LMFDB - Embedded newform 882.2.e.e.655.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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, 2]))

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (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:	$0$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			655.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.e.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-3.00000 - 5.19615i) q^{13} -3.46410i q^{15} +1.00000 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} +(-2.00000 + 3.46410i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} -5.19615i q^{27} +(2.00000 - 3.46410i) q^{29} +3.46410i q^{30} +6.00000 q^{31} -1.00000 q^{32} +(-1.50000 - 0.866025i) q^{33} +(2.50000 - 4.33013i) q^{34} +(1.50000 - 2.59808i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(3.50000 + 6.06218i) q^{38} +(-9.00000 - 5.19615i) q^{39} +(-1.00000 + 1.73205i) q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(2.00000 - 3.46410i) q^{46} +(1.50000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{50} +8.66025i q^{51} +(-3.00000 - 5.19615i) q^{52} +(-6.00000 + 10.3923i) q^{53} +5.19615i q^{54} -2.00000 q^{55} +(-10.5000 - 6.06218i) q^{57} +(-2.00000 + 3.46410i) q^{58} +7.00000 q^{59} -3.46410i q^{60} +12.0000 q^{61} -6.00000 q^{62} +1.00000 q^{64} -12.0000 q^{65} +(1.50000 + 0.866025i) q^{66} +13.0000 q^{67} +(-2.50000 + 4.33013i) q^{68} +6.92820i q^{69} -8.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(0.500000 - 0.866025i) 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} -6.00000 q^{79} +(1.00000 - 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(8.00000 - 13.8564i) q^{83} +(5.00000 + 8.66025i) q^{85} +(-0.500000 + 0.866025i) q^{86} -6.92820i q^{87} +(0.500000 + 0.866025i) 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} -14.0000 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 - 2 q^{2} + 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} - 2 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + 3 q^{12} - 6 q^{13} + 2 q^{16} - 5 q^{17} - 3 q^{18} - 7 q^{19} + 2 q^{20} + q^{22} - 4 q^{23} - 3 q^{24}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^6 - 2 * q^8 + 3 * q^9 - 2 * q^10 - q^11 + 3 * q^12 - 6 * q^13 + 2 * q^16 - 5 * q^17 - 3 * q^18 - 7 * q^19 + 2 * q^20 + q^22 - 4 * q^23 - 3 * q^24 + q^25 + 6 * q^26 + 4 * q^29 + 12 * q^31 - 2 * q^32 - 3 * q^33 + 5 * q^34 + 3 * q^36 - 2 * q^37 + 7 * q^38 - 18 * q^39 - 2 * q^40 + 3 * q^41 + q^43 - q^44 - 6 * q^45 + 4 * q^46 + 3 * q^48 - q^50 - 6 * q^52 - 12 * q^53 - 4 * q^55 - 21 * q^57 - 4 * q^58 + 14 * q^59 + 24 * q^61 - 12 * q^62 + 2 * q^64 - 24 * q^65 + 3 * q^66 + 26 * q^67 - 5 * q^68 - 16 * q^71 - 3 * q^72 + q^73 + 2 * q^74 + 3 * q^75 - 7 * q^76 + 18 * q^78 - 12 * q^79 + 2 * q^80 - 9 * q^81 - 3 * q^82 + 16 * q^83 + 10 * q^85 - q^86 + q^88 - 6 * q^89 + 6 * q^90 - 4 * q^92 + 18 * q^93 - 28 * q^95 - 3 * q^96 - 5 * q^97 - 6 * q^99

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$	1.00000			0.500000
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$	−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
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	0.780750	−	0.624844i	$-0.214837\pi$
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	−0.931505	+	0.363727i	$0.881504\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$	−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
$16$	1.00000			0.250000
$17$	−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
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	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	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$			3.46410i			0.632456i
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	−1.00000			−0.176777
$33$	−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
$37$	−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	$0.885902\pi$
$38$	3.50000	+	6.06218i	0.567775	+	0.983415i
$39$	−9.00000	−	5.19615i	−1.44115	−	0.832050i
$40$	−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	$0.142372\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	−3.00000	−	5.19615i	−0.447214	−	0.774597i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$		0			0
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$			8.66025i			1.21268i
$52$	−3.00000	−	5.19615i	−0.416025	−	0.720577i
$53$	−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	$0.858312\pi$
$54$			5.19615i			0.707107i
$55$	−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
$59$	7.00000			0.911322			0.455661	−	0.890153i	$-0.349403\pi$
$59$	7.00000			0.911322			0.455661	+	0.890153i	$0.349403\pi$
$60$		−	3.46410i		−	0.447214i
$61$	12.0000			1.53644			0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000			1.53644			0.768221	+	0.640184i	$0.221142\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	−12.0000			−1.48842
