LMFDB - Embedded newform 1169.1.f.c.667.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1169,1,Mod(333,1169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("1169.333");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1169 = 7 \cdot 167 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1169.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.583406999768$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{7}]$
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			667.3
Root			$0.981929 - 0.189251i$ of defining polynomial
Character	$\chi$	$=$	1169.667
Dual form			1169.1.f.c.333.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.415415 + 0.719520i) q^{2} +(-0.928368 - 1.60798i) q^{3} +(0.154861 + 0.268227i) q^{4} +1.54263 q^{6} +(0.0475819 + 0.998867i) q^{7} -1.08816 q^{8} +(-1.22373 + 2.11957i) q^{9} +(-0.981929 - 1.70075i) q^{11} +(0.287535 - 0.498026i) q^{12} +(-0.738471 - 0.380708i) q^{14} +(0.297176 - 0.514723i) q^{16} +(-1.01671 - 1.76100i) q^{18} +(0.959493 - 1.66189i) q^{19} +(1.56199 - 1.00383i) q^{21} +1.63163 q^{22} +(1.01021 + 1.74973i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.68757 q^{27} +(-0.260554 + 0.167448i) q^{28} -1.77767 q^{29} +(-0.580057 - 1.00469i) q^{31} +(-0.297176 - 0.514723i) q^{32} +(-1.82318 + 3.15784i) q^{33} -0.758033 q^{36} +(0.797176 + 1.38075i) q^{38} +(0.0734014 + 1.54088i) q^{42} +(0.304124 - 0.526759i) q^{44} +(-0.235759 + 0.408346i) q^{47} -1.10355 q^{48} +(-0.995472 + 0.0950560i) q^{49} +0.830830 q^{50} +(-1.11646 + 1.93376i) q^{54} +(-0.0517765 - 1.08692i) q^{56} -3.56305 q^{57} +(0.738471 - 1.27907i) q^{58} +(0.142315 - 0.246497i) q^{61} +0.963857 q^{62} +(-2.17540 - 1.12149i) q^{63} +1.08816 q^{64} +(-1.51475 - 2.62363i) q^{66} +(1.33161 - 2.30642i) q^{72} +(-0.928368 + 1.60798i) q^{75} +0.594351 q^{76} +(1.65210 - 1.06174i) q^{77} +(-1.27132 - 2.20198i) q^{81} +(0.511143 + 0.263513i) q^{84} +(1.65033 + 2.85846i) q^{87} +(1.06849 + 1.85068i) q^{88} +(0.786053 - 1.36148i) q^{89} +(-1.07701 + 1.86544i) q^{93} +(-0.195876 - 0.339266i) q^{94} +(-0.551777 + 0.955705i) q^{96} -1.30972 q^{97} +(0.345139 - 0.755750i) q^{98} +4.80648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - q^{3} - 8 q^{4} + 4 q^{6} + q^{7} - 8 q^{8} - 11 q^{9} - q^{11} - 3 q^{12} + 2 q^{14} - 6 q^{16} + 2 q^{19} + 2 q^{21} + 4 q^{22} - 4 q^{24} - 10 q^{25} - 2 q^{27} - 6 q^{28} + 2 q^{29}+ \cdots + 18 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - q^3 - 8 * q^4 + 4 * q^6 + q^7 - 8 * q^8 - 11 * q^9 - q^11 - 3 * q^12 + 2 * q^14 - 6 * q^16 + 2 * q^19 + 2 * q^21 + 4 * q^22 - 4 * q^24 - 10 * q^25 - 2 * q^27 - 6 * q^28 + 2 * q^29 - q^31 + 6 * q^32 + q^33 + 22 * q^36 + 4 * q^38 + 20 * q^42 + 8 * q^44 - q^47 - 12 * q^48 + q^49 - 4 * q^50 - 20 * q^54 + 4 * q^56 + 4 * q^57 - 2 * q^58 + 2 * q^61 - 18 * q^62 + 8 * q^64 + 2 * q^66 + 11 * q^72 - q^75 - 12 * q^76 + 2 * q^77 - 12 * q^81 + 19 * q^84 + q^87 - 4 * q^88 - q^89 + q^93 - 2 * q^94 - 6 * q^96 - 4 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1169\mathbb{Z}\right)^\times$.

