556975	+	0.569801i
$100$	−0.475719	+	2.95994i	−0.475719	+	2.95994i
$101$		0			0		−0.356242	−	0.934394i	$-0.615942\pi$
$101$		0			0		0.356242	+	0.934394i	$0.384058\pi$
$102$		0			0
$103$		0			0		0.907905	−	0.419177i	$-0.137681\pi$
$103$		0			0		−0.907905	+	0.419177i	$0.862319\pi$
$104$		0			0
$105$		0			0
$106$	−0.0808235	−	3.54970i	−0.0808235	−	3.54970i
$107$	1.08106	+	1.60800i	1.08106	+	1.60800i	0.746184	+	0.665740i	$0.231884\pi$
$107$	1.08106	+	1.60800i	1.08106	+	1.60800i	0.334880	+	0.942261i	$0.391304\pi$
$108$		0			0
$109$	−0.325617	−	0.535454i	−0.325617	−	0.535454i	0.648582	−	0.761145i	$-0.275362\pi$
$109$	−0.325617	−	0.535454i	−0.325617	−	0.535454i	−0.974199	+	0.225690i	$0.927536\pi$
$110$		0			0
$111$		0			0
$112$	4.00983	−	2.96947i	4.00983	−	2.96947i
$113$	0.00926262	−	0.0445742i	0.00926262	−	0.0445742i	−0.974199	−	0.225690i	$-0.927536\pi$
$113$	0.00926262	−	0.0445742i	0.00926262	−	0.0445742i	0.983462	+	0.181116i	$0.0579710\pi$
$114$		0			0
$115$		0			0
$116$	1.72885	+	2.99445i	1.72885	+	2.99445i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.364728	+	0.0166177i	−0.364728	+	0.0166177i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.99896	−	0.0455146i	−1.99896	−	0.0455146i
$127$	1.53048	+	0.391475i	1.53048	+	0.391475i	0.917211	−	0.398401i	$-0.130435\pi$
$127$	1.53048	+	0.391475i	1.53048	+	0.391475i	0.613267	+	0.789876i	$0.289855\pi$
$128$	−7.79012	+	1.61881i	−7.79012	+	1.61881i
$129$		0			0
$130$		0			0
$131$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$131$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$132$		0			0
$133$		0			0
$134$	2.73538	−	0.834019i	2.73538	−	0.834019i
$135$		0			0
$136$		0			0
$137$	−0.0410462	+	0.449511i	−0.0410462	+	0.449511i	0.949640	+	0.313344i	$0.101449\pi$
$137$	−0.0410462	+	0.449511i	−0.0410462	+	0.449511i	−0.990686	+	0.136167i	$0.956522\pi$
$138$		0			0
$139$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$139$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$140$		0			0
$141$		0			0
$142$	−0.664315	+	3.60723i	−0.664315	+	3.60723i
$143$		0			0
$144$	4.48133	+	2.19412i	4.48133	+	2.19412i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	1.02324	−	0.363661i	1.02324	−	0.363661i
$149$	0.0891252	−	0.0185204i	0.0891252	−	0.0185204i	−0.158683	−	0.987330i	$-0.550725\pi$
$149$	0.0891252	−	0.0185204i	0.0891252	−	0.0185204i	0.247808	+	0.968809i	$0.420290\pi$
$150$		0			0
$151$	0.960065	+	0.0218598i	0.960065	+	0.0218598i	0.500000	−	0.866025i	$-0.333333\pi$
$151$	0.960065	+	0.0218598i	0.960065	+	0.0218598i	0.460065	+	0.887885i	$0.347826\pi$
$152$		0			0
$153$		0			0
$154$	1.13931	+	1.11366i	1.13931	+	1.11366i
$155$		0			0
$156$		0			0
$157$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$157$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$158$	0.0822635	+	0.446691i	0.0822635	+	0.446691i
$159$		0			0
$160$		0			0
$161$	−0.949640	−	1.64482i	−0.949640	−	1.64482i
$162$	−0.879242	−	1.79579i	−0.879242	−	1.79579i
$163$	1.96188	−	0.224282i	1.96188	−	0.224282i	0.962917	−	0.269797i	$-0.0869565\pi$
$163$	1.96188	−	0.224282i	1.96188	−	0.224282i	0.998964	+	0.0455146i	$0.0144928\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.665740	−	0.746184i	$-0.731884\pi$
$167$		0			0		0.665740	+	0.746184i	$0.268116\pi$
$168$		0			0
$169$	0.854419	−	0.519584i	0.854419	−	0.519584i
$170$		0			0
$171$		0			0
$172$	−3.60477	−	2.79877i	−3.60477	−	2.79877i
$173$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$173$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$174$		0			0
$175$	−0.682553	−	0.730836i	−0.682553	−	0.730836i
$176$	−1.41633	−	3.71492i	−1.41633	−	3.71492i
$177$		0			0
$178$		0			0
$179$	0.606043	−	1.10716i	0.606043	−	1.10716i	−0.377419	−	0.926043i	$-0.623188\pi$
$179$	0.606043	−	1.10716i	0.606043	−	1.10716i	0.983462	−	0.181116i	$-0.0579710\pi$
$180$		0			0
$181$		0			0		0.356242	−	0.934394i	$-0.384058\pi$
$181$		0			0		−0.356242	+	0.934394i	$0.615942\pi$
$182$		0			0
$183$		0			0
$184$	0.689948	+	7.55584i	0.689948	+	7.55584i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.695737	−	1.50691i	−0.695737	−	1.50691i	−0.854419	−	0.519584i	$-0.826087\pi$
$191$	−0.695737	−	1.50691i	−0.695737	−	1.50691i	0.158683	−	0.987330i	$-0.449275\pi$
$192$		0			0
$193$	−0.119722	−	1.75028i	−0.119722	−	1.75028i	−0.538899	−	0.842371i	$-0.681159\pi$
$193$	−0.119722	−	1.75028i	−0.119722	−	1.75028i	0.419177	−	0.907905i	$-0.362319\pi$
$194$		0			0
$195$		0			0
$196$	−0.0682424	+	2.99715i	−0.0682424	+	2.99715i
$197$	−1.37638	+	0.880528i	−1.37638	+	0.880528i	−0.998964	−	0.0455146i	$-0.985507\pi$
$197$	−1.37638	+	0.880528i	−1.37638	+	0.880528i	−0.377419	+	0.926043i	$0.623188\pi$
