LMFDB - Embedded newform 1008.2.cs.b.703.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(271,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

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

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

chi := DirichletCharacter("1008.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cs (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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1008.703
Dual form			1008.2.cs.b.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +O(q^{10})$	$q+(-3.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(3.00000 + 1.73205i) q^{11} -1.73205i q^{13} +(2.50000 + 4.33013i) q^{19} +(-6.00000 + 3.46410i) q^{23} +(3.50000 - 6.06218i) q^{25} +(-2.50000 + 4.33013i) q^{31} +(3.00000 + 8.66025i) q^{35} +(5.50000 + 9.52628i) q^{37} +3.46410i q^{41} +8.66025i q^{43} +(3.00000 + 5.19615i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(6.00000 - 10.3923i) q^{53} -12.0000 q^{55} +(-6.00000 + 10.3923i) q^{59} +(-12.0000 + 6.92820i) q^{61} +(3.00000 + 5.19615i) q^{65} +(7.50000 + 4.33013i) q^{67} -3.46410i q^{71} +(-4.50000 - 2.59808i) q^{73} +(6.00000 - 6.92820i) q^{77} +(10.5000 - 6.06218i) q^{79} +18.0000 q^{83} +(-6.00000 + 3.46410i) q^{89} +(-4.50000 - 0.866025i) q^{91} +(-15.0000 - 8.66025i) q^{95} +6.92820i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{5} + q^{7}+O(q^{10}) $ 2 * q - 6 * q^5 + q^7	$ 2 q - 6 q^{5} + q^{7} + 6 q^{11} + 5 q^{19} - 12 q^{23} + 7 q^{25} - 5 q^{31} + 6 q^{35} + 11 q^{37} + 6 q^{47} - 13 q^{49} + 12 q^{53} - 24 q^{55} - 12 q^{59} - 24 q^{61} + 6 q^{65} + 15 q^{67} - 9 q^{73} + 12 q^{77} + 21 q^{79} + 36 q^{83} - 12 q^{89} - 9 q^{91} - 30 q^{95}+O(q^{100}) $ 2 * q - 6 * q^5 + q^7 + 6 * q^11 + 5 * q^19 - 12 * q^23 + 7 * q^25 - 5 * q^31 + 6 * q^35 + 11 * q^37 + 6 * q^47 - 13 * q^49 + 12 * q^53 - 24 * q^55 - 12 * q^59 - 24 * q^61 + 6 * q^65 + 15 * q^67 - 9 * q^73 + 12 * q^77 + 21 * q^79 + 36 * q^83 - 12 * q^89 - 9 * q^91 - 30 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$5$	−3.00000	+	1.73205i	−1.34164	+	0.774597i	−0.987048	−	0.160424i	$-0.948714\pi$
$5$	−3.00000	+	1.73205i	−1.34164	+	0.774597i	−0.354593	+	0.935021i	$0.615380\pi$
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.878668	−	0.477432i	$-0.158432\pi$
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.0258656	+	0.999665i	$0.491766\pi$
$12$		0			0
$13$		−	1.73205i		−	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$		−	1.73205i		−	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.00000	+	3.46410i	−1.25109	+	0.722315i	−0.971325	−	0.237754i	$-0.923589\pi$
$23$	−6.00000	+	3.46410i	−1.25109	+	0.722315i	−0.279761	+	0.960070i	$0.590255\pi$
$24$		0			0
$25$	3.50000	−	6.06218i	0.700000	−	1.21244i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.00000	+	8.66025i	0.507093	+	1.46385i
$36$		0			0
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.821995	+	0.569495i	$0.192861\pi$
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.0821995	+	0.996616i	$0.473806\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			3.46410i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$41$			3.46410i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$42$		0			0
$43$			8.66025i			1.32068i	0.750968	+	0.660338i	$0.229587\pi$
$43$			8.66025i			1.32068i	−0.750968	+	0.660338i	$0.770413\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$		0			0
$55$	−12.0000			−1.61808
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$		0			0
$61$	−12.0000	+	6.92820i	−1.53644	+	0.887066i	−0.537400	+	0.843328i	$0.680593\pi$
$61$	−12.0000	+	6.92820i	−1.53644	+	0.887066i	−0.999043	+	0.0437377i	$0.986073\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$		0			0
$67$	7.50000	+	4.33013i	0.916271	+	0.529009i	0.882443	−	0.470418i	$-0.155897\pi$
$67$	7.50000	+	4.33013i	0.916271	+	0.529009i	0.0338274	+	0.999428i	$0.489230\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	3.46410i		−	0.411113i	−0.978645	−	0.205557i	$-0.934100\pi$
$71$		−	3.46410i		−	0.411113i	0.978645	−	0.205557i	$-0.0659005\pi$
$72$		0			0
$73$	−4.50000	−	2.59808i	−0.526685	−	0.304082i	0.212980	−	0.977056i	$-0.431683\pi$
$73$	−4.50000	−	2.59808i	−0.526685	−	0.304082i	−0.739666	+	0.672975i	$0.765016\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.00000	−	6.92820i	0.683763	−	0.789542i
$78$		0			0
$79$	10.5000	−	6.06218i	1.18134	−	0.682048i	0.225018	−	0.974355i	$-0.427756\pi$
$79$	10.5000	−	6.06218i	1.18134	−	0.682048i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	18.0000			1.97576			0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000			1.97576			0.987878	+	0.155230i	$0.0496119\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.00000	+	3.46410i	−0.635999	+	0.367194i	−0.783072	−	0.621932i	$-0.786348\pi$
$89$	−6.00000	+	3.46410i	−0.635999	+	0.367194i	0.147073	+	0.989126i	$0.453015\pi$
$90$		0			0
