LMFDB - Embedded newform 2736.2.bm.s.1855.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(559,2736)]

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([3, 0, 0, 1]))

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

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

chi := DirichletCharacter("2736.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.bm (of order $6$, degree $2$, 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 $\Q(\zeta_{6})$
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} - 30x^{5} - 5x^{4} + 114x^{3} + 300x^{2} + 116x + 19 $ x^8 - 2x^7 - 30x^5 - 5x^4 + 114x^3 + 300x^2 + 116x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 912)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1855.2
Root			$-0.654220 - 2.95767i$ of defining polynomial
Character	$\chi$	$=$	2736.1855
Dual form			2736.2.bm.s.559.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.353597 + 0.612447i) q^{5} -0.0924751i q^{7} +O(q^{10})$	$q+(0.353597 + 0.612447i) q^{5} -0.0924751i q^{7} -4.18329i q^{11} +(3.54275 + 2.04541i) q^{13} +(-1.22649 - 2.12434i) q^{17} +(-4.26923 - 0.879564i) q^{19} +(-3.10354 - 1.79183i) q^{23} +(2.24994 - 3.89701i) q^{25} +(-7.24566 - 4.18329i) q^{29} -3.79268 q^{31} +(0.0566361 - 0.0326989i) q^{35} +1.91700i q^{37} +(-6.72637 + 3.88347i) q^{41} +(7.76371 - 4.48238i) q^{43} +(2.64088 + 1.52471i) q^{47} +6.99145 q^{49} +(1.58009 + 0.912263i) q^{53} +(2.56204 - 1.47920i) q^{55} +(-2.91564 - 5.05003i) q^{59} +(-5.70292 + 9.87774i) q^{61} +2.89299i q^{65} +(-0.334301 + 0.579026i) q^{67} +(-1.93368 - 3.34924i) q^{71} +(-1.20719 - 2.09092i) q^{73} -0.386850 q^{77} +(-5.60354 - 9.70561i) q^{79} -15.7095i q^{83} +(0.867365 - 1.50232i) q^{85} +(-4.77904 - 2.75918i) q^{89} +(0.189149 - 0.327616i) q^{91} +(-0.970900 - 2.92569i) q^{95} +(11.0427 - 6.37553i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{5}+O(q^{10}) $ 8 * q + 2 * q^5	$ 8 q + 2 q^{5} - 4 q^{17} + 6 q^{23} - 12 q^{25} + 12 q^{29} + 28 q^{31} + 18 q^{35} + 12 q^{41} + 18 q^{43} + 12 q^{47} - 24 q^{49} + 6 q^{53} - 12 q^{55} + 10 q^{59} - 4 q^{61} - 6 q^{67} - 8 q^{71} - 8 q^{73} - 28 q^{77} - 14 q^{79} - 8 q^{85} - 54 q^{89} - 26 q^{91} + 38 q^{95} + 60 q^{97}+O(q^{100}) $ 8 * q + 2 * q^5 - 4 * q^17 + 6 * q^23 - 12 * q^25 + 12 * q^29 + 28 * q^31 + 18 * q^35 + 12 * q^41 + 18 * q^43 + 12 * q^47 - 24 * q^49 + 6 * q^53 - 12 * q^55 + 10 * q^59 - 4 * q^61 - 6 * q^67 - 8 * q^71 - 8 * q^73 - 28 * q^77 - 14 * q^79 - 8 * q^85 - 54 * q^89 - 26 * q^91 + 38 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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
$5$	0.353597	+	0.612447i	0.158133	+	0.273895i	0.934195	−	0.356762i	$-0.116119\pi$
$5$	0.353597	+	0.612447i	0.158133	+	0.273895i	−0.776062	+	0.630656i	$0.782786\pi$
$6$		0			0
$7$		−	0.0924751i		−	0.0349523i	−0.999847	−	0.0174762i	$-0.994437\pi$
$7$		−	0.0924751i		−	0.0349523i	0.999847	−	0.0174762i	$-0.00556312\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	4.18329i		−	1.26131i	−0.776064	−	0.630654i	$-0.782787\pi$
$11$		−	4.18329i		−	1.26131i	0.776064	−	0.630654i	$-0.217213\pi$
$12$		0			0
$13$	3.54275	+	2.04541i	0.982581	+	0.567293i	0.903048	−	0.429539i	$-0.141324\pi$
$13$	3.54275	+	2.04541i	0.982581	+	0.567293i	0.0795325	+	0.996832i	$0.474657\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.22649	−	2.12434i	−0.297467	−	0.515229i	0.678088	−	0.734980i	$-0.262809\pi$
$17$	−1.22649	−	2.12434i	−0.297467	−	0.515229i	−0.975556	+	0.219752i	$0.929475\pi$
$18$		0			0
$19$	−4.26923	−	0.879564i	−0.979430	−	0.201786i
$19$	−4.26923	−	0.879564i	−0.979430	−	0.201786i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.10354	−	1.79183i	−0.647132	−	0.373622i	0.140225	−	0.990120i	$-0.455218\pi$
$23$	−3.10354	−	1.79183i	−0.647132	−	0.373622i	−0.787357	+	0.616498i	$0.788551\pi$
$24$		0			0
$25$	2.24994	−	3.89701i	0.449988	−	0.779402i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−7.24566	−	4.18329i	−1.34549	−	0.776817i	−0.357879	−	0.933768i	$-0.616500\pi$
$29$	−7.24566	−	4.18329i	−1.34549	−	0.776817i	−0.987606	+	0.156951i	$0.949833\pi$
$30$		0			0
$31$	−3.79268			−0.681186			−0.340593	−	0.940211i	$-0.610628\pi$
$31$	−3.79268			−0.681186			−0.340593	+	0.940211i	$0.610628\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.0566361	−	0.0326989i	0.00957326	−	0.00552712i
$36$		0			0
$37$			1.91700i			0.315153i	0.987507	+	0.157577i	$0.0503681\pi$
$37$			1.91700i			0.315153i	−0.987507	+	0.157577i	$0.949632\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.72637	+	3.88347i	−1.05048	+	0.606496i	−0.922784	−	0.385317i	$-0.874092\pi$
$41$	−6.72637	+	3.88347i	−1.05048	+	0.606496i	−0.127698	+	0.991813i	$0.540759\pi$
$42$		0			0
$43$	7.76371	−	4.48238i	1.18395	−	0.683556i	0.227028	−	0.973888i	$-0.427099\pi$
$43$	7.76371	−	4.48238i	1.18395	−	0.683556i	0.956926	+	0.290332i	$0.0937657\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.64088	+	1.52471i	0.385211	+	0.222402i	0.680083	−	0.733135i	$-0.261944\pi$
$47$	2.64088	+	1.52471i	0.385211	+	0.222402i	−0.294872	+	0.955537i	$0.595277\pi$
$48$		0			0
$49$	6.99145			0.998778
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.58009	+	0.912263i	0.217041	+	0.125309i	0.604580	−	0.796545i	$-0.293341\pi$
$53$	1.58009	+	0.912263i	0.217041	+	0.125309i	−0.387538	+	0.921854i	$0.626674\pi$
$54$		0			0
$55$	2.56204	−	1.47920i	0.345466	−	0.199455i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.91564	−	5.05003i	−0.379584	−	0.657458i	0.611418	−	0.791308i	$-0.290599\pi$
$59$	−2.91564	−	5.05003i	−0.379584	−	0.657458i	−0.991002	+	0.133849i	$0.957266\pi$
$60$		0			0
$61$	−5.70292	+	9.87774i	−0.730184	+	1.26472i	0.226621	+	0.973983i	$0.427232\pi$
$61$	−5.70292	+	9.87774i	−0.730184	+	1.26472i	−0.956804	+	0.290732i	$0.906101\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			2.89299i			0.358832i
$66$		0			0
