LMFDB - Embedded newform 3017.1.t.a.1091.1

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			1091.1
Root			$0.457242 + 0.889342i$ of defining polynomial
Character	$\chi$	$=$	3017.1091
Dual form			3017.1.t.a.1756.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173134 - 0.133690i) q^{2} +(-0.240831 - 0.921191i) q^{4} +(-0.181637 - 0.983366i) q^{7} +(-0.167009 + 0.393005i) q^{8} +(-0.181637 - 0.983366i) q^{9} +O(q^{10})$	\(q+(-0.173134 - 0.133690i) q^{2} +(-0.240831 - 0.921191i) q^{4} +(-0.181637 - 0.983366i) q^{7} +(-0.167009 + 0.393005i) q^{8} +(-0.181637 - 0.983366i) q^{9} +(1.13588 - 1.58766i) q^{11} +(-0.100018 + 0.194537i) q^{14} +(-0.748868 + 0.420285i) q^{16} +(-0.100018 + 0.194537i) q^{18} +(-0.408913 + 0.123024i) q^{22} +(-0.359402 - 0.0528931i) q^{23} +(0.744772 + 0.667319i) q^{25} +(-0.862124 + 0.404147i) q^{28} +(-0.0184753 + 0.0706689i) q^{29} +(0.608310 + 0.0895247i) q^{32} +(-0.862124 + 0.404147i) q^{36} +(0.0333988 - 0.0649611i) q^{37} +(-0.336403 + 0.551217i) q^{43} +(-1.73610 - 0.664001i) q^{44} +(0.0551535 + 0.0572060i) q^{46} +(-0.934016 + 0.357231i) q^{49} +(-0.0397317 - 0.215104i) q^{50} +(-1.45457 + 0.962337i) q^{53} +(0.416802 + 0.0928467i) q^{56} +(0.0126464 - 0.00976523i) q^{58} +(-0.934016 + 0.357231i) q^{63} +(0.502682 + 0.521389i) q^{64} +(0.532101 - 1.03494i) q^{67} +(1.06697 + 0.705902i) q^{71} +(0.416802 + 0.0928467i) q^{72} +(-0.0144671 + 0.00678190i) q^{74} +(-1.76757 - 0.828604i) q^{77} +(0.963478 - 0.999333i) q^{79} +(-0.934016 + 0.357231i) q^{81} +(0.131935 - 0.0504607i) q^{86} +(0.434258 + 0.711559i) q^{88} +(0.0378306 + 0.343817i) q^{92} +(0.209468 + 0.0630195i) q^{98} +(-1.76757 - 0.828604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3017\mathbb{Z}\right)^\times$.

$n$	$869$	$1725$
$\chi(n)$	$e\left(\frac{19}{43}\right)$	$-1$

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 $

$2$	−0.173134	−	0.133690i	−0.173134	−	0.133690i	0.520940	−	0.853593i	$-0.325581\pi$
$2$	−0.173134	−	0.133690i	−0.173134	−	0.133690i	−0.694074	+	0.719903i	$0.744186\pi$
$3$		0			0		0.639673	−	0.768647i	$-0.279070\pi$
$3$		0			0		−0.639673	+	0.768647i	$0.720930\pi$
$4$	−0.240831	−	0.921191i	−0.240831	−	0.921191i
$5$		0			0		−0.934016	−	0.357231i	$-0.883721\pi$
$5$		0			0		0.934016	+	0.357231i	$0.116279\pi$
$6$		0			0
$7$	−0.181637	−	0.983366i	−0.181637	−	0.983366i
$7$	−0.181637	−	0.983366i	−0.181637	−	0.983366i
$8$	−0.167009	+	0.393005i	−0.167009	+	0.393005i
$9$	−0.181637	−	0.983366i	−0.181637	−	0.983366i
$10$		0			0
$11$	1.13588	−	1.58766i	1.13588	−	1.58766i	0.391105	−	0.920346i	$-0.372093\pi$
$11$	1.13588	−	1.58766i	1.13588	−	1.58766i	0.744772	−	0.667319i	$-0.232558\pi$
$12$		0			0
$13$		0			0		0.791496	−	0.611174i	$-0.209302\pi$
$13$		0			0		−0.791496	+	0.611174i	$0.790698\pi$
$14$	−0.100018	+	0.194537i	−0.100018	+	0.194537i
$15$		0			0
$16$	−0.748868	+	0.420285i	−0.748868	+	0.420285i
$17$		0			0		0.581859	−	0.813290i	$-0.302326\pi$
$17$		0			0		−0.581859	+	0.813290i	$0.697674\pi$
$18$	−0.100018	+	0.194537i	−0.100018	+	0.194537i
$19$		0			0		0.934016	−	0.357231i	$-0.116279\pi$
$19$		0			0		−0.934016	+	0.357231i	$0.883721\pi$
$20$		0			0
$21$		0			0
$22$	−0.408913	+	0.123024i	−0.408913	+	0.123024i
$23$	−0.359402	−	0.0528931i	−0.359402	−	0.0528931i	−0.0365220	−	0.999333i	$-0.511628\pi$
$23$	−0.359402	−	0.0528931i	−0.359402	−	0.0528931i	−0.322880	+	0.946440i	$0.604651\pi$
$24$		0			0
$25$	0.744772	+	0.667319i	0.744772	+	0.667319i
$26$		0			0
$27$		0			0
$28$	−0.862124	+	0.404147i	−0.862124	+	0.404147i
$29$	−0.0184753	+	0.0706689i	−0.0184753	+	0.0706689i	−0.976076	−	0.217430i	$-0.930233\pi$
$29$	−0.0184753	+	0.0706689i	−0.0184753	+	0.0706689i	0.957601	+	0.288099i	$0.0930233\pi$
$30$		0			0
$31$		0			0		−0.976076	−	0.217430i	$-0.930233\pi$
$31$		0			0		0.976076	+	0.217430i	$0.0697674\pi$
$32$	0.608310	+	0.0895247i	0.608310	+	0.0895247i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.862124	+	0.404147i	−0.862124	+	0.404147i
$37$	0.0333988	−	0.0649611i	0.0333988	−	0.0649611i	−0.872049	−	0.489418i	$-0.837209\pi$
$37$	0.0333988	−	0.0649611i	0.0333988	−	0.0649611i	0.905448	+	0.424457i	$0.139535\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.872049	−	0.489418i	$-0.162791\pi$
$41$		0			0		−0.872049	+	0.489418i	$0.837209\pi$
$42$		0			0
$43$	−0.336403	+	0.551217i	−0.336403	+	0.551217i	−0.976076	−	0.217430i	$-0.930233\pi$
$43$	−0.336403	+	0.551217i	−0.336403	+	0.551217i	0.639673	+	0.768647i	$0.279070\pi$
$44$	−1.73610	−	0.664001i	−1.73610	−	0.664001i
$45$		0			0
$46$	0.0551535	+	0.0572060i	0.0551535	+	0.0572060i
$47$		0			0		−0.833998	−	0.551768i	$-0.813953\pi$
$47$		0			0		0.833998	+	0.551768i	$0.186047\pi$
$48$		0			0
$49$	−0.934016	+	0.357231i	−0.934016	+	0.357231i
$50$	−0.0397317	−	0.215104i	−0.0397317	−	0.215104i
$51$		0			0
$52$		0			0
$53$	−1.45457	+	0.962337i	−1.45457	+	0.962337i	−0.457242	+	0.889342i	$0.651163\pi$
$53$	−1.45457	+	0.962337i	−1.45457	+	0.962337i	−0.997332	+	0.0729953i	$0.976744\pi$
$54$		0			0
$55$		0			0
$56$	0.416802	+	0.0928467i	0.416802	+	0.0928467i
$57$		0			0
$58$	0.0126464	−	0.00976523i	0.0126464	−	0.00976523i
$59$		0			0		−0.791496	−	0.611174i	$-0.790698\pi$
$59$		0			0		0.791496	+	0.611174i	$0.209302\pi$
$60$		0			0
$61$		0			0		0.997332	−	0.0729953i	$-0.0232558\pi$
$61$		0			0		−0.997332	+	0.0729953i	$0.976744\pi$
$62$		0			0
$63$	−0.934016	+	0.357231i	−0.934016	+	0.357231i
$64$	0.502682	+	0.521389i	0.502682	+	0.521389i
$65$		0			0
$66$		0			0
$67$	0.532101	−	1.03494i	0.532101	−	1.03494i	−0.457242	−	0.889342i	$-0.651163\pi$