$91$	−4.50000	−	0.866025i	−0.471728	−	0.0907841i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−15.0000	−	8.66025i	−1.53897	−	0.888523i
$96$		0			0
$97$			6.92820i			0.703452i	0.936103	+	0.351726i	$0.114405\pi$
$97$			6.92820i			0.703452i	−0.936103	+	0.351726i	$0.885595\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.00000	−	5.19615i	−0.895533	−	0.517036i	−0.0197851	−	0.999804i	$-0.506298\pi$
$101$	−9.00000	−	5.19615i	−0.895533	−	0.517036i	−0.875748	+	0.482768i	$0.839632\pi$
$102$		0			0
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	0.716173	−	0.697923i	$-0.245892\pi$
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	−0.962505	+	0.271263i	$0.912559\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$		0			0
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	−0.648292	−	0.761392i	$-0.724516\pi$
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	0.983531	+	0.180741i	$0.0578495\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	12.0000	−	20.7846i	1.11901	−	1.93817i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			6.92820i			0.619677i
$126$		0			0
$127$			12.1244i			1.07586i	0.842989	+	0.537931i	$0.180794\pi$
$127$			12.1244i			1.07586i	−0.842989	+	0.537931i	$0.819206\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	12.5000	−	4.33013i	1.08389	−	0.375470i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−7.00000			−0.593732			−0.296866	−	0.954919i	$-0.595942\pi$
$139$	−7.00000			−0.593732			−0.296866	+	0.954919i	$0.595942\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	0.999953	−	0.00974235i	$-0.00310113\pi$
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	−0.508413	+	0.861113i	$0.669768\pi$
$150$		0			0
$151$	3.00000	+	1.73205i	0.244137	+	0.140952i	0.617076	−	0.786903i	$-0.288317\pi$
$151$	3.00000	+	1.73205i	0.244137	+	0.140952i	−0.372940	+	0.927855i	$0.621650\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	17.3205i		−	1.39122i
$156$		0			0
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.00000	+	17.3205i	0.472866	+	1.36505i
$162$		0			0
$163$	−3.00000	+	1.73205i	−0.234978	+	0.135665i	−0.612866	−	0.790186i	$-0.709984\pi$
$163$	−3.00000	+	1.73205i	−0.234978	+	0.135665i	0.377888	+	0.925851i	$0.376650\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.00000			0.464294			0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000			0.464294			0.232147	+	0.972681i	$0.425425\pi$
$168$		0			0
$169$	10.0000			0.769231
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.00000	+	3.46410i	−0.456172	+	0.263371i	−0.710433	−	0.703765i	$-0.751501\pi$
$173$	−6.00000	+	3.46410i	−0.456172	+	0.263371i	0.254262	+	0.967135i	$0.418168\pi$
$174$		0			0
$175$	−14.0000	−	12.1244i	−1.05830	−	0.916515i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.00000	+	5.19615i	0.672692	+	0.388379i	0.797096	−	0.603853i	$-0.206369\pi$
$179$	9.00000	+	5.19615i	0.672692	+	0.388379i	−0.124404	+	0.992232i	$0.539702\pi$
$180$		0			0
$181$		−	5.19615i		−	0.386227i	−0.981176	−	0.193113i	$-0.938141\pi$
$181$		−	5.19615i		−	0.386227i	0.981176	−	0.193113i	$-0.0618586\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−33.0000	−	19.0526i	−2.42621	−	1.40077i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−15.0000	+	8.66025i	−1.08536	+	0.626634i	−0.932338	−	0.361588i	$-0.882235\pi$
$191$	−15.0000	+	8.66025i	−1.08536	+	0.626634i	−0.153024	+	0.988222i	$0.548901\pi$
$192$		0			0
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	−0.597317	−	0.802005i	$-0.703766\pi$
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	0.993215	+	0.116289i	$0.0370998\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−24.0000			−1.70993			−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000			−1.70993			−0.854965	+	0.518686i	$0.826421\pi$
$198$		0			0
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−6.00000	−	10.3923i	−0.419058	−	0.725830i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			17.3205i			1.19808i
$210$		0			0
$211$			3.46410i			0.238479i	0.992866	+	0.119239i	$0.0380456\pi$
$211$			3.46410i			0.238479i	−0.992866	+	0.119239i	$0.961954\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−15.0000	−	25.9808i	−1.02299	−	1.77187i
$216$		0			0
$217$	10.0000	+	8.66025i	0.678844	+	0.587896i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$		0			0
$229$	7.50000	−	4.33013i	0.495614	−	0.286143i	−0.231287	−	0.972886i	$-0.574293\pi$
$229$	7.50000	−	4.33013i	0.495614	−	0.286143i	0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$	−18.0000	−	10.3923i	−1.17419	−	0.677919i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	10.3923i		−	0.672222i	−0.941822	−	0.336111i	$-0.890888\pi$
$239$		−	10.3923i		−	0.672222i	0.941822	−	0.336111i	$-0.109112\pi$
$240$		0			0
$241$	−12.0000	−	6.92820i	−0.772988	−	0.446285i	0.0609515	−	0.998141i	$-0.480586\pi$
$241$	−12.0000	−	6.92820i	−0.772988	−	0.446285i	−0.833939	+	0.551856i	$0.813920\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	24.0000	−	3.46410i	1.53330	−	0.221313i
