LMFDB - Embedded newform 737.1.w.a.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [737,1,Mod(10,737)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(737, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 16]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("737.10");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 737 = 11 \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	737.w (of order $66$, degree $20$, 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:	$0.367810914311$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 $ x^20 - x^19 + x^17 - x^16 + x^14 - x^13 + x^11 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{33}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{33} - \cdots)$

Embedding invariants

Embedding label			65.1
Root			$0.235759 - 0.971812i$ of defining polynomial
Character	$\chi$	$=$	737.65
Dual form			737.1.w.a.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61435 - 0.474017i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-1.21590 + 1.40323i) q^{5} +(1.54019 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.61435 - 0.474017i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-1.21590 + 1.40323i) q^{5} +(1.54019 + 0.989821i) q^{9} +(-0.327068 - 0.945001i) q^{11} +(1.56199 + 0.625325i) q^{12} +(2.62805 - 1.68895i) q^{15} +(0.981929 + 0.189251i) q^{16} +(1.34378 - 1.28129i) q^{20} +(-0.452418 - 1.86489i) q^{23} +(-0.348311 - 2.42256i) q^{25} +(-0.915415 - 1.05645i) q^{27} +(1.39734 + 1.09888i) q^{31} +(0.0800569 + 1.68060i) q^{33} +(-1.43913 - 1.13174i) q^{36} +(0.888835 + 1.53951i) q^{37} +(0.235759 + 0.971812i) q^{44} +(-3.26167 + 0.957713i) q^{45} +(0.0688733 - 0.0656706i) q^{47} +(-1.49547 - 0.770969i) q^{48} +(0.580057 - 0.814576i) q^{49} +(-0.271738 - 0.595023i) q^{53} +(1.72373 + 0.690079i) q^{55} +(0.0930932 - 0.647478i) q^{59} +(-2.77670 + 1.43149i) q^{60} +(-0.959493 - 0.281733i) q^{64} +(0.235759 - 0.971812i) q^{67} +(-0.153628 + 3.22505i) q^{69} +(0.283341 + 0.0270558i) q^{71} +(-0.586036 + 4.07597i) q^{75} +(-1.45949 + 1.14776i) q^{80} +(0.216476 + 0.474017i) q^{81} +(1.50842 - 0.442913i) q^{89} +(0.273100 + 1.89945i) q^{92} +(-1.73492 - 2.43635i) q^{93} +(-0.580057 - 1.00469i) q^{97} +(0.431635 - 1.77922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} + q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 20 * q - 4 * q^3 + q^4 + 2 * q^5 - 6 * q^9	$ 20 q - 4 q^{3} + q^{4} + 2 q^{5} - 6 q^{9} + q^{11} + 2 q^{12} + 4 q^{15} + q^{16} - q^{20} - 9 q^{23} - 8 q^{27} - q^{31} - 9 q^{33} + 3 q^{36} - q^{37} + q^{44} - 5 q^{45} - q^{47} - 9 q^{48} + q^{49} + 2 q^{53} + 21 q^{55} + 2 q^{59} - 2 q^{60} - 2 q^{64} + q^{67} + 4 q^{69} + 2 q^{71} - 12 q^{80} + 12 q^{81} + 2 q^{89} - 4 q^{92} - 13 q^{93} - q^{97} + 3 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 + q^4 + 2 * q^5 - 6 * q^9 + q^11 + 2 * q^12 + 4 * q^15 + q^16 - q^20 - 9 * q^23 - 8 * q^27 - q^31 - 9 * q^33 + 3 * q^36 - q^37 + q^44 - 5 * q^45 - q^47 - 9 * q^48 + q^49 + 2 * q^53 + 21 * q^55 + 2 * q^59 - 2 * q^60 - 2 * q^64 + q^67 + 4 * q^69 + 2 * q^71 - 12 * q^80 + 12 * q^81 + 2 * q^89 - 4 * q^92 - 13 * q^93 - q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/737\mathbb{Z}\right)^\times$.

$n$	$68$	$672$
$\chi(n)$	$-1$	$e\left(\frac{17}{33}\right)$

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		0.0475819	−	0.998867i	$-0.484848\pi$
$2$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$3$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$3$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$4$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$5$	−1.21590	+	1.40323i	−1.21590	+	1.40323i	−0.327068	+	0.945001i	$0.606061\pi$
$5$	−1.21590	+	1.40323i	−1.21590	+	1.40323i	−0.888835	+	0.458227i	$0.848485\pi$
$6$		0			0
$7$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$7$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$8$		0			0
$9$	1.54019	+	0.989821i	1.54019	+	0.989821i
$10$		0			0
$11$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$11$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$12$	1.56199	+	0.625325i	1.56199	+	0.625325i
$13$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$13$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$14$		0			0
$15$	2.62805	−	1.68895i	2.62805	−	1.68895i
$16$	0.981929	+	0.189251i	0.981929	+	0.189251i
$17$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$17$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$18$		0			0
$19$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$19$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$20$	1.34378	−	1.28129i	1.34378	−	1.28129i
$21$		0			0
$22$		0			0
$23$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	−0.500000	−	0.866025i	$-0.666667\pi$
$23$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	0.0475819	−	0.998867i	$-0.484848\pi$
$24$		0			0
$25$	−0.348311	−	2.42256i	−0.348311	−	2.42256i
$26$		0			0
$27$	−0.915415	−	1.05645i	−0.915415	−	1.05645i
$28$		0			0
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$		0			0
$31$	1.39734	+	1.09888i	1.39734	+	1.09888i	0.981929	+	0.189251i	$0.0606061\pi$
$31$	1.39734	+	1.09888i	1.39734	+	1.09888i	0.415415	+	0.909632i	$0.363636\pi$
$32$		0			0
$33$	0.0800569	+	1.68060i	0.0800569	+	1.68060i
$34$		0			0
$35$		0			0
$36$	−1.43913	−	1.13174i	−1.43913	−	1.13174i
$37$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.841254	+	0.540641i	$0.181818\pi$