$67$	0.532101	−	1.03494i	0.532101	−	1.03494i	0.989343	−	0.145601i	$-0.0465116\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.06697	+	0.705902i	1.06697	+	0.705902i	0.957601	−	0.288099i	$-0.0930233\pi$
$71$	1.06697	+	0.705902i	1.06697	+	0.705902i	0.109371	+	0.994001i	$0.465116\pi$
$72$	0.416802	+	0.0928467i	0.416802	+	0.0928467i
$73$		0			0		0.0365220	−	0.999333i	$-0.488372\pi$
$73$		0			0		−0.0365220	+	0.999333i	$0.511628\pi$
$74$	−0.0144671	+	0.00678190i	−0.0144671	+	0.00678190i
$75$		0			0
$76$		0			0
$77$	−1.76757	−	0.828604i	−1.76757	−	0.828604i
$78$		0			0
$79$	0.963478	−	0.999333i	0.963478	−	0.999333i	−0.0365220	−	0.999333i	$-0.511628\pi$
$79$	0.963478	−	0.999333i	0.963478	−	0.999333i	1.00000			$0$
$80$		0			0
$81$	−0.934016	+	0.357231i	−0.934016	+	0.357231i
$82$		0			0
$83$		0			0		0.639673	−	0.768647i	$-0.279070\pi$
$83$		0			0		−0.639673	+	0.768647i	$0.720930\pi$
$84$		0			0
$85$		0			0
$86$	0.131935	−	0.0504607i	0.131935	−	0.0504607i
$87$		0			0
$88$	0.434258	+	0.711559i	0.434258	+	0.711559i
$89$		0			0		0.109371	−	0.994001i	$-0.465116\pi$
$89$		0			0		−0.109371	+	0.994001i	$0.534884\pi$
$90$		0			0
$91$		0			0
$92$	0.0378306	+	0.343817i	0.0378306	+	0.343817i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.694074	−	0.719903i	$-0.744186\pi$
$97$		0			0		0.694074	+	0.719903i	$0.255814\pi$
$98$	0.209468	+	0.0630195i	0.209468	+	0.0630195i
$99$	−1.76757	−	0.828604i	−1.76757	−	0.828604i
$100$	0.435364	−	0.846789i	0.435364	−	0.846789i
$101$		0			0		0.694074	−	0.719903i	$-0.255814\pi$
$101$		0			0		−0.694074	+	0.719903i	$0.744186\pi$
$102$		0			0
$103$		0			0		−0.109371	−	0.994001i	$-0.534884\pi$
$103$		0			0		0.109371	+	0.994001i	$0.465116\pi$
$104$		0			0
$105$		0			0
$106$	0.380491	+	0.0278483i	0.380491	+	0.0278483i
$107$	−0.744399	−	1.04048i	−0.744399	−	1.04048i	−0.997332	−	0.0729953i	$-0.976744\pi$
$107$	−0.744399	−	1.04048i	−0.744399	−	1.04048i	0.252933	−	0.967484i	$-0.418605\pi$
$108$		0			0
$109$	0.532101	−	0.743741i	0.532101	−	0.743741i	−0.457242	−	0.889342i	$-0.651163\pi$
$109$	0.532101	−	0.743741i	0.532101	−	0.743741i	0.989343	+	0.145601i	$0.0465116\pi$
$110$		0			0
$111$		0			0
$112$	0.549316	+	0.660072i	0.549316	+	0.660072i
$113$	0.252139	−	0.261522i	0.252139	−	0.261522i	−0.581859	−	0.813290i	$-0.697674\pi$
$113$	0.252139	−	0.261522i	0.252139	−	0.261522i	0.833998	+	0.551768i	$0.186047\pi$
$114$		0			0
$115$		0			0
$116$	0.0695490			0.0695490
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.907583	−	2.66034i	−0.907583	−	2.66034i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.209468	+	0.0630195i	0.209468	+	0.0630195i
$127$	−0.744399	+	0.894488i	−0.744399	+	0.894488i	−0.997332	−	0.0729953i	$-0.976744\pi$
$127$	−0.744399	+	0.894488i	−0.744399	+	0.894488i	0.252933	+	0.967484i	$0.418605\pi$
$128$	−0.0845752	−	0.768647i	−0.0845752	−	0.768647i
$129$		0			0
$130$		0			0
$131$		0			0		−0.391105	−	0.920346i	$-0.627907\pi$
$131$		0			0		0.391105	+	0.920346i	$0.372093\pi$
$132$		0			0
$133$		0			0
$134$	−0.230486	+	0.108047i	−0.230486	+	0.108047i
$135$		0			0
$136$		0			0
$137$	−1.66355	+	1.10059i	−1.66355	+	1.10059i	−0.791496	+	0.611174i	$0.790698\pi$
$137$	−1.66355	+	1.10059i	−1.66355	+	1.10059i	−0.872049	+	0.489418i	$0.837209\pi$
$138$		0			0
$139$		0			0		0.976076	−	0.217430i	$-0.0697674\pi$
$139$		0			0		−0.976076	+	0.217430i	$0.930233\pi$
$140$		0			0
$141$		0			0
$142$	−0.0903572	−	0.264859i	−0.0903572	−	0.264859i
$143$		0			0
$144$	0.549316	+	0.660072i	0.549316	+	0.660072i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.0678851	−	0.0151221i	−0.0678851	−	0.0151221i
$149$	1.29655	+	0.495889i	1.29655	+	0.495889i	0.905448	−	0.424457i	$-0.139535\pi$
$149$	1.29655	+	0.495889i	1.29655	+	0.495889i	0.391105	+	0.920346i	$0.372093\pi$
$150$		0			0
$151$	1.39110	+	0.920346i	1.39110	+	0.920346i	1.00000			$0$
$151$	1.39110	+	0.920346i	1.39110	+	0.920346i	0.391105	+	0.920346i	$0.372093\pi$
$152$		0			0
$153$		0			0
$154$	0.195251	+	0.379765i	0.195251	+	0.379765i
$155$		0			0
$156$		0			0
$157$		0			0		−0.997332	−	0.0729953i	$-0.976744\pi$
$157$		0			0		0.997332	+	0.0729953i	$0.0232558\pi$
$158$	−0.300411	+	0.0442113i	−0.300411	+	0.0442113i
$159$		0			0
$160$		0			0
$161$	0.0132675	+	0.363031i	0.0132675	+	0.363031i
$162$	0.209468	+	0.0630195i	0.209468	+	0.0630195i
$163$	1.82334	+	0.406167i	1.82334	+	0.406167i	0.989343	−	0.145601i	$-0.0465116\pi$
$163$	1.82334	+	0.406167i	1.82334	+	0.406167i	0.833998	+	0.551768i	$0.186047\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.989343	−	0.145601i	$-0.953488\pi$
$167$		0			0		0.989343	+	0.145601i	$0.0465116\pi$
$168$		0			0
$169$	0.252933	−	0.967484i	0.252933	−	0.967484i
$170$		0			0
$171$		0			0
$172$	0.588792	+	0.177141i	0.588792	+	0.177141i
$173$		0			0		0.322880	−	0.946440i	$-0.395349\pi$
$173$		0			0		−0.322880	+	0.946440i	$0.604651\pi$
$174$		0			0
$175$	0.520940	−	0.853593i	0.520940	−	0.853593i
$176$	−0.183350	+	1.66634i	−0.183350	+	1.66634i
$177$		0			0
$178$		0			0
$179$	−1.16372	−	1.62658i	−1.16372	−	1.62658i	−0.581859	−	0.813290i	$-0.697674\pi$
$179$	−1.16372	−	1.62658i	−1.16372	−	1.62658i	−0.581859	−	0.813290i	$-0.697674\pi$
$180$		0			0
$181$		0			0		0.181637	−	0.983366i	$-0.441860\pi$
$181$		0			0		−0.181637	+	0.983366i	$0.558140\pi$
$182$		0			0
$183$		0			0
$184$	0.0808106	−	0.132413i	0.0808106	−	0.132413i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.336403	+	0.551217i	−0.336403	+	0.551217i	−0.976076	−	0.217430i	$-0.930233\pi$
$191$	−0.336403	+	0.551217i	−0.336403	+	0.551217i	0.639673	+	0.768647i	$0.279070\pi$
$192$		0			0
$193$	−0.762678	−	1.48342i	−0.762678	−	1.48342i	−0.872049	−	0.489418i	$-0.837209\pi$
