LMFDB - Embedded newform 882.2.f.f.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (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:	$7.04280545828$
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:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.295
Dual form			882.2.f.f.589.1

$q$-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} +(1.00000 + 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +2.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +1.73205i q^{12} +(-3.00000 - 5.19615i) q^{13} -3.46410i q^{15} +(-0.500000 + 0.866025i) q^{16} +5.00000 q^{17} +3.00000 q^{18} +7.00000 q^{19} +(1.00000 - 1.73205i) q^{20} +(0.500000 + 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(1.50000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} -6.00000 q^{26} -5.19615i q^{27} +(2.00000 - 3.46410i) q^{29} +(-3.00000 - 1.73205i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 0.866025i) q^{33} +(2.50000 - 4.33013i) q^{34} +(1.50000 - 2.59808i) q^{36} +2.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +10.3923i q^{39} +(-1.00000 - 1.73205i) q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +1.00000 q^{44} +(-3.00000 + 5.19615i) q^{45} -4.00000 q^{46} +(1.50000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{50} +(-7.50000 - 4.33013i) q^{51} +(-3.00000 + 5.19615i) q^{52} +12.0000 q^{53} +(-4.50000 - 2.59808i) q^{54} -2.00000 q^{55} +(-10.5000 - 6.06218i) q^{57} +(-2.00000 - 3.46410i) q^{58} +(-3.50000 - 6.06218i) q^{59} +(-3.00000 + 1.73205i) q^{60} +(-6.00000 + 10.3923i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} -1.73205i q^{66} +(-6.50000 - 11.2583i) q^{67} +(-2.50000 - 4.33013i) q^{68} +6.92820i q^{69} -8.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} -1.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-3.50000 - 6.06218i) q^{76} +(9.00000 + 5.19615i) q^{78} +(3.00000 - 5.19615i) q^{79} -2.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +3.00000 q^{82} +(8.00000 - 13.8564i) q^{83} +(5.00000 + 8.66025i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(-6.00000 + 3.46410i) q^{87} +(0.500000 - 0.866025i) q^{88} +6.00000 q^{89} +(3.00000 + 5.19615i) q^{90} +(-2.00000 + 3.46410i) q^{92} +10.3923i q^{93} +(7.00000 + 12.1244i) q^{95} -1.73205i q^{96} +(-2.50000 + 4.33013i) q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} - q^{4} + 2 q^{5} - 3 q^{6} - 2 q^{8} + 3 q^{9} + 4 q^{10} - q^{11} - 6 q^{13} - q^{16} + 10 q^{17} + 6 q^{18} + 14 q^{19} + 2 q^{20} + q^{22} - 4 q^{23} + 3 q^{24} + q^{25}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 - q^4 + 2 * q^5 - 3 * q^6 - 2 * q^8 + 3 * q^9 + 4 * q^10 - q^11 - 6 * q^13 - q^16 + 10 * q^17 + 6 * q^18 + 14 * q^19 + 2 * q^20 + q^22 - 4 * q^23 + 3 * q^24 + q^25 - 12 * q^26 + 4 * q^29 - 6 * q^30 - 6 * q^31 + q^32 + 3 * q^33 + 5 * q^34 + 3 * q^36 + 4 * q^37 + 7 * q^38 - 2 * q^40 + 3 * q^41 + q^43 + 2 * q^44 - 6 * q^45 - 8 * q^46 + 3 * q^48 - q^50 - 15 * q^51 - 6 * q^52 + 24 * q^53 - 9 * q^54 - 4 * q^55 - 21 * q^57 - 4 * q^58 - 7 * q^59 - 6 * q^60 - 12 * q^61 - 12 * q^62 + 2 * q^64 + 12 * q^65 - 13 * q^67 - 5 * q^68 - 16 * q^71 - 3 * q^72 - 2 * q^73 + 2 * q^74 - 3 * q^75 - 7 * q^76 + 18 * q^78 + 6 * q^79 - 4 * q^80 - 9 * q^81 + 6 * q^82 + 16 * q^83 + 10 * q^85 - q^86 - 12 * q^87 + q^88 + 12 * q^89 + 6 * q^90 - 4 * q^92 + 14 * q^95 - 5 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	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
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	2.00000			0.632456
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$			1.73205i			0.500000i
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$		0			0
$15$		−	3.46410i		−	0.894427i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.00000			1.21268			0.606339	−	0.795206i	$-0.292637\pi$
$17$	5.00000			1.21268			0.606339	+	0.795206i	$0.292637\pi$
$18$	3.00000			0.707107
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$		0			0
$22$	0.500000	+	0.866025i	0.106600	+	0.184637i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−6.00000			−1.17670
$27$		−	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	$0.0455477\pi$
$30$	−3.00000	−	1.73205i	−0.547723	−	0.316228i
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.50000	−	0.866025i	0.261116	−	0.150756i
$34$	2.50000	−	4.33013i	0.428746	−	0.742611i
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	3.50000	−	6.06218i	0.567775	−	0.983415i
$39$			10.3923i			1.66410i
$40$	−1.00000	−	1.73205i	−0.158114	−	0.273861i
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		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	$0.142372\pi$
$44$	1.00000			0.150756
$45$	−3.00000	+	5.19615i	−0.447214	+	0.774597i
$46$	−4.00000			−0.589768
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$		0			0
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−7.50000	−	4.33013i	−1.05021	−	0.606339i
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$	12.0000			1.64833			0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000			1.64833			0.824163	+	0.566352i	$0.191646\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	−2.00000			−0.269680
$56$		0			0
$57$	−10.5000	−	6.06218i	−1.39076	−	0.802955i
$58$	−2.00000	−	3.46410i	−0.262613	−	0.454859i
$59$	−3.50000	−	6.06218i	−0.455661	−	0.789228i	0.543065	−	0.839691i	$-0.317264\pi$
$59$	−3.50000	−	6.06218i	−0.455661	−	0.789228i	−0.998726	+	0.0504625i	$0.983930\pi$
$60$	−3.00000	+	1.73205i	−0.387298	+	0.223607i
$61$	−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	$0.887809\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	6.00000	−	10.3923i	0.744208	−	1.28901i
$66$		−	1.73205i		−	0.213201i
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	−0.923408	−	0.383819i	$-0.874609\pi$
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	0.129307	−	0.991605i	$-0.458725\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$			6.92820i			0.834058i
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	−1.50000	+	0.866025i	−0.173205	+	0.100000i
$76$	−3.50000	−	6.06218i	−0.401478	−	0.695379i
$77$		0			0
$78$	9.00000	+	5.19615i	1.01905	+	0.588348i
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$	−2.00000			−0.223607
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	3.00000			0.331295
$83$	8.00000	−	13.8564i	0.878114	−	1.52094i	0.0247060	−	0.999695i	$-0.492135\pi$
$83$	8.00000	−	13.8564i	0.878114	−	1.52094i	0.853408	−	0.521243i	$-0.174532\pi$
$84$		0			0
$85$	5.00000	+	8.66025i	0.542326	+	0.939336i
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$	−6.00000	+	3.46410i	−0.643268	+	0.371391i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	3.00000	+	5.19615i	0.316228	+	0.547723i
$91$		0			0
$92$	−2.00000	+	3.46410i	−0.208514	+	0.361158i
$93$			10.3923i			1.07763i
$94$		0			0
$95$	7.00000	+	12.1244i	0.718185	+	1.24393i
$96$		−	1.73205i		−	0.176777i
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$	−1.00000			−0.100000
$101$	−2.00000	+	3.46410i	−0.199007	+	0.344691i	−0.948207	−	0.317653i	$-0.897105\pi$
