LMFDB - Embedded newform 2646.2.e.a.1549.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(1549,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2646.1549"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,0,2,-1,0,0,-2,0,1,-2,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$21.1284163748$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1549.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2646.1549
Dual form			2646.2.e.a.2125.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(-3.50000 + 6.06218i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} +(1.50000 + 2.59808i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(-4.00000 - 6.92820i) q^{29} -4.00000 q^{31} -1.00000 q^{32} +(3.00000 - 5.19615i) q^{37} +(3.50000 - 6.06218i) q^{38} +(0.500000 + 0.866025i) q^{40} +(6.00000 - 10.3923i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{46} -8.00000 q^{47} +(-2.00000 + 3.46410i) q^{50} +(1.00000 - 1.73205i) q^{52} +(2.00000 + 3.46410i) q^{53} +2.00000 q^{55} +(4.00000 + 6.92820i) q^{58} +4.00000 q^{59} -13.0000 q^{61} +4.00000 q^{62} +1.00000 q^{64} -2.00000 q^{65} -2.00000 q^{67} +5.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-3.50000 + 6.06218i) q^{76} -11.0000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-6.00000 + 10.3923i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(-4.00000 - 6.92820i) q^{86} +(1.00000 - 1.73205i) q^{88} +(-7.00000 + 12.1244i) q^{89} +(1.50000 + 2.59808i) q^{92} +8.00000 q^{94} +7.00000 q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - q^{5} - 2 q^{8} + q^{10} - 2 q^{11} + 2 q^{13} + 2 q^{16} - 7 q^{19} - q^{20} + 2 q^{22} + 3 q^{23} + 4 q^{25} - 2 q^{26} - 8 q^{29} - 8 q^{31} - 2 q^{32} + 6 q^{37} + 7 q^{38}+ \cdots - 2 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - q^5 - 2 * q^8 + q^10 - 2 * q^11 + 2 * q^13 + 2 * q^16 - 7 * q^19 - q^20 + 2 * q^22 + 3 * q^23 + 4 * q^25 - 2 * q^26 - 8 * q^29 - 8 * q^31 - 2 * q^32 + 6 * q^37 + 7 * q^38 + q^40 + 12 * q^41 + 8 * q^43 - 2 * q^44 - 3 * q^46 - 16 * q^47 - 4 * q^50 + 2 * q^52 + 4 * q^53 + 4 * q^55 + 8 * q^58 + 8 * q^59 - 26 * q^61 + 8 * q^62 + 2 * q^64 - 4 * q^65 - 4 * q^67 + 10 * q^71 - 14 * q^73 - 6 * q^74 - 7 * q^76 - 22 * q^79 - q^80 - 12 * q^82 - 12 * q^83 - 8 * q^86 + 2 * q^88 - 14 * q^89 + 3 * q^92 + 16 * q^94 + 14 * q^95 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$		0			0
$28$		0			0
$29$	−4.00000	−	6.92820i	−0.742781	−	1.28654i	−0.951224	−	0.308500i	$-0.900173\pi$
$29$	−4.00000	−	6.92820i	−0.742781	−	1.28654i	0.208443	−	0.978035i	$-0.433160\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$	3.50000	−	6.06218i	0.567775	−	0.983415i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	6.00000	−	10.3923i	0.937043	−	1.62301i	0.166092	−	0.986110i	$-0.446885\pi$
$41$	6.00000	−	10.3923i	0.937043	−	1.62301i	0.770950	−	0.636895i	$-0.219782\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$		0			0
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$		0			0
$49$		0			0
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		0			0
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	0.970065	−	0.242846i	$-0.0780811\pi$
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	−0.695344	+	0.718677i	$0.744748\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$		0			0
$57$		0			0
$58$	4.00000	+	6.92820i	0.525226	+	0.909718i
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$		0			0
$61$	−13.0000			−1.66448			−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000			−1.66448			−0.832240	+	0.554416i	$0.812942\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000			−0.248069
$66$		0			0
$67$	−2.00000			−0.244339			−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000			−0.244339			−0.122169	+	0.992509i	$0.538985\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.00000			0.593391			0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000			0.593391			0.296695	+	0.954972i	$0.404115\pi$
$72$		0			0
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		0			0
$76$	−3.50000	+	6.06218i	−0.401478	+	0.695379i
$77$		0			0
$78$		0			0
$79$	−11.0000			−1.23760			−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000			−1.23760			−0.618798	+	0.785550i	$0.712380\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$		0			0
$85$		0			0
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$		0			0
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	0.209585	+	0.977790i	$0.432789\pi$
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	−0.951584	+	0.307389i	$0.900545\pi$
$90$		0			0
$91$		0			0
$92$	1.50000	+	2.59808i	0.156386	+	0.270868i
$93$		0			0
$94$	8.00000			0.825137
$95$	7.00000			0.718185
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$		0			0
$99$		0			0
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	5.50000	−	9.52628i	0.547270	−	0.947900i	−0.451190	−	0.892428i	$-0.649000\pi$
$101$	5.50000	−	9.52628i	0.547270	−	0.947900i	0.998460	−	0.0554722i	$-0.0176664\pi$
$102$		0			0
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	−2.00000	−	3.46410i	−0.194257	−	0.336463i
$107$	4.00000	−	6.92820i	0.386695	−	0.669775i	−0.605308	−	0.795991i	$-0.706950\pi$
$107$	4.00000	−	6.92820i	0.386695	−	0.669775i	0.992003	+	0.126217i	$0.0402834\pi$
$108$		0			0
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	0.754204	−	0.656640i	$-0.228023\pi$
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	−0.945769	+	0.324840i	$0.894690\pi$
$110$	−2.00000			−0.190693
$111$		0			0
$112$		0			0
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	−0.888585	−	0.458712i	$-0.848311\pi$
