LMFDB - Embedded newform 1040.2.df.b.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(49,1040)] 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("1040.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	1040.49
Dual form			1040.2.df.b.849.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{3} +(-2.18890 + 0.456850i) q^{5} +(0.866025 - 1.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(2.29129 - 1.32288i) q^{11} +(3.46410 - 1.00000i) q^{13} +(1.66722 - 1.49009i) q^{15} +(-3.96863 - 2.29129i) q^{17} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(-3.96863 + 2.29129i) q^{23} +(4.58258 - 2.00000i) q^{25} -5.00000i q^{27} +(2.29129 + 3.96863i) q^{29} +6.20520i q^{31} +(-1.32288 + 2.29129i) q^{33} +(-1.21037 + 3.67900i) q^{35} +(3.96863 + 6.87386i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(2.29129 - 1.32288i) q^{41} +(9.16478 + 5.29129i) q^{43} +(1.39761 - 4.24814i) q^{45} -1.82740 q^{47} +(2.00000 + 3.46410i) q^{49} +4.58258 q^{51} +7.58258i q^{53} +(-4.41105 + 3.94242i) q^{55} -1.73205 q^{57} +(12.0826 + 6.97588i) q^{59} +(0.708712 - 1.22753i) q^{61} +(1.73205 + 3.00000i) q^{63} +(-7.12573 + 3.77148i) q^{65} +(0.504525 + 0.873864i) q^{67} +(2.29129 - 3.96863i) q^{69} +(-6.08258 - 3.51178i) q^{71} +(-2.96863 + 4.02334i) q^{75} -4.58258i q^{77} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +6.01450 q^{83} +(9.73371 + 3.20233i) q^{85} +(-3.96863 - 2.29129i) q^{87} +(8.29129 - 4.78698i) q^{89} +(1.50000 - 6.06218i) q^{91} +(-3.10260 - 5.37386i) q^{93} +(-3.67900 - 1.21037i) q^{95} +(-5.70068 + 9.87386i) q^{97} +5.29150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{9} + 6 q^{15} + 12 q^{19} - 6 q^{35} - 20 q^{39} + 12 q^{45} + 16 q^{49} + 14 q^{55} + 60 q^{59} + 24 q^{61} - 24 q^{65} - 12 q^{71} + 8 q^{75} - 48 q^{79} - 4 q^{81} + 42 q^{85} + 48 q^{89}+ \cdots + 6 q^{95}+O(q^{100}) $ 8 * q - 8 * q^9 + 6 * q^15 + 12 * q^19 - 6 * q^35 - 20 * q^39 + 12 * q^45 + 16 * q^49 + 14 * q^55 + 60 * q^59 + 24 * q^61 - 24 * q^65 - 12 * q^71 + 8 * q^75 - 48 * q^79 - 4 * q^81 + 42 * q^85 + 48 * q^89 + 12 * q^91 + 6 * q^95

Character values

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

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i	−0.728714	−	0.684819i	$-0.759881\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i	0.228714	+	0.973494i	$0.426548\pi$
$4$		0			0
$5$	−2.18890	+	0.456850i	−0.978906	+	0.204310i
$5$	−2.18890	+	0.456850i	−0.978906	+	0.204310i
$6$		0			0
$7$	0.866025	−	1.50000i	0.327327	−	0.566947i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	0.866025	−	1.50000i	0.327327	−	0.566947i	0.981981	+	0.188982i	$0.0605189\pi$
$8$		0			0