$246$		0			0
$247$	7.50000	−	4.33013i	0.477214	−	0.275519i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	−24.0000			−1.50887
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.0000	−	8.66025i	0.935674	−	0.540212i	0.0470726	−	0.998891i	$-0.485011\pi$
$257$	15.0000	−	8.66025i	0.935674	−	0.540212i	0.888602	+	0.458680i	$0.151677\pi$
$258$		0			0
$259$	27.5000	−	9.52628i	1.70877	−	0.591934i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.0000	−	6.92820i	−0.739952	−	0.427211i	0.0821001	−	0.996624i	$-0.473837\pi$
$263$	−12.0000	−	6.92820i	−0.739952	−	0.427211i	−0.822052	+	0.569413i	$0.807171\pi$
$264$		0			0
$265$			41.5692i			2.55358i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	15.0000	+	8.66025i	0.914566	+	0.528025i	0.881897	−	0.471441i	$-0.156266\pi$
$269$	15.0000	+	8.66025i	0.914566	+	0.528025i	0.0326687	+	0.999466i	$0.489599\pi$
$270$		0			0
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	0.718580	−	0.695444i	$-0.244792\pi$
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	−0.961563	+	0.274586i	$0.911459\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	21.0000	−	12.1244i	1.26635	−	0.731126i
$276$		0			0
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	0.425684	+	0.904872i	$0.360033\pi$
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	−0.996484	+	0.0837823i	$0.973300\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		0			0
$283$	−3.50000	+	6.06218i	−0.208053	+	0.360359i	−0.951101	−	0.308879i	$-0.900046\pi$
$283$	−3.50000	+	6.06218i	−0.208053	+	0.360359i	0.743048	+	0.669238i	$0.233379\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.00000	+	1.73205i	0.531253	+	0.102240i
$288$		0			0
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			20.7846i			1.21425i	0.794606	+	0.607125i	$0.207677\pi$
$293$			20.7846i			1.21425i	−0.794606	+	0.607125i	$0.792323\pi$
$294$		0			0
$295$		−	41.5692i		−	2.42025i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	22.5000	+	4.33013i	1.29688	+	0.249584i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	24.0000	−	41.5692i	1.37424	−	2.38025i
$306$		0			0
$307$	−11.0000			−0.627803			−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000			−0.627803			−0.313902	+	0.949456i	$0.601636\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	−0.489585	−	0.871956i	$-0.662852\pi$
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	0.999928	−	0.0119847i	$-0.00381495\pi$
$312$		0			0
$313$	13.5000	−	7.79423i	0.763065	−	0.440556i	−0.0673300	−	0.997731i	$-0.521448\pi$
$313$	13.5000	−	7.79423i	0.763065	−	0.440556i	0.830395	+	0.557175i	$0.188115\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−10.5000	−	6.06218i	−0.582435	−	0.336269i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	15.0000	−	5.19615i	0.826977	−	0.286473i
$330$		0			0
$331$	13.5000	−	7.79423i	0.742027	−	0.428410i	−0.0807788	−	0.996732i	$-0.525741\pi$
$331$	13.5000	−	7.79423i	0.742027	−	0.428410i	0.822806	+	0.568323i	$0.192407\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−30.0000			−1.63908
$336$		0			0
$337$	−19.0000			−1.03500			−0.517498	−	0.855684i	$-0.673136\pi$
$337$	−19.0000			−1.03500			−0.517498	+	0.855684i	$0.673136\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.0000	+	8.66025i	−0.812296	+	0.468979i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	24.0000	+	13.8564i	1.28839	+	0.743851i	0.978367	−	0.206879i	$-0.0663306\pi$
$347$	24.0000	+	13.8564i	1.28839	+	0.743851i	0.310021	+	0.950730i	$0.399664\pi$
$348$		0			0
$349$		−	13.8564i		−	0.741716i	−0.928689	−	0.370858i	$-0.879064\pi$
$349$		−	13.8564i		−	0.741716i	0.928689	−	0.370858i	$-0.120936\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−21.0000	−	12.1244i	−1.11772	−	0.645314i	−0.176900	−	0.984229i	$-0.556607\pi$
$353$	−21.0000	−	12.1244i	−1.11772	−	0.645314i	−0.940817	+	0.338914i	$0.889940\pi$
$354$		0			0
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	18.0000	−	10.3923i	0.950004	−	0.548485i	0.0569216	−	0.998379i	$-0.481871\pi$
$359$	18.0000	−	10.3923i	0.950004	−	0.548485i	0.893082	+	0.449894i	$0.148538\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	18.0000			0.942163
$366$		0			0
$367$	5.50000	−	9.52628i	0.287098	−	0.497268i	−0.686018	−	0.727585i	$-0.740643\pi$
$367$	5.50000	−	9.52628i	0.287098	−	0.497268i	0.973116	+	0.230317i	$0.0739762\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−24.0000	−	20.7846i	−1.24602	−	1.07908i
$372$		0			0
$373$	0.500000	+	0.866025i	0.0258890	+	0.0448411i	0.878680	−	0.477412i	$-0.158425\pi$
$373$	0.500000	+	0.866025i	0.0258890	+	0.0448411i	−0.852791	+	0.522253i	$0.825092\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$			8.66025i			0.444847i	0.974950	+	0.222424i	$0.0713968\pi$
$379$			8.66025i			0.444847i	−0.974950	+	0.222424i	$0.928603\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	0.990702	+	0.136047i	$0.0434398\pi$
