LMFDB - Embedded newform 737.1.w.a.10.1

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			10.1
Root			$-0.786053 - 0.618159i$ of defining polynomial
Character	$\chi$	$=$	737.10
Dual form			737.1.w.a.516.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.273100 + 1.89945i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(0.815816 - 1.78639i) q^{5} +(-2.57385 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.273100 + 1.89945i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(0.815816 - 1.78639i) q^{5} +(-2.57385 + 0.755750i) q^{9} +(0.580057 + 0.814576i) q^{11} +(-1.88431 + 0.363170i) q^{12} +(3.61596 + 1.06174i) q^{15} +(-0.995472 + 0.0950560i) q^{16} +(1.82318 + 0.729892i) q^{20} +(0.223734 - 0.175946i) q^{23} +(-1.87076 - 2.15898i) q^{25} +(-1.34125 - 2.93694i) q^{27} +(-0.154218 - 0.445585i) q^{31} +(-1.38884 + 1.32425i) q^{33} +(-0.877362 - 2.53497i) q^{36} +(-0.235759 - 0.408346i) q^{37} +(-0.786053 + 0.618159i) q^{44} +(-0.749723 + 5.21444i) q^{45} +(1.34378 + 0.537970i) q^{47} +(-0.452418 - 1.86489i) q^{48} +(-0.888835 - 0.458227i) q^{49} +(0.975950 - 0.627205i) q^{53} +(1.92837 - 0.371662i) q^{55} +(-0.759713 + 0.876756i) q^{59} +(-0.888485 + 3.66238i) q^{60} +(-0.142315 - 0.989821i) q^{64} +(-0.786053 - 0.618159i) q^{67} +(0.395304 + 0.376921i) q^{69} +(-0.0623191 - 1.30824i) q^{71} +(3.58997 - 4.14305i) q^{75} +(-0.642315 + 1.85585i) q^{80} +(2.95561 - 1.89945i) q^{81} +(0.0930932 - 0.647478i) q^{89} +(0.186393 + 0.215109i) q^{92} +(0.804250 - 0.414620i) q^{93} +(0.888835 + 1.53951i) q^{97} +(-2.10859 - 1.65822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/737\mathbb{Z}\right)^\times$.

$n$	$68$	$672$
$\chi(n)$	$-1$	$e\left(\frac{8}{33}\right)$

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		−0.723734	−	0.690079i	$-0.757576\pi$
$2$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$3$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$3$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$4$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$5$	0.815816	−	1.78639i	0.815816	−	1.78639i	0.235759	−	0.971812i	$-0.424242\pi$
$5$	0.815816	−	1.78639i	0.815816	−	1.78639i	0.580057	−	0.814576i	$-0.303030\pi$
$6$		0			0
$7$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$7$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$8$		0			0
$9$	−2.57385	+	0.755750i	−2.57385	+	0.755750i
$10$		0			0
$11$	0.580057	+	0.814576i	0.580057	+	0.814576i
$11$	0.580057	+	0.814576i	0.580057	+	0.814576i
$12$	−1.88431	+	0.363170i	−1.88431	+	0.363170i
$13$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$13$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$14$		0			0
$15$	3.61596	+	1.06174i	3.61596	+	1.06174i
$16$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$17$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$17$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$18$		0			0
$19$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$19$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$20$	1.82318	+	0.729892i	1.82318	+	0.729892i
$21$		0			0
$22$		0			0
$23$	0.223734	−	0.175946i	0.223734	−	0.175946i	−0.500000	−	0.866025i	$-0.666667\pi$
$23$	0.223734	−	0.175946i	0.223734	−	0.175946i	0.723734	+	0.690079i	$0.242424\pi$
$24$		0			0
$25$	−1.87076	−	2.15898i	−1.87076	−	2.15898i
$26$		0			0
$27$	−1.34125	−	2.93694i	−1.34125	−	2.93694i
$28$		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
$31$	−0.154218	−	0.445585i	−0.154218	−	0.445585i	0.841254	−	0.540641i	$-0.181818\pi$
$31$	−0.154218	−	0.445585i	−0.154218	−	0.445585i	−0.995472	+	0.0950560i	$0.969697\pi$
$32$		0			0
$33$	−1.38884	+	1.32425i	−1.38884	+	1.32425i
$34$		0			0
$35$		0			0
$36$	−0.877362	−	2.53497i	−0.877362	−	2.53497i
$37$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	0.723734	−	0.690079i	$-0.242424\pi$
$37$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	−0.959493	+	0.281733i	$0.909091\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$41$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$42$		0			0
$43$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$43$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$44$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$45$	−0.749723	+	5.21444i	−0.749723	+	5.21444i
$46$		0			0
$47$	1.34378	+	0.537970i	1.34378	+	0.537970i	0.928368	−	0.371662i	$-0.121212\pi$
$47$	1.34378	+	0.537970i	1.34378	+	0.537970i	0.415415	+	0.909632i	$0.363636\pi$
$48$	−0.452418	−	1.86489i	−0.452418	−	1.86489i
$49$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.975950	−	0.627205i	0.975950	−	0.627205i	0.0475819	−	0.998867i	$-0.484848\pi$
$53$	0.975950	−	0.627205i	0.975950	−	0.627205i	0.928368	+	0.371662i	$0.121212\pi$
$54$		0			0
$55$	1.92837	−	0.371662i	1.92837	−	0.371662i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.759713	+	0.876756i	−0.759713	+	0.876756i	−0.995472	−	0.0950560i	$-0.969697\pi$
$59$	−0.759713	+	0.876756i	−0.759713	+	0.876756i	0.235759	+	0.971812i	$0.424242\pi$
$60$	−0.888485	+	3.66238i	−0.888485	+	3.66238i
$61$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$61$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$62$		0			0