$67$	−0.334301	+	0.579026i	−0.0408413	+	0.0707392i	−0.885723	−	0.464213i	$-0.846337\pi$
$67$	−0.334301	+	0.579026i	−0.0408413	+	0.0707392i	0.844882	+	0.534952i	$0.179670\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.93368	−	3.34924i	−0.229486	−	0.397481i	0.728170	−	0.685397i	$-0.240371\pi$
$71$	−1.93368	−	3.34924i	−0.229486	−	0.397481i	−0.957656	+	0.287915i	$0.907038\pi$
$72$		0			0
$73$	−1.20719	−	2.09092i	−0.141291	−	0.244724i	0.786692	−	0.617346i	$-0.211792\pi$
$73$	−1.20719	−	2.09092i	−0.141291	−	0.244724i	−0.927983	+	0.372622i	$0.878459\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.386850			−0.0440856
$78$		0			0
$79$	−5.60354	−	9.70561i	−0.630447	−	1.09197i	−0.987460	−	0.157867i	$-0.949538\pi$
$79$	−5.60354	−	9.70561i	−0.630447	−	1.09197i	0.357013	−	0.934099i	$-0.383795\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	15.7095i		−	1.72434i	−0.506622	−	0.862168i	$-0.669106\pi$
$83$		−	15.7095i		−	1.72434i	0.506622	−	0.862168i	$-0.330894\pi$
$84$		0			0
$85$	0.867365	−	1.50232i	0.0940789	−	0.162949i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.77904	−	2.75918i	−0.506577	−	0.292472i	0.224848	−	0.974394i	$-0.427811\pi$
$89$	−4.77904	−	2.75918i	−0.506577	−	0.292472i	−0.731426	+	0.681921i	$0.761145\pi$
$90$		0			0
$91$	0.189149	−	0.327616i	0.0198282	−	0.0343435i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.970900	−	2.92569i	−0.0996123	−	0.300170i
$96$		0			0
$97$	11.0427	−	6.37553i	1.12122	−	0.647337i	0.179509	−	0.983756i	$-0.442549\pi$
$97$	11.0427	−	6.37553i	1.12122	−	0.647337i	0.941712	+	0.336419i	$0.109216\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.56620	−	11.3730i	0.653361	−	1.13165i	−0.328941	−	0.944350i	$-0.606692\pi$
$101$	6.56620	−	11.3730i	0.653361	−	1.13165i	0.982302	−	0.187304i	$-0.0599749\pi$
$102$		0			0
$103$	1.83983			0.181284			0.0906418	−	0.995884i	$-0.471108\pi$
$103$	1.83983			0.181284			0.0906418	+	0.995884i	$0.471108\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−16.9998			−1.64343			−0.821714	−	0.569900i	$-0.806982\pi$
$107$	−16.9998			−1.64343			−0.821714	+	0.569900i	$0.806982\pi$
$108$		0			0
$109$	−5.20292	+	3.00391i	−0.498349	+	0.287722i	−0.728032	−	0.685544i	$-0.759565\pi$
$109$	−5.20292	+	3.00391i	−0.498349	+	0.287722i	0.229682	+	0.973266i	$0.426231\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			8.56778i			0.805989i	0.915202	+	0.402994i	$0.132031\pi$
$113$			8.56778i			0.805989i	−0.915202	+	0.402994i	$0.867969\pi$
$114$		0			0
$115$		−	2.53434i		−	0.236328i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.196449	+	0.113420i	−0.0180084	+	0.0103972i
$120$		0			0
$121$	−6.49988			−0.590898
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.71825			0.600898
$126$		0			0
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	−0.818241	−	0.574875i	$-0.805051\pi$
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	0.906977	+	0.421180i	$0.138384\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.67947	−	2.12434i	0.321477	−	0.185605i	−0.330574	−	0.943780i	$-0.607242\pi$
$131$	3.67947	−	2.12434i	0.321477	−	0.185605i	0.652051	+	0.758175i	$0.273909\pi$
$132$		0			0
$133$	−0.0813378	+	0.394798i	−0.00705288	+	0.0342333i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		0			0
$139$	−11.4820	−	6.62911i	−0.973887	−	0.562274i	−0.0734678	−	0.997298i	$-0.523407\pi$
$139$	−11.4820	−	6.62911i	−0.973887	−	0.562274i	−0.900419	+	0.435024i	$0.856740\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.55651	−	14.8203i	0.715532	−	1.23934i
$144$		0			0
$145$		−	5.91678i		−	0.491362i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.95838	+	13.7843i	0.651976	+	1.12926i	0.982643	+	0.185508i	$0.0593932\pi$
$149$	7.95838	+	13.7843i	0.651976	+	1.12926i	−0.330666	+	0.943748i	$0.607274\pi$
$150$		0			0
$151$	6.58561			0.535930			0.267965	−	0.963429i	$-0.413649\pi$
$151$	6.58561			0.535930			0.267965	+	0.963429i	$0.413649\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.34108	−	2.32282i	−0.107718	−	0.186573i
$156$		0			0
$157$	−5.95298	−	10.3109i	−0.475099	−	0.822896i	0.524494	−	0.851414i	$-0.324255\pi$
$157$	−5.95298	−	10.3109i	−0.475099	−	0.822896i	−0.999593	+	0.0285179i	$0.990921\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.165699	+	0.287000i	−0.0130589	+	0.0226188i
$162$		0			0
$163$			4.80999i			0.376748i	0.982097	+	0.188374i	$0.0603217\pi$
$163$			4.80999i			0.376748i	−0.982097	+	0.188374i	$0.939678\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.1035	−	20.9639i	0.936600	−	1.62224i	0.164843	−	0.986320i	$-0.447288\pi$
$167$	12.1035	−	20.9639i	0.936600	−	1.62224i	0.771756	−	0.635919i	$-0.219379\pi$
$168$		0			0
$169$	1.86736	+	3.23437i	0.143643	+	0.248798i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	14.4913	−	8.36657i	1.10176	−	0.636099i	0.165074	−	0.986281i	$-0.447214\pi$
$173$	14.4913	−	8.36657i	1.10176	−	0.636099i	0.936681	+	0.350183i	$0.113880\pi$
$174$		0			0
$175$	−0.360376	−	0.208063i	−0.0272419	−	0.0157281i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.98039			−0.671226			−0.335613	−	0.942000i	$-0.608943\pi$
$179$	−8.98039			−0.671226			−0.335613	+	0.942000i	$0.608943\pi$
$180$		0			0
$181$	−3.08134	−	1.77901i	−0.229034	−	0.132233i	0.381092	−	0.924537i	$-0.375548\pi$
$181$	−3.08134	−	1.77901i	−0.229034	−	0.132233i	−0.610126	+	0.792304i	$0.708881\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.17406	+	0.677845i	−0.0863188	+	0.0498362i
$186$		0			0
$187$	−8.88673	+	5.13075i	−0.649862	+	0.375198i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			3.71445i			0.268768i	0.990929	+	0.134384i	$0.0429056\pi$
$191$			3.71445i			0.268768i	−0.990929	+	0.134384i	$0.957094\pi$
$192$		0			0
$193$	−17.8714	+	10.3181i	−1.28641	+	0.742710i	−0.978012	−	0.208547i	$-0.933127\pi$
$193$	−17.8714	+	10.3181i	−1.28641	+	0.742710i	−0.308399	+	0.951257i	$0.599793\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.29281			0.377097			0.188548	−	0.982064i	$-0.439622\pi$