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	−0.377531	+	0.925997i	$0.623227\pi$
$384$		0			0
$385$	−6.00000	+	31.1769i	−0.305788	+	1.58892i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−21.0000	+	36.3731i	−1.05662	+	1.83013i
$396$		0			0
$397$	−1.50000	+	0.866025i	−0.0752828	+	0.0434646i	−0.537169	−	0.843475i	$-0.680506\pi$
$397$	−1.50000	+	0.866025i	−0.0752828	+	0.0434646i	0.461886	+	0.886939i	$0.347173\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	0.976050	−	0.217545i	$-0.0698049\pi$
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	−0.676425	+	0.736512i	$0.736472\pi$
$402$		0			0
$403$	7.50000	+	4.33013i	0.373602	+	0.215699i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			38.1051i			1.88880i
$408$		0			0
$409$	−19.5000	−	11.2583i	−0.964213	−	0.556689i	−0.0667458	−	0.997770i	$-0.521262\pi$
$409$	−19.5000	−	11.2583i	−0.964213	−	0.556689i	−0.897467	+	0.441081i	$0.854595\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0000	+	20.7846i	1.18096	+	1.02274i
$414$		0			0
$415$	−54.0000	+	31.1769i	−2.65076	+	1.53041i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.00000			0.293119			0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000			0.293119			0.146560	+	0.989202i	$0.453180\pi$
$420$		0			0
$421$	7.00000			0.341159			0.170580	−	0.985344i	$-0.445436\pi$
$421$	7.00000			0.341159			0.170580	+	0.985344i	$0.445436\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	12.0000	+	34.6410i	0.580721	+	1.67640i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−21.0000	−	12.1244i	−1.01153	−	0.584010i	−0.0998939	−	0.994998i	$-0.531850\pi$
$431$	−21.0000	−	12.1244i	−1.01153	−	0.584010i	−0.911641	+	0.410988i	$0.865184\pi$
$432$		0			0
$433$		−	1.73205i		−	0.0832370i	−0.999134	−	0.0416185i	$-0.986749\pi$
$433$		−	1.73205i		−	0.0832370i	0.999134	−	0.0416185i	$-0.0132514\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−30.0000	−	17.3205i	−1.43509	−	0.828552i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.0000	+	6.92820i	−0.570137	+	0.329169i	−0.757204	−	0.653178i	$-0.773435\pi$
$443$	−12.0000	+	6.92820i	−0.570137	+	0.329169i	0.187067	+	0.982347i	$0.440102\pi$
$444$		0			0
$445$	12.0000	−	20.7846i	0.568855	−	0.985285i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	−6.00000	+	10.3923i	−0.282529	+	0.489355i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	15.0000	−	5.19615i	0.703211	−	0.243599i
$456$		0			0
$457$	9.50000	+	16.4545i	0.444391	+	0.769708i	0.998010	−	0.0630623i	$-0.0200867\pi$
$457$	9.50000	+	16.4545i	0.444391	+	0.769708i	−0.553618	+	0.832771i	$0.686753\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			13.8564i			0.645357i	0.946509	+	0.322679i	$0.104583\pi$
$461$			13.8564i			0.645357i	−0.946509	+	0.322679i	$0.895417\pi$
$462$		0			0
$463$		−	15.5885i		−	0.724457i	−0.932089	−	0.362229i	$-0.882016\pi$
$463$		−	15.5885i		−	0.724457i	0.932089	−	0.362229i	$-0.117984\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	15.0000	+	25.9808i	0.694117	+	1.20225i	0.970477	+	0.241192i	$0.0775384\pi$
$467$	15.0000	+	25.9808i	0.694117	+	1.20225i	−0.276360	+	0.961054i	$0.589128\pi$
$468$		0			0
$469$	15.0000	−	17.3205i	0.692636	−	0.799787i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−15.0000	+	25.9808i	−0.689701	+	1.19460i
$474$		0			0
$475$	35.0000			1.60591
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	−0.969920	−	0.243426i	$-0.921729\pi$
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	0.695773	+	0.718262i	$0.255062\pi$
$480$		0			0
$481$	16.5000	−	9.52628i	0.752335	−	0.434361i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−12.0000	−	20.7846i	−0.544892	−	0.943781i
$486$		0			0
$487$	22.5000	+	12.9904i	1.01957	+	0.588650i	0.913980	−	0.405759i	$-0.132993\pi$
$487$	22.5000	+	12.9904i	1.01957	+	0.588650i	0.105592	+	0.994410i	$0.466326\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			34.6410i			1.56333i	0.623700	+	0.781664i	$0.285629\pi$
$491$			34.6410i			1.56333i	−0.623700	+	0.781664i	$0.714371\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.00000	−	1.73205i	−0.403705	−	0.0776931i
$498$		0			0
$499$	−28.5000	+	16.4545i	−1.27584	+	0.736604i	−0.976080	−	0.217412i	$-0.930238\pi$
$499$	−28.5000	+	16.4545i	−1.27584	+	0.736604i	−0.299755	+	0.954016i	$0.596905\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−27.0000	+	15.5885i	−1.19675	+	0.690946i	−0.959830	−	0.280582i	$-0.909473\pi$
$509$	−27.0000	+	15.5885i	−1.19675	+	0.690946i	−0.236924	+	0.971528i	$0.576139\pi$
$510$		0			0
$511$	−9.00000	+	10.3923i	−0.398137	+	0.459728i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	15.0000	+	8.66025i	0.660979	+	0.381616i
$516$		0			0
$517$			20.7846i			0.914106i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	12.0000	+	6.92820i	0.525730	+	0.303530i	0.739276	−	0.673403i	$-0.235168\pi$
$521$	12.0000	+	6.92820i	0.525730	+	0.303530i	−0.213546	+	0.976933i	$0.568501\pi$
$522$		0			0
