LMFDB - Embedded newform 1638.2.j.f.1171.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(235,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1638.1171
Dual form			1638.2.j.f.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(2.00000 + 3.46410i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{19} +4.00000 q^{20} -1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-5.50000 - 9.52628i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(-2.00000 + 1.73205i) q^{28} +9.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(10.0000 + 3.46410i) q^{35} +(4.00000 - 6.92820i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(2.00000 - 3.46410i) q^{40} +10.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(-5.50000 + 9.52628i) q^{47} +(-6.50000 + 2.59808i) q^{49} -11.0000 q^{50} +(0.500000 + 0.866025i) q^{52} +(0.500000 + 0.866025i) q^{53} +4.00000 q^{55} +(0.500000 + 2.59808i) q^{56} +(4.50000 - 7.79423i) q^{58} +(-2.50000 - 4.33013i) q^{59} +(7.50000 - 12.9904i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(2.50000 + 4.33013i) q^{67} +(1.50000 - 2.59808i) q^{68} +(8.00000 - 6.92820i) q^{70} +15.0000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-4.00000 - 6.92820i) q^{74} -1.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(1.00000 - 1.73205i) q^{79} +(-2.00000 - 3.46410i) q^{80} +8.00000 q^{83} -12.0000 q^{85} +(5.00000 - 8.66025i) q^{86} +(0.500000 + 0.866025i) q^{88} +(0.500000 + 2.59808i) q^{91} -6.00000 q^{92} +(5.50000 + 9.52628i) q^{94} +(2.00000 + 3.46410i) q^{95} +10.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 4 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - 4 * q^5 - q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - 4 q^{5} - q^{7} - 2 q^{8} + 4 q^{10} - q^{11} - 2 q^{13} - 5 q^{14} - q^{16} + 3 q^{17} + q^{19} + 8 q^{20} - 2 q^{22} + 6 q^{23} - 11 q^{25} - q^{26} - 4 q^{28} + 18 q^{29} + 8 q^{31} + q^{32} + 6 q^{34} + 20 q^{35} + 8 q^{37} - q^{38} + 4 q^{40} + 20 q^{43} - q^{44} - 6 q^{46} - 11 q^{47} - 13 q^{49} - 22 q^{50} + q^{52} + q^{53} + 8 q^{55} + q^{56} + 9 q^{58} - 5 q^{59} + 15 q^{61} + 16 q^{62} + 2 q^{64} + 4 q^{65} + 5 q^{67} + 3 q^{68} + 16 q^{70} + 30 q^{71} - 2 q^{73} - 8 q^{74} - 2 q^{76} - 4 q^{77} + 2 q^{79} - 4 q^{80} + 16 q^{83} - 24 q^{85} + 10 q^{86} + q^{88} + q^{91} - 12 q^{92} + 11 q^{94} + 4 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 4 * q^5 - q^7 - 2 * q^8 + 4 * q^10 - q^11 - 2 * q^13 - 5 * q^14 - q^16 + 3 * q^17 + q^19 + 8 * q^20 - 2 * q^22 + 6 * q^23 - 11 * q^25 - q^26 - 4 * q^28 + 18 * q^29 + 8 * q^31 + q^32 + 6 * q^34 + 20 * q^35 + 8 * q^37 - q^38 + 4 * q^40 + 20 * q^43 - q^44 - 6 * q^46 - 11 * q^47 - 13 * q^49 - 22 * q^50 + q^52 + q^53 + 8 * q^55 + q^56 + 9 * q^58 - 5 * q^59 + 15 * q^61 + 16 * q^62 + 2 * q^64 + 4 * q^65 + 5 * q^67 + 3 * q^68 + 16 * q^70 + 30 * q^71 - 2 * q^73 - 8 * q^74 - 2 * q^76 - 4 * q^77 + 2 * q^79 - 4 * q^80 + 16 * q^83 - 24 * q^85 + 10 * q^86 + q^88 + q^91 - 12 * q^92 + 11 * q^94 + 4 * q^95 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.00000	+	3.46410i	−0.894427	+	1.54919i	−0.0599153	+	0.998203i	$0.519083\pi$
$5$	−2.00000	+	3.46410i	−0.894427	+	1.54919i	−0.834512	+	0.550990i	$0.814250\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	2.00000	+	3.46410i	0.632456	+	1.09545i
$11$	−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	$0.881504\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−2.50000	−	0.866025i	−0.668153	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	4.00000			0.894427
$21$		0			0
$22$	−1.00000			−0.213201
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$	−5.50000	−	9.52628i	−1.10000	−	1.90526i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$		0			0
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$	10.0000	+	3.46410i	1.69031	+	0.585540i
$36$		0			0
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	−0.323640	−	0.946180i	$-0.604907\pi$
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	0.981236	−	0.192809i	$-0.0617599\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$		0			0
$40$	2.00000	−	3.46410i	0.316228	−	0.547723i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−5.50000	+	9.52628i	−0.802257	+	1.38955i	0.115870	+	0.993264i	$0.463035\pi$
$47$	−5.50000	+	9.52628i	−0.802257	+	1.38955i	−0.918127	+	0.396286i	$0.870299\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−11.0000			−1.55563
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	0.898321	−	0.439340i	$-0.144788\pi$
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	−0.829640	+	0.558298i	$0.811454\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$		0			0
$58$	4.50000	−	7.79423i	0.590879	−	1.02343i
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	0.656136	−	0.754643i	$-0.272190\pi$
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	−0.981608	+	0.190909i	$0.938857\pi$
$60$		0			0
$61$	7.50000	−	12.9904i	0.960277	−	1.66325i	0.238474	−	0.971149i	$-0.423353\pi$
$61$	7.50000	−	12.9904i	0.960277	−	1.66325i	0.721803	−	0.692099i	$-0.243314\pi$
$62$	8.00000			1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000	−	3.46410i	0.248069	−	0.429669i
$66$		0			0
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$	8.00000	−	6.92820i	0.956183	−	0.828079i
$71$	15.0000			1.78017			0.890086	−	0.455792i	$-0.150644\pi$
$71$	15.0000			1.78017			0.890086	+	0.455792i	$0.150644\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$		0			0
$76$	−1.00000			−0.114708
$77$	−2.00000	+	1.73205i	−0.227921	+	0.197386i
$78$		0			0
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	−0.804272	−	0.594261i	$-0.797445\pi$
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	0.916781	+	0.399390i	$0.130778\pi$
$80$	−2.00000	−	3.46410i	−0.223607	−	0.387298i
$81$		0			0
$82$		0			0
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$		0			0
$85$	−12.0000			−1.30158
$86$	5.00000	−	8.66025i	0.539164	−	0.933859i
$87$		0			0
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	0.500000	+	2.59808i	0.0524142	+	0.272352i
$92$	−6.00000			−0.625543
$93$		0			0
$94$	5.50000	+	9.52628i	0.567282	+	0.982561i
$95$	2.00000	+	3.46410i	0.205196	+	0.355409i
$96$		0			0
