LMFDB - Embedded newform 882.2.h.g.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, 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:	$7.04280545828$
Analytic rank:	$1$
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			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.67
Dual form			882.2.h.g.79.1

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

Character values

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

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

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
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−3.00000			−1.00000
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	0.0643593	+	0.997927i	$0.479500\pi$
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	−0.896410	+	0.443227i	$0.853834\pi$
$14$		0			0
$15$			3.46410i			0.894427i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$		0			0
$22$	0.500000	−	0.866025i	0.106600	−	0.184637i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$			1.73205i			0.353553i
$25$	−1.00000			−0.200000
$26$	3.00000	+	5.19615i	0.588348	+	1.01905i
$27$			5.19615i			1.00000i
$28$		0			0
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	0.989780	−	0.142605i	$-0.0455477\pi$
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	−0.618389	+	0.785872i	$0.712214\pi$
$30$	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
$33$		−	1.73205i		−	0.301511i
$34$	2.50000	+	4.33013i	0.428746	+	0.742611i
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−7.00000			−1.13555
$39$	9.00000	+	5.19615i	1.44115	+	0.832050i
$40$	2.00000			0.316228
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	6.00000			0.894427
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$		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
$52$	6.00000			0.832050
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$	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
$58$	4.00000			0.525226
$59$	−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
$66$	−1.50000	−	0.866025i	−0.184637	−	0.106600i
$67$	−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	$-0.458725\pi$
$68$	5.00000			0.606339
$69$		−	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	$0.657448\pi$
$72$	3.00000			0.353553
$73$	0.500000	−	0.866025i	0.0585206	−	0.101361i	−0.835281	−	0.549823i	$-0.814695\pi$
$73$	0.500000	−	0.866025i	0.0585206	−	0.101361i	0.893801	+	0.448463i	$0.148028\pi$
$74$	−2.00000			−0.232495
$75$			1.73205i			0.200000i
$76$	−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	$0.0570765\pi$
$80$	1.00000	−	1.73205i	0.111803	−	0.193649i
$81$	9.00000			1.00000
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$	8.00000	+	13.8564i	0.878114	+	1.52094i	0.853408	+	0.521243i	$0.174532\pi$
$83$	8.00000	+	13.8564i	0.878114	+	1.52094i	0.0247060	+	0.999695i	$0.492135\pi$
$84$		0			0
$85$	5.00000	−	8.66025i	0.542326	−	0.939336i
$86$	1.00000			0.107833
$87$	6.00000	−	3.46410i	0.643268	−	0.371391i
$88$	−1.00000			−0.106600
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	3.00000	−	5.19615i	0.316228	−	0.547723i
$91$		0			0
$92$	−2.00000	−	3.46410i	−0.208514	−	0.361158i
$93$	−9.00000	+	5.19615i	−0.933257	+	0.538816i
$94$		0			0
$95$	7.00000	+	12.1244i	0.718185	+	1.24393i
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	−2.50000	−	4.33013i	−0.253837	−	0.439658i	0.710742	−	0.703452i	$-0.248359\pi$
$97$	−2.50000	−	4.33013i	−0.253837	−	0.439658i	−0.964579	+	0.263795i	$0.915026\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	4.00000			0.398015			0.199007	−	0.979998i	$-0.436228\pi$
$101$	4.00000			0.398015			0.199007	+	0.979998i	$0.436228\pi$
$102$	7.50000	−	4.33013i	0.742611	−	0.428746i
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	3.00000	−	5.19615i	0.294174	−	0.509525i
$105$		0			0
$106$	6.00000	+	10.3923i	0.582772	+	1.00939i
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−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	−0.529065	−	0.848581i	$-0.677457\pi$
$113$	5.00000	−	8.66025i	0.470360	−	0.814688i	0.999425	+	0.0338931i	$0.0107906\pi$
$114$			12.1244i			1.13555i
$115$	−8.00000			−0.746004
$116$	2.00000	−	3.46410i	0.185695	−	0.321634i
$117$	9.00000	−	15.5885i	0.832050	−	1.44115i
$118$	−7.00000			−0.644402
$119$		0			0
$120$		−	3.46410i		−	0.316228i
$121$	−10.0000			−0.909091
$122$	6.00000	+	10.3923i	0.543214	+	0.940875i
$123$	−4.50000	−	2.59808i	−0.405751	−	0.234261i
$124$	−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
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$	−1.50000	+	0.866025i	−0.130558	+	0.0753778i
$133$		0			0
$134$	−13.0000			−1.12303
$135$		−	10.3923i		−	0.894427i
$136$	2.50000	−	4.33013i	0.214373	−	0.371305i
$137$	−19.0000			−1.62328			−0.811640	−	0.584158i	$-0.801425\pi$
$137$	−19.0000			−1.62328			−0.811640	+	0.584158i	$0.801425\pi$
$138$	−6.00000	−	3.46410i	−0.510754	−	0.294884i
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$		0			0
$142$	−4.00000	+	6.92820i	−0.335673	+	0.581402i