$101$	−2.00000	+	3.46410i	−0.199007	+	0.344691i	0.749199	+	0.662344i	$0.230438\pi$
$102$	−7.50000	+	4.33013i	−0.742611	+	0.428746i
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	−0.282194	+	0.959357i	$0.591062\pi$
$104$	3.00000	+	5.19615i	0.294174	+	0.509525i
$105$		0			0
$106$	6.00000	−	10.3923i	0.582772	−	1.00939i
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$	−3.00000	−	1.73205i	−0.284747	−	0.164399i
$112$		0			0
$113$	5.00000	+	8.66025i	0.470360	+	0.814688i	0.999425	−	0.0338931i	$-0.0107906\pi$
$113$	5.00000	+	8.66025i	0.470360	+	0.814688i	−0.529065	+	0.848581i	$0.677457\pi$
$114$	−10.5000	+	6.06218i	−0.983415	+	0.567775i
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$	−4.00000			−0.371391
$117$	9.00000	−	15.5885i	0.832050	−	1.44115i
$118$	−7.00000			−0.644402
$119$		0			0
$120$			3.46410i			0.316228i
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	6.00000	+	10.3923i	0.543214	+	0.940875i
$123$		−	5.19615i		−	0.468521i
$124$	−3.00000	+	5.19615i	−0.269408	+	0.466628i
$125$	12.0000			1.07331
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.50000	+	0.866025i	−0.132068	+	0.0762493i
$130$	−6.00000	−	10.3923i	−0.526235	−	0.911465i
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	0.765331	−	0.643637i	$-0.222575\pi$
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	−0.940072	+	0.340977i	$0.889242\pi$
$132$	−1.50000	−	0.866025i	−0.130558	−	0.0753778i
$133$		0			0
$134$	−13.0000			−1.12303
$135$	9.00000	−	5.19615i	0.774597	−	0.447214i
$136$	−5.00000			−0.428746
$137$	9.50000	−	16.4545i	0.811640	−	1.40580i	−0.100076	−	0.994980i	$-0.531909\pi$
$137$	9.50000	−	16.4545i	0.811640	−	1.40580i	0.911716	−	0.410822i	$-0.134758\pi$
$138$	6.00000	+	3.46410i	0.510754	+	0.294884i
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$		0			0
$142$	−4.00000	+	6.92820i	−0.335673	+	0.581402i
$143$	6.00000			0.501745
$144$	−3.00000			−0.250000
$145$	8.00000			0.664364
$146$	−0.500000	+	0.866025i	−0.0413803	+	0.0716728i
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	12.0000	+	20.7846i	0.983078	+	1.70274i	0.650183	+	0.759778i	$0.274692\pi$
$149$	12.0000	+	20.7846i	0.983078	+	1.70274i	0.332896	+	0.942964i	$0.391974\pi$
$150$			1.73205i			0.141421i
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$	−7.00000			−0.567775
$153$	7.50000	+	12.9904i	0.606339	+	1.05021i
$154$		0			0
$155$	6.00000	−	10.3923i	0.481932	−	0.834730i
$156$	9.00000	−	5.19615i	0.720577	−	0.416025i
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	0.903167	−	0.429289i	$-0.141236\pi$
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	−0.823359	+	0.567521i	$0.807902\pi$
$158$	−3.00000	−	5.19615i	−0.238667	−	0.413384i
$159$	−18.0000	−	10.3923i	−1.42749	−	0.824163i
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$		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	$0.550070\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$	3.00000	+	1.73205i	0.233550	+	0.134840i
$166$	−8.00000	−	13.8564i	−0.620920	−	1.07547i
$167$	10.0000	+	17.3205i	0.773823	+	1.34030i	0.935454	+	0.353450i	$0.114991\pi$
$167$	10.0000	+	17.3205i	0.773823	+	1.34030i	−0.161630	+	0.986851i	$0.551675\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	10.0000			0.766965
$171$	10.5000	+	18.1865i	0.802955	+	1.39076i
$172$	−1.00000			−0.0762493
$173$	1.00000	−	1.73205i	0.0760286	−	0.131685i	−0.825505	−	0.564396i	$-0.809109\pi$
$173$	1.00000	−	1.73205i	0.0760286	−	0.131685i	0.901533	+	0.432710i	$0.142443\pi$
$174$			6.92820i			0.525226i
$175$		0			0
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$			12.1244i			0.911322i
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$	6.00000			0.447214
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	18.0000	−	10.3923i	1.33060	−	0.768221i
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	9.00000	+	5.19615i	0.659912	+	0.381000i
$187$	−2.50000	+	4.33013i	−0.182818	+	0.316650i
$188$		0			0
$189$		0			0
$190$	14.0000			1.01567
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	−0.990930	−	0.134382i	$-0.957095\pi$
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	0.379086	−	0.925361i	$-0.376238\pi$
$194$	2.50000	+	4.33013i	0.179490	+	0.310885i
$195$	−18.0000	+	10.3923i	−1.28901	+	0.744208i
$196$		0			0
$197$	10.0000			0.712470			0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000			0.712470			0.356235	+	0.934396i	$0.384060\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$			22.5167i			1.58820i
$202$	2.00000	+	3.46410i	0.140720	+	0.243733i
$203$		0			0
$204$			8.66025i			0.606339i
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$	14.0000			0.975426
$207$	6.00000	−	10.3923i	0.417029	−	0.722315i
$208$	6.00000			0.416025
$209$	−3.50000	+	6.06218i	−0.242100	+	0.419330i
$210$		0			0
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$	12.0000	+	6.92820i	0.822226	+	0.474713i
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$	2.00000			0.136399
$216$			5.19615i			0.353553i
$217$		0			0
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$	1.50000	+	0.866025i	0.101361	+	0.0585206i
$220$	1.00000	+	1.73205i	0.0674200	+	0.116775i
$221$	−15.0000	−	25.9808i	−1.00901	−	1.74766i
$222$	−3.00000	+	1.73205i	−0.201347	+	0.116248i
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$	10.0000			0.665190
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$			12.1244i			0.802955i
$229$	−13.0000	−	22.5167i	−0.859064	−	1.48794i	−0.872823	−	0.488037i	$-0.837713\pi$
$229$	−13.0000	−	22.5167i	−0.859064	−	1.48794i	0.0137585	−	0.999905i	$-0.495620\pi$
$230$	−4.00000	−	6.92820i	−0.263752	−	0.456832i
$231$		0			0
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	−29.0000			−1.89985			−0.949927	−	0.312473i	$-0.898843\pi$
$233$	−29.0000			−1.89985			−0.949927	+	0.312473i	$0.898843\pi$
$234$	−9.00000	−	15.5885i	−0.588348	−	1.01905i
$235$		0			0
$236$	−3.50000	+	6.06218i	−0.227831	+	0.394614i
$237$	−9.00000	+	5.19615i	−0.584613	+	0.337526i
$238$		0			0
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$	3.00000	+	1.73205i	0.193649	+	0.111803i
$241$	11.5000	−	19.9186i	0.740780	−	1.28307i	−0.211360	−	0.977408i	$-0.567789\pi$
$241$	11.5000	−	19.9186i	0.740780	−	1.28307i	0.952141	−	0.305661i	$-0.0988773\pi$
$242$	10.0000			0.642824
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	12.0000			0.768221
$245$		0			0
$246$	−4.50000	−	2.59808i	−0.286910	−	0.165647i
$247$	−21.0000	−	36.3731i	−1.33620	−	2.31436i
$248$	3.00000	+	5.19615i	0.190500	+	0.329956i
$249$	−24.0000	+	13.8564i	−1.52094	+	0.878114i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$	−6.00000	+	10.3923i	−0.376473	+	0.652071i
$255$		−	17.3205i		−	1.08465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$			1.73205i			0.107833i
$259$		0			0
$260$	−12.0000			−0.744208
$261$	12.0000			0.742781
$262$	−4.00000			−0.247121
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$	−1.50000	+	0.866025i	−0.0923186	+	0.0533002i
$265$	12.0000	+	20.7846i	0.737154	+	1.27679i
$266$		0			0
