LMFDB - Embedded newform 1050.2.o.l.499.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(499,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.499
Dual form			1050.2.o.l.949.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(0.866025 + 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(0.866025 + 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} +(-0.866025 - 0.500000i) q^{12} +4.00000i q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.59808 + 1.50000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(3.00000 - 5.19615i) q^{19} +(-2.00000 - 1.73205i) q^{21} -4.00000i q^{22} +(-6.06218 - 3.50000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(-1.73205 + 2.00000i) q^{28} -4.00000 q^{29} +(2.50000 + 4.33013i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.46410 - 2.00000i) q^{33} +3.00000 q^{34} +1.00000 q^{36} +(1.73205 + 1.00000i) q^{37} +(-5.19615 + 3.00000i) q^{38} +(-2.00000 - 3.46410i) q^{39} +7.00000 q^{41} +(0.866025 + 2.50000i) q^{42} +2.00000i q^{43} +(-2.00000 + 3.46410i) q^{44} +(3.50000 + 6.06218i) q^{46} +(0.866025 + 0.500000i) q^{47} -1.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(1.50000 - 2.59808i) q^{51} +(-3.46410 + 2.00000i) q^{52} +(-1.73205 + 1.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.50000 - 0.866025i) q^{56} +6.00000i q^{57} +(3.46410 + 2.00000i) q^{58} +(-7.00000 - 12.1244i) q^{59} +(-6.00000 + 10.3923i) q^{61} -5.00000i q^{62} +(2.59808 + 0.500000i) q^{63} -1.00000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-10.3923 + 6.00000i) q^{67} +(-2.59808 - 1.50000i) q^{68} +7.00000 q^{69} -9.00000 q^{71} +(-0.866025 - 0.500000i) q^{72} +(5.19615 - 3.00000i) q^{73} +(-1.00000 - 1.73205i) q^{74} +6.00000 q^{76} +(-6.92820 + 8.00000i) q^{77} +4.00000i q^{78} +(-8.50000 + 14.7224i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.06218 - 3.50000i) q^{82} -4.00000i q^{83} +(0.500000 - 2.59808i) q^{84} +(1.00000 - 1.73205i) q^{86} +(3.46410 - 2.00000i) q^{87} +(3.46410 - 2.00000i) q^{88} +(-3.50000 + 6.06218i) q^{89} +(-10.0000 + 3.46410i) q^{91} -7.00000i q^{92} +(-4.33013 - 2.50000i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-0.500000 + 0.866025i) q^{96} +7.00000i q^{97} +(6.92820 - 1.00000i) q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} + 2 q^{14} - 2 q^{16} + 12 q^{19} - 8 q^{21} + 2 q^{24} + 8 q^{26} - 16 q^{29} + 10 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} + 28 q^{41} - 8 q^{44} + 14 q^{46} - 22 q^{49} + 6 q^{51} + 2 q^{54} + 10 q^{56} - 28 q^{59} - 24 q^{61} - 4 q^{64} + 8 q^{66} + 28 q^{69} - 36 q^{71} - 4 q^{74} + 24 q^{76} - 34 q^{79} - 2 q^{81} + 2 q^{84} + 4 q^{86} - 14 q^{89} - 40 q^{91} - 2 q^{94} - 2 q^{96} + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9 + 8 * q^11 + 2 * q^14 - 2 * q^16 + 12 * q^19 - 8 * q^21 + 2 * q^24 + 8 * q^26 - 16 * q^29 + 10 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 + 28 * q^41 - 8 * q^44 + 14 * q^46 - 22 * q^49 + 6 * q^51 + 2 * q^54 + 10 * q^56 - 28 * q^59 - 24 * q^61 - 4 * q^64 + 8 * q^66 + 28 * q^69 - 36 * q^71 - 4 * q^74 + 24 * q^76 - 34 * q^79 - 2 * q^81 + 2 * q^84 + 4 * q^86 - 14 * q^89 - 40 * q^91 - 2 * q^94 - 2 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.00000			0.408248
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	−0.780801	−	0.624780i	$-0.785189\pi$
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	0.150675	+	0.988583i	$0.451855\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$		0			0
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$		−	4.00000i		−	0.852803i
$23$	−6.06218	−	3.50000i	−1.26405	−	0.729800i	−0.290196	−	0.956967i	$-0.593720\pi$
$23$	−6.06218	−	3.50000i	−1.26405	−	0.729800i	−0.973856	+	0.227167i	$0.927054\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	2.00000	−	3.46410i	0.392232	−	0.679366i
$27$			1.00000i			0.192450i
$28$	−1.73205	+	2.00000i	−0.327327	+	0.377964i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	0.998322	−	0.0579057i	$-0.0184423\pi$
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	−0.549309	+	0.835619i	$0.685109\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−3.46410	−	2.00000i	−0.603023	−	0.348155i
$34$	3.00000			0.514496
$35$		0			0
$36$	1.00000			0.166667
$37$	1.73205	+	1.00000i	0.284747	+	0.164399i	0.635571	−	0.772043i	$-0.280765\pi$
$37$	1.73205	+	1.00000i	0.284747	+	0.164399i	−0.350823	+	0.936442i	$0.614098\pi$
$38$	−5.19615	+	3.00000i	−0.842927	+	0.486664i
$39$	−2.00000	−	3.46410i	−0.320256	−	0.554700i
$40$		0			0
$41$	7.00000			1.09322			0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000			1.09322			0.546608	+	0.837389i	$0.315919\pi$
$42$	0.866025	+	2.50000i	0.133631	+	0.385758i
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$		0			0
$46$	3.50000	+	6.06218i	0.516047	+	0.893819i
$47$	0.866025	+	0.500000i	0.126323	+	0.0729325i	0.561830	−	0.827253i	$-0.310098\pi$
$47$	0.866025	+	0.500000i	0.126323	+	0.0729325i	−0.435507	+	0.900185i	$0.643431\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$	−3.46410	+	2.00000i	−0.480384	+	0.277350i
$53$	−1.73205	+	1.00000i	−0.237915	+	0.137361i	−0.614218	−	0.789136i	$-0.710529\pi$
$53$	−1.73205	+	1.00000i	−0.237915	+	0.137361i	0.376303	+	0.926497i	$0.377195\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$			6.00000i			0.794719i
$58$	3.46410	+	2.00000i	0.454859	+	0.262613i
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.812198	−	0.583382i	$-0.801729\pi$
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.0991242	−	0.995075i	$-0.531604\pi$
$60$		0			0
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	0.170305	+	0.985391i	$0.445525\pi$
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	−0.938527	+	0.345207i	$0.887809\pi$
$62$		−	5.00000i		−	0.635001i
$63$	2.59808	+	0.500000i	0.327327	+	0.0629941i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.00000	+	3.46410i	0.246183	+	0.426401i
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.974916	−	0.222571i	$-0.928555\pi$
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.294706	+	0.955588i	$0.595222\pi$
$68$	−2.59808	−	1.50000i	−0.315063	−	0.181902i
$69$	7.00000			0.842701
$70$		0			0
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	5.19615	−	3.00000i	0.608164	−	0.351123i	−0.164083	−	0.986447i	$-0.552466\pi$
$73$	5.19615	−	3.00000i	0.608164	−	0.351123i	0.772246	+	0.635323i	$0.219133\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$		0			0
$76$	6.00000			0.688247
$77$	−6.92820	+	8.00000i	−0.789542	+	0.911685i
$78$			4.00000i			0.452911i
$79$	−8.50000	+	14.7224i	−0.956325	+	1.65640i	−0.225018	+	0.974355i	$0.572244\pi$
$79$	−8.50000	+	14.7224i	−0.956325	+	1.65640i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.06218	−	3.50000i	−0.669456	−	0.386510i
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$	0.500000	−	2.59808i	0.0545545	−	0.283473i
$85$		0			0
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	3.46410	−	2.00000i	0.371391	−	0.214423i
$88$	3.46410	−	2.00000i	0.369274	−	0.213201i
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	−0.989720	−	0.143022i	$-0.954318\pi$
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	0.618720	+	0.785611i	$0.287651\pi$
$90$		0			0
$91$	−10.0000	+	3.46410i	−1.04828	+	0.363137i
$92$		−	7.00000i		−	0.729800i
$93$	−4.33013	−	2.50000i	−0.449013	−	0.259238i
