LMFDB - Embedded newform 1512.2.q.c.1369.9

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			1369.9
Character	$\chi$	$=$	1512.1369
Dual form			1512.2.q.c.793.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.927957 - 1.60727i) q^{5} +(0.900017 + 2.48796i) q^{7} +O(q^{10})$	$q+(0.927957 - 1.60727i) q^{5} +(0.900017 + 2.48796i) q^{7} +(-1.28800 - 2.23089i) q^{11} +(2.82227 + 4.88832i) q^{13} +(-3.57951 + 6.19989i) q^{17} +(0.636599 + 1.10262i) q^{19} +(0.120639 - 0.208952i) q^{23} +(0.777791 + 1.34717i) q^{25} +(-0.923571 + 1.59967i) q^{29} -2.99103 q^{31} +(4.83401 + 0.862156i) q^{35} +(0.338260 + 0.585884i) q^{37} +(0.733933 + 1.27121i) q^{41} +(4.14269 - 7.17535i) q^{43} +12.3145 q^{47} +(-5.37994 + 4.47842i) q^{49} +(-3.35508 + 5.81117i) q^{53} -4.78085 q^{55} -2.08279 q^{59} +12.9595 q^{61} +10.4758 q^{65} -4.83102 q^{67} +1.53621 q^{71} +(-6.55954 + 11.3615i) q^{73} +(4.39115 - 5.21235i) q^{77} -3.72018 q^{79} +(3.00173 - 5.19915i) q^{83} +(6.64326 + 11.5065i) q^{85} +(-6.60349 - 11.4376i) q^{89} +(-9.62187 + 11.4213i) q^{91} +2.36294 q^{95} +(6.40860 - 11.1000i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.927957	−	1.60727i	0.414995	−	0.718793i	−0.580433	−	0.814308i	$-0.697117\pi$
$5$	0.927957	−	1.60727i	0.414995	−	0.718793i	0.995428	+	0.0955156i	$0.0304500\pi$
$6$		0			0
$7$	0.900017	+	2.48796i	0.340174	+	0.940362i
$7$	0.900017	+	2.48796i	0.340174	+	0.940362i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.28800	−	2.23089i	−0.388348	−	0.672638i	0.603880	−	0.797076i	$-0.293621\pi$
$11$	−1.28800	−	2.23089i	−0.388348	−	0.672638i	−0.992227	+	0.124437i	$0.960287\pi$
$12$		0			0
$13$	2.82227	+	4.88832i	0.782757	+	1.35578i	0.930330	+	0.366724i	$0.119521\pi$
$13$	2.82227	+	4.88832i	0.782757	+	1.35578i	−0.147573	+	0.989051i	$0.547146\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.57951	+	6.19989i	−0.868158	+	1.50369i	−0.00428199	+	0.999991i	$0.501363\pi$
$17$	−3.57951	+	6.19989i	−0.868158	+	1.50369i	−0.863876	+	0.503704i	$0.831970\pi$
$18$		0			0
$19$	0.636599	+	1.10262i	0.146046	+	0.252959i	0.929763	−	0.368160i	$-0.120012\pi$
$19$	0.636599	+	1.10262i	0.146046	+	0.252959i	−0.783717	+	0.621118i	$0.786679\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.120639	−	0.208952i	0.0251549	−	0.0435696i	−0.853174	−	0.521627i	$-0.825325\pi$
$23$	0.120639	−	0.208952i	0.0251549	−	0.0435696i	0.878329	+	0.478057i	$0.158659\pi$
$24$		0			0
$25$	0.777791	+	1.34717i	0.155558	+	0.269435i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.923571	+	1.59967i	−0.171503	+	0.297051i	−0.938945	−	0.344066i	$-0.888196\pi$
$29$	−0.923571	+	1.59967i	−0.171503	+	0.297051i	0.767443	+	0.641118i	$0.221529\pi$
$30$		0			0
$31$	−2.99103			−0.537205			−0.268602	−	0.963251i	$-0.586562\pi$
$31$	−2.99103			−0.537205			−0.268602	+	0.963251i	$0.586562\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.83401	+	0.862156i	0.817096	+	0.145731i
$36$		0			0
$37$	0.338260	+	0.585884i	0.0556097	+	0.0963188i	0.892490	−	0.451067i	$-0.148956\pi$
$37$	0.338260	+	0.585884i	0.0556097	+	0.0963188i	−0.836880	+	0.547386i	$0.815623\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.733933	+	1.27121i	0.114621	+	0.198529i	0.917628	−	0.397440i	$-0.130101\pi$
$41$	0.733933	+	1.27121i	0.114621	+	0.198529i	−0.803007	+	0.595969i	$0.796768\pi$
$42$		0			0
$43$	4.14269	−	7.17535i	0.631754	−	1.09423i	−0.355439	−	0.934700i	$-0.615669\pi$
$43$	4.14269	−	7.17535i	0.631754	−	1.09423i	0.987193	−	0.159531i	$-0.0509981\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	12.3145			1.79625			0.898124	−	0.439742i	$-0.144930\pi$
$47$	12.3145			1.79625			0.898124	+	0.439742i	$0.144930\pi$
$48$		0			0
$49$	−5.37994	+	4.47842i	−0.768563	+	0.639774i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.35508	+	5.81117i	−0.460856	+	0.798226i	−0.999004	−	0.0446243i	$-0.985791\pi$
$53$	−3.35508	+	5.81117i	−0.460856	+	0.798226i	0.538148	+	0.842851i	$0.319124\pi$
$54$		0			0
$55$	−4.78085			−0.644650
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.08279			−0.271156			−0.135578	−	0.990767i	$-0.543289\pi$
$59$	−2.08279			−0.271156			−0.135578	+	0.990767i	$0.543289\pi$
$60$		0			0
$61$	12.9595			1.65929			0.829644	−	0.558292i	$-0.188543\pi$
$61$	12.9595			1.65929			0.829644	+	0.558292i	$0.188543\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	10.4758			1.29936
$66$		0			0
$67$	−4.83102			−0.590203			−0.295102	−	0.955466i	$-0.595354\pi$
$67$	−4.83102			−0.590203			−0.295102	+	0.955466i	$0.595354\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.53621			0.182314			0.0911572	−	0.995837i	$-0.470943\pi$
$71$	1.53621			0.182314			0.0911572	+	0.995837i	$0.470943\pi$
$72$		0			0
$73$	−6.55954	+	11.3615i	−0.767736	+	1.32976i	0.171052	+	0.985262i	$0.445283\pi$
$73$	−6.55954	+	11.3615i	−0.767736	+	1.32976i	−0.938788	+	0.344496i	$0.888050\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.39115	−	5.21235i	0.500418	−	0.594002i
$78$		0			0
$79$	−3.72018			−0.418553			−0.209277	−	0.977856i	$-0.567111\pi$
$79$	−3.72018			−0.418553			−0.209277	+	0.977856i	$0.567111\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.00173	−	5.19915i	0.329483	−	0.570681i	−0.652926	−	0.757421i	$-0.726459\pi$
$83$	3.00173	−	5.19915i	0.329483	−	0.570681i	0.982409	+	0.186740i	$0.0597922\pi$
$84$		0			0
$85$	6.64326	+	11.5065i	0.720563	+	1.24805i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.60349	−	11.4376i	−0.699968	−	1.21238i	−0.968477	−	0.249103i	$-0.919864\pi$
$89$	−6.60349	−	11.4376i	−0.699968	−	1.21238i	0.268509	−	0.963277i	$-0.413469\pi$
$90$		0			0
$91$	−9.62187	+	11.4213i	−1.00865	+	1.19728i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.36294			0.242433
$96$		0			0