$198$	−0.464648	+	1.52393i	−0.464648	+	1.52393i
$199$		0			0		−0.907905	−	0.419177i	$-0.862319\pi$
$199$		0			0		0.907905	+	0.419177i	$0.137681\pi$
$200$	1.25175	+	3.79364i	1.25175	+	3.79364i
$201$		0			0
$202$		0			0
$203$	−1.14262	−	0.157049i	−1.14262	−	0.157049i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.02352	−	1.59990i	1.02352	−	1.59990i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.836060	−	0.680185i	−0.836060	−	0.680185i	0.113580	−	0.993529i	$-0.463768\pi$
$211$	−0.836060	−	0.680185i	−0.836060	−	0.680185i	−0.949640	+	0.313344i	$0.898551\pi$
$212$	−2.55618	−	4.66980i	−2.55618	−	4.66980i
$213$		0			0
$214$	3.39841	+	1.86024i	3.39841	+	1.86024i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.07063	−	0.651065i	−1.07063	−	0.651065i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$223$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$224$	2.63044	−	5.37249i	2.63044	−	5.37249i
$225$	0.334880	−	0.942261i	0.334880	−	0.942261i
$226$	−0.0245594	−	0.0876536i	−0.0245594	−	0.0876536i
$227$		0			0		0.595128	−	0.803631i	$-0.297101\pi$
$227$		0			0		−0.595128	+	0.803631i	$0.702899\pi$
$228$		0			0
$229$		0			0		0.746184	−	0.665740i	$-0.231884\pi$
$229$		0			0		−0.746184	+	0.665740i	$0.768116\pi$
$230$		0			0
$231$		0			0
$232$	3.88120	+	2.48296i	3.88120	+	2.48296i
$233$	−0.301058	+	0.447801i	−0.301058	+	0.447801i	−0.949640	−	0.313344i	$-0.898551\pi$
$233$	−0.301058	+	0.447801i	−0.301058	+	0.447801i	0.648582	+	0.761145i	$0.275362\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.454538	−	1.62227i	0.454538	−	1.62227i	−0.291646	−	0.956526i	$-0.594203\pi$
$239$	0.454538	−	1.62227i	0.454538	−	1.62227i	0.746184	−	0.665740i	$-0.231884\pi$
$240$		0			0
$241$		0			0		−0.158683	−	0.987330i	$-0.550725\pi$
$241$		0			0		0.158683	+	0.987330i	$0.449275\pi$
$242$	−0.632219	+	0.365012i	−0.632219	+	0.365012i
$243$		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		0.730836	−	0.682553i	$-0.239130\pi$
$251$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$252$	−2.69252	+	1.31829i	−2.69252	+	1.31829i
$253$	−1.46615	+	0.375020i	−1.46615	+	0.375020i
$254$	3.07719	−	0.712885i	3.07719	−	0.712885i
$255$		0			0
$256$	−6.93326	+	5.64062i	−6.93326	+	5.64062i
$257$		0			0		−0.926043	−	0.377419i	$-0.876812\pi$
$257$		0			0		0.926043	+	0.377419i	$0.123188\pi$
$258$		0			0
$259$	−0.113503	+	0.343990i	−0.113503	+	0.343990i
$260$		0			0
$261$	−0.386237	−	1.08677i	−0.386237	−	1.08677i
$262$		0			0
$263$	1.36878	+	1.40030i	1.36878	+	1.40030i	0.829885	+	0.557934i	$0.188406\pi$
$263$	1.36878	+	1.40030i	1.36878	+	1.40030i	0.538899	+	0.842371i	$0.318841\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	3.06617	−	2.99715i	3.06617	−	2.99715i
$269$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$269$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$270$		0			0
$271$		0			0		−0.761145	−	0.648582i	$-0.775362\pi$
$271$		0			0		0.761145	+	0.648582i	$0.224638\pi$
$272$		0			0
$273$		0			0
$274$	0.340631	+	0.835779i	0.340631	+	0.835779i
$275$	−0.707469	+	0.366581i	−0.707469	+	0.366581i
$276$		0			0
$277$	−0.158683	+	0.987330i	−0.158683	+	0.987330i
$277$	−0.158683	+	0.987330i	−0.158683	+	0.987330i
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.985454	+	1.39607i	−0.985454	+	1.39607i	−0.0682424	+	0.997669i	$0.521739\pi$
$281$	−0.985454	+	1.39607i	−0.985454	+	1.39607i	−0.917211	+	0.398401i	$0.869565\pi$
$282$		0			0
$283$		0			0		−0.761145	−	0.648582i	$-0.775362\pi$
$283$		0			0		0.761145	+	0.648582i	$0.224638\pi$
$284$	1.60390	+	5.26038i	1.60390	+	5.26038i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	5.98033	−	0.136167i	5.98033	−	0.136167i
$289$	0.974199	+	0.225690i	0.974199	+	0.225690i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$293$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$294$		0			0
$295$		0			0
$296$	0.987691	−	1.05756i	0.987691	−	1.05756i
$297$		0			0
$298$	0.141188	−	0.114865i	0.141188	−	0.114865i
$299$		0			0
$300$		0			0
$301$	1.47481	−	0.377235i	1.47481	−	0.377235i
$302$	1.72452	−	0.844348i	1.72452	−	0.844348i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$307$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$308$	2.28491	+	0.696671i	2.28491	+	0.696671i
$309$		0			0
$310$		0			0
$311$		0			0		0.934394	−	0.356242i	$-0.115942\pi$
$311$		0			0		−0.934394	+	0.356242i	$0.884058\pi$
$312$		0			0
$313$		0			0		−0.158683	−	0.987330i	$-0.550725\pi$
$313$		0			0		0.158683	+	0.987330i	$0.449275\pi$
$314$		0			0
$315$		0			0
$316$	0.417641	+	0.537914i	0.417641	+	0.537914i
$317$	−1.70176	+	0.155393i	−1.70176	+	0.155393i	−0.898128	−	0.439735i	$-0.855072\pi$