$94$	−0.500000	−	0.866025i	−0.0515711	−	0.0893237i
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			7.00000i			0.710742i	0.934725	+	0.355371i	$0.115646\pi$
$97$			7.00000i			0.710742i	−0.934725	+	0.355371i	$0.884354\pi$
$98$	6.92820	−	1.00000i	0.699854	−	0.101015i
$99$	4.00000			0.402015
$100$		0			0
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$	−2.59808	+	1.50000i	−0.257248	+	0.148522i
$103$	6.06218	+	3.50000i	0.597324	+	0.344865i	0.767988	−	0.640464i	$-0.221258\pi$
$103$	6.06218	+	3.50000i	0.597324	+	0.344865i	−0.170664	+	0.985329i	$0.554591\pi$
$104$	4.00000			0.392232
$105$		0			0
$106$	2.00000			0.194257
$107$	12.1244	+	7.00000i	1.17211	+	0.676716i	0.954175	−	0.299249i	$-0.0967360\pi$
$107$	12.1244	+	7.00000i	1.17211	+	0.676716i	0.217931	+	0.975964i	$0.430069\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	3.00000	+	5.19615i	0.287348	+	0.497701i	0.973176	−	0.230063i	$-0.0738931\pi$
$109$	3.00000	+	5.19615i	0.287348	+	0.497701i	−0.685828	+	0.727764i	$0.740560\pi$
$110$		0			0
$111$	−2.00000			−0.189832
$112$	−2.59808	−	0.500000i	−0.245495	−	0.0472456i
$113$		−	3.00000i		−	0.282216i	−0.989994	−	0.141108i	$-0.954933\pi$
$113$		−	3.00000i		−	0.282216i	0.989994	−	0.141108i	$-0.0450665\pi$
$114$	3.00000	−	5.19615i	0.280976	−	0.486664i
$115$		0			0
$116$	−2.00000	−	3.46410i	−0.185695	−	0.321634i
$117$	3.46410	+	2.00000i	0.320256	+	0.184900i
$118$			14.0000i			1.28880i
$119$	−6.00000	−	5.19615i	−0.550019	−	0.476331i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	10.3923	−	6.00000i	0.940875	−	0.543214i
$123$	−6.06218	+	3.50000i	−0.546608	+	0.315584i
$124$	−2.50000	+	4.33013i	−0.224507	+	0.388857i
$125$		0			0
$126$	−2.00000	−	1.73205i	−0.178174	−	0.154303i
$127$		−	16.0000i		−	1.41977i	−0.704317	−	0.709885i	$-0.748747\pi$
$127$		−	16.0000i		−	1.41977i	0.704317	−	0.709885i	$-0.251253\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−1.00000	−	1.73205i	−0.0880451	−	0.152499i
$130$		0			0
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	−0.636676	−	0.771132i	$-0.719691\pi$
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	0.986157	+	0.165812i	$0.0530244\pi$
$132$		−	4.00000i		−	0.348155i
$133$	15.5885	+	3.00000i	1.35169	+	0.260133i
$134$	12.0000			1.03664
$135$		0			0
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	−12.9904	+	7.50000i	−1.10984	+	0.640768i	−0.938789	−	0.344493i	$-0.888051\pi$
$137$	−12.9904	+	7.50000i	−1.10984	+	0.640768i	−0.171054	+	0.985262i	$0.554717\pi$
$138$	−6.06218	−	3.50000i	−0.516047	−	0.297940i
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$	−1.00000			−0.0842152
$142$	7.79423	+	4.50000i	0.654077	+	0.377632i
$143$	−13.8564	+	8.00000i	−1.15873	+	0.668994i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$		0			0
$146$	−6.00000			−0.496564
$147$	2.59808	−	6.50000i	0.214286	−	0.536111i
$148$			2.00000i			0.164399i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−12.0000	−	20.7846i	−0.976546	−	1.69143i	−0.674735	−	0.738060i	$-0.735742\pi$
$151$	−12.0000	−	20.7846i	−0.976546	−	1.69143i	−0.301811	−	0.953368i	$-0.597591\pi$
$152$	−5.19615	−	3.00000i	−0.421464	−	0.243332i
$153$			3.00000i			0.242536i
$154$	10.0000	−	3.46410i	0.805823	−	0.279145i
$155$		0			0
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	3.46410	−	2.00000i	0.276465	−	0.159617i	−0.355357	−	0.934731i	$-0.615641\pi$
$157$	3.46410	−	2.00000i	0.276465	−	0.159617i	0.631822	+	0.775113i	$0.282307\pi$
$158$	14.7224	−	8.50000i	1.17125	−	0.676224i
$159$	1.00000	−	1.73205i	0.0793052	−	0.137361i
$160$		0			0
$161$	3.50000	−	18.1865i	0.275839	−	1.43330i
$162$			1.00000i			0.0785674i
$163$	6.92820	+	4.00000i	0.542659	+	0.313304i	0.746156	−	0.665771i	$-0.231897\pi$
$163$	6.92820	+	4.00000i	0.542659	+	0.313304i	−0.203497	+	0.979076i	$0.565231\pi$
$164$	3.50000	+	6.06218i	0.273304	+	0.473377i
$165$		0			0
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$	−1.73205	+	2.00000i	−0.133631	+	0.154303i
$169$	−3.00000			−0.230769
$170$		0			0
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	−1.73205	+	1.00000i	−0.132068	+	0.0762493i
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	0.289292	−	0.957241i	$-0.406580\pi$
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	−0.684349	+	0.729155i	$0.739913\pi$
$174$	−4.00000			−0.303239
$175$		0			0
$176$	−4.00000			−0.301511
$177$	12.1244	+	7.00000i	0.911322	+	0.526152i
$178$	6.06218	−	3.50000i	0.454379	−	0.262336i
$179$	1.00000	+	1.73205i	0.0747435	+	0.129460i	0.900975	−	0.433872i	$-0.142853\pi$
$179$	1.00000	+	1.73205i	0.0747435	+	0.129460i	−0.826231	+	0.563331i	$0.809520\pi$
$180$		0			0
$181$	12.0000			0.891953			0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000			0.891953			0.445976	+	0.895045i	$0.352856\pi$
$182$	10.3923	+	2.00000i	0.770329	+	0.148250i
$183$		−	12.0000i		−	0.887066i
$184$	−3.50000	+	6.06218i	−0.258023	+	0.446910i
$185$		0			0
$186$	2.50000	+	4.33013i	0.183309	+	0.317500i
$187$	−10.3923	−	6.00000i	−0.759961	−	0.438763i
$188$			1.00000i			0.0729325i
$189$	−2.50000	+	0.866025i	−0.181848	+	0.0629941i
$190$		0			0
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	0.456068	+	0.889945i	$0.349257\pi$
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	−0.998749	+	0.0500060i	$0.984076\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	21.6506	−	12.5000i	1.55845	−	0.899770i	0.561041	−	0.827788i	$-0.310401\pi$
$193$	21.6506	−	12.5000i	1.55845	−	0.899770i	0.997406	−	0.0719816i	$-0.0229323\pi$
$194$	3.50000	−	6.06218i	0.251285	−	0.435239i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$		−	20.0000i		−	1.42494i	−0.701702	−	0.712470i	$-0.747576\pi$
$197$		−	20.0000i		−	1.42494i	0.701702	−	0.712470i	$-0.252424\pi$
$198$	−3.46410	−	2.00000i	−0.246183	−	0.142134i
$199$	7.50000	+	12.9904i	0.531661	+	0.920864i	0.999317	+	0.0369532i	$0.0117652\pi$
$199$	7.50000	+	12.9904i	0.531661	+	0.920864i	−0.467656	+	0.883911i	$0.654901\pi$
$200$		0			0
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$		−	18.0000i		−	1.26648i
$203$	−3.46410	−	10.0000i	−0.243132	−	0.701862i
$204$	3.00000			0.210042
$205$		0			0
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$	−6.06218	+	3.50000i	−0.421350	+	0.243267i
$208$	−3.46410	−	2.00000i	−0.240192	−	0.138675i
$209$	24.0000			1.66011
$210$		0			0
$211$	−22.0000			−1.51454			−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000			−1.51454			−0.757271	+	0.653101i	$0.773468\pi$
$212$	−1.73205	−	1.00000i	−0.118958	−	0.0686803i
$213$	7.79423	−	4.50000i	0.534052	−	0.308335i
$214$	−7.00000	−	12.1244i	−0.478510	−	0.828804i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−8.66025	+	10.0000i	−0.587896	+	0.678844i
$218$		−	6.00000i		−	0.406371i
$219$	−3.00000	+	5.19615i	−0.202721	+	0.351123i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	1.73205	+	1.00000i	0.116248	+	0.0671156i
$223$			9.00000i			0.602685i	0.953516	+	0.301342i	$0.0974347\pi$
$223$			9.00000i			0.602685i	−0.953516	+	0.301342i	$0.902565\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$		0			0
$226$	−1.50000	+	2.59808i	−0.0997785	+	0.172821i
$227$	19.0526	−	11.0000i	1.26456	−	0.730096i	0.290609	−	0.956842i	$-0.406142\pi$
$227$	19.0526	−	11.0000i	1.26456	−	0.730096i	0.973954	+	0.226746i	$0.0728088\pi$
$228$	−5.19615	+	3.00000i	−0.344124	+	0.198680i
