LMFDB - Embedded newform 414.2.e.a.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (of order $3$, degree $2$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	414.277
Dual form			414.2.e.a.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} +(1.50000 - 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} +(1.50000 - 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -4.00000 q^{10} +(1.50000 - 2.59808i) q^{11} -1.73205i q^{12} +(-2.00000 - 3.46410i) q^{13} -6.92820i q^{15} +(-0.500000 + 0.866025i) q^{16} +7.00000 q^{17} +3.00000 q^{18} -5.00000 q^{19} +(-2.00000 + 3.46410i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-5.50000 + 9.52628i) q^{25} -4.00000 q^{26} +5.19615i q^{27} +(2.00000 - 3.46410i) q^{29} +(-6.00000 - 3.46410i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.50000 - 2.59808i) q^{33} +(3.50000 - 6.06218i) q^{34} +(1.50000 - 2.59808i) q^{36} +8.00000 q^{37} +(-2.50000 + 4.33013i) q^{38} -6.92820i q^{39} +(2.00000 + 3.46410i) q^{40} +(3.50000 + 6.06218i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +(6.00000 - 10.3923i) q^{45} -1.00000 q^{46} +(-5.00000 + 8.66025i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(3.50000 + 6.06218i) q^{49} +(5.50000 + 9.52628i) q^{50} +(10.5000 + 6.06218i) q^{51} +(-2.00000 + 3.46410i) q^{52} +10.0000 q^{53} +(4.50000 + 2.59808i) q^{54} -12.0000 q^{55} +(-7.50000 - 4.33013i) q^{57} +(-2.00000 - 3.46410i) q^{58} +(-6.50000 - 11.2583i) q^{59} +(-6.00000 + 3.46410i) q^{60} +(-1.00000 + 1.73205i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-8.00000 + 13.8564i) q^{65} -5.19615i q^{66} +(3.50000 + 6.06218i) q^{67} +(-3.50000 - 6.06218i) q^{68} -1.73205i q^{69} +(-1.50000 - 2.59808i) q^{72} -9.00000 q^{73} +(4.00000 - 6.92820i) q^{74} +(-16.5000 + 9.52628i) q^{75} +(2.50000 + 4.33013i) q^{76} +(-6.00000 - 3.46410i) q^{78} +(-1.00000 + 1.73205i) q^{79} +4.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +7.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-14.0000 - 24.2487i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(6.00000 - 3.46410i) q^{87} +(-1.50000 + 2.59808i) q^{88} +18.0000 q^{89} +(-6.00000 - 10.3923i) q^{90} +(-0.500000 + 0.866025i) q^{92} +3.46410i q^{93} +(5.00000 + 8.66025i) q^{94} +(10.0000 + 17.3205i) q^{95} +1.73205i q^{96} +(-3.50000 + 6.06218i) q^{97} +7.00000 q^{98} +9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} - 4 q^{5} + 3 q^{6} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 - q^4 - 4 * q^5 + 3 * q^6 - 2 * q^8 + 3 * q^9	$ 2 q + q^{2} + 3 q^{3} - q^{4} - 4 q^{5} + 3 q^{6} - 2 q^{8} + 3 q^{9} - 8 q^{10} + 3 q^{11} - 4 q^{13} - q^{16} + 14 q^{17} + 6 q^{18} - 10 q^{19} - 4 q^{20} - 3 q^{22} - q^{23} - 3 q^{24} - 11 q^{25} - 8 q^{26} + 4 q^{29} - 12 q^{30} + 2 q^{31} + q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{36} + 16 q^{37} - 5 q^{38} + 4 q^{40} + 7 q^{41} + q^{43} - 6 q^{44} + 12 q^{45} - 2 q^{46} - 10 q^{47} - 3 q^{48} + 7 q^{49} + 11 q^{50} + 21 q^{51} - 4 q^{52} + 20 q^{53} + 9 q^{54} - 24 q^{55} - 15 q^{57} - 4 q^{58} - 13 q^{59} - 12 q^{60} - 2 q^{61} + 4 q^{62} + 2 q^{64} - 16 q^{65} + 7 q^{67} - 7 q^{68} - 3 q^{72} - 18 q^{73} + 8 q^{74} - 33 q^{75} + 5 q^{76} - 12 q^{78} - 2 q^{79} + 8 q^{80} - 9 q^{81} + 14 q^{82} - 4 q^{83} - 28 q^{85} - q^{86} + 12 q^{87} - 3 q^{88} + 36 q^{89} - 12 q^{90} - q^{92} + 10 q^{94} + 20 q^{95} - 7 q^{97} + 14 q^{98} + 18 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 - 4 * q^5 + 3 * q^6 - 2 * q^8 + 3 * q^9 - 8 * q^10 + 3 * q^11 - 4 * q^13 - q^16 + 14 * q^17 + 6 * q^18 - 10 * q^19 - 4 * q^20 - 3 * q^22 - q^23 - 3 * q^24 - 11 * q^25 - 8 * q^26 + 4 * q^29 - 12 * q^30 + 2 * q^31 + q^32 + 9 * q^33 + 7 * q^34 + 3 * q^36 + 16 * q^37 - 5 * q^38 + 4 * q^40 + 7 * q^41 + q^43 - 6 * q^44 + 12 * q^45 - 2 * q^46 - 10 * q^47 - 3 * q^48 + 7 * q^49 + 11 * q^50 + 21 * q^51 - 4 * q^52 + 20 * q^53 + 9 * q^54 - 24 * q^55 - 15 * q^57 - 4 * q^58 - 13 * q^59 - 12 * q^60 - 2 * q^61 + 4 * q^62 + 2 * q^64 - 16 * q^65 + 7 * q^67 - 7 * q^68 - 3 * q^72 - 18 * q^73 + 8 * q^74 - 33 * q^75 + 5 * q^76 - 12 * q^78 - 2 * q^79 + 8 * q^80 - 9 * q^81 + 14 * q^82 - 4 * q^83 - 28 * q^85 - q^86 + 12 * q^87 - 3 * q^88 + 36 * q^89 - 12 * q^90 - q^92 + 10 * q^94 + 20 * q^95 - 7 * q^97 + 14 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.834512	−	0.550990i	$-0.814250\pi$
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.0599153	−	0.998203i	$-0.519083\pi$
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−4.00000			−1.26491
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		−	1.73205i		−	0.500000i
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$		0			0
$15$		−	6.92820i		−	1.78885i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	7.00000			1.69775			0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000			1.69775			0.848875	+	0.528594i	$0.177281\pi$
$18$	3.00000			0.707107
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$	−2.00000	+	3.46410i	−0.447214	+	0.774597i
$21$		0			0
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	−4.00000			−0.784465
$27$			5.19615i			1.00000i
$28$		0			0
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$	−6.00000	−	3.46410i	−1.09545	−	0.632456i
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	4.50000	−	2.59808i	0.783349	−	0.452267i
$34$	3.50000	−	6.06218i	0.600245	−	1.03965i
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	−2.50000	+	4.33013i	−0.405554	+	0.702439i
$39$		−	6.92820i		−	1.10940i
$40$	2.00000	+	3.46410i	0.316228	+	0.547723i
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	0.998504	+	0.0546823i	$0.0174146\pi$
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	−0.451896	+	0.892071i	$0.649252\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−3.00000			−0.452267
$45$	6.00000	−	10.3923i	0.894427	−	1.54919i
$46$	−1.00000			−0.147442
$47$	−5.00000	+	8.66025i	−0.729325	+	1.26323i	0.227844	+	0.973698i	$0.426832\pi$
$47$	−5.00000	+	8.66025i	−0.729325	+	1.26323i	−0.957169	+	0.289530i	$0.906501\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$	5.50000	+	9.52628i	0.777817	+	1.34722i
$51$	10.5000	+	6.06218i	1.47029	+	0.848875i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	10.0000			1.37361			0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000			1.37361			0.686803	+	0.726844i	$0.259014\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	−12.0000			−1.61808
$56$		0			0
$57$	−7.50000	−	4.33013i	−0.993399	−	0.573539i
$58$	−2.00000	−	3.46410i	−0.262613	−	0.454859i
$59$	−6.50000	−	11.2583i	−0.846228	−	1.46571i	−0.884551	−	0.466444i	$-0.845535\pi$
$59$	−6.50000	−	11.2583i	−0.846228	−	1.46571i	0.0383226	−	0.999265i	$-0.487799\pi$
$60$	−6.00000	+	3.46410i	−0.774597	+	0.447214i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−8.00000	+	13.8564i	−0.992278	+	1.71868i
$66$		−	5.19615i		−	0.639602i
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	−3.50000	−	6.06218i	−0.424437	−	0.735147i
$69$		−	1.73205i		−	0.208514i
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−9.00000			−1.05337			−0.526685	−	0.850060i	$-0.676565\pi$
$73$	−9.00000			−1.05337			−0.526685	+	0.850060i	$0.676565\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$	−16.5000	+	9.52628i	−1.90526	+	1.10000i
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$		0			0
