LMFDB - Embedded newform 2736.2.bm.l.559.2

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.31726512.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 10x^{4} + 3x^{3} + 84x^{2} - 27x + 9 $ x^6 - x^5 + 10x^4 + 3x^3 + 84x^2 - 27x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 304)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.2
Root			$0.162698 - 0.281802i$ of defining polynomial
Character	$\chi$	$=$	2736.559
Dual form			2736.2.bm.l.1855.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.337302 + 0.584224i) q^{5} -3.59084i q^{7} +O(q^{10})$	$q+(-0.337302 + 0.584224i) q^{5} -3.59084i q^{7} +1.85879i q^{11} +(3.00000 - 1.73205i) q^{13} +(-2.77246 + 4.80203i) q^{17} +(-2.83730 + 3.30904i) q^{19} +(-3.10976 + 1.79542i) q^{23} +(2.27246 + 3.93601i) q^{25} +(1.98810 - 1.14783i) q^{29} +5.56872 q^{31} +(2.09785 + 1.21120i) q^{35} +2.29565i q^{37} +(8.84118 + 5.10446i) q^{41} +(-3.00000 - 1.73205i) q^{43} +(0.109757 - 0.0633682i) q^{47} -5.89412 q^{49} +(6.00000 - 3.46410i) q^{53} +(-1.08595 - 0.626972i) q^{55} +(7.60976 - 13.1805i) q^{59} +(-1.66270 - 2.87988i) q^{61} +2.33689i q^{65} +(4.93515 + 8.54794i) q^{67} +(3.00000 - 5.19615i) q^{71} +(-3.94706 + 6.83651i) q^{73} +6.67460 q^{77} +(2.67460 - 4.63255i) q^{79} -6.61807i q^{83} +(-1.87031 - 3.23947i) q^{85} +(-5.31737 + 3.06998i) q^{89} +(-6.21951 - 10.7725i) q^{91} +(-0.976190 - 2.77376i) q^{95} +(3.52381 + 2.03447i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{5}+O(q^{10}) $ 6 * q - 2 * q^5	$ 6 q - 2 q^{5} + 18 q^{13} + 2 q^{17} - 17 q^{19} - 5 q^{25} + 12 q^{29} - 4 q^{31} - 6 q^{35} - 3 q^{41} - 18 q^{43} - 18 q^{47} + 2 q^{49} + 36 q^{53} + 12 q^{55} + 27 q^{59} - 10 q^{61} + 11 q^{67} + 18 q^{71} - 5 q^{73} + 40 q^{77} + 16 q^{79} + 26 q^{85} + 24 q^{89} - 6 q^{95} + 21 q^{97}+O(q^{100}) $ 6 * q - 2 * q^5 + 18 * q^13 + 2 * q^17 - 17 * q^19 - 5 * q^25 + 12 * q^29 - 4 * q^31 - 6 * q^35 - 3 * q^41 - 18 * q^43 - 18 * q^47 + 2 * q^49 + 36 * q^53 + 12 * q^55 + 27 * q^59 - 10 * q^61 + 11 * q^67 + 18 * q^71 - 5 * q^73 + 40 * q^77 + 16 * q^79 + 26 * q^85 + 24 * q^89 - 6 * q^95 + 21 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.337302	+	0.584224i	−0.150846	+	0.261273i	−0.931539	−	0.363642i	$-0.881533\pi$
$5$	−0.337302	+	0.584224i	−0.150846	+	0.261273i	0.780693	+	0.624915i	$0.214866\pi$
$6$		0			0
$7$		−	3.59084i		−	1.35721i	−0.734504	−	0.678605i	$-0.762585\pi$
$7$		−	3.59084i		−	1.35721i	0.734504	−	0.678605i	$-0.237415\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$			1.85879i			0.560445i	0.959935	+	0.280223i	$0.0904083\pi$
$11$			1.85879i			0.560445i	−0.959935	+	0.280223i	$0.909592\pi$
$12$		0			0
$13$	3.00000	−	1.73205i	0.832050	−	0.480384i	−0.0225039	−	0.999747i	$-0.507164\pi$
$13$	3.00000	−	1.73205i	0.832050	−	0.480384i	0.854554	+	0.519362i	$0.173830\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.77246	+	4.80203i	−0.672419	+	1.16466i	0.304797	+	0.952417i	$0.401411\pi$
$17$	−2.77246	+	4.80203i	−0.672419	+	1.16466i	−0.977216	+	0.212247i	$0.931922\pi$
$18$		0			0
$19$	−2.83730	+	3.30904i	−0.650922	+	0.759145i
$19$	−2.83730	+	3.30904i	−0.650922	+	0.759145i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.10976	+	1.79542i	−0.648429	+	0.374371i	−0.787854	−	0.615862i	$-0.788808\pi$
$23$	−3.10976	+	1.79542i	−0.648429	+	0.374371i	0.139425	+	0.990233i	$0.455475\pi$
$24$		0			0
$25$	2.27246	+	3.93601i	0.454491	+	0.787202i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.98810	−	1.14783i	0.369180	−	0.213146i	−0.303920	−	0.952698i	$-0.598296\pi$
$29$	1.98810	−	1.14783i	0.369180	−	0.213146i	0.673100	+	0.739551i	$0.264962\pi$
$30$		0			0
$31$	5.56872			1.00017			0.500086	−	0.865976i	$-0.333302\pi$
$31$	5.56872			1.00017			0.500086	+	0.865976i	$0.333302\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.09785	+	1.21120i	0.354602	+	0.204729i
$36$		0			0
$37$			2.29565i			0.377403i	0.982034	+	0.188702i	$0.0604279\pi$
$37$			2.29565i			0.377403i	−0.982034	+	0.188702i	$0.939572\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.84118	+	5.10446i	1.38076	+	0.797182i	0.992249	−	0.124262i	$-0.0396565\pi$
$41$	8.84118	+	5.10446i	1.38076	+	0.797182i	0.388510	+	0.921444i	$0.372990\pi$
$42$		0			0
$43$	−3.00000	−	1.73205i	−0.457496	−	0.264135i	0.253495	−	0.967337i	$-0.418420\pi$
$43$	−3.00000	−	1.73205i	−0.457496	−	0.264135i	−0.710991	+	0.703201i	$0.751753\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.109757	−	0.0633682i	0.0160097	−	0.00924319i	−0.491974	−	0.870610i	$-0.663724\pi$
$47$	0.109757	−	0.0633682i	0.0160097	−	0.00924319i	0.507983	+	0.861367i	$0.330391\pi$
$48$		0			0
$49$	−5.89412			−0.842017
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.00000	−	3.46410i	0.824163	−	0.475831i	−0.0276867	−	0.999617i	$-0.508814\pi$
$53$	6.00000	−	3.46410i	0.824163	−	0.475831i	0.851850	+	0.523786i	$0.175481\pi$
$54$		0			0
$55$	−1.08595	−	0.626972i	−0.146429	−	0.0845409i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.60976	−	13.1805i	0.990706	−	1.71595i	0.377555	−	0.925987i	$-0.376765\pi$
$59$	7.60976	−	13.1805i	0.990706	−	1.71595i	0.613151	−	0.789966i	$-0.289902\pi$
$60$		0			0
$61$	−1.66270	−	2.87988i	−0.212887	−	0.368731i	0.739730	−	0.672904i	$-0.234953\pi$
$61$	−1.66270	−	2.87988i	−0.212887	−	0.368731i	−0.952617	+	0.304173i	$0.901620\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			2.33689i			0.289856i
$66$		0			0
$67$	4.93515	+	8.54794i	0.602925	+	1.04430i	0.992376	+	0.123249i	$0.0393315\pi$
$67$	4.93515	+	8.54794i	0.602925	+	1.04430i	−0.389451	+	0.921047i	$0.627335\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$	−3.94706	+	6.83651i	−0.461968	+	0.800152i	−0.999059	−	0.0433720i	$-0.986190\pi$
$73$	−3.94706	+	6.83651i	−0.461968	+	0.800152i	0.537091	+	0.843524i	$0.319523\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.67460			0.760642
$78$		0			0
