LMFDB - Embedded newform 1127.1.v.a.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1127,1,Mod(31,1127)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1127, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([11, 18]))

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

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

chi := DirichletCharacter("1127.31");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1127 = 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1127.v (of order $66$, degree $20$, not 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:	$0.562446269237$
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:	no (minimal twist has level 161)
Projective image:	$D_{11}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{11} - \cdots)$

Embedding invariants

Embedding label			325.1
Root			$-0.995472 - 0.0950560i$ of defining polynomial
Character	$\chi$	$=$	1127.325
Dual form			1127.1.v.a.215.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50842 - 1.18624i) q^{2} +(0.632425 - 2.60689i) q^{4} +(-1.34125 - 2.93694i) q^{8} +(-0.327068 + 0.945001i) q^{9} +(-0.653077 - 0.513585i) q^{11} +(-3.12278 - 1.60990i) q^{16} +(0.627639 + 1.81344i) q^{18} -1.59435 q^{22} +(0.981929 + 0.189251i) q^{23} +(0.928368 + 0.371662i) q^{25} +(0.273100 + 0.0801894i) q^{29} +(-3.44985 + 0.664903i) q^{32} +(2.25667 + 1.45027i) q^{36} +(-0.550294 + 1.58997i) q^{37} +(-0.544078 + 1.19136i) q^{43} +(-1.75188 + 1.37770i) q^{44} +(1.70566 - 0.879330i) q^{46} +(1.84125 - 0.540641i) q^{50} +(-0.0135432 - 0.284307i) q^{53} +(0.507075 - 0.203002i) q^{58} +(-2.11435 + 2.44009i) q^{64} +(-1.78153 - 0.713215i) q^{67} +(-0.118239 - 0.822373i) q^{71} +(3.21409 - 0.306908i) q^{72} +(1.05601 + 3.05113i) q^{74} +(-0.0135432 + 0.284307i) q^{79} +(-0.786053 - 0.618159i) q^{81} +(0.592542 + 2.44249i) q^{86} +(-0.632425 + 2.60689i) q^{88} +(1.11435 - 2.44009i) q^{92} +(0.698939 - 0.449181i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 3 q^{4} - 8 q^{8} + q^{9} + 2 q^{11} - 6 q^{16} + 2 q^{18} - 8 q^{22} + q^{23} + q^{25} - 4 q^{29} - 5 q^{32} + 16 q^{36} + 2 q^{37} - 4 q^{43} - 5 q^{44} + 2 q^{46} + 18 q^{50} + 2 q^{53}+ \cdots - 4 q^{99}+O(q^{100}) $ 20 * q + 2 * q^2 + 3 * q^4 - 8 * q^8 + q^9 + 2 * q^11 - 6 * q^16 + 2 * q^18 - 8 * q^22 + q^23 + q^25 - 4 * q^29 - 5 * q^32 + 16 * q^36 + 2 * q^37 - 4 * q^43 - 5 * q^44 + 2 * q^46 + 18 * q^50 + 2 * q^53 - 7 * q^58 - 14 * q^64 + 2 * q^67 - 4 * q^71 + 4 * q^72 - 7 * q^74 + 2 * q^79 + q^81 + 4 * q^86 - 3 * q^88 - 6 * q^92 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1127\mathbb{Z}\right)^\times$.

$n$	$346$	$442$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{11}\right)$

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 $

$2$	1.50842	−	1.18624i	1.50842	−	1.18624i	0.580057	−	0.814576i	$-0.303030\pi$
$2$	1.50842	−	1.18624i	1.50842	−	1.18624i	0.928368	−	0.371662i	$-0.121212\pi$
$3$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$3$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$4$	0.632425	−	2.60689i	0.632425	−	2.60689i
$5$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$5$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.34125	−	2.93694i	−1.34125	−	2.93694i
$9$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$10$		0			0
$11$	−0.653077	−	0.513585i	−0.653077	−	0.513585i	0.235759	−	0.971812i	$-0.424242\pi$
$11$	−0.653077	−	0.513585i	−0.653077	−	0.513585i	−0.888835	+	0.458227i	$0.848485\pi$
$12$		0			0
$13$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$13$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$14$		0			0
$15$		0			0
$16$	−3.12278	−	1.60990i	−3.12278	−	1.60990i
$17$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$17$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$18$	0.627639	+	1.81344i	0.627639	+	1.81344i
$19$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$19$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$20$		0			0
$21$		0			0
$22$	−1.59435			−1.59435
$23$	0.981929	+	0.189251i	0.981929	+	0.189251i
$23$	0.981929	+	0.189251i	0.981929	+	0.189251i
$24$		0			0
$25$	0.928368	+	0.371662i	0.928368	+	0.371662i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$29$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$30$		0			0
$31$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$31$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$32$	−3.44985	+	0.664903i	−3.44985	+	0.664903i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.25667	+	1.45027i	2.25667	+	1.45027i
$37$	−0.550294	+	1.58997i	−0.550294	+	1.58997i	0.235759	+	0.971812i	$0.424242\pi$
$37$	−0.550294	+	1.58997i	−0.550294	+	1.58997i	−0.786053	+	0.618159i	$0.787879\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$41$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$42$		0			0
$43$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$43$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$44$	−1.75188	+	1.37770i	−1.75188	+	1.37770i
$45$		0			0
$46$	1.70566	−	0.879330i	1.70566	−	0.879330i
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$		0			0
$49$		0			0
$50$	1.84125	−	0.540641i	1.84125	−	0.540641i
$51$		0			0
$52$		0			0
$53$	−0.0135432	−	0.284307i	−0.0135432	−	0.284307i	−0.995472	−	0.0950560i	$-0.969697\pi$