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$		0			0
$11$	2.29129	−	1.32288i	0.690849	−	0.398862i	−0.113081	−	0.993586i	$-0.536072\pi$
$11$	2.29129	−	1.32288i	0.690849	−	0.398862i	0.803930	+	0.594724i	$0.202739\pi$
$12$		0			0
$13$	3.46410	−	1.00000i	0.960769	−	0.277350i
$13$	3.46410	−	1.00000i	0.960769	−	0.277350i
$14$		0			0
$15$	1.66722	−	1.49009i	0.430474	−	0.384741i
$16$		0			0
$17$	−3.96863	−	2.29129i	−0.962533	−	0.555719i	−0.0655816	−	0.997847i	$-0.520890\pi$
$17$	−3.96863	−	2.29129i	−0.962533	−	0.555719i	−0.896952	+	0.442128i	$0.854224\pi$
$18$		0			0
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$		0			0
$21$			1.73205i			0.377964i
$22$		0			0
$23$	−3.96863	+	2.29129i	−0.827516	+	0.477767i	−0.853001	−	0.521909i	$-0.825220\pi$
$23$	−3.96863	+	2.29129i	−0.827516	+	0.477767i	0.0254855	+	0.999675i	$0.491887\pi$
$24$		0			0
$25$	4.58258	−	2.00000i	0.916515	−	0.400000i
$26$		0			0
$27$		−	5.00000i		−	0.962250i
$28$		0			0
$29$	2.29129	+	3.96863i	0.425481	+	0.736956i	0.996465	−	0.0840058i	$-0.0267714\pi$
$29$	2.29129	+	3.96863i	0.425481	+	0.736956i	−0.570984	+	0.820961i	$0.693438\pi$
$30$		0			0
$31$			6.20520i			1.11449i	0.830349	+	0.557244i	$0.188141\pi$
$31$			6.20520i			1.11449i	−0.830349	+	0.557244i	$0.811859\pi$
$32$		0			0
$33$	−1.32288	+	2.29129i	−0.230283	+	0.398862i
$34$		0			0
$35$	−1.21037	+	3.67900i	−0.204590	+	0.621864i
$36$		0			0
$37$	3.96863	+	6.87386i	0.652438	+	1.13006i	0.982529	+	0.186107i	$0.0595872\pi$
$37$	3.96863	+	6.87386i	0.652438	+	1.13006i	−0.330091	+	0.943949i	$0.607080\pi$
$38$		0			0
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$		0			0
$41$	2.29129	−	1.32288i	0.357839	−	0.206598i	−0.310293	−	0.950641i	$-0.600427\pi$
$41$	2.29129	−	1.32288i	0.357839	−	0.206598i	0.668132	+	0.744042i	$0.267094\pi$
$42$		0			0
$43$	9.16478	+	5.29129i	1.39762	+	0.806914i	0.994142	−	0.108078i	$-0.0344695\pi$
$43$	9.16478	+	5.29129i	1.39762	+	0.806914i	0.403473	+	0.914991i	$0.367803\pi$
$44$		0			0
$45$	1.39761	−	4.24814i	0.208344	−	0.633275i
$46$		0			0
$47$	−1.82740			−0.266554			−0.133277	−	0.991079i	$-0.542550\pi$
$47$	−1.82740			−0.266554			−0.133277	+	0.991079i	$0.542550\pi$
$48$		0			0
$49$	2.00000	+	3.46410i	0.285714	+	0.494872i
$50$		0			0
$51$	4.58258			0.641689
$52$		0			0
$53$			7.58258i			1.04155i	0.853695	+	0.520773i	$0.174356\pi$
$53$			7.58258i			1.04155i	−0.853695	+	0.520773i	$0.825644\pi$
$54$		0			0
$55$	−4.41105	+	3.94242i	−0.594785	+	0.531596i
$56$		0			0
$57$	−1.73205			−0.229416
$58$		0			0
$59$	12.0826	+	6.97588i	1.57302	+	0.908182i	0.995796	+	0.0915940i	$0.0291962\pi$
$59$	12.0826	+	6.97588i	1.57302	+	0.908182i	0.577221	+	0.816588i	$0.304137\pi$
$60$		0			0
