LMFDB - Embedded newform 737.1.w.a.351.1

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			351.1
Root			$0.580057 + 0.814576i$ of defining polynomial
Character	$\chi$	$=$	737.351
Dual form			737.1.w.a.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.544078 - 1.19136i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.0913090 + 0.0268107i) q^{5} +(-0.468468 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.544078 - 1.19136i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.0913090 + 0.0268107i) q^{5} +(-0.468468 + 0.540641i) q^{9} +(0.235759 - 0.971812i) q^{11} +(-0.0623191 - 1.30824i) q^{12} +(0.0816206 + 0.0941952i) q^{15} +(0.723734 + 0.690079i) q^{16} +(-0.0947329 - 0.00904590i) q^{20} +(0.481929 - 0.676774i) q^{23} +(-0.833635 + 0.535745i) q^{25} +(-0.357685 - 0.105026i) q^{27} +(0.581419 - 0.299742i) q^{31} +(-1.28605 + 0.247866i) q^{33} +(-0.635847 + 0.327802i) q^{36} +(0.327068 + 0.566498i) q^{37} +(0.580057 - 0.814576i) q^{44} +(0.0282804 - 0.0619254i) q^{45} +(-1.95496 - 0.186677i) q^{47} +(0.428368 - 1.23769i) q^{48} +(-0.786053 + 0.618159i) q^{49} +(-0.0671040 - 0.466718i) q^{53} +(0.00452808 + 0.0950560i) q^{55} +(0.396666 + 0.254922i) q^{59} +(0.0407651 + 0.117783i) q^{60} +(0.415415 + 0.909632i) q^{64} +(0.580057 + 0.814576i) q^{67} +(-1.06849 - 0.205935i) q^{69} +(1.56199 + 0.625325i) q^{71} +(1.09183 + 0.701676i) q^{75} +(-0.0845850 - 0.0436066i) q^{80} +(0.171292 + 1.19136i) q^{81} +(-0.738471 + 1.61703i) q^{89} +(0.698939 - 0.449181i) q^{92} +(-0.673440 - 0.529599i) q^{93} +(0.786053 + 1.36148i) q^{97} +(0.414955 + 0.582723i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/737\mathbb{Z}\right)^\times$.

$n$	$68$	$672$
$\chi(n)$	$-1$	$e\left(\frac{2}{33}\right)$

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		−0.981929	−	0.189251i	$-0.939394\pi$
$2$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$3$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$3$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$4$	0.928368	+	0.371662i	0.928368	+	0.371662i
$5$	−0.0913090	+	0.0268107i	−0.0913090	+	0.0268107i	−0.327068	−	0.945001i	$-0.606061\pi$
$5$	−0.0913090	+	0.0268107i	−0.0913090	+	0.0268107i	0.235759	+	0.971812i	$0.424242\pi$
$6$		0			0
$7$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$7$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$8$		0			0
$9$	−0.468468	+	0.540641i	−0.468468	+	0.540641i
$10$		0			0
$11$	0.235759	−	0.971812i	0.235759	−	0.971812i
$11$	0.235759	−	0.971812i	0.235759	−	0.971812i
$12$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i
$13$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$13$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$14$		0			0
$15$	0.0816206	+	0.0941952i	0.0816206	+	0.0941952i
$16$	0.723734	+	0.690079i	0.723734	+	0.690079i
$17$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$17$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$18$		0			0
$19$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$19$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$20$	−0.0947329	−	0.00904590i	−0.0947329	−	0.00904590i
$21$		0			0
$22$		0			0
$23$	0.481929	−	0.676774i	0.481929	−	0.676774i	−0.500000	−	0.866025i	$-0.666667\pi$
$23$	0.481929	−	0.676774i	0.481929	−	0.676774i	0.981929	+	0.189251i	$0.0606061\pi$
$24$		0			0
$25$	−0.833635	+	0.535745i	−0.833635	+	0.535745i
$26$		0			0
$27$	−0.357685	−	0.105026i	−0.357685	−	0.105026i
$28$		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
$31$	0.581419	−	0.299742i	0.581419	−	0.299742i	−0.142315	−	0.989821i	$-0.545455\pi$
$31$	0.581419	−	0.299742i	0.581419	−	0.299742i	0.723734	+	0.690079i	$0.242424\pi$
$32$		0			0
$33$	−1.28605	+	0.247866i	−1.28605	+	0.247866i
$34$		0			0
$35$		0			0
$36$	−0.635847	+	0.327802i	−0.635847	+	0.327802i
$37$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$37$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$41$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$42$		0			0
$43$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$43$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$44$	0.580057	−	0.814576i	0.580057	−	0.814576i
$45$	0.0282804	−	0.0619254i	0.0282804	−	0.0619254i
$46$		0			0
$47$	−1.95496	−	0.186677i	−1.95496	−	0.186677i	−0.959493	−	0.281733i	$-0.909091\pi$
$47$	−1.95496	−	0.186677i	−1.95496	−	0.186677i	−0.995472	+	0.0950560i	$0.969697\pi$
$48$	0.428368	−	1.23769i	0.428368	−	1.23769i
$49$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.0671040	−	0.466718i	−0.0671040	−	0.466718i	−0.995472	−	0.0950560i	$-0.969697\pi$
$53$	−0.0671040	−	0.466718i	−0.0671040	−	0.466718i	0.928368	−	0.371662i	$-0.121212\pi$
$54$		0			0
$55$	0.00452808	+	0.0950560i	0.00452808	+	0.0950560i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.396666	+	0.254922i	0.396666	+	0.254922i	0.723734	−	0.690079i	$-0.242424\pi$
$59$	0.396666	+	0.254922i	0.396666	+	0.254922i	−0.327068	+	0.945001i	$0.606061\pi$
$60$	0.0407651	+	0.117783i	0.0407651	+	0.117783i
$61$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$61$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$62$		0			0
$63$		0			0
$64$	0.415415	+	0.909632i	0.415415	+	0.909632i
$65$		0			0
$66$		0			0