$97$	6.40860	−	11.1000i	0.650695	−	1.12704i	−0.332260	−	0.943188i	$-0.607811\pi$
$97$	6.40860	−	11.1000i	0.650695	−	1.12704i	0.982955	−	0.183848i	$-0.0588556\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.10066	+	10.5667i	0.607039	+	1.05142i	0.991726	+	0.128375i	$0.0409760\pi$
$101$	6.10066	+	10.5667i	0.607039	+	1.05142i	−0.384687	+	0.923047i	$0.625691\pi$
$102$		0			0
$103$	−6.82163	+	11.8154i	−0.672155	+	1.16421i	0.305137	+	0.952309i	$0.401298\pi$
$103$	−6.82163	+	11.8154i	−0.672155	+	1.16421i	−0.977292	+	0.211898i	$0.932036\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.48002	+	11.2237i	0.626448	+	1.08504i	0.988259	+	0.152788i	$0.0488251\pi$
$107$	6.48002	+	11.2237i	0.626448	+	1.08504i	−0.361811	+	0.932251i	$0.617842\pi$
$108$		0			0
$109$	7.70089	−	13.3383i	0.737612	−	1.27758i	−0.215956	−	0.976403i	$-0.569287\pi$
$109$	7.70089	−	13.3383i	0.737612	−	1.27758i	0.953568	−	0.301178i	$-0.0973799\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.73446	+	13.3965i	0.727597	+	1.26023i	0.957896	+	0.287115i	$0.0926961\pi$
$113$	7.73446	+	13.3965i	0.727597	+	1.26023i	−0.230299	+	0.973120i	$0.573971\pi$
$114$		0			0
$115$	−0.223895	−	0.387797i	−0.0208783	−	0.0361623i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−18.6467	−	3.32569i	−1.70934	−	0.304865i
$120$		0			0
$121$	2.18209	−	3.77949i	0.198372	−	0.343590i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.1666			1.08821
$126$		0			0
$127$	−3.19404			−0.283425			−0.141713	−	0.989908i	$-0.545261\pi$
$127$	−3.19404			−0.283425			−0.141713	+	0.989908i	$0.545261\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.04338	−	12.1995i	0.615383	−	1.06587i	−0.374935	−	0.927051i	$-0.622335\pi$
$131$	7.04338	−	12.1995i	0.615383	−	1.06587i	0.990317	−	0.138823i	$-0.0443318\pi$
$132$		0			0
$133$	−2.17033	+	2.57621i	−0.188192	+	0.223386i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.84818	+	11.8614i	0.585079	+	1.01339i	0.994866	+	0.101206i	$0.0322700\pi$
$137$	6.84818	+	11.8614i	0.585079	+	1.01339i	−0.409786	+	0.912182i	$0.634397\pi$
$138$		0			0
$139$	−4.94131	−	8.55859i	−0.419116	−	0.725931i	0.576735	−	0.816932i	$-0.304327\pi$
$139$	−4.94131	−	8.55859i	−0.419116	−	0.725931i	−0.995851	+	0.0910010i	$0.970993\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.27019	−	12.5923i	0.607964	−	1.05302i
$144$		0			0
$145$	1.71407	+	2.96885i	0.142346	+	0.246550i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.96015	+	3.39507i	−0.160581	+	0.278135i	−0.935077	−	0.354444i	$-0.884670\pi$
$149$	−1.96015	+	3.39507i	−0.160581	+	0.278135i	0.774496	+	0.632579i	$0.218004\pi$
$150$		0			0
$151$	−9.78920	−	16.9554i	−0.796634	−	1.37981i	−0.921796	−	0.387674i	$-0.873278\pi$
$151$	−9.78920	−	16.9554i	−0.796634	−	1.37981i	0.125162	−	0.992136i	$-0.460055\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.77555	+	4.80739i	−0.222937	+	0.386139i
$156$		0			0
$157$	14.7927			1.18059			0.590295	−	0.807188i	$-0.299012\pi$
$157$	14.7927			1.18059			0.590295	+	0.807188i	$0.299012\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.628443	+	0.112084i	0.0495282	+	0.00883347i
$162$		0			0
$163$	7.54686	+	13.0715i	0.591116	+	1.02384i	0.994082	+	0.108628i	$0.0346456\pi$
$163$	7.54686	+	13.0715i	0.591116	+	1.02384i	−0.402967	+	0.915215i	$0.632021\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.92946	−	3.34192i	−0.149306	−	0.258605i	0.781665	−	0.623698i	$-0.214371\pi$
$167$	−1.92946	−	3.34192i	−0.149306	−	0.258605i	−0.930971	+	0.365093i	$0.881037\pi$
$168$		0			0
$169$	−9.43043	+	16.3340i	−0.725418	+	1.25646i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.651571			−0.0495380			−0.0247690	−	0.999693i	$-0.507885\pi$
$173$	−0.651571			−0.0495380			−0.0247690	+	0.999693i	$0.507885\pi$
$174$		0			0
$175$	−2.65170	+	3.14760i	−0.200449	+	0.237936i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−10.9059	+	18.8896i	−0.815145	+	1.41187i	0.0940781	+	0.995565i	$0.470010\pi$
$179$	−10.9059	+	18.8896i	−0.815145	+	1.41187i	−0.909223	+	0.416308i	$0.863324\pi$
$180$		0			0
$181$	−25.0338			−1.86075			−0.930374	−	0.366613i	$-0.880517\pi$
$181$	−25.0338			−1.86075			−0.930374	+	0.366613i	$0.880517\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.25556			0.0923109
$186$		0			0
$187$	18.4417			1.34859
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.66073			−0.626668			−0.313334	−	0.949643i	$-0.601446\pi$
$191$	−8.66073			−0.626668			−0.313334	+	0.949643i	$0.601446\pi$
$192$		0			0
$193$	1.61664			0.116369			0.0581843	−	0.998306i	$-0.481469\pi$
$193$	1.61664			0.116369			0.0581843	+	0.998306i	$0.481469\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.7746			−0.767659			−0.383829	−	0.923404i	$-0.625395\pi$
$197$	−10.7746			−0.767659			−0.383829	+	0.923404i	$0.625395\pi$
$198$		0			0
$199$	2.38768	−	4.13558i	0.169258	−	0.293163i	−0.768901	−	0.639368i	$-0.779196\pi$
$199$	2.38768	−	4.13558i	0.169258	−	0.293163i	0.938159	+	0.346204i	$0.112530\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.81115	−	0.858080i	−0.337677	−	0.0602254i
$204$		0			0
$205$	2.72423			0.190269
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.63988	−	2.84036i	0.113433	−	0.196472i
$210$		0			0
$211$	2.42787	+	4.20520i	0.167142	+	0.289498i	0.937414	−	0.348218i	$-0.113213\pi$
$211$	2.42787	+	4.20520i	0.167142	+	0.289498i	−0.770272	+	0.637715i	$0.779880\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−7.68848	−	13.3168i	−0.524350	−	0.908200i
$216$		0			0
$217$	−2.69198	−	7.44158i	−0.182743	−	0.505167i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−40.4094			−2.71823
$222$		0			0
$223$	3.86187	−	6.68896i	0.258610	−	0.447926i	−0.707260	−	0.706954i	$-0.750069\pi$