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$	−1.00000	+	6.92820i	−0.101015	+	0.699854i
$99$		0			0
$100$	−5.50000	+	9.52628i	−0.550000	+	0.952628i
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	−0.969664	−	0.244443i	$-0.921395\pi$
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	0.273138	−	0.961975i	$-0.411939\pi$
$102$		0			0
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	−0.975124	−	0.221660i	$-0.928852\pi$
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	0.679525	+	0.733652i	$0.262186\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	1.00000			0.0971286
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	−0.992003	−	0.126217i	$-0.959717\pi$
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	0.605308	+	0.795991i	$0.293050\pi$
$108$		0			0
$109$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$109$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$110$	2.00000	−	3.46410i	0.190693	−	0.330289i
$111$		0			0
$112$	2.50000	+	0.866025i	0.236228	+	0.0818317i
$113$	−5.00000			−0.470360			−0.235180	−	0.971952i	$-0.575568\pi$
$113$	−5.00000			−0.470360			−0.235180	+	0.971952i	$0.575568\pi$
$114$		0			0
$115$	12.0000	+	20.7846i	1.11901	+	1.93817i
$116$	−4.50000	−	7.79423i	−0.417815	−	0.723676i
$117$		0			0
$118$	−5.00000			−0.460287
$119$	6.00000	−	5.19615i	0.550019	−	0.476331i
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−7.50000	−	12.9904i	−0.679018	−	1.17609i
$123$		0			0
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	24.0000			2.14663
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	−0.906399	−	0.422423i	$-0.861180\pi$
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	0.819028	+	0.573753i	$0.194513\pi$
$132$		0			0
$133$	−2.50000	−	0.866025i	−0.216777	−	0.0750939i
$134$	5.00000			0.431934
$135$		0			0
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	0.643013	−	0.765855i	$-0.277684\pi$
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	−0.984757	+	0.173939i	$0.944351\pi$
$138$		0			0
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$	−2.00000	−	10.3923i	−0.169031	−	0.878310i
$141$		0			0
$142$	7.50000	−	12.9904i	0.629386	−	1.09013i
$143$	0.500000	+	0.866025i	0.0418121	+	0.0724207i
$144$		0			0
$145$	−18.0000	+	31.1769i	−1.49482	+	2.58910i
$146$	−2.00000			−0.165521
$147$		0			0
$148$	−8.00000			−0.657596
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$		0			0
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	0.162758	−	0.986666i	$-0.447961\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$		0			0
$154$	0.500000	+	2.59808i	0.0402911	+	0.209359i
$155$	−32.0000			−2.57030
$156$		0			0
$157$	−7.50000	−	12.9904i	−0.598565	−	1.03675i	−0.993033	−	0.117836i	$-0.962404\pi$
$157$	−7.50000	−	12.9904i	−0.598565	−	1.03675i	0.394468	−	0.918910i	$-0.370929\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$		0			0
$160$	−4.00000			−0.316228
$161$	−15.0000	−	5.19615i	−1.18217	−	0.409514i
$162$		0			0
$163$	−6.50000	+	11.2583i	−0.509119	+	0.881820i	0.490825	+	0.871258i	$0.336695\pi$
$163$	−6.50000	+	11.2583i	−0.509119	+	0.881820i	−0.999944	+	0.0105623i	$0.996638\pi$
$164$		0			0
$165$		0			0
$166$	4.00000	−	6.92820i	0.310460	−	0.537733i
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−6.00000	+	10.3923i	−0.460179	+	0.797053i
$171$		0			0
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	−0.803354	−	0.595502i	$-0.796953\pi$
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	0.917397	+	0.397974i	$0.130287\pi$
$174$		0			0
$175$	−22.0000	+	19.0526i	−1.66304	+	1.44024i
$176$	1.00000			0.0753778
$177$		0			0
$178$		0			0
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	−0.977138	−	0.212607i	$-0.931805\pi$
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	0.304446	−	0.952529i	$-0.401529\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	2.50000	+	0.866025i	0.185312	+	0.0641941i
$183$		0			0
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	16.0000	+	27.7128i	1.17634	+	2.03749i
$186$		0			0
$187$	1.50000	−	2.59808i	0.109691	−	0.189990i
$188$	11.0000			0.802257
$189$		0			0
$190$	4.00000			0.290191
$191$	−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	$0.309616\pi$
$192$		0			0
$193$	6.00000	+	10.3923i	0.431889	+	0.748054i	0.997036	−	0.0769360i	$-0.0245137\pi$
$193$	6.00000	+	10.3923i	0.431889	+	0.748054i	−0.565147	+	0.824991i	$0.691180\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$	5.50000	+	9.52628i	0.388909	+	0.673610i
$201$		0			0
$202$	−14.0000			−0.985037
$203$	−4.50000	−	23.3827i	−0.315838	−	1.64114i
$204$		0			0
$205$		0			0
$206$	3.00000	+	5.19615i	0.209020	+	0.362033i
$207$		0			0
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	−1.00000			−0.0691714
$210$		0			0
$211$	18.0000			1.23917			0.619586	−	0.784929i	$-0.287301\pi$
$211$	18.0000			1.23917			0.619586	+	0.784929i	$0.287301\pi$
$212$	0.500000	−	0.866025i	0.0343401	−	0.0594789i
$213$		0			0
$214$	4.00000	+	6.92820i	0.273434	+	0.473602i
$215$	−20.0000	+	34.6410i	−1.36399	+	2.36250i
$216$		0			0
$217$	16.0000	−	13.8564i	1.08615	−	0.940634i
$218$		0			0
$219$		0			0
$220$	−2.00000	−	3.46410i	−0.134840	−	0.233550i
$221$	−1.50000	−	2.59808i	−0.100901	−	0.174766i
$222$		0			0
$223$	19.0000			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$224$	2.00000	−	1.73205i	0.133631	−	0.115728i
$225$		0			0
$226$	−2.50000	+	4.33013i	−0.166298	+	0.288036i
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	−9.00000	+	15.5885i	−0.594737	+	1.03011i	0.398847	+	0.917017i	$0.369410\pi$
$229$	−9.00000	+	15.5885i	−0.594737	+	1.03011i	−0.993584	+	0.113097i	$0.963923\pi$
$230$	24.0000			1.58251
$231$		0			0
$232$	−9.00000			−0.590879
$233$	−7.50000	+	12.9904i	−0.491341	+	0.851028i	−0.999950	−	0.00996947i	$-0.996827\pi$
$233$	−7.50000	+	12.9904i	−0.491341	+	0.851028i	0.508609	+	0.860998i	$0.330160\pi$
$234$		0			0
$235$	−22.0000	−	38.1051i	−1.43512	−	2.48570i
$236$	−2.50000	+	4.33013i	−0.162736	+	0.281867i
$237$		0			0
$238$	−1.50000	−	7.79423i	−0.0972306	−	0.505225i
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$		0			0
$241$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$241$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$242$	−5.00000	−	8.66025i	−0.321412	−	0.556702i
