LMFDB - Embedded newform 3017.1.t.a.1105.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3017,1,Mod(6,3017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3017, base_ring=CyclotomicField(86))

chi = DirichletCharacter(H, H._module([43, 14]))

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

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

chi := DirichletCharacter("3017.6");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3017 = 7 \cdot 431 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3017.t (of order $86$, degree $42$, 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:	$1.50567914311$
Analytic rank:	$0$
Dimension:	$42$
Coefficient field:	$\Q(\zeta_{86})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{42} - x^{41} + x^{40} - x^{39} + x^{38} - x^{37} + x^{36} - x^{35} + x^{34} - x^{33} + x^{32} + \cdots + 1 $ x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{43}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{43} - \cdots)$

Embedding invariants

Embedding label			1105.1
Root			$-0.109371 - 0.994001i$ of defining polynomial
Character	$\chi$	$=$	3017.1105
Dual form			3017.1.t.a.1630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26571 + 1.52091i) q^{2} +(-0.529508 + 2.86671i) q^{4} +(-0.694074 - 0.719903i) q^{7} +(-3.30470 + 1.85469i) q^{8} +(-0.694074 - 0.719903i) q^{9} +O(q^{10})$	\(q+(1.26571 + 1.52091i) q^{2} +(-0.529508 + 2.86671i) q^{4} +(-0.694074 - 0.719903i) q^{7} +(-3.30470 + 1.85469i) q^{8} +(-0.694074 - 0.719903i) q^{9} +(-1.86938 + 0.416423i) q^{11} +(0.216411 - 1.96682i) q^{14} +(-4.28078 - 1.63726i) q^{16} +(0.216411 - 1.96682i) q^{18} +(-2.99944 - 2.31609i) q^{22} +(0.448206 + 1.31380i) q^{23} +(-0.997332 + 0.0729953i) q^{25} +(2.43127 - 1.60851i) q^{28} +(0.166104 + 0.899273i) q^{29} +(-1.70453 - 4.99638i) q^{32} +(2.43127 - 1.60851i) q^{36} +(-0.100018 + 0.908999i) q^{37} +(1.34871 + 1.20845i) q^{43} +(-0.203910 - 5.57947i) q^{44} +(-1.43087 + 2.34457i) q^{46} +(-0.0365220 + 0.999333i) q^{49} +(-1.37336 - 1.42446i) q^{50} +(-0.472488 - 1.80729i) q^{53} +(3.62891 + 1.09178i) q^{56} +(-1.15747 + 1.39085i) q^{58} +(-0.0365220 + 0.999333i) q^{63} +(3.05404 - 5.00423i) q^{64} +(-0.213509 + 1.94044i) q^{67} +(0.197847 - 0.756775i) q^{71} +(3.62891 + 1.09178i) q^{72} +(-1.50910 + 0.998412i) q^{74} +(1.59727 + 1.05675i) q^{77} +(0.542758 + 0.889342i) q^{79} +(-0.0365220 + 0.999333i) q^{81} +(-0.130866 + 3.58081i) q^{86} +(5.40542 - 4.84328i) q^{88} +(-4.00361 + 0.589209i) q^{92} +(-1.56612 + 1.20932i) q^{98} +(1.59727 + 1.05675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) $ 42 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9	$ 42 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9} - 2 q^{11} - 2 q^{14} - 5 q^{16} - 2 q^{18} - 4 q^{22} - 2 q^{23} - q^{25} - 3 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 2 q^{37} - 2 q^{43} - 6 q^{44} - 4 q^{46} - q^{49} - 2 q^{50} - 2 q^{53} - 4 q^{56} - 4 q^{58} - q^{63} - 7 q^{64} - 2 q^{67} - 2 q^{71} - 4 q^{72} - 4 q^{74} - 2 q^{77} + 41 q^{79} - q^{81} - 4 q^{86} + 35 q^{88} - 6 q^{92} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 42 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9 - 2 * q^11 - 2 * q^14 - 5 * q^16 - 2 * q^18 - 4 * q^22 - 2 * q^23 - q^25 - 3 * q^28 - 2 * q^29 - 6 * q^32 - 3 * q^36 - 2 * q^37 - 2 * q^43 - 6 * q^44 - 4 * q^46 - q^49 - 2 * q^50 - 2 * q^53 - 4 * q^56 - 4 * q^58 - q^63 - 7 * q^64 - 2 * q^67 - 2 * q^71 - 4 * q^72 - 4 * q^74 - 2 * q^77 + 41 * q^79 - q^81 - 4 * q^86 + 35 * q^88 - 6 * q^92 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3017\mathbb{Z}\right)^\times$.

$n$	$869$	$1725$
$\chi(n)$	$e\left(\frac{11}{43}\right)$	$-1$

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 $

$2$	1.26571	+	1.52091i	1.26571	+	1.52091i	0.744772	+	0.667319i	$0.232558\pi$
$2$	1.26571	+	1.52091i	1.26571	+	1.52091i	0.520940	+	0.853593i	$0.325581\pi$
$3$		0			0		0.391105	−	0.920346i	$-0.372093\pi$
$3$		0			0		−0.391105	+	0.920346i	$0.627907\pi$
$4$	−0.529508	+	2.86671i	−0.529508	+	2.86671i
$5$		0			0		−0.0365220	−	0.999333i	$-0.511628\pi$
$5$		0			0		0.0365220	+	0.999333i	$0.488372\pi$
$6$		0			0
$7$	−0.694074	−	0.719903i	−0.694074	−	0.719903i
$7$	−0.694074	−	0.719903i	−0.694074	−	0.719903i
$8$	−3.30470	+	1.85469i	−3.30470	+	1.85469i
$9$	−0.694074	−	0.719903i	−0.694074	−	0.719903i
$10$		0			0
$11$	−1.86938	+	0.416423i	−1.86938	+	0.416423i	−0.997332	−	0.0729953i	$-0.976744\pi$
$11$	−1.86938	+	0.416423i	−1.86938	+	0.416423i	−0.872049	+	0.489418i	$0.837209\pi$
$12$		0			0
$13$		0			0		0.639673	−	0.768647i	$-0.279070\pi$
$13$		0			0		−0.639673	+	0.768647i	$0.720930\pi$
$14$	0.216411	−	1.96682i	0.216411	−	1.96682i
$15$		0			0
$16$	−4.28078	−	1.63726i	−4.28078	−	1.63726i
$17$		0			0		0.976076	−	0.217430i	$-0.0697674\pi$
$17$		0			0		−0.976076	+	0.217430i	$0.930233\pi$
$18$	0.216411	−	1.96682i	0.216411	−	1.96682i
$19$		0			0		0.0365220	−	0.999333i	$-0.488372\pi$
$19$		0			0		−0.0365220	+	0.999333i	$0.511628\pi$
$20$		0			0
$21$		0			0
$22$	−2.99944	−	2.31609i	−2.99944	−	2.31609i
$23$	0.448206	+	1.31380i	0.448206	+	1.31380i	0.905448	+	0.424457i	$0.139535\pi$
$23$	0.448206	+	1.31380i	0.448206	+	1.31380i	−0.457242	+	0.889342i	$0.651163\pi$
$24$		0			0
$25$	−0.997332	+	0.0729953i	−0.997332	+	0.0729953i
$26$		0			0
$27$		0			0
$28$	2.43127	−	1.60851i	2.43127	−	1.60851i
$29$	0.166104	+	0.899273i	0.166104	+	0.899273i	0.957601	+	0.288099i	$0.0930233\pi$
$29$	0.166104	+	0.899273i	0.166104	+	0.899273i	−0.791496	+	0.611174i	$0.790698\pi$
$30$		0			0
$31$		0			0		−0.957601	−	0.288099i	$-0.906977\pi$
$31$		0			0		0.957601	+	0.288099i	$0.0930233\pi$
$32$	−1.70453	−	4.99638i	−1.70453	−	4.99638i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.43127	−	1.60851i	2.43127	−	1.60851i
$37$	−0.100018	+	0.908999i	−0.100018	+	0.908999i	0.833998	+	0.551768i	$0.186047\pi$