$223$	3.86187	−	6.68896i	0.258610	−	0.447926i	0.965870	+	0.259028i	$0.0834021\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.97457	−	12.0803i	−0.462919	−	0.801799i	0.536186	−	0.844100i	$-0.319864\pi$
$227$	−6.97457	−	12.0803i	−0.462919	−	0.801799i	−0.999105	+	0.0423011i	$0.986531\pi$
$228$		0			0
$229$	−0.800136	+	1.38588i	−0.0528745	+	0.0915812i	−0.891251	−	0.453510i	$-0.850172\pi$
$229$	−0.800136	+	1.38588i	−0.0528745	+	0.0915812i	0.838377	+	0.545091i	$0.183505\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.69939	−	6.40753i	−0.242355	−	0.419771i	0.719030	−	0.694979i	$-0.244587\pi$
$233$	−3.69939	−	6.40753i	−0.242355	−	0.419771i	−0.961385	+	0.275208i	$0.911253\pi$
$234$		0			0
$235$	11.4273	−	19.7926i	0.745434	−	1.29113i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.25117	+	2.16709i	0.0809316	+	0.140178i	0.903650	−	0.428271i	$-0.140877\pi$
$239$	1.25117	+	2.16709i	0.0809316	+	0.140178i	−0.822719	+	0.568449i	$0.807544\pi$
$240$		0			0
$241$	−2.12148	−	3.67452i	−0.136657	−	0.236697i	0.789572	−	0.613658i	$-0.210302\pi$
$241$	−2.12148	−	3.67452i	−0.136657	−	0.236697i	−0.926229	+	0.376961i	$0.876969\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.20567	+	12.8028i	0.140915	+	0.817940i
$246$		0			0
$247$	−3.59331	+	6.22379i	−0.228637	+	0.396010i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13.5381			0.854516			0.427258	−	0.904130i	$-0.359480\pi$
$251$	13.5381			0.854516			0.427258	+	0.904130i	$0.359480\pi$
$252$		0			0
$253$	−0.621532			−0.0390754
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.07747	+	5.33034i	−0.191968	+	0.332497i	−0.945902	−	0.324452i	$-0.894820\pi$
$257$	−3.07747	+	5.33034i	−0.191968	+	0.332497i	0.753935	+	0.656949i	$0.228153\pi$
$258$		0			0
$259$	−1.15322	+	1.36889i	−0.0716576	+	0.0850584i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.6706	−	21.9460i	−0.781300	−	1.35325i	−0.931185	−	0.364547i	$-0.881224\pi$
$263$	−12.6706	−	21.9460i	−0.781300	−	1.35325i	0.149885	−	0.988703i	$-0.452110\pi$
$264$		0			0
$265$	6.22675	+	10.7850i	0.382506	+	0.662520i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.42092	−	9.38931i	0.330519	−	0.572476i	−0.652095	−	0.758138i	$-0.726109\pi$
$269$	5.42092	−	9.38931i	0.330519	−	0.572476i	0.982614	+	0.185662i	$0.0594428\pi$
$270$		0			0
$271$	−15.0184	−	26.0127i	−0.912306	−	1.58016i	−0.810799	−	0.585325i	$-0.800967\pi$
$271$	−15.0184	−	26.0127i	−0.912306	−	1.58016i	−0.101507	−	0.994835i	$-0.532366\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.00360	−	3.47033i	0.120821	−	0.209269i
$276$		0			0
$277$	−9.88147	−	17.1152i	−0.593720	−	1.02835i	−0.993726	−	0.111841i	$-0.964325\pi$
$277$	−9.88147	−	17.1152i	−0.593720	−	1.02835i	0.400006	−	0.916513i	$-0.369008\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.98596	−	6.90388i	0.237782	−	0.411851i	−0.722295	−	0.691585i	$-0.756913\pi$
$281$	3.98596	−	6.90388i	0.237782	−	0.411851i	0.960078	+	0.279734i	$0.0902462\pi$
$282$		0			0
$283$	23.2127			1.37985			0.689926	−	0.723880i	$-0.257643\pi$
$283$	23.2127			1.37985			0.689926	+	0.723880i	$0.257643\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.50217	+	2.97011i	−0.147698	+	0.175320i
$288$		0			0
$289$	−17.1258	−	29.6627i	−1.00740	−	1.74486i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−11.8556	−	20.5345i	−0.692612	−	1.19964i	−0.970979	−	0.239164i	$-0.923126\pi$
$293$	−11.8556	−	20.5345i	−0.692612	−	1.19964i	0.278367	−	0.960475i	$-0.410207\pi$
$294$		0			0
$295$	−1.93274	+	3.34760i	−0.112528	+	0.194905i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.36190			0.0787607
$300$		0			0
$301$	21.5805	+	3.84893i	1.24388	+	0.221849i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.0258	−	20.8293i	0.688597	−	1.19268i
$306$		0			0
$307$	3.87810			0.221335			0.110668	−	0.993857i	$-0.464701\pi$
$307$	3.87810			0.221335			0.110668	+	0.993857i	$0.464701\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.92439			0.392646			0.196323	−	0.980539i	$-0.437100\pi$
$311$	6.92439			0.392646			0.196323	+	0.980539i	$0.437100\pi$
$312$		0			0
$313$	30.2313			1.70878			0.854388	−	0.519636i	$-0.173932\pi$
$313$	30.2313			1.70878			0.854388	+	0.519636i	$0.173932\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.37399			−0.526496			−0.263248	−	0.964728i	$-0.584794\pi$
$317$	−9.37399			−0.526496			−0.263248	+	0.964728i	$0.584794\pi$
$318$		0			0
$319$	4.75825			0.266411
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−9.11484			−0.507163
$324$		0			0
$325$	−4.39027	+	7.60418i	−0.243529	+	0.421804i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	11.0832	+	30.6379i	0.611038	+	1.68912i
$330$		0			0
$331$	27.5441			1.51396			0.756979	−	0.653439i	$-0.226674\pi$
$331$	27.5441			1.51396			0.756979	+	0.653439i	$0.226674\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.48298	+	7.76475i	−0.244931	+	0.424234i
$336$		0			0
$337$	−3.41673	−	5.91796i	−0.186121	−	0.322372i	0.757832	−	0.652449i	$-0.226258\pi$
$337$	−3.41673	−	5.91796i	−0.186121	−	0.322372i	−0.943954	+	0.330078i	$0.892925\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.85246	+	6.67266i	0.208622	+	0.361345i
$342$		0			0
$343$	−15.9842	−	9.35445i	−0.863065	−	0.505093i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.1919			−1.08396			−0.541979	−	0.840392i	$-0.682325\pi$
$347$	−20.1919			−1.08396			−0.541979	+	0.840392i	$0.682325\pi$
$348$		0			0
$349$	−4.25154	+	7.36388i	−0.227580	+	0.394180i	−0.957090	−	0.289790i	$-0.906415\pi$
$349$	−4.25154	+	7.36388i	−0.227580	+	0.394180i	0.729511	+	0.683970i	$0.239748\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.35452	+	4.07815i	0.125318	+	0.217058i	0.921857	−	0.387529i	$-0.126671\pi$
$353$	2.35452	+	4.07815i	0.125318	+	0.217058i	−0.796539	+	0.604587i	$0.793338\pi$
$354$		0			0