$243$		0			0
$244$	−15.0000			−0.960277
$245$	4.00000	−	27.7128i	0.255551	−	1.77051i
$246$		0			0
$247$	−0.500000	+	0.866025i	−0.0318142	+	0.0551039i
$248$	−4.00000	−	6.92820i	−0.254000	−	0.439941i
$249$		0			0
$250$	12.0000	−	20.7846i	0.758947	−	1.31453i
$251$	22.0000			1.38863			0.694314	−	0.719672i	$-0.255708\pi$
$251$	22.0000			1.38863			0.694314	+	0.719672i	$0.255708\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$		0			0
$259$	−20.0000	−	6.92820i	−1.24274	−	0.430498i
$260$	−4.00000			−0.248069
$261$		0			0
$262$	1.00000	+	1.73205i	0.0617802	+	0.107006i
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$		0			0
$265$	−4.00000			−0.245718
$266$	−2.00000	+	1.73205i	−0.122628	+	0.106199i
$267$		0			0
$268$	2.50000	−	4.33013i	0.152712	−	0.264505i
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	0.695606	−	0.718423i	$-0.255136\pi$
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	−0.969976	+	0.243201i	$0.921803\pi$
$270$		0			0
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	0.880812	+	0.473466i	$0.156997\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	−8.00000			−0.483298
$275$	−5.50000	+	9.52628i	−0.331662	+	0.574456i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	6.00000	−	10.3923i	0.359856	−	0.623289i
$279$		0			0
$280$	−10.0000	−	3.46410i	−0.597614	−	0.207020i
$281$	32.0000			1.90896			0.954480	−	0.298275i	$-0.0964112\pi$
$281$	32.0000			1.90896			0.954480	+	0.298275i	$0.0964112\pi$
$282$		0			0
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	−7.50000	−	12.9904i	−0.445043	−	0.770837i
$285$		0			0
$286$	1.00000			0.0591312
$287$		0			0
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	18.0000	+	31.1769i	1.05700	+	1.83077i
$291$		0			0
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		0			0
$295$	20.0000			1.16445
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$		0			0
$298$	5.00000	+	8.66025i	0.289642	+	0.501675i
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$		0			0
$301$	−5.00000	−	25.9808i	−0.288195	−	1.49751i
$302$	−19.0000			−1.09333
$303$		0			0
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$	30.0000	+	51.9615i	1.71780	+	2.97531i
$306$		0			0
$307$	27.0000			1.54097			0.770486	−	0.637457i	$-0.220014\pi$
$307$	27.0000			1.54097			0.770486	+	0.637457i	$0.220014\pi$
$308$	2.50000	+	0.866025i	0.142451	+	0.0493464i
$309$		0			0
$310$	−16.0000	+	27.7128i	−0.908739	+	1.57398i
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	0.956864	−	0.290537i	$-0.0938340\pi$
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	−0.730044	+	0.683400i	$0.760501\pi$
$312$		0			0
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	−0.597522	−	0.801852i	$-0.703848\pi$
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	0.993186	+	0.116543i	$0.0371814\pi$
$314$	−15.0000			−0.846499
$315$		0			0
$316$	−2.00000			−0.112509
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$	−2.00000	+	3.46410i	−0.111803	+	0.193649i
$321$		0			0
$322$	−12.0000	+	10.3923i	−0.668734	+	0.579141i
$323$	3.00000			0.166924
$324$		0			0
$325$	5.50000	+	9.52628i	0.305085	+	0.528423i
$326$	6.50000	+	11.2583i	0.360002	+	0.623541i
$327$		0			0
$328$		0			0
$329$	27.5000	+	9.52628i	1.51612	+	0.525201i
$330$		0			0
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	0.168320	+	0.985732i	$0.446166\pi$
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	−0.937829	+	0.347097i	$0.887167\pi$
$332$	−4.00000	−	6.92820i	−0.219529	−	0.380235i
$333$		0			0
$334$	−1.50000	+	2.59808i	−0.0820763	+	0.142160i
$335$	−20.0000			−1.09272
$336$		0			0
$337$	31.0000			1.68868			0.844339	−	0.535810i	$-0.179994\pi$
$337$	31.0000			1.68868			0.844339	+	0.535810i	$0.179994\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$		0			0
$340$	6.00000	+	10.3923i	0.325396	+	0.563602i
$341$	4.00000	−	6.92820i	0.216612	−	0.375183i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−10.0000			−0.539164
$345$		0			0
$346$	−1.50000	−	2.59808i	−0.0806405	−	0.139673i
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	0.807337	−	0.590091i	$-0.200908\pi$
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	−0.914702	+	0.404128i	$0.867575\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$	5.50000	+	28.5788i	0.293987	+	1.52760i
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$		0			0
$355$	−30.0000	+	51.9615i	−1.59223	+	2.75783i
$356$		0			0
$357$		0			0
$358$	−18.0000			−0.951330
$359$	4.00000	−	6.92820i	0.211112	−	0.365657i	−0.740951	−	0.671559i	$-0.765625\pi$
$359$	4.00000	−	6.92820i	0.211112	−	0.365657i	0.952063	+	0.305903i	$0.0989582\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−3.50000	+	6.06218i	−0.183956	+	0.318621i
$363$		0			0
$364$	2.00000	−	1.73205i	0.104828	−	0.0907841i
$365$	8.00000			0.418739
$366$		0			0
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	−0.975404	−	0.220423i	$-0.929256\pi$
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	0.296810	−	0.954937i	$-0.404077\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$		0			0
$370$	32.0000			1.66360
$371$	2.00000	−	1.73205i	0.103835	−	0.0899236i
$372$		0			0
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	−0.852791	−	0.522253i	$-0.825092\pi$
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	0.878680	+	0.477412i	$0.158425\pi$
$374$	−1.50000	−	2.59808i	−0.0775632	−	0.134343i
$375$		0			0
$376$	5.50000	−	9.52628i	0.283641	−	0.491280i
$377$	−9.00000			−0.463524
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	2.00000	−	3.46410i	0.102598	−	0.177705i
$381$		0			0
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	8.00000	−	13.8564i	0.408781	−	0.708029i	−0.585973	−	0.810331i	$-0.699287\pi$
$383$	8.00000	−	13.8564i	0.408781	−	0.708029i	0.994753	+	0.102302i	$0.0326207\pi$
$384$		0			0
$385$	−2.00000	−	10.3923i	−0.101929	−	0.529641i
$386$	12.0000			0.610784
$387$		0			0
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	−11.5000	−	19.9186i	−0.583073	−	1.00991i	−0.995113	−	0.0987463i	$-0.968517\pi$
$389$	−11.5000	−	19.9186i	−0.583073	−	1.00991i	0.412039	−	0.911166i	$-0.364817\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$		0			0