$37$	−0.100018	+	0.908999i	−0.100018	+	0.908999i	−0.934016	+	0.357231i	$0.883721\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.934016	−	0.357231i	$-0.883721\pi$
$41$		0			0		0.934016	+	0.357231i	$0.116279\pi$
$42$		0			0
$43$	1.34871	+	1.20845i	1.34871	+	1.20845i	0.957601	+	0.288099i	$0.0930233\pi$
$43$	1.34871	+	1.20845i	1.34871	+	1.20845i	0.391105	+	0.920346i	$0.372093\pi$
$44$	−0.203910	−	5.57947i	−0.203910	−	5.57947i
$45$		0			0
$46$	−1.43087	+	2.34457i	−1.43087	+	2.34457i
$47$		0			0		0.252933	−	0.967484i	$-0.418605\pi$
$47$		0			0		−0.252933	+	0.967484i	$0.581395\pi$
$48$		0			0
$49$	−0.0365220	+	0.999333i	−0.0365220	+	0.999333i
$50$	−1.37336	−	1.42446i	−1.37336	−	1.42446i
$51$		0			0
$52$		0			0
$53$	−0.472488	−	1.80729i	−0.472488	−	1.80729i	−0.581859	−	0.813290i	$-0.697674\pi$
$53$	−0.472488	−	1.80729i	−0.472488	−	1.80729i	0.109371	−	0.994001i	$-0.465116\pi$
$54$		0			0
$55$		0			0
$56$	3.62891	+	1.09178i	3.62891	+	1.09178i
$57$		0			0
$58$	−1.15747	+	1.39085i	−1.15747	+	1.39085i
$59$		0			0		−0.639673	−	0.768647i	$-0.720930\pi$
$59$		0			0		0.639673	+	0.768647i	$0.279070\pi$
$60$		0			0
$61$		0			0		−0.581859	−	0.813290i	$-0.697674\pi$
$61$		0			0		0.581859	+	0.813290i	$0.302326\pi$
$62$		0			0
$63$	−0.0365220	+	0.999333i	−0.0365220	+	0.999333i
$64$	3.05404	−	5.00423i	3.05404	−	5.00423i
$65$		0			0
$66$		0			0
$67$	−0.213509	+	1.94044i	−0.213509	+	1.94044i	0.109371	+	0.994001i	$0.465116\pi$
$67$	−0.213509	+	1.94044i	−0.213509	+	1.94044i	−0.322880	+	0.946440i	$0.604651\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.197847	−	0.756775i	0.197847	−	0.756775i	−0.791496	−	0.611174i	$-0.790698\pi$
$71$	0.197847	−	0.756775i	0.197847	−	0.756775i	0.989343	−	0.145601i	$-0.0465116\pi$
$72$	3.62891	+	1.09178i	3.62891	+	1.09178i
$73$		0			0		−0.457242	−	0.889342i	$-0.651163\pi$
$73$		0			0		0.457242	+	0.889342i	$0.348837\pi$
$74$	−1.50910	+	0.998412i	−1.50910	+	0.998412i
$75$		0			0
$76$		0			0
$77$	1.59727	+	1.05675i	1.59727	+	1.05675i
$78$		0			0
$79$	0.542758	+	0.889342i	0.542758	+	0.889342i	1.00000			$0$
$79$	0.542758	+	0.889342i	0.542758	+	0.889342i	−0.457242	+	0.889342i	$0.651163\pi$
$80$		0			0
$81$	−0.0365220	+	0.999333i	−0.0365220	+	0.999333i
$82$		0			0
$83$		0			0		0.391105	−	0.920346i	$-0.372093\pi$
$83$		0			0		−0.391105	+	0.920346i	$0.627907\pi$
$84$		0			0
$85$		0			0
$86$	−0.130866	+	3.58081i	−0.130866	+	3.58081i
$87$		0			0
$88$	5.40542	−	4.84328i	5.40542	−	4.84328i
$89$		0			0		−0.989343	−	0.145601i	$-0.953488\pi$
$89$		0			0		0.989343	+	0.145601i	$0.0465116\pi$
$90$		0			0
$91$		0			0
$92$	−4.00361	+	0.589209i	−4.00361	+	0.589209i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.520940	−	0.853593i	$-0.325581\pi$
$97$		0			0		−0.520940	+	0.853593i	$0.674419\pi$
$98$	−1.56612	+	1.20932i	−1.56612	+	1.20932i
$99$	1.59727	+	1.05675i	1.59727	+	1.05675i
$100$	0.318839	−	2.89771i	0.318839	−	2.89771i
$101$		0			0		−0.520940	−	0.853593i	$-0.674419\pi$
$101$		0			0		0.520940	+	0.853593i	$0.325581\pi$
$102$		0			0
$103$		0			0		0.989343	−	0.145601i	$-0.0465116\pi$
$103$		0			0		−0.989343	+	0.145601i	$0.953488\pi$
$104$		0			0
$105$		0			0
$106$	2.15070	−	3.00612i	2.15070	−	3.00612i
$107$	−0.763496	−	0.170076i	−0.763496	−	0.170076i	−0.181637	−	0.983366i	$-0.558140\pi$
$107$	−0.763496	−	0.170076i	−0.763496	−	0.170076i	−0.581859	+	0.813290i	$0.697674\pi$
$108$		0			0
$109$	−0.213509	+	0.0475612i	−0.213509	+	0.0475612i	−0.322880	−	0.946440i	$-0.604651\pi$
$109$	−0.213509	+	0.0475612i	−0.213509	+	0.0475612i	0.109371	+	0.994001i	$0.465116\pi$
$110$		0			0
$111$		0			0
$112$	1.79251	+	4.21813i	1.79251	+	4.21813i
$113$	−0.723142	−	1.18491i	−0.723142	−	1.18491i	−0.976076	−	0.217430i	$-0.930233\pi$
$113$	−0.723142	−	1.18491i	−0.723142	−	1.18491i	0.252933	−	0.967484i	$-0.418605\pi$
$114$		0			0
$115$		0			0
$116$	−2.66591			−2.66591
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.41573	−	1.13245i	2.41573	−	1.13245i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.56612	+	1.20932i	−1.56612	+	1.20932i
$127$	−0.763496	+	1.79666i	−0.763496	+	1.79666i	−0.181637	+	0.983366i	$0.558140\pi$
$127$	−0.763496	+	1.79666i	−0.763496	+	1.79666i	−0.581859	+	0.813290i	$0.697674\pi$
$128$	6.25365	−	0.920346i	6.25365	−	0.920346i
$129$		0			0
$130$		0			0
$131$		0			0		−0.872049	−	0.489418i	$-0.837209\pi$
$131$		0			0		0.872049	+	0.489418i	$0.162791\pi$
$132$		0			0
$133$		0			0
$134$	−3.22148	+	2.13131i	−3.22148	+	2.13131i
$135$		0			0
$136$		0			0
$137$	−0.294343	−	1.12588i	−0.294343	−	1.12588i	−0.934016	−	0.357231i	$-0.883721\pi$
$137$	−0.294343	−	1.12588i	−0.294343	−	1.12588i	0.639673	−	0.768647i	$-0.279070\pi$
$138$		0			0
$139$		0			0		0.957601	−	0.288099i	$-0.0930233\pi$
$139$		0			0		−0.957601	+	0.288099i	$0.906977\pi$
$140$		0			0
$141$		0			0
$142$	1.40141	−	0.656952i	1.40141	−	0.656952i
$143$		0			0
$144$	1.79251	+	4.21813i	1.79251	+	4.21813i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−2.55287	−	0.768045i	−2.55287	−	0.768045i
$149$	−0.0380516	−	1.04119i	−0.0380516	−	1.04119i	−0.872049	−	0.489418i	$-0.837209\pi$
$149$	−0.0380516	−	1.04119i	−0.0380516	−	1.04119i	0.833998	−	0.551768i	$-0.186047\pi$
$150$		0			0
$151$	0.127951	−	0.489418i	0.127951	−	0.489418i	−0.872049	−	0.489418i	$-0.837209\pi$
$151$	0.127951	−	0.489418i	0.127951	−	0.489418i	1.00000			$0$
$152$		0			0
$153$		0			0
$154$	0.414471	+	3.76685i	0.414471	+	3.76685i
$155$		0			0
$156$		0			0
$157$		0			0		0.581859	−	0.813290i	$-0.302326\pi$
$157$		0			0		−0.581859	+	0.813290i	$0.697674\pi$
$158$	−0.665636	+	1.95114i	−0.665636	+	1.95114i
$159$		0			0
$160$		0			0
$161$	0.634720	−	1.23454i	0.634720	−	1.23454i
$162$	−1.56612	+	1.20932i	−1.56612	+	1.20932i
$163$	−0.0699470	−	0.0210439i	−0.0699470	−	0.0210439i	0.252933	−	0.967484i	$-0.418605\pi$
