LMFDB - Embedded newform 3131.1.de.a.929.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3131,1,Mod(30,3131)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3131, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([25, 47]))

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

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

chi := DirichletCharacter("3131.30");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3131 = 31 \cdot 101 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3131.de (of order $50$, 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:	$1.56257255455$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{50})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{15} + x^{10} - x^{5} + 1 $ x^20 - x^15 + x^10 - x^5 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{50}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{50} - \cdots)$

Embedding invariants

Embedding label			929.1
Root			$0.637424 + 0.770513i$ of defining polynomial
Character	$\chi$	$=$	3131.929
Dual form			3131.1.de.a.1611.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05491 - 1.12336i) q^{2} +(-0.0863221 + 1.37205i) q^{4} +(-1.41213 - 1.32608i) q^{5} +(0.742395 + 1.35041i) q^{7} +(0.444986 - 0.368125i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})$	\(q+(-1.05491 - 1.12336i) q^{2} +(-0.0863221 + 1.37205i) q^{4} +(-1.41213 - 1.32608i) q^{5} +(0.742395 + 1.35041i) q^{7} +(0.444986 - 0.368125i) q^{8} +(0.929776 - 0.368125i) q^{9} +2.98522i q^{10} +(0.733842 - 2.25853i) q^{14} +(0.480968 + 0.0607603i) q^{16} +(-1.39436 - 0.656137i) q^{18} +(-1.73879 + 0.219661i) q^{19} +(1.94135 - 1.82305i) q^{20} +(0.172838 + 2.74718i) q^{25} +(-1.91692 + 0.902033i) q^{28} +(-0.876307 + 0.481754i) q^{31} +(-0.778577 - 1.07162i) q^{32} +(0.742395 - 2.89144i) q^{35} +(0.424825 + 1.30748i) q^{36} +(2.08102 + 1.72157i) q^{38} +(-1.11654 - 0.0702469i) q^{40} +(-0.992567 + 1.36615i) q^{41} +(-1.80113 - 0.713118i) q^{45} +(-1.56720 - 0.402389i) q^{47} +(-0.736635 + 1.16075i) q^{49} +(2.90375 - 3.09218i) q^{50} +(0.827475 + 0.327621i) q^{56} +(-0.246226 + 1.94908i) q^{59} +(1.46560 + 0.476203i) q^{62} +(1.18738 + 0.982287i) q^{63} +(-0.291649 + 1.52888i) q^{64} +(-0.246226 - 0.0469702i) q^{67} +(-4.03128 + 2.21622i) q^{70} +(0.371808 + 1.94908i) q^{71} +(0.278222 - 0.506084i) q^{72} +(-0.151289 - 2.40467i) q^{76} +(-0.598617 - 0.723604i) q^{80} +(0.728969 - 0.684547i) q^{81} +(2.58174 - 0.326150i) q^{82} +(1.09893 + 2.77559i) q^{90} +(1.20122 + 2.18501i) q^{94} +(2.74670 + 1.99559i) q^{95} +(0.101597 - 1.61484i) q^{97} +(2.08102 - 0.396976i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{8}+O(q^{10}) $ 20 * q + 20 * q^8	$ 20 q + 20 q^{8} - 10 q^{14} + 5 q^{16} - 5 q^{19} + 5 q^{20} + 5 q^{28} - 5 q^{36} + 5 q^{38} - 5 q^{40} - 5 q^{45} + 5 q^{50} - 20 q^{56} + 5 q^{59} + 20 q^{63} + 20 q^{64} + 5 q^{67} - 5 q^{70} - 5 q^{71} - 20 q^{72} - 5 q^{76} + 20 q^{82} + 5 q^{98}+O(q^{100}) $ 20 * q + 20 * q^8 - 10 * q^14 + 5 * q^16 - 5 * q^19 + 5 * q^20 + 5 * q^28 - 5 * q^36 + 5 * q^38 - 5 * q^40 - 5 * q^45 + 5 * q^50 - 20 * q^56 + 5 * q^59 + 20 * q^63 + 20 * q^64 + 5 * q^67 - 5 * q^70 - 5 * q^71 - 20 * q^72 - 5 * q^76 + 20 * q^82 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3131\mathbb{Z}\right)^\times$.

$n$	$809$	$2729$
$\chi(n)$	$-1$	$e\left(\frac{13}{50}\right)$

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 $

$2$	−1.05491	−	1.12336i	−1.05491	−	1.12336i	−0.992115	−	0.125333i	$-0.960000\pi$
$2$	−1.05491	−	1.12336i	−1.05491	−	1.12336i	−0.0627905	−	0.998027i	$-0.520000\pi$
$3$		0			0		0.982287	−	0.187381i	$-0.0600000\pi$
$3$		0			0		−0.982287	+	0.187381i	$0.940000\pi$
$4$	−0.0863221	+	1.37205i	−0.0863221	+	1.37205i
$5$	−1.41213	−	1.32608i	−1.41213	−	1.32608i	−0.876307	−	0.481754i	$-0.840000\pi$
$5$	−1.41213	−	1.32608i	−1.41213	−	1.32608i	−0.535827	−	0.844328i	$-0.680000\pi$
$6$		0			0
$7$	0.742395	+	1.35041i	0.742395	+	1.35041i	0.929776	+	0.368125i	$0.120000\pi$
$7$	0.742395	+	1.35041i	0.742395	+	1.35041i	−0.187381	+	0.982287i	$0.560000\pi$
$8$	0.444986	−	0.368125i	0.444986	−	0.368125i
$9$	0.929776	−	0.368125i	0.929776	−	0.368125i
$10$			2.98522i			2.98522i
$11$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$11$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$12$		0			0
$13$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$13$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$14$	0.733842	−	2.25853i	0.733842	−	2.25853i
$15$		0			0
$16$	0.480968	+	0.0607603i	0.480968	+	0.0607603i
$17$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$17$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$18$	−1.39436	−	0.656137i	−1.39436	−	0.656137i
$19$	−1.73879	+	0.219661i	−1.73879	+	0.219661i	−0.929776	−	0.368125i	$-0.880000\pi$
$19$	−1.73879	+	0.219661i	−1.73879	+	0.219661i	−0.809017	+	0.587785i	$0.800000\pi$
$20$	1.94135	−	1.82305i	1.94135	−	1.82305i
$21$		0			0
$22$		0			0
$23$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$23$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$24$		0			0
$25$	0.172838	+	2.74718i	0.172838	+	2.74718i
$26$		0			0
$27$		0			0
$28$	−1.91692	+	0.902033i	−1.91692	+	0.902033i
$29$		0			0		0.481754	−	0.876307i	$-0.340000\pi$
$29$		0			0		−0.481754	+	0.876307i	$0.660000\pi$
$30$		0			0
$31$	−0.876307	+	0.481754i	−0.876307	+	0.481754i
$31$	−0.876307	+	0.481754i	−0.876307	+	0.481754i
$32$	−0.778577	−	1.07162i	−0.778577	−	1.07162i
$33$		0			0
$34$		0			0
$35$	0.742395	−	2.89144i	0.742395	−	2.89144i
$36$	0.424825	+	1.30748i	0.424825	+	1.30748i
$37$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$37$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$38$	2.08102	+	1.72157i	2.08102	+	1.72157i
$39$		0			0
$40$	−1.11654	−	0.0702469i	−1.11654	−	0.0702469i