$197$	5.29281			0.377097			0.188548	+	0.982064i	$0.439622\pi$
$198$		0			0
$199$	10.7662	+	6.21587i	0.763196	+	0.440632i	0.830442	−	0.557105i	$-0.188088\pi$
$199$	10.7662	+	6.21587i	0.763196	+	0.440632i	−0.0672458	+	0.997736i	$0.521421\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.386850	+	0.670044i	−0.0271515	+	0.0470278i
$204$		0			0
$205$	−4.75684	−	2.74636i	−0.332232	−	0.191814i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.67947	+	17.8594i	−0.254514	+	1.23536i
$210$		0			0
$211$	−14.0094	−	24.2649i	−0.964445	−	1.67047i	−0.711099	−	0.703092i	$-0.751802\pi$
$211$	−14.0094	−	24.2649i	−0.964445	−	1.67047i	−0.253345	−	0.967376i	$-0.581531\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.49044	+	3.16991i	0.374445	+	0.216186i
$216$		0			0
$217$			0.350729i			0.0238090i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	10.0347i		−	0.675005i
$222$		0			0
$223$	8.89634	+	15.4089i	0.595743	+	1.03186i	0.993442	+	0.114341i	$0.0364757\pi$
$223$	8.89634	+	15.4089i	0.595743	+	1.03186i	−0.397698	+	0.917516i	$0.630191\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.9639			−0.926817			−0.463409	−	0.886145i	$-0.653374\pi$
$227$	−13.9639			−0.926817			−0.463409	+	0.886145i	$0.653374\pi$
$228$		0			0
$229$	−1.91426			−0.126498			−0.0632491	−	0.997998i	$-0.520146\pi$
$229$	−1.91426			−0.126498			−0.0632491	+	0.997998i	$0.520146\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.51930	+	6.09560i	0.230557	+	0.399336i	0.957972	−	0.286861i	$-0.0926119\pi$
$233$	3.51930	+	6.09560i	0.230557	+	0.399336i	−0.727415	+	0.686197i	$0.759279\pi$
$234$		0			0
$235$			2.15653i			0.140676i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			19.2931i			1.24797i	0.781437	+	0.623984i	$0.214487\pi$
$239$			19.2931i			1.24797i	−0.781437	+	0.623984i	$0.785513\pi$
$240$		0			0
$241$	−10.1515	−	5.86097i	−0.653915	−	0.377538i	0.136039	−	0.990703i	$-0.456563\pi$
$241$	−10.1515	−	5.86097i	−0.653915	−	0.377538i	−0.789955	+	0.613165i	$0.789896\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.47215	+	4.28189i	0.157940	+	0.273560i
$246$		0			0
$247$	−13.3257	−	11.8484i	−0.847897	−	0.753895i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.67966	+	1.54710i	0.169138	+	0.0976521i	0.582180	−	0.813060i	$-0.302200\pi$
$251$	2.67966	+	1.54710i	0.169138	+	0.0976521i	−0.413041	+	0.910712i	$0.635533\pi$
$252$		0			0
$253$	−7.49572	+	12.9830i	−0.471252	+	0.816233i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.82575	+	5.09555i	0.550535	+	0.317852i	0.749338	−	0.662188i	$-0.230372\pi$
$257$	8.82575	+	5.09555i	0.550535	+	0.317852i	−0.198803	+	0.980040i	$0.563705\pi$
$258$		0			0
$259$	0.177275			0.0110153
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.76496	−	4.48310i	0.478808	−	0.276440i	−0.241112	−	0.970497i	$-0.577512\pi$
$263$	7.76496	−	4.48310i	0.478808	−	0.276440i	0.719920	+	0.694058i	$0.244179\pi$
$264$		0			0
$265$			1.29029i			0.0792620i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.174251	+	0.100604i	−0.0106243	+	0.00613393i	−0.505303	−	0.862942i	$-0.668619\pi$
$269$	−0.174251	+	0.100604i	−0.0106243	+	0.00613393i	0.494678	+	0.869076i	$0.335286\pi$
$270$		0			0
$271$	25.6129	−	14.7876i	1.55587	−	0.898284i	0.558229	−	0.829687i	$-0.311481\pi$
$271$	25.6129	−	14.7876i	1.55587	−	0.898284i	0.997644	−	0.0685967i	$-0.0218522\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−16.3023	−	9.41214i	−0.983066	−	0.567573i
$276$		0			0
$277$	−26.8200			−1.61146			−0.805728	−	0.592286i	$-0.798226\pi$
$277$	−26.8200			−1.61146			−0.805728	+	0.592286i	$0.798226\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.34254	+	3.66187i	0.378364	+	0.218449i	0.677106	−	0.735885i	$-0.263234\pi$
$281$	6.34254	+	3.66187i	0.378364	+	0.218449i	−0.298742	+	0.954334i	$0.596567\pi$
$282$		0			0
$283$	6.32034	−	3.64905i	0.375705	−	0.216914i	−0.300243	−	0.953863i	$-0.597068\pi$
$283$	6.32034	−	3.64905i	0.375705	−	0.216914i	0.675948	+	0.736949i	$0.263734\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.359124	+	0.622022i	0.0211984	+	0.0367168i
$288$		0			0
$289$	5.49145	−	9.51147i	0.323026	−	0.559498i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	25.9262i		−	1.51462i	−0.653053	−	0.757312i	$-0.726512\pi$
$293$		−	25.9262i		−	1.51462i	0.653053	−	0.757312i	$-0.273488\pi$
$294$		0			0
$295$	2.06192	−	3.57135i	0.120050	−	0.207932i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.33002	−	12.6960i	−0.423906	−	0.734227i
$300$		0			0
$301$	−0.414509	−	0.717950i	−0.0238919	−	0.0413819i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−8.06613			−0.461865
$306$		0			0
$307$	2.26923	+	3.93043i	0.129512	+	0.224322i	0.923488	−	0.383628i	$-0.125326\pi$
$307$	2.26923	+	3.93043i	0.129512	+	0.224322i	−0.793976	+	0.607950i	$0.791992\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			5.20697i			0.295260i	0.989043	+	0.147630i	$0.0471645\pi$
$311$			5.20697i			0.295260i	−0.989043	+	0.147630i	$0.952835\pi$
$312$		0			0
$313$	−1.37414	+	2.38009i	−0.0776712	+	0.134531i	−0.902245	−	0.431224i	$-0.858082\pi$
$313$	−1.37414	+	2.38009i	−0.0776712	+	0.134531i	0.824574	+	0.565755i	$0.191415\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.1544	−	9.90410i	−0.963487	−	0.556270i	−0.0662426	−	0.997804i	$-0.521101\pi$
$317$	−17.1544	−	9.90410i	−0.963487	−	0.556270i	−0.897245	+	0.441534i	$0.854434\pi$
$318$		0			0
$319$	−17.4999	+	30.3107i	−0.979805	+	1.69707i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.36768	+	10.1481i	0.187383	+	0.564655i
$324$		0			0
$325$	15.9419	−	9.20407i	0.884299	−	0.510550i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.140998	−	0.244215i	0.00777346	−	0.0134640i
$330$		0			0
$331$	−20.2840			−1.11491			−0.557455	−	0.830207i	$-0.688222\pi$
$331$	−20.2840			−1.11491			−0.557455	+	0.830207i	$0.688222\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.472830			−0.0258335
$336$		0			0