$63$		0			0
$64$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$65$		0			0
$66$		0			0
$67$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$67$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$68$		0			0
$69$	0.395304	+	0.376921i	0.395304	+	0.376921i
$70$		0			0
$71$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i	−0.786053	−	0.618159i	$-0.787879\pi$
$71$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i	0.723734	−	0.690079i	$-0.242424\pi$
$72$		0			0
$73$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$73$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$74$		0			0
$75$	3.58997	−	4.14305i	3.58997	−	4.14305i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$79$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$80$	−0.642315	+	1.85585i	−0.642315	+	1.85585i
$81$	2.95561	−	1.89945i	2.95561	−	1.89945i
$82$		0			0
$83$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$83$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.0930932	−	0.647478i	0.0930932	−	0.647478i	−0.888835	−	0.458227i	$-0.848485\pi$
$89$	0.0930932	−	0.647478i	0.0930932	−	0.647478i	0.981929	−	0.189251i	$-0.0606061\pi$
$90$		0			0
$91$		0			0
$92$	0.186393	+	0.215109i	0.186393	+	0.215109i
$93$	0.804250	−	0.414620i	0.804250	−	0.414620i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.841254	+	0.540641i	$0.181818\pi$
$97$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.0475819	+	0.998867i	$0.484848\pi$
$98$		0			0
$99$	−2.10859	−	1.65822i	−2.10859	−	1.65822i
$100$	2.06752	−	1.97137i	2.06752	−	1.97137i
$101$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$101$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$102$		0			0
$103$	0.514186	+	1.48564i	0.514186	+	1.48564i	0.841254	+	0.540641i	$0.181818\pi$
$103$	0.514186	+	1.48564i	0.514186	+	1.48564i	−0.327068	+	0.945001i	$0.606061\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$107$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$108$	2.86979	−	1.47948i	2.86979	−	1.47948i
$109$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$109$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$110$		0			0
$111$	0.711249	−	0.559333i	0.711249	−	0.559333i
$112$		0			0
$113$	0.651174	+	0.0621796i	0.651174	+	0.0621796i	0.415415	−	0.909632i	$-0.363636\pi$
$113$	0.651174	+	0.0621796i	0.651174	+	0.0621796i	0.235759	+	0.971812i	$0.424242\pi$
$114$		0			0
$115$	−0.131783	−	0.543216i	−0.131783	−	0.543216i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$122$		0			0
$123$		0			0
$124$	0.437742	−	0.175245i	0.437742	−	0.175245i
$125$	−3.49866	+	1.02730i	−3.49866	+	1.02730i
$126$		0			0
$127$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$127$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$131$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$132$	−1.38884	−	1.32425i	−1.38884	−	1.32425i
$133$		0			0
$134$		0			0
$135$	−6.34072			−6.34072
$136$		0			0
$137$	0.142315	+	0.989821i	0.142315	+	0.989821i	0.928368	+	0.371662i	$0.121212\pi$
$137$	0.142315	+	0.989821i	0.142315	+	0.989821i	−0.786053	+	0.618159i	$0.787879\pi$
$138$		0			0
$139$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$139$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$140$		0			0
$141$	−0.654861	+	2.69937i	−0.654861	+	2.69937i
$142$		0			0
$143$		0			0
$144$	2.49035	−	0.996987i	2.49035	−	0.996987i
$145$		0			0
$146$		0			0
$147$	0.627639	−	1.81344i	0.627639	−	1.81344i
$148$	0.396666	−	0.254922i	0.396666	−	0.254922i
$149$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$149$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$150$		0			0
$151$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$151$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.921801	−	0.0880213i	−0.921801	−	0.0880213i
$156$		0			0
$157$	−0.0748038	+	0.0588264i	−0.0748038	+	0.0588264i	−0.654861	−	0.755750i	$-0.727273\pi$
$157$	−0.0748038	+	0.0588264i	−0.0748038	+	0.0588264i	0.580057	+	0.814576i	$0.303030\pi$
$158$		0			0
$159$	1.45788	+	1.68248i	1.45788	+	1.68248i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.327068	−	0.566498i	0.327068	−	0.566498i	−0.654861	−	0.755750i	$-0.727273\pi$
$163$	0.327068	−	0.566498i	0.327068	−	0.566498i	0.981929	+	0.189251i	$0.0606061\pi$
$164$		0			0
$165$	1.23259	+	3.56134i	1.23259	+	3.56134i
$166$		0			0
$167$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$167$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$168$		0			0
$169$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$173$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$174$		0			0
$175$		0			0
$176$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$177$	−1.87283	−	1.20360i	−1.87283	−	1.20360i
$178$		0			0
$179$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$179$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$180$	−5.24421	−	0.500761i	−5.24421	−	0.500761i
$181$	−1.21590	−	0.486774i	−1.21590	−	0.486774i	−0.327068	−	0.945001i	$-0.606061\pi$
$181$	−1.21590	−	0.486774i	−1.21590	−	0.486774i	−0.888835	+	0.458227i	$0.848485\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.921801	+	0.0880213i	−0.921801	+	0.0880213i
