LMFDB - Embedded newform 1512.2.q.c.1369.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(793,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1512.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.q (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1369.6
Character	$\chi$	$=$	1512.1369
Dual form			1512.2.q.c.793.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.240694 + 0.416893i) q^{5} +(-1.92765 - 1.81223i) q^{7} +O(q^{10})$	$q+(-0.240694 + 0.416893i) q^{5} +(-1.92765 - 1.81223i) q^{7} +(1.69080 + 2.92855i) q^{11} +(-2.86067 - 4.95482i) q^{13} +(-2.75605 + 4.77362i) q^{17} +(2.18023 + 3.77626i) q^{19} +(1.81293 - 3.14008i) q^{23} +(2.38413 + 4.12944i) q^{25} +(-1.53131 + 2.65231i) q^{29} -9.34918 q^{31} +(1.21948 - 0.367431i) q^{35} +(1.48552 + 2.57299i) q^{37} +(6.29558 + 10.9043i) q^{41} +(1.90827 - 3.30522i) q^{43} +3.76564 q^{47} +(0.431647 + 6.98668i) q^{49} +(-5.57860 + 9.66242i) q^{53} -1.62786 q^{55} -8.42282 q^{59} -7.28625 q^{61} +2.75418 q^{65} +2.57143 q^{67} +3.94304 q^{71} +(-0.862216 + 1.49340i) q^{73} +(2.04794 - 8.70932i) q^{77} -5.59960 q^{79} +(0.119494 - 0.206970i) q^{83} +(-1.32673 - 2.29796i) q^{85} +(-0.648116 - 1.12257i) q^{89} +(-3.46492 + 14.7353i) q^{91} -2.09907 q^{95} +(-7.02669 + 12.1706i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} - 5 q^{7}+O(q^{10}) $ 22 * q - 3 * q^5 - 5 * q^7	$ 22 q - 3 q^{5} - 5 q^{7} + 3 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} - 2 q^{23} - 10 q^{25} - 9 q^{29} + 8 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} + 10 q^{47} + 15 q^{49} - 11 q^{53} + 22 q^{55} - 38 q^{59} + 26 q^{61} + 26 q^{65} - 52 q^{67} + 48 q^{71} - 35 q^{73} - 17 q^{77} - 20 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} + 24 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q - 3 * q^5 - 5 * q^7 + 3 * q^11 - 3 * q^13 - 7 * q^17 - q^19 - 2 * q^23 - 10 * q^25 - 9 * q^29 + 8 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 + 10 * q^47 + 15 * q^49 - 11 * q^53 + 22 * q^55 - 38 * q^59 + 26 * q^61 + 26 * q^65 - 52 * q^67 + 48 * q^71 - 35 * q^73 - 17 * q^77 - 20 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 + 24 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−0.240694	+	0.416893i	−0.107641	+	0.186440i	−0.914814	−	0.403875i	$-0.867663\pi$
$5$	−0.240694	+	0.416893i	−0.107641	+	0.186440i	0.807173	+	0.590315i	$0.200997\pi$
$6$		0			0
$7$	−1.92765	−	1.81223i	−0.728582	−	0.684958i
$7$	−1.92765	−	1.81223i	−0.728582	−	0.684958i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.69080	+	2.92855i	0.509794	+	0.882990i	0.999936	+	0.0113468i	$0.00361188\pi$
$11$	1.69080	+	2.92855i	0.509794	+	0.882990i	−0.490141	+	0.871643i	$0.663055\pi$
$12$		0			0
$13$	−2.86067	−	4.95482i	−0.793406	−	1.37422i	−0.923846	−	0.382764i	$-0.874972\pi$
$13$	−2.86067	−	4.95482i	−0.793406	−	1.37422i	0.130440	−	0.991456i	$-0.458361\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.75605	+	4.77362i	−0.668440	+	1.15777i	0.309900	+	0.950769i	$0.399704\pi$
$17$	−2.75605	+	4.77362i	−0.668440	+	1.15777i	−0.978340	+	0.207003i	$0.933629\pi$
$18$		0			0
$19$	2.18023	+	3.77626i	0.500178	+	0.866334i	1.00000		0.000205746i	$6.54909e-5\pi$
$19$	2.18023	+	3.77626i	0.500178	+	0.866334i	−0.499822	+	0.866128i	$0.666601\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.81293	−	3.14008i	0.378021	−	0.654752i	−0.612753	−	0.790274i	$-0.709938\pi$
$23$	1.81293	−	3.14008i	0.378021	−	0.654752i	0.990774	+	0.135523i	$0.0432713\pi$
$24$		0			0
$25$	2.38413	+	4.12944i	0.476827	+	0.825888i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.53131	+	2.65231i	−0.284358	+	0.492522i	−0.972453	−	0.233098i	$-0.925114\pi$
$29$	−1.53131	+	2.65231i	−0.284358	+	0.492522i	0.688095	+	0.725620i	$0.258447\pi$
$30$		0			0
$31$	−9.34918			−1.67916			−0.839581	−	0.543235i	$-0.817199\pi$
$31$	−9.34918			−1.67916			−0.839581	+	0.543235i	$0.817199\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.21948	−	0.367431i	0.206130	−	0.0621072i
$36$		0			0
$37$	1.48552	+	2.57299i	0.244218	+	0.422997i	0.961911	−	0.273361i	$-0.0881355\pi$
$37$	1.48552	+	2.57299i	0.244218	+	0.422997i	−0.717694	+	0.696359i	$0.754802\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.29558	+	10.9043i	0.983204	+	1.70296i	0.649659	+	0.760226i	$0.274912\pi$
$41$	6.29558	+	10.9043i	0.983204	+	1.70296i	0.333545	+	0.942734i	$0.391755\pi$
$42$		0			0
$43$	1.90827	−	3.30522i	0.291009	−	0.504042i	−0.683040	−	0.730381i	$-0.739342\pi$
$43$	1.90827	−	3.30522i	0.291009	−	0.504042i	0.974049	+	0.226339i	$0.0726758\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.76564			0.549276			0.274638	−	0.961548i	$-0.411442\pi$
$47$	3.76564			0.549276			0.274638	+	0.961548i	$0.411442\pi$
$48$		0			0
$49$	0.431647	+	6.98668i	0.0616639	+	0.998097i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.57860	+	9.66242i	−0.766280	+	1.32724i	0.173287	+	0.984871i	$0.444561\pi$
$53$	−5.57860	+	9.66242i	−0.766280	+	1.32724i	−0.939567	+	0.342364i	$0.888772\pi$
$54$		0			0
$55$	−1.62786			−0.219500
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.42282			−1.09656			−0.548279	−	0.836296i	$-0.684717\pi$
$59$	−8.42282			−1.09656			−0.548279	+	0.836296i	$0.684717\pi$
$60$		0			0
$61$	−7.28625			−0.932908			−0.466454	−	0.884545i	$-0.654469\pi$
$61$	−7.28625			−0.932908			−0.466454	+	0.884545i	$0.654469\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.75418			0.341614
$66$		0			0
$67$	2.57143			0.314150			0.157075	−	0.987587i	$-0.449794\pi$
$67$	2.57143			0.314150			0.157075	+	0.987587i	$0.449794\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.94304			0.467953			0.233977	−	0.972242i	$-0.424826\pi$
$71$	3.94304			0.467953			0.233977	+	0.972242i	$0.424826\pi$
$72$		0			0
$73$	−0.862216	+	1.49340i	−0.100915	+	0.174790i	−0.912062	−	0.410053i	$-0.865510\pi$
$73$	−0.862216	+	1.49340i	−0.100915	+	0.174790i	0.811147	+	0.584842i	$0.198844\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.04794	−	8.70932i	0.233384	−	0.992519i