$37$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.0475819	+	0.998867i	$0.484848\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$41$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$42$		0			0
$43$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$43$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$44$	0.235759	+	0.971812i	0.235759	+	0.971812i
$45$	−3.26167	+	0.957713i	−3.26167	+	0.957713i
$46$		0			0
$47$	0.0688733	−	0.0656706i	0.0688733	−	0.0656706i	−0.654861	−	0.755750i	$-0.727273\pi$
$47$	0.0688733	−	0.0656706i	0.0688733	−	0.0656706i	0.723734	+	0.690079i	$0.242424\pi$
$48$	−1.49547	−	0.770969i	−1.49547	−	0.770969i
$49$	0.580057	−	0.814576i	0.580057	−	0.814576i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.271738	−	0.595023i	−0.271738	−	0.595023i	0.723734	−	0.690079i	$-0.242424\pi$
$53$	−0.271738	−	0.595023i	−0.271738	−	0.595023i	−0.995472	+	0.0950560i	$0.969697\pi$
$54$		0			0
$55$	1.72373	+	0.690079i	1.72373	+	0.690079i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.0930932	−	0.647478i	0.0930932	−	0.647478i	−0.888835	−	0.458227i	$-0.848485\pi$
$59$	0.0930932	−	0.647478i	0.0930932	−	0.647478i	0.981929	−	0.189251i	$-0.0606061\pi$
$60$	−2.77670	+	1.43149i	−2.77670	+	1.43149i
$61$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$61$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$62$		0			0
$63$		0			0
$64$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$65$		0			0
$66$		0			0
$67$	0.235759	−	0.971812i	0.235759	−	0.971812i
$67$	0.235759	−	0.971812i	0.235759	−	0.971812i
$68$		0			0
$69$	−0.153628	+	3.22505i	−0.153628	+	3.22505i
$70$		0			0
$71$	0.283341	+	0.0270558i	0.283341	+	0.0270558i	0.235759	−	0.971812i	$-0.424242\pi$
$71$	0.283341	+	0.0270558i	0.283341	+	0.0270558i	0.0475819	+	0.998867i	$0.484848\pi$
$72$		0			0
$73$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$73$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$74$		0			0
$75$	−0.586036	+	4.07597i	−0.586036	+	4.07597i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$79$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$80$	−1.45949	+	1.14776i	−1.45949	+	1.14776i
$81$	0.216476	+	0.474017i	0.216476	+	0.474017i
$82$		0			0
$83$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$83$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.50842	−	0.442913i	1.50842	−	0.442913i	0.580057	−	0.814576i	$-0.303030\pi$
$89$	1.50842	−	0.442913i	1.50842	−	0.442913i	0.928368	+	0.371662i	$0.121212\pi$
$90$		0			0
$91$		0			0
$92$	0.273100	+	1.89945i	0.273100	+	1.89945i
$93$	−1.73492	−	2.43635i	−1.73492	−	2.43635i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$97$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$98$		0			0
$99$	0.431635	−	1.77922i	0.431635	−	1.77922i
$100$	0.116455	+	2.44470i	0.116455	+	2.44470i
$101$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$101$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$102$		0			0
$103$	−0.370638	−	0.291473i	−0.370638	−	0.291473i	0.415415	−	0.909632i	$-0.363636\pi$
$103$	−0.370638	−	0.291473i	−0.370638	−	0.291473i	−0.786053	+	0.618159i	$0.787879\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$107$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$108$	0.810848	+	1.13868i	0.810848	+	1.13868i
$109$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$109$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$110$		0			0
$111$	−0.705142	−	2.90663i	−0.705142	−	2.90663i
$112$		0			0
$113$	−1.54370	+	0.297523i	−1.54370	+	0.297523i	−0.888835	−	0.458227i	$-0.848485\pi$
$113$	−1.54370	+	0.297523i	−1.54370	+	0.297523i	−0.654861	+	0.755750i	$0.727273\pi$
$114$		0			0
$115$	3.16697	+	1.63268i	3.16697	+	1.63268i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$122$		0			0
$123$		0			0
$124$	−1.28656	−	1.22673i	−1.28656	−	1.22673i
$125$	2.26092	+	1.45301i	2.26092	+	1.45301i
$126$		0			0
$127$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$127$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$131$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$132$	0.0800569	−	1.68060i	0.0800569	−	1.68060i
$133$		0			0
$134$		0			0
$135$	2.59549			2.59549
$136$		0			0
$137$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.723734	−	0.690079i	$-0.242424\pi$
$137$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.235759	+	0.971812i	$0.424242\pi$
$138$		0			0
$139$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$139$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$140$		0			0
$141$	−0.142315	+	0.0733684i	−0.142315	+	0.0733684i
$142$		0			0
$143$		0			0
$144$	1.32503	+	1.26342i	1.32503	+	1.26342i
$145$		0			0
$146$		0			0
$147$	−1.32254	+	1.04006i	−1.32254	+	1.04006i
$148$	−0.738471	−	1.61703i	−0.738471	−	1.61703i
$149$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$149$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$150$		0			0
$151$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$151$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.24102	+	0.624655i	−3.24102	+	0.624655i
$156$		0			0
$157$	−0.469383	−	1.93482i	−0.469383	−	1.93482i	−0.327068	−	0.945001i	$-0.606061\pi$
$157$	−0.469383	−	1.93482i	−0.469383	−	1.93482i	−0.142315	−	0.989821i	$-0.545455\pi$
$158$		0			0
$159$	0.156630	+	1.08939i	0.156630	+	1.08939i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$163$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$164$		0			0
$165$	−2.45561	−	1.93111i	−2.45561	−	1.93111i