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	0.841549	+	0.540181i	$0.181644\pi$
$114$		0			0
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	−4.00000	−	6.92820i	−0.371391	−	0.643268i
$117$		0			0
$118$	−4.00000			−0.368230
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	13.0000			1.17696
$123$		0			0
$124$	−4.00000			−0.359211
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−19.0000			−1.68598			−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000			−1.68598			−0.842989	+	0.537931i	$0.819206\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	2.00000			0.175412
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$		0			0
$133$		0			0
$134$	2.00000			0.172774
$135$		0			0
$136$		0			0
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$		0			0
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	−0.609618	−	0.792695i	$-0.708677\pi$
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	0.991303	+	0.131597i	$0.0420106\pi$
$140$		0			0
$141$		0			0
$142$	−5.00000			−0.419591
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$		0			0
$145$	−4.00000	+	6.92820i	−0.332182	+	0.575356i
$146$	7.00000	+	12.1244i	0.579324	+	1.00342i
$147$		0			0
$148$	3.00000	−	5.19615i	0.246598	−	0.427121i
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$		0			0
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	3.50000	−	6.06218i	0.283887	−	0.491708i
$153$		0			0
$154$		0			0
$155$	2.00000	+	3.46410i	0.160644	+	0.278243i
$156$		0			0
$157$	−11.0000			−0.877896			−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−11.0000			−0.877896			−0.438948	+	0.898513i	$0.644649\pi$
$158$	11.0000			0.875113
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$		0			0
$162$		0			0
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	−0.724288	−	0.689497i	$-0.757831\pi$
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	0.959266	+	0.282503i	$0.0911648\pi$
$164$	6.00000	−	10.3923i	0.468521	−	0.811503i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−1.00000	+	1.73205i	−0.0773823	+	0.134030i	−0.902120	−	0.431486i	$-0.857990\pi$
$167$	−1.00000	+	1.73205i	−0.0773823	+	0.134030i	0.824737	+	0.565516i	$0.191323\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$		0			0
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$	−22.0000			−1.67263			−0.836315	−	0.548250i	$-0.815294\pi$
$173$	−22.0000			−1.67263			−0.836315	+	0.548250i	$0.815294\pi$
$174$		0			0
$175$		0			0
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$		0			0
$178$	7.00000	−	12.1244i	0.524672	−	0.908759i
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.831408	−	0.555663i	$-0.812464\pi$
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.0655145	−	0.997852i	$-0.520869\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$		0			0
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	−6.00000			−0.441129
$186$		0			0
$187$		0			0
$188$	−8.00000			−0.583460
$189$		0			0
$190$	−7.00000			−0.507833
$191$	−3.00000			−0.217072			−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000			−0.217072			−0.108536	+	0.994092i	$0.534616\pi$
$192$		0			0
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$		0			0
$196$		0			0
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	0.503774	−	0.863836i	$-0.331945\pi$
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	−0.999990	+	0.00436292i	$0.998611\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	−5.50000	+	9.52628i	−0.386979	+	0.670267i
$203$		0			0
$204$		0			0
$205$	−12.0000			−0.838116
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$		0			0
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$	−7.00000	−	12.1244i	−0.484200	−	0.838659i
$210$		0			0
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$		0			0
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$	4.00000	−	6.92820i	0.272798	−	0.472500i
$216$		0			0
$217$		0			0
$218$	2.00000	+	3.46410i	0.135457	+	0.234619i
$219$		0			0
$220$	2.00000			0.134840
$221$		0			0
$222$		0			0
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	0.830599	−	0.556871i	$-0.187998\pi$
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	−0.897564	+	0.440884i	$0.854665\pi$
$224$		0			0
$225$		0			0
$226$	0.500000	−	0.866025i	0.0332595	−	0.0576072i
$227$	−8.50000	+	14.7224i	−0.564165	+	0.977162i	0.432962	+	0.901412i	$0.357468\pi$
$227$	−8.50000	+	14.7224i	−0.564165	+	0.977162i	−0.997127	+	0.0757500i	$0.975865\pi$
$228$		0			0
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	0.567300	−	0.823511i	$-0.307988\pi$
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	−0.996832	+	0.0795401i	$0.974655\pi$
$230$	−1.50000	+	2.59808i	−0.0989071	+	0.171312i
$231$		0			0
$232$	4.00000	+	6.92820i	0.262613	+	0.454859i
$233$	0.500000	−	0.866025i	0.0327561	−	0.0567352i	−0.849183	−	0.528099i	$-0.822905\pi$
$233$	0.500000	−	0.866025i	0.0327561	−	0.0567352i	0.881939	+	0.471364i	$0.156238\pi$
$234$		0			0
$235$	4.00000	+	6.92820i	0.260931	+	0.451946i
$236$	4.00000			0.260378
$237$		0			0
$238$		0			0
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	−0.999854	−	0.0170808i	$-0.994563\pi$
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	0.514719	+	0.857359i	$0.327896\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	−13.0000			−0.832240
$245$		0			0
$246$		0			0
$247$	7.00000	+	12.1244i	0.445399	+	0.771454i
$248$	4.00000			0.254000
$249$		0			0
$250$	9.00000			0.569210
$251$	7.00000			0.441836			0.220918	−	0.975292i	$-0.429095\pi$
$251$	7.00000			0.441836			0.220918	+	0.975292i	$0.429095\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	19.0000			1.19217
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	0.713878	−	0.700270i	$-0.246937\pi$