$79$	2.67460	−	4.63255i	0.300916	−	0.521202i	−0.675427	−	0.737426i	$-0.736041\pi$
$79$	2.67460	−	4.63255i	0.300916	−	0.521202i	0.976344	+	0.216224i	$0.0693742\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	6.61807i		−	0.726428i	−0.931706	−	0.363214i	$-0.881679\pi$
$83$		−	6.61807i		−	0.726428i	0.931706	−	0.363214i	$-0.118321\pi$
$84$		0			0
$85$	−1.87031	−	3.23947i	−0.202863	−	0.351370i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.31737	+	3.06998i	−0.563640	+	0.325417i	−0.754605	−	0.656179i	$-0.772172\pi$
$89$	−5.31737	+	3.06998i	−0.563640	+	0.325417i	0.190965	+	0.981597i	$0.438838\pi$
$90$		0			0
$91$	−6.21951	−	10.7725i	−0.651982	−	1.12927i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.976190	−	2.77376i	−0.100155	−	0.284582i
$96$		0			0
$97$	3.52381	+	2.03447i	0.357789	+	0.206569i	0.668110	−	0.744062i	$-0.267103\pi$
$97$	3.52381	+	2.03447i	0.357789	+	0.206569i	−0.310322	+	0.950632i	$0.600437\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.90602	+	13.6936i	0.786679	+	1.36257i	0.927991	+	0.372602i	$0.121534\pi$
$101$	7.90602	+	13.6936i	0.786679	+	1.36257i	−0.141313	+	0.989965i	$0.545132\pi$
$102$		0			0
$103$	13.0898			1.28978			0.644889	−	0.764276i	$-0.276904\pi$
$103$	13.0898			1.28978			0.644889	+	0.764276i	$0.276904\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.4390			1.20253			0.601263	−	0.799051i	$-0.294664\pi$
$107$	12.4390			1.20253			0.601263	+	0.799051i	$0.294664\pi$
$108$		0			0
$109$	2.02381	+	1.16845i	0.193846	+	0.111917i	0.593782	−	0.804626i	$-0.297634\pi$
$109$	2.02381	+	1.16845i	0.193846	+	0.111917i	−0.399936	+	0.916543i	$0.630968\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	1.73205i		−	0.162938i	−0.996676	−	0.0814688i	$-0.974039\pi$
$113$		−	1.73205i		−	0.162938i	0.996676	−	0.0814688i	$-0.0259611\pi$
$114$		0			0
$115$		−	2.42239i		−	0.225889i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	17.2433	+	9.95544i	1.58069	+	0.912613i
$120$		0			0
$121$	7.54491			0.685901
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.43903			−0.575924
$126$		0			0
$127$	9.54491	+	16.5323i	0.846974	+	1.46700i	0.883896	+	0.467684i	$0.154911\pi$
$127$	9.54491	+	16.5323i	0.846974	+	1.46700i	−0.0369221	+	0.999318i	$0.511755\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.70761	−	5.60469i	−0.848158	−	0.489684i	0.0118711	−	0.999930i	$-0.496221\pi$
$131$	−9.70761	−	5.60469i	−0.848158	−	0.489684i	−0.860029	+	0.510245i	$0.829555\pi$
$132$		0			0
$133$	11.8822	+	10.1883i	1.03032	+	0.883437i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.17460	+	8.96268i	0.442096	+	0.765733i	0.997845	−	0.0656173i	$-0.0209017\pi$
$137$	5.17460	+	8.96268i	0.442096	+	0.765733i	−0.555749	+	0.831350i	$0.687568\pi$
$138$		0			0
$139$	7.60976	−	4.39350i	0.645451	−	0.372651i	−0.141260	−	0.989973i	$-0.545115\pi$
$139$	7.60976	−	4.39350i	0.645451	−	0.372651i	0.786711	+	0.617321i	$0.211782\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.21951	+	5.57636i	0.269229	+	0.466319i
$144$		0			0
$145$			1.54866i			0.128609i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.55682	+	11.3567i	−0.537155	+	0.930380i	0.461900	+	0.886932i	$0.347168\pi$
$149$	−6.55682	+	11.3567i	−0.537155	+	0.930380i	−0.999056	+	0.0434484i	$0.986166\pi$
$150$		0			0
$151$	−19.9601			−1.62433			−0.812166	−	0.583426i	$-0.801712\pi$
$151$	−19.9601			−1.62433			−0.812166	+	0.583426i	$0.801712\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.87834	+	3.25338i	−0.150872	+	0.261318i
$156$		0			0
$157$	−5.89412	+	10.2089i	−0.470402	+	0.814760i	−0.999427	−	0.0338463i	$-0.989224\pi$
$157$	−5.89412	+	10.2089i	−0.470402	+	0.814760i	0.529025	+	0.848606i	$0.322558\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.44706	+	11.1666i	0.508099	+	0.880054i
$162$		0			0
$163$		−	18.0521i		−	1.41395i	−0.707239	−	0.706974i	$-0.750060\pi$
$163$		−	18.0521i		−	1.41395i	0.707239	−	0.706974i	$-0.249940\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.2433	+	19.4740i	0.870034	+	1.50694i	0.861960	+	0.506977i	$0.169237\pi$
$167$	11.2433	+	19.4740i	0.870034	+	1.50694i	0.00807463	+	0.999967i	$0.497430\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−15.0000	−	8.66025i	−1.14043	−	0.658427i	−0.193892	−	0.981023i	$-0.562111\pi$
$173$	−15.0000	−	8.66025i	−1.14043	−	0.658427i	−0.946537	+	0.322596i	$0.895445\pi$
$174$		0			0
$175$	14.1336	−	8.16002i	1.06840	−	0.616839i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−23.4628			−1.75369			−0.876847	−	0.480769i	$-0.840358\pi$
$179$	−23.4628			−1.75369			−0.876847	+	0.480769i	$0.840358\pi$
$180$		0			0
$181$	13.6704	−	7.89264i	1.01612	−	0.586655i	0.103140	−	0.994667i	$-0.467111\pi$
$181$	13.6704	−	7.89264i	1.01612	−	0.586655i	0.912977	+	0.408012i	$0.133778\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.34118	−	0.774328i	−0.0986052	−	0.0569297i
$186$		0			0
$187$	−8.92596	−	5.15340i	−0.652731	−	0.376854i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	21.2916i		−	1.54060i	−0.637680	−	0.770301i	$-0.720106\pi$
$191$		−	21.2916i		−	1.54060i	0.637680	−	0.770301i	$-0.279894\pi$
$192$		0			0
$193$	17.3174	+	9.99819i	1.24653	+	0.719685i	0.970416	−	0.241439i	$-0.0776195\pi$
$193$	17.3174	+	9.99819i	1.24653	+	0.719685i	0.276115	+	0.961125i	$0.410953\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.7644			1.26566			0.632831	−	0.774290i	$-0.281893\pi$
$197$	17.7644			1.26566			0.632831	+	0.774290i	$0.281893\pi$
$198$		0			0
$199$	−4.04762	+	2.33689i	−0.286928	+	0.165658i	−0.636556	−	0.771231i	$-0.719641\pi$
$199$	−4.04762	+	2.33689i	−0.286928	+	0.165658i	0.349628	+	0.936889i	$0.386308\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.12166	−	7.13893i	−0.289284	−	0.501054i
$204$		0			0
$205$	−5.96429	+	3.44348i	−0.416564	+	0.240503i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.15079	−	5.27394i	−0.425459	−	0.364806i