$41$	−0.992567	+	1.36615i	−0.992567	+	1.36615i	−0.0627905	+	0.998027i	$0.520000\pi$
$41$	−0.992567	+	1.36615i	−0.992567	+	1.36615i	−0.929776	+	0.368125i	$0.880000\pi$
$42$		0			0
$43$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$43$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$44$		0			0
$45$	−1.80113	−	0.713118i	−1.80113	−	0.713118i
$46$		0			0
$47$	−1.56720	−	0.402389i	−1.56720	−	0.402389i	−0.637424	−	0.770513i	$-0.720000\pi$
$47$	−1.56720	−	0.402389i	−1.56720	−	0.402389i	−0.929776	+	0.368125i	$0.880000\pi$
$48$		0			0
$49$	−0.736635	+	1.16075i	−0.736635	+	1.16075i
$50$	2.90375	−	3.09218i	2.90375	−	3.09218i
$51$		0			0
$52$		0			0
$53$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$53$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$54$		0			0
$55$		0			0
$56$	0.827475	+	0.327621i	0.827475	+	0.327621i
$57$		0			0
$58$		0			0
$59$	−0.246226	+	1.94908i	−0.246226	+	1.94908i	0.0627905	+	0.998027i	$0.480000\pi$
$59$	−0.246226	+	1.94908i	−0.246226	+	1.94908i	−0.309017	+	0.951057i	$0.600000\pi$
$60$		0			0
$61$		0			0		−0.998027	−	0.0627905i	$-0.980000\pi$
$61$		0			0		0.998027	+	0.0627905i	$0.0200000\pi$
$62$	1.46560	+	0.476203i	1.46560	+	0.476203i
$63$	1.18738	+	0.982287i	1.18738	+	0.982287i
$64$	−0.291649	+	1.52888i	−0.291649	+	1.52888i
$65$		0			0
$66$		0			0
$67$	−0.246226	−	0.0469702i	−0.246226	−	0.0469702i	0.0627905	−	0.998027i	$-0.480000\pi$
$67$	−0.246226	−	0.0469702i	−0.246226	−	0.0469702i	−0.309017	+	0.951057i	$0.600000\pi$
$68$		0			0
$69$		0			0
$70$	−4.03128	+	2.21622i	−4.03128	+	2.21622i
$71$	0.371808	+	1.94908i	0.371808	+	1.94908i	0.309017	+	0.951057i	$0.400000\pi$
$71$	0.371808	+	1.94908i	0.371808	+	1.94908i	0.0627905	+	0.998027i	$0.480000\pi$
$72$	0.278222	−	0.506084i	0.278222	−	0.506084i
$73$		0			0		0.904827	−	0.425779i	$-0.140000\pi$
$73$		0			0		−0.904827	+	0.425779i	$0.860000\pi$
$74$		0			0
$75$		0			0
$76$	−0.151289	−	2.40467i	−0.151289	−	2.40467i
$77$		0			0
$78$		0			0
$79$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$79$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$80$	−0.598617	−	0.723604i	−0.598617	−	0.723604i
$81$	0.728969	−	0.684547i	0.728969	−	0.684547i
$82$	2.58174	−	0.326150i	2.58174	−	0.326150i
$83$		0			0		−0.904827	−	0.425779i	$-0.860000\pi$
$83$		0			0		0.904827	+	0.425779i	$0.140000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.125333	−	0.992115i	$-0.540000\pi$
$89$		0			0		0.125333	+	0.992115i	$0.460000\pi$
$90$	1.09893	+	2.77559i	1.09893	+	2.77559i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	1.20122	+	2.18501i	1.20122	+	2.18501i
$95$	2.74670	+	1.99559i	2.74670	+	1.99559i
$96$		0			0
$97$	0.101597	−	1.61484i	0.101597	−	1.61484i	−0.535827	−	0.844328i	$-0.680000\pi$
$97$	0.101597	−	1.61484i	0.101597	−	1.61484i	0.637424	−	0.770513i	$-0.280000\pi$
$98$	2.08102	−	0.396976i	2.08102	−	0.396976i
$99$		0			0
$100$	−3.78419			−3.78419
$101$	−0.728969	−	0.684547i	−0.728969	−	0.684547i
$101$	−0.728969	−	0.684547i	−0.728969	−	0.684547i
$102$		0			0
$103$	−0.171593	−	0.182728i	−0.171593	−	0.182728i	0.637424	−	0.770513i	$-0.280000\pi$
$103$	−0.171593	−	0.182728i	−0.171593	−	0.182728i	−0.809017	+	0.587785i	$0.800000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	0.0627905	−	0.998027i	$-0.480000\pi$
$107$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	−0.929776	+	0.368125i	$0.880000\pi$
$108$		0			0
$109$	1.46560	−	1.21245i	1.46560	−	1.21245i	0.535827	−	0.844328i	$-0.320000\pi$
$109$	1.46560	−	1.21245i	1.46560	−	1.21245i	0.929776	−	0.368125i	$-0.120000\pi$
$110$		0			0
$111$		0			0
$112$	0.275017	+	0.694613i	0.275017	+	0.694613i
$113$	0.246226	+	1.94908i	0.246226	+	1.94908i	0.309017	+	0.951057i	$0.400000\pi$
$113$	0.246226	+	1.94908i	0.246226	+	1.94908i	−0.0627905	+	0.998027i	$0.520000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	2.44927	−	1.77950i	2.44927	−	1.77950i
$119$		0			0
$120$		0			0
$121$	−0.728969	+	0.684547i	−0.728969	+	0.684547i
$122$		0			0
$123$		0			0
$124$	−0.585345	−	1.24392i	−0.585345	−	1.24392i
$125$	2.16412	−	2.61597i	2.16412	−	2.61597i
$126$	−0.149113	−	2.37008i	−0.149113	−	2.37008i
$127$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$127$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$128$	0.906747	−	0.575439i	0.906747	−	0.575439i
$129$		0			0
$130$		0			0
$131$	0.159566	+	0.836475i	0.159566	+	0.836475i	0.968583	+	0.248690i	$0.0800000\pi$
$131$	0.159566	+	0.836475i	0.159566	+	0.836475i	−0.809017	+	0.587785i	$0.800000\pi$
$132$		0			0
$133$	−1.58750	−	2.18501i	−1.58750	−	2.18501i
$134$	0.206981	+	0.326150i	0.206981	+	0.326150i
$135$		0			0
$136$		0			0
$137$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$137$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$138$		0			0
$139$		0			0		−0.770513	−	0.637424i	$-0.780000\pi$
$139$		0			0		0.770513	+	0.637424i	$0.220000\pi$
$140$	3.90311	+	1.26820i	3.90311	+	1.26820i
$141$		0			0
$142$	1.79730	−	2.47377i	1.79730	−	2.47377i
$143$		0			0
$144$	0.469560	−	0.120562i	0.469560	−	0.120562i
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.68532	−	0.106032i	1.68532	−	0.106032i	0.809017	−	0.587785i	$-0.200000\pi$
$149$	1.68532	−	0.106032i	1.68532	−	0.106032i	0.876307	+	0.481754i	$0.160000\pi$
$150$		0			0
$151$		0			0		0.684547	−	0.728969i	$-0.260000\pi$
$151$		0			0		−0.684547	+	0.728969i	$0.740000\pi$
$152$	−0.692877	+	0.737839i	−0.692877	+	0.737839i
$153$		0			0
$154$		0			0
$155$	1.87631	+	0.481754i	1.87631	+	0.481754i
$156$		0			0
$157$	1.80113	+	0.713118i	1.80113	+	0.713118i	0.992115	+	0.125333i	$0.0400000\pi$
$157$	1.80113	+	0.713118i	1.80113	+	0.713118i	0.809017	+	0.587785i	$0.200000\pi$
$158$		0			0
$159$		0			0
$160$	−0.321600	+	2.54573i	−0.321600	+	2.54573i
$161$		0			0
$162$	−1.53799	−	0.0967619i	−1.53799	−	0.0967619i
