LMFDB - Embedded newform 1040.2.q.b.321.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(81,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1040.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.30444181021$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			321.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1040.321
Dual form			1040.2.q.b.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{3} +1.00000 q^{5} +(1.50000 + 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 2.59808i) q^{3} +1.00000 q^{5} +(1.50000 + 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(1.50000 - 2.59808i) q^{11} +(1.00000 + 3.46410i) q^{13} +(-1.50000 + 2.59808i) q^{15} +(3.50000 + 6.06218i) q^{17} +(0.500000 + 0.866025i) q^{19} -9.00000 q^{21} +(-3.50000 + 6.06218i) q^{23} +1.00000 q^{25} +9.00000 q^{27} +(2.50000 - 4.33013i) q^{29} +4.00000 q^{31} +(4.50000 + 7.79423i) q^{33} +(1.50000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) q^{37} +(-10.5000 - 2.59808i) q^{39} +(-3.50000 + 6.06218i) q^{41} +(-4.50000 - 7.79423i) q^{43} +(-3.00000 - 5.19615i) q^{45} -8.00000 q^{47} +(-1.00000 + 1.73205i) q^{49} -21.0000 q^{51} -6.00000 q^{53} +(1.50000 - 2.59808i) q^{55} -3.00000 q^{57} +(2.50000 + 4.33013i) q^{59} +(2.50000 + 4.33013i) q^{61} +(9.00000 - 15.5885i) q^{63} +(1.00000 + 3.46410i) q^{65} +(6.50000 - 11.2583i) q^{67} +(-10.5000 - 18.1865i) q^{69} +(-1.50000 - 2.59808i) q^{71} -14.0000 q^{73} +(-1.50000 + 2.59808i) q^{75} +9.00000 q^{77} +8.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} -12.0000 q^{83} +(3.50000 + 6.06218i) q^{85} +(7.50000 + 12.9904i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(-7.50000 + 7.79423i) q^{91} +(-6.00000 + 10.3923i) q^{93} +(0.500000 + 0.866025i) q^{95} +(5.50000 + 9.52628i) q^{97} -18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 2 q^{5} + 3 q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + 2 * q^5 + 3 * q^7 - 6 * q^9	$ 2 q - 3 q^{3} + 2 q^{5} + 3 q^{7} - 6 q^{9} + 3 q^{11} + 2 q^{13} - 3 q^{15} + 7 q^{17} + q^{19} - 18 q^{21} - 7 q^{23} + 2 q^{25} + 18 q^{27} + 5 q^{29} + 8 q^{31} + 9 q^{33} + 3 q^{35} + 3 q^{37} - 21 q^{39} - 7 q^{41} - 9 q^{43} - 6 q^{45} - 16 q^{47} - 2 q^{49} - 42 q^{51} - 12 q^{53} + 3 q^{55} - 6 q^{57} + 5 q^{59} + 5 q^{61} + 18 q^{63} + 2 q^{65} + 13 q^{67} - 21 q^{69} - 3 q^{71} - 28 q^{73} - 3 q^{75} + 18 q^{77} + 16 q^{79} - 9 q^{81} - 24 q^{83} + 7 q^{85} + 15 q^{87} - 7 q^{89} - 15 q^{91} - 12 q^{93} + q^{95} + 11 q^{97} - 36 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 2 * q^5 + 3 * q^7 - 6 * q^9 + 3 * q^11 + 2 * q^13 - 3 * q^15 + 7 * q^17 + q^19 - 18 * q^21 - 7 * q^23 + 2 * q^25 + 18 * q^27 + 5 * q^29 + 8 * q^31 + 9 * q^33 + 3 * q^35 + 3 * q^37 - 21 * q^39 - 7 * q^41 - 9 * q^43 - 6 * q^45 - 16 * q^47 - 2 * q^49 - 42 * q^51 - 12 * q^53 + 3 * q^55 - 6 * q^57 + 5 * q^59 + 5 * q^61 + 18 * q^63 + 2 * q^65 + 13 * q^67 - 21 * q^69 - 3 * q^71 - 28 * q^73 - 3 * q^75 + 18 * q^77 + 16 * q^79 - 9 * q^81 - 24 * q^83 + 7 * q^85 + 15 * q^87 - 7 * q^89 - 15 * q^91 - 12 * q^93 + q^95 + 11 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	0.996866	+	0.0791130i	$0.0252088\pi$
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	−0.429919	+	0.902867i	$0.641458\pi$
$8$		0			0
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$		0			0
$15$	−1.50000	+	2.59808i	−0.387298	+	0.670820i
$16$		0			0
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	0.882213	+	0.470850i	$0.156053\pi$
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	−0.0333386	+	0.999444i	$0.510614\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	−9.00000			−1.96396
$22$		0			0
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	0.227167	+	0.973856i	$0.427054\pi$
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	−0.956967	+	0.290196i	$0.906280\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	9.00000			1.73205
$28$		0			0
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	−0.534928	−	0.844897i	$-0.679661\pi$
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	0.999167	+	0.0408130i	$0.0129948\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	4.50000	+	7.79423i	0.783349	+	1.35680i
$34$		0			0
$35$	1.50000	+	2.59808i	0.253546	+	0.439155i
$36$		0			0
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	−0.715981	−	0.698119i	$-0.754020\pi$
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	0.962580	+	0.270998i	$0.0873538\pi$
$38$		0			0
$39$	−10.5000	−	2.59808i	−1.68135	−	0.416025i
$40$		0			0
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	0.451896	+	0.892071i	$0.350748\pi$
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	−0.998504	+	0.0546823i	$0.982585\pi$
$42$		0			0
$43$	−4.50000	−	7.79423i	−0.686244	−	1.18861i	−0.973044	−	0.230618i	$-0.925925\pi$
$43$	−4.50000	−	7.79423i	−0.686244	−	1.18861i	0.286801	−	0.957990i	$-0.407408\pi$
$44$		0			0
$45$	−3.00000	−	5.19615i	−0.447214	−	0.774597i
$46$		0			0
$47$	−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
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$		0			0
$51$	−21.0000			−2.94059
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	1.50000	−	2.59808i	0.202260	−	0.350325i
$56$		0			0
$57$	−3.00000			−0.397360
$58$		0			0
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	0.981608	−	0.190909i	$-0.0611434\pi$
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	−0.656136	+	0.754643i	$0.727810\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$		0			0
$63$	9.00000	−	15.5885i	1.13389	−	1.96396i
$64$		0			0
$65$	1.00000	+	3.46410i	0.124035	+	0.429669i
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$		0			0
$69$	−10.5000	−	18.1865i	−1.26405	−	2.18940i
$70$		0			0
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	0.763184	−	0.646181i	$-0.223635\pi$
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	−0.941201	+	0.337846i	$0.890302\pi$
$72$		0			0
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$		0			0