$523$	−5.50000	−	9.52628i	−0.240498	−	0.416555i	0.720358	−	0.693602i	$-0.243977\pi$
$523$	−5.50000	−	9.52628i	−0.240498	−	0.416555i	−0.960856	+	0.277047i	$0.910644\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	12.5000	−	21.6506i	0.543478	−	0.941332i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.00000			0.259889
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−15.0000	−	19.0526i	−0.646096	−	0.820652i
$540$		0			0
$541$	2.50000	+	4.33013i	0.107483	+	0.186167i	0.914750	−	0.404020i	$-0.132387\pi$
$541$	2.50000	+	4.33013i	0.107483	+	0.186167i	−0.807267	+	0.590187i	$0.799054\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			24.2487i			1.03870i
$546$		0			0
$547$		−	3.46410i		−	0.148114i	−0.997254	−	0.0740571i	$-0.976405\pi$
$547$		−	3.46410i		−	0.148114i	0.997254	−	0.0740571i	$-0.0235947\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−10.5000	−	30.3109i	−0.446505	−	1.28895i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	21.0000	−	36.3731i	0.889799	−	1.54118i	0.0496855	−	0.998765i	$-0.484178\pi$
$557$	21.0000	−	36.3731i	0.889799	−	1.54118i	0.840113	−	0.542411i	$-0.182489\pi$
$558$		0			0
$559$	15.0000			0.634432
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.00000	−	5.19615i	0.126435	−	0.218992i	−0.795858	−	0.605483i	$-0.792980\pi$
$563$	3.00000	−	5.19615i	0.126435	−	0.218992i	0.922293	+	0.386492i	$0.126313\pi$
$564$		0			0
$565$	−18.0000	+	10.3923i	−0.757266	+	0.437208i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.0000	+	36.3731i	0.880366	+	1.52484i	0.850935	+	0.525271i	$0.176036\pi$
$569$	21.0000	+	36.3731i	0.880366	+	1.52484i	0.0294311	+	0.999567i	$0.490630\pi$
$570$		0			0
$571$	−40.5000	−	23.3827i	−1.69487	−	0.978535i	−0.950477	−	0.310796i	$-0.899404\pi$
$571$	−40.5000	−	23.3827i	−1.69487	−	0.978535i	−0.744396	−	0.667739i	$-0.767262\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			48.4974i			2.02248i
$576$		0			0
$577$	10.5000	+	6.06218i	0.437121	+	0.252372i	0.702376	−	0.711807i	$-0.252123\pi$
$577$	10.5000	+	6.06218i	0.437121	+	0.252372i	−0.265255	+	0.964178i	$0.585456\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	9.00000	−	46.7654i	0.373383	−	1.94015i
$582$		0			0
$583$	36.0000	−	20.7846i	1.49097	−	0.860811i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	−25.0000			−1.03011
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.00000	+	1.73205i	−0.123195	+	0.0711268i	−0.560331	−	0.828269i	$-0.689326\pi$
$593$	−3.00000	+	1.73205i	−0.123195	+	0.0711268i	0.437136	+	0.899395i	$0.355993\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	42.0000	+	24.2487i	1.71607	+	0.990775i	0.925794	+	0.378030i	$0.123398\pi$
$599$	42.0000	+	24.2487i	1.71607	+	0.990775i	0.790280	+	0.612746i	$0.209935\pi$
$600$		0			0
$601$		−	39.8372i		−	1.62499i	−0.582967	−	0.812496i	$-0.698108\pi$
$601$		−	39.8372i		−	1.62499i	0.582967	−	0.812496i	$-0.301892\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.00000	−	1.73205i	−0.121967	−	0.0704179i
$606$		0			0
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	0.703429	−	0.710766i	$-0.251651\pi$
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	−0.967256	+	0.253804i	$0.918318\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.00000	−	5.19615i	0.364101	−	0.210214i
$612$		0			0
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$		0			0
$619$	0.500000	−	0.866025i	0.0200967	−	0.0348085i	−0.855802	−	0.517303i	$-0.826936\pi$
$619$	0.500000	−	0.866025i	0.0200967	−	0.0348085i	0.875899	+	0.482495i	$0.160269\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6.00000	+	17.3205i	0.240385	+	0.693932i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$			3.46410i			0.137904i	0.997620	+	0.0689519i	$0.0219655\pi$
$631$			3.46410i			0.137904i	−0.997620	+	0.0689519i	$0.978035\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−21.0000	−	36.3731i	−0.833360	−	1.44342i
$636$		0			0
$637$	−4.50000	+	11.2583i	−0.178296	+	0.446071i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	12.0000	−	20.7846i	0.473972	−	0.820943i	−0.525584	−	0.850741i	$-0.676153\pi$
$641$	12.0000	−	20.7846i	0.473972	−	0.820943i	0.999556	+	0.0297987i	$0.00948663\pi$
$642$		0			0
$643$	31.0000			1.22252			0.611260	−	0.791430i	$-0.290663\pi$
$643$	31.0000			1.22252			0.611260	+	0.791430i	$0.290663\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	15.0000	−	25.9808i	0.589711	−	1.02141i	−0.404559	−	0.914512i	$-0.632575\pi$
$647$	15.0000	−	25.9808i	0.589711	−	1.02141i	0.994270	−	0.106897i	$-0.0340916\pi$
$648$		0			0
$649$	−36.0000	+	20.7846i	−1.41312	+	0.815867i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$	18.0000	+	10.3923i	0.703318	+	0.406061i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	13.8564i		−	0.539769i	−0.962893	−	0.269884i	$-0.913014\pi$
$659$		−	13.8564i		−	0.539769i	0.962893	−	0.269884i	$-0.0869855\pi$
$660$		0			0
$661$	22.5000	+	12.9904i	0.875149	+	0.505267i	0.869056	−	0.494714i	$-0.164727\pi$