$61$	0.708712	−	1.22753i	0.0907413	−	0.157169i	−0.817082	−	0.576522i	$-0.804410\pi$
$61$	0.708712	−	1.22753i	0.0907413	−	0.157169i	0.907823	+	0.419353i	$0.137743\pi$
$62$		0			0
$63$	1.73205	+	3.00000i	0.218218	+	0.377964i
$64$		0			0
$65$	−7.12573	+	3.77148i	−0.883837	+	0.467794i
$66$		0			0
$67$	0.504525	+	0.873864i	0.0616376	+	0.106759i	0.895198	−	0.445670i	$-0.147034\pi$
$67$	0.504525	+	0.873864i	0.0616376	+	0.106759i	−0.833560	+	0.552429i	$0.813701\pi$
$68$		0			0
$69$	2.29129	−	3.96863i	0.275839	−	0.477767i
$70$		0			0
$71$	−6.08258	−	3.51178i	−0.721869	−	0.416771i	0.0935712	−	0.995613i	$-0.470172\pi$
$71$	−6.08258	−	3.51178i	−0.721869	−	0.416771i	−0.815440	+	0.578841i	$0.803505\pi$
$72$		0			0
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$		0			0
$75$	−2.96863	+	4.02334i	−0.342788	+	0.464575i
$76$		0			0
$77$		−	4.58258i		−	0.522233i
$78$		0			0
$79$	−6.00000			−0.675053			−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000			−0.675053			−0.337526	+	0.941316i	$0.609590\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	6.01450			0.660177			0.330089	−	0.943950i	$-0.392921\pi$
$83$	6.01450			0.660177			0.330089	+	0.943950i	$0.392921\pi$
$84$		0			0
$85$	9.73371	+	3.20233i	1.05577	+	0.347342i
$86$		0			0
$87$	−3.96863	−	2.29129i	−0.425481	−	0.245652i
$88$		0			0
$89$	8.29129	−	4.78698i	0.878875	−	0.507419i	0.00858752	−	0.999963i	$-0.497266\pi$
$89$	8.29129	−	4.78698i	0.878875	−	0.507419i	0.870287	+	0.492545i	$0.163933\pi$
$90$		0			0
$91$	1.50000	−	6.06218i	0.157243	−	0.635489i
$92$		0			0
$93$	−3.10260	−	5.37386i	−0.321725	−	0.557244i
$94$		0			0
$95$	−3.67900	−	1.21037i	−0.377457	−	0.124181i
$96$		0			0
$97$	−5.70068	+	9.87386i	−0.578816	+	1.00254i	0.416799	+	0.908999i	$0.363152\pi$
$97$	−5.70068	+	9.87386i	−0.578816	+	1.00254i	−0.995615	+	0.0935404i	$0.970182\pi$
$98$		0			0
$99$			5.29150i			0.531816i
$100$		0			0
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$		0			0
$103$		−	3.16515i		−	0.311872i	−0.987767	−	0.155936i	$-0.950161\pi$
$103$		−	3.16515i		−	0.311872i	0.987767	−	0.155936i	$-0.0498393\pi$
$104$		0			0
$105$	−0.791288	−	3.79129i	−0.0772218	−	0.369992i
$106$		0			0
$107$	−9.16478	+	5.29129i	−0.885993	+	0.511528i	−0.872630	−	0.488383i	$-0.837587\pi$
$107$	−9.16478	+	5.29129i	−0.885993	+	0.511528i	−0.0133631	+	0.999911i	$0.504254\pi$
$108$		0			0
$109$			13.1334i			1.25795i	0.777425	+	0.628976i	$0.216526\pi$
$109$			13.1334i			1.25795i	−0.777425	+	0.628976i	$0.783474\pi$
$110$		0			0
$111$	−6.87386	−	3.96863i	−0.652438	−	0.376685i
$112$		0			0
$113$	6.42368	+	3.70871i	0.604289	+	0.348886i	0.770727	−	0.637166i	$-0.219893\pi$
$113$	6.42368	+	3.70871i	0.604289	+	0.348886i	−0.166438	+	0.986052i	$0.553227\pi$