$143$	−3.00000	+	5.19615i	−0.250873	+	0.434524i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	−4.00000	−	6.92820i	−0.332182	−	0.575356i
$146$	−0.500000	−	0.866025i	−0.0413803	−	0.0716728i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	−24.0000			−1.96616			−0.983078	−	0.183186i	$-0.941359\pi$
$149$	−24.0000			−1.96616			−0.983078	+	0.183186i	$0.941359\pi$
$150$	1.50000	+	0.866025i	0.122474	+	0.0707107i
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$	3.50000	+	6.06218i	0.283887	+	0.491708i
$153$	7.50000	−	12.9904i	0.606339	−	1.05021i
$154$		0			0
$155$	6.00000	+	10.3923i	0.481932	+	0.834730i
$156$		−	10.3923i		−	0.832050i
$157$	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
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	−3.00000			−0.234261
$165$			3.46410i			0.269680i
$166$	16.0000			1.24184
$167$	10.0000	−	17.3205i	0.773823	−	1.34030i	−0.161630	−	0.986851i	$-0.551675\pi$
$167$	10.0000	−	17.3205i	0.773823	−	1.34030i	0.935454	−	0.353450i	$-0.114991\pi$
$168$		0			0
$169$	−11.5000	−	19.9186i	−0.884615	−	1.53220i
$170$	−5.00000	−	8.66025i	−0.383482	−	0.664211i
$171$	10.5000	+	18.1865i	0.802955	+	1.39076i
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	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
$177$	−10.5000	+	6.06218i	−0.789228	+	0.455661i
$178$	−6.00000			−0.449719
$179$	−12.0000	+	20.7846i	−0.896922	+	1.55351i	−0.0655145	+	0.997852i	$0.520869\pi$
$179$	−12.0000	+	20.7846i	−0.896922	+	1.55351i	−0.831408	+	0.555663i	$0.812464\pi$
$180$	−3.00000	−	5.19615i	−0.223607	−	0.387298i
$181$		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
$184$	−4.00000			−0.294884
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$			10.3923i			0.762001i
$187$	−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	$0.309616\pi$
$192$		−	1.73205i		−	0.125000i
$193$	−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	$-0.376238\pi$
$194$	−5.00000			−0.358979
$195$	−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
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	−0.503774	−	0.863836i	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$	1.00000			0.0707107
$201$	−19.5000	+	11.2583i	−1.37542	+	0.794101i
$202$	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
$206$	−7.00000	+	12.1244i	−0.487713	+	0.844744i
$207$	−12.0000			−0.834058
$208$	−3.00000	−	5.19615i	−0.208013	−	0.360288i
$209$	−3.50000	−	6.06218i	−0.242100	−	0.419330i
$210$		0			0
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	0.998221	−	0.0596196i	$-0.0189888\pi$
$212$	12.0000			0.824163
$213$			13.8564i			0.949425i
$214$	−3.00000			−0.205076
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$		−	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
$222$			3.46410i			0.232495i
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	0.791258	−	0.611482i	$-0.209426\pi$
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	−0.925188	+	0.379509i	$0.876093\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$	−5.00000	−	8.66025i	−0.332595	−	0.576072i
$227$	−3.00000			−0.199117			−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000			−0.199117			−0.0995585	+	0.995032i	$0.531743\pi$
$228$	10.5000	+	6.06218i	0.695379	+	0.401478i
$229$	26.0000			1.71813			0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000			1.71813			0.859064	+	0.511868i	$0.171046\pi$
$230$	−4.00000	+	6.92820i	−0.263752	+	0.456832i
$231$		0			0
$232$	−2.00000	−	3.46410i	−0.131306	−	0.227429i
$233$	14.5000	+	25.1147i	0.949927	+	1.64532i	0.745573	+	0.666424i	$0.232176\pi$
$233$	14.5000	+	25.1147i	0.949927	+	1.64532i	0.204354	+	0.978897i	$0.434491\pi$
$234$	−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	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$	−3.00000	−	1.73205i	−0.193649	−	0.111803i
$241$	−23.0000			−1.48156			−0.740780	−	0.671748i	$-0.765544\pi$
$241$	−23.0000			−1.48156			−0.740780	+	0.671748i	$0.765544\pi$
$242$	−5.00000	+	8.66025i	−0.321412	+	0.556702i
$243$		−	15.5885i		−	1.00000i
$244$	12.0000			0.768221
$245$		0			0
$246$	−4.50000	+	2.59808i	−0.286910	+	0.165647i
$247$	42.0000			2.67240
$248$	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
$255$	−15.0000	−	8.66025i	−0.939336	−	0.542326i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.0000			0.935674			0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000			0.935674			0.467837	+	0.883815i	$0.345033\pi$
$258$		−	1.73205i		−	0.107833i
$259$		0			0
$260$	−12.0000			−0.744208
$261$	−6.00000	−	10.3923i	−0.371391	−	0.643268i
$262$	2.00000	−	3.46410i	0.123560	−	0.214013i
$263$	18.0000			1.10993			0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000			1.10993			0.554964	+	0.831875i	$0.312732\pi$
$264$			1.73205i			0.106600i
$265$	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
$269$	10.0000	−	17.3205i	0.609711	−	1.05605i	−0.381577	−	0.924337i	$-0.624619\pi$
$269$	10.0000	−	17.3205i	0.609711	−	1.05605i	0.991288	−	0.131713i	$-0.0420477\pi$
$270$	−9.00000	−	5.19615i	−0.547723	−	0.316228i
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	0.760405	−	0.649449i	$-0.225000\pi$