$53$	−0.0135432	−	0.284307i	−0.0135432	−	0.284307i	0.981929	−	0.189251i	$-0.0606061\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.507075	−	0.203002i	0.507075	−	0.203002i
$59$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$59$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$60$		0			0
$61$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$61$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$62$		0			0
$63$		0			0
$64$	−2.11435	+	2.44009i	−2.11435	+	2.44009i
$65$		0			0
$66$		0			0
$67$	−1.78153	−	0.713215i	−1.78153	−	0.713215i	−0.995472	−	0.0950560i	$-0.969697\pi$
$67$	−1.78153	−	0.713215i	−1.78153	−	0.713215i	−0.786053	−	0.618159i	$-0.787879\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$71$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$72$	3.21409	−	0.306908i	3.21409	−	0.306908i
$73$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$73$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$74$	1.05601	+	3.05113i	1.05601	+	3.05113i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.0135432	+	0.284307i	−0.0135432	+	0.284307i	0.981929	+	0.189251i	$0.0606061\pi$
$79$	−0.0135432	+	0.284307i	−0.0135432	+	0.284307i	−0.995472	+	0.0950560i	$0.969697\pi$
$80$		0			0
$81$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$82$		0			0
$83$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$83$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$84$		0			0
$85$		0			0
$86$	0.592542	+	2.44249i	0.592542	+	2.44249i
$87$		0			0
$88$	−0.632425	+	2.60689i	−0.632425	+	2.60689i
$89$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$89$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$90$		0			0
$91$		0			0
$92$	1.11435	−	2.44009i	1.11435	−	2.44009i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$97$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$98$		0			0
$99$	0.698939	−	0.449181i	0.698939	−	0.449181i
$100$	1.55601	−	2.18511i	1.55601	−	2.18511i
$101$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$101$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$102$		0			0
$103$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$103$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$104$		0			0
$105$		0			0
$106$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$107$	0.975950	−	1.37053i	0.975950	−	1.37053i	0.0475819	−	0.998867i	$-0.484848\pi$
$107$	0.975950	−	1.37053i	0.975950	−	1.37053i	0.928368	−	0.371662i	$-0.121212\pi$
$108$		0			0
$109$	−1.38884	+	1.32425i	−1.38884	+	1.32425i	−0.500000	+	0.866025i	$0.666667\pi$
$109$	−1.38884	+	1.32425i	−1.38884	+	1.32425i	−0.888835	+	0.458227i	$0.848485\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$113$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$114$		0			0
$115$		0			0
$116$	0.381761	−	0.661229i	0.381761	−	0.661229i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.0730196	−	0.300991i	−0.0730196	−	0.300991i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$127$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$128$	−0.127639	+	2.67947i	−0.127639	+	2.67947i
$129$		0			0
$130$		0			0
$131$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$131$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$132$		0			0
$133$		0			0
$134$	−3.53334	+	1.03748i	−3.53334	+	1.03748i
$135$		0			0
$136$		0			0
$137$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$137$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$138$		0			0
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$		0			0
$141$		0			0
$142$	−1.15389	−	1.10023i	−1.15389	−	1.10023i
$143$		0			0
$144$	2.54272	−	2.42448i	2.54272	−	2.42448i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	3.79686	+	2.44009i	3.79686	+	2.44009i
$149$	−1.21590	+	0.486774i	−1.21590	+	0.486774i	−0.888835	−	0.458227i	$-0.848485\pi$
$149$	−1.21590	+	0.486774i	−1.21590	+	0.486774i	−0.327068	+	0.945001i	$0.606061\pi$
$150$		0			0
$151$	0.252989	−	0.130425i	0.252989	−	0.130425i	−0.327068	−	0.945001i	$-0.606061\pi$
$151$	0.252989	−	0.130425i	0.252989	−	0.130425i	0.580057	+	0.814576i	$0.303030\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$157$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$158$	0.316827	+	0.444922i	0.316827	+	0.444922i
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−1.91899			−1.91899
$163$	0.223734	−	0.175946i	0.223734	−	0.175946i	−0.500000	−	0.866025i	$-0.666667\pi$
$163$	0.223734	−	0.175946i	0.223734	−	0.175946i	0.723734	+	0.690079i	$0.242424\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$167$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$168$		0			0
$169$	0.415415	+	0.909632i	0.415415	+	0.909632i
$170$		0			0
$171$		0			0
$172$	2.76167	+	2.17180i	2.76167	+	2.17180i
$173$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$173$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$174$		0			0
$175$		0			0
$176$	1.21259	+	2.65520i	1.21259	+	2.65520i
$177$		0			0
$178$		0			0
$179$	0.428368	+	1.23769i	0.428368	+	1.23769i	0.928368	+	0.371662i	$0.121212\pi$
$179$	0.428368	+	1.23769i	0.428368	+	1.23769i	−0.500000	+	0.866025i	$0.666667\pi$
$180$		0			0
$181$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$181$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$182$		0			0
$183$		0			0
$184$	−0.761197	−	3.13770i	−0.761197	−	3.13770i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.49547	−	0.770969i	−1.49547	−	0.770969i	−0.500000	−	0.866025i	$-0.666667\pi$