$186$		0			0
$187$		0			0
$188$	−0.473420	+	1.36786i	−0.473420	+	1.36786i
$189$		0			0
$190$		0			0
$191$	−1.45949	+	0.584293i	−1.45949	+	0.584293i	−0.959493	−	0.281733i	$-0.909091\pi$
$191$	−1.45949	+	0.584293i	−1.45949	+	0.584293i	−0.500000	+	0.866025i	$0.666667\pi$
$192$	1.84125	−	0.540641i	1.84125	−	0.540641i
$193$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$193$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$194$		0			0
$195$		0			0
$196$	0.415415	−	0.909632i	0.415415	−	0.909632i
$197$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$197$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$198$		0			0
$199$	−0.723734	−	0.690079i	−0.723734	−	0.690079i	0.235759	−	0.971812i	$-0.424242\pi$
$199$	−0.723734	−	0.690079i	−0.723734	−	0.690079i	−0.959493	+	0.281733i	$0.909091\pi$
$200$		0			0
$201$	0.959493	−	1.66189i	0.959493	−	1.66189i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.442886	+	0.621946i	−0.442886	+	0.621946i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$211$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$212$	0.672932	+	0.945001i	0.672932	+	0.945001i
$213$	2.46792	−	0.475652i	2.46792	−	0.475652i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.462997	+	1.90850i	0.462997	+	1.90850i
$221$		0			0
$222$		0			0
$223$	−0.165101	+	1.14831i	−0.165101	+	1.14831i	0.723734	+	0.690079i	$0.242424\pi$
$223$	−0.165101	+	1.14831i	−0.165101	+	1.14831i	−0.888835	+	0.458227i	$0.848485\pi$
$224$		0			0
$225$	6.44671	+	4.14305i	6.44671	+	4.14305i
$226$		0			0
$227$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$227$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$228$		0			0
$229$	−1.95496	−	0.376789i	−1.95496	−	0.376789i	−0.995472	−	0.0950560i	$-0.969697\pi$
$229$	−1.95496	−	0.376789i	−1.95496	−	0.376789i	−0.959493	−	0.281733i	$-0.909091\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$233$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$234$		0			0
$235$	2.05730	−	1.96163i	2.05730	−	1.96163i
$236$	−0.911911	−	0.717135i	−0.911911	−	0.717135i
$237$		0			0
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$	−3.70051	−	0.713215i	−3.70051	−	0.713215i
$241$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$241$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$242$		0			0
$243$	2.30075	+	2.65520i	2.30075	+	2.65520i
$244$		0			0
$245$	−1.54370	+	1.21398i	−1.54370	+	1.21398i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.0947329	+	1.98869i	−0.0947329	+	1.98869i	0.0475819	+	0.998867i	$0.484848\pi$
$251$	−0.0947329	+	1.98869i	−0.0947329	+	1.98869i	−0.142315	+	0.989821i	$0.545455\pi$
$252$		0			0
$253$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$254$		0			0
$255$		0			0
$256$	0.981929	−	0.189251i	0.981929	−	0.189251i
$257$	−0.580057	−	0.814576i	−0.580057	−	0.814576i	0.415415	−	0.909632i	$-0.363636\pi$
$257$	−0.580057	−	0.814576i	−0.580057	−	0.814576i	−0.995472	+	0.0950560i	$0.969697\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$263$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$264$		0			0
$265$	−0.324236	−	2.25511i	−0.324236	−	2.25511i
$266$		0			0
$267$	1.25528			1.25528
$268$	0.580057	−	0.814576i	0.580057	−	0.814576i
$269$	1.96386			1.96386			0.981929	−	0.189251i	$-0.0606061\pi$
$269$	1.96386			1.96386			0.981929	+	0.189251i	$0.0606061\pi$
$270$		0			0
$271$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$271$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.673501	−	2.77621i	0.673501	−	2.77621i
$276$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$277$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$277$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$278$		0			0
$279$	0.733685	+	1.03032i	0.733685	+	1.03032i
$280$		0			0
$281$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$281$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$282$		0			0
$283$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$283$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$284$	1.30379	−	0.124497i	1.30379	−	0.124497i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$290$		0			0
$291$	−2.68148	+	2.10874i	−2.68148	+	2.10874i
$292$		0			0
$293$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$293$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$294$		0			0
$295$	0.946439	+	2.07241i	0.946439	+	2.07241i
$296$		0			0
$297$	1.61435	−	2.79614i	1.61435	−	2.79614i
$298$		0			0
$299$		0			0
$300$	4.30917	+	3.38877i	4.30917	+	3.38877i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$307$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$308$		0			0
$309$	−2.68148	+	1.38240i	−2.68148	+	1.38240i
$310$		0			0
$311$	−1.49547	−	0.961081i	−1.49547	−	0.961081i	−0.995472	−	0.0950560i	$-0.969697\pi$
$311$	−1.49547	−	0.961081i	−1.49547	−	0.961081i	−0.500000	−	0.866025i	$-0.666667\pi$
$312$		0			0
$313$	0.223734	−	1.55610i	0.223734	−	1.55610i	−0.500000	−	0.866025i	$-0.666667\pi$
$313$	0.223734	−	1.55610i	0.223734	−	1.55610i	0.723734	−	0.690079i	$-0.242424\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.39734	+	0.720381i	1.39734	+	0.720381i	0.981929	−	0.189251i	$-0.0606061\pi$