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	−0.942642	+	0.333805i	$0.891667\pi$
$272$	−2.50000	−	4.33013i	−0.151585	−	0.262553i
$273$		0			0
$274$	−9.50000	+	16.4545i	−0.573916	+	0.994052i
$275$	−1.00000			−0.0603023
$276$	−6.00000	+	3.46410i	−0.361158	+	0.208514i
$277$	2.00000			0.120168			0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000			0.120168			0.0600842	+	0.998193i	$0.480863\pi$
$278$	2.50000	+	4.33013i	0.149940	+	0.259704i
$279$	9.00000	+	15.5885i	0.538816	+	0.933257i
$280$		0			0
$281$	−11.0000	−	19.0526i	−0.656205	−	1.13658i	−0.981590	−	0.190999i	$-0.938827\pi$
$281$	−11.0000	−	19.0526i	−0.656205	−	1.13658i	0.325385	−	0.945582i	$-0.394506\pi$
$282$		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
$285$	21.0000	−	12.1244i	1.24393	−	0.718185i
$286$	3.00000	+	5.19615i	0.177394	+	0.307255i
$287$		0			0
$288$	−1.50000	−	2.59808i	−0.0883883	−	0.153093i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	−8.00000			−0.469776
$291$	−7.50000	+	4.33013i	−0.439658	+	0.253837i
$292$	−1.00000			−0.0585206
$293$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$293$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$294$		0			0
$295$	7.00000	+	12.1244i	0.407556	+	0.705907i
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$			5.19615i			0.301511i
$298$	−12.0000	+	20.7846i	−0.695141	+	1.20402i
$299$	−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
$303$		−	6.92820i		−	0.398015i
$304$	7.00000			0.401478
$305$	12.0000	−	20.7846i	0.687118	−	1.19012i
$306$	−7.50000	−	12.9904i	−0.428746	−	0.742611i
$307$	−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
$310$	12.0000			0.681554
$311$	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	$0.815274\pi$
$312$	−9.00000	−	5.19615i	−0.509525	−	0.294174i
$313$	−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
$320$	−2.00000			−0.111803
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$		0			0
$323$	35.0000			1.94745
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	3.00000	−	5.19615i	0.166410	−	0.288231i
$326$	4.00000			0.221540
$327$	−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	$0.237227\pi$
$332$	8.00000	−	13.8564i	0.439057	−	0.760469i
$333$	3.00000	+	5.19615i	0.164399	+	0.284747i
$334$	−10.0000	−	17.3205i	−0.547176	−	0.947736i
$335$	13.0000	+	22.5167i	0.710266	+	1.23022i
$336$		0			0
$337$	4.50000	−	7.79423i	0.245131	−	0.424579i	−0.717038	−	0.697034i	$-0.754502\pi$
$337$	4.50000	−	7.79423i	0.245131	−	0.424579i	0.962168	+	0.272456i	$0.0878358\pi$
$338$	−23.0000			−1.25104
$339$	−15.0000	−	8.66025i	−0.814688	−	0.470360i
$340$	−10.0000			−0.542326
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$	21.0000			1.13555
$343$		0			0
$344$	−0.500000	−	0.866025i	−0.0269582	−	0.0466930i
$345$			13.8564i			0.746004i
$346$	−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	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$		0			0
$351$	−27.0000	−	15.5885i	−1.44115	−	0.832050i
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	15.0000			0.798369			0.399185	−	0.916871i	$-0.369293\pi$
$353$	15.0000			0.798369			0.399185	+	0.916871i	$0.369293\pi$
$354$			12.1244i			0.644402i
$355$	16.0000			0.849192
$356$	−3.00000	+	5.19615i	−0.159000	+	0.275396i
$357$		0			0
$358$	12.0000	+	20.7846i	0.634220	+	1.09850i
$359$	−1.00000	−	1.73205i	−0.0527780	−	0.0914141i	0.838429	−	0.545010i	$-0.183474\pi$
$359$	−1.00000	−	1.73205i	−0.0527780	−	0.0914141i	−0.891207	+	0.453596i	$0.850141\pi$
$360$	−6.00000			−0.316228
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$		0			0
$363$			17.3205i			0.909091i
$364$		0			0
$365$	−1.00000	+	1.73205i	−0.0523424	+	0.0906597i
$366$	18.0000	−	10.3923i	0.940875	−	0.543214i
$367$	22.0000			1.14839			0.574195	−	0.818718i	$-0.305315\pi$
$367$	22.0000			1.14839			0.574195	+	0.818718i	$0.305315\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$	−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
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$	2.50000	+	4.33013i	0.129272	+	0.223906i
$375$		−	20.7846i		−	1.07331i
$376$		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
$381$			20.7846i			1.06483i
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	−4.00000			−0.204390			−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000			−0.204390			−0.102195	+	0.994764i	$0.532587\pi$
$384$	−1.50000	−	0.866025i	−0.0765466	−	0.0441942i
$385$		0			0
$386$	−17.0000			−0.865277
$387$	−1.50000	−	2.59808i	−0.0762493	−	0.132068i
$388$	−2.50000	+	4.33013i	−0.126918	+	0.219829i
$389$	8.00000			0.405616			0.202808	−	0.979219i	$-0.434993\pi$
$389$	8.00000			0.405616			0.202808	+	0.979219i	$0.434993\pi$
$390$	−18.0000	+	10.3923i	−0.911465	+	0.526235i
$391$	−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
$395$	−6.00000	+	10.3923i	−0.301893	+	0.522894i
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	0.998492	−	0.0549046i	$-0.0174855\pi$
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	−0.546795	+	0.837267i	$0.684152\pi$