$355$	1.42554	−	2.46910i	0.0756596	−	0.131046i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.03357	−	10.4504i	−0.318440	−	0.551554i	0.661723	−	0.749748i	$-0.269825\pi$
$359$	−6.03357	−	10.4504i	−0.318440	−	0.551554i	−0.980163	+	0.198195i	$0.936492\pi$
$360$		0			0
$361$	8.68948	−	15.0506i	0.457341	−	0.792138i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	12.1739	+	21.0859i	0.637213	+	1.10369i
$366$		0			0
$367$	−0.480356	−	0.832001i	−0.0250744	−	0.0434301i	0.853216	−	0.521558i	$-0.174649\pi$
$367$	−0.480356	−	0.832001i	−0.0250744	−	0.0434301i	−0.878290	+	0.478128i	$0.841316\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−17.4776	−	3.11717i	−0.907393	−	0.161836i
$372$		0			0
$373$	3.52499	−	6.10547i	0.182517	−	0.316129i	−0.760220	−	0.649666i	$-0.774909\pi$
$373$	3.52499	−	6.10547i	0.182517	−	0.316129i	0.942737	+	0.333537i	$0.108242\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.4263			−0.536980
$378$		0			0
$379$	−37.1330			−1.90739			−0.953697	−	0.300769i	$-0.902757\pi$
$379$	−37.1330			−1.90739			−0.953697	+	0.300769i	$0.902757\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.0988	−	27.8839i	0.822608	−	1.42480i	−0.0811254	−	0.996704i	$-0.525851\pi$
$383$	16.0988	−	27.8839i	0.822608	−	1.42480i	0.903734	−	0.428095i	$-0.140815\pi$
$384$		0			0
$385$	−4.30285	−	11.8946i	−0.219293	−	0.606204i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.8713	−	22.2937i	−0.652600	−	1.13034i	−0.982490	−	0.186317i	$-0.940345\pi$
$389$	−12.8713	−	22.2937i	−0.652600	−	1.13034i	0.329889	−	0.944020i	$-0.392989\pi$
$390$		0			0
$391$	0.863654	+	1.49589i	0.0436769	+	0.0756506i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.45217	+	5.97933i	−0.173697	+	0.300853i
$396$		0			0
$397$	9.44903	+	16.3662i	0.474233	+	0.821396i	0.999565	−	0.0295016i	$-0.00939202\pi$
$397$	9.44903	+	16.3662i	0.474233	+	0.821396i	−0.525332	+	0.850898i	$0.676059\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.60193	−	13.1669i	0.379622	−	0.657525i	−0.611385	−	0.791333i	$-0.709387\pi$
$401$	7.60193	−	13.1669i	0.379622	−	0.657525i	0.991007	+	0.133808i	$0.0427206\pi$
$402$		0			0
$403$	−8.44150	−	14.6211i	−0.420501	−	0.728329i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.871362	−	1.50924i	0.0431918	−	0.0748104i
$408$		0			0
$409$	−29.9458			−1.48073			−0.740363	−	0.672207i	$-0.765346\pi$
$409$	−29.9458			−1.48073			−0.740363	+	0.672207i	$0.765346\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.87454	−	5.18191i	−0.0922403	−	0.254985i
$414$		0			0
$415$	−5.57096	−	9.64918i	−0.273468	−	0.473660i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.2660	+	21.2453i	0.599231	+	1.03790i	0.992935	+	0.118661i	$0.0378603\pi$
$419$	12.2660	+	21.2453i	0.599231	+	1.03790i	−0.393704	+	0.919237i	$0.628806\pi$
$420$		0			0
$421$	−2.37791	+	4.11866i	−0.115892	+	0.200731i	−0.918136	−	0.396265i	$-0.870306\pi$
$421$	−2.37791	+	4.11866i	−0.115892	+	0.200731i	0.802244	+	0.596996i	$0.203639\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.1364			−0.540197
$426$		0			0
$427$	11.6637	+	32.2427i	0.564448	+	1.56033i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.36446	+	2.36331i	−0.0657237	+	0.113837i	−0.897015	−	0.442000i	$-0.854269\pi$
$431$	−1.36446	+	2.36331i	−0.0657237	+	0.113837i	0.831291	+	0.555837i	$0.187602\pi$
$432$		0			0
$433$	14.5592			0.699672			0.349836	−	0.936811i	$-0.386237\pi$
$433$	14.5592			0.699672			0.349836	+	0.936811i	$0.386237\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.307194			0.0146951
$438$		0			0
$439$	−2.88131			−0.137517			−0.0687587	−	0.997633i	$-0.521904\pi$
$439$	−2.88131			−0.137517			−0.0687587	+	0.997633i	$0.521904\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−24.9731			−1.18651			−0.593254	−	0.805016i	$-0.702157\pi$
$443$	−24.9731			−1.18651			−0.593254	+	0.805016i	$0.702157\pi$
$444$		0			0
$445$	−24.5110			−1.16193
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.99154			0.141180			0.0705898	−	0.997505i	$-0.477512\pi$
$449$	2.99154			0.141180			0.0705898	+	0.997505i	$0.477512\pi$
$450$		0			0
$451$	1.89062	−	3.27464i	0.0890257	−	0.154197i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	9.42838	+	26.0634i	0.442009	+	1.22187i
$456$		0			0
$457$	−25.6171			−1.19832			−0.599158	−	0.800631i	$-0.704498\pi$
$457$	−25.6171			−1.19832			−0.599158	+	0.800631i	$0.704498\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.45759	−	11.1849i	0.300760	−	0.520931i	−0.675548	−	0.737316i	$-0.736093\pi$
$461$	6.45759	−	11.1849i	0.300760	−	0.520931i	0.976308	+	0.216384i	$0.0694264\pi$
$462$		0			0
$463$	−12.2457	−	21.2102i	−0.569108	−	0.985724i	−0.996654	−	0.0817305i	$-0.973955\pi$
$463$	−12.2457	−	21.2102i	−0.569108	−	0.985724i	0.427547	−	0.903993i	$-0.359378\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.4087	+	18.0283i	0.481655	+	0.834251i	0.999778	−	0.0210550i	$-0.00670252\pi$
$467$	10.4087	+	18.0283i	0.481655	+	0.834251i	−0.518123	+	0.855306i	$0.673369\pi$
$468$		0			0
$469$	−4.34800	−	12.0194i	−0.200772	−	0.555005i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−21.3432			−0.981362
$474$		0			0
$475$	−0.990281	+	1.71522i	−0.0454372	+	0.0786996i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.7436	+	23.8047i	0.627962	+	1.08766i	0.987960	+	0.154709i	$0.0494441\pi$
$479$	13.7436	+	23.8047i	0.627962	+	1.08766i	−0.359998	+	0.932953i	$0.617223\pi$
$480$		0			0
$481$	−1.90932	+	3.30705i	−0.0870577	+	0.150788i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−11.8938	−	20.6007i	−0.540070	−	0.935429i
$486$		0			0
$487$	−6.32927	+	10.9626i	−0.286807	+	0.496763i	−0.973046	−	0.230613i	$-0.925927\pi$
