LMFDB - Embedded newform 2268.2.x.a.377.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(377,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2268.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.x (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.1100711784$
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 756)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			377.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2268.377
Dual form			2268.2.x.a.1889.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{5} +(-2.50000 - 0.866025i) q^{7} +O(q^{10})$	$q+(-1.50000 + 2.59808i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-4.50000 + 2.59808i) q^{11} +(3.00000 + 1.73205i) q^{13} -6.00000 q^{17} -1.73205i q^{19} +(-4.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(9.00000 - 5.19615i) q^{29} +(4.50000 + 2.59808i) q^{31} +(6.00000 - 5.19615i) q^{35} +1.00000 q^{37} +(1.50000 - 2.59808i) q^{41} +(-5.00000 - 8.66025i) q^{43} +(3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} -15.5885i q^{55} +(-3.00000 + 5.19615i) q^{59} +(12.0000 - 6.92820i) q^{61} +(-9.00000 + 5.19615i) q^{65} +(-1.00000 + 1.73205i) q^{67} +5.19615i q^{71} +3.46410i q^{73} +(13.5000 - 2.59808i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(-3.00000 - 5.19615i) q^{83} +(9.00000 - 15.5885i) q^{85} +9.00000 q^{89} +(-6.00000 - 6.92820i) q^{91} +(4.50000 + 2.59808i) q^{95} +(6.00000 - 3.46410i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{5} - 5 q^{7}+O(q^{10}) $ 2 * q - 3 * q^5 - 5 * q^7	$ 2 q - 3 q^{5} - 5 q^{7} - 9 q^{11} + 6 q^{13} - 12 q^{17} - 9 q^{23} - 4 q^{25} + 18 q^{29} + 9 q^{31} + 12 q^{35} + 2 q^{37} + 3 q^{41} - 10 q^{43} + 6 q^{47} + 11 q^{49} - 6 q^{59} + 24 q^{61} - 18 q^{65} - 2 q^{67} + 27 q^{77} - 14 q^{79} - 6 q^{83} + 18 q^{85} + 18 q^{89} - 12 q^{91} + 9 q^{95} + 12 q^{97}+O(q^{100}) $ 2 * q - 3 * q^5 - 5 * q^7 - 9 * q^11 + 6 * q^13 - 12 * q^17 - 9 * q^23 - 4 * q^25 + 18 * q^29 + 9 * q^31 + 12 * q^35 + 2 * q^37 + 3 * q^41 - 10 * q^43 + 6 * q^47 + 11 * q^49 - 6 * q^59 + 24 * q^61 - 18 * q^65 - 2 * q^67 + 27 * q^77 - 14 * q^79 - 6 * q^83 + 18 * q^85 + 18 * q^89 - 12 * q^91 + 9 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.50000	+	2.59808i	−1.35680	+	0.783349i	−0.989191	−	0.146631i	$-0.953157\pi$
$11$	−4.50000	+	2.59808i	−1.35680	+	0.783349i	−0.367610	+	0.929980i	$0.619824\pi$
$12$		0			0
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	0.854554	−	0.519362i	$-0.173830\pi$
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	−0.0225039	+	0.999747i	$0.507164\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$		−	1.73205i		−	0.397360i	−0.980064	−	0.198680i	$-0.936335\pi$
$19$		−	1.73205i		−	0.397360i	0.980064	−	0.198680i	$-0.0636654\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.50000	−	2.59808i	−0.938315	−	0.541736i	−0.0488832	−	0.998805i	$-0.515566\pi$
$23$	−4.50000	−	2.59808i	−0.938315	−	0.541736i	−0.889432	+	0.457068i	$0.848900\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	9.00000	−	5.19615i	1.67126	−	0.964901i	0.704323	−	0.709880i	$-0.251251\pi$
$29$	9.00000	−	5.19615i	1.67126	−	0.964901i	0.966935	−	0.255021i	$-0.0820825\pi$
$30$		0			0
$31$	4.50000	+	2.59808i	0.808224	+	0.466628i	0.846339	−	0.532645i	$-0.178802\pi$
$31$	4.50000	+	2.59808i	0.808224	+	0.466628i	−0.0381148	+	0.999273i	$0.512135\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.00000	−	5.19615i	1.01419	−	0.878310i
$36$		0			0
$37$	1.00000			0.164399			0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000			0.164399			0.0821995	+	0.996616i	$0.473806\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	−0.941562	−	0.336840i	$-0.890642\pi$
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	0.179069	−	0.983836i	$-0.442691\pi$
$44$		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
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$		−	15.5885i		−	2.10195i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.537400	−	0.843328i	$-0.319407\pi$
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.999043	−	0.0437377i	$-0.0139266\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.00000	+	5.19615i	−1.11631	+	0.644503i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			5.19615i			0.616670i	0.951278	+	0.308335i	$0.0997717\pi$
$71$			5.19615i			0.616670i	−0.951278	+	0.308335i	$0.900228\pi$
$72$		0			0
$73$			3.46410i			0.405442i	0.979236	+	0.202721i	$0.0649785\pi$
$73$			3.46410i			0.405442i	−0.979236	+	0.202721i	$0.935021\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	13.5000	−	2.59808i	1.53847	−	0.296078i
$78$		0			0
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	0.653079	−	0.757290i	$-0.273477\pi$
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	−0.982372	+	0.186938i	$0.940144\pi$
$84$		0			0
$85$	9.00000	−	15.5885i	0.976187	−	1.69081i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$		0			0
$91$	−6.00000	−	6.92820i	−0.628971	−	0.726273i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.50000	+	2.59808i	0.461690	+	0.266557i
$96$		0			0