$267$	−9.00000	−	5.19615i	−0.550791	−	0.317999i
$268$	−6.50000	+	11.2583i	−0.397051	+	0.687712i
$269$	−20.0000			−1.21942			−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−20.0000			−1.21942			−0.609711	+	0.792624i	$0.708714\pi$
$270$		−	10.3923i		−	0.632456i
$271$	6.00000			0.364474			0.182237	−	0.983255i	$-0.441666\pi$
$271$	6.00000			0.364474			0.182237	+	0.983255i	$0.441666\pi$
$272$	−2.50000	+	4.33013i	−0.151585	+	0.262553i
$273$		0			0
$274$	−9.50000	−	16.4545i	−0.573916	−	0.994052i
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	6.00000	−	3.46410i	0.361158	−	0.208514i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	−5.00000			−0.299880
$279$	9.00000	−	15.5885i	0.538816	−	0.933257i
$280$		0			0
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	0.325385	+	0.945582i	$0.394506\pi$
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	−0.981590	+	0.190999i	$0.938827\pi$
$282$		0			0
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	4.00000	+	6.92820i	0.237356	+	0.411113i
$285$		−	24.2487i		−	1.43637i
$286$	3.00000	−	5.19615i	0.177394	−	0.307255i
$287$		0			0
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	8.00000			0.470588
$290$	4.00000	−	6.92820i	0.234888	−	0.406838i
$291$	7.50000	−	4.33013i	0.439658	−	0.253837i
$292$	0.500000	+	0.866025i	0.0292603	+	0.0506803i
$293$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$293$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$294$		0			0
$295$	7.00000	−	12.1244i	0.407556	−	0.705907i
$296$	−2.00000			−0.116248
$297$	4.50000	+	2.59808i	0.261116	+	0.150756i
$298$	24.0000			1.39028
$299$	−12.0000	+	20.7846i	−0.693978	+	1.20201i
$300$	1.50000	+	0.866025i	0.0866025	+	0.0500000i
$301$		0			0
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$	6.00000	−	3.46410i	0.344691	−	0.199007i
$304$	−3.50000	+	6.06218i	−0.200739	+	0.347690i
$305$	−24.0000			−1.37424
$306$	15.0000			0.857493
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$		−	24.2487i		−	1.37946i
$310$	−6.00000	−	10.3923i	−0.340777	−	0.590243i
$311$	1.00000	+	1.73205i	0.0567048	+	0.0982156i	0.892984	−	0.450088i	$-0.148607\pi$
$311$	1.00000	+	1.73205i	0.0567048	+	0.0982156i	−0.836280	+	0.548303i	$0.815274\pi$
$312$		−	10.3923i		−	0.588348i
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	−0.999748	−	0.0224310i	$-0.992859\pi$
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	0.519300	+	0.854592i	$0.326193\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	−6.00000			−0.337526
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$	−18.0000	+	10.3923i	−1.00939	+	0.582772i
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$	1.00000	+	1.73205i	0.0559017	+	0.0968246i
$321$	−4.50000	−	2.59808i	−0.251166	−	0.145010i
$322$		0			0
$323$	35.0000			1.94745
$324$	9.00000			0.500000
$325$	−6.00000			−0.332820
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$	3.00000	+	1.73205i	0.165900	+	0.0957826i
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$		0			0
$330$	3.00000	−	1.73205i	0.165145	−	0.0953463i
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	−16.0000			−0.878114
$333$	3.00000	+	5.19615i	0.164399	+	0.284747i
$334$	20.0000			1.09435
$335$	13.0000	−	22.5167i	0.710266	−	1.23022i
$336$		0			0
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	0.962168	−	0.272456i	$-0.0878358\pi$
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	−0.717038	+	0.697034i	$0.754502\pi$
$338$	11.5000	+	19.9186i	0.625518	+	1.08343i
$339$		−	17.3205i		−	0.940721i
$340$	5.00000	−	8.66025i	0.271163	−	0.469668i
$341$	6.00000			0.324918
$342$	21.0000			1.13555
$343$		0			0
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$	−12.0000	+	6.92820i	−0.646058	+	0.373002i
$346$	−1.00000	−	1.73205i	−0.0537603	−	0.0931156i
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	0.903475	−	0.428640i	$-0.141007\pi$
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	−0.822951	+	0.568112i	$0.807674\pi$
$348$	6.00000	+	3.46410i	0.321634	+	0.185695i
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$		0			0
$351$	−27.0000	+	15.5885i	−1.44115	+	0.832050i
$352$	−1.00000			−0.0533002
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	−0.993626	−	0.112731i	$-0.964040\pi$
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	0.594441	+	0.804139i	$0.297373\pi$
$354$	10.5000	+	6.06218i	0.558069	+	0.322201i
$355$	−8.00000	−	13.8564i	−0.424596	−	0.735422i
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$		0			0
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$	2.00000			0.105556			0.0527780	−	0.998606i	$-0.483192\pi$
$359$	2.00000			0.105556			0.0527780	+	0.998606i	$0.483192\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	30.0000			1.57895
$362$		0			0
$363$		−	17.3205i		−	0.909091i
$364$		0			0
$365$	−1.00000	−	1.73205i	−0.0523424	−	0.0906597i
$366$		−	20.7846i		−	1.08643i
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	0.421933	+	0.906627i	$0.361352\pi$
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	−0.996129	+	0.0879086i	$0.971982\pi$
$368$	4.00000			0.208514
$369$	−4.50000	+	7.79423i	−0.234261	+	0.405751i
$370$	4.00000			0.207950
$371$		0			0
$372$	9.00000	−	5.19615i	0.466628	−	0.269408i
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	−0.996610	−	0.0822766i	$-0.973781\pi$
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	0.427051	−	0.904227i	$-0.359552\pi$
$374$	2.50000	+	4.33013i	0.129272	+	0.223906i
$375$	−18.0000	−	10.3923i	−0.929516	−	0.536656i
$376$		0			0
$377$	−24.0000			−1.23606
$378$		0			0
$379$	−17.0000			−0.873231			−0.436616	−	0.899648i	$-0.643823\pi$
$379$	−17.0000			−0.873231			−0.436616	+	0.899648i	$0.643823\pi$
$380$	7.00000	−	12.1244i	0.359092	−	0.621966i
$381$	18.0000	+	10.3923i	0.922168	+	0.532414i
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	2.00000	+	3.46410i	0.102195	+	0.177007i	0.912589	−	0.408879i	$-0.134080\pi$
$383$	2.00000	+	3.46410i	0.102195	+	0.177007i	−0.810394	+	0.585886i	$0.800747\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$		0			0
$386$	−17.0000			−0.865277
$387$	3.00000			0.152499
$388$	5.00000			0.253837
$389$	−4.00000	+	6.92820i	−0.202808	+	0.351274i	−0.949432	−	0.313972i	$-0.898340\pi$
$389$	−4.00000	+	6.92820i	−0.202808	+	0.351274i	0.746624	+	0.665246i	$0.231673\pi$
$390$			20.7846i			1.05247i
$391$	−10.0000	−	17.3205i	−0.505722	−	0.875936i
$392$		0			0
$393$			6.92820i			0.349482i
$394$	5.00000	−	8.66025i	0.251896	−	0.436297i
$395$	12.0000			0.603786
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−18.0000			−0.903394			−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000			−0.903394			−0.451697	+	0.892171i	$0.649181\pi$
$398$	−7.00000	+	12.1244i	−0.350878	+	0.607739i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−4.50000	−	7.79423i	−0.224719	−	0.389225i	0.731516	−	0.681824i	$-0.238813\pi$
$401$	−4.50000	−	7.79423i	−0.224719	−	0.389225i	−0.956235	+	0.292599i	$0.905480\pi$
$402$	19.5000	+	11.2583i	0.972572	+	0.561514i
$403$	−18.0000	+	31.1769i	−0.896644	+	1.55303i