$193$	−0.762678	−	1.48342i	−0.762678	−	1.48342i	0.109371	−	0.994001i	$-0.465116\pi$
$194$		0			0
$195$		0			0
$196$	0.554018	+	0.774375i	0.554018	+	0.774375i
$197$	0.316793	+	1.71509i	0.316793	+	1.71509i	0.639673	+	0.768647i	$0.279070\pi$
$197$	0.316793	+	1.71509i	0.316793	+	1.71509i	−0.322880	+	0.946440i	$0.604651\pi$
$198$	0.195251	+	0.379765i	0.195251	+	0.379765i
$199$		0			0		−0.791496	−	0.611174i	$-0.790698\pi$
$199$		0			0		0.791496	+	0.611174i	$0.209302\pi$
$200$	−0.386643	+	0.181251i	−0.386643	+	0.181251i
$201$		0			0
$202$		0			0
$203$	0.0728492	+	0.00533187i	0.0728492	+	0.00533187i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.0132675	+	0.363031i	0.0132675	+	0.363031i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.376755	+	0.337574i	0.376755	+	0.337574i	0.833998	−	0.551768i	$-0.186047\pi$
$211$	0.376755	+	0.337574i	0.376755	+	0.337574i	−0.457242	+	0.889342i	$0.651163\pi$
$212$	1.23680	+	1.10818i	1.23680	+	1.10818i
$213$		0			0
$214$	−0.0102206	+	0.279661i	−0.0102206	+	0.279661i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.191555	+	0.0576304i	−0.191555	+	0.0576304i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.391105	−	0.920346i	$-0.372093\pi$
$223$		0			0		−0.391105	+	0.920346i	$0.627907\pi$
$224$	−0.0224560	−	0.614452i	−0.0224560	−	0.614452i
$225$	0.520940	−	0.853593i	0.520940	−	0.853593i
$226$	−0.0786166	+	0.0115700i	−0.0786166	+	0.0115700i
$227$		0			0		0.872049	−	0.489418i	$-0.162791\pi$
$227$		0			0		−0.872049	+	0.489418i	$0.837209\pi$
$228$		0			0
$229$		0			0		0.989343	−	0.145601i	$-0.0465116\pi$
$229$		0			0		−0.989343	+	0.145601i	$0.953488\pi$
$230$		0			0
$231$		0			0
$232$	−0.0246877	−	0.0190632i	−0.0246877	−	0.0190632i
$233$	0.532101	+	1.03494i	0.532101	+	1.03494i	0.989343	+	0.145601i	$0.0465116\pi$
$233$	0.532101	+	1.03494i	0.532101	+	1.03494i	−0.457242	+	0.889342i	$0.651163\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.27593	+	0.0933863i	−1.27593	+	0.0933863i	−0.694074	−	0.719903i	$-0.744186\pi$
$239$	−1.27593	+	0.0933863i	−1.27593	+	0.0933863i	−0.581859	+	0.813290i	$0.697674\pi$
$240$		0			0
$241$		0			0		−0.791496	−	0.611174i	$-0.790698\pi$
$241$		0			0		0.791496	+	0.611174i	$0.209302\pi$
$242$	−0.198527	+	0.581930i	−0.198527	+	0.581930i
$243$		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		0.997332	−	0.0729953i	$-0.0232558\pi$
$251$		0			0		−0.997332	+	0.0729953i	$0.976744\pi$
$252$	0.554018	+	0.774375i	0.554018	+	0.774375i
$253$	−0.492213	+	0.510531i	−0.492213	+	0.510531i
$254$	0.248464	−	0.0553478i	0.248464	−	0.0553478i
$255$		0			0
$256$	0.289173	−	0.473828i	0.289173	−	0.473828i
$257$		0			0		0.0365220	−	0.999333i	$-0.488372\pi$
$257$		0			0		−0.0365220	+	0.999333i	$0.511628\pi$
$258$		0			0
$259$	−0.0699470	−	0.0210439i	−0.0699470	−	0.0210439i
$260$		0			0
$261$	0.0728492	+	0.00533187i	0.0728492	+	0.00533187i
$262$		0			0
$263$	0.0578141	−	0.0446426i	0.0578141	−	0.0446426i	−0.581859	−	0.813290i	$-0.697674\pi$
$263$	0.0578141	−	0.0446426i	0.0578141	−	0.0446426i	0.639673	+	0.768647i	$0.279070\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−1.08153	−	0.240920i	−1.08153	−	0.240920i
$269$		0			0		−0.957601	−	0.288099i	$-0.906977\pi$
$269$		0			0		0.957601	+	0.288099i	$0.0930233\pi$
$270$		0			0
$271$		0			0		−0.872049	−	0.489418i	$-0.837209\pi$
$271$		0			0		0.872049	+	0.489418i	$0.162791\pi$
$272$		0			0
$273$		0			0
$274$	0.435154	+	0.0318492i	0.435154	+	0.0318492i
$275$	1.90545	−	0.424457i	1.90545	−	0.424457i
$276$		0			0
$277$	0.723811	+	1.40782i	0.723811	+	1.40782i	0.905448	+	0.424457i	$0.139535\pi$
$277$	0.723811	+	1.40782i	0.723811	+	1.40782i	−0.181637	+	0.983366i	$0.558140\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.563135	+	0.316047i	0.563135	+	0.316047i	0.744772	−	0.667319i	$-0.232558\pi$
$281$	0.563135	+	0.316047i	0.563135	+	0.316047i	−0.181637	+	0.983366i	$0.558140\pi$
$282$		0			0
$283$		0			0		−0.976076	−	0.217430i	$-0.930233\pi$
$283$		0			0		0.976076	+	0.217430i	$0.0697674\pi$
$284$	0.393311	−	1.15289i	0.393311	−	1.15289i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0224560	−	0.614452i	−0.0224560	−	0.614452i
$289$	−0.322880	−	0.946440i	−0.322880	−	0.946440i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.997332	−	0.0729953i	$-0.0232558\pi$
$293$		0			0		−0.997332	+	0.0729953i	$0.976744\pi$
$294$		0			0
$295$		0			0
$296$	0.0199521	+	0.0239750i	0.0199521	+	0.0239750i
$297$		0			0
$298$	−0.158182	−	0.259191i	−0.158182	−	0.259191i
$299$		0			0
$300$		0			0
$301$	0.603151	+	0.230686i	0.603151	+	0.230686i
$302$	−0.117807	−	0.345319i	−0.117807	−	0.345319i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.0365220	−	0.999333i	$-0.511628\pi$
$307$		0			0		0.0365220	+	0.999333i	$0.488372\pi$
$308$	−0.337617	+	1.82783i	−0.337617	+	1.82783i
$309$		0			0
$310$		0			0
$311$		0			0		−0.109371	−	0.994001i	$-0.534884\pi$
$311$		0			0		0.109371	+	0.994001i	$0.465116\pi$
$312$		0			0
$313$		0			0		−0.252933	−	0.967484i	$-0.581395\pi$
$313$		0			0		0.252933	+	0.967484i	$0.418605\pi$
$314$		0			0
$315$		0			0
$316$	−1.15261	−	0.646877i	−1.15261	−	0.646877i
$317$	0.421892	−	0.279121i	0.421892	−	0.279121i	−0.322880	−	0.946440i	$-0.604651\pi$
$317$	0.421892	−	0.279121i	0.421892	−	0.279121i	0.744772	+	0.667319i	$0.232558\pi$
$318$		0			0
$319$	0.0912129	+	0.109604i	0.0912129	+	0.109604i
$320$		0			0
$321$		0			0
$322$	0.0462365	−	0.0646267i	0.0462365	−	0.0646267i
$323$		0			0
$324$	0.554018	+	0.774375i	0.554018	+	0.774375i
$325$		0			0
