LMFDB - Embedded newform 2736.2.s.y.577.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(577,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2736.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.s (of order $3$, degree $2$, not 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:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2696112.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 $ x^6 - x^5 + 5x^4 + 18x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.2
Root			$0.235342 + 0.407624i$ of defining polynomial
Character	$\chi$	$=$	2736.577
Dual form			2736.2.s.y.1873.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.235342 + 0.407624i) q^{5} +3.30777 q^{7} +O(q^{10})$	$q+(0.235342 + 0.407624i) q^{5} +3.30777 q^{7} +1.47068 q^{11} +(1.41855 - 2.45699i) q^{13} +(3.35991 + 5.81954i) q^{17} +(0.206025 + 4.35403i) q^{19} +(-0.235342 + 0.407624i) q^{23} +(2.38923 - 4.13827i) q^{25} +(2.48448 - 4.30325i) q^{29} -6.74742 q^{31} +(0.778457 + 1.34833i) q^{35} +4.74742 q^{37} +(-0.250859 - 0.434501i) q^{41} +(1.94786 + 3.37380i) q^{43} +(-5.95517 + 10.3146i) q^{47} +3.94137 q^{49} +(-2.35991 + 4.08749i) q^{53} +(0.346113 + 0.599486i) q^{55} +(-3.62457 - 6.27794i) q^{59} +(6.26294 - 10.8477i) q^{61} +1.33537 q^{65} +(-0.316797 + 0.548708i) q^{67} +(1.88923 + 3.27224i) q^{71} +(1.97068 + 3.41332i) q^{73} +4.86469 q^{77} +(-4.41855 - 7.65314i) q^{79} +9.14486 q^{83} +(-1.58145 + 2.73916i) q^{85} +(1.47718 - 2.55855i) q^{89} +(4.69223 - 8.12717i) q^{91} +(-1.72632 + 1.10866i) q^{95} +(-0.0293166 - 0.0507778i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5} + 4 q^{7}+O(q^{10}) $ 6 * q + q^5 + 4 * q^7	$ 6 q + q^{5} + 4 q^{7} + 8 q^{11} + q^{13} + 11 q^{17} - q^{23} + 6 q^{25} - 3 q^{29} + 12 q^{31} - 12 q^{35} - 24 q^{37} - 19 q^{41} + 5 q^{43} - 17 q^{47} + 22 q^{49} - 5 q^{53} + 10 q^{55} - 13 q^{59} + 3 q^{61} - 42 q^{65} - 9 q^{67} + 3 q^{71} + 11 q^{73} - 20 q^{77} - 19 q^{79} + 24 q^{83} - 17 q^{85} + 3 q^{89} + 44 q^{91} + 13 q^{95} - q^{97}+O(q^{100}) $ 6 * q + q^5 + 4 * q^7 + 8 * q^11 + q^13 + 11 * q^17 - q^23 + 6 * q^25 - 3 * q^29 + 12 * q^31 - 12 * q^35 - 24 * q^37 - 19 * q^41 + 5 * q^43 - 17 * q^47 + 22 * q^49 - 5 * q^53 + 10 * q^55 - 13 * q^59 + 3 * q^61 - 42 * q^65 - 9 * q^67 + 3 * q^71 + 11 * q^73 - 20 * q^77 - 19 * q^79 + 24 * q^83 - 17 * q^85 + 3 * q^89 + 44 * q^91 + 13 * q^95 - q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.235342	+	0.407624i	0.105248	+	0.182295i	0.913840	−	0.406076i	$-0.133103\pi$
$5$	0.235342	+	0.407624i	0.105248	+	0.182295i	−0.808591	+	0.588370i	$0.799770\pi$
$6$		0			0
$7$	3.30777			1.25022			0.625110	−	0.780536i	$-0.285054\pi$
$7$	3.30777			1.25022			0.625110	+	0.780536i	$0.285054\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.47068			0.443428			0.221714	−	0.975112i	$-0.428835\pi$
$11$	1.47068			0.443428			0.221714	+	0.975112i	$0.428835\pi$
$12$		0			0
$13$	1.41855	−	2.45699i	0.393434	−	0.681447i	−0.599466	−	0.800400i	$-0.704620\pi$
$13$	1.41855	−	2.45699i	0.393434	−	0.681447i	0.992900	+	0.118953i	$0.0379538\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.35991	+	5.81954i	0.814898	+	1.41145i	0.909401	+	0.415921i	$0.136541\pi$
$17$	3.35991	+	5.81954i	0.814898	+	1.41145i	−0.0945025	+	0.995525i	$0.530126\pi$
$18$		0			0
$19$	0.206025	+	4.35403i	0.0472654	+	0.998882i
$19$	0.206025	+	4.35403i	0.0472654	+	0.998882i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.235342	+	0.407624i	−0.0490721	+	0.0849954i	−0.889518	−	0.456900i	$-0.848960\pi$
$23$	−0.235342	+	0.407624i	−0.0490721	+	0.0849954i	0.840446	+	0.541895i	$0.182293\pi$
$24$		0			0
$25$	2.38923	−	4.13827i	0.477846	−	0.827653i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.48448	−	4.30325i	0.461357	−	0.799093i	−0.537672	−	0.843154i	$-0.680696\pi$
$29$	2.48448	−	4.30325i	0.461357	−	0.799093i	0.999029	+	0.0440607i	$0.0140295\pi$
$30$		0			0
$31$	−6.74742			−1.21187			−0.605936	−	0.795513i	$-0.707201\pi$
$31$	−6.74742			−1.21187			−0.605936	+	0.795513i	$0.707201\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.778457	+	1.34833i	0.131583	+	0.227909i
$36$		0			0
$37$	4.74742			0.780471			0.390236	−	0.920715i	$-0.372394\pi$
$37$	4.74742			0.780471			0.390236	+	0.920715i	$0.372394\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.250859	−	0.434501i	−0.0391777	−	0.0678577i	0.845772	−	0.533545i	$-0.179140\pi$
$41$	−0.250859	−	0.434501i	−0.0391777	−	0.0678577i	−0.884949	+	0.465687i	$0.845807\pi$
$42$		0			0
$43$	1.94786	+	3.37380i	0.297046	+	0.514499i	0.975459	−	0.220182i	$-0.0706652\pi$
$43$	1.94786	+	3.37380i	0.297046	+	0.514499i	−0.678413	+	0.734681i	$0.737332\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.95517	+	10.3146i	−0.868650	+	1.50455i	−0.00527366	+	0.999986i	$0.501679\pi$
$47$	−5.95517	+	10.3146i	−0.868650	+	1.50455i	−0.863377	+	0.504560i	$0.831655\pi$
$48$		0			0
$49$	3.94137			0.563052
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.35991	+	4.08749i	−0.324159	+	0.561460i	−0.981342	−	0.192272i	$-0.938415\pi$
$53$	−2.35991	+	4.08749i	−0.324159	+	0.561460i	0.657183	+	0.753731i	$0.271748\pi$
$54$		0			0
$55$	0.346113	+	0.599486i	0.0466699	+	0.0808346i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.62457	−	6.27794i	−0.471879	−	0.817318i	0.527603	−	0.849491i	$-0.323091\pi$
$59$	−3.62457	−	6.27794i	−0.471879	−	0.817318i	−0.999482	+	0.0321726i	$0.989757\pi$
$60$		0			0
$61$	6.26294	−	10.8477i	0.801887	−	1.38891i	−0.116485	−	0.993192i	$-0.537163\pi$
$61$	6.26294	−	10.8477i	0.801887	−	1.38891i	0.918373	−	0.395717i	$-0.129504\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.33537			0.165632
$66$		0			0
$67$	−0.316797	+	0.548708i	−0.0387029	+	0.0670353i	−0.884728	−	0.466108i	$-0.845656\pi$
$67$	−0.316797	+	0.548708i	−0.0387029	+	0.0670353i	0.846025	+	0.533143i	$0.178989\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.88923	+	3.27224i	0.224210	+	0.388343i	0.956082	−	0.293099i	$-0.0946865\pi$