$317$	1.39734	+	0.720381i	1.39734	+	0.720381i	0.415415	+	0.909632i	$0.363636\pi$
$318$		0			0
$319$		0			0
$320$	−1.88431	−	0.553283i	−1.88431	−	0.553283i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	2.03794	+	2.86188i	2.03794	+	2.86188i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.0883470	+	1.85463i	0.0883470	+	1.85463i	0.415415	+	0.909632i	$0.363636\pi$
$331$	0.0883470	+	1.85463i	0.0883470	+	1.85463i	−0.327068	+	0.945001i	$0.606061\pi$
$332$		0			0
$333$	0.915415	+	0.872846i	0.915415	+	0.872846i
$334$		0			0
$335$	−1.74555	+	0.899892i	−1.74555	+	0.899892i
$336$		0			0
$337$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$337$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$338$		0			0
$339$	0.0597285	+	1.25386i	0.0597285	+	1.25386i
$340$		0			0
$341$	0.273507	−	0.384087i	0.273507	−	0.384087i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.995823	−	0.398667i	0.995823	−	0.398667i
$346$		0			0
$347$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$347$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$348$		0			0
$349$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$349$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.327068	−	0.945001i	$-0.606061\pi$
$353$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.959493	+	0.281733i	$0.909091\pi$
$354$		0			0
$355$	−2.38786	−	0.955955i	−2.38786	−	0.955955i
$356$	0.651174	+	0.0621796i	0.651174	+	0.0621796i
$357$		0			0
$358$		0			0
$359$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$359$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$360$		0			0
$361$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$362$		0			0
$363$	−1.88431	−	0.363170i	−1.88431	−	0.363170i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.786053	+	0.618159i	0.786053	+	0.618159i	0.928368	−	0.371662i	$-0.121212\pi$
$367$	0.786053	+	0.618159i	0.786053	+	0.618159i	−0.142315	+	0.989821i	$0.545455\pi$
$368$	−0.205996	+	0.196417i	−0.205996	+	0.196417i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.452418	+	0.783611i	0.452418	+	0.783611i
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−2.90679	−	6.36499i	−2.90679	−	6.36499i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.653077	+	0.513585i	−0.653077	+	0.513585i	−0.888835	−	0.458227i	$-0.848485\pi$
$379$	−0.653077	+	0.513585i	−0.653077	+	0.513585i	0.235759	+	0.971812i	$0.424242\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.419102	−	1.72756i	−0.419102	−	1.72756i	−0.654861	−	0.755750i	$-0.727273\pi$
$383$	−0.419102	−	1.72756i	−0.419102	−	1.72756i	0.235759	−	0.971812i	$-0.424242\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−1.49547	+	0.961081i	−1.49547	+	0.961081i
$389$	0.514186	−	1.48564i	0.514186	−	1.48564i	−0.327068	−	0.945001i	$-0.606061\pi$
$389$	0.514186	−	1.48564i	0.514186	−	1.48564i	0.841254	−	0.540641i	$-0.181818\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$	1.55601	−	2.18511i	1.55601	−	2.18511i
$397$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$397$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$398$		0			0
$399$		0			0
$400$	2.06752	+	1.97137i	2.06752	+	1.97137i
$401$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$401$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.981929	−	6.82946i	−0.981929	−	6.82946i
$406$		0			0
$407$	0.195876	−	0.428908i	0.195876	−	0.428908i
$408$		0			0
$409$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$409$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$410$		0			0
$411$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$412$	−1.45949	+	0.584293i	−1.45949	+	0.584293i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i	0.235759	+	0.971812i	$0.424242\pi$
$419$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i	−0.327068	+	0.945001i	$0.606061\pi$
$420$		0			0
$421$	0.195876	+	0.807410i	0.195876	+	0.807410i	0.981929	+	0.189251i	$0.0606061\pi$
$421$	0.195876	+	0.807410i	0.195876	+	0.807410i	−0.786053	+	0.618159i	$0.787879\pi$
$422$		0			0
$423$	−3.86526	−	0.369088i	−3.86526	−	0.369088i
$424$		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	$0.666667\pi$
$432$	1.61435	+	2.79614i	1.61435	+	2.79614i
$433$	−0.607279	−	1.75462i	−0.607279	−	1.75462i	−0.654861	−	0.755750i	$-0.727273\pi$
$433$	−0.607279	−	1.75462i	−0.607279	−	1.75462i	0.0475819	−	0.998867i	$-0.484848\pi$
$434$		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
$441$	2.63403	+	0.507668i	2.63403	+	0.507668i
$442$		0			0
$443$	1.76962	−	0.912303i	1.76962	−	0.912303i	0.841254	−	0.540641i	$-0.181818\pi$
$443$	1.76962	−	0.912303i	1.76962	−	0.912303i	0.928368	−	0.371662i	$-0.121212\pi$
$444$	0.592542	+	0.683830i	0.592542	+	0.683830i
$445$	−1.08070	−	0.694523i	−1.08070	−	0.694523i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.928368	−	0.371662i	−0.928368	−	0.371662i	−0.142315	−	0.989821i	$-0.545455\pi$
$449$	−0.928368	−	0.371662i	−0.928368	−	0.371662i	−0.786053	+	0.618159i	$0.787879\pi$
$450$		0			0
$451$		0			0
$452$	−0.0311250	+	0.653395i	−0.0311250	+	0.653395i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$457$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$458$		0			0