$210$		0			0
$211$	−6.79626	+	11.7715i	−0.467874	+	0.810382i	−0.999326	−	0.0367066i	$-0.988313\pi$
$211$	−6.79626	+	11.7715i	−0.467874	+	0.810382i	0.531452	+	0.847088i	$0.321647\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.02381	−	1.16845i	0.138023	−	0.0796874i
$216$		0			0
$217$		−	19.9964i		−	1.35744i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			19.2081i			1.29208i
$222$		0			0
$223$	−6.65467	+	11.5262i	−0.445629	+	0.771853i	−0.998096	−	0.0616823i	$-0.980353\pi$
$223$	−6.65467	+	11.5262i	−0.445629	+	0.771853i	0.552466	+	0.833535i	$0.313687\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.97619			−0.463026			−0.231513	−	0.972832i	$-0.574368\pi$
$227$	−6.97619			−0.463026			−0.231513	+	0.972832i	$0.574368\pi$
$228$		0			0
$229$	0.650794			0.0430056			0.0215028	−	0.999769i	$-0.493155\pi$
$229$	0.650794			0.0430056			0.0215028	+	0.999769i	$0.493155\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.29626	−	10.9055i	0.412482	−	0.714440i	−0.582678	−	0.812703i	$-0.697995\pi$
$233$	6.29626	−	10.9055i	0.412482	−	0.714440i	0.995160	+	0.0982630i	$0.0313286\pi$
$234$		0			0
$235$			0.0854967i			0.00557719i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			1.38068i			0.0893088i	0.999002	+	0.0446544i	$0.0142187\pi$
$239$			1.38068i			0.0893088i	−0.999002	+	0.0446544i	$0.985781\pi$
$240$		0			0
$241$	−7.86499	+	4.54085i	−0.506628	+	0.292502i	−0.731447	−	0.681899i	$-0.761154\pi$
$241$	−7.86499	+	4.54085i	−0.506628	+	0.292502i	0.224818	+	0.974401i	$0.427821\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.98810	−	3.44348i	0.127015	−	0.219996i
$246$		0			0
$247$	−2.78049	+	14.8415i	−0.176918	+	0.944339i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−15.9271	+	9.19553i	−1.00531	+	0.580417i	−0.909815	−	0.415013i	$-0.863777\pi$
$251$	−15.9271	+	9.19553i	−1.00531	+	0.580417i	−0.0954957	+	0.995430i	$0.530444\pi$
$252$		0			0
$253$	−3.33730	−	5.78038i	−0.209814	−	0.363409i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.81737	+	2.20396i	−0.238121	+	0.137479i	−0.614313	−	0.789063i	$-0.710567\pi$
$257$	−3.81737	+	2.20396i	−0.238121	+	0.137479i	0.376192	+	0.926542i	$0.377233\pi$
$258$		0			0
$259$	8.24332			0.512215
$260$		0			0
$261$		0			0
$262$		0			0
$263$	22.8159	+	13.1728i	1.40689	+	0.812268i	0.995087	−	0.0990048i	$-0.0315659\pi$
$263$	22.8159	+	13.1728i	1.40689	+	0.812268i	0.411803	+	0.911273i	$0.364899\pi$
$264$		0			0
$265$			4.67379i			0.287109i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	25.6347	+	14.8002i	1.56298	+	0.902385i	0.996954	+	0.0779962i	$0.0248522\pi$
$269$	25.6347	+	14.8002i	1.56298	+	0.902385i	0.566024	+	0.824389i	$0.308481\pi$
$270$		0			0
$271$	−17.3531	−	10.0188i	−1.05412	−	0.608599i	−0.130323	−	0.991472i	$-0.541602\pi$
$271$	−17.3531	−	10.0188i	−1.05412	−	0.608599i	−0.923801	+	0.382872i	$0.874935\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.31620	+	4.22401i	−0.441184	+	0.254717i
$276$		0			0
$277$	−20.2511			−1.21677			−0.608384	−	0.793642i	$-0.708182\pi$
$277$	−20.2511			−1.21677			−0.608384	+	0.793642i	$0.708182\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	21.8174	−	12.5963i	1.30151	−	0.751430i	0.320851	−	0.947130i	$-0.396031\pi$
$281$	21.8174	−	12.5963i	1.30151	−	0.751430i	0.980664	+	0.195700i	$0.0626978\pi$
$282$		0			0
$283$	12.4881	+	7.21001i	0.742340	+	0.428590i	0.822920	−	0.568158i	$-0.192344\pi$
$283$	12.4881	+	7.21001i	0.742340	+	0.428590i	−0.0805794	+	0.996748i	$0.525677\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	18.3293	−	31.7472i	1.08194	−	1.87398i
$288$		0			0
$289$	−6.87302	−	11.9044i	−0.404295	−	0.700260i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	19.2494i		−	1.12456i	−0.826947	−	0.562280i	$-0.809924\pi$
$293$		−	19.2494i		−	1.12456i	0.826947	−	0.562280i	$-0.190076\pi$
$294$		0			0
$295$	5.13357	+	8.89160i	0.298888	+	0.517689i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.21951	+	10.7725i	−0.359684	+	0.622991i
$300$		0			0
$301$	−6.21951	+	10.7725i	−0.358487	+	0.620917i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.24332			0.128452
$306$		0			0
$307$	4.50387	−	7.80094i	0.257050	−	0.445223i	−0.708401	−	0.705811i	$-0.750583\pi$
$307$	4.50387	−	7.80094i	0.257050	−	0.445223i	0.965450	+	0.260588i	$0.0839163\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	11.3928i		−	0.646025i	−0.946395	−	0.323013i	$-0.895304\pi$
$311$		−	11.3928i		−	0.646025i	0.946395	−	0.323013i	$-0.104696\pi$
$312$		0			0
$313$	5.94706	+	10.3006i	0.336148	+	0.582225i	0.983705	−	0.179792i	$-0.0575426\pi$
$313$	5.94706	+	10.3006i	0.336148	+	0.582225i	−0.647557	+	0.762017i	$0.724209\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.6824	+	11.9410i	−1.16164	+	0.670671i	−0.951696	−	0.307043i	$-0.900660\pi$
$317$	−20.6824	+	11.9410i	−1.16164	+	0.670671i	−0.209941	+	0.977714i	$0.567327\pi$
$318$		0			0
$319$	2.13357	+	3.69545i	0.119457	+	0.206905i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.02381	−	22.7990i	−0.446457	−	1.26857i
$324$		0			0
$325$	13.6347	+	7.87202i	0.756319	+	0.436661i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.227545	−	0.394119i	−0.0125449	−	0.0217285i
$330$		0			0
$331$	−4.81204			−0.264494			−0.132247	−	0.991217i	$-0.542219\pi$
$331$	−4.81204			−0.264494			−0.132247	+	0.991217i	$0.542219\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.65854			−0.363795
$336$		0			0
$337$	−16.1824	−	9.34288i	−0.881509	−	0.508939i	−0.0103532	−	0.999946i	$-0.503296\pi$
$337$	−16.1824	−	9.34288i	−0.881509	−	0.508939i	−0.871156	+	0.491007i	$0.836629\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			10.3511i			0.560542i
$342$		0			0
$343$		−	3.97105i		−	0.214416i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	25.0012	+	14.4344i	1.34213	+	0.774881i	0.987120	−	0.159981i	$-0.0511432\pi$
$347$	25.0012	+	14.4344i	1.34213	+	0.774881i	0.355013	+	0.934861i	$0.384477\pi$