$398$	−7.00000	−	12.1244i	−0.350878	−	0.607739i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	9.00000			0.449439			0.224719	−	0.974424i	$-0.427853\pi$
$401$	9.00000			0.449439			0.224719	+	0.974424i	$0.427853\pi$
$402$			22.5167i			1.12303i
$403$	36.0000			1.79329
$404$	−2.00000	−	3.46410i	−0.0995037	−	0.172345i
$405$	−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
$411$			32.9090i			1.62328i
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$		0			0
$414$	−6.00000	+	10.3923i	−0.294884	+	0.510754i
$415$	−16.0000	−	27.7128i	−0.785409	−	1.36037i
$416$	−6.00000			−0.294174
$417$	7.50000	+	4.33013i	0.367277	+	0.212047i
$418$	−7.00000			−0.342381
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	−0.974546	−	0.224189i	$-0.928027\pi$
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	0.681426	+	0.731887i	$0.261360\pi$
$420$		0			0
$421$	6.00000	+	10.3923i	0.292422	+	0.506490i	0.974382	−	0.224900i	$-0.0722054\pi$
$421$	6.00000	+	10.3923i	0.292422	+	0.506490i	−0.681960	+	0.731390i	$0.738872\pi$
$422$	−8.00000	−	13.8564i	−0.389434	−	0.674519i
$423$		0			0
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	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
$430$	−2.00000			−0.0964486
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	−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
$436$	−2.00000			−0.0957826
$437$	−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	$0.219845\pi$
$444$	3.00000	+	1.73205i	0.142374	+	0.0821995i
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	−4.00000			−0.189405
$447$			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
$451$	1.50000	−	2.59808i	0.0706322	−	0.122339i
$452$	−10.0000			−0.470360
$453$		−	17.3205i		−	0.813788i
$454$	−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	$0.174112\pi$
$458$	13.0000	−	22.5167i	0.607450	−	1.05213i
$459$	−22.5000	−	12.9904i	−1.05021	−	0.606339i
$460$	4.00000	+	6.92820i	0.186501	+	0.323029i
$461$	7.00000	+	12.1244i	0.326023	+	0.564688i	0.981719	−	0.190337i	$-0.0609581\pi$
$461$	7.00000	+	12.1244i	0.326023	+	0.564688i	−0.655696	+	0.755025i	$0.727625\pi$
$462$		0			0
$463$	4.00000	−	6.92820i	0.185896	−	0.321981i	−0.757982	−	0.652275i	$-0.773815\pi$
$463$	4.00000	−	6.92820i	0.185896	−	0.321981i	0.943878	+	0.330294i	$0.107148\pi$
$464$	−4.00000			−0.185695
$465$	18.0000	−	10.3923i	0.834730	−	0.481932i
$466$	29.0000			1.34340
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	0.675530	−	0.737333i	$-0.263915\pi$
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	−0.976314	+	0.216359i	$0.930582\pi$
$468$	−18.0000			−0.832050
$469$		0			0
$470$		0			0
$471$	3.00000	−	1.73205i	0.138233	−	0.0798087i
$472$	3.50000	+	6.06218i	0.161101	+	0.279034i
$473$	0.500000	+	0.866025i	0.0229900	+	0.0398199i
$474$	−9.00000	+	5.19615i	−0.413384	+	0.238667i
$475$	3.50000	+	6.06218i	0.160591	+	0.278152i
$476$		0			0
$477$	18.0000	−	31.1769i	0.824163	−	1.42749i
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	20.0000			0.913823			0.456912	−	0.889512i	$-0.348956\pi$
$479$	20.0000			0.913823			0.456912	+	0.889512i	$0.348956\pi$
$480$	−3.00000	+	1.73205i	−0.136931	+	0.0790569i
$481$	12.0000			0.547153
$482$	−11.5000	+	19.9186i	−0.523811	+	0.907267i
$483$		0			0
$484$	5.00000	+	8.66025i	0.227273	+	0.393648i
$485$	5.00000	+	8.66025i	0.227038	+	0.393242i
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	5.00000	−	8.66025i	0.226572	−	0.392434i	−0.730218	−	0.683214i	$-0.760582\pi$
$487$	5.00000	−	8.66025i	0.226572	−	0.392434i	0.956790	+	0.290780i	$0.0939149\pi$
$488$	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	0.205731	+	0.978609i	$0.434043\pi$
$491$	−16.5000	+	28.5788i	−0.744635	+	1.28974i	−0.950365	+	0.311136i	$0.899290\pi$
$492$			5.19615i			0.234261i
$493$	−20.0000			−0.900755
$494$	21.0000	−	36.3731i	0.944835	−	1.63650i
$495$	6.00000			0.269680
$496$	6.00000			0.269408
$497$		0			0
$498$		−	27.7128i		−	1.24184i
$499$	−29.0000			−1.29822			−0.649109	−	0.760695i	$-0.724858\pi$
$499$	−29.0000			−1.29822			−0.649109	+	0.760695i	$0.724858\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$	−30.0000	−	17.3205i	−1.34030	−	0.773823i
$502$	−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
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$	−15.0000	+	8.66025i	−0.664211	+	0.383482i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	31.5000	−	18.1865i	1.39076	−	0.802955i
$514$	7.50000	−	12.9904i	0.330811	−	0.572981i
$515$	28.0000			1.23383
$516$	−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
$521$	−4.50000	+	7.79423i	−0.197149	+	0.341471i	−0.947603	−	0.319451i	$-0.896501\pi$
$521$	−4.50000	+	7.79423i	−0.197149	+	0.341471i	0.750454	+	0.660922i	$0.229835\pi$
$522$	−12.0000			−0.525226
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	−0.990873	−	0.134801i	$-0.956961\pi$
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	0.378695	−	0.925521i	$-0.376373\pi$
$524$	−2.00000	−	3.46410i	−0.0873704	−	0.151330i
$525$		0			0
$526$	9.00000	−	15.5885i	0.392419	−	0.679689i
$527$	30.0000			1.30682
$528$	1.50000	+	0.866025i	0.0652791	+	0.0376889i