$337$	20.1557	−	11.6369i	1.09795	−	0.633901i	0.162267	−	0.986747i	$-0.448119\pi$
$337$	20.1557	−	11.6369i	1.09795	−	0.633901i	0.935681	+	0.352846i	$0.114786\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			15.8659i			0.859186i
$342$		0			0
$343$		−	1.29386i		−	0.0698619i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.5482	+	7.82203i	−0.727303	+	0.419909i	−0.817435	−	0.576021i	$-0.804605\pi$
$347$	−13.5482	+	7.82203i	−0.727303	+	0.419909i	0.0901318	+	0.995930i	$0.471271\pi$
$348$		0			0
$349$	25.3337			1.35608			0.678040	−	0.735025i	$-0.262830\pi$
$349$	25.3337			1.35608			0.678040	+	0.735025i	$0.262830\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	17.6515			0.939494			0.469747	−	0.882801i	$-0.344345\pi$
$353$	17.6515			0.939494			0.469747	+	0.882801i	$0.344345\pi$
$354$		0			0
$355$	1.36749	−	2.36856i	0.0725787	−	0.125710i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.25397	−	5.34278i	0.488406	−	0.281981i	−0.235507	−	0.971873i	$-0.575675\pi$
$359$	9.25397	−	5.34278i	0.488406	−	0.281981i	0.723913	+	0.689891i	$0.242342\pi$
$360$		0			0
$361$	17.4527	+	7.51013i	0.918565	+	0.395270i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.853719	−	1.47868i	0.0446857	−	0.0773979i
$366$		0			0
$367$	−26.6890	−	15.4089i	−1.39316	−	0.804339i	−0.399493	−	0.916736i	$-0.630814\pi$
$367$	−26.6890	−	15.4089i	−1.39316	−	0.804339i	−0.993663	+	0.112398i	$0.964147\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.0843616	−	0.146119i	0.00437984	−	0.00758610i
$372$		0			0
$373$			19.2740i			0.997968i	0.866611	+	0.498984i	$0.166293\pi$
$373$			19.2740i			0.997968i	−0.866611	+	0.498984i	$0.833707\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−17.1130	−	29.6406i	−0.881366	−	1.52657i
$378$		0			0
$379$	34.8696			1.79113			0.895566	−	0.444928i	$-0.146771\pi$
$379$	34.8696			1.79113			0.895566	+	0.444928i	$0.146771\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.80242	+	8.31804i	0.245392	+	0.425032i	0.962242	−	0.272196i	$-0.0877499\pi$
$383$	4.80242	+	8.31804i	0.245392	+	0.425032i	−0.716850	+	0.697228i	$0.754417\pi$
$384$		0			0
$385$	−0.136789	−	0.236925i	−0.00697140	−	0.0120748i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.5246	+	25.1573i	−0.736425	+	1.27553i	0.217670	+	0.976022i	$0.430154\pi$
$389$	−14.5246	+	25.1573i	−0.736425	+	1.27553i	−0.954095	+	0.299504i	$0.903179\pi$
$390$		0			0
$391$			8.79063i			0.444561i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.96278	−	6.86374i	0.199389	−	0.345352i
$396$		0			0
$397$	1.67538	+	2.90184i	0.0840850	+	0.145639i	0.905001	−	0.425410i	$-0.139870\pi$
$397$	1.67538	+	2.90184i	0.0840850	+	0.145639i	−0.820916	+	0.571049i	$0.806537\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.59071	+	4.38250i	−0.379062	+	0.218851i	−0.677410	−	0.735606i	$-0.736898\pi$
$401$	−7.59071	+	4.38250i	−0.379062	+	0.218851i	0.298348	+	0.954457i	$0.403564\pi$
$402$		0			0
$403$	−13.4365	−	7.75758i	−0.669321	−	0.386432i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.01936			0.397505
$408$		0			0
$409$	3.79708	+	2.19225i	0.187754	+	0.108400i	0.590931	−	0.806722i	$-0.298761\pi$
$409$	3.79708	+	2.19225i	0.187754	+	0.108400i	−0.403177	+	0.915122i	$0.632094\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.467003	+	0.269624i	−0.0229797	+	0.0132673i
$414$		0			0
$415$	9.62121	−	5.55481i	0.472287	−	0.272675i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			30.8399i			1.50663i	0.657661	+	0.753314i	$0.271546\pi$
$419$			30.8399i			1.50663i	−0.657661	+	0.753314i	$0.728454\pi$
$420$		0			0
$421$	16.4208	−	9.48055i	0.800301	−	0.462054i	−0.0432755	−	0.999063i	$-0.513779\pi$
$421$	16.4208	−	9.48055i	0.800301	−	0.462054i	0.843576	+	0.537009i	$0.180446\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.0381			−0.535427
$426$		0			0
$427$	0.913446	+	0.527378i	0.0442047	+	0.0255216i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.67947	+	16.7653i	−0.466244	+	0.807558i	−0.999257	−	0.0385494i	$-0.987726\pi$
$431$	−9.67947	+	16.7653i	−0.466244	+	0.807558i	0.533013	+	0.846107i	$0.321060\pi$
$432$		0			0
$433$	1.94608	+	1.12357i	0.0935225	+	0.0539952i	0.546032	−	0.837764i	$-0.316138\pi$
$433$	1.94608	+	1.12357i	0.0935225	+	0.0539952i	−0.452509	+	0.891760i	$0.649471\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.6737	+	10.3795i	0.558429	+	0.496518i
$438$		0			0
$439$	10.7401	+	18.6025i	0.512599	+	0.887847i	0.999893	+	0.0146093i	$0.00465046\pi$
$439$	10.7401	+	18.6025i	0.512599	+	0.887847i	−0.487295	+	0.873238i	$0.662016\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	27.3672	+	15.8005i	1.30026	+	0.750704i	0.980448	−	0.196778i	$-0.0630479\pi$
$443$	27.3672	+	15.8005i	1.30026	+	0.750704i	0.319809	+	0.947482i	$0.396381\pi$
$444$		0			0
$445$		−	3.90255i		−	0.184998i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			14.3346i			0.676492i	0.941058	+	0.338246i	$0.109834\pi$
$449$			14.3346i			0.676492i	−0.941058	+	0.338246i	$0.890166\pi$
$450$		0			0
$451$	16.2457	+	28.1383i	0.764978	+	1.32498i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.267530			0.0125420
$456$		0			0
$457$	4.40559			0.206085			0.103042	−	0.994677i	$-0.467142\pi$
$457$	4.40559			0.206085			0.103042	+	0.994677i	$0.467142\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.41136	−	7.64070i	−0.205458	−	0.355863i	0.744821	−	0.667265i	$-0.232535\pi$
$461$	−4.41136	−	7.64070i	−0.205458	−	0.355863i	−0.950278	+	0.311401i	$0.899202\pi$
$462$		0			0
$463$			21.1162i			0.981353i	0.871342	+	0.490676i	$0.163250\pi$
$463$			21.1162i			0.981353i	−0.871342	+	0.490676i	$0.836750\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			18.0284i			0.834257i	0.908847	+	0.417129i	$0.136964\pi$
$467$			18.0284i			0.834257i	−0.908847	+	0.417129i	$0.863036\pi$
$468$		0			0
$469$	0.0535455	+	0.0309145i	0.00247250	+	0.00142750i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−18.7511	−	32.4778i	−0.862175	−	1.49333i
$474$		0			0