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	−0.963391	+	0.268101i	$0.913604\pi$
$258$		0			0
$259$		0			0
$260$	−2.00000			−0.124035
$261$		0			0
$262$	7.50000	+	12.9904i	0.463352	+	0.802548i
$263$	9.50000	−	16.4545i	0.585795	−	1.01463i	−0.408981	−	0.912543i	$-0.634116\pi$
$263$	9.50000	−	16.4545i	0.585795	−	1.01463i	0.994776	−	0.102084i	$-0.0325510\pi$
$264$		0			0
$265$	2.00000	−	3.46410i	0.122859	−	0.212798i
$266$		0			0
$267$		0			0
$268$	−2.00000			−0.122169
$269$	−3.50000	−	6.06218i	−0.213399	−	0.369618i	0.739377	−	0.673291i	$-0.235120\pi$
$269$	−3.50000	−	6.06218i	−0.213399	−	0.369618i	−0.952776	+	0.303674i	$0.901787\pi$
$270$		0			0
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	−0.571221	−	0.820796i	$-0.693530\pi$
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	0.996441	+	0.0842940i	$0.0268635\pi$
$272$		0			0
$273$		0			0
$274$	1.00000	−	1.73205i	0.0604122	−	0.104637i
$275$	4.00000	+	6.92820i	0.241209	+	0.417786i
$276$		0			0
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$	−4.50000	+	7.79423i	−0.269892	+	0.467467i
$279$		0			0
$280$		0			0
$281$	−7.50000	−	12.9904i	−0.447412	−	0.774941i	0.550804	−	0.834634i	$-0.314321\pi$
$281$	−7.50000	−	12.9904i	−0.447412	−	0.774941i	−0.998217	+	0.0596933i	$0.980988\pi$
$282$		0			0
$283$	−25.0000			−1.48610			−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−25.0000			−1.48610			−0.743048	+	0.669238i	$0.766621\pi$
$284$	5.00000			0.296695
$285$		0			0
$286$	−2.00000	−	3.46410i	−0.118262	−	0.204837i
$287$		0			0
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	4.00000	−	6.92820i	0.234888	−	0.406838i
$291$		0			0
$292$	−7.00000	−	12.1244i	−0.409644	−	0.709524i
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	−0.967009	−	0.254741i	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$		0			0
$295$	−2.00000	−	3.46410i	−0.116445	−	0.201688i
$296$	−3.00000	+	5.19615i	−0.174371	+	0.302020i
$297$		0			0
$298$	−5.00000	−	8.66025i	−0.289642	−	0.501675i
$299$	6.00000			0.346989
$300$		0			0
$301$		0			0
$302$	9.50000	−	16.4545i	0.546664	−	0.946849i
$303$		0			0
$304$	−3.50000	+	6.06218i	−0.200739	+	0.347690i
$305$	6.50000	+	11.2583i	0.372189	+	0.644650i
$306$		0			0
$307$	−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
$309$		0			0
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	−10.0000			−0.567048			−0.283524	−	0.958965i	$-0.591504\pi$
$311$	−10.0000			−0.567048			−0.283524	+	0.958965i	$0.591504\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	11.0000			0.620766
$315$		0			0
$316$	−11.0000			−0.618798
$317$	−24.0000			−1.34797			−0.673987	−	0.738743i	$-0.735420\pi$
$317$	−24.0000			−1.34797			−0.673987	+	0.738743i	$0.735420\pi$
$318$		0			0
$319$	16.0000			0.895828
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−4.00000	−	6.92820i	−0.221880	−	0.384308i
$326$	−3.00000	+	5.19615i	−0.166155	+	0.287788i
$327$		0			0
$328$	−6.00000	+	10.3923i	−0.331295	+	0.573819i
$329$		0			0
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$		0			0
$334$	1.00000	−	1.73205i	0.0547176	−	0.0947736i
$335$	1.00000	+	1.73205i	0.0546358	+	0.0946320i
$336$		0			0
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	−0.393730	−	0.919226i	$-0.628816\pi$
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	0.992938	−	0.118633i	$-0.0378512\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$		0			0
$340$		0			0
$341$	4.00000	−	6.92820i	0.216612	−	0.375183i
$342$		0			0
$343$		0			0
$344$	−4.00000	−	6.92820i	−0.215666	−	0.373544i
$345$		0			0
$346$	22.0000			1.18273
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$		0			0
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	−0.917679	−	0.397324i	$-0.869939\pi$
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	0.114747	−	0.993395i	$-0.463394\pi$
$350$		0			0
$351$		0			0
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$		0			0
$355$	−2.50000	−	4.33013i	−0.132686	−	0.229819i
$356$	−7.00000	+	12.1244i	−0.370999	+	0.642590i
$357$		0			0
$358$	12.0000	+	20.7846i	0.634220	+	1.09850i
$359$	14.5000	−	25.1147i	0.765281	−	1.32551i	−0.174817	−	0.984601i	$-0.555933\pi$
$359$	14.5000	−	25.1147i	0.765281	−	1.32551i	0.940098	−	0.340904i	$-0.110733\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	7.00000			0.367912
$363$		0			0
$364$		0			0
$365$	−7.00000	+	12.1244i	−0.366397	+	0.634618i
$366$		0			0
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	0.0586798	+	0.998277i	$0.481311\pi$
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	−0.893873	+	0.448320i	$0.852022\pi$
$368$	1.50000	+	2.59808i	0.0781929	+	0.135434i
$369$		0			0
$370$	6.00000			0.311925
$371$		0			0
$372$		0			0
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	0.899255	+	0.437425i	$0.144109\pi$
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	−0.0708063	+	0.997490i	$0.522557\pi$
$374$		0			0
$375$		0			0
$376$	8.00000			0.412568
$377$	−16.0000			−0.824042
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	7.00000			0.359092
$381$		0			0
$382$	3.00000			0.153493
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$		0			0
$385$		0			0
$386$	−5.00000			−0.254493
$387$		0			0
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−12.0000			−0.604551
$395$	5.50000	+	9.52628i	0.276735	+	0.479319i
$396$		0			0
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	−0.635161	−	0.772380i	$-0.719066\pi$
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	0.986481	+	0.163876i	$0.0523996\pi$
$398$	7.00000	+	12.1244i	0.350878	+	0.607739i
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$	5.50000	−	9.52628i	0.273635	−	0.473950i