$529$	−7.00000			−0.304348
$530$	−12.0000	−	20.7846i	−0.521247	−	0.902826i
$531$	10.5000	+	18.1865i	0.455661	+	0.789228i
$532$		0			0
$533$	9.00000	+	15.5885i	0.389833	+	0.675211i
$534$			10.3923i			0.449719i
$535$	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
$541$	12.0000	+	20.7846i	0.515920	+	0.893600i	0.999829	+	0.0184818i	$0.00588327\pi$
$541$	12.0000	+	20.7846i	0.515920	+	0.893600i	−0.483909	+	0.875118i	$0.660783\pi$
$542$	−6.00000			−0.257722
$543$		0			0
$544$	−5.00000			−0.214373
$545$	−2.00000	+	3.46410i	−0.0856706	+	0.148386i
$546$		0			0
$547$	10.5000	+	18.1865i	0.448948	+	0.777600i	0.998318	−	0.0579790i	$-0.0184657\pi$
$547$	10.5000	+	18.1865i	0.448948	+	0.777600i	−0.549370	+	0.835579i	$0.685132\pi$
$548$	9.50000	+	16.4545i	0.405820	+	0.702901i
$549$	18.0000	−	31.1769i	0.768221	−	1.33060i
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$	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
$555$	6.00000	−	3.46410i	0.254686	−	0.147043i
$556$	5.00000			0.212047
$557$	14.0000	−	24.2487i	0.593199	−	1.02745i	−0.400599	−	0.916253i	$-0.631198\pi$
$557$	14.0000	−	24.2487i	0.593199	−	1.02745i	0.993798	−	0.111198i	$-0.0354686\pi$
$558$	18.0000			0.762001
$559$	−6.00000			−0.253773
$560$		0			0
$561$	7.50000	+	4.33013i	0.316650	+	0.182818i
$562$	−22.0000			−0.928014
$563$	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	$0.0648579\pi$
$570$		−	24.2487i		−	1.01567i
$571$	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	$0.590722\pi$
$572$	6.00000			0.250873
$573$	18.0000	+	10.3923i	0.751961	+	0.434145i
$574$		0			0
$575$	−4.00000			−0.166812
$576$	−3.00000			−0.125000
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	0.228968	+	0.973434i	$0.426465\pi$
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−8.00000			−0.332756
$579$	−25.5000	+	14.7224i	−1.05974	+	0.611843i
$580$	−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
$584$	−0.500000	+	0.866025i	−0.0206901	+	0.0358364i
$585$	−18.0000	+	31.1769i	−0.744208	+	1.28901i
$586$		0			0
$587$	−23.5000	−	40.7032i	−0.969949	−	1.68000i	−0.695686	−	0.718346i	$-0.744900\pi$
$587$	−23.5000	−	40.7032i	−0.969949	−	1.68000i	−0.274263	−	0.961655i	$-0.588434\pi$
$588$		0			0
$589$	−21.0000	+	36.3731i	−0.865290	+	1.49873i
$590$	14.0000			0.576371
$591$		−	17.3205i		−	0.712470i
$592$	2.00000			0.0821995
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$	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	$0.996449\pi$
$600$		−	1.73205i		−	0.0707107i
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	0.604601	−	0.796528i	$-0.293332\pi$
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	−0.992114	+	0.125336i	$0.959999\pi$
$602$		0			0
$603$	19.5000	+	33.7750i	0.794101	+	1.37542i
$604$	−5.00000	−	8.66025i	−0.203447	−	0.352381i
$605$	20.0000			0.813116
$606$	−6.00000	−	3.46410i	−0.243733	−	0.140720i
$607$	24.0000			0.974130			0.487065	−	0.873366i	$-0.338067\pi$
$607$	24.0000			0.974130			0.487065	+	0.873366i	$0.338067\pi$
$608$	3.50000	−	6.06218i	0.141944	−	0.245854i
$609$		0			0
$610$	−12.0000	−	20.7846i	−0.485866	−	0.841544i
$611$		0			0
$612$	−15.0000			−0.606339
$613$	−21.0000	+	36.3731i	−0.848182	+	1.46909i	0.0346469	+	0.999400i	$0.488969\pi$
$613$	−21.0000	+	36.3731i	−0.848182	+	1.46909i	−0.882829	+	0.469695i	$0.844364\pi$
$614$	−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	−0.642643	−	0.766165i	$-0.722162\pi$
$617$	8.50000	−	14.7224i	0.342197	−	0.592703i	0.984840	+	0.173463i	$0.0554956\pi$
$618$	21.0000	+	12.1244i	0.844744	+	0.487713i
$619$	−37.0000			−1.48716			−0.743578	−	0.668649i	$-0.766873\pi$
$619$	−37.0000			−1.48716			−0.743578	+	0.668649i	$0.766873\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$			20.7846i			0.834058i
$622$	2.00000			0.0801927
$623$		0			0
$624$	−9.00000	+	5.19615i	−0.360288	+	0.208013i
$625$	−19.0000			−0.760000
$626$	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
$633$	−24.0000	−	13.8564i	−0.953914	−	0.550743i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	24.0000			0.952411
$636$		−	20.7846i		−	0.824163i
$637$		0			0
$638$	4.00000			0.158362
$639$	24.0000			0.949425
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	1.00000			0.0394976			0.0197488	−	0.999805i	$-0.493713\pi$
$641$	1.00000			0.0394976			0.0197488	+	0.999805i	$0.493713\pi$
$642$			5.19615i			0.205076i
$643$	−3.50000	+	6.06218i	−0.138027	+	0.239069i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$	−3.50000	+	6.06218i	−0.138027	+	0.239069i	0.788723	+	0.614749i	$0.210743\pi$
$644$		0			0
$645$	−3.00000	+	1.73205i	−0.118125	+	0.0681994i
$646$	17.5000	−	30.3109i	0.688528	−	1.19257i
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	−0.723645	−	0.690172i	$-0.757535\pi$
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	0.959529	+	0.281609i	$0.0908680\pi$
$648$	−9.00000			−0.353553
$649$	−3.50000	−	6.06218i	−0.137387	−	0.237961i
$650$	−3.00000	−	5.19615i	−0.117670	−	0.203810i
$651$		0			0
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$	−3.00000	+	1.73205i	−0.117309	+	0.0677285i