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$		0			0
$397$	15.0000	−	25.9808i	0.752828	−	1.30394i	−0.193618	−	0.981077i	$-0.562022\pi$
$397$	15.0000	−	25.9808i	0.752828	−	1.30394i	0.946447	−	0.322860i	$-0.104644\pi$
$398$	10.0000			0.501255
$399$		0			0
$400$	11.0000			0.550000
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	−0.199207	−	0.979957i	$-0.563837\pi$
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	0.948272	−	0.317460i	$-0.102830\pi$
$402$		0			0
$403$	−4.00000	−	6.92820i	−0.199254	−	0.345118i
$404$	−7.00000	+	12.1244i	−0.348263	+	0.603209i
$405$		0			0
$406$	−22.5000	−	7.79423i	−1.11666	−	0.386821i
$407$	−8.00000			−0.396545
$408$		0			0
$409$	4.00000	+	6.92820i	0.197787	+	0.342578i	0.947811	−	0.318834i	$-0.103291\pi$
$409$	4.00000	+	6.92820i	0.197787	+	0.342578i	−0.750023	+	0.661411i	$0.769958\pi$
$410$		0			0
$411$		0			0
$412$	6.00000			0.295599
$413$	−10.0000	+	8.66025i	−0.492068	+	0.426143i
$414$		0			0
$415$	−16.0000	+	27.7128i	−0.785409	+	1.36037i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$		0			0
$418$	−0.500000	+	0.866025i	−0.0244558	+	0.0423587i
$419$	14.0000			0.683945			0.341972	−	0.939710i	$-0.388905\pi$
$419$	14.0000			0.683945			0.341972	+	0.939710i	$0.388905\pi$
$420$		0			0
$421$	−30.0000			−1.46211			−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000			−1.46211			−0.731055	+	0.682318i	$0.760972\pi$
$422$	9.00000	−	15.5885i	0.438113	−	0.758834i
$423$		0			0
$424$	−0.500000	−	0.866025i	−0.0242821	−	0.0420579i
$425$	16.5000	−	28.5788i	0.800368	−	1.38628i
$426$		0			0
$427$	−37.5000	−	12.9904i	−1.81475	−	0.628649i
$428$	8.00000			0.386695
$429$		0			0
$430$	20.0000	+	34.6410i	0.964486	+	1.67054i
$431$	−4.00000	−	6.92820i	−0.192673	−	0.333720i	0.753462	−	0.657491i	$-0.228382\pi$
$431$	−4.00000	−	6.92820i	−0.192673	−	0.333720i	−0.946135	+	0.323772i	$0.895049\pi$
$432$		0			0
$433$	−11.0000			−0.528626			−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000			−0.528626			−0.264313	+	0.964437i	$0.585145\pi$
$434$	−4.00000	−	20.7846i	−0.192006	−	0.997693i
$435$		0			0
$436$		0			0
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$		0			0
$439$	1.00000	−	1.73205i	0.0477274	−	0.0826663i	−0.841175	−	0.540763i	$-0.818135\pi$
$439$	1.00000	−	1.73205i	0.0477274	−	0.0826663i	0.888902	+	0.458097i	$0.151469\pi$
$440$	−4.00000			−0.190693
$441$		0			0
$442$	−3.00000			−0.142695
$443$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$443$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$444$		0			0
$445$		0			0
$446$	9.50000	−	16.4545i	0.449838	−	0.779142i
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$	4.00000			0.188772			0.0943858	−	0.995536i	$-0.469911\pi$
$449$	4.00000			0.188772			0.0943858	+	0.995536i	$0.469911\pi$
$450$		0			0
$451$		0			0
$452$	2.50000	+	4.33013i	0.117590	+	0.203672i
$453$		0			0
$454$	−12.0000			−0.563188
$455$	−10.0000	−	3.46410i	−0.468807	−	0.162400i
$456$		0			0
$457$	−17.0000	+	29.4449i	−0.795226	+	1.37737i	0.127469	+	0.991843i	$0.459315\pi$
$457$	−17.0000	+	29.4449i	−0.795226	+	1.37737i	−0.922695	+	0.385530i	$0.874019\pi$
$458$	9.00000	+	15.5885i	0.420542	+	0.728401i
$459$		0			0
$460$	12.0000	−	20.7846i	0.559503	−	0.969087i
$461$	−40.0000			−1.86299			−0.931493	−	0.363760i	$-0.881493\pi$
$461$	−40.0000			−1.86299			−0.931493	+	0.363760i	$0.881493\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	−4.50000	+	7.79423i	−0.208907	+	0.361838i
$465$		0			0
$466$	7.50000	+	12.9904i	0.347431	+	0.601768i
$467$	15.0000	−	25.9808i	0.694117	−	1.20225i	−0.276360	−	0.961054i	$-0.589128\pi$
$467$	15.0000	−	25.9808i	0.694117	−	1.20225i	0.970477	−	0.241192i	$-0.0775384\pi$
$468$		0			0
$469$	10.0000	−	8.66025i	0.461757	−	0.399893i
$470$	−44.0000			−2.02957
$471$		0			0
$472$	2.50000	+	4.33013i	0.115072	+	0.199310i
$473$	−5.00000	−	8.66025i	−0.229900	−	0.398199i
$474$		0			0
$475$	−11.0000			−0.504715
$476$	−7.50000	−	2.59808i	−0.343762	−	0.119083i
$477$		0			0
$478$	−7.50000	+	12.9904i	−0.343042	+	0.594166i
$479$	2.50000	+	4.33013i	0.114228	+	0.197849i	0.917471	−	0.397803i	$-0.130227\pi$
$479$	2.50000	+	4.33013i	0.114228	+	0.197849i	−0.803243	+	0.595652i	$0.796894\pi$
$480$		0			0
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$		0			0
$483$		0			0
$484$	−10.0000			−0.454545
$485$	−20.0000	+	34.6410i	−0.908153	+	1.57297i
$486$		0			0
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	0.877132	−	0.480250i	$-0.159454\pi$
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	−0.854475	+	0.519493i	$0.826121\pi$
$488$	−7.50000	+	12.9904i	−0.339509	+	0.588047i
$489$		0			0
$490$	−22.0000	−	17.3205i	−0.993859	−	0.782461i
$491$	38.0000			1.71492			0.857458	−	0.514554i	$-0.172042\pi$
$491$	38.0000			1.71492			0.857458	+	0.514554i	$0.172042\pi$
$492$		0			0
$493$	13.5000	+	23.3827i	0.608009	+	1.05310i
$494$	0.500000	+	0.866025i	0.0224961	+	0.0389643i
$495$		0			0
$496$	−8.00000			−0.359211
$497$	−7.50000	−	38.9711i	−0.336421	−	1.74809i
$498$		0			0
$499$	−4.00000	+	6.92820i	−0.179065	+	0.310149i	−0.941560	−	0.336844i	$-0.890640\pi$
$499$	−4.00000	+	6.92820i	−0.179065	+	0.310149i	0.762496	+	0.646993i	$0.223974\pi$
$500$	−12.0000	−	20.7846i	−0.536656	−	0.929516i
$501$		0			0
$502$	11.0000	−	19.0526i	0.490954	−	0.850357i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	56.0000			2.49197
$506$	−3.00000	+	5.19615i	−0.133366	+	0.230997i
$507$		0			0
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$	20.0000	−	34.6410i	0.886484	−	1.53544i	0.0424816	−	0.999097i	$-0.486474\pi$
$509$	20.0000	−	34.6410i	0.886484	−	1.53544i	0.844003	−	0.536339i	$-0.180193\pi$
$510$		0			0
$511$	−4.00000	+	3.46410i	−0.176950	+	0.153243i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	3.00000	+	5.19615i	0.132324	+	0.229192i
$515$	−12.0000	−	20.7846i	−0.528783	−	0.915879i
$516$		0			0
$517$	11.0000			0.483779
$518$	−16.0000	+	13.8564i	−0.703000	+	0.608816i
$519$		0			0
$520$	−2.00000	+	3.46410i	−0.0877058	+	0.151911i
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	0.954519	−	0.298150i	$-0.0963696\pi$
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	−0.735465	+	0.677563i	$0.763036\pi$
$522$		0			0