$71$	1.88923	+	3.27224i	0.224210	+	0.388343i	−0.731872	+	0.681442i	$0.761353\pi$
$72$		0			0
$73$	1.97068	+	3.41332i	0.230651	+	0.399499i	0.958000	−	0.286769i	$-0.0925811\pi$
$73$	1.97068	+	3.41332i	0.230651	+	0.399499i	−0.727349	+	0.686268i	$0.759248\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.86469			0.554383
$78$		0			0
$79$	−4.41855	−	7.65314i	−0.497125	−	0.861046i	0.502869	−	0.864362i	$-0.332278\pi$
$79$	−4.41855	−	7.65314i	−0.497125	−	0.861046i	−0.999995	+	0.00331640i	$0.998944\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	9.14486			1.00378			0.501890	−	0.864932i	$-0.332638\pi$
$83$	9.14486			1.00378			0.501890	+	0.864932i	$0.332638\pi$
$84$		0			0
$85$	−1.58145	+	2.73916i	−0.171533	+	0.297104i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.47718	−	2.55855i	0.156581	−	0.271206i	−0.777053	−	0.629435i	$-0.783286\pi$
$89$	1.47718	−	2.55855i	0.156581	−	0.271206i	0.933633	+	0.358230i	$0.116620\pi$
$90$		0			0
$91$	4.69223	−	8.12717i	0.491879	−	0.851959i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.72632	+	1.10866i	−0.177117	+	0.113747i
$96$		0			0
$97$	−0.0293166	−	0.0507778i	−0.00297665	−	0.00515571i	0.864533	−	0.502576i	$-0.167614\pi$
$97$	−0.0293166	−	0.0507778i	−0.00297665	−	0.00515571i	−0.867510	+	0.497420i	$0.834281\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.79226	−	10.0325i	0.576351	−	0.998269i	−0.419542	−	0.907736i	$-0.637809\pi$
$101$	5.79226	−	10.0325i	0.576351	−	0.998269i	0.995893	−	0.0905335i	$-0.0288572\pi$
$102$		0			0
$103$	8.17246			0.805257			0.402628	−	0.915364i	$-0.368097\pi$
$103$	8.17246			0.805257			0.402628	+	0.915364i	$0.368097\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.498281			0.0481706			0.0240853	−	0.999710i	$-0.492333\pi$
$107$	0.498281			0.0481706			0.0240853	+	0.999710i	$0.492333\pi$
$108$		0			0
$109$	4.19700	+	7.26942i	0.402000	+	0.696284i	0.993967	−	0.109678i	$-0.0349819\pi$
$109$	4.19700	+	7.26942i	0.402000	+	0.696284i	−0.591967	+	0.805962i	$0.701649\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.83365			−0.454712			−0.227356	−	0.973812i	$-0.573008\pi$
$113$	−4.83365			−0.454712			−0.227356	+	0.973812i	$0.573008\pi$
$114$		0			0
$115$	−0.221543			−0.0206590
$116$		0			0
$117$		0			0
$118$		0			0
$119$	11.1138	+	19.2497i	1.01880	+	1.76462i
$120$		0			0
$121$	−8.83709			−0.803372
$122$		0			0
$123$		0			0
$124$		0			0
$125$	4.60256			0.411665
$126$		0			0
$127$	−9.22460	+	15.9775i	−0.818551	+	1.41777i	0.0881990	+	0.996103i	$0.471889\pi$
$127$	−9.22460	+	15.9775i	−0.818551	+	1.41777i	−0.906750	+	0.421669i	$0.861444\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.434063	−	0.751819i	−0.0379243	−	0.0656867i	0.846440	−	0.532484i	$-0.178741\pi$
$131$	−0.434063	−	0.751819i	−0.0379243	−	0.0656867i	−0.884365	+	0.466797i	$0.845408\pi$
$132$		0			0
$133$	0.681485	+	14.4021i	0.0590922	+	1.24882i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.27846	−	3.94640i	0.194662	−	0.337164i	−0.752128	−	0.659017i	$-0.770972\pi$
$137$	2.27846	−	3.94640i	0.194662	−	0.337164i	0.946790	+	0.321853i	$0.104306\pi$
$138$		0			0
$139$	−8.15389	+	14.1229i	−0.691604	+	1.19789i	0.279709	+	0.960085i	$0.409762\pi$
$139$	−8.15389	+	14.1229i	−0.691604	+	1.19789i	−0.971312	+	0.237808i	$0.923571\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.08623	−	3.61346i	0.174459	−	0.302173i
$144$		0			0
$145$	2.33881			0.194228
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.4534	+	18.1059i	0.856380	+	1.48329i	0.875359	+	0.483473i	$0.160625\pi$
$149$	10.4534	+	18.1059i	0.856380	+	1.48329i	−0.0189794	+	0.999820i	$0.506042\pi$
$150$		0			0
$151$	−1.75086			−0.142483			−0.0712415	−	0.997459i	$-0.522696\pi$
$151$	−1.75086			−0.142483			−0.0712415	+	0.997459i	$0.522696\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.58795	−	2.75041i	−0.127547	−	0.220918i
$156$		0			0
$157$	0.0797359	+	0.138107i	0.00636362	+	0.0110221i	0.869190	−	0.494479i	$-0.164641\pi$
$157$	0.0797359	+	0.138107i	0.00636362	+	0.0110221i	−0.862826	+	0.505501i	$0.831308\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.778457	+	1.34833i	−0.0613510	+	0.106263i
$162$		0			0
$163$	0.0862308			0.00675412			0.00337706	−	0.999994i	$-0.498925\pi$
$163$	0.0862308			0.00675412			0.00337706	+	0.999994i	$0.498925\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.13837	−	5.43581i	0.242854	−	0.420636i	−0.718672	−	0.695349i	$-0.755250\pi$
$167$	3.13837	−	5.43581i	0.242854	−	0.420636i	0.961526	+	0.274713i	$0.0885830\pi$
$168$		0			0
$169$	2.47546	+	4.28762i	0.190420	+	0.329817i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−5.41855	−	9.38520i	−0.411964	−	0.713543i	0.583140	−	0.812372i	$-0.301824\pi$
$173$	−5.41855	−	9.38520i	−0.411964	−	0.713543i	−0.995104	+	0.0988284i	$0.968491\pi$
$174$		0			0
$175$	7.90303	−	13.6884i	0.597413	−	1.03475i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.08967			0.529907			0.264953	−	0.964261i	$-0.414643\pi$
$179$	7.08967			0.529907			0.264953	+	0.964261i	$0.414643\pi$
$180$		0			0
$181$	6.17671	−	10.6984i	0.459111	−	0.795204i	−0.539803	−	0.841791i	$-0.681501\pi$
$181$	6.17671	−	10.6984i	0.459111	−	0.795204i	0.998914	+	0.0465875i	$0.0148346\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.11727	+	1.93516i	0.0821431	+	0.142276i
$186$		0			0
$187$	4.94137	+	8.55870i	0.361349	+	0.625874i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.99656			0.650968			0.325484	−	0.945547i	$-0.394473\pi$
$191$	8.99656			0.650968			0.325484	+	0.945547i	$0.394473\pi$
$192$		0			0
$193$	1.58145	+	2.73916i	0.113836	+	0.197169i	0.917314	−	0.398165i	$-0.130353\pi$
$193$	1.58145	+	2.73916i	0.113836	+	0.197169i	−0.803478	+	0.595334i	$0.797020\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	21.2457			1.51369			0.756847	−	0.653592i	$-0.226739\pi$
$197$	21.2457			1.51369			0.756847	+	0.653592i	$0.226739\pi$
$198$		0			0
$199$	4.94786	−	8.56995i	0.350745	−	0.607507i	−0.635635	−	0.771989i	$-0.719262\pi$