$163$	−1.30209	−	0.423073i	−1.30209	−	0.423073i	−0.425779	−	0.904827i	$-0.640000\pi$
$163$	−1.30209	−	0.423073i	−1.30209	−	0.423073i	−0.876307	+	0.481754i	$0.840000\pi$
$164$	−1.78875	−	1.47978i	−1.78875	−	1.47978i
$165$		0			0
$166$		0			0
$167$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$167$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$168$		0			0
$169$	0.535827	+	0.844328i	0.535827	+	0.844328i
$170$		0			0
$171$	−1.53583	+	0.844328i	−1.53583	+	0.844328i
$172$		0			0
$173$	−0.239615	+	0.435857i	−0.239615	+	0.435857i	−0.968583	−	0.248690i	$-0.920000\pi$
$173$	−0.239615	+	0.435857i	−0.239615	+	0.435857i	0.728969	+	0.684547i	$0.240000\pi$
$174$		0			0
$175$	−3.58151	+	2.27290i	−3.58151	+	2.27290i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$179$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$180$	1.13391	−	2.40968i	1.13391	−	2.40968i
$181$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$181$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.687381	−	2.11554i	0.687381	−	2.11554i
$189$		0			0
$190$	−0.655737	−	5.19069i	−0.655737	−	5.19069i
$191$	0.354691	+	0.895846i	0.354691	+	0.895846i	0.992115	+	0.125333i	$0.0400000\pi$
$191$	0.354691	+	0.895846i	0.354691	+	0.895846i	−0.637424	+	0.770513i	$0.720000\pi$
$192$		0			0
$193$	0.116762	−	0.0462295i	0.116762	−	0.0462295i	−0.309017	−	0.951057i	$-0.600000\pi$
$193$	0.116762	−	0.0462295i	0.116762	−	0.0462295i	0.425779	+	0.904827i	$0.360000\pi$
$194$	−1.92122	+	1.58937i	−1.92122	+	1.58937i
$195$		0			0
$196$	−1.52902	−	1.11090i	−1.52902	−	1.11090i
$197$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$197$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$198$		0			0
$199$		0			0		0.982287	−	0.187381i	$-0.0600000\pi$
$199$		0			0		−0.982287	+	0.187381i	$0.940000\pi$
$200$	1.08822	+	1.15883i	1.08822	+	1.15883i
$201$		0			0
$202$			1.54103i			1.54103i
$203$		0			0
$204$		0			0
$205$	3.21327	−	0.612963i	3.21327	−	0.612963i
$206$	−0.0242550	+	0.385521i	−0.0242550	+	0.385521i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.50441	+	0.595638i	−1.50441	+	0.595638i	−0.968583	−	0.248690i	$-0.920000\pi$
$211$	−1.50441	+	0.595638i	−1.50441	+	0.595638i	−0.535827	+	0.844328i	$0.680000\pi$
$212$		0			0
$213$		0			0
$214$	0.206981	+	1.63842i	0.206981	+	1.63842i
$215$		0			0
$216$		0			0
$217$	−1.30113	−	0.825723i	−1.30113	−	0.825723i
$218$	−2.90809	−	0.367378i	−2.90809	−	0.367378i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$223$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$224$	0.869115	−	1.84696i	0.869115	−	1.84696i
$225$	1.17201	+	2.49064i	1.17201	+	2.49064i
$226$	1.92978	−	2.33270i	1.92978	−	2.33270i
$227$	0.0235315	+	0.374023i	0.0235315	+	0.374023i	0.992115	+	0.125333i	$0.0400000\pi$
$227$	0.0235315	+	0.374023i	0.0235315	+	0.374023i	−0.968583	+	0.248690i	$0.920000\pi$
$228$		0			0
$229$		0			0		0.844328	−	0.535827i	$-0.180000\pi$
$229$		0			0		−0.844328	+	0.535827i	$0.820000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.41789	+	0.779494i	−1.41789	+	0.779494i	−0.992115	−	0.125333i	$-0.960000\pi$
$233$	−1.41789	+	0.779494i	−1.41789	+	0.779494i	−0.425779	+	0.904827i	$0.640000\pi$
$234$		0			0
$235$	1.67950	+	2.64646i	1.67950	+	2.64646i
$236$	−2.65298	−	0.506084i	−2.65298	−	0.506084i
$237$		0			0
$238$		0			0
$239$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$239$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$240$		0			0
$241$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$241$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$242$	1.53799	+	0.0967619i	1.53799	+	0.0967619i
$243$		0			0
$244$		0			0
$245$	2.57948	−	0.662297i	2.57948	−	0.662297i
$246$		0			0
$247$		0			0
$248$	−0.212599	+	0.536964i	−0.212599	+	0.536964i
$249$		0			0
$250$	−5.22162	+	0.328517i	−5.22162	+	0.328517i
$251$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$251$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$252$	−1.45024	+	1.54435i	−1.45024	+	1.54435i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.0954119	−	0.0244976i	−0.0954119	−	0.0244976i
$257$	0.432756	−	1.09302i	0.432756	−	1.09302i	−0.535827	−	0.844328i	$-0.680000\pi$
$257$	0.432756	−	1.09302i	0.432756	−	1.09302i	0.968583	−	0.248690i	$-0.0800000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.771335	−	1.06165i	0.771335	−	1.06165i
$263$		0			0		−0.998027	−	0.0627905i	$-0.980000\pi$
$263$		0			0		0.998027	+	0.0627905i	$0.0200000\pi$
$264$		0			0
$265$		0			0
$266$	−0.779889	+	4.08832i	−0.779889	+	4.08832i
$267$		0			0
$268$	0.0857002	−	0.333780i	0.0857002	−	0.333780i
$269$		0			0		−0.982287	−	0.187381i	$-0.940000\pi$
$269$		0			0		0.982287	+	0.187381i	$0.0600000\pi$
$270$		0			0
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$277$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$278$		0			0
$279$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$280$	−0.734054	−	1.55994i	−0.734054	−	1.55994i
$281$	−0.0534698	+	0.113629i	−0.0534698	+	0.113629i	−0.929776	−	0.368125i	$-0.880000\pi$
$281$	−0.0534698	+	0.113629i	−0.0534698	+	0.113629i	0.876307	+	0.481754i	$0.160000\pi$
$282$		0			0
$283$	−1.17950	+	1.10762i	−1.17950	+	1.10762i	−0.187381	+	0.982287i	$0.560000\pi$
$283$	−1.17950	+	1.10762i	−1.17950	+	1.10762i	−0.992115	+	0.125333i	$0.960000\pi$
$284$	−2.70633	+	0.341890i	−2.70633	+	0.341890i
$285$		0			0
$286$		0			0
$287$	−2.58174	−	0.326150i	−2.58174	−	0.326150i
$288$	−1.11839	−	0.709753i	−1.11839	−	0.709753i
$289$	0.309017	−	0.951057i	0.309017	−	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$293$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$294$		0			0
$295$	2.93235	−	2.42585i	2.93235	−	2.42585i
$296$		0			0
$297$		0			0
$298$	−1.89697	−	1.78137i	−1.89697	−	1.78137i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.849650			−0.849650
$305$		0			0
$306$		0			0