$163$	−0.0699470	−	0.0210439i	−0.0699470	−	0.0210439i	−0.322880	+	0.946440i	$0.604651\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.322880	−	0.946440i	$-0.604651\pi$
$167$		0			0		0.322880	+	0.946440i	$0.395349\pi$
$168$		0			0
$169$	−0.181637	−	0.983366i	−0.181637	−	0.983366i
$170$		0			0
$171$		0			0
$172$	−4.17841	+	3.22646i	−4.17841	+	3.22646i
$173$		0			0		−0.905448	−	0.424457i	$-0.860465\pi$
$173$		0			0		0.905448	+	0.424457i	$0.139535\pi$
$174$		0			0
$175$	0.744772	+	0.667319i	0.744772	+	0.667319i
$176$	8.68420	+	1.27805i	8.68420	+	1.27805i
$177$		0			0
$178$		0			0
$179$	−1.95215	−	0.434860i	−1.95215	−	0.434860i	−0.976076	−	0.217430i	$-0.930233\pi$
$179$	−1.95215	−	0.434860i	−1.95215	−	0.434860i	−0.976076	−	0.217430i	$-0.930233\pi$
$180$		0			0
$181$		0			0		0.694074	−	0.719903i	$-0.255814\pi$
$181$		0			0		−0.694074	+	0.719903i	$0.744186\pi$
$182$		0			0
$183$		0			0
$184$	−3.91788	−	3.51043i	−3.91788	−	3.51043i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.34871	+	1.20845i	1.34871	+	1.20845i	0.957601	+	0.288099i	$0.0930233\pi$
$191$	1.34871	+	1.20845i	1.34871	+	1.20845i	0.391105	+	0.920346i	$0.372093\pi$
$192$		0			0
$193$	0.0553273	+	0.502832i	0.0553273	+	0.502832i	0.989343	+	0.145601i	$0.0465116\pi$
$193$	0.0553273	+	0.502832i	0.0553273	+	0.502832i	−0.934016	+	0.357231i	$0.883721\pi$
$194$		0			0
$195$		0			0
$196$	−2.84546	−	0.633853i	−2.84546	−	0.633853i
$197$	1.29655	+	1.34480i	1.29655	+	1.34480i	0.905448	+	0.424457i	$0.139535\pi$
$197$	1.29655	+	1.34480i	1.29655	+	1.34480i	0.391105	+	0.920346i	$0.372093\pi$
$198$	0.414471	+	3.76685i	0.414471	+	3.76685i
$199$		0			0		−0.639673	−	0.768647i	$-0.720930\pi$
$199$		0			0		0.639673	+	0.768647i	$0.279070\pi$
$200$	3.16050	−	2.09097i	3.16050	−	2.09097i
$201$		0			0
$202$		0			0
$203$	0.532101	−	0.743741i	0.532101	−	0.743741i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.634720	−	1.23454i	0.634720	−	1.23454i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.362305	−	0.0265173i	0.362305	−	0.0265173i	0.109371	−	0.994001i	$-0.465116\pi$
$211$	0.362305	−	0.0265173i	0.362305	−	0.0265173i	0.252933	+	0.967484i	$0.418605\pi$
$212$	5.43116	−	0.397510i	5.43116	−	0.397510i
$213$		0			0
$214$	−0.707696	−	1.37648i	−0.707696	−	1.37648i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.342578	−	0.264530i	−0.342578	−	0.264530i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.872049	−	0.489418i	$-0.162791\pi$
$223$		0			0		−0.872049	+	0.489418i	$0.837209\pi$
$224$	−2.41384	+	4.69495i	−2.41384	+	4.69495i
$225$	0.744772	+	0.667319i	0.744772	+	0.667319i
$226$	0.886859	−	2.59960i	0.886859	−	2.59960i
$227$		0			0		−0.934016	−	0.357231i	$-0.883721\pi$
$227$		0			0		0.934016	+	0.357231i	$0.116279\pi$
$228$		0			0
$229$		0			0		0.322880	−	0.946440i	$-0.395349\pi$
$229$		0			0		−0.322880	+	0.946440i	$0.604651\pi$
$230$		0			0
$231$		0			0
$232$	−2.21680	−	2.66376i	−2.21680	−	2.66376i
$233$	−0.213509	−	1.94044i	−0.213509	−	1.94044i	−0.322880	−	0.946440i	$-0.604651\pi$
$233$	−0.213509	−	1.94044i	−0.213509	−	1.94044i	0.109371	−	0.994001i	$-0.465116\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.455136	−	0.636163i	−0.455136	−	0.636163i	0.520940	−	0.853593i	$-0.325581\pi$
$239$	−0.455136	−	0.636163i	−0.455136	−	0.636163i	−0.976076	+	0.217430i	$0.930233\pi$
$240$		0			0
$241$		0			0		−0.639673	−	0.768647i	$-0.720930\pi$
$241$		0			0		0.639673	+	0.768647i	$0.279070\pi$
$242$	4.77998	+	2.24076i	4.77998	+	2.24076i
$243$		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		−0.581859	−	0.813290i	$-0.697674\pi$
$251$		0			0		0.581859	+	0.813290i	$0.302326\pi$
$252$	−2.84546	−	0.633853i	−2.84546	−	0.633853i
$253$	−1.38496	−	2.26935i	−1.38496	−	2.26935i
$254$	−3.69892	+	1.11284i	−3.69892	+	1.11284i
$255$		0			0
$256$	4.94883	+	4.43417i	4.94883	+	4.43417i
$257$		0			0		−0.457242	−	0.889342i	$-0.651163\pi$
$257$		0			0		0.457242	+	0.889342i	$0.348837\pi$
$258$		0			0
$259$	0.723811	−	0.558909i	0.723811	−	0.558909i
$260$		0			0
$261$	0.532101	−	0.743741i	0.532101	−	0.743741i
$262$		0			0
$263$	−0.584971	+	0.702916i	−0.584971	+	0.702916i	−0.976076	−	0.217430i	$-0.930233\pi$
$263$	−0.584971	+	0.702916i	−0.584971	+	0.702916i	0.391105	+	0.920346i	$0.372093\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−5.44962	−	1.63955i	−5.44962	−	1.63955i
$269$		0			0		0.791496	−	0.611174i	$-0.209302\pi$
$269$		0			0		−0.791496	+	0.611174i	$0.790698\pi$
$270$		0			0
$271$		0			0		0.934016	−	0.357231i	$-0.116279\pi$
$271$		0			0		−0.934016	+	0.357231i	$0.883721\pi$
$272$		0			0
$273$		0			0
$274$	1.33981	−	1.87271i	1.33981	−	1.87271i
$275$	1.83400	−	0.551768i	1.83400	−	0.551768i
$276$		0			0
$277$	0.139924	+	1.27167i	0.139924	+	1.27167i	0.833998	+	0.551768i	$0.186047\pi$
$277$	0.139924	+	1.27167i	0.139924	+	1.27167i	−0.694074	+	0.719903i	$0.744186\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.69141	+	0.646908i	−1.69141	+	0.646908i	−0.997332	−	0.0729953i	$-0.976744\pi$
$281$	−1.69141	+	0.646908i	−1.69141	+	0.646908i	−0.694074	+	0.719903i	$0.744186\pi$
$282$		0			0
$283$		0			0		−0.957601	−	0.288099i	$-0.906977\pi$
$283$		0			0		0.957601	+	0.288099i	$0.0930233\pi$
$284$	2.06469	+	0.967888i	2.06469	+	0.967888i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.41384	+	4.69495i	−2.41384	+	4.69495i
$289$	0.905448	−	0.424457i	0.905448	−	0.424457i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.581859	−	0.813290i	$-0.697674\pi$
$293$		0			0		0.581859	+	0.813290i	$0.302326\pi$
$294$		0			0
$295$		0			0
$296$	−1.35538	−	3.18947i	−1.35538	−	3.18947i
$297$		0			0
$298$	1.53539	−	1.37571i	1.53539	−	1.37571i
$299$		0			0
$300$		0			0
$301$	−0.0661376	−	1.80969i	−0.0661376	−	1.80969i
$302$	0.906310	−	0.424861i	0.906310	−	0.424861i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.457242	−	0.889342i	$-0.348837\pi$
$307$		0			0		−0.457242	+	0.889342i	$0.651163\pi$