$78$		0			0
$79$	−5.59960			−0.630004			−0.315002	−	0.949091i	$-0.602005\pi$
$79$	−5.59960			−0.630004			−0.315002	+	0.949091i	$0.602005\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.119494	−	0.206970i	0.0131162	−	0.0227179i	−0.859393	−	0.511316i	$-0.829158\pi$
$83$	0.119494	−	0.206970i	0.0131162	−	0.0227179i	0.872509	+	0.488598i	$0.162492\pi$
$84$		0			0
$85$	−1.32673	−	2.29796i	−0.143904	−	0.249249i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.648116	−	1.12257i	−0.0687002	−	0.118992i	0.829629	−	0.558315i	$-0.188552\pi$
$89$	−0.648116	−	1.12257i	−0.0687002	−	0.118992i	−0.898329	+	0.439323i	$0.855219\pi$
$90$		0			0
$91$	−3.46492	+	14.7353i	−0.363222	+	1.54468i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.09907			−0.215360
$96$		0			0
$97$	−7.02669	+	12.1706i	−0.713452	+	1.23574i	0.250101	+	0.968220i	$0.419536\pi$
$97$	−7.02669	+	12.1706i	−0.713452	+	1.23574i	−0.963553	+	0.267516i	$0.913797\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.30322	+	9.18545i	0.527690	+	0.913986i	0.999479	+	0.0322748i	$0.0102752\pi$
$101$	5.30322	+	9.18545i	0.527690	+	0.913986i	−0.471789	+	0.881712i	$0.656391\pi$
$102$		0			0
$103$	0.0797078	−	0.138058i	0.00785385	−	0.0136033i	−0.862072	−	0.506786i	$-0.830833\pi$
$103$	0.0797078	−	0.138058i	0.00785385	−	0.0136033i	0.869926	+	0.493183i	$0.164167\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.99030	+	6.91140i	0.385757	+	0.668150i	0.991874	−	0.127225i	$-0.0406071\pi$
$107$	3.99030	+	6.91140i	0.385757	+	0.668150i	−0.606117	+	0.795375i	$0.707274\pi$
$108$		0			0
$109$	−6.85612	+	11.8751i	−0.656697	+	1.13743i	0.324769	+	0.945793i	$0.394714\pi$
$109$	−6.85612	+	11.8751i	−0.656697	+	1.13743i	−0.981466	+	0.191639i	$0.938620\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−8.98656	−	15.5652i	−0.845384	−	1.46425i	−0.885287	−	0.465045i	$-0.846038\pi$
$113$	−8.98656	−	15.5652i	−0.845384	−	1.46425i	0.0399031	−	0.999204i	$-0.487295\pi$
$114$		0			0
$115$	0.872719	+	1.51159i	0.0813814	+	0.140957i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	13.9636	−	4.20726i	1.28004	−	0.385679i
$120$		0			0
$121$	−0.217588	+	0.376874i	−0.0197807	+	0.0342613i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.70232			−0.420588
$126$		0			0
$127$	18.9684			1.68317			0.841587	−	0.540121i	$-0.181622\pi$
$127$	18.9684			1.68317			0.841587	+	0.540121i	$0.181622\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.44116	+	4.22821i	−0.213285	+	0.369420i	−0.952741	−	0.303785i	$-0.901750\pi$
$131$	−2.44116	+	4.22821i	−0.213285	+	0.369420i	0.739456	+	0.673205i	$0.235083\pi$
$132$		0			0
$133$	2.64075	−	11.2304i	0.228982	−	0.973797i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.23741	−	5.60736i	−0.276591	−	0.479069i	0.693945	−	0.720028i	$-0.255871\pi$
$137$	−3.23741	−	5.60736i	−0.276591	−	0.479069i	−0.970535	+	0.240959i	$0.922538\pi$
$138$		0			0
$139$	−11.3740	−	19.7003i	−0.964727	−	1.67096i	−0.710346	−	0.703852i	$-0.751462\pi$
$139$	−11.3740	−	19.7003i	−0.964727	−	1.67096i	−0.254381	−	0.967104i	$-0.581872\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.67362	−	16.7552i	0.808948	−	1.40114i
$144$		0			0
$145$	−0.737155	−	1.27679i	−0.0612174	−	0.106032i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.10230	+	12.3016i	−0.581843	+	1.00778i	0.413418	+	0.910542i	$0.364335\pi$
$149$	−7.10230	+	12.3016i	−0.581843	+	1.00778i	−0.995261	+	0.0972407i	$0.968998\pi$
$150$		0			0
$151$	−1.26129	−	2.18462i	−0.102643	−	0.177782i	0.810130	−	0.586250i	$-0.199396\pi$
$151$	−1.26129	−	2.18462i	−0.102643	−	0.177782i	−0.912773	+	0.408468i	$0.866063\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.25029	−	3.89761i	0.180747	−	0.313064i
$156$		0			0
$157$	17.4813			1.39516			0.697579	−	0.716508i	$-0.254261\pi$
$157$	17.4813			1.39516			0.697579	+	0.716508i	$0.254261\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−9.18523	+	2.76753i	−0.723897	+	0.218112i
$162$		0			0
$163$	0.881184	+	1.52625i	0.0690196	+	0.119546i	0.898470	−	0.439035i	$-0.144680\pi$
$163$	0.881184	+	1.52625i	0.0690196	+	0.119546i	−0.829450	+	0.558580i	$0.811346\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.57220	+	6.18723i	0.276425	+	0.478782i	0.970494	−	0.241127i	$-0.0775169\pi$
$167$	3.57220	+	6.18723i	0.276425	+	0.478782i	−0.694069	+	0.719909i	$0.744184\pi$
$168$		0			0
$169$	−9.86684	+	17.0899i	−0.758988	+	1.31461i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.89382			−0.752213			−0.376107	−	0.926576i	$-0.622737\pi$
$173$	−9.89382			−0.752213			−0.376107	+	0.926576i	$0.622737\pi$
$174$		0			0
$175$	2.88773	−	12.2807i	0.218292	−	0.928334i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.02967	+	3.51550i	−0.151705	+	0.262761i	−0.931854	−	0.362833i	$-0.881810\pi$
$179$	−2.02967	+	3.51550i	−0.151705	+	0.262761i	0.780149	+	0.625593i	$0.215143\pi$
$180$		0			0
$181$	4.58084			0.340491			0.170246	−	0.985402i	$-0.445544\pi$
$181$	4.58084			0.340491			0.170246	+	0.985402i	$0.445544\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.43022			−0.105152
$186$		0			0
$187$	−18.6397			−1.36307
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.1925			−0.809860			−0.404930	−	0.914348i	$-0.632704\pi$
$191$	−11.1925			−0.809860			−0.404930	+	0.914348i	$0.632704\pi$
$192$		0			0
$193$	16.2936			1.17284			0.586419	−	0.810008i	$-0.300537\pi$
$193$	16.2936			1.17284			0.586419	+	0.810008i	$0.300537\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.17438			0.226165			0.113082	−	0.993586i	$-0.463928\pi$
$197$	3.17438			0.226165			0.113082	+	0.993586i	$0.463928\pi$
$198$		0			0
$199$	1.44140	−	2.49658i	0.102178	−	0.176978i	−0.810404	−	0.585872i	$-0.800752\pi$
$199$	1.44140	−	2.49658i	0.102178	−	0.176978i	0.912582	+	0.408894i	$0.134085\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.75844	−	2.33763i	0.544536	−	0.164070i
$204$		0			0
$205$	−6.06122			−0.423334
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.37264	+	12.7698i	−0.509976	+	0.883305i