$78$	−6.00000	−	3.46410i	−0.679366	−	0.392232i
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$	4.00000			0.447214
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	7.00000			0.773021
$83$	−2.00000	+	3.46410i	−0.219529	+	0.380235i	−0.954664	−	0.297686i	$-0.903785\pi$
$83$	−2.00000	+	3.46410i	−0.219529	+	0.380235i	0.735135	+	0.677920i	$0.237119\pi$
$84$		0			0
$85$	−14.0000	−	24.2487i	−1.51851	−	2.63014i
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$	6.00000	−	3.46410i	0.643268	−	0.371391i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	18.0000			1.90800			0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000			1.90800			0.953998	+	0.299813i	$0.0969242\pi$
$90$	−6.00000	−	10.3923i	−0.632456	−	1.09545i
$91$		0			0
$92$	−0.500000	+	0.866025i	−0.0521286	+	0.0902894i
$93$			3.46410i			0.359211i
$94$	5.00000	+	8.66025i	0.515711	+	0.893237i
$95$	10.0000	+	17.3205i	1.02598	+	1.77705i
$96$			1.73205i			0.176777i
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	−0.987181	−	0.159602i	$-0.948979\pi$
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	0.631810	+	0.775123i	$0.282312\pi$
$98$	7.00000			0.707107
$99$	9.00000			0.904534
$100$	11.0000			1.10000
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	10.5000	−	6.06218i	1.03965	−	0.600245i
$103$	−1.00000	−	1.73205i	−0.0985329	−	0.170664i	0.812545	−	0.582899i	$-0.198082\pi$
$103$	−1.00000	−	1.73205i	−0.0985329	−	0.170664i	−0.911078	+	0.412235i	$0.864748\pi$
$104$	2.00000	+	3.46410i	0.196116	+	0.339683i
$105$		0			0
$106$	5.00000	−	8.66025i	0.485643	−	0.841158i
$107$	−5.00000			−0.483368			−0.241684	−	0.970355i	$-0.577700\pi$
$107$	−5.00000			−0.483368			−0.241684	+	0.970355i	$0.577700\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−6.00000	+	10.3923i	−0.572078	+	0.990867i
$111$	12.0000	+	6.92820i	1.13899	+	0.657596i
$112$		0			0
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	−0.884182	−	0.467143i	$-0.845283\pi$
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	0.0375328	−	0.999295i	$-0.488050\pi$
$114$	−7.50000	+	4.33013i	−0.702439	+	0.405554i
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$	−4.00000			−0.371391
$117$	6.00000	−	10.3923i	0.554700	−	0.960769i
$118$	−13.0000			−1.19675
$119$		0			0
$120$			6.92820i			0.632456i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	1.00000	+	1.73205i	0.0905357	+	0.156813i
$123$			12.1244i			1.09322i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	24.0000			2.14663
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	1.50000	−	0.866025i	0.132068	−	0.0762493i
$130$	8.00000	+	13.8564i	0.701646	+	1.21529i
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$	−4.50000	−	2.59808i	−0.391675	−	0.226134i
$133$		0			0
$134$	7.00000			0.604708
$135$	18.0000	−	10.3923i	1.54919	−	0.894427i
$136$	−7.00000			−0.600245
$137$	6.50000	−	11.2583i	0.555332	−	0.961864i	−0.442545	−	0.896746i	$-0.645924\pi$
$137$	6.50000	−	11.2583i	0.555332	−	0.961864i	0.997878	−	0.0651178i	$-0.0207423\pi$
$138$	−1.50000	−	0.866025i	−0.127688	−	0.0737210i
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$	−15.0000	+	8.66025i	−1.26323	+	0.729325i
$142$		0			0
$143$	−12.0000			−1.00349
$144$	−3.00000			−0.250000
$145$	−16.0000			−1.32873
$146$	−4.50000	+	7.79423i	−0.372423	+	0.645055i
$147$			12.1244i			1.00000i
$148$	−4.00000	−	6.92820i	−0.328798	−	0.569495i
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$			19.0526i			1.55563i
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	−0.0964061	−	0.995342i	$-0.530735\pi$
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	0.910195	−	0.414181i	$-0.135932\pi$
$152$	5.00000			0.405554
$153$	10.5000	+	18.1865i	0.848875	+	1.47029i
$154$		0			0
$155$	4.00000	−	6.92820i	0.321288	−	0.556487i
$156$	−6.00000	+	3.46410i	−0.480384	+	0.277350i
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	0.823359	−	0.567521i	$-0.192098\pi$
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	−0.903167	+	0.429289i	$0.858764\pi$
$158$	1.00000	+	1.73205i	0.0795557	+	0.137795i
$159$	15.0000	+	8.66025i	1.18958	+	0.686803i
$160$	2.00000	−	3.46410i	0.158114	−	0.273861i
$161$		0			0
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	3.50000	−	6.06218i	0.273304	−	0.473377i
$165$	−18.0000	−	10.3923i	−1.40130	−	0.809040i
$166$	2.00000	+	3.46410i	0.155230	+	0.268866i
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	−28.0000			−2.14750
$171$	−7.50000	−	12.9904i	−0.573539	−	0.993399i
$172$	−1.00000			−0.0762493
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	−0.991082	−	0.133250i	$-0.957459\pi$
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	0.610939	+	0.791677i	$0.290792\pi$
$174$		−	6.92820i		−	0.525226i
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		−	22.5167i		−	1.69246i
$178$	9.00000	−	15.5885i	0.674579	−	1.16840i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	−12.0000			−0.894427
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$		0			0
$183$	−3.00000	+	1.73205i	−0.221766	+	0.128037i
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−16.0000	−	27.7128i	−1.17634	−	2.03749i
$186$	3.00000	+	1.73205i	0.219971	+	0.127000i
$187$	10.5000	−	18.1865i	0.767836	−	1.32993i
$188$	10.0000			0.729325
$189$		0			0
$190$	20.0000			1.45095
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	0.847469	−	0.530845i	$-0.178125\pi$
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	−0.883460	+	0.468507i	$0.844792\pi$
$194$	3.50000	+	6.06218i	0.251285	+	0.435239i
$195$	−24.0000	+	13.8564i	−1.71868	+	0.992278i
$196$	3.50000	−	6.06218i	0.250000	−	0.433013i
$197$	−4.00000			−0.284988			−0.142494	−	0.989796i	$-0.545512\pi$
$197$	−4.00000			−0.284988			−0.142494	+	0.989796i	$0.545512\pi$
$198$	4.50000	−	7.79423i	0.319801	−	0.553912i
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$	5.50000	−	9.52628i	0.388909	−	0.673610i
$201$			12.1244i			0.855186i
$202$		0			0
$203$		0			0
$204$		−	12.1244i		−	0.848875i
$205$	14.0000	−	24.2487i	0.977802	−	1.69360i
$206$	−2.00000			−0.139347
$207$	1.50000	−	2.59808i	0.104257	−	0.180579i
$208$	4.00000			0.277350
$209$	−7.50000	+	12.9904i	−0.518786	+	0.898563i
$210$		0			0
$211$	6.00000	+	10.3923i	0.413057	+	0.715436i	0.995222	−	0.0976347i	$-0.0311277\pi$
$211$	6.00000	+	10.3923i	0.413057	+	0.715436i	−0.582165	+	0.813070i	$0.697794\pi$
$212$	−5.00000	−	8.66025i	−0.343401	−	0.594789i
$213$		0			0
$214$	−2.50000	+	4.33013i	−0.170896	+	0.296001i
$215$	−4.00000			−0.272798
$216$		−	5.19615i		−	0.353553i
$217$		0			0
$218$	−5.00000	+	8.66025i	−0.338643	+	0.586546i
$219$	−13.5000	−	7.79423i	−0.912245	−	0.526685i
$220$	6.00000	+	10.3923i	0.404520	+	0.700649i
$221$	−14.0000	−	24.2487i	−0.941742	−	1.63114i
$222$	12.0000	−	6.92820i	0.805387	−	0.464991i
$223$	−9.00000	+	15.5885i	−0.602685	+	1.04388i	0.389728	+	0.920930i	$0.372569\pi$
$223$	−9.00000	+	15.5885i	−0.602685	+	1.04388i	−0.992413	+	0.122950i	$0.960764\pi$
$224$		0			0
$225$	−33.0000			−2.20000
$226$	−18.0000			−1.19734
$227$	3.50000	−	6.06218i	0.232303	−	0.402361i	−0.726182	−	0.687502i	$-0.758707\pi$
$227$	3.50000	−	6.06218i	0.232303	−	0.402361i	0.958485	+	0.285141i	$0.0920405\pi$
$228$			8.66025i			0.573539i
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	0.947960	−	0.318390i	$-0.103142\pi$
