LMFDB - Embedded newform 2736.2.s.ba.577.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2736.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 1368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.3
Root			$1.39083 + 2.40898i$ of defining polynomial
Character	$\chi$	$=$	2736.577
Dual form			2736.2.s.ba.1873.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.412855 - 0.715087i) q^{5} +0.703158 q^{7} +O(q^{10})$	$q+(-0.412855 - 0.715087i) q^{5} +0.703158 q^{7} +1.17429 q^{11} +(-2.45594 + 4.25382i) q^{13} +(-0.296842 - 0.514145i) q^{17} +(-3.07850 + 3.08591i) q^{19} +(-3.85361 + 6.67465i) q^{23} +(2.15910 - 3.73967i) q^{25} +(4.73760 - 8.20576i) q^{29} -4.26647 q^{31} +(-0.290303 - 0.502819i) q^{35} -7.53293 q^{37} +(-5.03444 - 8.71990i) q^{41} +(-1.83639 - 3.18072i) q^{43} +(0.877447 - 1.51978i) q^{47} -6.50557 q^{49} +(-2.46459 + 4.26880i) q^{53} +(-0.484812 - 0.839718i) q^{55} +(6.15045 + 10.6529i) q^{59} +(-3.10736 + 5.38211i) q^{61} +4.05580 q^{65} +(-5.26346 + 9.11659i) q^{67} +(4.20873 + 7.28973i) q^{71} +(-0.151422 - 0.262271i) q^{73} +0.825711 q^{77} +(0.221348 + 0.383385i) q^{79} -8.41745 q^{83} +(-0.245106 + 0.424535i) q^{85} +(6.55677 - 11.3567i) q^{89} +(-1.72692 + 2.99111i) q^{91} +(3.47767 + 0.927354i) q^{95} +(0.747216 + 1.29422i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^5 + 4 * q^7	$ 8 q - 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{17} - 8 q^{19} + 8 q^{23} - 4 q^{25} + 4 q^{31} + 16 q^{37} - 4 q^{41} + 6 q^{43} + 4 q^{47} - 16 q^{49} - 16 q^{53} + 16 q^{55} + 12 q^{59} - 8 q^{61} - 48 q^{65} - 2 q^{67} - 4 q^{71} - 4 q^{73} + 8 q^{77} + 22 q^{79} + 8 q^{83} - 8 q^{85} + 12 q^{89} + 2 q^{91} + 32 q^{95} + 24 q^{97}+O(q^{100}) $ 8 * q - 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^17 - 8 * q^19 + 8 * q^23 - 4 * q^25 + 4 * q^31 + 16 * q^37 - 4 * q^41 + 6 * q^43 + 4 * q^47 - 16 * q^49 - 16 * q^53 + 16 * q^55 + 12 * q^59 - 8 * q^61 - 48 * q^65 - 2 * q^67 - 4 * q^71 - 4 * q^73 + 8 * q^77 + 22 * q^79 + 8 * q^83 - 8 * q^85 + 12 * q^89 + 2 * q^91 + 32 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.412855	−	0.715087i	−0.184635	−	0.319796i	0.758819	−	0.651302i	$-0.225777\pi$
$5$	−0.412855	−	0.715087i	−0.184635	−	0.319796i	−0.943453	+	0.331505i	$0.892443\pi$
$6$		0			0
$7$	0.703158			0.265769			0.132884	−	0.991132i	$-0.457576\pi$
$7$	0.703158			0.265769			0.132884	+	0.991132i	$0.457576\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.17429			0.354061			0.177031	−	0.984205i	$-0.443351\pi$
$11$	1.17429			0.354061			0.177031	+	0.984205i	$0.443351\pi$
$12$		0			0
$13$	−2.45594	+	4.25382i	−0.681156	+	1.17980i	0.293473	+	0.955968i	$0.405189\pi$
$13$	−2.45594	+	4.25382i	−0.681156	+	1.17980i	−0.974628	+	0.223829i	$0.928144\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.296842	−	0.514145i	−0.0719947	−	0.124698i	0.827781	−	0.561052i	$-0.189603\pi$
$17$	−0.296842	−	0.514145i	−0.0719947	−	0.124698i	−0.899775	+	0.436353i	$0.856270\pi$
$18$		0			0
$19$	−3.07850	+	3.08591i	−0.706255	+	0.707957i
$19$	−3.07850	+	3.08591i	−0.706255	+	0.707957i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.85361	+	6.67465i	−0.803533	+	1.39176i	0.113744	+	0.993510i	$0.463716\pi$
$23$	−3.85361	+	6.67465i	−0.803533	+	1.39176i	−0.917277	+	0.398250i	$0.869618\pi$
$24$		0			0
$25$	2.15910	−	3.73967i	0.431820	−	0.747934i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.73760	−	8.20576i	0.879749	−	1.52377i	0.0281338	−	0.999604i	$-0.491044\pi$
$29$	4.73760	−	8.20576i	0.879749	−	1.52377i	0.851616	−	0.524167i	$-0.175623\pi$
$30$		0			0
$31$	−4.26647			−0.766280			−0.383140	−	0.923690i	$-0.625157\pi$
$31$	−4.26647			−0.766280			−0.383140	+	0.923690i	$0.625157\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.290303	−	0.502819i	−0.0490701	−	0.0849919i
$36$		0			0
$37$	−7.53293			−1.23841			−0.619203	−	0.785231i	$-0.712544\pi$
$37$	−7.53293			−1.23841			−0.619203	+	0.785231i	$0.712544\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.03444	−	8.71990i	−0.786247	−	1.36182i	−0.928251	−	0.371954i	$-0.878688\pi$
$41$	−5.03444	−	8.71990i	−0.786247	−	1.36182i	0.142004	−	0.989866i	$-0.454645\pi$
$42$		0			0
$43$	−1.83639	−	3.18072i	−0.280047	−	0.485056i	0.691349	−	0.722521i	$-0.257017\pi$
$43$	−1.83639	−	3.18072i	−0.280047	−	0.485056i	−0.971396	+	0.237465i	$0.923683\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.877447	−	1.51978i	0.127989	−	0.221683i	−0.794908	−	0.606729i	$-0.792481\pi$
$47$	0.877447	−	1.51978i	0.127989	−	0.221683i	0.922897	+	0.385046i	$0.125814\pi$
$48$		0			0
$49$	−6.50557			−0.929367
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.46459	+	4.26880i	−0.338538	+	0.586365i	−0.984158	−	0.177294i	$-0.943266\pi$
$53$	−2.46459	+	4.26880i	−0.338538	+	0.586365i	0.645620	+	0.763659i	$0.276599\pi$
$54$		0			0
$55$	−0.484812	−	0.839718i	−0.0653720	−	0.113228i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.15045	+	10.6529i	0.800721	+	1.38689i	0.919142	+	0.393925i	$0.128883\pi$
$59$	6.15045	+	10.6529i	0.800721	+	1.38689i	−0.118422	+	0.992963i	$0.537784\pi$
$60$		0			0
$61$	−3.10736	+	5.38211i	−0.397857	+	0.689109i	−0.993461	−	0.114169i	$-0.963579\pi$
$61$	−3.10736	+	5.38211i	−0.397857	+	0.689109i	0.595604	+	0.803278i	$0.296913\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.05580			0.503060
$66$		0			0
$67$	−5.26346	+	9.11659i	−0.643034	+	1.11377i	0.341717	+	0.939803i	$0.388991\pi$
$67$	−5.26346	+	9.11659i	−0.643034	+	1.11377i	−0.984752	+	0.173966i	$0.944342\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.20873	+	7.28973i	0.499484	+	0.865132i	1.00000		0.000595758i	$-0.000189636\pi$
$71$	4.20873	+	7.28973i	0.499484	+	0.865132i	−0.500516	+	0.865727i	$0.666856\pi$
$72$		0			0
$73$	−0.151422	−	0.262271i	−0.0177226	−	0.0306964i	0.857028	−	0.515270i	$-0.172308\pi$
