LMFDB - Embedded newform 2646.2.h.n.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(361,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2646.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,2,0,-2,4,0,0,-4,0,2,-8,0,0] 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2646.361
Dual form			2646.2.h.n.667.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.44949 q^{5} -1.00000 q^{8} +(-0.724745 + 1.25529i) q^{10} -2.00000 q^{11} +(2.44949 - 4.24264i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(1.27526 + 2.20881i) q^{19} +(0.724745 + 1.25529i) q^{20} +(-1.00000 + 1.73205i) q^{22} +1.00000 q^{23} -2.89898 q^{25} +(-2.44949 - 4.24264i) q^{26} +(-3.44949 - 5.97469i) q^{29} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{34} +(-5.89898 - 10.2173i) q^{37} +2.55051 q^{38} +1.44949 q^{40} +(-4.89898 + 8.48528i) q^{41} +(-3.44949 - 5.97469i) q^{43} +(1.00000 + 1.73205i) q^{44} +(0.500000 - 0.866025i) q^{46} +(-4.89898 + 8.48528i) q^{47} +(-1.44949 + 2.51059i) q^{50} -4.89898 q^{52} +(-5.44949 + 9.43879i) q^{53} +2.89898 q^{55} -6.89898 q^{58} +(1.00000 + 1.73205i) q^{59} +(3.27526 - 5.67291i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(-3.55051 + 6.14966i) q^{65} +(6.44949 + 11.1708i) q^{67} +2.00000 q^{68} -0.101021 q^{71} +(-3.44949 + 5.97469i) q^{73} -11.7980 q^{74} +(1.27526 - 2.20881i) q^{76} +(0.949490 - 1.64456i) q^{79} +(0.724745 - 1.25529i) q^{80} +(4.89898 + 8.48528i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} -6.89898 q^{86} +2.00000 q^{88} +(8.44949 + 14.6349i) q^{89} +(-0.500000 - 0.866025i) q^{92} +(4.89898 + 8.48528i) q^{94} +(-1.84847 - 3.20164i) q^{95} +(1.44949 + 2.51059i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8} + 2 q^{10} - 8 q^{11} - 2 q^{16} - 4 q^{17} + 10 q^{19} - 2 q^{20} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{29} + 12 q^{31} + 2 q^{32} + 4 q^{34} - 4 q^{37} + 20 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^8 + 2 * q^10 - 8 * q^11 - 2 * q^16 - 4 * q^17 + 10 * q^19 - 2 * q^20 - 4 * q^22 + 4 * q^23 + 8 * q^25 - 4 * q^29 + 12 * q^31 + 2 * q^32 + 4 * q^34 - 4 * q^37 + 20 * q^38 - 4 * q^40 - 4 * q^43 + 4 * q^44 + 2 * q^46 + 4 * q^50 - 12 * q^53 - 8 * q^55 - 8 * q^58 + 4 * q^59 + 18 * q^61 + 24 * q^62 + 4 * q^64 - 24 * q^65 + 16 * q^67 + 8 * q^68 - 20 * q^71 - 4 * q^73 - 8 * q^74 + 10 * q^76 - 6 * q^79 - 2 * q^80 - 4 * q^83 - 4 * q^85 - 8 * q^86 + 8 * q^88 + 24 * q^89 - 2 * q^92 + 22 * q^95 - 4 * q^97

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.44949			−0.648232			−0.324116	−	0.946017i	$-0.605067\pi$
$5$	−1.44949			−0.648232			−0.324116	+	0.946017i	$0.605067\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.724745	+	1.25529i	−0.229184	+	0.396959i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	2.44949	−	4.24264i	0.679366	−	1.17670i	−0.295806	−	0.955248i	$-0.595588\pi$
$13$	2.44949	−	4.24264i	0.679366	−	1.17670i	0.975172	−	0.221449i	$-0.0710785\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	1.27526	+	2.20881i	0.292564	+	0.506735i	0.974415	−	0.224756i	$-0.0721584\pi$
$19$	1.27526	+	2.20881i	0.292564	+	0.506735i	−0.681852	+	0.731491i	$0.738825\pi$
$20$	0.724745	+	1.25529i	0.162058	+	0.280692i
$21$		0			0
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	1.00000			0.208514			0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000			0.208514			0.104257	+	0.994550i	$0.466753\pi$
$24$		0			0
$25$	−2.89898			−0.579796
$26$	−2.44949	−	4.24264i	−0.480384	−	0.832050i
$27$		0			0
$28$		0			0
$29$	−3.44949	−	5.97469i	−0.640554	−	1.10947i	−0.985309	−	0.170780i	$-0.945371\pi$
$29$	−3.44949	−	5.97469i	−0.640554	−	1.10947i	0.344755	−	0.938693i	$-0.387962\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$		0			0
$36$		0			0
$37$	−5.89898	−	10.2173i	−0.969786	−	1.67972i	−0.696165	−	0.717881i	$-0.745112\pi$
$37$	−5.89898	−	10.2173i	−0.969786	−	1.67972i	−0.273621	−	0.961838i	$-0.588221\pi$
$38$	2.55051			0.413747
$39$		0			0
$40$	1.44949			0.229184
$41$	−4.89898	+	8.48528i	−0.765092	+	1.32518i	0.175106	+	0.984550i	$0.443973\pi$
$41$	−4.89898	+	8.48528i	−0.765092	+	1.32518i	−0.940198	+	0.340629i	$0.889360\pi$
$42$		0			0
$43$	−3.44949	−	5.97469i	−0.526042	−	0.911132i	−0.999540	−	0.0303367i	$-0.990342\pi$
$43$	−3.44949	−	5.97469i	−0.526042	−	0.911132i	0.473497	−	0.880795i	$-0.342991\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−4.89898	+	8.48528i	−0.714590	+	1.23771i	0.248528	+	0.968625i	$0.420053\pi$
$47$	−4.89898	+	8.48528i	−0.714590	+	1.23771i	−0.963118	+	0.269081i	$0.913280\pi$
$48$		0			0
$49$		0			0
$50$	−1.44949	+	2.51059i	−0.204989	+	0.355051i
$51$		0			0
$52$	−4.89898			−0.679366
$53$	−5.44949	+	9.43879i	−0.748545	+	1.29652i	0.199975	+	0.979801i	$0.435914\pi$
$53$	−5.44949	+	9.43879i	−0.748545	+	1.29652i	−0.948520	+	0.316717i	$0.897419\pi$
$54$		0			0
$55$	2.89898			0.390898
$56$		0			0
$57$		0			0
$58$	−6.89898			−0.905880
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	0.923749	−	0.382998i	$-0.125108\pi$
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	−0.793560	+	0.608492i	$0.791775\pi$
$60$		0			0
$61$	3.27526	−	5.67291i	0.419353	−	0.726341i	−0.576521	−	0.817082i	$-0.695590\pi$
$61$	3.27526	−	5.67291i	0.419353	−	0.726341i	0.995875	+	0.0907408i	$0.0289235\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.55051	+	6.14966i	−0.440387	+	0.762772i
$66$		0			0
$67$	6.44949	+	11.1708i	0.787931	+	1.36474i	0.927233	+	0.374486i	$0.122181\pi$
$67$	6.44949	+	11.1708i	0.787931	+	1.36474i	−0.139302	+	0.990250i	$0.544486\pi$
$68$	2.00000			0.242536
$69$		0			0
$70$		0			0
$71$	−0.101021			−0.0119889			−0.00599446	−	0.999982i	$-0.501908\pi$
$71$	−0.101021			−0.0119889			−0.00599446	+	0.999982i	$0.501908\pi$
$72$		0			0
$73$	−3.44949	+	5.97469i	−0.403732	+	0.699285i	−0.994173	−	0.107796i	$-0.965621\pi$
$73$	−3.44949	+	5.97469i	−0.403732	+	0.699285i	0.590441	+	0.807081i	$0.298954\pi$
$74$	−11.7980			−1.37148
$75$		0			0
$76$	1.27526	−	2.20881i	0.146282	−	0.253368i
$77$		0			0
$78$		0			0
$79$	0.949490	−	1.64456i	0.106826	−	0.185028i	−0.807657	−	0.589653i	$-0.799265\pi$
$79$	0.949490	−	1.64456i	0.106826	−	0.185028i	0.914483	+	0.404625i	$0.132598\pi$
$80$	0.724745	−	1.25529i	0.0810289	−	0.140346i
$81$		0			0
$82$	4.89898	+	8.48528i	0.541002	+	0.937043i
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	0.805910	−	0.592037i	$-0.201676\pi$
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	−0.915675	+	0.401920i	$0.868343\pi$
$84$		0			0
$85$	1.44949	−	2.51059i	0.157219	−	0.272312i
$86$	−6.89898			−0.743936
$87$		0			0
$88$	2.00000			0.213201
$89$	8.44949	+	14.6349i	0.895644	+	1.55130i	0.833005	+	0.553265i	$0.186618\pi$