$348$		0			0
$349$	−5.95238			−0.318624			−0.159312	−	0.987228i	$-0.550928\pi$
$349$	−5.95238			−0.318624			−0.159312	+	0.987228i	$0.550928\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.78823			0.254852			0.127426	−	0.991848i	$-0.459328\pi$
$353$	4.78823			0.254852			0.127426	+	0.991848i	$0.459328\pi$
$354$		0			0
$355$	2.02381	+	3.50534i	0.107413	+	0.186044i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	19.0859	+	11.0193i	1.00732	+	0.581575i	0.910405	−	0.413718i	$-0.135770\pi$
$359$	19.0859	+	11.0193i	1.00732	+	0.581575i	0.0969126	+	0.995293i	$0.469103\pi$
$360$		0			0
$361$	−2.89944	−	18.7775i	−0.152602	−	0.988288i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.66270	−	4.61193i	−0.139372	−	0.241399i
$366$		0			0
$367$	20.2817	−	11.7096i	1.05869	−	0.611237i	0.133623	−	0.991032i	$-0.457339\pi$
$367$	20.2817	−	11.7096i	1.05869	−	0.611237i	0.925071	+	0.379795i	$0.124006\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−12.4390	−	21.5450i	−0.645802	−	1.11856i
$372$		0			0
$373$			18.0809i			0.936195i	0.883677	+	0.468097i	$0.155060\pi$
$373$			18.0809i			0.936195i	−0.883677	+	0.468097i	$0.844940\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.97619	−	6.88696i	0.204784	−	0.354697i
$378$		0			0
$379$	−9.10588			−0.467738			−0.233869	−	0.972268i	$-0.575139\pi$
$379$	−9.10588			−0.467738			−0.233869	+	0.972268i	$0.575139\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.89024	+	5.00605i	−0.147685	+	0.255797i	−0.930371	−	0.366619i	$-0.880515\pi$
$383$	−2.89024	+	5.00605i	−0.147685	+	0.255797i	0.782687	+	0.622416i	$0.213849\pi$
$384$		0			0
$385$	−2.25135	+	3.89946i	−0.114740	+	0.198735i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.54491	−	14.8002i	−0.433244	−	0.750401i	0.563906	−	0.825839i	$-0.309298\pi$
$389$	−8.54491	−	14.8002i	−0.433244	−	0.750401i	−0.997151	+	0.0754378i	$0.975965\pi$
$390$		0			0
$391$		−	19.9109i		−	1.00694i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.80430	+	3.12513i	0.0907840	+	0.157242i
$396$		0			0
$397$	16.8001	−	29.0987i	0.843175	−	1.46042i	−0.0440221	−	0.999031i	$-0.514017\pi$
$397$	16.8001	−	29.0987i	0.843175	−	1.46042i	0.887197	−	0.461391i	$-0.152649\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−21.1347	−	12.2021i	−1.05542	−	0.609346i	−0.131257	−	0.991348i	$-0.541901\pi$
$401$	−21.1347	−	12.2021i	−1.05542	−	0.609346i	−0.924161	+	0.382002i	$0.875235\pi$
$402$		0			0
$403$	16.7062	−	9.64531i	0.832193	−	0.480467i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.26713			−0.211514
$408$		0			0
$409$	−7.79356	+	4.49961i	−0.385367	+	0.222491i	−0.680151	−	0.733072i	$-0.738086\pi$
$409$	−7.79356	+	4.49961i	−0.385367	+	0.222491i	0.294784	+	0.955564i	$0.404752\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−47.3290	−	27.3254i	−2.32891	−	1.34460i
$414$		0			0
$415$	3.86643	+	2.23229i	0.189796	+	0.109579i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			5.46504i			0.266985i	0.991050	+	0.133492i	$0.0426192\pi$
$419$			5.46504i			0.266985i	−0.991050	+	0.133492i	$0.957381\pi$
$420$		0			0
$421$	−29.7181	−	17.1577i	−1.44837	−	0.836217i	−0.449985	−	0.893036i	$-0.648571\pi$
$421$	−29.7181	−	17.1577i	−1.44837	−	0.836217i	−0.998384	+	0.0568192i	$0.981904\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−25.2011			−1.22243
$426$		0			0
$427$	−10.3412	+	5.97048i	−0.500445	+	0.288932i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.43903	+	16.3489i	0.454662	+	0.787498i	0.998669	−	0.0515832i	$-0.0164267\pi$
$431$	9.43903	+	16.3489i	0.454662	+	0.787498i	−0.544007	+	0.839081i	$0.683093\pi$
$432$		0			0
$433$	13.4126	−	7.74377i	0.644569	−	0.372142i	−0.141804	−	0.989895i	$-0.545290\pi$
$433$	13.4126	−	7.74377i	0.644569	−	0.372142i	0.786372	+	0.617753i	$0.211957\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.88221	−	15.3844i	0.137875	−	0.735938i
$438$		0			0
$439$	−2.45896	+	4.25905i	−0.117360	+	0.203273i	−0.918721	−	0.394908i	$-0.870776\pi$
$439$	−2.45896	+	4.25905i	−0.117360	+	0.203273i	0.801361	+	0.598181i	$0.204110\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−24.9986	+	14.4329i	−1.18772	+	0.685729i	−0.957787	−	0.287478i	$-0.907183\pi$
$443$	−24.9986	+	14.4329i	−1.18772	+	0.685729i	−0.229930	+	0.973207i	$0.573850\pi$
$444$		0			0
$445$		−	4.14204i		−	0.196352i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	12.5458i		−	0.592073i	−0.955177	−	0.296037i	$-0.904335\pi$
$449$		−	12.5458i		−	0.592073i	0.955177	−	0.296037i	$-0.0956650\pi$
$450$		0			0
$451$	−9.48810	+	16.4339i	−0.446777	+	0.773840i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	8.39141			0.393395
$456$		0			0
$457$	35.6347			1.66692			0.833461	−	0.552578i	$-0.186356\pi$
$457$	35.6347			1.66692			0.833461	+	0.552578i	$0.186356\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.5211	+	21.6872i	−0.583166	+	1.01007i	0.411936	+	0.911213i	$0.364853\pi$
$461$	−12.5211	+	21.6872i	−0.583166	+	1.01007i	−0.995101	+	0.0988598i	$0.968480\pi$
$462$		0			0
$463$		−	10.4748i		−	0.486804i	−0.969925	−	0.243402i	$-0.921736\pi$
$463$		−	10.4748i		−	0.486804i	0.969925	−	0.243402i	$-0.0782635\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			2.98599i			0.138175i	0.997611	+	0.0690877i	$0.0220088\pi$
$467$			2.98599i			0.138175i	−0.997611	+	0.0690877i	$0.977991\pi$
$468$		0			0
$469$	30.6943	−	17.7213i	1.41733	−	0.818295i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.21951	−	5.57636i	0.148033	−	0.256401i
$474$		0			0
$475$	−19.4720	−	3.64801i	−0.893438	−	0.167382i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.21951	+	3.59084i	−0.284177	+	0.164070i	−0.635313	−	0.772255i	$-0.719129\pi$
$479$	−6.21951	+	3.59084i	−0.284177	+	0.164070i	0.351136	+	0.936324i	$0.385795\pi$
$480$		0			0
$481$	3.97619	+	6.88696i	0.181299	+	0.314019i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.37717	+	1.37246i	−0.107942	+	0.0623203i