$73$	−0.151422	−	0.262271i	−0.0177226	−	0.0306964i	−0.874751	+	0.484573i	$0.838975\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.825711			0.0940985
$78$		0			0
$79$	0.221348	+	0.383385i	0.0249036	+	0.0431342i	0.878209	−	0.478278i	$-0.158739\pi$
$79$	0.221348	+	0.383385i	0.0249036	+	0.0431342i	−0.853305	+	0.521412i	$0.825405\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.41745			−0.923936			−0.461968	−	0.886897i	$-0.652856\pi$
$83$	−8.41745			−0.923936			−0.461968	+	0.886897i	$0.652856\pi$
$84$		0			0
$85$	−0.245106	+	0.424535i	−0.0265854	+	0.0460473i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.55677	−	11.3567i	0.695016	−	1.20380i	−0.275159	−	0.961399i	$-0.588731\pi$
$89$	6.55677	−	11.3567i	0.695016	−	1.20380i	0.970175	−	0.242404i	$-0.0779361\pi$
$90$		0			0
$91$	−1.72692	+	2.99111i	−0.181030	+	0.313553i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.47767	+	0.927354i	0.356801	+	0.0951445i
$96$		0			0
$97$	0.747216	+	1.29422i	0.0758683	+	0.131408i	0.901464	−	0.432855i	$-0.142494\pi$
$97$	0.747216	+	1.29422i	0.0758683	+	0.131408i	−0.825595	+	0.564263i	$0.809160\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.35458	−	2.34620i	0.134786	−	0.233456i	−0.790730	−	0.612165i	$-0.790299\pi$
$101$	1.35458	−	2.34620i	0.134786	−	0.233456i	0.925516	+	0.378709i	$0.123632\pi$
$102$		0			0
$103$	−2.59969			−0.256155			−0.128077	−	0.991764i	$-0.540881\pi$
$103$	−2.59969			−0.256155			−0.128077	+	0.991764i	$0.540881\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.2878			−1.18791			−0.593954	−	0.804499i	$-0.702434\pi$
$107$	−12.2878			−1.18791			−0.593954	+	0.804499i	$0.702434\pi$
$108$		0			0
$109$	5.25278	+	9.09809i	0.503125	+	0.871439i	0.999993	+	0.00361277i	$0.00114998\pi$
$109$	5.25278	+	9.09809i	0.503125	+	0.871439i	−0.496868	+	0.867826i	$0.665517\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.76797			−0.354461			−0.177231	−	0.984169i	$-0.556714\pi$
$113$	−3.76797			−0.354461			−0.177231	+	0.984169i	$0.556714\pi$
$114$		0			0
$115$	6.36394			0.593440
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.208727	−	0.361525i	−0.0191339	−	0.0331410i
$120$		0			0
$121$	−9.62105			−0.874640
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.69414			−0.688185
$126$		0			0
$127$	−7.21473	+	12.4963i	−0.640204	+	1.10887i	0.345183	+	0.938535i	$0.387817\pi$
$127$	−7.21473	+	12.4963i	−0.640204	+	1.10887i	−0.985387	+	0.170330i	$0.945517\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.86015	+	3.22187i	0.162522	+	0.281496i	0.935773	−	0.352604i	$-0.114704\pi$
$131$	1.86015	+	3.22187i	0.162522	+	0.281496i	−0.773251	+	0.634101i	$0.781371\pi$
$132$		0			0
$133$	−2.16467	+	2.16989i	−0.187701	+	0.188153i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.79533	+	10.0378i	−0.495129	+	0.857588i	−0.999984	−	0.00561565i	$-0.998212\pi$
$137$	−5.79533	+	10.0378i	−0.495129	+	0.857588i	0.504855	+	0.863204i	$0.331546\pi$
$138$		0			0
$139$	3.83639	−	6.64482i	0.325398	−	0.563607i	−0.656194	−	0.754592i	$-0.727835\pi$
$139$	3.83639	−	6.64482i	0.325398	−	0.563607i	0.981593	+	0.190985i	$0.0611683\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.88399	+	4.99521i	−0.241171	+	0.417721i
$144$		0			0
$145$	−7.82377			−0.649729
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.0278987	−	0.0483219i	−0.00228555	−	0.00395868i	0.864880	−	0.501978i	$-0.167394\pi$
$149$	−0.0278987	−	0.0483219i	−0.00228555	−	0.00395868i	−0.867166	+	0.498019i	$0.834061\pi$
$150$		0			0
$151$	−19.6475			−1.59889			−0.799447	−	0.600737i	$-0.794874\pi$
$151$	−19.6475			−1.59889			−0.799447	+	0.600737i	$0.794874\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.76143	+	3.05089i	0.141482	+	0.245054i
$156$		0			0
$157$	1.39053	+	2.40846i	0.110976	+	0.192216i	0.916164	−	0.400804i	$-0.131269\pi$
$157$	1.39053	+	2.40846i	0.110976	+	0.192216i	−0.805188	+	0.593020i	$0.797936\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.70970	+	4.69333i	−0.213554	+	0.369886i
$162$		0			0
$163$	−20.2472			−1.58589			−0.792943	−	0.609296i	$-0.791452\pi$
$163$	−20.2472			−1.58589			−0.792943	+	0.609296i	$0.791452\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.6793	−	18.4971i	0.826391	−	1.43135i	−0.0744612	−	0.997224i	$-0.523724\pi$
$167$	10.6793	−	18.4971i	0.826391	−	1.43135i	0.900852	−	0.434127i	$-0.142943\pi$
$168$		0			0
$169$	−5.56331	−	9.63593i	−0.427947	−	0.741225i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.38902	+	4.13790i	0.181634	+	0.314599i	0.942437	−	0.334384i	$-0.108528\pi$
$173$	2.38902	+	4.13790i	0.181634	+	0.314599i	−0.760803	+	0.648983i	$0.775195\pi$
$174$		0			0
$175$	1.51819	−	2.62958i	0.114764	−	0.198778i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	15.8107			1.18175			0.590873	−	0.806764i	$-0.298783\pi$
$179$	15.8107			1.18175			0.590873	+	0.806764i	$0.298783\pi$
$180$		0			0
$181$	−9.78571	+	16.9494i	−0.727366	+	1.25984i	0.230626	+	0.973042i	$0.425923\pi$
$181$	−9.78571	+	16.9494i	−0.727366	+	1.25984i	−0.957993	+	0.286793i	$0.907411\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.11001	+	5.38670i	0.228653	+	0.396038i
$186$		0			0
$187$	−0.348578	−	0.603755i	−0.0254906	−	0.0441509i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−13.7680			−0.996216			−0.498108	−	0.867115i	$-0.665972\pi$
$191$	−13.7680			−0.996216			−0.498108	+	0.867115i	$0.665972\pi$
$192$		0			0
$193$	−6.96751	−	12.0681i	−0.501533	−	0.868680i	−0.999998	−	0.00177056i	$-0.999436\pi$
$193$	−6.96751	−	12.0681i	−0.501533	−	0.868680i	0.498466	−	0.866909i	$-0.333897\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.3009			1.30389			0.651943	−	0.758268i	$-0.273954\pi$
$197$	18.3009			1.30389			0.651943	+	0.758268i	$0.273954\pi$
$198$		0			0
$199$	1.53955	−	2.66658i	0.109136	−	0.189029i	−0.806285	−	0.591528i	$-0.798525\pi$
$199$	1.53955	−	2.66658i	0.109136	−	0.189029i	0.915420	+	0.402499i	$0.131858\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.33128	−	5.76995i	0.233810	−	0.404971i