$199$	4.94786	−	8.56995i	0.350745	−	0.607507i	0.986380	+	0.164482i	$0.0525952\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.21811	−	14.2342i	0.576798	−	0.999043i
$204$		0			0
$205$	0.118075	−	0.204513i	0.00824674	−	0.0142838i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.302998	+	6.40340i	0.0209588	+	0.442932i
$210$		0			0
$211$	9.55042	+	16.5418i	0.657478	+	1.13879i	0.981266	+	0.192656i	$0.0617101\pi$
$211$	9.55042	+	16.5418i	0.657478	+	1.13879i	−0.323788	+	0.946130i	$0.604957\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.916826	+	1.58799i	−0.0625270	+	0.108300i
$216$		0			0
$217$	−22.3189			−1.51511
$218$		0			0
$219$		0			0
$220$		0			0
$221$	19.0647			1.28243
$222$		0			0
$223$	−8.48448	−	14.6956i	−0.568163	−	0.984087i	−0.996748	−	0.0805855i	$-0.974321\pi$
$223$	−8.48448	−	14.6956i	−0.568163	−	0.984087i	0.428585	−	0.903502i	$-0.359012\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.646583			0.0429152			0.0214576	−	0.999770i	$-0.493169\pi$
$227$	0.646583			0.0429152			0.0214576	+	0.999770i	$0.493169\pi$
$228$		0			0
$229$	−8.55348			−0.565230			−0.282615	−	0.959233i	$-0.591202\pi$
$229$	−8.55348			−0.565230			−0.282615	+	0.959233i	$0.591202\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.85342	−	3.21021i	−0.121421	−	0.210308i	0.798907	−	0.601455i	$-0.205412\pi$
$233$	−1.85342	−	3.21021i	−0.121421	−	0.210308i	−0.920328	+	0.391147i	$0.872079\pi$
$234$		0			0
$235$	−5.60600			−0.365695
$236$		0			0
$237$		0			0
$238$		0			0
$239$	15.7655			1.01978			0.509892	−	0.860239i	$-0.329685\pi$
$239$	15.7655			1.01978			0.509892	+	0.860239i	$0.329685\pi$
$240$		0			0
$241$	8.05691	−	13.9550i	0.518991	−	0.898920i	−0.480765	−	0.876850i	$-0.659641\pi$
$241$	8.05691	−	13.9550i	0.518991	−	0.898920i	0.999756	−	0.0220701i	$-0.00702570\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.927568	+	1.60659i	0.0592601	+	0.102642i
$246$		0			0
$247$	10.9901	+	5.67018i	0.699281	+	0.360785i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.82807	−	13.5586i	0.494103	−	0.855812i	−0.505874	−	0.862608i	$-0.668830\pi$
$251$	7.82807	−	13.5586i	0.494103	−	0.855812i	0.999977	+	0.00679567i	$0.00216314\pi$
$252$		0			0
$253$	−0.346113	+	0.599486i	−0.0217599	+	0.0376893i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.9086	+	24.0904i	−0.867595	+	1.50272i	−0.00314859	+	0.999995i	$0.501002\pi$
$257$	−13.9086	+	24.0904i	−0.867595	+	1.50272i	−0.864447	+	0.502724i	$0.832331\pi$
$258$		0			0
$259$	15.7034			0.975762
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.42585	−	14.5940i	−0.519560	−	0.899905i	−0.999742	−	0.0227353i	$-0.992763\pi$
$263$	−8.42585	−	14.5940i	−0.519560	−	0.899905i	0.480181	−	0.877169i	$-0.340571\pi$
$264$		0			0
$265$	−2.22154			−0.136468
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−14.8125	−	25.6561i	−0.903137	−	1.56428i	−0.823399	−	0.567464i	$-0.807925\pi$
$269$	−14.8125	−	25.6561i	−0.903137	−	1.56428i	−0.0797386	−	0.996816i	$-0.525409\pi$
$270$		0			0
$271$	7.23534	+	12.5320i	0.439516	+	0.761264i	0.997652	−	0.0684857i	$-0.0218167\pi$
$271$	7.23534	+	12.5320i	0.439516	+	0.761264i	−0.558136	+	0.829749i	$0.688483\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.51380	−	6.08608i	0.211890	−	0.367004i
$276$		0			0
$277$	−12.4216			−0.746342			−0.373171	−	0.927763i	$-0.621729\pi$
$277$	−12.4216			−0.746342			−0.373171	+	0.927763i	$0.621729\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.14658	+	8.91414i	−0.307019	+	0.531773i	−0.977709	−	0.209965i	$-0.932665\pi$
$281$	−5.14658	+	8.91414i	−0.307019	+	0.531773i	0.670690	+	0.741738i	$0.265998\pi$
$282$		0			0
$283$	−7.93234	−	13.7392i	−0.471529	−	0.816712i	0.527941	−	0.849281i	$-0.322964\pi$
$283$	−7.93234	−	13.7392i	−0.471529	−	0.816712i	−0.999469	+	0.0325693i	$0.989631\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.829786	−	1.43723i	−0.0489807	−	0.0848371i
$288$		0			0
$289$	−14.0780	+	24.3838i	−0.828119	+	1.43434i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.1579			0.710269			0.355135	−	0.934815i	$-0.384435\pi$
$293$	12.1579			0.710269			0.355135	+	0.934815i	$0.384435\pi$
$294$		0			0
$295$	1.70603	−	2.95492i	0.0993286	−	0.172042i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.667686	+	1.15647i	0.0386133	+	0.0668801i
$300$		0			0
$301$	6.44309	+	11.1598i	0.371373	+	0.643237i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	5.89572			0.337588
$306$		0			0
$307$	−6.15045	−	10.6529i	−0.351025	−	0.607993i	0.635405	−	0.772179i	$-0.280833\pi$
$307$	−6.15045	−	10.6529i	−0.351025	−	0.607993i	−0.986429	+	0.164187i	$0.947500\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.519765			−0.0294732			−0.0147366	−	0.999891i	$-0.504691\pi$
$311$	−0.519765			−0.0294732			−0.0147366	+	0.999891i	$0.504691\pi$
$312$		0			0
$313$	−9.30605	+	16.1186i	−0.526009	+	0.911075i	0.473532	+	0.880777i	$0.342979\pi$
$313$	−9.30605	+	16.1186i	−0.526009	+	0.911075i	−0.999541	+	0.0302980i	$0.990354\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.41855	+	2.45699i	−0.0796734	+	0.137998i	−0.903109	−	0.429411i	$-0.858721\pi$
$317$	−1.41855	+	2.45699i	−0.0796734	+	0.137998i	0.823436	+	0.567410i	$0.192054\pi$
$318$		0			0
$319$	3.65389	−	6.32872i	0.204578	−	0.354340i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−24.6462	+	15.8281i	−1.37135	+	0.880700i
$324$		0			0
$325$	−6.77846	−	11.7406i	−0.376001	−	0.651253i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−19.6983	+	34.1185i	−1.08600	+	1.88102i
$330$		0			0
$331$	19.0276			1.04585			0.522926	−	0.852378i	$-0.324841\pi$
$331$	19.0276			1.04585			0.522926	+	0.852378i	$0.324841\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.298222			−0.0162936
$336$		0			0
$337$	7.36469	+	12.7560i	0.401180	+	0.694864i	0.993869	−	0.110567i	$-0.0352668\pi$
$337$	7.36469	+	12.7560i	0.401180	+	0.694864i	−0.592689	+	0.805432i	$0.701933\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−9.92332			−0.537378
$342$		0			0
$343$	−10.1173			−0.546281