$166$		0			0
$167$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$167$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$168$		0			0
$169$	0.235759	−	0.971812i	0.235759	−	0.971812i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$173$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$174$		0			0
$175$		0			0
$176$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$177$	−0.457201	+	1.00113i	−0.457201	+	1.00113i
$178$		0			0
$179$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$179$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$180$	3.33794	−	0.643335i	3.33794	−	0.643335i
$181$	−0.205996	+	0.196417i	−0.205996	+	0.196417i	−0.786053	−	0.618159i	$-0.787879\pi$
$181$	−0.205996	+	0.196417i	−0.205996	+	0.196417i	0.580057	+	0.814576i	$0.303030\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.24102	−	0.624655i	−3.24102	−	0.624655i
$186$		0			0
$187$		0			0
$188$	−0.0748038	+	0.0588264i	−0.0748038	+	0.0588264i
$189$		0			0
$190$		0			0
$191$	0.341254	+	0.325385i	0.341254	+	0.325385i	0.841254	−	0.540641i	$-0.181818\pi$
$191$	0.341254	+	0.325385i	0.341254	+	0.325385i	−0.500000	+	0.866025i	$0.666667\pi$
$192$	1.41542	+	0.909632i	1.41542	+	0.909632i
$193$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$193$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$194$		0			0
$195$		0			0
$196$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$197$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$197$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$198$		0			0
$199$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i	0.841254	+	0.540641i	$0.181818\pi$
$199$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i	−0.888835	+	0.458227i	$0.848485\pi$
$200$		0			0
$201$	−0.841254	+	1.45709i	−0.841254	+	1.45709i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.14910	−	3.32011i	1.14910	−	3.32011i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$211$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$212$	0.213947	+	0.618159i	0.213947	+	0.618159i
$213$	−0.444587	−	0.177986i	−0.444587	−	0.177986i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−1.65033	−	0.850806i	−1.65033	−	0.850806i
$221$		0			0
$222$		0			0
$223$	0.627639	−	0.184291i	0.627639	−	0.184291i	0.0475819	−	0.998867i	$-0.484848\pi$
$223$	0.627639	−	0.184291i	0.627639	−	0.184291i	0.580057	+	0.814576i	$0.303030\pi$
$224$		0			0
$225$	1.86143	−	4.07597i	1.86143	−	4.07597i
$226$		0			0
$227$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$227$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$228$		0			0
$229$	1.82318	−	0.729892i	1.82318	−	0.729892i	0.841254	−	0.540641i	$-0.181818\pi$
$229$	1.82318	−	0.729892i	1.82318	−	0.729892i	0.981929	−	0.189251i	$-0.0606061\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$233$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$234$		0			0
$235$	0.00840744	+	0.176494i	0.00840744	+	0.176494i
$236$	−0.154218	+	0.635697i	−0.154218	+	0.635697i
$237$		0			0
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$	2.90019	−	1.16106i	2.90019	−	1.16106i
$241$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$241$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$242$		0			0
$243$	0.0741615	+	0.515804i	0.0741615	+	0.515804i
$244$		0			0
$245$	0.437742	+	1.80440i	0.437742	+	1.80440i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.95496	+	0.186677i	−1.95496	+	0.186677i	−0.995472	−	0.0950560i	$-0.969697\pi$
$251$	−1.95496	+	0.186677i	−1.95496	+	0.186677i	−0.959493	+	0.281733i	$0.909091\pi$
$252$		0			0
$253$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$254$		0			0
$255$		0			0
$256$	0.928368	+	0.371662i	0.928368	+	0.371662i
$257$	0.327068	+	0.945001i	0.327068	+	0.945001i	0.981929	+	0.189251i	$0.0606061\pi$
$257$	0.327068	+	0.945001i	0.327068	+	0.945001i	−0.654861	+	0.755750i	$0.727273\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$263$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$264$		0			0
$265$	1.16536	+	0.342180i	1.16536	+	0.342180i
$266$		0			0
$267$	−2.64508			−2.64508
$268$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$269$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$269$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$270$		0			0
$271$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$271$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.17540	+	1.12149i	−2.17540	+	1.12149i
$276$	0.459493	−	3.19584i	0.459493	−	3.19584i
$277$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$277$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$278$		0			0
$279$	1.06448	+	3.07561i	1.06448	+	3.07561i
$280$		0			0
$281$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$281$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$282$		0			0
$283$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$283$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$284$	−0.279486	−	0.0538665i	−0.279486	−	0.0538665i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.981929	−	0.189251i	0.981929	−	0.189251i
$290$		0			0
$291$	0.460178	+	1.89688i	0.460178	+	1.89688i
$292$		0			0
$293$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$293$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$294$		0			0
$295$	0.795366	+	0.917901i	0.795366	+	0.917901i
$296$		0			0
$297$	−0.698939	+	1.21060i	−0.698939	+	1.21060i
$298$		0			0
$299$		0			0