$404$	4.00000			0.199007
$405$	−18.0000			−0.894427
$406$		0			0
$407$	−1.00000	+	1.73205i	−0.0495682	+	0.0858546i
$408$	7.50000	+	4.33013i	0.371305	+	0.214373i
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	0.969363	−	0.245633i	$-0.0789957\pi$
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	−0.697406	+	0.716677i	$0.745662\pi$
$410$	3.00000	+	5.19615i	0.148159	+	0.256620i
$411$	−28.5000	+	16.4545i	−1.40580	+	0.811640i
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$		0			0
$414$	−6.00000	−	10.3923i	−0.294884	−	0.510754i
$415$	32.0000			1.57082
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$			8.66025i			0.424094i
$418$	3.50000	+	6.06218i	0.171191	+	0.296511i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		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	$0.0722054\pi$
$422$	16.0000			0.778868
$423$		0			0
$424$	−12.0000			−0.582772
$425$	2.50000	−	4.33013i	0.121268	−	0.210042i
$426$	12.0000	−	6.92820i	0.581402	−	0.335673i
$427$		0			0
$428$	−1.50000	−	2.59808i	−0.0725052	−	0.125583i
$429$	−9.00000	−	5.19615i	−0.434524	−	0.250873i
$430$	1.00000	−	1.73205i	0.0482243	−	0.0835269i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	25.0000			1.20142			0.600712	−	0.799466i	$-0.294884\pi$
$433$	25.0000			1.20142			0.600712	+	0.799466i	$0.294884\pi$
$434$		0			0
$435$	−12.0000	−	6.92820i	−0.575356	−	0.332182i
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−14.0000	−	24.2487i	−0.669711	−	1.15997i
$438$	1.50000	−	0.866025i	0.0716728	−	0.0413803i
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	0.423556	+	0.905870i	$0.360782\pi$
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	−0.996284	+	0.0861252i	$0.972552\pi$
$440$	2.00000			0.0953463
$441$		0			0
$442$	−30.0000			−1.42695
$443$	−3.50000	+	6.06218i	−0.166290	+	0.288023i	−0.937113	−	0.349027i	$-0.886512\pi$
$443$	−3.50000	+	6.06218i	−0.166290	+	0.288023i	0.770823	+	0.637050i	$0.219845\pi$
$444$			3.46410i			0.164399i
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	2.00000	+	3.46410i	0.0947027	+	0.164030i
$447$		−	41.5692i		−	1.96616i
$448$		0			0
$449$	17.0000			0.802280			0.401140	−	0.916017i	$-0.368614\pi$
$449$	17.0000			0.802280			0.401140	+	0.916017i	$0.368614\pi$
$450$	1.50000	−	2.59808i	0.0707107	−	0.122474i
$451$	−3.00000			−0.141264
$452$	5.00000	−	8.66025i	0.235180	−	0.407344i
$453$	15.0000	−	8.66025i	0.704761	−	0.406894i
$454$	−1.50000	−	2.59808i	−0.0703985	−	0.121934i
$455$		0			0
$456$	10.5000	+	6.06218i	0.491708	+	0.283887i
$457$	−0.500000	+	0.866025i	−0.0233890	+	0.0405110i	−0.877483	−	0.479608i	$-0.840779\pi$
$457$	−0.500000	+	0.866025i	−0.0233890	+	0.0405110i	0.854094	+	0.520119i	$0.174112\pi$
$458$	−26.0000			−1.21490
$459$		−	25.9808i		−	1.21268i
$460$	−8.00000			−0.373002
$461$	7.00000	−	12.1244i	0.326023	−	0.564688i	−0.655696	−	0.755025i	$-0.727625\pi$
$461$	7.00000	−	12.1244i	0.326023	−	0.564688i	0.981719	+	0.190337i	$0.0609581\pi$
$462$		0			0
$463$	4.00000	+	6.92820i	0.185896	+	0.321981i	0.943878	−	0.330294i	$-0.107148\pi$
$463$	4.00000	+	6.92820i	0.185896	+	0.321981i	−0.757982	+	0.652275i	$0.773815\pi$
$464$	2.00000	+	3.46410i	0.0928477	+	0.160817i
$465$	−18.0000	+	10.3923i	−0.834730	+	0.481932i
$466$	−14.5000	+	25.1147i	−0.671700	+	1.16342i
$467$	13.0000			0.601568			0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000			0.601568			0.300784	+	0.953692i	$0.402752\pi$
$468$	−18.0000			−0.832050
$469$		0			0
$470$		0			0
$471$		−	3.46410i		−	0.159617i
$472$	3.50000	+	6.06218i	0.161101	+	0.279034i
$473$	0.500000	+	0.866025i	0.0229900	+	0.0398199i
$474$			10.3923i			0.477334i
$475$	3.50000	−	6.06218i	0.160591	−	0.278152i
$476$		0			0
$477$	18.0000	+	31.1769i	0.824163	+	1.42749i
$478$	−6.00000			−0.274434
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	−0.998796	−	0.0490589i	$-0.984378\pi$
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	0.541884	+	0.840453i	$0.317711\pi$
$480$	3.00000	−	1.73205i	0.136931	−	0.0790569i
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	−11.5000	−	19.9186i	−0.523811	−	0.907267i
$483$		0			0
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	−10.0000			−0.454077
$486$		−	15.5885i		−	0.707107i
$487$	−10.0000			−0.453143			−0.226572	−	0.973995i	$-0.572752\pi$
$487$	−10.0000			−0.453143			−0.226572	+	0.973995i	$0.572752\pi$
$488$	6.00000	−	10.3923i	0.271607	−	0.470438i
$489$	6.00000	+	3.46410i	0.271329	+	0.156652i
$490$		0			0
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	−0.950365	−	0.311136i	$-0.899290\pi$
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	0.205731	−	0.978609i	$-0.434043\pi$
$492$	−4.50000	+	2.59808i	−0.202876	+	0.117130i
$493$	10.0000	−	17.3205i	0.450377	−	0.780076i
$494$	−42.0000			−1.88967
$495$	−3.00000	−	5.19615i	−0.134840	−	0.233550i
$496$	6.00000			0.269408
$497$		0			0
$498$			27.7128i			1.24184i
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	0.983336	+	0.181797i	$0.0581915\pi$
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	−0.334227	+	0.942493i	$0.608475\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$		−	34.6410i		−	1.54765i
$502$	−1.50000	+	2.59808i	−0.0669483	+	0.115958i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$	−8.00000			−0.355995
$506$	2.00000	−	3.46410i	0.0889108	−	0.153998i
$507$	34.5000	−	19.9186i	1.53220	−	0.884615i
$508$	6.00000	+	10.3923i	0.266207	+	0.461084i
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	0.979322	+	0.202306i	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$	−15.0000	−	8.66025i	−0.664211	−	0.383482i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		−	36.3731i		−	1.60591i
$514$	−15.0000			−0.661622
$515$	−14.0000	+	24.2487i	−0.616914	+	1.06853i
$516$	1.50000	+	0.866025i	0.0660338	+	0.0381246i
$517$		0			0
$518$		0			0
$519$	−3.00000	+	1.73205i	−0.131685	+	0.0760286i
$520$	−6.00000	+	10.3923i	−0.263117	+	0.455733i
$521$	9.00000			0.394297			0.197149	−	0.980374i	$-0.436832\pi$
$521$	9.00000			0.394297			0.197149	+	0.980374i	$0.436832\pi$
$522$	6.00000	−	10.3923i	0.262613	−	0.454859i
$523$	28.0000			1.22435			0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000			1.22435			0.612177	+	0.790721i	$0.290294\pi$
$524$	−2.00000	+	3.46410i	−0.0873704	+	0.151330i
$525$		0			0
$526$	9.00000	+	15.5885i	0.392419	+	0.679689i
$527$	−15.0000	−	25.9808i	−0.653410	−	1.13174i
$528$			1.73205i			0.0753778i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	24.0000			1.04249
$531$	10.5000	−	18.1865i	0.455661	−	0.789228i
$532$		0			0
$533$	9.00000	−	15.5885i	0.389833	−	0.675211i
$534$	−9.00000	+	5.19615i	−0.389468	+	0.224860i
$535$	3.00000	+	5.19615i	0.129701	+	0.224649i
$536$	6.50000	+	11.2583i	0.280757	+	0.486286i
$537$	−36.0000	−	20.7846i	−1.55351	−	0.896922i
$538$	−10.0000	+	17.3205i	−0.431131	+	0.746740i
$539$		0			0
$540$	−9.00000	−	5.19615i	−0.387298	−	0.223607i
$541$	−24.0000			−1.03184			−0.515920	−	0.856637i	$-0.672550\pi$
$541$	−24.0000			−1.03184			−0.515920	+	0.856637i	$0.672550\pi$
$542$	3.00000	−	5.19615i	0.128861	−	0.223194i