$661$	22.5000	+	12.9904i	0.875149	+	0.505267i	0.00609283	+	0.999981i	$0.498061\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−30.0000	+	34.6410i	−1.16335	+	1.34332i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−48.0000			−1.85302
$672$		0			0
$673$	1.00000			0.0385472			0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000			0.0385472			0.0192736	+	0.999814i	$0.493865\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.00000	−	3.46410i	0.230599	−	0.133136i	−0.380250	−	0.924884i	$-0.624162\pi$
$677$	6.00000	−	3.46410i	0.230599	−	0.133136i	0.610848	+	0.791748i	$0.290829\pi$
$678$		0			0
$679$	18.0000	+	3.46410i	0.690777	+	0.132940i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−6.00000	−	3.46410i	−0.229584	−	0.132550i	0.380796	−	0.924659i	$-0.375650\pi$
$683$	−6.00000	−	3.46410i	−0.229584	−	0.132550i	−0.610380	+	0.792109i	$0.708983\pi$
$684$		0			0
$685$			41.5692i			1.58828i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−18.0000	−	10.3923i	−0.685745	−	0.395915i
$690$		0			0
$691$	−11.5000	−	19.9186i	−0.437481	−	0.757739i	0.560014	−	0.828483i	$-0.310796\pi$
$691$	−11.5000	−	19.9186i	−0.437481	−	0.757739i	−0.997494	+	0.0707446i	$0.977462\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.0000	−	12.1244i	0.796575	−	0.459903i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$		0			0
$703$	−27.5000	+	47.6314i	−1.03718	+	1.79645i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−18.0000	+	20.7846i	−0.676960	+	0.781686i
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	34.6410i		−	1.29732i
$714$		0			0
$715$			20.7846i			0.777300i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	0.997546	+	0.0700124i	$0.0223039\pi$
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	−0.438141	+	0.898906i	$0.644363\pi$
$720$		0			0
$721$	−12.5000	+	4.33013i	−0.465524	+	0.161262i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	23.0000			0.853023			0.426511	−	0.904482i	$-0.359742\pi$
$727$	23.0000			0.853023			0.426511	+	0.904482i	$0.359742\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−25.5000	+	14.7224i	−0.941864	+	0.543785i	−0.890544	−	0.454897i	$-0.849676\pi$
$733$	−25.5000	+	14.7224i	−0.941864	+	0.543785i	−0.0513199	+	0.998682i	$0.516343\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	15.0000	+	25.9808i	0.552532	+	0.957014i
$738$		0			0
$739$	−46.5000	−	26.8468i	−1.71053	−	0.987575i	−0.933839	−	0.357693i	$-0.883563\pi$
$739$	−46.5000	−	26.8468i	−1.71053	−	0.987575i	−0.776691	−	0.629882i	$-0.783103\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	3.46410i		−	0.127086i	−0.997979	−	0.0635428i	$-0.979760\pi$
$743$		−	3.46410i		−	0.127086i	0.997979	−	0.0635428i	$-0.0202399\pi$
$744$		0			0
$745$	−36.0000	−	20.7846i	−1.31894	−	0.761489i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−4.50000	+	2.59808i	−0.164207	+	0.0948051i	−0.579852	−	0.814722i	$-0.696889\pi$
$751$	−4.50000	+	2.59808i	−0.164207	+	0.0948051i	0.415644	+	0.909527i	$0.363556\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.0000			−0.436725
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	36.0000	−	20.7846i	1.30500	−	0.753442i	0.323742	−	0.946145i	$-0.395059\pi$
$761$	36.0000	−	20.7846i	1.30500	−	0.753442i	0.981257	+	0.192704i	$0.0617257\pi$
$762$		0			0
$763$	−14.0000	−	12.1244i	−0.506834	−	0.438931i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	18.0000	+	10.3923i	0.649942	+	0.375244i
$768$		0			0
$769$		−	15.5885i		−	0.562134i	−0.959688	−	0.281067i	$-0.909312\pi$
$769$		−	15.5885i		−	0.562134i	0.959688	−	0.281067i	$-0.0906883\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	39.0000	+	22.5167i	1.40273	+	0.809868i	0.994672	−	0.103087i	$-0.0328720\pi$
$773$	39.0000	+	22.5167i	1.40273	+	0.809868i	0.408060	+	0.912955i	$0.366205\pi$
$774$		0			0
$775$	17.5000	+	30.3109i	0.628619	+	1.08880i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−15.0000	+	8.66025i	−0.537431	+	0.310286i
$780$		0			0
$781$	6.00000	−	10.3923i	0.214697	−	0.371866i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	8.00000	−	13.8564i	0.285169	−	0.493928i	−0.687481	−	0.726202i	$-0.741284\pi$
$787$	8.00000	−	13.8564i	0.285169	−	0.493928i	0.972650	+	0.232275i	$0.0746169\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.00000	−	15.5885i	0.106668	−	0.554262i
$792$		0			0
$793$	12.0000	+	20.7846i	0.426132	+	0.738083i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	34.6410i		−	1.22705i	−0.789676	−	0.613524i	$-0.789751\pi$
$797$		−	34.6410i		−	1.22705i	0.789676	−	0.613524i	$-0.210249\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−9.00000	−	15.5885i	−0.317603	−	0.550105i
$804$		0			0
$805$	−48.0000	−	41.5692i	−1.69178	−	1.46512i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.00000	−	15.5885i	0.316423	−	0.548061i	−0.663316	−	0.748340i	$-0.730851\pi$
$809$	9.00000	−	15.5885i	0.316423	−	0.548061i	0.979739	+	0.200279i	$0.0641847\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.00000	−	10.3923i	0.210171	−	0.364027i