$655$	−8.00000			−0.312586
$656$	1.50000	+	2.59808i	0.0585652	+	0.101438i
$657$	−1.50000	+	2.59808i	−0.0585206	+	0.101361i
$658$		0			0
$659$	−8.00000	−	13.8564i	−0.311636	−	0.539769i	0.667081	−	0.744985i	$-0.267544\pi$
$659$	−8.00000	−	13.8564i	−0.311636	−	0.539769i	−0.978717	+	0.205216i	$0.934210\pi$
$660$	3.00000	−	1.73205i	0.116775	−	0.0674200i
$661$	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
$663$	−45.0000	+	25.9808i	−1.74766	+	1.00901i
$664$	−8.00000	−	13.8564i	−0.310460	−	0.537733i
$665$		0			0
$666$	6.00000			0.232495
$667$	8.00000	+	13.8564i	0.309761	+	0.536522i
$668$	−20.0000			−0.773823
$669$	−6.00000	+	3.46410i	−0.231973	+	0.133930i
$670$	26.0000			1.00447
$671$	−6.00000	+	10.3923i	−0.231627	+	0.401190i
$672$		0			0
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$	−4.50000	−	7.79423i	−0.173334	−	0.300222i
$675$		−	5.19615i		−	0.200000i
$676$	−11.5000	+	19.9186i	−0.442308	+	0.766099i
$677$	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
$681$			5.19615i			0.199117i
$682$	−6.00000			−0.229752
$683$	−19.5000	+	33.7750i	−0.746147	+	1.29236i	0.203510	+	0.979073i	$0.434765\pi$
$683$	−19.5000	+	33.7750i	−0.746147	+	1.29236i	−0.949657	+	0.313291i	$0.898568\pi$
$684$	10.5000	−	18.1865i	0.401478	−	0.695379i
$685$	38.0000			1.45191
$686$		0			0
$687$		−	45.0333i		−	1.71813i
$688$	−1.00000			−0.0381246
$689$	−36.0000	−	62.3538i	−1.37149	−	2.37549i
$690$	12.0000	+	6.92820i	0.456832	+	0.263752i
$691$	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
$698$	−14.0000			−0.529908
$699$	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	$0.451726\pi$
$702$	−27.0000	+	15.5885i	−1.01905	+	0.588348i
$703$	−7.00000	+	12.1244i	−0.264010	+	0.457279i
$704$	1.00000			0.0376889
$705$		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	$0.142735\pi$
$710$	8.00000	−	13.8564i	0.300235	−	0.520022i
$711$	−9.00000	+	15.5885i	−0.337526	+	0.584613i
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$		0			0
$715$	6.00000	−	10.3923i	0.224387	−	0.388650i
$716$	24.0000			0.896922
$717$	9.00000	+	5.19615i	0.336111	+	0.194054i
$718$	−2.00000			−0.0746393
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	0.916529	−	0.399969i	$-0.130979\pi$
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	−0.804648	+	0.593753i	$0.797646\pi$
$720$	−3.00000	+	5.19615i	−0.111803	+	0.193649i
$721$		0			0
$722$	15.0000	+	25.9808i	0.558242	+	0.966904i
$723$			39.8372i			1.48156i
$724$		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	0.706523	−	0.707690i	$-0.250263\pi$
$727$	−7.00000	−	12.1244i	−0.259616	−	0.449667i	−0.966139	+	0.258022i	$0.916929\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	1.00000	+	1.73205i	0.0370117	+	0.0641061i
$731$	−5.00000			−0.184932
$732$		−	20.7846i		−	0.768221i
$733$	18.0000			0.664845			0.332423	−	0.943131i	$-0.392134\pi$
$733$	18.0000			0.664845			0.332423	+	0.943131i	$0.392134\pi$
$734$	11.0000	−	19.0526i	0.406017	−	0.703243i
$735$		0			0
$736$	2.00000	+	3.46410i	0.0737210	+	0.127688i
$737$	−6.50000	−	11.2583i	−0.239431	−	0.414706i
$738$	4.50000	+	7.79423i	0.165647	+	0.286910i
$739$	16.5000	−	28.5788i	0.606962	−	1.05129i	−0.384776	−	0.923010i	$-0.625721\pi$
$739$	16.5000	−	28.5788i	0.606962	−	1.05129i	0.991738	−	0.128279i	$-0.0409454\pi$
$740$	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	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$	9.00000	−	5.19615i	0.329956	−	0.190500i
$745$	48.0000			1.75858
$746$	11.0000	−	19.0526i	0.402739	−	0.697564i
$747$	−24.0000	−	41.5692i	−0.878114	−	1.52094i
$748$	5.00000			0.182818
$749$		0			0
$750$	−18.0000	−	10.3923i	−0.657267	−	0.379473i
$751$	−18.0000			−0.656829			−0.328415	−	0.944534i	$-0.606514\pi$
$751$	−18.0000			−0.656829			−0.328415	+	0.944534i	$0.606514\pi$
$752$		0			0
$753$			5.19615i			0.189358i
$754$	−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
$759$		−	6.92820i		−	0.251478i
$760$	−7.00000	−	12.1244i	−0.253917	−	0.439797i
$761$	−10.0000			−0.362500			−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000			−0.362500			−0.181250	+	0.983437i	$0.558014\pi$
$762$	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
$766$	−2.00000	+	3.46410i	−0.0722629	+	0.125163i
$767$	42.0000			1.51653
$768$	−1.50000	+	0.866025i	−0.0541266	+	0.0312500i
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	−0.596643	−	0.802507i	$-0.703499\pi$
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	0.993313	+	0.115454i	$0.0368323\pi$
$770$		0			0
$771$		−	25.9808i		−	0.935674i
$772$	−8.50000	+	14.7224i	−0.305922	+	0.529872i
$773$	−26.0000	+	45.0333i	−0.935155	+	1.61974i	−0.160798	+	0.986987i	$0.551407\pi$
$773$	−26.0000	+	45.0333i	−0.935155	+	1.61974i	−0.774357	+	0.632749i	$0.781927\pi$
$774$	−3.00000			−0.107833
$775$	3.00000	+	5.19615i	0.107763	+	0.186651i
$776$	2.50000	+	4.33013i	0.0897448	+	0.155443i
$777$		0			0
$778$	4.00000	−	6.92820i	0.143407	−	0.248388i
$779$	−21.0000			−0.752403
$780$			20.7846i			0.744208i
$781$	−8.00000			−0.286263
$782$	10.0000	+	17.3205i	0.357599	+	0.619380i