$210$		0			0
$211$	−0.242718	−	0.420400i	−0.0167094	−	0.0289415i	0.857550	−	0.514401i	$-0.171986\pi$
$211$	−0.242718	−	0.420400i	−0.0167094	−	0.0289415i	−0.874259	+	0.485459i	$0.838652\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.918617	+	1.59109i	0.0626492	+	0.108512i
$216$		0			0
$217$	18.0219	+	16.9429i	1.22341	+	1.15016i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	31.5366			2.12138
$222$		0			0
$223$	2.14795	−	3.72037i	0.143838	−	0.249134i	−0.785101	−	0.619368i	$-0.787389\pi$
$223$	2.14795	−	3.72037i	0.143838	−	0.249134i	0.928939	+	0.370234i	$0.120722\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.69137	−	15.0539i	−0.576866	−	0.999162i	−0.995836	−	0.0911616i	$-0.970942\pi$
$227$	−8.69137	−	15.0539i	−0.576866	−	0.999162i	0.418970	−	0.908000i	$-0.362391\pi$
$228$		0			0
$229$	−3.66563	+	6.34905i	−0.242231	+	0.419557i	−0.961350	−	0.275331i	$-0.911213\pi$
$229$	−3.66563	+	6.34905i	−0.242231	+	0.419557i	0.719118	+	0.694888i	$0.244546\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.16624	+	3.75205i	0.141915	+	0.245805i	0.928218	−	0.372037i	$-0.121341\pi$
$233$	2.16624	+	3.75205i	0.141915	+	0.245805i	−0.786302	+	0.617842i	$0.788007\pi$
$234$		0			0
$235$	−0.906366	+	1.56987i	−0.0591248	+	0.102407i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.77960	−	3.08236i	−0.115113	−	0.199381i	0.802712	−	0.596367i	$-0.203390\pi$
$239$	−1.77960	−	3.08236i	−0.115113	−	0.199381i	−0.917825	+	0.396986i	$0.870056\pi$
$240$		0			0
$241$	−8.00925	−	13.8724i	−0.515921	−	0.893602i	−0.999829	−	0.0184829i	$-0.994116\pi$
$241$	−8.00925	−	13.8724i	−0.515921	−	0.893602i	0.483908	−	0.875119i	$-0.339217\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.01659	−	1.50170i	−0.192723	−	0.0959399i
$246$		0			0
$247$	12.4738	−	21.6053i	0.793689	−	1.37471i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.8007			0.807972			0.403986	−	0.914765i	$-0.367625\pi$
$251$	12.8007			0.807972			0.403986	+	0.914765i	$0.367625\pi$
$252$		0			0
$253$	12.2612			0.770852
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.20769	−	14.2161i	0.511981	−	0.886778i	−0.487922	−	0.872887i	$-0.662245\pi$
$257$	8.20769	−	14.2161i	0.511981	−	0.886778i	0.999904	−	0.0138906i	$-0.00442165\pi$
$258$		0			0
$259$	1.79930	−	7.65192i	0.111803	−	0.475467i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.8264	+	22.2160i	0.790910	+	1.36990i	0.925404	+	0.378982i	$0.123726\pi$
$263$	12.8264	+	22.2160i	0.790910	+	1.36990i	−0.134494	+	0.990914i	$0.542941\pi$
$264$		0			0
$265$	−2.68547	−	4.65136i	−0.164967	−	0.285731i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.35397	+	9.27335i	−0.326437	+	0.565406i	−0.981802	−	0.189906i	$-0.939182\pi$
$269$	−5.35397	+	9.27335i	−0.326437	+	0.565406i	0.655365	+	0.755313i	$0.272515\pi$
$270$		0			0
$271$	−12.7513	−	22.0859i	−0.774587	−	1.34162i	−0.935026	−	0.354578i	$-0.884624\pi$
$271$	−12.7513	−	22.0859i	−0.774587	−	1.34162i	0.160439	−	0.987046i	$-0.448709\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8.06217	+	13.9641i	−0.486167	+	0.842066i
$276$		0			0
$277$	6.39123	+	11.0699i	0.384012	+	0.665128i	0.991632	−	0.129100i	$-0.0412089\pi$
$277$	6.39123	+	11.0699i	0.384012	+	0.665128i	−0.607620	+	0.794228i	$0.707876\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.4763	−	18.1454i	0.624961	−	1.08246i	−0.363587	−	0.931560i	$-0.618448\pi$
$281$	10.4763	−	18.1454i	0.624961	−	1.08246i	0.988548	−	0.150904i	$-0.0482185\pi$
$282$		0			0
$283$	15.0617			0.895325			0.447663	−	0.894203i	$-0.352257\pi$
$283$	15.0617			0.895325			0.447663	+	0.894203i	$0.352257\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.62537	−	32.4286i	0.450112	−	1.91420i
$288$		0			0
$289$	−6.69162	−	11.5902i	−0.393625	−	0.681778i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.134459	−	0.232890i	−0.00785519	−	0.0136056i	0.862071	−	0.506787i	$-0.169167\pi$
$293$	−0.134459	−	0.232890i	−0.00785519	−	0.0136056i	−0.869926	+	0.493182i	$0.835834\pi$
$294$		0			0
$295$	2.02732	−	3.51142i	0.118035	−	0.204443i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−20.7447			−1.19970
$300$		0			0
$301$	−9.66830	+	2.91308i	−0.557272	+	0.167907i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.75375	−	3.03759i	0.100420	−	0.173932i
$306$		0			0
$307$	−5.03514			−0.287371			−0.143685	−	0.989623i	$-0.545895\pi$
$307$	−5.03514			−0.287371			−0.143685	+	0.989623i	$0.545895\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.47630			−0.253828			−0.126914	−	0.991914i	$-0.540507\pi$
$311$	−4.47630			−0.253828			−0.126914	+	0.991914i	$0.540507\pi$
$312$		0			0
$313$	10.9779			0.620508			0.310254	−	0.950654i	$-0.399586\pi$
$313$	10.9779			0.620508			0.310254	+	0.950654i	$0.399586\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−24.9652			−1.40218			−0.701092	−	0.713071i	$-0.747304\pi$
$317$	−24.9652			−1.40218			−0.701092	+	0.713071i	$0.747304\pi$
$318$		0			0
$319$	−10.3566			−0.579856
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−24.0352			−1.33736
$324$		0			0
$325$	13.6404	−	23.6259i	0.756635	−	1.31053i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.25883	−	6.82421i	−0.400193	−	0.376231i
$330$		0			0
$331$	12.0241			0.660905			0.330453	−	0.943823i	$-0.392799\pi$
$331$	12.0241			0.660905			0.330453	+	0.943823i	$0.392799\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.618925	+	1.07201i	−0.0338155	+	0.0585702i
$336$		0			0
$337$	−14.1286	−	24.4715i	−0.769636	−	1.33305i	−0.937761	−	0.347282i	$-0.887105\pi$
$337$	−14.1286	−	24.4715i	−0.769636	−	1.33305i	0.168125	−	0.985766i	$-0.446229\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.8076	−	27.3795i	−0.856027	−	1.48268i
$342$		0			0
$343$	11.8294	−	14.2501i	0.638728	−	0.769433i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−19.6059			−1.05250			−0.526249	−	0.850331i	$-0.676402\pi$
$347$	−19.6059			−1.05250			−0.526249	+	0.850331i	$0.676402\pi$
$348$		0			0