$308$	−3.87515	+	4.01936i	−3.87515	+	4.01936i
$309$		0			0
$310$		0			0
$311$		0			0		0.989343	−	0.145601i	$-0.0465116\pi$
$311$		0			0		−0.989343	+	0.145601i	$0.953488\pi$
$312$		0			0
$313$		0			0		0.181637	−	0.983366i	$-0.441860\pi$
$313$		0			0		−0.181637	+	0.983366i	$0.558140\pi$
$314$		0			0
$315$		0			0
$316$	−2.83688	+	1.08501i	−2.83688	+	1.08501i
$317$	−0.0918840	−	0.351461i	−0.0918840	−	0.351461i	0.905448	−	0.424457i	$-0.139535\pi$
$317$	−0.0918840	−	0.351461i	−0.0918840	−	0.351461i	−0.997332	+	0.0729953i	$0.976744\pi$
$318$		0			0
$319$	−0.684989	−	1.61191i	−0.684989	−	1.61191i
$320$		0			0
$321$		0			0
$322$	2.68100	−	0.597218i	2.68100	−	0.597218i
$323$		0			0
$324$	−2.84546	−	0.633853i	−2.84546	−	0.633853i
$325$		0			0
$326$	−0.0565269	−	0.133019i	−0.0565269	−	0.133019i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.204309	+	1.85683i	−0.204309	+	1.85683i	0.252933	+	0.967484i	$0.418605\pi$
$331$	−0.204309	+	1.85683i	−0.204309	+	1.85683i	−0.457242	+	0.889342i	$0.651163\pi$
$332$		0			0
$333$	0.723811	−	0.558909i	0.723811	−	0.558909i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.80607	+	0.846649i	−1.80607	+	0.846649i	−0.872049	+	0.489418i	$0.837209\pi$
$337$	−1.80607	+	0.846649i	−1.80607	+	0.846649i	−0.934016	+	0.357231i	$0.883721\pi$
$338$	1.26571	−	1.52091i	1.26571	−	1.52091i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.744772	−	0.667319i	0.744772	−	0.667319i
$344$	−6.69836	−	1.49212i	−6.69836	−	1.49212i
$345$		0			0
$346$		0			0
$347$	0.252139	+	1.36506i	0.252139	+	1.36506i	0.833998	+	0.551768i	$0.186047\pi$
$347$	0.252139	+	1.36506i	0.252139	+	1.36506i	−0.581859	+	0.813290i	$0.697674\pi$
$348$		0			0
$349$		0			0		−0.322880	−	0.946440i	$-0.604651\pi$
$349$		0			0		0.322880	+	0.946440i	$0.395349\pi$
$350$	−0.0722656	+	1.97737i	−0.0722656	+	1.97737i
$351$		0			0
$352$	5.26701	+	8.63033i	5.26701	+	8.63033i
$353$		0			0		0.391105	−	0.920346i	$-0.372093\pi$
$353$		0			0		−0.391105	+	0.920346i	$0.627907\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.80948	−	3.51946i	−1.80948	−	3.51946i
$359$	−1.67015	−	0.502473i	−1.67015	−	0.502473i	−0.694074	−	0.719903i	$-0.744186\pi$
$359$	−1.67015	−	0.502473i	−1.67015	−	0.502473i	−0.976076	+	0.217430i	$0.930233\pi$
$360$		0			0
$361$	−0.997332	−	0.0729953i	−0.997332	−	0.0729953i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.520940	−	0.853593i	$-0.325581\pi$
$367$		0			0		−0.520940	+	0.853593i	$0.674419\pi$
$368$	0.232359	−	6.35791i	0.232359	−	6.35791i
$369$		0			0
$370$		0			0
$371$	−0.973133	+	1.59454i	−0.973133	+	1.59454i
$372$		0			0
$373$	0.139924	−	0.168136i	0.139924	−	0.168136i	−0.694074	−	0.719903i	$-0.744186\pi$
$373$	0.139924	−	0.168136i	0.139924	−	0.168136i	0.833998	+	0.551768i	$0.186047\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.139924	+	0.168136i	0.139924	+	0.168136i	0.833998	−	0.551768i	$-0.186047\pi$
$379$	0.139924	+	0.168136i	0.139924	+	0.168136i	−0.694074	+	0.719903i	$0.744186\pi$
$380$		0			0
$381$		0			0
$382$	−0.130866	+	3.58081i	−0.130866	+	3.58081i
$383$		0			0		0.694074	−	0.719903i	$-0.255814\pi$
$383$		0			0		−0.694074	+	0.719903i	$0.744186\pi$
$384$		0			0
$385$		0			0
$386$	−0.694735	+	0.720589i	−0.694735	+	0.720589i
$387$	−0.0661376	−	1.80969i	−0.0661376	−	1.80969i
$388$		0			0
$389$	1.62902	+	0.914248i	1.62902	+	0.914248i	0.989343	+	0.145601i	$0.0465116\pi$
$389$	1.62902	+	0.914248i	1.62902	+	0.914248i	0.639673	+	0.768647i	$0.279070\pi$
$390$		0			0
$391$		0			0
$392$	−1.73276	−	3.37024i	−1.73276	−	3.37024i
$393$		0			0
$394$	−0.404263	+	3.67408i	−0.404263	+	3.67408i
$395$		0			0
$396$	−3.87515	+	4.01936i	−3.87515	+	4.01936i
$397$		0			0		−0.791496	−	0.611174i	$-0.790698\pi$
$397$		0			0		0.791496	+	0.611174i	$0.209302\pi$
$398$		0			0
$399$		0			0
$400$	4.38887	+	1.32041i	4.38887	+	1.32041i
$401$	0.208504	+	0.611174i	0.208504	+	0.611174i	1.00000			$0$
$401$	0.208504	+	0.611174i	0.208504	+	0.611174i	−0.791496	+	0.611174i	$0.790698\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	1.80465	−	0.132083i	1.80465	−	0.132083i
$407$	−0.191555	−	1.74092i	−0.191555	−	1.74092i
$408$		0			0
$409$		0			0		−0.791496	−	0.611174i	$-0.790698\pi$
$409$		0			0		0.791496	+	0.611174i	$0.209302\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	2.68100	−	0.597218i	2.68100	−	0.597218i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.833998	−	0.551768i	$-0.813953\pi$
$419$		0			0		0.833998	+	0.551768i	$0.186047\pi$
$420$		0			0
$421$	−0.270556	+	0.242419i	−0.270556	+	0.242419i	−0.791496	−	0.611174i	$-0.790698\pi$
$421$	−0.270556	+	0.242419i	−0.270556	+	0.242419i	0.520940	+	0.853593i	$0.325581\pi$
$422$	0.498904	+	0.517470i	0.498904	+	0.517470i
$423$		0			0
$424$	4.91340	+	5.09624i	4.91340	+	5.09624i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.891835	−	2.09866i	0.891835	−	2.09866i
$429$		0			0
$430$		0			0
$431$	−0.791496	+	0.611174i	−0.791496	+	0.611174i
$431$	−0.791496	+	0.611174i	−0.791496	+	0.611174i
$432$		0			0
$433$		0			0		−0.639673	−	0.768647i	$-0.720930\pi$
$433$		0			0		0.639673	+	0.768647i	$0.279070\pi$
$434$		0			0
$435$		0			0
$436$	−0.0232893	−	0.637253i	−0.0232893	−	0.637253i
$437$		0			0
$438$		0			0
$439$		0			0		0.872049	−	0.489418i	$-0.162791\pi$
$439$		0			0		−0.872049	+	0.489418i	$0.837209\pi$
$440$		0			0
$441$	0.744772	−	0.667319i	0.744772	−	0.667319i
$442$		0			0
$443$	0.421892	+	0.279121i	0.421892	+	0.279121i	0.744772	−	0.667319i	$-0.232558\pi$
$443$	0.421892	+	0.279121i	0.421892	+	0.279121i	−0.322880	+	0.946440i	$0.604651\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−5.72229	+	1.27469i	−5.72229	+	1.27469i
$449$	−0.218159	+	1.98270i	−0.218159	+	1.98270i	−0.0365220	+	0.999333i	$0.511628\pi$
$449$	−0.218159	+	1.98270i	−0.218159	+	1.98270i	−0.181637	+	0.983366i	$0.558140\pi$
$450$	−0.0722656	+	1.97737i	−0.0722656	+	1.97737i
$451$		0			0