$114$		0			0
$115$	7.64016	−	6.82847i	0.712448	−	0.636758i
$116$		0			0
$117$	−1.73205	+	7.00000i	−0.160128	+	0.647150i
$118$		0			0
$119$	−6.87386	+	3.96863i	−0.630126	+	0.363803i
$120$		0			0
$121$	−2.00000	+	3.46410i	−0.181818	+	0.314918i
$122$		0			0
$123$	−1.32288	+	2.29129i	−0.119280	+	0.206598i
$124$		0			0
$125$	−9.11710	+	6.47135i	−0.815459	+	0.578815i
$126$		0			0
$127$	15.3700	−	8.87386i	1.36387	−	0.787428i	0.373729	−	0.927538i	$-0.378079\pi$
$127$	15.3700	−	8.87386i	1.36387	−	0.787428i	0.990136	+	0.140110i	$0.0447455\pi$
$128$		0			0
$129$	−10.5826			−0.931744
$130$		0			0
$131$	7.58258			0.662493			0.331246	−	0.943544i	$-0.392531\pi$
$131$	7.58258			0.662493			0.331246	+	0.943544i	$0.392531\pi$
$132$		0			0
$133$	2.59808	−	1.50000i	0.225282	−	0.130066i
$134$		0			0
$135$	2.28425	+	10.9445i	0.196597	+	0.941953i
$136$		0			0
$137$	5.24383	−	9.08258i	0.448010	−	0.775977i	−0.550246	−	0.835003i	$-0.685466\pi$
$137$	5.24383	−	9.08258i	0.448010	−	0.775977i	0.998256	+	0.0590258i	$0.0187994\pi$
$138$		0			0
$139$	10.8739	−	18.8341i	0.922309	−	1.59749i	0.126476	−	0.991970i	$-0.459633\pi$
$139$	10.8739	−	18.8341i	0.922309	−	1.59749i	0.795833	−	0.605517i	$-0.207033\pi$
$140$		0			0
$141$	1.58258	−	0.913701i	0.133277	−	0.0769475i
$142$		0			0
$143$	6.61438	−	6.87386i	0.553122	−	0.574821i
$144$		0			0
$145$	−6.82847	−	7.64016i	−0.567074	−	0.634480i
$146$		0			0
$147$	−3.46410	−	2.00000i	−0.285714	−	0.164957i
$148$		0			0
$149$	−14.4564	−	8.34643i	−1.18432	−	0.683766i	−0.227308	−	0.973823i	$-0.572992\pi$
$149$	−14.4564	−	8.34643i	−1.18432	−	0.683766i	−0.957009	+	0.290057i	$0.906326\pi$
$150$		0			0
$151$		−	9.66930i		−	0.786877i	−0.919351	−	0.393438i	$-0.871285\pi$
$151$		−	9.66930i		−	0.786877i	0.919351	−	0.393438i	$-0.128715\pi$
$152$		0			0
$153$	7.93725	−	4.58258i	0.641689	−	0.370479i
$154$		0			0
$155$	−2.83485	−	13.5826i	−0.227701	−	1.09098i
$156$		0			0
$157$		−	9.16515i		−	0.731459i	−0.930721	−	0.365729i	$-0.880820\pi$
$157$		−	9.16515i		−	0.731459i	0.930721	−	0.365729i	$-0.119180\pi$
$158$		0			0
$159$	−3.79129	−	6.56670i	−0.300669	−	0.520773i
$160$		0			0
$161$			7.93725i			0.625543i
$162$		0			0
$163$	−10.5353	+	18.2477i	−0.825191	+	1.42927i	0.0765827	+	0.997063i	$0.475599\pi$
$163$	−10.5353	+	18.2477i	−0.825191	+	1.42927i	−0.901773	+	0.432209i	$0.857734\pi$
$164$		0			0
$165$	1.84887	−	5.61976i	0.143934	−	0.437498i
$166$		0			0
$167$	4.78698	+	8.29129i	0.370427	+	0.641599i	0.989631	−	0.143631i	$-0.0458779\pi$
$167$	4.78698	+	8.29129i	0.370427	+	0.641599i	−0.619204	+	0.785230i	$0.712545\pi$
$168$		0			0
$169$	11.0000	−	6.92820i	0.846154	−	0.532939i
$170$		0			0