$405$		0			0
$406$		0			0
$407$	6.00000	+	10.3923i	0.297409	+	0.515127i
$408$		0			0
$409$	24.0000			1.18672			0.593362	−	0.804936i	$-0.297800\pi$
$409$	24.0000			1.18672			0.593362	+	0.804936i	$0.297800\pi$
$410$	12.0000			0.592638
$411$		0			0
$412$	4.00000	+	6.92820i	0.197066	+	0.341328i
$413$		0			0
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$		0			0
$418$	7.00000	+	12.1244i	0.342381	+	0.593022i
$419$	2.50000	−	4.33013i	0.122133	−	0.211541i	−0.798476	−	0.602027i	$-0.794360\pi$
$419$	2.50000	−	4.33013i	0.122133	−	0.211541i	0.920609	+	0.390487i	$0.127693\pi$
$420$		0			0
$421$	18.0000	+	31.1769i	0.877266	+	1.51947i	0.854329	+	0.519733i	$0.173969\pi$
$421$	18.0000	+	31.1769i	0.877266	+	1.51947i	0.0229375	+	0.999737i	$0.492698\pi$
$422$	−11.0000	+	19.0526i	−0.535472	+	0.927464i
$423$		0			0
$424$	−2.00000	−	3.46410i	−0.0971286	−	0.168232i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	4.00000	−	6.92820i	0.193347	−	0.334887i
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	0.937184	+	0.348836i	$0.113423\pi$
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	−0.166491	+	0.986043i	$0.553244\pi$
$432$		0			0
$433$	28.0000			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$434$		0			0
$435$		0			0
$436$	−2.00000	−	3.46410i	−0.0957826	−	0.165900i
$437$	−21.0000			−1.00457
$438$		0			0
$439$	36.0000			1.71819			0.859093	−	0.511819i	$-0.171028\pi$
$439$	36.0000			1.71819			0.859093	+	0.511819i	$0.171028\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$		0			0
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$		0			0
$445$	14.0000			0.663664
$446$	1.00000	+	1.73205i	0.0473514	+	0.0820150i
$447$		0			0
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	12.0000	+	20.7846i	0.565058	+	0.978709i
$452$	−0.500000	+	0.866025i	−0.0235180	+	0.0407344i
$453$		0			0
$454$	8.50000	−	14.7224i	0.398925	−	0.690958i
$455$		0			0
$456$		0			0
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$	6.50000	+	11.2583i	0.303725	+	0.526067i
$459$		0			0
$460$	1.50000	−	2.59808i	0.0699379	−	0.121136i
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	0.951584	−	0.307388i	$-0.0994551\pi$
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	−0.741998	+	0.670402i	$0.766122\pi$
$462$		0			0
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$	−4.00000	−	6.92820i	−0.185695	−	0.321634i
$465$		0			0
$466$	−0.500000	+	0.866025i	−0.0231621	+	0.0401179i
$467$	14.0000	−	24.2487i	0.647843	−	1.12210i	−0.335794	−	0.941935i	$-0.609005\pi$
$467$	14.0000	−	24.2487i	0.647843	−	1.12210i	0.983637	−	0.180161i	$-0.0576619\pi$
$468$		0			0
$469$		0			0
$470$	−4.00000	−	6.92820i	−0.184506	−	0.319574i
$471$		0			0
$472$	−4.00000			−0.184115
$473$	−16.0000			−0.735681
$474$		0			0
$475$	14.0000	+	24.2487i	0.642364	+	1.11261i
$476$		0			0
$477$		0			0
$478$	7.50000	−	12.9904i	0.343042	−	0.594166i
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	−5.00000	+	8.66025i	−0.227744	+	0.394464i
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$		0			0
$487$	−12.5000	−	21.6506i	−0.566429	−	0.981084i	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$	−12.5000	−	21.6506i	−0.566429	−	0.981084i	0.430486	−	0.902597i	$-0.358342\pi$
$488$	13.0000			0.588482
$489$		0			0
$490$		0			0
$491$	3.00000	−	5.19615i	0.135388	−	0.234499i	−0.790358	−	0.612646i	$-0.790105\pi$
$491$	3.00000	−	5.19615i	0.135388	−	0.234499i	0.925746	+	0.378147i	$0.123439\pi$
$492$		0			0
$493$		0			0
$494$	−7.00000	−	12.1244i	−0.314945	−	0.545501i
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	−12.0000	−	20.7846i	−0.537194	−	0.930447i	−0.999054	−	0.0434940i	$-0.986151\pi$
$499$	−12.0000	−	20.7846i	−0.537194	−	0.930447i	0.461860	−	0.886953i	$-0.347182\pi$
$500$	−9.00000			−0.402492
$501$		0			0
$502$	−7.00000			−0.312425
$503$	14.0000			0.624229			0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000			0.624229			0.312115	+	0.950044i	$0.398963\pi$
$504$		0			0
$505$	−11.0000			−0.489494
$506$	6.00000			0.266733
$507$		0			0
$508$	−19.0000			−0.842989
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	0.946111	+	0.323843i	$0.104975\pi$
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	−0.192599	+	0.981278i	$0.561692\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	4.00000	+	6.92820i	0.176432	+	0.305590i
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$		0			0
$517$	8.00000	−	13.8564i	0.351840	−	0.609404i
$518$		0			0
$519$		0			0
$520$	2.00000			0.0877058
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	0.670957	−	0.741496i	$-0.265883\pi$
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	−0.977633	+	0.210318i	$0.932550\pi$
$522$		0			0
$523$	17.5000	−	30.3109i	0.765222	−	1.32540i	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	17.5000	−	30.3109i	0.765222	−	1.32540i	0.940129	−	0.340818i	$-0.110704\pi$
$524$	−7.50000	−	12.9904i	−0.327639	−	0.567487i
$525$		0			0
$526$	−9.50000	+	16.4545i	−0.414220	+	0.717450i
$527$		0			0
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−2.00000	+	3.46410i	−0.0868744	+	0.150471i
$531$		0			0
$532$		0			0
$533$	−12.0000	−	20.7846i	−0.519778	−	0.900281i
$534$		0			0
$535$	−8.00000			−0.345870
$536$	2.00000			0.0863868
$537$		0			0
$538$	3.50000	+	6.06218i	0.150896	+	0.261359i
$539$		0			0
$540$		0			0
$541$	10.0000	−	17.3205i	0.429934	−	0.744667i	−0.566933	−	0.823764i	$-0.691870\pi$
$541$	10.0000	−	17.3205i	0.429934	−	0.744667i	0.996867	+	0.0790969i	$0.0252036\pi$
$542$	−7.00000	+	12.1244i	−0.300676	+	0.520786i
$543$		0			0
$544$		0			0
$545$	−2.00000	+	3.46410i	−0.0856706	+	0.148386i
$546$		0			0