$229$	4.00000	−	6.92820i	0.264327	−	0.457829i	−0.703060	−	0.711131i	$-0.748183\pi$
$229$	4.00000	−	6.92820i	0.264327	−	0.457829i	0.967387	+	0.253302i	$0.0815167\pi$
$230$		0			0
$231$	2.00000	−	10.3923i	0.131590	−	0.683763i
$232$			4.00000i			0.262613i
$233$	5.19615	+	3.00000i	0.340411	+	0.196537i	0.660454	−	0.750867i	$-0.270364\pi$
$233$	5.19615	+	3.00000i	0.340411	+	0.196537i	−0.320043	+	0.947403i	$0.603697\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$		0			0
$236$	7.00000	−	12.1244i	0.455661	−	0.789228i
$237$		−	17.0000i		−	1.10427i
$238$	2.59808	+	7.50000i	0.168408	+	0.486153i
$239$	−3.00000			−0.194054			−0.0970269	−	0.995282i	$-0.530933\pi$
$239$	−3.00000			−0.194054			−0.0970269	+	0.995282i	$0.530933\pi$
$240$		0			0
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	0.896435	−	0.443176i	$-0.146148\pi$
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	−0.832019	+	0.554747i	$0.812815\pi$
$242$	4.33013	−	2.50000i	0.278351	−	0.160706i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−12.0000			−0.768221
$245$		0			0
$246$	7.00000			0.446304
$247$	20.7846	+	12.0000i	1.32249	+	0.763542i
$248$	4.33013	−	2.50000i	0.274963	−	0.158750i
$249$	2.00000	+	3.46410i	0.126745	+	0.219529i
$250$		0			0
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$	0.866025	+	2.50000i	0.0545545	+	0.157485i
$253$		−	28.0000i		−	1.76034i
$254$	−8.00000	+	13.8564i	−0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.73205	−	1.00000i	−0.108042	−	0.0623783i	0.445005	−	0.895528i	$-0.353202\pi$
$257$	−1.73205	−	1.00000i	−0.108042	−	0.0623783i	−0.553047	+	0.833150i	$0.686535\pi$
$258$			2.00000i			0.124515i
$259$	−1.00000	+	5.19615i	−0.0621370	+	0.322873i
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	−6.92820	+	4.00000i	−0.428026	+	0.247121i
$263$	−23.3827	+	13.5000i	−1.44184	+	0.832446i	−0.997972	−	0.0636476i	$-0.979727\pi$
$263$	−23.3827	+	13.5000i	−1.44184	+	0.832446i	−0.443866	+	0.896093i	$0.646393\pi$
$264$	−2.00000	+	3.46410i	−0.123091	+	0.213201i
$265$		0			0
$266$	−12.0000	−	10.3923i	−0.735767	−	0.637193i
$267$		−	7.00000i		−	0.428393i
$268$	−10.3923	−	6.00000i	−0.634811	−	0.366508i
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	0.672374	−	0.740212i	$-0.265275\pi$
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	−0.977229	+	0.212187i	$0.931941\pi$
$270$		0			0
$271$	−2.50000	+	4.33013i	−0.151864	+	0.263036i	−0.931913	−	0.362682i	$-0.881861\pi$
$271$	−2.50000	+	4.33013i	−0.151864	+	0.263036i	0.780049	+	0.625719i	$0.215194\pi$
$272$		−	3.00000i		−	0.181902i
$273$	6.92820	−	8.00000i	0.419314	−	0.484182i
$274$	15.0000			0.906183
$275$		0			0
$276$	3.50000	+	6.06218i	0.210675	+	0.364900i
$277$	13.8564	−	8.00000i	0.832551	−	0.480673i	−0.0221745	−	0.999754i	$-0.507059\pi$
$277$	13.8564	−	8.00000i	0.832551	−	0.480673i	0.854725	+	0.519081i	$0.173726\pi$
$278$	1.73205	+	1.00000i	0.103882	+	0.0599760i
$279$	5.00000			0.299342
$280$		0			0
$281$	17.0000			1.01413			0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000			1.01413			0.507067	+	0.861906i	$0.330729\pi$
$282$	0.866025	+	0.500000i	0.0515711	+	0.0297746i
$283$	−6.92820	+	4.00000i	−0.411839	+	0.237775i	−0.691580	−	0.722300i	$-0.743085\pi$
$283$	−6.92820	+	4.00000i	−0.411839	+	0.237775i	0.279741	+	0.960076i	$0.409752\pi$
$284$	−4.50000	−	7.79423i	−0.267026	−	0.462502i
$285$		0			0
$286$	16.0000			0.946100
$287$	6.06218	+	17.5000i	0.357839	+	1.03299i
$288$		−	1.00000i		−	0.0589256i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	−3.50000	−	6.06218i	−0.205174	−	0.355371i
$292$	5.19615	+	3.00000i	0.304082	+	0.175562i
$293$		−	12.0000i		−	0.701047i	−0.936554	−	0.350524i	$-0.886004\pi$
$293$		−	12.0000i		−	0.701047i	0.936554	−	0.350524i	$-0.113996\pi$
$294$	−5.50000	+	4.33013i	−0.320767	+	0.252538i
$295$		0			0
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	−3.46410	+	2.00000i	−0.201008	+	0.116052i
$298$	5.19615	−	3.00000i	0.301005	−	0.173785i
$299$	14.0000	−	24.2487i	0.809641	−	1.40234i
$300$		0			0
$301$	−5.00000	+	1.73205i	−0.288195	+	0.0998337i
$302$			24.0000i			1.38104i
$303$	−15.5885	−	9.00000i	−0.895533	−	0.517036i
$304$	3.00000	+	5.19615i	0.172062	+	0.298020i
$305$		0			0
$306$	1.50000	−	2.59808i	0.0857493	−	0.148522i
$307$		−	20.0000i		−	1.14146i	−0.821138	−	0.570730i	$-0.806660\pi$
$307$		−	20.0000i		−	1.14146i	0.821138	−	0.570730i	$-0.193340\pi$
$308$	−10.3923	−	2.00000i	−0.592157	−	0.113961i
$309$	−7.00000			−0.398216
$310$		0			0
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	−0.993490	−	0.113917i	$-0.963660\pi$
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	0.398090	−	0.917346i	$-0.369673\pi$
$312$	−3.46410	+	2.00000i	−0.196116	+	0.113228i
$313$	23.3827	+	13.5000i	1.32167	+	0.763065i	0.983995	−	0.178198i	$-0.0570269\pi$
$313$	23.3827	+	13.5000i	1.32167	+	0.763065i	0.337673	+	0.941263i	$0.390360\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−17.0000			−0.956325
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$	−1.73205	+	1.00000i	−0.0971286	+	0.0560772i
$319$	−8.00000	−	13.8564i	−0.447914	−	0.775810i
$320$		0			0
$321$	−14.0000			−0.781404
$322$	−12.1244	+	14.0000i	−0.675664	+	0.780189i
$323$			18.0000i			1.00155i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		0			0
$326$	−4.00000	−	6.92820i	−0.221540	−	0.383718i
$327$	−5.19615	−	3.00000i	−0.287348	−	0.165900i
$328$		−	7.00000i		−	0.386510i
$329$	−0.500000	+	2.59808i	−0.0275659	+	0.143237i
$330$		0			0
$331$	17.0000	−	29.4449i	0.934405	−	1.61844i	0.158712	−	0.987325i	$-0.449266\pi$
$331$	17.0000	−	29.4449i	0.934405	−	1.61844i	0.775692	−	0.631111i	$-0.217401\pi$
$332$	3.46410	−	2.00000i	0.190117	−	0.109764i
$333$	1.73205	−	1.00000i	0.0949158	−	0.0547997i
$334$		0			0
$335$		0			0
$336$	2.50000	−	0.866025i	0.136386	−	0.0472456i
$337$		−	3.00000i		−	0.163420i	−0.996656	−	0.0817102i	$-0.973962\pi$
$337$		−	3.00000i		−	0.163420i	0.996656	−	0.0817102i	$-0.0260382\pi$
$338$	2.59808	+	1.50000i	0.141317	+	0.0815892i
$339$	1.50000	+	2.59808i	0.0814688	+	0.141108i
$340$		0			0
$341$	−10.0000	+	17.3205i	−0.541530	+	0.937958i
$342$			6.00000i			0.324443i
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$	2.00000			0.107833
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−27.7128	+	16.0000i	−1.48770	+	0.858925i	−0.999902	−	0.0140303i	$-0.995534\pi$
$347$	−27.7128	+	16.0000i	−1.48770	+	0.858925i	−0.487800	+	0.872955i	$0.662201\pi$
$348$	3.46410	+	2.00000i	0.185695	+	0.107211i
$349$	18.0000			0.963518			0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000			0.963518			0.481759	+	0.876304i	$0.339998\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	3.46410	+	2.00000i	0.184637	+	0.106600i
$353$	−12.9904	+	7.50000i	−0.691408	+	0.399185i	−0.804139	−	0.594441i	$-0.797373\pi$
$353$	−12.9904	+	7.50000i	−0.691408	+	0.399185i	0.112731	+	0.993626i	$0.464040\pi$
$354$	−7.00000	−	12.1244i	−0.372046	−	0.644402i
$355$		0			0
$356$	−7.00000			−0.370999
$357$	7.79423	+	1.50000i	0.412514	+	0.0793884i
$358$		−	2.00000i		−	0.105703i
$359$	2.00000	−	3.46410i	0.105556	−	0.182828i	−0.808409	−	0.588621i	$-0.799671\pi$
$359$	2.00000	−	3.46410i	0.105556	−	0.182828i	0.913965	+	0.405793i	$0.133004\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−10.3923	−	6.00000i	−0.546207	−	0.315353i
$363$		−	5.00000i		−	0.262432i
$364$	−8.00000	−	6.92820i	−0.419314	−	0.363137i
$365$		0			0