$66$	1.50000	+	0.866025i	0.184637	+	0.106600i
$67$	13.0000			1.58820			0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000			1.58820			0.794101	+	0.607785i	$0.207942\pi$
$68$	−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
$73$	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	$0.148028\pi$
$74$	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
$79$	−6.00000			−0.675053			−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000			−0.675053			−0.337526	+	0.941316i	$0.609590\pi$
$80$	1.00000	−	1.73205i	0.111803	−	0.193649i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$	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
$87$		−	6.92820i		−	0.742781i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−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
$95$	−14.0000			−1.43637
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$	−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
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−2.00000	−	3.46410i	−0.199007	−	0.344691i	0.749199	−	0.662344i	$-0.230438\pi$
$101$	−2.00000	−	3.46410i	−0.199007	−	0.344691i	−0.948207	+	0.317653i	$0.897105\pi$
$102$		−	8.66025i		−	0.857493i
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	−0.282194	−	0.959357i	$-0.591062\pi$
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	0.971925	−	0.235291i	$-0.0756043\pi$
$104$	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	$0.879655\pi$
$108$		−	5.19615i		−	0.500000i
$109$	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	$0.136131\pi$
$110$	2.00000			0.190693
$111$	−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
$116$	2.00000	−	3.46410i	0.185695	−	0.321634i
$117$	−18.0000			−1.66410
$118$	−7.00000			−0.644402
$119$		0			0
$120$			3.46410i			0.316228i
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−12.0000			−1.08643
$123$	4.50000	+	2.59808i	0.405751	+	0.234261i
$124$	6.00000			0.538816
$125$	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	$0.678715\pi$
$128$	−1.00000			−0.0883883
$129$		−	1.73205i		−	0.152499i
$130$	12.0000			1.05247
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	−0.940072	−	0.340977i	$-0.889242\pi$
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	0.765331	+	0.643637i	$0.222575\pi$
$132$	−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
$136$	2.50000	−	4.33013i	0.214373	−	0.371305i
$137$	9.50000	+	16.4545i	0.811640	+	1.40580i	0.911716	+	0.410822i	$0.134758\pi$
$137$	9.50000	+	16.4545i	0.811640	+	1.40580i	−0.100076	+	0.994980i	$0.531909\pi$
$138$		−	6.92820i		−	0.589768i
$139$	−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
$142$	8.00000			0.671345
$143$	−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
$149$	12.0000	−	20.7846i	0.983078	−	1.70274i	0.332896	−	0.942964i	$-0.391974\pi$
$149$	12.0000	−	20.7846i	0.983078	−	1.70274i	0.650183	−	0.759778i	$-0.274692\pi$
$150$	−1.50000	−	0.866025i	−0.122474	−	0.0707107i
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	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
$156$	−9.00000	−	5.19615i	−0.720577	−	0.416025i
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$	6.00000			0.477334
$159$			20.7846i			1.64833i
$160$	−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	$0.783263\pi$
$164$	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
$170$	−5.00000	−	8.66025i	−0.383482	−	0.664211i
$171$	−21.0000			−1.60591
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	−2.00000			−0.152057			−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000			−0.152057			−0.0760286	+	0.997106i	$0.524224\pi$
$174$			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
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	−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
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	−4.00000			−0.294086
$186$	−9.00000	+	5.19615i	−0.659912	+	0.381000i
$187$	5.00000			0.365636
$188$		0			0
$189$		0			0
$190$	14.0000			1.01567
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	1.50000	−	0.866025i	0.108253	−	0.0625000i
$193$	17.0000			1.22369			0.611843	−	0.790979i	$-0.290428\pi$
$193$	17.0000			1.22369			0.611843	+	0.790979i	$0.290428\pi$
$194$	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	$0.384060\pi$
$198$	3.00000			0.213201
$199$	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	$0.00138876\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	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
$205$	6.00000			0.419058
$206$	−7.00000	+	12.1244i	−0.487713	+	0.844744i
$207$	6.00000	+	10.3923i	0.417029	+	0.722315i
$208$	−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	0.998221	+	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
$215$	−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
$219$		−	1.73205i		−	0.117041i
$220$	−2.00000			−0.134840
$221$	30.0000			2.01802
$222$	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
