LMFDB - Embedded newform 3024.2.q.k.2881.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, 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("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.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:	$24.1467615712$
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			2881.6
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.k.2305.6

$q$-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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			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	$-0.996388\pi$
$11$	−1.69080	−	2.92855i	−0.509794	−	0.882990i	0.490141	−	0.871643i	$-0.336945\pi$
$12$		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	$-0.999935\pi$
$19$	−2.18023	−	3.77626i	−0.500178	−	0.866334i	0.499822	−	0.866128i	$-0.333399\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.81293	+	3.14008i	−0.378021	+	0.654752i	−0.990774	−	0.135523i	$-0.956729\pi$
$23$	−1.81293	+	3.14008i	−0.378021	+	0.654752i	0.612753	+	0.790274i	$0.290062\pi$
$24$		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	$-0.182801\pi$
$31$	9.34918			1.67916			0.839581	+	0.543235i	$0.182801\pi$
$32$		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	−0.974049	−	0.226339i	$-0.927324\pi$
$43$	−1.90827	+	3.30522i	−0.291009	+	0.504042i	0.683040	+	0.730381i	$0.260658\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.76564			−0.549276			−0.274638	−	0.961548i	$-0.588558\pi$
$47$	−3.76564			−0.549276			−0.274638	+	0.961548i	$0.588558\pi$
$48$		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	$-0.315283\pi$
$59$	8.42282			1.09656			0.548279	+	0.836296i	$0.315283\pi$
$60$		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	$-0.550206\pi$
$67$	−2.57143			−0.314150			−0.157075	+	0.987587i	$0.550206\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.94304			−0.467953			−0.233977	−	0.972242i	$-0.575174\pi$
$71$	−3.94304			−0.467953			−0.233977	+	0.972242i	$0.575174\pi$
$72$		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	$-0.397995\pi$
$79$	5.59960			0.630004			0.315002	+	0.949091i	$0.397995\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.119494	+	0.206970i	−0.0131162	+	0.0227179i	−0.872509	−	0.488598i	$-0.837508\pi$
$83$	−0.119494	+	0.206970i	−0.0131162	+	0.0227179i	0.859393	+	0.511316i	$0.170842\pi$
$84$		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	−0.869926	−	0.493183i	$-0.835833\pi$
$103$	−0.0797078	+	0.138058i	−0.00785385	+	0.0136033i	0.862072	+	0.506786i	$0.169167\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.99030	−	6.91140i	−0.385757	−	0.668150i	0.606117	−	0.795375i	$-0.292726\pi$
$107$	−3.99030	−	6.91140i	−0.385757	−	0.668150i	−0.991874	+	0.127225i	$0.959393\pi$
$108$		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	$-0.818378\pi$
$127$	−18.9684			−1.68317			−0.841587	+	0.540121i	$0.818378\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.44116	−	4.22821i	0.213285	−	0.369420i	−0.739456	−	0.673205i	$-0.764917\pi$
$131$	2.44116	−	4.22821i	0.213285	−	0.369420i	0.952741	+	0.303785i	$0.0982504\pi$
$132$		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	$0.248538\pi$
$139$	11.3740	+	19.7003i	0.964727	+	1.67096i	0.254381	+	0.967104i	$0.418128\pi$
$140$		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	0.912773	−	0.408468i	$-0.133937\pi$
$151$	1.26129	+	2.18462i	0.102643	+	0.177782i	−0.810130	+	0.586250i	$0.800604\pi$
$152$		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	0.829450	−	0.558580i	$-0.188654\pi$
$163$	−0.881184	−	1.52625i	−0.0690196	−	0.119546i	−0.898470	+	0.439035i	$0.855320\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.57220	−	6.18723i	−0.276425	−	0.478782i	0.694069	−	0.719909i	$-0.255816\pi$
$167$	−3.57220	−	6.18723i	−0.276425	−	0.478782i	−0.970494	+	0.241127i	$0.922483\pi$
$168$		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	−0.780149	−	0.625593i	$-0.784857\pi$
$179$	2.02967	−	3.51550i	0.151705	−	0.262761i	0.931854	+	0.362833i	$0.118190\pi$