$487$	−6.32927	+	10.9626i	−0.286807	+	0.496763i	0.686239	+	0.727376i	$0.259260\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.40618	+	2.43557i	0.0634598	+	0.109916i	0.896010	−	0.444034i	$-0.146453\pi$
$491$	1.40618	+	2.43557i	0.0634598	+	0.109916i	−0.832550	+	0.553950i	$0.813120\pi$
$492$		0			0
$493$	−6.61186	−	11.4521i	−0.297783	−	0.515776i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.38261	+	3.82203i	0.0620187	+	0.171442i
$498$		0			0
$499$	2.12103	−	3.67373i	0.0949502	−	0.164459i	−0.814638	−	0.579970i	$-0.803064\pi$
$499$	2.12103	−	3.67373i	0.0949502	−	0.164459i	0.909588	+	0.415512i	$0.136397\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−22.2162			−0.990570			−0.495285	−	0.868730i	$-0.664936\pi$
$503$	−22.2162			−0.990570			−0.495285	+	0.868730i	$0.664936\pi$
$504$		0			0
$505$	22.6446			1.00767
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.42735	+	4.20429i	−0.107590	+	0.186352i	−0.914794	−	0.403922i	$-0.867647\pi$
$509$	−2.42735	+	4.20429i	−0.107590	+	0.186352i	0.807203	+	0.590273i	$0.200980\pi$
$510$		0			0
$511$	−34.1706	−	6.09440i	−1.51162	−	0.269601i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.6604	+	21.9284i	0.557882	+	0.966280i
$516$		0			0
$517$	−15.8611	−	27.4722i	−0.697569	−	1.20823i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.92316	+	13.7233i	−0.347120	+	0.601229i	−0.985737	−	0.168296i	$-0.946174\pi$
$521$	−7.92316	+	13.7233i	−0.347120	+	0.601229i	0.638617	+	0.769525i	$0.279507\pi$
$522$		0			0
$523$	10.7605	+	18.6377i	0.470524	+	0.814972i	0.999432	−	0.0337078i	$-0.0107316\pi$
$523$	10.7605	+	18.6377i	0.470524	+	0.814972i	−0.528908	+	0.848679i	$0.677398\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.7064	−	18.5441i	0.466379	−	0.807792i
$528$		0			0
$529$	11.4709	+	19.8682i	0.498734	+	0.863833i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.14271	+	7.17539i	−0.179441	+	0.310801i
$534$		0			0
$535$	24.0527			1.03989
$536$		0			0
$537$		0			0
$538$		0			0
$539$	16.9202	+	6.23382i	0.728806	+	0.268510i
$540$		0			0
$541$	7.55977	+	13.0939i	0.325020	+	0.562951i	0.981516	−	0.191378i	$-0.0612957\pi$
$541$	7.55977	+	13.0939i	0.325020	+	0.562951i	−0.656497	+	0.754329i	$0.727962\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−14.2922	−	24.7548i	−0.612211	−	1.06038i
$546$		0			0
$547$	−19.4532	+	33.6939i	−0.831757	+	1.44065i	0.0648863	+	0.997893i	$0.479332\pi$
$547$	−19.4532	+	33.6939i	−0.831757	+	1.44065i	−0.896644	+	0.442753i	$0.854002\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.35177			−0.100189
$552$		0			0
$553$	−3.34823	−	9.25568i	−0.142381	−	0.393592i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.37036	−	9.30173i	0.227549	−	0.394127i	−0.729532	−	0.683947i	$-0.760262\pi$
$557$	5.37036	−	9.30173i	0.227549	−	0.394127i	0.957081	+	0.289820i	$0.0935954\pi$
$558$		0			0
$559$	46.7672			1.97804
$560$		0			0
$561$		0			0
$562$		0			0
$563$	23.4760			0.989394			0.494697	−	0.869066i	$-0.335279\pi$
$563$	23.4760			0.989394			0.494697	+	0.869066i	$0.335279\pi$
$564$		0			0
$565$	28.7090			1.20780
$566$		0			0
$567$		0			0
$568$		0			0
$569$	37.9361			1.59037			0.795183	−	0.606370i	$-0.207375\pi$
$569$	37.9361			1.59037			0.795183	+	0.606370i	$0.207375\pi$
$570$		0			0
$571$	−4.31630			−0.180632			−0.0903158	−	0.995913i	$-0.528788\pi$
$571$	−4.31630			−0.180632			−0.0903158	+	0.995913i	$0.528788\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.375326			0.0156522
$576$		0			0
$577$	−5.05923	+	8.76284i	−0.210618	+	0.364802i	−0.951908	−	0.306383i	$-0.900881\pi$
$577$	−5.05923	+	8.76284i	−0.210618	+	0.364802i	0.741290	+	0.671185i	$0.234214\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	15.6369	+	2.78888i	0.648729	+	0.115702i
$582$		0			0
$583$	17.2854			0.715890
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.10992	−	7.11859i	0.169635	−	0.293816i	−0.768657	−	0.639661i	$-0.779075\pi$
$587$	4.10992	−	7.11859i	0.169635	−	0.293816i	0.938291	+	0.345846i	$0.112408\pi$
$588$		0			0
$589$	−1.90409	−	3.29797i	−0.0784565	−	0.135891i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−21.8434	−	37.8339i	−0.897002	−	1.55365i	−0.831307	−	0.555814i	$-0.812407\pi$
$593$	−21.8434	−	37.8339i	−0.897002	−	1.55365i	−0.0656957	−	0.997840i	$-0.520927\pi$
$594$		0			0
$595$	−22.6486	+	26.8842i	−0.928504	+	1.10215i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.2789			0.624280			0.312140	−	0.950036i	$-0.398954\pi$
$599$	15.2789			0.624280			0.312140	+	0.950036i	$0.398954\pi$
$600$		0			0
$601$	7.65696	−	13.2622i	0.312334	−	0.540978i	−0.666533	−	0.745475i	$-0.732223\pi$
$601$	7.65696	−	13.2622i	0.312334	−	0.540978i	0.978867	+	0.204497i	$0.0655559\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.04977	−	7.01441i	−0.164647	−	0.285176i
$606$		0			0
$607$	1.33490	−	2.31212i	0.0541821	−	0.0938461i	−0.837662	−	0.546189i	$-0.816078\pi$
$607$	1.33490	−	2.31212i	0.0541821	−	0.0938461i	0.891844	+	0.452342i	$0.149412\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	34.7547	+	60.1970i	1.40603	+	2.43531i
$612$		0			0
$613$	−13.5875	+	23.5343i	−0.548796	+	0.950542i	0.449562	+	0.893249i	$0.351580\pi$
$613$	−13.5875	+	23.5343i	−0.548796	+	0.950542i	−0.998357	+	0.0572929i	$0.981753\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17.6058	+	30.4942i	0.708785	+	1.22765i	0.965308	+	0.261113i	$0.0840895\pi$
$617$	17.6058	+	30.4942i	0.708785	+	1.22765i	−0.256524	+	0.966538i	$0.582577\pi$
$618$		0			0
$619$	15.6340	+	27.0790i	0.628385	+	1.08840i	0.987876	+	0.155247i	$0.0496172\pi$
$619$	15.6340	+	27.0790i	0.628385	+	1.08840i	−0.359490	+	0.933149i	$0.617049\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	22.5130	−	26.7233i	0.901966	−	1.07064i
$624$		0			0
$625$	7.40113	−	12.8191i	0.296045	−	0.512765i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.84322			−0.193112