$67$	0.580057	+	0.814576i	0.580057	+	0.814576i
$67$	0.580057	+	0.814576i	0.580057	+	0.814576i
$68$		0			0
$69$	−1.06849	−	0.205935i	−1.06849	−	0.205935i
$70$		0			0
$71$	1.56199	+	0.625325i	1.56199	+	0.625325i	0.981929	−	0.189251i	$-0.0606061\pi$
$71$	1.56199	+	0.625325i	1.56199	+	0.625325i	0.580057	+	0.814576i	$0.303030\pi$
$72$		0			0
$73$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$73$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$74$		0			0
$75$	1.09183	+	0.701676i	1.09183	+	0.701676i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$79$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$80$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i
$81$	0.171292	+	1.19136i	0.171292	+	1.19136i
$82$		0			0
$83$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$83$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.738471	+	1.61703i	−0.738471	+	1.61703i	0.0475819	+	0.998867i	$0.484848\pi$
$89$	−0.738471	+	1.61703i	−0.738471	+	1.61703i	−0.786053	+	0.618159i	$0.787879\pi$
$90$		0			0
$91$		0			0
$92$	0.698939	−	0.449181i	0.698939	−	0.449181i
$93$	−0.673440	−	0.529599i	−0.673440	−	0.529599i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.786053	+	1.36148i	0.786053	+	1.36148i	0.928368	+	0.371662i	$0.121212\pi$
$97$	0.786053	+	1.36148i	0.786053	+	1.36148i	−0.142315	+	0.989821i	$0.545455\pi$
$98$		0			0
$99$	0.414955	+	0.582723i	0.414955	+	0.582723i
$100$	−0.973036	+	0.187537i	−0.973036	+	0.187537i
$101$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$101$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$102$		0			0
$103$	−1.03115	+	0.531595i	−1.03115	+	0.531595i	−0.888835	−	0.458227i	$-0.848485\pi$
$103$	−1.03115	+	0.531595i	−1.03115	+	0.531595i	−0.142315	+	0.989821i	$0.545455\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$107$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$108$	−0.293029	−	0.230441i	−0.293029	−	0.230441i
$109$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$109$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$110$		0			0
$111$	0.496956	−	0.697876i	0.496956	−	0.697876i
$112$		0			0
$113$	−1.28656	+	1.22673i	−1.28656	+	1.22673i	−0.327068	+	0.945001i	$0.606061\pi$
$113$	−1.28656	+	1.22673i	−1.28656	+	1.22673i	−0.959493	+	0.281733i	$0.909091\pi$
$114$		0			0
$115$	−0.0258596	+	0.0747165i	−0.0258596	+	0.0747165i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$122$		0			0
$123$		0			0
$124$	0.651174	−	0.0621796i	0.651174	−	0.0621796i
$125$	0.124074	−	0.143189i	0.124074	−	0.143189i
$126$		0			0
$127$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$127$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$131$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$132$	−1.28605	−	0.247866i	−1.28605	−	0.247866i
$133$		0			0
$134$		0			0
$135$	0.0354757			0.0354757
$136$		0			0
$137$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	−0.995472	−	0.0950560i	$-0.969697\pi$
$137$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	0.580057	−	0.814576i	$-0.303030\pi$
$138$		0			0
$139$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$139$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$140$		0			0
$141$	0.841254	+	2.43064i	0.841254	+	2.43064i
$142$		0			0
$143$		0			0
$144$	−0.712131	+	0.0680003i	−0.712131	+	0.0680003i
$145$		0			0
$146$		0			0
$147$	1.16413	+	0.600149i	1.16413	+	0.600149i
$148$	0.0930932	+	0.647478i	0.0930932	+	0.647478i
$149$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$149$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$150$		0			0
$151$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$151$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.0450525	+	0.0429575i	−0.0450525	+	0.0429575i
$156$		0			0
$157$	1.07701	−	1.51245i	1.07701	−	1.51245i	0.235759	−	0.971812i	$-0.424242\pi$
$157$	1.07701	−	1.51245i	1.07701	−	1.51245i	0.841254	−	0.540641i	$-0.181818\pi$
$158$		0			0
$159$	−0.519522	+	0.333877i	−0.519522	+	0.333877i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$163$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$164$		0			0
$165$	0.110783	−	0.0571125i	0.110783	−	0.0571125i
$166$		0			0
$167$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$167$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$168$		0			0
$169$	0.580057	+	0.814576i	0.580057	+	0.814576i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$173$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$174$		0			0
$175$		0			0
$176$	0.841254	−	0.540641i	0.841254	−	0.540641i
$177$	0.0878875	−	0.611271i	0.0878875	−	0.611271i
$178$		0			0
$179$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$179$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$180$	0.0492699	−	0.0469788i	0.0492699	−	0.0469788i
$181$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.786053	−	0.618159i	$-0.787879\pi$
$181$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.888835	+	0.458227i	$0.848485\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.0450525	−	0.0429575i	−0.0450525	−	0.0429575i
$186$		0			0
$187$		0			0
$188$	−1.74555	−	0.899892i	−1.74555	−	0.899892i
$189$		0			0
$190$		0			0
$191$	−1.15486	+	0.110276i	−1.15486	+	0.110276i	−0.654861	−	0.755750i	$-0.727273\pi$