$486$		0			0
$487$	−8.82269			−0.399794			−0.199897	−	0.979817i	$-0.564061\pi$
$487$	−8.82269			−0.399794			−0.199897	+	0.979817i	$0.564061\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.90186	−	3.40744i	−0.266347	−	0.153776i	0.360879	−	0.932613i	$-0.382477\pi$
$491$	−5.90186	−	3.40744i	−0.266347	−	0.153776i	−0.627227	+	0.778837i	$0.715810\pi$
$492$		0			0
$493$			12.7292i			0.573294i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−18.6585	−	10.7725i	−0.836950	−	0.483213i
$498$		0			0
$499$	−14.8795	−	8.59069i	−0.666098	−	0.384572i	0.128499	−	0.991710i	$-0.458984\pi$
$499$	−14.8795	−	8.59069i	−0.666098	−	0.384572i	−0.794597	+	0.607138i	$0.792318\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−30.4506	+	17.5807i	−1.35773	+	0.783884i	−0.989317	−	0.145779i	$-0.953431\pi$
$503$	−30.4506	+	17.5807i	−1.35773	+	0.783884i	−0.368410	+	0.929663i	$0.620098\pi$
$504$		0			0
$505$	−10.6669			−0.474669
$506$		0			0
$507$		0			0
$508$		0			0
$509$	15.6585	−	9.04046i	0.694053	−	0.400711i	−0.111076	−	0.993812i	$-0.535430\pi$
$509$	15.6585	−	9.04046i	0.694053	−	0.400711i	0.805128	+	0.593100i	$0.202096\pi$
$510$		0			0
$511$	24.5488	+	14.1732i	1.08597	+	0.626988i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4.41522	+	7.64738i	−0.194558	+	0.336984i
$516$		0			0
$517$	0.117788	+	0.204015i	0.00518031	+	0.00897255i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			2.85926i			0.125266i	0.998037	+	0.0626332i	$0.0199498\pi$
$521$			2.85926i			0.125266i	−0.998037	+	0.0626332i	$0.980050\pi$
$522$		0			0
$523$	−15.3331	−	26.5578i	−0.670472	−	1.16129i	−0.977771	−	0.209678i	$-0.932758\pi$
$523$	−15.3331	−	26.5578i	−0.670472	−	1.16129i	0.307299	−	0.951613i	$-0.400575\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.4390	+	26.7412i	−0.672535	+	1.16486i
$528$		0			0
$529$	−5.05294	+	8.75195i	−0.219693	+	0.380520i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	35.3647			1.53182
$534$		0			0
$535$	−4.19570	+	7.26717i	−0.181396	+	0.314187i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	10.9559i		−	0.471904i
$540$		0			0
$541$	−4.10588	−	7.11160i	−0.176526	−	0.305751i	0.764163	−	0.645024i	$-0.223153\pi$
$541$	−4.10588	−	7.11160i	−0.176526	−	0.305751i	−0.940688	+	0.339272i	$0.889819\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.36527	+	0.788238i	−0.0584817	+	0.0337644i
$546$		0			0
$547$	−3.76442	−	6.52017i	−0.160955	−	0.278783i	0.774256	−	0.632872i	$-0.218124\pi$
$547$	−3.76442	−	6.52017i	−0.160955	−	0.278783i	−0.935212	+	0.354090i	$0.884791\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.84262	+	9.83541i	−0.0784984	+	0.419003i
$552$		0			0
$553$	−16.6347	−	9.60407i	−0.707381	−	0.408406i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.69841	+	4.67379i	0.114335	+	0.198035i	0.917514	−	0.397704i	$-0.130193\pi$
$557$	2.69841	+	4.67379i	0.114335	+	0.198035i	−0.803178	+	0.595738i	$0.796859\pi$
$558$		0			0
$559$	−12.0000			−0.507546
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.5372			−0.528378			−0.264189	−	0.964471i	$-0.585104\pi$
$563$	−12.5372			−0.528378			−0.264189	+	0.964471i	$0.585104\pi$
$564$		0			0
$565$	1.01190	+	0.584224i	0.0425712	+	0.0245785i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	6.22244i		−	0.260858i	−0.991458	−	0.130429i	$-0.958364\pi$
$569$		−	6.22244i		−	0.260858i	0.991458	−	0.130429i	$-0.0416355\pi$
$570$		0			0
$571$			32.1341i			1.34477i	0.740201	+	0.672386i	$0.234731\pi$
$571$			32.1341i			1.34477i	−0.740201	+	0.672386i	$0.765269\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−14.1336	−	8.16002i	−0.589410	−	0.340296i
$576$		0			0
$577$	−21.6508			−0.901334			−0.450667	−	0.892692i	$-0.648814\pi$
$577$	−21.6508			−0.901334			−0.450667	+	0.892692i	$0.648814\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−23.7644			−0.985914
$582$		0			0
$583$	6.43903	+	11.1527i	0.266677	+	0.461899i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.1957	+	7.61854i	0.544645	+	0.314451i	0.746959	−	0.664870i	$-0.231513\pi$
$587$	13.1957	+	7.61854i	0.544645	+	0.314451i	−0.202314	+	0.979321i	$0.564846\pi$
$588$		0			0
$589$	−15.8001	+	18.4271i	−0.651033	+	0.759275i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9.07675	−	15.7214i	−0.372737	−	0.645600i	0.617248	−	0.786769i	$-0.288247\pi$
$593$	−9.07675	−	15.7214i	−0.372737	−	0.645600i	−0.989986	+	0.141168i	$0.954914\pi$
$594$		0			0
$595$	−11.6324	+	6.71597i	−0.476882	+	0.275328i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−10.3055	−	17.8496i	−0.421070	−	0.729314i	0.574975	−	0.818171i	$-0.305012\pi$
$599$	−10.3055	−	17.8496i	−0.421070	−	0.729314i	−0.996044	+	0.0888571i	$0.971679\pi$
$600$		0			0
$601$		−	23.6985i		−	0.966683i	−0.875432	−	0.483342i	$-0.839423\pi$
$601$		−	23.6985i		−	0.966683i	0.875432	−	0.483342i	$-0.160577\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.54491	+	4.40791i	−0.103465	+	0.179207i
$606$		0			0
$607$	24.0077			0.974444			0.487222	−	0.873278i	$-0.338010\pi$
$607$	24.0077			0.974444			0.487222	+	0.873278i	$0.338010\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.219514	−	0.380209i	0.00888057	−	0.0153816i
$612$		0			0
$613$	5.56872	−	9.64531i	0.224918	−	0.389570i	−0.731376	−	0.681974i	$-0.761122\pi$
$613$	5.56872	−	9.64531i	0.224918	−	0.389570i	0.956295	+	0.292404i	$0.0944551\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.15079	+	10.6535i	0.247622	+	0.428893i	0.962865	−	0.269982i	$-0.0870177\pi$
$617$	6.15079	+	10.6535i	0.247622	+	0.428893i	−0.715244	+	0.698875i	$0.753684\pi$
$618$		0			0
$619$			48.5551i			1.95159i	0.218678	+	0.975797i	$0.429826\pi$
$619$			48.5551i			1.95159i	−0.218678	+	0.975797i	$0.570174\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.0238	+	19.0938i	0.441660	+	0.764977i
$624$		0			0