$326$	−0.261382	−	0.314083i	−0.261382	−	0.314083i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.797476	−	1.55110i	0.797476	−	1.55110i	−0.0365220	−	0.999333i	$-0.511628\pi$
$331$	0.797476	−	1.55110i	0.797476	−	1.55110i	0.833998	−	0.551768i	$-0.186047\pi$
$332$		0			0
$333$	−0.0699470	−	0.0210439i	−0.0699470	−	0.0210439i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.480945	−	1.40976i	−0.480945	−	1.40976i	−0.872049	−	0.489418i	$-0.837209\pi$
$337$	−0.480945	−	1.40976i	−0.480945	−	1.40976i	0.391105	−	0.920346i	$-0.372093\pi$
$338$	−0.173134	+	0.133690i	−0.173134	+	0.133690i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.520940	+	0.853593i	0.520940	+	0.853593i
$344$	−0.160449	−	0.224266i	−0.160449	−	0.224266i
$345$		0			0
$346$		0			0
$347$	−0.0918840	+	0.351461i	−0.0918840	+	0.351461i	−0.997332	−	0.0729953i	$-0.976744\pi$
$347$	−0.0918840	+	0.351461i	−0.0918840	+	0.351461i	0.905448	+	0.424457i	$0.139535\pi$
$348$		0			0
$349$		0			0		−0.989343	−	0.145601i	$-0.953488\pi$
$349$		0			0		0.989343	+	0.145601i	$0.0465116\pi$
$350$	−0.204309	+	0.0781415i	−0.204309	+	0.0781415i
$351$		0			0
$352$	0.833100	−	0.864103i	0.833100	−	0.864103i
$353$		0			0		0.639673	−	0.768647i	$-0.279070\pi$
$353$		0			0		−0.639673	+	0.768647i	$0.720930\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.0159778	+	0.437193i	−0.0159778	+	0.437193i
$359$	−0.763496	−	0.170076i	−0.763496	−	0.170076i	−0.181637	−	0.983366i	$-0.558140\pi$
$359$	−0.763496	−	0.170076i	−0.763496	−	0.170076i	−0.581859	+	0.813290i	$0.697674\pi$
$360$		0			0
$361$	0.744772	−	0.667319i	0.744772	−	0.667319i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.694074	−	0.719903i	$-0.744186\pi$
$367$		0			0		0.694074	+	0.719903i	$0.255814\pi$
$368$	0.291375	−	0.111442i	0.291375	−	0.111442i
$369$		0			0
$370$		0			0
$371$	1.21053	+	1.25558i	1.21053	+	1.25558i
$372$		0			0
$373$	0.723811	−	0.558909i	0.723811	−	0.558909i	−0.181637	−	0.983366i	$-0.558140\pi$
$373$	0.723811	−	0.558909i	0.723811	−	0.558909i	0.905448	+	0.424457i	$0.139535\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.723811	+	0.558909i	0.723811	+	0.558909i	0.905448	−	0.424457i	$-0.139535\pi$
$379$	0.723811	+	0.558909i	0.723811	+	0.558909i	−0.181637	+	0.983366i	$0.558140\pi$
$380$		0			0
$381$		0			0
$382$	0.131935	−	0.0504607i	0.131935	−	0.0504607i
$383$		0			0		0.181637	−	0.983366i	$-0.441860\pi$
$383$		0			0		−0.181637	+	0.983366i	$0.558140\pi$
$384$		0			0
$385$		0			0
$386$	−0.0662723	+	0.358792i	−0.0662723	+	0.358792i
$387$	0.603151	+	0.230686i	0.603151	+	0.230686i
$388$		0			0
$389$	−0.682125	−	1.60517i	−0.682125	−	1.60517i	−0.791496	−	0.611174i	$-0.790698\pi$
$389$	−0.682125	−	1.60517i	−0.682125	−	1.60517i	0.109371	−	0.994001i	$-0.465116\pi$
$390$		0			0
$391$		0			0
$392$	0.0155956	−	0.426734i	0.0155956	−	0.426734i
$393$		0			0
$394$	0.174442	−	0.339291i	0.174442	−	0.339291i
$395$		0			0
$396$	−0.337617	+	1.82783i	−0.337617	+	1.82783i
$397$		0			0		0.957601	−	0.288099i	$-0.0930233\pi$
$397$		0			0		−0.957601	+	0.288099i	$0.906977\pi$
$398$		0			0
$399$		0			0
$400$	−0.838200	−	0.186717i	−0.838200	−	0.186717i
$401$	1.95760	+	0.288099i	1.95760	+	0.288099i	1.00000			$0$
$401$	1.95760	+	0.288099i	1.95760	+	0.288099i	0.957601	+	0.288099i	$0.0930233\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.0118998	−	0.0106623i	−0.0118998	−	0.0106623i
$407$	−0.0651996	−	0.126814i	−0.0651996	−	0.126814i
$408$		0			0
$409$		0			0		0.957601	−	0.288099i	$-0.0930233\pi$
$409$		0			0		−0.957601	+	0.288099i	$0.906977\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.0462365	−	0.0646267i	0.0462365	−	0.0646267i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.905448	−	0.424457i	$-0.860465\pi$
$419$		0			0		0.905448	+	0.424457i	$0.139535\pi$
$420$		0			0
$421$	0.263526	+	0.431804i	0.263526	+	0.431804i	0.957601	−	0.288099i	$-0.0930233\pi$
$421$	0.263526	+	0.431804i	0.263526	+	0.431804i	−0.694074	+	0.719903i	$0.744186\pi$
$422$	−0.0200989	−	0.108814i	−0.0200989	−	0.108814i
$423$		0			0
$424$	−0.135276	−	0.732374i	−0.135276	−	0.732374i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.779206	+	0.936313i	−0.779206	+	0.936313i
$429$		0			0
$430$		0			0
$431$	0.957601	+	0.288099i	0.957601	+	0.288099i
$431$	0.957601	+	0.288099i	0.957601	+	0.288099i
$432$		0			0
$433$		0			0		−0.791496	−	0.611174i	$-0.790698\pi$
$433$		0			0		0.791496	+	0.611174i	$0.209302\pi$
$434$		0			0
$435$		0			0
$436$	−0.813274	−	0.311051i	−0.813274	−	0.311051i
$437$		0			0
$438$		0			0
$439$		0			0		0.391105	−	0.920346i	$-0.372093\pi$
$439$		0			0		−0.391105	+	0.920346i	$0.627907\pi$
$440$		0			0
$441$	0.520940	+	0.853593i	0.520940	+	0.853593i
$442$		0			0
$443$	1.51028	+	0.707992i	1.51028	+	0.707992i	0.989343	−	0.145601i	$-0.0465116\pi$
$443$	1.51028	+	0.707992i	1.51028	+	0.707992i	0.520940	+	0.853593i	$0.325581\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.421410	−	0.589024i	0.421410	−	0.589024i
$449$	−0.681083	+	1.32471i	−0.681083	+	1.32471i	0.252933	+	0.967484i	$0.418605\pi$
$449$	−0.681083	+	1.32471i	−0.681083	+	1.32471i	−0.934016	+	0.357231i	$0.883721\pi$
$450$	−0.204309	+	0.0781415i	−0.204309	+	0.0781415i
$451$		0			0
$452$	−0.301635	−	0.169286i	−0.301635	−	0.169286i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.38815			−1.38815			−0.694074	−	0.719903i	$-0.744186\pi$
$457$	−1.38815			−1.38815			−0.694074	+	0.719903i	$0.744186\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.989343	−	0.145601i	$-0.953488\pi$
$461$		0			0		0.989343	+	0.145601i	$0.0465116\pi$
$462$		0			0
$463$	1.79160	+	0.263669i	1.79160	+	0.263669i	0.957601	−	0.288099i	$-0.0930233\pi$