$75$	−1.50000	+	2.59808i	−0.173205	+	0.300000i
$76$		0			0
$77$	9.00000			1.02565
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	3.50000	+	6.06218i	0.379628	+	0.657536i
$86$		0			0
$87$	7.50000	+	12.9904i	0.804084	+	1.39272i
$88$		0			0
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	−0.989720	−	0.143022i	$-0.954318\pi$
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	0.618720	+	0.785611i	$0.287651\pi$
$90$		0			0
$91$	−7.50000	+	7.79423i	−0.786214	+	0.817057i
$92$		0			0
$93$	−6.00000	+	10.3923i	−0.622171	+	1.07763i
$94$		0			0
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$		0			0
$97$	5.50000	+	9.52628i	0.558440	+	0.967247i	0.997627	+	0.0688512i	$0.0219334\pi$
$97$	5.50000	+	9.52628i	0.558440	+	0.967247i	−0.439187	+	0.898396i	$0.644733\pi$
$98$		0			0
$99$	−18.0000			−1.80907
$100$		0			0
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$		0			0
$103$	16.0000			1.57653			0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000			1.57653			0.788263	+	0.615338i	$0.210980\pi$
$104$		0			0
$105$	−9.00000			−0.878310
$106$		0			0
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$		0			0
$109$	−14.0000			−1.34096			−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000			−1.34096			−0.670478	+	0.741929i	$0.733911\pi$
$110$		0			0
$111$	4.50000	+	7.79423i	0.427121	+	0.739795i
$112$		0			0
$113$	−6.50000	−	11.2583i	−0.611469	−	1.05909i	−0.990993	−	0.133913i	$-0.957246\pi$
$113$	−6.50000	−	11.2583i	−0.611469	−	1.05909i	0.379525	−	0.925182i	$-0.376088\pi$
$114$		0			0
$115$	−3.50000	+	6.06218i	−0.326377	+	0.565301i
$116$		0			0
$117$	15.0000	−	15.5885i	1.38675	−	1.44115i
$118$		0			0
$119$	−10.5000	+	18.1865i	−0.962533	+	1.66716i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	−10.5000	−	18.1865i	−0.946753	−	1.63982i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	0.887357	+	0.461084i	$0.152539\pi$
$128$		0			0
$129$	27.0000			2.37722
$130$		0			0
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$	−1.50000	+	2.59808i	−0.130066	+	0.225282i
$134$		0			0
$135$	9.00000			0.774597
$136$		0			0
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	0.998179	+	0.0603135i	$0.0192101\pi$
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	−0.446857	+	0.894606i	$0.647457\pi$
$140$		0			0
$141$	12.0000	−	20.7846i	1.01058	−	1.75038i
$142$		0			0
$143$	10.5000	+	2.59808i	0.878054	+	0.217262i
$144$		0			0
$145$	2.50000	−	4.33013i	0.207614	−	0.359597i
$146$		0			0
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$		0			0
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$		0			0
$153$	21.0000	−	36.3731i	1.69775	−	2.94059i
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	6.00000			0.478852			0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000			0.478852			0.239426	+	0.970915i	$0.423041\pi$
$158$		0			0
$159$	9.00000	−	15.5885i	0.713746	−	1.23625i
$160$		0			0
$161$	−21.0000			−1.65503
$162$		0			0
$163$	5.50000	+	9.52628i	0.430793	+	0.746156i	0.996942	−	0.0781474i	$-0.0249005\pi$
$163$	5.50000	+	9.52628i	0.430793	+	0.746156i	−0.566149	+	0.824303i	$0.691567\pi$
$164$		0			0
$165$	4.50000	+	7.79423i	0.350325	+	0.606780i
$166$		0			0
$167$	0.500000	−	0.866025i	0.0386912	−	0.0670151i	−0.846031	−	0.533133i	$-0.821014\pi$
$167$	0.500000	−	0.866025i	0.0386912	−	0.0670151i	0.884723	+	0.466118i	$0.154348\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	3.00000	−	5.19615i	0.229416	−	0.397360i
$172$		0			0
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$		0			0
$175$	1.50000	+	2.59808i	0.113389	+	0.196396i
$176$		0			0
$177$	−15.0000			−1.12747
$178$		0			0
$179$	9.50000	−	16.4545i	0.710063	−	1.22987i	−0.254770	−	0.967002i	$-0.582000\pi$
$179$	9.50000	−	16.4545i	0.710063	−	1.22987i	0.964833	−	0.262864i	$-0.0846670\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$	−15.0000			−1.10883
$184$		0			0
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$		0			0
$187$	21.0000			1.53567
$188$		0			0
$189$	13.5000	+	23.3827i	0.981981	+	1.70084i
$190$		0			0
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	0.806641	−	0.591041i	$-0.201283\pi$
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	−0.915177	+	0.403051i	$0.867950\pi$
$192$		0			0
$193$	7.50000	−	12.9904i	0.539862	−	0.935068i	−0.459049	−	0.888411i	$-0.651810\pi$
$193$	7.50000	−	12.9904i	0.539862	−	0.935068i	0.998911	−	0.0466572i	$-0.0148568\pi$
$194$		0			0
$195$	−10.5000	−	2.59808i	−0.751921	−	0.186052i
$196$		0			0
$197$	11.5000	−	19.9186i	0.819341	−	1.41914i	−0.0868274	−	0.996223i	$-0.527673\pi$
$197$	11.5000	−	19.9186i	0.819341	−	1.41914i	0.906168	−	0.422917i	$-0.138994\pi$
$198$		0			0
$199$	4.50000	+	7.79423i	0.318997	+	0.552518i	0.980279	−	0.197619i	$-0.0633208\pi$
$199$	4.50000	+	7.79423i	0.318997	+	0.552518i	−0.661282	+	0.750137i	$0.729987\pi$
$200$		0			0
$201$	19.5000	+	33.7750i	1.37542	+	2.38230i
$202$		0			0
$203$	15.0000			1.05279
$204$		0			0
$205$	−3.50000	+	6.06218i	−0.244451	+	0.423401i
$206$		0			0
$207$	42.0000			2.91920
$208$		0			0
$209$	3.00000			0.207514
$210$		0			0
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	−0.939156	−	0.343490i	$-0.888391\pi$
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	0.767049	+	0.641588i	$0.221724\pi$
$212$		0			0
$213$	9.00000			0.616670
$214$		0			0
$215$	−4.50000	−	7.79423i	−0.306897	−	0.531562i
$216$		0			0
$217$	6.00000	+	10.3923i	0.407307	+	0.705476i
$218$		0			0
$219$	21.0000	−	36.3731i	1.41905	−	2.45786i
$220$		0			0
$221$	−17.5000	+	18.1865i	−1.17718	+	1.22336i
$222$		0			0
$223$	−11.5000	+	19.9186i	−0.770097	+	1.33385i	0.167412	+	0.985887i	$0.446459\pi$
$223$	−11.5000	+	19.9186i	−0.770097	+	1.33385i	−0.937509	+	0.347960i	$0.886874\pi$
$224$		0			0
$225$	−3.00000	−	5.19615i	−0.200000	−	0.346410i
$226$		0			0
$227$	−0.500000	−	0.866025i	−0.0331862	−	0.0574801i	0.848955	−	0.528465i	$-0.177232\pi$
$227$	−0.500000	−	0.866025i	−0.0331862	−	0.0574801i	−0.882141	+	0.470985i	$0.843899\pi$