$191$	−1.15486	+	0.110276i	−1.15486	+	0.110276i	−0.500000	+	0.866025i	$0.666667\pi$
$192$	0.857685	−	0.989821i	0.857685	−	0.989821i
$193$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$193$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$194$		0			0
$195$		0			0
$196$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$197$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$197$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$198$		0			0
$199$	−0.981929	−	0.189251i	−0.981929	−	0.189251i	−0.327068	−	0.945001i	$-0.606061\pi$
$199$	−0.981929	−	0.189251i	−0.981929	−	0.189251i	−0.654861	+	0.755750i	$0.727273\pi$
$200$		0			0
$201$	0.654861	−	1.13425i	0.654861	−	1.13425i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.140124	+	0.577597i	0.140124	+	0.577597i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$211$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$212$	0.111165	−	0.458227i	0.111165	−	0.458227i
$213$	−0.104852	−	2.20112i	−0.104852	−	2.20112i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−0.0311250	+	0.0899299i	−0.0311250	+	0.0899299i
$221$		0			0
$222$		0			0
$223$	0.195876	−	0.428908i	0.195876	−	0.428908i	−0.786053	−	0.618159i	$-0.787879\pi$
$223$	0.195876	−	0.428908i	0.195876	−	0.428908i	0.981929	+	0.189251i	$0.0606061\pi$
$224$		0			0
$225$	0.100886	−	0.701676i	0.100886	−	0.701676i
$226$		0			0
$227$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$227$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$228$		0			0
$229$	0.0688733	−	1.44583i	0.0688733	−	1.44583i	−0.654861	−	0.755750i	$-0.727273\pi$
$229$	0.0688733	−	1.44583i	0.0688733	−	1.44583i	0.723734	−	0.690079i	$-0.242424\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$233$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$234$		0			0
$235$	0.183511	−	0.0353688i	0.183511	−	0.0353688i
$236$	0.273507	+	0.384087i	0.273507	+	0.384087i
$237$		0			0
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$	−0.00593052	+	0.124497i	−0.00593052	+	0.124497i
$241$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$241$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$242$		0			0
$243$	1.01255	−	0.650724i	1.01255	−	0.650724i
$244$		0			0
$245$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.34378	−	0.537970i	1.34378	−	0.537970i	0.415415	−	0.909632i	$-0.363636\pi$
$251$	1.34378	−	0.537970i	1.34378	−	0.537970i	0.928368	+	0.371662i	$0.121212\pi$
$252$		0			0
$253$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$254$		0			0
$255$		0			0
$256$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$257$	−0.235759	+	0.971812i	−0.235759	+	0.971812i	0.723734	+	0.690079i	$0.242424\pi$
$257$	−0.235759	+	0.971812i	−0.235759	+	0.971812i	−0.959493	+	0.281733i	$0.909091\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$263$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$264$		0			0
$265$	0.0186403	+	0.0408165i	0.0186403	+	0.0408165i
$266$		0			0
$267$	2.32825			2.32825
$268$	0.235759	+	0.971812i	0.235759	+	0.971812i
$269$	0.0951638			0.0951638			0.0475819	−	0.998867i	$-0.484848\pi$
$269$	0.0951638			0.0951638			0.0475819	+	0.998867i	$0.484848\pi$
$270$		0			0
$271$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$271$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.324106	+	0.936443i	0.324106	+	0.936443i
$276$	−0.915415	−	0.588302i	−0.915415	−	0.588302i
$277$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$277$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$278$		0			0
$279$	−0.110323	+	0.454759i	−0.110323	+	0.454759i
$280$		0			0
$281$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$281$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$282$		0			0
$283$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$283$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$284$	1.21769	+	1.16106i	1.21769	+	1.16106i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.723734	−	0.690079i	0.723734	−	0.690079i
$290$		0			0
$291$	1.19435	−	1.67723i	1.19435	−	1.67723i
$292$		0			0
$293$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$293$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$294$		0			0
$295$	−0.0430538	−	0.0126417i	−0.0430538	−	0.0126417i
$296$		0			0
$297$	−0.186393	+	0.322842i	−0.186393	+	0.322842i
$298$		0			0
$299$		0			0
$300$	0.752833	+	1.05721i	0.752833	+	1.05721i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$307$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$308$		0			0
$309$	1.19435	+	0.939247i	1.19435	+	0.939247i
$310$		0			0
$311$	0.223734	−	1.55610i	0.223734	−	1.55610i	−0.500000	−	0.866025i	$-0.666667\pi$
$311$	0.223734	−	1.55610i	0.223734	−	1.55610i	0.723734	−	0.690079i	$-0.242424\pi$
$312$		0			0
$313$	0.481929	−	1.05528i	0.481929	−	1.05528i	−0.500000	−	0.866025i	$-0.666667\pi$
$313$	0.481929	−	1.05528i	0.481929	−	1.05528i	0.981929	−	0.189251i	$-0.0606061\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.911911	+	0.717135i	−0.911911	+	0.717135i	−0.959493	−	0.281733i	$-0.909091\pi$
$317$	−0.911911	+	0.717135i	−0.911911	+	0.717135i	0.0475819	+	0.998867i	$0.484848\pi$
$318$		0			0
$319$		0			0