$300$	0.970828	−	4.00181i	0.970828	−	4.00181i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$307$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$308$		0			0
$309$	0.460178	+	0.646229i	0.460178	+	0.646229i
$310$		0			0
$311$	0.481929	−	1.05528i	0.481929	−	1.05528i	−0.500000	−	0.866025i	$-0.666667\pi$
$311$	0.481929	−	1.05528i	0.481929	−	1.05528i	0.981929	−	0.189251i	$-0.0606061\pi$
$312$		0			0
$313$	−0.452418	+	0.132842i	−0.452418	+	0.132842i	−0.500000	−	0.866025i	$-0.666667\pi$
$313$	−0.452418	+	0.132842i	−0.452418	+	0.132842i	0.0475819	+	0.998867i	$0.484848\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.273507	−	0.384087i	0.273507	−	0.384087i	−0.654861	−	0.755750i	$-0.727273\pi$
$317$	0.273507	−	0.384087i	0.273507	−	0.384087i	0.928368	+	0.371662i	$0.121212\pi$
$318$		0			0
$319$		0			0
$320$	1.56199	−	1.00383i	1.56199	−	1.00383i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.170438	−	0.492448i	−0.170438	−	0.492448i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.44091	−	0.137591i	−1.44091	−	0.137591i	−0.654861	−	0.755750i	$-0.727273\pi$
$331$	−1.44091	−	0.137591i	−1.44091	−	0.137591i	−0.786053	+	0.618159i	$0.787879\pi$
$332$		0			0
$333$	−0.154861	+	3.25093i	−0.154861	+	3.25093i
$334$		0			0
$335$	1.07701	+	1.51245i	1.07701	+	1.51245i
$336$		0			0
$337$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$337$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$338$		0			0
$339$	2.63310	+	0.251431i	2.63310	+	0.251431i
$340$		0			0
$341$	0.581419	−	1.67990i	0.581419	−	1.67990i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−4.33868	−	4.13692i	−4.33868	−	4.13692i
$346$		0			0
$347$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$347$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$348$		0			0
$349$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$349$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i	−0.786053	−	0.618159i	$-0.787879\pi$
$353$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i	0.841254	+	0.540641i	$0.181818\pi$
$354$		0			0
$355$	−0.382481	+	0.364694i	−0.382481	+	0.364694i
$356$	−1.54370	+	0.297523i	−1.54370	+	0.297523i
$357$		0			0
$358$		0			0
$359$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$359$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$360$		0			0
$361$	0.580057	+	0.814576i	0.580057	+	0.814576i
$362$		0			0
$363$	1.56199	−	0.625325i	1.56199	−	0.625325i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.235759	+	0.971812i	−0.235759	+	0.971812i	0.723734	+	0.690079i	$0.242424\pi$
$367$	−0.235759	+	0.971812i	−0.235759	+	0.971812i	−0.959493	+	0.281733i	$0.909091\pi$
$368$	−0.0913090	−	1.91681i	−0.0913090	−	1.91681i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	1.49547	+	2.59023i	1.49547	+	2.59023i
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−2.96118	−	3.41739i	−2.96118	−	3.41739i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.308779	−	1.27280i	−0.308779	−	1.27280i	−0.888835	−	0.458227i	$-0.848485\pi$
$379$	−0.308779	−	1.27280i	−0.308779	−	1.27280i	0.580057	−	0.814576i	$-0.303030\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.03115	−	0.531595i	−1.03115	−	0.531595i	−0.142315	−	0.989821i	$-0.545455\pi$
$383$	−1.03115	−	0.531595i	−1.03115	−	0.531595i	−0.888835	+	0.458227i	$0.848485\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	0.481929	+	1.05528i	0.481929	+	1.05528i
$389$	−0.370638	+	0.291473i	−0.370638	+	0.291473i	−0.786053	−	0.618159i	$-0.787879\pi$
$389$	−0.370638	+	0.291473i	−0.370638	+	0.291473i	0.415415	+	0.909632i	$0.363636\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−0.598806	+	1.73014i	−0.598806	+	1.73014i
$397$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$397$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$398$		0			0
$399$		0			0
$400$	0.116455	−	2.44470i	0.116455	−	2.44470i
$401$	0.0951638			0.0951638			0.0475819	−	0.998867i	$-0.484848\pi$
$401$	0.0951638			0.0951638			0.0475819	+	0.998867i	$0.484848\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.928368	−	0.272593i	−0.928368	−	0.272593i
$406$		0			0
$407$	1.16413	−	1.34347i	1.16413	−	1.34347i
$408$		0			0
$409$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$409$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$410$		0			0
$411$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$412$	0.341254	+	0.325385i	0.341254	+	0.325385i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.67489	+	0.159932i	−1.67489	+	0.159932i	−0.888835	−	0.458227i	$-0.848485\pi$
$419$	−1.67489	+	0.159932i	−1.67489	+	0.159932i	−0.786053	+	0.618159i	$0.787879\pi$
$420$		0			0
$421$	1.16413	+	0.600149i	1.16413	+	0.600149i	0.928368	−	0.371662i	$-0.121212\pi$
$421$	1.16413	+	0.600149i	1.16413	+	0.600149i	0.235759	+	0.971812i	$0.424242\pi$
$422$		0			0
$423$	0.171080	−	0.0329730i	0.171080	−	0.0329730i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	−0.698939	−	1.21060i	−0.698939	−	1.21060i
$433$	−1.13779	−	0.894765i	−1.13779	−	0.894765i	−0.142315	−	0.989821i	$-0.545455\pi$
$433$	−1.13779	−	0.894765i	−1.13779	−	0.894765i	−0.995472	+	0.0950560i	$0.969697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	1.69968	−	0.680451i	1.69968	−	0.680451i
$442$		0			0
$443$	1.13915	+	1.59971i	1.13915	+	1.59971i	0.723734	+	0.690079i	$0.242424\pi$
$443$	1.13915	+	1.59971i	1.13915	+	1.59971i	0.415415	+	0.909632i	$0.363636\pi$
$444$	0.425656	+	2.96050i	0.425656	+	2.96050i