$n$	$673$	$836$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	−0.995472	−	0.0950560i	$-0.969697\pi$
$2$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	0.580057	+	0.814576i	$0.303030\pi$
$3$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.786053	−	0.618159i	$-0.787879\pi$
$3$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.142315	−	0.989821i	$-0.545455\pi$
$4$	0.154861	+	0.268227i	0.154861	+	0.268227i
$5$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$5$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$6$	1.54263			1.54263
$7$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$7$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$8$	−1.08816			−1.08816
$9$	−1.22373	+	2.11957i	−1.22373	+	2.11957i
$10$		0			0
$11$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.654861	−	0.755750i	$-0.727273\pi$
$11$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.327068	−	0.945001i	$-0.606061\pi$
$12$	0.287535	−	0.498026i	0.287535	−	0.498026i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	−0.738471	−	0.380708i	−0.738471	−	0.380708i
$15$		0			0
$16$	0.297176	−	0.514723i	0.297176	−	0.514723i
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$	−1.01671	−	1.76100i	−1.01671	−	1.76100i
$19$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$19$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$20$		0			0
$21$	1.56199	−	1.00383i	1.56199	−	1.00383i
$22$	1.63163			1.63163
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$	1.01021	+	1.74973i	1.01021	+	1.74973i
$25$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$26$		0			0
$27$	2.68757			2.68757
$28$	−0.260554	+	0.167448i	−0.260554	+	0.167448i
$29$	−1.77767			−1.77767			−0.888835	−	0.458227i	$-0.848485\pi$
$29$	−1.77767			−1.77767			−0.888835	+	0.458227i	$0.848485\pi$
$30$		0			0
$31$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$31$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$32$	−0.297176	−	0.514723i	−0.297176	−	0.514723i
$33$	−1.82318	+	3.15784i	−1.82318	+	3.15784i
$34$		0			0
$35$		0			0
$36$	−0.758033			−0.758033
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	0.797176	+	1.38075i	0.797176	+	1.38075i
$39$		0			0
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	0.0734014	+	1.54088i	0.0734014	+	1.54088i
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	0.304124	−	0.526759i	0.304124	−	0.526759i
$45$		0			0
$46$		0			0
$47$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$47$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$48$	−1.10355			−1.10355
$49$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$50$	0.830830			0.830830
$51$		0			0
$52$		0			0
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	−1.11646	+	1.93376i	−1.11646	+	1.93376i
$55$		0			0
$56$	−0.0517765	−	1.08692i	−0.0517765	−	1.08692i
$57$	−3.56305			−3.56305
$58$	0.738471	−	1.27907i	0.738471	−	1.27907i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$		0			0
$61$	0.142315	−	0.246497i	0.142315	−	0.246497i	−0.786053	−	0.618159i	$-0.787879\pi$
$61$	0.142315	−	0.246497i	0.142315	−	0.246497i	0.928368	+	0.371662i	$0.121212\pi$
$62$	0.963857			0.963857
$63$	−2.17540	−	1.12149i	−2.17540	−	1.12149i
$64$	1.08816			1.08816
$65$		0			0
$66$	−1.51475	−	2.62363i	−1.51475	−	2.62363i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	1.33161	−	2.30642i	1.33161	−	2.30642i
$73$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$73$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$74$		0			0
$75$	−0.928368	+	1.60798i	−0.928368	+	1.60798i
$76$	0.594351			0.594351
$77$	1.65210	−	1.06174i	1.65210	−	1.06174i
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$		0			0
$81$	−1.27132	−	2.20198i	−1.27132	−	2.20198i
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	0.511143	+	0.263513i	0.511143	+	0.263513i
$85$		0			0
$86$		0			0
$87$	1.65033	+	2.85846i	1.65033	+	2.85846i
$88$	1.06849	+	1.85068i	1.06849	+	1.85068i
$89$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$89$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.07701	+	1.86544i	−1.07701	+	1.86544i
$94$	−0.195876	−	0.339266i	−0.195876	−	0.339266i
$95$		0			0
$96$	−0.551777	+	0.955705i	−0.551777	+	0.955705i
$97$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$97$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$98$	0.345139	−	0.755750i	0.345139	−	0.755750i
$99$	4.80648			4.80648
$100$	0.154861	−	0.268227i	0.154861	−	0.268227i
$101$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$101$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$102$		0			0
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$107$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$108$	0.416198	+	0.720877i	0.416198	+	0.720877i
$109$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$109$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$110$		0			0
$111$		0			0
$112$	0.528280	+	0.272347i	0.528280	+	0.272347i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	1.48014	−	2.56369i	1.48014	−	2.56369i
$115$		0			0
$116$	−0.275291	−	0.476819i	−0.275291	−	0.476819i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.42837	+	2.47401i	−1.42837	+	2.47401i
$122$	0.118239	+	0.204797i	0.118239	+	0.204797i
$123$		0			0
$124$	0.179656	−	0.311173i	0.179656	−	0.311173i
$125$		0			0
$126$	1.71063	−	1.09936i	1.71063	−	1.09936i
$127$	−0.654136			−0.654136			−0.327068	−	0.945001i	$-0.606061\pi$
$127$	−0.654136			−0.654136			−0.327068	+	0.945001i	$0.606061\pi$