$97$	6.00000	−	3.46410i	0.609208	−	0.351726i	−0.163448	−	0.986552i	$-0.552261\pi$
$97$	6.00000	−	3.46410i	0.609208	−	0.351726i	0.772655	+	0.634826i	$0.218928\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$		0			0
$103$	−7.50000	−	4.33013i	−0.738997	−	0.426660i	0.0827075	−	0.996574i	$-0.473643\pi$
$103$	−7.50000	−	4.33013i	−0.738997	−	0.426660i	−0.821705	+	0.569914i	$0.806977\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			10.3923i			1.00466i	0.864675	+	0.502331i	$0.167524\pi$
$107$			10.3923i			1.00466i	−0.864675	+	0.502331i	$0.832476\pi$
$108$		0			0
$109$	−11.0000			−1.05361			−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000			−1.05361			−0.526804	+	0.849987i	$0.676610\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$		0			0
$115$	13.5000	−	7.79423i	1.25888	−	0.726816i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	15.0000	+	5.19615i	1.37505	+	0.476331i
$120$		0			0
$121$	8.00000	−	13.8564i	0.727273	−	1.25967i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$		0			0
$133$	−1.50000	+	4.33013i	−0.130066	+	0.375470i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.00000	−	5.19615i	0.768922	−	0.443937i	−0.0635680	−	0.997978i	$-0.520248\pi$
$137$	9.00000	−	5.19615i	0.768922	−	0.443937i	0.832490	+	0.554040i	$0.186915\pi$
$138$		0			0
$139$	15.0000	+	8.66025i	1.27228	+	0.734553i	0.975417	−	0.220366i	$-0.0707252\pi$
$139$	15.0000	+	8.66025i	1.27228	+	0.734553i	0.296866	+	0.954919i	$0.404058\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−18.0000			−1.50524
$144$		0			0
$145$			31.1769i			2.58910i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$149$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$150$		0			0
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	0.773099	−	0.634285i	$-0.218706\pi$
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−13.5000	+	7.79423i	−1.08435	+	0.626048i
$156$		0			0
$157$	−9.00000	−	5.19615i	−0.718278	−	0.414698i	0.0958404	−	0.995397i	$-0.469446\pi$
$157$	−9.00000	−	5.19615i	−0.718278	−	0.414698i	−0.814119	+	0.580699i	$0.802779\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	9.00000	+	10.3923i	0.709299	+	0.819028i
$162$		0			0
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$		0			0
$175$	2.00000	+	10.3923i	0.151186	+	0.785584i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	10.3923i		−	0.776757i	−0.921500	−	0.388379i	$-0.873035\pi$
$179$		−	10.3923i		−	0.776757i	0.921500	−	0.388379i	$-0.126965\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.50000	+	2.59808i	−0.110282	+	0.191014i
$186$		0			0
$187$	27.0000	−	15.5885i	1.97444	−	1.13994i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.50000	−	2.59808i	0.325609	−	0.187990i	−0.328281	−	0.944580i	$-0.606469\pi$
$191$	4.50000	−	2.59808i	0.325609	−	0.187990i	0.653890	+	0.756590i	$0.273136\pi$
$192$		0			0
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	20.7846i		−	1.48084i	−0.672143	−	0.740421i	$-0.734626\pi$
$197$		−	20.7846i		−	1.48084i	0.672143	−	0.740421i	$-0.265374\pi$
$198$		0			0
$199$			1.73205i			0.122782i	0.998114	+	0.0613909i	$0.0195536\pi$
$199$			1.73205i			0.122782i	−0.998114	+	0.0613909i	$0.980446\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−27.0000	+	5.19615i	−1.89503	+	0.364698i
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.50000	+	7.79423i	0.311272	+	0.539138i
$210$		0			0
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	−0.283918	−	0.958849i	$-0.591634\pi$
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	0.972346	−	0.233544i	$-0.0750324\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	30.0000			2.04598
$216$		0			0
$217$	−9.00000	−	10.3923i	−0.610960	−	0.705476i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−18.0000	−	10.3923i	−1.21081	−	0.699062i
$222$		0			0
$223$	−22.5000	+	12.9904i	−1.50671	+	0.869900i	−0.506742	+	0.862098i	$0.669150\pi$
$223$	−22.5000	+	12.9904i	−1.50671	+	0.869900i	−0.999970	+	0.00780243i	$0.997516\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$		0			0
$229$	−18.0000	−	10.3923i	−1.18947	−	0.686743i	−0.231287	−	0.972886i	$-0.574293\pi$
$229$	−18.0000	−	10.3923i	−1.18947	−	0.686743i	−0.958187	+	0.286143i	$0.907627\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	20.7846i		−	1.36165i	−0.732448	−	0.680823i	$-0.761622\pi$
$233$		−	20.7846i		−	1.36165i	0.732448	−	0.680823i	$-0.238378\pi$
$234$		0			0
$235$	−18.0000			−1.17419
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.00000	+	5.19615i	0.582162	+	0.336111i	0.761992	−	0.647586i	$-0.224222\pi$
$239$	9.00000	+	5.19615i	0.582162	+	0.336111i	−0.179830	+	0.983698i	$0.557555\pi$
$240$		0			0
$241$	3.00000	−	1.73205i	0.193247	−	0.111571i	−0.400255	−	0.916404i	$-0.631078\pi$
$241$	3.00000	−	1.73205i	0.193247	−	0.111571i	0.593502	+	0.804833i	$0.297745\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−19.5000	+	7.79423i	−1.24581	+	0.497955i
$246$		0			0
$247$	3.00000	−	5.19615i	0.190885	−	0.330623i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$		0			0
$253$	27.0000			1.69748
