LMFDB - Embedded newform 469.1.bl.a.391.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [469,1,Mod(6,469)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(469, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 40]))

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

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

chi := DirichletCharacter("469.6");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 469 = 7 \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	469.bl (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:	$0.234061490925$
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			391.1
Root			$-0.995472 - 0.0950560i$ of defining polynomial
Character	$\chi$	$=$	469.391
Dual form			469.1.bl.a.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.627639 + 1.81344i) q^{2} +(-2.10859 + 1.65822i) q^{4} +(0.981929 + 0.189251i) q^{7} +(-2.71616 - 1.74557i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.627639 + 1.81344i) q^{2} +(-2.10859 + 1.65822i) q^{4} +(0.981929 + 0.189251i) q^{7} +(-2.71616 - 1.74557i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.473420 - 0.451405i) q^{11} +(0.273100 + 1.89945i) q^{14} +(0.828301 - 3.41430i) q^{16} +(-1.78153 - 0.713215i) q^{18} +(0.521461 - 1.14184i) q^{22} +(1.76962 + 0.168978i) q^{23} +(0.841254 - 0.540641i) q^{25} +(-2.38431 + 1.22920i) q^{28} +(-0.981929 - 1.70075i) q^{29} +(3.49743 - 0.333964i) q^{32} +(0.127639 - 2.67947i) q^{36} +(-0.235759 + 0.408346i) q^{37} +(-0.264241 + 1.83784i) q^{43} +(1.74678 + 0.166797i) q^{44} +(0.804250 + 3.31517i) q^{46} +(0.928368 + 0.371662i) q^{49} +(1.50842 + 1.18624i) q^{50} +(-0.165101 - 1.14831i) q^{53} +(-2.33673 - 2.22806i) q^{56} +(2.46792 - 2.84813i) q^{58} +(-0.786053 + 0.618159i) q^{63} +(1.34125 + 2.93694i) q^{64} +(0.235759 - 0.971812i) q^{67} +(-1.13779 + 0.894765i) q^{71} +(3.09792 - 0.909632i) q^{72} +(-0.888485 - 0.171241i) q^{74} +(-0.379436 - 0.532843i) q^{77} +(-0.738471 - 0.380708i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-3.49866 + 0.674312i) q^{86} +(0.497926 + 2.05248i) q^{88} +(-4.01161 + 2.57811i) q^{92} +(-0.0913090 + 1.91681i) q^{98} +(0.651174 - 0.0621796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 3 q^{4} + q^{7} - 8 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 3 * q^4 + q^7 - 8 * q^8 - 2 * q^9	$ 20 q + 2 q^{2} + 3 q^{4} + q^{7} - 8 q^{8} - 2 q^{9} - q^{11} - 4 q^{14} + 5 q^{16} + 2 q^{18} - 7 q^{22} - q^{23} - 2 q^{25} - 8 q^{28} - q^{29} + 6 q^{32} - 8 q^{36} - q^{37} - 9 q^{43} - 3 q^{44} - 13 q^{46} + q^{49} + 2 q^{50} + 2 q^{53} - 7 q^{56} + 4 q^{58} + q^{63} + 8 q^{64} + q^{67} - q^{71} + 14 q^{72} - 2 q^{74} - q^{77} + 2 q^{79} - 2 q^{81} - 2 q^{86} - 4 q^{88} - 5 q^{92} + 2 q^{98} - q^{99}+O(q^{100}) $ 20 * q + 2 * q^2 + 3 * q^4 + q^7 - 8 * q^8 - 2 * q^9 - q^11 - 4 * q^14 + 5 * q^16 + 2 * q^18 - 7 * q^22 - q^23 - 2 * q^25 - 8 * q^28 - q^29 + 6 * q^32 - 8 * q^36 - q^37 - 9 * q^43 - 3 * q^44 - 13 * q^46 + q^49 + 2 * q^50 + 2 * q^53 - 7 * q^56 + 4 * q^58 + q^63 + 8 * q^64 + q^67 - q^71 + 14 * q^72 - 2 * q^74 - q^77 + 2 * q^79 - 2 * q^81 - 2 * q^86 - 4 * q^88 - 5 * q^92 + 2 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/469\mathbb{Z}\right)^\times$.

$n$	$269$	$337$
$\chi(n)$	$-1$	$e\left(\frac{13}{33}\right)$

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 $

$2$	0.627639	+	1.81344i	0.627639	+	1.81344i	0.580057	+	0.814576i	$0.303030\pi$
$2$	0.627639	+	1.81344i	0.627639	+	1.81344i	0.0475819	+	0.998867i	$0.484848\pi$
$3$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$3$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$4$	−2.10859	+	1.65822i	−2.10859	+	1.65822i
$5$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$5$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$6$		0			0
$7$	0.981929	+	0.189251i	0.981929	+	0.189251i
$7$	0.981929	+	0.189251i	0.981929	+	0.189251i
$8$	−2.71616	−	1.74557i	−2.71616	−	1.74557i
$9$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$10$		0			0
$11$	−0.473420	−	0.451405i	−0.473420	−	0.451405i	0.415415	−	0.909632i	$-0.363636\pi$
$11$	−0.473420	−	0.451405i	−0.473420	−	0.451405i	−0.888835	+	0.458227i	$0.848485\pi$
$12$		0			0
$13$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$13$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$14$	0.273100	+	1.89945i	0.273100	+	1.89945i
$15$		0			0
$16$	0.828301	−	3.41430i	0.828301	−	3.41430i
$17$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$17$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$18$	−1.78153	−	0.713215i	−1.78153	−	0.713215i
$19$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$19$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$20$		0			0
$21$		0			0
$22$	0.521461	−	1.14184i	0.521461	−	1.14184i
$23$	1.76962	+	0.168978i	1.76962	+	0.168978i	0.928368	−	0.371662i	$-0.121212\pi$
$23$	1.76962	+	0.168978i	1.76962	+	0.168978i	0.841254	+	0.540641i	$0.181818\pi$
$24$		0			0
$25$	0.841254	−	0.540641i	0.841254	−	0.540641i
$26$		0			0
$27$		0			0
$28$	−2.38431	+	1.22920i	−2.38431	+	1.22920i
$29$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.654861	−	0.755750i	$-0.727273\pi$
$29$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.327068	−	0.945001i	$-0.606061\pi$
$30$		0			0
$31$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$31$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$32$	3.49743	−	0.333964i	3.49743	−	0.333964i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.127639	−	2.67947i	0.127639	−	2.67947i
$37$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$37$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$41$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$42$		0			0