$89$	8.44949	+	14.6349i	0.895644	+	1.55130i	0.0626387	+	0.998036i	$0.480048\pi$
$90$		0			0
$91$		0			0
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$		0			0
$94$	4.89898	+	8.48528i	0.505291	+	0.875190i
$95$	−1.84847	−	3.20164i	−0.189649	−	0.328482i
$96$		0			0
$97$	1.44949	+	2.51059i	0.147173	+	0.254912i	0.930182	−	0.367099i	$-0.119649\pi$
$97$	1.44949	+	2.51059i	0.147173	+	0.254912i	−0.783008	+	0.622011i	$0.786316\pi$
$98$		0			0
$99$		0			0
$100$	1.44949	+	2.51059i	0.144949	+	0.251059i
$101$	−17.2474			−1.71619			−0.858093	−	0.513495i	$-0.828351\pi$
$101$	−17.2474			−1.71619			−0.858093	+	0.513495i	$0.828351\pi$
$102$		0			0
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	−2.44949	+	4.24264i	−0.240192	+	0.416025i
$105$		0			0
$106$	5.44949	+	9.43879i	0.529301	+	0.916777i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$		0			0
$109$	−6.34847	+	10.9959i	−0.608073	+	1.05321i	0.383485	+	0.923547i	$0.374724\pi$
$109$	−6.34847	+	10.9959i	−0.608073	+	1.05321i	−0.991558	+	0.129666i	$0.958609\pi$
$110$	1.44949	−	2.51059i	0.138203	−	0.239375i
$111$		0			0
$112$		0			0
$113$	−3.05051	+	5.28364i	−0.286968	+	0.497043i	−0.973084	−	0.230449i	$-0.925981\pi$
$113$	−3.05051	+	5.28364i	−0.286968	+	0.497043i	0.686117	+	0.727492i	$0.259314\pi$
$114$		0			0
$115$	−1.44949			−0.135166
$116$	−3.44949	+	5.97469i	−0.320277	+	0.554736i
$117$		0			0
$118$	2.00000			0.184115
$119$		0			0
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−3.27526	−	5.67291i	−0.296528	−	0.513601i
$123$		0			0
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$	11.4495			1.02407
$126$		0			0
$127$	−3.00000			−0.266207			−0.133103	−	0.991102i	$-0.542494\pi$
$127$	−3.00000			−0.266207			−0.133103	+	0.991102i	$0.542494\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	3.55051	+	6.14966i	0.311400	+	0.539361i
$131$	−8.55051			−0.747062			−0.373531	−	0.927618i	$-0.621853\pi$
$131$	−8.55051			−0.747062			−0.373531	+	0.927618i	$0.621853\pi$
$132$		0			0
$133$		0			0
$134$	12.8990			1.11430
$135$		0			0
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	−7.79796			−0.666225			−0.333112	−	0.942887i	$-0.608099\pi$
$137$	−7.79796			−0.666225			−0.333112	+	0.942887i	$0.608099\pi$
$138$		0			0
$139$	2.27526	−	3.94086i	0.192985	−	0.334259i	−0.753253	−	0.657730i	$-0.771517\pi$
$139$	2.27526	−	3.94086i	0.192985	−	0.334259i	0.946238	+	0.323471i	$0.104850\pi$
$140$		0			0
$141$		0			0
$142$	−0.0505103	+	0.0874863i	−0.00423873	+	0.00734169i
$143$	−4.89898	+	8.48528i	−0.409673	+	0.709575i
$144$		0			0
$145$	5.00000	+	8.66025i	0.415227	+	0.719195i
$146$	3.44949	+	5.97469i	0.285482	+	0.494469i
$147$		0			0
$148$	−5.89898	+	10.2173i	−0.484893	+	0.839860i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$	−5.00000			−0.406894			−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000			−0.406894			−0.203447	+	0.979086i	$0.565214\pi$
$152$	−1.27526	−	2.20881i	−0.103437	−	0.179158i
$153$		0			0
$154$		0			0
$155$	−4.34847	−	7.53177i	−0.349277	−	0.604966i
$156$		0			0
$157$	−4.17423	−	7.22999i	−0.333140	−	0.577016i	0.649986	−	0.759947i	$-0.274775\pi$
$157$	−4.17423	−	7.22999i	−0.333140	−	0.577016i	−0.983126	+	0.182931i	$0.941442\pi$
$158$	−0.949490	−	1.64456i	−0.0755373	−	0.130835i
$159$		0			0
$160$	−0.724745	−	1.25529i	−0.0572961	−	0.0992398i
$161$		0			0
$162$		0			0
$163$	9.89898	+	17.1455i	0.775348	+	1.34294i	0.934599	+	0.355704i	$0.115759\pi$
$163$	9.89898	+	17.1455i	0.775348	+	1.34294i	−0.159251	+	0.987238i	$0.550908\pi$
$164$	9.79796			0.765092
$165$		0			0
$166$	−2.00000			−0.155230
$167$	5.34847	−	9.26382i	0.413877	−	0.716856i	−0.581433	−	0.813594i	$-0.697508\pi$
$167$	5.34847	−	9.26382i	0.413877	−	0.716856i	0.995310	+	0.0967384i	$0.0308410\pi$
$168$		0			0
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$	−1.44949	−	2.51059i	−0.111171	−	0.192553i
$171$		0			0
$172$	−3.44949	+	5.97469i	−0.263021	+	0.455566i
$173$	1.55051	−	2.68556i	0.117883	−	0.204180i	−0.801045	−	0.598604i	$-0.795723\pi$
$173$	1.55051	−	2.68556i	0.117883	−	0.204180i	0.918929	+	0.394424i	$0.129056\pi$
$174$		0			0
$175$		0			0
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$		0			0
$178$	16.8990			1.26663
$179$	10.3485	−	17.9241i	0.773481	−	1.33971i	−0.162163	−	0.986764i	$-0.551847\pi$
$179$	10.3485	−	17.9241i	0.773481	−	1.33971i	0.935644	−	0.352944i	$-0.114819\pi$
$180$		0			0
$181$	10.3485			0.769196			0.384598	−	0.923084i	$-0.374340\pi$
$181$	10.3485			0.769196			0.384598	+	0.923084i	$0.374340\pi$
$182$		0			0
$183$		0			0
$184$	−1.00000			−0.0737210
$185$	8.55051	+	14.8099i	0.628646	+	1.08885i
$186$		0			0
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	9.79796			0.714590
$189$		0			0
$190$	−3.69694			−0.268204
$191$	2.05051	−	3.55159i	0.148370	−	0.256984i	−0.782255	−	0.622958i	$-0.785931\pi$
$191$	2.05051	−	3.55159i	0.148370	−	0.256984i	0.930625	+	0.365974i	$0.119264\pi$
$192$		0			0
$193$	8.94949	+	15.5010i	0.644198	+	1.11578i	0.984486	+	0.175463i	$0.0561422\pi$
$193$	8.94949	+	15.5010i	0.644198	+	1.11578i	−0.340288	+	0.940321i	$0.610524\pi$
$194$	2.89898			0.208135
$195$		0			0
$196$		0			0
$197$	−16.6969			−1.18961			−0.594804	−	0.803871i	$-0.702770\pi$
$197$	−16.6969			−1.18961			−0.594804	+	0.803871i	$0.702770\pi$
$198$		0			0
$199$	−1.44949	+	2.51059i	−0.102752	+	0.177971i	−0.912817	−	0.408368i	$-0.866098\pi$
$199$	−1.44949	+	2.51059i	−0.102752	+	0.177971i	0.810066	+	0.586339i	$0.199431\pi$
$200$	2.89898			0.204989
$201$		0			0
$202$	−8.62372	+	14.9367i	−0.606763	+	1.05094i
$203$		0			0
$204$		0			0
$205$	7.10102	−	12.2993i	0.495957	−	0.859022i
$206$	−7.00000	+	12.1244i	−0.487713	+	0.844744i
$207$		0			0
$208$	2.44949	+	4.24264i	0.169842	+	0.294174i
$209$	−2.55051	−	4.41761i	−0.176422	−	0.305573i
$210$		0			0
$211$	−6.44949	+	11.1708i	−0.444001	+	0.769033i	−0.997982	−	0.0634968i	$-0.979775\pi$
$211$	−6.44949	+	11.1708i	−0.444001	+	0.769033i	0.553981	+	0.832529i	$0.313108\pi$
$212$	10.8990			0.748545
$213$		0			0
$214$	−12.0000			−0.820303
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$		0			0
$218$	6.34847	+	10.9959i	0.429973	+	0.744734i
$219$		0			0
$220$	−1.44949	−	2.51059i	−0.0977246	−	0.169264i
$221$	4.89898	+	8.48528i	0.329541	+	0.570782i
$222$		0			0
$223$	−5.55051	−	9.61377i	−0.371690	−	0.643785i	0.618136	−	0.786071i	$-0.287888\pi$
$223$	−5.55051	−	9.61377i	−0.371690	−	0.643785i	−0.989826	+	0.142286i	$0.954555\pi$
$224$		0			0
$225$		0			0
$226$	3.05051	+	5.28364i	0.202917	+	0.351462i
$227$	−5.44949			−0.361695			−0.180848	−	0.983511i	$-0.557884\pi$
$227$	−5.44949			−0.361695			−0.180848	+	0.983511i	$0.557884\pi$
$228$		0			0
$229$	−1.24745			−0.0824337			−0.0412169	−	0.999150i	$-0.513123\pi$