$226$	−5.00000	−	8.66025i	−0.332595	−	0.576072i
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$	−10.5000	−	6.06218i	−0.695379	−	0.401478i
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	0.0137585	+	0.999905i	$0.495620\pi$
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	−0.872823	+	0.488037i	$0.837713\pi$
$230$	−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	$0.434491\pi$
$234$	18.0000			1.17670
$235$		0			0
$236$	7.00000			0.455661
$237$	−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	$0.895497\pi$
$240$		−	3.46410i		−	0.223607i
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	0.952141	+	0.305661i	$0.0988773\pi$
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	−0.211360	+	0.977408i	$0.567789\pi$
$242$	−5.00000	+	8.66025i	−0.321412	+	0.556702i
$243$	−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
$248$	−6.00000			−0.381000
$249$		−	27.7128i		−	1.75623i
$250$	−12.0000			−0.758947
$251$	−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
$254$	12.0000			0.752947
$255$	15.0000	+	8.66025i	0.939336	+	0.542326i
$256$	1.00000			0.0625000
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$			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
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	−0.997906	−	0.0646755i	$-0.979399\pi$
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	0.442943	−	0.896550i	$-0.353935\pi$
$264$	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
$268$	13.0000			0.794101
$269$	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
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$			6.92820i			0.417029i
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	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	0.325385	+	0.945582i	$0.394506\pi$
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	−0.981590	+	0.190999i	$0.938827\pi$
$282$		0			0
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$	−8.00000			−0.474713
$285$	−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
$290$	4.00000	+	6.92820i	0.234888	+	0.406838i
$291$			8.66025i			0.507673i
$292$	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
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	−4.50000	+	2.59808i	−0.261116	+	0.150756i
$298$	−12.0000	+	20.7846i	−0.695141	+	1.20402i
$299$	24.0000			1.38796
$300$	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
$305$	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
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	−2.00000			−0.113410			−0.0567048	−	0.998391i	$-0.518059\pi$
$311$	−2.00000			−0.113410			−0.0567048	+	0.998391i	$0.518059\pi$
$312$	9.00000	+	5.19615i	0.509525	+	0.294174i
$313$	17.0000			0.960897			0.480448	−	0.877023i	$-0.340474\pi$
$313$	17.0000			0.960897			0.480448	+	0.877023i	$0.340474\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	−6.00000			−0.337526
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$		−	20.7846i		−	1.16554i
$319$	−4.00000			−0.223957
$320$	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
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	3.00000	−	5.19615i	0.166410	−	0.288231i
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$		−	3.46410i		−	0.191565i
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$		0			0
$330$	3.00000	−	1.73205i	0.165145	−	0.0953463i
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	8.00000	−	13.8564i	0.439057	−	0.760469i
$333$	−6.00000			−0.328798
$334$	−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	0.962168	−	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
$339$	15.0000	+	8.66025i	0.814688	+	0.470360i
$340$	5.00000	+	8.66025i	0.271163	+	0.469668i
$341$	−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
$345$	12.0000	+	6.92820i	0.646058	+	0.373002i
$346$	2.00000			0.107521
$347$	−3.00000			−0.161048			−0.0805242	−	0.996753i	$-0.525659\pi$
$347$	−3.00000			−0.161048			−0.0805242	+	0.996753i	$0.525659\pi$
$348$		−	6.92820i		−	0.371391i
$349$	−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
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	0.594441	−	0.804139i	$-0.297373\pi$
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	−0.993626	+	0.112731i	$0.964040\pi$
$354$	−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
$359$	−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	$0.850141\pi$
$360$	3.00000	+	5.19615i	0.158114	+	0.273861i
$361$	−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
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	−0.996129	−	0.0879086i	$-0.971982\pi$
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	0.421933	−	0.906627i	$-0.361352\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$	9.00000			0.468521
$370$	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	0.427051	+	0.904227i	$0.359552\pi$
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	−0.996610	+	0.0822766i	$0.973781\pi$