$43$	−0.264241	+	1.83784i	−0.264241	+	1.83784i	0.235759	+	0.971812i	$0.424242\pi$
$43$	−0.264241	+	1.83784i	−0.264241	+	1.83784i	−0.500000	+	0.866025i	$0.666667\pi$
$44$	1.74678	+	0.166797i	1.74678	+	0.166797i
$45$		0			0
$46$	0.804250	+	3.31517i	0.804250	+	3.31517i
$47$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$47$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$48$		0			0
$49$	0.928368	+	0.371662i	0.928368	+	0.371662i
$50$	1.50842	+	1.18624i	1.50842	+	1.18624i
$51$		0			0
$52$		0			0
$53$	−0.165101	−	1.14831i	−0.165101	−	1.14831i	−0.888835	−	0.458227i	$-0.848485\pi$
$53$	−0.165101	−	1.14831i	−0.165101	−	1.14831i	0.723734	−	0.690079i	$-0.242424\pi$
$54$		0			0
$55$		0			0
$56$	−2.33673	−	2.22806i	−2.33673	−	2.22806i
$57$		0			0
$58$	2.46792	−	2.84813i	2.46792	−	2.84813i
$59$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$59$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$60$		0			0
$61$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$61$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$62$		0			0
$63$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$64$	1.34125	+	2.93694i	1.34125	+	2.93694i
$65$		0			0
$66$		0			0
$67$	0.235759	−	0.971812i	0.235759	−	0.971812i
$67$	0.235759	−	0.971812i	0.235759	−	0.971812i
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.13779	+	0.894765i	−1.13779	+	0.894765i	−0.995472	−	0.0950560i	$-0.969697\pi$
$71$	−1.13779	+	0.894765i	−1.13779	+	0.894765i	−0.142315	+	0.989821i	$0.545455\pi$
$72$	3.09792	−	0.909632i	3.09792	−	0.909632i
$73$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$73$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$74$	−0.888485	−	0.171241i	−0.888485	−	0.171241i
$75$		0			0
$76$		0			0
$77$	−0.379436	−	0.532843i	−0.379436	−	0.532843i
$78$		0			0
$79$	−0.738471	−	0.380708i	−0.738471	−	0.380708i	0.0475819	−	0.998867i	$-0.484848\pi$
$79$	−0.738471	−	0.380708i	−0.738471	−	0.380708i	−0.786053	+	0.618159i	$0.787879\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$82$		0			0
$83$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$83$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$84$		0			0
$85$		0			0
$86$	−3.49866	+	0.674312i	−3.49866	+	0.674312i
$87$		0			0
$88$	0.497926	+	2.05248i	0.497926	+	2.05248i
$89$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$89$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$90$		0			0
$91$		0			0
$92$	−4.01161	+	2.57811i	−4.01161	+	2.57811i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i
$99$	0.651174	−	0.0621796i	0.651174	−	0.0621796i
$100$	−0.877362	+	2.53497i	−0.877362	+	2.53497i
$101$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$101$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$102$		0			0
$103$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$103$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$104$		0			0
$105$		0			0
$106$	1.97876	−	1.02012i	1.97876	−	1.02012i
$107$	−1.78153	−	0.523103i	−1.78153	−	0.523103i	−0.786053	−	0.618159i	$-0.787879\pi$
$107$	−1.78153	−	0.523103i	−1.78153	−	0.523103i	−0.995472	+	0.0950560i	$0.969697\pi$
$108$		0			0
$109$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i	−0.500000	−	0.866025i	$-0.666667\pi$
$109$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i	0.580057	+	0.814576i	$0.303030\pi$
$110$		0			0
$111$		0			0
$112$	1.45949	−	3.19584i	1.45949	−	3.19584i
$113$	−0.235759	−	0.971812i	−0.235759	−	0.971812i	−0.959493	−	0.281733i	$-0.909091\pi$
$113$	−0.235759	−	0.971812i	−0.235759	−	0.971812i	0.723734	−	0.690079i	$-0.242424\pi$
$114$		0			0
$115$		0			0
$116$	4.89070	+	1.95794i	4.89070	+	1.95794i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.0272219	−	0.571458i	−0.0272219	−	0.571458i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$127$	−0.279486	−	0.0538665i	−0.279486	−	0.0538665i	0.0475819	−	0.998867i	$-0.484848\pi$
$127$	−0.279486	−	0.0538665i	−0.279486	−	0.0538665i	−0.327068	+	0.945001i	$0.606061\pi$
$128$	−1.94142	+	1.85114i	−1.94142	+	1.85114i
$129$		0			0
$130$		0			0
$131$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$131$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$132$		0			0
$133$		0			0
$134$	1.91030	−	0.182411i	1.91030	−	0.182411i
$135$		0			0
$136$		0			0
$137$	−0.827068	−	1.81103i	−0.827068	−	1.81103i	−0.500000	−	0.866025i	$-0.666667\pi$
$137$	−0.827068	−	1.81103i	−0.827068	−	1.81103i	−0.327068	−	0.945001i	$-0.606061\pi$
$138$		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			0
$142$	−2.33673	−	1.50172i	−2.33673	−	1.50172i
$143$		0			0
$144$	2.03794	+	2.86188i	2.03794	+	2.86188i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.180007	−	1.25198i	−0.180007	−	1.25198i
$149$	0.654861	+	0.755750i	0.654861	+	0.755750i	0.981929	−	0.189251i	$-0.0606061\pi$
$149$	0.654861	+	0.755750i	0.654861	+	0.755750i	−0.327068	+	0.945001i	$0.606061\pi$
$150$		0			0
$151$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.981929	−	0.189251i	$-0.0606061\pi$
$151$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.0475819	+	0.998867i	$0.484848\pi$
$152$		0			0
$153$		0			0
$154$	0.728132	−	1.02252i	0.728132	−	1.02252i
$155$		0			0
$156$		0			0
$157$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$157$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$158$	0.226900	−	1.57812i	0.226900	−	1.57812i
$159$		0			0
$160$		0			0
$161$	1.70566	+	0.500828i	1.70566	+	0.500828i
$162$	1.70566	−	0.879330i	1.70566	−	0.879330i
$163$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.580057	+	0.814576i	$0.303030\pi$
$163$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.415415	+	0.909632i	$0.363636\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$167$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$168$		0			0