$128$	−0.154861	+	0.268227i	−0.154861	+	0.268227i
$129$		0			0
$130$		0			0
$131$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$131$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$132$	−1.12936			−1.12936
$133$	1.70566	+	0.879330i	1.70566	+	0.879330i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$137$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$138$		0			0
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$		0			0
$141$	0.875484			0.875484
$142$		0			0
$143$		0			0
$144$	0.727328	+	1.25977i	0.727328	+	1.25977i
$145$		0			0
$146$		0			0
$147$	1.07701	+	1.51245i	1.07701	+	1.51245i
$148$		0			0
$149$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$149$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$150$	−0.771316	−	1.33596i	−0.771316	−	1.33596i
$151$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$151$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$152$	−1.04408	+	1.80840i	−1.04408	+	1.80840i
$153$		0			0
$154$	0.0776362	+	1.62978i	0.0776362	+	1.62978i
$155$		0			0
$156$		0			0
$157$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.580057	+	0.814576i	$0.303030\pi$
$157$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.415415	+	0.909632i	$0.363636\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	2.11249			2.11249
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.00000			1.00000
$167$	1.00000			1.00000
$168$	−1.69968	+	1.09232i	−1.69968	+	1.09232i
$169$	1.00000			1.00000
$170$		0			0
$171$	2.34833	+	4.06742i	2.34833	+	4.06742i
$172$		0			0
$173$	0.327068	−	0.566498i	0.327068	−	0.566498i	−0.654861	−	0.755750i	$-0.727273\pi$
$173$	0.327068	−	0.566498i	0.327068	−	0.566498i	0.981929	+	0.189251i	$0.0606061\pi$
$174$	−2.74229			−2.74229
$175$	0.841254	−	0.540641i	0.841254	−	0.540641i
$176$	−1.16722			−1.16722
$177$		0			0
$178$	0.653077	+	1.13116i	0.653077	+	1.13116i
$179$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	0.723734	−	0.690079i	$-0.242424\pi$
$179$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	−0.959493	+	0.281733i	$0.909091\pi$
$180$		0			0
$181$	0.471518			0.471518			0.235759	−	0.971812i	$-0.424242\pi$
$181$	0.471518			0.471518			0.235759	+	0.971812i	$0.424242\pi$
$182$		0			0
$183$	−0.528482			−0.528482
$184$		0			0
$185$		0			0
$186$	−0.894814	−	1.54986i	−0.894814	−	1.54986i
$187$		0			0
$188$	−0.146039			−0.146039
$189$	0.127880	+	2.68452i	0.127880	+	2.68452i
$190$		0			0
$191$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$191$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$192$	−1.01021	−	1.74973i	−1.01021	−	1.74973i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$	0.544078	−	0.942371i	0.544078	−	0.942371i
$195$		0			0
$196$	−0.179656	−	0.252292i	−0.179656	−	0.252292i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−1.99668	+	3.45836i	−1.99668	+	3.45836i
$199$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$199$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$200$	0.544078	+	0.942371i	0.544078	+	0.942371i
$201$		0			0
$202$		0			0
$203$	−0.0845850	−	1.77566i	−0.0845850	−	1.77566i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.76861			−3.76861
$210$		0			0
$211$	−1.99094			−1.99094			−0.995472	−	0.0950560i	$-0.969697\pi$
$211$	−1.99094			−1.99094			−0.995472	+	0.0950560i	$0.969697\pi$
$212$		0			0
$213$		0			0
$214$	−0.0395325	−	0.0684723i	−0.0395325	−	0.0684723i
$215$		0			0
$216$	−2.92449			−2.92449
$217$	0.975950	−	0.627205i	0.975950	−	0.627205i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.57211			−1.57211			−0.786053	−	0.618159i	$-0.787879\pi$
$223$	−1.57211			−1.57211			−0.786053	+	0.618159i	$0.787879\pi$
$224$	0.500000	−	0.321330i	0.500000	−	0.321330i
$225$	2.44747			2.44747
$226$		0			0
$227$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$227$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$228$	−0.551777	−	0.955705i	−0.551777	−	0.955705i
$229$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$229$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$230$		0			0
$231$	−3.24102	−	1.67086i	−3.24102	−	1.67086i
$232$	1.93438			1.93438
$233$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$233$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$239$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$240$		0			0
$241$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$241$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$242$	−1.18673	−	2.05548i	−1.18673	−	2.05548i
$243$	−1.01671	+	1.76100i	−1.01671	+	1.76100i
$244$	0.0881559			0.0881559
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.631192	+	1.09326i	0.631192	+	1.09326i
$249$		0			0
$250$		0			0
$251$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$251$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$252$	−0.0360687	−	0.757175i	−0.0360687	−	0.757175i
$253$		0			0
$254$	0.271738	−	0.470664i	0.271738	−	0.470664i
$255$		0			0
$256$	0.415415	+	0.719520i	0.415415	+	0.719520i
$257$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$257$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	2.17540	−	3.76790i	2.17540	−	3.76790i
$262$		0			0
$263$	0.142315	+	0.246497i	0.142315	+	0.246497i	0.928368	−	0.371662i	$-0.121212\pi$
$263$	0.142315	+	0.246497i	0.142315	+	0.246497i	−0.786053	+	0.618159i	$0.787879\pi$
$264$	1.98391	−	3.43623i	1.98391	−	3.43623i
$265$		0			0
$266$	−1.34125	+	0.861971i	−1.34125	+	0.861971i
$267$	−2.91899			−2.91899
$268$		0			0