$816$		0			0
$817$	−37.5000	+	21.6506i	−1.31196	+	0.757460i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	−3.00000	−	1.73205i	−0.104573	−	0.0603755i	0.446801	−	0.894633i	$-0.352563\pi$
$823$	−3.00000	−	1.73205i	−0.104573	−	0.0603755i	−0.551375	+	0.834258i	$0.685896\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	38.1051i		−	1.32504i	−0.749042	−	0.662522i	$-0.769486\pi$
$827$		−	38.1051i		−	1.32504i	0.749042	−	0.662522i	$-0.230514\pi$
$828$		0			0
$829$	22.5000	+	12.9904i	0.781457	+	0.451175i	0.836947	−	0.547285i	$-0.184339\pi$
$829$	22.5000	+	12.9904i	0.781457	+	0.451175i	−0.0554892	+	0.998459i	$0.517672\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−18.0000	+	10.3923i	−0.622916	+	0.359641i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	48.0000			1.65714			0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000			1.65714			0.828572	+	0.559883i	$0.189154\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−30.0000	+	17.3205i	−1.03203	+	0.595844i
$846$		0			0
$847$	2.50000	−	0.866025i	0.0859010	−	0.0297570i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−66.0000	−	38.1051i	−2.26245	−	1.30623i
$852$		0			0
$853$		−	5.19615i		−	0.177913i	−0.996036	−	0.0889564i	$-0.971647\pi$
$853$		−	5.19615i		−	0.177913i	0.996036	−	0.0889564i	$-0.0283532\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.0000	−	6.92820i	−0.409912	−	0.236663i	0.280840	−	0.959755i	$-0.409387\pi$
$857$	−12.0000	−	6.92820i	−0.409912	−	0.236663i	−0.690752	+	0.723092i	$0.742720\pi$
$858$		0			0
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	0.998549	+	0.0538535i	$0.0171504\pi$
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	−0.452636	+	0.891695i	$0.649516\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.00000	+	5.19615i	−0.306364	+	0.176879i	−0.645298	−	0.763931i	$-0.723267\pi$
$863$	−9.00000	+	5.19615i	−0.306364	+	0.176879i	0.338935	+	0.940810i	$0.389933\pi$
$864$		0			0
$865$	12.0000	−	20.7846i	0.408012	−	0.706698i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	42.0000			1.42475
$870$		0			0
$871$	7.50000	−	12.9904i	0.254128	−	0.440162i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	18.0000	+	3.46410i	0.608511	+	0.117108i
$876$		0			0
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	6.92820i		−	0.233417i	−0.993166	−	0.116709i	$-0.962766\pi$
$881$		−	6.92820i		−	0.233417i	0.993166	−	0.116709i	$-0.0372343\pi$
$882$		0			0
$883$		−	46.7654i		−	1.57378i	−0.617093	−	0.786890i	$-0.711690\pi$
$883$		−	46.7654i		−	1.57378i	0.617093	−	0.786890i	$-0.288310\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	0.976632	−	0.214919i	$-0.0689488\pi$
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	−0.674441	+	0.738328i	$0.735615\pi$
$888$		0			0
$889$	31.5000	+	6.06218i	1.05648	+	0.203319i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−15.0000	+	25.9808i	−0.501956	+	0.869413i
$894$		0			0
$895$	−36.0000			−1.20335
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	9.00000	+	15.5885i	0.299170	+	0.518178i
$906$		0			0
$907$	28.5000	+	16.4545i	0.946327	+	0.546362i	0.891938	−	0.452158i	$-0.149346\pi$
$907$	28.5000	+	16.4545i	0.946327	+	0.546362i	0.0543890	+	0.998520i	$0.482679\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	41.5692i		−	1.37725i	−0.725118	−	0.688625i	$-0.758215\pi$
$911$		−	41.5692i		−	1.37725i	0.725118	−	0.688625i	$-0.241785\pi$
$912$		0			0
$913$	54.0000	+	31.1769i	1.78714	+	1.03181i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.0000	+	5.19615i	−0.495344	+	0.171592i
$918$		0			0
$919$	37.5000	−	21.6506i	1.23701	−	0.714189i	0.268529	−	0.963272i	$-0.413463\pi$
$919$	37.5000	−	21.6506i	1.23701	−	0.714189i	0.968482	+	0.249083i	$0.0801292\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.00000			−0.197492
$924$		0			0
$925$	77.0000			2.53174
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.00000	+	5.19615i	−0.295280	+	0.170480i	−0.640321	−	0.768108i	$-0.721199\pi$
$929$	−9.00000	+	5.19615i	−0.295280	+	0.170480i	0.345040	+	0.938588i	$0.387865\pi$
$930$		0			0
$931$	−5.00000	−	34.6410i	−0.163868	−	1.13531i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	53.6936i		−	1.75409i	−0.480406	−	0.877046i	$-0.659511\pi$
$937$		−	53.6936i		−	1.75409i	0.480406	−	0.877046i	$-0.340489\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	12.0000	+	6.92820i	0.391189	+	0.225853i	0.682675	−	0.730722i	$-0.260816\pi$
$941$	12.0000	+	6.92820i	0.391189	+	0.225853i	−0.291486	+	0.956575i	$0.594150\pi$
$942$		0			0
$943$	−12.0000	−	20.7846i	−0.390774	−	0.676840i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	39.0000	−	22.5167i	1.26733	−	0.731693i	0.292848	−	0.956159i	$-0.405397\pi$
$947$	39.0000	−	22.5167i	1.26733	−	0.731693i	0.974482	+	0.224466i	$0.0720637\pi$
$948$		0			0