$374$	−5.00000			−0.258544
$375$	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	$0.643823\pi$
$380$	−14.0000			−0.718185
$381$	−18.0000	+	10.3923i	−0.922168	+	0.532414i
$382$	−12.0000			−0.613973
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	−0.810394	−	0.585886i	$-0.800747\pi$
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	0.912589	+	0.408879i	$0.134080\pi$
$384$	−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
$389$	−4.00000	−	6.92820i	−0.202808	−	0.351274i	0.746624	−	0.665246i	$-0.231673\pi$
$389$	−4.00000	−	6.92820i	−0.202808	−	0.351274i	−0.949432	+	0.313972i	$0.898340\pi$
$390$	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
$394$	−10.0000			−0.503793
$395$	−6.00000	+	10.3923i	−0.301893	+	0.522894i
$396$	−3.00000			−0.150756
$397$	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
$401$	−4.50000	+	7.79423i	−0.224719	+	0.389225i	−0.956235	−	0.292599i	$-0.905480\pi$
$401$	−4.50000	+	7.79423i	−0.224719	+	0.389225i	0.731516	+	0.681824i	$0.238813\pi$
$402$	−19.5000	+	11.2583i	−0.972572	+	0.561514i
$403$	−18.0000	−	31.1769i	−0.896644	−	1.55303i
$404$	−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
$408$		−	8.66025i		−	0.428746i
$409$	−11.0000			−0.543915			−0.271957	−	0.962309i	$-0.587671\pi$
$409$	−11.0000			−0.543915			−0.271957	+	0.962309i	$0.587671\pi$
$410$	−6.00000			−0.296319
$411$	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
$415$	−16.0000	−	27.7128i	−0.785409	−	1.36037i
$416$	3.00000	+	5.19615i	0.147087	+	0.254762i
$417$	−7.50000	−	4.33013i	−0.367277	−	0.212047i
$418$	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	$0.0722054\pi$
$422$	−8.00000	−	13.8564i	−0.389434	−	0.674519i
$423$		0			0
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	−5.00000			−0.242536
$426$	12.0000	−	6.92820i	0.581402	−	0.335673i
$427$		0			0
$428$	−1.50000	−	2.59808i	−0.0725052	−	0.125583i
$429$			10.3923i			0.501745i
$430$	1.00000	+	1.73205i	0.0482243	+	0.0835269i
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$		−	5.19615i		−	0.250000i
$433$	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
$437$	28.0000			1.33942
$438$			1.73205i			0.0827606i
$439$	24.0000			1.14546			0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000			1.14546			0.572729	+	0.819745i	$0.305885\pi$
$440$	2.00000			0.0953463
$441$		0			0
$442$	−30.0000			−1.42695
$443$	7.00000			0.332580			0.166290	−	0.986077i	$-0.446821\pi$
$443$	7.00000			0.332580			0.166290	+	0.986077i	$0.446821\pi$
$444$	−3.00000	−	1.73205i	−0.142374	−	0.0821995i
$445$	−12.0000			−0.568855
$446$	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	$0.368614\pi$
$450$	−3.00000			−0.141421
$451$	1.50000	−	2.59808i	0.0706322	−	0.122339i
$452$	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
$457$	1.00000			0.0467780			0.0233890	−	0.999726i	$-0.492554\pi$
$457$	1.00000			0.0467780			0.0233890	+	0.999726i	$0.492554\pi$
$458$	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	−0.655696	−	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
$465$		−	20.7846i		−	0.963863i
$466$	−14.5000	−	25.1147i	−0.671700	−	1.16342i
$467$	−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
$472$	−7.00000			−0.322201
$473$	−1.00000			−0.0459800
$474$	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
$479$	−10.0000	−	17.3205i	−0.456912	−	0.791394i	0.541884	−	0.840453i	$-0.317711\pi$
$479$	−10.0000	−	17.3205i	−0.456912	−	0.791394i	−0.998796	+	0.0490589i	$0.984378\pi$
$480$			3.46410i			0.158114i
$481$	−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
$485$	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	$0.0939149\pi$
$488$	−12.0000			−0.543214
$489$	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
$494$	21.0000	−	36.3731i	0.944835	−	1.63650i
$495$	−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	−0.334227	−	0.942493i	$-0.608475\pi$
$499$	14.5000	−	25.1147i	0.649109	−	1.12429i	0.983336	−	0.181797i	$-0.0581915\pi$
$500$	12.0000			0.536656
$501$	30.0000	+	17.3205i	1.34030	+	0.773823i
$502$	3.00000			0.133897
$503$	−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
$506$	−4.00000			−0.177822
$507$			39.8372i			1.76923i
$508$	−12.0000			−0.532414
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$	−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
$515$	−14.0000	−	24.2487i	−0.616914	−	1.06853i
$516$		−	1.73205i		−	0.0762493i
$517$		0			0
$518$		0			0
$519$	−3.00000	+	1.73205i	−0.131685	+	0.0760286i
$520$	12.0000			0.526235
$521$	−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	$0.229835\pi$
$522$	6.00000	+	10.3923i	0.262613	+	0.454859i
$523$	−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
$527$	−15.0000	+	25.9808i	−0.653410	+	1.13174i
$528$	−1.50000	−	0.866025i	−0.0652791	−	0.0376889i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−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
$534$	9.00000	+	5.19615i	0.389468	+	0.224860i