$445$	−1.21259	+	2.65520i	−1.21259	+	2.65520i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.723734	+	0.690079i	−0.723734	+	0.690079i	−0.959493	−	0.281733i	$-0.909091\pi$
$449$	−0.723734	+	0.690079i	−0.723734	+	0.690079i	0.235759	+	0.971812i	$0.424242\pi$
$450$		0			0
$451$		0			0
$452$	1.56499	−	0.149438i	1.56499	−	0.149438i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$457$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$458$		0			0
$459$		0			0
$460$	−2.99743	−	1.92633i	−2.99743	−	1.92633i
$461$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$461$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$462$		0			0
$463$	0.0930932	−	0.268975i	0.0930932	−	0.268975i	−0.888835	−	0.458227i	$-0.848485\pi$
$463$	0.0930932	−	0.268975i	0.0930932	−	0.268975i	0.981929	+	0.189251i	$0.0606061\pi$
$464$		0			0
$465$	5.52825	+	0.527884i	5.52825	+	0.527884i
$466$		0			0
$467$	0.0883470	−	1.85463i	0.0883470	−	1.85463i	−0.327068	−	0.945001i	$-0.606061\pi$
$467$	0.0883470	−	1.85463i	0.0883470	−	1.85463i	0.415415	−	0.909632i	$-0.363636\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.159389	+	3.34598i	−0.159389	+	3.34598i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.170438	−	1.18542i	0.170438	−	1.18542i
$478$		0			0
$479$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$479$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.841254	−	0.540641i	0.841254	−	0.540641i
$485$	2.11510	+	0.407652i	2.11510	+	0.407652i
$486$		0			0
$487$	1.13915	−	1.59971i	1.13915	−	1.59971i	0.415415	−	0.909632i	$-0.363636\pi$
$487$	1.13915	−	1.59971i	1.13915	−	1.59971i	0.723734	−	0.690079i	$-0.242424\pi$
$488$		0			0
$489$	−1.91433	+	1.82531i	−1.91433	+	1.82531i
$490$		0			0
$491$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$491$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	1.97183	+	2.76904i	1.97183	+	2.76904i
$496$	1.16413	+	1.34347i	1.16413	+	1.34347i
$497$		0			0
$498$		0			0
$499$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	0.580057	−	0.814576i	$-0.303030\pi$
$499$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	−0.995472	+	0.0950560i	$0.969697\pi$
$500$	−2.11257	−	1.66134i	−2.11257	−	1.66134i
$501$		0			0
$502$		0			0
$503$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$503$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.841254	+	1.45709i	−0.841254	+	1.45709i
$508$		0			0
$509$	−0.947890	−	1.09392i	−0.947890	−	1.09392i	−0.995472	−	0.0950560i	$-0.969697\pi$
$509$	−0.947890	−	1.09392i	−0.947890	−	1.09392i	0.0475819	−	0.998867i	$-0.484848\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.859663	−	0.165686i	0.859663	−	0.165686i
$516$		0			0
$517$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$521$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$522$		0			0
$523$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$523$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$529$	−2.38431	+	1.22920i	−2.38431	+	1.22920i
$530$		0			0
$531$	0.784269	−	0.905095i	0.784269	−	0.905095i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.22871			−3.22871
$538$		0			0
$539$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$540$	−2.58374	−	0.246717i	−2.58374	−	0.246717i
$541$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$541$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$542$		0			0
$543$	0.425656	−	0.219441i	0.425656	−	0.219441i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$547$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$548$	−0.928368	−	0.371662i	−0.928368	−	0.371662i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	4.93605	+	2.54471i	4.93605	+	2.54471i
$556$		0			0
$557$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$557$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$563$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$564$	0.148645	−	0.0595083i	0.148645	−	0.0595083i
$565$	1.45949	−	2.52792i	1.45949	−	2.52792i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$569$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$570$		0			0
$571$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$571$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$572$		0			0
$573$	−0.396666	−	0.687046i	−0.396666	−	0.687046i
$574$		0			0
$575$	−4.36023	+	1.74557i	−4.36023	+	1.74557i
$576$	−1.19894	−	1.38365i	−1.19894	−	1.38365i
$577$	0.481929	+	0.676774i	0.481929	+	0.676774i	0.981929	−	0.189251i	$-0.0606061\pi$
$577$	0.481929	+	0.676774i	0.481929	+	0.676774i	−0.500000	+	0.866025i	$0.666667\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.473420	+	0.451405i	−0.473420	+	0.451405i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.74555	−	0.336426i	−1.74555	−	0.336426i	−0.786053	−	0.618159i	$-0.787879\pi$
$587$	−1.74555	−	0.336426i	−1.74555	−	0.336426i	−0.959493	+	0.281733i	$0.909091\pi$
$588$	1.41542	−	0.909632i	1.41542	−	0.909632i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.581419	+	1.67990i	0.581419	+	1.67990i
$593$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$593$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.550294	−	1.58997i	0.550294	−	1.58997i
$598$		0			0
$599$	−0.469383	−	0.0448206i	−0.469383	−	0.0448206i	−0.142315	−	0.989821i	$-0.545455\pi$
$599$	−0.469383	−	0.0448206i	−0.469383	−	0.0448206i	−0.327068	+	0.945001i	$0.606061\pi$
$600$		0			0
$601$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$601$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$602$		0			0
$603$	1.32503	−	1.26342i	1.32503	−	1.26342i