$366$	−6.00000	+	10.3923i	−0.313625	+	0.543214i
$367$	27.7128	−	16.0000i	1.44660	−	0.835193i	0.448320	−	0.893873i	$-0.352022\pi$
$367$	27.7128	−	16.0000i	1.44660	−	0.835193i	0.998277	+	0.0586798i	$0.0186891\pi$
$368$	6.06218	−	3.50000i	0.316013	−	0.182450i
$369$	3.50000	−	6.06218i	0.182203	−	0.315584i
$370$		0			0
$371$	−4.00000	−	3.46410i	−0.207670	−	0.179847i
$372$		−	5.00000i		−	0.259238i
$373$	−10.3923	−	6.00000i	−0.538093	−	0.310668i	0.206213	−	0.978507i	$-0.433886\pi$
$373$	−10.3923	−	6.00000i	−0.538093	−	0.310668i	−0.744306	+	0.667839i	$0.767219\pi$
$374$	6.00000	+	10.3923i	0.310253	+	0.537373i
$375$		0			0
$376$	0.500000	−	0.866025i	0.0257855	−	0.0446619i
$377$		−	16.0000i		−	0.824042i
$378$	2.59808	+	0.500000i	0.133631	+	0.0257172i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$	8.00000	+	13.8564i	0.409852	+	0.709885i
$382$	12.9904	−	7.50000i	0.664646	−	0.383733i
$383$	26.8468	+	15.5000i	1.37181	+	0.792013i	0.991155	−	0.132706i	$-0.0423665\pi$
$383$	26.8468	+	15.5000i	1.37181	+	0.792013i	0.380651	+	0.924719i	$0.375700\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−25.0000			−1.27247
$387$	1.73205	+	1.00000i	0.0880451	+	0.0508329i
$388$	−6.06218	+	3.50000i	−0.307760	+	0.177686i
$389$	5.00000	+	8.66025i	0.253510	+	0.439092i	0.964490	−	0.264120i	$-0.0850816\pi$
$389$	5.00000	+	8.66025i	0.253510	+	0.439092i	−0.710980	+	0.703213i	$0.751748\pi$
$390$		0			0
$391$	21.0000			1.06202
$392$	4.33013	+	5.50000i	0.218704	+	0.277792i
$393$			8.00000i			0.403547i
$394$	−10.0000	+	17.3205i	−0.503793	+	0.872595i
$395$		0			0
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	−19.0526	−	11.0000i	−0.956221	−	0.552074i	−0.0612128	−	0.998125i	$-0.519497\pi$
$397$	−19.0526	−	11.0000i	−0.956221	−	0.552074i	−0.895008	+	0.446051i	$0.852830\pi$
$398$		−	15.0000i		−	0.751882i
$399$	−15.0000	+	5.19615i	−0.750939	+	0.260133i
$400$		0			0
$401$	−17.0000	+	29.4449i	−0.848939	+	1.47041i	0.0332161	+	0.999448i	$0.489425\pi$
$401$	−17.0000	+	29.4449i	−0.848939	+	1.47041i	−0.882156	+	0.470958i	$0.843908\pi$
$402$	−10.3923	+	6.00000i	−0.518321	+	0.299253i
$403$	−17.3205	+	10.0000i	−0.862796	+	0.498135i
$404$	−9.00000	+	15.5885i	−0.447767	+	0.775555i
$405$		0			0
$406$	−2.00000	+	10.3923i	−0.0992583	+	0.515761i
$407$			8.00000i			0.396545i
$408$	−2.59808	−	1.50000i	−0.128624	−	0.0742611i
$409$	14.5000	+	25.1147i	0.716979	+	1.24184i	0.962191	+	0.272374i	$0.0878089\pi$
$409$	14.5000	+	25.1147i	0.716979	+	1.24184i	−0.245212	+	0.969469i	$0.578858\pi$
$410$		0			0
$411$	7.50000	−	12.9904i	0.369948	−	0.640768i
$412$			7.00000i			0.344865i
$413$	24.2487	−	28.0000i	1.19320	−	1.37779i
$414$	7.00000			0.344031
$415$		0			0
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$	1.73205	−	1.00000i	0.0848189	−	0.0489702i
$418$	−20.7846	−	12.0000i	−1.01661	−	0.586939i
$419$	26.0000			1.27018			0.635092	−	0.772437i	$-0.280962\pi$
$419$	26.0000			1.27018			0.635092	+	0.772437i	$0.280962\pi$
$420$		0			0
$421$	16.0000			0.779792			0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000			0.779792			0.389896	+	0.920859i	$0.372511\pi$
$422$	19.0526	+	11.0000i	0.927464	+	0.535472i
$423$	0.866025	−	0.500000i	0.0421076	−	0.0243108i
$424$	1.00000	+	1.73205i	0.0485643	+	0.0841158i
$425$		0			0
$426$	−9.00000			−0.436051
$427$	−31.1769	−	6.00000i	−1.50876	−	0.290360i
$428$			14.0000i			0.676716i
$429$	8.00000	−	13.8564i	0.386244	−	0.668994i
$430$		0			0
$431$	19.5000	+	33.7750i	0.939282	+	1.62688i	0.766814	+	0.641869i	$0.221841\pi$
$431$	19.5000	+	33.7750i	0.939282	+	1.62688i	0.172468	+	0.985015i	$0.444826\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			37.0000i			1.77811i	0.457804	+	0.889053i	$0.348636\pi$
$433$			37.0000i			1.77811i	−0.457804	+	0.889053i	$0.651364\pi$
$434$	12.5000	−	4.33013i	0.600019	−	0.207853i
$435$		0			0
$436$	−3.00000	+	5.19615i	−0.143674	+	0.248851i
$437$	−36.3731	+	21.0000i	−1.73996	+	1.00457i
$438$	5.19615	−	3.00000i	0.248282	−	0.143346i
$439$	8.50000	−	14.7224i	0.405683	−	0.702663i	−0.588718	−	0.808339i	$-0.700367\pi$
$439$	8.50000	−	14.7224i	0.405683	−	0.702663i	0.994401	+	0.105675i	$0.0337004\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$			12.0000i			0.570782i
$443$	22.5167	+	13.0000i	1.06980	+	0.617649i	0.928126	−	0.372265i	$-0.121419\pi$
$443$	22.5167	+	13.0000i	1.06980	+	0.617649i	0.141672	+	0.989914i	$0.454752\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$		0			0
$446$	4.50000	−	7.79423i	0.213081	−	0.369067i
$447$		−	6.00000i		−	0.283790i
$448$	−0.866025	−	2.50000i	−0.0409159	−	0.118114i
$449$	13.0000			0.613508			0.306754	−	0.951789i	$-0.400757\pi$
$449$	13.0000			0.613508			0.306754	+	0.951789i	$0.400757\pi$
$450$		0			0
$451$	14.0000	+	24.2487i	0.659234	+	1.14183i
$452$	2.59808	−	1.50000i	0.122203	−	0.0705541i
$453$	20.7846	+	12.0000i	0.976546	+	0.563809i
$454$	−22.0000			−1.03251
$455$		0			0
$456$	6.00000			0.280976
$457$	15.5885	+	9.00000i	0.729197	+	0.421002i	0.818128	−	0.575036i	$-0.195012\pi$
$457$	15.5885	+	9.00000i	0.729197	+	0.421002i	−0.0889312	+	0.996038i	$0.528345\pi$
$458$	−6.92820	+	4.00000i	−0.323734	+	0.186908i
$459$	−1.50000	−	2.59808i	−0.0700140	−	0.121268i
$460$		0			0
$461$	36.0000			1.67669			0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000			1.67669			0.838344	+	0.545142i	$0.183524\pi$
$462$	−6.92820	+	8.00000i	−0.322329	+	0.372194i
$463$		−	7.00000i		−	0.325318i	−0.986682	−	0.162659i	$-0.947993\pi$
$463$		−	7.00000i		−	0.325318i	0.986682	−	0.162659i	$-0.0520070\pi$
$464$	2.00000	−	3.46410i	0.0928477	−	0.160817i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$467$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$468$			4.00000i			0.184900i
$469$	−24.0000	−	20.7846i	−1.10822	−	0.959744i
$470$		0			0
$471$	−2.00000	+	3.46410i	−0.0921551	+	0.159617i
$472$	−12.1244	+	7.00000i	−0.558069	+	0.322201i
$473$	−6.92820	+	4.00000i	−0.318559	+	0.183920i
$474$	−8.50000	+	14.7224i	−0.390418	+	0.676224i
$475$		0			0
$476$	1.50000	−	7.79423i	0.0687524	−	0.357248i
$477$			2.00000i			0.0915737i
$478$	2.59808	+	1.50000i	0.118833	+	0.0686084i
$479$	0.500000	+	0.866025i	0.0228456	+	0.0395697i	0.877222	−	0.480085i	$-0.159394\pi$
$479$	0.500000	+	0.866025i	0.0228456	+	0.0395697i	−0.854377	+	0.519654i	$0.826061\pi$
$480$		0			0
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$		−	2.00000i		−	0.0910975i
$483$	6.06218	+	17.5000i	0.275839	+	0.796278i
$484$	−5.00000			−0.227273
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−4.33013	+	2.50000i	−0.196217	+	0.113286i	−0.594890	−	0.803807i	$-0.702804\pi$
$487$	−4.33013	+	2.50000i	−0.196217	+	0.113286i	0.398673	+	0.917093i	$0.369471\pi$
$488$	10.3923	+	6.00000i	0.470438	+	0.271607i
$489$	−8.00000			−0.361773
$490$		0			0
$491$	38.0000			1.71492			0.857458	−	0.514554i	$-0.172042\pi$
$491$	38.0000			1.71492			0.857458	+	0.514554i	$0.172042\pi$
$492$	−6.06218	−	3.50000i	−0.273304	−	0.157792i
$493$	10.3923	−	6.00000i	0.468046	−	0.270226i
$494$	−12.0000	−	20.7846i	−0.539906	−	0.935144i
$495$		0			0
$496$	−5.00000			−0.224507
$497$	−7.79423	−	22.5000i	−0.349619	−	1.00926i
$498$		−	4.00000i		−	0.179244i
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$		0			0
$501$		0			0
$502$	−3.46410	−	2.00000i	−0.154610	−	0.0892644i
$503$			36.0000i			1.60516i	0.596544	+	0.802580i	$0.296540\pi$
