LMFDB - Embedded newform 1296.2.i.r.865.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1296,2,Mod(433,1296)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1296, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1296.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1296 = 2^{4} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1296.i (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:	$10.3486121020$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 648)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1296.865
Dual form			1296.2.i.r.433.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.133975 - 0.232051i) q^{5} +(-1.73205 + 3.00000i) q^{7} +O(q^{10})$	$q+(-0.133975 - 0.232051i) q^{5} +(-1.73205 + 3.00000i) q^{7} +(1.00000 - 1.73205i) q^{11} +(-2.23205 - 3.86603i) q^{13} +5.73205 q^{17} +0.535898 q^{19} +(4.46410 + 7.73205i) q^{23} +(2.46410 - 4.26795i) q^{25} +(-3.86603 + 6.69615i) q^{29} +(1.46410 + 2.53590i) q^{31} +0.928203 q^{35} +6.46410 q^{37} +(3.46410 + 6.00000i) q^{41} +(-5.73205 + 9.92820i) q^{43} +(-3.46410 + 6.00000i) q^{47} +(-2.50000 - 4.33013i) q^{49} +2.92820 q^{53} -0.535898 q^{55} +(4.00000 + 6.92820i) q^{59} +(-1.76795 + 3.06218i) q^{61} +(-0.598076 + 1.03590i) q^{65} +(-3.73205 - 6.46410i) q^{67} +2.00000 q^{71} +1.00000 q^{73} +(3.46410 + 6.00000i) q^{77} +(3.73205 - 6.46410i) q^{79} +(5.46410 - 9.46410i) q^{83} +(-0.767949 - 1.33013i) q^{85} +5.19615 q^{89} +15.4641 q^{91} +(-0.0717968 - 0.124356i) q^{95} +(-7.92820 + 13.7321i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5}+O(q^{10}) $ 4 * q - 4 * q^5	$ 4 q - 4 q^{5} + 4 q^{11} - 2 q^{13} + 16 q^{17} + 16 q^{19} + 4 q^{23} - 4 q^{25} - 12 q^{29} - 8 q^{31} - 24 q^{35} + 12 q^{37} - 16 q^{43} - 10 q^{49} - 16 q^{53} - 16 q^{55} + 16 q^{59} - 14 q^{61} + 8 q^{65} - 8 q^{67} + 8 q^{71} + 4 q^{73} + 8 q^{79} + 8 q^{83} - 10 q^{85} + 48 q^{91} - 28 q^{95} - 4 q^{97}+O(q^{100}) $ 4 * q - 4 * q^5 + 4 * q^11 - 2 * q^13 + 16 * q^17 + 16 * q^19 + 4 * q^23 - 4 * q^25 - 12 * q^29 - 8 * q^31 - 24 * q^35 + 12 * q^37 - 16 * q^43 - 10 * q^49 - 16 * q^53 - 16 * q^55 + 16 * q^59 - 14 * q^61 + 8 * q^65 - 8 * q^67 + 8 * q^71 + 4 * q^73 + 8 * q^79 + 8 * q^83 - 10 * q^85 + 48 * q^91 - 28 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.133975	−	0.232051i	−0.0599153	−	0.103776i	0.834512	−	0.550990i	$-0.185750\pi$
$5$	−0.133975	−	0.232051i	−0.0599153	−	0.103776i	−0.894427	+	0.447214i	$0.852416\pi$
$6$		0			0
$7$	−1.73205	+	3.00000i	−0.654654	+	1.13389i	0.327327	+	0.944911i	$0.393852\pi$
$7$	−1.73205	+	3.00000i	−0.654654	+	1.13389i	−0.981981	+	0.188982i	$0.939481\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−2.23205	−	3.86603i	−0.619060	−	1.07224i	−0.989658	−	0.143449i	$-0.954181\pi$
$13$	−2.23205	−	3.86603i	−0.619060	−	1.07224i	0.370598	−	0.928793i	$-0.379153\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.73205			1.39023			0.695113	−	0.718900i	$-0.255354\pi$
$17$	5.73205			1.39023			0.695113	+	0.718900i	$0.255354\pi$
$18$		0			0
$19$	0.535898			0.122944			0.0614718	−	0.998109i	$-0.480421\pi$
$19$	0.535898			0.122944			0.0614718	+	0.998109i	$0.480421\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.46410	+	7.73205i	0.930830	+	1.61224i	0.781907	+	0.623395i	$0.214247\pi$
$23$	4.46410	+	7.73205i	0.930830	+	1.61224i	0.148923	+	0.988849i	$0.452419\pi$
$24$		0			0
$25$	2.46410	−	4.26795i	0.492820	−	0.853590i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.86603	+	6.69615i	−0.717903	+	1.24344i	0.243926	+	0.969794i	$0.421564\pi$
$29$	−3.86603	+	6.69615i	−0.717903	+	1.24344i	−0.961829	+	0.273651i	$0.911769\pi$
$30$		0			0
$31$	1.46410	+	2.53590i	0.262960	+	0.455461i	0.967027	−	0.254673i	$-0.0819678\pi$
$31$	1.46410	+	2.53590i	0.262960	+	0.455461i	−0.704067	+	0.710134i	$0.748634\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.928203			0.156895
$36$		0			0
$37$	6.46410			1.06269			0.531346	−	0.847155i	$-0.321686\pi$
$37$	6.46410			1.06269			0.531346	+	0.847155i	$0.321686\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.46410	+	6.00000i	0.541002	+	0.937043i	0.998847	+	0.0480106i	$0.0152881\pi$
$41$	3.46410	+	6.00000i	0.541002	+	0.937043i	−0.457845	+	0.889032i	$0.651379\pi$
$42$		0			0
$43$	−5.73205	+	9.92820i	−0.874130	+	1.51404i	−0.0164424	+	0.999865i	$0.505234\pi$
$43$	−5.73205	+	9.92820i	−0.874130	+	1.51404i	−0.857687	+	0.514172i	$0.828099\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.46410	+	6.00000i	−0.505291	+	0.875190i	0.494690	+	0.869069i	$0.335282\pi$
$47$	−3.46410	+	6.00000i	−0.505291	+	0.875190i	−0.999981	+	0.00612051i	$0.998052\pi$
$48$		0			0
$49$	−2.50000	−	4.33013i	−0.357143	−	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.92820			0.402220			0.201110	−	0.979569i	$-0.435545\pi$
$53$	2.92820			0.402220			0.201110	+	0.979569i	$0.435545\pi$
$54$		0			0
$55$	−0.535898			−0.0722605
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	−1.76795	+	3.06218i	−0.226363	+	0.392072i	−0.956727	−	0.290986i	$-0.906017\pi$
$61$	−1.76795	+	3.06218i	−0.226363	+	0.392072i	0.730365	+	0.683057i	$0.239350\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.598076	+	1.03590i	−0.0741822	+	0.128487i
$66$		0			0
$67$	−3.73205	−	6.46410i	−0.455943	−	0.789716i	0.542799	−	0.839862i	$-0.317364\pi$
$67$	−3.73205	−	6.46410i	−0.455943	−	0.789716i	−0.998742	+	0.0501467i	$0.984031\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	1.00000			0.117041			0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000			0.117041			0.0585206	+	0.998286i	$0.481362\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.46410	+	6.00000i	0.394771	+	0.683763i
$78$		0			0
$79$	3.73205	−	6.46410i	0.419889	−	0.727268i	−0.576039	−	0.817422i	$-0.695403\pi$