$191$	−1.49547	−	0.770969i	−1.49547	−	0.770969i	−0.995472	+	0.0950560i	$0.969697\pi$
$192$		0			0
$193$	0.815816	−	0.157236i	0.815816	−	0.157236i	0.235759	−	0.971812i	$-0.424242\pi$
$193$	0.815816	−	0.157236i	0.815816	−	0.157236i	0.580057	+	0.814576i	$0.303030\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$197$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$198$	0.521461	−	1.50666i	0.521461	−	1.50666i
$199$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$199$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$200$	−0.153628	−	3.22505i	−0.153628	−	3.22505i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$211$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$212$	−0.749723	−	0.144497i	−0.749723	−	0.144497i
$213$		0			0
$214$	−0.153628	−	3.22505i	−0.153628	−	3.22505i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.524075	+	3.64502i	−0.524075	+	3.64502i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$223$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$224$		0			0
$225$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$226$	1.81899	+	1.73440i	1.81899	+	1.73440i
$227$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$227$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$228$		0			0
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$		0			0
$231$		0			0
$232$	−0.130785	−	0.909632i	−0.130785	−	0.909632i
$233$	−1.67489	+	0.159932i	−1.67489	+	0.159932i	−0.888835	−	0.458227i	$-0.848485\pi$
$233$	−1.67489	+	0.159932i	−1.67489	+	0.159932i	−0.786053	+	0.618159i	$0.787879\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$239$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$240$		0			0
$241$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$241$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$242$	−0.467192	−	0.367404i	−0.467192	−	0.367404i
$243$		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		−0.142315	−	0.989821i	$-0.545455\pi$
$251$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$252$		0			0
$253$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$254$	−1.25667	−	2.17661i	−1.25667	−	2.17661i
$255$		0			0
$256$	1.11312	+	1.56316i	1.11312	+	1.56316i
$257$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$257$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.165101	+	0.231852i	−0.165101	+	0.231852i
$262$		0			0
$263$	1.70566	−	0.879330i	1.70566	−	0.879330i	0.723734	−	0.690079i	$-0.242424\pi$
$263$	1.70566	−	0.879330i	1.70566	−	0.879330i	0.981929	−	0.189251i	$-0.0606061\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−2.98596	+	4.19319i	−2.98596	+	4.19319i
$269$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$269$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$270$		0			0
$271$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$271$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$272$		0			0
$273$		0			0
$274$	−0.524075	−	3.64502i	−0.524075	−	3.64502i
$275$	−0.415415	−	0.719520i	−0.415415	−	0.719520i
$276$		0			0
$277$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	0.0475819	+	0.998867i	$0.484848\pi$
$277$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	−0.888835	+	0.458227i	$0.848485\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$281$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$282$		0			0
$283$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$283$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$284$	−2.21862	−	0.211852i	−2.21862	−	0.211852i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.500000	−	3.47758i	0.500000	−	3.47758i
$289$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$293$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$294$		0			0
$295$		0			0
$296$	5.40773	−	0.516375i	5.40773	−	0.516375i
$297$		0			0
$298$	−1.25667	+	2.17661i	−1.25667	+	2.17661i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	0.226900	−	0.496841i	0.226900	−	0.496841i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$307$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$311$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$312$		0			0
$313$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$313$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$314$		0			0
$315$		0			0
$316$	0.732593	+	0.215109i	0.732593	+	0.215109i
$317$	1.65210	+	0.318417i	1.65210	+	0.318417i	0.928368	−	0.371662i	$-0.121212\pi$
$317$	1.65210	+	0.318417i	1.65210	+	0.318417i	0.723734	+	0.690079i	$0.242424\pi$
$318$		0			0
$319$	−0.137171	−	0.192630i	−0.137171	−	0.192630i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−2.10859	+	1.65822i	−2.10859	+	1.65822i
$325$		0			0
$326$	0.128772	−	0.530804i	0.128772	−	0.530804i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.428368	−	1.23769i	0.428368	−	1.23769i	−0.500000	−	0.866025i	$-0.666667\pi$
$331$	0.428368	−	1.23769i	0.428368	−	1.23769i	0.928368	−	0.371662i	$-0.121212\pi$
$332$		0			0
$333$	−1.32254	−	1.04006i	−1.32254	−	1.04006i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$337$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$338$	1.70566	+	0.879330i	1.70566	+	0.879330i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	4.22871			4.22871
$345$		0			0
$346$		0			0
$347$	1.56199	+	0.625325i	1.56199	+	0.625325i	0.981929	−	0.189251i	$-0.0606061\pi$
$347$	1.56199	+	0.625325i	1.56199	+	0.625325i	0.580057	+	0.814576i	$0.303030\pi$