$228$		0			0
$229$	26.0000			1.71813			0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000			1.71813			0.859064	+	0.511868i	$0.171046\pi$
$230$		0			0
$231$	−13.5000	+	23.3827i	−0.888235	+	1.53847i
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	−8.00000			−0.521862
$236$		0			0
$237$	−12.0000	+	20.7846i	−0.779484	+	1.35011i
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.00000	+	1.73205i	−0.0638877	+	0.110657i
$246$		0			0
$247$	−2.50000	+	2.59808i	−0.159071	+	0.165312i
$248$		0			0
$249$	18.0000	−	31.1769i	1.14070	−	1.97576i
$250$		0			0
$251$	2.50000	+	4.33013i	0.157799	+	0.273315i	0.934075	−	0.357078i	$-0.116227\pi$
$251$	2.50000	+	4.33013i	0.157799	+	0.273315i	−0.776276	+	0.630393i	$0.782894\pi$
$252$		0			0
$253$	10.5000	+	18.1865i	0.660129	+	1.14338i
$254$		0			0
$255$	−21.0000			−1.31507
$256$		0			0
$257$	9.50000	−	16.4545i	0.592594	−	1.02640i	−0.401288	−	0.915952i	$-0.631437\pi$
$257$	9.50000	−	16.4545i	0.592594	−	1.02640i	0.993882	−	0.110450i	$-0.0352294\pi$
$258$		0			0
$259$	9.00000			0.559233
$260$		0			0
$261$	−30.0000			−1.85695
$262$		0			0
$263$	−3.50000	+	6.06218i	−0.215819	+	0.373810i	−0.953526	−	0.301312i	$-0.902576\pi$
$263$	−3.50000	+	6.06218i	−0.215819	+	0.373810i	0.737706	+	0.675122i	$0.235909\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	−10.5000	−	18.1865i	−0.642590	−	1.11300i
$268$		0			0
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	0.816668	−	0.577108i	$-0.195819\pi$
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	−0.908124	+	0.418701i	$0.862486\pi$
$270$		0			0
$271$	11.5000	−	19.9186i	0.698575	−	1.20997i	−0.270385	−	0.962752i	$-0.587151\pi$
$271$	11.5000	−	19.9186i	0.698575	−	1.20997i	0.968960	−	0.247216i	$-0.0795156\pi$
$272$		0			0
$273$	−9.00000	−	31.1769i	−0.544705	−	1.88691i
$274$		0			0
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	11.5000	+	19.9186i	0.690968	+	1.19679i	0.971521	+	0.236953i	$0.0761488\pi$
$277$	11.5000	+	19.9186i	0.690968	+	1.19679i	−0.280553	+	0.959839i	$0.590518\pi$
$278$		0			0
$279$	−12.0000	−	20.7846i	−0.718421	−	1.24434i
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$		0			0
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	−0.850782	−	0.525519i	$-0.823871\pi$
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	0.880504	+	0.474039i	$0.157204\pi$
$284$		0			0
$285$	−3.00000			−0.177705
$286$		0			0
$287$	−21.0000			−1.23959
$288$		0			0
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$		0			0
$291$	−33.0000			−1.93449
$292$		0			0
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$	2.50000	+	4.33013i	0.145556	+	0.252110i
$296$		0			0
$297$	13.5000	−	23.3827i	0.783349	−	1.35680i
$298$		0			0
$299$	−24.5000	−	6.06218i	−1.41687	−	0.350585i
$300$		0			0
$301$	13.5000	−	23.3827i	0.778127	−	1.34776i
$302$		0			0
$303$	13.5000	+	23.3827i	0.775555	+	1.34330i
$304$		0			0
$305$	2.50000	+	4.33013i	0.143150	+	0.247942i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$	−24.0000	+	41.5692i	−1.36531	+	2.36479i
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$		0			0
$315$	9.00000	−	15.5885i	0.507093	−	0.878310i
$316$		0			0
$317$	−2.00000			−0.112331			−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000			−0.112331			−0.0561656	+	0.998421i	$0.517887\pi$
$318$		0			0
$319$	−7.50000	−	12.9904i	−0.419919	−	0.727322i
$320$		0			0
$321$	−4.50000	−	7.79423i	−0.251166	−	0.435031i
$322$		0			0
$323$	−3.50000	+	6.06218i	−0.194745	+	0.337309i
$324$		0			0
$325$	1.00000	+	3.46410i	0.0554700	+	0.192154i
$326$		0			0
$327$	21.0000	−	36.3731i	1.16130	−	2.01144i
$328$		0			0
$329$	−12.0000	−	20.7846i	−0.661581	−	1.14589i
$330$		0			0
$331$	6.50000	+	11.2583i	0.357272	+	0.618814i	0.987504	−	0.157593i	$-0.0503735\pi$
$331$	6.50000	+	11.2583i	0.357272	+	0.618814i	−0.630232	+	0.776407i	$0.717040\pi$
$332$		0			0
$333$	−18.0000			−0.986394
$334$		0			0
$335$	6.50000	−	11.2583i	0.355133	−	0.615108i
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$		0			0
$339$	39.0000			2.11819
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	15.0000			0.809924
$344$		0			0
$345$	−10.5000	−	18.1865i	−0.565301	−	0.979130i
$346$		0			0
$347$	−6.50000	−	11.2583i	−0.348938	−	0.604379i	0.637123	−	0.770762i	$-0.280124\pi$
$347$	−6.50000	−	11.2583i	−0.348938	−	0.604379i	−0.986061	+	0.166383i	$0.946791\pi$
$348$		0			0
$349$	12.5000	−	21.6506i	0.669110	−	1.15893i	−0.309044	−	0.951048i	$-0.600009\pi$
$349$	12.5000	−	21.6506i	0.669110	−	1.15893i	0.978153	−	0.207884i	$-0.0666577\pi$
$350$		0			0
$351$	9.00000	+	31.1769i	0.480384	+	1.66410i
$352$		0			0
$353$	−10.5000	+	18.1865i	−0.558859	+	0.967972i	0.438733	+	0.898617i	$0.355427\pi$
$353$	−10.5000	+	18.1865i	−0.558859	+	0.967972i	−0.997592	+	0.0693543i	$0.977906\pi$
$354$		0			0
$355$	−1.50000	−	2.59808i	−0.0796117	−	0.137892i
$356$		0			0
$357$	−31.5000	−	54.5596i	−1.66716	−	2.88760i
$358$		0			0
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	−6.00000			−0.314918
$364$		0			0
$365$	−14.0000			−0.732793
$366$		0			0
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	−0.724345	−	0.689438i	$-0.757858\pi$
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	0.959243	+	0.282582i	$0.0911910\pi$
$368$		0			0
$369$	42.0000			2.18643
$370$		0			0
$371$	−9.00000	−	15.5885i	−0.467257	−	0.809312i
$372$		0			0
$373$	13.5000	+	23.3827i	0.699004	+	1.21071i	0.968812	+	0.247796i	$0.0797062\pi$
$373$	13.5000	+	23.3827i	0.699004	+	1.21071i	−0.269809	+	0.962914i	$0.586961\pi$
$374$		0			0
$375$	−1.50000	+	2.59808i	−0.0774597	+	0.134164i
$376$		0			0
$377$	17.5000	+	4.33013i	0.901296	+	0.223013i
$378$		0			0
$379$	−4.50000	+	7.79423i	−0.231149	+	0.400363i	−0.958147	−	0.286278i	$-0.907582\pi$
$379$	−4.50000	+	7.79423i	−0.231149	+	0.400363i	0.726997	+	0.686640i	$0.240915\pi$
$380$		0			0
$381$	1.50000	+	2.59808i	0.0768473	+	0.133103i
$382$		0			0
$383$	−6.50000	−	11.2583i	−0.332134	−	0.575274i	0.650796	−	0.759253i	$-0.274435\pi$