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.50000	+	7.79423i	−0.280702	+	0.486191i	−0.971558	−	0.236802i	$-0.923901\pi$
$257$	−4.50000	+	7.79423i	−0.280702	+	0.486191i	0.690856	+	0.722993i	$0.257234\pi$
$258$		0			0
$259$	−2.50000	−	0.866025i	−0.155342	−	0.0538122i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.50000	−	2.59808i	0.277482	−	0.160204i	−0.354801	−	0.934942i	$-0.615451\pi$
$263$	4.50000	−	2.59808i	0.277482	−	0.160204i	0.632283	+	0.774738i	$0.282118\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−21.0000			−1.28039			−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000			−1.28039			−0.640196	+	0.768211i	$0.721147\pi$
$270$		0			0
$271$		−	3.46410i		−	0.210429i	−0.994450	−	0.105215i	$-0.966447\pi$
$271$		−	3.46410i		−	0.210429i	0.994450	−	0.105215i	$-0.0335529\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	18.0000	+	10.3923i	1.08544	+	0.626680i
$276$		0			0
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.00000	+	5.19615i	−0.536895	+	0.309976i	−0.743820	−	0.668380i	$-0.766988\pi$
$281$	−9.00000	+	5.19615i	−0.536895	+	0.309976i	0.206925	+	0.978357i	$0.433655\pi$
$282$		0			0
$283$	−9.00000	−	5.19615i	−0.534994	−	0.308879i	0.208053	−	0.978117i	$-0.433287\pi$
$283$	−9.00000	−	5.19615i	−0.534994	−	0.308879i	−0.743048	+	0.669238i	$0.766621\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.00000	+	5.19615i	−0.354169	+	0.306719i
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$		0			0
$295$	−9.00000	−	15.5885i	−0.524000	−	0.907595i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−9.00000	−	15.5885i	−0.520483	−	0.901504i
$300$		0			0
$301$	5.00000	+	25.9808i	0.288195	+	1.49751i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			41.5692i			2.38025i
$306$		0			0
$307$		−	15.5885i		−	0.889680i	−0.895610	−	0.444840i	$-0.853260\pi$
$307$		−	15.5885i		−	0.889680i	0.895610	−	0.444840i	$-0.146740\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	−3.00000	+	1.73205i	−0.169570	+	0.0979013i	−0.582383	−	0.812914i	$-0.697880\pi$
$313$	−3.00000	+	1.73205i	−0.169570	+	0.0979013i	0.412813	+	0.910816i	$0.364546\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	27.0000	−	15.5885i	1.51647	−	0.875535i	0.516658	−	0.856192i	$-0.327176\pi$
$317$	27.0000	−	15.5885i	1.51647	−	0.875535i	0.999813	−	0.0193432i	$-0.00615753\pi$
$318$		0			0
$319$	−27.0000	+	46.7654i	−1.51171	+	2.61836i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			10.3923i			0.578243i
$324$		0			0
$325$		−	13.8564i		−	0.768615i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.00000	−	15.5885i	−0.165395	−	0.859419i
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.00000	−	5.19615i	−0.163908	−	0.283896i
$336$		0			0
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	0.926049	−	0.377403i	$-0.123183\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−27.0000			−1.46213
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.50000	+	2.59808i	0.241573	+	0.139472i	0.615899	−	0.787825i	$-0.288793\pi$
$347$	4.50000	+	2.59808i	0.241573	+	0.139472i	−0.374327	+	0.927297i	$0.622126\pi$
$348$		0			0
$349$	−24.0000	+	13.8564i	−1.28469	+	0.741716i	−0.977702	−	0.209997i	$-0.932655\pi$
$349$	−24.0000	+	13.8564i	−1.28469	+	0.741716i	−0.306988	+	0.951713i	$0.599321\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	0.993626	−	0.112731i	$-0.0359599\pi$
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	−0.594441	+	0.804139i	$0.702627\pi$
$354$		0			0
$355$	−13.5000	−	7.79423i	−0.716506	−	0.413675i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	10.3923i		−	0.548485i	−0.961661	−	0.274242i	$-0.911573\pi$
$359$		−	10.3923i		−	0.548485i	0.961661	−	0.274242i	$-0.0884271\pi$
$360$		0			0
$361$	16.0000			0.842105
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−9.00000	−	5.19615i	−0.471082	−	0.271979i
$366$		0			0
$367$	1.50000	−	0.866025i	0.0782994	−	0.0452062i	−0.460339	−	0.887743i	$-0.652272\pi$
$367$	1.50000	−	0.866025i	0.0782994	−	0.0452062i	0.538639	+	0.842537i	$0.318939\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	0.196663	+	0.980471i	$0.436990\pi$
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	−0.947444	+	0.319921i	$0.896344\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	36.0000			1.85409
$378$		0			0
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	−0.671027	−	0.741433i	$-0.734147\pi$
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	0.977613	+	0.210411i	$0.0674801\pi$
$384$		0			0
$385$	−13.5000	+	38.9711i	−0.688024	+	1.98615i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−18.0000	+	10.3923i	−0.912636	+	0.526911i	−0.881278	−	0.472597i	$-0.843316\pi$
$389$	−18.0000	+	10.3923i	−0.912636	+	0.526911i	−0.0313578	+	0.999508i	$0.509983\pi$
$390$		0			0
$391$	27.0000	+	15.5885i	1.36545	+	0.788342i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	42.0000			2.11325
$396$		0			0
$397$			20.7846i			1.04315i	0.853206	+	0.521575i	$0.174655\pi$
$397$			20.7846i			1.04315i	−0.853206	+	0.521575i	$0.825345\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.00000	+	5.19615i	0.449439	+	0.259483i	0.707593	−	0.706620i	$-0.249781\pi$