$79$	3.73205	−	6.46410i	0.419889	−	0.727268i	0.995928	+	0.0901537i	$0.0287358\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.46410	−	9.46410i	0.599763	−	1.03882i	−0.393093	−	0.919499i	$-0.628595\pi$
$83$	5.46410	−	9.46410i	0.599763	−	1.03882i	0.992856	−	0.119321i	$-0.0380718\pi$
$84$		0			0
$85$	−0.767949	−	1.33013i	−0.0832958	−	0.144273i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.19615			0.550791			0.275396	−	0.961331i	$-0.411191\pi$
$89$	5.19615			0.550791			0.275396	+	0.961331i	$0.411191\pi$
$90$		0			0
$91$	15.4641			1.62108
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0717968	−	0.124356i	−0.00736619	−	0.0127586i
$96$		0			0
$97$	−7.92820	+	13.7321i	−0.804987	+	1.39428i	0.111313	+	0.993785i	$0.464494\pi$
$97$	−7.92820	+	13.7321i	−0.804987	+	1.39428i	−0.916300	+	0.400493i	$0.868839\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	−0.396236	−	0.918149i	$-0.629684\pi$
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	0.993258	−	0.115924i	$-0.0369830\pi$
$102$		0			0
$103$	−1.46410	−	2.53590i	−0.144262	−	0.249869i	0.784835	−	0.619704i	$-0.212748\pi$
$103$	−1.46410	−	2.53590i	−0.144262	−	0.249869i	−0.929097	+	0.369835i	$0.879414\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	18.9282			1.82986			0.914929	−	0.403614i	$-0.132246\pi$
$107$	18.9282			1.82986			0.914929	+	0.403614i	$0.132246\pi$
$108$		0			0
$109$	−2.46410			−0.236018			−0.118009	−	0.993013i	$-0.537651\pi$
$109$	−2.46410			−0.236018			−0.118009	+	0.993013i	$0.537651\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.866025	−	1.50000i	−0.0814688	−	0.141108i	0.822412	−	0.568892i	$-0.192628\pi$
$113$	−0.866025	−	1.50000i	−0.0814688	−	0.141108i	−0.903881	+	0.427784i	$0.859294\pi$
$114$		0			0
$115$	1.19615	−	2.07180i	0.111542	−	0.193196i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.92820	+	17.1962i	−0.910117	+	1.57637i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.66025			−0.237940
$126$		0			0
$127$	−7.46410			−0.662332			−0.331166	−	0.943573i	$-0.607442\pi$
$127$	−7.46410			−0.662332			−0.331166	+	0.943573i	$0.607442\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−10.4641	−	18.1244i	−0.914253	−	1.58353i	−0.807992	−	0.589194i	$-0.799445\pi$
$131$	−10.4641	−	18.1244i	−0.914253	−	1.58353i	−0.106261	−	0.994338i	$-0.533888\pi$
$132$		0			0
$133$	−0.928203	+	1.60770i	−0.0804854	+	0.139405i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.66987	+	2.89230i	−0.142667	+	0.247106i	−0.928500	−	0.371332i	$-0.878901\pi$
$137$	−1.66987	+	2.89230i	−0.142667	+	0.247106i	0.785833	+	0.618439i	$0.212234\pi$
$138$		0			0
$139$	−9.46410	−	16.3923i	−0.802735	−	1.39038i	−0.917810	−	0.397020i	$-0.870044\pi$
$139$	−9.46410	−	16.3923i	−0.802735	−	1.39038i	0.115075	−	0.993357i	$-0.463289\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.92820			−0.746614
$144$		0			0
$145$	2.07180			0.172053
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.13397	+	10.6244i	0.502515	+	0.870381i	0.999996	+	0.00290625i	$0.000925091\pi$
$149$	6.13397	+	10.6244i	0.502515	+	0.870381i	−0.497481	+	0.867475i	$0.665742\pi$
$150$		0			0
$151$	7.46410	−	12.9282i	0.607420	−	1.05208i	−0.384244	−	0.923232i	$-0.625538\pi$
$151$	7.46410	−	12.9282i	0.607420	−	1.05208i	0.991664	−	0.128851i	$-0.0411288\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.392305	−	0.679492i	0.0315107	−	0.0545781i
$156$		0			0
$157$	7.69615	+	13.3301i	0.614220	+	1.06386i	0.990521	+	0.137362i	$0.0438625\pi$
$157$	7.69615	+	13.3301i	0.614220	+	1.06386i	−0.376301	+	0.926497i	$0.622804\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−30.9282			−2.43748
$162$		0			0
$163$		0			0			−	1.00000i	$-0.5\pi$
$163$		0			0				1.00000i	$0.5\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	0.969693	+	0.244328i	$0.0785675\pi$
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	−0.273252	+	0.961943i	$0.588099\pi$
$168$		0			0
$169$	−3.46410	+	6.00000i	−0.266469	+	0.461538i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.13397	−	3.69615i	0.162243	−	0.281013i	−0.773430	−	0.633882i	$-0.781460\pi$
$173$	2.13397	−	3.69615i	0.162243	−	0.281013i	0.935673	+	0.352869i	$0.114794\pi$
$174$		0			0
$175$	8.53590	+	14.7846i	0.645253	+	1.11761i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.92820			−0.517838			−0.258919	−	0.965899i	$-0.583366\pi$
$179$	−6.92820			−0.517838			−0.258919	+	0.965899i	$0.583366\pi$
$180$		0			0
$181$	−19.8564			−1.47592			−0.737958	−	0.674847i	$-0.764210\pi$
$181$	−19.8564			−1.47592			−0.737958	+	0.674847i	$0.764210\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.866025	−	1.50000i	−0.0636715	−	0.110282i
$186$		0			0
$187$	5.73205	−	9.92820i	0.419169	−	0.726022i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.92820	+	6.80385i	−0.284235	+	0.492309i	−0.972423	−	0.233223i	$-0.925073\pi$
$191$	−3.92820	+	6.80385i	−0.284235	+	0.492309i	0.688189	+	0.725532i	$0.258406\pi$
$192$		0			0
$193$	−2.03590	−	3.52628i	−0.146547	−	0.253827i	0.783402	−	0.621515i	$-0.213483\pi$
$193$	−2.03590	−	3.52628i	−0.146547	−	0.253827i	−0.929949	+	0.367688i	$0.880149\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.6603			1.04450			0.522250	−	0.852792i	$-0.325093\pi$
$197$	14.6603			1.04450			0.522250	+	0.852792i	$0.325093\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−13.3923	−	23.1962i	−0.939956	−	1.62805i
$204$		0			0
$205$	0.928203	−	1.60770i	0.0648285	−	0.112286i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.535898	−	0.928203i	0.0370689	−	0.0642052i
$210$		0			0
$211$	4.66025	+	8.07180i	0.320825	+	0.555685i	0.980659	−	0.195727i	$-0.0627065\pi$
$211$	4.66025	+	8.07180i	0.320825	+	0.555685i	−0.659833	+	0.751412i	$0.729373\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.07180			0.209495