$169$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$170$		0			0
$171$		0			0
$172$	−2.49035	−	4.31342i	−2.49035	−	4.31342i
$173$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$173$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$174$		0			0
$175$	0.928368	−	0.371662i	0.928368	−	0.371662i
$176$	−1.93337	+	1.24250i	−1.93337	+	1.24250i
$177$		0			0
$178$		0			0
$179$	−0.653077	+	1.43004i	−0.653077	+	1.43004i	0.235759	+	0.971812i	$0.424242\pi$
$179$	−0.653077	+	1.43004i	−0.653077	+	1.43004i	−0.888835	+	0.458227i	$0.848485\pi$
$180$		0			0
$181$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$181$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$182$		0			0
$183$		0			0
$184$	−4.51161	−	3.54797i	−4.51161	−	3.54797i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.839614	+	1.17907i	0.839614	+	1.17907i	0.981929	+	0.189251i	$0.0606061\pi$
$191$	0.839614	+	1.17907i	0.839614	+	1.17907i	−0.142315	+	0.989821i	$0.545455\pi$
$192$		0			0
$193$	−1.67489	−	1.07639i	−1.67489	−	1.07639i	−0.888835	−	0.458227i	$-0.848485\pi$
$193$	−1.67489	−	1.07639i	−1.67489	−	1.07639i	−0.786053	−	0.618159i	$-0.787879\pi$
$194$		0			0
$195$		0			0
$196$	−2.57385	+	0.755750i	−2.57385	+	0.755750i
$197$	−0.370638	+	0.291473i	−0.370638	+	0.291473i	−0.786053	−	0.618159i	$-0.787879\pi$
$197$	−0.370638	+	0.291473i	−0.370638	+	0.291473i	0.415415	+	0.909632i	$0.363636\pi$
$198$	0.521461	+	1.14184i	0.521461	+	1.14184i
$199$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$199$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$200$	−3.22871			−3.22871
$201$		0			0
$202$		0			0
$203$	−0.642315	−	1.85585i	−0.642315	−	1.85585i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.28656	+	1.22673i	−1.28656	+	1.22673i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.580057	−	0.814576i	−0.580057	−	0.814576i	0.415415	−	0.909632i	$-0.363636\pi$
$211$	−0.580057	−	0.814576i	−0.580057	−	0.814576i	−0.995472	+	0.0950560i	$0.969697\pi$
$212$	2.25227	+	2.14754i	2.25227	+	2.14754i
$213$		0			0
$214$	−0.169537	−	3.55901i	−0.169537	−	3.55901i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.143547	+	0.112887i	0.143547	+	0.112887i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$223$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$224$	3.49743	+	0.333964i	3.49743	+	0.333964i
$225$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$226$	1.61435	−	1.03748i	1.61435	−	1.03748i
$227$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$227$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$228$		0			0
$229$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$229$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$230$		0			0
$231$		0			0
$232$	−0.301704	+	6.33354i	−0.301704	+	6.33354i
$233$	−1.95496	+	0.186677i	−1.95496	+	0.186677i	−0.995472	−	0.0950560i	$-0.969697\pi$
$233$	−1.95496	+	0.186677i	−1.95496	+	0.186677i	−0.959493	+	0.281733i	$0.909091\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.841254	+	0.540641i	$0.181818\pi$
$239$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.0475819	+	0.998867i	$0.484848\pi$
$240$		0			0
$241$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$241$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$242$	1.01922	−	0.408035i	1.01922	−	0.408035i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$251$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$252$	0.632425	−	2.60689i	0.632425	−	2.60689i
$253$	−0.761497	−	0.878815i	−0.761497	−	0.878815i
$254$	−0.0777324	−	0.540641i	−0.0777324	−	0.540641i
$255$		0			0
$256$	−1.70566	−	0.879330i	−1.70566	−	0.879330i
$257$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$257$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$258$		0			0
$259$	−0.308779	+	0.356349i	−0.308779	+	0.356349i
$260$		0			0
$261$	1.92837	+	0.371662i	1.92837	+	0.371662i
$262$		0			0
$263$	1.50842	−	0.442913i	1.50842	−	0.442913i	0.580057	−	0.814576i	$-0.303030\pi$
$263$	1.50842	−	0.442913i	1.50842	−	0.442913i	0.928368	+	0.371662i	$0.121212\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	1.11435	+	2.44009i	1.11435	+	2.44009i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		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
$274$	2.76509	−	2.63651i	2.76509	−	2.63651i
$275$	−0.642315	−	0.123796i	−0.642315	−	0.123796i
$276$		0			0
$277$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$277$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.0800569	+	1.68060i	0.0800569	+	1.68060i	0.580057	+	0.814576i	$0.303030\pi$
$281$	0.0800569	+	1.68060i	0.0800569	+	1.68060i	−0.500000	+	0.866025i	$0.666667\pi$
$282$		0			0
$283$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$283$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$284$	0.915415	−	3.77339i	0.915415	−	3.77339i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.03794	+	2.86188i	−2.03794	+	2.86188i
$289$	0.235759	+	0.971812i	0.235759	+	0.971812i
$290$		0			0
$291$		0			0
$292$		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			0
$296$	1.35316	−	0.697601i	1.35316	−	0.697601i
$297$		0			0
$298$	−0.959493	+	1.66189i	−0.959493	+	1.66189i
$299$		0			0
$300$		0			0
$301$	−0.607279	+	1.75462i	−0.607279	+	1.75462i
$302$	−0.822032	+	2.37511i	−0.822032	+	2.37511i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$307$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$308$	1.68365	+	0.494363i	1.68365	+	0.494363i
$309$		0			0
$310$		0			0
$311$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$311$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$312$		0			0