$307$	−0.0388067	+	0.616814i	−0.0388067	+	0.616814i	0.929776	+	0.368125i	$0.120000\pi$
$307$	−0.0388067	+	0.616814i	−0.0388067	+	0.616814i	−0.968583	+	0.248690i	$0.920000\pi$
$308$		0			0
$309$		0			0
$310$	−1.43814	−	2.61597i	−1.43814	−	2.61597i
$311$	1.46560	−	1.21245i	1.46560	−	1.21245i	0.535827	−	0.844328i	$-0.320000\pi$
$311$	1.46560	−	1.21245i	1.46560	−	1.21245i	0.929776	−	0.368125i	$-0.120000\pi$
$312$		0			0
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$	−1.09893	−	2.77559i	−1.09893	−	2.77559i
$315$	−0.374148	−	2.96169i	−0.374148	−	2.96169i
$316$		0			0
$317$	0.613161	−	1.88711i	0.613161	−	1.88711i	0.187381	−	0.982287i	$-0.440000\pi$
$317$	0.613161	−	1.88711i	0.613161	−	1.88711i	0.425779	−	0.904827i	$-0.360000\pi$
$318$		0			0
$319$		0			0
$320$	2.43926	−	1.77223i	2.43926	−	1.77223i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.876307	+	1.05927i	0.876307	+	1.05927i
$325$		0			0
$326$	0.898314	+	1.90901i	0.898314	+	1.90901i
$327$		0			0
$328$	0.0612353	+	0.973307i	0.0612353	+	0.973307i
$329$	−0.620092	−	2.41510i	−0.620092	−	2.41510i
$330$		0			0
$331$		0			0		0.904827	−	0.425779i	$-0.140000\pi$
$331$		0			0		−0.904827	+	0.425779i	$0.860000\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.285418	+	0.392845i	0.285418	+	0.392845i
$336$		0			0
$337$		0			0		−0.982287	−	0.187381i	$-0.940000\pi$
$337$		0			0		0.982287	+	0.187381i	$0.0600000\pi$
$338$	0.383238	−	1.49261i	0.383238	−	1.49261i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	2.56864	+	0.834600i	2.56864	+	0.834600i
$343$	−0.576380	−	0.0362627i	−0.576380	−	0.0362627i
$344$		0			0
$345$		0			0
$346$	0.742395	−	0.190615i	0.742395	−	0.190615i
$347$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$347$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$348$		0			0
$349$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$349$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$350$	6.33144	+	1.62564i	6.33144	+	1.62564i
$351$		0			0
$352$		0			0
$353$		0			0		0.684547	−	0.728969i	$-0.260000\pi$
$353$		0			0		−0.684547	+	0.728969i	$0.740000\pi$
$354$		0			0
$355$	2.05960	−	3.24541i	2.05960	−	3.24541i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.791759	−	0.313480i	−0.791759	−	0.313480i	−0.0627905	−	0.998027i	$-0.520000\pi$
$359$	−0.791759	−	0.313480i	−0.791759	−	0.313480i	−0.728969	+	0.684547i	$0.760000\pi$
$360$	−1.06400	+	0.345713i	−1.06400	+	0.345713i
$361$	2.00657	−	0.515199i	2.00657	−	0.515199i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$367$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$368$		0			0
$369$	−0.419952	+	1.63560i	−0.419952	+	1.63560i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.62954	+	0.895846i	−1.62954	+	0.895846i	−0.637424	+	0.770513i	$0.720000\pi$
$373$	−1.62954	+	0.895846i	−1.62954	+	0.895846i	−0.992115	+	0.125333i	$0.960000\pi$
$374$		0			0
$375$		0			0
$376$	−0.845512	+	0.397868i	−0.845512	+	0.397868i
$377$		0			0
$378$		0			0
$379$	0.110048	+	1.74915i	0.110048	+	1.74915i	0.535827	+	0.844328i	$0.320000\pi$
$379$	0.110048	+	1.74915i	0.110048	+	1.74915i	−0.425779	+	0.904827i	$0.640000\pi$
$380$	−2.97515	+	3.59634i	−2.97515	+	3.59634i
$381$		0			0
$382$	0.632193	−	1.34348i	0.632193	−	1.34348i
$383$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$383$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$384$		0			0
$385$		0			0
$386$	−0.175105	−	0.0823984i	−0.175105	−	0.0823984i
$387$		0			0
$388$	2.20687	+	0.278793i	2.20687	+	0.278793i
$389$		0			0		−0.844328	−	0.535827i	$-0.820000\pi$
$389$		0			0		0.844328	+	0.535827i	$0.180000\pi$
$390$		0			0
$391$		0			0
$392$	0.0995085	+	0.787691i	0.0995085	+	0.787691i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−0.813516	−	1.47978i	−0.813516	−	1.47978i	−0.876307	−	0.481754i	$-0.840000\pi$
$397$	−0.813516	−	1.47978i	−0.813516	−	1.47978i	0.0627905	−	0.998027i	$-0.480000\pi$
$398$		0			0
$399$		0			0
$400$	−0.0837902	+	1.33181i	−0.0837902	+	1.33181i
$401$		0			0		0.982287	−	0.187381i	$-0.0600000\pi$
$401$		0			0		−0.982287	+	0.187381i	$0.940000\pi$
$402$		0			0
$403$		0			0
$404$	1.00216	−	0.941090i	1.00216	−	0.941090i
$405$	−1.93717			−1.93717
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$409$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$410$	−4.07827	−	2.96304i	−4.07827	−	2.96304i
$411$		0			0
$412$	0.265524	−	0.219661i	0.265524	−	0.219661i
$413$	−2.81486	+	1.11448i	−2.81486	+	1.11448i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.992567	+	0.629902i	0.992567	+	0.629902i	0.929776	−	0.368125i	$-0.120000\pi$
$419$	0.992567	+	0.629902i	0.992567	+	0.629902i	0.0627905	+	0.998027i	$0.480000\pi$
$420$		0			0
$421$	−0.688925	+	0.500534i	−0.688925	+	0.500534i	−0.876307	−	0.481754i	$-0.840000\pi$
$421$	−0.688925	+	0.500534i	−0.688925	+	0.500534i	0.187381	+	0.982287i	$0.440000\pi$
$422$	2.25613	+	1.06165i	2.25613	+	1.06165i
$423$	−1.60528	+	0.202793i	−1.60528	+	0.202793i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.939097	−	1.13517i	0.939097	−	1.13517i
$429$		0			0
$430$		0			0
$431$	−0.419952	+	0.266509i	−0.419952	+	0.266509i	−0.728969	−	0.684547i	$-0.760000\pi$
$431$	−0.419952	+	0.266509i	−0.419952	+	0.266509i	0.309017	+	0.951057i	$0.400000\pi$
$432$		0			0
$433$		0			0		0.481754	−	0.876307i	$-0.340000\pi$
$433$		0			0		−0.481754	+	0.876307i	$0.660000\pi$
$434$	0.444986	+	2.33270i	0.444986	+	2.33270i
$435$		0			0
$436$	1.53703	+	2.11554i	1.53703	+	2.11554i
$437$		0			0
$438$		0			0
$439$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$439$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$440$		0			0
$441$	−0.257605	+	1.35041i	−0.257605	+	1.35041i
$442$		0			0
$443$	−1.72108	−	0.559214i	−1.72108	−	0.559214i	−0.728969	−	0.684547i	$-0.760000\pi$