$216$		0			0
$217$	−10.1436			−0.688592
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−12.7942	−	22.1603i	−0.860633	−	1.49066i
$222$		0			0
$223$	3.73205	−	6.46410i	0.249917	−	0.432868i	−0.713586	−	0.700568i	$-0.752930\pi$
$223$	3.73205	−	6.46410i	0.249917	−	0.432868i	0.963502	+	0.267700i	$0.0862635\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.3923	−	23.1962i	0.888878	−	1.53958i	0.0476758	−	0.998863i	$-0.484819\pi$
$227$	13.3923	−	23.1962i	0.888878	−	1.53958i	0.841203	−	0.540720i	$-0.181848\pi$
$228$		0			0
$229$	7.23205	+	12.5263i	0.477907	+	0.827760i	0.999679	−	0.0253252i	$-0.00806212\pi$
$229$	7.23205	+	12.5263i	0.477907	+	0.827760i	−0.521772	+	0.853085i	$0.674729\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.26795			0.410627			0.205314	−	0.978696i	$-0.434179\pi$
$233$	6.26795			0.410627			0.205314	+	0.978696i	$0.434179\pi$
$234$		0			0
$235$	1.85641			0.121099
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.46410	−	2.53590i	−0.0947049	−	0.164034i	0.814781	−	0.579770i	$-0.196857\pi$
$239$	−1.46410	−	2.53590i	−0.0947049	−	0.164034i	−0.909485	+	0.415736i	$0.863524\pi$
$240$		0			0
$241$	10.9641	−	18.9904i	0.706260	−	1.22328i	−0.259975	−	0.965615i	$-0.583714\pi$
$241$	10.9641	−	18.9904i	0.706260	−	1.22328i	0.966235	−	0.257663i	$-0.0829523\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.669873	+	1.16025i	−0.0427966	+	0.0741259i
$246$		0			0
$247$	−1.19615	−	2.07180i	−0.0761094	−	0.131825i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−10.0000			−0.631194			−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000			−0.631194			−0.315597	+	0.948893i	$0.602205\pi$
$252$		0			0
$253$	17.8564			1.12262
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.52628	−	9.57180i	−0.344720	−	0.597072i	0.640583	−	0.767889i	$-0.278693\pi$
$257$	−5.52628	−	9.57180i	−0.344720	−	0.597072i	−0.985303	+	0.170817i	$0.945359\pi$
$258$		0			0
$259$	−11.1962	+	19.3923i	−0.695695	+	1.20498i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.39230	+	11.0718i	−0.394166	+	0.682716i	−0.992994	−	0.118161i	$-0.962300\pi$
$263$	−6.39230	+	11.0718i	−0.394166	+	0.682716i	0.598828	+	0.800878i	$0.295633\pi$
$264$		0			0
$265$	−0.392305	−	0.679492i	−0.0240991	−	0.0417409i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−24.5167			−1.49481			−0.747404	−	0.664370i	$-0.768700\pi$
$269$	−24.5167			−1.49481			−0.747404	+	0.664370i	$0.768700\pi$
$270$		0			0
$271$	−23.4641			−1.42534			−0.712671	−	0.701498i	$-0.752515\pi$
$271$	−23.4641			−1.42534			−0.712671	+	0.701498i	$0.752515\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.92820	−	8.53590i	−0.297182	−	0.514734i
$276$		0			0
$277$	7.00000	−	12.1244i	0.420589	−	0.728482i	−0.575408	−	0.817867i	$-0.695157\pi$
$277$	7.00000	−	12.1244i	0.420589	−	0.728482i	0.995997	+	0.0893846i	$0.0284900\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.0622	−	17.4282i	0.600259	−	1.03968i	−0.392522	−	0.919742i	$-0.628397\pi$
$281$	10.0622	−	17.4282i	0.600259	−	1.03968i	0.992782	−	0.119937i	$-0.0382692\pi$
$282$		0			0
$283$	4.92820	+	8.53590i	0.292951	+	0.507406i	0.974506	−	0.224360i	$-0.0720293\pi$
$283$	4.92820	+	8.53590i	0.292951	+	0.507406i	−0.681555	+	0.731767i	$0.738696\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−24.0000			−1.41668
$288$		0			0
$289$	15.8564			0.932730
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.06218	−	15.6962i	−0.529418	−	0.916979i	−0.999411	−	0.0343090i	$-0.989077\pi$
$293$	−9.06218	−	15.6962i	−0.529418	−	0.916979i	0.469993	−	0.882670i	$-0.344256\pi$
$294$		0			0
$295$	1.07180	−	1.85641i	0.0624024	−	0.108084i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	19.9282	−	34.5167i	1.15248	−	1.99615i
$300$		0			0
$301$	−19.8564	−	34.3923i	−1.14450	−	1.98234i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.947441			0.0542503
$306$		0			0
$307$	5.07180			0.289463			0.144731	−	0.989471i	$-0.453768\pi$
$307$	5.07180			0.289463			0.144731	+	0.989471i	$0.453768\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	8.89230	−	15.4019i	0.502623	−	0.870568i	−0.497373	−	0.867537i	$-0.665702\pi$
$313$	8.89230	−	15.4019i	0.502623	−	0.870568i	0.999995	−	0.00303119i	$-0.000964858\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.13397	+	3.69615i	−0.119856	+	0.207597i	−0.919710	−	0.392597i	$-0.871577\pi$
$317$	−2.13397	+	3.69615i	−0.119856	+	0.207597i	0.799855	+	0.600194i	$0.204910\pi$
$318$		0			0
$319$	7.73205	+	13.3923i	0.432912	+	0.749825i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.07180			0.170919
$324$		0			0
$325$	−22.0000			−1.22034
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−12.0000	−	20.7846i	−0.661581	−	1.14589i
$330$		0			0
$331$	−14.1244	+	24.4641i	−0.776345	+	1.34467i	0.157691	+	0.987489i	$0.449595\pi$
$331$	−14.1244	+	24.4641i	−0.776345	+	1.34467i	−0.934036	+	0.357180i	$0.883738\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.00000	+	1.73205i	−0.0546358	+	0.0946320i
$336$		0			0
$337$	9.92820	+	17.1962i	0.540824	+	0.936734i	0.998857	+	0.0477991i	$0.0152207\pi$
$337$	9.92820	+	17.1962i	0.540824	+	0.936734i	−0.458033	+	0.888935i	$0.651446\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.85641			0.317142
$342$		0			0
$343$	−6.92820			−0.374088
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.53590	+	9.58846i	0.297183	+	0.514735i	0.975490	−	0.220043i	$-0.0706197\pi$
$347$	5.53590	+	9.58846i	0.297183	+	0.514735i	−0.678308	+	0.734778i	$0.737286\pi$
$348$		0			0
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	−0.774493	−	0.632583i	$-0.781995\pi$
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	0.935079	+	0.354439i	$0.115328\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.9282	+	25.8564i	−0.794548	+	1.37620i	0.128578	+	0.991699i	$0.458959\pi$