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	0.938779	−	0.344519i	$-0.111958\pi$
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	−0.767752	+	0.640747i	$0.778625\pi$
$548$	−1.00000	+	1.73205i	−0.0427179	+	0.0739895i
$549$		0			0
$550$	−4.00000	−	6.92820i	−0.170561	−	0.295420i
$551$	56.0000			2.38568
$552$		0			0
$553$		0			0
$554$	−1.00000	+	1.73205i	−0.0424859	+	0.0735878i
$555$		0			0
$556$	4.50000	−	7.79423i	0.190843	−	0.330549i
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	0.991254	−	0.131965i	$-0.0421286\pi$
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	−0.609912	+	0.792469i	$0.708795\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$	7.50000	+	12.9904i	0.316368	+	0.547966i
$563$	11.0000			0.463595			0.231797	−	0.972764i	$-0.425539\pi$
$563$	11.0000			0.463595			0.231797	+	0.972764i	$0.425539\pi$
$564$		0			0
$565$	1.00000			0.0420703
$566$	25.0000			1.05083
$567$		0			0
$568$	−5.00000			−0.209795
$569$	18.0000			0.754599			0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000			0.754599			0.377300	+	0.926091i	$0.376853\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$		0			0
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	14.0000	+	24.2487i	0.582828	+	1.00949i	0.995142	+	0.0984456i	$0.0313871\pi$
$577$	14.0000	+	24.2487i	0.582828	+	1.00949i	−0.412315	+	0.911041i	$0.635280\pi$
$578$	−8.50000	+	14.7224i	−0.353553	+	0.612372i
$579$		0			0
$580$	−4.00000	+	6.92820i	−0.166091	+	0.287678i
$581$		0			0
$582$		0			0
$583$	−8.00000			−0.331326
$584$	7.00000	+	12.1244i	0.289662	+	0.501709i
$585$		0			0
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$	11.5000	+	19.9186i	0.474656	+	0.822128i	0.999579	−	0.0290218i	$-0.00923921\pi$
$587$	11.5000	+	19.9186i	0.474656	+	0.822128i	−0.524923	+	0.851150i	$0.675906\pi$
$588$		0			0
$589$	14.0000	−	24.2487i	0.576860	−	0.999151i
$590$	2.00000	+	3.46410i	0.0823387	+	0.142615i
$591$		0			0
$592$	3.00000	−	5.19615i	0.123299	−	0.213561i
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	0.00727173	+	0.999974i	$0.497685\pi$
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	−0.869638	+	0.493689i	$0.835648\pi$
$594$		0			0
$595$		0			0
$596$	5.00000	+	8.66025i	0.204808	+	0.354738i
$597$		0			0
$598$	−6.00000			−0.245358
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$		0			0
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	−0.469095	+	0.883148i	$0.655420\pi$
$602$		0			0
$603$		0			0
$604$	−9.50000	+	16.4545i	−0.386550	+	0.669523i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$		0			0
$607$	−3.00000	−	5.19615i	−0.121766	−	0.210905i	0.798698	−	0.601732i	$-0.205522\pi$
$607$	−3.00000	−	5.19615i	−0.121766	−	0.210905i	−0.920464	+	0.390827i	$0.872189\pi$
$608$	3.50000	−	6.06218i	0.141944	−	0.245854i
$609$		0			0
$610$	−6.50000	−	11.2583i	−0.263177	−	0.455836i
$611$	−8.00000	+	13.8564i	−0.323645	+	0.560570i
$612$		0			0
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	0.949156	−	0.314806i	$-0.101939\pi$
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	7.00000			0.282497
$615$		0			0
$616$		0			0
$617$	−11.0000	+	19.0526i	−0.442843	+	0.767027i	−0.997899	−	0.0647859i	$-0.979364\pi$
$617$	−11.0000	+	19.0526i	−0.442843	+	0.767027i	0.555056	+	0.831813i	$0.312697\pi$
$618$		0			0
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	−0.955131	−	0.296183i	$-0.904286\pi$
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	0.734068	+	0.679076i	$0.237620\pi$
$620$	2.00000	+	3.46410i	0.0803219	+	0.139122i
$621$		0			0
$622$	10.0000			0.400963
$623$		0			0
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	6.00000			0.239808
$627$		0			0
$628$	−11.0000			−0.438948
$629$		0			0
$630$		0			0
$631$	9.00000			0.358284			0.179142	−	0.983823i	$-0.442668\pi$
$631$	9.00000			0.358284			0.179142	+	0.983823i	$0.442668\pi$
$632$	11.0000			0.437557
$633$		0			0
$634$	24.0000			0.953162
$635$	9.50000	+	16.4545i	0.376996	+	0.652976i
$636$		0			0
$637$		0			0
$638$	−16.0000			−0.633446
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	23.5000	−	40.7032i	0.928194	−	1.60768i	0.141852	−	0.989888i	$-0.454694\pi$
$641$	23.5000	−	40.7032i	0.928194	−	1.60768i	0.786342	−	0.617792i	$-0.211973\pi$
$642$		0			0
$643$	−6.00000	+	10.3923i	−0.236617	+	0.409832i	−0.959741	−	0.280885i	$-0.909372\pi$
$643$	−6.00000	+	10.3923i	−0.236617	+	0.409832i	0.723124	+	0.690718i	$0.242705\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	0.901464	+	0.432855i	$0.142494\pi$
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	−0.0758684	+	0.997118i	$0.524173\pi$
$648$		0			0
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$	4.00000	+	6.92820i	0.156893	+	0.271746i
$651$		0			0
$652$	3.00000	−	5.19615i	0.117489	−	0.203497i
$653$	−16.0000	−	27.7128i	−0.626128	−	1.08449i	−0.988322	−	0.152383i	$-0.951305\pi$
$653$	−16.0000	−	27.7128i	−0.626128	−	1.08449i	0.362193	−	0.932103i	$-0.382028\pi$
$654$		0			0
$655$	−7.50000	+	12.9904i	−0.293049	+	0.507576i
$656$	6.00000	−	10.3923i	0.234261	−	0.405751i
$657$		0			0
$658$		0			0
$659$	10.0000	+	17.3205i	0.389545	+	0.674711i	0.992388	−	0.123148i	$-0.0392990\pi$
$659$	10.0000	+	17.3205i	0.389545	+	0.674711i	−0.602844	+	0.797859i	$0.705966\pi$
$660$		0			0
$661$	31.0000			1.20576			0.602880	−	0.797832i	$-0.294020\pi$
$661$	31.0000			1.20576			0.602880	+	0.797832i	$0.294020\pi$
$662$	4.00000			0.155464
$663$		0			0
$664$	6.00000	+	10.3923i	0.232845	+	0.403300i
$665$		0			0
$666$		0			0
$667$	12.0000	−	20.7846i	0.464642	−	0.804783i
$668$	−1.00000	+	1.73205i	−0.0386912	+	0.0670151i
$669$		0			0
$670$	−1.00000	−	1.73205i	−0.0386334	−	0.0669150i
$671$	13.0000	−	22.5167i	0.501859	−	0.869246i
$672$		0			0