$204$		0			0
$205$	−4.15699	+	7.20012i	−0.290337	+	0.502878i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.61504	+	3.62376i	−0.250058	+	0.250660i
$210$		0			0
$211$	1.21535	+	2.10504i	0.0836678	+	0.144917i	0.904823	−	0.425788i	$-0.140003\pi$
$211$	1.21535	+	2.10504i	0.0836678	+	0.144917i	−0.821155	+	0.570705i	$0.806670\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.51633	+	2.62636i	−0.103413	+	0.179116i
$216$		0			0
$217$	−3.00000			−0.203653
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.91611			0.196158
$222$		0			0
$223$	10.3937	+	18.0024i	0.696013	+	1.20553i	0.969838	+	0.243751i	$0.0783779\pi$
$223$	10.3937	+	18.0024i	0.696013	+	1.20553i	−0.273825	+	0.961780i	$0.588289\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.60676			−0.571251			−0.285625	−	0.958341i	$-0.592201\pi$
$227$	−8.60676			−0.571251			−0.285625	+	0.958341i	$0.592201\pi$
$228$		0			0
$229$	15.0274			0.993036			0.496518	−	0.868026i	$-0.334612\pi$
$229$	15.0274			0.993036			0.496518	+	0.868026i	$0.334612\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.45805	−	9.45362i	−0.357569	−	0.619328i	0.629985	−	0.776607i	$-0.283061\pi$
$233$	−5.45805	−	9.45362i	−0.357569	−	0.619328i	−0.987554	+	0.157280i	$0.949728\pi$
$234$		0			0
$235$	−1.44904			−0.0945247
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.17429			−0.334697			−0.167348	−	0.985898i	$-0.553520\pi$
$239$	−5.17429			−0.334697			−0.167348	+	0.985898i	$0.553520\pi$
$240$		0			0
$241$	2.71473	−	4.70205i	0.174871	−	0.302886i	−0.765246	−	0.643738i	$-0.777382\pi$
$241$	2.71473	−	4.70205i	0.174871	−	0.302886i	0.940117	+	0.340853i	$0.110716\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.68586	+	4.65205i	0.171593	+	0.297208i
$246$		0			0
$247$	−5.56631	−	20.6742i	−0.354176	−	1.31547i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.4175	−	21.5077i	0.783783	−	1.35755i	−0.145941	−	0.989293i	$-0.546621\pi$
$251$	12.4175	−	21.5077i	0.783783	−	1.35755i	0.929724	−	0.368258i	$-0.120046\pi$
$252$		0			0
$253$	−4.52525	+	7.83797i	−0.284500	+	0.492769i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.41692	+	7.65032i	−0.275520	+	0.477214i	−0.970266	−	0.242041i	$-0.922183\pi$
$257$	−4.41692	+	7.65032i	−0.275520	+	0.477214i	0.694746	+	0.719255i	$0.255517\pi$
$258$		0			0
$259$	−5.29684			−0.329130
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.4538	−	18.1066i	−0.644611	−	1.11650i	−0.984391	−	0.175994i	$-0.943686\pi$
$263$	−10.4538	−	18.1066i	−0.644611	−	1.11650i	0.339780	−	0.940505i	$-0.389647\pi$
$264$		0			0
$265$	4.07008			0.250023
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.76549	+	15.1823i	0.534442	+	0.925680i	0.999190	+	0.0402373i	$0.0128114\pi$
$269$	8.76549	+	15.1823i	0.534442	+	0.925680i	−0.464749	+	0.885443i	$0.653855\pi$
$270$		0			0
$271$	11.3871	+	19.7230i	0.691716	+	1.19809i	0.971275	+	0.237958i	$0.0764782\pi$
$271$	11.3871	+	19.7230i	0.691716	+	1.19809i	−0.279560	+	0.960128i	$0.590188\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.53541	−	4.39146i	0.152891	−	0.264815i
$276$		0			0
$277$	−16.4448			−0.988073			−0.494037	−	0.869441i	$-0.664479\pi$
$277$	−16.4448			−0.988073			−0.494037	+	0.869441i	$0.664479\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.41286	+	11.1074i	−0.382559	+	0.662611i	−0.991427	−	0.130660i	$-0.958290\pi$
$281$	−6.41286	+	11.1074i	−0.382559	+	0.662611i	0.608868	+	0.793271i	$0.291624\pi$
$282$		0			0
$283$	4.02736	+	6.97560i	0.239402	+	0.414656i	0.960543	−	0.278132i	$-0.0897153\pi$
$283$	4.02736	+	6.97560i	0.239402	+	0.414656i	−0.721141	+	0.692788i	$0.756382\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.54001	−	6.13147i	−0.208960	−	0.361929i
$288$		0			0
$289$	8.32377	−	14.4172i	0.489634	−	0.848070i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−32.3687			−1.89100			−0.945500	−	0.325622i	$-0.894426\pi$
$293$	−32.3687			−1.89100			−0.945500	+	0.325622i	$0.894426\pi$
$294$		0			0
$295$	5.07850	−	8.79621i	0.295681	−	0.512135i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−18.9285	−	32.7851i	−1.09466	−	1.89601i
$300$		0			0
$301$	−1.29127	−	2.23655i	−0.0744278	−	0.128913i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	5.13157			0.293833
$306$		0			0
$307$	4.22435	+	7.31679i	0.241096	+	0.417591i	0.961027	−	0.276455i	$-0.0891597\pi$
$307$	4.22435	+	7.31679i	0.241096	+	0.417591i	−0.719931	+	0.694046i	$0.755826\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	27.8450			1.57894			0.789472	−	0.613787i	$-0.210355\pi$
$311$	27.8450			1.57894			0.789472	+	0.613787i	$0.210355\pi$
$312$		0			0
$313$	3.40977	−	5.90590i	0.192732	−	0.333821i	−0.753423	−	0.657536i	$-0.771599\pi$
$313$	3.40977	−	5.90590i	0.192732	−	0.333821i	0.946155	+	0.323715i	$0.104932\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.32880	+	10.9618i	−0.355461	+	0.615676i	−0.987197	−	0.159507i	$-0.949009\pi$
$317$	−6.32880	+	10.9618i	−0.355461	+	0.615676i	0.631736	+	0.775184i	$0.282343\pi$
$318$		0			0
$319$	5.56331	−	9.63593i	0.311485	−	0.539509i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.50043	+	0.666765i	0.139128	+	0.0370998i
$324$		0			0
$325$	10.6053	+	18.3688i	0.588274	+	1.01892i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.616984	−	1.06865i	0.0340154	−	0.0589165i
$330$		0			0
$331$	−17.0791			−0.938752			−0.469376	−	0.882998i	$-0.655521\pi$
$331$	−17.0791			−0.938752			−0.469376	+	0.882998i	$0.655521\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.69220			0.474906
$336$		0			0
$337$	3.97173	+	6.87924i	0.216354	+	0.374736i	0.953691	−	0.300789i	$-0.0972501\pi$
$337$	3.97173	+	6.87924i	0.216354	+	0.374736i	−0.737336	+	0.675526i	$0.763917\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.01006			−0.271310
$342$		0			0
$343$	−9.49655			−0.512766