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.06766	+	8.77744i	0.272046	+	0.471198i	0.969386	−	0.245543i	$-0.0789664\pi$
$347$	5.06766	+	8.77744i	0.272046	+	0.471198i	−0.697340	+	0.716741i	$0.745633\pi$
$348$		0			0
$349$	2.56035			0.137053			0.0685263	−	0.997649i	$-0.478170\pi$
$349$	2.56035			0.137053			0.0685263	+	0.997649i	$0.478170\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−20.4458			−1.08822			−0.544109	−	0.839015i	$-0.683132\pi$
$353$	−20.4458			−1.08822			−0.544109	+	0.839015i	$0.683132\pi$
$354$		0			0
$355$	−0.889229	+	1.54019i	−0.0471954	+	0.0817447i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.29397	+	12.6335i	0.384961	+	0.666772i	0.991764	−	0.128080i	$-0.0408815\pi$
$359$	7.29397	+	12.6335i	0.384961	+	0.666772i	−0.606803	+	0.794853i	$0.707548\pi$
$360$		0			0
$361$	−18.9151	+	1.79408i	−0.995532	+	0.0944252i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.927568	+	1.60659i	−0.0485511	+	0.0840930i
$366$		0			0
$367$	14.5397	−	25.1835i	0.758965	−	1.31457i	−0.184414	−	0.982849i	$-0.559039\pi$
$367$	14.5397	−	25.1835i	0.758965	−	1.31457i	0.943379	−	0.331717i	$-0.107628\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.80605	+	13.5205i	−0.405270	+	0.701949i
$372$		0			0
$373$	20.7880			1.07636			0.538181	−	0.842829i	$-0.319112\pi$
$373$	20.7880			1.07636			0.538181	+	0.842829i	$0.319112\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.04870	−	12.2087i	−0.363027	−	0.628780i
$378$		0			0
$379$	−19.7034			−1.01210			−0.506048	−	0.862505i	$-0.668894\pi$
$379$	−19.7034			−1.01210			−0.506048	+	0.862505i	$0.668894\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.2319	−	24.6504i	−0.727216	−	1.25958i	−0.958055	−	0.286584i	$-0.907480\pi$
$383$	−14.2319	−	24.6504i	−0.727216	−	1.25958i	0.230839	−	0.972992i	$-0.425853\pi$
$384$		0			0
$385$	1.14486	+	1.98296i	0.0583477	+	0.101061i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.85819	−	3.21848i	0.0942141	−	0.163184i	−0.815066	−	0.579368i	$-0.803300\pi$
$389$	1.85819	−	3.21848i	0.0942141	−	0.163184i	0.909280	+	0.416184i	$0.136633\pi$
$390$		0			0
$391$	−3.16291			−0.159955
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.07974	−	3.60221i	0.104643	−	0.181247i
$396$		0			0
$397$	−8.81985	−	15.2764i	−0.442656	−	0.766702i	0.555230	−	0.831697i	$-0.312630\pi$
$397$	−8.81985	−	15.2764i	−0.442656	−	0.766702i	−0.997886	+	0.0649947i	$0.979297\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.2785	−	26.4631i	−0.762970	−	1.32150i	−0.941313	−	0.337534i	$-0.890407\pi$
$401$	−15.2785	−	26.4631i	−0.762970	−	1.32150i	0.178344	−	0.983968i	$-0.442926\pi$
$402$		0			0
$403$	−9.57152	+	16.5784i	−0.476791	+	0.825827i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.98195			0.346083
$408$		0			0
$409$	15.6138	−	27.0439i	0.772054	−	1.33724i	−0.164381	−	0.986397i	$-0.552563\pi$
$409$	15.6138	−	27.0439i	0.772054	−	1.33724i	0.936435	−	0.350840i	$-0.114104\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−11.9893	−	20.7660i	−0.589953	−	1.02183i
$414$		0			0
$415$	2.15217	+	3.72766i	0.105646	+	0.182984i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−28.9966			−1.41657			−0.708287	−	0.705924i	$-0.750532\pi$
$419$	−28.9966			−1.41657			−0.708287	+	0.705924i	$0.750532\pi$
$420$		0			0
$421$	−15.6293	−	27.0708i	−0.761728	−	1.31935i	−0.941959	−	0.335727i	$-0.891018\pi$
$421$	−15.6293	−	27.0708i	−0.761728	−	1.31935i	0.180232	−	0.983624i	$-0.442315\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	32.1104			1.55758
$426$		0			0
$427$	20.7164	−	35.8818i	1.00254	−	1.73644i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.43315	−	12.8746i	0.358042	−	0.620148i	−0.629591	−	0.776926i	$-0.716778\pi$
$431$	7.43315	−	12.8746i	0.358042	−	0.620148i	0.987634	+	0.156779i	$0.0501110\pi$
$432$		0			0
$433$	−19.7815	+	34.2626i	−0.950639	+	1.64655i	−0.206592	+	0.978427i	$0.566237\pi$
$433$	−19.7815	+	34.2626i	−0.950639	+	1.64655i	−0.744047	+	0.668128i	$0.767096\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.82329	−	0.940703i	−0.0872199	−	0.0450000i
$438$		0			0
$439$	−5.79226	−	10.0325i	−0.276449	−	0.478824i	0.694050	−	0.719926i	$-0.255824\pi$
$439$	−5.79226	−	10.0325i	−0.276449	−	0.478824i	−0.970500	+	0.241102i	$0.922491\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.4617	+	25.0483i	−0.687094	+	1.19008i	0.285680	+	0.958325i	$0.407781\pi$
$443$	−14.4617	+	25.0483i	−0.687094	+	1.19008i	−0.972774	+	0.231757i	$0.925553\pi$
$444$		0			0
$445$	1.39057			0.0659192
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−31.2147			−1.47311			−0.736556	−	0.676377i	$-0.763549\pi$
$449$	−31.2147			−1.47311			−0.736556	+	0.676377i	$0.763549\pi$
$450$		0			0
$451$	−0.368935	−	0.639014i	−0.0173725	−	0.0300900i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.41711			0.207077
$456$		0			0
$457$	17.2215			0.805590			0.402795	−	0.915290i	$-0.368039\pi$
$457$	17.2215			0.805590			0.402795	+	0.915290i	$0.368039\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.4151	−	28.4318i	−0.764528	−	1.32420i	−0.940496	−	0.339805i	$-0.889639\pi$
$461$	−16.4151	−	28.4318i	−0.764528	−	1.32420i	0.175968	−	0.984396i	$-0.443694\pi$
$462$		0			0
$463$	−6.28973			−0.292308			−0.146154	−	0.989262i	$-0.546690\pi$
$463$	−6.28973			−0.292308			−0.146154	+	0.989262i	$0.546690\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.47068			−0.438251			−0.219125	−	0.975697i	$-0.570320\pi$
$467$	−9.47068			−0.438251			−0.219125	+	0.975697i	$0.570320\pi$
$468$		0			0
$469$	−1.04789	+	1.81500i	−0.0483871	+	0.0838090i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.86469	+	4.96179i	0.131718	+	0.228143i
$474$		0			0
$475$	18.5104	+	9.55018i	0.849314	+	0.438192i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.0341	+	22.5757i	−0.595543	+	1.03151i	0.397927	+	0.917417i	$0.369730\pi$
$479$	−13.0341	+	22.5757i	−0.595543	+	1.03151i	−0.993470	+	0.114094i	$0.963604\pi$
$480$		0			0