$535$	−6.00000			−0.259403
$536$	−13.0000			−0.561514
$537$			41.5692i			1.79384i
$538$	−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	$0.660783\pi$
$542$	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	$0.0184657\pi$
$548$	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
$551$	−28.0000			−1.19284
$552$		−	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
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	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	$-0.0354686\pi$
$558$	−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
$563$	−31.0000			−1.30649			−0.653247	−	0.757145i	$-0.726594\pi$
$563$	−31.0000			−1.30649			−0.653247	+	0.757145i	$0.726594\pi$
$564$		0			0
$565$	20.0000			0.841406
$566$	4.00000			0.168133
$567$		0			0
$568$	8.00000			0.335673
$569$	−15.0000			−0.628833			−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000			−0.628833			−0.314416	+	0.949285i	$0.601809\pi$
$570$	21.0000	−	12.1244i	0.879593	−	0.507833i
$571$	−33.0000			−1.38101			−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000			−1.38101			−0.690504	+	0.723329i	$0.742611\pi$
$572$	−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
$577$	−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	$0.906868\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$	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
$583$	12.0000			0.496989
$584$	−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	−0.274263	+	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
$593$	−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
$597$		−	24.2487i		−	0.992434i
$598$	−24.0000			−0.981433
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$	−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
$604$	−5.00000	−	8.66025i	−0.203447	−	0.352381i
$605$	−10.0000	−	17.3205i	−0.406558	−	0.704179i
$606$	6.00000	+	3.46410i	0.243733	+	0.140720i
$607$	−12.0000	+	20.7846i	−0.487065	+	0.843621i	−0.999889	−	0.0148722i	$-0.995266\pi$
$607$	−12.0000	+	20.7846i	−0.487065	+	0.843621i	0.512824	+	0.858494i	$0.328599\pi$
$608$	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
$613$	−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	$0.844364\pi$
$614$	7.00000			0.282497
$615$	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	$0.722162\pi$
$618$			24.2487i			0.975426i
$619$	18.5000	+	32.0429i	0.743578	+	1.28791i	0.950856	+	0.309633i	$0.100206\pi$
$619$	18.5000	+	32.0429i	0.743578	+	1.28791i	−0.207279	+	0.978282i	$0.566461\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$	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
$626$	−17.0000			−0.679457
$627$			12.1244i			0.484200i
$628$	−2.00000			−0.0798087
$629$	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	$0.449096\pi$
$632$	6.00000			0.238667
$633$	24.0000	+	13.8564i	0.953914	+	0.550743i
$634$	6.00000			0.238290
$635$	−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
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	−0.500000	−	0.866025i	−0.0197488	−	0.0342059i	0.855982	−	0.517005i	$-0.172953\pi$
$641$	−0.500000	−	0.866025i	−0.0197488	−	0.0342059i	−0.875731	+	0.482800i	$0.839620\pi$
$642$	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
$646$	−35.0000			−1.37706
$647$	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	$0.0908680\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	−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
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$			3.46410i			0.135457i
$655$	4.00000	+	6.92820i	0.156293	+	0.270707i
$656$	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	−0.978717	−	0.205216i	$-0.934210\pi$
$659$	−8.00000	+	13.8564i	−0.311636	+	0.539769i	0.667081	+	0.744985i	$0.267544\pi$
$660$	−3.00000	+	1.73205i	−0.116775	+	0.0674200i
$661$	−28.0000			−1.08907			−0.544537	−	0.838737i	$-0.683295\pi$
$661$	−28.0000			−1.08907			−0.544537	+	0.838737i	$0.683295\pi$
$662$	−8.00000			−0.310929
$663$	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
$668$	10.0000	+	17.3205i	0.386912	+	0.670151i
$669$			6.92820i			0.267860i
$670$	−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	$0.253634\pi$
$674$	−4.50000	−	7.79423i	−0.173334	−	0.300222i
$675$	4.50000	−	2.59808i	0.173205	−	0.100000i
$676$	−11.5000	+	19.9186i	−0.442308	+	0.766099i
$677$	−30.0000			−1.15299			−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000			−1.15299			−0.576497	+	0.817099i	$0.695581\pi$
$678$	−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
$683$	−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	$0.898568\pi$
$684$	−21.0000			−0.802955
$685$	38.0000			1.45191
$686$		0			0
$687$			45.0333i			1.71813i
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	72.0000			2.74298
$690$	−12.0000	−	6.92820i	−0.456832	−	0.263752i
$691$	−32.0000			−1.21734			−0.608669	−	0.793424i	$-0.708296\pi$
$691$	−32.0000			−1.21734			−0.608669	+	0.793424i	$0.708296\pi$