$452$	3.77971	−	1.44562i	3.77971	−	1.44562i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.04188			1.04188			0.520940	−	0.853593i	$-0.325581\pi$
$457$	1.04188			1.04188			0.520940	+	0.853593i	$0.325581\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.322880	−	0.946440i	$-0.604651\pi$
$461$		0			0		0.322880	+	0.946440i	$0.395349\pi$
$462$		0			0
$463$	−0.538563	−	1.57866i	−0.538563	−	1.57866i	−0.791496	−	0.611174i	$-0.790698\pi$
$463$	−0.538563	−	1.57866i	−0.538563	−	1.57866i	0.252933	−	0.967484i	$-0.418605\pi$
$464$	0.761288	−	4.12154i	0.761288	−	4.12154i
$465$		0			0
$466$	2.68100	−	2.78077i	2.68100	−	2.78077i
$467$		0			0		0.833998	−	0.551768i	$-0.186047\pi$
$467$		0			0		−0.833998	+	0.551768i	$0.813953\pi$
$468$		0			0
$469$	1.54512	−	1.19310i	1.54512	−	1.19310i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.02447	−	1.69741i	−3.02447	−	1.69741i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.973133	+	1.59454i	−0.973133	+	1.59454i
$478$	0.391477	−	1.49742i	0.391477	−	1.49742i
$479$		0			0		0.694074	−	0.719903i	$-0.255814\pi$
$479$		0			0		−0.694074	+	0.719903i	$0.744186\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.96725	+	7.52484i	1.96725	+	7.52484i
$485$		0			0
$486$		0			0
$487$	−0.0699470	−	0.0210439i	−0.0699470	−	0.0210439i	0.252933	−	0.967484i	$-0.418605\pi$
$487$	−0.0699470	−	0.0210439i	−0.0699470	−	0.0210439i	−0.322880	+	0.946440i	$0.604651\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.01695	+	1.66634i	−1.01695	+	1.66634i	−0.322880	+	0.946440i	$0.604651\pi$
$491$	−1.01695	+	1.66634i	−1.01695	+	1.66634i	−0.694074	+	0.719903i	$0.744186\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.682125	+	0.382827i	−0.682125	+	0.382827i
$498$		0			0
$499$	0.0712965	+	1.95085i	0.0712965	+	1.95085i	0.252933	+	0.967484i	$0.418605\pi$
$499$	0.0712965	+	1.95085i	0.0712965	+	1.95085i	−0.181637	+	0.983366i	$0.558140\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.957601	−	0.288099i	$-0.906977\pi$
$503$		0			0		0.957601	+	0.288099i	$0.0930233\pi$
$504$	−1.73276	−	3.37024i	−1.73276	−	3.37024i
$505$		0			0
$506$	1.69851	−	4.97875i	1.69851	−	4.97875i
$507$		0			0
$508$	−4.74621	−	3.14006i	−4.74621	−	3.14006i
$509$		0			0		0.391105	−	0.920346i	$-0.372093\pi$
$509$		0			0		−0.391105	+	0.920346i	$0.627907\pi$
$510$		0			0
$511$		0			0
$512$	−0.249331	+	6.82232i	−0.249331	+	6.82232i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	1.76619	+	0.393435i	1.76619	+	0.393435i
$519$		0			0
$520$		0			0
$521$		0			0		−0.997332	−	0.0729953i	$-0.976744\pi$
$521$		0			0		0.997332	+	0.0729953i	$0.0232558\pi$
$522$	1.80465	−	0.132083i	1.80465	−	0.132083i
$523$		0			0		0.989343	−	0.145601i	$-0.0465116\pi$
$523$		0			0		−0.989343	+	0.145601i	$0.953488\pi$
$524$		0			0
$525$		0			0
$526$	−1.80948			−1.80948
$527$		0			0
$528$		0			0
$529$	−0.733682	+	0.566531i	−0.733682	+	0.566531i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−2.89333	−	6.80858i	−2.89333	−	6.80858i
$537$		0			0
$538$		0			0
$539$	−0.347871	−	1.88334i	−0.347871	−	1.88334i
$540$		0			0
$541$	−0.970538	+	1.35656i	−0.970538	+	1.35656i	−0.0365220	+	0.999333i	$0.511628\pi$
$541$	−0.970538	+	1.35656i	−0.970538	+	1.35656i	−0.934016	+	0.357231i	$0.883721\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.48954			1.48954			0.744772	−	0.667319i	$-0.232558\pi$
$547$	1.48954			1.48954			0.744772	+	0.667319i	$0.232558\pi$
$548$	3.38342	−	0.247635i	3.38342	−	0.247635i
$549$		0			0
$550$	3.16050	+	2.09097i	3.16050	+	2.09097i
$551$		0			0
$552$		0			0
$553$	0.263526	−	1.00800i	0.263526	−	1.00800i
$554$	−1.75700	+	1.82238i	−1.75700	+	1.82238i
$555$		0			0
$556$		0			0
$557$	0.0578141	−	0.0446426i	0.0578141	−	0.0446426i	−0.581859	−	0.813290i	$-0.697674\pi$
$557$	0.0578141	−	0.0446426i	0.0578141	−	0.0446426i	0.639673	+	0.768647i	$0.279070\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−3.12472	−	1.75368i	−3.12472	−	1.75368i
$563$		0			0		−0.934016	−	0.357231i	$-0.883721\pi$
$563$		0			0		0.934016	+	0.357231i	$0.116279\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.744772	−	0.667319i	0.744772	−	0.667319i
$568$	0.749757	+	2.86786i	0.749757	+	2.86786i
$569$	−0.294343	−	0.411416i	−0.294343	−	0.411416i	0.639673	−	0.768647i	$-0.279070\pi$
$569$	−0.294343	−	0.411416i	−0.294343	−	0.411416i	−0.934016	+	0.357231i	$0.883721\pi$
$570$		0			0
$571$	0.532101	+	0.743741i	0.532101	+	0.743741i	0.989343	−	0.145601i	$-0.0465116\pi$
$571$	0.532101	+	0.743741i	0.532101	+	0.743741i	−0.457242	+	0.889342i	$0.651163\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.542911	−	1.27758i	−0.542911	−	1.27758i
$576$	−5.72229	+	1.27469i	−5.72229	+	1.27469i
$577$		0			0		0.391105	−	0.920346i	$-0.372093\pi$
$577$		0			0		−0.391105	+	0.920346i	$0.627907\pi$
$578$	1.79160	+	0.839867i	1.79160	+	0.839867i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.63586	+	3.18176i	1.63586	+	3.18176i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.957601	−	0.288099i	$-0.0930233\pi$
$587$		0			0		−0.957601	+	0.288099i	$0.906977\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.91642	−	3.72747i	1.91642	−	3.72747i
$593$		0			0		0.791496	−	0.611174i	$-0.209302\pi$
$593$		0			0		−0.791496	+	0.611174i	$0.790698\pi$
$594$		0			0
$595$		0			0
$596$	3.00492	+	0.442233i	3.00492	+	0.442233i
$597$		0			0
$598$		0			0
$599$	1.22510	−	1.47211i	1.22510	−	1.47211i	0.391105	−	0.920346i	$-0.372093\pi$
$599$	1.22510	−	1.47211i	1.22510	−	1.47211i	0.833998	−	0.551768i	$-0.186047\pi$
$600$		0			0
$601$		0			0		0.581859	−	0.813290i	$-0.302326\pi$
$601$		0			0		−0.581859	+	0.813290i	$0.697674\pi$
$602$	2.66867	−	2.39113i	2.66867	−	2.39113i
$603$	1.54512	−	1.19310i	1.54512	−	1.19310i
$604$	1.33527	+	0.625948i	1.33527	+	0.625948i
$605$		0			0
$606$		0			0
$607$		0			0		−0.989343	−	0.145601i	$-0.953488\pi$