$180$		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	$-0.367296\pi$
$191$	11.1925			0.809860			0.404930	+	0.914348i	$0.367296\pi$
$192$		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	−0.912582	−	0.408894i	$-0.865915\pi$
$199$	−1.44140	+	2.49658i	−0.102178	+	0.176978i	0.810404	+	0.585872i	$0.199248\pi$
$200$		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	0.874259	−	0.485459i	$-0.161348\pi$
$211$	0.242718	+	0.420400i	0.0167094	+	0.0289415i	−0.857550	+	0.514401i	$0.828014\pi$
$212$		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	−0.928939	−	0.370234i	$-0.879278\pi$
$223$	−2.14795	+	3.72037i	−0.143838	+	0.249134i	0.785101	+	0.619368i	$0.212611\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.69137	+	15.0539i	0.576866	+	0.999162i	0.995836	+	0.0911616i	$0.0290580\pi$
$227$	8.69137	+	15.0539i	0.576866	+	0.999162i	−0.418970	+	0.908000i	$0.637609\pi$
$228$		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	0.917825	−	0.396986i	$-0.129944\pi$
$239$	1.77960	+	3.08236i	0.115113	+	0.199381i	−0.802712	+	0.596367i	$0.796610\pi$
$240$		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	$-0.632375\pi$
$251$	−12.8007			−0.807972			−0.403986	+	0.914765i	$0.632375\pi$
$252$		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	$-0.876274\pi$
$263$	−12.8264	−	22.2160i	−0.790910	−	1.36990i	0.134494	−	0.990914i	$-0.457059\pi$
$264$		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	$0.115376\pi$
$271$	12.7513	+	22.0859i	0.774587	+	1.34162i	−0.160439	+	0.987046i	$0.551291\pi$
$272$		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	$-0.647743\pi$
$283$	−15.0617			−0.895325			−0.447663	+	0.894203i	$0.647743\pi$
$284$		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	$-0.454105\pi$
$307$	5.03514			0.287371			0.143685	+	0.989623i	$0.454105\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.47630			0.253828			0.126914	−	0.991914i	$-0.459493\pi$
$311$	4.47630			0.253828			0.126914	+	0.991914i	$0.459493\pi$
$312$		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	$-0.607201\pi$
$331$	−12.0241			−0.660905			−0.330453	+	0.943823i	$0.607201\pi$
$332$		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	$-0.323598\pi$
$347$	19.6059			1.05250			0.526249	+	0.850331i	$0.323598\pi$
$348$		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	0.995561	−	0.0941231i	$-0.0300047\pi$
$359$	7.88714	+	13.6609i	0.416267	+	0.720996i	−0.579293	+	0.815119i	$0.696671\pi$
$360$		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	0.999947	−	0.0103233i	$-0.00328606\pi$
$367$	9.40684	+	16.2931i	0.491033	+	0.850494i	−0.508914	+	0.860818i	$0.669953\pi$
$368$		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	$-0.845904\pi$
$379$	−34.4618			−1.77018			−0.885091	+	0.465419i	$0.845904\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	11.3705	−	19.6943i	0.581005	−	1.00633i	−0.414356	−	0.910115i	$-0.635993\pi$
$383$	11.3705	−	19.6943i	0.581005	−	1.00633i	0.995361	−	0.0962145i	$-0.0306735\pi$
$384$		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	0.684791	−	0.728739i	$-0.259893\pi$
$419$	−5.90976	−	10.2360i	−0.288711	−	0.500062i	−0.973502	+	0.228677i	$0.926560\pi$
$420$		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	$0.509837\pi$
$431$	−18.2913	+	31.6815i	−0.881062	+	1.52604i	−0.850162	+	0.526522i	$0.823496\pi$
$432$		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	$-0.336909\pi$
$439$	20.5434			0.980482			0.490241	+	0.871587i	$0.336909\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−33.6802			−1.60020			−0.800098	−	0.599870i	$-0.795219\pi$
$443$	−33.6802			−1.60020			−0.800098	+	0.599870i	$0.795219\pi$
$444$		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	0.520080	−	0.854117i	$-0.325902\pi$
$463$	−10.3208	−	17.8761i	−0.479647	−	0.830773i	−0.999727	+	0.0233441i	$0.992569\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.68477	−	15.0425i	−0.401883	−	0.696082i	0.592070	−	0.805887i	$-0.298311\pi$