$630$		0			0
$631$	15.5090			0.617403			0.308702	−	0.951159i	$-0.400106\pi$
$631$	15.5090			0.617403			0.308702	+	0.951159i	$0.400106\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.96393	+	5.13369i	−0.117620	+	0.203724i
$636$		0			0
$637$	−37.0756	−	13.6595i	−1.46899	−	0.541210i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.7655	−	29.0387i	−0.662198	−	1.14696i	−0.980037	−	0.198816i	$-0.936290\pi$
$641$	−16.7655	−	29.0387i	−0.662198	−	1.14696i	0.317839	−	0.948145i	$-0.397043\pi$
$642$		0			0
$643$	−10.2721	−	17.7918i	−0.405093	−	0.701641i	0.589239	−	0.807958i	$-0.299427\pi$
$643$	−10.2721	−	17.7918i	−0.405093	−	0.701641i	−0.994332	+	0.106317i	$0.966094\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.8855	−	29.2465i	0.663836	−	1.14980i	−0.315763	−	0.948838i	$-0.602261\pi$
$647$	16.8855	−	29.2465i	0.663836	−	1.14980i	0.979599	−	0.200960i	$-0.0644061\pi$
$648$		0			0
$649$	2.68264	+	4.64647i	0.105303	+	0.182390i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.00576	−	15.5984i	0.352423	−	0.610414i	−0.634251	−	0.773127i	$-0.718691\pi$
$653$	9.00576	−	15.5984i	0.352423	−	0.610414i	0.986673	+	0.162714i	$0.0520247\pi$
$654$		0			0
$655$	−13.0719	−	22.6412i	−0.510762	−	0.884665i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.42710	+	2.47180i	−0.0555918	+	0.0962878i	−0.892482	−	0.451083i	$-0.851038\pi$
$659$	−1.42710	+	2.47180i	−0.0555918	+	0.0962878i	0.836890	+	0.547371i	$0.184371\pi$
$660$		0			0
$661$	14.0549			0.546673			0.273337	−	0.961918i	$-0.411873\pi$
$661$	14.0549			0.546673			0.273337	+	0.961918i	$0.411873\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.12669	+	5.87892i	0.0824695	+	0.227975i
$666$		0			0
$667$	0.222837	+	0.385964i	0.00862827	+	0.0149446i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−16.6918	−	28.9111i	−0.644381	−	1.11610i
$672$		0			0
$673$	−7.54157	+	13.0624i	−0.290706	+	0.503518i	−0.973977	−	0.226647i	$-0.927223\pi$
$673$	−7.54157	+	13.0624i	−0.290706	+	0.503518i	0.683271	+	0.730165i	$0.260557\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	36.2187			1.39200			0.695998	−	0.718043i	$-0.254962\pi$
$677$	36.2187			1.39200			0.695998	+	0.718043i	$0.254962\pi$
$678$		0			0
$679$	33.3843	+	5.95417i	1.28117	+	0.228500i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.84350	+	15.3174i	−0.338387	+	0.586104i	−0.984130	−	0.177452i	$-0.943215\pi$
$683$	−8.84350	+	15.3174i	−0.338387	+	0.586104i	0.645742	+	0.763555i	$0.276548\pi$
$684$		0			0
$685$	25.4193			0.971220
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−37.8758			−1.44295
$690$		0			0
$691$	22.4097			0.852506			0.426253	−	0.904604i	$-0.359833\pi$
$691$	22.4097			0.852506			0.426253	+	0.904604i	$0.359833\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−18.3413			−0.695725
$696$		0			0
$697$	−10.5085			−0.398037
$698$		0			0
$699$		0			0
$700$		0			0
$701$	31.1776			1.17756			0.588781	−	0.808293i	$-0.299608\pi$
$701$	31.1776			1.17756			0.588781	+	0.808293i	$0.299608\pi$
$702$		0			0
$703$	−0.430672	+	0.745946i	−0.0162431	+	0.0281339i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−20.7988	+	24.6884i	−0.782218	+	0.928503i
$708$		0			0
$709$	−8.04985			−0.302318			−0.151159	−	0.988509i	$-0.548301\pi$
$709$	−8.04985			−0.302318			−0.151159	+	0.988509i	$0.548301\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.360834	+	0.624982i	−0.0135133	+	0.0234058i
$714$		0			0
$715$	−13.4929	−	23.3703i	−0.504604	−	0.874000i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.9980	+	36.3696i	0.783093	+	1.35636i	0.930132	+	0.367226i	$0.119692\pi$
$719$	20.9980	+	36.3696i	0.783093	+	1.35636i	−0.147039	+	0.989131i	$0.546974\pi$
$720$		0			0
$721$	−35.5359	−	6.33791i	−1.32343	−	0.236036i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.87338			−0.106715
$726$		0			0
$727$	0.668774	−	1.15835i	0.0248035	−	0.0429609i	−0.853357	−	0.521327i	$-0.825437\pi$
$727$	0.668774	−	1.15835i	0.0248035	−	0.0429609i	0.878161	+	0.478366i	$0.158771\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	29.6576	+	51.3684i	1.09693	+	1.89993i
$732$		0			0
$733$	−14.7374	+	25.5260i	−0.544340	+	0.942824i	0.454308	+	0.890845i	$0.349886\pi$
$733$	−14.7374	+	25.5260i	−0.544340	+	0.942824i	−0.998648	+	0.0519798i	$0.983447\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.22238	+	10.7775i	0.229204	+	0.396993i
$738$		0			0
$739$	9.52146	−	16.4916i	0.350252	−	0.606655i	−0.636041	−	0.771655i	$-0.719429\pi$
$739$	9.52146	−	16.4916i	0.350252	−	0.606655i	0.986294	+	0.165000i	$0.0527625\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.6613	−	37.5185i	−0.794676	−	1.37642i	−0.923045	−	0.384693i	$-0.874307\pi$
$743$	−21.6613	−	37.5185i	−0.794676	−	1.37642i	0.128369	−	0.991726i	$-0.459026\pi$
$744$		0			0
$745$	3.63786	+	6.30097i	0.133281	+	0.230850i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−22.0921	+	26.2236i	−0.807228	+	0.958190i
$750$		0			0
$751$	−17.4381	+	30.2037i	−0.636327	+	1.10215i	0.349906	+	0.936785i	$0.386214\pi$
$751$	−17.4381	+	30.2037i	−0.636327	+	1.10215i	−0.986232	+	0.165365i	$0.947120\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−36.3358			−1.32240
$756$		0			0
$757$	8.67255			0.315209			0.157605	−	0.987502i	$-0.449623\pi$
$757$	8.67255			0.315209			0.157605	+	0.987502i	$0.449623\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.74489	+	4.75428i	−0.0995021	+	0.172343i	−0.911479	−	0.411347i	$-0.865058\pi$
$761$	−2.74489	+	4.75428i	−0.0995021	+	0.172343i	0.811977	+	0.583690i	$0.198392\pi$
$762$		0			0
$763$	40.1163	+	7.15482i	1.45231	+	0.259022i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.87819	−	10.1813i	−0.212249	−	0.367627i
$768$		0			0
$769$	1.81365	+	3.14134i	0.0654021	+	0.113280i	0.896872	−	0.442290i	$-0.145834\pi$