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	−0.749714	+	0.661762i	$0.769809\pi$
$230$	2.00000	+	3.46410i	0.131876	+	0.228416i
$231$		0			0
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	−5.00000			−0.327561			−0.163780	−	0.986497i	$-0.552369\pi$
$233$	−5.00000			−0.327561			−0.163780	+	0.986497i	$0.552369\pi$
$234$	−6.00000	−	10.3923i	−0.392232	−	0.679366i
$235$	40.0000			2.60931
$236$	−6.50000	+	11.2583i	−0.423114	+	0.732855i
$237$	−3.00000	+	1.73205i	−0.194871	+	0.112509i
$238$		0			0
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$	6.00000	+	3.46410i	0.387298	+	0.223607i
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	2.00000			0.128565
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	2.00000			0.128037
$245$	14.0000	−	24.2487i	0.894427	−	1.54919i
$246$	10.5000	+	6.06218i	0.669456	+	0.386510i
$247$	10.0000	+	17.3205i	0.636285	+	1.10208i
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$	−6.00000	+	3.46410i	−0.380235	+	0.219529i
$250$	12.0000	−	20.7846i	0.758947	−	1.31453i
$251$	1.00000			0.0631194			0.0315597	−	0.999502i	$-0.489953\pi$
$251$	1.00000			0.0631194			0.0315597	+	0.999502i	$0.489953\pi$
$252$		0			0
$253$	−3.00000			−0.188608
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$		−	48.4974i		−	3.03703i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	0.981901	+	0.189396i	$0.0606529\pi$
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	−0.326929	+	0.945049i	$0.606014\pi$
$258$		−	1.73205i		−	0.107833i
$259$		0			0
$260$	16.0000			0.992278
$261$	12.0000			0.742781
$262$	12.0000			0.741362
$263$	−11.0000	+	19.0526i	−0.678289	+	1.17483i	0.297207	+	0.954813i	$0.403945\pi$
$263$	−11.0000	+	19.0526i	−0.678289	+	1.17483i	−0.975496	+	0.220018i	$0.929388\pi$
$264$	−4.50000	+	2.59808i	−0.276956	+	0.159901i
$265$	−20.0000	−	34.6410i	−1.22859	−	2.12798i
$266$		0			0
$267$	27.0000	+	15.5885i	1.65237	+	0.953998i
$268$	3.50000	−	6.06218i	0.213797	−	0.370306i
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$		−	20.7846i		−	1.26491i
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	−3.50000	+	6.06218i	−0.212219	+	0.367574i
$273$		0			0
$274$	−6.50000	−	11.2583i	−0.392679	−	0.680141i
$275$	16.5000	+	28.5788i	0.994987	+	1.72337i
$276$	−1.50000	+	0.866025i	−0.0902894	+	0.0521286i
$277$	−2.00000	+	3.46410i	−0.120168	+	0.208138i	−0.919834	−	0.392308i	$-0.871677\pi$
$277$	−2.00000	+	3.46410i	−0.120168	+	0.208138i	0.799666	+	0.600446i	$0.205010\pi$
$278$	5.00000			0.299880
$279$	−3.00000	+	5.19615i	−0.179605	+	0.311086i
$280$		0			0
$281$	13.0000	−	22.5167i	0.775515	−	1.34323i	−0.158990	−	0.987280i	$-0.550824\pi$
$281$	13.0000	−	22.5167i	0.775515	−	1.34323i	0.934505	−	0.355951i	$-0.115843\pi$
$282$			17.3205i			1.03142i
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$		0			0
$285$			34.6410i			2.05196i
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$		0			0
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	32.0000			1.88235
$290$	−8.00000	+	13.8564i	−0.469776	+	0.813676i
$291$	−10.5000	+	6.06218i	−0.615521	+	0.355371i
$292$	4.50000	+	7.79423i	0.263343	+	0.456123i
$293$	−12.0000	−	20.7846i	−0.701047	−	1.21425i	−0.968099	−	0.250568i	$-0.919383\pi$
$293$	−12.0000	−	20.7846i	−0.701047	−	1.21425i	0.267052	−	0.963682i	$-0.413951\pi$
$294$	10.5000	+	6.06218i	0.612372	+	0.353553i
$295$	−26.0000	+	45.0333i	−1.51378	+	2.62194i
$296$	−8.00000			−0.464991
$297$	13.5000	+	7.79423i	0.783349	+	0.452267i
$298$	−10.0000			−0.579284
$299$	−2.00000	+	3.46410i	−0.115663	+	0.200334i
$300$	16.5000	+	9.52628i	0.952628	+	0.550000i
$301$		0			0
$302$	−10.0000	−	17.3205i	−0.575435	−	0.996683i
$303$		0			0
$304$	2.50000	−	4.33013i	0.143385	−	0.248350i
$305$	8.00000			0.458079
$306$	21.0000			1.20049
$307$	23.0000			1.31268			0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000			1.31268			0.656340	+	0.754466i	$0.272104\pi$
$308$		0			0
$309$		−	3.46410i		−	0.197066i
$310$	−4.00000	−	6.92820i	−0.227185	−	0.393496i
$311$	−10.0000	−	17.3205i	−0.567048	−	0.982156i	−0.996856	−	0.0792356i	$-0.974752\pi$
$311$	−10.0000	−	17.3205i	−0.567048	−	0.982156i	0.429808	−	0.902920i	$-0.358581\pi$
$312$			6.92820i			0.392232i
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	−2.00000			−0.112867
$315$		0			0
$316$	2.00000			0.112509
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	−0.836576	−	0.547852i	$-0.815446\pi$
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	0.892741	+	0.450570i	$0.148779\pi$
$318$	15.0000	−	8.66025i	0.841158	−	0.485643i
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$	−2.00000	−	3.46410i	−0.111803	−	0.193649i
$321$	−7.50000	−	4.33013i	−0.418609	−	0.241684i
$322$		0			0
$323$	−35.0000			−1.94745
$324$	9.00000			0.500000
$325$	44.0000			2.44068
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$	−15.0000	−	8.66025i	−0.829502	−	0.478913i
$328$	−3.50000	−	6.06218i	−0.193255	−	0.334728i
$329$		0			0
$330$	−18.0000	+	10.3923i	−0.990867	+	0.572078i
$331$	−16.0000	+	27.7128i	−0.879440	+	1.52323i	−0.0274825	+	0.999622i	$0.508749\pi$
$331$	−16.0000	+	27.7128i	−0.879440	+	1.52323i	−0.851957	+	0.523612i	$0.824584\pi$
$332$	4.00000			0.219529
$333$	12.0000	+	20.7846i	0.657596	+	1.13899i
$334$	−12.0000			−0.656611
$335$	14.0000	−	24.2487i	0.764902	−	1.32485i
$336$		0			0
$337$	−4.50000	−	7.79423i	−0.245131	−	0.424579i	0.717038	−	0.697034i	$-0.245498\pi$
$337$	−4.50000	−	7.79423i	−0.245131	−	0.424579i	−0.962168	+	0.272456i	$0.912164\pi$
$338$	1.50000	+	2.59808i	0.0815892	+	0.141317i
$339$		−	31.1769i		−	1.69330i
$340$	−14.0000	+	24.2487i	−0.759257	+	1.31507i
$341$	6.00000			0.324918
$342$	−15.0000			−0.811107
$343$		0			0
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$	−6.00000	+	3.46410i	−0.323029	+	0.186501i
$346$	5.00000	+	8.66025i	0.268802	+	0.465578i
$347$	−13.5000	−	23.3827i	−0.724718	−	1.25525i	−0.959090	−	0.283101i	$-0.908637\pi$
$347$	−13.5000	−	23.3827i	−0.724718	−	1.25525i	0.234372	−	0.972147i	$-0.424697\pi$
$348$	−6.00000	−	3.46410i	−0.321634	−	0.185695i
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	−0.774493	−	0.632583i	$-0.781995\pi$
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	0.935079	+	0.354439i	$0.115328\pi$
$350$		0			0
$351$	18.0000	−	10.3923i	0.960769	−	0.554700i
$352$	3.00000			0.159901
$353$	12.5000	−	21.6506i	0.665308	−	1.15235i	−0.313894	−	0.949458i	$-0.601634\pi$
$353$	12.5000	−	21.6506i	0.665308	−	1.15235i	0.979202	−	0.202889i	$-0.0650330\pi$
$354$	−19.5000	−	11.2583i	−1.03641	−	0.598374i
$355$		0			0
$356$	−9.00000	−	15.5885i	−0.476999	−	0.826187i
$357$		0			0
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$	−6.00000	+	10.3923i	−0.316228	+	0.547723i
$361$	6.00000			0.315789
$362$	−4.00000	+	6.92820i	−0.210235	+	0.364138i
$363$			3.46410i			0.181818i
$364$		0			0
$365$	18.0000	+	31.1769i	0.942163	+	1.63187i
$366$			3.46410i			0.181071i
$367$	−12.0000	+	20.7846i	−0.626395	+	1.08495i	0.361874	+	0.932227i	$0.382137\pi$
$367$	−12.0000	+	20.7846i	−0.626395	+	1.08495i	−0.988269	+	0.152721i	$0.951196\pi$
$368$	1.00000			0.0521286
$369$	−10.5000	+	18.1865i	−0.546608	+	0.946753i
$370$	−32.0000			−1.66360
$371$		0			0
$372$	3.00000	−	1.73205i	0.155543	−	0.0898027i
$373$	18.0000	+	31.1769i	0.932005	+	1.61428i	0.779890	+	0.625917i	$0.215275\pi$
$373$	18.0000	+	31.1769i	0.932005	+	1.61428i	0.152115	+	0.988363i	$0.451392\pi$