$269$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$269$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$270$		0			0
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$		0			0
$273$		0			0
$274$	−0.543476			−0.543476
$275$	−0.981929	+	1.70075i	−0.981929	+	1.70075i
$276$		0			0
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$	2.83934			2.83934
$280$		0			0
$281$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$281$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$282$	−0.363689	+	0.629928i	−0.363689	+	0.629928i
$283$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.654861	−	0.755750i	$-0.727273\pi$
$283$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.327068	−	0.945001i	$-0.606061\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.45466			1.45466
$289$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$290$		0			0
$291$	1.21590	+	2.10601i	1.21590	+	2.10601i
$292$		0			0
$293$	1.16011			1.16011			0.580057	−	0.814576i	$-0.303030\pi$
$293$	1.16011			1.16011			0.580057	+	0.814576i	$0.303030\pi$
$294$	−1.53565	+	0.146636i	−1.53565	+	0.146636i
$295$		0			0
$296$		0			0
$297$	−2.63900	−	4.57088i	−2.63900	−	4.57088i
$298$		0			0
$299$		0			0
$300$	−0.575071			−0.575071
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.570276	−	0.987747i	−0.570276	−	0.987747i
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	0.540633	+	0.278716i	0.540633	+	0.278716i
$309$		0			0
$310$		0			0
$311$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$311$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	−1.65414			−1.65414
$315$		0			0
$316$		0			0
$317$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$317$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$318$		0			0
$319$	1.74555	+	3.02337i	1.74555	+	3.02337i
$320$		0			0
$321$	0.176694			0.176694
$322$		0			0
$323$		0			0
$324$	0.393754	−	0.682002i	0.393754	−	0.682002i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.419102	−	0.216062i	−0.419102	−	0.216062i
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$		0			0
$334$	−0.415415	+	0.719520i	−0.415415	+	0.719520i
$335$		0			0
$336$	−0.0525092	−	1.10230i	−0.0525092	−	1.10230i
$337$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$337$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$338$	−0.415415	+	0.719520i	−0.415415	+	0.719520i
$339$		0			0
$340$		0			0
$341$	−1.13915	+	1.97306i	−1.13915	+	1.97306i
$342$	−3.90212			−3.90212
$343$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$344$		0			0
$345$		0			0
$346$	0.271738	+	0.470664i	0.271738	+	0.470664i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	−0.511143	+	0.885326i	−0.511143	+	0.885326i
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$	0.0395325	+	0.829889i	0.0395325	+	0.829889i
$351$		0			0
$352$	−0.583610	+	1.01084i	−0.583610	+	1.01084i
$353$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	0.841254	−	0.540641i	$-0.181818\pi$
$353$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	−0.888835	+	0.458227i	$0.848485\pi$
$354$		0			0
$355$		0			0
$356$	0.486915			0.486915
$357$		0			0
$358$	0.391751			0.391751
$359$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$359$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$360$		0			0
$361$	−1.34125	−	2.32312i	−1.34125	−	2.32312i
$362$	−0.195876	+	0.339266i	−0.195876	+	0.339266i
$363$	5.30420			5.30420
$364$		0			0
$365$		0			0
$366$	0.219539	−	0.380253i	0.219539	−	0.380253i
$367$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	−0.959493	−	0.281733i	$-0.909091\pi$
$367$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	0.235759	−	0.971812i	$-0.424242\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.667148			−0.667148
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$		0			0
$376$	0.256542	−	0.444345i	0.256542	−	0.444345i
$377$		0			0
$378$	−1.98469	−	1.02318i	−1.98469	−	1.02318i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	0.607279	+	1.05184i	0.607279	+	1.05184i
$382$	0.827068	+	1.43252i	0.827068	+	1.43252i
$383$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$383$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$384$	0.575071			0.575071
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−0.202824	−	0.351302i	−0.202824	−	0.351302i
$389$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$389$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$390$		0			0
$391$		0			0
$392$	1.08323	−	0.103436i	1.08323	−	0.103436i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	0.744335	+	1.28923i	0.744335	+	1.28923i
$397$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$397$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$398$	−0.543476			−0.543476
$399$	−0.169537	−	3.55901i	−0.169537	−	3.55901i
$400$	−0.594351			−0.594351
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	1.31276	+	0.676774i	1.31276	+	0.676774i
$407$		0			0
$408$		0			0
$409$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$409$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$410$		0			0
$411$	0.607279	−	1.05184i	0.607279	−	1.05184i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$	1.56554	−	2.71159i	1.56554	−	2.71159i
$419$	−1.99094			−1.99094			−0.995472	−	0.0950560i	$-0.969697\pi$
$419$	−1.99094			−1.99094			−0.995472	+	0.0950560i	$0.969697\pi$
$420$		0			0
$421$	0.0951638			0.0951638			0.0475819	−	0.998867i	$-0.484848\pi$
$421$	0.0951638			0.0951638			0.0475819	+	0.998867i	$0.484848\pi$