$353$	−14.9282	+	25.8564i	−0.794548	+	1.37620i	−0.923126	+	0.384498i	$0.874374\pi$
$354$		0			0
$355$	−0.267949	−	0.464102i	−0.0142213	−	0.0246320i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.7846			−1.41364			−0.706819	−	0.707395i	$-0.749870\pi$
$359$	−26.7846			−1.41364			−0.706819	+	0.707395i	$0.749870\pi$
$360$		0			0
$361$	−18.7128			−0.984885
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.133975	−	0.232051i	−0.00701255	−	0.0121461i
$366$		0			0
$367$	4.53590	−	7.85641i	0.236772	−	0.410101i	−0.723014	−	0.690833i	$-0.757244\pi$
$367$	4.53590	−	7.85641i	0.236772	−	0.410101i	0.959786	+	0.280732i	$0.0905772\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.07180	+	8.78461i	−0.263315	+	0.456074i
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	34.5167			1.77770
$378$		0			0
$379$	−16.7846			−0.862167			−0.431084	−	0.902312i	$-0.641869\pi$
$379$	−16.7846			−0.862167			−0.431084	+	0.902312i	$0.641869\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	0.998954	−	0.0457244i	$-0.0145596\pi$
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	−0.539076	+	0.842257i	$0.681226\pi$
$384$		0			0
$385$	0.928203	−	1.60770i	0.0473056	−	0.0819357i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.53590	+	11.3205i	−0.331383	+	0.573973i	−0.982783	−	0.184762i	$-0.940849\pi$
$389$	−6.53590	+	11.3205i	−0.331383	+	0.573973i	0.651400	+	0.758734i	$0.274182\pi$
$390$		0			0
$391$	25.5885	+	44.3205i	1.29406	+	2.24138i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.00000			−0.100631
$396$		0			0
$397$	21.3923			1.07365			0.536825	−	0.843694i	$-0.319624\pi$
$397$	21.3923			1.07365			0.536825	+	0.843694i	$0.319624\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.40192	+	5.89230i	0.169884	+	0.294248i	0.938379	−	0.345608i	$-0.112327\pi$
$401$	3.40192	+	5.89230i	0.169884	+	0.294248i	−0.768495	+	0.639856i	$0.778994\pi$
$402$		0			0
$403$	6.53590	−	11.3205i	0.325576	−	0.563915i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.46410	−	11.1962i	0.320414	−	0.554973i
$408$		0			0
$409$	−1.03590	−	1.79423i	−0.0512219	−	0.0887189i	0.839278	−	0.543703i	$-0.182978\pi$
$409$	−1.03590	−	1.79423i	−0.0512219	−	0.0887189i	−0.890500	+	0.454984i	$0.849645\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−27.7128			−1.36366
$414$		0			0
$415$	−2.92820			−0.143740
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.928203	−	1.60770i	−0.0453457	−	0.0785410i	0.842462	−	0.538756i	$-0.181106\pi$
$419$	−0.928203	−	1.60770i	−0.0453457	−	0.0785410i	−0.887807	+	0.460215i	$0.847772\pi$
$420$		0			0
$421$	8.69615	−	15.0622i	0.423825	−	0.734086i	−0.572485	−	0.819915i	$-0.694021\pi$
$421$	8.69615	−	15.0622i	0.423825	−	0.734086i	0.996310	+	0.0858293i	$0.0273540\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	14.1244	−	24.4641i	0.685132	−	1.18668i
$426$		0			0
$427$	−6.12436	−	10.6077i	−0.296378	−	0.513342i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.0718			0.629646			0.314823	−	0.949150i	$-0.398055\pi$
$431$	13.0718			0.629646			0.314823	+	0.949150i	$0.398055\pi$
$432$		0			0
$433$	−13.7846			−0.662446			−0.331223	−	0.943552i	$-0.607461\pi$
$433$	−13.7846			−0.662446			−0.331223	+	0.943552i	$0.607461\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.39230	+	4.14359i	0.114439	+	0.198215i
$438$		0			0
$439$	−6.00000	+	10.3923i	−0.286364	+	0.495998i	−0.972939	−	0.231062i	$-0.925780\pi$
$439$	−6.00000	+	10.3923i	−0.286364	+	0.495998i	0.686575	+	0.727059i	$0.259113\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.46410	+	12.9282i	−0.354630	+	0.614237i	−0.987055	−	0.160385i	$-0.948727\pi$
$443$	−7.46410	+	12.9282i	−0.354630	+	0.614237i	0.632424	+	0.774622i	$0.282060\pi$
$444$		0			0
$445$	−0.696152	−	1.20577i	−0.0330008	−	0.0571590i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−12.7846			−0.603343			−0.301672	−	0.953412i	$-0.597545\pi$
$449$	−12.7846			−0.603343			−0.301672	+	0.953412i	$0.597545\pi$
$450$		0			0
$451$	13.8564			0.652473
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.07180	−	3.58846i	−0.0971273	−	0.168229i
$456$		0			0
$457$	12.0359	−	20.8468i	0.563016	−	0.975172i	−0.434216	−	0.900809i	$-0.642974\pi$
$457$	12.0359	−	20.8468i	0.563016	−	0.975172i	0.997231	−	0.0743627i	$-0.0236922\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−8.39230	+	14.5359i	−0.390869	+	0.677004i	−0.992564	−	0.121721i	$-0.961159\pi$
$461$	−8.39230	+	14.5359i	−0.390869	+	0.677004i	0.601696	+	0.798725i	$0.294492\pi$
$462$		0			0
$463$	−20.0000	−	34.6410i	−0.929479	−	1.60990i	−0.784195	−	0.620515i	$-0.786924\pi$
$463$	−20.0000	−	34.6410i	−0.929479	−	1.60990i	−0.145284	−	0.989390i	$-0.546410\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	15.7128			0.727102			0.363551	−	0.931574i	$-0.381564\pi$
$467$	15.7128			0.727102			0.363551	+	0.931574i	$0.381564\pi$
$468$		0			0
$469$	25.8564			1.19394
$470$		0			0
$471$		0			0
$472$		0			0
$473$	11.4641	+	19.8564i	0.527120	+	0.912999i
$474$		0			0
$475$	1.32051	−	2.28719i	0.0605891	−	0.104943i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.92820	+	13.7321i	−0.362249	+	0.627433i	−0.988331	−	0.152324i	$-0.951324\pi$
$479$	−7.92820	+	13.7321i	−0.362249	+	0.627433i	0.626082	+	0.779757i	$0.284658\pi$
$480$		0			0
$481$	−14.4282	−	24.9904i	−0.657869	−	1.13946i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.24871			0.192924
$486$		0			0
$487$	−21.0718			−0.954854			−0.477427	−	0.878671i	$-0.658431\pi$
$487$	−21.0718			−0.954854			−0.477427	+	0.878671i	$0.658431\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.07180	−	13.9808i	−0.364275	−	0.630943i	0.624384	−	0.781117i	$-0.285350\pi$
$491$	−8.07180	−	13.9808i	−0.364275	−	0.630943i	−0.988660	+	0.150174i	$0.952017\pi$