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$	−11.0000	+	19.0526i	−0.423704	+	0.733877i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$	−5.00000	−	8.66025i	−0.191320	−	0.331375i	0.754368	−	0.656452i	$-0.227943\pi$
$683$	−5.00000	−	8.66025i	−0.191320	−	0.331375i	−0.945688	+	0.325076i	$0.894610\pi$
$684$		0			0
$685$	2.00000			0.0764161
$686$		0			0
$687$		0			0
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	8.00000			0.304776
$690$		0			0
$691$	29.0000			1.10321			0.551606	−	0.834105i	$-0.314015\pi$
$691$	29.0000			1.10321			0.551606	+	0.834105i	$0.314015\pi$
$692$	−22.0000			−0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	−9.00000			−0.341389
$696$		0			0
$697$		0			0
$698$	15.0000	+	25.9808i	0.567758	+	0.983386i
$699$		0			0
$700$		0			0
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$	21.0000	+	36.3731i	0.792030	+	1.37184i
$704$	−1.00000	+	1.73205i	−0.0376889	+	0.0652791i
$705$		0			0
$706$	12.0000	−	20.7846i	0.451626	−	0.782239i
$707$		0			0
$708$		0			0
$709$	−32.0000			−1.20179			−0.600893	−	0.799330i	$-0.705188\pi$
$709$	−32.0000			−1.20179			−0.600893	+	0.799330i	$0.705188\pi$
$710$	2.50000	+	4.33013i	0.0938233	+	0.162507i
$711$		0			0
$712$	7.00000	−	12.1244i	0.262336	−	0.454379i
$713$	−6.00000	−	10.3923i	−0.224702	−	0.389195i
$714$		0			0
$715$	2.00000	−	3.46410i	0.0747958	−	0.129550i
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$		0			0
$718$	−14.5000	+	25.1147i	−0.541135	+	0.937274i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$		0			0
$722$	15.0000	+	25.9808i	0.558242	+	0.966904i
$723$		0			0
$724$	−7.00000			−0.260153
$725$	−32.0000			−1.18845
$726$		0			0
$727$	13.0000	+	22.5167i	0.482143	+	0.835097i	0.999790	−	0.0204978i	$-0.00652512\pi$
$727$	13.0000	+	22.5167i	0.482143	+	0.835097i	−0.517647	+	0.855595i	$0.673192\pi$
$728$		0			0
$729$		0			0
$730$	7.00000	−	12.1244i	0.259082	−	0.448743i
$731$		0			0
$732$		0			0
$733$	0.500000	+	0.866025i	0.0184679	+	0.0319874i	0.875112	−	0.483921i	$-0.160788\pi$
$733$	0.500000	+	0.866025i	0.0184679	+	0.0319874i	−0.856644	+	0.515908i	$0.827454\pi$
$734$	16.0000	−	27.7128i	0.590571	−	1.02290i
$735$		0			0
$736$	−1.50000	−	2.59808i	−0.0552907	−	0.0957664i
$737$	2.00000	−	3.46410i	0.0736709	−	0.127602i
$738$		0			0
$739$	19.0000	+	32.9090i	0.698926	+	1.21058i	0.968839	+	0.247691i	$0.0796718\pi$
$739$	19.0000	+	32.9090i	0.698926	+	1.21058i	−0.269913	+	0.962885i	$0.586995\pi$
$740$	−6.00000			−0.220564
$741$		0			0
$742$		0			0
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.0296605	−	0.999560i	$-0.490557\pi$
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.850814	−	0.525467i	$-0.176109\pi$
$744$		0			0
$745$	5.00000	−	8.66025i	0.183186	−	0.317287i
$746$	−16.0000	−	27.7128i	−0.585802	−	1.01464i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	19.5000	+	33.7750i	0.711565	+	1.23247i	0.964269	+	0.264923i	$0.0853467\pi$
$751$	19.5000	+	33.7750i	0.711565	+	1.23247i	−0.252704	+	0.967544i	$0.581320\pi$
$752$	−8.00000			−0.291730
$753$		0			0
$754$	16.0000			0.582686
$755$	19.0000			0.691481
$756$		0			0
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$	12.0000			0.435860
$759$		0			0
$760$	−7.00000			−0.253917
$761$	10.0000	+	17.3205i	0.362500	+	0.627868i	0.988372	−	0.152058i	$-0.0485900\pi$
$761$	10.0000	+	17.3205i	0.362500	+	0.627868i	−0.625872	+	0.779926i	$0.715257\pi$
$762$		0			0
$763$		0			0
$764$	−3.00000			−0.108536
$765$		0			0
$766$	−3.00000	−	5.19615i	−0.108394	−	0.187745i
$767$	4.00000	−	6.92820i	0.144432	−	0.250163i
$768$		0			0
$769$	1.00000	−	1.73205i	0.0360609	−	0.0624593i	−0.847432	−	0.530904i	$-0.821852\pi$
$769$	1.00000	−	1.73205i	0.0360609	−	0.0624593i	0.883493	+	0.468445i	$0.155186\pi$
$770$		0			0
$771$		0			0
$772$	5.00000			0.179954
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	0.613062	−	0.790034i	$-0.289937\pi$
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	−0.990721	+	0.135910i	$0.956604\pi$
$774$		0			0
$775$	−8.00000	+	13.8564i	−0.287368	+	0.497737i
$776$	1.00000	+	1.73205i	0.0358979	+	0.0621770i
$777$		0			0
$778$	15.0000	−	25.9808i	0.537776	−	0.931455i
$779$	42.0000	+	72.7461i	1.50481	+	2.60640i
$780$		0			0
$781$	−5.00000	+	8.66025i	−0.178914	+	0.309888i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.50000	+	9.52628i	0.196303	+	0.340007i
$786$		0			0
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$	12.0000			0.427482
$789$		0			0
$790$	−5.50000	−	9.52628i	−0.195681	−	0.338930i
$791$		0			0
$792$		0			0
$793$	−13.0000	+	22.5167i	−0.461644	+	0.799590i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	−7.00000	−	12.1244i	−0.248108	−	0.429736i
$797$	−25.5000	+	44.1673i	−0.903256	+	1.56449i	−0.0800155	+	0.996794i	$0.525497\pi$
$797$	−25.5000	+	44.1673i	−0.903256	+	1.56449i	−0.823241	+	0.567692i	$0.807836\pi$
$798$		0			0
$799$		0			0
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$		0			0
$802$	−1.50000	−	2.59808i	−0.0529668	−	0.0917413i
$803$	28.0000			0.988099
$804$		0			0
$805$		0			0
$806$	4.00000	−	6.92820i	0.140894	−	0.244036i
$807$		0			0
$808$	−5.50000	+	9.52628i	−0.193489	+	0.335133i
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	0.979739	−	0.200279i	$-0.0641847\pi$
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	−0.663316	+	0.748340i	$0.730851\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$		0			0
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$	−6.00000			−0.210171
$816$		0			0
$817$	−56.0000			−1.95919
$818$	−24.0000			−0.839140
$819$		0			0
$820$	−12.0000			−0.419058
$821$	32.0000			1.11681			0.558404	−	0.829569i	$-0.311414\pi$
$821$	32.0000			1.11681			0.558404	+	0.829569i	$0.311414\pi$