$383$	−6.50000	−	11.2583i	−0.332134	−	0.575274i	−0.982930	+	0.183979i	$0.941102\pi$
$384$		0			0
$385$	9.00000			0.458682
$386$		0			0
$387$	−27.0000	+	46.7654i	−1.37249	+	2.37722i
$388$		0			0
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	−49.0000			−2.47804
$392$		0			0
$393$	6.00000	−	10.3923i	0.302660	−	0.524222i
$394$		0			0
$395$	8.00000			0.402524
$396$		0			0
$397$	−16.5000	−	28.5788i	−0.828111	−	1.43433i	−0.899518	−	0.436884i	$-0.856082\pi$
$397$	−16.5000	−	28.5788i	−0.828111	−	1.43433i	0.0714068	−	0.997447i	$-0.477251\pi$
$398$		0			0
$399$	−4.50000	−	7.79423i	−0.225282	−	0.390199i
$400$		0			0
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$		0			0
$403$	4.00000	+	13.8564i	0.199254	+	0.690237i
$404$		0			0
$405$	−4.50000	+	7.79423i	−0.223607	+	0.387298i
$406$		0			0
$407$	−4.50000	−	7.79423i	−0.223057	−	0.386346i
$408$		0			0
$409$	0.500000	+	0.866025i	0.0247234	+	0.0428222i	0.878122	−	0.478436i	$-0.158796\pi$
$409$	0.500000	+	0.866025i	0.0247234	+	0.0428222i	−0.853399	+	0.521258i	$0.825463\pi$
$410$		0			0
$411$	−9.00000			−0.443937
$412$		0			0
$413$	−7.50000	+	12.9904i	−0.369051	+	0.639215i
$414$		0			0
$415$	−12.0000			−0.589057
$416$		0			0
$417$	−39.0000			−1.90984
$418$		0			0
$419$	−16.5000	+	28.5788i	−0.806078	+	1.39617i	0.109483	+	0.993989i	$0.465080\pi$
$419$	−16.5000	+	28.5788i	−0.806078	+	1.39617i	−0.915561	+	0.402179i	$0.868253\pi$
$420$		0			0
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$		0			0
$423$	24.0000	+	41.5692i	1.16692	+	2.02116i
$424$		0			0
$425$	3.50000	+	6.06218i	0.169775	+	0.294059i
$426$		0			0
$427$	−7.50000	+	12.9904i	−0.362950	+	0.628649i
$428$		0			0
$429$	−22.5000	+	23.3827i	−1.08631	+	1.12893i
$430$		0			0
$431$	−4.50000	+	7.79423i	−0.216757	+	0.375435i	−0.953815	−	0.300395i	$-0.902881\pi$
$431$	−4.50000	+	7.79423i	−0.216757	+	0.375435i	0.737057	+	0.675830i	$0.236215\pi$
$432$		0			0
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	0.853761	−	0.520665i	$-0.174316\pi$
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	−0.877790	+	0.479046i	$0.840983\pi$
$434$		0			0
$435$	7.50000	+	12.9904i	0.359597	+	0.622841i
$436$		0			0
$437$	−7.00000			−0.334855
$438$		0			0
$439$	1.50000	−	2.59808i	0.0715911	−	0.123999i	−0.828008	−	0.560717i	$-0.810526\pi$
$439$	1.50000	−	2.59808i	0.0715911	−	0.123999i	0.899599	+	0.436717i	$0.143859\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$		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
$445$	−3.50000	+	6.06218i	−0.165916	+	0.287375i
$446$		0			0
$447$	9.00000			0.425685
$448$		0			0
$449$	10.5000	+	18.1865i	0.495526	+	0.858276i	0.999987	−	0.00515887i	$-0.00164213\pi$
$449$	10.5000	+	18.1865i	0.495526	+	0.858276i	−0.504461	+	0.863434i	$0.668309\pi$
$450$		0			0
$451$	10.5000	+	18.1865i	0.494426	+	0.856370i
$452$		0			0
$453$	−12.0000	+	20.7846i	−0.563809	+	0.976546i
$454$		0			0
$455$	−7.50000	+	7.79423i	−0.351605	+	0.365399i
$456$		0			0
$457$	11.5000	−	19.9186i	0.537947	−	0.931752i	−0.461067	−	0.887365i	$-0.652533\pi$
$457$	11.5000	−	19.9186i	0.537947	−	0.931752i	0.999014	−	0.0443868i	$-0.0141334\pi$
$458$		0			0
$459$	31.5000	+	54.5596i	1.47029	+	2.54662i
$460$		0			0
$461$	−5.50000	−	9.52628i	−0.256161	−	0.443683i	0.709050	−	0.705159i	$-0.249124\pi$
$461$	−5.50000	−	9.52628i	−0.256161	−	0.443683i	−0.965210	+	0.261476i	$0.915791\pi$
$462$		0			0
$463$	28.0000			1.30127			0.650635	−	0.759390i	$-0.274503\pi$
$463$	28.0000			1.30127			0.650635	+	0.759390i	$0.274503\pi$
$464$		0			0
$465$	−6.00000	+	10.3923i	−0.278243	+	0.481932i
$466$		0			0
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$		0			0
$469$	39.0000			1.80085
$470$		0			0
$471$	−9.00000	+	15.5885i	−0.414698	+	0.718278i
$472$		0			0
$473$	−27.0000			−1.24146
$474$		0			0
$475$	0.500000	+	0.866025i	0.0229416	+	0.0397360i
$476$		0			0
$477$	18.0000	+	31.1769i	0.824163	+	1.42749i
$478$		0			0
$479$	−0.500000	+	0.866025i	−0.0228456	+	0.0395697i	−0.877222	−	0.480085i	$-0.840606\pi$
$479$	−0.500000	+	0.866025i	−0.0228456	+	0.0395697i	0.854377	+	0.519654i	$0.173939\pi$
$480$		0			0
$481$	10.5000	+	2.59808i	0.478759	+	0.118462i
$482$		0			0
$483$	31.5000	−	54.5596i	1.43330	−	2.48255i
$484$		0			0
$485$	5.50000	+	9.52628i	0.249742	+	0.432566i
$486$		0			0
$487$	−8.50000	−	14.7224i	−0.385172	−	0.667137i	0.606621	−	0.794991i	$-0.292524\pi$
$487$	−8.50000	−	14.7224i	−0.385172	−	0.667137i	−0.991793	+	0.127854i	$0.959191\pi$
$488$		0			0
$489$	−33.0000			−1.49231
$490$		0			0
$491$	11.5000	−	19.9186i	0.518988	−	0.898913i	−0.480769	−	0.876847i	$-0.659642\pi$
$491$	11.5000	−	19.9186i	0.518988	−	0.898913i	0.999757	−	0.0220657i	$-0.00702431\pi$
$492$		0			0
$493$	35.0000			1.57632
$494$		0			0
$495$	−18.0000			−0.809040
$496$		0			0
$497$	4.50000	−	7.79423i	0.201853	−	0.349619i
$498$		0			0
$499$	16.0000			0.716258			0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000			0.716258			0.358129	+	0.933672i	$0.383415\pi$
$500$		0			0
$501$	1.50000	+	2.59808i	0.0670151	+	0.116073i
$502$		0			0
$503$	5.50000	+	9.52628i	0.245233	+	0.424756i	0.962197	−	0.272354i	$-0.0878022\pi$
$503$	5.50000	+	9.52628i	0.245233	+	0.424756i	−0.716964	+	0.697110i	$0.754469\pi$
$504$		0			0
$505$	4.50000	−	7.79423i	0.200247	−	0.346839i
$506$		0			0
$507$	−1.50000	−	38.9711i	−0.0666173	−	1.73077i
$508$		0			0
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$		0			0
$511$	−21.0000	−	36.3731i	−0.928985	−	1.60905i
$512$		0			0
$513$	4.50000	+	7.79423i	0.198680	+	0.344124i
$514$		0			0
$515$	16.0000			0.705044
$516$		0			0
$517$	−12.0000	+	20.7846i	−0.527759	+	0.914106i
$518$		0			0
$519$	−45.0000			−1.97528
$520$		0			0
$521$	−34.0000			−1.48957			−0.744784	−	0.667306i	$-0.767447\pi$
$521$	−34.0000			−1.48957			−0.744784	+	0.667306i	$0.767447\pi$
$522$		0			0
$523$	−11.5000	+	19.9186i	−0.502860	+	0.870979i	0.497135	+	0.867673i	$0.334385\pi$
$523$	−11.5000	+	19.9186i	−0.502860	+	0.870979i	−0.999995	+	0.00330547i	$0.998948\pi$