$349$	−8.22904	+	14.2531i	−0.440490	+	0.762952i	−0.997726	−	0.0674029i	$-0.978529\pi$
$349$	−8.22904	+	14.2531i	−0.440490	+	0.762952i	0.557236	+	0.830354i	$0.311862\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.6854	−	23.7039i	−0.728402	−	1.26163i	−0.957558	−	0.288240i	$-0.906930\pi$
$353$	−13.6854	−	23.7039i	−0.728402	−	1.26163i	0.229156	−	0.973390i	$-0.426403\pi$
$354$		0			0
$355$	−0.949065	+	1.64383i	−0.0503711	+	0.0872453i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.88714	−	13.6609i	−0.416267	−	0.720996i	0.579293	−	0.815119i	$-0.303329\pi$
$359$	−7.88714	−	13.6609i	−0.416267	−	0.720996i	−0.995561	+	0.0941231i	$0.969995\pi$
$360$		0			0
$361$	−0.00677168	+	0.0117289i	−0.000356404	+	0.000617310i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.415060	−	0.718905i	−0.0217252	−	0.0376292i
$366$		0			0
$367$	−9.40684	−	16.2931i	−0.491033	−	0.850494i	0.508914	−	0.860818i	$-0.330047\pi$
$367$	−9.40684	−	16.2931i	−0.491033	−	0.850494i	−0.999947	+	0.0103233i	$0.996714\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	28.2641	−	8.51603i	1.46740	−	0.442130i
$372$		0			0
$373$	8.78687	−	15.2193i	0.454967	−	0.788026i	−0.543719	−	0.839267i	$-0.682984\pi$
$373$	8.78687	−	15.2193i	0.454967	−	0.788026i	0.998686	+	0.0512414i	$0.0163178\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	17.5223			0.902446
$378$		0			0
$379$	34.4618			1.77018			0.885091	−	0.465419i	$-0.154096\pi$
$379$	34.4618			1.77018			0.885091	+	0.465419i	$0.154096\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.3705	+	19.6943i	−0.581005	+	1.00633i	0.414356	+	0.910115i	$0.364007\pi$
$383$	−11.3705	+	19.6943i	−0.581005	+	1.00633i	−0.995361	+	0.0962145i	$0.969327\pi$
$384$		0			0
$385$	3.13793	+	2.95005i	0.159924	+	0.150348i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.88189	+	13.6518i	0.399628	+	0.692175i	0.993680	−	0.112251i	$-0.0358061\pi$
$389$	7.88189	+	13.6518i	0.399628	+	0.692175i	−0.594052	+	0.804426i	$0.702473\pi$
$390$		0			0
$391$	9.99303	+	17.3084i	0.505369	+	0.875325i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.34779	−	2.33444i	0.0678145	−	0.117458i
$396$		0			0
$397$	−5.39875	−	9.35091i	−0.270955	−	0.469308i	0.698151	−	0.715950i	$-0.254006\pi$
$397$	−5.39875	−	9.35091i	−0.270955	−	0.469308i	−0.969107	+	0.246642i	$0.920673\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.16473	−	10.6776i	0.307852	−	0.533215i	−0.670040	−	0.742325i	$-0.733723\pi$
$401$	6.16473	−	10.6776i	0.307852	−	0.533215i	0.977892	+	0.209110i	$0.0670566\pi$
$402$		0			0
$403$	26.7449	+	46.3235i	1.33226	+	2.30754i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.02342	+	8.70082i	−0.249002	+	0.431284i
$408$		0			0
$409$	18.6354			0.921462			0.460731	−	0.887540i	$-0.347587\pi$
$409$	18.6354			0.921462			0.460731	+	0.887540i	$0.347587\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.2362	+	15.2641i	0.798932	+	0.751096i
$414$		0			0
$415$	0.0575230	+	0.0996328i	0.00282369	+	0.00489078i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.90976	+	10.2360i	0.288711	+	0.500062i	0.973502	−	0.228677i	$-0.0734400\pi$
$419$	5.90976	+	10.2360i	0.288711	+	0.500062i	−0.684791	+	0.728739i	$0.740107\pi$
$420$		0			0
$421$	4.81800	−	8.34503i	0.234815	−	0.406712i	−0.724404	−	0.689376i	$-0.757885\pi$
$421$	4.81800	−	8.34503i	0.234815	−	0.406712i	0.959219	+	0.282664i	$0.0912182\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−26.2832			−1.27492
$426$		0			0
$427$	14.0453	+	13.2044i	0.679700	+	0.639003i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	18.2913	−	31.6815i	0.881062	−	1.52604i	0.0309004	−	0.999522i	$-0.490163\pi$
$431$	18.2913	−	31.6815i	0.881062	−	1.52604i	0.850162	−	0.526522i	$-0.176504\pi$
$432$		0			0
$433$	−7.69388			−0.369744			−0.184872	−	0.982763i	$-0.559187\pi$
$433$	−7.69388			−0.369744			−0.184872	+	0.982763i	$0.559187\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.8104			0.756312
$438$		0			0
$439$	−20.5434			−0.980482			−0.490241	−	0.871587i	$-0.663091\pi$
$439$	−20.5434			−0.980482			−0.490241	+	0.871587i	$0.663091\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	33.6802			1.60020			0.800098	−	0.599870i	$-0.204781\pi$
$443$	33.6802			1.60020			0.800098	+	0.599870i	$0.204781\pi$
$444$		0			0
$445$	0.623990			0.0295799
$446$		0			0
$447$		0			0
$448$		0			0
$449$	22.5141			1.06250			0.531252	−	0.847214i	$-0.321722\pi$
$449$	22.5141			1.06250			0.531252	+	0.847214i	$0.321722\pi$
$450$		0			0
$451$	−21.2891	+	36.8738i	−1.00246	+	1.73632i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.30908	−	4.99120i	−0.248894	−	0.233991i
$456$		0			0
$457$	−23.7117			−1.10919			−0.554594	−	0.832121i	$-0.687126\pi$
$457$	−23.7117			−1.10919			−0.554594	+	0.832121i	$0.687126\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.57340	−	9.65342i	0.259579	−	0.449605i	−0.706550	−	0.707663i	$-0.749749\pi$
$461$	5.57340	−	9.65342i	0.259579	−	0.449605i	0.966129	+	0.258059i	$0.0830828\pi$
$462$		0			0
$463$	10.3208	+	17.8761i	0.479647	+	0.830773i	0.999727	−	0.0233441i	$-0.00743133\pi$
$463$	10.3208	+	17.8761i	0.479647	+	0.830773i	−0.520080	+	0.854117i	$0.674098\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.68477	+	15.0425i	0.401883	+	0.696082i	0.993953	−	0.109804i	$-0.0350224\pi$
$467$	8.68477	+	15.0425i	0.401883	+	0.696082i	−0.592070	+	0.805887i	$0.701689\pi$
$468$		0			0
$469$	−4.95680	−	4.66001i	−0.228884	−	0.215179i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.9060			0.593419
$474$		0			0
$475$	−10.3959	+	18.0062i	−0.476997	+	0.826182i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.04517	−	3.54233i	−0.0934461	−	0.161853i	0.815513	−	0.578739i	$-0.196455\pi$
$479$	−2.04517	−	3.54233i	−0.0934461	−	0.161853i	−0.908959	+	0.416886i	$0.863122\pi$
$480$		0			0
$481$	8.49915	−	14.7210i	0.387528	−	0.671218i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.38256	−	5.85876i	−0.153594	−	0.266033i
$486$		0			0
$487$	−0.843065	+	1.46023i	−0.0382029	+	0.0661694i	−0.884495	−	0.466550i	$-0.845497\pi$