$374$	−10.5000	−	18.1865i	−0.542942	−	0.940403i
$375$	36.0000	+	20.7846i	1.85903	+	1.07331i
$376$	5.00000	−	8.66025i	0.257855	−	0.446619i
$377$	−16.0000			−0.824042
$378$		0			0
$379$	−1.00000			−0.0513665			−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000			−0.0513665			−0.0256833	+	0.999670i	$0.508176\pi$
$380$	10.0000	−	17.3205i	0.512989	−	0.888523i
$381$	24.0000	+	13.8564i	1.22956	+	0.709885i
$382$	3.00000	+	5.19615i	0.153493	+	0.265858i
$383$	−13.0000	−	22.5167i	−0.664269	−	1.15055i	−0.979483	−	0.201527i	$-0.935410\pi$
$383$	−13.0000	−	22.5167i	−0.664269	−	1.15055i	0.315214	−	0.949021i	$-0.397924\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$		0			0
$386$	−1.00000			−0.0508987
$387$	3.00000			0.152499
$388$	7.00000			0.355371
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	−0.964490	−	0.264120i	$-0.914918\pi$
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	0.710980	+	0.703213i	$0.248252\pi$
$390$			27.7128i			1.40329i
$391$	−3.50000	−	6.06218i	−0.177003	−	0.306578i
$392$	−3.50000	−	6.06218i	−0.176777	−	0.306186i
$393$			20.7846i			1.04844i
$394$	−2.00000	+	3.46410i	−0.100759	+	0.174519i
$395$	8.00000			0.402524
$396$	−4.50000	−	7.79423i	−0.226134	−	0.391675i
$397$		0			0			−	1.00000i	$-0.5\pi$
$397$		0			0				1.00000i	$0.5\pi$
$398$	−7.00000	+	12.1244i	−0.350878	+	0.607739i
$399$		0			0
$400$	−5.50000	−	9.52628i	−0.275000	−	0.476314i
$401$	18.5000	+	32.0429i	0.923846	+	1.60015i	0.793407	+	0.608692i	$0.208305\pi$
$401$	18.5000	+	32.0429i	0.923846	+	1.60015i	0.130439	+	0.991456i	$0.458361\pi$
$402$	10.5000	+	6.06218i	0.523692	+	0.302354i
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$		0			0
$405$	36.0000			1.78885
$406$		0			0
$407$	12.0000	−	20.7846i	0.594818	−	1.03025i
$408$	−10.5000	−	6.06218i	−0.519827	−	0.300123i
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$	−14.0000	−	24.2487i	−0.691411	−	1.19756i
$411$	19.5000	−	11.2583i	0.961864	−	0.555332i
$412$	−1.00000	+	1.73205i	−0.0492665	+	0.0853320i
$413$		0			0
$414$	−1.50000	−	2.59808i	−0.0737210	−	0.127688i
$415$	16.0000			0.785409
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$			8.66025i			0.424094i
$418$	7.50000	+	12.9904i	0.366837	+	0.635380i
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$	6.00000	−	10.3923i	0.292422	−	0.506490i	−0.681960	−	0.731390i	$-0.738872\pi$
$421$	6.00000	−	10.3923i	0.292422	−	0.506490i	0.974382	+	0.224900i	$0.0722054\pi$
$422$	12.0000			0.584151
$423$	−30.0000			−1.45865
$424$	−10.0000			−0.485643
$425$	−38.5000	+	66.6840i	−1.86752	+	3.23465i
$426$		0			0
$427$		0			0
$428$	2.50000	+	4.33013i	0.120842	+	0.209305i
$429$	−18.0000	−	10.3923i	−0.869048	−	0.501745i
$430$	−2.00000	+	3.46410i	−0.0964486	+	0.167054i
$431$	36.0000			1.73406			0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000			1.73406			0.867029	+	0.498257i	$0.166026\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−1.00000			−0.0480569			−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000			−0.0480569			−0.0240285	+	0.999711i	$0.507649\pi$
$434$		0			0
$435$	−24.0000	−	13.8564i	−1.15071	−	0.664364i
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	2.50000	+	4.33013i	0.119591	+	0.207138i
$438$	−13.5000	+	7.79423i	−0.645055	+	0.372423i
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	0.310228	+	0.950662i	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$	12.0000			0.572078
$441$	−10.5000	+	18.1865i	−0.500000	+	0.866025i
$442$	−28.0000			−1.33182
$443$	−14.5000	+	25.1147i	−0.688916	+	1.19324i	0.283273	+	0.959039i	$0.408580\pi$
$443$	−14.5000	+	25.1147i	−0.688916	+	1.19324i	−0.972189	+	0.234198i	$0.924754\pi$
$444$		−	13.8564i		−	0.657596i
$445$	−36.0000	−	62.3538i	−1.70656	−	2.95585i
$446$	9.00000	+	15.5885i	0.426162	+	0.738135i
$447$		−	17.3205i		−	0.819232i
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	−16.5000	+	28.5788i	−0.777817	+	1.34722i
$451$	21.0000			0.988851
$452$	−9.00000	+	15.5885i	−0.423324	+	0.733219i
$453$	30.0000	−	17.3205i	1.40952	−	0.813788i
$454$	−3.50000	−	6.06218i	−0.164263	−	0.284512i
$455$		0			0
$456$	7.50000	+	4.33013i	0.351220	+	0.202777i
$457$	−13.5000	+	23.3827i	−0.631503	+	1.09380i	0.355741	+	0.934585i	$0.384228\pi$
$457$	−13.5000	+	23.3827i	−0.631503	+	1.09380i	−0.987245	+	0.159211i	$0.949105\pi$
$458$	6.00000			0.280362
$459$			36.3731i			1.69775i
$460$	4.00000			0.186501
$461$	−21.0000	+	36.3731i	−0.978068	+	1.69406i	−0.308651	+	0.951175i	$0.599877\pi$
$461$	−21.0000	+	36.3731i	−0.978068	+	1.69406i	−0.669417	+	0.742887i	$0.733456\pi$
$462$		0			0
$463$	−3.00000	−	5.19615i	−0.139422	−	0.241486i	0.787856	−	0.615859i	$-0.211191\pi$
$463$	−3.00000	−	5.19615i	−0.139422	−	0.241486i	−0.927278	+	0.374374i	$0.877858\pi$
$464$	2.00000	+	3.46410i	0.0928477	+	0.160817i
$465$	12.0000	−	6.92820i	0.556487	−	0.321288i
$466$	−2.50000	+	4.33013i	−0.115810	+	0.200589i
$467$	−39.0000			−1.80470			−0.902352	−	0.430999i	$-0.858161\pi$
$467$	−39.0000			−1.80470			−0.902352	+	0.430999i	$0.858161\pi$
$468$	−12.0000			−0.554700
$469$		0			0
$470$	20.0000	−	34.6410i	0.922531	−	1.59787i
$471$		−	3.46410i		−	0.159617i
$472$	6.50000	+	11.2583i	0.299187	+	0.518207i
$473$	−1.50000	−	2.59808i	−0.0689701	−	0.119460i
$474$			3.46410i			0.159111i
$475$	27.5000	−	47.6314i	1.26179	−	2.18548i
$476$		0			0
$477$	15.0000	+	25.9808i	0.686803	+	1.18958i
$478$		0			0
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	6.00000	−	3.46410i	0.273861	−	0.158114i
$481$	−16.0000	−	27.7128i	−0.729537	−	1.26360i
$482$	−0.500000	−	0.866025i	−0.0227744	−	0.0394464i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	28.0000			1.27141
$486$			15.5885i			0.707107i
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$	−6.00000	−	3.46410i	−0.271329	−	0.156652i
$490$	−14.0000	−	24.2487i	−0.632456	−	1.09545i
$491$	12.5000	+	21.6506i	0.564117	+	0.977079i	0.997131	+	0.0756923i	$0.0241167\pi$
$491$	12.5000	+	21.6506i	0.564117	+	0.977079i	−0.433014	+	0.901387i	$0.642550\pi$
$492$	10.5000	−	6.06218i	0.473377	−	0.273304i
$493$	14.0000	−	24.2487i	0.630528	−	1.09211i
$494$	20.0000			0.899843
$495$	−18.0000	−	31.1769i	−0.809040	−	1.40130i
$496$	−2.00000			−0.0898027
$497$		0			0
$498$			6.92820i			0.310460i
$499$	17.5000	+	30.3109i	0.783408	+	1.35690i	0.929946	+	0.367697i	$0.119854\pi$
$499$	17.5000	+	30.3109i	0.783408	+	1.35690i	−0.146538	+	0.989205i	$0.546813\pi$
$500$	−12.0000	−	20.7846i	−0.536656	−	0.929516i
$501$		−	20.7846i		−	0.928588i
$502$	0.500000	−	0.866025i	0.0223161	−	0.0386526i
$503$	−16.0000			−0.713405			−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000			−0.713405			−0.356702	+	0.934218i	$0.616099\pi$
$504$		0			0
$505$		0			0
$506$	−1.50000	+	2.59808i	−0.0666831	+	0.115499i
$507$	−4.50000	+	2.59808i	−0.199852	+	0.115385i
$508$	−8.00000	−	13.8564i	−0.354943	−	0.614779i
$509$	18.0000	+	31.1769i	0.797836	+	1.38189i	0.921023	+	0.389509i	$0.127355\pi$
$509$	18.0000	+	31.1769i	0.797836	+	1.38189i	−0.123187	+	0.992384i	$0.539311\pi$
$510$	−42.0000	−	24.2487i	−1.85979	−	1.07375i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		−	25.9808i		−	1.14708i
$514$	21.0000			0.926270
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$	−1.50000	−	0.866025i	−0.0660338	−	0.0381246i
$517$	15.0000	+	25.9808i	0.659699	+	1.14263i
$518$		0			0
$519$	−15.0000	+	8.66025i	−0.658427	+	0.380143i