$229$	−1.24745			−0.0824337			−0.0412169	+	0.999150i	$0.513123\pi$
$230$	−0.724745	+	1.25529i	−0.0477883	+	0.0827717i
$231$		0			0
$232$	3.44949	+	5.97469i	0.226470	+	0.392258i
$233$	−3.50000	−	6.06218i	−0.229293	−	0.397146i	0.728306	−	0.685252i	$-0.240308\pi$
$233$	−3.50000	−	6.06218i	−0.229293	−	0.397146i	−0.957599	+	0.288106i	$0.906975\pi$
$234$		0			0
$235$	7.10102	−	12.2993i	0.463220	−	0.802320i
$236$	1.00000	−	1.73205i	0.0650945	−	0.112747i
$237$		0			0
$238$		0			0
$239$	3.39898	−	5.88721i	0.219862	−	0.380812i	−0.734904	−	0.678171i	$-0.762773\pi$
$239$	3.39898	−	5.88721i	0.219862	−	0.380812i	0.954766	+	0.297360i	$0.0961061\pi$
$240$		0			0
$241$	−0.898979			−0.0579084			−0.0289542	−	0.999581i	$-0.509218\pi$
$241$	−0.898979			−0.0579084			−0.0289542	+	0.999581i	$0.509218\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	−6.55051			−0.419353
$245$		0			0
$246$		0			0
$247$	12.4949			0.795031
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$		0			0
$250$	5.72474	−	9.91555i	0.362065	−	0.627114i
$251$	17.4495			1.10140			0.550701	−	0.834703i	$-0.314360\pi$
$251$	17.4495			1.10140			0.550701	+	0.834703i	$0.314360\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$	−1.50000	+	2.59808i	−0.0941184	+	0.163018i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.20204			0.511629			0.255815	−	0.966726i	$-0.417656\pi$
$257$	8.20204			0.511629			0.255815	+	0.966726i	$0.417656\pi$
$258$		0			0
$259$		0			0
$260$	7.10102			0.440387
$261$		0			0
$262$	−4.27526	+	7.40496i	−0.264126	+	0.457480i
$263$	−25.8990			−1.59700			−0.798500	−	0.601995i	$-0.794373\pi$
$263$	−25.8990			−1.59700			−0.798500	+	0.601995i	$0.794373\pi$
$264$		0			0
$265$	7.89898	−	13.6814i	0.485230	−	0.840444i
$266$		0			0
$267$		0			0
$268$	6.44949	−	11.1708i	0.393965	−	0.682368i
$269$	9.17423	−	15.8902i	0.559363	−	0.968845i	−0.438187	−	0.898884i	$-0.644379\pi$
$269$	9.17423	−	15.8902i	0.559363	−	0.968845i	0.997550	−	0.0699611i	$-0.0222875\pi$
$270$		0			0
$271$	3.55051	+	6.14966i	0.215678	+	0.373565i	0.953482	−	0.301450i	$-0.0974705\pi$
$271$	3.55051	+	6.14966i	0.215678	+	0.373565i	−0.737804	+	0.675015i	$0.764137\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$		0			0
$274$	−3.89898	+	6.75323i	−0.235546	+	0.407978i
$275$	5.79796			0.349630
$276$		0			0
$277$	−18.6969			−1.12339			−0.561695	−	0.827344i	$-0.689851\pi$
$277$	−18.6969			−1.12339			−0.561695	+	0.827344i	$0.689851\pi$
$278$	−2.27526	−	3.94086i	−0.136461	−	0.236357i
$279$		0			0
$280$		0			0
$281$	−9.50000	−	16.4545i	−0.566722	−	0.981592i	−0.996887	−	0.0788417i	$-0.974878\pi$
$281$	−9.50000	−	16.4545i	−0.566722	−	0.981592i	0.430165	−	0.902750i	$-0.358455\pi$
$282$		0			0
$283$	−12.7247	−	22.0399i	−0.756408	−	1.31014i	−0.944672	−	0.328018i	$-0.893619\pi$
$283$	−12.7247	−	22.0399i	−0.756408	−	1.31014i	0.188264	−	0.982118i	$-0.439714\pi$
$284$	0.0505103	+	0.0874863i	0.00299723	+	0.00519136i
$285$		0			0
$286$	4.89898	+	8.48528i	0.289683	+	0.501745i
$287$		0			0
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	10.0000			0.587220
$291$		0			0
$292$	6.89898			0.403732
$293$	−1.37628	+	2.38378i	−0.0804029	+	0.139262i	−0.903423	−	0.428750i	$-0.858954\pi$
$293$	−1.37628	+	2.38378i	−0.0804029	+	0.139262i	0.823020	+	0.568012i	$0.192287\pi$
$294$		0			0
$295$	−1.44949	−	2.51059i	−0.0843926	−	0.146172i
$296$	5.89898	+	10.2173i	0.342871	+	0.593870i
$297$		0			0
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	2.44949	−	4.24264i	0.141658	−	0.245358i
$300$		0			0
$301$		0			0
$302$	−2.50000	+	4.33013i	−0.143859	+	0.249171i
$303$		0			0
$304$	−2.55051			−0.146282
$305$	−4.74745	+	8.22282i	−0.271838	+	0.470837i
$306$		0			0
$307$	−25.2474			−1.44095			−0.720474	−	0.693482i	$-0.756076\pi$
$307$	−25.2474			−1.44095			−0.720474	+	0.693482i	$0.756076\pi$
$308$		0			0
$309$		0			0
$310$	−8.69694			−0.493953
$311$	−15.3485	−	26.5843i	−0.870332	−	1.50746i	−0.861654	−	0.507497i	$-0.830571\pi$
$311$	−15.3485	−	26.5843i	−0.870332	−	1.50746i	−0.00867810	−	0.999962i	$-0.502762\pi$
$312$		0			0
$313$	−2.34847	+	4.06767i	−0.132743	+	0.229918i	−0.924733	−	0.380616i	$-0.875712\pi$
$313$	−2.34847	+	4.06767i	−0.132743	+	0.229918i	0.791990	+	0.610534i	$0.209045\pi$
$314$	−8.34847			−0.471131
$315$		0			0
$316$	−1.89898			−0.106826
$317$	10.3485	−	17.9241i	0.581228	−	1.00672i	−0.414106	−	0.910229i	$-0.635906\pi$
$317$	10.3485	−	17.9241i	0.581228	−	1.00672i	0.995334	−	0.0964878i	$-0.0307609\pi$
$318$		0			0
$319$	6.89898	+	11.9494i	0.386269	+	0.669037i
$320$	−1.44949			−0.0810289
$321$		0			0
$322$		0			0
$323$	−5.10102			−0.283828
$324$		0			0
$325$	−7.10102	+	12.2993i	−0.393894	+	0.682244i
$326$	19.7980			1.09651
$327$		0			0
$328$	4.89898	−	8.48528i	0.270501	−	0.468521i
$329$		0			0
$330$		0			0
$331$	−2.34847	+	4.06767i	−0.129084	+	0.223579i	−0.923322	−	0.384027i	$-0.874537\pi$
$331$	−2.34847	+	4.06767i	−0.129084	+	0.223579i	0.794238	+	0.607606i	$0.207870\pi$
$332$	−1.00000	+	1.73205i	−0.0548821	+	0.0950586i
$333$		0			0
$334$	−5.34847	−	9.26382i	−0.292655	−	0.506894i
$335$	−9.34847	−	16.1920i	−0.510761	−	0.884665i
$336$		0			0
$337$	11.6969	−	20.2597i	0.637173	−	1.10362i	−0.348877	−	0.937168i	$-0.613437\pi$
$337$	11.6969	−	20.2597i	0.637173	−	1.10362i	0.986050	−	0.166447i	$-0.0532296\pi$
$338$	−11.0000			−0.598321
$339$		0			0
$340$	−2.89898			−0.157219
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$		0			0
$343$		0			0
$344$	3.44949	+	5.97469i	0.185984	+	0.322134i
$345$		0			0
$346$	−1.55051	−	2.68556i	−0.0833559	−	0.144377i
$347$	9.79796	+	16.9706i	0.525982	+	0.911028i	0.999542	+	0.0302659i	$0.00963541\pi$
$347$	9.79796	+	16.9706i	0.525982	+	0.911028i	−0.473560	+	0.880762i	$0.657031\pi$
$348$		0			0
$349$	5.55051	+	9.61377i	0.297112	+	0.514613i	0.975474	−	0.220115i	$-0.0706432\pi$
$349$	5.55051	+	9.61377i	0.297112	+	0.514613i	−0.678362	+	0.734728i	$0.737310\pi$
$350$		0			0
$351$		0			0
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$	0.146428			0.00777160
$356$	8.44949	−	14.6349i	0.447822	−	0.775651i
$357$		0			0
$358$	−10.3485	−	17.9241i	−0.546934	−	0.947317i
$359$	−4.39898	−	7.61926i	−0.232169	−	0.402129i	0.726277	−	0.687402i	$-0.241249\pi$
$359$	−4.39898	−	7.61926i	−0.232169	−	0.402129i	−0.958446	+	0.285273i	$0.907916\pi$
$360$		0			0
$361$	6.24745	−	10.8209i	0.328813	−	0.569521i
$362$	5.17423	−	8.96204i	0.271952	−	0.471034i
$363$		0			0
$364$		0			0
$365$	5.00000	−	8.66025i	0.261712	−	0.453298i
$366$		0			0
$367$	13.7980			0.720248			0.360124	−	0.932905i	$-0.382734\pi$
$367$	13.7980			0.720248			0.360124	+	0.932905i	$0.382734\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$		0			0