$401$	9.00000	+	5.19615i	0.449439	+	0.259483i	−0.258154	+	0.966104i	$0.583114\pi$
$402$		0			0
$403$	9.00000	+	15.5885i	0.448322	+	0.776516i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.50000	+	2.59808i	−0.223057	+	0.128782i
$408$		0			0
$409$	15.0000	+	8.66025i	0.741702	+	0.428222i	0.822688	−	0.568493i	$-0.192473\pi$
$409$	15.0000	+	8.66025i	0.741702	+	0.428222i	−0.0809857	+	0.996715i	$0.525807\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	12.0000	−	10.3923i	0.590481	−	0.511372i
$414$		0			0
$415$	18.0000			0.883585
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	−0.408481	−	0.912767i	$-0.633942\pi$
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	0.994720	−	0.102628i	$-0.0327251\pi$
$420$		0			0
$421$	−2.50000	−	4.33013i	−0.121843	−	0.211037i	0.798652	−	0.601793i	$-0.205547\pi$
$421$	−2.50000	−	4.33013i	−0.121843	−	0.211037i	−0.920494	+	0.390756i	$0.872214\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.0000	+	20.7846i	0.582086	+	1.00820i
$426$		0			0
$427$	−36.0000	+	6.92820i	−1.74216	+	0.335279i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	36.3731i		−	1.75203i	−0.482285	−	0.876014i	$-0.660193\pi$
$431$		−	36.3731i		−	1.75203i	0.482285	−	0.876014i	$-0.339807\pi$
$432$		0			0
$433$			10.3923i			0.499422i	0.968320	+	0.249711i	$0.0803357\pi$
$433$			10.3923i			0.499422i	−0.968320	+	0.249711i	$0.919664\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.50000	+	7.79423i	−0.215264	+	0.372849i
$438$		0			0
$439$	−27.0000	+	15.5885i	−1.28864	+	0.743996i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−27.0000	+	15.5885i	−1.28864	+	0.743996i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13.5000	−	7.79423i	0.641404	−	0.370315i	−0.143751	−	0.989614i	$-0.545916\pi$
$443$	13.5000	−	7.79423i	0.641404	−	0.370315i	0.785155	+	0.619299i	$0.212583\pi$
$444$		0			0
$445$	−13.5000	+	23.3827i	−0.639961	+	1.10845i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			20.7846i			0.980886i	0.871473	+	0.490443i	$0.163165\pi$
$449$			20.7846i			0.980886i	−0.871473	+	0.490443i	$0.836835\pi$
$450$		0			0
$451$			15.5885i			0.734032i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	27.0000	−	5.19615i	1.26578	−	0.243599i
$456$		0			0
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	0.993431	−	0.114433i	$-0.0365053\pi$
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	−0.595818	+	0.803120i	$0.703172\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	0.636817	−	0.771015i	$-0.280251\pi$
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	−0.986127	+	0.165992i	$0.946917\pi$
$462$		0			0
$463$	8.00000	−	13.8564i	0.371792	−	0.643962i	−0.618050	−	0.786139i	$-0.712077\pi$
$463$	8.00000	−	13.8564i	0.371792	−	0.643962i	0.989841	+	0.142177i	$0.0454103\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.0000			−0.832941			−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000			−0.832941			−0.416470	+	0.909149i	$0.636733\pi$
$468$		0			0
$469$	4.00000	−	3.46410i	0.184703	−	0.159957i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	45.0000	+	25.9808i	2.06910	+	1.19460i
$474$		0			0
$475$	−6.00000	+	3.46410i	−0.275299	+	0.158944i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$		0			0
$481$	3.00000	+	1.73205i	0.136788	+	0.0789747i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			20.7846i			0.943781i
$486$		0			0
$487$	−26.0000			−1.17817			−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000			−1.17817			−0.589086	+	0.808070i	$0.700512\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.5000	−	7.79423i	−0.609246	−	0.351749i	0.163424	−	0.986556i	$-0.447746\pi$
$491$	−13.5000	−	7.79423i	−0.609246	−	0.351749i	−0.772670	+	0.634807i	$0.781079\pi$
$492$		0			0
$493$	−54.0000	+	31.1769i	−2.43204	+	1.40414i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.50000	−	12.9904i	0.201853	−	0.582698i
$498$		0			0
$499$	7.00000	−	12.1244i	0.313363	−	0.542761i	−0.665725	−	0.746197i	$-0.731878\pi$
$499$	7.00000	−	12.1244i	0.313363	−	0.542761i	0.979088	+	0.203436i	$0.0652110\pi$
$500$		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
$505$	54.0000			2.40297
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−21.0000	+	36.3731i	−0.930809	+	1.61221i	−0.148866	+	0.988857i	$0.547562\pi$
$509$	−21.0000	+	36.3731i	−0.930809	+	1.61221i	−0.781943	+	0.623350i	$0.785771\pi$
$510$		0			0
$511$	3.00000	−	8.66025i	0.132712	−	0.383107i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	22.5000	−	12.9904i	0.991468	−	0.572425i
$516$		0			0
$517$	−27.0000	−	15.5885i	−1.18746	−	0.685580i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	33.0000			1.44576			0.722878	−	0.690976i	$-0.242819\pi$
$521$	33.0000			1.44576			0.722878	+	0.690976i	$0.242819\pi$
$522$		0			0
$523$			12.1244i			0.530161i	0.964226	+	0.265081i	$0.0853985\pi$
$523$			12.1244i			0.530161i	−0.964226	+	0.265081i	$0.914601\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−27.0000	−	15.5885i	−1.17614	−	0.679044i
$528$		0			0
$529$	2.00000	+	3.46410i	0.0869565	+	0.150613i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.00000	−	5.19615i	0.389833	−	0.225070i