$317$	−1.70176	+	0.155393i	−1.70176	+	0.155393i	−0.803631	+	0.595128i	$0.797101\pi$
$318$		0			0
$319$	−0.366131	+	0.842917i	−0.366131	+	0.842917i
$320$		0			0
$321$		0			0
$322$	−3.19897	−	2.04651i	−3.19897	−	2.04651i
$323$		0			0
$324$	−2.40923	−	1.78415i	−2.40923	−	1.78415i
$325$		0			0
$326$	3.27663	−	2.20289i	3.27663	−	2.20289i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.18748	+	0.0812259i	−1.18748	+	0.0812259i	−0.648582	−	0.761145i	$-0.724638\pi$
$331$	−1.18748	+	0.0812259i	−1.18748	+	0.0812259i	−0.538899	+	0.842371i	$0.681159\pi$
$332$		0			0
$333$	−0.357643	+	0.0574800i	−0.357643	+	0.0574800i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			0.539594i			0.539594i	0.962917	+	0.269797i	$0.0869565\pi$
$337$			0.539594i			0.539594i	−0.962917	+	0.269797i	$0.913043\pi$
$338$	1.03890	−	1.70840i	1.03890	−	1.70840i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.775711	−	0.631088i	−0.775711	−	0.631088i
$344$	−5.98070	−	1.10142i	−5.98070	−	1.10142i
$345$		0			0
$346$		0			0
$347$	0.699040	−	1.09269i	0.699040	−	1.09269i	−0.291646	−	0.956526i	$-0.594203\pi$
$347$	0.699040	−	1.09269i	0.699040	−	1.09269i	0.990686	−	0.136167i	$-0.0434783\pi$
$348$		0			0
$349$		0			0		−0.595128	−	0.803631i	$-0.702899\pi$
$349$		0			0		0.595128	+	0.803631i	$0.297101\pi$
$350$	−1.88403	−	0.669586i	−1.88403	−	0.669586i
$351$		0			0
$352$	−3.55659	−	3.17317i	−3.55659	−	3.17317i
$353$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$353$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.0574474	−	2.52304i	0.0574474	−	2.52304i
$359$	1.06322	−	1.30687i	1.06322	−	1.30687i	0.113580	−	0.993529i	$-0.463768\pi$
$359$	1.06322	−	1.30687i	1.06322	−	1.30687i	0.949640	−	0.313344i	$-0.101449\pi$
$360$		0			0
$361$	−0.0682424	−	0.997669i	−0.0682424	−	0.997669i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.995857	−	0.0909349i	$-0.971014\pi$
$367$		0			0		0.995857	+	0.0909349i	$0.0289855\pi$
$368$	5.10699	+	7.98291i	5.10699	+	7.98291i
$369$		0			0
$370$		0			0
$371$	1.75327	+	0.281784i	1.75327	+	0.281784i
$372$		0			0
$373$	−0.617029	+	1.61842i	−0.617029	+	1.61842i	0.158683	+	0.987330i	$0.449275\pi$
$373$	−0.617029	+	1.61842i	−0.617029	+	1.61842i	−0.775711	+	0.631088i	$0.782609\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.837174	−	0.896395i	−0.837174	−	0.896395i	0.158683	−	0.987330i	$-0.449275\pi$
$379$	−0.837174	−	0.896395i	−0.837174	−	0.896395i	−0.995857	+	0.0909349i	$0.971014\pi$
$380$		0			0
$381$		0			0
$382$	−2.62135	−	2.03524i	−2.62135	−	2.03524i
$383$		0			0		−0.0227632	−	0.999741i	$-0.507246\pi$
$383$		0			0		0.0227632	+	0.999741i	$0.492754\pi$
$384$		0			0
$385$		0			0
$386$	−1.82261	−	2.99715i	−1.82261	−	2.99715i
$387$	1.01345	+	1.13591i	1.01345	+	1.13591i
$388$		0			0
$389$	−0.803631	+	0.595128i	−0.803631	+	0.595128i	−0.917211	−	0.398401i	$-0.869565\pi$
$389$	−0.803631	+	0.595128i	−0.803631	+	0.595128i	0.113580	+	0.993529i	$0.463768\pi$
$390$		0			0
$391$		0			0
$392$	1.75666	+	3.58786i	1.75666	+	3.58786i
$393$		0			0
$394$	−1.63352	+	2.82933i	−1.63352	+	2.82933i
$395$		0			0
$396$	0.432642	+	2.34925i	0.432642	+	2.34925i
$397$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$397$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$398$		0			0
$399$		0			0
$400$	3.56814	+	3.48782i	3.56814	+	3.48782i
$401$	−1.29061	+	1.00204i	−1.29061	+	1.00204i	−0.291646	+	0.956526i	$0.594203\pi$
$401$	−1.29061	+	1.00204i	−1.29061	+	1.00204i	−0.998964	+	0.0455146i	$0.985507\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−2.17297	+	0.772274i	−2.17297	+	0.772274i
$407$	0.239528	+	0.161035i	0.239528	+	0.161035i
$408$		0			0
$409$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$409$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.345332	−	3.78184i	0.345332	−	3.78184i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.181116	−	0.983462i	$-0.442029\pi$
$419$		0			0		−0.181116	+	0.983462i	$0.557971\pi$
$420$		0			0
$421$	−1.76655	−	0.864925i	−1.76655	−	0.864925i	−0.962917	−	0.269797i	$-0.913043\pi$
$421$	−1.76655	−	0.864925i	−1.76655	−	0.864925i	−0.803631	−	0.595128i	$-0.797101\pi$
$422$	−2.10996	−	0.438455i	−2.10996	−	0.438455i
$423$		0			0
$424$	−5.88711	−	3.95792i	−5.88711	−	3.95792i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	5.80733	+	0.132228i	5.80733	+	0.132228i
$429$		0			0
$430$		0			0
$431$	−0.927614	−	0.906734i	−0.927614	−	0.906734i	0.0682424	−	0.997669i	$-0.478261\pi$
$431$	−0.927614	−	0.906734i	−0.927614	−	0.906734i	−0.995857	+	0.0909349i	$0.971014\pi$
$432$		0			0
$433$		0			0		0.998964	−	0.0455146i	$-0.0144928\pi$
$433$		0			0		−0.998964	+	0.0455146i	$0.985507\pi$