$822$		0			0
$823$	−44.0000			−1.53374			−0.766872	−	0.641800i	$-0.778188\pi$
$823$	−44.0000			−1.53374			−0.766872	+	0.641800i	$0.778188\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$		0			0
$826$		0			0
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	0.718481	−	0.695546i	$-0.244838\pi$
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	−0.961601	+	0.274450i	$0.911504\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$		0			0
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$		0			0
$834$		0			0
$835$	2.00000			0.0692129
$836$	−7.00000	−	12.1244i	−0.242100	−	0.419330i
$837$		0			0
$838$	−2.50000	+	4.33013i	−0.0863611	+	0.149582i
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	0.999785	+	0.0207443i	$0.00660359\pi$
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	−0.481927	+	0.876211i	$0.660063\pi$
$840$		0			0
$841$	−17.5000	+	30.3109i	−0.603448	+	1.04520i
$842$	−18.0000	−	31.1769i	−0.620321	−	1.07443i
$843$		0			0
$844$	11.0000	−	19.0526i	0.378636	−	0.655816i
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$		0			0
$848$	2.00000	+	3.46410i	0.0686803	+	0.118958i
$849$		0			0
$850$		0			0
$851$	18.0000			0.617032
$852$		0			0
$853$	−18.5000	−	32.0429i	−0.633428	−	1.09713i	−0.986846	−	0.161664i	$-0.948314\pi$
$853$	−18.5000	−	32.0429i	−0.633428	−	1.09713i	0.353418	−	0.935466i	$-0.385019\pi$
$854$		0			0
$855$		0			0
$856$	−4.00000	+	6.92820i	−0.136717	+	0.236801i
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	0.990533	+	0.137277i	$0.0438352\pi$
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	−0.376381	+	0.926465i	$0.622831\pi$
$860$	4.00000	−	6.92820i	0.136399	−	0.236250i
$861$		0			0
$862$	−16.0000	−	27.7128i	−0.544962	−	0.943902i
$863$	28.5000	−	49.3634i	0.970151	−	1.68035i	0.275064	−	0.961426i	$-0.411301\pi$
$863$	28.5000	−	49.3634i	0.970151	−	1.68035i	0.695087	−	0.718925i	$-0.255366\pi$
$864$		0			0
$865$	11.0000	+	19.0526i	0.374011	+	0.647806i
$866$	−28.0000			−0.951479
$867$		0			0
$868$		0			0
$869$	11.0000	−	19.0526i	0.373149	−	0.646314i
$870$		0			0
$871$	−2.00000	+	3.46410i	−0.0677674	+	0.117377i
$872$	2.00000	+	3.46410i	0.0677285	+	0.117309i
$873$		0			0
$874$	21.0000			0.710336
$875$		0			0
$876$		0			0
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	0.589135	−	0.808035i	$-0.299469\pi$
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	−0.994346	+	0.106188i	$0.966135\pi$
$878$	−36.0000			−1.21494
$879$		0			0
$880$	2.00000			0.0674200
$881$	28.0000			0.943344			0.471672	−	0.881774i	$-0.343651\pi$
$881$	28.0000			0.943344			0.471672	+	0.881774i	$0.343651\pi$
$882$		0			0
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$		0			0
$885$		0			0
$886$	24.0000			0.806296
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	−0.992149	−	0.125061i	$-0.960087\pi$
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	0.387768	−	0.921757i	$-0.373246\pi$
$888$		0			0
$889$		0			0
$890$	−14.0000			−0.469281
$891$		0			0
$892$	−1.00000	−	1.73205i	−0.0334825	−	0.0579934i
$893$	28.0000	−	48.4974i	0.936984	−	1.62290i
$894$		0			0
$895$	−12.0000	+	20.7846i	−0.401116	+	0.694753i
$896$		0			0
$897$		0			0
$898$	9.00000			0.300334
$899$	16.0000	+	27.7128i	0.533630	+	0.924274i
$900$		0			0
$901$		0			0
$902$	−12.0000	−	20.7846i	−0.399556	−	0.692052i
$903$		0			0
$904$	0.500000	−	0.866025i	0.0166298	−	0.0288036i
$905$	3.50000	+	6.06218i	0.116344	+	0.201514i
$906$		0			0
$907$	1.00000	−	1.73205i	0.0332045	−	0.0575118i	−0.848946	−	0.528480i	$-0.822762\pi$
$907$	1.00000	−	1.73205i	0.0332045	−	0.0575118i	0.882150	+	0.470968i	$0.156095\pi$
$908$	−8.50000	+	14.7224i	−0.282082	+	0.488581i
$909$		0			0
$910$		0			0
$911$	−0.500000	−	0.866025i	−0.0165657	−	0.0286927i	0.857624	−	0.514278i	$-0.171940\pi$
$911$	−0.500000	−	0.866025i	−0.0165657	−	0.0286927i	−0.874189	+	0.485585i	$0.838607\pi$
$912$		0			0
$913$	24.0000			0.794284
$914$	−17.0000			−0.562310
$915$		0			0
$916$	−6.50000	−	11.2583i	−0.214766	−	0.371986i
$917$		0			0
$918$		0			0
$919$	−7.50000	+	12.9904i	−0.247402	+	0.428513i	−0.962804	−	0.270200i	$-0.912910\pi$
$919$	−7.50000	+	12.9904i	−0.247402	+	0.428513i	0.715402	+	0.698713i	$0.246244\pi$
$920$	−1.50000	+	2.59808i	−0.0494535	+	0.0856560i
$921$		0			0
$922$	−4.50000	−	7.79423i	−0.148200	−	0.256689i
$923$	5.00000	−	8.66025i	0.164577	−	0.285056i
$924$		0			0
$925$	−12.0000	−	20.7846i	−0.394558	−	0.683394i
$926$	−0.500000	+	0.866025i	−0.0164310	+	0.0284594i
$927$		0			0
$928$	4.00000	+	6.92820i	0.131306	+	0.227429i
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$		0			0
$931$		0			0
$932$	0.500000	−	0.866025i	0.0163780	−	0.0283676i
$933$		0			0
$934$	−14.0000	+	24.2487i	−0.458094	+	0.793442i
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	−3.00000			−0.0977972			−0.0488986	−	0.998804i	$-0.515571\pi$
$941$	−3.00000			−0.0977972			−0.0488986	+	0.998804i	$0.515571\pi$
$942$		0			0
$943$	36.0000			1.17232
$944$	4.00000			0.130189
$945$		0			0
$946$	16.0000			0.520205
$947$	−10.0000			−0.324956			−0.162478	−	0.986712i	$-0.551949\pi$
$947$	−10.0000			−0.324956			−0.162478	+	0.986712i	$0.551949\pi$
$948$		0			0
$949$	−28.0000			−0.908918
$950$	−14.0000	−	24.2487i	−0.454220	−	0.786732i
$951$		0			0
$952$		0			0
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$		0			0
$955$	1.50000	+	2.59808i	0.0485389	+	0.0840718i
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$		0			0
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$		0			0
$960$		0			0
$961$	−15.0000			−0.483871
$962$	6.00000	+	10.3923i	0.193448	+	0.335061i
$963$		0			0