$503$			36.0000i			1.60516i	−0.596544	+	0.802580i	$0.703460\pi$
$504$	0.500000	−	2.59808i	0.0222718	−	0.115728i
$505$		0			0
$506$	−14.0000	+	24.2487i	−0.622376	+	1.07799i
$507$	2.59808	−	1.50000i	0.115385	−	0.0666173i
$508$	13.8564	−	8.00000i	0.614779	−	0.354943i
$509$	−8.00000	+	13.8564i	−0.354594	+	0.614174i	−0.987048	−	0.160423i	$-0.948714\pi$
$509$	−8.00000	+	13.8564i	−0.354594	+	0.614174i	0.632455	+	0.774597i	$0.282047\pi$
$510$		0			0
$511$	12.0000	+	10.3923i	0.530849	+	0.459728i
$512$			1.00000i			0.0441942i
$513$	5.19615	+	3.00000i	0.229416	+	0.132453i
$514$	1.00000	+	1.73205i	0.0441081	+	0.0763975i
$515$		0			0
$516$	1.00000	−	1.73205i	0.0440225	−	0.0762493i
$517$			4.00000i			0.175920i
$518$	3.46410	−	4.00000i	0.152204	−	0.175750i
$519$	6.00000			0.263371
$520$		0			0
$521$	4.50000	+	7.79423i	0.197149	+	0.341471i	0.947603	−	0.319451i	$-0.103499\pi$
$521$	4.50000	+	7.79423i	0.197149	+	0.341471i	−0.750454	+	0.660922i	$0.770165\pi$
$522$	3.46410	−	2.00000i	0.151620	−	0.0875376i
$523$	−38.1051	−	22.0000i	−1.66622	−	0.961993i	−0.969648	−	0.244507i	$-0.921374\pi$
$523$	−38.1051	−	22.0000i	−1.66622	−	0.961993i	−0.696573	−	0.717486i	$-0.745293\pi$
$524$	8.00000			0.349482
$525$		0			0
$526$	27.0000			1.17726
$527$	−12.9904	−	7.50000i	−0.565870	−	0.326705i
$528$	3.46410	−	2.00000i	0.150756	−	0.0870388i
$529$	13.0000	+	22.5167i	0.565217	+	0.978985i
$530$		0			0
$531$	−14.0000			−0.607548
$532$	5.19615	+	15.0000i	0.225282	+	0.650332i
$533$			28.0000i			1.21281i
$534$	−3.50000	+	6.06218i	−0.151460	+	0.262336i
$535$		0			0
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	−1.73205	−	1.00000i	−0.0747435	−	0.0431532i
$538$			10.0000i			0.431131i
$539$	−26.0000	−	10.3923i	−1.11990	−	0.447628i
$540$		0			0
$541$	−16.0000	+	27.7128i	−0.687894	+	1.19147i	0.284624	+	0.958639i	$0.408131\pi$
$541$	−16.0000	+	27.7128i	−0.687894	+	1.19147i	−0.972518	+	0.232828i	$0.925202\pi$
$542$	4.33013	−	2.50000i	0.185995	−	0.107384i
$543$	−10.3923	+	6.00000i	−0.445976	+	0.257485i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$		0			0
$546$	−10.0000	+	3.46410i	−0.427960	+	0.148250i
$547$		−	22.0000i		−	0.940652i	−0.882493	−	0.470326i	$-0.844136\pi$
$547$		−	22.0000i		−	0.940652i	0.882493	−	0.470326i	$-0.155864\pi$
$548$	−12.9904	−	7.50000i	−0.554922	−	0.320384i
$549$	6.00000	+	10.3923i	0.256074	+	0.443533i
$550$		0			0
$551$	−12.0000	+	20.7846i	−0.511217	+	0.885454i
$552$		−	7.00000i		−	0.297940i
$553$	−44.1673	−	8.50000i	−1.87818	−	0.361457i
$554$	−16.0000			−0.679775
$555$		0			0
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	−25.9808	+	15.0000i	−1.10084	+	0.635570i	−0.936442	−	0.350824i	$-0.885902\pi$
$557$	−25.9808	+	15.0000i	−1.10084	+	0.635570i	−0.164399	+	0.986394i	$0.552568\pi$
$558$	−4.33013	−	2.50000i	−0.183309	−	0.105833i
$559$	−8.00000			−0.338364
$560$		0			0
$561$	12.0000			0.506640
$562$	−14.7224	−	8.50000i	−0.621028	−	0.358551i
$563$	−1.73205	+	1.00000i	−0.0729972	+	0.0421450i	−0.536054	−	0.844183i	$-0.680086\pi$
$563$	−1.73205	+	1.00000i	−0.0729972	+	0.0421450i	0.463057	+	0.886328i	$0.346752\pi$
$564$	−0.500000	−	0.866025i	−0.0210538	−	0.0364662i
$565$		0			0
$566$	8.00000			0.336265
$567$	1.73205	−	2.00000i	0.0727393	−	0.0839921i
$568$			9.00000i			0.377632i
$569$	−22.5000	+	38.9711i	−0.943249	+	1.63376i	−0.184030	+	0.982921i	$0.558914\pi$
$569$	−22.5000	+	38.9711i	−0.943249	+	1.63376i	−0.759220	+	0.650835i	$0.774419\pi$
$570$		0			0
$571$	−20.0000	−	34.6410i	−0.836974	−	1.44968i	−0.892413	−	0.451219i	$-0.850989\pi$
$571$	−20.0000	−	34.6410i	−0.836974	−	1.44968i	0.0554391	−	0.998462i	$-0.482344\pi$
$572$	−13.8564	−	8.00000i	−0.579365	−	0.334497i
$573$		−	15.0000i		−	0.626634i
$574$	3.50000	−	18.1865i	0.146087	−	0.759091i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	1.73205	−	1.00000i	0.0721062	−	0.0416305i	−0.463513	−	0.886090i	$-0.653411\pi$
$577$	1.73205	−	1.00000i	0.0721062	−	0.0416305i	0.535620	+	0.844459i	$0.320078\pi$
$578$	6.92820	−	4.00000i	0.288175	−	0.166378i
$579$	−12.5000	+	21.6506i	−0.519482	+	0.899770i
$580$		0			0
$581$	10.0000	−	3.46410i	0.414870	−	0.143715i
$582$			7.00000i			0.290159i
$583$	−6.92820	−	4.00000i	−0.286937	−	0.165663i
$584$	−3.00000	−	5.19615i	−0.124141	−	0.215018i
$585$		0			0
$586$	−6.00000	+	10.3923i	−0.247858	+	0.429302i
$587$		−	42.0000i		−	1.73353i	−0.498721	−	0.866763i	$-0.666197\pi$
$587$		−	42.0000i		−	1.73353i	0.498721	−	0.866763i	$-0.333803\pi$
$588$	6.92820	−	1.00000i	0.285714	−	0.0412393i
$589$	30.0000			1.23613
$590$		0			0
$591$	10.0000	+	17.3205i	0.411345	+	0.712470i
$592$	−1.73205	+	1.00000i	−0.0711868	+	0.0410997i
$593$	−11.2583	−	6.50000i	−0.462324	−	0.266923i	0.250697	−	0.968066i	$-0.419340\pi$
$593$	−11.2583	−	6.50000i	−0.462324	−	0.266923i	−0.713021	+	0.701143i	$0.752674\pi$
$594$	4.00000			0.164122
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−12.9904	−	7.50000i	−0.531661	−	0.306955i
$598$	−24.2487	+	14.0000i	−0.991604	+	0.572503i
$599$	−15.5000	−	26.8468i	−0.633313	−	1.09693i	−0.986870	−	0.161517i	$-0.948361\pi$
$599$	−15.5000	−	26.8468i	−0.633313	−	1.09693i	0.353557	−	0.935413i	$-0.384972\pi$
$600$		0			0
$601$	46.0000			1.87638			0.938190	−	0.346122i	$-0.112502\pi$
$601$	46.0000			1.87638			0.938190	+	0.346122i	$0.112502\pi$
$602$	5.19615	+	1.00000i	0.211779	+	0.0407570i
$603$			12.0000i			0.488678i
$604$	12.0000	−	20.7846i	0.488273	−	0.845714i
$605$		0			0
$606$	9.00000	+	15.5885i	0.365600	+	0.633238i
$607$	25.1147	+	14.5000i	1.01938	+	0.588537i	0.913923	−	0.405887i	$-0.133038\pi$
$607$	25.1147	+	14.5000i	1.01938	+	0.588537i	0.105453	+	0.994424i	$0.466371\pi$
$608$		−	6.00000i		−	0.243332i
$609$	8.00000	+	6.92820i	0.324176	+	0.280745i
$610$		0			0
$611$	−2.00000	+	3.46410i	−0.0809113	+	0.140143i
$612$	−2.59808	+	1.50000i	−0.105021	+	0.0606339i
$613$	3.46410	−	2.00000i	0.139914	−	0.0807792i	−0.428409	−	0.903585i	$-0.640926\pi$
$613$	3.46410	−	2.00000i	0.139914	−	0.0807792i	0.568323	+	0.822806i	$0.307592\pi$
$614$	−10.0000	+	17.3205i	−0.403567	+	0.698999i
$615$		0			0
$616$	8.00000	+	6.92820i	0.322329	+	0.279145i
$617$		−	1.00000i		−	0.0402585i	−0.999797	−	0.0201292i	$-0.993592\pi$
$617$		−	1.00000i		−	0.0402585i	0.999797	−	0.0201292i	$-0.00640777\pi$
$618$	6.06218	+	3.50000i	0.243857	+	0.140791i
$619$	−8.00000	−	13.8564i	−0.321547	−	0.556936i	0.659260	−	0.751915i	$-0.270870\pi$
$619$	−8.00000	−	13.8564i	−0.321547	−	0.556936i	−0.980807	+	0.194979i	$0.937536\pi$
$620$		0			0
$621$	3.50000	−	6.06218i	0.140450	−	0.243267i
$622$			21.0000i			0.842023i
$623$	−18.1865	−	3.50000i	−0.728628	−	0.140225i
$624$	4.00000			0.160128
$625$		0			0
$626$	−13.5000	−	23.3827i	−0.539569	−	0.934560i
$627$	−20.7846	+	12.0000i	−0.830057	+	0.479234i
$628$	3.46410	+	2.00000i	0.138233	+	0.0798087i
$629$	−6.00000			−0.239236
$630$		0			0
$631$	7.00000			0.278666			0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000			0.278666			0.139333	+	0.990246i	$0.455504\pi$
$632$	14.7224	+	8.50000i	0.585627	+	0.338112i
$633$	19.0526	−	11.0000i	0.757271	−	0.437211i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$		0			0
$636$	2.00000			0.0793052
$637$	−17.3205	−	22.0000i	−0.686264	−	0.871672i
$638$			16.0000i			0.633446i
$639$	−4.50000	+	7.79423i	−0.178017	+	0.308335i
$640$		0			0
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$	12.1244	+	7.00000i	0.478510	+	0.276268i