$443$	−1.72108	−	0.559214i	−1.72108	−	0.559214i	−0.992115	+	0.125333i	$0.960000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−2.28113	+	0.741184i	−2.28113	+	0.741184i
$449$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$449$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$450$	1.56153	−	3.94397i	1.56153	−	3.94397i
$451$		0			0
$452$	−2.69549	+	0.169586i	−2.69549	+	0.169586i
$453$		0			0
$454$	0.395339	−	0.420993i	0.395339	−	0.420993i
$455$		0			0
$456$		0			0
$457$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$457$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$461$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$462$		0			0
$463$		0			0		0.125333	−	0.992115i	$-0.460000\pi$
$463$		0			0		−0.125333	+	0.992115i	$0.540000\pi$
$464$		0			0
$465$		0			0
$466$	2.37140	+	0.770513i	2.37140	+	0.770513i
$467$	1.46560	+	1.21245i	1.46560	+	1.21245i	0.929776	+	0.368125i	$0.120000\pi$
$467$	1.46560	+	1.21245i	1.46560	+	1.21245i	0.535827	+	0.844328i	$0.320000\pi$
$468$		0			0
$469$	−0.119368	−	0.367378i	−0.119368	−	0.367378i
$470$	1.20122	−	4.67845i	1.20122	−	4.67845i
$471$		0			0
$472$	0.607938	+	0.957957i	0.607938	+	0.957957i
$473$		0			0
$474$		0			0
$475$	−0.903977	−	4.73882i	−0.903977	−	4.73882i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.450043	−	1.75280i	−0.450043	−	1.75280i	−0.637424	−	0.770513i	$-0.720000\pi$
$479$	−0.450043	−	1.75280i	−0.450043	−	1.75280i	0.187381	−	0.982287i	$-0.440000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.876307	−	1.05927i	−0.876307	−	1.05927i
$485$	−2.28488	+	2.14565i	−2.28488	+	2.14565i
$486$		0			0
$487$		0			0		−0.904827	−	0.425779i	$-0.860000\pi$
$487$		0			0		0.904827	+	0.425779i	$0.140000\pi$
$488$		0			0
$489$		0			0
$490$	−3.46510	−	2.19902i	−3.46510	−	2.19902i
$491$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$491$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.450747	+	0.178463i	−0.450747	+	0.178463i
$497$	−2.35604	+	1.94908i	−2.35604	+	1.94908i
$498$		0			0
$499$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$499$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$500$	3.40243	+	3.19510i	3.40243	+	3.19510i
$501$		0			0
$502$		0			0
$503$	−0.171593	−	0.182728i	−0.171593	−	0.182728i	0.637424	−	0.770513i	$-0.280000\pi$
$503$	−0.171593	−	0.182728i	−0.171593	−	0.182728i	−0.809017	+	0.587785i	$0.800000\pi$
$504$	0.889972			0.889972
$505$	0.121636	+	1.93334i	0.121636	+	1.93334i
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$509$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$510$		0			0
$511$		0			0
$512$	−0.444238	−	0.808065i	−0.444238	−	0.808065i
$513$		0			0
$514$	−1.68437	+	0.666889i	−1.68437	+	0.666889i
$515$			0.485583i			0.485583i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.124591	+	0.0157395i	0.124591	+	0.0157395i	0.187381	−	0.982287i	$-0.440000\pi$
$521$	0.124591	+	0.0157395i	0.124591	+	0.0157395i	−0.0627905	+	0.998027i	$0.520000\pi$
$522$		0			0
$523$		0			0		−0.904827	−	0.425779i	$-0.860000\pi$
$523$		0			0		0.904827	+	0.425779i	$0.140000\pi$
$524$	−1.16146	+	0.146726i	−1.16146	+	0.146726i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$530$		0			0
$531$	0.488570	+	1.90285i	0.488570	+	1.90285i
$532$	3.13498	−	1.98952i	3.13498	−	1.98952i
$533$		0			0
$534$		0			0
$535$	0.388998	+	2.03920i	0.388998	+	2.03920i
$536$	−0.126858	+	0.0697409i	−0.126858	+	0.0697409i
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.450527	+	1.38658i	0.450527	+	1.38658i	0.876307	+	0.481754i	$0.160000\pi$
$541$	0.450527	+	1.38658i	0.450527	+	1.38658i	−0.425779	+	0.904827i	$0.640000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.67744	−	0.231365i	−3.67744	−	0.231365i
$546$		0			0
$547$	0.250172	−	1.98031i	0.250172	−	1.98031i	0.0627905	−	0.998027i	$-0.480000\pi$
$547$	0.250172	−	1.98031i	0.250172	−	1.98031i	0.187381	−	0.982287i	$-0.440000\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$557$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$558$	1.53799	−	0.0967619i	1.53799	−	0.0967619i
$559$		0			0
$560$	0.532753	−	1.34558i	0.532753	−	1.34558i
$561$		0			0
$562$	0.184052	−	0.0598021i	0.184052	−	0.0598021i
$563$	−1.69755	+	0.435857i	−1.69755	+	0.435857i	−0.968583	−	0.248690i	$-0.920000\pi$
$563$	−1.69755	+	0.435857i	−1.69755	+	0.435857i	−0.728969	+	0.684547i	$0.760000\pi$
$564$		0			0
$565$	2.23694	−	3.07888i	2.23694	−	3.07888i
$566$	2.48851	+	0.156564i	2.48851	+	0.156564i
$567$	1.46560	+	0.476203i	1.46560	+	0.476203i
$568$	0.882955	+	0.730444i	0.882955	+	0.730444i
$569$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$569$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$570$		0			0
$571$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$571$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$572$		0			0
$573$		0			0
$574$	2.35711	+	3.24429i	2.35711	+	3.24429i
$575$		0			0
$576$	0.291649	+	1.52888i	0.291649	+	1.52888i
$577$	−0.659566	+	1.19975i	−0.659566	+	1.19975i	0.309017	+	0.951057i	$0.400000\pi$
$577$	−0.659566	+	1.19975i	−0.659566	+	1.19975i	−0.968583	+	0.248690i	$0.920000\pi$
$578$	−1.39436	+	0.656137i	−1.39436	+	0.656137i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	1.32059	−	1.24012i	1.32059	−	1.24012i
$587$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$587$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$588$		0			0
$589$	1.41789	−	1.03016i	1.41789	−	1.03016i
$590$	−5.81845	−	0.735041i	−5.81845	−	0.735041i
$591$		0			0
$592$		0			0
$593$	0.541587	+	0.297740i	0.541587	+	0.297740i	0.728969	−	0.684547i	$-0.240000\pi$
$593$	0.541587	+	0.297740i	0.541587	+	0.297740i	−0.187381	+	0.982287i	$0.560000\pi$
$594$		0			0
$595$		0			0
$596$			2.32150i			2.32150i
$597$		0			0
$598$		0			0
$599$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$599$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$600$		0			0