$348$		0			0
$349$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$349$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$350$		0			0
$351$		0			0
$352$	2.59450	+	1.33756i	2.59450	+	1.33756i
$353$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$353$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	2.11435	+	1.35881i	2.11435	+	1.35881i
$359$	0.428368	−	1.23769i	0.428368	−	1.23769i	−0.500000	−	0.866025i	$-0.666667\pi$
$359$	0.428368	−	1.23769i	0.428368	−	1.23769i	0.928368	−	0.371662i	$-0.121212\pi$
$360$		0			0
$361$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	−2.76167	−	2.17180i	−2.76167	−	2.17180i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.815816	+	0.157236i	0.815816	+	0.157236i	0.580057	−	0.814576i	$-0.303030\pi$
$373$	0.815816	+	0.157236i	0.815816	+	0.157236i	0.235759	+	0.971812i	$0.424242\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$379$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$380$		0			0
$381$		0			0
$382$	−3.17036	+	0.611037i	−3.17036	+	0.611037i
$383$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$383$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$384$		0			0
$385$		0			0
$386$	1.04408	−	1.20493i	1.04408	−	1.20493i
$387$	−0.947890	−	0.903811i	−0.947890	−	0.903811i
$388$		0			0
$389$	0.771316	+	0.308788i	0.771316	+	0.308788i	0.723734	−	0.690079i	$-0.242424\pi$
$389$	0.771316	+	0.308788i	0.771316	+	0.308788i	0.0475819	+	0.998867i	$0.484848\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−2.50196	+	0.238908i	−2.50196	+	0.238908i
$395$		0			0
$396$	−0.728939	−	2.10613i	−0.728939	−	2.10613i
$397$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$397$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$398$		0			0
$399$		0			0
$400$	−2.30075	−	2.65520i	−2.30075	−	2.65520i
$401$	0.0800569	−	1.68060i	0.0800569	−	1.68060i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	0.0800569	−	1.68060i	0.0800569	−	1.68060i	0.580057	−	0.814576i	$-0.303030\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.17597	−	0.755750i	1.17597	−	0.755750i
$408$		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			0
$412$		0			0
$413$		0			0
$414$	0.273100	+	1.89945i	0.273100	+	1.89945i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$419$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$420$		0			0
$421$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$421$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$422$	−0.924814	+	1.29872i	−0.924814	+	1.29872i
$423$		0			0
$424$	−0.816827	+	0.421104i	−0.816827	+	0.421104i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−2.95561	−	3.41095i	−2.95561	−	3.41095i
$429$		0			0
$430$		0			0
$431$	−0.947890	+	0.903811i	−0.947890	+	0.903811i	−0.995472	−	0.0950560i	$-0.969697\pi$
$431$	−0.947890	+	0.903811i	−0.947890	+	0.903811i	0.0475819	+	0.998867i	$0.484848\pi$
$432$		0			0
$433$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$433$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$434$		0			0
$435$		0			0
$436$	2.57385	+	4.45803i	2.57385	+	4.45803i
$437$		0			0
$438$		0			0
$439$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$439$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.195876	+	0.807410i	0.195876	+	0.807410i	0.981929	+	0.189251i	$0.0606061\pi$
$443$	0.195876	+	0.807410i	0.195876	+	0.807410i	−0.786053	+	0.618159i	$0.787879\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$449$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$450$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i
$451$		0			0
$452$	3.49743	+	0.333964i	3.49743	+	0.333964i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.283341	−	0.0270558i	0.283341	−	0.0270558i	0.0475819	−	0.998867i	$-0.484848\pi$
$457$	0.283341	−	0.0270558i	0.283341	−	0.0270558i	0.235759	+	0.971812i	$0.424242\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$463$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$464$	−0.723734	−	0.690079i	−0.723734	−	0.690079i
$465$		0			0
$466$	−2.33673	+	2.22806i	−2.33673	+	2.22806i
$467$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$467$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.967192	−	0.498622i	0.967192	−	0.498622i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$478$	−3.17036	−	0.611037i	−3.17036	−	0.611037i
$479$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$479$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.830830			−0.830830
$485$		0			0
$486$		0			0
$487$	−0.308779	+	1.27280i	−0.308779	+	1.27280i	0.580057	+	0.814576i	$0.303030\pi$
$487$	−0.308779	+	1.27280i	−0.308779	+	1.27280i	−0.888835	+	0.458227i	$0.848485\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$491$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.70566	+	0.879330i	1.70566	+	0.879330i	0.981929	+	0.189251i	$0.0606061\pi$
$499$	1.70566	+	0.879330i	1.70566	+	0.879330i	0.723734	+	0.690079i	$0.242424\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$503$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$504$		0			0
$505$		0			0
$506$	−1.56554	−	0.301733i	−1.56554	−	0.301733i
$507$		0			0
$508$	−3.26167	−	1.30578i	−3.26167	−	1.30578i
$509$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$509$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$510$		0			0
$511$		0			0