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.6429	+	25.3623i	0.786074	+	1.36152i	0.928355	+	0.371694i	$0.121223\pi$
$347$	14.6429	+	25.3623i	0.786074	+	1.36152i	−0.142281	+	0.989826i	$0.545444\pi$
$348$		0			0
$349$	4.79641			0.256746			0.128373	−	0.991726i	$-0.459025\pi$
$349$	4.79641			0.256746			0.128373	+	0.991726i	$0.459025\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	37.3548			1.98819			0.994097	−	0.108499i	$-0.0346043\pi$
$353$	37.3548			1.98819			0.994097	+	0.108499i	$0.0346043\pi$
$354$		0			0
$355$	3.47519	−	6.01921i	0.184444	−	0.319466i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.5329	−	18.2436i	−0.555907	−	0.962859i	−0.997832	−	0.0658071i	$-0.979038\pi$
$359$	−10.5329	−	18.2436i	−0.555907	−	0.962859i	0.441926	−	0.897052i	$-0.354296\pi$
$360$		0			0
$361$	−0.0457341	−	18.9999i	−0.00240706	−	0.999997i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.125031	+	0.216560i	−0.00654441	+	0.0113352i
$366$		0			0
$367$	5.77865	−	10.0089i	0.301643	−	0.522461i	−0.674865	−	0.737941i	$-0.735798\pi$
$367$	5.77865	−	10.0089i	0.301643	−	0.522461i	0.976508	+	0.215480i	$0.0691315\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.73300	+	3.00164i	−0.0899728	+	0.155837i
$372$		0			0
$373$	−2.94347			−0.152407			−0.0762035	−	0.997092i	$-0.524280\pi$
$373$	−2.94347			−0.152407			−0.0762035	+	0.997092i	$0.524280\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	23.2705	+	40.3057i	1.19849	+	2.07585i
$378$		0			0
$379$	31.1441			1.59976			0.799882	−	0.600157i	$-0.204895\pi$
$379$	31.1441			1.59976			0.799882	+	0.600157i	$0.204895\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.76744	+	4.79334i	0.141409	+	0.244928i	0.928028	−	0.372512i	$-0.121503\pi$
$383$	2.76744	+	4.79334i	0.141409	+	0.244928i	−0.786618	+	0.617440i	$0.788170\pi$
$384$		0			0
$385$	−0.340899	−	0.590455i	−0.0173738	−	0.0300924i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.03390	+	12.1831i	−0.356633	+	0.617706i	−0.987396	−	0.158269i	$-0.949409\pi$
$389$	−7.03390	+	12.1831i	−0.356633	+	0.617706i	0.630763	+	0.775975i	$0.282742\pi$
$390$		0			0
$391$	4.57565			0.231401
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.182769	−	0.316565i	0.00919611	−	0.0159281i
$396$		0			0
$397$	13.5826	+	23.5257i	0.681689	+	1.18072i	0.974465	+	0.224539i	$0.0720876\pi$
$397$	13.5826	+	23.5257i	0.681689	+	1.18072i	−0.292776	+	0.956181i	$0.594579\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.0320	−	20.8400i	−0.600847	−	1.04070i	−0.992693	−	0.120667i	$-0.961497\pi$
$401$	−12.0320	−	20.8400i	−0.600847	−	1.04070i	0.391846	−	0.920031i	$-0.371837\pi$
$402$		0			0
$403$	10.4782	−	18.1488i	0.521956	−	0.904054i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.84584			−0.438472
$408$		0			0
$409$	16.1878	−	28.0381i	0.800436	−	1.38640i	−0.118894	−	0.992907i	$-0.537935\pi$
$409$	16.1878	−	28.0381i	0.800436	−	1.38640i	0.919330	−	0.393488i	$-0.128732\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.32474	+	7.49067i	0.212807	+	0.368592i
$414$		0			0
$415$	3.47519	+	6.01921i	0.170590	+	0.295471i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−21.2778			−1.03949			−0.519743	−	0.854322i	$-0.673972\pi$
$419$	−21.2778			−1.03949			−0.519743	+	0.854322i	$0.673972\pi$
$420$		0			0
$421$	11.9773	+	20.7453i	0.583738	+	1.01106i	0.995031	+	0.0995609i	$0.0317438\pi$
$421$	11.9773	+	20.7453i	0.583738	+	1.01106i	−0.411293	+	0.911503i	$0.634923\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.56365			−0.124355
$426$		0			0
$427$	−2.18497	+	3.78448i	−0.105738	+	0.183144i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.64348	+	13.2389i	−0.368173	+	0.637695i	−0.989280	−	0.146031i	$-0.953350\pi$
$431$	−7.64348	+	13.2389i	−0.368173	+	0.637695i	0.621107	+	0.783726i	$0.286683\pi$
$432$		0			0
$433$	12.6920	−	21.9832i	0.609940	−	1.05645i	−0.381310	−	0.924447i	$-0.624527\pi$
$433$	12.6920	−	21.9832i	0.609940	−	1.05645i	0.991250	−	0.132000i	$-0.0421398\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.73407	−	32.4398i	−0.417807	−	1.55181i
$438$		0			0
$439$	−2.74767	−	4.75911i	−0.131139	−	0.227140i	0.792977	−	0.609252i	$-0.208530\pi$
$439$	−2.74767	−	4.75911i	−0.131139	−	0.227140i	−0.924116	+	0.382112i	$0.875197\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.85307	−	8.40577i	0.230576	−	0.399370i	−0.727401	−	0.686212i	$-0.759272\pi$
$443$	4.85307	−	8.40577i	0.230576	−	0.399370i	0.957978	+	0.286842i	$0.0926055\pi$
$444$		0			0
$445$	−10.8280			−0.513296
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−12.9850			−0.612799			−0.306400	−	0.951903i	$-0.599124\pi$
$449$	−12.9850			−0.612799			−0.306400	+	0.951903i	$0.599124\pi$
$450$		0			0
$451$	−5.91188	−	10.2397i	−0.278380	−	0.482168i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.85187			0.133698
$456$		0			0
$457$	9.99578			0.467583			0.233791	−	0.972287i	$-0.424887\pi$
$457$	9.99578			0.467583			0.233791	+	0.972287i	$0.424887\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.65196	−	13.2536i	−0.356387	−	0.617281i	0.630967	−	0.775810i	$-0.282658\pi$
$461$	−7.65196	−	13.2536i	−0.356387	−	0.617281i	−0.987354	+	0.158529i	$0.949325\pi$
$462$		0			0
$463$	−1.78349			−0.0828858			−0.0414429	−	0.999141i	$-0.513195\pi$
$463$	−1.78349			−0.0828858			−0.0414429	+	0.999141i	$0.513195\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.4325			−0.714130			−0.357065	−	0.934080i	$-0.616222\pi$
$467$	−15.4325			−0.714130			−0.357065	+	0.934080i	$0.616222\pi$
$468$		0			0
$469$	−3.70105	+	6.41040i	−0.170899	+	0.296005i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.15645	−	3.73509i	−0.0991538	−	0.171739i
$474$		0			0
$475$	4.89353	+	18.1754i	0.224530	+	0.833943i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.4277	−	18.0613i	0.476453	−	0.825240i	−0.523183	−	0.852220i	$-0.675256\pi$