$492$		0			0
$493$	−22.1603	+	38.3827i	−0.998048	+	1.72867i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.46410	+	6.00000i	−0.155386	+	0.269137i
$498$		0			0
$499$	−12.1244	−	21.0000i	−0.542761	−	0.940089i	−0.998744	−	0.0501009i	$-0.984046\pi$
$499$	−12.1244	−	21.0000i	−0.542761	−	0.940089i	0.455983	−	0.889988i	$-0.349288\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.85641			0.0827731			0.0413865	−	0.999143i	$-0.486822\pi$
$503$	1.85641			0.0827731			0.0413865	+	0.999143i	$0.486822\pi$
$504$		0			0
$505$	−3.21539			−0.143083
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.39230	−	7.60770i	−0.194685	−	0.337205i	0.752112	−	0.659035i	$-0.229035\pi$
$509$	−4.39230	−	7.60770i	−0.194685	−	0.337205i	−0.946797	+	0.321830i	$0.895702\pi$
$510$		0			0
$511$	−1.73205	+	3.00000i	−0.0766214	+	0.132712i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.392305	+	0.679492i	−0.0172870	+	0.0299420i
$516$		0			0
$517$	6.92820	+	12.0000i	0.304702	+	0.527759i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	12.7846			0.560104			0.280052	−	0.959985i	$-0.409648\pi$
$521$	12.7846			0.560104			0.280052	+	0.959985i	$0.409648\pi$
$522$		0			0
$523$	28.5359			1.24779			0.623894	−	0.781509i	$-0.285550\pi$
$523$	28.5359			1.24779			0.623894	+	0.781509i	$0.285550\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.39230	+	14.5359i	0.365575	+	0.633194i
$528$		0			0
$529$	−28.3564	+	49.1147i	−1.23289	+	2.13542i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	15.4641	−	26.7846i	0.669825	−	1.16017i
$534$		0			0
$535$	−2.53590	−	4.39230i	−0.109636	−	0.189896i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.0000			−0.430730
$540$		0			0
$541$	−13.3923			−0.575780			−0.287890	−	0.957663i	$-0.592954\pi$
$541$	−13.3923			−0.575780			−0.287890	+	0.957663i	$0.592954\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.330127	+	0.571797i	0.0141411	+	0.0244931i
$546$		0			0
$547$	4.92820	−	8.53590i	0.210715	−	0.364969i	−0.741224	−	0.671258i	$-0.765754\pi$
$547$	4.92820	−	8.53590i	0.210715	−	0.364969i	0.951938	+	0.306289i	$0.0990875\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.07180	+	3.58846i	−0.0882615	+	0.152873i
$552$		0			0
$553$	12.9282	+	22.3923i	0.549763	+	0.952218i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.5885			0.745247			0.372623	−	0.927983i	$-0.378458\pi$
$557$	17.5885			0.745247			0.372623	+	0.927983i	$0.378458\pi$
$558$		0			0
$559$	51.1769			2.16455
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.46410	+	12.9282i	0.314574	+	0.544859i	0.979347	−	0.202187i	$-0.0648049\pi$
$563$	7.46410	+	12.9282i	0.314574	+	0.544859i	−0.664773	+	0.747046i	$0.731472\pi$
$564$		0			0
$565$	−0.232051	+	0.401924i	−0.00976245	+	0.0169091i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.20577	−	10.7487i	0.260159	−	0.450609i	−0.706125	−	0.708088i	$-0.749558\pi$
$569$	6.20577	−	10.7487i	0.260159	−	0.450609i	0.966284	+	0.257478i	$0.0828915\pi$
$570$		0			0
$571$	6.92820	+	12.0000i	0.289936	+	0.502184i	0.973794	−	0.227431i	$-0.0730325\pi$
$571$	6.92820	+	12.0000i	0.289936	+	0.502184i	−0.683858	+	0.729615i	$0.739699\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	44.0000			1.83493
$576$		0			0
$577$	24.8564			1.03479			0.517393	−	0.855748i	$-0.326903\pi$
$577$	24.8564			1.03479			0.517393	+	0.855748i	$0.326903\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	18.9282	+	32.7846i	0.785274	+	1.36013i
$582$		0			0
$583$	2.92820	−	5.07180i	0.121274	−	0.210052i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.0000	−	22.5167i	0.536567	−	0.929362i	−0.462518	−	0.886610i	$-0.653054\pi$
$587$	13.0000	−	22.5167i	0.536567	−	0.929362i	0.999086	−	0.0427523i	$-0.0136126\pi$
$588$		0			0
$589$	0.784610	+	1.35898i	0.0323293	+	0.0559960i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−31.5885			−1.29718			−0.648591	−	0.761137i	$-0.724642\pi$
$593$	−31.5885			−1.29718			−0.648591	+	0.761137i	$0.724642\pi$
$594$		0			0
$595$	5.32051			0.218120
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.53590	−	4.39230i	−0.103614	−	0.179465i	0.809557	−	0.587041i	$-0.199707\pi$
$599$	−2.53590	−	4.39230i	−0.103614	−	0.179465i	−0.913171	+	0.407576i	$0.866374\pi$
$600$		0			0
$601$	−10.4282	+	18.0622i	−0.425375	+	0.736772i	−0.996455	−	0.0841227i	$-0.973191\pi$
$601$	−10.4282	+	18.0622i	−0.425375	+	0.736772i	0.571080	+	0.820894i	$0.306525\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.937822	−	1.62436i	0.0381279	−	0.0660394i
$606$		0			0
$607$	−11.5885	−	20.0718i	−0.470361	−	0.814689i	0.529065	−	0.848582i	$-0.322543\pi$
$607$	−11.5885	−	20.0718i	−0.470361	−	0.814689i	−0.999425	+	0.0338925i	$0.989210\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	30.9282			1.25122
$612$		0			0
$613$	−23.8564			−0.963551			−0.481776	−	0.876295i	$-0.660008\pi$
$613$	−23.8564			−0.963551			−0.481776	+	0.876295i	$0.660008\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.7224	+	25.5000i	0.592703	+	1.02659i	0.993867	+	0.110585i	$0.0352725\pi$
$617$	14.7224	+	25.5000i	0.592703	+	1.02659i	−0.401164	+	0.916006i	$0.631394\pi$
$618$		0			0
$619$	18.3923	−	31.8564i	0.739249	−	1.28042i	−0.213585	−	0.976925i	$-0.568514\pi$
$619$	18.3923	−	31.8564i	0.739249	−	1.28042i	0.952834	−	0.303493i	$-0.0981527\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−9.00000	+	15.5885i	−0.360577	+	0.624538i
$624$		0			0
$625$	−11.9641	−	20.7224i	−0.478564	−	0.828897i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	37.0526			1.47738
$630$		0			0
$631$	28.7846			1.14590			0.572949	−	0.819591i	$-0.305799\pi$
$631$	28.7846			1.14590			0.572949	+	0.819591i	$0.305799\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.00000	+	1.73205i	0.0396838	+	0.0687343i