$467$	−8.68477	−	15.0425i	−0.401883	−	0.696082i	−0.993953	+	0.109804i	$0.964978\pi$
$468$		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	0.908959	−	0.416886i	$-0.136878\pi$
$479$	2.04517	+	3.54233i	0.0934461	+	0.161853i	−0.815513	+	0.578739i	$0.803545\pi$
$480$		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	−0.846292	−	0.532720i	$-0.821170\pi$
$487$	0.843065	−	1.46023i	0.0382029	−	0.0661694i	0.884495	+	0.466550i	$0.154503\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.85070	+	11.8658i	0.309168	+	0.535494i	0.978181	−	0.207757i	$-0.0666162\pi$
$491$	6.85070	+	11.8658i	0.309168	+	0.535494i	−0.669013	+	0.743251i	$0.733283\pi$
$492$		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	−0.930027	−	0.367492i	$-0.880216\pi$
$499$	−3.27827	+	5.67813i	−0.146756	+	0.254188i	0.783271	+	0.621680i	$0.213550\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	26.8584			1.19756			0.598779	−	0.800914i	$-0.295653\pi$
$503$	26.8584			1.19756			0.598779	+	0.800914i	$0.295653\pi$
$504$		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	0.999679	−	0.0253481i	$-0.00806942\pi$
$523$	10.9289	+	18.9294i	0.477887	+	0.827725i	−0.521791	+	0.853073i	$0.674736\pi$
$524$		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	−0.819429	−	0.573181i	$-0.805709\pi$
$547$	2.02714	−	3.51112i	0.0866744	−	0.150124i	0.906103	+	0.423056i	$0.139043\pi$
$548$		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	$-0.113579\pi$
$563$	44.4662			1.87403			0.937013	+	0.349295i	$0.113579\pi$
$564$		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	$-0.320639\pi$
$571$	25.5267			1.06826			0.534130	+	0.845402i	$0.320639\pi$
$572$		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	$-0.617372\pi$
$587$	15.2055	−	26.3366i	0.627597	−	1.08703i	0.988033	−	0.154245i	$-0.0492947\pi$
$588$		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	$-0.864137\pi$
$599$	−44.5574			−1.82057			−0.910284	+	0.413985i	$0.864137\pi$
$600$		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	−0.687847	−	0.725856i	$-0.741444\pi$
$607$	7.01391	−	12.1484i	0.284686	−	0.493090i	0.972533	+	0.232765i	$0.0747774\pi$
$608$		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	0.890550	−	0.454885i	$-0.150320\pi$
$619$	1.27715	+	2.21209i	0.0513331	+	0.0889116i	−0.839217	+	0.543797i	$0.816986\pi$
$620$		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	$-0.764600\pi$
$631$	−37.1162			−1.47757			−0.738786	+	0.673941i	$0.764600\pi$
$632$		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	0.621654	−	0.783292i	$-0.286461\pi$
$643$	−9.31948	−	16.1418i	−0.367524	−	0.636571i	−0.989178	+	0.146722i	$0.953128\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.78509	−	8.28801i	0.188121	−	0.325835i	−0.756503	−	0.653991i	$-0.773094\pi$
$647$	4.78509	−	8.28801i	0.188121	−	0.325835i	0.944624	+	0.328155i	$0.106427\pi$
$648$		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	$-0.416435\pi$
$659$	24.8011	−	42.9568i	0.966114	−	1.67336i	0.706593	−	0.707620i	$-0.250231\pi$
$660$		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	$-0.502299\pi$
$683$	22.5380	−	39.0369i	0.862391	−	1.49371i	0.869614	−	0.493732i	$-0.164367\pi$
$684$		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	$-0.792523\pi$
$691$	−41.7955			−1.58998			−0.794988	+	0.606625i	$0.792523\pi$
$692$		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	0.945123	−	0.326715i	$-0.105942\pi$
$719$	5.08444	+	8.80650i	0.189617	+	0.328427i	−0.755505	+	0.655143i	$0.772609\pi$
$720$		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	−0.864325	−	0.502934i	$-0.832254\pi$
$727$	0.0914356	−	0.158371i	0.00339116	−	0.00587366i	0.867716	+	0.497060i	$0.165587\pi$
$728$		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	−0.563107	−	0.826384i	$-0.690394\pi$
$739$	11.8013	−	20.4404i	0.434116	−	0.751911i	0.997223	+	0.0744729i	$0.0237274\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.1821	−	19.3680i	−0.410233	−	0.710544i	0.584682	−	0.811263i	$-0.301219\pi$