$512$	0.959493	+	0.281733i	0.959493	+	0.281733i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$521$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$522$	0.0259893	+	0.545582i	0.0259893	+	0.545582i
$523$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$523$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$524$		0			0
$525$		0			0
$526$	1.52977	−	3.34973i	1.52977	−	3.34973i
$527$		0			0
$528$		0			0
$529$	0.928368	+	0.371662i	0.928368	+	0.371662i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.294810	+	6.18883i	0.294810	+	6.18883i
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.78153	+	0.713215i	−1.78153	+	0.713215i	−0.786053	+	0.618159i	$0.787879\pi$
$541$	−1.78153	+	0.713215i	−1.78153	+	0.713215i	−0.995472	+	0.0950560i	$0.969697\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$547$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$548$	−3.72556	−	3.55232i	−3.72556	−	3.55232i
$549$		0			0
$550$	−1.48014	−	0.592560i	−1.48014	−	0.592560i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.459493	+	3.19584i	0.459493	+	3.19584i
$555$		0			0
$556$		0			0
$557$	−0.654136	−	1.89000i	−0.654136	−	1.89000i	−0.327068	−	0.945001i	$-0.606061\pi$
$557$	−0.654136	−	1.89000i	−0.654136	−	1.89000i	−0.327068	−	0.945001i	$-0.606061\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.0259893	−	0.545582i	0.0259893	−	0.545582i
$563$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$563$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−2.25667	+	1.45027i	−2.25667	+	1.45027i
$569$	0.396666	+	1.63508i	0.396666	+	1.63508i	0.723734	+	0.690079i	$0.242424\pi$
$569$	0.396666	+	1.63508i	0.396666	+	1.63508i	−0.327068	+	0.945001i	$0.606061\pi$
$570$		0			0
$571$	0.396666	−	1.63508i	0.396666	−	1.63508i	−0.327068	−	0.945001i	$-0.606061\pi$
$571$	0.396666	−	1.63508i	0.396666	−	1.63508i	0.723734	−	0.690079i	$-0.242424\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.841254	+	0.540641i	0.841254	+	0.540641i
$576$	−1.61435	−	2.79614i	−1.61435	−	2.79614i
$577$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$577$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$578$	−1.11312	−	1.56316i	−1.11312	−	1.56316i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.137171	+	0.192630i	−0.137171	+	0.192630i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$587$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	4.27815	−	4.07921i	4.27815	−	4.07921i
$593$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$593$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$594$		0			0
$595$		0			0
$596$	0.500000	+	3.47758i	0.500000	+	3.47758i
$597$		0			0
$598$		0			0
$599$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$599$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$600$		0			0
$601$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$601$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$602$		0			0
$603$	1.25667	−	1.45027i	1.25667	−	1.45027i
$604$	−0.180007	−	0.741999i	−0.180007	−	0.741999i
$605$		0			0
$606$		0			0
$607$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$607$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.91030	+	0.182411i	1.91030	+	0.182411i	0.981929	−	0.189251i	$-0.0606061\pi$
$613$	1.91030	+	0.182411i	1.91030	+	0.182411i	0.928368	+	0.371662i	$0.121212\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$617$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$618$		0			0
$619$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$619$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.723734	+	0.690079i	0.723734	+	0.690079i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$631$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$632$	0.853157	−	0.341553i	0.853157	−	0.341553i
$633$		0			0
$634$	2.86979	−	1.47948i	2.86979	−	1.47948i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.435418	−	0.127850i	−0.435418	−	0.127850i
$639$	0.815816	+	0.157236i	0.815816	+	0.157236i
$640$		0			0
$641$	1.16011	+	1.62915i	1.16011	+	1.62915i	0.580057	+	0.814576i	$0.303030\pi$
$641$	1.16011	+	1.62915i	1.16011	+	1.62915i	0.580057	+	0.814576i	$0.303030\pi$
$642$		0			0
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$647$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$648$	−0.761197	+	3.13770i	−0.761197	+	3.13770i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.317178	−	0.694523i	−0.317178	−	0.694523i
$653$	0.627639	−	1.81344i	0.627639	−	1.81344i	0.0475819	−	0.998867i	$-0.484848\pi$
$653$	0.627639	−	1.81344i	0.627639	−	1.81344i	0.580057	−	0.814576i	$-0.303030\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$659$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$660$		0			0
$661$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$661$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$662$	−0.822032	−	2.37511i	−0.822032	−	2.37511i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−3.22871			−3.22871
$667$	0.252989	+	0.130425i	0.252989	+	0.130425i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$673$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$674$	1.41712	+	0.730574i	1.41712	+	0.730574i
$675$		0			0
$676$	2.63403	−	0.507668i	2.63403	−	0.507668i
$677$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$677$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.0800569	+	1.68060i	0.0800569	+	1.68060i	0.580057	+	0.814576i	$0.303030\pi$