$604$		0			0
$605$	0.0883470	−	1.85463i	0.0883470	−	1.85463i
$606$		0			0
$607$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$607$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$613$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.601300	+	1.31666i	0.601300	+	1.31666i	0.928368	+	0.371662i	$0.121212\pi$
$617$	0.601300	+	1.31666i	0.601300	+	1.31666i	−0.327068	+	0.945001i	$0.606061\pi$
$618$		0			0
$619$	−1.88431	−	0.363170i	−1.88431	−	0.363170i	−0.888835	−	0.458227i	$-0.848485\pi$
$619$	−1.88431	−	0.363170i	−1.88431	−	0.363170i	−0.995472	+	0.0950560i	$0.969697\pi$
$620$	3.28572	−	0.313748i	3.28572	−	0.313748i
$621$	−1.55601	+	2.18511i	−1.55601	+	2.18511i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−2.43964	+	0.716342i	−2.43964	+	0.716342i
$626$		0			0
$627$		0			0
$628$	0.283341	+	1.97068i	0.283341	+	1.97068i
$629$		0			0
$630$		0			0
$631$	−0.264241	+	0.105786i	−0.264241	+	0.105786i	−0.500000	−	0.866025i	$-0.666667\pi$
$631$	−0.264241	+	0.105786i	−0.264241	+	0.105786i	0.235759	+	0.971812i	$0.424242\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.0523681	−	1.09934i	−0.0523681	−	1.09934i
$637$		0			0
$638$		0			0
$639$	0.409619	+	0.322128i	0.409619	+	0.322128i
$640$		0			0
$641$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$641$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$642$		0			0
$643$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$643$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.341254	+	1.40667i	0.341254	+	1.40667i	0.841254	+	0.540641i	$0.181818\pi$
$647$	0.341254	+	1.40667i	0.341254	+	1.40667i	−0.500000	+	0.866025i	$0.666667\pi$
$648$		0			0
$649$	−0.642315	+	0.123796i	−0.642315	+	0.123796i
$650$		0			0
$651$		0			0
$652$	−0.911911	+	1.28060i	−0.911911	+	1.28060i
$653$	1.98193	−	0.189251i	1.98193	−	0.189251i	0.981929	−	0.189251i	$-0.0606061\pi$
$653$	1.98193	−	0.189251i	1.98193	−	0.189251i	1.00000			$0$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$659$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$660$	2.26092	+	2.15579i	2.26092	+	2.15579i
$661$	0.396666	+	0.254922i	0.396666	+	0.254922i	0.723734	−	0.690079i	$-0.242424\pi$
$661$	0.396666	+	0.254922i	0.396666	+	0.254922i	−0.327068	+	0.945001i	$0.606061\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−1.10059			−1.10059
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$673$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$674$		0			0
$675$	−2.24045	+	2.58562i	−2.24045	+	2.58562i
$676$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$677$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$677$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.02951	−	0.809616i	1.02951	−	0.809616i	0.0475819	−	0.998867i	$-0.484848\pi$
$683$	1.02951	−	0.809616i	1.02951	−	0.809616i	0.981929	+	0.189251i	$0.0606061\pi$
$684$		0			0
$685$	−1.56199	+	1.00383i	−1.56199	+	1.00383i
$686$		0			0
$687$	−3.28924	+	0.314085i	−3.28924	+	0.314085i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.981929	+	0.189251i	−0.981929	+	0.189251i	−0.654861	−	0.755750i	$-0.727273\pi$
$691$	−0.981929	+	0.189251i	−0.981929	+	0.189251i	−0.327068	+	0.945001i	$0.606061\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$701$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$702$		0			0
$703$		0			0
$704$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$705$	0.0700886	−	0.288909i	0.0700886	−	0.288909i
$706$		0			0
$707$		0			0
$708$	0.550294	−	0.953137i	0.550294	−	0.953137i
$709$	−1.84833	+	0.739959i	−1.84833	+	0.739959i	−0.888835	+	0.458227i	$0.848485\pi$
$709$	−1.84833	+	0.739959i	−1.84833	+	0.739959i	−0.959493	+	0.281733i	$0.909091\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.41712	−	3.10305i	1.41712	−	3.10305i
$714$		0			0
$715$		0			0
$716$	−1.88431	+	0.363170i	−1.88431	+	0.363170i
$717$		0			0
$718$		0			0
$719$	−1.15486	+	1.62177i	−1.15486	+	1.62177i	−0.500000	+	0.866025i	$0.666667\pi$
$719$	−1.15486	+	1.62177i	−1.15486	+	1.62177i	−0.654861	+	0.755750i	$0.727273\pi$
$720$	−3.38398	+	0.323130i	−3.38398	+	0.323130i
$721$		0			0
$722$		0			0
$723$		0			0
$724$	0.223734	−	0.175946i	0.223734	−	0.175946i
$725$		0			0
$726$		0			0
$727$	−0.947890	−	0.903811i	−0.947890	−	0.903811i	0.0475819	−	0.998867i	$-0.484848\pi$
$727$	−0.947890	−	0.903811i	−0.947890	−	0.903811i	−0.995472	+	0.0950560i	$0.969697\pi$
$728$		0			0
$729$	0.198939	−	1.38365i	0.198939	−	1.38365i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$733$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$734$		0			0
$735$	0.148645	−	3.12043i	0.148645	−	3.12043i
$736$		0			0
$737$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$738$		0			0
$739$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$739$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$740$	3.16697	+	0.929905i	3.16697	+	0.929905i
$741$		0			0
$742$		0			0
$743$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$743$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.0395325	+	0.0865641i	0.0395325	+	0.0865641i	0.928368	−	0.371662i	$-0.121212\pi$
$751$	0.0395325	+	0.0865641i	0.0395325	+	0.0865641i	−0.888835	+	0.458227i	$0.848485\pi$
$752$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i
$753$	3.24449	+	0.625325i	3.24449	+	0.625325i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.42131	−	1.35522i	1.42131	−	1.35522i	0.580057	−	0.814576i	$-0.303030\pi$
$757$	1.42131	−	1.35522i	1.42131	−	1.35522i	0.841254	−	0.540641i	$-0.181818\pi$