$370$	17.1010			0.889040
$371$		0			0
$372$		0			0
$373$	−6.89898			−0.357216			−0.178608	−	0.983920i	$-0.557159\pi$
$373$	−6.89898			−0.357216			−0.178608	+	0.983920i	$0.557159\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$		0			0
$376$	4.89898	−	8.48528i	0.252646	−	0.437595i
$377$	−33.7980			−1.74068
$378$		0			0
$379$	22.4949			1.15549			0.577743	−	0.816219i	$-0.303934\pi$
$379$	22.4949			1.15549			0.577743	+	0.816219i	$0.303934\pi$
$380$	−1.84847	+	3.20164i	−0.0948245	+	0.164241i
$381$		0			0
$382$	−2.05051	−	3.55159i	−0.104913	−	0.181715i
$383$	−2.89898			−0.148131			−0.0740655	−	0.997253i	$-0.523597\pi$
$383$	−2.89898			−0.148131			−0.0740655	+	0.997253i	$0.523597\pi$
$384$		0			0
$385$		0			0
$386$	17.8990			0.911034
$387$		0			0
$388$	1.44949	−	2.51059i	0.0735867	−	0.127456i
$389$	24.8990			1.26243			0.631214	−	0.775609i	$-0.282557\pi$
$389$	24.8990			1.26243			0.631214	+	0.775609i	$0.282557\pi$
$390$		0			0
$391$	−1.00000	+	1.73205i	−0.0505722	+	0.0875936i
$392$		0			0
$393$		0			0
$394$	−8.34847	+	14.4600i	−0.420590	+	0.728483i
$395$	−1.37628	+	2.38378i	−0.0692479	+	0.119941i
$396$		0			0
$397$	19.3485	+	33.5125i	0.971072	+	1.68195i	0.692332	+	0.721579i	$0.256583\pi$
$397$	19.3485	+	33.5125i	0.971072	+	1.68195i	0.278740	+	0.960367i	$0.410083\pi$
$398$	1.44949	+	2.51059i	0.0726564	+	0.125844i
$399$		0			0
$400$	1.44949	−	2.51059i	0.0724745	−	0.125529i
$401$	19.8990			0.993708			0.496854	−	0.867834i	$-0.334489\pi$
$401$	19.8990			0.993708			0.496854	+	0.867834i	$0.334489\pi$
$402$		0			0
$403$	29.3939			1.46421
$404$	8.62372	+	14.9367i	0.429046	+	0.743130i
$405$		0			0
$406$		0			0
$407$	11.7980	+	20.4347i	0.584803	+	1.01291i
$408$		0			0
$409$	−6.89898	−	11.9494i	−0.341133	−	0.590859i	0.643511	−	0.765437i	$-0.277477\pi$
$409$	−6.89898	−	11.9494i	−0.341133	−	0.590859i	−0.984643	+	0.174578i	$0.944144\pi$
$410$	−7.10102	−	12.2993i	−0.350694	−	0.607421i
$411$		0			0
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$		0			0
$414$		0			0
$415$	1.44949	+	2.51059i	0.0711527	+	0.123240i
$416$	4.89898			0.240192
$417$		0			0
$418$	−5.10102			−0.249499
$419$	−14.7247	+	25.5040i	−0.719351	+	1.24595i	0.241906	+	0.970300i	$0.422227\pi$
$419$	−14.7247	+	25.5040i	−0.719351	+	1.24595i	−0.961257	+	0.275653i	$0.911106\pi$
$420$		0			0
$421$	−11.4495	−	19.8311i	−0.558014	−	0.966509i	−0.997662	−	0.0683385i	$-0.978230\pi$
$421$	−11.4495	−	19.8311i	−0.558014	−	0.966509i	0.439648	−	0.898170i	$-0.355103\pi$
$422$	6.44949	+	11.1708i	0.313956	+	0.543788i
$423$		0			0
$424$	5.44949	−	9.43879i	0.264651	−	0.458388i
$425$	2.89898	−	5.02118i	0.140621	−	0.243563i
$426$		0			0
$427$		0			0
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$	10.0000			0.482243
$431$	15.7980	−	27.3629i	0.760961	−	1.31802i	−0.181395	−	0.983410i	$-0.558061\pi$
$431$	15.7980	−	27.3629i	0.760961	−	1.31802i	0.942356	−	0.334613i	$-0.108605\pi$
$432$		0			0
$433$	7.79796			0.374746			0.187373	−	0.982289i	$-0.440003\pi$
$433$	7.79796			0.374746			0.187373	+	0.982289i	$0.440003\pi$
$434$		0			0
$435$		0			0
$436$	12.6969			0.608073
$437$	1.27526	+	2.20881i	0.0610037	+	0.105662i
$438$		0			0
$439$	1.10102	−	1.90702i	0.0525488	−	0.0910173i	−0.838554	−	0.544818i	$-0.816599\pi$
$439$	1.10102	−	1.90702i	0.0525488	−	0.0910173i	0.891103	+	0.453801i	$0.149932\pi$
$440$	−2.89898			−0.138203
$441$		0			0
$442$	9.79796			0.466041
$443$	−7.44949	+	12.9029i	−0.353936	+	0.613035i	−0.986935	−	0.161117i	$-0.948490\pi$
$443$	−7.44949	+	12.9029i	−0.353936	+	0.613035i	0.632999	+	0.774152i	$0.281824\pi$
$444$		0			0
$445$	−12.2474	−	21.2132i	−0.580585	−	1.00560i
$446$	−11.1010			−0.525649
$447$		0			0
$448$		0			0
$449$	−20.5959			−0.971981			−0.485991	−	0.873964i	$-0.661541\pi$
$449$	−20.5959			−0.971981			−0.485991	+	0.873964i	$0.661541\pi$
$450$		0			0
$451$	9.79796	−	16.9706i	0.461368	−	0.799113i
$452$	6.10102			0.286968
$453$		0			0
$454$	−2.72474	+	4.71940i	−0.127879	+	0.221492i
$455$		0			0
$456$		0			0
$457$	8.74745	−	15.1510i	0.409188	−	0.708735i	−0.585611	−	0.810593i	$-0.699145\pi$
$457$	8.74745	−	15.1510i	0.409188	−	0.708735i	0.994799	+	0.101857i	$0.0324785\pi$
$458$	−0.623724	+	1.08032i	−0.0291447	+	0.0504801i
$459$		0			0
$460$	0.724745	+	1.25529i	0.0337914	+	0.0585284i
$461$	−2.82577	−	4.89437i	−0.131609	−	0.227954i	0.792688	−	0.609628i	$-0.208681\pi$
$461$	−2.82577	−	4.89437i	−0.131609	−	0.227954i	−0.924297	+	0.381674i	$0.875348\pi$
$462$		0			0
$463$	−1.84847	+	3.20164i	−0.0859057	+	0.148793i	−0.905777	−	0.423755i	$-0.860712\pi$
$463$	−1.84847	+	3.20164i	−0.0859057	+	0.148793i	0.819871	+	0.572548i	$0.194045\pi$
$464$	6.89898			0.320277
$465$		0			0
$466$	−7.00000			−0.324269
$467$	−5.00000	−	8.66025i	−0.231372	−	0.400749i	0.726840	−	0.686807i	$-0.240988\pi$
$467$	−5.00000	−	8.66025i	−0.231372	−	0.400749i	−0.958212	+	0.286058i	$0.907655\pi$
$468$		0			0
$469$		0			0
$470$	−7.10102	−	12.2993i	−0.327546	−	0.567326i
$471$		0			0
$472$	−1.00000	−	1.73205i	−0.0460287	−	0.0797241i
$473$	6.89898	+	11.9494i	0.317215	+	0.549433i
$474$		0			0
$475$	−3.69694	−	6.40329i	−0.169627	−	0.293803i
$476$		0			0
$477$		0			0
$478$	−3.39898	−	5.88721i	−0.155466	−	0.269274i
$479$	9.59592			0.438449			0.219224	−	0.975674i	$-0.429647\pi$
$479$	9.59592			0.438449			0.219224	+	0.975674i	$0.429647\pi$
$480$		0			0
$481$	−57.7980			−2.63536
$482$	−0.449490	+	0.778539i	−0.0204737	+	0.0354615i
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−2.10102	−	3.63907i	−0.0954024	−	0.165242i
$486$		0			0
$487$	18.1969	−	31.5180i	0.824582	−	1.42822i	−0.0776564	−	0.996980i	$-0.524744\pi$
$487$	18.1969	−	31.5180i	0.824582	−	1.42822i	0.902238	−	0.431238i	$-0.141923\pi$
$488$	−3.27526	+	5.67291i	−0.148264	+	0.256800i
$489$		0			0
$490$		0			0
$491$	7.89898	−	13.6814i	0.356476	−	0.617434i	−0.630893	−	0.775869i	$-0.717312\pi$
$491$	7.89898	−	13.6814i	0.356476	−	0.617434i	0.987369	+	0.158435i	$0.0506448\pi$
$492$		0			0
$493$	13.7980			0.621429
$494$	6.24745	−	10.8209i	0.281086	−	0.486855i
$495$		0			0
$496$	−6.00000			−0.269408
$497$		0			0
$498$		0			0
$499$	−25.3939			−1.13679			−0.568393	−	0.822757i	$-0.692435\pi$
$499$	−25.3939			−1.13679			−0.568393	+	0.822757i	$0.692435\pi$
$500$	−5.72474	−	9.91555i	−0.256018	−	0.443437i
$501$		0			0
$502$	8.72474	−	15.1117i	0.389404	−	0.674468i
$503$	−24.4949			−1.09217			−0.546087	−	0.837729i	$-0.683883\pi$
$503$	−24.4949			−1.09217			−0.546087	+	0.837729i	$0.683883\pi$
$504$		0			0
$505$	25.0000			1.11249
$506$	−1.00000	+	1.73205i	−0.0444554	+	0.0769991i
$507$		0			0
$508$	1.50000	+	2.59808i	0.0665517	+	0.115271i
$509$	−7.10102			−0.314747			−0.157374	−	0.987539i	$-0.550303\pi$