$320$	−0.0623191	−	0.0719200i	−0.0623191	−	0.0719200i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.283763	+	1.16969i	−0.283763	+	1.16969i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.84833	−	0.739959i	−1.84833	−	0.739959i	−0.959493	−	0.281733i	$-0.909091\pi$
$331$	−1.84833	−	0.739959i	−1.84833	−	0.739959i	−0.888835	−	0.458227i	$-0.848485\pi$
$332$		0			0
$333$	−0.459493	−	0.0885600i	−0.459493	−	0.0885600i
$334$		0			0
$335$	−0.0748038	−	0.0588264i	−0.0748038	−	0.0588264i
$336$		0			0
$337$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$337$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$338$		0			0
$339$	2.16148	+	0.865325i	2.16148	+	0.865325i
$340$		0			0
$341$	−0.154218	−	0.635697i	−0.154218	−	0.635697i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.103084	−	0.00984335i	0.103084	−	0.00984335i
$346$		0			0
$347$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$347$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$348$		0			0
$349$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$349$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.54370	+	1.21398i	−1.54370	+	1.21398i	−0.654861	+	0.755750i	$0.727273\pi$
$353$	−1.54370	+	1.21398i	−1.54370	+	1.21398i	−0.888835	+	0.458227i	$0.848485\pi$
$354$		0			0
$355$	−0.159389	−	0.0152198i	−0.159389	−	0.0152198i
$356$	−1.28656	+	1.22673i	−1.28656	+	1.22673i
$357$		0			0
$358$		0			0
$359$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$359$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$360$		0			0
$361$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$362$		0			0
$363$	−0.0623191	+	1.30824i	−0.0623191	+	1.30824i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.580057	−	0.814576i	−0.580057	−	0.814576i	0.415415	−	0.909632i	$-0.363636\pi$
$367$	−0.580057	−	0.814576i	−0.580057	−	0.814576i	−0.995472	+	0.0950560i	$0.969697\pi$
$368$	0.815816	−	0.157236i	0.815816	−	0.157236i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.428368	−	0.741955i	−0.428368	−	0.741955i
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−0.238096	−	0.0699112i	−0.238096	−	0.0699112i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.11312	+	1.56316i	−1.11312	+	1.56316i	−0.327068	+	0.945001i	$0.606061\pi$
$379$	−1.11312	+	1.56316i	−1.11312	+	1.56316i	−0.786053	+	0.618159i	$0.787879\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.514186	−	1.48564i	0.514186	−	1.48564i	−0.327068	−	0.945001i	$-0.606061\pi$
$383$	0.514186	−	1.48564i	0.514186	−	1.48564i	0.841254	−	0.540641i	$-0.181818\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	0.223734	+	1.55610i	0.223734	+	1.55610i
$389$	−1.03115	−	0.531595i	−1.03115	−	0.531595i	−0.142315	−	0.989821i	$-0.545455\pi$
$389$	−1.03115	−	0.531595i	−1.03115	−	0.531595i	−0.888835	+	0.458227i	$0.848485\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$	0.168655	+	0.695205i	0.168655	+	0.695205i
$397$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$397$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$398$		0			0
$399$		0			0
$400$	−0.973036	−	0.187537i	−0.973036	−	0.187537i
$401$	1.96386			1.96386			0.981929	−	0.189251i	$-0.0606061\pi$
$401$	1.96386			1.96386			0.981929	+	0.189251i	$0.0606061\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.0475819	−	0.104190i	−0.0475819	−	0.104190i
$406$		0			0
$407$	0.627639	−	0.184291i	0.627639	−	0.184291i
$408$		0			0
$409$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$409$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$410$		0			0
$411$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$412$	−1.15486	+	0.110276i	−1.15486	+	0.110276i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.21590	+	0.486774i	−1.21590	+	0.486774i	−0.888835	−	0.458227i	$-0.848485\pi$
$419$	−1.21590	+	0.486774i	−1.21590	+	0.486774i	−0.327068	+	0.945001i	$0.606061\pi$
$420$		0			0
$421$	0.627639	−	1.81344i	0.627639	−	1.81344i	0.0475819	−	0.998867i	$-0.484848\pi$
$421$	0.627639	−	1.81344i	0.627639	−	1.81344i	0.580057	−	0.814576i	$-0.303030\pi$
$422$		0			0
$423$	1.01676	−	0.969482i	1.01676	−	0.969482i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	−0.186393	−	0.322842i	−0.186393	−	0.322842i
$433$	1.76962	−	0.912303i	1.76962	−	0.912303i	0.841254	−	0.540641i	$-0.181818\pi$
$433$	1.76962	−	0.912303i	1.76962	−	0.912303i	0.928368	−	0.371662i	$-0.121212\pi$
$434$		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
$441$	0.0340387	−	0.714560i	0.0340387	−	0.714560i
$442$		0			0
$443$	−1.13779	−	0.894765i	−1.13779	−	0.894765i	−0.142315	−	0.989821i	$-0.545455\pi$
$443$	−1.13779	−	0.894765i	−1.13779	−	0.894765i	−0.995472	+	0.0950560i	$0.969697\pi$
$444$	0.720732	−	0.463186i	0.720732	−	0.463186i
$445$	0.0240754	−	0.167448i	0.0240754	−	0.167448i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.995472	+	0.0950560i	0.995472	+	0.0950560i	0.580057	−	0.814576i	$-0.303030\pi$
$449$	0.995472	+	0.0950560i	0.995472	+	0.0950560i	0.415415	+	0.909632i	$0.363636\pi$
$450$		0			0
$451$		0			0
$452$	−1.65033	+	0.660694i	−1.65033	+	0.660694i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$457$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$458$		0			0
$459$		0			0
$460$	−0.0517765	+	0.0597533i	−0.0517765	+	0.0597533i