$487$	−0.843065	+	1.46023i	−0.0382029	+	0.0661694i	0.846292	+	0.532720i	$0.178830\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.85070	−	11.8658i	−0.309168	−	0.535494i	0.669013	−	0.743251i	$-0.266717\pi$
$491$	−6.85070	−	11.8658i	−0.309168	−	0.535494i	−0.978181	+	0.207757i	$0.933384\pi$
$492$		0			0
$493$	−8.44076	−	14.6198i	−0.380153	−	0.658444i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.60079	−	7.14570i	−0.340942	−	0.320528i
$498$		0			0
$499$	3.27827	−	5.67813i	0.146756	−	0.254188i	−0.783271	−	0.621680i	$-0.786450\pi$
$499$	3.27827	−	5.67813i	0.146756	−	0.254188i	0.930027	+	0.367492i	$0.119784\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−26.8584			−1.19756			−0.598779	−	0.800914i	$-0.704347\pi$
$503$	−26.8584			−1.19756			−0.598779	+	0.800914i	$0.704347\pi$
$504$		0			0
$505$	−5.10580			−0.227205
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−19.8669	+	34.4104i	−0.880584	+	1.52522i	−0.0298904	+	0.999553i	$0.509516\pi$
$509$	−19.8669	+	34.4104i	−0.880584	+	1.52522i	−0.850693	+	0.525662i	$0.823817\pi$
$510$		0			0
$511$	4.36844	−	1.31622i	0.193248	−	0.0582261i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.0383703	+	0.0664593i	0.00169080	+	0.00292855i
$516$		0			0
$517$	6.36694	+	11.0279i	0.280018	+	0.485005i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−11.7585	+	20.3663i	−0.515148	+	0.892262i	0.484698	+	0.874682i	$0.338930\pi$
$521$	−11.7585	+	20.3663i	−0.515148	+	0.892262i	−0.999845	+	0.0175802i	$0.994404\pi$
$522$		0			0
$523$	−10.9289	−	18.9294i	−0.477887	−	0.827725i	0.521791	−	0.853073i	$-0.325264\pi$
$523$	−10.9289	−	18.9294i	−0.477887	−	0.827725i	−0.999679	+	0.0253481i	$0.991931\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	25.7668	−	44.6294i	1.12242	−	1.94409i
$528$		0			0
$529$	4.92660	+	8.53312i	0.214200	+	0.371005i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	36.0191	−	62.3869i	1.56016	−	2.70228i
$534$		0			0
$535$	−3.84175			−0.166094
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19.7310	+	13.0772i	−0.849874	+	0.563273i
$540$		0			0
$541$	14.0063	+	24.2596i	0.602178	+	1.04300i	0.992491	+	0.122320i	$0.0390334\pi$
$541$	14.0063	+	24.2596i	0.602178	+	1.04300i	−0.390313	+	0.920682i	$0.627633\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.30045	−	5.71654i	−0.141376	−	0.244870i
$546$		0			0
$547$	−2.02714	+	3.51112i	−0.0866744	+	0.150124i	−0.906103	−	0.423056i	$-0.860957\pi$
$547$	−2.02714	+	3.51112i	−0.0866744	+	0.150124i	0.819429	+	0.573181i	$0.194291\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−13.3544			−0.568919
$552$		0			0
$553$	10.7941	+	10.1478i	0.459010	+	0.431527i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.926620	−	1.60495i	0.0392621	−	0.0680040i	−0.845727	−	0.533616i	$-0.820833\pi$
$557$	0.926620	−	1.60495i	0.0392621	−	0.0680040i	0.884989	+	0.465612i	$0.154166\pi$
$558$		0			0
$559$	−21.8357			−0.923553
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−44.4662			−1.87403			−0.937013	−	0.349295i	$-0.886421\pi$
$563$	−44.4662			−1.87403			−0.937013	+	0.349295i	$0.886421\pi$
$564$		0			0
$565$	8.65202			0.363993
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.2623			−0.639830			−0.319915	−	0.947446i	$-0.603654\pi$
$569$	−15.2623			−0.639830			−0.319915	+	0.947446i	$0.603654\pi$
$570$		0			0
$571$	−25.5267			−1.06826			−0.534130	−	0.845402i	$-0.679361\pi$
$571$	−25.5267			−1.06826			−0.534130	+	0.845402i	$0.679361\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	17.2890			0.721002
$576$		0			0
$577$	−3.26981	+	5.66348i	−0.136124	+	0.235774i	−0.926026	−	0.377459i	$-0.876798\pi$
$577$	−3.26981	+	5.66348i	−0.136124	+	0.235774i	0.789902	+	0.613233i	$0.210131\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.605420	+	0.182414i	−0.0251171	+	0.00756783i
$582$		0			0
$583$	−37.7291			−1.56258
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−15.2055	+	26.3366i	−0.627597	+	1.08703i	0.360436	+	0.932784i	$0.382628\pi$
$587$	−15.2055	+	26.3366i	−0.627597	+	1.08703i	−0.988033	+	0.154245i	$0.950705\pi$
$588$		0			0
$589$	−20.3833	−	35.3049i	−0.839880	−	1.45471i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	21.3291	+	36.9432i	0.875883	+	1.51707i	0.855819	+	0.517275i	$0.173053\pi$
$593$	21.3291	+	36.9432i	0.875883	+	1.51707i	0.0200633	+	0.999799i	$0.493613\pi$
$594$		0			0
$595$	−1.60697	+	6.83399i	−0.0658792	+	0.280166i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	44.5574			1.82057			0.910284	−	0.413985i	$-0.135863\pi$
$599$	44.5574			1.82057			0.910284	+	0.413985i	$0.135863\pi$
$600$		0			0
$601$	14.1961	−	24.5884i	0.579071	−	1.00298i	−0.416515	−	0.909129i	$-0.636749\pi$
$601$	14.1961	−	24.5884i	0.579071	−	1.00298i	0.995586	−	0.0938518i	$-0.0299180\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.104744	−	0.181422i	−0.00425845	−	0.00737586i
$606$		0			0
$607$	−7.01391	+	12.1484i	−0.284686	+	0.493090i	−0.972533	−	0.232765i	$-0.925223\pi$
$607$	−7.01391	+	12.1484i	−0.284686	+	0.493090i	0.687847	+	0.725856i	$0.258556\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.7723	−	18.6581i	−0.435799	−	0.754826i
$612$		0			0
$613$	−9.97062	+	17.2696i	−0.402709	+	0.697513i	−0.994052	−	0.108907i	$-0.965265\pi$
$613$	−9.97062	+	17.2696i	−0.402709	+	0.697513i	0.591342	+	0.806421i	$0.298598\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.51584	+	2.62551i	0.0610254	+	0.105699i	0.894924	−	0.446219i	$-0.147230\pi$
$617$	1.51584	+	2.62551i	0.0610254	+	0.105699i	−0.833899	+	0.551918i	$0.813896\pi$
$618$		0			0
$619$	−1.27715	−	2.21209i	−0.0513331	−	0.0889116i	0.839217	−	0.543797i	$-0.183014\pi$
$619$	−1.27715	−	2.21209i	−0.0513331	−	0.0889116i	−0.890550	+	0.454885i	$0.849680\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.785016	+	3.33846i	−0.0314510	+	0.133752i
$624$		0			0
$625$	−10.7888	+	18.6868i	−0.431554	+	0.747473i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−16.3766			−0.652980
$630$		0			0