$607$		0			0		0.989343	+	0.145601i	$0.0465116\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.03385	−	1.07233i	−1.03385	−	1.07233i	−0.997332	−	0.0729953i	$-0.976744\pi$
$613$	−1.03385	−	1.07233i	−1.03385	−	1.07233i	−0.0365220	−	0.999333i	$-0.511628\pi$
$614$		0			0
$615$		0			0
$616$	−7.23845	−	0.529786i	−7.23845	−	0.529786i
$617$	1.97869			1.97869			0.989343	−	0.145601i	$-0.0465116\pi$
$617$	1.97869			1.97869			0.989343	+	0.145601i	$0.0465116\pi$
$618$		0			0
$619$		0			0		−0.905448	−	0.424457i	$-0.860465\pi$
$619$		0			0		0.905448	+	0.424457i	$0.139535\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.989343	−	0.145601i	0.989343	−	0.145601i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.868926	−	0.574876i	0.868926	−	0.574876i	−0.0365220	−	0.999333i	$-0.511628\pi$
$631$	0.868926	−	0.574876i	0.868926	−	0.574876i	0.905448	+	0.424457i	$0.139535\pi$
$632$	−3.44311	−	1.93237i	−3.44311	−	1.93237i
$633$		0			0
$634$	0.418243	−	0.584597i	0.418243	−	0.584597i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	1.58458	−	3.08203i	1.58458	−	3.08203i
$639$	−0.682125	+	0.382827i	−0.682125	+	0.382827i
$640$		0			0
$641$	0.0333988	−	0.0649611i	0.0333988	−	0.0649611i	−0.872049	−	0.489418i	$-0.837209\pi$
$641$	0.0333988	−	0.0649611i	0.0333988	−	0.0649611i	0.905448	+	0.424457i	$0.139535\pi$
$642$		0			0
$643$		0			0		0.997332	−	0.0729953i	$-0.0232558\pi$
$643$		0			0		−0.997332	+	0.0729953i	$0.976744\pi$
$644$	3.20297	+	2.47326i	3.20297	+	2.47326i
$645$		0			0
$646$		0			0
$647$		0			0		0.639673	−	0.768647i	$-0.279070\pi$
$647$		0			0		−0.639673	+	0.768647i	$0.720930\pi$
$648$	−1.73276	−	3.37024i	−1.73276	−	3.37024i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.0973643	−	0.189375i	0.0973643	−	0.189375i
$653$	0.362305	+	1.96148i	0.362305	+	1.96148i	0.252933	+	0.967484i	$0.418605\pi$
$653$	0.362305	+	1.96148i	0.362305	+	1.96148i	0.109371	+	0.994001i	$0.465116\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.08693	−	1.51925i	1.08693	−	1.51925i	0.252933	−	0.967484i	$-0.418605\pi$
$659$	1.08693	−	1.51925i	1.08693	−	1.51925i	0.833998	−	0.551768i	$-0.186047\pi$
$660$		0			0
$661$		0			0		−0.872049	−	0.489418i	$-0.837209\pi$
$661$		0			0		0.872049	+	0.489418i	$0.162791\pi$
$662$	−3.08266	+	2.03947i	−3.08266	+	2.03947i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.76619	+	0.393435i	1.76619	+	0.393435i
$667$	−1.10701	+	0.621287i	−1.10701	+	0.621287i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.15838	+	0.543027i	1.15838	+	0.543027i	0.905448	−	0.424457i	$-0.139535\pi$
$673$	1.15838	+	0.543027i	1.15838	+	0.543027i	0.252933	+	0.967484i	$0.418605\pi$
$674$	−3.57364	−	1.67525i	−3.57364	−	1.67525i
$675$		0			0
$676$	2.91520			2.91520
$677$		0			0		−0.997332	−	0.0729953i	$-0.976744\pi$
$677$		0			0		0.997332	+	0.0729953i	$0.0232558\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.54512	+	0.344190i	1.54512	+	0.344190i	0.905448	−	0.424457i	$-0.139535\pi$
$683$	1.54512	+	0.344190i	1.54512	+	0.344190i	0.639673	+	0.768647i	$0.279070\pi$
$684$		0			0
$685$		0			0
$686$	1.95760	+	0.288099i	1.95760	+	0.288099i
$687$		0			0
$688$	−3.79497	−	7.38127i	−3.79497	−	7.38127i
$689$		0			0
$690$		0			0
$691$		0			0		0.744772	−	0.667319i	$-0.232558\pi$
$691$		0			0		−0.744772	+	0.667319i	$0.767442\pi$
$692$		0			0
$693$	−0.347871	−	1.88334i	−0.347871	−	1.88334i
$694$	−1.75700	+	2.11125i	−1.75700	+	2.11125i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−2.30737	+	1.78169i	−2.30737	+	1.78169i
$701$	−0.100018	+	0.194537i	−0.100018	+	0.194537i	−0.934016	−	0.357231i	$-0.883721\pi$
$701$	−0.100018	+	0.194537i	−0.100018	+	0.194537i	0.833998	+	0.551768i	$0.186047\pi$
$702$		0			0
$703$		0			0
$704$	−3.62528	+	10.6266i	−3.62528	+	10.6266i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.970538	−	0.642102i	−0.970538	−	0.642102i	−0.0365220	−	0.999333i	$-0.511628\pi$
$709$	−0.970538	−	0.642102i	−0.970538	−	0.642102i	−0.934016	+	0.357231i	$0.883721\pi$
$710$		0			0
$711$	0.263526	−	1.00800i	0.263526	−	1.00800i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	2.28030	−	5.36599i	2.28030	−	5.36599i
$717$		0			0
$718$	−1.34971	−	3.17614i	−1.34971	−	3.17614i
$719$		0			0		0.457242	−	0.889342i	$-0.348837\pi$
$719$		0			0		−0.457242	+	0.889342i	$0.651163\pi$
$720$		0			0
$721$		0			0
$722$	−1.15132	−	1.60925i	−1.15132	−	1.60925i
$723$		0			0
$724$		0			0
$725$	−0.231304	−	0.884749i	−0.231304	−	0.884749i
$726$		0			0
$727$		0			0		−0.391105	−	0.920346i	$-0.627907\pi$
$727$		0			0		0.391105	+	0.920346i	$0.372093\pi$
$728$		0			0
$729$	0.744772	−	0.667319i	0.744772	−	0.667319i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.905448	−	0.424457i	$-0.139535\pi$
$733$		0			0		−0.905448	+	0.424457i	$0.860465\pi$
$734$		0			0
$735$		0			0
$736$	5.80025	−	4.47881i	5.80025	−	4.47881i
$737$	−0.408913	−	3.71633i	−0.408913	−	3.71633i
$738$		0			0
$739$	1.35494	−	1.40536i	1.35494	−	1.40536i	0.520940	−	0.853593i	$-0.325581\pi$
$739$	1.35494	−	1.40536i	1.35494	−	1.40536i	0.833998	−	0.551768i	$-0.186047\pi$
$740$		0			0
$741$		0			0
$742$	−3.65686	+	0.538178i	−3.65686	+	0.538178i
$743$	−1.32021	−	0.873444i	−1.32021	−	0.873444i	−0.322880	−	0.946440i	$-0.604651\pi$
$743$	−1.32021	−	0.873444i	−1.32021	−	0.873444i	−0.997332	+	0.0729953i	$0.976744\pi$
$744$		0			0
$745$		0			0
$746$	0.432823			0.432823
$747$		0			0
$748$		0			0
$749$	0.407484	+	0.667689i	0.407484	+	0.667689i
$750$		0			0
$751$	0.0636980	+	0.0357491i	0.0636980	+	0.0357491i	0.520940	−	0.853593i	$-0.325581\pi$
$751$	0.0636980	+	0.0357491i	0.0636980	+	0.0357491i	−0.457242	+	0.889342i	$0.651163\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.142078	−	0.334338i	−0.142078	−	0.334338i	0.833998	−	0.551768i	$-0.186047\pi$
$757$	−0.142078	−	0.334338i	−0.142078	−	0.334338i	−0.976076	+	0.217430i	$0.930233\pi$
$758$	−0.0786166	+	0.425623i	−0.0786166	+	0.425623i
$759$		0			0
$760$		0			0