$461$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$461$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$462$		0			0
$463$	0.396666	+	1.63508i	0.396666	+	1.63508i	0.723734	+	0.690079i	$0.242424\pi$
$463$	0.396666	+	1.63508i	0.396666	+	1.63508i	−0.327068	+	0.945001i	$0.606061\pi$
$464$		0			0
$465$	0.0756901	+	0.0303017i	0.0756901	+	0.0303017i
$466$		0			0
$467$	0.0934441	+	0.0180099i	0.0934441	+	0.0180099i	0.235759	−	0.971812i	$-0.424242\pi$
$467$	0.0934441	+	0.0180099i	0.0934441	+	0.0180099i	−0.142315	+	0.989821i	$0.545455\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2.38786	−	0.460222i	−2.38786	−	0.460222i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.283763	+	0.182363i	0.283763	+	0.182363i
$478$		0			0
$479$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$479$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$485$	−0.108276	−	0.103241i	−0.108276	−	0.103241i
$486$		0			0
$487$	−1.13779	+	0.894765i	−1.13779	+	0.894765i	−0.995472	−	0.0950560i	$-0.969697\pi$
$487$	−1.13779	+	0.894765i	−1.13779	+	0.894765i	−0.142315	+	0.989821i	$0.545455\pi$
$488$		0			0
$489$	−2.31771	−	0.221315i	−2.31771	−	0.221315i
$490$		0			0
$491$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$491$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−0.0535124	−	0.0420826i	−0.0535124	−	0.0420826i
$496$	0.627639	+	0.184291i	0.627639	+	0.184291i
$497$		0			0
$498$		0			0
$499$	0.142315	+	0.246497i	0.142315	+	0.246497i	0.928368	−	0.371662i	$-0.121212\pi$
$499$	0.142315	+	0.246497i	0.142315	+	0.246497i	−0.786053	+	0.618159i	$0.787879\pi$
$500$	0.168404	−	0.0868183i	0.168404	−	0.0868183i
$501$		0			0
$502$		0			0
$503$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$503$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.654861	−	1.13425i	0.654861	−	1.13425i
$508$		0			0
$509$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.981929	+	0.189251i	$0.0606061\pi$
$509$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.928368	+	0.371662i	$0.121212\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.0799009	−	0.0761853i	0.0799009	−	0.0761853i
$516$		0			0
$517$	−0.642315	+	1.85585i	−0.642315	+	1.85585i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$521$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$522$		0			0
$523$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$523$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$529$	0.101300	+	0.292687i	0.101300	+	0.292687i
$530$		0			0
$531$	−0.323646	+	0.0950312i	−0.323646	+	0.0950312i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.08816			−1.08816
$538$		0			0
$539$	0.415415	+	0.909632i	0.415415	+	0.909632i
$540$	0.0329345	+	0.0131850i	0.0329345	+	0.0131850i
$541$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$541$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$542$		0			0
$543$	0.720732	+	2.08242i	0.720732	+	2.08242i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$547$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$548$	−0.0475819	−	0.998867i	−0.0475819	−	0.998867i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.0266659	+	0.0770462i	−0.0266659	+	0.0770462i
$556$		0			0
$557$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$557$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$563$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$564$	−0.122386	+	2.56919i	−0.122386	+	2.56919i
$565$	0.0845850	−	0.146505i	0.0845850	−	0.146505i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$569$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$570$		0			0
$571$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$571$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$572$		0			0
$573$	0.759713	+	1.31586i	0.759713	+	1.31586i
$574$		0			0
$575$	−0.0391745	+	0.822373i	−0.0391745	+	0.822373i
$576$	−0.686393	−	0.201543i	−0.686393	−	0.201543i
$577$	0.223734	+	0.175946i	0.223734	+	0.175946i	0.723734	−	0.690079i	$-0.242424\pi$
$577$	0.223734	+	0.175946i	0.223734	+	0.175946i	−0.500000	+	0.866025i	$0.666667\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.469383	−	0.0448206i	−0.469383	−	0.0448206i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.473420	−	0.451405i	−0.473420	−	0.451405i	0.415415	−	0.909632i	$-0.363636\pi$
$587$	−0.473420	−	0.451405i	−0.473420	−	0.451405i	−0.888835	+	0.458227i	$0.848485\pi$
$588$	0.857685	+	0.989821i	0.857685	+	0.989821i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.154218	+	0.635697i	−0.154218	+	0.635697i
$593$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$593$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.308779	+	1.27280i	0.308779	+	1.27280i
$598$		0			0
$599$	1.07701	+	0.431171i	1.07701	+	0.431171i	0.841254	−	0.540641i	$-0.181818\pi$
$599$	1.07701	+	0.431171i	1.07701	+	0.431171i	0.235759	+	0.971812i	$0.424242\pi$
$600$		0			0
$601$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$601$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$602$		0			0
$603$	−0.712131	−	0.0680003i	−0.712131	−	0.0680003i
$604$		0			0
$605$	0.0934441	+	0.0180099i	0.0934441	+	0.0180099i
$606$		0			0
$607$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$607$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$613$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.283341	+	1.97068i	0.283341	+	1.97068i	0.235759	+	0.971812i	$0.424242\pi$