$524$		0			0
$525$	−9.00000			−0.392792
$526$		0			0
$527$	14.0000	+	24.2487i	0.609850	+	1.05629i
$528$		0			0
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$		0			0
$531$	15.0000	−	25.9808i	0.650945	−	1.12747i
$532$		0			0
$533$	−24.5000	−	6.06218i	−1.06121	−	0.262582i
$534$		0			0
$535$	−1.50000	+	2.59808i	−0.0648507	+	0.112325i
$536$		0			0
$537$	28.5000	+	49.3634i	1.22987	+	2.13019i
$538$		0			0
$539$	3.00000	+	5.19615i	0.129219	+	0.223814i
$540$		0			0
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$		0			0
$543$	21.0000	−	36.3731i	0.901196	−	1.56092i
$544$		0			0
$545$	−14.0000			−0.599694
$546$		0			0
$547$	16.0000			0.684111			0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000			0.684111			0.342055	+	0.939680i	$0.388877\pi$
$548$		0			0
$549$	15.0000	−	25.9808i	0.640184	−	1.10883i
$550$		0			0
$551$	5.00000			0.213007
$552$		0			0
$553$	12.0000	+	20.7846i	0.510292	+	0.883852i
$554$		0			0
$555$	4.50000	+	7.79423i	0.191014	+	0.330847i
$556$		0			0
$557$	9.50000	−	16.4545i	0.402528	−	0.697199i	−0.591502	−	0.806303i	$-0.701465\pi$
$557$	9.50000	−	16.4545i	0.402528	−	0.697199i	0.994030	+	0.109104i	$0.0347983\pi$
$558$		0			0
$559$	22.5000	−	23.3827i	0.951649	−	0.988982i
$560$		0			0
$561$	−31.5000	+	54.5596i	−1.32993	+	2.30351i
$562$		0			0
$563$	−22.5000	−	38.9711i	−0.948262	−	1.64244i	−0.749085	−	0.662474i	$-0.769506\pi$
$563$	−22.5000	−	38.9711i	−0.948262	−	1.64244i	−0.199177	−	0.979963i	$-0.563827\pi$
$564$		0			0
$565$	−6.50000	−	11.2583i	−0.273457	−	0.473642i
$566$		0			0
$567$	−27.0000			−1.13389
$568$		0			0
$569$	−9.50000	+	16.4545i	−0.398261	+	0.689808i	−0.993511	−	0.113732i	$-0.963719\pi$
$569$	−9.50000	+	16.4545i	−0.398261	+	0.689808i	0.595251	+	0.803540i	$0.297053\pi$
$570$		0			0
$571$	40.0000			1.67395			0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000			1.67395			0.836974	+	0.547243i	$0.184323\pi$
$572$		0			0
$573$	9.00000			0.375980
$574$		0			0
$575$	−3.50000	+	6.06218i	−0.145960	+	0.252810i
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$		0			0
$579$	22.5000	+	38.9711i	0.935068	+	1.61959i
$580$		0			0
$581$	−18.0000	−	31.1769i	−0.746766	−	1.29344i
$582$		0			0
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$		0			0
$585$	15.0000	−	15.5885i	0.620174	−	0.644503i
$586$		0			0
$587$	18.5000	−	32.0429i	0.763577	−	1.32255i	−0.177419	−	0.984135i	$-0.556775\pi$
$587$	18.5000	−	32.0429i	0.763577	−	1.32255i	0.940996	−	0.338418i	$-0.109892\pi$
$588$		0			0
$589$	2.00000	+	3.46410i	0.0824086	+	0.142736i
$590$		0			0
$591$	34.5000	+	59.7558i	1.41914	+	2.45802i
$592$		0			0
$593$	26.0000			1.06769			0.533846	−	0.845582i	$-0.320746\pi$
$593$	26.0000			1.06769			0.533846	+	0.845582i	$0.320746\pi$
$594$		0			0
$595$	−10.5000	+	18.1865i	−0.430458	+	0.745575i
$596$		0			0
$597$	−27.0000			−1.10504
$598$		0			0
$599$	−8.00000			−0.326871			−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000			−0.326871			−0.163436	+	0.986554i	$0.552258\pi$
$600$		0			0
$601$	6.50000	−	11.2583i	0.265141	−	0.459237i	−0.702460	−	0.711723i	$-0.747915\pi$
$601$	6.50000	−	11.2583i	0.265141	−	0.459237i	0.967600	+	0.252486i	$0.0812483\pi$
$602$		0			0
$603$	−78.0000			−3.17641
$604$		0			0
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$		0			0
$607$	−4.50000	−	7.79423i	−0.182649	−	0.316358i	0.760133	−	0.649768i	$-0.225134\pi$
$607$	−4.50000	−	7.79423i	−0.182649	−	0.316358i	−0.942782	+	0.333410i	$0.891801\pi$
$608$		0			0
$609$	−22.5000	+	38.9711i	−0.911746	+	1.57919i
$610$		0			0
$611$	−8.00000	−	27.7128i	−0.323645	−	1.12114i
$612$		0			0
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	−0.362300	−	0.932062i	$-0.618008\pi$
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	0.988339	−	0.152270i	$-0.0486583\pi$
$614$		0			0
$615$	−10.5000	−	18.1865i	−0.423401	−	0.733352i
$616$		0			0
$617$	−14.5000	−	25.1147i	−0.583748	−	1.01108i	−0.995030	−	0.0995732i	$-0.968252\pi$
$617$	−14.5000	−	25.1147i	−0.583748	−	1.01108i	0.411282	−	0.911508i	$-0.365081\pi$
$618$		0			0
$619$	−12.0000			−0.482321			−0.241160	−	0.970485i	$-0.577528\pi$
$619$	−12.0000			−0.482321			−0.241160	+	0.970485i	$0.577528\pi$
$620$		0			0
$621$	−31.5000	+	54.5596i	−1.26405	+	2.18940i
$622$		0			0
$623$	−21.0000			−0.841347
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−4.50000	+	7.79423i	−0.179713	+	0.311272i
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	−7.50000	−	12.9904i	−0.298570	−	0.517139i	0.677239	−	0.735763i	$-0.263176\pi$
$631$	−7.50000	−	12.9904i	−0.298570	−	0.517139i	−0.975809	+	0.218624i	$0.929843\pi$
$632$		0			0
$633$	−7.50000	−	12.9904i	−0.298098	−	0.516321i
$634$		0			0
$635$	0.500000	−	0.866025i	0.0198419	−	0.0343672i
$636$		0			0
$637$	−7.00000	−	1.73205i	−0.277350	−	0.0686264i
$638$		0			0
$639$	−9.00000	+	15.5885i	−0.356034	+	0.616670i
$640$		0			0
$641$	10.5000	+	18.1865i	0.414725	+	0.718325i	0.995400	−	0.0958109i	$-0.0305444\pi$
$641$	10.5000	+	18.1865i	0.414725	+	0.718325i	−0.580674	+	0.814136i	$0.697211\pi$
$642$		0			0
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	0.926750	−	0.375680i	$-0.122591\pi$
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	−0.788723	+	0.614749i	$0.789257\pi$
$644$		0			0
$645$	27.0000			1.06312
$646$		0			0
$647$	8.50000	−	14.7224i	0.334169	−	0.578799i	−0.649155	−	0.760656i	$-0.724878\pi$
$647$	8.50000	−	14.7224i	0.334169	−	0.578799i	0.983325	+	0.181857i	$0.0582109\pi$
$648$		0			0
$649$	15.0000			0.588802
$650$		0			0
$651$	−36.0000			−1.41095
$652$		0			0
$653$	5.50000	−	9.52628i	0.215232	−	0.372792i	−0.738113	−	0.674678i	$-0.764283\pi$
$653$	5.50000	−	9.52628i	0.215232	−	0.372792i	0.953344	+	0.301885i	$0.0976160\pi$
$654$		0			0
$655$	−4.00000			−0.156293
$656$		0			0
$657$	42.0000	+	72.7461i	1.63858	+	2.83810i
$658$		0			0
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	0.682161	−	0.731202i	$-0.261040\pi$
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	−0.974320	+	0.225168i	$0.927707\pi$