$422$	0.827068	−	1.43252i	0.827068	−	1.43252i
$423$	−0.577012	−	0.999415i	−0.577012	−	0.999415i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.252989	+	0.130425i	0.252989	+	0.130425i
$428$	−0.0294743			−0.0294743
$429$		0			0
$430$		0			0
$431$	0.786053	+	1.36148i	0.786053	+	1.36148i	0.928368	+	0.371662i	$0.121212\pi$
$431$	0.786053	+	1.36148i	0.786053	+	1.36148i	−0.142315	+	0.989821i	$0.545455\pi$
$432$	0.798679	−	1.38335i	0.798679	−	1.38335i
$433$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$433$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$434$	0.0458622	+	0.962766i	0.0458622	+	0.962766i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	1.01671	−	2.22630i	1.01671	−	2.22630i
$442$		0			0
$443$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$443$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$444$		0			0
$445$		0			0
$446$	0.653077	−	1.13116i	0.653077	−	1.13116i
$447$		0			0
$448$	0.0517765	+	1.08692i	0.0517765	+	1.08692i
$449$	0.471518			0.471518			0.235759	−	0.971812i	$-0.424242\pi$
$449$	0.471518			0.471518			0.235759	+	0.971812i	$0.424242\pi$
$450$	−1.01671	+	1.76100i	−1.01671	+	1.76100i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	3.87715			3.87715
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	0.738471	+	1.27907i	0.738471	+	1.27907i
$459$		0			0
$460$		0			0
$461$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$461$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$462$	2.54859	−	1.63788i	2.54859	−	1.63788i
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$	−0.528280	+	0.915008i	−0.528280	+	0.915008i
$465$		0			0
$466$	−0.481929	−	0.834725i	−0.481929	−	0.834725i
$467$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$467$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.84833	−	3.20140i	1.84833	−	3.20140i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−1.91899			−1.91899
$476$		0			0
$477$		0			0
$478$	−0.771316	+	1.33596i	−0.771316	+	1.33596i
$479$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$479$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.884792			−0.884792
$485$		0			0
$486$	−0.844717	−	1.46309i	−0.844717	−	1.46309i
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$	−0.154861	+	0.268227i	−0.154861	+	0.268227i
$489$		0			0
$490$		0			0
$491$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$491$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.689515			−0.689515
$497$		0			0
$498$		0			0
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$		0			0
$501$	−0.928368	−	1.60798i	−0.928368	−	1.60798i
$502$	−0.698939	+	1.21060i	−0.698939	+	1.21060i
$503$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$503$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$504$	2.36717	+	1.22036i	2.36717	+	1.22036i
$505$		0			0
$506$		0			0
$507$	−0.928368	−	1.60798i	−0.928368	−	1.60798i
$508$	−0.101300	−	0.175457i	−0.101300	−	0.175457i
$509$	0.654861	−	1.13425i	0.654861	−	1.13425i	−0.327068	−	0.945001i	$-0.606061\pi$
$509$	0.654861	−	1.13425i	0.654861	−	1.13425i	0.981929	−	0.189251i	$-0.0606061\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−1.00000
$513$	2.57870	−	4.46644i	2.57870	−	4.46644i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.925994			0.925994
$518$		0			0
$519$	−1.21456			−1.21456
$520$		0			0
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$	1.80738	+	3.13048i	1.80738	+	3.13048i
$523$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$523$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$524$		0			0
$525$	−1.65033	−	0.850806i	−1.65033	−	0.850806i
$526$	−0.236479			−0.236479
$527$		0			0
$528$	1.08361	+	1.87687i	1.08361	+	1.87687i
$529$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$530$		0			0
$531$		0			0
$532$	0.0282804	+	0.593678i	0.0282804	+	0.593678i
$533$		0			0
$534$	1.21259	−	2.10027i	1.21259	−	2.10027i
$535$		0			0
$536$		0			0
$537$	−0.437742	+	0.758192i	−0.437742	+	0.758192i
$538$		0			0
$539$	1.13915	+	1.59971i	1.13915	+	1.59971i
$540$		0			0
$541$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$541$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$542$		0			0
$543$	−0.437742	−	0.758192i	−0.437742	−	0.758192i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	−0.101300	+	0.175457i	−0.101300	+	0.175457i
$549$	0.348311	+	0.603292i	0.348311	+	0.603292i
$550$	−0.815816	−	1.41303i	−0.815816	−	1.41303i
$551$	−1.70566	+	2.95429i	−1.70566	+	2.95429i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.654861	+	1.13425i	0.654861	+	1.13425i	0.981929	+	0.189251i	$0.0606061\pi$
$557$	0.654861	+	1.13425i	0.654861	+	1.13425i	−0.327068	+	0.945001i	$0.606061\pi$
$558$	−1.17951	+	2.04296i	−1.17951	+	2.04296i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.118239	−	0.204797i	0.118239	−	0.204797i
$563$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	−0.959493	−	0.281733i	$-0.909091\pi$
$563$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	0.235759	−	0.971812i	$-0.424242\pi$
$564$	0.135578	+	0.234828i	0.135578	+	0.234828i
$565$		0			0
$566$	1.63163			1.63163
$567$	2.13900	−	1.37465i	2.13900	−	1.37465i
$568$		0			0
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$571$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$572$		0			0
$573$	−3.69666			−3.69666
$574$		0			0
$575$		0			0
$576$	−1.33161	+	2.30642i	−1.33161	+	2.30642i
$577$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	0.580057	−	0.814576i	$-0.303030\pi$