$643$			14.0000i			0.552106i	0.961142	+	0.276053i	$0.0890266\pi$
$643$			14.0000i			0.552106i	−0.961142	+	0.276053i	$0.910973\pi$
$644$	17.5000	−	6.06218i	0.689597	−	0.238883i
$645$		0			0
$646$	9.00000	−	15.5885i	0.354100	−	0.613320i
$647$	27.7128	−	16.0000i	1.08950	−	0.629025i	0.156059	−	0.987748i	$-0.450121\pi$
$647$	27.7128	−	16.0000i	1.08950	−	0.629025i	0.933444	+	0.358723i	$0.116788\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	28.0000	−	48.4974i	1.09910	−	1.90369i
$650$		0			0
$651$	2.50000	−	12.9904i	0.0979827	−	0.509133i
$652$			8.00000i			0.313304i
$653$	−13.8564	−	8.00000i	−0.542243	−	0.313064i	0.203744	−	0.979024i	$-0.434689\pi$
$653$	−13.8564	−	8.00000i	−0.542243	−	0.313064i	−0.745988	+	0.665960i	$0.768022\pi$
$654$	3.00000	+	5.19615i	0.117309	+	0.203186i
$655$		0			0
$656$	−3.50000	+	6.06218i	−0.136652	+	0.236688i
$657$		−	6.00000i		−	0.234082i
$658$	1.73205	−	2.00000i	0.0675224	−	0.0779681i
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	−0.995069	−	0.0991864i	$-0.968376\pi$
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	0.411636	−	0.911348i	$-0.364957\pi$
$662$	−29.4449	+	17.0000i	−1.14441	+	0.660724i
$663$	10.3923	+	6.00000i	0.403604	+	0.233021i
$664$	−4.00000			−0.155230
$665$		0			0
$666$	−2.00000			−0.0774984
$667$	24.2487	+	14.0000i	0.938914	+	0.542082i
$668$		0			0
$669$	−4.50000	−	7.79423i	−0.173980	−	0.301342i
$670$		0			0
$671$	−48.0000			−1.85302
$672$	−2.59808	−	0.500000i	−0.100223	−	0.0192879i
$673$		−	11.0000i		−	0.424019i	−0.977268	−	0.212009i	$-0.931999\pi$
$673$		−	11.0000i		−	0.424019i	0.977268	−	0.212009i	$-0.0680008\pi$
$674$	−1.50000	+	2.59808i	−0.0577778	+	0.100074i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	27.7128	+	16.0000i	1.06509	+	0.614930i	0.926836	−	0.375467i	$-0.122518\pi$
$677$	27.7128	+	16.0000i	1.06509	+	0.614930i	0.138254	+	0.990397i	$0.455851\pi$
$678$		−	3.00000i		−	0.115214i
$679$	−17.5000	+	6.06218i	−0.671588	+	0.232645i
$680$		0			0
$681$	−11.0000	+	19.0526i	−0.421521	+	0.730096i
$682$	17.3205	−	10.0000i	0.663237	−	0.382920i
$683$	19.0526	−	11.0000i	0.729026	−	0.420903i	−0.0890398	−	0.996028i	$-0.528380\pi$
$683$	19.0526	−	11.0000i	0.729026	−	0.420903i	0.818066	+	0.575125i	$0.195047\pi$
$684$	3.00000	−	5.19615i	0.114708	−	0.198680i
$685$		0			0
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$			8.00000i			0.305219i
$688$	−1.73205	−	1.00000i	−0.0660338	−	0.0381246i
$689$	−4.00000	−	6.92820i	−0.152388	−	0.263944i
$690$		0			0
$691$	12.0000	−	20.7846i	0.456502	−	0.790684i	−0.542272	−	0.840203i	$-0.682436\pi$
$691$	12.0000	−	20.7846i	0.456502	−	0.790684i	0.998773	+	0.0495194i	$0.0157690\pi$
$692$		−	6.00000i		−	0.228086i
$693$	3.46410	+	10.0000i	0.131590	+	0.379869i
$694$	32.0000			1.21470
$695$		0			0
$696$	−2.00000	−	3.46410i	−0.0758098	−	0.131306i
$697$	−18.1865	+	10.5000i	−0.688864	+	0.397716i
$698$	−15.5885	−	9.00000i	−0.590032	−	0.340655i
$699$	−6.00000			−0.226941
$700$		0			0
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$	3.46410	+	2.00000i	0.130744	+	0.0754851i
$703$	10.3923	−	6.00000i	0.391953	−	0.226294i
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$		0			0
$706$	15.0000			0.564532
$707$	−31.1769	+	36.0000i	−1.17253	+	1.35392i
$708$			14.0000i			0.526152i
$709$	7.00000	−	12.1244i	0.262891	−	0.455340i	−0.704118	−	0.710083i	$-0.748658\pi$
$709$	7.00000	−	12.1244i	0.262891	−	0.455340i	0.967009	+	0.254743i	$0.0819909\pi$
$710$		0			0
$711$	8.50000	+	14.7224i	0.318775	+	0.552134i
$712$	6.06218	+	3.50000i	0.227190	+	0.131168i
$713$		−	35.0000i		−	1.31076i
$714$	−6.00000	−	5.19615i	−0.224544	−	0.194461i
$715$		0			0
$716$	−1.00000	+	1.73205i	−0.0373718	+	0.0647298i
$717$	2.59808	−	1.50000i	0.0970269	−	0.0560185i
$718$	−3.46410	+	2.00000i	−0.129279	+	0.0746393i
$719$	−3.50000	+	6.06218i	−0.130528	+	0.226081i	−0.923880	−	0.382682i	$-0.875001\pi$
$719$	−3.50000	+	6.06218i	−0.130528	+	0.226081i	0.793352	+	0.608763i	$0.208334\pi$
$720$		0			0
$721$	−3.50000	+	18.1865i	−0.130347	+	0.677302i
$722$			17.0000i			0.632674i
$723$	−1.73205	−	1.00000i	−0.0644157	−	0.0371904i
$724$	6.00000	+	10.3923i	0.222988	+	0.386227i
$725$		0			0
$726$	−2.50000	+	4.33013i	−0.0927837	+	0.160706i
$727$			49.0000i			1.81731i	0.417548	+	0.908655i	$0.362889\pi$
$727$			49.0000i			1.81731i	−0.417548	+	0.908655i	$0.637111\pi$
$728$	3.46410	+	10.0000i	0.128388	+	0.370625i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−3.00000	−	5.19615i	−0.110959	−	0.192187i
$732$	10.3923	−	6.00000i	0.384111	−	0.221766i
$733$	8.66025	+	5.00000i	0.319874	+	0.184679i	0.651336	−	0.758789i	$-0.274209\pi$
$733$	8.66025	+	5.00000i	0.319874	+	0.184679i	−0.331463	+	0.943468i	$0.607542\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	−7.00000			−0.258023
$737$	−41.5692	−	24.0000i	−1.53122	−	0.884051i
$738$	−6.06218	+	3.50000i	−0.223152	+	0.128837i
$739$	7.00000	+	12.1244i	0.257499	+	0.446002i	0.965571	−	0.260138i	$-0.0837682\pi$
$739$	7.00000	+	12.1244i	0.257499	+	0.446002i	−0.708072	+	0.706140i	$0.750435\pi$
$740$		0			0
$741$	−24.0000			−0.881662
$742$	1.73205	+	5.00000i	0.0635856	+	0.183556i
$743$			1.00000i			0.0366864i	0.999832	+	0.0183432i	$0.00583916\pi$
$743$			1.00000i			0.0366864i	−0.999832	+	0.0183432i	$0.994161\pi$
$744$	−2.50000	+	4.33013i	−0.0916544	+	0.158750i
$745$		0			0
$746$	6.00000	+	10.3923i	0.219676	+	0.380489i
$747$	−3.46410	−	2.00000i	−0.126745	−	0.0731762i
$748$		−	12.0000i		−	0.438763i
$749$	−7.00000	+	36.3731i	−0.255774	+	1.32904i
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	−0.866025	+	0.500000i	−0.0315807	+	0.0182331i
$753$	−3.46410	+	2.00000i	−0.126239	+	0.0728841i
$754$	−8.00000	+	13.8564i	−0.291343	+	0.504621i
$755$		0			0
$756$	−2.00000	−	1.73205i	−0.0727393	−	0.0629941i
$757$			16.0000i			0.581530i	0.956795	+	0.290765i	$0.0939098\pi$
$757$			16.0000i			0.581530i	−0.956795	+	0.290765i	$0.906090\pi$
$758$	17.3205	+	10.0000i	0.629109	+	0.363216i
$759$	14.0000	+	24.2487i	0.508168	+	0.880172i
$760$		0			0
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	−0.610527	−	0.791995i	$-0.709042\pi$
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	0.991152	+	0.132734i	$0.0423756\pi$
$762$		−	16.0000i		−	0.579619i
$763$	−10.3923	+	12.0000i	−0.376227	+	0.434429i
$764$	−15.0000			−0.542681
$765$		0			0
$766$	−15.5000	−	26.8468i	−0.560038	−	0.970014i
$767$	48.4974	−	28.0000i	1.75114	−	1.01102i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$		0			0
$771$	2.00000			0.0720282
$772$	21.6506	+	12.5000i	0.779223	+	0.449885i
$773$	−15.5885	+	9.00000i	−0.560678	+	0.323708i	−0.753418	−	0.657542i	$-0.771596\pi$
$773$	−15.5885	+	9.00000i	−0.560678	+	0.323708i	0.192740	+	0.981250i	$0.438263\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$		0			0
$776$	7.00000			0.251285
$777$	−1.73205	−	5.00000i	−0.0621370	−	0.179374i
$778$		−	10.0000i		−	0.358517i
$779$	21.0000	−	36.3731i	0.752403	−	1.30320i
$780$		0			0
$781$	−18.0000	−	31.1769i	−0.644091	−	1.11560i
$782$	−18.1865	−	10.5000i	−0.650349	−	0.375479i
$783$		−	4.00000i		−	0.142948i
$784$	−1.00000	−	6.92820i	−0.0357143	−	0.247436i
$785$		0			0
$786$	4.00000	−	6.92820i	0.142675	−	0.247121i
$787$	−19.0526	+	11.0000i	−0.679150	+	0.392108i	−0.799535	−	0.600620i	$-0.794921\pi$
$787$	−19.0526	+	11.0000i	−0.679150	+	0.392108i	0.120384	+	0.992727i	$0.461587\pi$