$523$	7.00000	−	12.1244i	0.306089	−	0.530161i	−0.671414	−	0.741082i	$-0.734313\pi$
$523$	7.00000	−	12.1244i	0.306089	−	0.530161i	0.977503	+	0.210921i	$0.0676463\pi$
$524$	2.00000			0.0873704
$525$		0			0
$526$	24.0000			1.04645
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−2.00000	+	3.46410i	−0.0868744	+	0.150471i
$531$		0			0
$532$	0.500000	+	2.59808i	0.0216777	+	0.112641i
$533$		0			0
$534$		0			0
$535$	−16.0000	−	27.7128i	−0.691740	−	1.19813i
$536$	−2.50000	−	4.33013i	−0.107984	−	0.187033i
$537$		0			0
$538$	−9.00000			−0.388018
$539$	5.50000	+	4.33013i	0.236902	+	0.186512i
$540$		0			0
$541$	14.0000	−	24.2487i	0.601907	−	1.04253i	−0.390625	−	0.920550i	$-0.627741\pi$
$541$	14.0000	−	24.2487i	0.601907	−	1.04253i	0.992532	−	0.121984i	$-0.0389256\pi$
$542$	−0.500000	−	0.866025i	−0.0214768	−	0.0371990i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$		0			0
$546$		0			0
$547$	−42.0000			−1.79579			−0.897895	−	0.440209i	$-0.854904\pi$
$547$	−42.0000			−1.79579			−0.897895	+	0.440209i	$0.854904\pi$
$548$	−4.00000	+	6.92820i	−0.170872	+	0.295958i
$549$		0			0
$550$	5.50000	+	9.52628i	0.234521	+	0.406202i
$551$	4.50000	−	7.79423i	0.191706	−	0.332045i
$552$		0			0
$553$	−5.00000	−	1.73205i	−0.212622	−	0.0736543i
$554$	1.00000			0.0424859
$555$		0			0
$556$	−6.00000	−	10.3923i	−0.254457	−	0.440732i
$557$	17.0000	+	29.4449i	0.720313	+	1.24762i	0.960874	+	0.276985i	$0.0893352\pi$
$557$	17.0000	+	29.4449i	0.720313	+	1.24762i	−0.240561	+	0.970634i	$0.577331\pi$
$558$		0			0
$559$	−10.0000			−0.422955
$560$	−8.00000	+	6.92820i	−0.338062	+	0.292770i
$561$		0			0
$562$	16.0000	−	27.7128i	0.674919	−	1.16899i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$	10.0000	−	17.3205i	0.420703	−	0.728679i
$566$	14.0000			0.588464
$567$		0			0
$568$	−15.0000			−0.629386
$569$	−9.50000	+	16.4545i	−0.398261	+	0.689808i	−0.993511	−	0.113732i	$-0.963719\pi$
$569$	−9.50000	+	16.4545i	−0.398261	+	0.689808i	0.595251	+	0.803540i	$0.297053\pi$
$570$		0			0
$571$	−8.00000	−	13.8564i	−0.334790	−	0.579873i	0.648655	−	0.761083i	$-0.275332\pi$
$571$	−8.00000	−	13.8564i	−0.334790	−	0.579873i	−0.983444	+	0.181210i	$0.941999\pi$
$572$	0.500000	−	0.866025i	0.0209061	−	0.0362103i
$573$		0			0
$574$		0			0
$575$	−66.0000			−2.75239
$576$		0			0
$577$	7.00000	+	12.1244i	0.291414	+	0.504744i	0.974144	−	0.225927i	$-0.0725410\pi$
$577$	7.00000	+	12.1244i	0.291414	+	0.504744i	−0.682730	+	0.730670i	$0.739208\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	36.0000			1.49482
$581$	−4.00000	−	20.7846i	−0.165948	−	0.862291i
$582$		0			0
$583$	0.500000	−	0.866025i	0.0207079	−	0.0358671i
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$		0			0
$586$	−7.00000	+	12.1244i	−0.289167	+	0.500853i
$587$	−47.0000			−1.93990			−0.969949	−	0.243309i	$-0.921767\pi$
$587$	−47.0000			−1.93990			−0.969949	+	0.243309i	$0.921767\pi$
$588$		0			0
$589$	8.00000			0.329634
$590$	10.0000	−	17.3205i	0.411693	−	0.713074i
$591$		0			0
$592$	4.00000	+	6.92820i	0.164399	+	0.284747i
$593$	−6.00000	+	10.3923i	−0.246390	+	0.426761i	−0.962522	−	0.271205i	$-0.912578\pi$
$593$	−6.00000	+	10.3923i	−0.246390	+	0.426761i	0.716131	+	0.697966i	$0.245911\pi$
$594$		0			0
$595$	6.00000	+	31.1769i	0.245976	+	1.27813i
$596$	10.0000			0.409616
$597$		0			0
$598$	3.00000	+	5.19615i	0.122679	+	0.212486i
$599$	−2.00000	−	3.46410i	−0.0817178	−	0.141539i	0.822270	−	0.569097i	$-0.192707\pi$
$599$	−2.00000	−	3.46410i	−0.0817178	−	0.141539i	−0.903988	+	0.427558i	$0.859374\pi$
$600$		0			0
$601$	17.0000			0.693444			0.346722	−	0.937968i	$-0.387295\pi$
$601$	17.0000			0.693444			0.346722	+	0.937968i	$0.387295\pi$
$602$	−25.0000	−	8.66025i	−1.01892	−	0.352966i
$603$		0			0
$604$	−9.50000	+	16.4545i	−0.386550	+	0.669523i
$605$	20.0000	+	34.6410i	0.813116	+	1.40836i
$606$		0			0
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	0.688274	+	0.725450i	$0.258368\pi$
$608$	1.00000			0.0405554
$609$		0			0
$610$	60.0000			2.42933
$611$	5.50000	−	9.52628i	0.222506	−	0.385392i
$612$		0			0
$613$	12.0000	+	20.7846i	0.484675	+	0.839482i	0.999845	−	0.0176058i	$-0.00560439\pi$
$613$	12.0000	+	20.7846i	0.484675	+	0.839482i	−0.515170	+	0.857088i	$0.672271\pi$
$614$	13.5000	−	23.3827i	0.544816	−	0.943648i
$615$		0			0
$616$	2.00000	−	1.73205i	0.0805823	−	0.0697863i
$617$	30.0000			1.20775			0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000			1.20775			0.603877	+	0.797077i	$0.293622\pi$
$618$		0			0
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.846566	+	0.532284i	$0.178666\pi$
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.0376891	+	0.999290i	$0.488000\pi$
$620$	16.0000	+	27.7128i	0.642575	+	1.11297i
$621$		0			0
$622$	8.00000			0.320771
$623$		0			0
$624$		0			0
$625$	−20.5000	+	35.5070i	−0.820000	+	1.42028i
$626$	−7.00000	−	12.1244i	−0.279776	−	0.484587i
$627$		0			0
$628$	−7.50000	+	12.9904i	−0.299283	+	0.518373i
$629$	24.0000			0.956943
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	−1.00000	+	1.73205i	−0.0397779	+	0.0688973i
$633$		0			0
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$		0			0
$637$	6.50000	−	2.59808i	0.257539	−	0.102940i
$638$	−9.00000			−0.356313
$639$		0			0
$640$	2.00000	+	3.46410i	0.0790569	+	0.136931i
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$		0			0
$643$	−49.0000			−1.93237			−0.966186	−	0.257847i	$-0.916987\pi$
$643$	−49.0000			−1.93237			−0.966186	+	0.257847i	$0.916987\pi$
$644$	3.00000	+	15.5885i	0.118217	+	0.614271i
$645$		0			0
$646$	1.50000	−	2.59808i	0.0590167	−	0.102220i
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	0.885013	−	0.465566i	$-0.154149\pi$
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	−0.845699	+	0.533660i	$0.820816\pi$
$648$		0			0
$649$	−2.50000	+	4.33013i	−0.0981336	+	0.169972i
$650$	11.0000			0.431455
$651$		0			0
$652$	13.0000			0.509119
$653$	17.0000	−	29.4449i	0.665261	−	1.15227i	−0.313953	−	0.949439i	$-0.601653\pi$
$653$	17.0000	−	29.4449i	0.665261	−	1.15227i	0.979214	−	0.202828i	$-0.0650132\pi$
$654$		0			0
$655$	−4.00000	−	6.92820i	−0.156293	−	0.270707i
$656$		0			0
$657$		0			0
$658$	22.0000	−	19.0526i	0.857649	−	0.742746i
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$	−8.00000	−	13.8564i	−0.311164	−	0.538952i	0.667451	−	0.744654i	$-0.267385\pi$