$520$	8.00000	−	13.8564i	0.350823	−	0.607644i
$521$	−29.0000			−1.27051			−0.635257	−	0.772301i	$-0.719106\pi$
$521$	−29.0000			−1.27051			−0.635257	+	0.772301i	$0.719106\pi$
$522$	6.00000	−	10.3923i	0.262613	−	0.454859i
$523$	−12.0000			−0.524723			−0.262362	−	0.964970i	$-0.584501\pi$
$523$	−12.0000			−0.524723			−0.262362	+	0.964970i	$0.584501\pi$
$524$	6.00000	−	10.3923i	0.262111	−	0.453990i
$525$		0			0
$526$	11.0000	+	19.0526i	0.479623	+	0.830731i
$527$	7.00000	+	12.1244i	0.304925	+	0.528145i
$528$			5.19615i			0.226134i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−40.0000			−1.73749
$531$	19.5000	−	33.7750i	0.846228	−	1.46571i
$532$		0			0
$533$	14.0000	−	24.2487i	0.606407	−	1.05033i
$534$	27.0000	−	15.5885i	1.16840	−	0.674579i
$535$	10.0000	+	17.3205i	0.432338	+	0.748831i
$536$	−3.50000	−	6.06218i	−0.151177	−	0.261846i
$537$	−18.0000	−	10.3923i	−0.776757	−	0.448461i
$538$	−5.00000	+	8.66025i	−0.215565	+	0.373370i
$539$	21.0000			0.904534
$540$	−18.0000	−	10.3923i	−0.774597	−	0.447214i
$541$	26.0000			1.11783			0.558914	−	0.829226i	$-0.311218\pi$
$541$	26.0000			1.11783			0.558914	+	0.829226i	$0.311218\pi$
$542$	1.00000	−	1.73205i	0.0429537	−	0.0743980i
$543$	−12.0000	−	6.92820i	−0.514969	−	0.297318i
$544$	3.50000	+	6.06218i	0.150061	+	0.259914i
$545$	20.0000	+	34.6410i	0.856706	+	1.48386i
$546$		0			0
$547$	−0.500000	+	0.866025i	−0.0213785	+	0.0370286i	−0.876517	−	0.481371i	$-0.840139\pi$
$547$	−0.500000	+	0.866025i	−0.0213785	+	0.0370286i	0.855138	+	0.518400i	$0.173472\pi$
$548$	−13.0000			−0.555332
$549$	−6.00000			−0.256074
$550$	33.0000			1.40712
$551$	−10.0000	+	17.3205i	−0.426014	+	0.737878i
$552$			1.73205i			0.0737210i
$553$		0			0
$554$	2.00000	+	3.46410i	0.0849719	+	0.147176i
$555$		−	55.4256i		−	2.35269i
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	−32.0000			−1.35588			−0.677942	−	0.735116i	$-0.737128\pi$
$557$	−32.0000			−1.35588			−0.677942	+	0.735116i	$0.737128\pi$
$558$	3.00000	+	5.19615i	0.127000	+	0.219971i
$559$	−4.00000			−0.169182
$560$		0			0
$561$	31.5000	−	18.1865i	1.32993	−	0.767836i
$562$	−13.0000	−	22.5167i	−0.548372	−	0.949808i
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	0.904320	+	0.426855i	$0.140378\pi$
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	−0.0824933	+	0.996592i	$0.526288\pi$
$564$	15.0000	+	8.66025i	0.631614	+	0.364662i
$565$	−36.0000	+	62.3538i	−1.51453	+	2.62325i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.5000	−	32.0429i	0.775560	−	1.34331i	−0.158919	−	0.987292i	$-0.550801\pi$
$569$	18.5000	−	32.0429i	0.775560	−	1.34331i	0.934479	−	0.356018i	$-0.115866\pi$
$570$	30.0000	+	17.3205i	1.25656	+	0.725476i
$571$	−3.50000	−	6.06218i	−0.146470	−	0.253694i	0.783450	−	0.621455i	$-0.213458\pi$
$571$	−3.50000	−	6.06218i	−0.146470	−	0.253694i	−0.929921	+	0.367760i	$0.880125\pi$
$572$	6.00000	+	10.3923i	0.250873	+	0.434524i
$573$	−9.00000	+	5.19615i	−0.375980	+	0.217072i
$574$		0			0
$575$	11.0000			0.458732
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	3.00000			0.124892			0.0624458	−	0.998048i	$-0.480110\pi$
$577$	3.00000			0.124892			0.0624458	+	0.998048i	$0.480110\pi$
$578$	16.0000	−	27.7128i	0.665512	−	1.15270i
$579$		−	1.73205i		−	0.0719816i
$580$	8.00000	+	13.8564i	0.332182	+	0.575356i
$581$		0			0
$582$			12.1244i			0.502571i
$583$	15.0000	−	25.9808i	0.621237	−	1.07601i
$584$	9.00000			0.372423
$585$	−48.0000			−1.98456
$586$	−24.0000			−0.991431
$587$	−4.50000	+	7.79423i	−0.185735	+	0.321702i	−0.943824	−	0.330449i	$-0.892800\pi$
$587$	−4.50000	+	7.79423i	−0.185735	+	0.321702i	0.758089	+	0.652151i	$0.226133\pi$
$588$	10.5000	−	6.06218i	0.433013	−	0.250000i
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$	26.0000	+	45.0333i	1.07040	+	1.85399i
$591$	−6.00000	−	3.46410i	−0.246807	−	0.142494i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	−34.0000			−1.39621			−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000			−1.39621			−0.698106	+	0.715994i	$0.745974\pi$
$594$	13.5000	−	7.79423i	0.553912	−	0.319801i
$595$		0			0
$596$	−5.00000	+	8.66025i	−0.204808	+	0.354738i
$597$	−21.0000	−	12.1244i	−0.859473	−	0.496217i
$598$	2.00000	+	3.46410i	0.0817861	+	0.141658i
$599$	21.0000	+	36.3731i	0.858037	+	1.48616i	0.873799	+	0.486287i	$0.161649\pi$
$599$	21.0000	+	36.3731i	0.858037	+	1.48616i	−0.0157622	+	0.999876i	$0.505017\pi$
$600$	16.5000	−	9.52628i	0.673610	−	0.388909i
$601$	10.5000	−	18.1865i	0.428304	−	0.741844i	−0.568419	−	0.822739i	$-0.692445\pi$
$601$	10.5000	−	18.1865i	0.428304	−	0.741844i	0.996723	+	0.0808953i	$0.0257779\pi$
$602$		0			0
$603$	−10.5000	+	18.1865i	−0.427593	+	0.740613i
$604$	−20.0000			−0.813788
$605$	4.00000	−	6.92820i	0.162623	−	0.281672i
$606$		0			0
$607$	9.00000	+	15.5885i	0.365299	+	0.632716i	0.988824	−	0.149087i	$-0.0476335\pi$
$607$	9.00000	+	15.5885i	0.365299	+	0.632716i	−0.623525	+	0.781803i	$0.714300\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$		0			0
$610$	4.00000	−	6.92820i	0.161955	−	0.280515i
$611$	40.0000			1.61823
$612$	10.5000	−	18.1865i	0.424437	−	0.735147i
$613$	−2.00000			−0.0807792			−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000			−0.0807792			−0.0403896	+	0.999184i	$0.512860\pi$
$614$	11.5000	−	19.9186i	0.464102	−	0.803849i
$615$	42.0000	−	24.2487i	1.69360	−	0.977802i
$616$		0			0
$617$	7.50000	+	12.9904i	0.301939	+	0.522973i	0.976575	−	0.215177i	$-0.0690329\pi$
$617$	7.50000	+	12.9904i	0.301939	+	0.522973i	−0.674636	+	0.738150i	$0.735700\pi$
$618$	−3.00000	−	1.73205i	−0.120678	−	0.0696733i
$619$	12.5000	−	21.6506i	0.502417	−	0.870212i	−0.497579	−	0.867419i	$-0.665777\pi$
$619$	12.5000	−	21.6506i	0.502417	−	0.870212i	0.999996	−	0.00279365i	$-0.000889247\pi$
$620$	−8.00000			−0.321288
$621$	4.50000	−	2.59808i	0.180579	−	0.104257i
$622$	−20.0000			−0.801927
$623$		0			0
$624$	6.00000	+	3.46410i	0.240192	+	0.138675i
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$	−22.5000	+	12.9904i	−0.898563	+	0.518786i
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	56.0000			2.23287
$630$		0			0
$631$	42.0000			1.67199			0.835997	−	0.548734i	$-0.184890\pi$
$631$	42.0000			1.67199			0.835997	+	0.548734i	$0.184890\pi$
$632$	1.00000	−	1.73205i	0.0397779	−	0.0688973i
$633$			20.7846i			0.826114i
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$	−32.0000	−	55.4256i	−1.26988	−	2.19950i
$636$		−	17.3205i		−	0.686803i
$637$	14.0000	−	24.2487i	0.554700	−	0.960769i
$638$	−12.0000			−0.475085
$639$		0			0
$640$	−4.00000			−0.158114
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	0.466029	+	0.884769i	$0.345684\pi$
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	−0.999247	+	0.0387913i	$0.987649\pi$
$642$	−7.50000	+	4.33013i	−0.296001	+	0.170896i
$643$	−21.5000	−	37.2391i	−0.847877	−	1.46857i	−0.883099	−	0.469187i	$-0.844547\pi$
$643$	−21.5000	−	37.2391i	−0.847877	−	1.46857i	0.0352216	−	0.999380i	$-0.488786\pi$
$644$		0			0
$645$	−6.00000	−	3.46410i	−0.236250	−	0.136399i
$646$	−17.5000	+	30.3109i	−0.688528	+	1.19257i
$647$	−36.0000			−1.41531			−0.707653	−	0.706560i	$-0.750246\pi$
$647$	−36.0000			−1.41531			−0.707653	+	0.706560i	$0.750246\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−39.0000			−1.53088
$650$	22.0000	−	38.1051i	0.862911	−	1.49461i
$651$		0			0