$758$		0			0
$759$	3.09792	−	0.909632i	3.09792	−	0.909632i
$760$		0			0
$761$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$761$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$762$		0			0
$763$		0			0
$764$	−0.308779	−	0.356349i	−0.308779	−	0.356349i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.32254	−	1.04006i	−1.32254	−	1.04006i
$769$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$769$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$770$		0			0
$771$	−0.0800569	−	1.68060i	−0.0800569	−	1.68060i
$772$		0			0
$773$	1.39734	+	1.09888i	1.39734	+	1.09888i	0.981929	+	0.189251i	$0.0606061\pi$
$773$	1.39734	+	1.09888i	1.39734	+	1.09888i	0.415415	+	0.909632i	$0.363636\pi$
$774$		0			0
$775$	2.17540	−	3.76790i	2.17540	−	3.76790i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i
$782$		0			0
$783$		0			0
$784$	0.723734	−	0.690079i	0.723734	−	0.690079i
$785$	3.28572	+	1.69391i	3.28572	+	1.69391i
$786$		0			0
$787$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$787$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−1.71910	−	1.10480i	−1.71910	−	1.10480i
$796$	0.142315	−	0.989821i	0.142315	−	0.989821i
$797$	1.16413	−	0.600149i	1.16413	−	0.600149i	0.235759	−	0.971812i	$-0.424242\pi$
$797$	1.16413	−	0.600149i	1.16413	−	0.600149i	0.928368	+	0.371662i	$0.121212\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	2.76167	+	0.810899i	2.76167	+	0.810899i
$802$		0			0
$803$		0			0
$804$	0.975950	−	1.37053i	0.975950	−	1.37053i
$805$		0			0
$806$		0			0
$807$	−2.99743	−	0.880124i	−2.99743	−	0.880124i
$808$		0			0
$809$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$809$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$810$		0			0
$811$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$811$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.954707	+	2.75844i	0.954707	+	2.75844i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$821$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$822$		0			0
$823$	−1.03115	−	0.531595i	−1.03115	−	0.531595i	−0.142315	−	0.989821i	$-0.545455\pi$
$823$	−1.03115	−	0.531595i	−1.03115	−	0.531595i	−0.888835	+	0.458227i	$0.848485\pi$
$824$		0			0
$825$	4.04347	−	0.779314i	4.04347	−	0.779314i
$826$		0			0
$827$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$827$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$828$	−1.45949	+	3.19584i	−1.45949	+	3.19584i
$829$	−0.279486	−	1.94387i	−0.279486	−	1.94387i	−0.327068	−	0.945001i	$-0.606061\pi$
$829$	−0.279486	−	1.94387i	−0.279486	−	1.94387i	0.0475819	−	0.998867i	$-0.484848\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.118239	−	2.48215i	−0.118239	−	2.48215i
$838$		0			0
$839$	0.273507	−	1.12741i	0.273507	−	1.12741i	−0.654861	−	0.755750i	$-0.727273\pi$
$839$	0.273507	−	1.12741i	0.273507	−	1.12741i	0.928368	−	0.371662i	$-0.121212\pi$
$840$		0			0
$841$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.07701	+	1.51245i	1.07701	+	1.51245i
$846$		0			0
$847$		0			0
$848$	−0.154218	−	0.635697i	−0.154218	−	0.635697i
$849$		0			0
$850$		0			0
$851$	2.46889	−	2.35408i	2.46889	−	2.35408i
$852$	0.425656	+	0.219441i	0.425656	+	0.219441i
$853$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$853$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$857$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$858$		0			0
$859$	1.56199	+	0.625325i	1.56199	+	0.625325i	0.981929	−	0.189251i	$-0.0606061\pi$
$859$	1.56199	+	0.625325i	1.56199	+	0.625325i	0.580057	+	0.814576i	$0.303030\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.279486	+	1.94387i	−0.279486	+	1.94387i	0.0475819	+	0.998867i	$0.484848\pi$
$863$	−0.279486	+	1.94387i	−0.279486	+	1.94387i	−0.327068	+	0.945001i	$0.606061\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.67489	−	0.159932i	−1.67489	−	0.159932i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.101063	−	2.12157i	0.101063	−	2.12157i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$877$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$878$		0			0
$879$		0			0
$880$	1.56199	+	1.00383i	1.56199	+	1.00383i
$881$	0.839614	+	0.800570i	0.839614	+	0.800570i	0.981929	−	0.189251i	$-0.0606061\pi$
$881$	0.839614	+	0.800570i	0.839614	+	0.800570i	−0.142315	+	0.989821i	$0.545455\pi$
$882$		0			0
$883$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i	0.415415	−	0.909632i	$-0.363636\pi$
$883$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i	−0.327068	+	0.945001i	$0.606061\pi$
$884$		0			0
$885$	−0.848901	−	1.85883i	−0.848901	−	1.85883i
$886$		0			0
$887$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$887$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.377144	−	0.359606i	0.377144	−	0.359606i
$892$	−0.642315	+	0.123796i	−0.642315	+	0.123796i
$893$		0			0
$894$		0			0
$895$	−1.48014	+	3.24106i	−1.48014	+	3.24106i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−2.24045	+	3.88057i	−2.24045	+	3.88057i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.0251462	−	0.527884i	−0.0251462	−	0.527884i
$906$		0			0
$907$	−1.54370	−	1.21398i	−1.54370	−	1.21398i	−0.888835	−	0.458227i	$-0.848485\pi$
$907$	−1.54370	−	1.21398i	−1.54370	−	1.21398i	−0.654861	−	0.755750i	$-0.727273\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.30379	+	1.50465i	1.30379	+	1.50465i	0.723734	+	0.690079i	$0.242424\pi$
$911$	1.30379	+	1.50465i	1.30379	+	1.50465i	0.580057	+	0.814576i	$0.303030\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.88431	+	0.553283i	−1.88431	+	0.553283i