$783$	−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
$789$		−	31.1769i		−	1.10993i
$790$	6.00000	+	10.3923i	0.213470	+	0.369742i
$791$		0			0
$792$	3.00000			0.106600
$793$	−36.0000	−	62.3538i	−1.27840	−	2.21425i
$794$	18.0000			0.638796
$795$	−36.0000	−	20.7846i	−1.27679	−	0.737154i
$796$	−14.0000			−0.496217
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	−0.952506	−	0.304520i	$-0.901504\pi$
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	0.739975	+	0.672634i	$0.234837\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$	4.50000	−	7.79423i	0.158901	−	0.275224i
$803$	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
$808$	−4.00000			−0.140720
$809$	21.5000	−	37.2391i	0.755900	−	1.30926i	−0.189026	−	0.981972i	$-0.560533\pi$
$809$	21.5000	−	37.2391i	0.755900	−	1.30926i	0.944926	−	0.327285i	$-0.106134\pi$
$810$	−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
$814$	−2.00000			−0.0701000
$815$	−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	$0.870060\pi$
$822$	28.5000	+	16.4545i	0.994052	+	0.573916i
$823$	−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	$-0.368558\pi$
$824$	14.0000			0.487713
$825$			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	$0.433096\pi$
$828$	6.00000	+	10.3923i	0.208514	+	0.361158i
$829$	2.00000	−	3.46410i	0.0694629	−	0.120313i	−0.829202	−	0.558949i	$-0.811205\pi$
$829$	2.00000	−	3.46410i	0.0694629	−	0.120313i	0.898665	+	0.438636i	$0.144538\pi$
$830$	−32.0000			−1.11074
$831$		−	3.46410i		−	0.120168i
$832$	−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
$836$	−3.50000	+	6.06218i	−0.121050	+	0.209665i
$837$	27.0000	−	15.5885i	0.933257	−	0.538816i
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$	−10.0000	−	17.3205i	−0.345238	−	0.597970i	0.640159	−	0.768243i	$-0.278869\pi$
$839$	−10.0000	−	17.3205i	−0.345238	−	0.597970i	−0.985397	+	0.170272i	$0.945535\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	12.0000			0.413547
$843$	−33.0000	+	19.0526i	−1.13658	+	0.656205i
$844$	−16.0000			−0.550743
$845$	23.0000	+	39.8372i	0.791224	+	1.37044i
$846$		0			0
$847$		0			0
$848$	−6.00000	−	10.3923i	−0.206041	−	0.356873i
$849$	6.00000	−	3.46410i	0.205919	−	0.118888i
$850$	−2.50000	−	4.33013i	−0.0857493	−	0.148522i
$851$	−4.00000	−	6.92820i	−0.137118	−	0.237496i
$852$	12.0000	−	6.92820i	0.411113	−	0.237356i
$853$	22.0000	+	38.1051i	0.753266	+	1.30469i	0.946232	+	0.323489i	$0.104856\pi$
$853$	22.0000	+	38.1051i	0.753266	+	1.30469i	−0.192966	+	0.981205i	$0.561811\pi$
$854$		0			0
$855$	−21.0000	−	36.3731i	−0.718185	−	1.24393i
$856$	1.50000	+	2.59808i	0.0512689	+	0.0888004i
$857$	−30.0000			−1.02478			−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000			−1.02478			−0.512390	+	0.858753i	$0.671240\pi$
$858$	9.00000	−	5.19615i	0.307255	−	0.177394i
$859$	−29.0000			−0.989467			−0.494734	−	0.869045i	$-0.664734\pi$
$859$	−29.0000			−0.989467			−0.494734	+	0.869045i	$0.664734\pi$
$860$	−1.00000	+	1.73205i	−0.0340997	+	0.0590624i
$861$		0			0
$862$		0			0
$863$	−19.0000	−	32.9090i	−0.646768	−	1.12023i	−0.983890	−	0.178774i	$-0.942787\pi$
$863$	−19.0000	−	32.9090i	−0.646768	−	1.12023i	0.337123	−	0.941461i	$-0.390546\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	−2.00000	+	3.46410i	−0.0680020	+	0.117783i
$866$	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
$870$			13.8564i			0.469776i
$871$	78.0000			2.64293
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$	7.50000	+	12.9904i	0.253837	+	0.439658i
$874$	−28.0000			−0.947114
$875$		0			0
$876$			1.73205i			0.0585206i
$877$	16.0000			0.540282			0.270141	−	0.962821i	$-0.412930\pi$
$877$	16.0000			0.540282			0.270141	+	0.962821i	$0.412930\pi$
$878$	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
$887$	6.00000			0.201460			0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000			0.201460			0.100730	+	0.994914i	$0.467882\pi$
$888$	3.00000	−	1.73205i	0.100673	−	0.0581238i
$889$		0			0
$890$	12.0000			0.402241
$891$	9.00000			0.301511
$892$	−2.00000	+	3.46410i	−0.0669650	+	0.115987i
$893$		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
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$	−1.50000	−	2.59808i	−0.0500000	−	0.0866025i
$901$	−30.0000	−	51.9615i	−0.999445	−	1.73109i
$902$	−1.50000	−	2.59808i	−0.0499445	−	0.0865065i
$903$		0			0
$904$	−5.00000	+	8.66025i	−0.166298	+	0.288036i
$905$		0			0
$906$	−15.0000	−	8.66025i	−0.498342	−	0.287718i
$907$	−27.0000			−0.896520			−0.448260	−	0.893903i	$-0.647956\pi$
$907$	−27.0000			−0.896520			−0.448260	+	0.893903i	$0.647956\pi$
$908$	1.50000	+	2.59808i	0.0497792	+	0.0862202i
$909$	−12.0000			−0.398015
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$		−	12.1244i		−	0.401478i
$913$	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
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	0.703378	−	0.710816i	$-0.251674\pi$
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	−0.967274	+	0.253735i	$0.918341\pi$
$920$	8.00000			0.263752
$921$			12.1244i			0.399511i
$922$	14.0000			0.461065