$509$	−7.10102			−0.314747			−0.157374	+	0.987539i	$0.550303\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	4.10102	−	7.10318i	0.180888	−	0.313308i
$515$	20.2929			0.894210
$516$		0			0
$517$	9.79796	−	16.9706i	0.430914	−	0.746364i
$518$		0			0
$519$		0			0
$520$	3.55051	−	6.14966i	0.155700	−	0.269681i
$521$	4.65153	−	8.05669i	0.203787	−	0.352970i	−0.745958	−	0.665993i	$-0.768008\pi$
$521$	4.65153	−	8.05669i	0.203787	−	0.352970i	0.949746	+	0.313023i	$0.101342\pi$
$522$		0			0
$523$	−7.17423	−	12.4261i	−0.313707	−	0.543357i	0.665455	−	0.746438i	$-0.268238\pi$
$523$	−7.17423	−	12.4261i	−0.313707	−	0.543357i	−0.979162	+	0.203081i	$0.934904\pi$
$524$	4.27526	+	7.40496i	0.186765	+	0.323487i
$525$		0			0
$526$	−12.9495	+	22.4292i	−0.564625	+	0.977958i
$527$	−12.0000			−0.522728
$528$		0			0
$529$	−22.0000			−0.956522
$530$	−7.89898	−	13.6814i	−0.343110	−	0.594284i
$531$		0			0
$532$		0			0
$533$	24.0000	+	41.5692i	1.03956	+	1.80056i
$534$		0			0
$535$	8.69694	+	15.0635i	0.376001	+	0.651254i
$536$	−6.44949	−	11.1708i	−0.278576	−	0.482507i
$537$		0			0
$538$	−9.17423	−	15.8902i	−0.395529	−	0.685077i
$539$		0			0
$540$		0			0
$541$	9.24745	+	16.0171i	0.397579	+	0.688627i	0.993427	−	0.114471i	$-0.0365172\pi$
$541$	9.24745	+	16.0171i	0.397579	+	0.688627i	−0.595848	+	0.803097i	$0.703184\pi$
$542$	7.10102			0.305015
$543$		0			0
$544$	−2.00000			−0.0857493
$545$	9.20204	−	15.9384i	0.394172	−	0.682726i
$546$		0			0
$547$	3.79796	+	6.57826i	0.162389	+	0.281266i	0.935725	−	0.352730i	$-0.114747\pi$
$547$	3.79796	+	6.57826i	0.162389	+	0.281266i	−0.773336	+	0.633996i	$0.781413\pi$
$548$	3.89898	+	6.75323i	0.166556	+	0.288484i
$549$		0			0
$550$	2.89898	−	5.02118i	0.123613	−	0.214104i
$551$	8.79796	−	15.2385i	0.374806	−	0.649182i
$552$		0			0
$553$		0			0
$554$	−9.34847	+	16.1920i	−0.397178	+	0.687933i
$555$		0			0
$556$	−4.55051			−0.192985
$557$	−6.44949	+	11.1708i	−0.273274	+	0.473324i	−0.969698	−	0.244306i	$-0.921440\pi$
$557$	−6.44949	+	11.1708i	−0.273274	+	0.473324i	0.696424	+	0.717630i	$0.254773\pi$
$558$		0			0
$559$	−33.7980			−1.42950
$560$		0			0
$561$		0			0
$562$	−19.0000			−0.801467
$563$	19.9722	+	34.5929i	0.841728	+	1.45791i	0.888433	+	0.459006i	$0.151794\pi$
$563$	19.9722	+	34.5929i	0.841728	+	1.45791i	−0.0467054	+	0.998909i	$0.514872\pi$
$564$		0			0
$565$	4.42168	−	7.65858i	0.186022	−	0.322199i
$566$	−25.4495			−1.06972
$567$		0			0
$568$	0.101021			0.00423873
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		0			0
$571$	−16.8990	−	29.2699i	−0.707200	−	1.22491i	−0.965892	−	0.258947i	$-0.916625\pi$
$571$	−16.8990	−	29.2699i	−0.707200	−	1.22491i	0.258691	−	0.965960i	$-0.416709\pi$
$572$	9.79796			0.409673
$573$		0			0
$574$		0			0
$575$	−2.89898			−0.120896
$576$		0			0
$577$	−7.79796	+	13.5065i	−0.324633	+	0.562281i	−0.981438	−	0.191779i	$-0.938574\pi$
$577$	−7.79796	+	13.5065i	−0.324633	+	0.562281i	0.656805	+	0.754061i	$0.271908\pi$
$578$	13.0000			0.540729
$579$		0			0
$580$	5.00000	−	8.66025i	0.207614	−	0.359597i
$581$		0			0
$582$		0			0
$583$	10.8990	−	18.8776i	0.451390	−	0.781830i
$584$	3.44949	−	5.97469i	0.142741	−	0.247234i
$585$		0			0
$586$	1.37628	+	2.38378i	0.0568534	+	0.0984730i
$587$	−8.07321	−	13.9832i	−0.333217	−	0.577149i	0.649924	−	0.760000i	$-0.274801\pi$
$587$	−8.07321	−	13.9832i	−0.333217	−	0.577149i	−0.983141	+	0.182850i	$0.941468\pi$
$588$		0			0
$589$	−7.65153	+	13.2528i	−0.315276	+	0.546074i
$590$	−2.89898			−0.119349
$591$		0			0
$592$	11.7980			0.484893
$593$	−7.34847	−	12.7279i	−0.301765	−	0.522673i	0.674770	−	0.738028i	$-0.264243\pi$
$593$	−7.34847	−	12.7279i	−0.301765	−	0.522673i	−0.976536	+	0.215355i	$0.930909\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	−2.44949	−	4.24264i	−0.100167	−	0.173494i
$599$	−16.8990	−	29.2699i	−0.690474	−	1.19594i	−0.971683	−	0.236289i	$-0.924069\pi$
$599$	−16.8990	−	29.2699i	−0.690474	−	1.19594i	0.281209	−	0.959646i	$-0.409264\pi$
$600$		0			0
$601$	8.34847	+	14.4600i	0.340541	+	0.589835i	0.984533	−	0.175198i	$-0.0560564\pi$
$601$	8.34847	+	14.4600i	0.340541	+	0.589835i	−0.643992	+	0.765032i	$0.722723\pi$
$602$		0			0
$603$		0			0
$604$	2.50000	+	4.33013i	0.101724	+	0.176190i
$605$	10.1464			0.412511
$606$		0			0
$607$	−20.6969			−0.840063			−0.420031	−	0.907510i	$-0.637981\pi$
$607$	−20.6969			−0.840063			−0.420031	+	0.907510i	$0.637981\pi$
$608$	−1.27526	+	2.20881i	−0.0517184	+	0.0895789i
$609$		0			0
$610$	4.74745	+	8.22282i	0.192219	+	0.332932i
$611$	24.0000	+	41.5692i	0.970936	+	1.68171i
$612$		0			0
$613$	7.34847	−	12.7279i	0.296802	−	0.514076i	−0.678601	−	0.734508i	$-0.737413\pi$
$613$	7.34847	−	12.7279i	0.296802	−	0.514076i	0.975402	+	0.220432i	$0.0707466\pi$
$614$	−12.6237	+	21.8649i	−0.509452	+	0.882397i
$615$		0			0
$616$		0			0
$617$	−7.69694	+	13.3315i	−0.309867	+	0.536706i	−0.978333	−	0.207037i	$-0.933618\pi$
$617$	−7.69694	+	13.3315i	−0.309867	+	0.536706i	0.668466	+	0.743743i	$0.266951\pi$
$618$		0			0
$619$	−30.1464			−1.21169			−0.605844	−	0.795584i	$-0.707164\pi$
$619$	−30.1464			−1.21169			−0.605844	+	0.795584i	$0.707164\pi$
$620$	−4.34847	+	7.53177i	−0.174639	+	0.302483i
$621$		0			0
$622$	−30.6969			−1.23084
$623$		0			0
$624$		0			0
$625$	−2.10102			−0.0840408
$626$	2.34847	+	4.06767i	0.0938637	+	0.162577i
$627$		0			0
$628$	−4.17423	+	7.22999i	−0.166570	+	0.288508i
$629$	23.5959			0.940831
$630$		0			0
$631$	27.8990			1.11064			0.555320	−	0.831636i	$-0.312596\pi$
$631$	27.8990			1.11064			0.555320	+	0.831636i	$0.312596\pi$
$632$	−0.949490	+	1.64456i	−0.0377687	+	0.0654173i
$633$		0			0
$634$	−10.3485	−	17.9241i	−0.410990	−	0.711856i
$635$	4.34847			0.172564
$636$		0			0
$637$		0			0
$638$	13.7980			0.546266
$639$		0			0
$640$	−0.724745	+	1.25529i	−0.0286481	+	0.0496199i
$641$	7.49490			0.296031			0.148015	−	0.988985i	$-0.452712\pi$
$641$	7.49490			0.296031			0.148015	+	0.988985i	$0.452712\pi$
$642$		0			0
$643$	−19.6969	+	34.1161i	−0.776771	+	1.34541i	0.157022	+	0.987595i	$0.449811\pi$
$643$	−19.6969	+	34.1161i	−0.776771	+	1.34541i	−0.933793	+	0.357812i	$0.883523\pi$
$644$		0			0
$645$		0			0
$646$	−2.55051	+	4.41761i	−0.100348	+	0.173809i
$647$	25.3485	−	43.9048i	0.996551	−	1.72608i	0.426412	−	0.904529i	$-0.359777\pi$
$647$	25.3485	−	43.9048i	0.996551	−	1.72608i	0.570139	−	0.821548i	$-0.306889\pi$
$648$		0			0
$649$	−2.00000	−	3.46410i	−0.0785069	−	0.135978i
$650$	7.10102	+	12.2993i	0.278525	+	0.482419i
$651$		0			0
$652$	9.89898	−	17.1455i	0.387674	−	0.671471i
$653$	−9.79796			−0.383424			−0.191712	−	0.981451i	$-0.561404\pi$
$653$	−9.79796			−0.383424			−0.191712	+	0.981451i	$0.561404\pi$
$654$		0			0
$655$	12.3939			0.484269
$656$	−4.89898	−	8.48528i	−0.191273	−	0.331295i