$660$		0			0
$661$	8.50000	−	14.7224i	0.330612	−	0.572636i	−0.652020	−	0.758202i	$-0.726078\pi$
$661$	8.50000	−	14.7224i	0.330612	−	0.572636i	0.982632	+	0.185565i	$0.0594116\pi$
$662$		0			0
$663$	−21.0000	−	72.7461i	−0.815572	−	2.82523i
$664$		0			0
$665$	−1.50000	+	2.59808i	−0.0581675	+	0.100749i
$666$		0			0
$667$	17.5000	+	30.3109i	0.677603	+	1.17364i
$668$		0			0
$669$	−34.5000	−	59.7558i	−1.33385	−	2.31029i
$670$		0			0
$671$	15.0000			0.579069
$672$		0			0
$673$	−6.50000	+	11.2583i	−0.250557	+	0.433977i	−0.963679	−	0.267063i	$-0.913947\pi$
$673$	−6.50000	+	11.2583i	−0.250557	+	0.433977i	0.713123	+	0.701039i	$0.247280\pi$
$674$		0			0
$675$	9.00000			0.346410
$676$		0			0
$677$	22.0000			0.845529			0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000			0.845529			0.422764	+	0.906240i	$0.361060\pi$
$678$		0			0
$679$	−16.5000	+	28.5788i	−0.633212	+	1.09676i
$680$		0			0
$681$	3.00000			0.114960
$682$		0			0
$683$	15.5000	+	26.8468i	0.593091	+	1.02726i	0.993813	+	0.111064i	$0.0354259\pi$
$683$	15.5000	+	26.8468i	0.593091	+	1.02726i	−0.400722	+	0.916200i	$0.631241\pi$
$684$		0			0
$685$	1.50000	+	2.59808i	0.0573121	+	0.0992674i
$686$		0			0
$687$	−39.0000	+	67.5500i	−1.48794	+	2.57719i
$688$		0			0
$689$	−6.00000	−	20.7846i	−0.228582	−	0.791831i
$690$		0			0
$691$	−12.5000	+	21.6506i	−0.475522	+	0.823629i	−0.999607	−	0.0280373i	$-0.991074\pi$
$691$	−12.5000	+	21.6506i	−0.475522	+	0.823629i	0.524084	+	0.851666i	$0.324408\pi$
$692$		0			0
$693$	−27.0000	−	46.7654i	−1.02565	−	1.77647i
$694$		0			0
$695$	6.50000	+	11.2583i	0.246559	+	0.427053i
$696$		0			0
$697$	−49.0000			−1.85601
$698$		0			0
$699$	−27.0000	+	46.7654i	−1.02123	+	1.76883i
$700$		0			0
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$		0			0
$703$	3.00000			0.113147
$704$		0			0
$705$	12.0000	−	20.7846i	0.451946	−	0.782794i
$706$		0			0
$707$	27.0000			1.01544
$708$		0			0
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	−0.981331	−	0.192328i	$-0.938396\pi$
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	0.324104	−	0.946021i	$-0.394937\pi$
$710$		0			0
$711$	−24.0000	−	41.5692i	−0.900070	−	1.55897i
$712$		0			0
$713$	−14.0000	+	24.2487i	−0.524304	+	0.908121i
$714$		0			0
$715$	10.5000	+	2.59808i	0.392678	+	0.0971625i
$716$		0			0
$717$	−24.0000	+	41.5692i	−0.896296	+	1.55243i
$718$		0			0
$719$	0.500000	+	0.866025i	0.0186469	+	0.0322973i	0.875198	−	0.483764i	$-0.160731\pi$
$719$	0.500000	+	0.866025i	0.0186469	+	0.0322973i	−0.856551	+	0.516062i	$0.827398\pi$
$720$		0			0
$721$	24.0000	+	41.5692i	0.893807	+	1.54812i
$722$		0			0
$723$	−3.00000			−0.111571
$724$		0			0
$725$	2.50000	−	4.33013i	0.0928477	−	0.160817i
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	31.5000	−	54.5596i	1.16507	−	2.01796i
$732$		0			0
$733$	14.0000			0.517102			0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000			0.517102			0.258551	+	0.965998i	$0.416755\pi$
$734$		0			0
$735$	−3.00000	−	5.19615i	−0.110657	−	0.191663i
$736$		0			0
$737$	−19.5000	−	33.7750i	−0.718292	−	1.24412i
$738$		0			0
$739$	19.5000	−	33.7750i	0.717319	−	1.24243i	−0.244739	−	0.969589i	$-0.578702\pi$
$739$	19.5000	−	33.7750i	0.717319	−	1.24243i	0.962058	−	0.272844i	$-0.0879643\pi$
$740$		0			0
$741$	−3.00000	−	10.3923i	−0.110208	−	0.381771i
$742$		0			0
$743$	0.500000	−	0.866025i	0.0183432	−	0.0317714i	−0.856708	−	0.515802i	$-0.827494\pi$
$743$	0.500000	−	0.866025i	0.0183432	−	0.0317714i	0.875051	+	0.484030i	$0.160828\pi$
$744$		0			0
$745$	−1.50000	−	2.59808i	−0.0549557	−	0.0951861i
$746$		0			0
$747$	36.0000	+	62.3538i	1.31717	+	2.28141i
$748$		0			0
$749$	−9.00000			−0.328853
$750$		0			0
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	−0.959906	−	0.280321i	$-0.909559\pi$
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	0.722718	+	0.691143i	$0.242893\pi$
$752$		0			0
$753$	−15.0000			−0.546630
$754$		0			0
$755$	8.00000			0.291150
$756$		0			0
$757$	−0.500000	+	0.866025i	−0.0181728	+	0.0314762i	−0.874969	−	0.484179i	$-0.839118\pi$
$757$	−0.500000	+	0.866025i	−0.0181728	+	0.0314762i	0.856796	+	0.515656i	$0.172452\pi$
$758$		0			0
$759$	−63.0000			−2.28676
$760$		0			0
$761$	−25.5000	−	44.1673i	−0.924374	−	1.60106i	−0.792564	−	0.609788i	$-0.791255\pi$
$761$	−25.5000	−	44.1673i	−0.924374	−	1.60106i	−0.131810	−	0.991275i	$-0.542079\pi$
$762$		0			0
$763$	−21.0000	−	36.3731i	−0.760251	−	1.31679i
$764$		0			0
$765$	21.0000	−	36.3731i	0.759257	−	1.31507i
$766$		0			0
$767$	−12.5000	+	12.9904i	−0.451349	+	0.469055i
$768$		0			0
$769$	2.50000	−	4.33013i	0.0901523	−	0.156148i	−0.817423	−	0.576038i	$-0.804598\pi$
$769$	2.50000	−	4.33013i	0.0901523	−	0.156148i	0.907575	+	0.419890i	$0.137931\pi$
$770$		0			0
$771$	28.5000	+	49.3634i	1.02640	+	1.77778i
$772$		0			0
$773$	−12.5000	−	21.6506i	−0.449594	−	0.778719i	0.548766	−	0.835976i	$-0.315098\pi$
$773$	−12.5000	−	21.6506i	−0.449594	−	0.778719i	−0.998359	+	0.0572570i	$0.981765\pi$
$774$		0			0
$775$	4.00000			0.143684
$776$		0			0
$777$	−13.5000	+	23.3827i	−0.484310	+	0.838849i
$778$		0			0
$779$	−7.00000			−0.250801
$780$		0			0
$781$	−9.00000			−0.322045
$782$		0			0
$783$	22.5000	−	38.9711i	0.804084	−	1.39272i
$784$		0			0
$785$	6.00000			0.214149
$786$		0			0
$787$	−0.500000	−	0.866025i	−0.0178231	−	0.0308705i	0.856976	−	0.515356i	$-0.172340\pi$
$787$	−0.500000	−	0.866025i	−0.0178231	−	0.0308705i	−0.874799	+	0.484485i	$0.839007\pi$
$788$		0			0
$789$	−10.5000	−	18.1865i	−0.373810	−	0.647458i
$790$		0			0
$791$	19.5000	−	33.7750i	0.693340	−	1.20090i
$792$		0			0
$793$	−12.5000	+	12.9904i	−0.443888	+	0.461302i
$794$		0			0
$795$	9.00000	−	15.5885i	0.319197	−	0.552866i
$796$		0			0
$797$	3.50000	+	6.06218i	0.123976	+	0.214733i	0.921332	−	0.388776i	$-0.127102\pi$
$797$	3.50000	+	6.06218i	0.123976	+	0.214733i	−0.797356	+	0.603509i	$0.793769\pi$
$798$		0			0
$799$	−28.0000	−	48.4974i	−0.990569	−	1.71572i
$800$		0			0
$801$	42.0000			1.48400
$802$		0			0