$543$		0			0
$544$	2.50000	+	4.33013i	0.107187	+	0.185653i
$545$	−2.00000	−	3.46410i	−0.0856706	−	0.148386i
$546$		0			0
$547$	10.5000	−	18.1865i	0.448948	−	0.777600i	−0.549370	−	0.835579i	$-0.685132\pi$
$547$	10.5000	−	18.1865i	0.448948	−	0.777600i	0.998318	+	0.0579790i	$0.0184657\pi$
$548$	−19.0000			−0.811640
$549$	−36.0000			−1.53644
$550$	1.00000			0.0426401
$551$	14.0000	−	24.2487i	0.596420	−	1.03303i
$552$		−	6.92820i		−	0.294884i
$553$		0			0
$554$	1.00000	+	1.73205i	0.0424859	+	0.0735878i
$555$		−	6.92820i		−	0.294086i
$556$	−2.50000	+	4.33013i	−0.106024	+	0.183638i
$557$	−28.0000			−1.18640			−0.593199	−	0.805056i	$-0.702135\pi$
$557$	−28.0000			−1.18640			−0.593199	+	0.805056i	$0.702135\pi$
$558$	−9.00000	−	15.5885i	−0.381000	−	0.659912i
$559$	−6.00000			−0.253773
$560$		0			0
$561$	7.50000	−	4.33013i	0.316650	−	0.182818i
$562$	11.0000	+	19.0526i	0.464007	+	0.803684i
$563$	15.5000	+	26.8468i	0.653247	+	1.13146i	0.982330	+	0.187156i	$0.0599271\pi$
$563$	15.5000	+	26.8468i	0.653247	+	1.13146i	−0.329083	+	0.944301i	$0.606740\pi$
$564$		0			0
$565$	−10.0000	+	17.3205i	−0.420703	+	0.728679i
$566$	4.00000			0.168133
$567$		0			0
$568$	8.00000			0.335673
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	−0.664897	−	0.746935i	$-0.731525\pi$
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	0.979313	+	0.202350i	$0.0648579\pi$
$570$	−21.0000	−	12.1244i	−0.879593	−	0.507833i
$571$	16.5000	+	28.5788i	0.690504	+	1.19599i	0.971673	+	0.236329i	$0.0759443\pi$
$571$	16.5000	+	28.5788i	0.690504	+	1.19599i	−0.281170	+	0.959658i	$0.590722\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$	18.0000	−	10.3923i	0.751961	−	0.434145i
$574$		0			0
$575$	−4.00000			−0.166812
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	35.0000			1.45707			0.728535	−	0.685009i	$-0.240202\pi$
$577$	35.0000			1.45707			0.728535	+	0.685009i	$0.240202\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$			29.4449i			1.22369i
$580$	−4.00000	−	6.92820i	−0.166091	−	0.287678i
$581$		0			0
$582$		−	8.66025i		−	0.358979i
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$	1.00000			0.0413803
$585$	36.0000			1.48842
$586$		0			0
$587$	−23.5000	+	40.7032i	−0.969949	+	1.68000i	−0.274263	+	0.961655i	$0.588434\pi$
$587$	−23.5000	+	40.7032i	−0.969949	+	1.68000i	−0.695686	+	0.718346i	$0.744900\pi$
$588$		0			0
$589$	−21.0000	−	36.3731i	−0.865290	−	1.49873i
$590$	−7.00000	−	12.1244i	−0.288185	−	0.499152i
$591$	−15.0000	−	8.66025i	−0.617018	−	0.356235i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$	4.50000	−	2.59808i	0.184637	−	0.106600i
$595$		0			0
$596$	12.0000	−	20.7846i	0.491539	−	0.851371i
$597$	21.0000	+	12.1244i	0.859473	+	0.496217i
$598$	12.0000	+	20.7846i	0.490716	+	0.849946i
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$	1.50000	−	0.866025i	0.0612372	−	0.0353553i
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	−0.992114	−	0.125336i	$-0.959999\pi$
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	0.604601	+	0.796528i	$0.293332\pi$
$602$		0			0
$603$	19.5000	−	33.7750i	0.794101	−	1.37542i
$604$	10.0000			0.406894
$605$	−10.0000	+	17.3205i	−0.406558	+	0.704179i
$606$		−	6.92820i		−	0.281439i
$607$	−12.0000	−	20.7846i	−0.487065	−	0.843621i	0.512824	−	0.858494i	$-0.328599\pi$
$607$	−12.0000	−	20.7846i	−0.487065	−	0.843621i	−0.999889	+	0.0148722i	$0.995266\pi$
$608$	3.50000	+	6.06218i	0.141944	+	0.245854i
$609$		0			0
$610$	−12.0000	+	20.7846i	−0.485866	+	0.841544i
$611$		0			0
$612$	7.50000	−	12.9904i	0.303170	−	0.525105i
$613$	42.0000			1.69636			0.848182	−	0.529705i	$-0.177697\pi$
$613$	42.0000			1.69636			0.848182	+	0.529705i	$0.177697\pi$
$614$	−3.50000	+	6.06218i	−0.141249	+	0.244650i
$615$	9.00000	−	5.19615i	0.362915	−	0.209529i
$616$		0			0
$617$	8.50000	+	14.7224i	0.342197	+	0.592703i	0.984840	−	0.173463i	$-0.0554956\pi$
$617$	8.50000	+	14.7224i	0.342197	+	0.592703i	−0.642643	+	0.766165i	$0.722162\pi$
$618$	−21.0000	−	12.1244i	−0.844744	−	0.487713i
$619$	18.5000	−	32.0429i	0.743578	−	1.28791i	−0.207279	−	0.978282i	$-0.566461\pi$
$619$	18.5000	−	32.0429i	0.743578	−	1.28791i	0.950856	−	0.309633i	$-0.100206\pi$
$620$	−12.0000			−0.481932
$621$	−18.0000	+	10.3923i	−0.722315	+	0.417029i
$622$	2.00000			0.0801927
$623$		0			0
$624$	−9.00000	−	5.19615i	−0.360288	−	0.208013i
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	8.50000	+	14.7224i	0.339728	+	0.588427i
$627$	10.5000	−	6.06218i	0.419330	−	0.242100i
$628$	1.00000	−	1.73205i	0.0399043	−	0.0691164i
$629$	10.0000			0.398726
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−3.00000	+	5.19615i	−0.119334	+	0.206692i
$633$		−	27.7128i		−	1.10149i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	−12.0000	−	20.7846i	−0.476205	−	0.824812i
$636$			20.7846i			0.824163i
$637$		0			0
$638$	4.00000			0.158362
$639$	−12.0000	−	20.7846i	−0.474713	−	0.822226i
$640$	2.00000			0.0790569
$641$	−0.500000	+	0.866025i	−0.0197488	+	0.0342059i	−0.875731	−	0.482800i	$-0.839620\pi$
$641$	−0.500000	+	0.866025i	−0.0197488	+	0.0342059i	0.855982	+	0.517005i	$0.172953\pi$
$642$	−4.50000	+	2.59808i	−0.177601	+	0.102538i
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	0.788723	−	0.614749i	$-0.210743\pi$
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	−0.926750	+	0.375680i	$0.877409\pi$
$644$		0			0
$645$	−3.00000	−	1.73205i	−0.118125	−	0.0681994i
$646$	17.5000	−	30.3109i	0.688528	−	1.19257i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	7.00000			0.274774
$650$	−3.00000	+	5.19615i	−0.117670	+	0.203810i
$651$		0			0
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$	3.00000	−	1.73205i	0.117309	−	0.0677285i
$655$	4.00000	−	6.92820i	0.156293	−	0.270707i
$656$	−3.00000			−0.117130
$657$	−1.50000	−	2.59808i	−0.0585206	−	0.101361i
$658$		0			0
$659$	−8.00000	+	13.8564i	−0.311636	+	0.539769i	−0.978717	−	0.205216i	$-0.934210\pi$
$659$	−8.00000	+	13.8564i	−0.311636	+	0.539769i	0.667081	+	0.744985i	$0.267544\pi$
$660$		−	3.46410i		−	0.134840i
$661$	14.0000	+	24.2487i	0.544537	+	0.943166i	0.998636	+	0.0522143i	$0.0166279\pi$
$661$	14.0000	+	24.2487i	0.544537	+	0.943166i	−0.454099	+	0.890951i	$0.650039\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$			51.9615i			2.01802i
$664$	−8.00000	+	13.8564i	−0.310460	+	0.537733i
$665$		0			0
$666$	6.00000			0.232495
$667$	−16.0000			−0.619522
$668$	10.0000	−	17.3205i	0.386912	−	0.670151i
$669$	6.00000	−	3.46410i	0.231973	−	0.133930i
$670$	−13.0000	−	22.5167i	−0.502234	−	0.869894i
$671$	−6.00000	−	10.3923i	−0.231627	−	0.401190i
$672$		0			0
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	9.00000			0.346667
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$	23.0000			0.884615
$677$	15.0000	−	25.9808i	0.576497	−	0.998522i	−0.419380	−	0.907811i	$-0.637753\pi$
$677$	15.0000	−	25.9808i	0.576497	−	0.998522i	0.995877	−	0.0907112i	$-0.0289140\pi$
$678$	−15.0000	−	8.66025i	−0.576072	−	0.332595i
$679$		0			0
$680$	−5.00000	−	8.66025i	−0.191741	−	0.332106i