$631$	37.1162			1.47757			0.738786	−	0.673941i	$-0.235400\pi$
$631$	37.1162			1.47757			0.738786	+	0.673941i	$0.235400\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.56557	+	7.90780i	−0.181179	+	0.313812i
$636$		0			0
$637$	33.3830	−	22.1253i	1.32268	−	0.876636i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.5484	+	18.2704i	0.416638	+	0.721638i	0.995599	−	0.0937176i	$-0.0298751\pi$
$641$	10.5484	+	18.2704i	0.416638	+	0.721638i	−0.578961	+	0.815355i	$0.696542\pi$
$642$		0			0
$643$	9.31948	+	16.1418i	0.367524	+	0.636571i	0.989178	−	0.146722i	$-0.0468722\pi$
$643$	9.31948	+	16.1418i	0.367524	+	0.636571i	−0.621654	+	0.783292i	$0.713539\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.78509	+	8.28801i	−0.188121	+	0.325835i	−0.944624	−	0.328155i	$-0.893573\pi$
$647$	−4.78509	+	8.28801i	−0.188121	+	0.325835i	0.756503	+	0.653991i	$0.226906\pi$
$648$		0			0
$649$	−14.2413	−	24.6666i	−0.559019	−	0.968249i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−16.4280	+	28.4541i	−0.642877	+	1.11350i	0.341911	+	0.939732i	$0.388926\pi$
$653$	−16.4280	+	28.4541i	−0.642877	+	1.11350i	−0.984788	+	0.173763i	$0.944407\pi$
$654$		0			0
$655$	−1.17514	−	2.03541i	−0.0459166	−	0.0795299i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−24.8011	+	42.9568i	−0.966114	+	1.67336i	−0.259521	+	0.965738i	$0.583565\pi$
$659$	−24.8011	+	42.9568i	−0.966114	+	1.67336i	−0.706593	+	0.707620i	$0.749769\pi$
$660$		0			0
$661$	−3.31789			−0.129051			−0.0645255	−	0.997916i	$-0.520553\pi$
$661$	−3.31789			−0.129051			−0.0645255	+	0.997916i	$0.520553\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.04626	+	3.80399i	0.156907	+	0.147512i
$666$		0			0
$667$	5.55232	+	9.61690i	0.214987	+	0.372368i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−12.3196	−	21.3381i	−0.475591	−	0.823748i
$672$		0			0
$673$	21.8005	−	37.7597i	0.840349	−	1.45553i	−0.0492503	−	0.998786i	$-0.515683\pi$
$673$	21.8005	−	37.7597i	0.840349	−	1.45553i	0.889600	−	0.456741i	$-0.150983\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.2808			0.702587			0.351294	−	0.936265i	$-0.385742\pi$
$677$	18.2808			0.702587			0.351294	+	0.936265i	$0.385742\pi$
$678$		0			0
$679$	35.6009	−	10.7266i	1.36624	−	0.411650i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−22.5380	+	39.0369i	−0.862391	+	1.49371i	0.00722317	+	0.999974i	$0.497701\pi$
$683$	−22.5380	+	39.0369i	−0.862391	+	1.49371i	−0.869614	+	0.493732i	$0.835633\pi$
$684$		0			0
$685$	3.11689			0.119090
$686$		0			0
$687$		0			0
$688$		0			0
$689$	63.8341			2.43189
$690$		0			0
$691$	41.7955			1.58998			0.794988	−	0.606625i	$-0.207477\pi$
$691$	41.7955			1.58998			0.794988	+	0.606625i	$0.207477\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	10.9506			0.415378
$696$		0			0
$697$	−69.4037			−2.62885
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−19.3967			−0.732604			−0.366302	−	0.930496i	$-0.619376\pi$
$701$	−19.3967			−0.732604			−0.366302	+	0.930496i	$0.619376\pi$
$702$		0			0
$703$	−6.47753	+	11.2194i	−0.244305	+	0.423148i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.42340	−	27.3170i	0.241577	−	1.02736i
$708$		0			0
$709$	−17.2308			−0.647118			−0.323559	−	0.946208i	$-0.604879\pi$
$709$	−17.2308			−0.647118			−0.323559	+	0.946208i	$0.604879\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−16.9494	+	29.3572i	−0.634759	+	1.09943i
$714$		0			0
$715$	4.65675	+	8.06573i	0.174153	+	0.301641i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.08444	−	8.80650i	−0.189617	−	0.328427i	0.755505	−	0.655143i	$-0.227391\pi$
$719$	−5.08444	−	8.80650i	−0.189617	−	0.328427i	−0.945123	+	0.326715i	$0.894058\pi$
$720$		0			0
$721$	−0.403841	+	0.121678i	−0.0150398	+	0.00453153i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−14.6034			−0.542358
$726$		0			0
$727$	−0.0914356	+	0.158371i	−0.00339116	+	0.00587366i	−0.867716	−	0.497060i	$-0.834413\pi$
$727$	−0.0914356	+	0.158371i	−0.00339116	+	0.00587366i	0.864325	+	0.502934i	$0.167746\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	10.5186	+	18.2187i	0.389044	+	0.673844i
$732$		0			0
$733$	−20.9672	+	36.3162i	−0.774440	+	1.34137i	0.160669	+	0.987008i	$0.448635\pi$
$733$	−20.9672	+	36.3162i	−0.774440	+	1.34137i	−0.935109	+	0.354361i	$0.884698\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.34776	+	7.53054i	0.160152	+	0.277391i
$738$		0			0
$739$	−11.8013	+	20.4404i	−0.434116	+	0.751911i	−0.997223	−	0.0744729i	$-0.976273\pi$
$739$	−11.8013	+	20.4404i	−0.434116	+	0.751911i	0.563107	+	0.826384i	$0.309606\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	11.1821	+	19.3680i	0.410233	+	0.710544i	0.994915	−	0.100718i	$-0.0321141\pi$
$743$	11.1821	+	19.3680i	0.410233	+	0.710544i	−0.584682	+	0.811263i	$0.698781\pi$
$744$		0			0
$745$	−3.41896	−	5.92181i	−0.125261	−	0.216958i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.83315	−	20.5541i	0.176600	−	0.751029i
$750$		0			0
$751$	−15.5231	+	26.8868i	−0.566445	+	0.981112i	0.430468	+	0.902606i	$0.358348\pi$
$751$	−15.5231	+	26.8868i	−0.566445	+	0.981112i	−0.996914	+	0.0785064i	$0.974985\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.21434			0.0441943
$756$		0			0
$757$	−44.0639			−1.60153			−0.800764	−	0.598980i	$-0.795573\pi$
$757$	−44.0639			−1.60153			−0.800764	+	0.598980i	$0.795573\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.87470	−	4.97913i	0.104208	−	0.180493i	−0.809206	−	0.587524i	$-0.800103\pi$
$761$	2.87470	−	4.97913i	0.104208	−	0.180493i	0.913414	+	0.407031i	$0.133436\pi$
$762$		0			0
$763$	34.7367	−	10.4662i	1.25755	−	0.378903i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	24.0949	+	41.7336i	0.870016	+	1.50691i
$768$		0			0
$769$	−7.48401	−	12.9627i	−0.269880	−	0.467446i	0.698950	−	0.715170i	$-0.253651\pi$
$769$	−7.48401	−	12.9627i	−0.269880	−	0.467446i	−0.968831	+	0.247724i	$0.920317\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	10.0605	−	17.4253i	0.361850	−	0.626743i	−0.626415	−	0.779490i	$-0.715479\pi$