$481$	6.73443	−	11.6644i	0.307064	−	0.531850i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.0137988	−	0.0239003i	0.000626573	−	0.00108526i
$486$		0			0
$487$	−16.8939			−0.765536			−0.382768	−	0.923845i	$-0.625029\pi$
$487$	−16.8939			−0.765536			−0.382768	+	0.923845i	$0.625029\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.94442	−	15.4922i	−0.403656	−	0.699153i	0.590508	−	0.807032i	$-0.298927\pi$
$491$	−8.94442	−	15.4922i	−0.403656	−	0.699153i	−0.994164	+	0.107879i	$0.965594\pi$
$492$		0			0
$493$	33.3906			1.50384
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.24914	+	10.8238i	0.280312	+	0.485515i
$498$		0			0
$499$	−14.7108	−	25.4799i	−0.658546	−	1.14063i	−0.980992	−	0.194047i	$-0.937839\pi$
$499$	−14.7108	−	25.4799i	−0.658546	−	1.14063i	0.322446	−	0.946588i	$-0.395495\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.53968	+	7.86295i	−0.202414	+	0.350592i	−0.949306	−	0.314354i	$-0.898212\pi$
$503$	−4.53968	+	7.86295i	−0.202414	+	0.350592i	0.746892	+	0.664946i	$0.231545\pi$
$504$		0			0
$505$	5.45264			0.242639
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.1970	+	17.6617i	−0.451974	+	0.782842i	−0.998509	−	0.0545944i	$-0.982613\pi$
$509$	−10.1970	+	17.6617i	−0.451974	+	0.782842i	0.546534	+	0.837437i	$0.315947\pi$
$510$		0			0
$511$	6.51857	+	11.2905i	0.288365	+	0.499462i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.92332	+	3.33129i	0.0847517	+	0.146794i
$516$		0			0
$517$	−8.75816	+	15.1696i	−0.385184	+	0.667158i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	14.8697			0.651455			0.325728	−	0.945464i	$-0.394391\pi$
$521$	14.8697			0.651455			0.325728	+	0.945464i	$0.394391\pi$
$522$		0			0
$523$	−5.44958	+	9.43895i	−0.238294	+	0.412736i	−0.960225	−	0.279228i	$-0.909921\pi$
$523$	−5.44958	+	9.43895i	−0.238294	+	0.412736i	0.721931	+	0.691965i	$0.243255\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−22.6707	−	39.2669i	−0.987553	−	1.71049i
$528$		0			0
$529$	11.3892	+	19.7267i	0.495184	+	0.857684i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.42342			−0.0616552
$534$		0			0
$535$	0.117266	+	0.203111i	0.00506987	+	0.00878126i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.79650			0.249673
$540$		0			0
$541$	−5.97546	+	10.3498i	−0.256905	+	0.444973i	−0.965411	−	0.260732i	$-0.916036\pi$
$541$	−5.97546	+	10.3498i	−0.256905	+	0.444973i	0.708506	+	0.705705i	$0.249369\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.97546	+	3.42160i	−0.0846194	+	0.146565i
$546$		0			0
$547$	−2.00306	+	3.46940i	−0.0856445	+	0.148341i	−0.905666	−	0.423993i	$-0.860628\pi$
$547$	−2.00306	+	3.46940i	−0.0856445	+	0.148341i	0.820021	+	0.572333i	$0.193962\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	19.2483	+	9.93093i	0.820006	+	0.423072i
$552$		0			0
$553$	−14.6155	−	25.3149i	−0.621516	−	1.07650i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.35991	−	9.28364i	0.227107	−	0.393360i	−0.729843	−	0.683615i	$-0.760407\pi$
$557$	5.35991	−	9.28364i	0.227107	−	0.393360i	0.956949	+	0.290255i	$0.0937400\pi$
$558$		0			0
$559$	11.0525			0.467472
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.18096			0.302641			0.151321	−	0.988485i	$-0.451647\pi$
$563$	7.18096			0.302641			0.151321	+	0.988485i	$0.451647\pi$
$564$		0			0
$565$	−1.13756	−	1.97031i	−0.0478575	−	0.0828916i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−31.4328			−1.31773			−0.658865	−	0.752261i	$-0.728963\pi$
$569$	−31.4328			−1.31773			−0.658865	+	0.752261i	$0.728963\pi$
$570$		0			0
$571$	−8.08623			−0.338398			−0.169199	−	0.985582i	$-0.554118\pi$
$571$	−8.08623			−0.338398			−0.169199	+	0.985582i	$0.554118\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.12457	+	1.94781i	0.0468978	+	0.0812294i
$576$		0			0
$577$	4.95779			0.206396			0.103198	−	0.994661i	$-0.467093\pi$
$577$	4.95779			0.206396			0.103198	+	0.994661i	$0.467093\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	30.2491			1.25495
$582$		0			0
$583$	−3.47068	+	6.01140i	−0.143741	+	0.248967i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.8858	−	20.5868i	−0.490579	−	0.849708i	0.509362	−	0.860552i	$-0.329881\pi$
$587$	−11.8858	−	20.5868i	−0.490579	−	0.849708i	−0.999941	+	0.0108444i	$0.996548\pi$
$588$		0			0
$589$	−1.39014	−	29.3785i	−0.0572797	−	1.21052i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−21.2018	+	36.7226i	−0.870653	+	1.50801i	−0.00932994	+	0.999956i	$0.502970\pi$
$593$	−21.2018	+	36.7226i	−0.870653	+	1.50801i	−0.861323	+	0.508058i	$0.830363\pi$
$594$		0			0
$595$	−5.23109	+	9.06052i	−0.214454	+	0.371445i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−21.4258	+	37.1107i	−0.875436	+	1.51630i	−0.0191394	+	0.999817i	$0.506093\pi$
$599$	−21.4258	+	37.1107i	−0.875436	+	1.51630i	−0.856297	+	0.516484i	$0.827241\pi$
$600$		0			0
$601$	−15.1855			−0.619427			−0.309714	−	0.950830i	$-0.600233\pi$
$601$	−15.1855			−0.619427			−0.309714	+	0.950830i	$0.600233\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.07974	−	3.60221i	−0.0845533	−	0.146451i
$606$		0			0
$607$	32.3336			1.31238			0.656189	−	0.754596i	$-0.272167\pi$
$607$	32.3336			1.31238			0.656189	+	0.754596i	$0.272167\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	16.8953	+	29.2636i	0.683512	+	1.18388i
$612$		0			0
$613$	3.91683	+	6.78414i	0.158199	+	0.274009i	0.934219	−	0.356699i	$-0.116098\pi$
$613$	3.91683	+	6.78414i	0.158199	+	0.274009i	−0.776020	+	0.630708i	$0.782765\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.13359	+	3.69549i	−0.0858952	+	0.148775i	−0.905772	−	0.423765i	$-0.860708\pi$
$617$	−2.13359	+	3.69549i	−0.0858952	+	0.148775i	0.819877	+	0.572540i	$0.194042\pi$
$618$		0			0
$619$	−42.8363			−1.72174			−0.860869	−	0.508827i	$-0.830079\pi$
$619$	−42.8363			−1.72174			−0.860869	+	0.508827i	$0.830079\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.88617	−	8.46310i	0.195760	−	0.339067i
$624$		0			0
$625$	−10.8630	−	18.8152i	−0.434519	−	0.752609i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	15.9509	+	27.6278i	0.636005	+	1.10159i
$630$		0			0