$434$		0			0
$435$		0			0
$436$	−1.87439	−	0.128211i	−1.87439	−	0.128211i
$437$		0			0
$438$		0			0
$439$		0			0		−0.439735	−	0.898128i	$-0.644928\pi$
$439$		0			0		0.439735	+	0.898128i	$0.355072\pi$
$440$		0			0
$441$	0.203456	−	0.979084i	0.203456	−	0.979084i
$442$		0			0
$443$	0.251841	−	1.08708i	0.251841	−	1.08708i	−0.682553	−	0.730836i	$-0.739130\pi$
$443$	0.251841	−	1.08708i	0.251841	−	1.08708i	0.934394	−	0.356242i	$-0.115942\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.158683	−	6.96921i	−0.158683	−	6.96921i
$449$	−1.48854	−	1.15571i	−1.48854	−	1.15571i	−0.949640	−	0.313344i	$-0.898551\pi$
$449$	−1.48854	−	1.15571i	−1.48854	−	1.15571i	−0.538899	−	0.842371i	$-0.681159\pi$
$450$	−0.272263	−	1.98086i	−0.272263	−	1.98086i
$451$		0			0
$452$	−0.0931581	−	0.0997480i	−0.0931581	−	0.0997480i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.814426	+	0.331929i	−0.814426	+	0.331929i	−0.746184	−	0.665740i	$-0.768116\pi$
$457$	−0.814426	+	0.331929i	−0.814426	+	0.331929i	−0.0682424	+	0.997669i	$0.521739\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.0909349	−	0.995857i	$-0.528986\pi$
$461$		0			0		0.0909349	+	0.995857i	$0.471014\pi$
$462$		0			0
$463$	0.495857	+	0.775091i	0.495857	+	0.775091i	0.995857	−	0.0909349i	$-0.0289855\pi$
$463$	0.495857	+	0.775091i	0.495857	+	0.775091i	−0.500000	+	0.866025i	$0.666667\pi$
$464$	5.73101	+	0.523317i	5.73101	+	0.523317i
$465$		0			0
$466$	−0.122543	+	1.07193i	−0.122543	+	1.07193i
$467$		0			0		−0.998964	−	0.0455146i	$-0.985507\pi$
$467$		0			0		0.998964	+	0.0455146i	$0.0144928\pi$
$468$		0			0
$469$	0.162445	+	1.42096i	0.162445	+	1.42096i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.0276109	−	1.21265i	0.0276109	−	1.21265i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.556427	+	1.68634i	0.556427	+	1.68634i
$478$	−0.685364	−	3.29815i	−0.685364	−	3.29815i
$479$		0			0		−0.746184	−	0.665740i	$-0.768116\pi$
$479$		0			0		0.746184	+	0.665740i	$0.231884\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.589858	+	0.922027i	−0.589858	+	0.922027i
$485$		0			0
$486$		0			0
$487$	1.83788	+	0.338468i	1.83788	+	0.338468i	0.983462	−	0.181116i	$-0.0579710\pi$
$487$	1.83788	+	0.338468i	1.83788	+	0.338468i	0.854419	+	0.519584i	$0.173913\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.278387	+	0.152385i	0.278387	+	0.152385i	0.613267	−	0.789876i	$-0.289855\pi$
$491$	0.278387	+	0.152385i	0.278387	+	0.152385i	−0.334880	+	0.942261i	$0.608696\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.71407	−	0.653498i	−1.71407	−	0.653498i
$498$		0			0
$499$	−0.122817	−	0.480157i	−0.122817	−	0.480157i	0.877183	−	0.480157i	$-0.159420\pi$
$499$	−0.122817	−	0.480157i	−0.122817	−	0.480157i	−1.00000			$\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$503$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$504$	−2.37743	+	3.21036i	−2.37743	+	3.21036i
$505$		0			0
$506$	−2.25789	+	2.01447i	−2.25789	+	2.01447i
$507$		0			0
$508$	3.60477	−	3.07167i	3.60477	−	3.07167i
$509$		0			0		−0.842371	−	0.538899i	$-0.818841\pi$
$509$		0			0		0.842371	+	0.538899i	$0.181159\pi$
$510$		0			0
$511$		0			0
$512$	−3.95003	+	9.09388i	−3.95003	+	9.09388i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.114930	+	0.715100i	0.114930	+	0.715100i
$519$		0			0
$520$		0			0
$521$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$521$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$522$	−1.68540	−	1.57405i	−1.68540	−	1.57405i
$523$		0			0		−0.956526	−	0.291646i	$-0.905797\pi$
$523$		0			0		0.956526	+	0.291646i	$0.0942029\pi$
$524$		0			0
$525$		0			0
$526$	3.71814	+	1.22684i	3.71814	+	1.22684i
$527$		0			0
$528$		0			0
$529$	2.34165	−	1.14650i	2.34165	−	1.14650i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	1.79028	−	5.42573i	1.79028	−	5.42573i
$537$		0			0
$538$		0			0
$539$	−0.650963	+	0.459500i	−0.650963	+	0.459500i
$540$		0			0
$541$	1.43703	−	0.402636i	1.43703	−	0.402636i	0.538899	−	0.842371i	$-0.318841\pi$
$541$	1.43703	−	0.402636i	1.43703	−	0.402636i	0.898128	+	0.439735i	$0.144928\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.0398052	+	0.130551i	0.0398052	+	0.130551i	0.974199	−	0.225690i	$-0.0724638\pi$
$547$	0.0398052	+	0.130551i	0.0398052	+	0.130551i	−0.934394	+	0.356242i	$0.884058\pi$
$548$	1.02999	+	0.877666i	1.02999	+	0.877666i
$549$		0			0
$550$	−0.918762	+	1.30159i	−0.918762	+	1.30159i
$551$		0			0
$552$		0			0
$553$	−0.227160			−0.227160
$554$	0.626526	+	1.89879i	0.626526	+	1.89879i
$555$		0			0
$556$		0			0
$557$	−0.747808	−	1.83483i	−0.747808	−	1.83483i	−0.500000	−	0.866025i	$-0.666667\pi$