$683$	0.0800569	+	1.68060i	0.0800569	+	1.68060i	−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$	3.61702	−	2.84445i	3.61702	−	2.84445i
$689$		0			0
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$		0			0
$694$	3.09792	−	0.909632i	3.09792	−	0.909632i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$701$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$702$		0			0
$703$		0			0
$704$	2.63403	−	0.507668i	2.63403	−	0.507668i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.601300	+	0.573338i	0.601300	+	0.573338i	0.928368	−	0.371662i	$-0.121212\pi$
$709$	0.601300	+	0.573338i	0.601300	+	0.573338i	−0.327068	+	0.945001i	$0.606061\pi$
$710$		0			0
$711$	−0.264241	−	0.105786i	−0.264241	−	0.105786i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	3.49743	−	0.333964i	3.49743	−	0.333964i
$717$		0			0
$718$	−0.822032	−	2.37511i	−0.822032	−	2.37511i
$719$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$719$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$720$		0			0
$721$		0			0
$722$	1.25667	+	1.45027i	1.25667	+	1.45027i
$723$		0			0
$724$		0			0
$725$	0.223734	+	0.175946i	0.223734	+	0.175946i
$726$		0			0
$727$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$727$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.841254	−	0.540641i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$733$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$734$		0			0
$735$		0			0
$736$	−3.51334			−3.51334
$737$	0.797176	+	1.38075i	0.797176	+	1.38075i
$738$		0			0
$739$	−1.11312	−	1.56316i	−1.11312	−	1.56316i	−0.786053	−	0.618159i	$-0.787879\pi$
$739$	−1.11312	−	1.56316i	−1.11312	−	1.56316i	−0.327068	−	0.945001i	$-0.606061\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$743$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$744$		0			0
$745$		0			0
$746$	1.41712	−	0.730574i	1.41712	−	0.730574i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−0.165101	+	0.231852i	−0.165101	+	0.231852i	−0.888835	−	0.458227i	$-0.848485\pi$
$751$	−0.165101	+	0.231852i	−0.165101	+	0.231852i	0.723734	+	0.690079i	$0.242424\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$757$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$758$	−0.273100	−	0.473023i	−0.273100	−	0.473023i
$759$		0			0
$760$		0			0
$761$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$761$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$762$		0			0
$763$		0			0
$764$	−2.95561	+	3.41095i	−2.95561	+	3.41095i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$769$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$770$		0			0
$771$		0			0
$772$	0.106046	−	2.22618i	0.106046	−	2.22618i
$773$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$773$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$774$	−2.50196	−	0.238908i	−2.50196	−	0.238908i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.52977	−	0.449181i	1.52977	−	0.449181i
$779$		0			0
$780$		0			0
$781$	−0.345139	+	0.597799i	−0.345139	+	0.597799i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$787$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$788$	−2.54272	+	2.42448i	−2.54272	+	2.42448i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−2.25667	−	1.45027i	−2.25667	−	1.45027i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$797$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$798$		0			0
$799$		0			0
$800$	−3.44985	−	0.664903i	−3.44985	−	0.664903i
$801$		0			0
$802$	−1.87283	−	2.63003i	−1.87283	−	2.63003i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.0671040	+	0.276606i	−0.0671040	+	0.276606i	−0.995472	−	0.0950560i	$-0.969697\pi$
$809$	−0.0671040	+	0.276606i	−0.0671040	+	0.276606i	0.928368	+	0.371662i	$0.121212\pi$
$810$		0			0
$811$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$811$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$812$		0			0
$813$		0			0
$814$	0.877362	−	2.53497i	0.877362	−	2.53497i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.738471	−	0.380708i	−0.738471	−	0.380708i	0.0475819	−	0.998867i	$-0.484848\pi$
$821$	−0.738471	−	0.380708i	−0.738471	−	0.380708i	−0.786053	+	0.618159i	$0.787879\pi$
$822$		0			0
$823$	0.0930932	+	0.268975i	0.0930932	+	0.268975i	0.981929	−	0.189251i	$-0.0606061\pi$
$823$	0.0930932	+	0.268975i	0.0930932	+	0.268975i	−0.888835	+	0.458227i	$0.848485\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$827$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$828$	1.94142	+	1.85114i	1.94142	+	1.85114i
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		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		0.142315	−	0.989821i	$-0.454545\pi$
$839$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$840$		0			0
$841$	−0.773100	−	0.496841i	−0.773100	−	0.496841i
$842$	−0.822032	+	2.37511i	−0.822032	+	2.37511i
$843$		0			0
$844$	0.106046	+	2.22618i	0.106046	+	2.22618i
$845$		0			0
$846$		0			0
$847$		0			0
$848$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$849$		0			0
$850$		0			0
$851$	−0.841254	+	1.45709i	−0.841254	+	1.45709i
$852$		0			0
$853$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$853$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$854$		0			0
$855$		0			0
$856$	−5.33415	−	1.02807i	−5.33415	−	1.02807i
$857$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$857$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$858$		0			0