$631$	−18.1552	+	31.4458i	−0.722748	+	1.25184i	0.237146	+	0.971474i	$0.423788\pi$
$631$	−18.1552	+	31.4458i	−0.722748	+	1.25184i	−0.959894	+	0.280362i	$0.909545\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.68373			−0.344603
$636$		0			0
$637$	5.59101	−	9.68391i	0.221524	−	0.383690i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−24.8043	−	42.9624i	−0.979712	−	1.69691i	−0.663415	−	0.748251i	$-0.730894\pi$
$641$	−24.8043	−	42.9624i	−0.979712	−	1.69691i	−0.316297	−	0.948660i	$-0.602440\pi$
$642$		0			0
$643$	−2.49270	−	4.31748i	−0.0983023	−	0.170265i	0.812680	−	0.582711i	$-0.198008\pi$
$643$	−2.49270	−	4.31748i	−0.0983023	−	0.170265i	−0.910982	+	0.412446i	$0.864675\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−43.2863			−1.70176			−0.850880	−	0.525360i	$-0.823931\pi$
$647$	−43.2863			−1.70176			−0.850880	+	0.525360i	$0.823931\pi$
$648$		0			0
$649$	−5.33060	−	9.23286i	−0.209244	−	0.362422i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.43965			0.212870			0.106435	−	0.994320i	$-0.466056\pi$
$653$	5.43965			0.212870			0.106435	+	0.994320i	$0.466056\pi$
$654$		0			0
$655$	0.204306	−	0.353869i	0.00798290	−	0.0138268i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.87462	−	4.97899i	0.111979	−	0.193954i	−0.804589	−	0.593832i	$-0.797614\pi$
$659$	2.87462	−	4.97899i	0.111979	−	0.193954i	0.916568	+	0.399878i	$0.130948\pi$
$660$		0			0
$661$	5.12763	−	8.88131i	0.199442	−	0.345443i	−0.748906	−	0.662676i	$-0.769421\pi$
$661$	5.12763	−	8.88131i	0.199442	−	0.345443i	0.948348	+	0.317233i	$0.102754\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.71027	+	3.66721i	−0.221435	+	0.142208i
$666$		0			0
$667$	1.16940	+	2.02547i	0.0452795	+	0.0784264i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	9.21080	−	15.9536i	0.355579	−	0.615881i
$672$		0			0
$673$	−29.9379			−1.15402			−0.577011	−	0.816736i	$-0.695781\pi$
$673$	−29.9379			−1.15402			−0.577011	+	0.816736i	$0.695781\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.8827			0.456691			0.228345	−	0.973580i	$-0.426668\pi$
$677$	11.8827			0.456691			0.228345	+	0.973580i	$0.426668\pi$
$678$		0			0
$679$	−0.0969726	−	0.167961i	−0.00372147	−	0.00644577i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	6.35180			0.243045			0.121522	−	0.992589i	$-0.461222\pi$
$683$	6.35180			0.243045			0.121522	+	0.992589i	$0.461222\pi$
$684$		0			0
$685$	2.14486			0.0819510
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.69528	+	11.5966i	0.255070	+	0.441794i
$690$		0			0
$691$	−28.9966			−1.10308			−0.551541	−	0.834148i	$-0.685960\pi$
$691$	−28.9966			−1.10308			−0.551541	+	0.834148i	$0.685960\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.67580			−0.291160
$696$		0			0
$697$	1.68573	−	2.91977i	0.0638516	−	0.110594i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	2.00081	+	3.46550i	0.0755695	+	0.130890i	0.901334	−	0.433125i	$-0.142589\pi$
$701$	2.00081	+	3.46550i	0.0755695	+	0.130890i	−0.825764	+	0.564015i	$0.809256\pi$
$702$		0			0
$703$	0.978088	+	20.6704i	0.0368893	+	0.779599i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	19.1595	−	33.1852i	0.720566	−	1.24806i
$708$		0			0
$709$	8.23190	−	14.2581i	0.309156	−	0.535473i	−0.669022	−	0.743242i	$-0.733287\pi$
$709$	8.23190	−	14.2581i	0.309156	−	0.535473i	0.978178	+	0.207769i	$0.0666203\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.58795	−	2.75041i	0.0594692	−	0.103004i
$714$		0			0
$715$	1.96391			0.0734460
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.60561	−	16.6374i	−0.358229	−	0.620471i	0.629436	−	0.777052i	$-0.283286\pi$
$719$	−9.60561	−	16.6374i	−0.358229	−	0.620471i	−0.987665	+	0.156581i	$0.949953\pi$
$720$		0			0
$721$	27.0327			1.00675
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−11.8720	−	20.5629i	−0.440915	−	0.763687i
$726$		0			0
$727$	9.08317	+	15.7325i	0.336876	+	0.583487i	0.983843	−	0.179031i	$-0.0572963\pi$
$727$	9.08317	+	15.7325i	0.336876	+	0.583487i	−0.646967	+	0.762518i	$0.723963\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−13.0893	+	22.6713i	−0.484125	+	0.838529i
$732$		0			0
$733$	50.2423			1.85574			0.927870	−	0.372903i	$-0.121638\pi$
$733$	50.2423			1.85574			0.927870	+	0.372903i	$0.121638\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.465907	+	0.806975i	−0.0171619	+	0.0297253i
$738$		0			0
$739$	−14.8883	−	25.7873i	−0.547676	−	0.948602i	−0.998433	−	0.0559557i	$-0.982179\pi$
$739$	−14.8883	−	25.7873i	−0.547676	−	0.948602i	0.450758	−	0.892646i	$-0.351154\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−19.7578	−	34.2215i	−0.724843	−	1.25546i	−0.959039	−	0.283275i	$-0.908579\pi$
$743$	−19.7578	−	34.2215i	−0.724843	−	1.25546i	0.234196	−	0.972189i	$-0.424754\pi$
$744$		0			0
$745$	−4.92026	+	8.52215i	−0.180265	+	0.312227i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.64820			0.0602240
$750$		0			0
$751$	−9.05214	+	15.6788i	−0.330317	+	0.572126i	−0.982574	−	0.185872i	$-0.940489\pi$
$751$	−9.05214	+	15.6788i	−0.330317	+	0.572126i	0.652257	+	0.757998i	$0.273822\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.412050	−	0.713692i	−0.0149960	−	0.0259739i
$756$		0			0
$757$	11.7996	+	20.4374i	0.428862	+	0.742811i	0.996772	−	0.0802793i	$-0.0255812\pi$
$757$	11.7996	+	20.4374i	0.428862	+	0.742811i	−0.567910	+	0.823091i	$0.692248\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.69061			0.0612845			0.0306422	−	0.999530i	$-0.490245\pi$
$761$	1.69061			0.0612845			0.0306422	+	0.999530i	$0.490245\pi$
$762$		0			0
$763$	13.8827	+	24.0456i	0.502589	+	0.870509i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−20.5665			−0.742612
$768$		0			0
$769$	26.0583	−	45.1342i	0.939685	−	1.62758i	0.173625	−	0.984812i	$-0.444452\pi$
$769$	26.0583	−	45.1342i	0.939685	−	1.62758i	0.766059	−	0.642770i	$-0.222215\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	22.5397	−	39.0399i	0.810696	−	1.40417i	−0.101682	−	0.994817i	$-0.532422\pi$
$773$	22.5397	−	39.0399i	0.810696	−	1.40417i	0.912378	−	0.409349i	$-0.134244\pi$