$557$	−0.747808	−	1.83483i	−0.747808	−	1.83483i	−0.247808	−	0.968809i	$-0.579710\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.465253	+	3.38497i	−0.465253	+	3.38497i
$563$		0			0		0.715110	−	0.699012i	$-0.246377\pi$
$563$		0			0		−0.715110	+	0.699012i	$0.753623\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.962917	−	0.269797i	0.962917	−	0.269797i
$568$	5.12249	+	5.24046i	5.12249	+	5.24046i
$569$	−1.08778	+	0.767838i	−1.08778	+	0.767838i	−0.974199	−	0.225690i	$-0.927536\pi$
$569$	−1.08778	+	0.767838i	−1.08778	+	0.767838i	−0.113580	+	0.993529i	$0.536232\pi$
$570$		0			0
$571$	1.38898	+	0.158788i	1.38898	+	0.158788i	0.775711	−	0.631088i	$-0.217391\pi$
$571$	1.38898	+	0.158788i	1.38898	+	0.158788i	0.613267	+	0.789876i	$0.289855\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.47329	−	1.19861i	1.47329	−	1.19861i
$576$	6.11485	−	3.34718i	6.11485	−	3.34718i
$577$		0			0		0.974199	−	0.225690i	$-0.0724638\pi$
$577$		0			0		−0.974199	+	0.225690i	$0.927536\pi$
$578$	1.93712	−	0.495487i	1.93712	−	0.495487i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.593109	−	1.28463i	0.593109	−	1.28463i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$587$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.487633	−	1.74039i	0.487633	−	1.74039i
$593$		0			0		−0.613267	−	0.789876i	$-0.710145\pi$
$593$		0			0		0.613267	+	0.789876i	$0.289855\pi$
$594$		0			0
$595$		0			0
$596$	0.108723	−	0.250306i	0.108723	−	0.250306i
$597$		0			0
$598$		0			0
$599$	−1.06322	−	0.680185i	−1.06322	−	0.680185i	−0.113580	−	0.993529i	$-0.536232\pi$
$599$	−1.06322	−	0.680185i	−1.06322	−	0.680185i	−0.949640	+	0.313344i	$0.898551\pi$
$600$		0			0
$601$		0			0		−0.803631	−	0.595128i	$-0.797101\pi$
$601$		0			0		0.803631	+	0.595128i	$0.202899\pi$
$602$	2.27123	−	2.02637i	2.27123	−	2.02637i
$603$	−1.18692	+	0.797968i	−1.18692	+	0.797968i
$604$	1.71334	−	2.31361i	1.71334	−	2.31361i
$605$		0			0
$606$		0			0
$607$		0			0		0.439735	−	0.898128i	$-0.355072\pi$
$607$		0			0		−0.439735	+	0.898128i	$0.644928\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.854419	+	0.519584i	0.854419	+	0.519584i	0.877183	−	0.480157i	$-0.159420\pi$
$613$	0.854419	+	0.519584i	0.854419	+	0.519584i	−0.0227632	+	0.999741i	$0.507246\pi$
$614$		0			0
$615$		0			0
$616$	3.13044	−	0.576508i	3.13044	−	0.576508i
$617$	−0.356936	−	0.195382i	−0.356936	−	0.195382i	0.291646	−	0.956526i	$-0.405797\pi$
$617$	−0.356936	−	0.195382i	−0.356936	−	0.195382i	−0.648582	+	0.761145i	$0.724638\pi$
$618$		0			0
$619$		0			0		−0.480157	−	0.877183i	$-0.659420\pi$
$619$		0			0		0.480157	+	0.877183i	$0.340580\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.613267	−	0.789876i	0.613267	−	0.789876i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.599444	+	1.81671i	0.599444	+	1.81671i	0.576680	+	0.816970i	$0.304348\pi$
$631$	0.599444	+	1.81671i	0.599444	+	1.81671i	0.0227632	+	0.999741i	$0.492754\pi$
$632$	0.823891	+	0.380388i	0.823891	+	0.380388i
$633$		0			0
$634$	−2.87821	+	1.84130i	−2.87821	+	1.84130i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.125397	+	1.83324i	0.125397	+	1.83324i
$639$	−0.208354	−	1.82255i	−0.208354	−	1.82255i
$640$		0			0
$641$	0.495102	+	0.0225577i	0.495102	+	0.0225577i	0.291646	−	0.956526i	$-0.405797\pi$
$641$	0.495102	+	0.0225577i	0.495102	+	0.0225577i	0.203456	+	0.979084i	$0.434783\pi$
$642$		0			0
$643$		0			0		0.949640	−	0.313344i	$-0.101449\pi$
$643$		0			0		−0.949640	+	0.313344i	$0.898551\pi$
$644$	−5.67031	−	0.517774i	−5.67031	−	0.517774i
$645$		0			0
$646$		0			0
$647$		0			0		−0.0909349	−	0.995857i	$-0.528986\pi$
$647$		0			0		0.0909349	+	0.995857i	$0.471014\pi$
$648$	−3.94420	−	0.633908i	−3.94420	−	0.633908i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	2.84247	−	5.19282i	2.84247	−	5.19282i
$653$	−1.26927	+	1.29850i	−1.26927	+	1.29850i	−0.334880	+	0.942261i	$0.608696\pi$
$653$	−1.26927	+	1.29850i	−1.26927	+	1.29850i	−0.934394	+	0.356242i	$0.884058\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.56953	+	1.21860i	1.56953	+	1.21860i	0.854419	+	0.519584i	$0.173913\pi$
$659$	1.56953	+	1.21860i	1.56953	+	1.21860i	0.715110	+	0.699012i	$0.246377\pi$
$660$		0			0
$661$		0			0		−0.557934	−	0.829885i	$-0.688406\pi$
$661$		0			0		0.557934	+	0.829885i	$0.311594\pi$
$662$	−2.03343	+	1.23655i	−2.03343	+	1.23655i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.582052	+	0.431037i	−0.582052	+	0.431037i
$667$	0.445681	−	2.14474i	0.445681	−	2.14474i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.0164869	−	0.0895237i	−0.0164869	−	0.0895237i	0.974199	−	0.225690i	$-0.0724638\pi$
$673$	−0.0164869	−	0.0895237i	−0.0164869	−	0.0895237i	−0.990686	+	0.136167i	$0.956522\pi$