$923$	24.0000	−	41.5692i	0.789970	−	1.36827i
$924$		0			0
$925$	1.00000	+	1.73205i	0.0328798	+	0.0569495i
$926$	−4.00000	−	6.92820i	−0.131448	−	0.227675i
$927$	42.0000			1.37946
$928$	−2.00000	+	3.46410i	−0.0656532	+	0.113715i
$929$	−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
$933$	3.00000	−	1.73205i	0.0982156	−	0.0567048i
$934$	−13.0000			−0.425373
$935$	5.00000	−	8.66025i	0.163517	−	0.283221i
$936$	−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	$0.727636\pi$
$942$		−	3.46410i		−	0.112867i
$943$	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	$-0.0386316\pi$
$948$			10.3923i			0.337526i
$949$	3.00000	+	5.19615i	0.0973841	+	0.168674i
$950$	7.00000			0.227110
$951$	−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	$0.691850\pi$
$954$	−18.0000	−	31.1769i	−0.582772	−	1.00939i
$955$	12.0000	−	20.7846i	0.388311	−	0.672574i
$956$	6.00000			0.194054
$957$	6.00000	−	3.46410i	0.193952	−	0.111979i
$958$	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
$962$	6.00000	−	10.3923i	0.193448	−	0.335061i
$963$	4.50000	+	7.79423i	0.145010	+	0.251166i
$964$	11.5000	+	19.9186i	0.370390	+	0.641534i
$965$	17.0000	+	29.4449i	0.547249	+	0.947864i
$966$		0			0
$967$	−7.00000	+	12.1244i	−0.225105	+	0.389893i	−0.956351	−	0.292221i	$-0.905606\pi$
$967$	−7.00000	+	12.1244i	−0.225105	+	0.389893i	0.731246	+	0.682114i	$0.238939\pi$
$968$	10.0000			0.321412
$969$		−	60.6218i		−	1.94745i
$970$	10.0000			0.321081
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$	−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	$0.756204\pi$
$978$		−	6.92820i		−	0.221540i
$979$	−3.00000	−	5.19615i	−0.0958804	−	0.166070i
$980$		0			0
$981$	−3.00000	+	5.19615i	−0.0957826	+	0.165900i
$982$	16.5000	+	28.5788i	0.526536	+	0.911987i
$983$	60.0000			1.91370			0.956851	−	0.290578i	$-0.0938475\pi$
$983$	60.0000			1.91370			0.956851	+	0.290578i	$0.0938475\pi$
$984$	4.50000	+	2.59808i	0.143455	+	0.0828236i
$985$	−20.0000			−0.637253
$986$	−10.0000	+	17.3205i	−0.318465	+	0.551597i
$987$		0			0
$988$	−21.0000	−	36.3731i	−0.668099	−	1.15718i
$989$	2.00000	+	3.46410i	0.0635963	+	0.110152i
$990$	3.00000	−	5.19615i	0.0953463	−	0.165145i
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	−0.553308	−	0.832977i	$-0.686635\pi$
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	0.998033	+	0.0626908i	$0.0199682\pi$
$992$	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
$997$	−2.00000			−0.0633406			−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000			−0.0633406			−0.0316703	+	0.999498i	$0.510083\pi$
$998$	−14.5000	+	25.1147i	−0.458989	+	0.794993i
$999$	9.00000	−	5.19615i	0.284747	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.g.67.1		2
3.2	odd	2		2646.2.h.c.361.1		2
7.2	even	3		882.2.e.e.373.1		2
7.3	odd	6		126.2.f.b.85.1	yes	2
7.4	even	3		882.2.f.f.589.1		2
7.5	odd	6		882.2.e.a.373.1		2
7.6	odd	2		882.2.h.h.67.1		2
9.2	odd	6		2646.2.e.h.2125.1		2
9.7	even	3		882.2.e.e.655.1		2
21.2	odd	6		2646.2.e.h.1549.1		2
21.5	even	6		2646.2.e.i.1549.1		2
21.11	odd	6		2646.2.f.b.1765.1		2
21.17	even	6		378.2.f.b.253.1		2
21.20	even	2		2646.2.h.b.361.1		2
28.3	even	6		1008.2.r.a.337.1		2
63.2	odd	6		2646.2.h.c.667.1		2
63.4	even	3		7938.2.a.e.1.1		1
63.11	odd	6		2646.2.f.b.883.1		2
63.16	even	3	inner	882.2.h.g.79.1		2
63.20	even	6		2646.2.e.i.2125.1		2
63.25	even	3		882.2.f.f.295.1		2
63.31	odd	6		1134.2.a.c.1.1		1
63.32	odd	6		7938.2.a.bb.1.1		1
63.34	odd	6		882.2.e.a.655.1		2
63.38	even	6		378.2.f.b.127.1		2
63.47	even	6		2646.2.h.b.667.1		2
63.52	odd	6		126.2.f.b.43.1	✓	2
63.59	even	6		1134.2.a.f.1.1		1
63.61	odd	6		882.2.h.h.79.1		2
84.59	odd	6		3024.2.r.c.1009.1		2
252.31	even	6		9072.2.a.t.1.1		1
252.59	odd	6		9072.2.a.f.1.1		1
252.115	even	6		1008.2.r.a.673.1		2
252.227	odd	6		3024.2.r.c.2017.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.b.43.1	✓	2	63.52	odd	6
126.2.f.b.85.1	yes	2	7.3	odd	6
378.2.f.b.127.1		2	63.38	even	6
378.2.f.b.253.1		2	21.17	even	6
882.2.e.a.373.1		2	7.5	odd	6
882.2.e.a.655.1		2	63.34	odd	6
882.2.e.e.373.1		2	7.2	even	3
882.2.e.e.655.1		2	9.7	even	3
882.2.f.f.295.1		2	63.25	even	3
882.2.f.f.589.1		2	7.4	even	3
882.2.h.g.67.1		2	1.1	even	1	trivial
882.2.h.g.79.1		2	63.16	even	3	inner
882.2.h.h.67.1		2	7.6	odd	2
882.2.h.h.79.1		2	63.61	odd	6
1008.2.r.a.337.1		2	28.3	even	6
1008.2.r.a.673.1		2	252.115	even	6
1134.2.a.c.1.1		1	63.31	odd	6
1134.2.a.f.1.1		1	63.59	even	6
2646.2.e.h.1549.1		2	21.2	odd	6
2646.2.e.h.2125.1		2	9.2	odd	6
2646.2.e.i.1549.1		2	21.5	even	6
2646.2.e.i.2125.1		2	63.20	even	6
2646.2.f.b.883.1		2	63.11	odd	6
2646.2.f.b.1765.1		2	21.11	odd	6
2646.2.h.b.361.1		2	21.20	even	2
2646.2.h.b.667.1		2	63.47	even	6
2646.2.h.c.361.1		2	3.2	odd	2
2646.2.h.c.667.1		2	63.2	odd	6
3024.2.r.c.1009.1		2	84.59	odd	6
3024.2.r.c.2017.1		2	252.227	odd	6
7938.2.a.e.1.1		1	63.4	even	3
7938.2.a.bb.1.1		1	63.32	odd	6
9072.2.a.f.1.1		1	252.59	odd	6
9072.2.a.t.1.1		1	252.31	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.h (of order \(3\), degree \(2\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more