$601$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$601$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$602$		0			0
$603$	−0.246226	+	0.0469702i	−0.246226	+	0.0469702i
$604$		0			0
$605$	1.93717			1.93717
$606$		0			0
$607$	−0.125581			−0.125581			−0.0627905	−	0.998027i	$-0.520000\pi$
$607$	−0.125581			−0.125581			−0.0627905	+	0.998027i	$0.520000\pi$
$608$	1.58918	+	1.69230i	1.58918	+	1.69230i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$613$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$614$	0.733842	−	0.607087i	0.733842	−	0.607087i
$615$		0			0
$616$		0			0
$617$	−0.621636	−	1.57007i	−0.621636	−	1.57007i	−0.809017	−	0.587785i	$-0.800000\pi$
$617$	−0.621636	−	1.57007i	−0.621636	−	1.57007i	0.187381	−	0.982287i	$-0.440000\pi$
$618$		0			0
$619$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$619$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$620$	−0.822957	+	2.53280i	−0.822957	+	2.53280i
$621$		0			0
$622$	−2.90809	−	0.367378i	−2.90809	−	0.367378i
$623$		0			0
$624$		0			0
$625$	−3.79411	+	0.479308i	−3.79411	+	0.479308i
$626$		0			0
$627$		0			0
$628$	−1.13391	+	2.40968i	−1.13391	+	2.40968i
$629$		0			0
$630$	−2.93235	+	3.54460i	−2.93235	+	3.54460i
$631$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$631$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$632$		0			0
$633$		0			0
$634$	−2.76673	+	1.30193i	−2.76673	+	1.30193i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.06320	+	1.67534i	1.06320	+	1.67534i
$640$	−2.04353	−	0.389824i	−2.04353	−	0.389824i
$641$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$641$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$642$		0			0
$643$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$643$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$647$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$648$	0.0723823	−	0.572965i	0.0723823	−	0.572965i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.692877	−	1.75001i	0.692877	−	1.75001i
$653$	−1.41213	−	0.362574i	−1.41213	−	0.362574i	−0.535827	−	0.844328i	$-0.680000\pi$
$653$	−1.41213	−	0.362574i	−1.41213	−	0.362574i	−0.876307	+	0.481754i	$0.840000\pi$
$654$		0			0
$655$	0.883906	−	1.39281i	0.883906	−	1.39281i
$656$	−0.560400	+	0.596766i	−0.560400	+	0.596766i
$657$		0			0
$658$	−2.05889	+	3.24429i	−2.05889	+	3.24429i
$659$	1.36639	−	0.0859661i	1.36639	−	0.0859661i	0.637424	−	0.770513i	$-0.280000\pi$
$659$	1.36639	−	0.0859661i	1.36639	−	0.0859661i	0.728969	+	0.684547i	$0.240000\pi$
$660$		0			0
$661$	−0.0922765	+	0.233064i	−0.0922765	+	0.233064i	−0.968583	−	0.248690i	$-0.920000\pi$
$661$	−0.0922765	+	0.233064i	−0.0922765	+	0.233064i	0.876307	+	0.481754i	$0.160000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.655737	+	5.19069i	−0.655737	+	5.19069i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	0.140217	−	0.735041i	0.140217	−	0.735041i
$671$		0			0
$672$		0			0
$673$		0			0		−0.982287	−	0.187381i	$-0.940000\pi$
$673$		0			0		0.982287	+	0.187381i	$0.0600000\pi$
$674$		0			0
$675$		0			0
$676$	−1.20471	+	0.662297i	−1.20471	+	0.662297i
$677$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$677$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$678$		0			0
$679$	2.25613	−	1.06165i	2.25613	−	1.06165i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.929324	−	1.12336i	0.929324	−	1.12336i	−0.0627905	−	0.998027i	$-0.520000\pi$
$683$	0.929324	−	1.12336i	0.929324	−	1.12336i	0.992115	−	0.125333i	$-0.0400000\pi$
$684$	−1.02588	−	2.18012i	−1.02588	−	2.18012i
$685$		0			0
$686$	0.567290	+	0.685735i	0.567290	+	0.685735i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	1.44644	+	0.182728i	1.44644	+	0.182728i	0.809017	−	0.587785i	$-0.200000\pi$
$691$	1.44644	+	0.182728i	1.44644	+	0.182728i	0.637424	+	0.770513i	$0.280000\pi$
$692$	−0.577334	−	0.366387i	−0.577334	−	0.366387i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−2.80936	−	5.11021i	−2.80936	−	5.11021i
$701$	−1.03137	−	0.749337i	−1.03137	−	0.749337i	−0.0627905	−	0.998027i	$-0.520000\pi$
$701$	−1.03137	−	0.749337i	−1.03137	−	0.749337i	−0.968583	+	0.248690i	$0.920000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.383238	−	1.49261i	0.383238	−	1.49261i
$708$		0			0
$709$		0			0		−0.684547	−	0.728969i	$-0.740000\pi$
$709$		0			0		0.684547	+	0.728969i	$0.260000\pi$
$710$	−5.81845	+	1.10993i	−5.81845	+	1.10993i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	0.483080	+	1.22012i	0.483080	+	1.22012i
$719$		0			0		−0.125333	−	0.992115i	$-0.540000\pi$
$719$		0			0		0.125333	+	0.992115i	$0.460000\pi$
$720$	−0.822957	−	0.452424i	−0.822957	−	0.452424i
$721$	0.119368	−	0.367378i	0.119368	−	0.367378i
$722$	−2.69549	−	1.71061i	−2.69549	−	1.71061i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	1.06279	−	0.998027i	1.06279	−	0.998027i	0.0627905	−	0.998027i	$-0.480000\pi$
$727$	1.06279	−	0.998027i	1.06279	−	0.998027i	1.00000			$0$
$728$		0			0
$729$	0.425779	−	0.904827i	0.425779	−	0.904827i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.123693	−	0.481754i	−0.123693	−	0.481754i	0.876307	−	0.481754i	$-0.160000\pi$
$733$	−0.123693	−	0.481754i	−0.123693	−	0.481754i	−1.00000			$\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	2.28038	−	1.25365i	2.28038	−	1.25365i
$739$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$739$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$743$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$744$		0			0
$745$	−2.52051	−	2.08515i	−2.52051	−	2.08515i
$746$	2.72537	+	0.885525i	2.72537	+	0.885525i
$747$		0			0
$748$		0			0
$749$	0.206981	−	1.63842i	0.206981	−	1.63842i
$750$		0			0
$751$	−1.11803	+	0.363271i	−1.11803	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$751$	−1.11803	+	0.363271i	−1.11803	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$752$	−0.729323	−	0.288760i	−0.729323	−	0.288760i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.684547	−	0.728969i	$-0.260000\pi$