$479$	10.4277	−	18.0613i	0.476453	−	0.825240i	0.999636	+	0.0269799i	$0.00858902\pi$
$480$		0			0
$481$	18.5004	−	32.0437i	0.843548	−	1.46107i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.616984	−	1.06865i	0.0280158	−	0.0485248i
$486$		0			0
$487$	7.07189			0.320458			0.160229	−	0.987080i	$-0.448777\pi$
$487$	7.07189			0.320458			0.160229	+	0.987080i	$0.448777\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.23187	+	12.5260i	0.326370	+	0.565289i	0.981789	−	0.189977i	$-0.0608413\pi$
$491$	7.23187	+	12.5260i	0.326370	+	0.565289i	−0.655419	+	0.755266i	$0.727508\pi$
$492$		0			0
$493$	−5.62527			−0.253349
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.95940	+	5.12583i	0.132747	+	0.229925i
$498$		0			0
$499$	−14.0355	−	24.3102i	−0.628315	−	1.08827i	−0.987890	−	0.155157i	$-0.950412\pi$
$499$	−14.0355	−	24.3102i	−0.628315	−	1.08827i	0.359575	−	0.933116i	$-0.382922\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	7.43475	−	12.8774i	0.331499	−	0.574173i	−0.651307	−	0.758814i	$-0.725779\pi$
$503$	7.43475	−	12.8774i	0.331499	−	0.574173i	0.982806	+	0.184641i	$0.0591122\pi$
$504$		0			0
$505$	−2.23698			−0.0995445
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.3486	+	24.8525i	−0.635990	+	1.10157i	0.350315	+	0.936632i	$0.386075\pi$
$509$	−14.3486	+	24.8525i	−0.635990	+	1.10157i	−0.986305	+	0.164934i	$0.947259\pi$
$510$		0			0
$511$	−0.106474	−	0.184418i	−0.00471011	−	0.00815816i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.07329	+	1.85900i	0.0472950	+	0.0819174i
$516$		0			0
$517$	1.03038	−	1.78466i	0.0453159	−	0.0784895i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−38.8946			−1.70400			−0.852001	−	0.523540i	$-0.824611\pi$
$521$	−38.8946			−1.70400			−0.852001	+	0.523540i	$0.824611\pi$
$522$		0			0
$523$	8.29384	−	14.3654i	0.362664	−	0.628153i	−0.625734	−	0.780036i	$-0.715200\pi$
$523$	8.29384	−	14.3654i	0.362664	−	0.628153i	0.988398	+	0.151883i	$0.0485338\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.26647	+	2.19358i	0.0551681	+	0.0955539i
$528$		0			0
$529$	−18.2006	−	31.5244i	−0.791331	−	1.37063i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	49.4572			2.14223
$534$		0			0
$535$	5.07310	+	8.78686i	0.219329	+	0.379889i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−7.63942			−0.329053
$540$		0			0
$541$	−16.0958	+	27.8787i	−0.692013	+	1.19860i	0.279165	+	0.960243i	$0.409942\pi$
$541$	−16.0958	+	27.8787i	−0.692013	+	1.19860i	−0.971177	+	0.238358i	$0.923391\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.33728	−	7.51239i	0.185789	−	0.321796i
$546$		0			0
$547$	5.13323	−	8.89102i	0.219481	−	0.380153i	−0.735168	−	0.677885i	$-0.762897\pi$
$547$	5.13323	−	8.89102i	0.219481	−	0.380153i	0.954649	+	0.297732i	$0.0962302\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	10.7376	+	39.8812i	0.457437	+	1.69900i
$552$		0			0
$553$	0.155642	+	0.269581i	0.00661859	+	0.0114637i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.8065	−	32.5738i	0.796856	−	1.38019i	−0.124798	−	0.992182i	$-0.539828\pi$
$557$	18.8065	−	32.5738i	0.796856	−	1.38019i	0.921654	−	0.388013i	$-0.126838\pi$
$558$		0			0
$559$	18.0403			0.763023
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10.1723			0.428713			0.214357	−	0.976755i	$-0.431235\pi$
$563$	10.1723			0.428713			0.214357	+	0.976755i	$0.431235\pi$
$564$		0			0
$565$	1.55563	+	2.69443i	0.0654458	+	0.113355i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	24.3221			1.01964			0.509818	−	0.860282i	$-0.329713\pi$
$569$	24.3221			1.01964			0.509818	+	0.860282i	$0.329713\pi$
$570$		0			0
$571$	41.3131			1.72890			0.864449	−	0.502720i	$-0.167667\pi$
$571$	41.3131			1.72890			0.864449	+	0.502720i	$0.167667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	16.6407	+	28.8225i	0.693964	+	1.20198i
$576$		0			0
$577$	9.80841			0.408330			0.204165	−	0.978937i	$-0.434552\pi$
$577$	9.80841			0.408330			0.204165	+	0.978937i	$0.434552\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.91880			−0.245553
$582$		0			0
$583$	−2.89414	+	5.01280i	−0.119863	+	0.207609i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.53963	+	2.66672i	0.0635473	+	0.110067i	0.896049	−	0.443956i	$-0.146425\pi$
$587$	1.53963	+	2.66672i	0.0635473	+	0.110067i	−0.832501	+	0.554023i	$0.813092\pi$
$588$		0			0
$589$	13.1343	−	13.1659i	0.541189	−	0.542493i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.92037	+	6.79027i	−0.160990	+	0.278843i	−0.935224	−	0.354056i	$-0.884802\pi$
$593$	−3.92037	+	6.79027i	−0.160990	+	0.278843i	0.774234	+	0.632900i	$0.218135\pi$
$594$		0			0
$595$	−0.172348	+	0.298515i	−0.00706558	+	0.0122379i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.5912	+	25.2727i	−0.596180	+	1.03261i	0.397199	+	0.917733i	$0.369982\pi$
$599$	−14.5912	+	25.2727i	−0.596180	+	1.03261i	−0.993379	+	0.114882i	$0.963351\pi$
$600$		0			0
$601$	41.8442			1.70686			0.853431	−	0.521206i	$-0.174518\pi$
$601$	41.8442			1.70686			0.853431	+	0.521206i	$0.174518\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.97210	+	6.87988i	0.161489	+	0.279707i
$606$		0			0
$607$	2.16299			0.0877932			0.0438966	−	0.999036i	$-0.486023\pi$
$607$	2.16299			0.0877932			0.0438966	+	0.999036i	$0.486023\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.30992	+	7.46500i	0.174361	+	0.302002i
$612$		0			0
$613$	16.7553	+	29.0211i	0.676742	+	1.17215i	0.975957	+	0.217965i	$0.0699420\pi$
$613$	16.7553	+	29.0211i	0.676742	+	1.17215i	−0.299215	+	0.954186i	$0.596725\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.39962	−	12.8165i	0.297897	−	0.515973i	−0.677757	−	0.735286i	$-0.737048\pi$
$617$	7.39962	−	12.8165i	0.297897	−	0.515973i	0.975655	+	0.219312i	$0.0703813\pi$
$618$		0			0
$619$	−3.26256			−0.131133			−0.0655667	−	0.997848i	$-0.520886\pi$
$619$	−3.26256			−0.131133			−0.0655667	+	0.997848i	$0.520886\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.61045	−	7.98553i	0.184714	−	0.319933i