$681$	−4.50000	+	2.59808i	−0.172440	+	0.0995585i
$682$	3.00000	−	5.19615i	0.114876	−	0.198971i
$683$	39.0000			1.49229			0.746147	−	0.665782i	$-0.231902\pi$
$683$	39.0000			1.49229			0.746147	+	0.665782i	$0.231902\pi$
$684$	10.5000	−	18.1865i	0.401478	−	0.695379i
$685$	38.0000			1.45191
$686$		0			0
$687$			45.0333i			1.71813i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	−36.0000	−	62.3538i	−1.37149	−	2.37549i
$690$			13.8564i			0.527504i
$691$	16.0000	−	27.7128i	0.608669	−	1.05425i	−0.382791	−	0.923835i	$-0.625037\pi$
$691$	16.0000	−	27.7128i	0.608669	−	1.05425i	0.991460	−	0.130410i	$-0.0416295\pi$
$692$	−2.00000			−0.0760286
$693$		0			0
$694$	3.00000			0.113878
$695$	5.00000	−	8.66025i	0.189661	−	0.328502i
$696$	6.00000	−	3.46410i	0.227429	−	0.131306i
$697$	7.50000	+	12.9904i	0.284083	+	0.492046i
$698$	7.00000	+	12.1244i	0.264954	+	0.458914i
$699$	43.5000	+	25.1147i	1.64532	+	0.949927i
$700$		0			0
$701$	8.00000			0.302156			0.151078	−	0.988522i	$-0.451726\pi$
$701$	8.00000			0.302156			0.151078	+	0.988522i	$0.451726\pi$
$702$			31.1769i			1.17670i
$703$	14.0000			0.528020
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	7.50000	+	12.9904i	0.282266	+	0.488899i
$707$		0			0
$708$	10.5000	−	6.06218i	0.394614	−	0.227831i
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	−0.826023	−	0.563636i	$-0.809402\pi$
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	0.901135	+	0.433539i	$0.142735\pi$
$710$	−16.0000			−0.600469
$711$	18.0000			0.675053
$712$	−6.00000			−0.224860
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$		0			0
$715$	6.00000	+	10.3923i	0.224387	+	0.388650i
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$			10.3923i			0.388108i
$718$	1.00000	−	1.73205i	0.0373197	−	0.0646396i
$719$	−6.00000			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$720$	−3.00000	−	5.19615i	−0.111803	−	0.193649i
$721$		0			0
$722$	15.0000	−	25.9808i	0.558242	−	0.966904i
$723$	−34.5000	+	19.9186i	−1.28307	+	0.740780i
$724$		0			0
$725$	−2.00000	−	3.46410i	−0.0742781	−	0.128654i
$726$	−15.0000	−	8.66025i	−0.556702	−	0.321412i
$727$	−7.00000	+	12.1244i	−0.259616	+	0.449667i	−0.966139	−	0.258022i	$-0.916929\pi$
$727$	−7.00000	+	12.1244i	−0.259616	+	0.449667i	0.706523	+	0.707690i	$0.250263\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−2.00000			−0.0740233
$731$	2.50000	−	4.33013i	0.0924658	−	0.160156i
$732$	−18.0000	−	10.3923i	−0.665299	−	0.384111i
$733$	−9.00000	−	15.5885i	−0.332423	−	0.575773i	0.650564	−	0.759452i	$-0.274533\pi$
$733$	−9.00000	−	15.5885i	−0.332423	−	0.575773i	−0.982986	+	0.183679i	$0.941199\pi$
$734$	11.0000	+	19.0526i	0.406017	+	0.703243i
$735$		0			0
$736$	2.00000	−	3.46410i	0.0737210	−	0.127688i
$737$	13.0000			0.478861
$738$	4.50000	+	7.79423i	0.165647	+	0.286910i
$739$	−33.0000			−1.21392			−0.606962	−	0.794731i	$-0.707612\pi$
$739$	−33.0000			−1.21392			−0.606962	+	0.794731i	$0.707612\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$			72.7461i			2.67240i
$742$		0			0
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$		−	10.3923i		−	0.381000i
$745$	−24.0000	+	41.5692i	−0.879292	+	1.52298i
$746$	−22.0000			−0.805477
$747$	48.0000			1.75623
$748$	5.00000			0.182818
$749$		0			0
$750$	−18.0000	+	10.3923i	−0.657267	+	0.379473i
$751$	9.00000	+	15.5885i	0.328415	+	0.568831i	0.982197	−	0.187851i	$-0.0601523\pi$
$751$	9.00000	+	15.5885i	0.328415	+	0.568831i	−0.653783	+	0.756682i	$0.726819\pi$
$752$		0			0
$753$	4.50000	+	2.59808i	0.163989	+	0.0946792i
$754$	−12.0000	+	20.7846i	−0.437014	+	0.756931i
$755$	−20.0000			−0.727875
$756$		0			0
$757$	−48.0000			−1.74459			−0.872295	−	0.488980i	$-0.837369\pi$
$757$	−48.0000			−1.74459			−0.872295	+	0.488980i	$0.837369\pi$
$758$	−8.50000	+	14.7224i	−0.308734	+	0.534743i
$759$	−6.00000	−	3.46410i	−0.217786	−	0.125739i
$760$	−7.00000	−	12.1244i	−0.253917	−	0.439797i
$761$	5.00000	+	8.66025i	0.181250	+	0.313934i	0.942306	−	0.334752i	$-0.108652\pi$
$761$	5.00000	+	8.66025i	0.181250	+	0.313934i	−0.761057	+	0.648686i	$0.775319\pi$
$762$	18.0000	−	10.3923i	0.652071	−	0.376473i
$763$		0			0
$764$	12.0000			0.434145
$765$	−15.0000	+	25.9808i	−0.542326	+	0.939336i
$766$	4.00000			0.144526
$767$	−21.0000	+	36.3731i	−0.758266	+	1.31336i
$768$			1.73205i			0.0625000i
$769$	11.0000	+	19.0526i	0.396670	+	0.687053i	0.993313	−	0.115454i	$-0.0368323\pi$
$769$	11.0000	+	19.0526i	0.396670	+	0.687053i	−0.596643	+	0.802507i	$0.703499\pi$
$770$		0			0
$771$			25.9808i			0.935674i
$772$	−8.50000	+	14.7224i	−0.305922	+	0.529872i
$773$	52.0000			1.87031			0.935155	−	0.354239i	$-0.115260\pi$
$773$	52.0000			1.87031			0.935155	+	0.354239i	$0.115260\pi$
$774$	1.50000	−	2.59808i	0.0539164	−	0.0933859i
$775$	−6.00000			−0.215526
$776$	2.50000	−	4.33013i	0.0897448	−	0.155443i
$777$		0			0
$778$	4.00000	+	6.92820i	0.143407	+	0.248388i
$779$	10.5000	+	18.1865i	0.376202	+	0.651600i
$780$	18.0000	+	10.3923i	0.644503	+	0.372104i
$781$	4.00000	−	6.92820i	0.143131	−	0.247911i
$782$	−20.0000			−0.715199
$783$	−18.0000	−	10.3923i	−0.643268	−	0.371391i
$784$		0			0
$785$	−2.00000	+	3.46410i	−0.0713831	+	0.123639i
$786$	6.00000	+	3.46410i	0.214013	+	0.123560i
$787$	−6.00000	−	10.3923i	−0.213877	−	0.370446i	0.739048	−	0.673653i	$-0.235276\pi$
$787$	−6.00000	−	10.3923i	−0.213877	−	0.370446i	−0.952925	+	0.303207i	$0.901942\pi$
$788$	−5.00000	−	8.66025i	−0.178118	−	0.308509i
$789$	27.0000	−	15.5885i	0.961225	−	0.554964i
$790$	6.00000	−	10.3923i	0.213470	−	0.369742i
$791$		0			0
$792$	3.00000			0.106600
$793$	72.0000			2.55679
$794$	−9.00000	+	15.5885i	−0.319398	+	0.553214i
$795$		−	41.5692i		−	1.47431i
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	0.739975	−	0.672634i	$-0.234837\pi$
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	−0.952506	+	0.304520i	$0.901504\pi$
$798$		0			0
$799$		0			0
$800$	1.00000			0.0353553
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$	−9.00000			−0.317801
$803$	0.500000	−	0.866025i	0.0176446	−	0.0305614i
$804$	19.5000	−	11.2583i	0.687712	−	0.397051i
$805$		0			0
$806$	18.0000	+	31.1769i	0.634023	+	1.09816i
$807$	30.0000	+	17.3205i	1.05605	+	0.609711i
$808$	2.00000	−	3.46410i	0.0703598	−	0.121867i
$809$	−43.0000			−1.51180			−0.755900	−	0.654687i	$-0.772800\pi$
$809$	−43.0000			−1.51180			−0.755900	+	0.654687i	$0.772800\pi$
$810$	−9.00000	+	15.5885i	−0.316228	+	0.547723i
$811$	−31.0000			−1.08856			−0.544279	−	0.838905i	$-0.683197\pi$
$811$	−31.0000			−1.08856			−0.544279	+	0.838905i	$0.683197\pi$
$812$		0			0
$813$	−9.00000	−	5.19615i	−0.315644	−	0.182237i
$814$	1.00000	+	1.73205i	0.0350500	+	0.0607083i
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$	7.50000	−	4.33013i	0.262553	−	0.151585i
$817$	3.50000	−	6.06218i	0.122449	−	0.212089i
$818$	11.0000			0.384606
$819$		0			0
$820$	6.00000			0.209529
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	0.115124	+	0.993351i	$0.463274\pi$
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	−0.917829	+	0.396976i	$0.870060\pi$
$822$			32.9090i			1.14783i