$625$	−9.19038	+	15.9182i	−0.367615	+	0.636728i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−11.0238	−	6.36460i	−0.439548	−	0.253773i
$630$		0			0
$631$	−10.8159	+	6.24457i	−0.430575	+	0.248593i	−0.699592	−	0.714543i	$-0.746635\pi$
$631$	−10.8159	+	6.24457i	−0.430575	+	0.248593i	0.269017	+	0.963136i	$0.413301\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.8781			−0.511050
$636$		0			0
$637$	−17.6824	+	10.2089i	−0.700600	+	0.404492i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	35.4521	+	20.4683i	1.40027	+	0.808448i	0.994420	−	0.105490i	$-0.0336411\pi$
$641$	35.4521	+	20.4683i	1.40027	+	0.808448i	0.405853	+	0.913938i	$0.366974\pi$
$642$		0			0
$643$	−3.17045	−	1.83046i	−0.125030	−	0.0721862i	0.436180	−	0.899859i	$-0.356331\pi$
$643$	−3.17045	−	1.83046i	−0.125030	−	0.0721862i	−0.561211	+	0.827673i	$0.689664\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			29.3470i			1.15375i	0.816833	+	0.576874i	$0.195728\pi$
$647$			29.3470i			1.15375i	−0.816833	+	0.576874i	$0.804272\pi$
$648$		0			0
$649$	24.4997	+	14.1449i	0.961698	+	0.555237i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.25397			0.205604			0.102802	−	0.994702i	$-0.467219\pi$
$653$	5.25397			0.205604			0.102802	+	0.994702i	$0.467219\pi$
$654$		0			0
$655$	6.54878	−	3.78094i	0.255882	−	0.147734i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−16.4866	−	28.5557i	−0.642229	−	1.11237i	−0.984934	−	0.172930i	$-0.944677\pi$
$659$	−16.4866	−	28.5557i	−0.642229	−	1.11237i	0.342706	−	0.939443i	$-0.388657\pi$
$660$		0			0
$661$	−33.3052	+	19.2288i	−1.29542	+	0.747912i	−0.979610	−	0.200910i	$-0.935610\pi$
$661$	−33.3052	+	19.2288i	−1.29542	+	0.747912i	−0.315812	+	0.948822i	$0.602277\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−9.96013	+	3.50534i	−0.386237	+	0.135931i
$666$		0			0
$667$	−4.12166	+	7.13893i	−0.159591	+	0.276420i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.35308	−	3.09060i	0.206653	−	0.119311i
$672$		0			0
$673$		−	3.12513i		−	0.120465i	−0.998184	−	0.0602325i	$-0.980816\pi$
$673$		−	3.12513i		−	0.120465i	0.998184	−	0.0602325i	$-0.0191842\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	5.43421i		−	0.208854i	−0.994533	−	0.104427i	$-0.966699\pi$
$677$		−	5.43421i		−	0.208854i	0.994533	−	0.104427i	$-0.0333008\pi$
$678$		0			0
$679$	7.30546	−	12.6534i	0.280358	−	0.485594i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−48.8781			−1.87027			−0.935133	−	0.354296i	$-0.884721\pi$
$683$	−48.8781			−1.87027			−0.935133	+	0.354296i	$0.884721\pi$
$684$		0			0
$685$	−6.98161			−0.266754
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$		−	15.0661i		−	0.573141i	−0.958059	−	0.286571i	$-0.907485\pi$
$691$		−	15.0661i		−	0.573141i	0.958059	−	0.286571i	$-0.0925153\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			5.92773i			0.224852i
$696$		0			0
$697$	−49.0235	+	28.3037i	−1.85690	+	1.07208i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	20.8001	−	36.0269i	0.785610	−	1.36072i	−0.143023	−	0.989719i	$-0.545682\pi$
$701$	20.8001	−	36.0269i	0.785610	−	1.36072i	0.928634	−	0.370998i	$-0.120984\pi$
$702$		0			0
$703$	−7.59640	−	6.51346i	−0.286504	−	0.245660i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	49.1716	−	28.3892i	1.84929	−	1.06769i
$708$		0			0
$709$	−11.7763	−	20.3972i	−0.442269	−	0.766033i	0.555588	−	0.831458i	$-0.312493\pi$
$709$	−11.7763	−	20.3972i	−0.442269	−	0.766033i	−0.997858	+	0.0654247i	$0.979160\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−17.3174	+	9.99819i	−0.648540	+	0.374435i
$714$		0			0
$715$	−4.34379			−0.162448
$716$		0			0
$717$		0			0
$718$		0			0
$719$	27.3676	+	15.8007i	1.02064	+	0.589266i	0.914289	−	0.405062i	$-0.132750\pi$
$719$	27.3676	+	15.8007i	1.02064	+	0.589266i	0.106350	+	0.994329i	$0.466084\pi$
$720$		0			0
$721$		−	47.0034i		−	1.75050i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	9.03571	+	5.21677i	0.335578	+	0.193746i
$726$		0			0
$727$	41.6824	+	24.0653i	1.54591	+	0.892533i	0.998447	+	0.0557050i	$0.0177406\pi$
$727$	41.6824	+	24.0653i	1.54591	+	0.892533i	0.547466	+	0.836828i	$0.315593\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	16.6347	−	9.60407i	0.615258	−	0.355219i
$732$		0			0
$733$	33.4574			1.23578			0.617889	−	0.786265i	$-0.287988\pi$
$733$	33.4574			1.23578			0.617889	+	0.786265i	$0.287988\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−15.8888	+	9.17340i	−0.585271	+	0.337907i
$738$		0			0
$739$	−15.6336	−	9.02604i	−0.575090	−	0.332028i	0.184090	−	0.982909i	$-0.441066\pi$
$739$	−15.6336	−	9.02604i	−0.575090	−	0.332028i	−0.759180	+	0.650881i	$0.774400\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.15738	+	7.20079i	−0.152519	+	0.264171i	−0.932153	−	0.362065i	$-0.882072\pi$
$743$	−4.15738	+	7.20079i	−0.152519	+	0.264171i	0.779634	+	0.626236i	$0.215405\pi$
$744$		0			0
$745$	−4.42325	−	7.66129i	−0.162055	−	0.280688i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	44.6665i		−	1.63208i
$750$		0			0
$751$	−12.3254	−	21.3482i	−0.449760	−	0.779007i	0.548610	−	0.836078i	$-0.315157\pi$
$751$	−12.3254	−	21.3482i	−0.449760	−	0.779007i	−0.998370	+	0.0570710i	$0.981824\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.73258	−	11.6612i	0.245024	−	0.424394i
$756$		0			0
$757$	27.1136	−	46.9622i	0.985462	−	1.70687i	0.345595	−	0.938384i	$-0.387677\pi$
$757$	27.1136	−	46.9622i	0.985462	−	1.70687i	0.639867	−	0.768486i	$-0.278990\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−24.1374			−0.874982			−0.437491	−	0.899223i	$-0.644133\pi$
$761$	−24.1374			−0.874982			−0.437491	+	0.899223i	$0.644133\pi$
$762$		0			0
$763$	4.19570	−	7.26717i	0.151895	−	0.263089i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	52.7219i		−	1.90368i
$768$		0			0
$769$	1.22754	+	2.12617i	0.0442664	+	0.0766716i	0.887310	−	0.461174i	$-0.152572\pi$