$774$		0			0
$775$	−16.1211	+	27.9226i	−0.579088	+	1.00301i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.84015	−	1.18177i	0.0659301	−	0.0423412i
$780$		0			0
$781$	2.77846	+	4.81243i	0.0994210	+	0.172202i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.0375304	+	0.0650045i	−0.00133952	+	0.00232011i
$786$		0			0
$787$	38.1414			1.35960			0.679798	−	0.733400i	$-0.262068\pi$
$787$	38.1414			1.35960			0.679798	+	0.733400i	$0.262068\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−15.9886			−0.568490
$792$		0			0
$793$	−17.7685	−	30.7760i	−0.630979	−	1.09289i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.7148			0.485802			0.242901	−	0.970051i	$-0.421901\pi$
$797$	13.7148			0.485802			0.242901	+	0.970051i	$0.421901\pi$
$798$		0			0
$799$	−80.0353			−2.83145
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.89825	+	5.01992i	0.102277	+	0.177149i
$804$		0			0
$805$	−0.732814			−0.0258283
$806$		0			0
$807$		0			0
$808$		0			0
$809$	21.6285			0.760419			0.380209	−	0.924900i	$-0.375852\pi$
$809$	21.6285			0.760419			0.380209	+	0.924900i	$0.375852\pi$
$810$		0			0
$811$	−3.27024	+	5.66423i	−0.114834	+	0.198898i	−0.917713	−	0.397243i	$-0.869967\pi$
$811$	−3.27024	+	5.66423i	−0.114834	+	0.198898i	0.802880	+	0.596141i	$0.203300\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.0202937	+	0.0351497i	0.000710858	+	0.00123124i
$816$		0			0
$817$	−14.2883	+	9.17613i	−0.499884	+	0.321032i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	20.8091	−	36.0424i	0.726243	−	1.25789i	−0.232217	−	0.972664i	$-0.574598\pi$
$821$	20.8091	−	36.0424i	0.726243	−	1.25789i	0.958460	−	0.285226i	$-0.0920686\pi$
$822$		0			0
$823$	−2.72632	+	4.72212i	−0.0950335	+	0.164603i	−0.909623	−	0.415436i	$-0.863629\pi$
$823$	−2.72632	+	4.72212i	−0.0950335	+	0.164603i	0.814589	+	0.580038i	$0.196962\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.34439	−	2.32856i	0.0467492	−	0.0809719i	−0.841704	−	0.539939i	$-0.818447\pi$
$827$	1.34439	−	2.32856i	0.0467492	−	0.0809719i	0.888453	+	0.458967i	$0.151781\pi$
$828$		0			0
$829$	−27.4328			−0.952780			−0.476390	−	0.879234i	$-0.658055\pi$
$829$	−27.4328			−0.952780			−0.476390	+	0.879234i	$0.658055\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	13.2426	+	22.9369i	0.458830	+	0.794718i
$834$		0			0
$835$	2.95436			0.102240
$836$		0			0
$837$		0			0
$838$		0			0
$839$	13.7206	+	23.7648i	0.473689	+	0.820453i	0.999546	−	0.0301195i	$-0.00958880\pi$
$839$	13.7206	+	23.7648i	0.473689	+	0.820453i	−0.525857	+	0.850573i	$0.676255\pi$
$840$		0			0
$841$	2.15470	+	3.73204i	0.0742999	+	0.128691i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.16516	+	2.01811i	−0.0400826	+	0.0694252i
$846$		0			0
$847$	−29.2311			−1.00439
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.11727	+	1.93516i	−0.0382994	+	0.0663365i
$852$		0			0
$853$	−18.1936	−	31.5122i	−0.622936	−	1.07896i	−0.988936	−	0.148342i	$-0.952606\pi$
$853$	−18.1936	−	31.5122i	−0.622936	−	1.07896i	0.366000	−	0.930615i	$-0.380727\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−24.5647	−	42.5474i	−0.839116	−	1.45339i	−0.890635	−	0.454719i	$-0.849740\pi$
$857$	−24.5647	−	42.5474i	−0.839116	−	1.45339i	0.0515191	−	0.998672i	$-0.483594\pi$
$858$		0			0
$859$	25.9565	−	44.9580i	0.885624	−	1.53395i	0.0406283	−	0.999174i	$-0.487064\pi$
$859$	25.9565	−	44.9580i	0.885624	−	1.53395i	0.844996	−	0.534772i	$-0.179603\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	27.9785			0.952400			0.476200	−	0.879337i	$-0.342014\pi$
$863$	27.9785			0.952400			0.476200	+	0.879337i	$0.342014\pi$
$864$		0			0
$865$	2.55042	−	4.41746i	0.0867169	−	0.150198i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.49828	−	11.2554i	−0.220439	−	0.381812i
$870$		0			0
$871$	0.898780	+	1.55673i	0.0304540	+	0.0527479i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	15.2242			0.514673
$876$		0			0
$877$	6.20087	+	10.7402i	0.209388	+	0.362671i	0.951522	−	0.307581i	$-0.0995194\pi$
$877$	6.20087	+	10.7402i	0.209388	+	0.362671i	−0.742134	+	0.670252i	$0.766186\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−17.8923			−0.602806			−0.301403	−	0.953497i	$-0.597455\pi$
$881$	−17.8923			−0.602806			−0.301403	+	0.953497i	$0.597455\pi$
$882$		0			0
$883$	−5.51686	+	9.55547i	−0.185657	+	0.321567i	−0.943798	−	0.330524i	$-0.892775\pi$
$883$	−5.51686	+	9.55547i	−0.185657	+	0.321567i	0.758141	+	0.652091i	$0.226108\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.1970	−	34.9822i	0.678149	−	1.17459i	−0.297389	−	0.954756i	$-0.596116\pi$
$887$	20.1970	−	34.9822i	0.678149	−	1.17459i	0.975538	−	0.219832i	$-0.0705509\pi$
$888$		0			0
$889$	−30.5129	+	52.8499i	−1.02337	+	1.77253i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−46.1372	−	23.8039i	−1.54392	−	0.796566i
$894$		0			0
$895$	1.66849	+	2.88992i	0.0557716	+	0.0965993i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−16.7638	+	29.0358i	−0.559106	+	0.968399i
$900$		0			0
$901$	−31.7164			−1.05663
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.81455			0.193282
$906$		0			0
$907$	−19.5755	−	33.9057i	−0.649993	−	1.12582i	−0.983124	−	0.182941i	$-0.941438\pi$
$907$	−19.5755	−	33.9057i	−0.649993	−	1.12582i	0.333130	−	0.942881i	$-0.391895\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−27.3561			−0.906348			−0.453174	−	0.891422i	$-0.649708\pi$
$911$	−27.3561			−0.906348			−0.453174	+	0.891422i	$0.649708\pi$
$912$		0			0
$913$	13.4492			0.445104
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.43578	−	2.48685i	−0.0474137	−	0.0821229i
$918$		0			0
$919$	0.948243			0.0312796			0.0156398	−	0.999878i	$-0.495021\pi$
$919$	0.948243			0.0312796			0.0156398	+	0.999878i	$0.495021\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	10.7198			0.352847
$924$		0			0
$925$	11.3427	−	19.6461i	0.372945	−	0.645959i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2.63026	+	4.55574i	0.0862959	+	0.149469i	0.905943	−	0.423400i	$-0.139164\pi$