$475$	−13.0332	+	14.6583i	−0.598004	+	0.672568i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	19.0961	+	11.0251i	0.872524	+	0.503752i	0.868186	−	0.496239i	$-0.165286\pi$
$479$	19.0961	+	11.0251i	0.872524	+	0.503752i	0.00433763	+	0.999991i	$0.498619\pi$
$480$		0			0
$481$	−3.92104	+	6.79145i	−0.178784	+	0.309663i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.80935	+	4.50873i	0.354605	+	0.204731i
$486$		0			0
$487$	43.2479			1.95975			0.979875	−	0.199611i	$-0.0639678\pi$
$487$	43.2479			1.95975			0.979875	+	0.199611i	$0.0639678\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	17.2899	−	9.98231i	0.780281	−	0.450495i	−0.0562489	−	0.998417i	$-0.517914\pi$
$491$	17.2899	−	9.98231i	0.780281	−	0.450495i	0.836530	+	0.547921i	$0.184581\pi$
$492$		0			0
$493$			20.5230i			0.924310i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.309721	+	0.178818i	−0.0138929	+	0.00802106i
$498$		0			0
$499$	−19.7399	+	11.3968i	−0.883679	+	0.510192i	−0.871870	−	0.489738i	$-0.837092\pi$
$499$	−19.7399	+	11.3968i	−0.883679	+	0.510192i	−0.0118092	+	0.999930i	$0.503759\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.6901	+	10.7907i	0.833350	+	0.481135i	0.854998	−	0.518631i	$-0.173558\pi$
$503$	18.6901	+	10.7907i	0.833350	+	0.481135i	−0.0216484	+	0.999766i	$0.506891\pi$
$504$		0			0
$505$	9.28714			0.413272
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−27.8034	−	16.0523i	−1.23236	−	0.711505i	−0.264841	−	0.964292i	$-0.585319\pi$
$509$	−27.8034	−	16.0523i	−1.23236	−	0.711505i	−0.967522	+	0.252787i	$0.918653\pi$
$510$		0			0
$511$	−0.193358	+	0.111635i	−0.00855366	+	0.00493846i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.650557	+	1.12680i	0.0286670	+	0.0496526i
$516$		0			0
$517$	6.37830	−	11.0475i	0.280517	−	0.485870i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	3.71946i		−	0.162953i	−0.996675	−	0.0814763i	$-0.974036\pi$
$521$		−	3.71946i		−	0.162953i	0.996675	−	0.0814763i	$-0.0259635\pi$
$522$		0			0
$523$	−9.49698	+	16.4492i	−0.415274	+	0.719275i	−0.995457	−	0.0952106i	$-0.969648\pi$
$523$	−9.49698	+	16.4492i	−0.415274	+	0.719275i	0.580183	+	0.814486i	$0.302981\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.65169	+	8.05696i	0.202631	+	0.350967i
$528$		0			0
$529$	−5.07871	−	8.79659i	−0.220814	−	0.382460i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−31.7731			−1.37624
$534$		0			0
$535$	−6.01106	−	10.4115i	−0.259881	−	0.450126i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	29.2472i		−	1.25977i
$540$		0			0
$541$	−2.40596	+	4.16724i	−0.103440	+	0.179164i	−0.913100	−	0.407736i	$-0.866318\pi$
$541$	−2.40596	+	4.16724i	−0.103440	+	0.179164i	0.809660	+	0.586900i	$0.199652\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.67947	−	2.12434i	−0.157611	−	0.0909968i
$546$		0			0
$547$	−8.93493	+	15.4758i	−0.382030	+	0.661696i	−0.991352	−	0.131227i	$-0.958108\pi$
$547$	−8.93493	+	15.4758i	−0.382030	+	0.661696i	0.609322	+	0.792923i	$0.291442\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	27.2540	+	24.2325i	1.16106	+	1.03234i
$552$		0			0
$553$	−0.897527	+	0.518188i	−0.0381667	+	0.0220356i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.20707	+	15.9471i	−0.390116	+	0.675701i	−0.992465	−	0.122532i	$-0.960898\pi$
$557$	−9.20707	+	15.9471i	−0.390116	+	0.675701i	0.602348	+	0.798233i	$0.294232\pi$
$558$		0			0
$559$	36.6731			1.55111
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−45.1320			−1.90209			−0.951044	−	0.309056i	$-0.899987\pi$
$563$	−45.1320			−1.90209			−0.951044	+	0.309056i	$0.899987\pi$
$564$		0			0
$565$	−5.24731	+	3.02954i	−0.220756	+	0.127454i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			22.6348i			0.948899i	0.880283	+	0.474449i	$0.157353\pi$
$569$			22.6348i			0.948899i	−0.880283	+	0.474449i	$0.842647\pi$
$570$		0			0
$571$		−	40.6503i		−	1.70116i	−0.525845	−	0.850580i	$-0.676251\pi$
$571$		−	40.6503i		−	1.70116i	0.525845	−	0.850580i	$-0.323749\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−13.9655	+	8.06300i	−0.582403	+	0.336250i
$576$		0			0
$577$	−16.3115			−0.679059			−0.339529	−	0.940595i	$-0.610268\pi$
$577$	−16.3115			−0.679059			−0.339529	+	0.940595i	$0.610268\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.45273			−0.0602696
$582$		0			0
$583$	3.81626	−	6.60995i	0.158053	−	0.273756i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−27.6778	+	15.9798i	−1.14239	+	0.659557i	−0.947021	−	0.321173i	$-0.895923\pi$
$587$	−27.6778	+	15.9798i	−1.14239	+	0.659557i	−0.195366	+	0.980730i	$0.562590\pi$
$588$		0			0
$589$	16.1919	+	3.33591i	0.667174	+	0.137454i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	8.86453	−	15.3538i	0.364023	−	0.630506i	−0.624596	−	0.780948i	$-0.714736\pi$
$593$	8.86453	−	15.3538i	0.364023	−	0.630506i	0.988619	+	0.150442i	$0.0480697\pi$
$594$		0			0
$595$	−0.138927	−	0.0802097i	−0.00569546	−	0.00328828i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	5.07600	−	8.79189i	0.207400	−	0.359227i	−0.743495	−	0.668742i	$-0.766833\pi$
$599$	5.07600	−	8.79189i	0.207400	−	0.359227i	0.950895	+	0.309515i	$0.100167\pi$
$600$		0			0
$601$			19.3856i			0.790754i	0.918519	+	0.395377i	$0.129386\pi$
$601$			19.3856i			0.790754i	−0.918519	+	0.395377i	$0.870614\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.29833	−	3.98083i	−0.0934406	−	0.161844i
$606$		0			0
$607$	−23.9466			−0.971961			−0.485981	−	0.873970i	$-0.661537\pi$
$607$	−23.9466			−0.971961			−0.485981	+	0.873970i	$0.661537\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.23730	+	10.8033i	0.252334	+	0.437056i
$612$		0			0
$613$	0.0427457	+	0.0740378i	0.00172648	+	0.00299036i	0.866887	−	0.498504i	$-0.166117\pi$
$613$	0.0427457	+	0.0740378i	0.00172648	+	0.00299036i	−0.865161	+	0.501494i	$0.832784\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.9388	−	29.3388i	0.681929	−	1.18114i	−0.292462	−	0.956277i	$-0.594474\pi$
$617$	16.9388	−	29.3388i	0.681929	−	1.18114i	0.974391	−	0.224859i	$-0.0721922\pi$