$761$		0			0		−0.520940	−	0.853593i	$-0.674419\pi$
$761$		0			0		0.520940	+	0.853593i	$0.325581\pi$
$762$		0			0
$763$	0.182431	+	0.120695i	0.182431	+	0.120695i
$764$	−4.17841	+	3.22646i	−4.17841	+	3.22646i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.639673	−	0.768647i	$-0.279070\pi$
$769$		0			0		−0.639673	+	0.768647i	$0.720930\pi$
$770$		0			0
$771$		0			0
$772$	−1.47077	−	0.107646i	−1.47077	−	0.107646i
$773$		0			0		−0.989343	−	0.145601i	$-0.953488\pi$
$773$		0			0		0.989343	+	0.145601i	$0.0465116\pi$
$774$	2.66867	−	2.39113i	2.66867	−	2.39113i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.671375	+	3.63477i	0.671375	+	3.63477i
$779$		0			0
$780$		0			0
$781$	−0.0547132	+	1.49709i	−0.0547132	+	1.49709i
$782$		0			0
$783$		0			0
$784$	1.79251	−	4.21813i	1.79251	−	4.21813i
$785$		0			0
$786$		0			0
$787$		0			0		0.322880	−	0.946440i	$-0.395349\pi$
$787$		0			0		−0.322880	+	0.946440i	$0.604651\pi$
$788$	−4.54169	+	3.00476i	−4.54169	+	3.00476i
$789$		0			0
$790$		0			0
$791$	−0.351109	+	1.34301i	−0.351109	+	1.34301i
$792$	−7.23845	−	0.529786i	−7.23845	−	0.529786i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.791496	−	0.611174i	$-0.790698\pi$
$797$		0			0		0.791496	+	0.611174i	$0.209302\pi$
$798$		0			0
$799$		0			0
$800$	2.06469	+	4.85862i	2.06469	+	4.85862i
$801$		0			0
$802$	−0.665636	+	1.09069i	−0.665636	+	1.09069i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.323589	+	1.23775i	0.323589	+	1.23775i	0.905448	+	0.424457i	$0.139535\pi$
$809$	0.323589	+	1.23775i	0.323589	+	1.23775i	−0.581859	+	0.813290i	$0.697674\pi$
$810$		0			0
$811$		0			0		0.181637	−	0.983366i	$-0.441860\pi$
$811$		0			0		−0.181637	+	0.983366i	$0.558140\pi$
$812$	1.85034	+	1.91920i	1.85034	+	1.91920i
$813$		0			0
$814$	2.40532	−	2.49484i	2.40532	−	2.49484i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.854143	+	0.326682i	0.854143	+	0.326682i	0.744772	−	0.667319i	$-0.232558\pi$
$821$	0.854143	+	0.326682i	0.854143	+	0.326682i	0.109371	+	0.994001i	$0.465116\pi$
$822$		0			0
$823$	0.912045	+	1.77394i	0.912045	+	1.77394i	0.520940	+	0.853593i	$0.325581\pi$
$823$	0.912045	+	1.77394i	0.912045	+	1.77394i	0.391105	+	0.920346i	$0.372093\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.21053	−	1.25558i	1.21053	−	1.25558i	0.252933	−	0.967484i	$-0.418605\pi$
$827$	1.21053	−	1.25558i	1.21053	−	1.25558i	0.957601	−	0.288099i	$-0.0930233\pi$
$828$	3.20297	+	2.47326i	3.20297	+	2.47326i
$829$		0			0		0.181637	−	0.983366i	$-0.441860\pi$
$829$		0			0		−0.181637	+	0.983366i	$0.558140\pi$
$830$		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		−0.322880	−	0.946440i	$-0.604651\pi$
$839$		0			0		0.322880	+	0.946440i	$0.395349\pi$
$840$		0			0
$841$	0.152915	−	0.0584851i	0.152915	−	0.0584851i
$842$	−0.711145	−	0.104659i	−0.711145	−	0.104659i
$843$		0			0
$844$	−0.115826	+	1.05266i	−0.115826	+	1.05266i
$845$		0			0
$846$		0			0
$847$	−2.49195	−	0.953090i	−2.49195	−	0.953090i
$848$	−0.936388	+	8.51020i	−0.936388	+	8.51020i
$849$		0			0
$850$		0			0
$851$	−1.23907	+	0.276015i	−1.23907	+	0.276015i
$852$		0			0
$853$		0			0		−0.694074	−	0.719903i	$-0.744186\pi$
$853$		0			0		0.694074	+	0.719903i	$0.255814\pi$
$854$		0			0
$855$		0			0
$856$	2.83857	−	0.853997i	2.83857	−	0.853997i
$857$		0			0		−0.0365220	−	0.999333i	$-0.511628\pi$
$857$		0			0		0.0365220	+	0.999333i	$0.488372\pi$
$858$		0			0
$859$		0			0		0.391105	−	0.920346i	$-0.372093\pi$
$859$		0			0		−0.391105	+	0.920346i	$0.627907\pi$
$860$		0			0
$861$		0			0
$862$	−1.93135	−	0.430226i	−1.93135	−	0.430226i
$863$	−1.74410			−1.74410			−0.872049	−	0.489418i	$-0.837209\pi$
$863$	−1.74410			−1.74410			−0.872049	+	0.489418i	$0.837209\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.38496	−	1.43650i	−1.38496	−	1.43650i
$870$		0			0
$871$		0			0
$872$	0.617373	−	0.553169i	0.617373	−	0.553169i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.47854	+	0.565494i	1.47854	+	0.565494i	0.957601	−	0.288099i	$-0.0930233\pi$
$877$	1.47854	+	0.565494i	1.47854	+	0.565494i	0.520940	+	0.853593i	$0.325581\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.0365220	−	0.999333i	$-0.488372\pi$
$881$		0			0		−0.0365220	+	0.999333i	$0.511628\pi$
$882$	1.95760	+	0.288099i	1.95760	+	0.288099i
$883$	0.603151	−	0.230686i	0.603151	−	0.230686i	−0.0365220	−	0.999333i	$-0.511628\pi$
$883$	0.603151	−	0.230686i	0.603151	−	0.230686i	0.639673	+	0.768647i	$0.279070\pi$
$884$		0			0
$885$		0			0
$886$	0.109475	+	0.994947i	0.109475	+	0.994947i
$887$		0			0		0.997332	−	0.0729953i	$-0.0232558\pi$
$887$		0			0		−0.997332	+	0.0729953i	$0.976744\pi$
$888$		0			0
$889$	1.82334	−	0.697369i	1.82334	−	0.697369i
$890$		0			0
$891$	−0.347871	−	1.88334i	−0.347871	−	1.88334i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−5.00306	−	3.86323i	−5.00306	−	3.86323i
$897$		0			0
$898$	−3.29164	+	2.17773i	−3.29164	+	2.17773i
$899$		0			0
$900$	−2.30737	+	1.78169i	−2.30737	+	1.78169i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	4.58742	+	2.57458i	4.58742	+	2.57458i
$905$		0			0
$906$		0			0
$907$	−1.32929	+	1.37876i	−1.32929	+	1.37876i	−0.457242	+	0.889342i	$0.651163\pi$
$907$	−1.32929	+	1.37876i	−1.32929	+	1.37876i	−0.872049	+	0.489418i	$0.837209\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.0722656	+	1.97737i	−0.0722656	+	1.97737i	0.109371	+	0.994001i	$0.465116\pi$
$911$	−0.0722656	+	1.97737i	−0.0722656	+	1.97737i	−0.181637	+	0.983366i	$0.558140\pi$
$912$		0			0
$913$		0			0
$914$	1.31872	+	1.58461i	1.31872	+	1.58461i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.328926	−	0.154194i	−0.328926	−	0.154194i	0.252933	−	0.967484i	$-0.418605\pi$
$919$	−0.328926	−	0.154194i	−0.328926	−	0.154194i	−0.581859	+	0.813290i	$0.697674\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.0333988	−	0.913875i	0.0333988	−	0.913875i
$926$	1.71933	−	2.81723i	1.71933	−	2.81723i
$927$		0			0