$949$	−4.50000	+	7.79423i	−0.146076	+	0.253011i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−24.0000			−0.777436			−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000			−0.777436			−0.388718	+	0.921357i	$0.627082\pi$
$954$		0			0
$955$	30.0000	−	51.9615i	0.970777	−	1.68144i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−24.0000	−	20.7846i	−0.775000	−	0.671170i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			38.1051i			1.22665i
$966$		0			0
$967$		−	8.66025i		−	0.278495i	−0.990258	−	0.139247i	$-0.955532\pi$
$967$		−	8.66025i		−	0.278495i	0.990258	−	0.139247i	$-0.0444684\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$		0			0
$973$	−3.50000	+	18.1865i	−0.112205	+	0.583033i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	0.305530	+	0.952183i	$0.401167\pi$
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	−0.977379	+	0.211495i	$0.932167\pi$
$978$		0			0
$979$	−24.0000			−0.767043
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.00000	−	10.3923i	0.191370	−	0.331463i	−0.754334	−	0.656490i	$-0.772040\pi$
$983$	6.00000	−	10.3923i	0.191370	−	0.331463i	0.945705	+	0.325027i	$0.105374\pi$
$984$		0			0
$985$	72.0000	−	41.5692i	2.29411	−	1.32451i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−30.0000	−	51.9615i	−0.953945	−	1.65228i
$990$		0			0
$991$	34.5000	+	19.9186i	1.09593	+	0.632735i	0.935149	−	0.354256i	$-0.115266\pi$
$991$	34.5000	+	19.9186i	1.09593	+	0.632735i	0.160780	+	0.986990i	$0.448599\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	55.4256i		−	1.75711i
$996$		0			0
$997$	−16.5000	−	9.52628i	−0.522560	−	0.301700i	0.215421	−	0.976521i	$-0.430888\pi$
$997$	−16.5000	−	9.52628i	−0.522560	−	0.301700i	−0.737982	+	0.674821i	$0.764221\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cs.b.703.1		2
3.2	odd	2		336.2.bl.d.31.1	✓	2
4.3	odd	2		1008.2.cs.a.703.1		2
7.3	odd	6		7056.2.b.k.1567.2		2
7.4	even	3		7056.2.b.d.1567.1		2
7.5	odd	6		1008.2.cs.a.271.1		2
12.11	even	2		336.2.bl.h.31.1	yes	2
21.2	odd	6		2352.2.bl.a.607.1		2
21.5	even	6		336.2.bl.h.271.1	yes	2
21.11	odd	6		2352.2.b.e.1567.2		2
21.17	even	6		2352.2.b.d.1567.1		2
21.20	even	2		2352.2.bl.g.31.1		2
24.5	odd	2		1344.2.bl.e.703.1		2
24.11	even	2		1344.2.bl.a.703.1		2
28.3	even	6		7056.2.b.d.1567.2		2
28.11	odd	6		7056.2.b.k.1567.1		2
28.19	even	6	inner	1008.2.cs.b.271.1		2
84.11	even	6		2352.2.b.d.1567.2		2
84.23	even	6		2352.2.bl.g.607.1		2
84.47	odd	6		336.2.bl.d.271.1	yes	2
84.59	odd	6		2352.2.b.e.1567.1		2
84.83	odd	2		2352.2.bl.a.31.1		2
168.5	even	6		1344.2.bl.a.1279.1		2
168.131	odd	6		1344.2.bl.e.1279.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bl.d.31.1	✓	2	3.2	odd	2
336.2.bl.d.271.1	yes	2	84.47	odd	6
336.2.bl.h.31.1	yes	2	12.11	even	2
336.2.bl.h.271.1	yes	2	21.5	even	6
1008.2.cs.a.271.1		2	7.5	odd	6
1008.2.cs.a.703.1		2	4.3	odd	2
1008.2.cs.b.271.1		2	28.19	even	6	inner
1008.2.cs.b.703.1		2	1.1	even	1	trivial
1344.2.bl.a.703.1		2	24.11	even	2
1344.2.bl.a.1279.1		2	168.5	even	6
1344.2.bl.e.703.1		2	24.5	odd	2
1344.2.bl.e.1279.1		2	168.131	odd	6
2352.2.b.d.1567.1		2	21.17	even	6
2352.2.b.d.1567.2		2	84.11	even	6
2352.2.b.e.1567.1		2	84.59	odd	6
2352.2.b.e.1567.2		2	21.11	odd	6
2352.2.bl.a.31.1		2	84.83	odd	2
2352.2.bl.a.607.1		2	21.2	odd	6
2352.2.bl.g.31.1		2	21.20	even	2
2352.2.bl.g.607.1		2	84.23	even	6
7056.2.b.d.1567.1		2	7.4	even	3
7056.2.b.d.1567.2		2	28.3	even	6
7056.2.b.k.1567.1		2	28.11	odd	6
7056.2.b.k.1567.2		2	7.3	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +O(q^{10})\)	\(q+(-3.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(3.00000 + 1.73205i) q^{11} -1.73205i q^{13} +(2.50000 + 4.33013i) q^{19} +(-6.00000 + 3.46410i) q^{23} +(3.50000 - 6.06218i) q^{25} +(-2.50000 + 4.33013i) q^{31} +(3.00000 + 8.66025i) q^{35} +(5.50000 + 9.52628i) q^{37} +3.46410i q^{41} +8.66025i q^{43} +(3.00000 + 5.19615i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(6.00000 - 10.3923i) q^{53} -12.0000 q^{55} +(-6.00000 + 10.3923i) q^{59} +(-12.0000 + 6.92820i) q^{61} +(3.00000 + 5.19615i) q^{65} +(7.50000 + 4.33013i) q^{67} -3.46410i q^{71} +(-4.50000 - 2.59808i) q^{73} +(6.00000 - 6.92820i) q^{77} +(10.5000 - 6.06218i) q^{79} +18.0000 q^{83} +(-6.00000 + 3.46410i) q^{89} +(-4.50000 - 0.866025i) q^{91} +(-15.0000 - 8.66025i) q^{95} +6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{5} + q^{7}+O(q^{10}) \) 2 * q - 6 * q^5 + q^7	\( 2 q - 6 q^{5} + q^{7} + 6 q^{11} + 5 q^{19} - 12 q^{23} + 7 q^{25} - 5 q^{31} + 6 q^{35} + 11 q^{37} + 6 q^{47} - 13 q^{49} + 12 q^{53} - 24 q^{55} - 12 q^{59} - 24 q^{61} + 6 q^{65} + 15 q^{67} - 9 q^{73} + 12 q^{77} + 21 q^{79} + 36 q^{83} - 12 q^{89} - 9 q^{91} - 30 q^{95}+O(q^{100}) \) 2 * q - 6 * q^5 + q^7 + 6 * q^11 + 5 * q^19 - 12 * q^23 + 7 * q^25 - 5 * q^31 + 6 * q^35 + 11 * q^37 + 6 * q^47 - 13 * q^49 + 12 * q^53 - 24 * q^55 - 12 * q^59 - 24 * q^61 + 6 * q^65 + 15 * q^67 - 9 * q^73 + 12 * q^77 + 21 * q^79 + 36 * q^83 - 12 * q^89 - 9 * q^91 - 30 * q^95

Introduction

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