$917$		0			0
$918$		0			0
$919$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$919$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	3.41995	−	2.68948i	3.41995	−	2.68948i
$926$		0			0
$927$	−0.282348	−	0.815790i	−0.282348	−	0.815790i
$928$		0			0
$929$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$929$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.27822	+	1.47515i	−1.27822	+	1.47515i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$	0.793332			0.793332
$940$	0.00840744	−	0.176494i	0.00840744	−	0.176494i
$941$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$941$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$942$		0			0
$943$		0			0
$944$	0.213947	−	0.618159i	0.213947	−	0.618159i
$945$		0			0
$946$		0			0
$947$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$947$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−0.623601	+	0.490405i	−0.623601	+	0.490405i
$952$		0			0
$953$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$953$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$954$		0			0
$955$	−0.871520	+	0.0832201i	−0.871520	+	0.0832201i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−2.99743	+	0.880124i	−2.99743	+	0.880124i
$961$	0.509266	+	2.09922i	0.509266	+	2.09922i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$967$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i	−0.786053	−	0.618159i	$-0.787879\pi$
$971$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i	0.723734	−	0.690079i	$-0.242424\pi$
$972$	−0.0247953	−	0.520518i	−0.0247953	−	0.520518i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.72373	−	0.690079i	1.72373	−	0.690079i	0.723734	−	0.690079i	$-0.242424\pi$
$977$	1.72373	−	0.690079i	1.72373	−	0.690079i	1.00000			$0$
$978$		0			0
$979$	−0.911911	−	1.28060i	−0.911911	−	1.28060i
$980$	−0.264241	−	1.83784i	−0.264241	−	1.83784i
$981$		0			0
$982$		0			0
$983$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$983$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.827068	−	1.81103i	−0.827068	−	1.81103i	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	−0.827068	−	1.81103i	−0.827068	−	1.81103i	−0.327068	−	0.945001i	$-0.606061\pi$
$992$		0			0
$993$	2.26092	+	0.905138i	2.26092	+	0.905138i
$994$		0			0
$995$	−1.34378	−	1.28129i	−1.34378	−	1.28129i
$996$		0			0
$997$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$997$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$998$		0			0
$999$	0.812753	−	2.34829i	0.812753	−	2.34829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	737.1.w.a.65.1	✓	20
11.10	odd	2	CM	737.1.w.a.65.1	✓	20
67.33	even	33	inner	737.1.w.a.703.1	yes	20
737.703	odd	66	inner	737.1.w.a.703.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
737.1.w.a.65.1	✓	20	1.1	even	1	trivial
737.1.w.a.65.1	✓	20	11.10	odd	2	CM
737.1.w.a.703.1	yes	20	67.33	even	33	inner
737.1.w.a.703.1	yes	20	737.703	odd	66	inner

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:	\( N \)	\(=\)	\( 737 = 11 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	737.w (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61435 - 0.474017i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-1.21590 + 1.40323i) q^{5} +(1.54019 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.61435 - 0.474017i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-1.21590 + 1.40323i) q^{5} +(1.54019 + 0.989821i) q^{9} +(-0.327068 - 0.945001i) q^{11} +(1.56199 + 0.625325i) q^{12} +(2.62805 - 1.68895i) q^{15} +(0.981929 + 0.189251i) q^{16} +(1.34378 - 1.28129i) q^{20} +(-0.452418 - 1.86489i) q^{23} +(-0.348311 - 2.42256i) q^{25} +(-0.915415 - 1.05645i) q^{27} +(1.39734 + 1.09888i) q^{31} +(0.0800569 + 1.68060i) q^{33} +(-1.43913 - 1.13174i) q^{36} +(0.888835 + 1.53951i) q^{37} +(0.235759 + 0.971812i) q^{44} +(-3.26167 + 0.957713i) q^{45} +(0.0688733 - 0.0656706i) q^{47} +(-1.49547 - 0.770969i) q^{48} +(0.580057 - 0.814576i) q^{49} +(-0.271738 - 0.595023i) q^{53} +(1.72373 + 0.690079i) q^{55} +(0.0930932 - 0.647478i) q^{59} +(-2.77670 + 1.43149i) q^{60} +(-0.959493 - 0.281733i) q^{64} +(0.235759 - 0.971812i) q^{67} +(-0.153628 + 3.22505i) q^{69} +(0.283341 + 0.0270558i) q^{71} +(-0.586036 + 4.07597i) q^{75} +(-1.45949 + 1.14776i) q^{80} +(0.216476 + 0.474017i) q^{81} +(1.50842 - 0.442913i) q^{89} +(0.273100 + 1.89945i) q^{92} +(-1.73492 - 2.43635i) q^{93} +(-0.580057 - 1.00469i) q^{97} +(0.431635 - 1.77922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} + q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 20 * q - 4 * q^3 + q^4 + 2 * q^5 - 6 * q^9	\( 20 q - 4 q^{3} + q^{4} + 2 q^{5} - 6 q^{9} + q^{11} + 2 q^{12} + 4 q^{15} + q^{16} - q^{20} - 9 q^{23} - 8 q^{27} - q^{31} - 9 q^{33} + 3 q^{36} - q^{37} + q^{44} - 5 q^{45} - q^{47} - 9 q^{48} + q^{49} + 2 q^{53} + 21 q^{55} + 2 q^{59} - 2 q^{60} - 2 q^{64} + q^{67} + 4 q^{69} + 2 q^{71} - 12 q^{80} + 12 q^{81} + 2 q^{89} - 4 q^{92} - 13 q^{93} - q^{97} + 3 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 + q^4 + 2 * q^5 - 6 * q^9 + q^11 + 2 * q^12 + 4 * q^15 + q^16 - q^20 - 9 * q^23 - 8 * q^27 - q^31 - 9 * q^33 + 3 * q^36 - q^37 + q^44 - 5 * q^45 - q^47 - 9 * q^48 + q^49 + 2 * q^53 + 21 * q^55 + 2 * q^59 - 2 * q^60 - 2 * q^64 + q^67 + 4 * q^69 + 2 * q^71 - 12 * q^80 + 12 * q^81 + 2 * q^89 - 4 * q^92 - 13 * q^93 - q^97 + 3 * q^99

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