$534$		0			0
$535$	−27.0000	−	15.5885i	−1.16731	−	0.673948i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−36.0000	−	5.19615i	−1.55063	−	0.223814i
$540$		0			0
$541$	17.0000			0.730887			0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000			0.730887			0.365444	+	0.930834i	$0.380917\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.5000	−	28.5788i	0.706782	−	1.22418i
$546$		0			0
$547$	20.0000	+	34.6410i	0.855138	+	1.48114i	0.876517	+	0.481371i	$0.159861\pi$
$547$	20.0000	+	34.6410i	0.855138	+	1.48114i	−0.0213785	+	0.999771i	$0.506805\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.00000	−	15.5885i	−0.383413	−	0.664091i
$552$		0			0
$553$	7.00000	+	36.3731i	0.297670	+	1.54674i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	20.7846i		−	0.880672i	−0.897833	−	0.440336i	$-0.854859\pi$
$557$		−	20.7846i		−	0.880672i	0.897833	−	0.440336i	$-0.145141\pi$
$558$		0			0
$559$		−	34.6410i		−	1.46516i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.00000	−	15.5885i	0.379305	−	0.656975i	−0.611656	−	0.791123i	$-0.709497\pi$
$563$	9.00000	−	15.5885i	0.379305	−	0.656975i	0.990961	+	0.134148i	$0.0428299\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−36.0000	+	20.7846i	−1.50920	+	0.871336i	−0.509256	+	0.860615i	$0.670079\pi$
$569$	−36.0000	+	20.7846i	−1.50920	+	0.871336i	−0.999943	+	0.0107211i	$0.996587\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			20.7846i			0.866778i
$576$		0			0
$577$			34.6410i			1.44212i	0.692870	+	0.721062i	$0.256346\pi$
$577$			34.6410i			1.44212i	−0.692870	+	0.721062i	$0.743654\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.00000	+	15.5885i	0.124461	+	0.646718i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.0000	+	31.1769i	0.742940	+	1.28681i	0.951151	+	0.308725i	$0.0999023\pi$
$587$	18.0000	+	31.1769i	0.742940	+	1.28681i	−0.208212	+	0.978084i	$0.566764\pi$
$588$		0			0
$589$	4.50000	−	7.79423i	0.185419	−	0.321156i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−39.0000			−1.60154			−0.800769	−	0.598973i	$-0.795576\pi$
$593$	−39.0000			−1.60154			−0.800769	+	0.598973i	$0.795576\pi$
$594$		0			0
$595$	−36.0000	+	31.1769i	−1.47586	+	1.27813i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−22.5000	−	12.9904i	−0.919325	−	0.530773i	−0.0359054	−	0.999355i	$-0.511431\pi$
$599$	−22.5000	−	12.9904i	−0.919325	−	0.530773i	−0.883420	+	0.468583i	$0.844765\pi$
$600$		0			0
$601$	9.00000	−	5.19615i	0.367118	−	0.211955i	−0.305081	−	0.952326i	$-0.598683\pi$
$601$	9.00000	−	5.19615i	0.367118	−	0.211955i	0.672198	+	0.740371i	$0.265350\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	24.0000	+	41.5692i	0.975739	+	1.69003i
$606$		0			0
$607$	−15.0000	−	8.66025i	−0.608831	−	0.351509i	0.163677	−	0.986514i	$-0.447665\pi$
$607$	−15.0000	−	8.66025i	−0.608831	−	0.351509i	−0.772508	+	0.635005i	$0.780998\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			20.7846i			0.840855i
$612$		0			0
$613$	−19.0000			−0.767403			−0.383701	−	0.923457i	$-0.625351\pi$
$613$	−19.0000			−0.767403			−0.383701	+	0.923457i	$0.625351\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−27.0000	−	15.5885i	−1.08698	−	0.627568i	−0.154209	−	0.988038i	$-0.549283\pi$
$617$	−27.0000	−	15.5885i	−1.08698	−	0.627568i	−0.932771	+	0.360471i	$0.882616\pi$
$618$		0			0
$619$	28.5000	−	16.4545i	1.14551	−	0.661361i	0.197722	−	0.980258i	$-0.436646\pi$
$619$	28.5000	−	16.4545i	1.14551	−	0.661361i	0.947790	+	0.318897i	$0.103312\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−22.5000	−	7.79423i	−0.901443	−	0.312269i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−6.00000			−0.239236
$630$		0			0
$631$	26.0000			1.03504			0.517522	−	0.855670i	$-0.326855\pi$
$631$	26.0000			1.03504			0.517522	+	0.855670i	$0.326855\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.00000	+	5.19615i	−0.119051	+	0.206203i
$636$		0			0
$637$	9.00000	+	22.5167i	0.356593	+	0.892143i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−18.0000	+	10.3923i	−0.710957	+	0.410471i	−0.811415	−	0.584470i	$-0.801302\pi$
$641$	−18.0000	+	10.3923i	−0.710957	+	0.410471i	0.100458	+	0.994941i	$0.467969\pi$
$642$		0			0
$643$	−40.5000	−	23.3827i	−1.59716	−	0.922123i	−0.992030	−	0.125999i	$-0.959786\pi$
$643$	−40.5000	−	23.3827i	−1.59716	−	0.922123i	−0.605134	−	0.796124i	$-0.706880\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$		0			0
$649$		−	31.1769i		−	1.22380i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.00000	−	5.19615i	−0.352197	−	0.203341i	0.313455	−	0.949603i	$-0.398513\pi$
$653$	−9.00000	−	5.19615i	−0.352197	−	0.203341i	−0.665653	+	0.746262i	$0.731847\pi$
$654$		0			0
$655$	27.0000	+	46.7654i	1.05498	+	1.82727i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	31.5000	−	18.1865i	1.22707	−	0.708447i	0.260651	−	0.965433i	$-0.416063\pi$
$659$	31.5000	−	18.1865i	1.22707	−	0.708447i	0.966415	+	0.256986i	$0.0827296\pi$
$660$		0			0
$661$	21.0000	+	12.1244i	0.816805	+	0.471583i	0.849314	−	0.527889i	$-0.177016\pi$