$624$		0			0
$625$	−7.61894	−	13.1964i	−0.304757	−	0.527855i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.23609	+	3.87302i	0.0891587	+	0.154427i
$630$		0			0
$631$	−2.26346	+	3.92043i	−0.0901071	+	0.156070i	−0.907556	−	0.419931i	$-0.862054\pi$
$631$	−2.26346	+	3.92043i	−0.0901071	+	0.156070i	0.817449	+	0.576001i	$0.195388\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	11.9146			0.472815
$636$		0			0
$637$	15.9773	−	27.6735i	0.633044	−	1.09646i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.21879	−	15.9674i	−0.364120	−	0.630675i	0.624514	−	0.781013i	$-0.285297\pi$
$641$	−9.21879	−	15.9674i	−0.364120	−	0.630675i	−0.988635	+	0.150339i	$0.951964\pi$
$642$		0			0
$643$	−19.6869	−	34.0987i	−0.776376	−	1.34472i	−0.934018	−	0.357227i	$-0.883722\pi$
$643$	−19.6869	−	34.0987i	−0.776376	−	1.34472i	0.157641	−	0.987496i	$-0.449611\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−28.0809			−1.10397			−0.551987	−	0.833853i	$-0.686130\pi$
$647$	−28.0809			−1.10397			−0.551987	+	0.833853i	$0.686130\pi$
$648$		0			0
$649$	7.22241	+	12.5096i	0.283504	+	0.491044i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−14.1257			−0.552783			−0.276392	−	0.961045i	$-0.589139\pi$
$653$	−14.1257			−0.552783			−0.276392	+	0.961045i	$0.589139\pi$
$654$		0			0
$655$	1.53595	−	2.66034i	0.0600143	−	0.103948i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.1909	+	21.1152i	−0.474890	+	0.822533i	−0.999586	−	0.0287561i	$-0.990845\pi$
$659$	−12.1909	+	21.1152i	−0.474890	+	0.822533i	0.524697	+	0.851289i	$0.324179\pi$
$660$		0			0
$661$	2.53595	−	4.39239i	0.0986368	−	0.170844i	−0.812484	−	0.582984i	$-0.801885\pi$
$661$	2.53595	−	4.39239i	0.0986368	−	0.170844i	0.911121	+	0.412140i	$0.135218\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.44535	+	0.652077i	0.0948267	+	0.0252865i
$666$		0			0
$667$	36.5137	+	63.2436i	1.41382	+	2.44880i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.64894	+	6.32016i	−0.140866	+	0.243987i
$672$		0			0
$673$	−7.25234			−0.279557			−0.139779	−	0.990183i	$-0.544639\pi$
$673$	−7.25234			−0.279557			−0.139779	+	0.990183i	$0.544639\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.3251			0.512126			0.256063	−	0.966660i	$-0.417575\pi$
$677$	13.3251			0.512126			0.256063	+	0.966660i	$0.417575\pi$
$678$		0			0
$679$	0.525411	+	0.910038i	0.0201634	+	0.0349241i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.60461			−0.176191			−0.0880953	−	0.996112i	$-0.528078\pi$
$683$	−4.60461			−0.176191			−0.0880953	+	0.996112i	$0.528078\pi$
$684$		0			0
$685$	9.57054			0.365672
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−12.1058	−	20.9678i	−0.461194	−	0.798811i
$690$		0			0
$691$	32.3994			1.23253			0.616266	−	0.787538i	$-0.288645\pi$
$691$	32.3994			1.23253			0.616266	+	0.787538i	$0.288645\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.33550			−0.240319
$696$		0			0
$697$	−2.98886	+	5.17686i	−0.113211	+	0.196088i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−22.4341	−	38.8569i	−0.847323	−	1.46761i	−0.883589	−	0.468264i	$-0.844880\pi$
$701$	−22.4341	−	38.8569i	−0.847323	−	1.46761i	0.0362662	−	0.999342i	$-0.488454\pi$
$702$		0			0
$703$	23.1901	−	23.2460i	0.874631	−	0.876739i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.952484	−	1.64975i	0.0358219	−	0.0620453i
$708$		0			0
$709$	−2.09536	+	3.62927i	−0.0786929	+	0.136300i	−0.902686	−	0.430299i	$-0.858408\pi$
$709$	−2.09536	+	3.62927i	−0.0786929	+	0.136300i	0.823993	+	0.566600i	$0.191741\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	16.4413	−	28.4772i	0.615731	−	1.06648i
$714$		0			0
$715$	4.76268			0.178114
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.4990	−	32.0413i	−0.689897	−	1.19494i	−0.971871	−	0.235515i	$-0.924322\pi$
$719$	−18.4990	−	32.0413i	−0.689897	−	1.19494i	0.281973	−	0.959422i	$-0.409011\pi$
$720$		0			0
$721$	−1.82799			−0.0680779
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−20.4579	−	35.4341i	−0.759787	−	1.31599i
$726$		0			0
$727$	−0.487813	−	0.844916i	−0.0180920	−	0.0313362i	0.856838	−	0.515586i	$-0.172426\pi$
$727$	−0.487813	−	0.844916i	−0.0180920	−	0.0313362i	−0.874930	+	0.484250i	$0.839093\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.09024	+	1.88834i	−0.0403238	+	0.0698429i
$732$		0			0
$733$	25.3344			0.935749			0.467875	−	0.883795i	$-0.345020\pi$
$733$	25.3344			0.935749			0.467875	+	0.883795i	$0.345020\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.18083	+	10.7055i	−0.227674	+	0.394342i
$738$		0			0
$739$	−12.5937	−	21.8129i	−0.463266	−	0.802400i	0.535856	−	0.844310i	$-0.319989\pi$
$739$	−12.5937	−	21.8129i	−0.463266	−	0.802400i	−0.999121	+	0.0419099i	$0.986656\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	20.0795	+	34.7787i	0.736645	+	1.27591i	0.953998	+	0.299813i	$0.0969242\pi$
$743$	20.0795	+	34.7787i	0.736645	+	1.27591i	−0.217354	+	0.976093i	$0.569742\pi$
$744$		0			0
$745$	−0.0230362	+	0.0398999i	−0.000843982	+	0.00146182i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−8.64028			−0.315709
$750$		0			0
$751$	23.9778	−	41.5307i	0.874961	−	1.51548i	0.0181564	−	0.999835i	$-0.494220\pi$
$751$	23.9778	−	41.5307i	0.874961	−	1.51548i	0.856804	−	0.515642i	$-0.172446\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	8.11159	+	14.0497i	0.295211	+	0.511321i
$756$		0			0
$757$	−1.46016	−	2.52908i	−0.0530705	−	0.0919208i	0.838270	−	0.545256i	$-0.183567\pi$
$757$	−1.46016	−	2.52908i	−0.0530705	−	0.0919208i	−0.891340	+	0.453335i	$0.850234\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.14001			0.113825			0.0569126	−	0.998379i	$-0.481874\pi$
$761$	3.14001			0.113825			0.0569126	+	0.998379i	$0.481874\pi$
$762$		0			0
$763$	3.69354	+	6.39740i	0.133715	+	0.231601i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−60.4206			−2.18166
$768$		0			0