$743$	−11.1821	−	19.3680i	−0.410233	−	0.710544i	−0.994915	+	0.100718i	$0.967886\pi$
$744$		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	$-0.641652\pi$
$751$	15.5231	−	26.8868i	0.566445	−	0.981112i	0.996914	−	0.0785064i	$-0.0250151\pi$
$752$		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	$-0.358586\pi$
$787$	24.1145			0.859588			0.429794	+	0.902927i	$0.358586\pi$
$788$		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	$-0.362898\pi$
$811$	23.7806			0.835049			0.417525	+	0.908666i	$0.362898\pi$
$812$		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	$-0.447312\pi$
$823$	9.45383			0.329540			0.164770	+	0.986332i	$0.447312\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.95385			−0.276582			−0.138291	−	0.990392i	$-0.544161\pi$
$827$	−7.95385			−0.276582			−0.138291	+	0.990392i	$0.544161\pi$
$828$		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	$0.450103\pi$
$839$	−22.5163	+	38.9994i	−0.777350	+	1.34641i	−0.933464	+	0.358671i	$0.883230\pi$
$840$		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	$-0.532849\pi$
$859$	23.7374	−	41.1144i	0.809910	−	1.40280i	0.912926	−	0.408125i	$-0.133817\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.1445	−	27.9630i	−0.549564	−	0.951873i	−0.998304	−	0.0582109i	$-0.981460\pi$
$863$	−16.1445	−	27.9630i	−0.549564	−	0.951873i	0.448740	−	0.893662i	$-0.351873\pi$
$864$		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	$-0.524948\pi$
$883$	−4.65312			−0.156590			−0.0782950	+	0.996930i	$0.524948\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23.6434	−	40.9515i	0.793866	−	1.37502i	−0.129691	−	0.991554i	$-0.541398\pi$
$887$	23.6434	−	40.9515i	0.793866	−	1.37502i	0.923557	−	0.383462i	$-0.125268\pi$
$888$		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	0.811267	−	0.584676i	$-0.198778\pi$
$907$	−3.03306	−	5.25342i	−0.100711	−	0.174437i	−0.911978	+	0.410239i	$0.865445\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.3223	−	19.6109i	0.375126	−	0.649737i	−0.615220	−	0.788356i	$-0.710933\pi$
$911$	11.3223	−	19.6109i	0.375126	−	0.649737i	0.990346	+	0.138618i	$0.0442661\pi$
$912$		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	$0.0978388\pi$
$919$	22.3902	+	38.7810i	0.738585	+	1.27927i	−0.214548	+	0.976713i	$0.568828\pi$
$920$		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	$-0.450624\pi$
$947$	9.50893			0.308999			0.154499	+	0.987993i	$0.450624\pi$
$948$		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	$0.0289735\pi$
$967$	17.9319	+	31.0589i	0.576649	+	0.998786i	−0.419211	+	0.907889i	$0.637693\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−3.72746	−	6.45615i	−0.119620	−	0.207188i	0.799997	−	0.600004i	$-0.204834\pi$
$971$	−3.72746	−	6.45615i	−0.119620	−	0.207188i	−0.919617	+	0.392816i	$0.871501\pi$
$972$		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	0.791396	−	0.611304i	$-0.209355\pi$
$983$	−4.19208	−	7.26090i	−0.133707	−	0.231587i	−0.925103	+	0.379717i	$0.876021\pi$
$984$		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	$-0.597677\pi$
$991$	21.2345	−	36.7792i	0.674536	−	1.16833i	0.976604	−	0.215044i	$-0.0689896\pi$
$992$		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	3024.2.q.k.2881.6		22
3.2	odd	2		1008.2.q.k.529.7		22
4.3	odd	2		1512.2.q.c.1369.6		22
7.2	even	3		3024.2.t.l.289.6		22
9.4	even	3		3024.2.t.l.1873.6		22
9.5	odd	6		1008.2.t.k.193.9		22
12.11	even	2		504.2.q.d.25.5	✓	22
21.2	odd	6		1008.2.t.k.961.9		22
28.23	odd	6		1512.2.t.d.289.6		22
36.23	even	6		504.2.t.d.193.3	yes	22
36.31	odd	6		1512.2.t.d.361.6		22
63.23	odd	6		1008.2.q.k.625.7		22
63.58	even	3	inner	3024.2.q.k.2305.6		22
84.23	even	6		504.2.t.d.457.3	yes	22
252.23	even	6		504.2.q.d.121.5	yes	22
252.247	odd	6		1512.2.q.c.793.6		22

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

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.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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