$618$		0			0
$619$		−	33.7408i		−	1.35616i	−0.734989	−	0.678079i	$-0.762813\pi$
$619$		−	33.7408i		−	1.35616i	0.734989	−	0.678079i	$-0.237187\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.255155	+	0.441942i	−0.0102226	+	0.0177060i
$624$		0			0
$625$	−8.87414	−	15.3705i	−0.354966	−	0.614819i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	4.07237	−	2.35118i	0.162376	−	0.0937477i
$630$		0			0
$631$	9.03569	+	5.21676i	0.359705	+	0.207676i	0.668951	−	0.743306i	$-0.266743\pi$
$631$	9.03569	+	5.21676i	0.359705	+	0.207676i	−0.309246	+	0.950982i	$0.600077\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.41439			0.0561282
$636$		0			0
$637$	24.7689	+	14.3003i	0.981380	+	0.566600i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−5.43380	+	3.13721i	−0.214622	+	0.123912i	−0.603458	−	0.797395i	$-0.706211\pi$
$641$	−5.43380	+	3.13721i	−0.214622	+	0.123912i	0.388835	+	0.921307i	$0.372877\pi$
$642$		0			0
$643$	−24.6075	+	14.2071i	−0.970425	+	0.560275i	−0.899366	−	0.437197i	$-0.855971\pi$
$643$	−24.6075	+	14.2071i	−0.970425	+	0.560275i	−0.0710593	+	0.997472i	$0.522638\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			34.0508i			1.33867i	0.742959	+	0.669337i	$0.233422\pi$
$647$			34.0508i			1.33867i	−0.742959	+	0.669337i	$0.766578\pi$
$648$		0			0
$649$	−21.1257	+	12.1969i	−0.829258	+	0.478772i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	47.3806			1.85414			0.927072	−	0.374883i	$-0.122317\pi$
$653$	47.3806			1.85414			0.927072	+	0.374883i	$0.122317\pi$
$654$		0			0
$655$	2.60209	+	1.50232i	0.101672	+	0.0587005i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−18.2939	+	31.6860i	−0.712631	+	1.23431i	0.251236	+	0.967926i	$0.419163\pi$
$659$	−18.2939	+	31.6860i	−0.712631	+	1.23431i	−0.963866	+	0.266386i	$0.914170\pi$
$660$		0			0
$661$	−19.2482	−	11.1129i	−0.748667	−	0.432243i	0.0765451	−	0.997066i	$-0.475611\pi$
$661$	−19.2482	−	11.1129i	−0.748667	−	0.432243i	−0.825212	+	0.564823i	$0.808944\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.270554	+	0.0897841i	−0.0104916	+	0.00348168i
$666$		0			0
$667$	14.9914	+	25.9660i	0.580471	+	1.00541i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	41.3214	+	23.8569i	1.59520	+	0.920987i
$672$		0			0
$673$		−	9.89639i		−	0.381478i	−0.981641	−	0.190739i	$-0.938912\pi$
$673$		−	9.89639i		−	0.381478i	0.981641	−	0.190739i	$-0.0610884\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			40.2095i			1.54538i	0.634785	+	0.772689i	$0.281089\pi$
$677$			40.2095i			1.54538i	−0.634785	+	0.772689i	$0.718911\pi$
$678$		0			0
$679$	−0.589578	−	1.02118i	−0.0226259	−	0.0391893i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−19.2073			−0.734947			−0.367474	−	0.930034i	$-0.619777\pi$
$683$	−19.2073			−0.734947			−0.367474	+	0.930034i	$0.619777\pi$
$684$		0			0
$685$	4.24316			0.162123
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.73189	+	6.46383i	0.142174	+	0.246252i
$690$		0			0
$691$			51.2975i			1.95145i	0.219000	+	0.975725i	$0.429720\pi$
$691$			51.2975i			1.95145i	−0.219000	+	0.975725i	$0.570280\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	9.37612i		−	0.355657i
$696$		0			0
$697$	16.4996	+	9.52607i	0.624968	+	0.360826i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.0994	−	24.4208i	−0.532526	−	0.922363i	−0.999279	−	0.0379746i	$-0.987909\pi$
$701$	−14.0994	−	24.4208i	−0.532526	−	0.922363i	0.466752	−	0.884388i	$-0.345424\pi$
$702$		0			0
$703$	1.68613	−	8.18413i	0.0635934	−	0.308670i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.05172	−	0.607210i	−0.0395539	−	0.0228365i
$708$		0			0
$709$	22.1942	−	38.4416i	0.833522	−	1.44370i	−0.0617056	−	0.998094i	$-0.519654\pi$
$709$	22.1942	−	38.4416i	0.833522	−	1.44370i	0.895228	−	0.445609i	$-0.147013\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	11.7707	+	6.79583i	0.440817	+	0.254506i
$714$		0			0
$715$	12.1022			0.452597
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.33858	−	2.50488i	0.161802	−	0.0934162i	−0.416913	−	0.908946i	$-0.636888\pi$
$719$	4.33858	−	2.50488i	0.161802	−	0.0934162i	0.578714	+	0.815530i	$0.303555\pi$
$720$		0			0
$721$		−	0.170138i		−	0.00633628i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−32.6046	+	18.8243i	−1.21090	+	0.699116i
$726$		0			0
$727$	23.4351	−	13.5302i	0.869158	−	0.501809i	0.00208975	−	0.999998i	$-0.499335\pi$
$727$	23.4351	−	13.5302i	0.869158	−	0.501809i	0.867068	+	0.498189i	$0.166001\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−19.0442	−	10.9952i	−0.704375	−	0.406671i
$732$		0			0
$733$	19.0852			0.704930			0.352465	−	0.935825i	$-0.385344\pi$
$733$	19.0852			0.704930			0.352465	+	0.935825i	$0.385344\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.42223	+	1.39847i	0.0892240	+	0.0515135i
$738$		0			0
$739$	11.0884	−	6.40189i	0.407893	−	0.235497i	−0.281991	−	0.959417i	$-0.590995\pi$
$739$	11.0884	−	6.40189i	0.407893	−	0.235497i	0.689884	+	0.723920i	$0.257661\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	15.4264	+	26.7193i	0.565939	+	0.980235i	0.996962	+	0.0778941i	$0.0248196\pi$
$743$	15.4264	+	26.7193i	0.565939	+	0.980235i	−0.431023	+	0.902341i	$0.641847\pi$
$744$		0			0
$745$	−5.62811	+	9.74818i	−0.206198	+	0.357146i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			1.57205i			0.0574416i
$750$		0			0
$751$	−11.7237	+	20.3060i	−0.427802	+	0.740975i	−0.996678	−	0.0814486i	$-0.974045\pi$
$751$	−11.7237	+	20.3060i	−0.427802	+	0.740975i	0.568875	+	0.822424i	$0.307379\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.32865	+	4.03334i	0.0847483	+	0.146788i
$756$		0			0
$757$	−22.4209	−	38.8342i	−0.814902	−	1.41145i	−0.909398	−	0.415927i	$-0.863457\pi$
$757$	−22.4209	−	38.8342i	−0.814902	−	1.41145i	0.0944958	−	0.995525i	$-0.469876\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	46.3138			1.67887			0.839437	−	0.543457i	$-0.182885\pi$
$761$	46.3138			1.67887			0.839437	+	0.543457i	$0.182885\pi$