$788$	17.3205	−	10.0000i	0.617018	−	0.356235i
$789$	13.5000	−	23.3827i	0.480613	−	0.832446i
$790$		0			0
$791$	7.50000	−	2.59808i	0.266669	−	0.0923770i
$792$		−	4.00000i		−	0.142134i
$793$	−41.5692	−	24.0000i	−1.47617	−	0.852265i
$794$	11.0000	+	19.0526i	0.390375	+	0.676150i
$795$		0			0
$796$	−7.50000	+	12.9904i	−0.265830	+	0.460432i
$797$			12.0000i			0.425062i	0.977154	+	0.212531i	$0.0681706\pi$
$797$			12.0000i			0.425062i	−0.977154	+	0.212531i	$0.931829\pi$
$798$	15.5885	+	3.00000i	0.551825	+	0.106199i
$799$	−3.00000			−0.106132
$800$		0			0
$801$	3.50000	+	6.06218i	0.123666	+	0.214197i
$802$	29.4449	−	17.0000i	1.03973	−	0.600291i
$803$	20.7846	+	12.0000i	0.733473	+	0.423471i
$804$	12.0000			0.423207
$805$		0			0
$806$	20.0000			0.704470
$807$	8.66025	+	5.00000i	0.304855	+	0.176008i
$808$	15.5885	−	9.00000i	0.548400	−	0.316619i
$809$	27.0000	+	46.7654i	0.949269	+	1.64418i	0.746968	+	0.664860i	$0.231509\pi$
$809$	27.0000	+	46.7654i	0.949269	+	1.64418i	0.202301	+	0.979323i	$0.435158\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	6.92820	−	8.00000i	0.243132	−	0.280745i
$813$		−	5.00000i		−	0.175358i
$814$	4.00000	−	6.92820i	0.140200	−	0.242833i
$815$		0			0
$816$	1.50000	+	2.59808i	0.0525105	+	0.0909509i
$817$	10.3923	+	6.00000i	0.363581	+	0.209913i
$818$		−	29.0000i		−	1.01396i
$819$	−2.00000	+	10.3923i	−0.0698857	+	0.363137i
$820$		0			0
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$	−12.9904	+	7.50000i	−0.453092	+	0.261593i
$823$	−20.7846	+	12.0000i	−0.724506	+	0.418294i	−0.816409	−	0.577474i	$-0.804038\pi$
$823$	−20.7846	+	12.0000i	−0.724506	+	0.418294i	0.0919029	+	0.995768i	$0.470705\pi$
$824$	3.50000	−	6.06218i	0.121928	−	0.211186i
$825$		0			0
$826$	−35.0000	+	12.1244i	−1.21781	+	0.421860i
$827$		−	20.0000i		−	0.695468i	−0.937593	−	0.347734i	$-0.886951\pi$
$827$		−	20.0000i		−	0.695468i	0.937593	−	0.347734i	$-0.113049\pi$
$828$	−6.06218	−	3.50000i	−0.210675	−	0.121633i
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	−0.980642	−	0.195810i	$-0.937266\pi$
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	0.320745	−	0.947166i	$-0.396067\pi$
$830$		0			0
$831$	−8.00000	+	13.8564i	−0.277517	+	0.480673i
$832$		−	4.00000i		−	0.138675i
$833$	7.79423	−	19.5000i	0.270054	−	0.675635i
$834$	−2.00000			−0.0692543
$835$		0			0
$836$	12.0000	+	20.7846i	0.415029	+	0.718851i
$837$	−4.33013	+	2.50000i	−0.149671	+	0.0864126i
$838$	−22.5167	−	13.0000i	−0.777825	−	0.449078i
$839$	25.0000			0.863096			0.431548	−	0.902090i	$-0.357968\pi$
$839$	25.0000			0.863096			0.431548	+	0.902090i	$0.357968\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−13.8564	−	8.00000i	−0.477523	−	0.275698i
$843$	−14.7224	+	8.50000i	−0.507067	+	0.292756i
$844$	−11.0000	−	19.0526i	−0.378636	−	0.655816i
$845$		0			0
$846$	−1.00000			−0.0343807
$847$	−12.9904	−	2.50000i	−0.446355	−	0.0859010i
$848$		−	2.00000i		−	0.0686803i
$849$	4.00000	−	6.92820i	0.137280	−	0.237775i
$850$		0			0
$851$	−7.00000	−	12.1244i	−0.239957	−	0.415618i
$852$	7.79423	+	4.50000i	0.267026	+	0.154167i
$853$		−	2.00000i		−	0.0684787i	−0.999414	−	0.0342393i	$-0.989099\pi$
$853$		−	2.00000i		−	0.0684787i	0.999414	−	0.0342393i	$-0.0109009\pi$
$854$	24.0000	+	20.7846i	0.821263	+	0.711235i
$855$		0			0
$856$	7.00000	−	12.1244i	0.239255	−	0.414402i
$857$	22.5167	−	13.0000i	0.769154	−	0.444072i	−0.0634184	−	0.997987i	$-0.520200\pi$
$857$	22.5167	−	13.0000i	0.769154	−	0.444072i	0.832573	+	0.553915i	$0.186867\pi$
$858$	−13.8564	+	8.00000i	−0.473050	+	0.273115i
$859$	12.0000	−	20.7846i	0.409435	−	0.709162i	−0.585392	−	0.810751i	$-0.699059\pi$
$859$	12.0000	−	20.7846i	0.409435	−	0.709162i	0.994826	+	0.101589i	$0.0323926\pi$
$860$		0			0
$861$	−14.0000	−	12.1244i	−0.477119	−	0.413197i
$862$		−	39.0000i		−	1.32835i
$863$	9.52628	+	5.50000i	0.324278	+	0.187222i	0.653298	−	0.757101i	$-0.273385\pi$
$863$	9.52628	+	5.50000i	0.324278	+	0.187222i	−0.329020	+	0.944323i	$0.606718\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	18.5000	−	32.0429i	0.628656	−	1.08886i
$867$		−	8.00000i		−	0.271694i
$868$	−12.9904	−	2.50000i	−0.440922	−	0.0848555i
$869$	−68.0000			−2.30674
$870$		0			0
$871$	−24.0000	−	41.5692i	−0.813209	−	1.40852i
$872$	5.19615	−	3.00000i	0.175964	−	0.101593i
$873$	6.06218	+	3.50000i	0.205174	+	0.118457i
$874$	42.0000			1.42067
$875$		0			0
$876$	−6.00000			−0.202721
$877$	32.9090	+	19.0000i	1.11126	+	0.641584i	0.939155	−	0.343495i	$-0.111611\pi$
$877$	32.9090	+	19.0000i	1.11126	+	0.641584i	0.172102	+	0.985079i	$0.444944\pi$
$878$	−14.7224	+	8.50000i	−0.496858	+	0.286861i
$879$	6.00000	+	10.3923i	0.202375	+	0.350524i
$880$		0			0
$881$	−35.0000			−1.17918			−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000			−1.17918			−0.589590	+	0.807703i	$0.700711\pi$
$882$	2.59808	−	6.50000i	0.0874818	−	0.218866i
$883$			6.00000i			0.201916i	0.994891	+	0.100958i	$0.0321908\pi$
$883$			6.00000i			0.201916i	−0.994891	+	0.100958i	$0.967809\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$	−13.0000	−	22.5167i	−0.436744	−	0.756462i
$887$	48.4974	+	28.0000i	1.62838	+	0.940148i	0.984575	+	0.174962i	$0.0559801\pi$
$887$	48.4974	+	28.0000i	1.62838	+	0.940148i	0.643809	+	0.765186i	$0.277353\pi$
$888$			2.00000i			0.0671156i
$889$	40.0000	−	13.8564i	1.34156	−	0.464729i
$890$		0			0
$891$	2.00000	−	3.46410i	0.0670025	−	0.116052i
$892$	−7.79423	+	4.50000i	−0.260970	+	0.150671i
$893$	5.19615	−	3.00000i	0.173883	−	0.100391i
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$		0			0
$896$	−0.500000	+	2.59808i	−0.0167038	+	0.0867956i
$897$			28.0000i			0.934893i
$898$	−11.2583	−	6.50000i	−0.375695	−	0.216908i
$899$	−10.0000	−	17.3205i	−0.333519	−	0.577671i
$900$		0			0
$901$	3.00000	−	5.19615i	0.0999445	−	0.173109i
$902$		−	28.0000i		−	0.932298i
$903$	3.46410	−	4.00000i	0.115278	−	0.133112i
$904$	−3.00000			−0.0997785
$905$		0			0
$906$	−12.0000	−	20.7846i	−0.398673	−	0.690522i
$907$	24.2487	−	14.0000i	0.805165	−	0.464862i	−0.0401089	−	0.999195i	$-0.512770\pi$
$907$	24.2487	−	14.0000i	0.805165	−	0.464862i	0.845274	+	0.534333i	$0.179437\pi$
$908$	19.0526	+	11.0000i	0.632281	+	0.365048i
$909$	18.0000			0.597022
$910$		0			0
$911$	19.0000			0.629498			0.314749	−	0.949175i	$-0.398080\pi$
$911$	19.0000			0.629498			0.314749	+	0.949175i	$0.398080\pi$
$912$	−5.19615	−	3.00000i	−0.172062	−	0.0993399i
$913$	13.8564	−	8.00000i	0.458580	−	0.264761i
$914$	−9.00000	−	15.5885i	−0.297694	−	0.515620i
$915$		0			0
$916$	8.00000			0.264327
$917$	20.7846	+	4.00000i	0.686368	+	0.132092i
$918$			3.00000i			0.0990148i
$919$	−19.5000	+	33.7750i	−0.643246	+	1.11413i	0.341458	+	0.939897i	$0.389079\pi$
$919$	−19.5000	+	33.7750i	−0.643246	+	1.11413i	−0.984704	+	0.174237i	$0.944254\pi$
$920$		0			0
$921$	10.0000	+	17.3205i	0.329511	+	0.570730i
$922$	−31.1769	−	18.0000i	−1.02676	−	0.592798i
$923$		−	36.0000i		−	1.18495i
$924$	10.0000	−	3.46410i	0.328976	−	0.113961i
$925$		0			0
$926$	−3.50000	+	6.06218i	−0.115017	+	0.199216i
$927$	6.06218	−	3.50000i	0.199108	−	0.114955i
$928$	−3.46410	+	2.00000i	−0.113715	+	0.0656532i
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$		0			0
$931$	6.00000	+	41.5692i	0.196642	+	1.36238i
$932$			6.00000i			0.196537i
$933$	18.1865	+	10.5000i	0.595400	+	0.343755i
$934$		0			0
$935$		0			0
$936$	2.00000	−	3.46410i	0.0653720	−	0.113228i