$692$	−2.00000			−0.0760286
$693$		0			0
$694$	3.00000			0.113878
$695$	−10.0000			−0.379322
$696$			6.92820i			0.262613i
$697$	−15.0000			−0.568166
$698$	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	$0.451726\pi$
$702$	27.0000	−	15.5885i	1.01905	−	0.588348i
$703$	−7.00000	+	12.1244i	−0.264010	+	0.457279i
$704$	−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
$709$	−4.00000			−0.150223			−0.0751116	−	0.997175i	$-0.523931\pi$
$709$	−4.00000			−0.150223			−0.0751116	+	0.997175i	$0.523931\pi$
$710$	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
$716$	−12.0000	+	20.7846i	−0.448461	+	0.776757i
$717$	−9.00000	−	5.19615i	−0.336111	−	0.194054i
$718$	1.00000	+	1.73205i	0.0373197	+	0.0646396i
$719$	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
$723$	34.5000	+	19.9186i	1.28307	+	0.740780i
$724$		0			0
$725$	4.00000			0.148556
$726$			17.3205i			0.642824i
$727$	−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
$730$	1.00000	+	1.73205i	0.0370117	+	0.0641061i
$731$	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	−0.982986	−	0.183679i	$-0.941199\pi$
$733$	−9.00000	+	15.5885i	−0.332423	+	0.575773i	0.650564	+	0.759452i	$0.274533\pi$
$734$	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
$738$	−9.00000			−0.331295
$739$	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	$-0.0409454\pi$
$740$	−4.00000			−0.147043
$741$			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	$0.798229\pi$
$744$	−9.00000	+	5.19615i	−0.329956	+	0.190500i
$745$	−24.0000	−	41.5692i	−0.879292	−	1.52298i
$746$	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
$751$	9.00000	−	15.5885i	0.328415	−	0.568831i	−0.653783	−	0.756682i	$-0.726819\pi$
$751$	9.00000	−	15.5885i	0.328415	−	0.568831i	0.982197	+	0.187851i	$0.0601523\pi$
$752$		0			0
$753$	−4.50000	+	2.59808i	−0.163989	+	0.0946792i
$754$	24.0000			0.874028
$755$	−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	$0.837369\pi$
$758$	17.0000			0.617468
$759$	6.00000	−	3.46410i	0.217786	−	0.125739i
$760$	14.0000			0.507833
$761$	5.00000	−	8.66025i	0.181250	−	0.313934i	−0.761057	−	0.648686i	$-0.775319\pi$
$761$	5.00000	−	8.66025i	0.181250	−	0.313934i	0.942306	+	0.334752i	$0.108652\pi$
$762$	18.0000	−	10.3923i	0.652071	−	0.376473i
$763$		0			0
$764$	12.0000			0.434145
$765$	30.0000			1.08465
$766$	−2.00000	+	3.46410i	−0.0722629	+	0.125163i
$767$	−21.0000	−	36.3731i	−0.758266	−	1.31336i
$768$	1.50000	−	0.866025i	0.0541266	−	0.0312500i
$769$	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
$772$	17.0000			0.611843
$773$	−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	$0.781927\pi$
$774$	1.50000	+	2.59808i	0.0539164	+	0.0933859i
$775$	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
$779$	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
$782$	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
$786$		−	6.92820i		−	0.247121i
$787$	12.0000			0.427754			0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000			0.427754			0.213877	+	0.976861i	$0.431391\pi$
$788$	10.0000			0.356235
$789$	−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
$793$	−36.0000	−	62.3538i	−1.27840	−	2.21425i
$794$	−9.00000	−	15.5885i	−0.319398	−	0.553214i
$795$	36.0000	+	20.7846i	1.27679	+	0.737154i
$796$	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
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−18.0000			−0.635999
$802$	4.50000	−	7.79423i	0.158901	−	0.275224i
$803$	−1.00000			−0.0352892
$804$	19.5000	−	11.2583i	0.687712	−	0.397051i
$805$		0			0
$806$	18.0000	+	31.1769i	0.634023	+	1.09816i
$807$		−	34.6410i		−	1.21942i
$808$	2.00000	+	3.46410i	0.0703598	+	0.121867i
$809$	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	$-0.106134\pi$
$810$	18.0000			0.632456
$811$	−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
$815$	8.00000			0.280228
$816$			8.66025i			0.303170i
$817$	−7.00000			−0.244899
$818$	11.0000			0.384606
$819$		0			0
$820$	6.00000			0.209529
$821$	46.0000			1.60541			0.802706	−	0.596376i	$-0.203393\pi$
$821$	46.0000			1.60541			0.802706	+	0.596376i	$0.203393\pi$
$822$	−28.5000	−	16.4545i	−0.994052	−	0.573916i
$823$	34.0000			1.18517			0.592583	−	0.805510i	$-0.298108\pi$
$823$	34.0000			1.18517			0.592583	+	0.805510i	$0.298108\pi$
$824$	−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	$0.433096\pi$
$828$	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	$0.144538\pi$
$830$	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
$835$	40.0000			1.38426
$836$	−3.50000	+	6.06218i	−0.121050	+	0.209665i
$837$		−	31.1769i		−	1.07763i
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$	−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
$843$			38.1051i			1.31241i
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	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
$850$	5.00000			0.171499
$851$	8.00000			0.274236
$852$	−12.0000	+	6.92820i	−0.411113	+	0.237356i