$463$	1.79160	+	0.263669i	1.79160	+	0.263669i	0.833998	+	0.551768i	$0.186047\pi$
$464$	−0.0158655	−	0.0606866i	−0.0158655	−	0.0606866i
$465$		0			0
$466$	0.0462365	−	0.250320i	0.0462365	−	0.250320i
$467$		0			0		0.905448	−	0.424457i	$-0.139535\pi$
$467$		0			0		−0.905448	+	0.424457i	$0.860465\pi$
$468$		0			0
$469$	−1.11438	−	0.335266i	−1.11438	−	0.335266i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.493036	+	1.16021i	0.493036	+	1.16021i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.21053	+	1.25558i	1.21053	+	1.25558i
$478$	0.233392	+	0.154411i	0.233392	+	0.154411i
$479$		0			0		0.181637	−	0.983366i	$-0.441860\pi$
$479$		0			0		−0.181637	+	0.983366i	$0.558140\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−2.23211	+	1.47675i	−2.23211	+	1.47675i
$485$		0			0
$486$		0			0
$487$	1.82334	+	0.406167i	1.82334	+	0.406167i	0.989343	−	0.145601i	$-0.0465116\pi$
$487$	1.82334	+	0.406167i	1.82334	+	0.406167i	0.833998	+	0.551768i	$0.186047\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.807707	+	0.837765i	0.807707	+	0.837765i	0.989343	−	0.145601i	$-0.0465116\pi$
$491$	0.807707	+	0.837765i	0.807707	+	0.837765i	−0.181637	+	0.983366i	$0.558140\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.500358	−	1.17744i	0.500358	−	1.17744i
$498$		0			0
$499$	1.08693	+	0.415716i	1.08693	+	0.415716i	0.833998	−	0.551768i	$-0.186047\pi$
$499$	1.08693	+	0.415716i	1.08693	+	0.415716i	0.252933	+	0.967484i	$0.418605\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.976076	−	0.217430i	$-0.930233\pi$
$503$		0			0		0.976076	+	0.217430i	$0.0697674\pi$
$504$	0.0155956	−	0.426734i	0.0155956	−	0.426734i
$505$		0			0
$506$	0.153471	−	0.0225863i	0.153471	−	0.0225863i
$507$		0			0
$508$	1.00327	+	0.470313i	1.00327	+	0.470313i
$509$		0			0		0.639673	−	0.768647i	$-0.279070\pi$
$509$		0			0		−0.639673	+	0.768647i	$0.720930\pi$
$510$		0			0
$511$		0			0
$512$	−0.835673	+	0.319618i	−0.835673	+	0.319618i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.00929684	+	0.0129946i	0.00929684	+	0.0129946i
$519$		0			0
$520$		0			0
$521$		0			0		0.744772	−	0.667319i	$-0.232558\pi$
$521$		0			0		−0.744772	+	0.667319i	$0.767442\pi$
$522$	−0.0118998	−	0.0106623i	−0.0118998	−	0.0106623i
$523$		0			0		−0.109371	−	0.994001i	$-0.534884\pi$
$523$		0			0		0.109371	+	0.994001i	$0.465116\pi$
$524$		0			0
$525$		0			0
$526$	−0.0159778			−0.0159778
$527$		0			0
$528$		0			0
$529$	−0.831228	−	0.250079i	−0.831228	−	0.250079i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.317872	+	0.381963i	0.317872	+	0.381963i
$537$		0			0
$538$		0			0
$539$	−0.493764	+	1.88867i	−0.493764	+	1.88867i
$540$		0			0
$541$	−1.80607	−	0.132187i	−1.80607	−	0.132187i	−0.872049	−	0.489418i	$-0.837209\pi$
$541$	−1.80607	−	0.132187i	−1.80607	−	0.132187i	−0.934016	+	0.357231i	$0.883721\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.04188			1.04188			0.520940	−	0.853593i	$-0.325581\pi$
$547$	1.04188			1.04188			0.520940	+	0.853593i	$0.325581\pi$
$548$	1.41449	+	1.26739i	1.41449	+	1.26739i
$549$		0			0
$550$	−0.386643	−	0.181251i	−0.386643	−	0.181251i
$551$		0			0
$552$		0			0
$553$	−1.15771	−	0.765936i	−1.15771	−	0.765936i
$554$	0.0628950	−	0.340508i	0.0628950	−	0.340508i
$555$		0			0
$556$		0			0
$557$	−1.78883	−	0.538178i	−1.78883	−	0.538178i	−0.791496	−	0.611174i	$-0.790698\pi$
$557$	−1.78883	−	0.538178i	−1.78883	−	0.538178i	−0.997332	+	0.0729953i	$0.976744\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.0552456	−	0.130004i	−0.0552456	−	0.130004i
$563$		0			0		0.872049	−	0.489418i	$-0.162791\pi$
$563$		0			0		−0.872049	+	0.489418i	$0.837209\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.520940	+	0.853593i	0.520940	+	0.853593i
$568$	−0.455617	+	0.301433i	−0.455617	+	0.301433i
$569$	−1.66355	+	0.121756i	−1.66355	+	0.121756i	−0.872049	−	0.489418i	$-0.837209\pi$
$569$	−1.66355	+	0.121756i	−1.66355	+	0.121756i	−0.791496	+	0.611174i	$0.790698\pi$
$570$		0			0
$571$	0.0728492	−	0.00533187i	0.0728492	−	0.00533187i	−0.0365220	−	0.999333i	$-0.511628\pi$
$571$	0.0728492	−	0.00533187i	0.0728492	−	0.00533187i	0.109371	+	0.994001i	$0.465116\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.232376	−	0.279229i	−0.232376	−	0.279229i
$576$	0.421410	−	0.589024i	0.421410	−	0.589024i
$577$		0			0		0.639673	−	0.768647i	$-0.279070\pi$
$577$		0			0		−0.639673	+	0.768647i	$0.720930\pi$
$578$	−0.0706276	+	0.207027i	−0.0706276	+	0.207027i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.124348	+	3.40247i	−0.124348	+	3.40247i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.976076	−	0.217430i	$-0.0697674\pi$
$587$		0			0		−0.976076	+	0.217430i	$0.930233\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.00229089	+	0.0626843i	0.00229089	+	0.0626843i
$593$		0			0		−0.957601	−	0.288099i	$-0.906977\pi$
$593$		0			0		0.957601	+	0.288099i	$0.0930233\pi$
$594$		0			0
$595$		0			0
$596$	0.144559	−	1.31380i	0.144559	−	1.31380i
$597$		0			0
$598$		0			0
$599$	1.54512	−	1.19310i	1.54512	−	1.19310i	0.639673	−	0.768647i	$-0.279070\pi$
$599$	1.54512	−	1.19310i	1.54512	−	1.19310i	0.905448	−	0.424457i	$-0.139535\pi$
$600$		0			0
$601$		0			0		−0.997332	−	0.0729953i	$-0.976744\pi$
$601$		0			0		0.997332	+	0.0729953i	$0.0232558\pi$
$602$	−0.0735856	−	0.120575i	−0.0735856	−	0.120575i
$603$	−1.11438	−	0.335266i	−1.11438	−	0.335266i
$604$	0.512794	−	1.50312i	0.512794	−	1.50312i
$605$		0			0
$606$		0			0
$607$		0			0		0.109371	−	0.994001i	$-0.465116\pi$
$607$		0			0		−0.109371	+	0.994001i	$0.534884\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.189244	−	1.02455i	−0.189244	−	1.02455i	−0.934016	−	0.357231i	$-0.883721\pi$