$773$	10.0605	−	17.4253i	0.361850	−	0.626743i	0.988265	+	0.152747i	$0.0488119\pi$
$774$		0			0
$775$	−22.2897	−	38.6069i	−0.800669	−	1.38680i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−27.4516	+	47.5475i	−0.983555	+	1.70357i
$780$		0			0
$781$	6.66688	+	11.5474i	0.238560	+	0.413198i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.20763	+	7.28783i	−0.150177	+	0.260114i
$786$		0			0
$787$	−24.1145			−0.859588			−0.429794	−	0.902927i	$-0.641414\pi$
$787$	−24.1145			−0.859588			−0.429794	+	0.902927i	$0.641414\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−10.8848	+	46.2899i	−0.387017	+	1.64588i
$792$		0			0
$793$	20.8435	+	36.1021i	0.740175	+	1.28202i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.54611	+	2.67794i	0.0547661	+	0.0948576i	0.892109	−	0.451821i	$-0.149225\pi$
$797$	1.54611	+	2.67794i	0.0547661	+	0.0948576i	−0.837343	+	0.546678i	$0.815892\pi$
$798$		0			0
$799$	−10.3783	+	17.9758i	−0.367158	+	0.635936i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.83133			−0.205783
$804$		0			0
$805$	1.05706	−	4.49539i	0.0372565	−	0.158442i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.32067	−	5.75157i	0.116749	−	0.202215i	−0.801729	−	0.597688i	$-0.796086\pi$
$809$	3.32067	−	5.75157i	0.116749	−	0.202215i	0.918477	+	0.395473i	$0.129419\pi$
$810$		0			0
$811$	−23.7806			−0.835049			−0.417525	−	0.908666i	$-0.637102\pi$
$811$	−23.7806			−0.835049			−0.417525	+	0.908666i	$0.637102\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.848381			−0.0297175
$816$		0			0
$817$	16.6419			0.582225
$818$		0			0
$819$		0			0
$820$		0			0
$821$	49.8303			1.73909			0.869544	−	0.493856i	$-0.164413\pi$
$821$	49.8303			1.73909			0.869544	+	0.493856i	$0.164413\pi$
$822$		0			0
$823$	−9.45383			−0.329540			−0.164770	−	0.986332i	$-0.552688\pi$
$823$	−9.45383			−0.329540			−0.164770	+	0.986332i	$0.552688\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	7.95385			0.276582			0.138291	−	0.990392i	$-0.455839\pi$
$827$	7.95385			0.276582			0.138291	+	0.990392i	$0.455839\pi$
$828$		0			0
$829$	6.22333	−	10.7791i	0.216145	−	0.374374i	−0.737481	−	0.675368i	$-0.763985\pi$
$829$	6.22333	−	10.7791i	0.216145	−	0.374374i	0.953626	+	0.300993i	$0.0973182\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−34.5414	−	17.1951i	−1.19679	−	0.595775i
$834$		0			0
$835$	−3.43922			−0.119019
$836$		0			0
$837$		0			0
$838$		0			0
$839$	22.5163	−	38.9994i	0.777350	−	1.34641i	−0.156114	−	0.987739i	$-0.549897\pi$
$839$	22.5163	−	38.9994i	0.777350	−	1.34641i	0.933464	−	0.358671i	$-0.116770\pi$
$840$		0			0
$841$	9.81015	+	16.9917i	0.338281	+	0.585920i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.74977	−	8.22684i	−0.163397	−	0.283012i
$846$		0			0
$847$	1.10242	−	0.332160i	0.0378794	−	0.0114131i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.7725			0.369278
$852$		0			0
$853$	−1.15007	+	1.99198i	−0.0393777	+	0.0682042i	−0.885043	−	0.465510i	$-0.845871\pi$
$853$	−1.15007	+	1.99198i	−0.0393777	+	0.0682042i	0.845665	+	0.533714i	$0.179204\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.33473	+	10.9721i	0.216390	+	0.374799i	0.953702	−	0.300754i	$-0.0972384\pi$
$857$	6.33473	+	10.9721i	0.216390	+	0.374799i	−0.737312	+	0.675553i	$0.763905\pi$
$858$		0			0
$859$	−23.7374	+	41.1144i	−0.809910	+	1.40280i	0.103016	+	0.994680i	$0.467151\pi$
$859$	−23.7374	+	41.1144i	−0.809910	+	1.40280i	−0.912926	+	0.408125i	$0.866183\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.1445	+	27.9630i	0.549564	+	0.951873i	0.998304	+	0.0582109i	$0.0185396\pi$
$863$	16.1445	+	27.9630i	0.549564	+	0.951873i	−0.448740	+	0.893662i	$0.648127\pi$
$864$		0			0
$865$	2.38138	−	4.12467i	0.0809693	−	0.140243i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.46779	−	16.3987i	−0.321173	−	0.556287i
$870$		0			0
$871$	−7.35599	−	12.7410i	−0.249248	−	0.431711i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	9.06441	+	8.52168i	0.306433	+	0.288085i
$876$		0			0
$877$	−13.8795	+	24.0399i	−0.468676	+	0.811771i	−0.999359	−	0.0357996i	$-0.988602\pi$
$877$	−13.8795	+	24.0399i	−0.468676	+	0.811771i	0.530683	+	0.847570i	$0.321936\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	22.7696			0.767126			0.383563	−	0.923515i	$-0.374697\pi$
$881$	22.7696			0.767126			0.383563	+	0.923515i	$0.374697\pi$
$882$		0			0
$883$	4.65312			0.156590			0.0782950	−	0.996930i	$-0.475052\pi$
$883$	4.65312			0.156590			0.0782950	+	0.996930i	$0.475052\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−23.6434	+	40.9515i	−0.793866	+	1.37502i	0.129691	+	0.991554i	$0.458602\pi$
$887$	−23.6434	+	40.9515i	−0.793866	+	1.37502i	−0.923557	+	0.383462i	$0.874732\pi$
$888$		0			0
$889$	−36.5644	−	34.3751i	−1.22633	−	1.15290i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.20996	+	14.2201i	0.274736	+	0.475856i
$894$		0			0
$895$	−0.977058	−	1.69231i	−0.0326595	−	0.0565678i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	14.3165	−	24.7970i	0.477483	−	0.827025i
$900$		0			0
$901$	−30.7498	−	53.2602i	−1.02442	−	1.77436i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.10258	+	1.90972i	−0.0366510	+	0.0634813i
$906$		0			0
$907$	3.03306	+	5.25342i	0.100711	+	0.174437i	0.911978	−	0.410239i	$-0.134555\pi$
$907$	3.03306	+	5.25342i	0.100711	+	0.174437i	−0.811267	+	0.584676i	$0.801222\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−11.3223	+	19.6109i	−0.375126	+	0.649737i	−0.990346	−	0.138618i	$-0.955734\pi$
$911$	−11.3223	+	19.6109i	−0.375126	+	0.649737i	0.615220	+	0.788356i	$0.289067\pi$
$912$		0			0
$913$	0.808162			0.0267463
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.3682	−	3.72656i	0.408433	−	0.123062i
$918$		0			0
$919$	−22.3902	−	38.7810i	−0.738585	−	1.27927i	−0.953133	−	0.302553i	$-0.902161\pi$
$919$	−22.3902	−	38.7810i	−0.738585	−	1.27927i	0.214548	−	0.976713i	$-0.431172\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−11.2797	−	19.5371i	−0.371277	−	0.643071i
$924$		0			0