$929$	2.63026	+	4.55574i	0.0862959	+	0.149469i	−0.819647	+	0.572869i	$0.805830\pi$
$930$		0			0
$931$	0.812021	+	17.1608i	0.0266129	+	0.562423i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.32582	+	4.02844i	−0.0760624	+	0.131744i
$936$		0			0
$937$	−22.9638	+	39.7745i	−0.750195	+	1.29938i	0.197533	+	0.980296i	$0.436707\pi$
$937$	−22.9638	+	39.7745i	−0.750195	+	1.29938i	−0.947728	+	0.319079i	$0.896626\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−22.2978	+	38.6210i	−0.726889	+	1.25901i	0.231303	+	0.972882i	$0.425701\pi$
$941$	−22.2978	+	38.6210i	−0.726889	+	1.25901i	−0.958192	+	0.286127i	$0.907632\pi$
$942$		0			0
$943$	0.236151			0.00769013
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.00811	+	12.1384i	0.227733	+	0.394445i	0.957136	−	0.289639i	$-0.0935353\pi$
$947$	7.00811	+	12.1384i	0.227733	+	0.394445i	−0.729403	+	0.684084i	$0.760202\pi$
$948$		0			0
$949$	11.1820			0.362984
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.42332	+	2.46526i	0.0461059	+	0.0798577i	0.888157	−	0.459539i	$-0.151986\pi$
$953$	1.42332	+	2.46526i	0.0461059	+	0.0798577i	−0.842051	+	0.539397i	$0.818652\pi$
$954$		0			0
$955$	2.11727	+	3.66721i	0.0685131	+	0.118668i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.53662	−	13.0538i	0.243370	−	0.421529i
$960$		0			0
$961$	14.5277			0.468635
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.744365	+	1.28928i	−0.0239619	+	0.0415033i
$966$		0			0
$967$	−0.830595	−	1.43863i	−0.0267101	−	0.0462633i	0.852361	−	0.522953i	$-0.175170\pi$
$967$	−0.830595	−	1.43863i	−0.0267101	−	0.0462633i	−0.879071	+	0.476690i	$0.841836\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−20.2091	−	35.0032i	−0.648540	−	1.12330i	−0.983472	−	0.181062i	$-0.942046\pi$
$971$	−20.2091	−	35.0032i	−0.648540	−	1.12330i	0.334931	−	0.942243i	$-0.391287\pi$
$972$		0			0
$973$	−26.9712	+	46.7155i	−0.864657	+	1.49763i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.5439			−0.337330			−0.168665	−	0.985673i	$-0.553946\pi$
$977$	−10.5439			−0.337330			−0.168665	+	0.985673i	$0.553946\pi$
$978$		0			0
$979$	2.17246	−	3.76281i	0.0694322	−	0.120260i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4.91683	+	8.51619i	0.156822	+	0.271624i	0.933721	−	0.358001i	$-0.116542\pi$
$983$	4.91683	+	8.51619i	0.156822	+	0.271624i	−0.776899	+	0.629626i	$0.783208\pi$
$984$		0			0
$985$	5.00000	+	8.66025i	0.159313	+	0.275939i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.83365			−0.0583068
$990$		0			0
$991$	10.1349	+	17.5542i	0.321947	+	0.557628i	0.980890	−	0.194565i	$-0.0623295\pi$
$991$	10.1349	+	17.5542i	0.321947	+	0.557628i	−0.658943	+	0.752193i	$0.728996\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.65775			0.147661
$996$		0			0
$997$	−7.66038	+	13.2682i	−0.242607	+	0.420207i	−0.961456	−	0.274959i	$-0.911336\pi$
$997$	−7.66038	+	13.2682i	−0.242607	+	0.420207i	0.718849	+	0.695166i	$0.244669\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.s.y.577.2		6
3.2	odd	2		304.2.i.f.273.3		6
4.3	odd	2		1368.2.s.k.577.2		6
12.11	even	2		152.2.i.c.121.1	yes	6
19.11	even	3	inner	2736.2.s.y.1873.2		6
24.5	odd	2		1216.2.i.m.577.1		6
24.11	even	2		1216.2.i.n.577.3		6
57.11	odd	6		304.2.i.f.49.3		6
57.26	odd	6		5776.2.a.bk.1.1		3
57.50	even	6		5776.2.a.bq.1.3		3
76.11	odd	6		1368.2.s.k.505.2		6
228.11	even	6		152.2.i.c.49.1	✓	6
228.83	even	6		2888.2.a.r.1.3		3
228.107	odd	6		2888.2.a.n.1.1		3
456.11	even	6		1216.2.i.n.961.3		6
456.125	odd	6		1216.2.i.m.961.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.i.c.49.1	✓	6	228.11	even	6
152.2.i.c.121.1	yes	6	12.11	even	2
304.2.i.f.49.3		6	57.11	odd	6
304.2.i.f.273.3		6	3.2	odd	2
1216.2.i.m.577.1		6	24.5	odd	2
1216.2.i.m.961.1		6	456.125	odd	6
1216.2.i.n.577.3		6	24.11	even	2
1216.2.i.n.961.3		6	456.11	even	6
1368.2.s.k.505.2		6	76.11	odd	6
1368.2.s.k.577.2		6	4.3	odd	2
2736.2.s.y.577.2		6	1.1	even	1	trivial
2736.2.s.y.1873.2		6	19.11	even	3	inner
2888.2.a.n.1.1		3	228.107	odd	6
2888.2.a.r.1.3		3	228.83	even	6
5776.2.a.bk.1.1		3	57.26	odd	6
5776.2.a.bq.1.3		3	57.50	even	6

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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.235342 + 0.407624i) q^{5} +3.30777 q^{7} +O(q^{10})\)	\(q+(0.235342 + 0.407624i) q^{5} +3.30777 q^{7} +1.47068 q^{11} +(1.41855 - 2.45699i) q^{13} +(3.35991 + 5.81954i) q^{17} +(0.206025 + 4.35403i) q^{19} +(-0.235342 + 0.407624i) q^{23} +(2.38923 - 4.13827i) q^{25} +(2.48448 - 4.30325i) q^{29} -6.74742 q^{31} +(0.778457 + 1.34833i) q^{35} +4.74742 q^{37} +(-0.250859 - 0.434501i) q^{41} +(1.94786 + 3.37380i) q^{43} +(-5.95517 + 10.3146i) q^{47} +3.94137 q^{49} +(-2.35991 + 4.08749i) q^{53} +(0.346113 + 0.599486i) q^{55} +(-3.62457 - 6.27794i) q^{59} +(6.26294 - 10.8477i) q^{61} +1.33537 q^{65} +(-0.316797 + 0.548708i) q^{67} +(1.88923 + 3.27224i) q^{71} +(1.97068 + 3.41332i) q^{73} +4.86469 q^{77} +(-4.41855 - 7.65314i) q^{79} +9.14486 q^{83} +(-1.58145 + 2.73916i) q^{85} +(1.47718 - 2.55855i) q^{89} +(4.69223 - 8.12717i) q^{91} +(-1.72632 + 1.10866i) q^{95} +(-0.0293166 - 0.0507778i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} + 4 q^{7}+O(q^{10}) \) 6 * q + q^5 + 4 * q^7	\( 6 q + q^{5} + 4 q^{7} + 8 q^{11} + q^{13} + 11 q^{17} - q^{23} + 6 q^{25} - 3 q^{29} + 12 q^{31} - 12 q^{35} - 24 q^{37} - 19 q^{41} + 5 q^{43} - 17 q^{47} + 22 q^{49} - 5 q^{53} + 10 q^{55} - 13 q^{59} + 3 q^{61} - 42 q^{65} - 9 q^{67} + 3 q^{71} + 11 q^{73} - 20 q^{77} - 19 q^{79} + 24 q^{83} - 17 q^{85} + 3 q^{89} + 44 q^{91} + 13 q^{95} - q^{97}+O(q^{100}) \) 6 * q + q^5 + 4 * q^7 + 8 * q^11 + q^13 + 11 * q^17 - q^23 + 6 * q^25 - 3 * q^29 + 12 * q^31 - 12 * q^35 - 24 * q^37 - 19 * q^41 + 5 * q^43 - 17 * q^47 + 22 * q^49 - 5 * q^53 + 10 * q^55 - 13 * q^59 + 3 * q^61 - 42 * q^65 - 9 * q^67 + 3 * q^71 + 11 * q^73 - 20 * q^77 - 19 * q^79 + 24 * q^83 - 17 * q^85 + 3 * q^89 + 44 * q^91 + 13 * q^95 - q^97

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