$613$	−0.189244	−	1.02455i	−0.189244	−	1.02455i	0.744772	−	0.667319i	$-0.232558\pi$
$614$		0			0
$615$		0			0
$616$	0.620846	−	0.556280i	0.620846	−	0.556280i
$617$	0.218742			0.218742			0.109371	−	0.994001i	$-0.465116\pi$
$617$	0.218742			0.218742			0.109371	+	0.994001i	$0.465116\pi$
$618$		0			0
$619$		0			0		0.322880	−	0.946440i	$-0.395349\pi$
$619$		0			0		−0.322880	+	0.946440i	$0.604651\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.109371	+	0.994001i	0.109371	+	0.994001i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.25690	+	0.589209i	−1.25690	+	0.589209i	−0.934016	−	0.357231i	$-0.883721\pi$
$631$	−1.25690	+	0.589209i	−1.25690	+	0.589209i	−0.322880	+	0.946440i	$0.604651\pi$
$632$	0.231833	+	0.545549i	0.231833	+	0.545549i
$633$		0			0
$634$	−0.110359	−	0.00807726i	−0.110359	−	0.00807726i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.00113916	−	0.0311703i	−0.00113916	−	0.0311703i
$639$	0.500358	−	1.17744i	0.500358	−	1.17744i
$640$		0			0
$641$	0.0682243	+	1.86679i	0.0682243	+	1.86679i	0.391105	+	0.920346i	$0.372093\pi$
$641$	0.0682243	+	1.86679i	0.0682243	+	1.86679i	−0.322880	+	0.946440i	$0.604651\pi$
$642$		0			0
$643$		0			0		−0.744772	−	0.667319i	$-0.767442\pi$
$643$		0			0		0.744772	+	0.667319i	$0.232558\pi$
$644$	0.331226	−	0.0996511i	0.331226	−	0.0996511i
$645$		0			0
$646$		0			0
$647$		0			0		0.791496	−	0.611174i	$-0.209302\pi$
$647$		0			0		−0.791496	+	0.611174i	$0.790698\pi$
$648$	0.0155956	−	0.426734i	0.0155956	−	0.426734i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.0649599	−	1.77746i	−0.0649599	−	1.77746i
$653$	0.376755	−	1.44111i	0.376755	−	1.44111i	−0.457242	−	0.889342i	$-0.651163\pi$
$653$	0.376755	−	1.44111i	0.376755	−	1.44111i	0.833998	−	0.551768i	$-0.186047\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.73945	+	0.127311i	1.73945	+	0.127311i	0.905448	−	0.424457i	$-0.139535\pi$
$659$	1.73945	+	0.127311i	1.73945	+	0.127311i	0.833998	+	0.551768i	$0.186047\pi$
$660$		0			0
$661$		0			0		−0.391105	−	0.920346i	$-0.627907\pi$
$661$		0			0		0.391105	+	0.920346i	$0.372093\pi$
$662$	−0.345436	+	0.161934i	−0.345436	+	0.161934i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.00929684	+	0.0129946i	0.00929684	+	0.0129946i
$667$	0.0103780	−	0.0244214i	0.0103780	−	0.0244214i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.511117	−	1.49821i	0.511117	−	1.49821i	−0.322880	−	0.946440i	$-0.604651\pi$
$673$	0.511117	−	1.49821i	0.511117	−	1.49821i	0.833998	−	0.551768i	$-0.186047\pi$
$674$	−0.105203	+	0.308375i	−0.105203	+	0.308375i
$675$		0			0
$676$	−0.952152			−0.952152
$677$		0			0		0.744772	−	0.667319i	$-0.232558\pi$
$677$		0			0		−0.744772	+	0.667319i	$0.767442\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.11438	−	1.55761i	−1.11438	−	1.55761i	−0.791496	−	0.611174i	$-0.790698\pi$
$683$	−1.11438	−	1.55761i	−1.11438	−	1.55761i	−0.322880	−	0.946440i	$-0.604651\pi$
$684$		0			0
$685$		0			0
$686$	0.0239241	−	0.217430i	0.0239241	−	0.217430i
$687$		0			0
$688$	0.0202531	−	0.554174i	0.0202531	−	0.554174i
$689$		0			0
$690$		0			0
$691$		0			0		−0.520940	−	0.853593i	$-0.674419\pi$
$691$		0			0		0.520940	+	0.853593i	$0.325581\pi$
$692$		0			0
$693$	−0.493764	+	1.88867i	−0.493764	+	1.88867i
$694$	0.0628950	−	0.0485659i	0.0628950	−	0.0485659i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.911781	−	0.274314i	−0.911781	−	0.274314i
$701$	0.0333988	+	0.913875i	0.0333988	+	0.913875i	0.905448	+	0.424457i	$0.139535\pi$
$701$	0.0333988	+	0.913875i	0.0333988	+	0.913875i	−0.872049	+	0.489418i	$0.837209\pi$
$702$		0			0
$703$		0			0
$704$	1.39878	−	0.205857i	1.39878	−	0.205857i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.80607	−	0.846649i	−1.80607	−	0.846649i	−0.934016	−	0.357231i	$-0.883721\pi$
$709$	−1.80607	−	0.846649i	−1.80607	−	0.846649i	−0.872049	−	0.489418i	$-0.837209\pi$
$710$		0			0
$711$	−1.15771	−	0.765936i	−1.15771	−	0.765936i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.21813	+	1.46374i	−1.21813	+	1.46374i
$717$		0			0
$718$	0.109450	+	0.131517i	0.109450	+	0.131517i
$719$		0			0		−0.0365220	−	0.999333i	$-0.511628\pi$
$719$		0			0		0.0365220	+	0.999333i	$0.488372\pi$
$720$		0			0
$721$		0			0
$722$	−0.218159	+	0.0159672i	−0.218159	+	0.0159672i
$723$		0			0
$724$		0			0
$725$	−0.0609186	+	0.0403033i	−0.0609186	+	0.0403033i
$726$		0			0
$727$		0			0		−0.639673	−	0.768647i	$-0.720930\pi$
$727$		0			0		0.639673	+	0.768647i	$0.279070\pi$
$728$		0			0
$729$	0.520940	+	0.853593i	0.520940	+	0.853593i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.322880	−	0.946440i	$-0.604651\pi$
$733$		0			0		0.322880	+	0.946440i	$0.395349\pi$
$734$		0			0
$735$		0			0
$736$	−0.213893	−	0.0643508i	−0.213893	−	0.0643508i
$737$	−1.03874	−	2.02037i	−1.03874	−	2.02037i
$738$		0			0
$739$	0.211374	−	1.14436i	0.211374	−	1.14436i	−0.694074	−	0.719903i	$-0.744186\pi$
$739$	0.211374	−	1.14436i	0.211374	−	1.14436i	0.905448	−	0.424457i	$-0.139535\pi$
$740$		0			0
$741$		0			0
$742$	−0.0417260	−	0.379220i	−0.0417260	−	0.379220i
$743$	1.73412	+	0.812920i	1.73412	+	0.812920i	0.989343	+	0.145601i	$0.0465116\pi$
$743$	1.73412	+	0.812920i	1.73412	+	0.812920i	0.744772	+	0.667319i	$0.232558\pi$
$744$		0			0
$745$		0			0
$746$	−0.200037			−0.200037
$747$		0			0
$748$		0			0
$749$	−0.887961	+	0.921006i	−0.887961	+	0.921006i
$750$		0			0
$751$	−0.730596	−	1.71924i	−0.730596	−	1.71924i	−0.694074	−	0.719903i	$-0.744186\pi$
$751$	−0.730596	−	1.71924i	−0.730596	−	1.71924i	−0.0365220	−	0.999333i	$-0.511628\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.323589	+	0.388833i	0.323589	+	0.388833i	0.905448	−	0.424457i	$-0.139535\pi$