$577$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	−0.995472	+	0.0950560i	$0.969697\pi$
$578$	−0.415415	−	0.719520i	−0.415415	−	0.719520i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	−2.02042			−2.02042
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.481929	+	0.834725i	−0.481929	+	0.834725i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−0.238893	+	0.523103i	−0.238893	+	0.523103i
$589$	−2.22624			−2.22624
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$593$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$594$	4.38512			4.38512
$595$		0			0
$596$		0			0
$597$	0.607279	−	1.05184i	0.607279	−	1.05184i
$598$		0			0
$599$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	−0.888835	−	0.458227i	$-0.848485\pi$
$599$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	0.0475819	−	0.998867i	$-0.484848\pi$
$600$	1.01021	−	1.74973i	1.01021	−	1.74973i
$601$	0.0951638			0.0951638			0.0475819	−	0.998867i	$-0.484848\pi$
$601$	0.0951638			0.0951638			0.0475819	+	0.998867i	$0.484848\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	−1.14055			−1.14055
$609$	−2.77670	+	1.78447i	−2.77670	+	1.78447i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.580057	+	0.814576i	$0.303030\pi$
$613$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.415415	+	0.909632i	$0.363636\pi$
$614$		0			0
$615$		0			0
$616$	−1.79774	+	1.15534i	−1.79774	+	1.15534i
$617$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$617$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$618$		0			0
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$		0			0
$622$	−0.830830			−0.830830
$623$	1.39734	+	0.720381i	1.39734	+	0.720381i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$626$		0			0
$627$	3.49866	+	6.05986i	3.49866	+	6.05986i
$628$	−0.308319	+	0.534024i	−0.308319	+	0.534024i
$629$		0			0
$630$		0			0
$631$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$631$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$632$		0			0
$633$	1.84833	+	3.20140i	1.84833	+	3.20140i
$634$	−0.771316	−	1.33596i	−0.771316	−	1.33596i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−2.90050			−2.90050
$639$		0			0
$640$		0			0
$641$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$641$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$642$	−0.0734014	+	0.127135i	−0.0734014	+	0.127135i
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$647$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$648$	1.38339	+	2.39610i	1.38339	+	2.39610i
$649$		0			0
$650$		0			0
$651$	−1.91457	−	0.987031i	−1.91457	−	0.987031i
$652$		0			0
$653$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$653$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	0.329562	−	0.211797i	0.329562	−	0.211797i
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$661$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.154861	+	0.268227i	0.154861	+	0.268227i
$669$	1.45949	+	2.52792i	1.45949	+	2.52792i
$670$		0			0
$671$	−0.558972			−0.558972
$672$	−0.980877	−	0.505677i	−0.980877	−	0.505677i
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$	0.797176	−	1.38075i	0.797176	−	1.38075i
$675$	−1.34378	−	2.32750i	−1.34378	−	2.32750i
$676$	0.154861	+	0.268227i	0.154861	+	0.268227i
$677$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$677$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$678$		0			0
$679$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i
$680$		0			0
$681$		0			0
$682$	−0.946439	−	1.63928i	−0.946439	−	1.63928i
$683$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$683$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$684$	−0.727328	+	1.25977i	−0.727328	+	1.25977i
$685$		0			0
$686$	0.771316	+	0.308788i	0.771316	+	0.308788i
$687$	−3.30067			−3.30067
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$	0.202600			0.202600
$693$	0.228701	+	4.80103i	0.228701	+	4.80103i
$694$		0			0
$695$		0			0
$696$	−1.79582	−	3.11045i	−1.79582	−	3.11045i
$697$		0			0
$698$		0			0
$699$	2.15402			2.15402
$700$	0.275291	+	0.141923i	0.275291	+	0.141923i
$701$	−1.57211			−1.57211			−0.786053	−	0.618159i	$-0.787879\pi$
$701$	−1.57211			−1.57211			−0.786053	+	0.618159i	$0.787879\pi$
$702$		0			0
$703$		0			0
$704$	−1.06849	−	1.85068i	−1.06849	−	1.85068i
$705$		0			0
$706$	0.0790650			0.0790650
$707$		0			0
$708$		0			0
$709$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$709$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$	−0.855348	+	1.48151i	−0.855348	+	1.48151i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.0730196	−	0.126474i	0.0730196	−	0.126474i
$717$	−1.72373	−	2.98559i	−1.72373	−	2.98559i
$718$	−0.481929	−	0.834725i	−0.481929	−	0.834725i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$		0			0
$721$		0			0
$722$	2.22871			2.22871
$723$		0			0
$724$	0.0730196	+	0.126474i	0.0730196	+	0.126474i
$725$	0.888835	+	1.53951i	0.888835	+	1.53951i
$726$	−2.20345	+	3.81648i	−2.20345	+	3.81648i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	1.23291			1.23291
$730$		0			0
$731$		0			0
$732$	−0.0818411	−	0.141753i	−0.0818411	−	0.141753i
$733$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	0.235759	+	0.971812i	$0.424242\pi$
$733$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	−0.959493	+	0.281733i	$0.909091\pi$
$734$	1.20260			1.20260
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$743$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$744$	1.17196	−	2.02989i	1.17196	−	2.02989i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i