$769$	3.78360	−	6.55339i	0.136440	−	0.236321i	−0.789706	−	0.613485i	$-0.789767\pi$
$769$	3.78360	−	6.55339i	0.136440	−	0.236321i	0.926147	+	0.377163i	$0.123100\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.3484	−	23.1201i	0.480109	−	0.831574i	−0.519630	−	0.854391i	$-0.673930\pi$
$773$	13.3484	−	23.1201i	0.480109	−	0.831574i	0.999740	+	0.0228175i	$0.00726368\pi$
$774$		0			0
$775$	−9.21173	+	15.9552i	−0.330895	+	0.573127i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	42.4074	+	11.3083i	1.51940	+	0.405163i
$780$		0			0
$781$	4.94226	+	8.56025i	0.176848	+	0.306310i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.14817	−	1.98869i	0.0409800	−	0.0709795i
$786$		0			0
$787$	−40.9017			−1.45799			−0.728993	−	0.684521i	$-0.760012\pi$
$787$	−40.9017			−1.45799			−0.728993	+	0.684521i	$0.760012\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.64948			−0.0942047
$792$		0			0
$793$	−15.2630	−	26.4363i	−0.542006	−	0.938781i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.68515			0.236800			0.118400	−	0.992966i	$-0.462223\pi$
$797$	6.68515			0.236800			0.118400	+	0.992966i	$0.462223\pi$
$798$		0			0
$799$	−1.04185			−0.0368581
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.177813	−	0.307981i	−0.00627489	−	0.0108684i
$804$		0			0
$805$	4.47485			0.157718
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.26361			0.325691			0.162846	−	0.986652i	$-0.447933\pi$
$809$	9.26361			0.325691			0.162846	+	0.986652i	$0.447933\pi$
$810$		0			0
$811$	−11.8511	+	20.5268i	−0.416150	+	0.720792i	−0.995548	−	0.0942520i	$-0.969954\pi$
$811$	−11.8511	+	20.5268i	−0.416150	+	0.720792i	0.579399	+	0.815044i	$0.303287\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.35918	+	14.4785i	0.292809	+	0.507160i
$816$		0			0
$817$	15.4688	+	4.12489i	0.541183	+	0.144312i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−24.2474	+	41.9977i	−0.846240	+	1.46573i	0.0383008	+	0.999266i	$0.487805\pi$
$821$	−24.2474	+	41.9977i	−0.846240	+	1.46573i	−0.884540	+	0.466464i	$0.845528\pi$
$822$		0			0
$823$	3.38708	−	5.86659i	0.118066	−	0.204496i	−0.800935	−	0.598751i	$-0.795664\pi$
$823$	3.38708	−	5.86659i	0.118066	−	0.204496i	0.919001	+	0.394255i	$0.128997\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−16.9827	+	29.4149i	−0.590546	+	1.02286i	0.403613	+	0.914930i	$0.367754\pi$
$827$	−16.9827	+	29.4149i	−0.590546	+	1.02286i	−0.994159	+	0.107926i	$0.965579\pi$
$828$		0			0
$829$	−0.537151			−0.0186560			−0.00932801	−	0.999956i	$-0.502969\pi$
$829$	−0.537151			−0.0186560			−0.00932801	+	0.999956i	$0.502969\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.93112	+	3.34481i	0.0669095	+	0.115891i
$834$		0			0
$835$	−17.6361			−0.610321
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.4515	+	19.8346i	0.395350	+	0.684767i	0.993146	−	0.116882i	$-0.0372899\pi$
$839$	11.4515	+	19.8346i	0.395350	+	0.684767i	−0.597796	+	0.801649i	$0.703957\pi$
$840$		0			0
$841$	−30.3896	−	52.6364i	−1.04792	−	1.81505i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.59368	+	7.95649i	−0.158028	+	0.273712i
$846$		0			0
$847$	−6.76512			−0.232452
$848$		0			0
$849$		0			0
$850$		0			0
$851$	29.0290	−	50.2797i	0.995100	−	1.72356i
$852$		0			0
$853$	−1.70873	−	2.95960i	−0.0585057	−	0.101335i	0.835289	−	0.549811i	$-0.185300\pi$
$853$	−1.70873	−	2.95960i	−0.0585057	−	0.101335i	−0.893795	+	0.448476i	$0.851967\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.6972	−	21.9921i	−0.433727	−	0.751236i	0.563464	−	0.826141i	$-0.309468\pi$
$857$	−12.6972	−	21.9921i	−0.433727	−	0.751236i	−0.997191	+	0.0749040i	$0.976135\pi$
$858$		0			0
$859$	9.03851	−	15.6552i	0.308390	−	0.534147i	−0.669620	−	0.742704i	$-0.733543\pi$
$859$	9.03851	−	15.6552i	0.308390	−	0.534147i	0.978010	+	0.208556i	$0.0668765\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	54.6752			1.86117			0.930583	−	0.366080i	$-0.119300\pi$
$863$	54.6752			1.86117			0.930583	+	0.366080i	$0.119300\pi$
$864$		0			0
$865$	1.97264	−	3.41671i	0.0670717	−	0.116172i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.259926	+	0.450205i	0.00881739	+	0.0152722i
$870$		0			0
$871$	−25.8535	−	44.7796i	−0.876013	−	1.51730i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.41020			−0.182898
$876$		0			0
$877$	14.7207	+	25.4971i	0.497084	+	0.860974i	0.999994	−	0.00336411i	$-0.00107083\pi$
$877$	14.7207	+	25.4971i	0.497084	+	0.860974i	−0.502911	+	0.864338i	$0.667737\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	49.0227			1.65162			0.825809	−	0.563950i	$-0.190719\pi$
$881$	49.0227			1.65162			0.825809	+	0.563950i	$0.190719\pi$
$882$		0			0
$883$	−17.9934	+	31.1655i	−0.605525	+	1.04880i	0.386443	+	0.922313i	$0.373704\pi$
$883$	−17.9934	+	31.1655i	−0.605525	+	1.04880i	−0.991968	+	0.126488i	$0.959630\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.9731	−	24.2022i	0.469172	−	0.812630i	−0.530207	−	0.847868i	$-0.677886\pi$
$887$	13.9731	−	24.2022i	0.469172	−	0.812630i	0.999379	+	0.0352381i	$0.0112190\pi$
$888$		0			0
$889$	−5.07310	+	8.78686i	−0.170146	+	0.294702i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.98870	+	7.38637i	0.0665494	+	0.247176i
$894$		0			0
$895$	−6.52753	−	11.3060i	−0.218191	−	0.377918i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−20.2128	+	35.0096i	−0.674134	+	1.16763i
$900$		0			0
$901$	2.92638			0.0974917
$902$		0			0
$903$		0			0
$904$		0			0
$905$	16.1603			0.537188
$906$		0			0
$907$	0.838789	+	1.45283i	0.0278515	+	0.0482403i	0.879615	−	0.475686i	$-0.157800\pi$
$907$	0.838789	+	1.45283i	0.0278515	+	0.0482403i	−0.851764	+	0.523926i	$0.824467\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4.85079			0.160714			0.0803570	−	0.996766i	$-0.474394\pi$
$911$	4.85079			0.160714			0.0803570	+	0.996766i	$0.474394\pi$
$912$		0			0
$913$	−9.88452			−0.327130
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.30798	+	2.26549i	0.0431933	+	0.0748129i