$762$		0			0
$763$	0.277787	+	0.481141i	0.0100566	+	0.0174185i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	23.8546i		−	0.861341i
$768$		0			0
$769$	9.41426	−	16.3060i	0.339487	−	0.588009i	−0.644849	−	0.764310i	$-0.723080\pi$
$769$	9.41426	−	16.3060i	0.339487	−	0.588009i	0.984336	+	0.176301i	$0.0564132\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	45.9828	+	26.5482i	1.65389	+	0.954873i	0.975452	+	0.220213i	$0.0706753\pi$
$773$	45.9828	+	26.5482i	1.65389	+	0.954873i	0.678436	+	0.734659i	$0.262658\pi$
$774$		0			0
$775$	−8.53331	+	14.7801i	−0.306525	+	0.530918i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	32.1322	−	10.6632i	1.15126	−	0.382048i
$780$		0			0
$781$	−14.0108	+	8.08915i	−0.501346	+	0.289452i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.20991	−	7.29177i	0.150258	−	0.260254i
$786$		0			0
$787$	−11.3143			−0.403311			−0.201656	−	0.979457i	$-0.564632\pi$
$787$	−11.3143			−0.403311			−0.201656	+	0.979457i	$0.564632\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.792307			0.0281712
$792$		0			0
$793$	−40.4080	+	23.3296i	−1.43493	+	0.828457i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			16.9600i			0.600753i	0.953821	+	0.300377i	$0.0971124\pi$
$797$			16.9600i			0.600753i	−0.953821	+	0.300377i	$0.902888\pi$
$798$		0			0
$799$		−	7.48016i		−	0.264629i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.74692	+	5.05003i	−0.308672	+	0.178212i
$804$		0			0
$805$	−0.234363			−0.00826021
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−23.7069			−0.833492			−0.416746	−	0.909023i	$-0.636830\pi$
$809$	−23.7069			−0.833492			−0.416746	+	0.909023i	$0.636830\pi$
$810$		0			0
$811$	8.04690	−	13.9376i	0.282565	−	0.489417i	−0.689451	−	0.724332i	$-0.742148\pi$
$811$	8.04690	−	13.9376i	0.282565	−	0.489417i	0.972016	+	0.234916i	$0.0754814\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.94587	+	1.70080i	−0.103189	+	0.0595763i
$816$		0			0
$817$	−37.0876	+	12.3076i	−1.29753	+	0.430590i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.6129	−	39.1667i	0.789196	−	1.36693i	−0.137264	−	0.990534i	$-0.543831\pi$
$821$	22.6129	−	39.1667i	0.789196	−	1.36693i	0.926460	−	0.376393i	$-0.122836\pi$
$822$		0			0
$823$	−26.7648	−	15.4526i	−0.932961	−	0.538645i	−0.0452143	−	0.998977i	$-0.514397\pi$
$823$	−26.7648	−	15.4526i	−0.932961	−	0.538645i	−0.887747	+	0.460332i	$0.847730\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.91426	+	11.9759i	−0.240433	+	0.416441i	−0.960838	−	0.277112i	$-0.910623\pi$
$827$	−6.91426	+	11.9759i	−0.240433	+	0.416441i	0.720405	+	0.693554i	$0.243956\pi$
$828$		0			0
$829$		−	19.5734i		−	0.679813i	−0.940459	−	0.339907i	$-0.889605\pi$
$829$		−	19.5734i		−	0.679813i	0.940459	−	0.339907i	$-0.110395\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−8.57494	−	14.8522i	−0.297104	−	0.514599i
$834$		0			0
$835$	17.1191			0.592430
$836$		0			0
$837$		0			0
$838$		0			0
$839$	25.3517	+	43.9104i	0.875238	+	1.51596i	0.856509	+	0.516132i	$0.172629\pi$
$839$	25.3517	+	43.9104i	0.875238	+	1.51596i	0.0187289	+	0.999825i	$0.494038\pi$
$840$		0			0
$841$	20.4998	+	35.5066i	0.706888	+	1.22437i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.32059	+	2.28732i	−0.0454296	+	0.0786864i
$846$		0			0
$847$			0.601077i			0.0206533i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.43493	−	5.94948i	0.117748	−	0.203946i
$852$		0			0
$853$	−19.6130	−	33.9708i	−0.671537	−	1.16314i	−0.977468	−	0.211083i	$-0.932301\pi$
$853$	−19.6130	−	33.9708i	−0.671537	−	1.16314i	0.305931	−	0.952054i	$-0.401032\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	48.5793	−	28.0473i	1.65944	−	0.958077i	0.686464	−	0.727164i	$-0.259162\pi$
$857$	48.5793	−	28.0473i	1.65944	−	0.958077i	0.972974	−	0.230913i	$-0.0741712\pi$
$858$		0			0
$859$	−22.0523	−	12.7319i	−0.752415	−	0.434407i	0.0741509	−	0.997247i	$-0.476375\pi$
$859$	−22.0523	−	12.7319i	−0.752415	−	0.434407i	−0.826566	+	0.562840i	$0.809709\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	12.4525			0.423888			0.211944	−	0.977282i	$-0.432021\pi$
$863$	12.4525			0.423888			0.211944	+	0.977282i	$0.432021\pi$
$864$		0			0
$865$	10.2482	+	5.91678i	0.348448	+	0.201177i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−40.6013	+	23.4412i	−1.37731	+	0.795188i
$870$		0			0
$871$	−2.36868	+	1.36756i	−0.0802598	+	0.0463380i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		−	0.621271i		−	0.0210028i
$876$		0			0
$877$	−14.2839	+	8.24681i	−0.482333	+	0.278475i	−0.721388	−	0.692531i	$-0.756496\pi$
$877$	−14.2839	+	8.24681i	−0.482333	+	0.278475i	0.239055	+	0.971006i	$0.423162\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	55.1042			1.85651			0.928254	−	0.371946i	$-0.121309\pi$
$881$	55.1042			1.85651			0.928254	+	0.371946i	$0.121309\pi$
$882$		0			0
$883$	32.0841	+	18.5237i	1.07971	+	0.623373i	0.930819	−	0.365480i	$-0.119095\pi$
$883$	32.0841	+	18.5237i	1.07971	+	0.623373i	0.148895	+	0.988853i	$0.452428\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.2468	−	35.0685i	0.679821	−	1.17748i	−0.295214	−	0.955431i	$-0.595391\pi$
$887$	20.2468	−	35.0685i	0.679821	−	1.17748i	0.975035	−	0.222053i	$-0.0712758\pi$
$888$		0			0
$889$	−0.160172	−	0.0924751i	−0.00537198	−	0.00310152i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.93344	−	8.83217i	−0.332410	−	0.295557i
$894$		0			0
$895$	−3.17544	−	5.50002i	−0.106143	−	0.183845i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	27.4805	+	15.8659i	0.916526	+	0.529157i
$900$		0			0
$901$		−	4.47552i		−	0.149101i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	2.51621i		−	0.0836416i
$906$		0			0
$907$	−12.2457	−	21.2101i	−0.406611	−	0.704270i	0.587897	−	0.808936i	$-0.299956\pi$
$907$	−12.2457	−	21.2101i	−0.406611	−	0.704270i	−0.994507	+	0.104666i	$0.966623\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−44.1701			−1.46342			−0.731711	−	0.681615i	$-0.761278\pi$