$313$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$313$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$314$		0			0
$315$		0			0
$316$	2.18843	−	0.421786i	2.18843	−	0.421786i
$317$	−0.264241	−	0.105786i	−0.264241	−	0.105786i	0.235759	−	0.971812i	$-0.424242\pi$
$317$	−0.264241	−	0.105786i	−0.264241	−	0.105786i	−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$	−0.302863	+	1.24842i	−0.302863	+	1.24842i
$320$		0			0
$321$		0			0
$322$	0.162317	+	3.40746i	0.162317	+	3.40746i
$323$		0			0
$324$	1.94142	+	1.85114i	1.94142	+	1.85114i
$325$		0			0
$326$	−2.50196	+	2.88741i	−2.50196	+	2.88741i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.56499	−	1.23072i	1.56499	−	1.23072i	0.723734	−	0.690079i	$-0.242424\pi$
$331$	1.56499	−	1.23072i	1.56499	−	1.23072i	0.841254	−	0.540641i	$-0.181818\pi$
$332$		0			0
$333$	−0.154218	−	0.445585i	−0.154218	−	0.445585i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.514186	+	1.48564i	0.514186	+	1.48564i	0.841254	+	0.540641i	$0.181818\pi$
$337$	0.514186	+	1.48564i	0.514186	+	1.48564i	−0.327068	+	0.945001i	$0.606061\pi$
$338$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.841254	+	0.540641i	0.841254	+	0.540641i
$344$	3.92580	−	4.53061i	3.92580	−	4.53061i
$345$		0			0
$346$		0			0
$347$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i	0.415415	−	0.909632i	$-0.363636\pi$
$347$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i	−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$349$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$350$	1.25667	+	1.45027i	1.25667	+	1.45027i
$351$		0			0
$352$	−1.80651	−	1.42065i	−1.80651	−	1.42065i
$353$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$353$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−3.00319	−	0.286770i	−3.00319	−	0.286770i
$359$	−0.0135432	+	0.0941952i	−0.0135432	+	0.0941952i	−0.995472	−	0.0950560i	$-0.969697\pi$
$359$	−0.0135432	+	0.0941952i	−0.0135432	+	0.0941952i	0.981929	+	0.189251i	$0.0606061\pi$
$360$		0			0
$361$	0.928368	−	0.371662i	0.928368	−	0.371662i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$367$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$368$	2.04272	−	5.90206i	2.04272	−	5.90206i
$369$		0			0
$370$		0			0
$371$	0.0552004	−	1.15880i	0.0552004	−	1.15880i
$372$		0			0
$373$	0.786053	+	1.36148i	0.786053	+	1.36148i	0.928368	+	0.371662i	$0.121212\pi$
$373$	0.786053	+	1.36148i	0.786053	+	1.36148i	−0.142315	+	0.989821i	$0.545455\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.786053	−	0.618159i	$-0.787879\pi$
$379$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.888835	+	0.458227i	$0.848485\pi$
$380$		0			0
$381$		0			0
$382$	−1.61121	+	2.26262i	−1.61121	+	2.26262i
$383$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$383$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$384$		0			0
$385$		0			0
$386$	0.900739	−	3.71290i	0.900739	−	3.71290i
$387$	−1.21590	−	1.40323i	−1.21590	−	1.40323i
$388$		0			0
$389$	0.0552004	+	1.15880i	0.0552004	+	1.15880i	0.841254	+	0.540641i	$0.181818\pi$
$389$	0.0552004	+	1.15880i	0.0552004	+	1.15880i	−0.786053	+	0.618159i	$0.787879\pi$
$390$		0			0
$391$		0			0
$392$	−1.87283	−	2.63003i	−1.87283	−	2.63003i
$393$		0			0
$394$	−0.761197	−	0.489191i	−0.761197	−	0.489191i
$395$		0			0
$396$	−1.26995	+	1.21090i	−1.26995	+	1.21090i
$397$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$397$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$398$		0			0
$399$		0			0
$400$	−1.14910	−	3.32011i	−1.14910	−	3.32011i
$401$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$401$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	2.96233	−	2.32960i	2.96233	−	2.32960i
$407$	0.295943	−	0.0868967i	0.295943	−	0.0868967i
$408$		0			0
$409$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$409$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−3.03211	−	1.56316i	−3.03211	−	1.56316i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$419$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$420$		0			0
$421$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i	−0.142315	−	0.989821i	$-0.545455\pi$
$421$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i	0.235759	+	0.971812i	$0.424242\pi$
$422$	1.11312	−	1.56316i	1.11312	−	1.56316i
$423$		0			0
$424$	−1.55601	+	3.40718i	−1.55601	+	3.40718i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	4.62393	−	1.85114i	4.62393	−	1.85114i
$429$		0			0
$430$		0			0
$431$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$431$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$432$		0			0
$433$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$433$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$434$		0			0
$435$		0			0
$436$	−0.0834931	+	0.241238i	−0.0834931	+	0.241238i
$437$		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
$441$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$442$		0			0
$443$	−0.264241	+	0.105786i	−0.264241	+	0.105786i	−0.500000	−	0.866025i	$-0.666667\pi$
$443$	−0.264241	+	0.105786i	−0.264241	+	0.105786i	0.235759	+	0.971812i	$0.424242\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.761197	+	3.13770i	0.761197	+	3.13770i
$449$	−0.165101	+	0.231852i	−0.165101	+	0.231852i	−0.888835	−	0.458227i	$-0.848485\pi$
$449$	−0.165101	+	0.231852i	−0.165101	+	0.231852i	0.723734	+	0.690079i	$0.242424\pi$
$450$	−1.88431	+	0.363170i	−1.88431	+	0.363170i
$451$		0			0
$452$	2.10859	+	1.65822i	2.10859	+	1.65822i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.327068	−	0.945001i	$-0.606061\pi$
$457$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.959493	+	0.281733i	$0.909091\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$461$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$462$		0			0