$617$	0.283341	+	1.97068i	0.283341	+	1.97068i	0.0475819	+	0.998867i	$0.484848\pi$
$618$		0			0
$619$	0.601300	+	0.573338i	0.601300	+	0.573338i	0.928368	−	0.371662i	$-0.121212\pi$
$619$	0.601300	+	0.573338i	0.601300	+	0.573338i	−0.327068	+	0.945001i	$0.606061\pi$
$620$	−0.0577910	+	0.0231360i	−0.0577910	+	0.0231360i
$621$	−0.243458	+	0.191457i	−0.243458	+	0.191457i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.404163	−	0.884993i	0.404163	−	0.884993i
$626$		0			0
$627$		0			0
$628$	1.56199	−	1.00383i	1.56199	−	1.00383i
$629$		0			0
$630$		0			0
$631$	0.0800569	−	1.68060i	0.0800569	−	1.68060i	−0.500000	−	0.866025i	$-0.666667\pi$
$631$	0.0800569	−	1.68060i	0.0800569	−	1.68060i	0.580057	−	0.814576i	$-0.303030\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.606397	+	0.116873i	−0.606397	+	0.116873i
$637$		0			0
$638$		0			0
$639$	−1.06982	+	0.551529i	−1.06982	+	0.551529i
$640$		0			0
$641$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$641$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$642$		0			0
$643$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$643$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.15486	+	1.62177i	−1.15486	+	1.62177i	−0.500000	+	0.866025i	$0.666667\pi$
$647$	−1.15486	+	1.62177i	−1.15486	+	1.62177i	−0.654861	+	0.755750i	$0.727273\pi$
$648$		0			0
$649$	0.341254	−	0.325385i	0.341254	−	0.325385i
$650$		0			0
$651$		0			0
$652$	1.39734	−	1.09888i	1.39734	−	1.09888i
$653$	1.72373	−	0.690079i	1.72373	−	0.690079i	0.723734	−	0.690079i	$-0.242424\pi$
$653$	1.72373	−	0.690079i	1.72373	−	0.690079i	1.00000			$0$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$659$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$660$	0.124074	−	0.0118476i	0.124074	−	0.0118476i
$661$	−0.759713	+	0.876756i	−0.759713	+	0.876756i	−0.995472	−	0.0950560i	$-0.969697\pi$
$661$	−0.759713	+	0.876756i	−0.759713	+	0.876756i	0.235759	+	0.971812i	$0.424242\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.617557			−0.617557
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$673$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$674$		0			0
$675$	0.354446	−	0.104075i	0.354446	−	0.104075i
$676$	0.235759	+	0.971812i	0.235759	+	0.971812i
$677$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$677$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.70566	+	0.879330i	1.70566	+	0.879330i	0.981929	+	0.189251i	$0.0606061\pi$
$683$	1.70566	+	0.879330i	1.70566	+	0.879330i	0.723734	+	0.690079i	$0.242424\pi$
$684$		0			0
$685$	0.0623191	+	0.0719200i	0.0623191	+	0.0719200i
$686$		0			0
$687$	−1.75998	+	0.704590i	−1.75998	+	0.704590i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.723734	+	0.690079i	−0.723734	+	0.690079i	−0.959493	−	0.281733i	$-0.909091\pi$
$691$	−0.723734	+	0.690079i	−0.723734	+	0.690079i	0.235759	+	0.971812i	$0.424242\pi$
$692$		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		0.888835	−	0.458227i	$-0.151515\pi$
$701$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$702$		0			0
$703$		0			0
$704$	0.981929	−	0.189251i	0.981929	−	0.189251i
$705$	−0.141981	−	0.199385i	−0.141981	−	0.199385i
$706$		0			0
$707$		0			0
$708$	0.308779	−	0.534820i	0.308779	−	0.534820i
$709$	0.0883470	−	1.85463i	0.0883470	−	1.85463i	−0.327068	−	0.945001i	$-0.606061\pi$
$709$	0.0883470	−	1.85463i	0.0883470	−	1.85463i	0.415415	−	0.909632i	$-0.363636\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.0773447	−	0.537944i	0.0773447	−	0.537944i
$714$		0			0
$715$		0			0
$716$	0.601300	−	0.573338i	0.601300	−	0.573338i
$717$		0			0
$718$		0			0
$719$	−1.45949	+	1.14776i	−1.45949	+	1.14776i	−0.500000	+	0.866025i	$0.666667\pi$
$719$	−1.45949	+	1.14776i	−1.45949	+	1.14776i	−0.959493	+	0.281733i	$0.909091\pi$
$720$	0.0632009	−	0.0253018i	0.0632009	−	0.0253018i
$721$		0			0
$722$		0			0
$723$		0			0
$724$	−1.49547	−	0.770969i	−1.49547	−	0.770969i
$725$		0			0
$726$		0			0
$727$	1.91030	−	0.182411i	1.91030	−	0.182411i	0.928368	−	0.371662i	$-0.121212\pi$
$727$	1.91030	−	0.182411i	1.91030	−	0.182411i	0.981929	+	0.189251i	$0.0606061\pi$
$728$		0			0
$729$	−0.313607	−	0.201543i	−0.313607	−	0.201543i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$733$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$734$		0			0
$735$	−0.122386	−	0.0235879i	−0.122386	−	0.0235879i
$736$		0			0
$737$	0.928368	−	0.371662i	0.928368	−	0.371662i
$738$		0			0
$739$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$739$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$740$	−0.0258596	−	0.0566247i	−0.0258596	−	0.0566247i
$741$		0			0
$742$		0			0
$743$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$743$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−0.279486	−	1.94387i	−0.279486	−	1.94387i	−0.327068	−	0.945001i	$-0.606061\pi$
$751$	−0.279486	−	1.94387i	−0.279486	−	1.94387i	0.0475819	−	0.998867i	$-0.484848\pi$
$752$	−1.28605	−	1.48418i	−1.28605	−	1.48418i
$753$	−1.37204	−	1.30824i	−1.37204	−	1.30824i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.44091	−	0.137591i	−1.44091	−	0.137591i	−0.654861	−	0.755750i	$-0.727273\pi$