$657$		0			0
$658$		0			0
$659$	−12.3485	−	21.3882i	−0.481028	−	0.833165i	0.518735	−	0.854935i	$-0.326403\pi$
$659$	−12.3485	−	21.3882i	−0.481028	−	0.833165i	−0.999763	+	0.0217701i	$0.993070\pi$
$660$		0			0
$661$	2.27526	+	3.94086i	0.0884972	+	0.153282i	0.906876	−	0.421397i	$-0.138460\pi$
$661$	2.27526	+	3.94086i	0.0884972	+	0.153282i	−0.818379	+	0.574679i	$0.805127\pi$
$662$	2.34847	+	4.06767i	0.0912758	+	0.158094i
$663$		0			0
$664$	1.00000	+	1.73205i	0.0388075	+	0.0672166i
$665$		0			0
$666$		0			0
$667$	−3.44949	−	5.97469i	−0.133565	−	0.231341i
$668$	−10.6969			−0.413877
$669$		0			0
$670$	−18.6969			−0.722326
$671$	−6.55051	+	11.3458i	−0.252880	+	0.438000i
$672$		0			0
$673$	4.29796	+	7.44428i	0.165674	+	0.286956i	0.936894	−	0.349612i	$-0.113687\pi$
$673$	4.29796	+	7.44428i	0.165674	+	0.286956i	−0.771220	+	0.636568i	$0.780353\pi$
$674$	−11.6969	−	20.2597i	−0.450549	−	0.780374i
$675$		0			0
$676$	−5.50000	+	9.52628i	−0.211538	+	0.366395i
$677$	−7.34847	+	12.7279i	−0.282425	+	0.489174i	−0.971981	−	0.235058i	$-0.924472\pi$
$677$	−7.34847	+	12.7279i	−0.282425	+	0.489174i	0.689557	+	0.724232i	$0.257805\pi$
$678$		0			0
$679$		0			0
$680$	−1.44949	+	2.51059i	−0.0555854	+	0.0962767i
$681$		0			0
$682$	−12.0000			−0.459504
$683$	25.8990	−	44.8583i	0.990997	−	1.71646i	0.379551	−	0.925171i	$-0.376079\pi$
$683$	25.8990	−	44.8583i	0.990997	−	1.71646i	0.611446	−	0.791286i	$-0.290588\pi$
$684$		0			0
$685$	11.3031			0.431868
$686$		0			0
$687$		0			0
$688$	6.89898			0.263021
$689$	26.6969	+	46.2405i	1.01707	+	1.76162i
$690$		0			0
$691$	25.5227	−	44.2066i	0.970929	−	1.68170i	0.278168	−	0.960533i	$-0.410273\pi$
$691$	25.5227	−	44.2066i	0.970929	−	1.68170i	0.692762	−	0.721167i	$-0.256394\pi$
$692$	−3.10102			−0.117883
$693$		0			0
$694$	19.5959			0.743851
$695$	−3.29796	+	5.71223i	−0.125099	+	0.216677i
$696$		0			0
$697$	−9.79796	−	16.9706i	−0.371124	−	0.642806i
$698$	11.1010			0.420180
$699$		0			0
$700$		0			0
$701$	7.39388			0.279263			0.139631	−	0.990204i	$-0.455408\pi$
$701$	7.39388			0.279263			0.139631	+	0.990204i	$0.455408\pi$
$702$		0			0
$703$	15.0454	−	26.0594i	0.567448	−	0.982849i
$704$	−2.00000			−0.0753778
$705$		0			0
$706$	−3.00000	+	5.19615i	−0.112906	+	0.195560i
$707$		0			0
$708$		0			0
$709$	−13.7980	+	23.8988i	−0.518193	+	0.897537i	0.481583	+	0.876400i	$0.340062\pi$
$709$	−13.7980	+	23.8988i	−0.518193	+	0.897537i	−0.999777	+	0.0211367i	$0.993271\pi$
$710$	0.0732141	−	0.126811i	0.00274768	−	0.00475911i
$711$		0			0
$712$	−8.44949	−	14.6349i	−0.316658	−	0.548468i
$713$	3.00000	+	5.19615i	0.112351	+	0.194597i
$714$		0			0
$715$	7.10102	−	12.2993i	0.265563	−	0.459969i
$716$	−20.6969			−0.773481
$717$		0			0
$718$	−8.79796			−0.328337
$719$	−4.89898	−	8.48528i	−0.182701	−	0.316448i	0.760098	−	0.649808i	$-0.225151\pi$
$719$	−4.89898	−	8.48528i	−0.182701	−	0.316448i	−0.942799	+	0.333360i	$0.891817\pi$
$720$		0			0
$721$		0			0
$722$	−6.24745	−	10.8209i	−0.232506	−	0.402712i
$723$		0			0
$724$	−5.17423	−	8.96204i	−0.192299	−	0.333071i
$725$	10.0000	+	17.3205i	0.371391	+	0.643268i
$726$		0			0
$727$	−4.24745	−	7.35680i	−0.157529	−	0.272848i	0.776448	−	0.630181i	$-0.217019\pi$
$727$	−4.24745	−	7.35680i	−0.157529	−	0.272848i	−0.933977	+	0.357333i	$0.883686\pi$
$728$		0			0
$729$		0			0
$730$	−5.00000	−	8.66025i	−0.185058	−	0.320530i
$731$	13.7980			0.510336
$732$		0			0
$733$	17.4495			0.644512			0.322256	−	0.946653i	$-0.395559\pi$
$733$	17.4495			0.644512			0.322256	+	0.946653i	$0.395559\pi$
$734$	6.89898	−	11.9494i	0.254646	−	0.441060i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−12.8990	−	22.3417i	−0.475140	−	0.822967i
$738$		0			0
$739$	−6.79796	+	11.7744i	−0.250067	+	0.433129i	−0.963544	−	0.267550i	$-0.913786\pi$
$739$	−6.79796	+	11.7744i	−0.250067	+	0.433129i	0.713477	+	0.700679i	$0.247119\pi$
$740$	8.55051	−	14.8099i	0.314323	−	0.544423i
$741$		0			0
$742$		0			0
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	−0.320166	−	0.947361i	$-0.603739\pi$
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	0.980522	−	0.196409i	$-0.0629279\pi$
$744$		0			0
$745$	−8.69694			−0.318631
$746$	−3.44949	+	5.97469i	−0.126295	+	0.218749i
$747$		0			0
$748$	−4.00000			−0.146254
$749$		0			0
$750$		0			0
$751$	1.40408			0.0512357			0.0256178	−	0.999672i	$-0.491845\pi$
$751$	1.40408			0.0512357			0.0256178	+	0.999672i	$0.491845\pi$
$752$	−4.89898	−	8.48528i	−0.178647	−	0.309426i
$753$		0			0
$754$	−16.8990	+	29.2699i	−0.615425	+	1.06595i
$755$	7.24745			0.263762
$756$		0			0
$757$	−35.3939			−1.28641			−0.643206	−	0.765693i	$-0.722396\pi$
$757$	−35.3939			−1.28641			−0.643206	+	0.765693i	$0.722396\pi$
$758$	11.2474	−	19.4812i	0.408526	−	0.707587i
$759$		0			0
$760$	1.84847	+	3.20164i	0.0670510	+	0.116136i
$761$	2.00000			0.0724999			0.0362500	−	0.999343i	$-0.488459\pi$
$761$	2.00000			0.0724999			0.0362500	+	0.999343i	$0.488459\pi$
$762$		0			0
$763$		0			0
$764$	−4.10102			−0.148370
$765$		0			0
$766$	−1.44949	+	2.51059i	−0.0523722	+	0.0907113i
$767$	9.79796			0.353784
$768$		0			0
$769$	−17.0454	+	29.5235i	−0.614673	+	1.06465i	0.375769	+	0.926714i	$0.377379\pi$
$769$	−17.0454	+	29.5235i	−0.614673	+	1.06465i	−0.990442	+	0.137932i	$0.955955\pi$
$770$		0			0
$771$		0			0
$772$	8.94949	−	15.5010i	0.322099	−	0.557892i
$773$	−16.9722	+	29.3967i	−0.610447	+	1.05733i	0.380718	+	0.924691i	$0.375677\pi$
$773$	−16.9722	+	29.3967i	−0.610447	+	1.05733i	−0.991165	+	0.132635i	$0.957656\pi$
$774$		0			0
$775$	−8.69694	−	15.0635i	−0.312403	−	0.541098i
$776$	−1.44949	−	2.51059i	−0.0520336	−	0.0901249i
$777$		0			0
$778$	12.4495	−	21.5631i	0.446336	−	0.773076i
$779$	−24.9898			−0.895352
$780$		0			0
$781$	0.202041			0.00722960
$782$	1.00000	+	1.73205i	0.0357599	+	0.0619380i
$783$		0			0
$784$		0			0
$785$	6.05051	+	10.4798i	0.215952	+	0.374040i
$786$		0			0
$787$	−5.69694	−	9.86739i	−0.203074	−	0.351734i	0.746443	−	0.665449i	$-0.231760\pi$
$787$	−5.69694	−	9.86739i	−0.203074	−	0.351734i	−0.949517	+	0.313715i	$0.898427\pi$
$788$	8.34847	+	14.4600i	0.297402	+	0.515115i
$789$		0			0
$790$	1.37628	+	2.38378i	0.0489657	+	0.0848111i
$791$		0			0
$792$		0			0
$793$	−16.0454	−	27.7915i	−0.569789	−	0.986904i
$794$	38.6969			1.37330
$795$		0			0
$796$	2.89898			0.102752
$797$	8.97219	−	15.5403i	0.317811	−	0.550465i	−0.662220	−	0.749310i	$-0.730385\pi$
$797$	8.97219	−	15.5403i	0.317811	−	0.550465i	0.980031	+	0.198844i	$0.0637188\pi$
$798$		0			0
$799$	−9.79796	−	16.9706i	−0.346627	−	0.600375i
$800$	−1.44949	−	2.51059i	−0.0512472	−	0.0887628i
$801$		0			0
$802$	9.94949	−	17.2330i	0.351329	−	0.608519i
$803$	6.89898	−	11.9494i	0.243460	−	0.421685i
$804$		0			0
$805$		0			0