$463$	0.0688733	−	0.0656706i	0.0688733	−	0.0656706i	−0.654861	−	0.755750i	$-0.727273\pi$
$463$	0.0688733	−	0.0656706i	0.0688733	−	0.0656706i	0.723734	+	0.690079i	$0.242424\pi$
$464$	−6.62021	+	1.94387i	−6.62021	+	1.94387i
$465$		0			0
$466$	−1.56554	−	3.42805i	−1.56554	−	3.42805i
$467$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$467$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$468$		0			0
$469$	0.415415	−	0.909632i	0.415415	−	0.909632i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.954707	−	0.750790i	0.954707	−	0.750790i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.975950	+	0.627205i	0.975950	+	0.627205i
$478$	−2.23394	+	2.57811i	−2.23394	+	2.57811i
$479$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$479$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.00500	+	1.15983i	1.00500	+	1.15983i
$485$		0			0
$486$		0			0
$487$	0.437742	+	0.175245i	0.437742	+	0.175245i	0.580057	−	0.814576i	$-0.303030\pi$
$487$	0.437742	+	0.175245i	0.437742	+	0.175245i	−0.142315	+	0.989821i	$0.545455\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$491$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.28656	+	0.663268i	−1.28656	+	0.663268i
$498$		0			0
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$503$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$504$	3.21409	−	0.306908i	3.21409	−	0.306908i
$505$		0			0
$506$	1.11574	−	1.93251i	1.11574	−	1.93251i
$507$		0			0
$508$	0.678645	−	0.349866i	0.678645	−	0.349866i
$509$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$509$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$510$		0			0
$511$		0			0
$512$	0.142315	−	0.989821i	0.142315	−	0.989821i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.840021	−	0.336294i	−0.840021	−	0.336294i
$519$		0			0
$520$		0			0
$521$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$521$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$522$	0.536330	+	3.73026i	0.536330	+	3.73026i
$523$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$523$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$524$		0			0
$525$		0			0
$526$	1.74994	+	2.45745i	1.74994	+	2.45745i
$527$		0			0
$528$		0			0
$529$	2.12108	+	0.408804i	2.12108	+	0.408804i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−2.33673	+	2.22806i	−2.33673	+	2.22806i
$537$		0			0
$538$		0			0
$539$	−0.271738	−	0.595023i	−0.271738	−	0.595023i
$540$		0			0
$541$	−1.88431	+	0.553283i	−1.88431	+	0.553283i	−0.888835	+	0.458227i	$0.848485\pi$
$541$	−1.88431	+	0.553283i	−1.88431	+	0.553283i	−0.995472	+	0.0950560i	$0.969697\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.28656	−	1.22673i	−1.28656	−	1.22673i	−0.959493	−	0.281733i	$-0.909091\pi$
$547$	−1.28656	−	1.22673i	−1.28656	−	1.22673i	−0.327068	−	0.945001i	$-0.606061\pi$
$548$	4.74702	+	2.44726i	4.74702	+	2.44726i
$549$		0			0
$550$	−0.178645	−	1.24250i	−0.178645	−	1.24250i
$551$		0			0
$552$		0			0
$553$	−0.653077	−	0.513585i	−0.653077	−	0.513585i
$554$	2.33330	+	0.934113i	2.33330	+	0.934113i
$555$		0			0
$556$		0			0
$557$	0.195876	+	0.807410i	0.195876	+	0.807410i	0.981929	+	0.189251i	$0.0606061\pi$
$557$	0.195876	+	0.807410i	0.195876	+	0.807410i	−0.786053	+	0.618159i	$0.787879\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−2.99743	+	1.19999i	−2.99743	+	1.19999i
$563$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$563$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$568$	4.65229	−	0.444240i	4.65229	−	0.444240i
$569$	0.627639	−	1.81344i	0.627639	−	1.81344i	0.0475819	−	0.998867i	$-0.484848\pi$
$569$	0.627639	−	1.81344i	0.627639	−	1.81344i	0.580057	−	0.814576i	$-0.303030\pi$
$570$		0			0
$571$	0.651174	−	0.0621796i	0.651174	−	0.0621796i	0.235759	−	0.971812i	$-0.424242\pi$
$571$	0.651174	−	0.0621796i	0.651174	−	0.0621796i	0.415415	+	0.909632i	$0.363636\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.58006	−	0.814576i	1.58006	−	0.814576i
$576$	−3.09792	−	0.909632i	−3.09792	−	0.909632i
$577$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$577$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$578$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.440189	+	0.618159i	−0.440189	+	0.618159i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$587$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.19894	+	1.14319i	1.19894	+	1.14319i
$593$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$593$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$594$		0			0
$595$		0			0
$596$	−2.63403	−	0.507668i	−2.63403	−	0.507668i
$597$		0			0
$598$		0			0
$599$	−0.911911	+	0.717135i	−0.911911	+	0.717135i	−0.959493	−	0.281733i	$-0.909091\pi$
$599$	−0.911911	+	0.717135i	−0.911911	+	0.717135i	0.0475819	+	0.998867i	$0.484848\pi$
$600$		0			0
$601$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$601$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$602$	−3.56305			−3.56305
$603$	0.580057	+	0.814576i	0.580057	+	0.814576i
$604$	−3.51334			−3.51334
$605$		0			0
$606$		0			0
$607$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$607$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.839614	+	1.17907i	0.839614	+	1.17907i	0.981929	+	0.189251i	$0.0606061\pi$
$613$	0.839614	+	1.17907i	0.839614	+	1.17907i	−0.142315	+	0.989821i	$0.545455\pi$
$614$		0			0
$615$		0			0
$616$	0.100494	+	2.10962i	0.100494	+	2.10962i
$617$	−0.264241	−	1.83784i	−0.264241	−	1.83784i	−0.500000	−	0.866025i	$-0.666667\pi$
$617$	−0.264241	−	1.83784i	−0.264241	−	1.83784i	0.235759	−	0.971812i	$-0.424242\pi$
$618$		0			0