$928$	4.20998	−	2.36275i	4.20998	−	2.36275i
$929$		0			0		0.109371	−	0.994001i	$-0.465116\pi$
$929$		0			0		−0.109371	+	0.994001i	$0.534884\pi$
$930$		0			0
$931$		0			0
$932$	5.67573	+	0.415410i	5.67573	+	0.415410i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.322880	−	0.946440i	$-0.395349\pi$
$937$		0			0		−0.322880	+	0.946440i	$0.604651\pi$
$938$	3.77029	+	0.839867i	3.77029	+	0.839867i
$939$		0			0
$940$		0			0
$941$		0			0		−0.520940	−	0.853593i	$-0.674419\pi$
$941$		0			0		0.520940	+	0.853593i	$0.325581\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−1.24649	−	6.74839i	−1.24649	−	6.74839i
$947$	0.421892	+	1.61376i	0.421892	+	1.61376i	0.744772	+	0.667319i	$0.232558\pi$
$947$	0.421892	+	1.61376i	0.421892	+	1.61376i	−0.322880	+	0.946440i	$0.604651\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.94694	−	0.142498i	1.94694	−	0.142498i	0.957601	−	0.288099i	$-0.0930233\pi$
$953$	1.94694	−	0.142498i	1.94694	−	0.142498i	0.989343	+	0.145601i	$0.0465116\pi$
$954$	−3.65686	+	0.538178i	−3.65686	+	0.538178i
$955$		0			0
$956$	2.06469	−	0.967888i	2.06469	−	0.967888i
$957$		0			0
$958$		0			0
$959$	−0.606228	+	0.993341i	−0.606228	+	0.993341i
$960$		0			0
$961$	0.833998	+	0.551768i	0.833998	+	0.551768i
$962$		0			0
$963$	0.407484	+	0.667689i	0.407484	+	0.667689i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.305926	+	0.719903i	0.305926	+	0.719903i	1.00000			$0$
$967$	0.305926	+	0.719903i	0.305926	+	0.719903i	−0.694074	+	0.719903i	$0.744186\pi$
$968$	−5.88294	+	8.22284i	−5.88294	+	8.22284i
$969$		0			0
$970$		0			0
$971$		0			0		0.976076	−	0.217430i	$-0.0697674\pi$
$971$		0			0		−0.976076	+	0.217430i	$0.930233\pi$
$972$		0			0
$973$		0			0
$974$	−0.0565269	−	0.133019i	−0.0565269	−	0.133019i
$975$		0			0
$976$		0			0
$977$	−0.472488	+	0.180711i	−0.472488	+	0.180711i	−0.581859	−	0.813290i	$-0.697674\pi$
$977$	−0.472488	+	0.180711i	−0.472488	+	0.180711i	0.109371	+	0.994001i	$0.465116\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.182431	+	0.120695i	0.182431	+	0.120695i
$982$	−3.82153	+	0.562413i	−3.82153	+	0.562413i
$983$		0			0		0.905448	−	0.424457i	$-0.139535\pi$
$983$		0			0		−0.905448	+	0.424457i	$0.860465\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.983156	+	2.31356i	−0.983156	+	2.31356i
$990$		0			0
$991$	−1.57919	+	0.740294i	−1.57919	+	0.740294i	−0.997332	−	0.0729953i	$-0.976744\pi$
$991$	−1.57919	+	0.740294i	−1.57919	+	0.740294i	−0.581859	+	0.813290i	$0.697674\pi$
$992$		0			0
$993$		0			0
$994$	−1.44562	−	0.552903i	−1.44562	−	0.552903i
$995$		0			0
$996$		0			0
$997$		0			0		−0.391105	−	0.920346i	$-0.627907\pi$
$997$		0			0		0.391105	+	0.920346i	$0.372093\pi$
$998$	−2.87683	+	2.57765i	−2.87683	+	2.57765i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3017.1.t.a.1105.1	✓	42
7.6	odd	2	CM	3017.1.t.a.1105.1	✓	42
431.337	even	43	inner	3017.1.t.a.1630.1	yes	42
3017.1630	odd	86	inner	3017.1.t.a.1630.1	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3017.1.t.a.1105.1	✓	42	1.1	even	1	trivial
3017.1.t.a.1105.1	✓	42	7.6	odd	2	CM
3017.1.t.a.1630.1	yes	42	431.337	even	43	inner
3017.1.t.a.1630.1	yes	42	3017.1630	odd	86	inner

Overview	Random
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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:	\( N \)	\(=\)	\( 3017 = 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3017.t (of order \(86\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26571 + 1.52091i) q^{2} +(-0.529508 + 2.86671i) q^{4} +(-0.694074 - 0.719903i) q^{7} +(-3.30470 + 1.85469i) q^{8} +(-0.694074 - 0.719903i) q^{9} +O(q^{10})\)	\(q+(1.26571 + 1.52091i) q^{2} +(-0.529508 + 2.86671i) q^{4} +(-0.694074 - 0.719903i) q^{7} +(-3.30470 + 1.85469i) q^{8} +(-0.694074 - 0.719903i) q^{9} +(-1.86938 + 0.416423i) q^{11} +(0.216411 - 1.96682i) q^{14} +(-4.28078 - 1.63726i) q^{16} +(0.216411 - 1.96682i) q^{18} +(-2.99944 - 2.31609i) q^{22} +(0.448206 + 1.31380i) q^{23} +(-0.997332 + 0.0729953i) q^{25} +(2.43127 - 1.60851i) q^{28} +(0.166104 + 0.899273i) q^{29} +(-1.70453 - 4.99638i) q^{32} +(2.43127 - 1.60851i) q^{36} +(-0.100018 + 0.908999i) q^{37} +(1.34871 + 1.20845i) q^{43} +(-0.203910 - 5.57947i) q^{44} +(-1.43087 + 2.34457i) q^{46} +(-0.0365220 + 0.999333i) q^{49} +(-1.37336 - 1.42446i) q^{50} +(-0.472488 - 1.80729i) q^{53} +(3.62891 + 1.09178i) q^{56} +(-1.15747 + 1.39085i) q^{58} +(-0.0365220 + 0.999333i) q^{63} +(3.05404 - 5.00423i) q^{64} +(-0.213509 + 1.94044i) q^{67} +(0.197847 - 0.756775i) q^{71} +(3.62891 + 1.09178i) q^{72} +(-1.50910 + 0.998412i) q^{74} +(1.59727 + 1.05675i) q^{77} +(0.542758 + 0.889342i) q^{79} +(-0.0365220 + 0.999333i) q^{81} +(-0.130866 + 3.58081i) q^{86} +(5.40542 - 4.84328i) q^{88} +(-4.00361 + 0.589209i) q^{92} +(-1.56612 + 1.20932i) q^{98} +(1.59727 + 1.05675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 42 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9	\( 42 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9} - 2 q^{11} - 2 q^{14} - 5 q^{16} - 2 q^{18} - 4 q^{22} - 2 q^{23} - q^{25} - 3 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 2 q^{37} - 2 q^{43} - 6 q^{44} - 4 q^{46} - q^{49} - 2 q^{50} - 2 q^{53} - 4 q^{56} - 4 q^{58} - q^{63} - 7 q^{64} - 2 q^{67} - 2 q^{71} - 4 q^{72} - 4 q^{74} - 2 q^{77} + 41 q^{79} - q^{81} - 4 q^{86} + 35 q^{88} - 6 q^{92} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 42 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9 - 2 * q^11 - 2 * q^14 - 5 * q^16 - 2 * q^18 - 4 * q^22 - 2 * q^23 - q^25 - 3 * q^28 - 2 * q^29 - 6 * q^32 - 3 * q^36 - 2 * q^37 - 2 * q^43 - 6 * q^44 - 4 * q^46 - q^49 - 2 * q^50 - 2 * q^53 - 4 * q^56 - 4 * q^58 - q^63 - 7 * q^64 - 2 * q^67 - 2 * q^71 - 4 * q^72 - 4 * q^74 - 2 * q^77 + 41 * q^79 - q^81 - 4 * q^86 + 35 * q^88 - 6 * q^92 - 2 * q^98 - 2 * q^99

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