$674$	0.496368	+	0.957946i	0.496368	+	0.957946i
$675$		0			0
$676$	0.204586	−	2.99094i	0.204586	−	2.99094i
$677$		0			0		−0.715110	−	0.699012i	$-0.753623\pi$
$677$		0			0		0.715110	+	0.699012i	$0.246377\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.979167	−	0.347996i	0.979167	−	0.347996i	0.203456	−	0.979084i	$-0.434783\pi$
$683$	0.979167	−	0.347996i	0.979167	−	0.347996i	0.775711	+	0.631088i	$0.217391\pi$
$684$		0			0
$685$		0			0
$686$	−1.95766	−	0.406807i	−1.95766	−	0.406807i
$687$		0			0
$688$	−7.26547	+	2.21525i	−7.26547	+	2.21525i
$689$		0			0
$690$		0			0
$691$		0			0		0.0909349	−	0.995857i	$-0.471014\pi$
$691$		0			0		−0.0909349	+	0.995857i	$0.528986\pi$
$692$		0			0
$693$	−0.707469	−	0.366581i	−0.707469	−	0.366581i
$694$	0.235854	−	2.58291i	0.235854	−	2.58291i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−2.97000	+	0.408218i	−2.97000	+	0.408218i
$701$	−1.13288	−	0.761639i	−1.13288	−	0.761639i	−0.158683	−	0.987330i	$-0.550725\pi$
$701$	−1.13288	−	0.761639i	−1.13288	−	0.761639i	−0.974199	+	0.225690i	$0.927536\pi$
$702$		0			0
$703$		0			0
$704$	−5.38127	−	1.37645i	−5.38127	−	1.37645i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.00310683	+	0.0454203i	−0.00310683	+	0.0454203i	−0.998964	−	0.0455146i	$-0.985507\pi$
$709$	−0.00310683	+	0.0454203i	−0.00310683	+	0.0454203i	0.995857	+	0.0909349i	$0.0289855\pi$
$710$		0			0
$711$	−0.104509	−	0.201692i	−0.104509	−	0.201692i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.66392	−	3.39844i	−1.66392	−	3.39844i
$717$		0			0
$718$	0.685364	−	3.29815i	0.685364	−	3.29815i
$719$		0			0		0.803631	−	0.595128i	$-0.202899\pi$
$719$		0			0		−0.803631	+	0.595128i	$0.797101\pi$
$720$		0			0
$721$		0			0
$722$	−1.03890	−	1.70840i	−1.03890	−	1.70840i
$723$		0			0
$724$		0			0
$725$	−0.0262542	−	1.15306i	−0.0262542	−	1.15306i
$726$		0			0
$727$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$727$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$728$		0			0
$729$	0.682553	+	0.730836i	0.682553	+	0.730836i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.480157	−	0.877183i	$-0.340580\pi$
$733$		0			0		−0.480157	+	0.877183i	$0.659420\pi$
$734$		0			0
$735$		0			0
$736$	9.83914	+	5.68063i	9.83914	+	5.68063i
$737$	1.12516	+	0.180835i	1.12516	+	0.180835i
$738$		0			0
$739$	−0.726847	+	1.78340i	−0.726847	+	1.78340i	−0.113580	+	0.993529i	$0.536232\pi$
$739$	−0.726847	+	1.78340i	−0.726847	+	1.78340i	−0.613267	+	0.789876i	$0.710145\pi$
$740$		0			0
$741$		0			0
$742$	3.37181	−	1.11257i	3.37181	−	1.11257i
$743$	−0.223404	+	1.95420i	−0.223404	+	1.95420i	0.0682424	+	0.997669i	$0.478261\pi$
$743$	−0.223404	+	1.95420i	−0.223404	+	1.95420i	−0.291646	+	0.956526i	$0.594203\pi$
$744$		0			0
$745$		0			0
$746$	0.393351	+	3.44079i	0.393351	+	3.44079i
$747$		0			0
$748$		0			0
$749$	−1.22281	+	1.50303i	−1.22281	+	1.50303i
$750$		0			0
$751$	−0.600175	+	0.383956i	−0.600175	+	0.383956i	−0.803631	−	0.595128i	$-0.797101\pi$
$751$	−0.600175	+	0.383956i	−0.600175	+	0.383956i	0.203456	+	0.979084i	$0.434783\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.93025	+	0.265307i	1.93025	+	0.265307i	0.995857	−	0.0909349i	$-0.0289855\pi$
$757$	1.93025	+	0.265307i	1.93025	+	0.265307i	0.934394	+	0.356242i	$0.115942\pi$
$758$	−2.31083	−	0.821269i	−2.31083	−	0.821269i
$759$		0			0
$760$		0			0
$761$		0			0		0.538899	−	0.842371i	$-0.318841\pi$
$761$		0			0		−0.538899	+	0.842371i	$0.681159\pi$
$762$		0			0
$763$	0.417211	−	0.467624i	0.417211	−	0.467624i
$764$	−4.89358	−	0.901211i	−4.89358	−	0.901211i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.983462	−	0.181116i	$-0.0579710\pi$
$769$		0			0		−0.983462	+	0.181116i	$0.942029\pi$
$770$		0			0
$771$		0			0
$772$	−4.49378	−	2.73273i	−4.49378	−	2.73273i
$773$		0			0		−0.0455146	−	0.998964i	$-0.514493\pi$
$773$		0			0		0.0455146	+	0.998964i	$0.485507\pi$
$774$	2.84410	+	1.08432i	2.84410	+	1.08432i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.879242	+	1.79579i	−0.879242	+	1.79579i
$779$		0			0
$780$		0			0
$781$	−0.869882	+	1.17465i	−0.869882	+	1.17465i
$782$		0			0
$783$		0			0
$784$	4.00983	+	2.96947i	4.00983	+	2.96947i
$785$		0			0
$786$		0			0
$787$		0			0		0.557934	−	0.829885i	$-0.311594\pi$
$787$		0			0		−0.557934	+	0.829885i	$0.688406\pi$
$788$	−0.222950	+	4.89336i	−0.222950	+	4.89336i
$789$		0			0
$790$		0			0
$791$	0.0453378	−	0.00413994i	0.0453378	−	0.00413994i
$792$	1.95208	+	2.51424i	1.95208	+	2.51424i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.934394	−	0.356242i	$-0.115942\pi$
$797$		0			0		−0.934394	+	0.356242i	$0.884058\pi$
$798$		0			0
$799$		0			0
$800$	5.72182	+	1.74459i	5.72182	+	1.74459i