$619$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$619$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.415415	−	0.909632i	0.415415	−	0.909632i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.74555	+	0.899892i	−1.74555	+	0.899892i	−0.786053	+	0.618159i	$0.787879\pi$
$631$	−1.74555	+	0.899892i	−1.74555	+	0.899892i	−0.959493	+	0.281733i	$0.909091\pi$
$632$	1.34125	+	2.32312i	1.34125	+	2.32312i
$633$		0			0
$634$	0.0259893	−	0.545582i	0.0259893	−	0.545582i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−2.45402	+	0.234331i	−2.45402	+	0.234331i
$639$	0.0688733	−	1.44583i	0.0688733	−	1.44583i
$640$		0			0
$641$	0.142315	+	0.246497i	0.142315	+	0.246497i	0.928368	−	0.371662i	$-0.121212\pi$
$641$	0.142315	+	0.246497i	0.142315	+	0.246497i	−0.786053	+	0.618159i	$0.787879\pi$
$642$		0			0
$643$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$643$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$644$	−4.42703	+	1.77232i	−4.42703	+	1.77232i
$645$		0			0
$646$		0			0
$647$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$647$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$648$	−1.34125	+	2.93694i	−1.34125	+	2.93694i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−4.95815	−	1.98495i	−4.95815	−	1.98495i
$653$	−0.653077	−	0.513585i	−0.653077	−	0.513585i	0.235759	−	0.971812i	$-0.424242\pi$
$653$	−0.653077	−	0.513585i	−0.653077	−	0.513585i	−0.888835	+	0.458227i	$0.848485\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.0688733	+	0.0656706i	0.0688733	+	0.0656706i	0.723734	−	0.690079i	$-0.242424\pi$
$659$	0.0688733	+	0.0656706i	0.0688733	+	0.0656706i	−0.654861	+	0.755750i	$0.727273\pi$
$660$		0			0
$661$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$661$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$662$	3.21409	+	2.06557i	3.21409	+	2.06557i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.711249	−	0.559333i	0.711249	−	0.559333i
$667$	−1.45025	−	3.17561i	−1.45025	−	3.17561i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.195876	+	0.428908i	0.195876	+	0.428908i	0.981929	−	0.189251i	$-0.0606061\pi$
$673$	0.195876	+	0.428908i	0.195876	+	0.428908i	−0.786053	+	0.618159i	$0.787879\pi$
$674$	−2.37140	+	1.86489i	−2.37140	+	1.86489i
$675$		0			0
$676$	1.94142	−	1.85114i	1.94142	−	1.85114i
$677$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$677$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.0688733	+	1.44583i	0.0688733	+	1.44583i	0.723734	+	0.690079i	$0.242424\pi$
$683$	0.0688733	+	1.44583i	0.0688733	+	1.44583i	−0.654861	+	0.755750i	$0.727273\pi$
$684$		0			0
$685$		0			0
$686$	−0.452418	+	1.86489i	−0.452418	+	1.86489i
$687$		0			0
$688$	6.05606	+	2.42448i	6.05606	+	2.42448i
$689$		0			0
$690$		0			0
$691$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$691$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$692$		0			0
$693$	0.651174	+	0.0621796i	0.651174	+	0.0621796i
$694$	0.0259893	−	0.180759i	0.0259893	−	0.180759i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−1.34125	+	2.32312i	−1.34125	+	2.32312i
$701$	0.0800569	−	1.68060i	0.0800569	−	1.68060i	−0.500000	−	0.866025i	$-0.666667\pi$
$701$	0.0800569	−	1.68060i	0.0800569	−	1.68060i	0.580057	−	0.814576i	$-0.303030\pi$
$702$		0			0
$703$		0			0
$704$	0.690772	−	1.99585i	0.690772	−	1.99585i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.70566	−	0.879330i	1.70566	−	0.879330i	0.723734	−	0.690079i	$-0.242424\pi$
$709$	1.70566	−	0.879330i	1.70566	−	0.879330i	0.981929	−	0.189251i	$-0.0606061\pi$
$710$		0			0
$711$	0.771316	−	0.308788i	0.771316	−	0.308788i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.994239	−	4.09831i	−0.994239	−	4.09831i
$717$		0			0
$718$	−0.179318	+	0.0345607i	−0.179318	+	0.0345607i
$719$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$719$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$720$		0			0
$721$		0			0
$722$	1.25667	+	1.45027i	1.25667	+	1.45027i
$723$		0			0
$724$		0			0
$725$	−1.74555	−	0.899892i	−1.74555	−	0.899892i
$726$		0			0
$727$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$727$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.841254	+	0.540641i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$733$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$734$		0			0
$735$		0			0
$736$	6.24556			6.24556
$737$	−0.550294	+	0.353653i	−0.550294	+	0.353653i
$738$		0			0
$739$	−0.379436	−	1.09631i	−0.379436	−	1.09631i	−0.959493	−	0.281733i	$-0.909091\pi$
$739$	−0.379436	−	1.09631i	−0.379436	−	1.09631i	0.580057	−	0.814576i	$-0.303030\pi$
$740$		0			0
$741$		0			0
$742$	2.13606	−	0.627205i	2.13606	−	0.627205i
$743$	0.601300	−	0.573338i	0.601300	−	0.573338i	−0.327068	−	0.945001i	$-0.606061\pi$
$743$	0.601300	−	0.573338i	0.601300	−	0.573338i	0.928368	+	0.371662i	$0.121212\pi$
$744$		0			0
$745$		0			0
$746$	−1.97562	+	2.27998i	−1.97562	+	2.27998i
$747$		0			0
$748$		0			0
$749$	−1.65033	−	0.850806i	−1.65033	−	0.850806i
$750$		0			0
$751$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$751$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.975950	−	1.37053i	0.975950	−	1.37053i	0.0475819	−	0.998867i	$-0.484848\pi$
$757$	0.975950	−	1.37053i	0.975950	−	1.37053i	0.928368	−	0.371662i	$-0.121212\pi$
$758$	−0.761197	−	3.13770i	−0.761197	−	3.13770i
$759$		0			0
$760$		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
$763$	0.0883470	−	0.0353688i	0.0883470	−	0.0353688i
$764$	−3.72556	−	1.09392i	−3.72556	−	1.09392i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$769$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$770$		0			0
$771$		0			0
$772$	5.31654	−	0.507668i	5.31654	−	0.507668i
$773$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$773$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$774$	1.78153	−	3.08569i	1.78153	−	3.08569i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−2.06677	+	0.827411i	−2.06677	+	0.827411i