$661$	−8.00000	−	13.8564i	−0.311164	−	0.538952i	−0.978615	+	0.205702i	$0.934052\pi$
$662$	14.0000	+	24.2487i	0.544125	+	0.942453i
$663$		0			0
$664$	−8.00000			−0.310460
$665$	8.00000	−	6.92820i	0.310227	−	0.268664i
$666$		0			0
$667$	27.0000	−	46.7654i	1.04544	−	1.81076i
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$		0			0
$670$	−10.0000	+	17.3205i	−0.386334	+	0.669150i
$671$	−15.0000			−0.579069
$672$		0			0
$673$	−18.0000			−0.693849			−0.346925	−	0.937893i	$-0.612774\pi$
$673$	−18.0000			−0.693849			−0.346925	+	0.937893i	$0.612774\pi$
$674$	15.5000	−	26.8468i	0.597038	−	1.03410i
$675$		0			0
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	0.500000	−	0.866025i	0.0192166	−	0.0332841i	−0.856257	−	0.516550i	$-0.827216\pi$
$677$	0.500000	−	0.866025i	0.0192166	−	0.0332841i	0.875474	+	0.483266i	$0.160549\pi$
$678$		0			0
$679$	−5.00000	−	25.9808i	−0.191882	−	0.997050i
$680$	12.0000			0.460179
$681$		0			0
$682$	−4.00000	−	6.92820i	−0.153168	−	0.265295i
$683$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$683$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$684$		0			0
$685$	32.0000			1.22266
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$		0			0
$688$	−5.00000	+	8.66025i	−0.190623	+	0.330169i
$689$	−0.500000	−	0.866025i	−0.0190485	−	0.0329929i
$690$		0			0
$691$	−2.50000	+	4.33013i	−0.0951045	+	0.164726i	−0.909652	−	0.415371i	$-0.863652\pi$
$691$	−2.50000	+	4.33013i	−0.0951045	+	0.164726i	0.814548	+	0.580097i	$0.196985\pi$
$692$	−3.00000			−0.114043
$693$		0			0
$694$	−4.00000			−0.151838
$695$	−24.0000	+	41.5692i	−0.910372	+	1.57681i
$696$		0			0
$697$		0			0
$698$	−5.00000	+	8.66025i	−0.189253	+	0.327795i
$699$		0			0
$700$	27.5000	+	9.52628i	1.03940	+	0.360060i
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$		0			0
$703$	−4.00000	−	6.92820i	−0.150863	−	0.261302i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$		0			0
$706$	18.0000			0.677439
$707$	−28.0000	+	24.2487i	−1.05305	+	0.911967i
$708$		0			0
$709$	−15.0000	+	25.9808i	−0.563337	+	0.975728i	0.433865	+	0.900978i	$0.357149\pi$
$709$	−15.0000	+	25.9808i	−0.563337	+	0.975728i	−0.997202	+	0.0747503i	$0.976184\pi$
$710$	30.0000	+	51.9615i	1.12588	+	1.95008i
$711$		0			0
$712$		0			0
$713$	48.0000			1.79761
$714$		0			0
$715$	−4.00000			−0.149592
$716$	−9.00000	+	15.5885i	−0.336346	+	0.582568i
$717$		0			0
$718$	−4.00000	−	6.92820i	−0.149279	−	0.258558i
$719$	−13.0000	+	22.5167i	−0.484818	+	0.839730i	−0.999848	−	0.0174426i	$-0.994448\pi$
$719$	−13.0000	+	22.5167i	−0.484818	+	0.839730i	0.515030	+	0.857172i	$0.327781\pi$
$720$		0			0
$721$	15.0000	+	5.19615i	0.558629	+	0.193515i
$722$	18.0000			0.669891
$723$		0			0
$724$	3.50000	+	6.06218i	0.130076	+	0.225299i
$725$	−49.5000	−	85.7365i	−1.83838	−	3.18417i
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	−0.500000	−	2.59808i	−0.0185312	−	0.0962911i
$729$		0			0
$730$	4.00000	−	6.92820i	0.148047	−	0.256424i
$731$	15.0000	+	25.9808i	0.554795	+	0.960933i
$732$		0			0
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	−0.883902	−	0.467671i	$-0.845093\pi$
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	0.846967	+	0.531646i	$0.178426\pi$
$734$	−26.0000			−0.959678
$735$		0			0
$736$	6.00000			0.221163
$737$	2.50000	−	4.33013i	0.0920887	−	0.159502i
$738$		0			0
$739$	−2.00000	−	3.46410i	−0.0735712	−	0.127429i	0.826893	−	0.562360i	$-0.190106\pi$
$739$	−2.00000	−	3.46410i	−0.0735712	−	0.127429i	−0.900464	+	0.434930i	$0.856773\pi$
$740$	16.0000	−	27.7128i	0.588172	−	1.01874i
$741$		0			0
$742$	−0.500000	−	2.59808i	−0.0183556	−	0.0953784i
$743$	5.00000			0.183432			0.0917161	−	0.995785i	$-0.470765\pi$
$743$	5.00000			0.183432			0.0917161	+	0.995785i	$0.470765\pi$
$744$		0			0
$745$	−20.0000	−	34.6410i	−0.732743	−	1.26915i
$746$	−0.500000	−	0.866025i	−0.0183063	−	0.0317074i
$747$		0			0
$748$	−3.00000			−0.109691
$749$	20.0000	+	6.92820i	0.730784	+	0.253151i
$750$		0			0
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$	−5.50000	−	9.52628i	−0.200564	−	0.347388i
$753$		0			0
$754$	−4.50000	+	7.79423i	−0.163880	+	0.283849i
$755$	76.0000			2.76592
$756$		0			0
$757$	−47.0000			−1.70824			−0.854122	−	0.520073i	$-0.825905\pi$
$757$	−47.0000			−1.70824			−0.854122	+	0.520073i	$0.825905\pi$
$758$	−10.0000	+	17.3205i	−0.363216	+	0.629109i
$759$		0			0
$760$	−2.00000	−	3.46410i	−0.0725476	−	0.125656i
$761$	−8.00000	+	13.8564i	−0.290000	+	0.502294i	−0.973809	−	0.227366i	$-0.926989\pi$
$761$	−8.00000	+	13.8564i	−0.290000	+	0.502294i	0.683810	+	0.729661i	$0.260322\pi$
$762$		0			0
$763$		0			0
$764$	12.0000			0.434145
$765$		0			0
$766$	−8.00000	−	13.8564i	−0.289052	−	0.500652i
$767$	2.50000	+	4.33013i	0.0902698	+	0.156352i
$768$		0			0
$769$	22.0000			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$770$	−10.0000	−	3.46410i	−0.360375	−	0.124838i
$771$		0			0
$772$	6.00000	−	10.3923i	0.215945	−	0.374027i
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$		0			0
$775$	44.0000	−	76.2102i	1.58053	−	2.73755i
$776$	−10.0000			−0.358979
$777$		0			0
$778$	−23.0000			−0.824590
$779$		0			0
$780$		0			0
$781$	−7.50000	−	12.9904i	−0.268371	−	0.464832i
$782$	9.00000	−	15.5885i	0.321839	−	0.557442i
$783$		0			0
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	60.0000			2.14149
$786$		0			0
$787$	7.50000	+	12.9904i	0.267346	+	0.463057i	0.968176	−	0.250272i	$-0.0805200\pi$
$787$	7.50000	+	12.9904i	0.267346	+	0.463057i	−0.700830	+	0.713329i	$0.747187\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$		0			0
$790$	8.00000			0.284627
$791$	2.50000	+	12.9904i	0.0888898	+	0.461885i
$792$		0			0
$793$	−7.50000	+	12.9904i	−0.266333	+	0.461302i
$794$	−15.0000	−	25.9808i	−0.532330	−	0.922023i
$795$		0			0
$796$	5.00000	−	8.66025i	0.177220	−	0.306955i
$797$	−54.0000			−1.91278			−0.956389	−	0.292096i	$-0.905647\pi$
$797$	−54.0000			−1.91278			−0.956389	+	0.292096i	$0.905647\pi$
$798$		0			0
$799$	−33.0000			−1.16746
$800$	5.50000	−	9.52628i	0.194454	−	0.336805i
$801$		0			0
$802$	−15.0000	−	25.9808i	−0.529668	−	0.917413i
$803$	−1.00000	+	1.73205i	−0.0352892	+	0.0611227i
$804$		0			0