$750$		0			0
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$	0.140124	+	0.242701i	0.140124	+	0.242701i
$753$	−1.56199	−	2.70544i	−1.56199	−	2.70544i
$754$		0			0
$755$		0			0
$756$	−0.700257	+	0.450028i	−0.700257	+	0.450028i
$757$	1.96386			1.96386			0.981929	−	0.189251i	$-0.0606061\pi$
$757$	1.96386			1.96386			0.981929	+	0.189251i	$0.0606061\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.142315	−	0.246497i	0.142315	−	0.246497i	−0.786053	−	0.618159i	$-0.787879\pi$
$761$	0.142315	−	0.246497i	0.142315	−	0.246497i	0.928368	+	0.371662i	$0.121212\pi$
$762$	−1.00909			−1.00909
$763$		0			0
$764$	0.616638			0.616638
$765$		0			0
$766$	0.738471	+	1.27907i	0.738471	+	1.27907i
$767$		0			0
$768$	0.771316	−	1.33596i	0.771316	−	1.33596i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$		0			0
$775$	−0.580057	+	1.00469i	−0.580057	+	1.00469i
$776$	1.42518			1.42518
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−4.77761			−4.77761
$784$	−0.246902	+	0.540641i	−0.246902	+	0.540641i
$785$		0			0
$786$		0			0
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$		0			0
$789$	0.264241	−	0.457679i	0.264241	−	0.457679i
$790$		0			0
$791$		0			0
$792$	−5.23020			−5.23020
$793$		0			0
$794$	0.653077	+	1.13116i	0.653077	+	1.13116i
$795$		0			0
$796$	−0.101300	+	0.175457i	−0.101300	+	0.175457i
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$	2.63121	+	1.35648i	2.63121	+	1.35648i
$799$		0			0
$800$	−0.297176	+	0.514723i	−0.297176	+	0.514723i
$801$	1.92384	+	3.33219i	1.92384	+	3.33219i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.654861	+	1.13425i	0.654861	+	1.13425i	0.981929	+	0.189251i	$0.0606061\pi$
$809$	0.654861	+	1.13425i	0.654861	+	1.13425i	−0.327068	+	0.945001i	$0.606061\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	0.463180	−	0.297668i	0.463180	−	0.297668i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.543476			−0.543476
$819$		0			0
$820$		0			0
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	0.504545	+	0.873898i	0.504545	+	0.873898i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	3.64636			3.64636
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$829$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−0.583610	−	1.01084i	−0.583610	−	1.01084i
$837$	−1.55894	−	2.70017i	−1.55894	−	2.70017i
$838$	0.827068	−	1.43252i	0.827068	−	1.43252i
$839$	−1.57211			−1.57211			−0.786053	−	0.618159i	$-0.787879\pi$
$839$	−1.57211			−1.57211			−0.786053	+	0.618159i	$0.787879\pi$
$840$		0			0
$841$	2.16011			2.16011
$842$	−0.0395325	+	0.0684723i	−0.0395325	+	0.0684723i
$843$	0.264241	+	0.457679i	0.264241	+	0.457679i
$844$	−0.308319	−	0.534024i	−0.308319	−	0.534024i
$845$		0			0
$846$	0.958799			0.958799
$847$	−2.53917	−	1.30903i	−2.53917	−	1.30903i
$848$		0			0
$849$	−1.82318	+	3.15784i	−1.82318	+	3.15784i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.654136			−0.654136			−0.327068	−	0.945001i	$-0.606061\pi$
$853$	−0.654136			−0.654136			−0.327068	+	0.945001i	$0.606061\pi$
$854$	−0.198939	+	0.127850i	−0.198939	+	0.127850i
$855$		0			0
$856$	0.0517765	−	0.0896796i	0.0517765	−	0.0896796i
$857$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.723734	+	0.690079i	$0.242424\pi$
$857$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.235759	+	0.971812i	$0.424242\pi$
$858$		0			0
$859$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	0.0475819	+	0.998867i	$0.484848\pi$
$859$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	−0.888835	+	0.458227i	$0.848485\pi$
$860$		0			0
$861$		0			0
$862$	−1.30615			−1.30615
$863$	0.654861	−	1.13425i	0.654861	−	1.13425i	−0.327068	−	0.945001i	$-0.606061\pi$
$863$	0.654861	−	1.13425i	0.654861	−	1.13425i	0.981929	−	0.189251i	$-0.0606061\pi$
$864$	−0.798679	−	1.38335i	−0.798679	−	1.38335i
$865$		0			0
$866$	−0.601300	+	1.04148i	−0.601300	+	1.04148i
$867$	1.85674			1.85674
$868$	0.319369	+	0.164646i	0.319369	+	0.164646i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.60275	−	2.77605i	1.60275	−	2.77605i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$877$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$878$		0			0
$879$	−1.07701	−	1.86544i	−1.07701	−	1.86544i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	1.17951	+	1.65638i	1.17951	+	1.65638i
$883$	−1.77767			−1.77767			−0.888835	−	0.458227i	$-0.848485\pi$
$883$	−1.77767			−1.77767			−0.888835	+	0.458227i	$0.848485\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$		0			0
$889$	−0.0311250	−	0.653395i	−0.0311250	−	0.653395i
$890$		0			0
$891$	−2.49668	+	4.32438i	−2.49668	+	4.32438i
$892$	−0.243458	−	0.421681i	−0.243458	−	0.421681i
$893$	0.452418	+	0.783611i	0.452418	+	0.783611i
$894$		0			0
$895$		0			0
$896$	−0.275291	−	0.141923i	−0.275291	−	0.141923i
$897$		0			0
$898$	−0.195876	+	0.339266i	−0.195876	+	0.339266i
$899$	1.03115	+	1.78600i	1.03115	+	1.78600i
$900$	0.379017	+	0.656476i	0.379017	+	0.656476i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.786053	−	0.618159i	$-0.787879\pi$
$907$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.142315	−	0.989821i	$-0.545455\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$911$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$912$	−1.05885	+	1.83398i	−1.05885	+	1.83398i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.550583			0.550583
$917$		0			0
$918$		0			0