$779$		0			0
$780$		0			0
$781$	0.942554	+	0.0900029i	0.942554	+	0.0900029i
$782$		0			0
$783$		0			0
$784$	2.03794	−	2.86188i	2.03794	−	2.86188i
$785$		0			0
$786$		0			0
$787$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$787$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$788$	0.298200	−	1.22920i	0.298200	−	1.22920i
$789$		0			0
$790$		0			0
$791$	−0.0475819	−	0.998867i	−0.0475819	−	0.998867i
$792$	−1.87723	−	0.967781i	−1.87723	−	0.967781i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$797$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$798$		0			0
$799$		0			0
$800$	2.76167	−	2.17180i	2.76167	−	2.17180i
$801$		0			0
$802$	0.521461	+	1.50666i	0.521461	+	1.50666i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.78153	+	0.523103i	−1.78153	+	0.523103i	−0.995472	−	0.0950560i	$-0.969697\pi$
$809$	−1.78153	+	0.523103i	−1.78153	+	0.523103i	−0.786053	+	0.618159i	$0.787879\pi$
$810$		0			0
$811$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$811$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$812$	4.43178	+	2.84813i	4.43178	+	2.84813i
$813$		0			0
$814$	0.343327	+	0.482136i	0.343327	+	0.482136i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.56499	+	1.23072i	1.56499	+	1.23072i	0.841254	+	0.540641i	$0.181818\pi$
$821$	1.56499	+	1.23072i	1.56499	+	1.23072i	0.723734	+	0.690079i	$0.242424\pi$
$822$		0			0
$823$	−0.981929	+	0.189251i	−0.981929	+	0.189251i	−0.654861	−	0.755750i	$-0.727273\pi$
$823$	−0.981929	+	0.189251i	−0.981929	+	0.189251i	−0.327068	+	0.945001i	$0.606061\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.56499	+	0.149438i	1.56499	+	0.149438i	0.841254	−	0.540641i	$-0.181818\pi$
$827$	1.56499	+	0.149438i	1.56499	+	0.149438i	0.723734	+	0.690079i	$0.242424\pi$
$828$	0.678645	−	4.72008i	0.678645	−	4.72008i
$829$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$829$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$839$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$840$		0			0
$841$	−1.42837	+	2.47401i	−1.42837	+	2.47401i
$842$	0.0913090	+	0.158152i	0.0913090	+	0.158152i
$843$		0			0
$844$	2.57385	+	0.755750i	2.57385	+	0.755750i
$845$		0			0
$846$		0			0
$847$	0.0814192	−	0.566283i	0.0814192	−	0.566283i
$848$	−4.05742	−	0.387436i	−4.05742	−	0.387436i
$849$		0			0
$850$		0			0
$851$	−0.486206	+	0.682780i	−0.486206	+	0.682780i
$852$		0			0
$853$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$853$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$854$		0			0
$855$		0			0
$856$	3.92580	+	4.53061i	3.92580	+	4.53061i
$857$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$857$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$858$		0			0
$859$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$859$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$860$		0			0
$861$		0			0
$862$	−0.822032	+	0.948676i	−0.822032	+	0.948676i
$863$	0.975950	+	0.627205i	0.975950	+	0.627205i	0.928368	−	0.371662i	$-0.121212\pi$
$863$	0.975950	+	0.627205i	0.975950	+	0.627205i	0.0475819	+	0.998867i	$0.484848\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.177754	+	0.513585i	0.177754	+	0.513585i
$870$		0			0
$871$		0			0
$872$	−0.307256			−0.307256
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.38884	+	1.32425i	−1.38884	+	1.32425i	−0.500000	+	0.866025i	$0.666667\pi$
$877$	−1.38884	+	1.32425i	−1.38884	+	1.32425i	−0.888835	+	0.458227i	$0.848485\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$881$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$882$	−1.38884	−	1.32425i	−1.38884	−	1.32425i
$883$	−1.03115	−	0.531595i	−1.03115	−	0.531595i	−0.142315	−	0.989821i	$-0.545455\pi$
$883$	−1.03115	−	0.531595i	−1.03115	−	0.531595i	−0.888835	+	0.458227i	$0.848485\pi$
$884$		0			0
$885$		0			0
$886$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$887$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$887$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$888$		0			0
$889$	−0.264241	−	0.105786i	−0.264241	−	0.105786i
$890$		0			0
$891$	−0.379436	+	0.532843i	−0.379436	+	0.532843i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−2.25667	+	1.45027i	−2.25667	+	1.45027i
$897$		0			0
$898$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$899$		0			0
$900$	−1.34125	−	2.32312i	−1.34125	−	2.32312i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−1.05601	+	3.05113i	−1.05601	+	3.05113i
$905$		0			0
$906$		0			0
$907$	−0.0311250	+	0.653395i	−0.0311250	+	0.653395i	0.928368	+	0.371662i	$0.121212\pi$
$907$	−0.0311250	+	0.653395i	−0.0311250	+	0.653395i	−0.959493	+	0.281733i	$0.909091\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.981929	+	0.189251i	$0.0606061\pi$
$911$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.928368	+	0.371662i	$0.121212\pi$
$912$		0			0
$913$		0			0
$914$	0.395304	−	2.74940i	0.395304	−	2.74940i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.54370	+	0.297523i	−1.54370	+	0.297523i	−0.888835	−	0.458227i	$-0.848485\pi$
$919$	−1.54370	+	0.297523i	−1.54370	+	0.297523i	−0.654861	+	0.755750i	$0.727273\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.0224357	+	0.470984i	0.0224357	+	0.470984i
$926$	0.162317	+	0.0836804i	0.162317	+	0.0836804i
$927$		0			0
$928$	−4.00221	−	5.62032i	−4.00221	−	5.62032i
$929$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$929$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$930$		0			0
$931$		0			0
$932$	3.81268	−	3.63538i	3.81268	−	3.63538i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	1.91030	+	0.182411i	1.91030	+	0.182411i
$939$		0			0
$940$		0			0