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	−14.0000	−	24.2487i	−0.547862	−	0.948925i	−0.998421	−	0.0561784i	$-0.982108\pi$
$653$	−14.0000	−	24.2487i	−0.547862	−	0.948925i	0.450558	−	0.892747i	$-0.351225\pi$
$654$	−15.0000	+	8.66025i	−0.586546	+	0.338643i
$655$	24.0000	−	41.5692i	0.937758	−	1.62424i
$656$	−7.00000			−0.273304
$657$	−13.5000	−	23.3827i	−0.526685	−	0.912245i
$658$		0			0
$659$	22.0000	−	38.1051i	0.856998	−	1.48436i	−0.0177803	−	0.999842i	$-0.505660\pi$
$659$	22.0000	−	38.1051i	0.856998	−	1.48436i	0.874779	−	0.484523i	$-0.161007\pi$
$660$			20.7846i			0.809040i
$661$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$661$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$662$	16.0000	+	27.7128i	0.621858	+	1.07709i
$663$		−	48.4974i		−	1.88348i
$664$	2.00000	−	3.46410i	0.0776151	−	0.134433i
$665$		0			0
$666$	24.0000			0.929981
$667$	−4.00000			−0.154881
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$	−27.0000	+	15.5885i	−1.04388	+	0.602685i
$670$	−14.0000	−	24.2487i	−0.540867	−	0.936809i
$671$	3.00000	+	5.19615i	0.115814	+	0.200595i
$672$		0			0
$673$	3.00000	−	5.19615i	0.115642	−	0.200297i	−0.802395	−	0.596794i	$-0.796441\pi$
$673$	3.00000	−	5.19615i	0.115642	−	0.200297i	0.918036	+	0.396497i	$0.129774\pi$
$674$	−9.00000			−0.346667
$675$	−49.5000	−	28.5788i	−1.90526	−	1.10000i
$676$	3.00000			0.115385
$677$	4.00000	−	6.92820i	0.153732	−	0.266272i	−0.778864	−	0.627192i	$-0.784204\pi$
$677$	4.00000	−	6.92820i	0.153732	−	0.266272i	0.932597	+	0.360920i	$0.117537\pi$
$678$	−27.0000	−	15.5885i	−1.03693	−	0.598671i
$679$		0			0
$680$	14.0000	+	24.2487i	0.536875	+	0.929896i
$681$	10.5000	−	6.06218i	0.402361	−	0.232303i
$682$	3.00000	−	5.19615i	0.114876	−	0.198971i
$683$	1.00000			0.0382639			0.0191320	−	0.999817i	$-0.493910\pi$
$683$	1.00000			0.0382639			0.0191320	+	0.999817i	$0.493910\pi$
$684$	−7.50000	+	12.9904i	−0.286770	+	0.496700i
$685$	−52.0000			−1.98682
$686$		0			0
$687$			10.3923i			0.396491i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	−20.0000	−	34.6410i	−0.761939	−	1.31972i
$690$			6.92820i			0.263752i
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	0.999276	−	0.0380440i	$-0.0121127\pi$
$692$	10.0000			0.380143
$693$		0			0
$694$	−27.0000			−1.02491
$695$	10.0000	−	17.3205i	0.379322	−	0.657004i
$696$	−6.00000	+	3.46410i	−0.227429	+	0.131306i
$697$	24.5000	+	42.4352i	0.928004	+	1.60735i
$698$	−3.00000	−	5.19615i	−0.113552	−	0.196677i
$699$	−7.50000	−	4.33013i	−0.283676	−	0.163780i
$700$		0			0
$701$	24.0000			0.906467			0.453234	−	0.891392i	$-0.350270\pi$
$701$	24.0000			0.906467			0.453234	+	0.891392i	$0.350270\pi$
$702$		−	20.7846i		−	0.784465i
$703$	−40.0000			−1.50863
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$	60.0000	+	34.6410i	2.25973	+	1.30466i
$706$	−12.5000	−	21.6506i	−0.470444	−	0.814832i
$707$		0			0
$708$	−19.5000	+	11.2583i	−0.732855	+	0.423114i
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	0.347325	+	0.937745i	$0.387090\pi$
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	−0.985773	+	0.168080i	$0.946243\pi$
$710$		0			0
$711$	−6.00000			−0.225018
$712$	−18.0000			−0.674579
$713$	1.00000	−	1.73205i	0.0374503	−	0.0648658i
$714$		0			0
$715$	24.0000	+	41.5692i	0.897549	+	1.55460i
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$	6.00000	+	10.3923i	0.223607	+	0.387298i
$721$		0			0
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$	1.50000	−	0.866025i	0.0557856	−	0.0322078i
$724$	4.00000	+	6.92820i	0.148659	+	0.257485i
$725$	22.0000	+	38.1051i	0.817059	+	1.41519i
$726$	3.00000	+	1.73205i	0.111340	+	0.0642824i
$727$	−6.00000	+	10.3923i	−0.222528	+	0.385429i	−0.955575	−	0.294749i	$-0.904764\pi$
$727$	−6.00000	+	10.3923i	−0.222528	+	0.385429i	0.733047	+	0.680178i	$0.238097\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	36.0000			1.33242
$731$	3.50000	−	6.06218i	0.129452	−	0.224218i
$732$	3.00000	+	1.73205i	0.110883	+	0.0640184i
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	0.916096	−	0.400959i	$-0.131323\pi$
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	−0.805289	+	0.592883i	$0.797990\pi$
$734$	12.0000	+	20.7846i	0.442928	+	0.767174i
$735$	42.0000	−	24.2487i	1.54919	−	0.894427i
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	21.0000			0.773545
$738$	10.5000	+	18.1865i	0.386510	+	0.669456i
$739$	−11.0000			−0.404642			−0.202321	−	0.979319i	$-0.564848\pi$
$739$	−11.0000			−0.404642			−0.202321	+	0.979319i	$0.564848\pi$
$740$	−16.0000	+	27.7128i	−0.588172	+	1.01874i
$741$			34.6410i			1.27257i
$742$		0			0
$743$	−15.0000	−	25.9808i	−0.550297	−	0.953142i	−0.998253	−	0.0590862i	$-0.981181\pi$
$743$	−15.0000	−	25.9808i	−0.550297	−	0.953142i	0.447956	−	0.894055i	$-0.352152\pi$
$744$		−	3.46410i		−	0.127000i
$745$	−20.0000	+	34.6410i	−0.732743	+	1.26915i
$746$	36.0000			1.31805
$747$	−12.0000			−0.439057
$748$	−21.0000			−0.767836
$749$		0			0
$750$	36.0000	−	20.7846i	1.31453	−	0.758947i
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	0.760263	−	0.649616i	$-0.225070\pi$
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	−0.942715	+	0.333599i	$0.891737\pi$
$752$	−5.00000	−	8.66025i	−0.182331	−	0.315807i
$753$	1.50000	+	0.866025i	0.0546630	+	0.0315597i
$754$	−8.00000	+	13.8564i	−0.291343	+	0.504621i
$755$	−80.0000			−2.91150
$756$		0			0
$757$	−20.0000			−0.726912			−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000			−0.726912			−0.363456	+	0.931611i	$0.618403\pi$
$758$	−0.500000	+	0.866025i	−0.0181608	+	0.0314555i
$759$	−4.50000	−	2.59808i	−0.163340	−	0.0943042i
$760$	−10.0000	−	17.3205i	−0.362738	−	0.628281i
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$	24.0000	−	13.8564i	0.869428	−	0.501965i
$763$		0			0
$764$	6.00000			0.217072
$765$	42.0000	−	72.7461i	1.51851	−	2.63014i
$766$	−26.0000			−0.939418
$767$	−26.0000	+	45.0333i	−0.938806	+	1.62606i
$768$		−	1.73205i		−	0.0625000i
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$		0			0
$771$			36.3731i			1.30994i
$772$	−0.500000	+	0.866025i	−0.0179954	+	0.0311689i
$773$	−4.00000			−0.143870			−0.0719350	−	0.997409i	$-0.522917\pi$
$773$	−4.00000			−0.143870			−0.0719350	+	0.997409i	$0.522917\pi$
$774$	1.50000	−	2.59808i	0.0539164	−	0.0933859i
$775$	−22.0000			−0.790263
$776$	3.50000	−	6.06218i	0.125643	−	0.217620i
$777$		0			0
$778$	5.00000	+	8.66025i	0.179259	+	0.310485i
$779$	−17.5000	−	30.3109i	−0.627003	−	1.08600i
$780$	24.0000	+	13.8564i	0.859338	+	0.496139i
$781$		0			0
$782$	−7.00000			−0.250319
$783$	18.0000	+	10.3923i	0.643268	+	0.371391i
$784$	−7.00000			−0.250000
$785$	−4.00000	+	6.92820i	−0.142766	+	0.247278i
$786$	18.0000	+	10.3923i	0.642039	+	0.370681i
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	2.00000	+	3.46410i	0.0712470	+	0.123404i
$789$	−33.0000	+	19.0526i	−1.17483	+	0.678289i
$790$	4.00000	−	6.92820i	0.142314	−	0.246494i
$791$		0			0
$792$	−9.00000			−0.319801
$793$	8.00000			0.284088
$794$		0			0
$795$		−	69.2820i		−	2.45718i
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$	13.0000	+	22.5167i	0.460484	+	0.797581i	0.998985	−	0.0450436i	$-0.0143427\pi$
$797$	13.0000	+	22.5167i	0.460484	+	0.797581i	−0.538501	+	0.842625i	$0.681009\pi$
$798$		0			0
$799$	−35.0000	+	60.6218i	−1.23821	+	2.14464i
$800$	−11.0000			−0.388909
$801$	27.0000	+	46.7654i	0.953998	+	1.65237i
$802$	37.0000			1.30652