$803$	−21.0000	+	36.3731i	−0.741074	+	1.28358i
$804$		0			0
$805$	−21.0000			−0.740153
$806$		0			0
$807$	9.00000			0.316815
$808$		0			0
$809$	12.5000	−	21.6506i	0.439477	−	0.761196i	−0.558173	−	0.829725i	$-0.688497\pi$
$809$	12.5000	−	21.6506i	0.439477	−	0.761196i	0.997649	+	0.0685291i	$0.0218306\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	34.5000	+	59.7558i	1.20997	+	2.09573i
$814$		0			0
$815$	5.50000	+	9.52628i	0.192657	+	0.333691i
$816$		0			0
$817$	4.50000	−	7.79423i	0.157435	−	0.272686i
$818$		0			0
$819$	63.0000	+	15.5885i	2.20140	+	0.544705i
$820$		0			0
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	−0.966708	−	0.255884i	$-0.917634\pi$
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	0.704956	+	0.709251i	$0.250967\pi$
$822$		0			0
$823$	23.5000	+	40.7032i	0.819159	+	1.41882i	0.906303	+	0.422628i	$0.138892\pi$
$823$	23.5000	+	40.7032i	0.819159	+	1.41882i	−0.0871445	+	0.996196i	$0.527774\pi$
$824$		0			0
$825$	4.50000	+	7.79423i	0.156670	+	0.271360i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	−0.730791	−	0.682601i	$-0.760849\pi$
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	0.956545	+	0.291583i	$0.0941820\pi$
$830$		0			0
$831$	−69.0000			−2.39358
$832$		0			0
$833$	−14.0000			−0.485071
$834$		0			0
$835$	0.500000	−	0.866025i	0.0173032	−	0.0299700i
$836$		0			0
$837$	36.0000			1.24434
$838$		0			0
$839$	6.50000	+	11.2583i	0.224405	+	0.388681i	0.956141	−	0.292908i	$-0.0946228\pi$
$839$	6.50000	+	11.2583i	0.224405	+	0.388681i	−0.731736	+	0.681588i	$0.761290\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$		0			0
$843$	15.0000	−	25.9808i	0.516627	−	0.894825i
$844$		0			0
$845$	−11.0000	+	6.92820i	−0.378412	+	0.238337i
$846$		0			0
$847$	−3.00000	+	5.19615i	−0.103081	+	0.178542i
$848$		0			0
$849$	1.50000	+	2.59808i	0.0514799	+	0.0891657i
$850$		0			0
$851$	10.5000	+	18.1865i	0.359935	+	0.623426i
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$		0			0
$855$	3.00000	−	5.19615i	0.102598	−	0.177705i
$856$		0			0
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	−44.0000			−1.50126			−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000			−1.50126			−0.750630	+	0.660722i	$0.770250\pi$
$860$		0			0
$861$	31.5000	−	54.5596i	1.07352	−	1.85939i
$862$		0			0
$863$	−16.0000			−0.544646			−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000			−0.544646			−0.272323	+	0.962206i	$0.587792\pi$
$864$		0			0
$865$	7.50000	+	12.9904i	0.255008	+	0.441686i
$866$		0			0
$867$	−48.0000	−	83.1384i	−1.63017	−	2.82353i
$868$		0			0
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$		0			0
$871$	45.5000	+	11.2583i	1.54171	+	0.381474i
$872$		0			0
$873$	33.0000	−	57.1577i	1.11688	−	1.93449i
$874$		0			0
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$		0			0
$877$	−2.50000	−	4.33013i	−0.0844190	−	0.146218i	0.820724	−	0.571324i	$-0.193570\pi$
$877$	−2.50000	−	4.33013i	−0.0844190	−	0.146218i	−0.905143	+	0.425106i	$0.860237\pi$
$878$		0			0
$879$	27.0000			0.910687
$880$		0			0
$881$	−5.50000	+	9.52628i	−0.185300	+	0.320949i	−0.943677	−	0.330867i	$-0.892659\pi$
$881$	−5.50000	+	9.52628i	−0.185300	+	0.320949i	0.758378	+	0.651815i	$0.225992\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$		0			0
$885$	−15.0000			−0.504219
$886$		0			0
$887$	−9.50000	+	16.4545i	−0.318979	+	0.552487i	−0.980275	−	0.197637i	$-0.936673\pi$
$887$	−9.50000	+	16.4545i	−0.318979	+	0.552487i	0.661296	+	0.750125i	$0.270007\pi$
$888$		0			0
$889$	3.00000			0.100617
$890$		0			0
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$		0			0
$893$	−4.00000	−	6.92820i	−0.133855	−	0.231843i
$894$		0			0
$895$	9.50000	−	16.4545i	0.317550	−	0.550013i
$896$		0			0
$897$	52.5000	−	54.5596i	1.75292	−	1.82169i
$898$		0			0
$899$	10.0000	−	17.3205i	0.333519	−	0.577671i
$900$		0			0
$901$	−21.0000	−	36.3731i	−0.699611	−	1.21176i
$902$		0			0
$903$	40.5000	+	70.1481i	1.34776	+	2.33438i
$904$		0			0
$905$	−14.0000			−0.465376
$906$		0			0
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	−0.689698	−	0.724097i	$-0.742257\pi$
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	0.971936	+	0.235247i	$0.0755899\pi$
$908$		0			0
$909$	−54.0000			−1.79107
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	−18.0000	+	31.1769i	−0.595713	+	1.03181i
$914$		0			0
$915$	−15.0000			−0.495885
$916$		0			0
$917$	−6.00000	−	10.3923i	−0.198137	−	0.343184i
$918$		0			0
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	−0.965147	−	0.261708i	$-0.915714\pi$
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	0.255927	−	0.966696i	$-0.417619\pi$
$920$		0			0
$921$	42.0000	−	72.7461i	1.38395	−	2.39707i
$922$		0			0
$923$	7.50000	−	7.79423i	0.246866	−	0.256550i
$924$		0			0
$925$	1.50000	−	2.59808i	0.0493197	−	0.0854242i
$926$		0			0
$927$	−48.0000	−	83.1384i	−1.57653	−	2.73062i
$928$		0			0
$929$	26.5000	+	45.8993i	0.869437	+	1.50591i	0.862573	+	0.505932i	$0.168851\pi$
$929$	26.5000	+	45.8993i	0.869437	+	1.50591i	0.00686358	+	0.999976i	$0.497815\pi$
$930$		0			0
$931$	−2.00000			−0.0655474
$932$		0			0
$933$	−36.0000	+	62.3538i	−1.17859	+	2.04137i
$934$		0			0
$935$	21.0000			0.686773
$936$		0			0
$937$	50.0000			1.63343			0.816714	−	0.577042i	$-0.195793\pi$
$937$	50.0000			1.63343			0.816714	+	0.577042i	$0.195793\pi$
$938$		0			0
$939$	9.00000	−	15.5885i	0.293704	−	0.508710i
$940$		0			0
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$		0			0
$943$	−24.5000	−	42.4352i	−0.797830	−	1.38188i
$944$		0			0
$945$	13.5000	+	23.3827i	0.439155	+	0.760639i
$946$		0			0
$947$	−27.5000	+	47.6314i	−0.893630	+	1.54781i	−0.0581388	+	0.998309i	$0.518517\pi$
$947$	−27.5000	+	47.6314i	−0.893630	+	1.54781i	−0.835491	+	0.549504i	$0.814817\pi$
$948$		0			0
$949$	−14.0000	−	48.4974i	−0.454459	−	1.57429i
$950$		0			0
$951$	3.00000	−	5.19615i	0.0972817	−	0.168497i
$952$		0			0
$953$	15.5000	+	26.8468i	0.502094	+	0.869653i	0.999997	+	0.00241992i	$0.000770286\pi$