$823$	−17.0000	−	29.4449i	−0.592583	−	1.02638i	−0.993883	−	0.110437i	$-0.964775\pi$
$823$	−17.0000	−	29.4449i	−0.592583	−	1.02638i	0.401300	−	0.915947i	$-0.368558\pi$
$824$	−7.00000	−	12.1244i	−0.243857	−	0.422372i
$825$		−	1.73205i		−	0.0603023i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	−12.0000			−0.417029
$829$	−4.00000			−0.138926			−0.0694629	−	0.997585i	$-0.522129\pi$
$829$	−4.00000			−0.138926			−0.0694629	+	0.997585i	$0.522129\pi$
$830$	16.0000	−	27.7128i	0.555368	−	0.961926i
$831$	3.00000	−	1.73205i	0.104069	−	0.0600842i
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$		0			0
$834$	7.50000	+	4.33013i	0.259704	+	0.149940i
$835$	−20.0000	+	34.6410i	−0.692129	+	1.19880i
$836$	7.00000			0.242100
$837$	−27.0000	+	15.5885i	−0.933257	+	0.538816i
$838$	−12.0000			−0.414533
$839$	−10.0000	+	17.3205i	−0.345238	+	0.597970i	−0.985397	−	0.170272i	$-0.945535\pi$
$839$	−10.0000	+	17.3205i	−0.345238	+	0.597970i	0.640159	+	0.768243i	$0.278869\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	−6.00000	−	10.3923i	−0.206774	−	0.358142i
$843$	33.0000	−	19.0526i	1.13658	−	0.656205i
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	−46.0000			−1.58245
$846$		0			0
$847$		0			0
$848$	−6.00000	+	10.3923i	−0.206041	+	0.356873i
$849$		−	6.92820i		−	0.237775i
$850$	−2.50000	−	4.33013i	−0.0857493	−	0.148522i
$851$	−4.00000	−	6.92820i	−0.137118	−	0.237496i
$852$		−	13.8564i		−	0.474713i
$853$	22.0000	−	38.1051i	0.753266	−	1.30469i	−0.192966	−	0.981205i	$-0.561811\pi$
$853$	22.0000	−	38.1051i	0.753266	−	1.30469i	0.946232	−	0.323489i	$-0.104856\pi$
$854$		0			0
$855$	−21.0000	+	36.3731i	−0.718185	+	1.24393i
$856$	−3.00000			−0.102538
$857$	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	$-0.00457319\pi$
$858$	−9.00000	+	5.19615i	−0.307255	+	0.177394i
$859$	14.5000	+	25.1147i	0.494734	+	0.856904i	0.999982	−	0.00607046i	$-0.00193230\pi$
$859$	14.5000	+	25.1147i	0.494734	+	0.856904i	−0.505248	+	0.862974i	$0.668599\pi$
$860$	−1.00000	−	1.73205i	−0.0340997	−	0.0590624i
$861$		0			0
$862$		0			0
$863$	38.0000			1.29354			0.646768	−	0.762687i	$-0.276120\pi$
$863$	38.0000			1.29354			0.646768	+	0.762687i	$0.276120\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$	4.00000			0.136004
$866$	12.5000	−	21.6506i	0.424767	−	0.735719i
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$		0			0
$869$	3.00000	+	5.19615i	0.101768	+	0.176267i
$870$	−12.0000	+	6.92820i	−0.406838	+	0.234888i
$871$	−39.0000	+	67.5500i	−1.32146	+	2.28884i
$872$	2.00000			0.0677285
$873$	−15.0000			−0.507673
$874$	−28.0000			−0.947114
$875$		0			0
$876$		−	1.73205i		−	0.0585206i
$877$	−8.00000	−	13.8564i	−0.270141	−	0.467898i	0.698757	−	0.715359i	$-0.253737\pi$
$877$	−8.00000	−	13.8564i	−0.270141	−	0.467898i	−0.968898	+	0.247462i	$0.920404\pi$
$878$	12.0000	+	20.7846i	0.404980	+	0.701447i
$879$		0			0
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$	53.0000			1.78359			0.891796	−	0.452438i	$-0.149446\pi$
$883$	53.0000			1.78359			0.891796	+	0.452438i	$0.149446\pi$
$884$	−15.0000	+	25.9808i	−0.504505	+	0.873828i
$885$	−21.0000	+	12.1244i	−0.705907	+	0.407556i
$886$	3.50000	+	6.06218i	0.117585	+	0.203663i
$887$	−3.00000	−	5.19615i	−0.100730	−	0.174470i	0.811256	−	0.584692i	$-0.198785\pi$
$887$	−3.00000	−	5.19615i	−0.100730	−	0.174470i	−0.911986	+	0.410222i	$0.865451\pi$
$888$	3.00000	+	1.73205i	0.100673	+	0.0581238i
$889$		0			0
$890$	12.0000			0.402241
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$	4.00000			0.133930
$893$		0			0
$894$	−36.0000	−	20.7846i	−1.20402	−	0.695141i
$895$	24.0000	+	41.5692i	0.802232	+	1.38951i
$896$		0			0
$897$	36.0000	−	20.7846i	1.20201	−	0.693978i
$898$	8.50000	−	14.7224i	0.283649	−	0.491294i
$899$	−24.0000			−0.800445
$900$	−1.50000	−	2.59808i	−0.0500000	−	0.0866025i
$901$	60.0000			1.99889
$902$	−1.50000	+	2.59808i	−0.0499445	+	0.0865065i
$903$		0			0
$904$	−5.00000	−	8.66025i	−0.166298	−	0.288036i
$905$		0			0
$906$		−	17.3205i		−	0.575435i
$907$	13.5000	−	23.3827i	0.448260	−	0.776409i	−0.550013	−	0.835156i	$-0.685377\pi$
$907$	13.5000	−	23.3827i	0.448260	−	0.776409i	0.998273	+	0.0587469i	$0.0187105\pi$
$908$	−3.00000			−0.0995585
$909$	−12.0000			−0.398015
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$	10.5000	−	6.06218i	0.347690	−	0.200739i
$913$	8.00000	+	13.8564i	0.264761	+	0.458580i
$914$	0.500000	+	0.866025i	0.0165385	+	0.0286456i
$915$	36.0000	+	20.7846i	1.19012	+	0.687118i
$916$	−13.0000	+	22.5167i	−0.429532	+	0.743971i
$917$		0			0
$918$	−22.5000	−	12.9904i	−0.742611	−	0.428746i
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$	−4.00000	+	6.92820i	−0.131876	+	0.228416i
$921$	10.5000	+	6.06218i	0.345987	+	0.199756i
$922$	−7.00000	−	12.1244i	−0.230533	−	0.399294i
$923$	24.0000	+	41.5692i	0.789970	+	1.36827i
$924$		0			0
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	8.00000			0.262896
$927$	−21.0000	+	36.3731i	−0.689730	+	1.19465i
$928$	4.00000			0.131306
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	−0.975050	−	0.221985i	$-0.928746\pi$
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	0.679770	+	0.733426i	$0.262080\pi$
$930$			20.7846i			0.681554i
$931$		0			0
$932$	14.5000	+	25.1147i	0.474963	+	0.822661i
$933$		−	3.46410i		−	0.113410i
$934$	6.50000	−	11.2583i	0.212686	−	0.368384i
$935$	−10.0000			−0.327035
$936$	−9.00000	+	15.5885i	−0.294174	+	0.509525i
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$	25.5000	−	14.7224i	0.832161	−	0.480448i
$940$		0			0
$941$	10.0000	+	17.3205i	0.325991	+	0.564632i	0.981712	−	0.190370i	$-0.0609689\pi$
$941$	10.0000	+	17.3205i	0.325991	+	0.564632i	−0.655722	+	0.755003i	$0.727636\pi$
$942$	−3.00000	−	1.73205i	−0.0977453	−	0.0564333i
$943$	6.00000	−	10.3923i	0.195387	−	0.338420i
$944$	7.00000			0.227831
$945$		0			0
$946$	1.00000			0.0325128
$947$	18.5000	−	32.0429i	0.601169	−	1.04126i	−0.391475	−	0.920189i	$-0.628035\pi$
$947$	18.5000	−	32.0429i	0.601169	−	1.04126i	0.992644	−	0.121067i	$-0.0386316\pi$
$948$	9.00000	+	5.19615i	0.292306	+	0.168763i
$949$	3.00000	+	5.19615i	0.0973841	+	0.168674i
$950$	−3.50000	−	6.06218i	−0.113555	−	0.196683i
$951$	−9.00000	+	5.19615i	−0.291845	+	0.168497i
$952$		0			0
$953$	−35.0000			−1.13376			−0.566881	−	0.823800i	$-0.691850\pi$
$953$	−35.0000			−1.13376			−0.566881	+	0.823800i	$0.691850\pi$
$954$	36.0000			1.16554
$955$	−24.0000			−0.776622
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$		−	6.92820i		−	0.223957i
$958$	10.0000	+	17.3205i	0.323085	+	0.559600i
$959$		0			0
$960$		−	3.46410i		−	0.111803i
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	−12.0000			−0.386896
$963$	4.50000	+	7.79423i	0.145010	+	0.251166i
$964$	−23.0000			−0.740780
$965$	17.0000	−	29.4449i	0.547249	−	0.947864i
$966$		0			0
$967$	−7.00000	−	12.1244i	−0.225105	−	0.389893i	0.731246	−	0.682114i	$-0.238939\pi$
$967$	−7.00000	−	12.1244i	−0.225105	−	0.389893i	−0.956351	+	0.292221i	$0.905606\pi$
$968$	−5.00000	−	8.66025i	−0.160706	−	0.278351i
$969$	−52.5000	−	30.3109i	−1.68654	−	0.973726i