$459$		0			0
$460$	0.536330	−	0.157481i	0.536330	−	0.157481i
$461$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$461$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$462$		0			0
$463$	−0.759713	+	1.06687i	−0.759713	+	1.06687i	0.235759	+	0.971812i	$0.424242\pi$
$463$	−0.759713	+	1.06687i	−0.759713	+	1.06687i	−0.995472	+	0.0950560i	$0.969697\pi$
$464$		0			0
$465$	−0.0845516	−	1.77496i	−0.0845516	−	1.77496i
$466$		0			0
$467$	1.42131	+	1.35522i	1.42131	+	1.35522i	0.841254	+	0.540641i	$0.181818\pi$
$467$	1.42131	+	1.35522i	1.42131	+	1.35522i	0.580057	+	0.814576i	$0.303030\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.132167	−	0.126021i	−0.132167	−	0.126021i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−2.03794	+	2.35190i	−2.03794	+	2.35190i
$478$		0			0
$479$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$479$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$485$	3.47528	−	0.331849i	3.47528	−	0.331849i
$486$		0			0
$487$	1.76962	+	0.912303i	1.76962	+	0.912303i	0.928368	+	0.371662i	$0.121212\pi$
$487$	1.76962	+	0.912303i	1.76962	+	0.912303i	0.841254	+	0.540641i	$0.181818\pi$
$488$		0			0
$489$	1.16536	+	0.466540i	1.16536	+	0.466540i
$490$		0			0
$491$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$491$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−4.68244	+	2.41397i	−4.68244	+	2.41397i
$496$	0.195876	+	0.428908i	0.195876	+	0.428908i
$497$		0			0
$498$		0			0
$499$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	−0.888835	−	0.458227i	$-0.848485\pi$
$499$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	0.0475819	−	0.998867i	$-0.484848\pi$
$500$	−1.19261	−	3.44582i	−1.19261	−	3.44582i
$501$		0			0
$502$		0			0
$503$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$503$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.959493	−	1.66189i	0.959493	−	1.66189i
$508$		0			0
$509$	0.771316	+	1.68895i	0.771316	+	1.68895i	0.723734	+	0.690079i	$0.242424\pi$
$509$	0.771316	+	1.68895i	0.771316	+	1.68895i	0.0475819	+	0.998867i	$0.484848\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.07341	+	0.293475i	3.07341	+	0.293475i
$516$		0			0
$517$	0.341254	+	1.40667i	0.341254	+	1.40667i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$521$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$522$		0			0
$523$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$523$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.25667	−	1.45027i	1.25667	−	1.45027i
$529$	−0.216659	+	0.893081i	−0.216659	+	0.893081i
$530$		0			0
$531$	1.29278	−	2.83079i	1.29278	−	2.83079i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.546200			0.546200
$538$		0			0
$539$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$540$	−0.301704	−	6.33354i	−0.301704	−	6.33354i
$541$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$541$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$542$		0			0
$543$	0.592542	−	2.44249i	0.592542	−	2.44249i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$547$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$548$	−0.981929	+	0.189251i	−0.981929	+	0.189251i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.418936	−	1.72688i	−0.418936	−	1.72688i
$556$		0			0
$557$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$557$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$563$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$564$	−2.72747	−	0.525678i	−2.72747	−	0.525678i
$565$	0.642315	−	1.11252i	0.642315	−	1.11252i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$569$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$570$		0			0
$571$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$571$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$572$		0			0
$573$	−1.50842	−	2.61267i	−1.50842	−	2.61267i
$574$		0			0
$575$	−0.798418	−	0.153882i	−0.798418	−	0.153882i
$576$	1.11435	+	2.44009i	1.11435	+	2.44009i
$577$	−1.49547	+	0.770969i	−1.49547	+	0.770969i	−0.995472	−	0.0950560i	$-0.969697\pi$
$577$	−1.49547	+	0.770969i	−1.49547	+	0.770969i	−0.500000	+	0.866025i	$0.666667\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.07701	+	0.431171i	1.07701	+	0.431171i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.469383	+	0.0448206i	−0.469383	+	0.0448206i	−0.327068	−	0.945001i	$-0.606061\pi$
$587$	−0.469383	+	0.0448206i	−0.469383	+	0.0448206i	−0.142315	+	0.989821i	$0.545455\pi$
$588$	1.84125	+	0.540641i	1.84125	+	0.540641i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.273507	+	0.384087i	0.273507	+	0.384087i
$593$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$593$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.11312	−	1.56316i	1.11312	−	1.56316i
$598$		0			0
$599$	−0.0748038	−	1.57033i	−0.0748038	−	1.57033i	−0.654861	−	0.755750i	$-0.727273\pi$
$599$	−0.0748038	−	1.57033i	−0.0748038	−	1.57033i	0.580057	−	0.814576i	$-0.303030\pi$
$600$		0			0
$601$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$601$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$602$		0			0
$603$	2.49035	+	0.996987i	2.49035	+	0.996987i