$859$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$859$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$860$		0			0
$861$		0			0
$862$	−0.357685	+	2.48775i	−0.357685	+	2.48775i
$863$	0.771316	−	0.308788i	0.771316	−	0.308788i	0.0475819	−	0.998867i	$-0.484848\pi$
$863$	0.771316	−	0.308788i	0.771316	−	0.308788i	0.723734	+	0.690079i	$0.242424\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.154861	−	0.178719i	0.154861	−	0.178719i
$870$		0			0
$871$		0			0
$872$	5.75202	+	2.30276i	5.75202	+	2.30276i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.827068	+	0.0789754i	−0.827068	+	0.0789754i	−0.500000	−	0.866025i	$-0.666667\pi$
$877$	−0.827068	+	0.0789754i	−0.827068	+	0.0789754i	−0.327068	+	0.945001i	$0.606061\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$881$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$882$		0			0
$883$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$883$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$884$		0			0
$885$		0			0
$886$	1.25324	+	0.985562i	1.25324	+	0.985562i
$887$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$887$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.195876	+	0.807410i	0.195876	+	0.807410i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.61435	+	2.79614i	1.61435	+	2.79614i
$899$		0			0
$900$	1.55601	+	2.18511i	1.55601	+	2.18511i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	3.55742	−	2.28621i	3.55742	−	2.28621i
$905$		0			0
$906$		0			0
$907$	1.70566	−	0.879330i	1.70566	−	0.879330i	0.723734	−	0.690079i	$-0.242424\pi$
$907$	1.70566	−	0.879330i	1.70566	−	0.879330i	0.981929	−	0.189251i	$-0.0606061\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$911$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$912$		0			0
$913$		0			0
$914$	0.395304	−	0.376921i	0.395304	−	0.376921i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	−0.888835	−	0.458227i	$-0.848485\pi$
$919$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	0.0475819	−	0.998867i	$-0.484848\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$926$	0.868184	+	3.57870i	0.868184	+	3.57870i
$927$		0			0
$928$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$929$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$929$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$930$		0			0
$931$		0			0
$932$	−0.642315	+	4.46740i	−0.642315	+	4.46740i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$937$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$941$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.867451	−	1.89945i	0.867451	−	1.89945i
$947$	1.21769	+	1.16106i	1.21769	+	1.16106i	0.981929	+	0.189251i	$0.0606061\pi$
$947$	1.21769	+	1.16106i	1.21769	+	1.16106i	0.235759	+	0.971812i	$0.424242\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$953$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$954$	0.507075	−	0.203002i	0.507075	−	0.203002i
$955$		0			0
$956$	−4.01161	+	2.06813i	−4.01161	+	2.06813i
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.981929	+	0.189251i	0.981929	+	0.189251i
$962$		0			0
$963$	0.975950	+	1.37053i	0.975950	+	1.37053i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$967$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$968$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$969$		0			0
$970$		0			0
$971$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$971$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$972$		0			0
$973$		0			0
$974$	1.04408	+	2.28621i	1.04408	+	2.28621i
$975$		0			0
$976$		0			0
$977$	−1.57211	−	1.23632i	−1.57211	−	1.23632i	−0.786053	−	0.618159i	$-0.787879\pi$
$977$	−1.57211	−	1.23632i	−1.57211	−	1.23632i	−0.786053	−	0.618159i	$-0.787879\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$982$	−3.27314	−	1.68742i	−3.27314	−	1.68742i
$983$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$983$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.759713	+	1.06687i	−0.759713	+	1.06687i
$990$		0			0
$991$	−1.78153	−	0.713215i	−1.78153	−	0.713215i	−0.995472	−	0.0950560i	$-0.969697\pi$
$991$	−1.78153	−	0.713215i	−1.78153	−	0.713215i	−0.786053	−	0.618159i	$-0.787879\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$997$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$998$	3.61596	−	0.696919i	3.61596	−	0.696919i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1127.1.v.a.325.1		20
7.2	even	3	inner	1127.1.v.a.509.1		20
7.3	odd	6		161.1.l.a.118.1	✓	10
7.4	even	3		161.1.l.a.118.1	✓	10
7.5	odd	6	inner	1127.1.v.a.509.1		20
7.6	odd	2	CM	1127.1.v.a.325.1		20
21.11	odd	6		1449.1.bq.a.118.1		10
21.17	even	6		1449.1.bq.a.118.1		10
23.8	even	11	inner	1127.1.v.a.31.1		20
28.3	even	6		2576.1.cj.a.1889.1		10
28.11	odd	6		2576.1.cj.a.1889.1		10
161.3	odd	66		3703.1.l.c.2603.1		10
161.4	even	33		3703.1.l.b.3429.1		10
161.10	even	66		3703.1.b.b.1588.1		5
161.11	odd	66		3703.1.l.i.2617.1		10
161.17	even	66		3703.1.l.e.706.1		10
161.18	even	33		3703.1.l.c.2582.1		10
161.25	even	33		3703.1.l.b.1392.1		10
161.31	odd	66		161.1.l.a.146.1	yes	10
161.32	even	33		3703.1.l.a.2911.1		10
161.38	even	66		3703.1.l.f.3044.1		10
161.39	even	33		3703.1.l.h.699.1		10
161.45	even	6		3703.1.l.f.118.1		10
161.52	odd	66		3703.1.l.a.706.1		10
161.53	odd	66		3703.1.l.i.699.1		10
161.54	odd	66	inner	1127.1.v.a.215.1		20
161.59	odd	66		3703.1.b.c.1588.1		5
161.60	odd	66		3703.1.l.e.2911.1		10