$769$	1.81365	+	3.14134i	0.0654021	+	0.113280i	−0.831470	+	0.555569i	$0.812500\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.96717	−	12.0675i	0.250592	−	0.434037i	−0.713097	−	0.701065i	$-0.752708\pi$
$773$	6.96717	−	12.0675i	0.250592	−	0.434037i	0.963689	+	0.267028i	$0.0860415\pi$
$774$		0			0
$775$	−2.32640	−	4.02944i	−0.0835666	−	0.144742i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.934441	+	1.61850i	−0.0334798	+	0.0579888i
$780$		0			0
$781$	−1.97864	−	3.42711i	−0.0708014	−	0.122632i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	13.7270	−	23.7759i	0.489939	−	0.848599i
$786$		0			0
$787$	17.5785			0.626604			0.313302	−	0.949654i	$-0.398565\pi$
$787$	17.5785			0.626604			0.313302	+	0.949654i	$0.398565\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−26.3688	+	31.3001i	−0.937567	+	1.11290i
$792$		0			0
$793$	36.5751	+	63.3499i	1.29882	+	2.24962i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.57971	−	9.66434i	−0.197644	−	0.342329i	0.750120	−	0.661301i	$-0.229996\pi$
$797$	−5.57971	−	9.66434i	−0.197644	−	0.342329i	−0.947764	+	0.318973i	$0.896662\pi$
$798$		0			0
$799$	−44.0797	+	76.3483i	−1.55943	+	2.70101i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	33.7949			1.19259
$804$		0			0
$805$	0.763317	−	0.906067i	0.0269034	−	0.0319347i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−14.3481	+	24.8517i	−0.504453	+	0.873738i	0.495534	+	0.868589i	$0.334972\pi$
$809$	−14.3481	+	24.8517i	−0.504453	+	0.873738i	−0.999987	+	0.00514935i	$0.998361\pi$
$810$		0			0
$811$	47.1695			1.65635			0.828173	−	0.560473i	$-0.189380\pi$
$811$	47.1695			1.65635			0.828173	+	0.560473i	$0.189380\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	28.0126			0.981240
$816$		0			0
$817$	10.5489			0.369060
$818$		0			0
$819$		0			0
$820$		0			0
$821$	38.7707			1.35311			0.676554	−	0.736393i	$-0.263472\pi$
$821$	38.7707			1.35311			0.676554	+	0.736393i	$0.263472\pi$
$822$		0			0
$823$	−22.7840			−0.794202			−0.397101	−	0.917775i	$-0.629984\pi$
$823$	−22.7840			−0.794202			−0.397101	+	0.917775i	$0.629984\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.55152			0.0539515			0.0269758	−	0.999636i	$-0.491412\pi$
$827$	1.55152			0.0539515			0.0269758	+	0.999636i	$0.491412\pi$
$828$		0			0
$829$	−23.8972	+	41.3911i	−0.829983	+	1.43757i	0.0680673	+	0.997681i	$0.478317\pi$
$829$	−23.8972	+	41.3911i	−0.829983	+	1.43757i	−0.898051	+	0.439892i	$0.855017\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−8.50818	−	49.3856i	−0.294791	−	1.71111i
$834$		0			0
$835$	−7.16181			−0.247845
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−19.5804	+	33.9142i	−0.675990	+	1.17085i	0.300188	+	0.953880i	$0.402951\pi$
$839$	−19.5804	+	33.9142i	−0.675990	+	1.17085i	−0.976178	+	0.216970i	$0.930383\pi$
$840$		0			0
$841$	12.7940	+	22.1599i	0.441174	+	0.764135i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	17.5021	+	30.3145i	0.602089	+	1.04285i
$846$		0			0
$847$	11.3672	+	2.02736i	0.390580	+	0.0696609i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.163229			0.00559542
$852$		0			0
$853$	14.5234	−	25.1552i	0.497270	−	0.861298i	−0.502725	−	0.864447i	$-0.667669\pi$
$853$	14.5234	−	25.1552i	0.497270	−	0.861298i	0.999995	+	0.00314895i	$0.00100234\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−24.1292	−	41.7930i	−0.824239	−	1.42762i	−0.902500	−	0.430690i	$-0.858270\pi$
$857$	−24.1292	−	41.7930i	−0.824239	−	1.42762i	0.0782612	−	0.996933i	$-0.475063\pi$
$858$		0			0
$859$	5.07528	−	8.79063i	0.173166	−	0.299933i	−0.766359	−	0.642413i	$-0.777934\pi$
$859$	5.07528	−	8.79063i	0.173166	−	0.299933i	0.939525	+	0.342480i	$0.111267\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−25.7981	−	44.6837i	−0.878179	−	1.52105i	−0.853338	−	0.521359i	$-0.825425\pi$
$863$	−25.7981	−	44.6837i	−0.878179	−	1.52105i	−0.0248411	−	0.999691i	$-0.507908\pi$
$864$		0			0
$865$	−0.604630	+	1.04725i	−0.0205580	+	0.0356076i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.79161	+	8.29931i	0.162544	+	0.281535i
$870$		0			0
$871$	−13.6345	−	23.6156i	−0.461986	−	0.800183i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	10.9501	+	30.2701i	0.370182	+	1.02332i
$876$		0			0
$877$	5.19891	−	9.00477i	0.175555	−	0.304069i	−0.764798	−	0.644270i	$-0.777161\pi$
$877$	5.19891	−	9.00477i	0.175555	−	0.304069i	0.940353	+	0.340200i	$0.110495\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−23.6562			−0.796996			−0.398498	−	0.917169i	$-0.630468\pi$
$881$	−23.6562			−0.796996			−0.398498	+	0.917169i	$0.630468\pi$
$882$		0			0
$883$	41.8601			1.40871			0.704353	−	0.709850i	$-0.251237\pi$
$883$	41.8601			1.40871			0.704353	+	0.709850i	$0.251237\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	21.1252	−	36.5900i	0.709316	−	1.22857i	−0.255795	−	0.966731i	$-0.582337\pi$
$887$	21.1252	−	36.5900i	0.709316	−	1.22857i	0.965111	−	0.261840i	$-0.0843294\pi$
$888$		0			0
$889$	−2.87469	−	7.94667i	−0.0964141	−	0.266523i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.83937	+	13.5782i	0.262334	+	0.454377i
$894$		0			0
$895$	20.2404	+	35.0574i	0.676563	+	1.17184i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.76243	−	4.78467i	0.0921321	−	0.159578i
$900$		0			0
$901$	−24.0191	−	41.6023i	−0.800192	−	1.38597i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−23.2303	+	40.2360i	−0.772201	+	1.33749i
$906$		0			0
$907$	20.4404	+	35.4037i	0.678711	+	1.17556i	0.975369	+	0.220578i	$0.0707945\pi$
$907$	20.4404	+	35.4037i	0.678711	+	1.17556i	−0.296658	+	0.954984i	$0.595872\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14.4235	+	24.9823i	−0.477873	+	0.827701i	−0.999678	−	0.0253641i	$-0.991925\pi$