$769$	1.22754	+	2.12617i	0.0442664	+	0.0766716i	−0.843043	+	0.537846i	$0.819238\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.89286	+	1.67019i	−0.104049	+	0.0600726i	−0.551121	−	0.834425i	$-0.685800\pi$
$773$	−2.89286	+	1.67019i	−0.104049	+	0.0600726i	0.447073	+	0.894498i	$0.352467\pi$
$774$		0			0
$775$	12.6547	+	21.9185i	0.454569	+	0.787337i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−41.9759	+	14.7729i	−1.50394	+	0.529294i
$780$		0			0
$781$	9.65854	+	5.57636i	0.345610	+	0.199538i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.97619	−	6.88696i	−0.141916	−	0.245806i
$786$		0			0
$787$	−22.6003			−0.805613			−0.402806	−	0.915285i	$-0.631965\pi$
$787$	−22.6003			−0.805613			−0.402806	+	0.915285i	$0.631965\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6.21951			−0.221140
$792$		0			0
$793$	−9.97619	−	5.75976i	−0.354265	−	0.204535i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	16.5457i		−	0.586078i	−0.956100	−	0.293039i	$-0.905333\pi$
$797$		−	16.5457i		−	0.586078i	0.956100	−	0.293039i	$-0.0946666\pi$
$798$		0			0
$799$			0.702741i			0.0248612i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−12.7076	−	7.33674i	−0.448442	−	0.258908i
$804$		0			0
$805$	−8.69841			−0.306579
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−19.5027			−0.685679			−0.342839	−	0.939394i	$-0.611389\pi$
$809$	−19.5027			−0.685679			−0.342839	+	0.939394i	$0.611389\pi$
$810$		0			0
$811$	−14.0316	−	24.3034i	−0.492715	−	0.853407i	0.507250	−	0.861799i	$-0.330662\pi$
$811$	−14.0316	−	24.3034i	−0.492715	−	0.853407i	−0.999965	+	0.00839210i	$0.997329\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.5465	+	6.08900i	0.369426	+	0.213288i
$816$		0			0
$817$	14.2433	−	5.01276i	0.498311	−	0.175374i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.3331	−	43.8783i	−0.884133	−	1.53136i	−0.846704	−	0.532064i	$-0.821417\pi$
$821$	−25.3331	−	43.8783i	−0.884133	−	1.53136i	−0.0374285	−	0.999299i	$-0.511917\pi$
$822$		0			0
$823$	−21.1214	+	12.1944i	−0.736245	+	0.425071i	−0.820702	−	0.571356i	$-0.806418\pi$
$823$	−21.1214	+	12.1944i	−0.736245	+	0.425071i	0.0844575	+	0.996427i	$0.473084\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.75523	+	3.04014i	0.0610353	+	0.105716i	0.894928	−	0.446210i	$-0.147226\pi$
$827$	1.75523	+	3.04014i	0.0610353	+	0.105716i	−0.833893	+	0.551926i	$0.813893\pi$
$828$		0			0
$829$		−	48.8086i		−	1.69519i	−0.530642	−	0.847596i	$-0.678049\pi$
$829$		−	48.8086i		−	1.69519i	0.530642	−	0.847596i	$-0.321951\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	16.3412	−	28.3037i	0.566188	−	0.980667i
$834$		0			0
$835$	−15.1696			−0.524964
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−18.5488	+	32.1274i	−0.640375	+	1.10916i	0.344974	+	0.938612i	$0.387888\pi$
$839$	−18.5488	+	32.1274i	−0.640375	+	1.10916i	−0.985349	+	0.170550i	$0.945446\pi$
$840$		0			0
$841$	−11.8650	+	20.5508i	−0.409137	+	0.708647i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.337302	−	0.584224i	−0.0116035	−	0.0200979i
$846$		0			0
$847$		−	27.0926i		−	0.930911i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.12166	−	7.13893i	−0.141289	−	0.244719i
$852$		0			0
$853$	4.10588	−	7.11160i	0.140583	−	0.243496i	−0.787133	−	0.616783i	$-0.788436\pi$
$853$	4.10588	−	7.11160i	0.140583	−	0.243496i	0.927716	+	0.373286i	$0.121769\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	15.4524	+	8.92144i	0.527843	+	0.304750i	0.740138	−	0.672455i	$-0.234760\pi$
$857$	15.4524	+	8.92144i	0.527843	+	0.304750i	−0.212294	+	0.977206i	$0.568094\pi$
$858$		0			0
$859$	17.6600	−	10.1960i	0.602551	−	0.347883i	−0.167493	−	0.985873i	$-0.553567\pi$
$859$	17.6600	−	10.1960i	0.602551	−	0.347883i	0.770045	+	0.637990i	$0.220234\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	40.7062			1.38565			0.692827	−	0.721104i	$-0.256365\pi$
$863$	40.7062			1.38565			0.692827	+	0.721104i	$0.256365\pi$
$864$		0			0
$865$	10.1190	−	5.84224i	0.344058	−	0.198642i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	8.61092	+	4.97152i	0.292106	+	0.168647i
$870$		0			0
$871$	29.6109	+	17.0959i	1.00333	+	0.579272i
$872$		0			0
$873$		0			0
$874$		0			0
$875$			23.1215i			0.781649i
$876$		0			0
$877$	16.5990	+	9.58345i	0.560509	+	0.323610i	0.753350	−	0.657620i	$-0.228437\pi$
$877$	16.5990	+	9.58345i	0.560509	+	0.323610i	−0.192841	+	0.981230i	$0.561770\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−44.9839			−1.51555			−0.757774	−	0.652517i	$-0.773713\pi$
$881$	−44.9839			−1.51555			−0.757774	+	0.652517i	$0.773713\pi$
$882$		0			0
$883$	−12.7790	+	7.37798i	−0.430049	+	0.248289i	−0.699367	−	0.714762i	$-0.746535\pi$
$883$	−12.7790	+	7.37798i	−0.430049	+	0.248289i	0.269319	+	0.963051i	$0.413202\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.2433	+	24.6702i	0.478244	+	0.828343i	0.999689	−	0.0249421i	$-0.00794013\pi$
$887$	14.2433	+	24.6702i	0.478244	+	0.828343i	−0.521445	+	0.853285i	$0.674607\pi$
$888$		0			0
$889$	59.3647	−	34.2742i	1.99103	−	1.14952i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.101726	+	0.542984i	−0.00340412	+	0.0181703i
$894$		0			0
$895$	7.91405	−	13.7075i	0.264538	−	0.458193i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11.0711	−	6.39193i	0.369243	−	0.213183i
$900$		0			0
$901$			38.4163i			1.27983i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			10.6488i			0.353978i
$906$		0			0
$907$	9.95896	−	17.2494i	0.330682	−	0.572758i	−0.651964	−	0.758250i	$-0.726055\pi$
$907$	9.95896	−	17.2494i	0.330682	−	0.572758i	0.982646	+	0.185492i	$0.0593879\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−11.3415			−0.375759			−0.187880	−	0.982192i	$-0.560161\pi$
$911$	−11.3415			−0.375759			−0.187880	+	0.982192i	$0.560161\pi$
$912$		0			0
$913$	12.3016			0.407123
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20.1255	+	34.8585i	−0.664604	+	1.15113i
$918$		0			0
$919$		−	29.8539i		−	0.984790i	−0.870372	−	0.492395i	$-0.836122\pi$