$805$	48.0000	−	41.5692i	1.69178	−	1.46512i
$806$	−8.00000			−0.281788
$807$		0			0
$808$	7.00000	+	12.1244i	0.246259	+	0.426533i
$809$	−1.50000	−	2.59808i	−0.0527372	−	0.0913435i	0.838452	−	0.544976i	$-0.183461\pi$
$809$	−1.50000	−	2.59808i	−0.0527372	−	0.0913435i	−0.891189	+	0.453632i	$0.850128\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−18.0000	+	15.5885i	−0.631676	+	0.547048i
$813$		0			0
$814$	−4.00000	+	6.92820i	−0.140200	+	0.242833i
$815$	−26.0000	−	45.0333i	−0.910740	−	1.57745i
$816$		0			0
$817$	5.00000	−	8.66025i	0.174928	−	0.302984i
$818$	8.00000			0.279713
$819$		0			0
$820$		0			0
$821$	20.0000	−	34.6410i	0.698005	−	1.20898i	−0.271152	−	0.962536i	$-0.587405\pi$
$821$	20.0000	−	34.6410i	0.698005	−	1.20898i	0.969157	−	0.246443i	$-0.0792619\pi$
$822$		0			0
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	3.00000	−	5.19615i	0.104510	−	0.181017i
$825$		0			0
$826$	2.50000	+	12.9904i	0.0869861	+	0.451993i
$827$	−17.0000			−0.591148			−0.295574	−	0.955320i	$-0.595511\pi$
$827$	−17.0000			−0.591148			−0.295574	+	0.955320i	$0.595511\pi$
$828$		0			0
$829$	−21.5000	−	37.2391i	−0.746726	−	1.29337i	−0.949384	−	0.314118i	$-0.898291\pi$
$829$	−21.5000	−	37.2391i	−0.746726	−	1.29337i	0.202658	−	0.979250i	$-0.435042\pi$
$830$	16.0000	+	27.7128i	0.555368	+	0.961926i
$831$		0			0
$832$	−1.00000			−0.0346688
$833$	−16.5000	−	12.9904i	−0.571691	−	0.450090i
$834$		0			0
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$	0.500000	+	0.866025i	0.0172929	+	0.0299521i
$837$		0			0
$838$	7.00000	−	12.1244i	0.241811	−	0.418829i
$839$	−5.00000			−0.172619			−0.0863096	−	0.996268i	$-0.527507\pi$
$839$	−5.00000			−0.172619			−0.0863096	+	0.996268i	$0.527507\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	−15.0000	+	25.9808i	−0.516934	+	0.895356i
$843$		0			0
$844$	−9.00000	−	15.5885i	−0.309793	−	0.536577i
$845$	−2.00000	+	3.46410i	−0.0688021	+	0.119169i
$846$		0			0
$847$	−25.0000	−	8.66025i	−0.859010	−	0.297570i
$848$	−1.00000			−0.0343401
$849$		0			0
$850$	−16.5000	−	28.5788i	−0.565945	−	0.980246i
$851$	−24.0000	−	41.5692i	−0.822709	−	1.42497i
$852$		0			0
$853$	2.00000			0.0684787			0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000			0.0684787			0.0342393	+	0.999414i	$0.489099\pi$
$854$	−30.0000	+	25.9808i	−1.02658	+	0.889043i
$855$		0			0
$856$	4.00000	−	6.92820i	0.136717	−	0.236801i
$857$	4.50000	+	7.79423i	0.153717	+	0.266246i	0.932591	−	0.360935i	$-0.117542\pi$
$857$	4.50000	+	7.79423i	0.153717	+	0.266246i	−0.778874	+	0.627180i	$0.784209\pi$
$858$		0			0
$859$	4.00000	−	6.92820i	0.136478	−	0.236387i	−0.789683	−	0.613515i	$-0.789755\pi$
$859$	4.00000	−	6.92820i	0.136478	−	0.236387i	0.926161	+	0.377128i	$0.123088\pi$
$860$	40.0000			1.36399
$861$		0			0
$862$	−8.00000			−0.272481
$863$	−2.00000	+	3.46410i	−0.0680808	+	0.117919i	−0.898056	−	0.439880i	$-0.855021\pi$
$863$	−2.00000	+	3.46410i	−0.0680808	+	0.117919i	0.829976	+	0.557800i	$0.188354\pi$
$864$		0			0
$865$	6.00000	+	10.3923i	0.204006	+	0.353349i
$866$	−5.50000	+	9.52628i	−0.186898	+	0.323716i
$867$		0			0
$868$	−20.0000	−	6.92820i	−0.678844	−	0.235159i
$869$	−2.00000			−0.0678454
$870$		0			0
$871$	−2.50000	−	4.33013i	−0.0847093	−	0.146721i
$872$		0			0
$873$		0			0
$874$	−6.00000			−0.202953
$875$	−12.0000	−	62.3538i	−0.405674	−	2.10794i
$876$		0			0
$877$	−12.0000	+	20.7846i	−0.405211	+	0.701846i	−0.994346	−	0.106188i	$-0.966135\pi$
$877$	−12.0000	+	20.7846i	−0.405211	+	0.701846i	0.589135	+	0.808035i	$0.299469\pi$
$878$	−1.00000	−	1.73205i	−0.0337484	−	0.0584539i
$879$		0			0
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	−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
$883$	24.0000			0.807664			0.403832	−	0.914833i	$-0.367678\pi$
$883$	24.0000			0.807664			0.403832	+	0.914833i	$0.367678\pi$
$884$	−1.50000	+	2.59808i	−0.0504505	+	0.0873828i
$885$		0			0
$886$		0			0
$887$	−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	$0.198785\pi$
$888$		0			0
$889$	−1.00000	−	5.19615i	−0.0335389	−	0.174273i
$890$		0			0
$891$		0			0
$892$	−9.50000	−	16.4545i	−0.318084	−	0.550937i
$893$	5.50000	+	9.52628i	0.184050	+	0.318785i
$894$		0			0
$895$	72.0000			2.40669
$896$	−2.50000	−	0.866025i	−0.0835191	−	0.0289319i
$897$		0			0
$898$	2.00000	−	3.46410i	0.0667409	−	0.115599i
$899$	36.0000	+	62.3538i	1.20067	+	2.07962i
$900$		0			0
$901$	−1.50000	+	2.59808i	−0.0499722	+	0.0865545i
$902$		0			0
$903$		0			0
$904$	5.00000			0.166298
$905$	14.0000	−	24.2487i	0.465376	−	0.806054i
$906$		0			0
$907$	−9.00000	−	15.5885i	−0.298840	−	0.517606i	0.677031	−	0.735955i	$-0.263266\pi$
$907$	−9.00000	−	15.5885i	−0.298840	−	0.517606i	−0.975871	+	0.218348i	$0.929933\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$		0			0
$910$	−8.00000	+	6.92820i	−0.265197	+	0.229668i
$911$	−2.00000			−0.0662630			−0.0331315	−	0.999451i	$-0.510548\pi$
$911$	−2.00000			−0.0662630			−0.0331315	+	0.999451i	$0.510548\pi$
$912$		0			0
$913$	−4.00000	−	6.92820i	−0.132381	−	0.229290i
$914$	17.0000	+	29.4449i	0.562310	+	0.973950i
$915$		0			0
$916$	18.0000			0.594737
$917$	5.00000	+	1.73205i	0.165115	+	0.0571974i
$918$		0			0
$919$	11.0000	−	19.0526i	0.362857	−	0.628486i	−0.625573	−	0.780165i	$-0.715135\pi$
$919$	11.0000	−	19.0526i	0.362857	−	0.628486i	0.988430	+	0.151680i	$0.0484682\pi$
$920$	−12.0000	−	20.7846i	−0.395628	−	0.685248i
$921$		0			0
$922$	−20.0000	+	34.6410i	−0.658665	+	1.14084i
$923$	−15.0000			−0.493731
$924$		0			0
$925$	−88.0000			−2.89342
$926$		0			0
$927$		0			0
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$	5.00000	−	8.66025i	0.164045	−	0.284134i	−0.772271	−	0.635293i	$-0.780879\pi$
$929$	5.00000	−	8.66025i	0.164045	−	0.284134i	0.936316	+	0.351160i	$0.114213\pi$
$930$		0			0
$931$	−1.00000	+	6.92820i	−0.0327737	+	0.227063i
$932$	15.0000			0.491341
$933$		0			0
$934$	−15.0000	−	25.9808i	−0.490815	−	0.850117i
$935$	6.00000	+	10.3923i	0.196221	+	0.339865i
$936$		0			0
$937$	−49.0000			−1.60076			−0.800380	−	0.599493i	$-0.795369\pi$
$937$	−49.0000			−1.60076			−0.800380	+	0.599493i	$0.795369\pi$
$938$	−2.50000	−	12.9904i	−0.0816279	−	0.424151i
$939$		0			0
$940$	−22.0000	+	38.1051i	−0.717561	+	1.24285i