$941$		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			0
$945$		0			0
$946$	1.96073	+	1.26008i	1.96073	+	1.26008i
$947$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$947$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.759713	−	0.876756i	−0.759713	−	0.876756i	0.235759	−	0.971812i	$-0.424242\pi$
$953$	−0.759713	−	0.876756i	−0.759713	−	0.876756i	−0.995472	+	0.0950560i	$0.969697\pi$
$954$	−0.524856	+	2.16349i	−0.524856	+	2.16349i
$955$		0			0
$956$	−4.42703	−	1.77232i	−4.42703	−	1.77232i
$957$		0			0
$958$		0			0
$959$	−0.469383	−	1.93482i	−0.469383	−	1.93482i
$960$		0			0
$961$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$962$		0			0
$963$	1.56199	−	1.00383i	1.56199	−	1.00383i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	0.723734	−	0.690079i	$-0.242424\pi$
$967$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	−0.959493	+	0.281733i	$0.909091\pi$
$968$	−0.923582	+	1.59969i	−0.923582	+	1.59969i
$969$		0			0
$970$		0			0
$971$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$971$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$972$		0			0
$973$		0			0
$974$	−0.0430538	+	0.903811i	−0.0430538	+	0.903811i
$975$		0			0
$976$		0			0
$977$	0.888835	−	0.458227i	0.888835	−	0.458227i	0.0475819	−	0.998867i	$-0.484848\pi$
$977$	0.888835	−	0.458227i	0.888835	−	0.458227i	0.841254	+	0.540641i	$0.181818\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.0135432	+	0.0941952i	−0.0135432	+	0.0941952i
$982$	1.58713	+	0.151553i	1.58713	+	0.151553i
$983$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$983$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.778161	+	3.20762i	−0.778161	+	3.20762i
$990$		0			0
$991$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$991$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$992$		0			0
$993$		0			0
$994$	−2.01029	−	1.91681i	−2.01029	−	1.91681i
$995$		0			0
$996$		0			0
$997$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$997$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$998$	1.88431	+	0.363170i	1.88431	+	0.363170i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	469.1.bl.a.391.1	yes	20
7.2	even	3		3283.1.bw.a.2334.1		20
7.3	odd	6		3283.1.cd.a.1195.1		20
7.4	even	3		3283.1.cd.a.1195.1		20
7.5	odd	6		3283.1.bw.a.2334.1		20
7.6	odd	2	CM	469.1.bl.a.391.1	yes	20
67.6	even	33	inner	469.1.bl.a.6.1	✓	20
469.6	odd	66	inner	469.1.bl.a.6.1	✓	20
469.73	odd	66		3283.1.bw.a.3155.1		20
469.207	even	33		3283.1.bw.a.3155.1		20
469.341	odd	66		3283.1.cd.a.1011.1		20
469.408	even	33		3283.1.cd.a.1011.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
469.1.bl.a.6.1	✓	20	67.6	even	33	inner
469.1.bl.a.6.1	✓	20	469.6	odd	66	inner
469.1.bl.a.391.1	yes	20	1.1	even	1	trivial
469.1.bl.a.391.1	yes	20	7.6	odd	2	CM
3283.1.bw.a.2334.1		20	7.2	even	3
3283.1.bw.a.2334.1		20	7.5	odd	6
3283.1.bw.a.3155.1		20	469.73	odd	66
3283.1.bw.a.3155.1		20	469.207	even	33
3283.1.cd.a.1011.1		20	469.341	odd	66
3283.1.cd.a.1011.1		20	469.408	even	33
3283.1.cd.a.1195.1		20	7.3	odd	6
3283.1.cd.a.1195.1		20	7.4	even	3

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:	\( N \)	\(=\)	\( 469 = 7 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	469.bl (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.627639 + 1.81344i) q^{2} +(-2.10859 + 1.65822i) q^{4} +(0.981929 + 0.189251i) q^{7} +(-2.71616 - 1.74557i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.627639 + 1.81344i) q^{2} +(-2.10859 + 1.65822i) q^{4} +(0.981929 + 0.189251i) q^{7} +(-2.71616 - 1.74557i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.473420 - 0.451405i) q^{11} +(0.273100 + 1.89945i) q^{14} +(0.828301 - 3.41430i) q^{16} +(-1.78153 - 0.713215i) q^{18} +(0.521461 - 1.14184i) q^{22} +(1.76962 + 0.168978i) q^{23} +(0.841254 - 0.540641i) q^{25} +(-2.38431 + 1.22920i) q^{28} +(-0.981929 - 1.70075i) q^{29} +(3.49743 - 0.333964i) q^{32} +(0.127639 - 2.67947i) q^{36} +(-0.235759 + 0.408346i) q^{37} +(-0.264241 + 1.83784i) q^{43} +(1.74678 + 0.166797i) q^{44} +(0.804250 + 3.31517i) q^{46} +(0.928368 + 0.371662i) q^{49} +(1.50842 + 1.18624i) q^{50} +(-0.165101 - 1.14831i) q^{53} +(-2.33673 - 2.22806i) q^{56} +(2.46792 - 2.84813i) q^{58} +(-0.786053 + 0.618159i) q^{63} +(1.34125 + 2.93694i) q^{64} +(0.235759 - 0.971812i) q^{67} +(-1.13779 + 0.894765i) q^{71} +(3.09792 - 0.909632i) q^{72} +(-0.888485 - 0.171241i) q^{74} +(-0.379436 - 0.532843i) q^{77} +(-0.738471 - 0.380708i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-3.49866 + 0.674312i) q^{86} +(0.497926 + 2.05248i) q^{88} +(-4.01161 + 2.57811i) q^{92} +(-0.0913090 + 1.91681i) q^{98} +(0.651174 - 0.0621796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 3 q^{4} + q^{7} - 8 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 3 * q^4 + q^7 - 8 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 3 q^{4} + q^{7} - 8 q^{8} - 2 q^{9} - q^{11} - 4 q^{14} + 5 q^{16} + 2 q^{18} - 7 q^{22} - q^{23} - 2 q^{25} - 8 q^{28} - q^{29} + 6 q^{32} - 8 q^{36} - q^{37} - 9 q^{43} - 3 q^{44} - 13 q^{46} + q^{49} + 2 q^{50} + 2 q^{53} - 7 q^{56} + 4 q^{58} + q^{63} + 8 q^{64} + q^{67} - q^{71} + 14 q^{72} - 2 q^{74} - q^{77} + 2 q^{79} - 2 q^{81} - 2 q^{86} - 4 q^{88} - 5 q^{92} + 2 q^{98} - q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 3 * q^4 + q^7 - 8 * q^8 - 2 * q^9 - q^11 - 4 * q^14 + 5 * q^16 + 2 * q^18 - 7 * q^22 - q^23 - 2 * q^25 - 8 * q^28 - q^29 + 6 * q^32 - 8 * q^36 - q^37 - 9 * q^43 - 3 * q^44 - 13 * q^46 + q^49 + 2 * q^50 + 2 * q^53 - 7 * q^56 + 4 * q^58 + q^63 + 8 * q^64 + q^67 - q^71 + 14 * q^72 - 2 * q^74 - q^77 + 2 * q^79 - 2 * q^81 - 2 * q^86 - 4 * q^88 - 5 * q^92 + 2 * q^98 - q^99

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