$636$		0			0
$637$	−11.1603	+	19.3301i	−0.442185	+	0.765888i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.9904	+	19.0359i	−0.434094	+	0.751873i	−0.997221	−	0.0744974i	$-0.976265\pi$
$641$	−10.9904	+	19.0359i	−0.434094	+	0.751873i	0.563127	+	0.826370i	$0.309598\pi$
$642$		0			0
$643$	−4.39230	−	7.60770i	−0.173216	−	0.300018i	0.766327	−	0.642451i	$-0.222082\pi$
$643$	−4.39230	−	7.60770i	−0.173216	−	0.300018i	−0.939542	+	0.342433i	$0.888749\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17.7128			0.696363			0.348181	−	0.937427i	$-0.386799\pi$
$647$	17.7128			0.696363			0.348181	+	0.937427i	$0.386799\pi$
$648$		0			0
$649$	16.0000			0.628055
$650$		0			0
$651$		0			0
$652$		0			0
$653$	16.3923	+	28.3923i	0.641480	+	1.11108i	0.985102	+	0.171969i	$0.0550128\pi$
$653$	16.3923	+	28.3923i	0.641480	+	1.11108i	−0.343622	+	0.939108i	$0.611654\pi$
$654$		0			0
$655$	−2.80385	+	4.85641i	−0.109555	+	0.189756i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.3923	+	33.5885i	−0.755417	+	1.30842i	0.189750	+	0.981832i	$0.439232\pi$
$659$	−19.3923	+	33.5885i	−0.755417	+	1.30842i	−0.945167	+	0.326588i	$0.894101\pi$
$660$		0			0
$661$	−2.16025	−	3.74167i	−0.0840241	−	0.145534i	0.820951	−	0.570999i	$-0.193444\pi$
$661$	−2.16025	−	3.74167i	−0.0840241	−	0.145534i	−0.904975	+	0.425465i	$0.860111\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.497423			0.0192892
$666$		0			0
$667$	−69.0333			−2.67298
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.53590	+	6.12436i	0.136502	+	0.236428i
$672$		0			0
$673$	−6.03590	+	10.4545i	−0.232667	+	0.402991i	−0.958592	−	0.284783i	$-0.908078\pi$
$673$	−6.03590	+	10.4545i	−0.232667	+	0.402991i	0.725925	+	0.687774i	$0.241412\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.3205	−	33.4641i	0.742547	−	1.28613i	−0.208784	−	0.977962i	$-0.566951\pi$
$677$	19.3205	−	33.4641i	0.742547	−	1.28613i	0.951332	−	0.308168i	$-0.0997160\pi$
$678$		0			0
$679$	−27.4641	−	47.5692i	−1.05398	−	1.82554i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−14.9282			−0.571212			−0.285606	−	0.958347i	$-0.592195\pi$
$683$	−14.9282			−0.571212			−0.285606	+	0.958347i	$0.592195\pi$
$684$		0			0
$685$	0.894882			0.0341917
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.53590	−	11.3205i	−0.248998	−	0.431277i
$690$		0			0
$691$	−19.1962	+	33.2487i	−0.730256	+	1.26484i	0.226518	+	0.974007i	$0.427266\pi$
$691$	−19.1962	+	33.2487i	−0.730256	+	1.26484i	−0.956774	+	0.290834i	$0.906067\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.53590	+	4.39230i	−0.0961921	+	0.166610i
$696$		0			0
$697$	19.8564	+	34.3923i	0.752115	+	1.30270i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−23.4449			−0.885500			−0.442750	−	0.896645i	$-0.645997\pi$
$701$	−23.4449			−0.885500			−0.442750	+	0.896645i	$0.645997\pi$
$702$		0			0
$703$	3.46410			0.130651
$704$		0			0
$705$		0			0
$706$		0			0
$707$	20.7846	+	36.0000i	0.781686	+	1.35392i
$708$		0			0
$709$	6.16025	−	10.6699i	0.231353	−	0.400715i	−0.726853	−	0.686793i	$-0.759018\pi$
$709$	6.16025	−	10.6699i	0.231353	−	0.400715i	0.958207	+	0.286077i	$0.0923514\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−13.0718	+	22.6410i	−0.489543	+	0.847913i
$714$		0			0
$715$	1.19615	+	2.07180i	0.0447336	+	0.0774808i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.92820			0.183791			0.0918955	−	0.995769i	$-0.470707\pi$
$719$	4.92820			0.183791			0.0918955	+	0.995769i	$0.470707\pi$
$720$		0			0
$721$	10.1436			0.377767
$722$		0			0
$723$		0			0
$724$		0			0
$725$	19.0526	+	33.0000i	0.707594	+	1.22559i
$726$		0			0
$727$	15.5885	−	27.0000i	0.578144	−	1.00137i	−0.417548	−	0.908655i	$-0.637111\pi$
$727$	15.5885	−	27.0000i	0.578144	−	1.00137i	0.995692	−	0.0927199i	$-0.0295561\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−32.8564	+	56.9090i	−1.21524	+	2.10485i
$732$		0			0
$733$	−6.07180	−	10.5167i	−0.224267	−	0.388442i	0.731832	−	0.681485i	$-0.238665\pi$
$733$	−6.07180	−	10.5167i	−0.224267	−	0.388442i	−0.956099	+	0.293043i	$0.905332\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−14.9282			−0.549887
$738$		0			0
$739$	28.0000			1.03000			0.514998	−	0.857191i	$-0.327793\pi$
$739$	28.0000			1.03000			0.514998	+	0.857191i	$0.327793\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.53590	−	7.85641i	−0.166406	−	0.288224i	0.770748	−	0.637140i	$-0.219883\pi$
$743$	−4.53590	−	7.85641i	−0.166406	−	0.288224i	−0.937154	+	0.348917i	$0.886550\pi$
$744$		0			0
$745$	1.64359	−	2.84679i	0.0602166	−	0.104298i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−32.7846	+	56.7846i	−1.19792	+	2.07486i
$750$		0			0
$751$	8.66025	+	15.0000i	0.316017	+	0.547358i	0.979653	−	0.200698i	$-0.0643209\pi$
$751$	8.66025	+	15.0000i	0.316017	+	0.547358i	−0.663636	+	0.748056i	$0.730988\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.00000			−0.145575
$756$		0			0
$757$	−8.14359			−0.295984			−0.147992	−	0.988989i	$-0.547281\pi$
$757$	−8.14359			−0.295984			−0.147992	+	0.988989i	$0.547281\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	19.4019	+	33.6051i	0.703319	+	1.21818i	0.967295	+	0.253655i	$0.0816329\pi$
$761$	19.4019	+	33.6051i	0.703319	+	1.21818i	−0.263976	+	0.964529i	$0.585034\pi$
$762$		0			0
$763$	4.26795	−	7.39230i	0.154510	−	0.267619i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	17.8564	−	30.9282i	0.644757	−	1.11675i
$768$		0			0
$769$	−15.8923	−	27.5263i	−0.573091	−	0.992623i	−0.996246	−	0.0865657i	$-0.972411\pi$
$769$	−15.8923	−	27.5263i	−0.573091	−	0.992623i	0.423155	−	0.906057i	$-0.360923\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	31.7321			1.14132			0.570661	−	0.821186i	$-0.306687\pi$
$773$	31.7321			1.14132			0.570661	+	0.821186i	$0.306687\pi$
$774$		0			0