$801$		0			0
$802$	−1.36946	+	2.96615i	−1.36946	+	2.96615i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.40986	−	0.771738i	1.40986	−	0.771738i	0.419177	−	0.907905i	$-0.362319\pi$
$809$	1.40986	−	0.771738i	1.40986	−	0.771738i	0.990686	+	0.136167i	$0.0434783\pi$
$810$		0			0
$811$		0			0		−0.926043	−	0.377419i	$-0.876812\pi$
$811$		0			0		0.926043	+	0.377419i	$0.123188\pi$
$812$	−2.36006	+	2.52701i	−2.36006	+	2.52701i
$813$		0			0
$814$	0.573371	+	0.0655478i	0.573371	+	0.0655478i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.27571	+	1.49711i	1.27571	+	1.49711i	0.775711	+	0.631088i	$0.217391\pi$
$821$	1.27571	+	1.49711i	1.27571	+	1.49711i	0.500000	+	0.866025i	$0.333333\pi$
$822$		0			0
$823$	−0.235848	+	1.71592i	−0.235848	+	1.71592i	0.377419	+	0.926043i	$0.376812\pi$
$823$	−0.235848	+	1.71592i	−0.235848	+	1.71592i	−0.613267	+	0.789876i	$0.710145\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.386237	−	0.547173i	0.386237	−	0.547173i	−0.576680	−	0.816970i	$-0.695652\pi$
$827$	0.386237	−	0.547173i	0.386237	−	0.547173i	0.962917	+	0.269797i	$0.0869565\pi$
$828$	−2.14899	−	5.27280i	−2.14899	−	5.27280i
$829$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$829$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$830$		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		0.136167	−	0.990686i	$-0.456522\pi$
$839$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$840$		0			0
$841$	−0.214188	−	0.251361i	−0.214188	−	0.251361i
$842$	−3.93181	+	0.0895237i	−3.93181	+	0.0895237i
$843$		0			0
$844$	−3.11134	+	0.871756i	−3.11134	+	0.871756i
$845$		0			0
$846$		0			0
$847$	−0.122267	−	0.344025i	−0.122267	−	0.344025i
$848$	−8.80312	−	1.00637i	−8.80312	−	1.00637i
$849$		0			0
$850$		0			0
$851$	−0.637099	−	0.259657i	−0.637099	−	0.259657i
$852$		0			0
$853$		0			0		0.877183	−	0.480157i	$-0.159420\pi$
$853$		0			0		−0.877183	+	0.480157i	$0.840580\pi$
$854$		0			0
$855$		0			0
$856$	6.95190	−	3.40374i	6.95190	−	3.40374i
$857$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$857$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$858$		0			0
$859$		0			0		−0.949640	−	0.313344i	$-0.898551\pi$
$859$		0			0		0.949640	+	0.313344i	$0.101449\pi$
$860$		0			0
$861$		0			0
$862$	−2.48090	−	0.756429i	−2.48090	−	0.756429i
$863$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$863$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.0488337	+	0.174290i	−0.0488337	+	0.174290i
$870$		0			0
$871$		0			0
$872$	−2.29624	+	0.997399i	−2.29624	+	0.997399i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.138429	−	0.117957i	0.138429	−	0.117957i	−0.576680	−	0.816970i	$-0.695652\pi$
$877$	0.138429	−	0.117957i	0.138429	−	0.117957i	0.715110	+	0.699012i	$0.246377\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.595128	−	0.803631i	$-0.297101\pi$
$881$		0			0		−0.595128	+	0.803631i	$0.702899\pi$
$882$	−0.539454	−	1.92534i	−0.539454	−	1.92534i
$883$	−0.165972	+	0.466999i	−0.165972	+	0.466999i	−0.995857	−	0.0909349i	$-0.971014\pi$
$883$	−0.165972	+	0.466999i	−0.165972	+	0.466999i	0.829885	+	0.557934i	$0.188406\pi$
$884$		0			0
$885$		0			0
$886$	−0.552898	−	2.16157i	−0.552898	−	2.16157i
$887$		0			0		0.987330	−	0.158683i	$-0.0507246\pi$
$887$		0			0		−0.987330	+	0.158683i	$0.949275\pi$
$888$		0			0
$889$	0.0719018	+	1.57811i	0.0719018	+	1.57811i
$890$		0			0
$891$		−	0.796802i		−	0.796802i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−3.82039	−	6.97934i	−3.82039	−	6.97934i
$897$		0			0
$898$	−3.70575	−	0.682458i	−3.70575	−	0.682458i
$899$		0			0
$900$	−1.72885	−	2.44922i	−1.72885	−	2.44922i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.171369	−	0.0609045i	−0.171369	−	0.0609045i
$905$		0			0
$906$		0			0
$907$	0.170568	+	0.820818i	0.170568	+	0.820818i	0.974199	+	0.225690i	$0.0724638\pi$
$907$	0.170568	+	0.820818i	0.170568	+	0.820818i	−0.803631	+	0.595128i	$0.797101\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.229406	+	0.146760i	−0.229406	+	0.146760i	−0.648582	−	0.761145i	$-0.724638\pi$
$911$	−0.229406	+	0.146760i	−0.229406	+	0.146760i	0.419177	+	0.907905i	$0.362319\pi$
$912$		0			0
$913$		0			0
$914$	−1.14052	+	1.33846i	−1.14052	+	1.33846i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.113580	+	0.993529i	−0.113580	+	0.993529i	0.803631	+	0.595128i	$0.202899\pi$
$919$	−0.113580	+	0.993529i	−0.113580	+	0.993529i	−0.917211	+	0.398401i	$0.869565\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.357643	−	0.0574800i	−0.357643	−	0.0574800i
$926$	1.59330	+	0.919892i	1.59330	+	0.919892i
$927$		0			0
$928$	6.38901	−	2.60391i	6.38901	−	2.60391i
$929$		0			0		0.480157	−	0.877183i	$-0.340580\pi$