$604$		0			0
$605$	1.42131	+	1.35522i	1.42131	+	1.35522i
$606$		0			0
$607$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$607$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$613$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.56199	−	1.00383i	1.56199	−	1.00383i	0.580057	−	0.814576i	$-0.303030\pi$
$617$	1.56199	−	1.00383i	1.56199	−	1.00383i	0.981929	−	0.189251i	$-0.0606061\pi$
$618$		0			0
$619$	0.283341	−	0.0270558i	0.283341	−	0.0270558i	0.0475819	−	0.998867i	$-0.484848\pi$
$619$	0.283341	−	0.0270558i	0.283341	−	0.0270558i	0.235759	+	0.971812i	$0.424242\pi$
$620$	0.0440606	−	0.924945i	0.0440606	−	0.924945i
$621$	−0.816827	−	0.421104i	−0.816827	−	0.421104i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.612552	+	4.26039i	−0.612552	+	4.26039i
$626$		0			0
$627$		0			0
$628$	−0.0623191	−	0.0719200i	−0.0623191	−	0.0719200i
$629$		0			0
$630$		0			0
$631$	−1.28605	−	0.247866i	−1.28605	−	0.247866i	−0.500000	−	0.866025i	$-0.666667\pi$
$631$	−1.28605	−	0.247866i	−1.28605	−	0.247866i	−0.786053	+	0.618159i	$0.787879\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−1.61121	+	1.53628i	−1.61121	+	1.53628i
$637$		0			0
$638$		0			0
$639$	1.14910	+	3.32011i	1.14910	+	3.32011i
$640$		0			0
$641$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$641$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$642$		0			0
$643$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$643$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.45949	+	1.14776i	−1.45949	+	1.14776i	−0.500000	+	0.866025i	$0.666667\pi$
$647$	−1.45949	+	1.14776i	−1.45949	+	1.14776i	−0.959493	+	0.281733i	$0.909091\pi$
$648$		0			0
$649$	−1.15486	−	0.110276i	−1.15486	−	0.110276i
$650$		0			0
$651$		0			0
$652$	0.581419	+	0.299742i	0.581419	+	0.299742i
$653$	0.00452808	−	0.0950560i	0.00452808	−	0.0950560i	−0.995472	−	0.0950560i	$-0.969697\pi$
$653$	0.00452808	−	0.0950560i	0.00452808	−	0.0950560i	1.00000			$0$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$659$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$660$	−3.49866	+	1.40065i	−3.49866	+	1.40065i
$661$	1.50842	−	0.442913i	1.50842	−	0.442913i	0.580057	−	0.814576i	$-0.303030\pi$
$661$	1.50842	−	0.442913i	1.50842	−	0.442913i	0.928368	+	0.371662i	$0.121212\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−2.22624			−2.22624
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$673$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$674$		0			0
$675$	−3.83161	+	8.39005i	−3.83161	+	8.39005i
$676$	0.580057	−	0.814576i	0.580057	−	0.814576i
$677$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$677$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.271738	+	0.785135i	−0.271738	+	0.785135i	0.723734	+	0.690079i	$0.242424\pi$
$683$	−0.271738	+	0.785135i	−0.271738	+	0.785135i	−0.995472	+	0.0950560i	$0.969697\pi$
$684$		0			0
$685$	1.88431	+	0.553283i	1.88431	+	0.553283i
$686$		0			0
$687$	0.181791	−	3.81627i	0.181791	−	3.81627i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.995472	+	0.0950560i	0.995472	+	0.0950560i	0.580057	−	0.814576i	$-0.303030\pi$
$691$	0.995472	+	0.0950560i	0.995472	+	0.0950560i	0.415415	+	0.909632i	$0.363636\pi$
$692$		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		−0.327068	−	0.945001i	$-0.606061\pi$
$701$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$702$		0			0
$703$		0			0
$704$	0.723734	−	0.690079i	0.723734	−	0.690079i
$705$	4.28788	+	3.37203i	4.28788	+	3.37203i
$706$		0			0
$707$		0			0
$708$	1.11312	−	1.92798i	1.11312	−	1.92798i
$709$	0.0934441	+	0.0180099i	0.0934441	+	0.0180099i	0.235759	−	0.971812i	$-0.424242\pi$
$709$	0.0934441	+	0.0180099i	0.0934441	+	0.0180099i	−0.142315	+	0.989821i	$0.545455\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.112903	−	0.0725583i	−0.112903	−	0.0725583i
$714$		0			0
$715$		0			0
$716$	0.283341	+	0.0270558i	0.283341	+	0.0270558i
$717$		0			0
$718$		0			0
$719$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i	0.415415	−	0.909632i	$-0.363636\pi$
$719$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i	−0.500000	+	0.866025i	$0.666667\pi$
$720$	0.250664	−	5.26209i	0.250664	−	5.26209i
$721$		0			0
$722$		0			0
$723$		0			0
$724$	0.428368	−	1.23769i	0.428368	−	1.23769i
$725$		0			0
$726$		0			0
$727$	0.771316	−	0.308788i	0.771316	−	0.308788i	0.0475819	−	0.998867i	$-0.484848\pi$
$727$	0.771316	−	0.308788i	0.771316	−	0.308788i	0.723734	+	0.690079i	$0.242424\pi$
$728$		0			0
$729$	−2.11435	+	2.44009i	−2.11435	+	2.44009i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$733$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$734$		0			0
$735$	−2.72747	−	2.60064i	−2.72747	−	2.60064i
$736$		0			0
$737$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$738$		0			0
$739$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$739$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$740$	−0.131783	−	0.916569i	−0.131783	−	0.916569i
$741$		0			0
$742$		0			0
$743$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$743$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.21769	−	0.782560i	1.21769	−	0.782560i	0.235759	−	0.971812i	$-0.424242\pi$