$775$	14.4308			0.518369
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.85641	+	3.21539i	0.0665127	+	0.115203i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.06218	−	3.57180i	0.0736023	−	0.127483i
$786$		0			0
$787$	6.26795	+	10.8564i	0.223428	+	0.386989i	0.955847	−	0.293866i	$-0.0949418\pi$
$787$	6.26795	+	10.8564i	0.223428	+	0.386989i	−0.732418	+	0.680855i	$0.761608\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	6.00000			0.213335
$792$		0			0
$793$	15.7846			0.560528
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−24.2583	−	42.0167i	−0.859274	−	1.48831i	−0.872622	−	0.488396i	$-0.837582\pi$
$797$	−24.2583	−	42.0167i	−0.859274	−	1.48831i	0.0133482	−	0.999911i	$-0.495751\pi$
$798$		0			0
$799$	−19.8564	+	34.3923i	−0.702469	+	1.21671i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.00000	−	1.73205i	0.0352892	−	0.0611227i
$804$		0			0
$805$	4.14359	+	7.17691i	0.146042	+	0.252953i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	26.2679			0.923532			0.461766	−	0.887002i	$-0.347216\pi$
$809$	26.2679			0.923532			0.461766	+	0.887002i	$0.347216\pi$
$810$		0			0
$811$	49.5692			1.74061			0.870305	−	0.492513i	$-0.163921\pi$
$811$	49.5692			1.74061			0.870305	+	0.492513i	$0.163921\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.07180	+	5.32051i	−0.107469	+	0.186141i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	13.3301	−	23.0885i	0.465225	−	0.805793i	−0.533987	−	0.845493i	$-0.679307\pi$
$821$	13.3301	−	23.0885i	0.465225	−	0.805793i	0.999212	+	0.0397000i	$0.0126402\pi$
$822$		0			0
$823$	10.0000	+	17.3205i	0.348578	+	0.603755i	0.985997	−	0.166762i	$-0.0533313\pi$
$823$	10.0000	+	17.3205i	0.348578	+	0.603755i	−0.637419	+	0.770517i	$0.719998\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	15.8564			0.551381			0.275691	−	0.961246i	$-0.411093\pi$
$827$	15.8564			0.551381			0.275691	+	0.961246i	$0.411093\pi$
$828$		0			0
$829$	−3.85641			−0.133939			−0.0669693	−	0.997755i	$-0.521333\pi$
$829$	−3.85641			−0.133939			−0.0669693	+	0.997755i	$0.521333\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−14.3301	−	24.8205i	−0.496509	−	0.859980i
$834$		0			0
$835$	2.41154	−	4.17691i	0.0834549	−	0.144548i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.4641	−	31.9808i	0.637452	−	1.10410i	−0.348538	−	0.937294i	$-0.613322\pi$
$839$	18.4641	−	31.9808i	0.637452	−	1.10410i	0.985990	−	0.166804i	$-0.0533447\pi$
$840$		0			0
$841$	−15.3923	−	26.6603i	−0.530769	−	0.919319i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.85641			0.0638623
$846$		0			0
$847$	−24.2487			−0.833196
$848$		0			0
$849$		0			0
$850$		0			0
$851$	28.8564	+	49.9808i	0.989185	+	1.71332i
$852$		0			0
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	−0.960621	−	0.277862i	$-0.910374\pi$
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	0.720946	+	0.692992i	$0.243708\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.79423	−	3.10770i	0.0612897	−	0.106157i	−0.833752	−	0.552138i	$-0.813812\pi$
$857$	1.79423	−	3.10770i	0.0612897	−	0.106157i	0.895042	+	0.445982i	$0.147145\pi$
$858$		0			0
$859$	0.928203	+	1.60770i	0.0316699	+	0.0548539i	0.881426	−	0.472322i	$-0.156584\pi$
$859$	0.928203	+	1.60770i	0.0316699	+	0.0548539i	−0.849756	+	0.527176i	$0.823251\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−19.0718			−0.649212			−0.324606	−	0.945849i	$-0.605232\pi$
$863$	−19.0718			−0.649212			−0.324606	+	0.945849i	$0.605232\pi$
$864$		0			0
$865$	−1.14359			−0.0388833
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.46410	−	12.9282i	−0.253202	−	0.438559i
$870$		0			0
$871$	−16.6603	+	28.8564i	−0.564511	+	0.977762i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.60770	−	7.98076i	0.155769	−	0.269799i
$876$		0			0
$877$	7.16025	+	12.4019i	0.241785	+	0.418783i	0.961223	−	0.275773i	$-0.0889339\pi$
$877$	7.16025	+	12.4019i	0.241785	+	0.418783i	−0.719438	+	0.694557i	$0.755601\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18.6410			−0.628032			−0.314016	−	0.949418i	$-0.601675\pi$
$881$	−18.6410			−0.628032			−0.314016	+	0.949418i	$0.601675\pi$
$882$		0			0
$883$	−50.9282			−1.71387			−0.856935	−	0.515424i	$-0.827634\pi$
$883$	−50.9282			−1.71387			−0.856935	+	0.515424i	$0.827634\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.3205	−	21.3397i	−0.413682	−	0.716519i	0.581607	−	0.813470i	$-0.302424\pi$
$887$	−12.3205	−	21.3397i	−0.413682	−	0.716519i	−0.995289	+	0.0969514i	$0.969091\pi$
$888$		0			0
$889$	12.9282	−	22.3923i	0.433598	−	0.751014i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.85641	+	3.21539i	−0.0621223	+	0.107599i
$894$		0			0
$895$	0.928203	+	1.60770i	0.0310264	+	0.0537393i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−22.6410			−0.755120
$900$		0			0
$901$	16.7846			0.559176
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.66025	+	4.60770i	0.0884298	+	0.153165i
$906$		0			0
$907$	−2.39230	+	4.14359i	−0.0794352	+	0.137586i	−0.903006	−	0.429627i	$-0.858645\pi$
$907$	−2.39230	+	4.14359i	−0.0794352	+	0.137586i	0.823571	+	0.567213i	$0.191978\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	23.3923	−	40.5167i	0.775022	−	1.34238i	−0.159761	−	0.987156i	$-0.551072\pi$
$911$	23.3923	−	40.5167i	0.775022	−	1.34238i	0.934782	−	0.355221i	$-0.115594\pi$
$912$		0			0
$913$	−10.9282	−	18.9282i	−0.361671	−	0.626432i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	72.4974			2.39408
$918$		0			0
$919$	−35.1769			−1.16038			−0.580190	−	0.814481i	$-0.697022\pi$
$919$	−35.1769			−1.16038			−0.580190	+	0.814481i	$0.697022\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.46410	−	7.73205i	−0.146938	−	0.254504i
$924$		0			0
$925$	15.9282	−	27.5885i	0.523716	−	0.907103i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2.20577	−	3.82051i	0.0723690	−	0.125347i	−0.827570	−	0.561362i	$-0.810277\pi$