$918$		0			0
$919$	−31.0634			−1.02469			−0.512344	−	0.858780i	$-0.671223\pi$
$919$	−31.0634			−1.02469			−0.512344	+	0.858780i	$0.671223\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−41.3456			−1.36091
$924$		0			0
$925$	−16.2644	+	28.1707i	−0.534769	+	0.926247i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.13315	+	10.6229i	0.201222	+	0.348527i	0.948922	−	0.315509i	$-0.102175\pi$
$929$	6.13315	+	10.6229i	0.201222	+	0.348527i	−0.747700	+	0.664036i	$0.768842\pi$
$930$		0			0
$931$	20.0274	−	20.0756i	0.656370	−	0.657952i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.287825	+	0.498527i	−0.00941287	+	0.0163036i
$936$		0			0
$937$	−12.0060	+	20.7950i	−0.392219	+	0.679344i	−0.992742	−	0.120264i	$-0.961626\pi$
$937$	−12.0060	+	20.7950i	−0.392219	+	0.679344i	0.600523	+	0.799608i	$0.294959\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	23.4144	−	40.5550i	0.763289	−	1.32206i	−0.177858	−	0.984056i	$-0.556917\pi$
$941$	23.4144	−	40.5550i	0.763289	−	1.32206i	0.941147	−	0.337999i	$-0.109750\pi$
$942$		0			0
$943$	77.6030			2.52710
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−20.9868	−	36.3501i	−0.681978	−	1.18122i	−0.974376	−	0.224924i	$-0.927787\pi$
$947$	−20.9868	−	36.3501i	−0.681978	−	1.18122i	0.292398	−	0.956297i	$-0.405547\pi$
$948$		0			0
$949$	1.48753			0.0482874
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−24.1769	−	41.8757i	−0.783168	−	1.35649i	−0.930087	−	0.367338i	$-0.880269\pi$
$953$	−24.1769	−	41.8757i	−0.783168	−	1.35649i	0.146919	−	0.989148i	$-0.453064\pi$
$954$		0			0
$955$	5.68418	+	9.84529i	0.183936	+	0.318586i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.07504	+	7.05817i	−0.131590	+	0.227920i
$960$		0			0
$961$	−12.7973			−0.412815
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5.75315	+	9.96475i	−0.185201	+	0.320777i
$966$		0			0
$967$	13.9095	+	24.0919i	0.447299	+	0.774744i	0.998209	−	0.0598200i	$-0.0190527\pi$
$967$	13.9095	+	24.0919i	0.447299	+	0.774744i	−0.550910	+	0.834564i	$0.685719\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.1195	+	24.4558i	0.453118	+	0.784823i	0.998578	−	0.0533141i	$-0.0169785\pi$
$971$	14.1195	+	24.4558i	0.453118	+	0.784823i	−0.545460	+	0.838137i	$0.683645\pi$
$972$		0			0
$973$	2.69759	−	4.67236i	0.0864808	−	0.149789i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.98074			−0.0953623			−0.0476812	−	0.998863i	$-0.515183\pi$
$977$	−2.98074			−0.0953623			−0.0476812	+	0.998863i	$0.515183\pi$
$978$		0			0
$979$	7.69954	−	13.3360i	0.246078	−	0.426220i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.6410	−	37.4833i	−0.690241	−	1.19553i	−0.971759	−	0.235976i	$-0.924171\pi$
$983$	−21.6410	−	37.4833i	−0.690241	−	1.19553i	0.281518	−	0.959556i	$-0.409162\pi$
$984$		0			0
$985$	−7.55563	−	13.0867i	−0.240742	−	0.416978i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	28.3069			0.900108
$990$		0			0
$991$	24.3531	+	42.1808i	0.773602	+	1.33992i	0.935577	+	0.353122i	$0.114880\pi$
$991$	24.3531	+	42.1808i	0.773602	+	1.33992i	−0.161975	+	0.986795i	$0.551787\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.54244			−0.0806009
$996$		0			0
$997$	10.2459	−	17.7464i	0.324490	−	0.562034i	−0.656919	−	0.753961i	$-0.728141\pi$
$997$	10.2459	−	17.7464i	0.324490	−	0.562034i	0.981409	+	0.191928i	$0.0614739\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.s.ba.577.3		8
3.2	odd	2		2736.2.s.bc.577.2		8
4.3	odd	2		1368.2.s.l.577.3	yes	8
12.11	even	2		1368.2.s.m.577.2	yes	8
19.11	even	3	inner	2736.2.s.ba.1873.3		8
57.11	odd	6		2736.2.s.bc.1873.2		8
76.11	odd	6		1368.2.s.l.505.3	✓	8
228.11	even	6		1368.2.s.m.505.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.s.l.505.3	✓	8	76.11	odd	6
1368.2.s.l.577.3	yes	8	4.3	odd	2
1368.2.s.m.505.2	yes	8	228.11	even	6
1368.2.s.m.577.2	yes	8	12.11	even	2
2736.2.s.ba.577.3		8	1.1	even	1	trivial
2736.2.s.ba.1873.3		8	19.11	even	3	inner
2736.2.s.bc.577.2		8	3.2	odd	2
2736.2.s.bc.1873.2		8	57.11	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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.412855 - 0.715087i) q^{5} +0.703158 q^{7} +O(q^{10})\)	\(q+(-0.412855 - 0.715087i) q^{5} +0.703158 q^{7} +1.17429 q^{11} +(-2.45594 + 4.25382i) q^{13} +(-0.296842 - 0.514145i) q^{17} +(-3.07850 + 3.08591i) q^{19} +(-3.85361 + 6.67465i) q^{23} +(2.15910 - 3.73967i) q^{25} +(4.73760 - 8.20576i) q^{29} -4.26647 q^{31} +(-0.290303 - 0.502819i) q^{35} -7.53293 q^{37} +(-5.03444 - 8.71990i) q^{41} +(-1.83639 - 3.18072i) q^{43} +(0.877447 - 1.51978i) q^{47} -6.50557 q^{49} +(-2.46459 + 4.26880i) q^{53} +(-0.484812 - 0.839718i) q^{55} +(6.15045 + 10.6529i) q^{59} +(-3.10736 + 5.38211i) q^{61} +4.05580 q^{65} +(-5.26346 + 9.11659i) q^{67} +(4.20873 + 7.28973i) q^{71} +(-0.151422 - 0.262271i) q^{73} +0.825711 q^{77} +(0.221348 + 0.383385i) q^{79} -8.41745 q^{83} +(-0.245106 + 0.424535i) q^{85} +(6.55677 - 11.3567i) q^{89} +(-1.72692 + 2.99111i) q^{91} +(3.47767 + 0.927354i) q^{95} +(0.747216 + 1.29422i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^5 + 4 * q^7	\( 8 q - 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{17} - 8 q^{19} + 8 q^{23} - 4 q^{25} + 4 q^{31} + 16 q^{37} - 4 q^{41} + 6 q^{43} + 4 q^{47} - 16 q^{49} - 16 q^{53} + 16 q^{55} + 12 q^{59} - 8 q^{61} - 48 q^{65} - 2 q^{67} - 4 q^{71} - 4 q^{73} + 8 q^{77} + 22 q^{79} + 8 q^{83} - 8 q^{85} + 12 q^{89} + 2 q^{91} + 32 q^{95} + 24 q^{97}+O(q^{100}) \) 8 * q - 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^17 - 8 * q^19 + 8 * q^23 - 4 * q^25 + 4 * q^31 + 16 * q^37 - 4 * q^41 + 6 * q^43 + 4 * q^47 - 16 * q^49 - 16 * q^53 + 16 * q^55 + 12 * q^59 - 8 * q^61 - 48 * q^65 - 2 * q^67 - 4 * q^71 - 4 * q^73 + 8 * q^77 + 22 * q^79 + 8 * q^83 - 8 * q^85 + 12 * q^89 + 2 * q^91 + 32 * q^95 + 24 * q^97

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