$757$	−1.44091	−	0.137591i	−1.44091	−	0.137591i	−0.786053	+	0.618159i	$0.787879\pi$
$758$		0			0
$759$	−0.452036	+	0.989821i	−0.452036	+	0.989821i
$760$		0			0
$761$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$761$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$762$		0			0
$763$		0			0
$764$	−1.11312	−	0.326842i	−1.11312	−	0.326842i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.16413	−	0.600149i	1.16413	−	0.600149i
$769$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$769$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$770$		0			0
$771$	1.28605	−	0.247866i	1.28605	−	0.247866i
$772$		0			0
$773$	0.581419	−	0.299742i	0.581419	−	0.299742i	−0.142315	−	0.989821i	$-0.545455\pi$
$773$	0.581419	−	0.299742i	0.581419	−	0.299742i	0.723734	+	0.690079i	$0.242424\pi$
$774$		0			0
$775$	−0.324106	+	0.561368i	−0.324106	+	0.561368i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	0.975950	−	1.37053i	0.975950	−	1.37053i
$782$		0			0
$783$		0			0
$784$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$785$	−0.0577910	+	0.166976i	−0.0577910	+	0.166976i
$786$		0			0
$787$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$787$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.0384856	−	0.0444147i	0.0384856	−	0.0444147i
$796$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$797$	0.627639	+	1.81344i	0.627639	+	1.81344i	0.580057	+	0.814576i	$0.303030\pi$
$797$	0.627639	+	1.81344i	0.627639	+	1.81344i	0.0475819	+	0.998867i	$0.484848\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−0.528280	−	1.15677i	−0.528280	−	1.15677i
$802$		0			0
$803$		0			0
$804$	1.02951	−	0.809616i	1.02951	−	0.809616i
$805$		0			0
$806$		0			0
$807$	−0.0517765	−	0.113375i	−0.0517765	−	0.113375i
$808$		0			0
$809$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$809$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$810$		0			0
$811$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$811$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.0398833	+	0.164401i	−0.0398833	+	0.164401i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$821$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$822$		0			0
$823$	0.514186	−	1.48564i	0.514186	−	1.48564i	−0.327068	−	0.945001i	$-0.606061\pi$
$823$	0.514186	−	1.48564i	0.514186	−	1.48564i	0.841254	−	0.540641i	$-0.181818\pi$
$824$		0			0
$825$	0.939306	−	0.895626i	0.939306	−	0.895626i
$826$		0			0
$827$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$827$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$828$	−0.0845850	+	0.588302i	−0.0845850	+	0.588302i
$829$	1.21769	−	0.782560i	1.21769	−	0.782560i	0.235759	−	0.971812i	$-0.424242\pi$
$829$	1.21769	−	0.782560i	1.21769	−	0.782560i	0.981929	+	0.189251i	$0.0606061\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.239446	+	0.0461494i	−0.239446	+	0.0461494i
$838$		0			0
$839$	−0.911911	−	1.28060i	−0.911911	−	1.28060i	−0.959493	−	0.281733i	$-0.909091\pi$
$839$	−0.911911	−	1.28060i	−0.911911	−	1.28060i	0.0475819	−	0.998867i	$-0.484848\pi$
$840$		0			0
$841$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.0748038	−	0.0588264i	−0.0748038	−	0.0588264i
$846$		0			0
$847$		0			0
$848$	0.273507	−	0.384087i	0.273507	−	0.384087i
$849$		0			0
$850$		0			0
$851$	0.541015	+	0.0516607i	0.541015	+	0.0516607i
$852$	0.720732	−	2.08242i	0.720732	−	2.08242i
$853$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$853$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$857$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$858$		0			0
$859$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i	−0.786053	−	0.618159i	$-0.787879\pi$
$859$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i	0.723734	−	0.690079i	$-0.242424\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.21769	+	0.782560i	1.21769	+	0.782560i	0.981929	−	0.189251i	$-0.0606061\pi$
$863$	1.21769	+	0.782560i	1.21769	+	0.782560i	0.235759	+	0.971812i	$0.424242\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.21590	−	0.486774i	−1.21590	−	0.486774i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.10431	−	0.212839i	−1.10431	−	0.212839i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$877$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$878$		0			0
$879$		0			0
$880$	−0.0623191	+	0.0719200i	−0.0623191	+	0.0719200i
$881$	1.56499	−	0.149438i	1.56499	−	0.149438i	0.723734	−	0.690079i	$-0.242424\pi$
$881$	1.56499	−	0.149438i	1.56499	−	0.149438i	0.841254	+	0.540641i	$0.181818\pi$
$882$		0			0
$883$	0.0934441	+	1.96163i	0.0934441	+	1.96163i	0.235759	+	0.971812i	$0.424242\pi$
$883$	0.0934441	+	1.96163i	0.0934441	+	1.96163i	−0.142315	+	0.989821i	$0.545455\pi$
$884$		0			0
$885$	0.00836371	+	0.0581709i	0.00836371	+	0.0581709i
$886$		0			0
$887$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$887$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.19817	+	0.114411i	1.19817	+	0.114411i
$892$	0.341254	−	0.325385i	0.341254	−	0.325385i
$893$		0			0
$894$		0			0
$895$	−0.0112521	+	0.0782602i	−0.0112521	+	0.0782602i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.354446	−	0.613918i	0.354446	−	0.613918i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.157220	−	0.0303017i	0.157220	−	0.0303017i