$929$	2.20577	−	3.82051i	0.0723690	−	0.125347i	0.899939	+	0.436016i	$0.143611\pi$
$930$		0			0
$931$	−1.33975	−	2.32051i	−0.0439084	−	0.0760516i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.07180			−0.100458
$936$		0			0
$937$	−50.5692			−1.65202			−0.826012	−	0.563652i	$-0.809396\pi$
$937$	−50.5692			−1.65202			−0.826012	+	0.563652i	$0.809396\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.06218	+	15.6962i	0.295419	+	0.511680i	0.975082	−	0.221844i	$-0.0712076\pi$
$941$	9.06218	+	15.6962i	0.295419	+	0.511680i	−0.679664	+	0.733524i	$0.737874\pi$
$942$		0			0
$943$	−30.9282	+	53.5692i	−1.00716	+	1.74445i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.46410	+	11.1962i	−0.210055	+	0.363826i	−0.951732	−	0.306932i	$-0.900698\pi$
$947$	−6.46410	+	11.1962i	−0.210055	+	0.363826i	0.741676	+	0.670758i	$0.234031\pi$
$948$		0			0
$949$	−2.23205	−	3.86603i	−0.0724554	−	0.125496i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	13.9808			0.452881			0.226441	−	0.974025i	$-0.427291\pi$
$953$	13.9808			0.452881			0.226441	+	0.974025i	$0.427291\pi$
$954$		0			0
$955$	2.10512			0.0681200
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.78461	−	10.0192i	−0.186795	−	0.323538i
$960$		0			0
$961$	11.2128	−	19.4212i	0.361704	−	0.626489i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.545517	+	0.944864i	−0.0175608	+	0.0304162i
$966$		0			0
$967$	−4.66025	−	8.07180i	−0.149864	−	0.259571i	0.781313	−	0.624139i	$-0.214550\pi$
$967$	−4.66025	−	8.07180i	−0.149864	−	0.259571i	−0.931177	+	0.364568i	$0.881217\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.928203			−0.0297875			−0.0148937	−	0.999889i	$-0.504741\pi$
$971$	−0.928203			−0.0297875			−0.0148937	+	0.999889i	$0.504741\pi$
$972$		0			0
$973$	65.5692			2.10205
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.53590	−	14.7846i	−0.273088	−	0.473002i	0.696563	−	0.717495i	$-0.254712\pi$
$977$	−8.53590	−	14.7846i	−0.273088	−	0.473002i	−0.969651	+	0.244494i	$0.921378\pi$
$978$		0			0
$979$	5.19615	−	9.00000i	0.166070	−	0.287641i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	−0.422027	−	0.906583i	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$		0			0
$985$	−1.96410	−	3.40192i	−0.0625815	−	0.108394i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−102.354			−3.25466
$990$		0			0
$991$	46.1051			1.46458			0.732289	−	0.680994i	$-0.238452\pi$
$991$	46.1051			1.46458			0.732289	+	0.680994i	$0.238452\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.535898	+	0.928203i	0.0169891	+	0.0294260i
$996$		0			0
$997$	24.0885	−	41.7224i	0.762889	−	1.32136i	−0.178466	−	0.983946i	$-0.557114\pi$
$997$	24.0885	−	41.7224i	0.762889	−	1.32136i	0.941355	−	0.337417i	$-0.109553\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1296.2.i.r.865.2		4
3.2	odd	2		1296.2.i.t.865.1		4
4.3	odd	2		648.2.i.i.217.2		4
9.2	odd	6		1296.2.a.m.1.2		2
9.4	even	3	inner	1296.2.i.r.433.2		4
9.5	odd	6		1296.2.i.t.433.1		4
9.7	even	3		1296.2.a.q.1.1		2
12.11	even	2		648.2.i.j.217.1		4
36.7	odd	6		648.2.a.h.1.1	yes	2
36.11	even	6		648.2.a.e.1.2	✓	2
36.23	even	6		648.2.i.j.433.1		4
36.31	odd	6		648.2.i.i.433.2		4
72.11	even	6		5184.2.a.cb.1.1		2
72.29	odd	6		5184.2.a.bz.1.1		2
72.43	odd	6		5184.2.a.bg.1.2		2
72.61	even	6		5184.2.a.bi.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
648.2.a.e.1.2	✓	2	36.11	even	6
648.2.a.h.1.1	yes	2	36.7	odd	6
648.2.i.i.217.2		4	4.3	odd	2
648.2.i.i.433.2		4	36.31	odd	6
648.2.i.j.217.1		4	12.11	even	2
648.2.i.j.433.1		4	36.23	even	6
1296.2.a.m.1.2		2	9.2	odd	6
1296.2.a.q.1.1		2	9.7	even	3
1296.2.i.r.433.2		4	9.4	even	3	inner
1296.2.i.r.865.2		4	1.1	even	1	trivial
1296.2.i.t.433.1		4	9.5	odd	6
1296.2.i.t.865.1		4	3.2	odd	2
5184.2.a.bg.1.2		2	72.43	odd	6
5184.2.a.bi.1.2		2	72.61	even	6
5184.2.a.bz.1.1		2	72.29	odd	6
5184.2.a.cb.1.1		2	72.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1296.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.133975 - 0.232051i) q^{5} +(-1.73205 + 3.00000i) q^{7} +O(q^{10})\)	\(q+(-0.133975 - 0.232051i) q^{5} +(-1.73205 + 3.00000i) q^{7} +(1.00000 - 1.73205i) q^{11} +(-2.23205 - 3.86603i) q^{13} +5.73205 q^{17} +0.535898 q^{19} +(4.46410 + 7.73205i) q^{23} +(2.46410 - 4.26795i) q^{25} +(-3.86603 + 6.69615i) q^{29} +(1.46410 + 2.53590i) q^{31} +0.928203 q^{35} +6.46410 q^{37} +(3.46410 + 6.00000i) q^{41} +(-5.73205 + 9.92820i) q^{43} +(-3.46410 + 6.00000i) q^{47} +(-2.50000 - 4.33013i) q^{49} +2.92820 q^{53} -0.535898 q^{55} +(4.00000 + 6.92820i) q^{59} +(-1.76795 + 3.06218i) q^{61} +(-0.598076 + 1.03590i) q^{65} +(-3.73205 - 6.46410i) q^{67} +2.00000 q^{71} +1.00000 q^{73} +(3.46410 + 6.00000i) q^{77} +(3.73205 - 6.46410i) q^{79} +(5.46410 - 9.46410i) q^{83} +(-0.767949 - 1.33013i) q^{85} +5.19615 q^{89} +15.4641 q^{91} +(-0.0717968 - 0.124356i) q^{95} +(-7.92820 + 13.7321i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5}+O(q^{10}) \) 4 * q - 4 * q^5	\( 4 q - 4 q^{5} + 4 q^{11} - 2 q^{13} + 16 q^{17} + 16 q^{19} + 4 q^{23} - 4 q^{25} - 12 q^{29} - 8 q^{31} - 24 q^{35} + 12 q^{37} - 16 q^{43} - 10 q^{49} - 16 q^{53} - 16 q^{55} + 16 q^{59} - 14 q^{61} + 8 q^{65} - 8 q^{67} + 8 q^{71} + 4 q^{73} + 8 q^{79} + 8 q^{83} - 10 q^{85} + 48 q^{91} - 28 q^{95} - 4 q^{97}+O(q^{100}) \) 4 * q - 4 * q^5 + 4 * q^11 - 2 * q^13 + 16 * q^17 + 16 * q^19 + 4 * q^23 - 4 * q^25 - 12 * q^29 - 8 * q^31 - 24 * q^35 + 12 * q^37 - 16 * q^43 - 10 * q^49 - 16 * q^53 - 16 * q^55 + 16 * q^59 - 14 * q^61 + 8 * q^65 - 8 * q^67 + 8 * q^71 + 4 * q^73 + 8 * q^79 + 8 * q^83 - 10 * q^85 + 48 * q^91 - 28 * q^95 - 4 * q^97

Introduction

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