$919$		−	29.8539i		−	0.984790i	0.870372	−	0.492395i	$-0.163878\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	20.7846i		−	0.684134i
$924$		0			0
$925$	−9.03571	+	5.21677i	−0.297092	+	0.171526i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.26442	+	2.19005i	−0.0414844	+	0.0718531i	−0.886022	−	0.463643i	$-0.846542\pi$
$929$	−1.26442	+	2.19005i	−0.0414844	+	0.0718531i	0.844538	+	0.535496i	$0.179875\pi$
$930$		0			0
$931$	16.7234	−	19.5038i	0.548087	−	0.639213i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6.02148	−	3.47650i	0.196923	−	0.113694i
$936$		0			0
$937$	18.7936	+	32.5514i	0.613959	+	1.06341i	0.990566	+	0.137035i	$0.0437572\pi$
$937$	18.7936	+	32.5514i	0.613959	+	1.06341i	−0.376608	+	0.926373i	$0.622909\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−27.6585	+	15.9687i	−0.901643	+	0.520564i	−0.877733	−	0.479150i	$-0.840945\pi$
$941$	−27.6585	+	15.9687i	−0.901643	+	0.520564i	−0.0239099	+	0.999714i	$0.507611\pi$
$942$		0			0
$943$	−36.6585			−1.19377
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.8043	+	6.23786i	0.351092	+	0.202703i	0.665166	−	0.746695i	$-0.268361\pi$
$947$	10.8043	+	6.23786i	0.351092	+	0.202703i	−0.314074	+	0.949399i	$0.601694\pi$
$948$		0			0
$949$			27.3460i			0.887689i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−9.81737	−	5.66806i	−0.318016	−	0.183606i	0.332492	−	0.943106i	$-0.392111\pi$
$953$	−9.81737	−	5.66806i	−0.318016	−	0.183606i	−0.650508	+	0.759500i	$0.725444\pi$
$954$		0			0
$955$	12.4390	+	7.18168i	0.402517	+	0.232394i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	32.1835	−	18.5812i	1.03926	−	0.600017i
$960$		0			0
$961$	0.0106443			0.000343365
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−11.6824	+	6.74481i	−0.376068	+	0.217123i
$966$		0			0
$967$	18.5105	+	10.6870i	0.595256	+	0.343671i	0.767173	−	0.641440i	$-0.221663\pi$
$967$	18.5105	+	10.6870i	0.595256	+	0.343671i	−0.171917	+	0.985111i	$0.554996\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−15.8531	+	27.4583i	−0.508750	+	0.881180i	0.491199	+	0.871047i	$0.336559\pi$
$971$	−15.8531	+	27.4583i	−0.508750	+	0.881180i	−0.999949	+	0.0101328i	$0.996775\pi$
$972$		0			0
$973$	−15.7763	−	27.3254i	−0.505766	−	0.876012i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			30.2878i			0.968991i	0.874794	+	0.484496i	$0.160997\pi$
$977$			30.2878i			0.968991i	−0.874794	+	0.484496i	$0.839003\pi$
$978$		0			0
$979$	−5.70644	−	9.88385i	−0.182379	−	0.315889i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.65854	−	16.7291i	0.308060	−	0.533575i	−0.669878	−	0.742471i	$-0.733654\pi$
$983$	9.65854	−	16.7291i	0.308060	−	0.533575i	0.977938	+	0.208896i	$0.0669870\pi$
$984$		0			0
$985$	−5.99197	+	10.3784i	−0.190920	+	0.330683i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.4390			0.395538
$990$		0			0
$991$	−24.8703	+	43.0766i	−0.790031	+	1.36837i	0.135915	+	0.990720i	$0.456602\pi$
$991$	−24.8703	+	43.0766i	−0.790031	+	1.36837i	−0.925947	+	0.377654i	$0.876731\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	3.15295i		−	0.0999553i
$996$		0			0
$997$	15.0435	+	26.0560i	0.476431	+	0.825203i	0.999635	−	0.0270043i	$-0.00859679\pi$
$997$	15.0435	+	26.0560i	0.476431	+	0.825203i	−0.523204	+	0.852207i	$0.675263\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.bm.l.559.2		6
3.2	odd	2		304.2.n.d.255.2	yes	6
4.3	odd	2		2736.2.bm.m.559.2		6
12.11	even	2		304.2.n.e.255.2	yes	6
19.12	odd	6		2736.2.bm.m.1855.2		6
24.5	odd	2		1216.2.n.e.255.2		6
24.11	even	2		1216.2.n.d.255.2		6
57.50	even	6		304.2.n.e.31.2	yes	6
76.31	even	6	inner	2736.2.bm.l.1855.2		6
228.107	odd	6		304.2.n.d.31.2	✓	6
456.107	odd	6		1216.2.n.e.639.2		6
456.221	even	6		1216.2.n.d.639.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.n.d.31.2	✓	6	228.107	odd	6
304.2.n.d.255.2	yes	6	3.2	odd	2
304.2.n.e.31.2	yes	6	57.50	even	6
304.2.n.e.255.2	yes	6	12.11	even	2
1216.2.n.d.255.2		6	24.11	even	2
1216.2.n.d.639.2		6	456.221	even	6
1216.2.n.e.255.2		6	24.5	odd	2
1216.2.n.e.639.2		6	456.107	odd	6
2736.2.bm.l.559.2		6	1.1	even	1	trivial
2736.2.bm.l.1855.2		6	76.31	even	6	inner
2736.2.bm.m.559.2		6	4.3	odd	2
2736.2.bm.m.1855.2		6	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.337302 + 0.584224i) q^{5} -3.59084i q^{7} +O(q^{10})\)	\(q+(-0.337302 + 0.584224i) q^{5} -3.59084i q^{7} +1.85879i q^{11} +(3.00000 - 1.73205i) q^{13} +(-2.77246 + 4.80203i) q^{17} +(-2.83730 + 3.30904i) q^{19} +(-3.10976 + 1.79542i) q^{23} +(2.27246 + 3.93601i) q^{25} +(1.98810 - 1.14783i) q^{29} +5.56872 q^{31} +(2.09785 + 1.21120i) q^{35} +2.29565i q^{37} +(8.84118 + 5.10446i) q^{41} +(-3.00000 - 1.73205i) q^{43} +(0.109757 - 0.0633682i) q^{47} -5.89412 q^{49} +(6.00000 - 3.46410i) q^{53} +(-1.08595 - 0.626972i) q^{55} +(7.60976 - 13.1805i) q^{59} +(-1.66270 - 2.87988i) q^{61} +2.33689i q^{65} +(4.93515 + 8.54794i) q^{67} +(3.00000 - 5.19615i) q^{71} +(-3.94706 + 6.83651i) q^{73} +6.67460 q^{77} +(2.67460 - 4.63255i) q^{79} -6.61807i q^{83} +(-1.87031 - 3.23947i) q^{85} +(-5.31737 + 3.06998i) q^{89} +(-6.21951 - 10.7725i) q^{91} +(-0.976190 - 2.77376i) q^{95} +(3.52381 + 2.03447i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{5}+O(q^{10}) \) 6 * q - 2 * q^5	\( 6 q - 2 q^{5} + 18 q^{13} + 2 q^{17} - 17 q^{19} - 5 q^{25} + 12 q^{29} - 4 q^{31} - 6 q^{35} - 3 q^{41} - 18 q^{43} - 18 q^{47} + 2 q^{49} + 36 q^{53} + 12 q^{55} + 27 q^{59} - 10 q^{61} + 11 q^{67} + 18 q^{71} - 5 q^{73} + 40 q^{77} + 16 q^{79} + 26 q^{85} + 24 q^{89} - 6 q^{95} + 21 q^{97}+O(q^{100}) \) 6 * q - 2 * q^5 + 18 * q^13 + 2 * q^17 - 17 * q^19 - 5 * q^25 + 12 * q^29 - 4 * q^31 - 6 * q^35 - 3 * q^41 - 18 * q^43 - 18 * q^47 + 2 * q^49 + 36 * q^53 + 12 * q^55 + 27 * q^59 - 10 * q^61 + 11 * q^67 + 18 * q^71 - 5 * q^73 + 40 * q^77 + 16 * q^79 + 26 * q^85 + 24 * q^89 - 6 * q^95 + 21 * q^97

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