$751$	1.21769	−	0.782560i	1.21769	−	0.782560i	0.981929	+	0.189251i	$0.0606061\pi$
$752$	−1.38884	−	0.407799i	−1.38884	−	0.407799i
$753$	−3.80329	+	0.363170i	−3.80329	+	0.363170i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.84833	−	0.739959i	−1.84833	−	0.739959i	−0.959493	−	0.281733i	$-0.909091\pi$
$757$	−1.84833	−	0.739959i	−1.84833	−	0.739959i	−0.888835	−	0.458227i	$-0.848485\pi$
$758$		0			0
$759$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$760$		0			0
$761$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$761$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$762$		0			0
$763$		0			0
$764$	−0.653077	−	1.43004i	−0.653077	−	1.43004i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.627639	+	1.81344i	0.627639	+	1.81344i
$769$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$769$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$770$		0			0
$771$	1.38884	−	1.32425i	1.38884	−	1.32425i
$772$		0			0
$773$	−0.154218	−	0.445585i	−0.154218	−	0.445585i	0.841254	−	0.540641i	$-0.181818\pi$
$773$	−0.154218	−	0.445585i	−0.154218	−	0.445585i	−0.995472	+	0.0950560i	$0.969697\pi$
$774$		0			0
$775$	−0.673501	+	1.16654i	−0.673501	+	1.16654i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	1.02951	−	0.809616i	1.02951	−	0.809616i
$782$		0			0
$783$		0			0
$784$	0.928368	+	0.371662i	0.928368	+	0.371662i
$785$	0.0440606	+	0.181620i	0.0440606	+	0.181620i
$786$		0			0
$787$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$787$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	4.19492	−	1.23174i	4.19492	−	1.23174i
$796$	0.654861	−	0.755750i	0.654861	−	0.755750i
$797$	0.195876	−	0.807410i	0.195876	−	0.807410i	−0.786053	−	0.618159i	$-0.787879\pi$
$797$	0.195876	−	0.807410i	0.195876	−	0.807410i	0.981929	−	0.189251i	$-0.0606061\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	0.249723	+	1.73686i	0.249723	+	1.73686i
$802$		0			0
$803$		0			0
$804$	1.70566	+	0.879330i	1.70566	+	0.879330i
$805$		0			0
$806$		0			0
$807$	0.536330	+	3.73026i	0.536330	+	3.73026i
$808$		0			0
$809$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$809$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$810$		0			0
$811$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$811$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.745158	−	1.04643i	−0.745158	−	1.04643i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$821$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$822$		0			0
$823$	−0.419102	−	1.72756i	−0.419102	−	1.72756i	−0.654861	−	0.755750i	$-0.727273\pi$
$823$	−0.419102	−	1.72756i	−0.419102	−	1.72756i	0.235759	−	0.971812i	$-0.424242\pi$
$824$		0			0
$825$	5.45721	+	0.521101i	5.45721	+	0.521101i
$826$		0			0
$827$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$827$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$828$	−0.642315	−	0.412791i	−0.642315	−	0.412791i
$829$	1.30379	+	1.50465i	1.30379	+	1.50465i	0.723734	+	0.690079i	$0.242424\pi$
$829$	1.30379	+	1.50465i	1.30379	+	1.50465i	0.580057	+	0.814576i	$0.303030\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.10181	+	1.05057i	−1.10181	+	1.05057i
$838$		0			0
$839$	1.39734	+	1.09888i	1.39734	+	1.09888i	0.981929	+	0.189251i	$0.0606061\pi$
$839$	1.39734	+	1.09888i	1.39734	+	1.09888i	0.415415	+	0.909632i	$0.363636\pi$
$840$		0			0
$841$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.74555	+	0.899892i	−1.74555	+	0.899892i
$846$		0			0
$847$		0			0
$848$	−0.911911	+	0.717135i	−0.911911	+	0.717135i
$849$		0			0
$850$		0			0
$851$	−0.124594	−	0.0498801i	−0.124594	−	0.0498801i
$852$	0.592542	+	2.44249i	0.592542	+	2.44249i
$853$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$853$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$857$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$858$		0			0
$859$	−1.88431	+	0.363170i	−1.88431	+	0.363170i	−0.995472	−	0.0950560i	$-0.969697\pi$
$859$	−1.88431	+	0.363170i	−1.88431	+	0.363170i	−0.888835	+	0.458227i	$0.848485\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.30379	−	1.50465i	1.30379	−	1.50465i	0.580057	−	0.814576i	$-0.303030\pi$
$863$	1.30379	−	1.50465i	1.30379	−	1.50465i	0.723734	−	0.690079i	$-0.242424\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.0913090	−	1.91681i	−0.0913090	−	1.91681i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−3.45121	−	3.29072i	−3.45121	−	3.29072i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$877$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$878$		0			0
$879$		0			0
$880$	−1.88431	+	0.553283i	−1.88431	+	0.553283i
$881$	−1.65033	+	0.660694i	−1.65033	+	0.660694i	−0.995472	−	0.0950560i	$-0.969697\pi$
$881$	−1.65033	+	0.660694i	−1.65033	+	0.660694i	−0.654861	+	0.755750i	$0.727273\pi$
$882$		0			0
$883$	1.42131	−	0.273935i	1.42131	−	0.273935i	0.580057	−	0.814576i	$-0.303030\pi$
$883$	1.42131	−	0.273935i	1.42131	−	0.273935i	0.841254	+	0.540641i	$0.181818\pi$
$884$		0			0
$885$	−3.67798	+	2.36369i	−3.67798	+	2.36369i
$886$		0			0
$887$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$887$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	3.26167	+	1.30578i	3.26167	+	1.30578i