$941$	−24.0000	−	41.5692i	−0.782378	−	1.35512i	−0.930553	−	0.366157i	$-0.880673\pi$
$941$	−24.0000	−	41.5692i	−0.782378	−	1.35512i	0.148176	−	0.988961i	$-0.452660\pi$
$942$		0			0
$943$		0			0
$944$	5.00000			0.162736
$945$		0			0
$946$	−10.0000			−0.325128
$947$	−16.5000	+	28.5788i	−0.536178	+	0.928687i	0.462927	+	0.886396i	$0.346799\pi$
$947$	−16.5000	+	28.5788i	−0.536178	+	0.928687i	−0.999105	+	0.0422912i	$0.986534\pi$
$948$		0			0
$949$	1.00000	+	1.73205i	0.0324614	+	0.0562247i
$950$	−5.50000	+	9.52628i	−0.178444	+	0.309073i
$951$		0			0
$952$	−6.00000	+	5.19615i	−0.194461	+	0.168408i
$953$	−13.0000			−0.421111			−0.210556	−	0.977582i	$-0.567527\pi$
$953$	−13.0000			−0.421111			−0.210556	+	0.977582i	$0.567527\pi$
$954$		0			0
$955$	−24.0000	−	41.5692i	−0.776622	−	1.34515i
$956$	7.50000	+	12.9904i	0.242567	+	0.420139i
$957$		0			0
$958$	5.00000			0.161543
$959$	−16.0000	+	13.8564i	−0.516667	+	0.447447i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	4.00000	+	6.92820i	0.128965	+	0.223374i
$963$		0			0
$964$		0			0
$965$	−48.0000			−1.54517
$966$		0			0
$967$	13.0000			0.418052			0.209026	−	0.977910i	$-0.432971\pi$
$967$	13.0000			0.418052			0.209026	+	0.977910i	$0.432971\pi$
$968$	−5.00000	+	8.66025i	−0.160706	+	0.278351i
$969$		0			0
$970$	20.0000	+	34.6410i	0.642161	+	1.11226i
$971$	20.0000	−	34.6410i	0.641831	−	1.11168i	−0.343193	−	0.939265i	$-0.611509\pi$
$971$	20.0000	−	34.6410i	0.641831	−	1.11168i	0.985024	−	0.172418i	$-0.0551581\pi$
$972$		0			0
$973$	−6.00000	−	31.1769i	−0.192351	−	0.999486i
$974$	1.00000			0.0320421
$975$		0			0
$976$	7.50000	+	12.9904i	0.240069	+	0.415812i
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	0.814038	−	0.580812i	$-0.197265\pi$
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	−0.910017	+	0.414572i	$0.863931\pi$
$978$		0			0
$979$		0			0
$980$	−26.0000	+	10.3923i	−0.830540	+	0.331970i
$981$		0			0
$982$	19.0000	−	32.9090i	0.606314	−	1.05017i
$983$	−2.50000	−	4.33013i	−0.0797376	−	0.138110i	0.823399	−	0.567463i	$-0.192075\pi$
$983$	−2.50000	−	4.33013i	−0.0797376	−	0.138110i	−0.903137	+	0.429353i	$0.858742\pi$
$984$		0			0
$985$	36.0000	−	62.3538i	1.14706	−	1.98676i
$986$	27.0000			0.859855
$987$		0			0
$988$	1.00000			0.0318142
$989$	30.0000	−	51.9615i	0.953945	−	1.65228i
$990$		0			0
$991$	28.0000	+	48.4974i	0.889449	+	1.54057i	0.840528	+	0.541769i	$0.182245\pi$
$991$	28.0000	+	48.4974i	0.889449	+	1.54057i	0.0489218	+	0.998803i	$0.484422\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$		0			0
$994$	−37.5000	−	12.9904i	−1.18943	−	0.412030i
$995$	−40.0000			−1.26809
$996$		0			0
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	0.999945	−	0.0104877i	$-0.00333839\pi$
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	−0.509055	+	0.860734i	$0.670005\pi$
$998$	4.00000	+	6.92820i	0.126618	+	0.219308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.j.f.1171.1		2
3.2	odd	2		546.2.i.c.79.1	✓	2
7.4	even	3	inner	1638.2.j.f.235.1		2
21.2	odd	6		3822.2.a.ba.1.1		1
21.5	even	6		3822.2.a.z.1.1		1
21.11	odd	6		546.2.i.c.235.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.c.79.1	✓	2	3.2	odd	2
546.2.i.c.235.1	yes	2	21.11	odd	6
1638.2.j.f.235.1		2	7.4	even	3	inner
1638.2.j.f.1171.1		2	1.1	even	1	trivial
3822.2.a.z.1.1		1	21.5	even	6
3822.2.a.ba.1.1		1	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(2.00000 + 3.46410i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{19} +4.00000 q^{20} -1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-5.50000 - 9.52628i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(-2.00000 + 1.73205i) q^{28} +9.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(10.0000 + 3.46410i) q^{35} +(4.00000 - 6.92820i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(2.00000 - 3.46410i) q^{40} +10.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(-5.50000 + 9.52628i) q^{47} +(-6.50000 + 2.59808i) q^{49} -11.0000 q^{50} +(0.500000 + 0.866025i) q^{52} +(0.500000 + 0.866025i) q^{53} +4.00000 q^{55} +(0.500000 + 2.59808i) q^{56} +(4.50000 - 7.79423i) q^{58} +(-2.50000 - 4.33013i) q^{59} +(7.50000 - 12.9904i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(2.50000 + 4.33013i) q^{67} +(1.50000 - 2.59808i) q^{68} +(8.00000 - 6.92820i) q^{70} +15.0000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-4.00000 - 6.92820i) q^{74} -1.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(1.00000 - 1.73205i) q^{79} +(-2.00000 - 3.46410i) q^{80} +8.00000 q^{83} -12.0000 q^{85} +(5.00000 - 8.66025i) q^{86} +(0.500000 + 0.866025i) q^{88} +(0.500000 + 2.59808i) q^{91} -6.00000 q^{92} +(5.50000 + 9.52628i) q^{94} +(2.00000 + 3.46410i) q^{95} +10.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 4 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - 4 * q^5 - q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - 4 q^{5} - q^{7} - 2 q^{8} + 4 q^{10} - q^{11} - 2 q^{13} - 5 q^{14} - q^{16} + 3 q^{17} + q^{19} + 8 q^{20} - 2 q^{22} + 6 q^{23} - 11 q^{25} - q^{26} - 4 q^{28} + 18 q^{29} + 8 q^{31} + q^{32} + 6 q^{34} + 20 q^{35} + 8 q^{37} - q^{38} + 4 q^{40} + 20 q^{43} - q^{44} - 6 q^{46} - 11 q^{47} - 13 q^{49} - 22 q^{50} + q^{52} + q^{53} + 8 q^{55} + q^{56} + 9 q^{58} - 5 q^{59} + 15 q^{61} + 16 q^{62} + 2 q^{64} + 4 q^{65} + 5 q^{67} + 3 q^{68} + 16 q^{70} + 30 q^{71} - 2 q^{73} - 8 q^{74} - 2 q^{76} - 4 q^{77} + 2 q^{79} - 4 q^{80} + 16 q^{83} - 24 q^{85} + 10 q^{86} + q^{88} + q^{91} - 12 q^{92} + 11 q^{94} + 4 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 4 * q^5 - q^7 - 2 * q^8 + 4 * q^10 - q^11 - 2 * q^13 - 5 * q^14 - q^16 + 3 * q^17 + q^19 + 8 * q^20 - 2 * q^22 + 6 * q^23 - 11 * q^25 - q^26 - 4 * q^28 + 18 * q^29 + 8 * q^31 + q^32 + 6 * q^34 + 20 * q^35 + 8 * q^37 - q^38 + 4 * q^40 + 20 * q^43 - q^44 - 6 * q^46 - 11 * q^47 - 13 * q^49 - 22 * q^50 + q^52 + q^53 + 8 * q^55 + q^56 + 9 * q^58 - 5 * q^59 + 15 * q^61 + 16 * q^62 + 2 * q^64 + 4 * q^65 + 5 * q^67 + 3 * q^68 + 16 * q^70 + 30 * q^71 - 2 * q^73 - 8 * q^74 - 2 * q^76 - 4 * q^77 + 2 * q^79 - 4 * q^80 + 16 * q^83 - 24 * q^85 + 10 * q^86 + q^88 + q^91 - 12 * q^92 + 11 * q^94 + 4 * q^95 + 20 * q^97 - 2 * q^98

Introduction

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