$937$			6.00000i			0.196011i	0.995186	+	0.0980057i	$0.0312463\pi$
$937$			6.00000i			0.196011i	−0.995186	+	0.0980057i	$0.968754\pi$
$938$	10.3923	+	30.0000i	0.339321	+	0.979535i
$939$	−27.0000			−0.881112
$940$		0			0
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	−0.973568	−	0.228395i	$-0.926652\pi$
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	0.288988	−	0.957333i	$-0.406681\pi$
$942$	3.46410	−	2.00000i	0.112867	−	0.0651635i
$943$	−42.4352	−	24.5000i	−1.38188	−	0.797830i
$944$	14.0000			0.455661
$945$		0			0
$946$	8.00000			0.260102
$947$	−27.7128	−	16.0000i	−0.900545	−	0.519930i	−0.0231683	−	0.999732i	$-0.507375\pi$
$947$	−27.7128	−	16.0000i	−0.900545	−	0.519930i	−0.877377	+	0.479801i	$0.840709\pi$
$948$	14.7224	−	8.50000i	0.478162	−	0.276067i
$949$	12.0000	+	20.7846i	0.389536	+	0.674697i
$950$		0			0
$951$	−18.0000			−0.583690
$952$	−5.19615	+	6.00000i	−0.168408	+	0.194461i
$953$		−	26.0000i		−	0.842223i	−0.907009	−	0.421111i	$-0.861640\pi$
$953$		−	26.0000i		−	0.842223i	0.907009	−	0.421111i	$-0.138360\pi$
$954$	1.00000	−	1.73205i	0.0323762	−	0.0560772i
$955$		0			0
$956$	−1.50000	−	2.59808i	−0.0485135	−	0.0840278i
$957$	13.8564	+	8.00000i	0.447914	+	0.258603i
$958$		−	1.00000i		−	0.0323085i
$959$	−30.0000	−	25.9808i	−0.968751	−	0.838963i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	6.92820	−	4.00000i	0.223374	−	0.128965i
$963$	12.1244	−	7.00000i	0.390702	−	0.225572i
$964$	−1.00000	+	1.73205i	−0.0322078	+	0.0557856i
$965$		0			0
$966$	3.50000	−	18.1865i	0.112611	−	0.585142i
$967$			29.0000i			0.932577i	0.884633	+	0.466289i	$0.154409\pi$
$967$			29.0000i			0.932577i	−0.884633	+	0.466289i	$0.845591\pi$
$968$	4.33013	+	2.50000i	0.139176	+	0.0803530i
$969$	−9.00000	−	15.5885i	−0.289122	−	0.500773i
$970$		0			0
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$			1.00000i			0.0320750i
$973$	−1.73205	−	5.00000i	−0.0555270	−	0.160293i
$974$	5.00000			0.160210
$975$		0			0
$976$	−6.00000	−	10.3923i	−0.192055	−	0.332650i
$977$	−2.59808	+	1.50000i	−0.0831198	+	0.0479893i	−0.540984	−	0.841033i	$-0.681948\pi$
$977$	−2.59808	+	1.50000i	−0.0831198	+	0.0479893i	0.457864	+	0.889022i	$0.348615\pi$
$978$	6.92820	+	4.00000i	0.221540	+	0.127906i
$979$	−28.0000			−0.894884
$980$		0			0
$981$	6.00000			0.191565
$982$	−32.9090	−	19.0000i	−1.05017	−	0.606314i
$983$	24.2487	−	14.0000i	0.773414	−	0.446531i	−0.0606773	−	0.998157i	$-0.519326\pi$
$983$	24.2487	−	14.0000i	0.773414	−	0.446531i	0.834091	+	0.551627i	$0.185993\pi$
$984$	3.50000	+	6.06218i	0.111576	+	0.193255i
$985$		0			0
$986$	−12.0000			−0.382158
$987$	−0.866025	−	2.50000i	−0.0275659	−	0.0795759i
$988$			24.0000i			0.763542i
$989$	7.00000	−	12.1244i	0.222587	−	0.385532i
$990$		0			0
$991$	−3.50000	−	6.06218i	−0.111181	−	0.192571i	0.805066	−	0.593186i	$-0.202130\pi$
$991$	−3.50000	−	6.06218i	−0.111181	−	0.192571i	−0.916247	+	0.400614i	$0.868797\pi$
$992$	4.33013	+	2.50000i	0.137482	+	0.0793751i
$993$			34.0000i			1.07896i
$994$	−4.50000	+	23.3827i	−0.142731	+	0.741654i
$995$		0			0
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	13.8564	−	8.00000i	0.438837	−	0.253363i	−0.264267	−	0.964449i	$-0.585130\pi$
$997$	13.8564	−	8.00000i	0.438837	−	0.253363i	0.703104	+	0.711087i	$0.251797\pi$
$998$	−24.2487	+	14.0000i	−0.767580	+	0.443162i
$999$	−1.00000	+	1.73205i	−0.0316386	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.o.l.499.1		4
5.2	odd	4		1050.2.i.r.751.1	yes	2
5.3	odd	4		1050.2.i.d.751.1	yes	2
5.4	even	2	inner	1050.2.o.l.499.2		4
7.4	even	3	inner	1050.2.o.l.949.2		4
35.2	odd	12		7350.2.a.e.1.1		1
35.4	even	6	inner	1050.2.o.l.949.1		4
35.12	even	12		7350.2.a.v.1.1		1
35.18	odd	12		1050.2.i.d.151.1	✓	2
35.23	odd	12		7350.2.a.ci.1.1		1
35.32	odd	12		1050.2.i.r.151.1	yes	2
35.33	even	12		7350.2.a.bs.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.d.151.1	✓	2	35.18	odd	12
1050.2.i.d.751.1	yes	2	5.3	odd	4
1050.2.i.r.151.1	yes	2	35.32	odd	12
1050.2.i.r.751.1	yes	2	5.2	odd	4
1050.2.o.l.499.1		4	1.1	even	1	trivial
1050.2.o.l.499.2		4	5.4	even	2	inner
1050.2.o.l.949.1		4	35.4	even	6	inner
1050.2.o.l.949.2		4	7.4	even	3	inner
7350.2.a.e.1.1		1	35.2	odd	12
7350.2.a.v.1.1		1	35.12	even	12
7350.2.a.bs.1.1		1	35.33	even	12
7350.2.a.ci.1.1		1	35.23	odd	12

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(0.866025 + 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(0.866025 + 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} +(-0.866025 - 0.500000i) q^{12} +4.00000i q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.59808 + 1.50000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(3.00000 - 5.19615i) q^{19} +(-2.00000 - 1.73205i) q^{21} -4.00000i q^{22} +(-6.06218 - 3.50000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(-1.73205 + 2.00000i) q^{28} -4.00000 q^{29} +(2.50000 + 4.33013i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.46410 - 2.00000i) q^{33} +3.00000 q^{34} +1.00000 q^{36} +(1.73205 + 1.00000i) q^{37} +(-5.19615 + 3.00000i) q^{38} +(-2.00000 - 3.46410i) q^{39} +7.00000 q^{41} +(0.866025 + 2.50000i) q^{42} +2.00000i q^{43} +(-2.00000 + 3.46410i) q^{44} +(3.50000 + 6.06218i) q^{46} +(0.866025 + 0.500000i) q^{47} -1.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(1.50000 - 2.59808i) q^{51} +(-3.46410 + 2.00000i) q^{52} +(-1.73205 + 1.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.50000 - 0.866025i) q^{56} +6.00000i q^{57} +(3.46410 + 2.00000i) q^{58} +(-7.00000 - 12.1244i) q^{59} +(-6.00000 + 10.3923i) q^{61} -5.00000i q^{62} +(2.59808 + 0.500000i) q^{63} -1.00000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-10.3923 + 6.00000i) q^{67} +(-2.59808 - 1.50000i) q^{68} +7.00000 q^{69} -9.00000 q^{71} +(-0.866025 - 0.500000i) q^{72} +(5.19615 - 3.00000i) q^{73} +(-1.00000 - 1.73205i) q^{74} +6.00000 q^{76} +(-6.92820 + 8.00000i) q^{77} +4.00000i q^{78} +(-8.50000 + 14.7224i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.06218 - 3.50000i) q^{82} -4.00000i q^{83} +(0.500000 - 2.59808i) q^{84} +(1.00000 - 1.73205i) q^{86} +(3.46410 - 2.00000i) q^{87} +(3.46410 - 2.00000i) q^{88} +(-3.50000 + 6.06218i) q^{89} +(-10.0000 + 3.46410i) q^{91} -7.00000i q^{92} +(-4.33013 - 2.50000i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-0.500000 + 0.866025i) q^{96} +7.00000i q^{97} +(6.92820 - 1.00000i) q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} + 2 q^{14} - 2 q^{16} + 12 q^{19} - 8 q^{21} + 2 q^{24} + 8 q^{26} - 16 q^{29} + 10 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} + 28 q^{41} - 8 q^{44} + 14 q^{46} - 22 q^{49} + 6 q^{51} + 2 q^{54} + 10 q^{56} - 28 q^{59} - 24 q^{61} - 4 q^{64} + 8 q^{66} + 28 q^{69} - 36 q^{71} - 4 q^{74} + 24 q^{76} - 34 q^{79} - 2 q^{81} + 2 q^{84} + 4 q^{86} - 14 q^{89} - 40 q^{91} - 2 q^{94} - 2 q^{96} + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9 + 8 * q^11 + 2 * q^14 - 2 * q^16 + 12 * q^19 - 8 * q^21 + 2 * q^24 + 8 * q^26 - 16 * q^29 + 10 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 + 28 * q^41 - 8 * q^44 + 14 * q^46 - 22 * q^49 + 6 * q^51 + 2 * q^54 + 10 * q^56 - 28 * q^59 - 24 * q^61 - 4 * q^64 + 8 * q^66 + 28 * q^69 - 36 * q^71 - 4 * q^74 + 24 * q^76 - 34 * q^79 - 2 * q^81 + 2 * q^84 + 4 * q^86 - 14 * q^89 - 40 * q^91 - 2 * q^94 - 2 * q^96 + 16 * q^99

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