$929$		0			0		−0.480157	+	0.877183i	$0.659420\pi$
$930$		0			0
$931$		0			0
$932$	0.576279	+	1.51153i	0.576279	+	1.51153i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.0227632	−	0.999741i	$-0.507246\pi$
$937$		0			0		0.0227632	+	0.999741i	$0.492754\pi$
$938$	1.59552	+	2.37322i	1.59552	+	2.37322i
$939$		0			0
$940$		0			0
$941$		0			0		−0.665740	−	0.746184i	$-0.731884\pi$
$941$		0			0		0.665740	+	0.746184i	$0.268116\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−1.06649	−	2.17823i	−1.06649	−	2.17823i
$947$	0.974199	+	1.68736i	0.974199	+	1.68736i	0.682553	+	0.730836i	$0.260870\pi$
$947$	0.974199	+	1.68736i	0.974199	+	1.68736i	0.291646	+	0.956526i	$0.405797\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.00931405	+	0.136167i	−0.00931405	+	0.136167i	0.990686	+	0.136167i	$0.0434783\pi$
$953$	−0.00931405	+	0.136167i	−0.00931405	+	0.136167i	−1.00000			$\pi$
$954$	2.53908	+	2.48193i	2.53908	+	2.48193i
$955$		0			0
$956$	−3.18746	−	3.91791i	−3.18746	−	3.91791i
$957$		0			0
$958$		0			0
$959$	−0.441940	+	0.0918361i	−0.441940	+	0.0918361i
$960$		0			0
$961$	0.829885	+	0.557934i	0.829885	+	0.557934i
$962$		0			0
$963$	−1.89709	−	0.394220i	−1.89709	−	0.394220i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.100836	−	0.394220i	0.100836	−	0.394220i	−0.898128	−	0.439735i	$-0.855072\pi$
$967$	0.100836	−	0.394220i	0.100836	−	0.394220i	0.998964	+	0.0455146i	$0.0144928\pi$
$968$	−0.132632	+	1.45249i	−0.132632	+	1.45249i
$969$		0			0
$970$		0			0
$971$		0			0		0.0909349	−	0.995857i	$-0.471014\pi$
$971$		0			0		−0.0909349	+	0.995857i	$0.528986\pi$
$972$		0			0
$973$		0			0
$974$	3.57416	−	1.08977i	3.57416	−	1.08977i
$975$		0			0
$976$		0			0
$977$	−1.90790	+	0.262234i	−1.90790	+	0.262234i	−0.990686	−	0.136167i	$-0.956522\pi$
$977$	−1.90790	+	0.262234i	−1.90790	+	0.262234i	−0.917211	+	0.398401i	$0.869565\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.607141	+	0.155298i	0.607141	+	0.155298i
$982$	0.634401	+	0.0144447i	0.634401	+	0.0144447i
$983$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$983$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.523653	+	2.84344i	0.523653	+	2.84344i
$990$		0			0
$991$	0.990686	−	1.71592i	0.990686	−	1.71592i	0.377419	−	0.926043i	$-0.376812\pi$
$991$	0.990686	−	1.71592i	0.990686	−	1.71592i	0.613267	−	0.789876i	$-0.289855\pi$
$992$		0			0
$993$		0			0
$994$	−3.64416	+	0.416600i	−3.64416	+	0.416600i
$995$		0			0
$996$		0			0
$997$		0			0		0.225690	−	0.974199i	$-0.427536\pi$
$997$		0			0		−0.225690	+	0.974199i	$0.572464\pi$
$998$	−0.659731	−	0.739449i	−0.659731	−	0.739449i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1939.1.by.a.867.1	yes	44
7.6	odd	2	CM	1939.1.by.a.867.1	yes	44
277.177	even	138	inner	1939.1.by.a.454.1	✓	44
1939.454	odd	138	inner	1939.1.by.a.454.1	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1939.1.by.a.454.1	✓	44	277.177	even	138	inner
1939.1.by.a.454.1	✓	44	1939.454	odd	138	inner
1939.1.by.a.867.1	yes	44	1.1	even	1	trivial
1939.1.by.a.867.1	yes	44	7.6	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(1.77531 - 0.919892i) q^{2} +(1.72885 - 2.44922i) q^{4} +(0.291646 + 0.956526i) q^{7} +(0.543961 - 3.95761i) q^{8} +(-0.715110 + 0.699012i) q^{9} +O(q^{10})\)	\(q+(1.77531 - 0.919892i) q^{2} +(1.72885 - 2.44922i) q^{4} +(0.291646 + 0.956526i) q^{7} +(0.543961 - 3.95761i) q^{8} +(-0.715110 + 0.699012i) q^{9} +(0.796596 - 0.0181378i) q^{11} +(1.39766 + 1.42985i) q^{14} +(-1.67093 - 4.70154i) q^{16} +(-0.626526 + 1.89879i) q^{18} +(1.39752 - 0.764982i) q^{22} +(-1.85028 + 0.428649i) q^{23} +(-0.898128 + 0.439735i) q^{25} +(2.84695 + 0.939382i) q^{28} +(-0.483462 + 1.04714i) q^{29} +(-4.37177 - 4.08295i) q^{32} +(0.475719 + 2.95994i) q^{36} +(0.295933 + 0.208892i) q^{37} +(0.0692864 - 1.52071i) q^{43} +(1.33277 - 1.98239i) q^{44} +(-2.89050 + 2.46304i) q^{46} +(-0.829885 + 0.557934i) q^{49} +(-1.18995 + 1.60685i) q^{50} +(0.780868 - 1.59487i) q^{53} +(3.94420 - 0.633908i) q^{56} +(0.104962 + 2.30373i) q^{58} +(-0.877183 - 0.480157i) q^{63} +(-6.71251 - 1.88076i) q^{64} +(1.40657 + 0.259036i) q^{67} +(-1.12499 + 1.44897i) q^{71} +(2.37743 + 3.21036i) q^{72} +(0.717531 + 0.0986224i) q^{74} +(0.249673 + 0.756675i) q^{77} +(-0.0662504 + 0.217285i) q^{79} +(0.0227632 - 0.999741i) q^{81} +(-1.27589 - 2.76347i) q^{86} +(0.361535 - 3.16248i) q^{88} +(-2.14899 + 5.27280i) q^{92} +(-0.960065 + 1.75391i) q^{98} +(-0.556975 + 0.569801i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{4} + q^{7} + q^{9}+O(q^{10}) \) 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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