$757$	0.323589	+	0.388833i	0.323589	+	0.388833i	−0.581859	+	0.813290i	$0.697674\pi$
$758$	−0.0505959	−	0.193532i	−0.0505959	−	0.193532i
$759$		0			0
$760$		0			0
$761$		0			0		0.694074	−	0.719903i	$-0.255814\pi$
$761$		0			0		−0.694074	+	0.719903i	$0.744186\pi$
$762$		0			0
$763$	−0.828019	−	0.388159i	−0.828019	−	0.388159i
$764$	0.588792	+	0.177141i	0.588792	+	0.177141i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.791496	−	0.611174i	$-0.209302\pi$
$769$		0			0		−0.791496	+	0.611174i	$0.790698\pi$
$770$		0			0
$771$		0			0
$772$	−1.18284	+	1.05983i	−1.18284	+	1.05983i
$773$		0			0		0.109371	−	0.994001i	$-0.465116\pi$
$773$		0			0		−0.109371	+	0.994001i	$0.534884\pi$
$774$	−0.0735856	−	0.120575i	−0.0735856	−	0.120575i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.0964962	+	0.369103i	−0.0964962	+	0.369103i
$779$		0			0
$780$		0			0
$781$	2.33268	−	0.892176i	2.33268	−	0.892176i
$782$		0			0
$783$		0			0
$784$	0.549316	−	0.660072i	0.549316	−	0.660072i
$785$		0			0
$786$		0			0
$787$		0			0		0.989343	−	0.145601i	$-0.0465116\pi$
$787$		0			0		−0.989343	+	0.145601i	$0.953488\pi$
$788$	1.50363	−	0.704873i	1.50363	−	0.704873i
$789$		0			0
$790$		0			0
$791$	−0.302969	−	0.200443i	−0.302969	−	0.200443i
$792$	0.620846	−	0.556280i	0.620846	−	0.556280i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.957601	−	0.288099i	$-0.0930233\pi$
$797$		0			0		−0.957601	+	0.288099i	$0.906977\pi$
$798$		0			0
$799$		0			0
$800$	0.393311	+	0.472612i	0.393311	+	0.472612i
$801$		0			0
$802$	−0.300411	−	0.311591i	−0.300411	−	0.311591i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.32021	+	0.873444i	−1.32021	+	0.873444i	−0.997332	−	0.0729953i	$-0.976744\pi$
$809$	−1.32021	+	0.873444i	−1.32021	+	0.873444i	−0.322880	+	0.946440i	$0.604651\pi$
$810$		0			0
$811$		0			0		−0.252933	−	0.967484i	$-0.581395\pi$
$811$		0			0		0.252933	+	0.967484i	$0.418605\pi$
$812$	−0.0126327	−	0.0683921i	−0.0126327	−	0.0683921i
$813$		0			0
$814$	−0.00566546	+	0.0306723i	−0.00566546	+	0.0306723i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.0636980	−	0.0357491i	0.0636980	−	0.0357491i	−0.457242	−	0.889342i	$-0.651163\pi$
$821$	0.0636980	−	0.0357491i	0.0636980	−	0.0357491i	0.520940	+	0.853593i	$0.325581\pi$
$822$		0			0
$823$	−0.0544012	+	1.48855i	−0.0544012	+	1.48855i	0.639673	+	0.768647i	$0.279070\pi$
$823$	−0.0544012	+	1.48855i	−0.0544012	+	1.48855i	−0.694074	+	0.719903i	$0.744186\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.142078	+	0.769198i	−0.142078	+	0.769198i	0.833998	+	0.551768i	$0.186047\pi$
$827$	−0.142078	+	0.769198i	−0.142078	+	0.769198i	−0.976076	+	0.217430i	$0.930233\pi$
$828$	0.331226	−	0.0996511i	0.331226	−	0.0996511i
$829$		0			0		−0.252933	−	0.967484i	$-0.581395\pi$
$829$		0			0		0.252933	+	0.967484i	$0.418605\pi$
$830$		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		−0.989343	−	0.145601i	$-0.953488\pi$
$839$		0			0		0.989343	+	0.145601i	$0.0465116\pi$
$840$		0			0
$841$	0.867397	+	0.486807i	0.867397	+	0.486807i
$842$	0.0121024	−	0.109991i	0.0121024	−	0.109991i
$843$		0			0
$844$	0.220236	−	0.428362i	0.220236	−	0.428362i
$845$		0			0
$846$		0			0
$847$	−2.45124	+	1.37570i	−2.45124	+	1.37570i
$848$	0.684828	−	1.33200i	0.684828	−	1.33200i
$849$		0			0
$850$		0			0
$851$	−0.0154396	+	0.0215806i	−0.0154396	+	0.0215806i
$852$		0			0
$853$		0			0		−0.181637	−	0.983366i	$-0.558140\pi$
$853$		0			0		0.181637	+	0.983366i	$0.441860\pi$
$854$		0			0
$855$		0			0
$856$	0.533234	−	0.118783i	0.533234	−	0.118783i
$857$		0			0		−0.934016	−	0.357231i	$-0.883721\pi$
$857$		0			0		0.934016	+	0.357231i	$0.116279\pi$
$858$		0			0
$859$		0			0		0.639673	−	0.768647i	$-0.279070\pi$
$859$		0			0		−0.639673	+	0.768647i	$0.720930\pi$
$860$		0			0
$861$		0			0
$862$	−0.127277	−	0.177901i	−0.127277	−	0.177901i
$863$	0.782209			0.782209			0.391105	−	0.920346i	$-0.372093\pi$
$863$	0.782209			0.782209			0.391105	+	0.920346i	$0.372093\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.492213	−	2.66480i	−0.492213	−	2.66480i
$870$		0			0
$871$		0			0
$872$	0.203428	+	0.333330i	0.203428	+	0.333330i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.67015	+	0.937334i	−1.67015	+	0.937334i	−0.694074	+	0.719903i	$0.744186\pi$
$877$	−1.67015	+	0.937334i	−1.67015	+	0.937334i	−0.976076	+	0.217430i	$0.930233\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.934016	−	0.357231i	$-0.116279\pi$
$881$		0			0		−0.934016	+	0.357231i	$0.883721\pi$
$882$	0.0239241	−	0.217430i	0.0239241	−	0.217430i
$883$	−1.72551	−	0.968405i	−1.72551	−	0.968405i	−0.934016	−	0.357231i	$-0.883721\pi$
$883$	−1.72551	−	0.968405i	−1.72551	−	0.968405i	−0.791496	−	0.611174i	$-0.790698\pi$
$884$		0			0
$885$		0			0
$886$	−0.166830	−	0.324487i	−0.166830	−	0.324487i
$887$		0			0		−0.744772	−	0.667319i	$-0.767442\pi$
$887$		0			0		0.744772	+	0.667319i	$0.232558\pi$
$888$		0			0
$889$	1.01482	+	0.569544i	1.01482	+	0.569544i
$890$		0			0
$891$	−0.493764	+	1.88867i	−0.493764	+	1.88867i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.740499	+	0.222783i	−0.740499	+	0.222783i
$897$		0			0
$898$	0.295019	−	0.138299i	0.295019	−	0.138299i
$899$		0			0
$900$	−0.911781	−	0.274314i	−0.911781	−	0.274314i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.0606699	+	0.142768i	0.0606699	+	0.142768i
$905$		0			0
$906$		0			0
$907$	0.354583	−	1.91968i	0.354583	−	1.91968i	−0.0365220	−	0.999333i	$-0.511628\pi$
$907$	0.354583	−	1.91968i	0.354583	−	1.91968i	0.391105	−	0.920346i	$-0.372093\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.204309	+	0.0781415i	−0.204309	+	0.0781415i	−0.457242	−	0.889342i	$-0.651163\pi$