$803$	−13.5000	+	23.3827i	−0.476405	+	0.825157i
$804$	10.5000	−	6.06218i	0.370306	−	0.213797i
$805$		0			0
$806$	−4.00000	−	6.92820i	−0.140894	−	0.244036i
$807$	−15.0000	−	8.66025i	−0.528025	−	0.304855i
$808$		0			0
$809$	41.0000			1.44148			0.720742	−	0.693204i	$-0.243801\pi$
$809$	41.0000			1.44148			0.720742	+	0.693204i	$0.243801\pi$
$810$	18.0000	−	31.1769i	0.632456	−	1.09545i
$811$	−49.0000			−1.72062			−0.860311	−	0.509769i	$-0.829731\pi$
$811$	−49.0000			−1.72062			−0.860311	+	0.509769i	$0.829731\pi$
$812$		0			0
$813$	3.00000	+	1.73205i	0.105215	+	0.0607457i
$814$	−12.0000	−	20.7846i	−0.420600	−	0.728500i
$815$	8.00000	+	13.8564i	0.280228	+	0.485369i
$816$	−10.5000	+	6.06218i	−0.367574	+	0.212219i
$817$	−2.50000	+	4.33013i	−0.0874639	+	0.151492i
$818$	−5.00000			−0.174821
$819$		0			0
$820$	−28.0000			−0.977802
$821$	−4.00000	+	6.92820i	−0.139601	+	0.241796i	−0.927346	−	0.374206i	$-0.877915\pi$
$821$	−4.00000	+	6.92820i	−0.139601	+	0.241796i	0.787745	+	0.616002i	$0.211249\pi$
$822$		−	22.5167i		−	0.785359i
$823$	19.0000	+	32.9090i	0.662298	+	1.14713i	0.980010	+	0.198947i	$0.0637522\pi$
$823$	19.0000	+	32.9090i	0.662298	+	1.14713i	−0.317712	+	0.948187i	$0.602914\pi$
$824$	1.00000	+	1.73205i	0.0348367	+	0.0603388i
$825$			57.1577i			1.98997i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	−3.00000			−0.104257
$829$	4.00000			0.138926			0.0694629	−	0.997585i	$-0.477871\pi$
$829$	4.00000			0.138926			0.0694629	+	0.997585i	$0.477871\pi$
$830$	8.00000	−	13.8564i	0.277684	−	0.480963i
$831$	−6.00000	+	3.46410i	−0.208138	+	0.120168i
$832$	−2.00000	−	3.46410i	−0.0693375	−	0.120096i
$833$	24.5000	+	42.4352i	0.848875	+	1.47029i
$834$	7.50000	+	4.33013i	0.259704	+	0.149940i
$835$	−24.0000	+	41.5692i	−0.830554	+	1.43856i
$836$	15.0000			0.518786
$837$	−9.00000	+	5.19615i	−0.311086	+	0.179605i
$838$		0			0
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	−0.829435	−	0.558604i	$-0.811337\pi$
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	0.898482	+	0.439010i	$0.144671\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	−6.00000	−	10.3923i	−0.206774	−	0.358142i
$843$	39.0000	−	22.5167i	1.34323	−	0.775515i
$844$	6.00000	−	10.3923i	0.206529	−	0.357718i
$845$	12.0000			0.412813
$846$	−15.0000	+	25.9808i	−0.515711	+	0.893237i
$847$		0			0
$848$	−5.00000	+	8.66025i	−0.171701	+	0.297394i
$849$		0			0
$850$	38.5000	+	66.6840i	1.32054	+	2.28724i
$851$	−4.00000	−	6.92820i	−0.137118	−	0.237496i
$852$		0			0
$853$	13.0000	−	22.5167i	0.445112	−	0.770956i	−0.552948	−	0.833215i	$-0.686497\pi$
$853$	13.0000	−	22.5167i	0.445112	−	0.770956i	0.998060	+	0.0622597i	$0.0198307\pi$
$854$		0			0
$855$	−30.0000	+	51.9615i	−1.02598	+	1.77705i
$856$	5.00000			0.170896
$857$	15.0000	−	25.9808i	0.512390	−	0.887486i	−0.487507	−	0.873119i	$-0.662093\pi$
$857$	15.0000	−	25.9808i	0.512390	−	0.887486i	0.999897	−	0.0143666i	$-0.00457319\pi$
$858$	−18.0000	+	10.3923i	−0.614510	+	0.354787i
$859$	7.50000	+	12.9904i	0.255897	+	0.443226i	0.965139	−	0.261739i	$-0.0842960\pi$
$859$	7.50000	+	12.9904i	0.255897	+	0.443226i	−0.709242	+	0.704965i	$0.750963\pi$
$860$	2.00000	+	3.46410i	0.0681994	+	0.118125i
$861$		0			0
$862$	18.0000	−	31.1769i	0.613082	−	1.06189i
$863$	−14.0000			−0.476566			−0.238283	−	0.971196i	$-0.576585\pi$
$863$	−14.0000			−0.476566			−0.238283	+	0.971196i	$0.576585\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	40.0000			1.36004
$866$	−0.500000	+	0.866025i	−0.0169907	+	0.0294287i
$867$	48.0000	+	27.7128i	1.63017	+	0.941176i
$868$		0			0
$869$	3.00000	+	5.19615i	0.101768	+	0.176267i
$870$	−24.0000	+	13.8564i	−0.813676	+	0.469776i
$871$	14.0000	−	24.2487i	0.474372	−	0.821636i
$872$	10.0000			0.338643
$873$	−21.0000			−0.710742
$874$	5.00000			0.169128
$875$		0			0
$876$			15.5885i			0.526685i
$877$	−14.0000	−	24.2487i	−0.472746	−	0.818821i	0.526767	−	0.850010i	$-0.323404\pi$
$877$	−14.0000	−	24.2487i	−0.472746	−	0.818821i	−0.999514	+	0.0311889i	$0.990071\pi$
$878$	14.0000	+	24.2487i	0.472477	+	0.818354i
$879$		−	41.5692i		−	1.40209i
$880$	6.00000	−	10.3923i	0.202260	−	0.350325i
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$	10.5000	+	18.1865i	0.353553	+	0.612372i
$883$	7.00000			0.235569			0.117784	−	0.993039i	$-0.462421\pi$
$883$	7.00000			0.235569			0.117784	+	0.993039i	$0.462421\pi$
$884$	−14.0000	+	24.2487i	−0.470871	+	0.815572i
$885$	−78.0000	+	45.0333i	−2.62194	+	1.51378i
$886$	14.5000	+	25.1147i	0.487137	+	0.843746i
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	0.976632	−	0.214919i	$-0.0689488\pi$
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	−0.674441	+	0.738328i	$0.735615\pi$
$888$	−12.0000	−	6.92820i	−0.402694	−	0.232495i
$889$		0			0
$890$	−72.0000			−2.41345
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$	18.0000			0.602685
$893$	25.0000	−	43.3013i	0.836593	−	1.44902i
$894$	−15.0000	−	8.66025i	−0.501675	−	0.289642i
$895$	24.0000	+	41.5692i	0.802232	+	1.38951i
$896$		0			0
$897$	−6.00000	+	3.46410i	−0.200334	+	0.115663i
$898$	4.50000	−	7.79423i	0.150167	−	0.260097i
$899$	8.00000			0.266815
$900$	16.5000	+	28.5788i	0.550000	+	0.952628i
$901$	70.0000			2.33204
$902$	10.5000	−	18.1865i	0.349612	−	0.605545i
$903$		0			0
$904$	9.00000	+	15.5885i	0.299336	+	0.518464i
$905$	16.0000	+	27.7128i	0.531858	+	0.921205i
$906$		−	34.6410i		−	1.15087i
$907$	25.5000	−	44.1673i	0.846714	−	1.46655i	−0.0374111	−	0.999300i	$-0.511911\pi$
$907$	25.5000	−	44.1673i	0.846714	−	1.46655i	0.884125	−	0.467251i	$-0.154756\pi$
$908$	−7.00000			−0.232303
$909$		0			0
$910$		0			0
$911$	23.0000	−	39.8372i	0.762024	−	1.31986i	−0.179782	−	0.983707i	$-0.557539\pi$
$911$	23.0000	−	39.8372i	0.762024	−	1.31986i	0.941806	−	0.336158i	$-0.109128\pi$
$912$	7.50000	−	4.33013i	0.248350	−	0.143385i
$913$	6.00000	+	10.3923i	0.198571	+	0.343935i
$914$	13.5000	+	23.3827i	0.446540	+	0.773431i
$915$	12.0000	+	6.92820i	0.396708	+	0.229039i
$916$	3.00000	−	5.19615i	0.0991228	−	0.171686i
$917$		0			0
$918$	31.5000	+	18.1865i	1.03965	+	0.600245i
$919$	−38.0000			−1.25350			−0.626752	−	0.779219i	$-0.715616\pi$
$919$	−38.0000			−1.25350			−0.626752	+	0.779219i	$0.715616\pi$
$920$	2.00000	−	3.46410i	0.0659380	−	0.114208i
$921$	34.5000	+	19.9186i	1.13681	+	0.656340i
$922$	21.0000	+	36.3731i	0.691598	+	1.19788i
$923$		0			0
$924$		0			0
$925$	−44.0000	+	76.2102i	−1.44671	+	2.50578i
$926$	−6.00000			−0.197172
$927$	3.00000	−	5.19615i	0.0985329	−	0.170664i
$928$	4.00000			0.131306
$929$	11.0000	−	19.0526i	0.360898	−	0.625094i	−0.627211	−	0.778850i	$-0.715803\pi$
$929$	11.0000	−	19.0526i	0.360898	−	0.625094i	0.988109	+	0.153755i	$0.0491368\pi$
$930$		−	13.8564i		−	0.454369i
$931$	−17.5000	−	30.3109i	−0.573539	−	0.993399i
$932$	2.50000	+	4.33013i	0.0818902	+	0.141838i
$933$		−	34.6410i		−	1.13410i
$934$	−19.5000	+	33.7750i	−0.638059	+	1.10515i
$935$	−84.0000			−2.74709
$936$	−6.00000	+	10.3923i	−0.196116	+	0.339683i
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$	1.50000	−	0.866025i	0.0489506	−	0.0282617i
$940$	−20.0000	−	34.6410i	−0.652328	−	1.12987i
$941$	−16.0000	−	27.7128i	−0.521585	−	0.903412i	−0.999685	−	0.0251063i	$-0.992008\pi$
$941$	−16.0000	−	27.7128i	−0.521585	−	0.903412i	0.478100	−	0.878306i	$-0.341326\pi$
$942$	−3.00000	−	1.73205i	−0.0977453	−	0.0564333i
$943$	3.50000	−	6.06218i	0.113976	−	0.197412i