$806$	14.6969	−	25.4558i	0.517678	−	0.896644i
$807$		0			0
$808$	17.2474			0.606763
$809$	−8.10102	+	14.0314i	−0.284817	+	0.493317i	−0.972565	−	0.232632i	$-0.925266\pi$
$809$	−8.10102	+	14.0314i	−0.284817	+	0.493317i	0.687748	+	0.725950i	$0.258599\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$		0			0
$814$	23.5959			0.827036
$815$	−14.3485	−	24.8523i	−0.502605	−	0.870537i
$816$		0			0
$817$	8.79796	−	15.2385i	0.307802	−	0.533128i
$818$	−13.7980			−0.482434
$819$		0			0
$820$	−14.2020			−0.495957
$821$	0.202041	−	0.349945i	0.00705128	−	0.0122132i	−0.862478	−	0.506094i	$-0.831089\pi$
$821$	0.202041	−	0.349945i	0.00705128	−	0.0122132i	0.869530	+	0.493881i	$0.164422\pi$
$822$		0			0
$823$	6.69694	+	11.5994i	0.233441	+	0.404331i	0.958818	−	0.284020i	$-0.0916682\pi$
$823$	6.69694	+	11.5994i	0.233441	+	0.404331i	−0.725378	+	0.688351i	$0.758335\pi$
$824$	14.0000			0.487713
$825$		0			0
$826$		0			0
$827$	36.4949			1.26905			0.634526	−	0.772902i	$-0.281195\pi$
$827$	36.4949			1.26905			0.634526	+	0.772902i	$0.281195\pi$
$828$		0			0
$829$	0.651531	−	1.12848i	0.0226286	−	0.0391939i	−0.854489	−	0.519469i	$-0.826130\pi$
$829$	0.651531	−	1.12848i	0.0226286	−	0.0391939i	0.877118	+	0.480275i	$0.159463\pi$
$830$	2.89898			0.100625
$831$		0			0
$832$	2.44949	−	4.24264i	0.0849208	−	0.147087i
$833$		0			0
$834$		0			0
$835$	−7.75255	+	13.4278i	−0.268288	+	0.464689i
$836$	−2.55051	+	4.41761i	−0.0882112	+	0.152786i
$837$		0			0
$838$	14.7247	+	25.5040i	0.508658	+	0.881021i
$839$	17.5505	+	30.3984i	0.605911	+	1.04947i	0.991907	+	0.126968i	$0.0405245\pi$
$839$	17.5505	+	30.3984i	0.605911	+	1.04947i	−0.385996	+	0.922500i	$0.626142\pi$
$840$		0			0
$841$	−9.29796	+	16.1045i	−0.320619	+	0.555329i
$842$	−22.8990			−0.789151
$843$		0			0
$844$	12.8990			0.444001
$845$	7.97219	+	13.8082i	0.274252	+	0.475018i
$846$		0			0
$847$		0			0
$848$	−5.44949	−	9.43879i	−0.187136	−	0.324129i
$849$		0			0
$850$	−2.89898	−	5.02118i	−0.0994342	−	0.172225i
$851$	−5.89898	−	10.2173i	−0.202214	−	0.350246i
$852$		0			0
$853$	12.4217	+	21.5150i	0.425310	+	0.736659i	0.996449	−	0.0841942i	$-0.0268316\pi$
$853$	12.4217	+	21.5150i	0.425310	+	0.736659i	−0.571139	+	0.820853i	$0.693498\pi$
$854$		0			0
$855$		0			0
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	−34.8990			−1.19213			−0.596063	−	0.802938i	$-0.703269\pi$
$857$	−34.8990			−1.19213			−0.596063	+	0.802938i	$0.703269\pi$
$858$		0			0
$859$	10.0000			0.341196			0.170598	−	0.985341i	$-0.445430\pi$
$859$	10.0000			0.341196			0.170598	+	0.985341i	$0.445430\pi$
$860$	5.00000	−	8.66025i	0.170499	−	0.295312i
$861$		0			0
$862$	−15.7980	−	27.3629i	−0.538081	−	0.931983i
$863$	5.94949	+	10.3048i	0.202523	+	0.350780i	0.949341	−	0.314249i	$-0.101753\pi$
$863$	5.94949	+	10.3048i	0.202523	+	0.350780i	−0.746818	+	0.665029i	$0.768419\pi$
$864$		0			0
$865$	−2.24745	+	3.89270i	−0.0764155	+	0.132356i
$866$	3.89898	−	6.75323i	0.132493	−	0.229484i
$867$		0			0
$868$		0			0
$869$	−1.89898	+	3.28913i	−0.0644185	+	0.111576i
$870$		0			0
$871$	63.1918			2.14117
$872$	6.34847	−	10.9959i	0.214986	−	0.372367i
$873$		0			0
$874$	2.55051			0.0862723
$875$		0			0
$876$		0			0
$877$	22.4949			0.759599			0.379799	−	0.925069i	$-0.375993\pi$
$877$	22.4949			0.759599			0.379799	+	0.925069i	$0.375993\pi$
$878$	−1.10102	−	1.90702i	−0.0371576	−	0.0643589i
$879$		0			0
$880$	−1.44949	+	2.51059i	−0.0488623	+	0.0846320i
$881$	19.5959			0.660203			0.330102	−	0.943945i	$-0.392917\pi$
$881$	19.5959			0.660203			0.330102	+	0.943945i	$0.392917\pi$
$882$		0			0
$883$	−19.7980			−0.666254			−0.333127	−	0.942882i	$-0.608104\pi$
$883$	−19.7980			−0.666254			−0.333127	+	0.942882i	$0.608104\pi$
$884$	4.89898	−	8.48528i	0.164771	−	0.285391i
$885$		0			0
$886$	7.44949	+	12.9029i	0.250271	+	0.433481i
$887$	−14.2020			−0.476858			−0.238429	−	0.971160i	$-0.576632\pi$
$887$	−14.2020			−0.476858			−0.238429	+	0.971160i	$0.576632\pi$
$888$		0			0
$889$		0			0
$890$	−24.4949			−0.821071
$891$		0			0
$892$	−5.55051	+	9.61377i	−0.185845	+	0.321893i
$893$	−24.9898			−0.836252
$894$		0			0
$895$	−15.0000	+	25.9808i	−0.501395	+	0.868441i
$896$		0			0
$897$		0			0
$898$	−10.2980	+	17.8366i	−0.343647	+	0.595215i
$899$	20.6969	−	35.8481i	0.690282	−	1.19560i
$900$		0			0
$901$	−10.8990	−	18.8776i	−0.363098	−	0.628904i
$902$	−9.79796	−	16.9706i	−0.326236	−	0.565058i
$903$		0			0
$904$	3.05051	−	5.28364i	0.101458	−	0.175731i
$905$	−15.0000			−0.498617
$906$		0			0
$907$	2.69694			0.0895504			0.0447752	−	0.998997i	$-0.485743\pi$
$907$	2.69694			0.0895504			0.0447752	+	0.998997i	$0.485743\pi$
$908$	2.72474	+	4.71940i	0.0904238	+	0.156619i
$909$		0			0
$910$		0			0
$911$	25.9949	+	45.0245i	0.861249	+	1.49173i	0.870724	+	0.491773i	$0.163651\pi$
$911$	25.9949	+	45.0245i	0.861249	+	1.49173i	−0.00947432	+	0.999955i	$0.503016\pi$
$912$		0			0
$913$	2.00000	+	3.46410i	0.0661903	+	0.114645i
$914$	−8.74745	−	15.1510i	−0.289340	−	0.501151i
$915$		0			0
$916$	0.623724	+	1.08032i	0.0206084	+	0.0356949i
$917$		0			0
$918$		0			0
$919$	12.8485	+	22.2542i	0.423832	+	0.734098i	0.996311	−	0.0858213i	$-0.0273514\pi$
$919$	12.8485	+	22.2542i	0.423832	+	0.734098i	−0.572479	+	0.819920i	$0.694018\pi$
$920$	1.44949			0.0477883
$921$		0			0
$922$	−5.65153			−0.186123
$923$	−0.247449	+	0.428594i	−0.00814487	+	0.0141073i
$924$		0			0
$925$	17.1010	+	29.6198i	0.562278	+	0.973894i
$926$	1.84847	+	3.20164i	0.0607445	+	0.105213i
$927$		0			0
$928$	3.44949	−	5.97469i	0.113235	−	0.196129i
$929$	−17.1464	+	29.6985i	−0.562556	+	0.974376i	0.434716	+	0.900567i	$0.356849\pi$
$929$	−17.1464	+	29.6985i	−0.562556	+	0.974376i	−0.997272	+	0.0738083i	$0.976485\pi$
$930$		0			0
$931$		0			0
$932$	−3.50000	+	6.06218i	−0.114646	+	0.198573i
$933$		0			0
$934$	−10.0000			−0.327210
$935$	−2.89898	+	5.02118i	−0.0948068	+	0.164210i
$936$		0			0
$937$	−45.5959			−1.48955			−0.744777	−	0.667314i	$-0.767444\pi$
$937$	−45.5959			−1.48955			−0.744777	+	0.667314i	$0.767444\pi$
$938$		0			0
$939$		0			0
$940$	−14.2020			−0.463220
$941$	0.724745	+	1.25529i	0.0236260	+	0.0409214i	0.877597	−	0.479400i	$-0.159146\pi$
$941$	0.724745	+	1.25529i	0.0236260	+	0.0409214i	−0.853971	+	0.520321i	$0.825812\pi$
$942$		0			0
$943$	−4.89898	+	8.48528i	−0.159533	+	0.276319i
$944$	−2.00000			−0.0650945
$945$		0			0
$946$	13.7980			0.448610
$947$	26.2474	−	45.4619i	0.852927	−	1.47731i	−0.0256270	−	0.999672i	$-0.508158\pi$
$947$	26.2474	−	45.4619i	0.852927	−	1.47731i	0.878554	−	0.477642i	$-0.158508\pi$
$948$		0			0
$949$	16.8990	+	29.2699i	0.548564	+	0.950141i
$950$	−7.39388			−0.239889
$951$		0			0
$952$		0			0
$953$	3.39388			0.109938			0.0549692	−	0.998488i	$-0.482494\pi$