$970$	−5.00000	+	8.66025i	−0.160540	+	0.278064i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$		0			0
$974$	−5.00000	+	8.66025i	−0.160210	+	0.277492i
$975$	9.00000	+	5.19615i	0.288231	+	0.166410i
$976$	−6.00000	−	10.3923i	−0.192055	−	0.332650i
$977$	7.50000	+	12.9904i	0.239946	+	0.415599i	0.960699	−	0.277594i	$-0.0895368\pi$
$977$	7.50000	+	12.9904i	0.239946	+	0.415599i	−0.720752	+	0.693193i	$0.756204\pi$
$978$	6.00000	−	3.46410i	0.191859	−	0.110770i
$979$	−3.00000	+	5.19615i	−0.0958804	+	0.166070i
$980$		0			0
$981$	−3.00000	−	5.19615i	−0.0957826	−	0.165900i
$982$	−33.0000			−1.05307
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.226778	+	0.973946i	$0.572819\pi$
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.730073	+	0.683369i	$0.760514\pi$
$984$			5.19615i			0.165647i
$985$	10.0000	+	17.3205i	0.318626	+	0.551877i
$986$	−10.0000	−	17.3205i	−0.318465	−	0.551597i
$987$		0			0
$988$	−21.0000	+	36.3731i	−0.668099	+	1.15718i
$989$	−4.00000			−0.127193
$990$	−6.00000			−0.190693
$991$	−28.0000			−0.889449			−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000			−0.889449			−0.444725	+	0.895667i	$0.646698\pi$
$992$	3.00000	−	5.19615i	0.0952501	−	0.164978i
$993$	12.0000	−	6.92820i	0.380808	−	0.219860i
$994$		0			0
$995$	−14.0000	−	24.2487i	−0.443830	−	0.768736i
$996$	24.0000	+	13.8564i	0.760469	+	0.439057i
$997$	1.00000	−	1.73205i	0.0316703	−	0.0548546i	−0.849756	−	0.527176i	$-0.823251\pi$
$997$	1.00000	−	1.73205i	0.0316703	−	0.0548546i	0.881426	+	0.472322i	$0.156584\pi$
$998$	29.0000			0.917979
$999$		−	10.3923i		−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.f.295.1		2
3.2	odd	2		2646.2.f.b.883.1		2
7.2	even	3		882.2.e.e.655.1		2
7.3	odd	6		882.2.h.h.79.1		2
7.4	even	3		882.2.h.g.79.1		2
7.5	odd	6		882.2.e.a.655.1		2
7.6	odd	2		126.2.f.b.43.1	✓	2
9.2	odd	6		7938.2.a.bb.1.1		1
9.4	even	3	inner	882.2.f.f.589.1		2
9.5	odd	6		2646.2.f.b.1765.1		2
9.7	even	3		7938.2.a.e.1.1		1
21.2	odd	6		2646.2.e.h.2125.1		2
21.5	even	6		2646.2.e.i.2125.1		2
21.11	odd	6		2646.2.h.c.667.1		2
21.17	even	6		2646.2.h.b.667.1		2
21.20	even	2		378.2.f.b.127.1		2
28.27	even	2		1008.2.r.a.673.1		2
63.4	even	3		882.2.e.e.373.1		2
63.5	even	6		2646.2.h.b.361.1		2
63.13	odd	6		126.2.f.b.85.1	yes	2
63.20	even	6		1134.2.a.f.1.1		1
63.23	odd	6		2646.2.h.c.361.1		2
63.31	odd	6		882.2.e.a.373.1		2
63.32	odd	6		2646.2.e.h.1549.1		2
63.34	odd	6		1134.2.a.c.1.1		1
63.40	odd	6		882.2.h.h.67.1		2
63.41	even	6		378.2.f.b.253.1		2
63.58	even	3		882.2.h.g.67.1		2
63.59	even	6		2646.2.e.i.1549.1		2
84.83	odd	2		3024.2.r.c.2017.1		2
252.83	odd	6		9072.2.a.f.1.1		1
252.139	even	6		1008.2.r.a.337.1		2
252.167	odd	6		3024.2.r.c.1009.1		2
252.223	even	6		9072.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.b.43.1	✓	2	7.6	odd	2
126.2.f.b.85.1	yes	2	63.13	odd	6
378.2.f.b.127.1		2	21.20	even	2
378.2.f.b.253.1		2	63.41	even	6
882.2.e.a.373.1		2	63.31	odd	6
882.2.e.a.655.1		2	7.5	odd	6
882.2.e.e.373.1		2	63.4	even	3
882.2.e.e.655.1		2	7.2	even	3
882.2.f.f.295.1		2	1.1	even	1	trivial
882.2.f.f.589.1		2	9.4	even	3	inner
882.2.h.g.67.1		2	63.58	even	3
882.2.h.g.79.1		2	7.4	even	3
882.2.h.h.67.1		2	63.40	odd	6
882.2.h.h.79.1		2	7.3	odd	6
1008.2.r.a.337.1		2	252.139	even	6
1008.2.r.a.673.1		2	28.27	even	2
1134.2.a.c.1.1		1	63.34	odd	6
1134.2.a.f.1.1		1	63.20	even	6
2646.2.e.h.1549.1		2	63.32	odd	6
2646.2.e.h.2125.1		2	21.2	odd	6
2646.2.e.i.1549.1		2	63.59	even	6
2646.2.e.i.2125.1		2	21.5	even	6
2646.2.f.b.883.1		2	3.2	odd	2
2646.2.f.b.1765.1		2	9.5	odd	6
2646.2.h.b.361.1		2	63.5	even	6
2646.2.h.b.667.1		2	21.17	even	6
2646.2.h.c.361.1		2	63.23	odd	6
2646.2.h.c.667.1		2	21.11	odd	6
3024.2.r.c.1009.1		2	252.167	odd	6
3024.2.r.c.2017.1		2	84.83	odd	2
7938.2.a.e.1.1		1	9.7	even	3
7938.2.a.bb.1.1		1	9.2	odd	6
9072.2.a.f.1.1		1	252.83	odd	6
9072.2.a.t.1.1		1	252.223	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (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} +(1.00000 + 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +2.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +1.73205i q^{12} +(-3.00000 - 5.19615i) q^{13} -3.46410i q^{15} +(-0.500000 + 0.866025i) q^{16} +5.00000 q^{17} +3.00000 q^{18} +7.00000 q^{19} +(1.00000 - 1.73205i) q^{20} +(0.500000 + 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(1.50000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} -6.00000 q^{26} -5.19615i q^{27} +(2.00000 - 3.46410i) q^{29} +(-3.00000 - 1.73205i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 0.866025i) q^{33} +(2.50000 - 4.33013i) q^{34} +(1.50000 - 2.59808i) q^{36} +2.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +10.3923i q^{39} +(-1.00000 - 1.73205i) q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +1.00000 q^{44} +(-3.00000 + 5.19615i) q^{45} -4.00000 q^{46} +(1.50000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{50} +(-7.50000 - 4.33013i) q^{51} +(-3.00000 + 5.19615i) q^{52} +12.0000 q^{53} +(-4.50000 - 2.59808i) q^{54} -2.00000 q^{55} +(-10.5000 - 6.06218i) q^{57} +(-2.00000 - 3.46410i) q^{58} +(-3.50000 - 6.06218i) q^{59} +(-3.00000 + 1.73205i) q^{60} +(-6.00000 + 10.3923i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} -1.73205i q^{66} +(-6.50000 - 11.2583i) q^{67} +(-2.50000 - 4.33013i) q^{68} +6.92820i q^{69} -8.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} -1.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-3.50000 - 6.06218i) q^{76} +(9.00000 + 5.19615i) q^{78} +(3.00000 - 5.19615i) q^{79} -2.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +3.00000 q^{82} +(8.00000 - 13.8564i) q^{83} +(5.00000 + 8.66025i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(-6.00000 + 3.46410i) q^{87} +(0.500000 - 0.866025i) q^{88} +6.00000 q^{89} +(3.00000 + 5.19615i) q^{90} +(-2.00000 + 3.46410i) q^{92} +10.3923i q^{93} +(7.00000 + 12.1244i) q^{95} -1.73205i q^{96} +(-2.50000 + 4.33013i) q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} - q^{4} + 2 q^{5} - 3 q^{6} - 2 q^{8} + 3 q^{9} + 4 q^{10} - q^{11} - 6 q^{13} - q^{16} + 10 q^{17} + 6 q^{18} + 14 q^{19} + 2 q^{20} + q^{22} - 4 q^{23} + 3 q^{24} + q^{25}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 - q^4 + 2 * q^5 - 3 * q^6 - 2 * q^8 + 3 * q^9 + 4 * q^10 - q^11 - 6 * q^13 - q^16 + 10 * q^17 + 6 * q^18 + 14 * q^19 + 2 * q^20 + q^22 - 4 * q^23 + 3 * q^24 + q^25 - 12 * q^26 + 4 * q^29 - 6 * q^30 - 6 * q^31 + q^32 + 3 * q^33 + 5 * q^34 + 3 * q^36 + 4 * q^37 + 7 * q^38 - 2 * q^40 + 3 * q^41 + q^43 + 2 * q^44 - 6 * q^45 - 8 * q^46 + 3 * q^48 - q^50 - 15 * q^51 - 6 * q^52 + 24 * q^53 - 9 * q^54 - 4 * q^55 - 21 * q^57 - 4 * q^58 - 7 * q^59 - 6 * q^60 - 12 * q^61 - 12 * q^62 + 2 * q^64 + 12 * q^65 - 13 * q^67 - 5 * q^68 - 16 * q^71 - 3 * q^72 - 2 * q^73 + 2 * q^74 - 3 * q^75 - 7 * q^76 + 18 * q^78 + 6 * q^79 - 4 * q^80 - 9 * q^81 + 6 * q^82 + 16 * q^83 + 10 * q^85 - q^86 - 12 * q^87 + q^88 + 12 * q^89 + 6 * q^90 - 4 * q^92 + 14 * q^95 - 5 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more