$906$		0			0
$907$	−1.28656	+	0.663268i	−1.28656	+	0.663268i	−0.959493	−	0.281733i	$-0.909091\pi$
$907$	−1.28656	+	0.663268i	−1.28656	+	0.663268i	−0.327068	+	0.945001i	$0.606061\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.78153	−	0.523103i	−1.78153	−	0.523103i	−0.786053	−	0.618159i	$-0.787879\pi$
$911$	−1.78153	−	0.523103i	−1.78153	−	0.523103i	−0.995472	+	0.0950560i	$0.969697\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.601300	−	1.31666i	0.601300	−	1.31666i
$917$		0			0
$918$		0			0
$919$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$919$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.576154	−	0.297028i	−0.576154	−	0.297028i
$926$		0			0
$927$	0.195659	−	0.806517i	0.195659	−	0.806517i
$928$		0			0
$929$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$929$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.97562	+	0.580093i	−1.97562	+	0.580093i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$	−1.51943			−1.51943
$940$	0.183511	+	0.0353688i	0.183511	+	0.0353688i
$941$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$941$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$942$		0			0
$943$		0			0
$944$	0.111165	+	0.458227i	0.111165	+	0.458227i
$945$		0			0
$946$		0			0
$947$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$947$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	1.35052	+	0.696241i	1.35052	+	0.696241i
$952$		0			0
$953$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$953$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$954$		0			0
$955$	0.102493	−	0.0410319i	0.102493	−	0.0410319i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.0517765	+	0.113375i	−0.0517765	+	0.113375i
$961$	−0.331854	+	0.466024i	−0.331854	+	0.466024i
$962$		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
$971$	−1.88431	+	0.363170i	−1.88431	+	0.363170i	−0.995472	−	0.0950560i	$-0.969697\pi$
$971$	−1.88431	+	0.363170i	−1.88431	+	0.363170i	−0.888835	+	0.458227i	$0.848485\pi$
$972$	1.18186	−	0.227786i	1.18186	−	0.227786i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.00452808	−	0.0950560i	0.00452808	−	0.0950560i	−0.995472	−	0.0950560i	$-0.969697\pi$
$977$	0.00452808	−	0.0950560i	0.00452808	−	0.0950560i	1.00000			$0$
$978$		0			0
$979$	1.39734	+	1.09888i	1.39734	+	1.09888i
$980$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i
$981$		0			0
$982$		0			0
$983$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$983$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.264241	−	1.83784i	−0.264241	−	1.83784i	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	−0.264241	−	1.83784i	−0.264241	−	1.83784i	0.235759	−	0.971812i	$-0.424242\pi$
$992$		0			0
$993$	0.124074	+	2.60463i	0.124074	+	2.60463i
$994$		0			0
$995$	0.0947329	−	0.00904590i	0.0947329	−	0.00904590i
$996$		0			0
$997$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$997$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$998$		0			0
$999$	−0.0574904	−	0.236979i	−0.0574904	−	0.236979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	737.1.w.a.351.1	yes	20
11.10	odd	2	CM	737.1.w.a.351.1	yes	20
67.21	even	33	inner	737.1.w.a.21.1	✓	20
737.21	odd	66	inner	737.1.w.a.21.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
737.1.w.a.21.1	✓	20	67.21	even	33	inner
737.1.w.a.21.1	✓	20	737.21	odd	66	inner
737.1.w.a.351.1	yes	20	1.1	even	1	trivial
737.1.w.a.351.1	yes	20	11.10	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:	\( N \)	\(=\)	\( 737 = 11 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	737.w (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.544078 - 1.19136i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.0913090 + 0.0268107i) q^{5} +(-0.468468 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.544078 - 1.19136i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.0913090 + 0.0268107i) q^{5} +(-0.468468 + 0.540641i) q^{9} +(0.235759 - 0.971812i) q^{11} +(-0.0623191 - 1.30824i) q^{12} +(0.0816206 + 0.0941952i) q^{15} +(0.723734 + 0.690079i) q^{16} +(-0.0947329 - 0.00904590i) q^{20} +(0.481929 - 0.676774i) q^{23} +(-0.833635 + 0.535745i) q^{25} +(-0.357685 - 0.105026i) q^{27} +(0.581419 - 0.299742i) q^{31} +(-1.28605 + 0.247866i) q^{33} +(-0.635847 + 0.327802i) q^{36} +(0.327068 + 0.566498i) q^{37} +(0.580057 - 0.814576i) q^{44} +(0.0282804 - 0.0619254i) q^{45} +(-1.95496 - 0.186677i) q^{47} +(0.428368 - 1.23769i) q^{48} +(-0.786053 + 0.618159i) q^{49} +(-0.0671040 - 0.466718i) q^{53} +(0.00452808 + 0.0950560i) q^{55} +(0.396666 + 0.254922i) q^{59} +(0.0407651 + 0.117783i) q^{60} +(0.415415 + 0.909632i) q^{64} +(0.580057 + 0.814576i) q^{67} +(-1.06849 - 0.205935i) q^{69} +(1.56199 + 0.625325i) q^{71} +(1.09183 + 0.701676i) q^{75} +(-0.0845850 - 0.0436066i) q^{80} +(0.171292 + 1.19136i) q^{81} +(-0.738471 + 1.61703i) q^{89} +(0.698939 - 0.449181i) q^{92} +(-0.673440 - 0.529599i) q^{93} +(0.786053 + 1.36148i) q^{97} +(0.414955 + 0.582723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} + q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 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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