$911$	−14.4235	+	24.9823i	−0.477873	+	0.827701i	0.521805	+	0.853065i	$0.325259\pi$
$912$		0			0
$913$	−15.4650			−0.511816
$914$		0			0
$915$		0			0
$916$		0			0
$917$	36.6910	+	6.54393i	1.21165	+	0.216100i
$918$		0			0
$919$	21.8195	+	37.7925i	0.719760	+	1.24666i	0.961095	+	0.276219i	$0.0890815\pi$
$919$	21.8195	+	37.7925i	0.719760	+	1.24666i	−0.241335	+	0.970442i	$0.577585\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4.33560	+	7.50947i	0.142708	+	0.247177i
$924$		0			0
$925$	−0.526192	+	0.911391i	−0.0173011	+	0.0299663i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	27.4754			0.901438			0.450719	−	0.892666i	$-0.351168\pi$
$929$	27.4754			0.901438			0.450719	+	0.892666i	$0.351168\pi$
$930$		0			0
$931$	−8.36286	−	3.08108i	−0.274082	−	0.100978i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	17.1131	−	29.6408i	0.559658	−	0.969356i
$936$		0			0
$937$	−3.11920			−0.101900			−0.0509500	−	0.998701i	$-0.516225\pi$
$937$	−3.11920			−0.101900			−0.0509500	+	0.998701i	$0.516225\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	26.1215			0.851538			0.425769	−	0.904832i	$-0.360004\pi$
$941$	26.1215			0.851538			0.425769	+	0.904832i	$0.360004\pi$
$942$		0			0
$943$	0.354163			0.0115331
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.18031			0.233329			0.116664	−	0.993171i	$-0.462780\pi$
$947$	7.18031			0.233329			0.116664	+	0.993171i	$0.462780\pi$
$948$		0			0
$949$	−74.0512			−2.40380
$950$		0			0
$951$		0			0
$952$		0			0
$953$	32.1187			1.04043			0.520214	−	0.854036i	$-0.325852\pi$
$953$	32.1187			1.04043			0.520214	+	0.854036i	$0.325852\pi$
$954$		0			0
$955$	−8.03678	+	13.9201i	−0.260064	+	0.450444i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−23.3473	+	27.7135i	−0.753922	+	0.894915i
$960$		0			0
$961$	−22.0537			−0.711411
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.50018	−	2.59838i	0.0482924	−	0.0836449i
$966$		0			0
$967$	−27.4860	−	47.6071i	−0.883890	−	1.53094i	−0.846981	−	0.531623i	$-0.821582\pi$
$967$	−27.4860	−	47.6071i	−0.883890	−	1.53094i	−0.0369085	−	0.999319i	$-0.511751\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−20.8518	−	36.1163i	−0.669165	−	1.15903i	−0.978138	−	0.207957i	$-0.933319\pi$
$971$	−20.8518	−	36.1163i	−0.669165	−	1.15903i	0.308973	−	0.951071i	$-0.400015\pi$
$972$		0			0
$973$	16.8462	−	19.9967i	0.540065	−	0.641064i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5.22874			−0.167282			−0.0836412	−	0.996496i	$-0.526655\pi$
$977$	−5.22874			−0.167282			−0.0836412	+	0.996496i	$0.526655\pi$
$978$		0			0
$979$	−17.0106	+	29.4633i	−0.543662	+	0.941651i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.45349	+	5.98162i	0.110149	+	0.190784i	0.915830	−	0.401566i	$-0.131534\pi$
$983$	3.45349	+	5.98162i	0.110149	+	0.190784i	−0.805681	+	0.592349i	$0.798200\pi$
$984$		0			0
$985$	−9.99837	+	17.3177i	−0.318575	+	0.551788i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.999537	−	1.73125i	−0.0317834	−	0.0550505i
$990$		0			0
$991$	2.19861	−	3.80811i	0.0698412	−	0.120968i	−0.828990	−	0.559263i	$-0.811084\pi$
$991$	2.19861	−	3.80811i	0.0698412	−	0.120968i	0.898831	+	0.438295i	$0.144417\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.43133	−	7.67528i	−0.140482	−	0.243323i
$996$		0			0
$997$	14.0180	+	24.2798i	0.443954	+	0.768950i	0.997979	−	0.0635498i	$-0.0202422\pi$
$997$	14.0180	+	24.2798i	0.443954	+	0.768950i	−0.554025	+	0.832500i	$0.686909\pi$
$998$		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.1369.9		22
3.2	odd	2		504.2.q.d.25.7	✓	22
4.3	odd	2		3024.2.q.k.2881.9		22
7.2	even	3		1512.2.t.d.289.3		22
9.4	even	3		1512.2.t.d.361.3		22
9.5	odd	6		504.2.t.d.193.8	yes	22
12.11	even	2		1008.2.q.k.529.5		22
21.2	odd	6		504.2.t.d.457.8	yes	22
28.23	odd	6		3024.2.t.l.289.3		22
36.23	even	6		1008.2.t.k.193.4		22
36.31	odd	6		3024.2.t.l.1873.3		22
63.23	odd	6		504.2.q.d.121.7	yes	22
63.58	even	3	inner	1512.2.q.c.793.9		22
84.23	even	6		1008.2.t.k.961.4		22
252.23	even	6		1008.2.q.k.625.5		22
252.247	odd	6		3024.2.q.k.2305.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.7	✓	22	3.2	odd	2
504.2.q.d.121.7	yes	22	63.23	odd	6
504.2.t.d.193.8	yes	22	9.5	odd	6
504.2.t.d.457.8	yes	22	21.2	odd	6
1008.2.q.k.529.5		22	12.11	even	2
1008.2.q.k.625.5		22	252.23	even	6
1008.2.t.k.193.4		22	36.23	even	6
1008.2.t.k.961.4		22	84.23	even	6
1512.2.q.c.793.9		22	63.58	even	3	inner
1512.2.q.c.1369.9		22	1.1	even	1	trivial
1512.2.t.d.289.3		22	7.2	even	3
1512.2.t.d.361.3		22	9.4	even	3
3024.2.q.k.2305.9		22	252.247	odd	6
3024.2.q.k.2881.9		22	4.3	odd	2
3024.2.t.l.289.3		22	28.23	odd	6
3024.2.t.l.1873.3		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)

\(f(q)\)	\(=\)	\(q+(0.927957 - 1.60727i) q^{5} +(0.900017 + 2.48796i) q^{7} +O(q^{10})\)	\(q+(0.927957 - 1.60727i) q^{5} +(0.900017 + 2.48796i) q^{7} +(-1.28800 - 2.23089i) q^{11} +(2.82227 + 4.88832i) q^{13} +(-3.57951 + 6.19989i) q^{17} +(0.636599 + 1.10262i) q^{19} +(0.120639 - 0.208952i) q^{23} +(0.777791 + 1.34717i) q^{25} +(-0.923571 + 1.59967i) q^{29} -2.99103 q^{31} +(4.83401 + 0.862156i) q^{35} +(0.338260 + 0.585884i) q^{37} +(0.733933 + 1.27121i) q^{41} +(4.14269 - 7.17535i) q^{43} +12.3145 q^{47} +(-5.37994 + 4.47842i) q^{49} +(-3.35508 + 5.81117i) q^{53} -4.78085 q^{55} -2.08279 q^{59} +12.9595 q^{61} +10.4758 q^{65} -4.83102 q^{67} +1.53621 q^{71} +(-6.55954 + 11.3615i) q^{73} +(4.39115 - 5.21235i) q^{77} -3.72018 q^{79} +(3.00173 - 5.19915i) q^{83} +(6.64326 + 11.5065i) q^{85} +(-6.60349 - 11.4376i) q^{89} +(-9.62187 + 11.4213i) q^{91} +2.36294 q^{95} +(6.40860 - 11.1000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 5 q^{7}+O(q^{10}) \) 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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