$757$		0			0		−0.684547	+	0.728969i	$0.740000\pi$
$758$	1.84884	−	1.96882i	1.84884	−	1.96882i
$759$		0			0
$760$	1.95687	−	0.123116i	1.95687	−	0.123116i
$761$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$761$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$762$		0			0
$763$	2.72537	+	1.07905i	2.72537	+	1.07905i
$764$	−1.25976	+	0.409322i	−1.25976	+	0.409322i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$769$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$770$		0			0
$771$		0			0
$772$	0.0533500	+	0.164194i	0.0533500	+	0.164194i
$773$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$773$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$774$		0			0
$775$	−1.47492	−	2.32411i	−1.47492	−	2.32411i
$776$	−0.549253	−	0.755982i	−0.549253	−	0.755982i
$777$		0			0
$778$		0			0
$779$	1.42578	−	2.59348i	1.42578	−	2.59348i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.424825	+	0.513525i	−0.424825	+	0.513525i
$785$	−1.59779	−	3.39547i	−1.59779	−	3.39547i
$786$		0			0
$787$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$787$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.44927	+	1.77950i	−2.44927	+	1.77950i
$792$		0			0
$793$		0			0
$794$	−0.804144	+	2.47490i	−0.804144	+	2.47490i
$795$		0			0
$796$		0			0
$797$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$797$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$798$		0			0
$799$		0			0
$800$	2.80936	−	2.32411i	2.80936	−	2.32411i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.576380	−	0.0362627i	−0.576380	−	0.0362627i
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$	2.04353	+	2.17614i	2.04353	+	2.17614i
$811$	−1.51373	+	0.288760i	−1.51373	+	0.288760i	−0.876307	−	0.481754i	$-0.840000\pi$
$811$	−1.51373	+	0.288760i	−1.51373	+	0.288760i	−0.637424	+	0.770513i	$0.720000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.27769	+	2.32411i	1.27769	+	2.32411i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	0.563640	+	4.46167i	0.563640	+	4.46167i
$821$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$821$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$822$		0			0
$823$		0			0		−0.844328	−	0.535827i	$-0.820000\pi$
$823$		0			0		0.844328	+	0.535827i	$0.180000\pi$
$824$	−0.143623	−	0.0181438i	−0.143623	−	0.0181438i
$825$		0			0
$826$	4.22138	+	1.98643i	4.22138	+	1.98643i
$827$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$827$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$828$		0			0
$829$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$829$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−0.339457	−	1.77950i	−0.339457	−	1.77950i
$839$	−1.11716	+	0.614163i	−1.11716	+	0.614163i	−0.929776	−	0.368125i	$-0.880000\pi$
$839$	−1.11716	+	0.614163i	−1.11716	+	0.614163i	−0.187381	+	0.982287i	$0.560000\pi$
$840$		0			0
$841$	−0.535827	−	0.844328i	−0.535827	−	0.844328i
$842$	1.28903	+	0.245896i	1.28903	+	0.245896i
$843$		0			0
$844$	−0.687381	−	2.11554i	−0.687381	−	2.11554i
$845$	0.362989	−	1.90285i	0.362989	−	1.90285i
$846$	1.92122	+	1.58937i	1.92122	+	1.58937i
$847$	−1.46560	−	0.476203i	−1.46560	−	0.476203i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−1.62954	−	0.645180i	−1.62954	−	0.645180i	−0.637424	−	0.770513i	$-0.720000\pi$
$853$	−1.62954	−	0.645180i	−1.62954	−	0.645180i	−0.992115	+	0.125333i	$0.960000\pi$
$854$		0			0
$855$	3.28844	+	0.844328i	3.28844	+	0.844328i
$856$	−0.617679	+	0.0388611i	−0.617679	+	0.0388611i
$857$	0.331159	−	0.521823i	0.331159	−	0.521823i	−0.637424	−	0.770513i	$-0.720000\pi$
$857$	0.331159	−	0.521823i	0.331159	−	0.521823i	0.968583	+	0.248690i	$0.0800000\pi$
$858$		0			0
$859$		0			0		0.684547	−	0.728969i	$-0.260000\pi$
$859$		0			0		−0.684547	+	0.728969i	$0.740000\pi$
$860$		0			0
$861$		0			0
$862$	0.742395	+	0.190615i	0.742395	+	0.190615i
$863$		0			0		0.368125	−	0.929776i	$-0.380000\pi$
$863$		0			0		−0.368125	+	0.929776i	$0.620000\pi$
$864$		0			0
$865$	0.916350	−	0.297740i	0.916350	−	0.297740i
$866$		0			0
$867$		0			0
$868$	1.24525	−	1.71394i	1.24525	−	1.71394i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.205840	−	1.07905i	0.205840	−	1.07905i
$873$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$874$		0			0
$875$	5.13927	+	0.980369i	5.13927	+	0.980369i
$876$		0			0
$877$	0.432756	+	0.595638i	0.432756	+	0.595638i	0.968583	−	0.248690i	$-0.0800000\pi$
$877$	0.432756	+	0.595638i	0.432756	+	0.595638i	−0.535827	+	0.844328i	$0.680000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.904827	−	0.425779i	$-0.140000\pi$
$881$		0			0		−0.904827	+	0.425779i	$0.860000\pi$
$882$	1.78875	−	1.13517i	1.78875	−	1.13517i
$883$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$883$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$884$		0			0
$885$		0			0
$886$	1.18738	+	2.52331i	1.18738	+	2.52331i
$887$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	0.535827	+	0.844328i	$0.320000\pi$
$887$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	−0.992115	+	0.125333i	$0.960000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.81343	+	0.355418i	2.81343	+	0.355418i
$894$		0			0
$895$		0			0
$896$	1.45024	+	0.797279i	1.45024	+	0.797279i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−3.51845	+	1.39305i	−3.51845	+	1.39305i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.827073	+	0.776673i	0.827073	+	0.776673i
$905$		0			0
$906$		0			0
$907$	−1.15596	−	1.23098i	−1.15596	−	1.23098i	−0.968583	−	0.248690i	$-0.920000\pi$
$907$	−1.15596	−	1.23098i	−1.15596	−	1.23098i	−0.187381	−	0.982287i	$-0.560000\pi$
$908$	−0.515210			−0.515210
$909$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$910$		0			0
$911$		0			0		−0.684547	−	0.728969i	$-0.740000\pi$