$919$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$919$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$920$		0			0
$921$		0			0
$922$	0.797176	−	1.38075i	0.797176	−	1.38075i
$923$		0			0
$924$	−0.0537370	−	1.12808i	−0.0537370	−	1.12808i
$925$		0			0
$926$		0			0
$927$		0			0
$928$	0.528280	+	0.915008i	0.528280	+	0.915008i
$929$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	−0.995472	−	0.0950560i	$-0.969697\pi$
$929$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	0.580057	+	0.814576i	$0.303030\pi$
$930$		0			0
$931$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$932$	−0.359312			−0.359312
$933$	0.928368	−	1.60798i	0.928368	−	1.60798i
$934$	−0.0395325	−	0.0684723i	−0.0395325	−	0.0684723i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$941$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$942$	1.53565	+	2.65982i	1.53565	+	2.65982i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$947$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$948$		0			0
$949$		0			0
$950$	0.797176	−	1.38075i	0.797176	−	1.38075i
$951$	3.44747			3.44747
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$	0.287535	+	0.498026i	0.287535	+	0.498026i
$957$	3.24102	−	5.61361i	3.24102	−	5.61361i
$958$		0			0
$959$	−0.550294	+	0.353653i	−0.550294	+	0.353653i
$960$		0			0
$961$	−0.172932	+	0.299527i	−0.172932	+	0.299527i
$962$		0			0
$963$	−0.116455	−	0.201706i	−0.116455	−	0.201706i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.16011			1.16011			0.580057	−	0.814576i	$-0.303030\pi$
$967$	1.16011			1.16011			0.580057	+	0.814576i	$0.303030\pi$
$968$	1.55429	−	2.69210i	1.55429	−	2.69210i
$969$		0			0
$970$		0			0
$971$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$971$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$972$	−0.629797			−0.629797
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.0845850	−	0.146505i	−0.0845850	−	0.146505i
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$	−3.08739			−3.08739
$980$		0			0
$981$		0			0
$982$	0.415415	−	0.719520i	0.415415	−	0.719520i
$983$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$983$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.0416572	+	0.874493i	0.0416572	+	0.874493i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$	−0.344757	+	0.597137i	−0.344757	+	0.597137i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	−0.888835	−	0.458227i	$-0.848485\pi$
$997$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	0.0475819	−	0.998867i	$-0.484848\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1169.1.f.c.667.3	yes	20
7.4	even	3	inner	1169.1.f.c.333.3	✓	20
167.166	odd	2	CM	1169.1.f.c.667.3	yes	20
1169.333	odd	6	inner	1169.1.f.c.333.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1169.1.f.c.333.3	✓	20	7.4	even	3	inner
1169.1.f.c.333.3	✓	20	1169.333	odd	6	inner
1169.1.f.c.667.3	yes	20	1.1	even	1	trivial
1169.1.f.c.667.3	yes	20	167.166	odd	2	CM

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:	\( N \)	\(=\)	\( 1169 = 7 \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1169.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.719520i) q^{2} +(-0.928368 - 1.60798i) q^{3} +(0.154861 + 0.268227i) q^{4} +1.54263 q^{6} +(0.0475819 + 0.998867i) q^{7} -1.08816 q^{8} +(-1.22373 + 2.11957i) q^{9} +(-0.981929 - 1.70075i) q^{11} +(0.287535 - 0.498026i) q^{12} +(-0.738471 - 0.380708i) q^{14} +(0.297176 - 0.514723i) q^{16} +(-1.01671 - 1.76100i) q^{18} +(0.959493 - 1.66189i) q^{19} +(1.56199 - 1.00383i) q^{21} +1.63163 q^{22} +(1.01021 + 1.74973i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.68757 q^{27} +(-0.260554 + 0.167448i) q^{28} -1.77767 q^{29} +(-0.580057 - 1.00469i) q^{31} +(-0.297176 - 0.514723i) q^{32} +(-1.82318 + 3.15784i) q^{33} -0.758033 q^{36} +(0.797176 + 1.38075i) q^{38} +(0.0734014 + 1.54088i) q^{42} +(0.304124 - 0.526759i) q^{44} +(-0.235759 + 0.408346i) q^{47} -1.10355 q^{48} +(-0.995472 + 0.0950560i) q^{49} +0.830830 q^{50} +(-1.11646 + 1.93376i) q^{54} +(-0.0517765 - 1.08692i) q^{56} -3.56305 q^{57} +(0.738471 - 1.27907i) q^{58} +(0.142315 - 0.246497i) q^{61} +0.963857 q^{62} +(-2.17540 - 1.12149i) q^{63} +1.08816 q^{64} +(-1.51475 - 2.62363i) q^{66} +(1.33161 - 2.30642i) q^{72} +(-0.928368 + 1.60798i) q^{75} +0.594351 q^{76} +(1.65210 - 1.06174i) q^{77} +(-1.27132 - 2.20198i) q^{81} +(0.511143 + 0.263513i) q^{84} +(1.65033 + 2.85846i) q^{87} +(1.06849 + 1.85068i) q^{88} +(0.786053 - 1.36148i) q^{89} +(-1.07701 + 1.86544i) q^{93} +(-0.195876 - 0.339266i) q^{94} +(-0.551777 + 0.955705i) q^{96} -1.30972 q^{97} +(0.345139 - 0.755750i) q^{98} +4.80648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - q^{3} - 8 q^{4} + 4 q^{6} + q^{7} - 8 q^{8} - 11 q^{9} - q^{11} - 3 q^{12} + 2 q^{14} - 6 q^{16} + 2 q^{19} + 2 q^{21} + 4 q^{22} - 4 q^{24} - 10 q^{25} - 2 q^{27} - 6 q^{28} + 2 q^{29}+ \cdots + 18 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - q^3 - 8 * q^4 + 4 * q^6 + q^7 - 8 * q^8 - 11 * q^9 - q^11 - 3 * q^12 + 2 * q^14 - 6 * q^16 + 2 * q^19 + 2 * q^21 + 4 * q^22 - 4 * q^24 - 10 * q^25 - 2 * q^27 - 6 * q^28 + 2 * q^29 - q^31 + 6 * q^32 + q^33 + 22 * q^36 + 4 * q^38 + 20 * q^42 + 8 * q^44 - q^47 - 12 * q^48 + q^49 - 4 * q^50 - 20 * q^54 + 4 * q^56 + 4 * q^57 - 2 * q^58 + 2 * q^61 - 18 * q^62 + 8 * q^64 + 2 * q^66 + 11 * q^72 - q^75 - 12 * q^76 + 2 * q^77 - 12 * q^81 + 19 * q^84 + q^87 - 4 * q^88 - q^89 + q^93 - 2 * q^94 - 6 * q^96 - 4 * q^97 + 18 * q^98

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