$953$	15.5000	+	26.8468i	0.502094	+	0.869653i	−0.497903	+	0.867233i	$0.665896\pi$
$954$		0			0
$955$	−1.50000	−	2.59808i	−0.0485389	−	0.0840718i
$956$		0			0
$957$	45.0000			1.45464
$958$		0			0
$959$	−4.50000	+	7.79423i	−0.145313	+	0.251689i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	18.0000			0.580042
$964$		0			0
$965$	7.50000	−	12.9904i	0.241434	−	0.418175i
$966$		0			0
$967$	48.0000			1.54358			0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000			1.54358			0.771788	+	0.635880i	$0.219363\pi$
$968$		0			0
$969$	−10.5000	−	18.1865i	−0.337309	−	0.584236i
$970$		0			0
$971$	−21.5000	−	37.2391i	−0.689968	−	1.19506i	−0.971848	−	0.235610i	$-0.924291\pi$
$971$	−21.5000	−	37.2391i	−0.689968	−	1.19506i	0.281880	−	0.959450i	$-0.409042\pi$
$972$		0			0
$973$	−19.5000	+	33.7750i	−0.625141	+	1.08278i
$974$		0			0
$975$	−10.5000	−	2.59808i	−0.336269	−	0.0832050i
$976$		0			0
$977$	1.50000	−	2.59808i	0.0479893	−	0.0831198i	−0.841033	−	0.540984i	$-0.818052\pi$
$977$	1.50000	−	2.59808i	0.0479893	−	0.0831198i	0.889022	+	0.457864i	$0.151385\pi$
$978$		0			0
$979$	10.5000	+	18.1865i	0.335581	+	0.581244i
$980$		0			0
$981$	42.0000	+	72.7461i	1.34096	+	2.32261i
$982$		0			0
$983$	−36.0000			−1.14822			−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000			−1.14822			−0.574111	+	0.818778i	$0.694652\pi$
$984$		0			0
$985$	11.5000	−	19.9186i	0.366420	−	0.634659i
$986$		0			0
$987$	72.0000			2.29179
$988$		0			0
$989$	63.0000			2.00328
$990$		0			0
$991$	−6.50000	+	11.2583i	−0.206479	+	0.357633i	−0.950603	−	0.310409i	$-0.899534\pi$
$991$	−6.50000	+	11.2583i	−0.206479	+	0.357633i	0.744124	+	0.668042i	$0.232867\pi$
$992$		0			0
$993$	−39.0000			−1.23763
$994$		0			0
$995$	4.50000	+	7.79423i	0.142660	+	0.247094i
$996$		0			0
$997$	−6.50000	−	11.2583i	−0.205857	−	0.356555i	0.744548	−	0.667568i	$-0.232665\pi$
$997$	−6.50000	−	11.2583i	−0.205857	−	0.356555i	−0.950405	+	0.311014i	$0.899332\pi$
$998$		0			0
$999$	13.5000	−	23.3827i	0.427121	−	0.739795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.q.b.321.1		2
4.3	odd	2		260.2.i.d.61.1	✓	2
12.11	even	2		2340.2.q.a.1621.1		2
13.3	even	3	inner	1040.2.q.b.81.1		2
20.3	even	4		1300.2.bb.e.1049.2		4
20.7	even	4		1300.2.bb.e.1049.1		4
20.19	odd	2		1300.2.i.a.1101.1		2
52.3	odd	6		260.2.i.d.81.1	yes	2
52.7	even	12		3380.2.f.a.3041.2		2
52.19	even	12		3380.2.f.a.3041.1		2
52.35	odd	6		3380.2.a.b.1.1		1
52.43	odd	6		3380.2.a.a.1.1		1
156.107	even	6		2340.2.q.a.2161.1		2
260.3	even	12		1300.2.bb.e.549.1		4
260.107	even	12		1300.2.bb.e.549.2		4
260.159	odd	6		1300.2.i.a.601.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.i.d.61.1	✓	2	4.3	odd	2
260.2.i.d.81.1	yes	2	52.3	odd	6
1040.2.q.b.81.1		2	13.3	even	3	inner
1040.2.q.b.321.1		2	1.1	even	1	trivial
1300.2.i.a.601.1		2	260.159	odd	6
1300.2.i.a.1101.1		2	20.19	odd	2
1300.2.bb.e.549.1		4	260.3	even	12
1300.2.bb.e.549.2		4	260.107	even	12
1300.2.bb.e.1049.1		4	20.7	even	4
1300.2.bb.e.1049.2		4	20.3	even	4
2340.2.q.a.1621.1		2	12.11	even	2
2340.2.q.a.2161.1		2	156.107	even	6
3380.2.a.a.1.1		1	52.43	odd	6
3380.2.a.b.1.1		1	52.35	odd	6
3380.2.f.a.3041.1		2	52.19	even	12
3380.2.f.a.3041.2		2	52.7	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +1.00000 q^{5} +(1.50000 + 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{3} +1.00000 q^{5} +(1.50000 + 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(1.50000 - 2.59808i) q^{11} +(1.00000 + 3.46410i) q^{13} +(-1.50000 + 2.59808i) q^{15} +(3.50000 + 6.06218i) q^{17} +(0.500000 + 0.866025i) q^{19} -9.00000 q^{21} +(-3.50000 + 6.06218i) q^{23} +1.00000 q^{25} +9.00000 q^{27} +(2.50000 - 4.33013i) q^{29} +4.00000 q^{31} +(4.50000 + 7.79423i) q^{33} +(1.50000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) q^{37} +(-10.5000 - 2.59808i) q^{39} +(-3.50000 + 6.06218i) q^{41} +(-4.50000 - 7.79423i) q^{43} +(-3.00000 - 5.19615i) q^{45} -8.00000 q^{47} +(-1.00000 + 1.73205i) q^{49} -21.0000 q^{51} -6.00000 q^{53} +(1.50000 - 2.59808i) q^{55} -3.00000 q^{57} +(2.50000 + 4.33013i) q^{59} +(2.50000 + 4.33013i) q^{61} +(9.00000 - 15.5885i) q^{63} +(1.00000 + 3.46410i) q^{65} +(6.50000 - 11.2583i) q^{67} +(-10.5000 - 18.1865i) q^{69} +(-1.50000 - 2.59808i) q^{71} -14.0000 q^{73} +(-1.50000 + 2.59808i) q^{75} +9.00000 q^{77} +8.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} -12.0000 q^{83} +(3.50000 + 6.06218i) q^{85} +(7.50000 + 12.9904i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(-7.50000 + 7.79423i) q^{91} +(-6.00000 + 10.3923i) q^{93} +(0.500000 + 0.866025i) q^{95} +(5.50000 + 9.52628i) q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 2 q^{5} + 3 q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + 2 * q^5 + 3 * q^7 - 6 * q^9	\( 2 q - 3 q^{3} + 2 q^{5} + 3 q^{7} - 6 q^{9} + 3 q^{11} + 2 q^{13} - 3 q^{15} + 7 q^{17} + q^{19} - 18 q^{21} - 7 q^{23} + 2 q^{25} + 18 q^{27} + 5 q^{29} + 8 q^{31} + 9 q^{33} + 3 q^{35} + 3 q^{37} - 21 q^{39} - 7 q^{41} - 9 q^{43} - 6 q^{45} - 16 q^{47} - 2 q^{49} - 42 q^{51} - 12 q^{53} + 3 q^{55} - 6 q^{57} + 5 q^{59} + 5 q^{61} + 18 q^{63} + 2 q^{65} + 13 q^{67} - 21 q^{69} - 3 q^{71} - 28 q^{73} - 3 q^{75} + 18 q^{77} + 16 q^{79} - 9 q^{81} - 24 q^{83} + 7 q^{85} + 15 q^{87} - 7 q^{89} - 15 q^{91} - 12 q^{93} + q^{95} + 11 q^{97} - 36 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 2 * q^5 + 3 * q^7 - 6 * q^9 + 3 * q^11 + 2 * q^13 - 3 * q^15 + 7 * q^17 + q^19 - 18 * q^21 - 7 * q^23 + 2 * q^25 + 18 * q^27 + 5 * q^29 + 8 * q^31 + 9 * q^33 + 3 * q^35 + 3 * q^37 - 21 * q^39 - 7 * q^41 - 9 * q^43 - 6 * q^45 - 16 * q^47 - 2 * q^49 - 42 * q^51 - 12 * q^53 + 3 * q^55 - 6 * q^57 + 5 * q^59 + 5 * q^61 + 18 * q^63 + 2 * q^65 + 13 * q^67 - 21 * q^69 - 3 * q^71 - 28 * q^73 - 3 * q^75 + 18 * q^77 + 16 * q^79 - 9 * q^81 - 24 * q^83 + 7 * q^85 + 15 * q^87 - 7 * q^89 - 15 * q^91 - 12 * q^93 + q^95 + 11 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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