$661$	21.0000	+	12.1244i	0.816805	+	0.471583i	−0.0325082	+	0.999471i	$0.510350\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−9.00000	−	10.3923i	−0.349005	−	0.402996i
$666$		0			0
$667$	−54.0000			−2.09089
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−36.0000	+	62.3538i	−1.38976	+	2.40714i
$672$		0			0
$673$	−11.0000	−	19.0526i	−0.424019	−	0.734422i	0.572309	−	0.820038i	$-0.306048\pi$
$673$	−11.0000	−	19.0526i	−0.424019	−	0.734422i	−0.996328	+	0.0856156i	$0.972714\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	−0.999760	−	0.0219013i	$-0.993028\pi$
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	0.480913	−	0.876768i	$-0.340305\pi$
$678$		0			0
$679$	−18.0000	+	3.46410i	−0.690777	+	0.132940i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			15.5885i			0.596476i	0.954492	+	0.298238i	$0.0963989\pi$
$683$			15.5885i			0.596476i	−0.954492	+	0.298238i	$0.903601\pi$
$684$		0			0
$685$			31.1769i			1.19121i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	9.00000	−	5.19615i	0.342376	−	0.197671i	−0.318946	−	0.947773i	$-0.603329\pi$
$691$	9.00000	−	5.19615i	0.342376	−	0.197671i	0.661322	+	0.750102i	$0.269996\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−45.0000	+	25.9808i	−1.70695	+	0.985506i
$696$		0			0
$697$	−9.00000	+	15.5885i	−0.340899	+	0.590455i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	31.1769i		−	1.17754i	−0.808302	−	0.588768i	$-0.799613\pi$
$701$		−	31.1769i		−	1.17754i	0.808302	−	0.588768i	$-0.200387\pi$
$702$		0			0
$703$		−	1.73205i		−	0.0653255i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.00000	+	46.7654i	0.338480	+	1.75879i
$708$		0			0
$709$	11.5000	+	19.9186i	0.431892	+	0.748058i	0.997036	−	0.0769337i	$-0.0245130\pi$
$709$	11.5000	+	19.9186i	0.431892	+	0.748058i	−0.565145	+	0.824992i	$0.691180\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−13.5000	−	23.3827i	−0.505579	−	0.875688i
$714$		0			0
$715$	27.0000	−	46.7654i	1.00974	−	1.74893i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$		0			0
$721$	15.0000	+	17.3205i	0.558629	+	0.645049i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−36.0000	−	20.7846i	−1.33701	−	0.771921i
$726$		0			0
$727$	27.0000	−	15.5885i	1.00137	−	0.578144i	0.0927199	−	0.995692i	$-0.470444\pi$
$727$	27.0000	−	15.5885i	1.00137	−	0.578144i	0.908655	+	0.417548i	$0.137111\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	30.0000	+	51.9615i	1.10959	+	1.92187i
$732$		0			0
$733$	9.00000	+	5.19615i	0.332423	+	0.191924i	0.656916	−	0.753964i	$-0.271861\pi$
$733$	9.00000	+	5.19615i	0.332423	+	0.191924i	−0.324494	+	0.945888i	$0.605194\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	10.3923i		−	0.382805i
$738$		0			0
$739$	−16.0000			−0.588570			−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000			−0.588570			−0.294285	+	0.955718i	$0.595081\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	31.5000	+	18.1865i	1.15562	+	0.667199i	0.950251	−	0.311485i	$-0.100826\pi$
$743$	31.5000	+	18.1865i	1.15562	+	0.667199i	0.205372	+	0.978684i	$0.434160\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.00000	−	25.9808i	0.328853	−	0.949316i
$750$		0			0
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	−0.847203	−	0.531269i	$-0.821715\pi$
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	0.883694	+	0.468065i	$0.155049\pi$
$752$		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	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	−0.915264	−	0.402854i	$-0.868018\pi$
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	0.806514	+	0.591215i	$0.201351\pi$
$762$		0			0
$763$	27.5000	+	9.52628i	0.995567	+	0.344874i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−18.0000	+	10.3923i	−0.649942	+	0.375244i
$768$		0			0
$769$	−3.00000	−	1.73205i	−0.108183	−	0.0624593i	0.444932	−	0.895564i	$-0.353228\pi$
$769$	−3.00000	−	1.73205i	−0.108183	−	0.0624593i	−0.553115	+	0.833105i	$0.686561\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	39.0000			1.40273			0.701366	−	0.712801i	$-0.252574\pi$
$773$	39.0000			1.40273			0.701366	+	0.712801i	$0.252574\pi$
$774$		0			0
$775$		−	20.7846i		−	0.746605i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.50000	−	2.59808i	−0.161229	−	0.0930857i
$780$		0			0
$781$	−13.5000	−	23.3827i	−0.483068	−	0.836698i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	27.0000	−	15.5885i	0.963671	−	0.556376i
$786$		0			0
$787$	−33.0000	−	19.0526i	−1.17632	−	0.679150i	−0.221162	−	0.975237i	$-0.570985\pi$
$787$	−33.0000	−	19.0526i	−1.17632	−	0.679150i	−0.955161	+	0.296087i	$0.904318\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	48.0000			1.70453
$794$		0			0
$795$		0			0
$796$		0			0
$797$	22.5000	−	38.9711i	0.796991	−	1.38043i	−0.124576	−	0.992210i	$-0.539757\pi$
$797$	22.5000	−	38.9711i	0.796991	−	1.38043i	0.921567	−	0.388219i	$-0.126909\pi$
$798$		0			0
$799$	−18.0000	−	31.1769i	−0.636794	−	1.10296i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−9.00000	−	15.5885i	−0.317603	−	0.550105i
$804$		0			0
$805$	−40.5000	+	7.79423i	−1.42744	+	0.274710i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	31.1769i		−	1.09612i	−0.836438	−	0.548061i	$-0.815366\pi$