161.66	even	66		3703.1.l.g.2603.1		10
161.67	odd	66		3703.1.l.d.1392.1		10
161.73	odd	66		3703.1.l.b.3429.1		10
161.74	odd	66		3703.1.l.g.2582.1		10
161.80	even	66		3703.1.l.i.2617.1		10
161.81	even	33		3703.1.l.h.2617.1		10
161.87	odd	66		3703.1.l.c.2582.1		10
161.88	odd	66		3703.1.l.d.3429.1		10
161.94	odd	66		3703.1.l.b.1392.1		10
161.95	even	33		3703.1.l.c.2603.1		10
161.100	even	33	inner	1127.1.v.a.215.1		20
161.101	odd	66		3703.1.l.a.2911.1		10
161.102	odd	66		3703.1.b.b.1588.1		5
161.108	odd	66		3703.1.l.h.699.1		10
161.109	odd	66		3703.1.l.e.706.1		10
161.122	even	66		3703.1.l.i.699.1		10
161.123	even	33		161.1.l.a.146.1	yes	10
161.129	even	66		3703.1.l.e.2911.1		10
161.130	odd	66		3703.1.l.f.3044.1		10
161.136	even	66		3703.1.l.d.1392.1		10
161.137	odd	6		3703.1.l.f.118.1		10
161.143	even	66		3703.1.l.g.2582.1		10
161.144	even	33		3703.1.l.a.706.1		10
161.146	odd	22	inner	1127.1.v.a.31.1		20
161.150	odd	66		3703.1.l.h.2617.1		10
161.151	even	33		3703.1.b.c.1588.1		5
161.157	even	66		3703.1.l.d.3429.1		10
161.158	odd	66		3703.1.l.g.2603.1		10
483.284	odd	66		1449.1.bq.a.307.1		10
483.353	even	66		1449.1.bq.a.307.1		10
644.31	even	66		2576.1.cj.a.2561.1		10
644.123	odd	66		2576.1.cj.a.2561.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.1.l.a.118.1	✓	10	7.3	odd	6
161.1.l.a.118.1	✓	10	7.4	even	3
161.1.l.a.146.1	yes	10	161.31	odd	66
161.1.l.a.146.1	yes	10	161.123	even	33
1127.1.v.a.31.1		20	23.8	even	11	inner
1127.1.v.a.31.1		20	161.146	odd	22	inner
1127.1.v.a.215.1		20	161.54	odd	66	inner
1127.1.v.a.215.1		20	161.100	even	33	inner
1127.1.v.a.325.1		20	1.1	even	1	trivial
1127.1.v.a.325.1		20	7.6	odd	2	CM
1127.1.v.a.509.1		20	7.2	even	3	inner
1127.1.v.a.509.1		20	7.5	odd	6	inner
1449.1.bq.a.118.1		10	21.11	odd	6
1449.1.bq.a.118.1		10	21.17	even	6
1449.1.bq.a.307.1		10	483.284	odd	66
1449.1.bq.a.307.1		10	483.353	even	66
2576.1.cj.a.1889.1		10	28.3	even	6
2576.1.cj.a.1889.1		10	28.11	odd	6
2576.1.cj.a.2561.1		10	644.31	even	66
2576.1.cj.a.2561.1		10	644.123	odd	66
3703.1.b.b.1588.1		5	161.10	even	66
3703.1.b.b.1588.1		5	161.102	odd	66
3703.1.b.c.1588.1		5	161.59	odd	66
3703.1.b.c.1588.1		5	161.151	even	33
3703.1.l.a.706.1		10	161.52	odd	66
3703.1.l.a.706.1		10	161.144	even	33
3703.1.l.a.2911.1		10	161.32	even	33
3703.1.l.a.2911.1		10	161.101	odd	66
3703.1.l.b.1392.1		10	161.25	even	33
3703.1.l.b.1392.1		10	161.94	odd	66
3703.1.l.b.3429.1		10	161.4	even	33
3703.1.l.b.3429.1		10	161.73	odd	66
3703.1.l.c.2582.1		10	161.18	even	33
3703.1.l.c.2582.1		10	161.87	odd	66
3703.1.l.c.2603.1		10	161.3	odd	66
3703.1.l.c.2603.1		10	161.95	even	33
3703.1.l.d.1392.1		10	161.67	odd	66
3703.1.l.d.1392.1		10	161.136	even	66
3703.1.l.d.3429.1		10	161.88	odd	66
3703.1.l.d.3429.1		10	161.157	even	66
3703.1.l.e.706.1		10	161.17	even	66
3703.1.l.e.706.1		10	161.109	odd	66
3703.1.l.e.2911.1		10	161.60	odd	66
3703.1.l.e.2911.1		10	161.129	even	66
3703.1.l.f.118.1		10	161.45	even	6
3703.1.l.f.118.1		10	161.137	odd	6
3703.1.l.f.3044.1		10	161.38	even	66
3703.1.l.f.3044.1		10	161.130	odd	66
3703.1.l.g.2582.1		10	161.74	odd	66
3703.1.l.g.2582.1		10	161.143	even	66
3703.1.l.g.2603.1		10	161.66	even	66
3703.1.l.g.2603.1		10	161.158	odd	66
3703.1.l.h.699.1		10	161.39	even	33
3703.1.l.h.699.1		10	161.108	odd	66
3703.1.l.h.2617.1		10	161.81	even	33
3703.1.l.h.2617.1		10	161.150	odd	66
3703.1.l.i.699.1		10	161.53	odd	66
3703.1.l.i.699.1		10	161.122	even	66
3703.1.l.i.2617.1		10	161.11	odd	66
3703.1.l.i.2617.1		10	161.80	even	66

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:	\( N \)	\(=\)	\( 1127 = 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1127.v (of order \(66\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50842 - 1.18624i) q^{2} +(0.632425 - 2.60689i) q^{4} +(-1.34125 - 2.93694i) q^{8} +(-0.327068 + 0.945001i) q^{9} +(-0.653077 - 0.513585i) q^{11} +(-3.12278 - 1.60990i) q^{16} +(0.627639 + 1.81344i) q^{18} -1.59435 q^{22} +(0.981929 + 0.189251i) q^{23} +(0.928368 + 0.371662i) q^{25} +(0.273100 + 0.0801894i) q^{29} +(-3.44985 + 0.664903i) q^{32} +(2.25667 + 1.45027i) q^{36} +(-0.550294 + 1.58997i) q^{37} +(-0.544078 + 1.19136i) q^{43} +(-1.75188 + 1.37770i) q^{44} +(1.70566 - 0.879330i) q^{46} +(1.84125 - 0.540641i) q^{50} +(-0.0135432 - 0.284307i) q^{53} +(0.507075 - 0.203002i) q^{58} +(-2.11435 + 2.44009i) q^{64} +(-1.78153 - 0.713215i) q^{67} +(-0.118239 - 0.822373i) q^{71} +(3.21409 - 0.306908i) q^{72} +(1.05601 + 3.05113i) q^{74} +(-0.0135432 + 0.284307i) q^{79} +(-0.786053 - 0.618159i) q^{81} +(0.592542 + 2.44249i) q^{86} +(-0.632425 + 2.60689i) q^{88} +(1.11435 - 2.44009i) q^{92} +(0.698939 - 0.449181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 3 q^{4} - 8 q^{8} + q^{9} + 2 q^{11} - 6 q^{16} + 2 q^{18} - 8 q^{22} + q^{23} + q^{25} - 4 q^{29} - 5 q^{32} + 16 q^{36} + 2 q^{37} - 4 q^{43} - 5 q^{44} + 2 q^{46} + 18 q^{50} + 2 q^{53}+ \cdots - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 3 * q^4 - 8 * q^8 + q^9 + 2 * q^11 - 6 * q^16 + 2 * q^18 - 8 * q^22 + q^23 + q^25 - 4 * q^29 - 5 * q^32 + 16 * q^36 + 2 * q^37 - 4 * q^43 - 5 * q^44 + 2 * q^46 + 18 * q^50 + 2 * q^53 - 7 * q^58 - 14 * q^64 + 2 * q^67 - 4 * q^71 + 4 * q^72 - 7 * q^74 + 2 * q^79 + q^81 + 4 * q^86 - 3 * q^88 - 6 * q^92 - 4 * q^99

Introduction

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