$925$	−7.08335	+	12.2687i	−0.232899	+	0.403393i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.10524			0.0362618			0.0181309	−	0.999836i	$-0.494228\pi$
$929$	1.10524			0.0362618			0.0181309	+	0.999836i	$0.494228\pi$
$930$		0			0
$931$	−25.4424	+	16.8626i	−0.833842	+	0.552648i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.48645	−	7.77076i	0.146723	−	0.254131i
$936$		0			0
$937$	44.7012			1.46033			0.730163	−	0.683273i	$-0.239444\pi$
$937$	44.7012			1.46033			0.730163	+	0.683273i	$0.239444\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.49932			0.0488765			0.0244383	−	0.999701i	$-0.492220\pi$
$941$	1.49932			0.0488765			0.0244383	+	0.999701i	$0.492220\pi$
$942$		0			0
$943$	45.6537			1.48669
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.50893			−0.308999			−0.154499	−	0.987993i	$-0.549376\pi$
$947$	−9.50893			−0.308999			−0.154499	+	0.987993i	$0.549376\pi$
$948$		0			0
$949$	9.86606			0.320266
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−15.2064			−0.492585			−0.246292	−	0.969196i	$-0.579212\pi$
$953$	−15.2064			−0.492585			−0.246292	+	0.969196i	$0.579212\pi$
$954$		0			0
$955$	2.69396	−	4.66607i	0.0871745	−	0.150991i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.92124	+	16.6759i	−0.126623	+	0.538494i
$960$		0			0
$961$	56.4071			1.81958
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.92176	+	6.79268i	−0.126246	+	0.218664i
$966$		0			0
$967$	−17.9319	−	31.0589i	−0.576649	−	0.998786i	−0.995860	−	0.0908973i	$-0.971027\pi$
$967$	−17.9319	−	31.0589i	−0.576649	−	0.998786i	0.419211	−	0.907889i	$-0.362307\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.72746	+	6.45615i	0.119620	+	0.207188i	0.919617	−	0.392816i	$-0.128499\pi$
$971$	3.72746	+	6.45615i	0.119620	+	0.207188i	−0.799997	+	0.600004i	$0.795166\pi$
$972$		0			0
$973$	−13.7765	+	58.5874i	−0.441653	+	1.87823i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	39.9512			1.27815			0.639076	−	0.769143i	$-0.279317\pi$
$977$	39.9512			1.27815			0.639076	+	0.769143i	$0.279317\pi$
$978$		0			0
$979$	2.19167	−	3.79608i	0.0700460	−	0.121323i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4.19208	+	7.26090i	0.133707	+	0.231587i	0.925103	−	0.379717i	$-0.123979\pi$
$983$	4.19208	+	7.26090i	0.133707	+	0.231587i	−0.791396	+	0.611304i	$0.790645\pi$
$984$		0			0
$985$	−0.764052	+	1.32338i	−0.0243447	+	0.0421663i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.91911	−	11.9843i	−0.220015	−	0.381077i
$990$		0			0
$991$	−21.2345	+	36.7792i	−0.674536	+	1.16833i	0.302068	+	0.953286i	$0.402323\pi$
$991$	−21.2345	+	36.7792i	−0.674536	+	1.16833i	−0.976604	+	0.215044i	$0.931010\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.693871	+	1.20182i	0.0219972	+	0.0381003i
$996$		0			0
$997$	15.4816	+	26.8149i	0.490306	+	0.849236i	0.999938	−	0.0111572i	$-0.00355152\pi$
$997$	15.4816	+	26.8149i	0.490306	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.q.c.1369.6		22
3.2	odd	2		504.2.q.d.25.5	✓	22
4.3	odd	2		3024.2.q.k.2881.6		22
7.2	even	3		1512.2.t.d.289.6		22
9.4	even	3		1512.2.t.d.361.6		22
9.5	odd	6		504.2.t.d.193.3	yes	22
12.11	even	2		1008.2.q.k.529.7		22
21.2	odd	6		504.2.t.d.457.3	yes	22
28.23	odd	6		3024.2.t.l.289.6		22
36.23	even	6		1008.2.t.k.193.9		22
36.31	odd	6		3024.2.t.l.1873.6		22
63.23	odd	6		504.2.q.d.121.5	yes	22
63.58	even	3	inner	1512.2.q.c.793.6		22
84.23	even	6		1008.2.t.k.961.9		22
252.23	even	6		1008.2.q.k.625.7		22
252.247	odd	6		3024.2.q.k.2305.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.5	✓	22	3.2	odd	2
504.2.q.d.121.5	yes	22	63.23	odd	6
504.2.t.d.193.3	yes	22	9.5	odd	6
504.2.t.d.457.3	yes	22	21.2	odd	6
1008.2.q.k.529.7		22	12.11	even	2
1008.2.q.k.625.7		22	252.23	even	6
1008.2.t.k.193.9		22	36.23	even	6
1008.2.t.k.961.9		22	84.23	even	6
1512.2.q.c.793.6		22	63.58	even	3	inner
1512.2.q.c.1369.6		22	1.1	even	1	trivial
1512.2.t.d.289.6		22	7.2	even	3
1512.2.t.d.361.6		22	9.4	even	3
3024.2.q.k.2305.6		22	252.247	odd	6
3024.2.q.k.2881.6		22	4.3	odd	2
3024.2.t.l.289.6		22	28.23	odd	6
3024.2.t.l.1873.6		22	36.31	odd	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.240694 + 0.416893i) q^{5} +(-1.92765 - 1.81223i) q^{7} +O(q^{10})\)	\(q+(-0.240694 + 0.416893i) q^{5} +(-1.92765 - 1.81223i) q^{7} +(1.69080 + 2.92855i) q^{11} +(-2.86067 - 4.95482i) q^{13} +(-2.75605 + 4.77362i) q^{17} +(2.18023 + 3.77626i) q^{19} +(1.81293 - 3.14008i) q^{23} +(2.38413 + 4.12944i) q^{25} +(-1.53131 + 2.65231i) q^{29} -9.34918 q^{31} +(1.21948 - 0.367431i) q^{35} +(1.48552 + 2.57299i) q^{37} +(6.29558 + 10.9043i) q^{41} +(1.90827 - 3.30522i) q^{43} +3.76564 q^{47} +(0.431647 + 6.98668i) q^{49} +(-5.57860 + 9.66242i) q^{53} -1.62786 q^{55} -8.42282 q^{59} -7.28625 q^{61} +2.75418 q^{65} +2.57143 q^{67} +3.94304 q^{71} +(-0.862216 + 1.49340i) q^{73} +(2.04794 - 8.70932i) q^{77} -5.59960 q^{79} +(0.119494 - 0.206970i) q^{83} +(-1.32673 - 2.29796i) q^{85} +(-0.648116 - 1.12257i) q^{89} +(-3.46492 + 14.7353i) q^{91} -2.09907 q^{95} +(-7.02669 + 12.1706i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 5 q^{7}+O(q^{10}) \) 22 * q - 3 * q^5 - 5 * q^7	\( 22 q - 3 q^{5} - 5 q^{7} + 3 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} - 2 q^{23} - 10 q^{25} - 9 q^{29} + 8 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} + 10 q^{47} + 15 q^{49} - 11 q^{53} + 22 q^{55} - 38 q^{59} + 26 q^{61} + 26 q^{65} - 52 q^{67} + 48 q^{71} - 35 q^{73} - 17 q^{77} - 20 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} + 24 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q - 3 * q^5 - 5 * q^7 + 3 * q^11 - 3 * q^13 - 7 * q^17 - q^19 - 2 * q^23 - 10 * q^25 - 9 * q^29 + 8 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 + 10 * q^47 + 15 * q^49 - 11 * q^53 + 22 * q^55 - 38 * q^59 + 26 * q^61 + 26 * q^65 - 52 * q^67 + 48 * q^71 - 35 * q^73 - 17 * q^77 - 20 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 + 24 * q^95 - 29 * q^97

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