$853$	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
$856$	1.50000	+	2.59808i	0.0512689	+	0.0888004i
$857$	15.0000	+	25.9808i	0.512390	+	0.887486i	0.999897	+	0.0143666i	$0.00457319\pi$
$857$	15.0000	+	25.9808i	0.512390	+	0.887486i	−0.487507	+	0.873119i	$0.662093\pi$
$858$		−	10.3923i		−	0.354787i
$859$	14.5000	−	25.1147i	0.494734	−	0.856904i	−0.505248	−	0.862974i	$-0.668599\pi$
$859$	14.5000	−	25.1147i	0.494734	−	0.856904i	0.999982	+	0.00607046i	$0.00193230\pi$
$860$	−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	$-0.390546\pi$
$864$			5.19615i			0.176777i
$865$	−2.00000	+	3.46410i	−0.0680020	+	0.117783i
$866$	−25.0000			−0.849535
$867$	−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
$872$	−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
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	−0.968898	−	0.247462i	$-0.920404\pi$
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	0.698757	+	0.715359i	$0.253737\pi$
$878$	−24.0000			−0.809961
$879$		0			0
$880$	−2.00000			−0.0674200
$881$	−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	$0.149446\pi$
$884$	30.0000			1.00901
$885$		−	24.2487i		−	0.815112i
$886$	−7.00000			−0.235170
$887$	−3.00000	+	5.19615i	−0.100730	+	0.174470i	−0.911986	−	0.410222i	$-0.865451\pi$
$887$	−3.00000	+	5.19615i	−0.100730	+	0.174470i	0.811256	+	0.584692i	$0.198785\pi$
$888$	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
$892$	−2.00000	+	3.46410i	−0.0669650	+	0.115987i
$893$		0			0
$894$			41.5692i			1.39028i
$895$	24.0000	+	41.5692i	0.802232	+	1.38951i
$896$		0			0
$897$	36.0000	−	20.7846i	1.20201	−	0.693978i
$898$	−17.0000			−0.567297
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$	3.00000			0.100000
$901$	−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
$907$	13.5000	+	23.3827i	0.448260	+	0.776409i	0.998273	−	0.0587469i	$-0.0187105\pi$
$907$	13.5000	+	23.3827i	0.448260	+	0.776409i	−0.550013	+	0.835156i	$0.685377\pi$
$908$	1.50000	+	2.59808i	0.0497792	+	0.0862202i
$909$	−12.0000			−0.398015
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$	−10.5000	−	6.06218i	−0.347690	−	0.200739i
$913$	−16.0000			−0.529523
$914$	−1.00000			−0.0330771
$915$		−	41.5692i		−	1.37424i
$916$	−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	$0.918341\pi$
$920$	−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
$926$	−4.00000	−	6.92820i	−0.131448	−	0.227675i
$927$	−21.0000	−	36.3731i	−0.689730	−	1.19465i
$928$	−2.00000	+	3.46410i	−0.0656532	+	0.113715i
$929$	18.0000			0.590561			0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000			0.590561			0.295280	+	0.955411i	$0.404587\pi$
$930$			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
$934$	6.50000	+	11.2583i	0.212686	+	0.368384i
$935$	5.00000	−	8.66025i	0.163517	−	0.283221i
$936$	18.0000			0.588348
$937$	−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
$941$	−20.0000			−0.651981			−0.325991	−	0.945373i	$-0.605698\pi$
$941$	−20.0000			−0.651981			−0.325991	+	0.945373i	$0.605698\pi$
$942$	3.00000	−	1.73205i	0.0977453	−	0.0564333i
$943$	−12.0000			−0.390774
$944$	7.00000			0.227831
$945$		0			0
$946$	1.00000			0.0325128
$947$	−37.0000			−1.20234			−0.601169	−	0.799122i	$-0.705298\pi$
$947$	−37.0000			−1.20234			−0.601169	+	0.799122i	$0.705298\pi$
$948$	−9.00000	+	5.19615i	−0.292306	+	0.168763i
$949$	−6.00000			−0.194768
$950$	−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	$0.691850\pi$
$954$	−18.0000	−	31.1769i	−0.582772	−	1.00939i
$955$	12.0000	−	20.7846i	0.388311	−	0.672574i
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$	−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
$961$	5.00000			0.161290
$962$	6.00000	−	10.3923i	0.193448	−	0.335061i
$963$	−9.00000			−0.290021
$964$	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	0.731246	−	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
$971$	−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
$975$		−	10.3923i		−	0.332820i
$976$	12.0000			0.384111
$977$	−15.0000			−0.479893			−0.239946	−	0.970786i	$-0.577130\pi$
$977$	−15.0000			−0.479893			−0.239946	+	0.970786i	$0.577130\pi$
$978$	−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
$982$	16.5000	+	28.5788i	0.526536	+	0.911987i
$983$	−30.0000	−	51.9615i	−0.956851	−	1.65732i	−0.730073	−	0.683369i	$-0.760514\pi$
$983$	−30.0000	−	51.9615i	−0.956851	−	1.65732i	−0.226778	−	0.973946i	$-0.572819\pi$
$984$	−4.50000	−	2.59808i	−0.143455	−	0.0828236i
$985$	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
$989$	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	$0.0199682\pi$
$992$	−6.00000			−0.190500
$993$	12.0000	−	6.92820i	0.380808	−	0.219860i
$994$		0			0
$995$	−14.0000	−	24.2487i	−0.443830	−	0.768736i
$996$		−	27.7128i		−	0.878114i
$997$	1.00000	+	1.73205i	0.0316703	+	0.0548546i	0.881426	−	0.472322i	$-0.156584\pi$
$997$	1.00000	+	1.73205i	0.0316703	+	0.0548546i	−0.849756	+	0.527176i	$0.823251\pi$