$809$		−	31.1769i		−	1.09612i	0.836438	−	0.548061i	$-0.184634\pi$
$810$		0			0
$811$			5.19615i			0.182462i	0.995830	+	0.0912308i	$0.0290801\pi$
$811$			5.19615i			0.182462i	−0.995830	+	0.0912308i	$0.970920\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	15.0000	−	25.9808i	0.525427	−	0.910066i
$816$		0			0
$817$	−15.0000	+	8.66025i	−0.524784	+	0.302984i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	27.0000	−	15.5885i	0.942306	−	0.544041i	0.0516239	−	0.998667i	$-0.483560\pi$
$821$	27.0000	−	15.5885i	0.942306	−	0.544041i	0.890683	+	0.454626i	$0.150227\pi$
$822$		0			0
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	−0.985997	−	0.166762i	$-0.946669\pi$
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	0.637419	+	0.770517i	$0.280002\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	46.7654i		−	1.62619i	−0.582130	−	0.813096i	$-0.697781\pi$
$827$		−	46.7654i		−	1.62619i	0.582130	−	0.813096i	$-0.302219\pi$
$828$		0			0
$829$		−	45.0333i		−	1.56407i	−0.623233	−	0.782036i	$-0.714181\pi$
$829$		−	45.0333i		−	1.56407i	0.623233	−	0.782036i	$-0.285819\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−33.0000	−	25.9808i	−1.14338	−	0.900180i
$834$		0			0
$835$	−18.0000	−	31.1769i	−0.622916	−	1.07892i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.0000	+	36.3731i	0.725001	+	1.25574i	0.958974	+	0.283495i	$0.0914938\pi$
$839$	21.0000	+	36.3731i	0.725001	+	1.25574i	−0.233973	+	0.972243i	$0.575173\pi$
$840$		0			0
$841$	39.5000	−	68.4160i	1.36207	−	2.35917i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.00000			0.103203
$846$		0			0
$847$	−32.0000	+	27.7128i	−1.09953	+	0.952224i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.50000	−	2.59808i	−0.154258	−	0.0890609i
$852$		0			0
$853$	42.0000	−	24.2487i	1.43805	−	0.830260i	0.440338	−	0.897832i	$-0.354859\pi$
$853$	42.0000	−	24.2487i	1.43805	−	0.830260i	0.997714	+	0.0675719i	$0.0215252\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	0.629066	−	0.777352i	$-0.283437\pi$
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	−0.987739	+	0.156112i	$0.950104\pi$
$858$		0			0
$859$	25.5000	+	14.7224i	0.870049	+	0.502323i	0.867364	−	0.497674i	$-0.165812\pi$
$859$	25.5000	+	14.7224i	0.870049	+	0.502323i	0.00268433	+	0.999996i	$0.499146\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	10.3923i		−	0.353758i	−0.984233	−	0.176879i	$-0.943400\pi$
$863$		−	10.3923i		−	0.353758i	0.984233	−	0.176879i	$-0.0566002\pi$
$864$		0			0
$865$	−27.0000			−0.918028
$866$		0			0
$867$		0			0
$868$		0			0
$869$	63.0000	+	36.3731i	2.13713	+	1.23387i
$870$		0			0
$871$	−6.00000	+	3.46410i	−0.203302	+	0.117377i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	7.50000	+	2.59808i	0.253546	+	0.0878310i
$876$		0			0
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	−0.882415	−	0.470471i	$-0.844084\pi$
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	0.848648	+	0.528958i	$0.177417\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−27.0000			−0.909653			−0.454827	−	0.890580i	$-0.650299\pi$
$881$	−27.0000			−0.909653			−0.454827	+	0.890580i	$0.650299\pi$
$882$		0			0
$883$	28.0000			0.942275			0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000			0.942275			0.471138	+	0.882060i	$0.343844\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	−0.261540	−	0.965193i	$-0.584230\pi$
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	0.966651	−	0.256096i	$-0.0824362\pi$
$888$		0			0
$889$	−5.00000	−	1.73205i	−0.167695	−	0.0580911i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.00000	−	5.19615i	0.301174	−	0.173883i
$894$		0			0
$895$	27.0000	+	15.5885i	0.902510	+	0.521065i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	54.0000			1.80100
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18.0000	−	10.3923i	−0.598340	−	0.345452i
$906$		0			0
$907$	16.0000	+	27.7128i	0.531271	+	0.920189i	0.999334	+	0.0364935i	$0.0116188\pi$
$907$	16.0000	+	27.7128i	0.531271	+	0.920189i	−0.468063	+	0.883695i	$0.655048\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	9.00000	−	5.19615i	0.298183	−	0.172156i	−0.343443	−	0.939173i	$-0.611593\pi$
$911$	9.00000	−	5.19615i	0.298183	−	0.172156i	0.641626	+	0.767017i	$0.278260\pi$
$912$		0			0
$913$	27.0000	+	15.5885i	0.893570	+	0.515903i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−36.0000	+	31.1769i	−1.18882	+	1.02955i
$918$		0			0
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.00000	+	15.5885i	−0.296239	+	0.513100i
$924$		0			0
$925$	−2.00000	−	3.46410i	−0.0657596	−	0.113899i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$		0			0
$931$	7.50000	−	9.52628i	0.245803	−	0.312211i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			93.5307i			3.05878i
$936$		0			0
$937$			55.4256i			1.81068i	0.424691	+	0.905338i	$0.360383\pi$
$937$			55.4256i			1.81068i	−0.424691	+	0.905338i	$0.639617\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	−0.642567	−	0.766229i	$-0.722131\pi$
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	0.984858	+	0.173365i	$0.0554641\pi$
$942$		0			0