$892$	−1.15486	−	0.110276i	−1.15486	−	0.110276i
$893$		0			0
$894$		0			0
$895$	−0.470237	−	0.302203i	−0.470237	−	0.302203i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−3.83161	+	6.63654i	−3.83161	+	6.63654i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.86152	+	1.77496i	−1.86152	+	1.77496i
$906$		0			0
$907$	0.651174	+	1.88144i	0.651174	+	1.88144i	0.415415	+	0.909632i	$0.363636\pi$
$907$	0.651174	+	1.88144i	0.651174	+	1.88144i	0.235759	+	0.971812i	$0.424242\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.0395325	+	0.0865641i	0.0395325	+	0.0865641i	0.928368	−	0.371662i	$-0.121212\pi$
$911$	0.0395325	+	0.0865641i	0.0395325	+	0.0865641i	−0.888835	+	0.458227i	$0.848485\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.283341	−	1.97068i	0.283341	−	1.97068i
$917$		0			0
$918$		0			0
$919$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$919$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.440561	+	1.27292i	−0.440561	+	1.27292i
$926$		0			0
$927$	−2.44621	−	3.43522i	−2.44621	−	3.43522i
$928$		0			0
$929$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$929$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.41712	−	3.10305i	1.41712	−	3.10305i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$	3.01685			3.01685
$940$	2.05730	+	1.96163i	2.05730	+	1.96163i
$941$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$941$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$942$		0			0
$943$		0			0
$944$	0.672932	−	0.945001i	0.672932	−	0.945001i
$945$		0			0
$946$		0			0
$947$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$947$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−0.986715	+	2.85093i	−0.986715	+	2.85093i
$952$		0			0
$953$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$953$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$954$		0			0
$955$	−0.146904	+	3.08390i	−0.146904	+	3.08390i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.536330	−	3.73026i	0.536330	−	3.73026i
$961$	0.611291	−	0.480724i	0.611291	−	0.480724i
$962$		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
$971$	0.601300	−	0.573338i	0.601300	−	0.573338i	−0.327068	−	0.945001i	$-0.606061\pi$
$971$	0.601300	−	0.573338i	0.601300	−	0.573338i	0.928368	+	0.371662i	$0.121212\pi$
$972$	−2.54272	+	2.42448i	−2.54272	+	2.42448i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.92837	+	0.371662i	1.92837	+	0.371662i	1.00000			$0$
$977$	1.92837	+	0.371662i	1.92837	+	0.371662i	0.928368	+	0.371662i	$0.121212\pi$
$978$		0			0
$979$	0.581419	−	0.299742i	0.581419	−	0.299742i
$980$	−1.28605	−	1.48418i	−1.28605	−	1.48418i
$981$		0			0
$982$		0			0
$983$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$983$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i	0.580057	+	0.814576i	$0.303030\pi$
$992$		0			0
$993$	−3.49866	+	0.674312i	−3.49866	+	0.674312i
$994$		0			0
$995$	−1.82318	+	0.729892i	−1.82318	+	0.729892i
$996$		0			0
$997$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$997$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$998$		0			0
$999$	−0.883075	+	1.24010i	−0.883075	+	1.24010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	737.1.w.a.10.1	✓	20
11.10	odd	2	CM	737.1.w.a.10.1	✓	20
67.47	even	33	inner	737.1.w.a.516.1	yes	20
737.516	odd	66	inner	737.1.w.a.516.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
737.1.w.a.10.1	✓	20	1.1	even	1	trivial
737.1.w.a.10.1	✓	20	11.10	odd	2	CM
737.1.w.a.516.1	yes	20	67.47	even	33	inner
737.1.w.a.516.1	yes	20	737.516	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)

\(f(q)\)	\(=\)	\(q+(0.273100 + 1.89945i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(0.815816 - 1.78639i) q^{5} +(-2.57385 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.273100 + 1.89945i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(0.815816 - 1.78639i) q^{5} +(-2.57385 + 0.755750i) q^{9} +(0.580057 + 0.814576i) q^{11} +(-1.88431 + 0.363170i) q^{12} +(3.61596 + 1.06174i) q^{15} +(-0.995472 + 0.0950560i) q^{16} +(1.82318 + 0.729892i) q^{20} +(0.223734 - 0.175946i) q^{23} +(-1.87076 - 2.15898i) q^{25} +(-1.34125 - 2.93694i) q^{27} +(-0.154218 - 0.445585i) q^{31} +(-1.38884 + 1.32425i) q^{33} +(-0.877362 - 2.53497i) q^{36} +(-0.235759 - 0.408346i) q^{37} +(-0.786053 + 0.618159i) q^{44} +(-0.749723 + 5.21444i) q^{45} +(1.34378 + 0.537970i) q^{47} +(-0.452418 - 1.86489i) q^{48} +(-0.888835 - 0.458227i) q^{49} +(0.975950 - 0.627205i) q^{53} +(1.92837 - 0.371662i) q^{55} +(-0.759713 + 0.876756i) q^{59} +(-0.888485 + 3.66238i) q^{60} +(-0.142315 - 0.989821i) q^{64} +(-0.786053 - 0.618159i) q^{67} +(0.395304 + 0.376921i) q^{69} +(-0.0623191 - 1.30824i) q^{71} +(3.58997 - 4.14305i) q^{75} +(-0.642315 + 1.85585i) q^{80} +(2.95561 - 1.89945i) q^{81} +(0.0930932 - 0.647478i) q^{89} +(0.186393 + 0.215109i) q^{92} +(0.804250 - 0.414620i) q^{93} +(0.888835 + 1.53951i) q^{97} +(-2.10859 - 1.65822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} + q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 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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