$998$	−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.e.e.655.1		2
3.2	odd	2		2646.2.e.h.2125.1		2
7.2	even	3		882.2.h.g.79.1		2
7.3	odd	6		126.2.f.b.43.1	✓	2
7.4	even	3		882.2.f.f.295.1		2
7.5	odd	6		882.2.h.h.79.1		2
7.6	odd	2		882.2.e.a.655.1		2
9.4	even	3		882.2.h.g.67.1		2
9.5	odd	6		2646.2.h.c.361.1		2
21.2	odd	6		2646.2.h.c.667.1		2
21.5	even	6		2646.2.h.b.667.1		2
21.11	odd	6		2646.2.f.b.883.1		2
21.17	even	6		378.2.f.b.127.1		2
21.20	even	2		2646.2.e.i.2125.1		2
28.3	even	6		1008.2.r.a.673.1		2
63.4	even	3		882.2.f.f.589.1		2
63.5	even	6		2646.2.e.i.1549.1		2
63.11	odd	6		7938.2.a.bb.1.1		1
63.13	odd	6		882.2.h.h.67.1		2
63.23	odd	6		2646.2.e.h.1549.1		2
63.25	even	3		7938.2.a.e.1.1		1
63.31	odd	6		126.2.f.b.85.1	yes	2
63.32	odd	6		2646.2.f.b.1765.1		2
63.38	even	6		1134.2.a.f.1.1		1
63.40	odd	6		882.2.e.a.373.1		2
63.41	even	6		2646.2.h.b.361.1		2
63.52	odd	6		1134.2.a.c.1.1		1
63.58	even	3	inner	882.2.e.e.373.1		2
63.59	even	6		378.2.f.b.253.1		2
84.59	odd	6		3024.2.r.c.2017.1		2
252.31	even	6		1008.2.r.a.337.1		2
252.59	odd	6		3024.2.r.c.1009.1		2
252.115	even	6		9072.2.a.t.1.1		1
252.227	odd	6		9072.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.b.43.1	✓	2	7.3	odd	6
126.2.f.b.85.1	yes	2	63.31	odd	6
378.2.f.b.127.1		2	21.17	even	6
378.2.f.b.253.1		2	63.59	even	6
882.2.e.a.373.1		2	63.40	odd	6
882.2.e.a.655.1		2	7.6	odd	2
882.2.e.e.373.1		2	63.58	even	3	inner
882.2.e.e.655.1		2	1.1	even	1	trivial
882.2.f.f.295.1		2	7.4	even	3
882.2.f.f.589.1		2	63.4	even	3
882.2.h.g.67.1		2	9.4	even	3
882.2.h.g.79.1		2	7.2	even	3
882.2.h.h.67.1		2	63.13	odd	6
882.2.h.h.79.1		2	7.5	odd	6
1008.2.r.a.337.1		2	252.31	even	6
1008.2.r.a.673.1		2	28.3	even	6
1134.2.a.c.1.1		1	63.52	odd	6
1134.2.a.f.1.1		1	63.38	even	6
2646.2.e.h.1549.1		2	63.23	odd	6
2646.2.e.h.2125.1		2	3.2	odd	2
2646.2.e.i.1549.1		2	63.5	even	6
2646.2.e.i.2125.1		2	21.20	even	2
2646.2.f.b.883.1		2	21.11	odd	6
2646.2.f.b.1765.1		2	63.32	odd	6
2646.2.h.b.361.1		2	63.41	even	6
2646.2.h.b.667.1		2	21.5	even	6
2646.2.h.c.361.1		2	9.5	odd	6
2646.2.h.c.667.1		2	21.2	odd	6
3024.2.r.c.1009.1		2	252.59	odd	6
3024.2.r.c.2017.1		2	84.59	odd	6
7938.2.a.e.1.1		1	63.25	even	3
7938.2.a.bb.1.1		1	63.11	odd	6
9072.2.a.f.1.1		1	252.227	odd	6
9072.2.a.t.1.1		1	252.115	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-3.00000 - 5.19615i) q^{13} -3.46410i q^{15} +1.00000 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} +(-2.00000 + 3.46410i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} -5.19615i q^{27} +(2.00000 - 3.46410i) q^{29} +3.46410i q^{30} +6.00000 q^{31} -1.00000 q^{32} +(-1.50000 - 0.866025i) q^{33} +(2.50000 - 4.33013i) q^{34} +(1.50000 - 2.59808i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(3.50000 + 6.06218i) q^{38} +(-9.00000 - 5.19615i) q^{39} +(-1.00000 + 1.73205i) q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(2.00000 - 3.46410i) q^{46} +(1.50000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{50} +8.66025i q^{51} +(-3.00000 - 5.19615i) q^{52} +(-6.00000 + 10.3923i) q^{53} +5.19615i q^{54} -2.00000 q^{55} +(-10.5000 - 6.06218i) q^{57} +(-2.00000 + 3.46410i) q^{58} +7.00000 q^{59} -3.46410i q^{60} +12.0000 q^{61} -6.00000 q^{62} +1.00000 q^{64} -12.0000 q^{65} +(1.50000 + 0.866025i) q^{66} +13.0000 q^{67} +(-2.50000 + 4.33013i) q^{68} +6.92820i q^{69} -8.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(0.500000 - 0.866025i) 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} -6.00000 q^{79} +(1.00000 - 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(8.00000 - 13.8564i) q^{83} +(5.00000 + 8.66025i) q^{85} +(-0.500000 + 0.866025i) q^{86} -6.92820i q^{87} +(0.500000 + 0.866025i) 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} -14.0000 q^{95} +(-1.50000 + 0.866025i) q^{96} +(-2.50000 + 4.33013i) q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} - 2 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + 3 q^{12} - 6 q^{13} + 2 q^{16} - 5 q^{17} - 3 q^{18} - 7 q^{19} + 2 q^{20} + q^{22} - 4 q^{23} - 3 q^{24}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^6 - 2 * q^8 + 3 * q^9 - 2 * q^10 - q^11 + 3 * q^12 - 6 * q^13 + 2 * q^16 - 5 * q^17 - 3 * q^18 - 7 * q^19 + 2 * q^20 + q^22 - 4 * q^23 - 3 * q^24 + q^25 + 6 * q^26 + 4 * q^29 + 12 * q^31 - 2 * q^32 - 3 * q^33 + 5 * q^34 + 3 * q^36 - 2 * q^37 + 7 * q^38 - 18 * q^39 - 2 * q^40 + 3 * q^41 + q^43 - q^44 - 6 * q^45 + 4 * q^46 + 3 * q^48 - q^50 - 6 * q^52 - 12 * q^53 - 4 * q^55 - 21 * q^57 - 4 * q^58 + 14 * q^59 + 24 * q^61 - 12 * q^62 + 2 * q^64 - 24 * q^65 + 3 * q^66 + 26 * q^67 - 5 * q^68 - 16 * q^71 - 3 * q^72 + q^73 + 2 * q^74 + 3 * q^75 - 7 * q^76 + 18 * q^78 - 12 * q^79 + 2 * q^80 - 9 * q^81 - 3 * q^82 + 16 * q^83 + 10 * q^85 - q^86 + q^88 - 6 * q^89 + 6 * q^90 - 4 * q^92 + 18 * q^93 - 28 * q^95 - 3 * q^96 - 5 * q^97 - 6 * q^99

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