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	−2.50000	−	4.33013i	−0.0804778	−	0.139392i
$966$		0			0
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	−0.951408	−	0.307933i	$-0.900363\pi$
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	0.742382	+	0.669977i	$0.233696\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		0			0
$970$	1.00000	−	1.73205i	0.0321081	−	0.0556128i
$971$	17.5000	−	30.3109i	0.561602	−	0.972723i	−0.435755	−	0.900065i	$-0.643519\pi$
$971$	17.5000	−	30.3109i	0.561602	−	0.972723i	0.997357	−	0.0726575i	$-0.0231480\pi$
$972$		0			0
$973$		0			0
$974$	12.5000	+	21.6506i	0.400526	+	0.693731i
$975$		0			0
$976$	−13.0000			−0.416120
$977$	2.00000			0.0639857			0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000			0.0639857			0.0319928	+	0.999488i	$0.489815\pi$
$978$		0			0
$979$	−14.0000	−	24.2487i	−0.447442	−	0.774992i
$980$		0			0
$981$		0			0
$982$	−3.00000	+	5.19615i	−0.0957338	+	0.165816i
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	−0.489608	−	0.871943i	$-0.662860\pi$
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	0.999928	−	0.0119587i	$-0.00380665\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$		0			0
$987$		0			0
$988$	7.00000	+	12.1244i	0.222700	+	0.385727i
$989$	−12.0000	+	20.7846i	−0.381578	+	0.660912i
$990$		0			0
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	−0.999954	−	0.00956046i	$-0.996957\pi$
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	0.491698	−	0.870766i	$-0.336377\pi$
$992$	4.00000			0.127000
$993$		0			0
$994$		0			0
$995$	−7.00000	+	12.1244i	−0.221915	+	0.384368i
$996$		0			0
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	−0.699457	−	0.714675i	$-0.746575\pi$
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	0.968655	+	0.248410i	$0.0799082\pi$
$998$	12.0000	+	20.7846i	0.379853	+	0.657925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.e.a.1549.1		2
3.2	odd	2		882.2.e.j.373.1		2
7.2	even	3		2646.2.f.f.1765.1		2
7.3	odd	6		2646.2.h.g.361.1		2
7.4	even	3		2646.2.h.j.361.1		2
7.5	odd	6		2646.2.f.h.1765.1		2
7.6	odd	2		2646.2.e.d.1549.1		2
9.2	odd	6		882.2.h.a.79.1		2
9.7	even	3		2646.2.h.j.667.1		2
21.2	odd	6		882.2.f.c.589.1	yes	2
21.5	even	6		882.2.f.b.589.1	yes	2
21.11	odd	6		882.2.h.a.67.1		2
21.17	even	6		882.2.h.d.67.1		2
21.20	even	2		882.2.e.f.373.1		2
63.2	odd	6		882.2.f.c.295.1	yes	2
63.5	even	6		7938.2.a.ba.1.1		1
63.11	odd	6		882.2.e.j.655.1		2
63.16	even	3		2646.2.f.f.883.1		2
63.20	even	6		882.2.h.d.79.1		2
63.23	odd	6		7938.2.a.v.1.1		1
63.25	even	3	inner	2646.2.e.a.2125.1		2
63.34	odd	6		2646.2.h.g.667.1		2
63.38	even	6		882.2.e.f.655.1		2
63.40	odd	6		7938.2.a.f.1.1		1
63.47	even	6		882.2.f.b.295.1	✓	2
63.52	odd	6		2646.2.e.d.2125.1		2
63.58	even	3		7938.2.a.k.1.1		1
63.61	odd	6		2646.2.f.h.883.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.f.373.1		2	21.20	even	2
882.2.e.f.655.1		2	63.38	even	6
882.2.e.j.373.1		2	3.2	odd	2
882.2.e.j.655.1		2	63.11	odd	6
882.2.f.b.295.1	✓	2	63.47	even	6
882.2.f.b.589.1	yes	2	21.5	even	6
882.2.f.c.295.1	yes	2	63.2	odd	6
882.2.f.c.589.1	yes	2	21.2	odd	6
882.2.h.a.67.1		2	21.11	odd	6
882.2.h.a.79.1		2	9.2	odd	6
882.2.h.d.67.1		2	21.17	even	6
882.2.h.d.79.1		2	63.20	even	6
2646.2.e.a.1549.1		2	1.1	even	1	trivial
2646.2.e.a.2125.1		2	63.25	even	3	inner
2646.2.e.d.1549.1		2	7.6	odd	2
2646.2.e.d.2125.1		2	63.52	odd	6
2646.2.f.f.883.1		2	63.16	even	3
2646.2.f.f.1765.1		2	7.2	even	3
2646.2.f.h.883.1		2	63.61	odd	6
2646.2.f.h.1765.1		2	7.5	odd	6
2646.2.h.g.361.1		2	7.3	odd	6
2646.2.h.g.667.1		2	63.34	odd	6
2646.2.h.j.361.1		2	7.4	even	3
2646.2.h.j.667.1		2	9.7	even	3
7938.2.a.f.1.1		1	63.40	odd	6
7938.2.a.k.1.1		1	63.58	even	3
7938.2.a.v.1.1		1	63.23	odd	6
7938.2.a.ba.1.1		1	63.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(-3.50000 + 6.06218i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} +(1.50000 + 2.59808i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(-4.00000 - 6.92820i) q^{29} -4.00000 q^{31} -1.00000 q^{32} +(3.00000 - 5.19615i) q^{37} +(3.50000 - 6.06218i) q^{38} +(0.500000 + 0.866025i) q^{40} +(6.00000 - 10.3923i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{46} -8.00000 q^{47} +(-2.00000 + 3.46410i) q^{50} +(1.00000 - 1.73205i) q^{52} +(2.00000 + 3.46410i) q^{53} +2.00000 q^{55} +(4.00000 + 6.92820i) q^{58} +4.00000 q^{59} -13.0000 q^{61} +4.00000 q^{62} +1.00000 q^{64} -2.00000 q^{65} -2.00000 q^{67} +5.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-3.50000 + 6.06218i) q^{76} -11.0000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-6.00000 + 10.3923i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(-4.00000 - 6.92820i) q^{86} +(1.00000 - 1.73205i) q^{88} +(-7.00000 + 12.1244i) q^{89} +(1.50000 + 2.59808i) q^{92} +8.00000 q^{94} +7.00000 q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - q^{5} - 2 q^{8} + q^{10} - 2 q^{11} + 2 q^{13} + 2 q^{16} - 7 q^{19} - q^{20} + 2 q^{22} + 3 q^{23} + 4 q^{25} - 2 q^{26} - 8 q^{29} - 8 q^{31} - 2 q^{32} + 6 q^{37} + 7 q^{38}+ \cdots - 2 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - q^5 - 2 * q^8 + q^10 - 2 * q^11 + 2 * q^13 + 2 * q^16 - 7 * q^19 - q^20 + 2 * q^22 + 3 * q^23 + 4 * q^25 - 2 * q^26 - 8 * q^29 - 8 * q^31 - 2 * q^32 + 6 * q^37 + 7 * q^38 + q^40 + 12 * q^41 + 8 * q^43 - 2 * q^44 - 3 * q^46 - 16 * q^47 - 4 * q^50 + 2 * q^52 + 4 * q^53 + 4 * q^55 + 8 * q^58 + 8 * q^59 - 26 * q^61 + 8 * q^62 + 2 * q^64 - 4 * q^65 - 4 * q^67 + 10 * q^71 - 14 * q^73 - 6 * q^74 - 7 * q^76 - 22 * q^79 - q^80 - 12 * q^82 - 12 * q^83 - 8 * q^86 + 2 * q^88 - 14 * q^89 + 3 * q^92 + 16 * q^94 + 14 * q^95 - 2 * q^97

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