$911$		0			0		0.684547	+	0.728969i	$0.260000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.01112	+	0.836475i	−1.01112	+	0.836475i
$918$		0			0
$919$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$919$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.226810	−	0.106729i	−0.226810	−	0.106729i
$928$		0			0
$929$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$929$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$930$		0			0
$931$	1.02588	−	2.18012i	1.02588	−	2.18012i
$932$	−0.947109	−	2.01271i	−0.947109	−	2.01271i
$933$		0			0
$934$	−0.184052	−	2.92542i	−0.184052	−	2.92542i
$935$		0			0
$936$		0			0
$937$	0.450043	−	0.211774i	0.450043	−	0.211774i	−0.187381	−	0.982287i	$-0.560000\pi$
$937$	0.450043	−	0.211774i	0.450043	−	0.211774i	0.637424	+	0.770513i	$0.280000\pi$
$938$	−0.286775	+	0.521642i	−0.286775	+	0.521642i
$939$		0			0
$940$	−3.77606	+	2.07590i	−3.77606	+	2.07590i
$941$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$941$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$942$		0			0
$943$		0			0
$944$	−0.236854	+	0.922485i	−0.236854	+	0.922485i
$945$		0			0
$946$		0			0
$947$		0			0		−0.770513	−	0.637424i	$-0.780000\pi$
$947$		0			0		0.770513	+	0.637424i	$0.220000\pi$
$948$		0			0
$949$		0			0
$950$	−4.36979	+	6.01449i	−4.36979	+	6.01449i
$951$		0			0
$952$		0			0
$953$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$953$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$954$		0			0
$955$	0.687095	−	1.73540i	0.687095	−	1.73540i
$956$		0			0
$957$		0			0
$958$	−1.49427	+	2.35460i	−1.49427	+	2.35460i
$959$		0			0
$960$		0			0
$961$	0.535827	−	0.844328i	0.535827	−	0.844328i
$962$		0			0
$963$	−1.03799	−	0.266509i	−1.03799	−	0.266509i
$964$		0			0
$965$	−0.226188	−	0.0895542i	−0.226188	−	0.0895542i
$966$		0			0
$967$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$967$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$968$	−0.0723823	+	0.572965i	−0.0723823	+	0.572965i
$969$		0			0
$970$	4.82066	+	0.303290i	4.82066	+	0.303290i
$971$	1.30209	+	0.423073i	1.30209	+	0.423073i	0.876307	−	0.481754i	$-0.160000\pi$
$971$	1.30209	+	0.423073i	1.30209	+	0.423073i	0.425779	+	0.904827i	$0.360000\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.06320	+	1.67534i	1.06320	+	1.67534i	0.637424	+	0.770513i	$0.280000\pi$
$977$	1.06320	+	1.67534i	1.06320	+	1.67534i	0.425779	+	0.904827i	$0.360000\pi$
$978$		0			0
$979$		0			0
$980$	0.686039	+	3.59634i	0.686039	+	3.59634i
$981$	0.916350	−	1.66683i	0.916350	−	1.66683i
$982$		0			0
$983$		0			0		0.844328	−	0.535827i	$-0.180000\pi$
$983$		0			0		−0.844328	+	0.535827i	$0.820000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$991$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$992$	1.19853	+	0.563985i	1.19853	+	0.563985i
$993$		0			0
$994$	4.67492	+	0.590579i	4.67492	+	0.590579i
$995$		0			0
$996$		0			0
$997$	1.41789	+	0.779494i	1.41789	+	0.779494i	0.992115	−	0.125333i	$-0.0400000\pi$
$997$	1.41789	+	0.779494i	1.41789	+	0.779494i	0.425779	+	0.904827i	$0.360000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3131.1.de.a.929.1	✓	20
31.30	odd	2	CM	3131.1.de.a.929.1	✓	20
101.96	even	50	inner	3131.1.de.a.1611.1	yes	20
3131.1611	odd	50	inner	3131.1.de.a.1611.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3131.1.de.a.929.1	✓	20	1.1	even	1	trivial
3131.1.de.a.929.1	✓	20	31.30	odd	2	CM
3131.1.de.a.1611.1	yes	20	101.96	even	50	inner
3131.1.de.a.1611.1	yes	20	3131.1611	odd	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3131 = 31 \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3131.de (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05491 - 1.12336i) q^{2} +(-0.0863221 + 1.37205i) q^{4} +(-1.41213 - 1.32608i) q^{5} +(0.742395 + 1.35041i) q^{7} +(0.444986 - 0.368125i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})\)	\(q+(-1.05491 - 1.12336i) q^{2} +(-0.0863221 + 1.37205i) q^{4} +(-1.41213 - 1.32608i) q^{5} +(0.742395 + 1.35041i) q^{7} +(0.444986 - 0.368125i) q^{8} +(0.929776 - 0.368125i) q^{9} +2.98522i q^{10} +(0.733842 - 2.25853i) q^{14} +(0.480968 + 0.0607603i) q^{16} +(-1.39436 - 0.656137i) q^{18} +(-1.73879 + 0.219661i) q^{19} +(1.94135 - 1.82305i) q^{20} +(0.172838 + 2.74718i) q^{25} +(-1.91692 + 0.902033i) q^{28} +(-0.876307 + 0.481754i) q^{31} +(-0.778577 - 1.07162i) q^{32} +(0.742395 - 2.89144i) q^{35} +(0.424825 + 1.30748i) q^{36} +(2.08102 + 1.72157i) q^{38} +(-1.11654 - 0.0702469i) q^{40} +(-0.992567 + 1.36615i) q^{41} +(-1.80113 - 0.713118i) q^{45} +(-1.56720 - 0.402389i) q^{47} +(-0.736635 + 1.16075i) q^{49} +(2.90375 - 3.09218i) q^{50} +(0.827475 + 0.327621i) q^{56} +(-0.246226 + 1.94908i) q^{59} +(1.46560 + 0.476203i) q^{62} +(1.18738 + 0.982287i) q^{63} +(-0.291649 + 1.52888i) q^{64} +(-0.246226 - 0.0469702i) q^{67} +(-4.03128 + 2.21622i) q^{70} +(0.371808 + 1.94908i) q^{71} +(0.278222 - 0.506084i) q^{72} +(-0.151289 - 2.40467i) q^{76} +(-0.598617 - 0.723604i) q^{80} +(0.728969 - 0.684547i) q^{81} +(2.58174 - 0.326150i) q^{82} +(1.09893 + 2.77559i) q^{90} +(1.20122 + 2.18501i) q^{94} +(2.74670 + 1.99559i) q^{95} +(0.101597 - 1.61484i) q^{97} +(2.08102 - 0.396976i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{8}+O(q^{10}) \) 20 * q + 20 * q^8	\( 20 q + 20 q^{8} - 10 q^{14} + 5 q^{16} - 5 q^{19} + 5 q^{20} + 5 q^{28} - 5 q^{36} + 5 q^{38} - 5 q^{40} - 5 q^{45} + 5 q^{50} - 20 q^{56} + 5 q^{59} + 20 q^{63} + 20 q^{64} + 5 q^{67} - 5 q^{70} - 5 q^{71} - 20 q^{72} - 5 q^{76} + 20 q^{82} + 5 q^{98}+O(q^{100}) \) 20 * q + 20 * q^8 - 10 * q^14 + 5 * q^16 - 5 * q^19 + 5 * q^20 + 5 * q^28 - 5 * q^36 + 5 * q^38 - 5 * q^40 - 5 * q^45 + 5 * q^50 - 20 * q^56 + 5 * q^59 + 20 * q^63 + 20 * q^64 + 5 * q^67 - 5 * q^70 - 5 * q^71 - 20 * q^72 - 5 * q^76 + 20 * q^82 + 5 * q^98

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