$911$	−0.204309	+	0.0781415i	−0.204309	+	0.0781415i	0.252933	+	0.967484i	$0.418605\pi$
$912$		0			0
$913$		0			0
$914$	0.240335	+	0.185581i	0.240335	+	0.185581i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.163334	+	0.478772i	−0.163334	+	0.478772i	−0.997332	−	0.0729953i	$-0.976744\pi$
$919$	−0.163334	+	0.478772i	−0.163334	+	0.478772i	0.833998	+	0.551768i	$0.186047\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.0682243	−	0.0260936i	0.0682243	−	0.0260936i
$926$	−0.274937	−	0.285168i	−0.274937	−	0.285168i
$927$		0			0
$928$	−0.0175653	+	0.0413346i	−0.0175653	+	0.0413346i
$929$		0			0		0.457242	−	0.889342i	$-0.348837\pi$
$929$		0			0		−0.457242	+	0.889342i	$0.651163\pi$
$930$		0			0
$931$		0			0
$932$	0.825234	−	0.739413i	0.825234	−	0.739413i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.989343	−	0.145601i	$-0.0465116\pi$
$937$		0			0		−0.989343	+	0.145601i	$0.953488\pi$
$938$	0.148115	+	0.207027i	0.148115	+	0.207027i
$939$		0			0
$940$		0			0
$941$		0			0		0.694074	−	0.719903i	$-0.255814\pi$
$941$		0			0		−0.694074	+	0.719903i	$0.744186\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.0697468	−	0.266785i	0.0697468	−	0.266785i
$947$	1.51028	−	0.999194i	1.51028	−	0.999194i	0.520940	−	0.853593i	$-0.325581\pi$
$947$	1.51028	−	0.999194i	1.51028	−	0.999194i	0.989343	−	0.145601i	$-0.0465116\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.866705	−	0.776571i	−0.866705	−	0.776571i	0.109371	−	0.994001i	$-0.465116\pi$
$953$	−0.866705	−	0.776571i	−0.866705	−	0.776571i	−0.976076	+	0.217430i	$0.930233\pi$
$954$	−0.0417260	−	0.379220i	−0.0417260	−	0.379220i
$955$		0			0
$956$	0.393311	+	1.15289i	0.393311	+	1.15289i
$957$		0			0
$958$		0			0
$959$	1.38445	+	1.43597i	1.38445	+	1.43597i
$960$		0			0
$961$	0.905448	+	0.424457i	0.905448	+	0.424457i
$962$		0			0
$963$	−0.887961	+	0.921006i	−0.887961	+	0.921006i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.818363	+	0.983366i	0.818363	+	0.983366i	1.00000			$0$
$967$	0.818363	+	0.983366i	0.818363	+	0.983366i	−0.181637	+	0.983366i	$0.558140\pi$
$968$	1.19710	+	0.0876166i	1.19710	+	0.0876166i
$969$		0			0
$970$		0			0
$971$		0			0		0.581859	−	0.813290i	$-0.302326\pi$
$971$		0			0		−0.581859	+	0.813290i	$0.697674\pi$
$972$		0			0
$973$		0			0
$974$	−0.261382	−	0.314083i	−0.261382	−	0.314083i
$975$		0			0
$976$		0			0
$977$	−1.45457	−	0.816347i	−1.45457	−	0.816347i	−0.457242	−	0.889342i	$-0.651163\pi$
$977$	−1.45457	−	0.816347i	−1.45457	−	0.816347i	−0.997332	+	0.0729953i	$0.976744\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.828019	−	0.388159i	−0.828019	−	0.388159i
$982$	−0.0278409	−	0.253027i	−0.0278409	−	0.253027i
$983$		0			0		−0.322880	−	0.946440i	$-0.604651\pi$
$983$		0			0		0.322880	+	0.946440i	$0.395349\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.150060	−	0.180315i	0.150060	−	0.180315i
$990$		0			0
$991$	−0.252560	−	0.740314i	−0.252560	−	0.740314i	−0.997332	−	0.0729953i	$-0.976744\pi$
$991$	−0.252560	−	0.740314i	−0.252560	−	0.740314i	0.744772	−	0.667319i	$-0.232558\pi$
$992$		0			0
$993$		0			0
$994$	−0.244041	+	0.136962i	−0.244041	+	0.136962i
$995$		0			0
$996$		0			0
$997$		0			0		−0.639673	−	0.768647i	$-0.720930\pi$
$997$		0			0		0.639673	+	0.768647i	$0.279070\pi$
$998$	−0.132608	−	0.217286i	−0.132608	−	0.217286i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3017.1.t.a.1091.1	✓	42
7.6	odd	2	CM	3017.1.t.a.1091.1	✓	42
431.32	even	43	inner	3017.1.t.a.1756.1	yes	42
3017.1756	odd	86	inner	3017.1.t.a.1756.1	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3017.1.t.a.1091.1	✓	42	1.1	even	1	trivial
3017.1.t.a.1091.1	✓	42	7.6	odd	2	CM
3017.1.t.a.1756.1	yes	42	431.32	even	43	inner
3017.1.t.a.1756.1	yes	42	3017.1756	odd	86	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:	\( N \)	\(=\)	\( 3017 = 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3017.t (of order \(86\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173134 - 0.133690i) q^{2} +(-0.240831 - 0.921191i) q^{4} +(-0.181637 - 0.983366i) q^{7} +(-0.167009 + 0.393005i) q^{8} +(-0.181637 - 0.983366i) q^{9} +O(q^{10})\)	\(q+(-0.173134 - 0.133690i) q^{2} +(-0.240831 - 0.921191i) q^{4} +(-0.181637 - 0.983366i) q^{7} +(-0.167009 + 0.393005i) q^{8} +(-0.181637 - 0.983366i) q^{9} +(1.13588 - 1.58766i) q^{11} +(-0.100018 + 0.194537i) q^{14} +(-0.748868 + 0.420285i) q^{16} +(-0.100018 + 0.194537i) q^{18} +(-0.408913 + 0.123024i) q^{22} +(-0.359402 - 0.0528931i) q^{23} +(0.744772 + 0.667319i) q^{25} +(-0.862124 + 0.404147i) q^{28} +(-0.0184753 + 0.0706689i) q^{29} +(0.608310 + 0.0895247i) q^{32} +(-0.862124 + 0.404147i) q^{36} +(0.0333988 - 0.0649611i) q^{37} +(-0.336403 + 0.551217i) q^{43} +(-1.73610 - 0.664001i) q^{44} +(0.0551535 + 0.0572060i) q^{46} +(-0.934016 + 0.357231i) q^{49} +(-0.0397317 - 0.215104i) q^{50} +(-1.45457 + 0.962337i) q^{53} +(0.416802 + 0.0928467i) q^{56} +(0.0126464 - 0.00976523i) q^{58} +(-0.934016 + 0.357231i) q^{63} +(0.502682 + 0.521389i) q^{64} +(0.532101 - 1.03494i) q^{67} +(1.06697 + 0.705902i) q^{71} +(0.416802 + 0.0928467i) q^{72} +(-0.0144671 + 0.00678190i) q^{74} +(-1.76757 - 0.828604i) q^{77} +(0.963478 - 0.999333i) q^{79} +(-0.934016 + 0.357231i) q^{81} +(0.131935 - 0.0504607i) q^{86} +(0.434258 + 0.711559i) q^{88} +(0.0378306 + 0.343817i) q^{92} +(0.209468 + 0.0630195i) q^{98} +(-1.76757 - 0.828604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 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

Introduction

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