$944$	13.0000			0.423114
$945$		0			0
$946$	−3.00000			−0.0975384
$947$	−18.5000	+	32.0429i	−0.601169	+	1.04126i	0.391475	+	0.920189i	$0.371965\pi$
$947$	−18.5000	+	32.0429i	−0.601169	+	1.04126i	−0.992644	+	0.121067i	$0.961368\pi$
$948$	3.00000	+	1.73205i	0.0974355	+	0.0562544i
$949$	18.0000	+	31.1769i	0.584305	+	1.01205i
$950$	−27.5000	−	47.6314i	−0.892218	−	1.54537i
$951$	3.00000	−	1.73205i	0.0972817	−	0.0561656i
$952$		0			0
$953$	−53.0000			−1.71684			−0.858419	−	0.512949i	$-0.828553\pi$
$953$	−53.0000			−1.71684			−0.858419	+	0.512949i	$0.828553\pi$
$954$	30.0000			0.971286
$955$	24.0000			0.776622
$956$		0			0
$957$		−	20.7846i		−	0.671871i
$958$		0			0
$959$		0			0
$960$		−	6.92820i		−	0.223607i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−32.0000			−1.03172
$963$	−7.50000	−	12.9904i	−0.241684	−	0.418609i
$964$	−1.00000			−0.0322078
$965$	−2.00000	+	3.46410i	−0.0643823	+	0.111513i
$966$		0			0
$967$	−11.0000	−	19.0526i	−0.353736	−	0.612689i	0.633165	−	0.774017i	$-0.281756\pi$
$967$	−11.0000	−	19.0526i	−0.353736	−	0.612689i	−0.986901	+	0.161328i	$0.948422\pi$
$968$	−1.00000	−	1.73205i	−0.0321412	−	0.0556702i
$969$	−52.5000	−	30.3109i	−1.68654	−	0.973726i
$970$	14.0000	−	24.2487i	0.449513	−	0.778579i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$		0			0
$974$	−16.0000	+	27.7128i	−0.512673	+	0.887976i
$975$	66.0000	+	38.1051i	2.11369	+	1.22034i
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	0.500000	+	0.866025i	0.0159964	+	0.0277066i	0.873913	−	0.486083i	$-0.161575\pi$
$977$	0.500000	+	0.866025i	0.0159964	+	0.0277066i	−0.857916	+	0.513789i	$0.828241\pi$
$978$	−6.00000	+	3.46410i	−0.191859	+	0.110770i
$979$	27.0000	−	46.7654i	0.862924	−	1.49463i
$980$	−28.0000			−0.894427
$981$	−15.0000	−	25.9808i	−0.478913	−	0.829502i
$982$	25.0000			0.797782
$983$	−27.0000	+	46.7654i	−0.861166	+	1.49158i	0.00963785	+	0.999954i	$0.496932\pi$
$983$	−27.0000	+	46.7654i	−0.861166	+	1.49158i	−0.870804	+	0.491630i	$0.836401\pi$
$984$		−	12.1244i		−	0.386510i
$985$	8.00000	+	13.8564i	0.254901	+	0.441502i
$986$	−14.0000	−	24.2487i	−0.445851	−	0.772236i
$987$		0			0
$988$	10.0000	−	17.3205i	0.318142	−	0.551039i
$989$	−1.00000			−0.0317982
$990$	−36.0000			−1.14416
$991$	52.0000			1.65183			0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000			1.65183			0.825917	+	0.563791i	$0.190658\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$	−48.0000	+	27.7128i	−1.52323	+	0.879440i
$994$		0			0
$995$	28.0000	+	48.4974i	0.887660	+	1.53747i
$996$	6.00000	+	3.46410i	0.190117	+	0.109764i
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	0.934274	+	0.356555i	$0.116049\pi$
$998$	35.0000			1.10791
$999$			41.5692i			1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.a.277.1	yes	2
3.2	odd	2		1242.2.e.a.829.1		2
9.2	odd	6		3726.2.a.e.1.1		1
9.4	even	3	inner	414.2.e.a.139.1	✓	2
9.5	odd	6		1242.2.e.a.415.1		2
9.7	even	3		3726.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.a.139.1	✓	2	9.4	even	3	inner
414.2.e.a.277.1	yes	2	1.1	even	1	trivial
1242.2.e.a.415.1		2	9.5	odd	6
1242.2.e.a.829.1		2	3.2	odd	2
3726.2.a.d.1.1		1	9.7	even	3
3726.2.a.e.1.1		1	9.2	odd	6

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} +(1.50000 - 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} +(1.50000 - 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -4.00000 q^{10} +(1.50000 - 2.59808i) q^{11} -1.73205i q^{12} +(-2.00000 - 3.46410i) q^{13} -6.92820i q^{15} +(-0.500000 + 0.866025i) q^{16} +7.00000 q^{17} +3.00000 q^{18} -5.00000 q^{19} +(-2.00000 + 3.46410i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-5.50000 + 9.52628i) q^{25} -4.00000 q^{26} +5.19615i q^{27} +(2.00000 - 3.46410i) q^{29} +(-6.00000 - 3.46410i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.50000 - 2.59808i) q^{33} +(3.50000 - 6.06218i) q^{34} +(1.50000 - 2.59808i) q^{36} +8.00000 q^{37} +(-2.50000 + 4.33013i) q^{38} -6.92820i q^{39} +(2.00000 + 3.46410i) q^{40} +(3.50000 + 6.06218i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +(6.00000 - 10.3923i) q^{45} -1.00000 q^{46} +(-5.00000 + 8.66025i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(3.50000 + 6.06218i) q^{49} +(5.50000 + 9.52628i) q^{50} +(10.5000 + 6.06218i) q^{51} +(-2.00000 + 3.46410i) q^{52} +10.0000 q^{53} +(4.50000 + 2.59808i) q^{54} -12.0000 q^{55} +(-7.50000 - 4.33013i) q^{57} +(-2.00000 - 3.46410i) q^{58} +(-6.50000 - 11.2583i) q^{59} +(-6.00000 + 3.46410i) q^{60} +(-1.00000 + 1.73205i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-8.00000 + 13.8564i) q^{65} -5.19615i q^{66} +(3.50000 + 6.06218i) q^{67} +(-3.50000 - 6.06218i) q^{68} -1.73205i q^{69} +(-1.50000 - 2.59808i) q^{72} -9.00000 q^{73} +(4.00000 - 6.92820i) q^{74} +(-16.5000 + 9.52628i) q^{75} +(2.50000 + 4.33013i) q^{76} +(-6.00000 - 3.46410i) q^{78} +(-1.00000 + 1.73205i) q^{79} +4.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +7.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-14.0000 - 24.2487i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(6.00000 - 3.46410i) q^{87} +(-1.50000 + 2.59808i) q^{88} +18.0000 q^{89} +(-6.00000 - 10.3923i) q^{90} +(-0.500000 + 0.866025i) q^{92} +3.46410i q^{93} +(5.00000 + 8.66025i) q^{94} +(10.0000 + 17.3205i) q^{95} +1.73205i q^{96} +(-3.50000 + 6.06218i) q^{97} +7.00000 q^{98} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} - 4 q^{5} + 3 q^{6} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 - q^4 - 4 * q^5 + 3 * q^6 - 2 * q^8 + 3 * q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} - 4 q^{5} + 3 q^{6} - 2 q^{8} + 3 q^{9} - 8 q^{10} + 3 q^{11} - 4 q^{13} - q^{16} + 14 q^{17} + 6 q^{18} - 10 q^{19} - 4 q^{20} - 3 q^{22} - q^{23} - 3 q^{24} - 11 q^{25} - 8 q^{26} + 4 q^{29} - 12 q^{30} + 2 q^{31} + q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{36} + 16 q^{37} - 5 q^{38} + 4 q^{40} + 7 q^{41} + q^{43} - 6 q^{44} + 12 q^{45} - 2 q^{46} - 10 q^{47} - 3 q^{48} + 7 q^{49} + 11 q^{50} + 21 q^{51} - 4 q^{52} + 20 q^{53} + 9 q^{54} - 24 q^{55} - 15 q^{57} - 4 q^{58} - 13 q^{59} - 12 q^{60} - 2 q^{61} + 4 q^{62} + 2 q^{64} - 16 q^{65} + 7 q^{67} - 7 q^{68} - 3 q^{72} - 18 q^{73} + 8 q^{74} - 33 q^{75} + 5 q^{76} - 12 q^{78} - 2 q^{79} + 8 q^{80} - 9 q^{81} + 14 q^{82} - 4 q^{83} - 28 q^{85} - q^{86} + 12 q^{87} - 3 q^{88} + 36 q^{89} - 12 q^{90} - q^{92} + 10 q^{94} + 20 q^{95} - 7 q^{97} + 14 q^{98} + 18 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 - 4 * q^5 + 3 * q^6 - 2 * q^8 + 3 * q^9 - 8 * q^10 + 3 * q^11 - 4 * q^13 - q^16 + 14 * q^17 + 6 * q^18 - 10 * q^19 - 4 * q^20 - 3 * q^22 - q^23 - 3 * q^24 - 11 * q^25 - 8 * q^26 + 4 * q^29 - 12 * q^30 + 2 * q^31 + q^32 + 9 * q^33 + 7 * q^34 + 3 * q^36 + 16 * q^37 - 5 * q^38 + 4 * q^40 + 7 * q^41 + q^43 - 6 * q^44 + 12 * q^45 - 2 * q^46 - 10 * q^47 - 3 * q^48 + 7 * q^49 + 11 * q^50 + 21 * q^51 - 4 * q^52 + 20 * q^53 + 9 * q^54 - 24 * q^55 - 15 * q^57 - 4 * q^58 - 13 * q^59 - 12 * q^60 - 2 * q^61 + 4 * q^62 + 2 * q^64 - 16 * q^65 + 7 * q^67 - 7 * q^68 - 3 * q^72 - 18 * q^73 + 8 * q^74 - 33 * q^75 + 5 * q^76 - 12 * q^78 - 2 * q^79 + 8 * q^80 - 9 * q^81 + 14 * q^82 - 4 * q^83 - 28 * q^85 - q^86 + 12 * q^87 - 3 * q^88 + 36 * q^89 - 12 * q^90 - q^92 + 10 * q^94 + 20 * q^95 - 7 * q^97 + 14 * q^98 + 18 * q^99

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