$953$	3.39388			0.109938			0.0549692	+	0.998488i	$0.482494\pi$
$954$		0			0
$955$	−2.97219	+	5.14799i	−0.0961779	+	0.166585i
$956$	−6.79796			−0.219862
$957$		0			0
$958$	4.79796	−	8.31031i	0.155015	−	0.268494i
$959$		0			0
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	−28.8990	+	50.0545i	−0.931740	+	1.61382i
$963$		0			0
$964$	0.449490	+	0.778539i	0.0144771	+	0.0250751i
$965$	−12.9722	−	22.4685i	−0.417590	−	0.723287i
$966$		0			0
$967$	−12.2980	+	21.3007i	−0.395476	+	0.684984i	−0.993162	−	0.116746i	$-0.962754\pi$
$967$	−12.2980	+	21.3007i	−0.395476	+	0.684984i	0.597686	+	0.801730i	$0.296087\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	−4.20204			−0.134919
$971$	0.0278064	+	0.0481621i	0.000892350	+	0.00154560i	0.866471	−	0.499227i	$-0.166383\pi$
$971$	0.0278064	+	0.0481621i	0.000892350	+	0.00154560i	−0.865579	+	0.500773i	$0.833049\pi$
$972$		0			0
$973$		0			0
$974$	−18.1969	−	31.5180i	−0.583068	−	1.00990i
$975$		0			0
$976$	3.27526	+	5.67291i	0.104838	+	0.181585i
$977$	−18.7980	−	32.5590i	−0.601400	−	1.04166i	−0.992609	−	0.121354i	$-0.961276\pi$
$977$	−18.7980	−	32.5590i	−0.601400	−	1.04166i	0.391209	−	0.920302i	$-0.372057\pi$
$978$		0			0
$979$	−16.8990	−	29.2699i	−0.540094	−	0.935470i
$980$		0			0
$981$		0			0
$982$	−7.89898	−	13.6814i	−0.252067	−	0.436592i
$983$	−33.1918			−1.05866			−0.529328	−	0.848418i	$-0.677556\pi$
$983$	−33.1918			−1.05866			−0.529328	+	0.848418i	$0.677556\pi$
$984$		0			0
$985$	24.2020			0.771141
$986$	6.89898	−	11.9494i	0.219708	−	0.380546i
$987$		0			0
$988$	−6.24745	−	10.8209i	−0.198758	−	0.344259i
$989$	−3.44949	−	5.97469i	−0.109687	−	0.189984i
$990$		0			0
$991$	0.898979	−	1.55708i	0.0285570	−	0.0494622i	−0.851394	−	0.524527i	$-0.824242\pi$
$991$	0.898979	−	1.55708i	0.0285570	−	0.0494622i	0.879951	+	0.475065i	$0.157575\pi$
$992$	−3.00000	+	5.19615i	−0.0952501	+	0.164978i
$993$		0			0
$994$		0			0
$995$	2.10102	−	3.63907i	0.0666068	−	0.115366i
$996$		0			0
$997$	−52.1464			−1.65149			−0.825747	−	0.564041i	$-0.809246\pi$
$997$	−52.1464			−1.65149			−0.825747	+	0.564041i	$0.809246\pi$
$998$	−12.6969	+	21.9917i	−0.401915	+	0.696136i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.n.361.1		4
3.2	odd	2		882.2.h.l.67.1		4
7.2	even	3		2646.2.e.k.1549.2		4
7.3	odd	6		378.2.f.d.253.1		4
7.4	even	3		2646.2.f.k.1765.2		4
7.5	odd	6		2646.2.e.l.1549.1		4
7.6	odd	2		2646.2.h.m.361.2		4
9.2	odd	6		882.2.e.n.655.2		4
9.7	even	3		2646.2.e.k.2125.2		4
21.2	odd	6		882.2.e.n.373.2		4
21.5	even	6		882.2.e.m.373.1		4
21.11	odd	6		882.2.f.j.589.2		4
21.17	even	6		126.2.f.c.85.1	yes	4
21.20	even	2		882.2.h.k.67.2		4
28.3	even	6		3024.2.r.e.1009.1		4
63.2	odd	6		882.2.h.l.79.1		4
63.4	even	3		7938.2.a.bm.1.1		2
63.11	odd	6		882.2.f.j.295.1		4
63.16	even	3	inner	2646.2.h.n.667.1		4
63.20	even	6		882.2.e.m.655.1		4
63.25	even	3		2646.2.f.k.883.2		4
63.31	odd	6		1134.2.a.i.1.2		2
63.32	odd	6		7938.2.a.bn.1.2		2
63.34	odd	6		2646.2.e.l.2125.1		4
63.38	even	6		126.2.f.c.43.2	✓	4
63.47	even	6		882.2.h.k.79.2		4
63.52	odd	6		378.2.f.d.127.1		4
63.59	even	6		1134.2.a.p.1.1		2
63.61	odd	6		2646.2.h.m.667.2		4
84.59	odd	6		1008.2.r.e.337.2		4
252.31	even	6		9072.2.a.bd.1.2		2
252.59	odd	6		9072.2.a.bk.1.1		2
252.115	even	6		3024.2.r.e.2017.1		4
252.227	odd	6		1008.2.r.e.673.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.2	✓	4	63.38	even	6
126.2.f.c.85.1	yes	4	21.17	even	6
378.2.f.d.127.1		4	63.52	odd	6
378.2.f.d.253.1		4	7.3	odd	6
882.2.e.m.373.1		4	21.5	even	6
882.2.e.m.655.1		4	63.20	even	6
882.2.e.n.373.2		4	21.2	odd	6
882.2.e.n.655.2		4	9.2	odd	6
882.2.f.j.295.1		4	63.11	odd	6
882.2.f.j.589.2		4	21.11	odd	6
882.2.h.k.67.2		4	21.20	even	2
882.2.h.k.79.2		4	63.47	even	6
882.2.h.l.67.1		4	3.2	odd	2
882.2.h.l.79.1		4	63.2	odd	6
1008.2.r.e.337.2		4	84.59	odd	6
1008.2.r.e.673.1		4	252.227	odd	6
1134.2.a.i.1.2		2	63.31	odd	6
1134.2.a.p.1.1		2	63.59	even	6
2646.2.e.k.1549.2		4	7.2	even	3
2646.2.e.k.2125.2		4	9.7	even	3
2646.2.e.l.1549.1		4	7.5	odd	6
2646.2.e.l.2125.1		4	63.34	odd	6
2646.2.f.k.883.2		4	63.25	even	3
2646.2.f.k.1765.2		4	7.4	even	3
2646.2.h.m.361.2		4	7.6	odd	2
2646.2.h.m.667.2		4	63.61	odd	6
2646.2.h.n.361.1		4	1.1	even	1	trivial
2646.2.h.n.667.1		4	63.16	even	3	inner
3024.2.r.e.1009.1		4	28.3	even	6
3024.2.r.e.2017.1		4	252.115	even	6
7938.2.a.bm.1.1		2	63.4	even	3
7938.2.a.bn.1.2		2	63.32	odd	6
9072.2.a.bd.1.2		2	252.31	even	6
9072.2.a.bk.1.1		2	252.59	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.44949 q^{5} -1.00000 q^{8} +(-0.724745 + 1.25529i) q^{10} -2.00000 q^{11} +(2.44949 - 4.24264i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(1.27526 + 2.20881i) q^{19} +(0.724745 + 1.25529i) q^{20} +(-1.00000 + 1.73205i) q^{22} +1.00000 q^{23} -2.89898 q^{25} +(-2.44949 - 4.24264i) q^{26} +(-3.44949 - 5.97469i) q^{29} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{34} +(-5.89898 - 10.2173i) q^{37} +2.55051 q^{38} +1.44949 q^{40} +(-4.89898 + 8.48528i) q^{41} +(-3.44949 - 5.97469i) q^{43} +(1.00000 + 1.73205i) q^{44} +(0.500000 - 0.866025i) q^{46} +(-4.89898 + 8.48528i) q^{47} +(-1.44949 + 2.51059i) q^{50} -4.89898 q^{52} +(-5.44949 + 9.43879i) q^{53} +2.89898 q^{55} -6.89898 q^{58} +(1.00000 + 1.73205i) q^{59} +(3.27526 - 5.67291i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(-3.55051 + 6.14966i) q^{65} +(6.44949 + 11.1708i) q^{67} +2.00000 q^{68} -0.101021 q^{71} +(-3.44949 + 5.97469i) q^{73} -11.7980 q^{74} +(1.27526 - 2.20881i) q^{76} +(0.949490 - 1.64456i) q^{79} +(0.724745 - 1.25529i) q^{80} +(4.89898 + 8.48528i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} -6.89898 q^{86} +2.00000 q^{88} +(8.44949 + 14.6349i) q^{89} +(-0.500000 - 0.866025i) q^{92} +(4.89898 + 8.48528i) q^{94} +(-1.84847 - 3.20164i) q^{95} +(1.44949 + 2.51059i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8} + 2 q^{10} - 8 q^{11} - 2 q^{16} - 4 q^{17} + 10 q^{19} - 2 q^{20} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{29} + 12 q^{31} + 2 q^{32} + 4 q^{34} - 4 q^{37} + 20 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^8 + 2 * q^10 - 8 * q^11 - 2 * q^16 - 4 * q^17 + 10 * q^19 - 2 * q^20 - 4 * q^22 + 4 * q^23 + 8 * q^25 - 4 * q^29 + 12 * q^31 + 2 * q^32 + 4 * q^34 - 4 * q^37 + 20 * q^38 - 4 * q^40 - 4 * q^43 + 4 * q^44 + 2 * q^46 + 4 * q^50 - 12 * q^53 - 8 * q^55 - 8 * q^58 + 4 * q^59 + 18 * q^61 + 24 * q^62 + 4 * q^64 - 24 * q^65 + 16 * q^67 + 8 * q^68 - 20 * q^71 - 4 * q^73 - 8 * q^74 + 10 * q^76 - 6 * q^79 - 2 * q^80 - 4 * q^83 - 4 * q^85 - 8 * q^86 + 8 * q^88 + 24 * q^89 - 2 * q^92 + 22 * q^95 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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