$943$	−13.5000	+	7.79423i	−0.439620	+	0.253815i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−22.5000	+	12.9904i	−0.731152	+	0.422131i	−0.818843	−	0.574017i	$-0.805384\pi$
$947$	−22.5000	+	12.9904i	−0.731152	+	0.422131i	0.0876916	+	0.996148i	$0.472051\pi$
$948$		0			0
$949$	−6.00000	+	10.3923i	−0.194768	+	0.337348i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			31.1769i			1.00992i	0.863143	+	0.504960i	$0.168493\pi$
$953$			31.1769i			1.00992i	−0.863143	+	0.504960i	$0.831507\pi$
$954$		0			0
$955$			15.5885i			0.504431i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−27.0000	+	5.19615i	−0.871875	+	0.167793i
$960$		0			0
$961$	−2.00000	−	3.46410i	−0.0645161	−	0.111745i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.00000	+	5.19615i	0.0965734	+	0.167270i
$966$		0			0
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	−0.708245	−	0.705967i	$-0.750513\pi$
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	0.965508	+	0.260375i	$0.0838461\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6.00000			0.192549			0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000			0.192549			0.0962746	+	0.995355i	$0.469307\pi$
$972$		0			0
$973$	−30.0000	−	34.6410i	−0.961756	−	1.11054i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	36.0000	+	20.7846i	1.15174	+	0.664959i	0.949311	−	0.314338i	$-0.101783\pi$
$977$	36.0000	+	20.7846i	1.15174	+	0.664959i	0.202431	+	0.979297i	$0.435116\pi$
$978$		0			0
$979$	−40.5000	+	23.3827i	−1.29439	+	0.747314i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.0000	−	36.3731i	−0.669796	−	1.16012i	−0.977961	−	0.208788i	$-0.933048\pi$
$983$	−21.0000	−	36.3731i	−0.669796	−	1.16012i	0.308165	−	0.951333i	$-0.400285\pi$
$984$		0			0
$985$	54.0000	+	31.1769i	1.72058	+	0.993379i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			51.9615i			1.65228i
$990$		0			0
$991$	10.0000			0.317660			0.158830	−	0.987306i	$-0.449228\pi$
$991$	10.0000			0.317660			0.158830	+	0.987306i	$0.449228\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.50000	−	2.59808i	−0.142660	−	0.0823646i
$996$		0			0
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.x.a.377.1		2
3.2	odd	2		2268.2.x.g.377.1		2
7.6	odd	2		2268.2.x.h.377.1		2
9.2	odd	6		2268.2.x.h.1889.1		2
9.4	even	3		756.2.f.c.377.1	yes	2
9.5	odd	6		756.2.f.a.377.1	✓	2
9.7	even	3		2268.2.x.b.1889.1		2
21.20	even	2		2268.2.x.b.377.1		2
36.23	even	6		3024.2.k.a.1889.2		2
36.31	odd	6		3024.2.k.d.1889.2		2
63.13	odd	6		756.2.f.a.377.2	yes	2
63.20	even	6	inner	2268.2.x.a.1889.1		2
63.34	odd	6		2268.2.x.g.1889.1		2
63.41	even	6		756.2.f.c.377.2	yes	2
252.139	even	6		3024.2.k.a.1889.1		2
252.167	odd	6		3024.2.k.d.1889.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.f.a.377.1	✓	2	9.5	odd	6
756.2.f.a.377.2	yes	2	63.13	odd	6
756.2.f.c.377.1	yes	2	9.4	even	3
756.2.f.c.377.2	yes	2	63.41	even	6
2268.2.x.a.377.1		2	1.1	even	1	trivial
2268.2.x.a.1889.1		2	63.20	even	6	inner
2268.2.x.b.377.1		2	21.20	even	2
2268.2.x.b.1889.1		2	9.7	even	3
2268.2.x.g.377.1		2	3.2	odd	2
2268.2.x.g.1889.1		2	63.34	odd	6
2268.2.x.h.377.1		2	7.6	odd	2
2268.2.x.h.1889.1		2	9.2	odd	6
3024.2.k.a.1889.1		2	252.139	even	6
3024.2.k.a.1889.2		2	36.23	even	6
3024.2.k.d.1889.1		2	252.167	odd	6
3024.2.k.d.1889.2		2	36.31	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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.x (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{5} +(-2.50000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-4.50000 + 2.59808i) q^{11} +(3.00000 + 1.73205i) q^{13} -6.00000 q^{17} -1.73205i q^{19} +(-4.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(9.00000 - 5.19615i) q^{29} +(4.50000 + 2.59808i) q^{31} +(6.00000 - 5.19615i) q^{35} +1.00000 q^{37} +(1.50000 - 2.59808i) q^{41} +(-5.00000 - 8.66025i) q^{43} +(3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} -15.5885i q^{55} +(-3.00000 + 5.19615i) q^{59} +(12.0000 - 6.92820i) q^{61} +(-9.00000 + 5.19615i) q^{65} +(-1.00000 + 1.73205i) q^{67} +5.19615i q^{71} +3.46410i q^{73} +(13.5000 - 2.59808i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(-3.00000 - 5.19615i) q^{83} +(9.00000 - 15.5885i) q^{85} +9.00000 q^{89} +(-6.00000 - 6.92820i) q^{91} +(4.50000 + 2.59808i) q^{95} +(6.00000 - 3.46410i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{5} - 5 q^{7}+O(q^{10}) \) 2 * q - 3 * q^5 - 5 * q^7	\( 2 q - 3 q^{5} - 5 q^{7} - 9 q^{11} + 6 q^{13} - 12 q^{17} - 9 q^{23} - 4 q^{25} + 18 q^{29} + 9 q^{31} + 12 q^{35} + 2 q^{37} + 3 q^{41} - 10 q^{43} + 6 q^{47} + 11 q^{49} - 6 q^{59} + 24 q^{61} - 18 q^{65} - 2 q^{67} + 27 q^{77} - 14 q^{79} - 6 q^{83} + 18 q^{85} + 18 q^{89} - 12 q^{91} + 9 q^{95} + 12 q^{97}+O(q^{100}) \) 2 * q - 3 * q^5 - 5 * q^7 - 9 * q^11 + 6 * q^13 - 12 * q^17 - 9 * q^23 - 4 * q^25 + 18 * q^29 + 9 * q^31 + 12 * q^35 + 2 * q^37 + 3 * q^41 - 10 * q^43 + 6 * q^47 + 11 * q^49 - 6 * q^59 + 24 * q^61 - 18 * q^65 - 2 * q^67 + 27 * q^77 - 14 * q^79 - 6 * q^83 + 18 * q^85 + 18 * q^89 - 12 * q^91 + 9 * q^95 + 12 * q^97

Introduction

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