$911$	−44.1701			−1.46342			−0.731711	+	0.681615i	$0.761278\pi$
$912$		0			0
$913$	−65.7171			−2.17492
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.196449	−	0.340259i	−0.00648731	−	0.0112364i
$918$		0			0
$919$			38.3854i			1.26622i	0.774062	+	0.633109i	$0.218222\pi$
$919$			38.3854i			1.26622i	−0.774062	+	0.633109i	$0.781778\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	15.8207i		−	0.520743i
$924$		0			0
$925$	7.47057	+	4.31314i	0.245631	+	0.141815i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.56091	−	2.70358i	−0.0512119	−	0.0887015i	0.839283	−	0.543695i	$-0.182975\pi$
$929$	−1.56091	−	2.70358i	−0.0512119	−	0.0887015i	−0.890495	+	0.454993i	$0.849642\pi$
$930$		0			0
$931$	−29.8481	−	6.14943i	−0.978233	−	0.201539i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.28463	−	3.62843i	−0.205529	−	0.118663i
$936$		0			0
$937$	−2.80802	+	4.86363i	−0.0917339	+	0.158888i	−0.908241	−	0.418448i	$-0.862574\pi$
$937$	−2.80802	+	4.86363i	−0.0917339	+	0.158888i	0.816507	+	0.577336i	$0.195908\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	36.8034	+	21.2484i	1.19976	+	0.692679i	0.960501	−	0.278278i	$-0.0897636\pi$
$941$	36.8034	+	21.2484i	1.19976	+	0.692679i	0.239255	+	0.970957i	$0.423097\pi$
$942$		0			0
$943$	27.8340			0.906401
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−20.8692	+	12.0488i	−0.678158	+	0.391534i	−0.799161	−	0.601118i	$-0.794722\pi$
$947$	−20.8692	+	12.0488i	−0.678158	+	0.391534i	0.121003	+	0.992652i	$0.461389\pi$
$948$		0			0
$949$		−	9.87680i		−	0.320614i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−20.5110	+	11.8420i	−0.664417	+	0.383601i	−0.793958	−	0.607973i	$-0.791983\pi$
$953$	−20.5110	+	11.8420i	−0.664417	+	0.383601i	0.129541	+	0.991574i	$0.458650\pi$
$954$		0			0
$955$	−2.27490	+	1.31342i	−0.0736142	+	0.0425012i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.480515	−	0.277425i	−0.0155166	−	0.00895853i
$960$		0			0
$961$	−16.6155			−0.535985
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.6385	−	7.29686i	−0.406849	−	0.234894i
$966$		0			0
$967$	−39.3127	+	22.6972i	−1.26421	+	0.729893i	−0.973887	−	0.227034i	$-0.927097\pi$
$967$	−39.3127	+	22.6972i	−1.26421	+	0.729893i	−0.290326	+	0.956928i	$0.593764\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−10.2734	−	17.7940i	−0.329689	−	0.571038i	0.652761	−	0.757564i	$-0.273610\pi$
$971$	−10.2734	−	17.7940i	−0.329689	−	0.571038i	−0.982450	+	0.186526i	$0.940277\pi$
$972$		0			0
$973$	−0.613028	+	1.06180i	−0.0196528	+	0.0340396i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			16.8292i			0.538413i	0.963082	+	0.269207i	$0.0867615\pi$
$977$			16.8292i			0.538413i	−0.963082	+	0.269207i	$0.913239\pi$
$978$		0			0
$979$	−11.5424	+	19.9921i	−0.368898	+	0.638950i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−28.5754	−	49.4941i	−0.911415	−	1.57862i	−0.812067	−	0.583565i	$-0.801658\pi$
$983$	−28.5754	−	49.4941i	−0.911415	−	1.57862i	−0.0993483	−	0.995053i	$-0.531676\pi$
$984$		0			0
$985$	1.87152	+	3.24157i	0.0596315	+	0.103285i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−32.1266			−1.02157
$990$		0			0
$991$	13.5478	+	23.4655i	0.430361	+	0.745408i	0.996904	−	0.0786245i	$-0.0250528\pi$
$991$	13.5478	+	23.4655i	0.430361	+	0.745408i	−0.566543	+	0.824032i	$0.691719\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			8.79165i			0.278714i
$996$		0			0
$997$	−8.46141	+	14.6556i	−0.267975	+	0.464147i	−0.968339	−	0.249639i	$-0.919688\pi$
$997$	−8.46141	+	14.6556i	−0.267975	+	0.464147i	0.700363	+	0.713786i	$0.253021\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.bm.s.1855.2		8
3.2	odd	2		912.2.bb.g.31.3	✓	8
4.3	odd	2		2736.2.bm.r.1855.2		8
12.11	even	2		912.2.bb.h.31.3	yes	8
19.8	odd	6		2736.2.bm.r.559.2		8
57.8	even	6		912.2.bb.h.559.3	yes	8
76.27	even	6	inner	2736.2.bm.s.559.2		8
228.179	odd	6		912.2.bb.g.559.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.g.31.3	✓	8	3.2	odd	2
912.2.bb.g.559.3	yes	8	228.179	odd	6
912.2.bb.h.31.3	yes	8	12.11	even	2
912.2.bb.h.559.3	yes	8	57.8	even	6
2736.2.bm.r.559.2		8	19.8	odd	6
2736.2.bm.r.1855.2		8	4.3	odd	2
2736.2.bm.s.559.2		8	76.27	even	6	inner
2736.2.bm.s.1855.2		8	1.1	even	1	trivial

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.353597 + 0.612447i) q^{5} -0.0924751i q^{7} +O(q^{10})\)	\(q+(0.353597 + 0.612447i) q^{5} -0.0924751i q^{7} -4.18329i q^{11} +(3.54275 + 2.04541i) q^{13} +(-1.22649 - 2.12434i) q^{17} +(-4.26923 - 0.879564i) q^{19} +(-3.10354 - 1.79183i) q^{23} +(2.24994 - 3.89701i) q^{25} +(-7.24566 - 4.18329i) q^{29} -3.79268 q^{31} +(0.0566361 - 0.0326989i) q^{35} +1.91700i q^{37} +(-6.72637 + 3.88347i) q^{41} +(7.76371 - 4.48238i) q^{43} +(2.64088 + 1.52471i) q^{47} +6.99145 q^{49} +(1.58009 + 0.912263i) q^{53} +(2.56204 - 1.47920i) q^{55} +(-2.91564 - 5.05003i) q^{59} +(-5.70292 + 9.87774i) q^{61} +2.89299i q^{65} +(-0.334301 + 0.579026i) q^{67} +(-1.93368 - 3.34924i) q^{71} +(-1.20719 - 2.09092i) q^{73} -0.386850 q^{77} +(-5.60354 - 9.70561i) q^{79} -15.7095i q^{83} +(0.867365 - 1.50232i) q^{85} +(-4.77904 - 2.75918i) q^{89} +(0.189149 - 0.327616i) q^{91} +(-0.970900 - 2.92569i) q^{95} +(11.0427 - 6.37553i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5}+O(q^{10}) \) 8 * q + 2 * q^5	\( 8 q + 2 q^{5} - 4 q^{17} + 6 q^{23} - 12 q^{25} + 12 q^{29} + 28 q^{31} + 18 q^{35} + 12 q^{41} + 18 q^{43} + 12 q^{47} - 24 q^{49} + 6 q^{53} - 12 q^{55} + 10 q^{59} - 4 q^{61} - 6 q^{67} - 8 q^{71} - 8 q^{73} - 28 q^{77} - 14 q^{79} - 8 q^{85} - 54 q^{89} - 26 q^{91} + 38 q^{95} + 60 q^{97}+O(q^{100}) \) 8 * q + 2 * q^5 - 4 * q^17 + 6 * q^23 - 12 * q^25 + 12 * q^29 + 28 * q^31 + 18 * q^35 + 12 * q^41 + 18 * q^43 + 12 * q^47 - 24 * q^49 + 6 * q^53 - 12 * q^55 + 10 * q^59 - 4 * q^61 - 6 * q^67 - 8 * q^71 - 8 * q^73 - 28 * q^77 - 14 * q^79 - 8 * q^85 - 54 * q^89 - 26 * q^91 + 38 * q^95 + 60 * q^97

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