$171$	−3.00000	+	1.73205i	−0.229416	+	0.132453i
$172$		0			0
$173$	14.3609	+	8.29129i	1.09184	+	0.630375i	0.934066	−	0.357100i	$-0.116234\pi$
$173$	14.3609	+	8.29129i	1.09184	+	0.630375i	0.157775	+	0.987475i	$0.449568\pi$
$174$		0			0
$175$	0.968627	−	8.60591i	0.0732213	−	0.650546i
$176$		0			0
$177$	−13.9518			−1.04868
$178$		0			0
$179$	−9.08258	−	15.7315i	−0.678864	−	1.17583i	−0.975323	−	0.220781i	$-0.929139\pi$
$179$	−9.08258	−	15.7315i	−0.678864	−	1.17583i	0.296460	−	0.955045i	$-0.404194\pi$
$180$		0			0
$181$	8.74773			0.650213			0.325107	−	0.945677i	$-0.394600\pi$
$181$	8.74773			0.650213			0.325107	+	0.945677i	$0.394600\pi$
$182$		0			0
$183$			1.41742i			0.104779i
$184$		0			0
$185$	−11.8273	−	13.2331i	−0.869557	−	0.972920i
$186$		0			0
$187$	−12.1244			−0.886621
$188$		0			0
$189$	−7.50000	−	4.33013i	−0.545545	−	0.314970i
$190$		0			0
$191$	−8.29129	+	14.3609i	−0.599937	+	1.03912i	0.392893	+	0.919584i	$0.371474\pi$
$191$	−8.29129	+	14.3609i	−0.599937	+	1.03912i	−0.992830	+	0.119536i	$0.961859\pi$
$192$		0			0
$193$	7.43273	+	12.8739i	0.535020	+	0.926681i	0.999162	+	0.0409206i	$0.0130291\pi$
$193$	7.43273	+	12.8739i	0.535020	+	0.926681i	−0.464143	+	0.885760i	$0.653638\pi$
$194$		0			0
$195$	4.28532	−	6.82906i	0.306878	−	0.489039i
$196$		0			0
$197$	−7.33738	−	12.7087i	−0.522767	−	0.905458i	−0.999649	−	0.0264912i	$-0.991567\pi$
$197$	−7.33738	−	12.7087i	−0.522767	−	0.905458i	0.476882	−	0.878967i	$-0.341767\pi$
$198$		0			0
$199$	−5.29129	+	9.16478i	−0.375089	+	0.649674i	−0.990340	−	0.138657i	$-0.955721\pi$
$199$	−5.29129	+	9.16478i	−0.375089	+	0.649674i	0.615251	+	0.788331i	$0.289055\pi$
$200$		0			0
$201$	−0.873864	−	0.504525i	−0.0616376	−	0.0355865i
$202$		0			0
$203$	7.93725			0.557086
$204$		0			0
$205$	−4.41105	+	3.94242i	−0.308081	+	0.275351i
$206$		0			0
$207$		−	9.16515i		−	0.637022i
$208$		0			0
$209$	4.58258			0.316983
$210$		0			0
$211$	−0.0825757	−	0.143025i	−0.00568475	−	0.00984627i	0.863169	−	0.504915i	$-0.168476\pi$
$211$	−0.0825757	−	0.143025i	−0.00568475	−	0.00984627i	−0.868854	+	0.495069i	$0.835143\pi$
$212$		0			0
$213$	7.02355			0.481246
$214$		0			0
$215$	−22.4781	−	7.39517i	−1.53300	−	0.504347i
$216$		0			0
$217$	9.30780	+	5.37386i	0.631855	+	0.364802i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−16.0390	−	3.96863i	−1.07890	−	0.266959i
$222$		0			0
$223$	4.33013	+	7.50000i	0.289967	+	0.502237i	0.973801	−	0.227400i	$-0.0730224\pi$
$223$	4.33013	+	7.50000i	0.289967	+	0.502237i	−0.683835	+	0.729637i	$0.739689\pi$
$224$		0			0
$225$	−1.11847	+	9.93725i	−0.0745649	+	0.662484i
$226$		0			0
$227$	−0.409175	+	0.708712i	−0.0271579	+	0.0470389i	−0.879285	−	0.476296i	$-0.841979\pi$
$227$	−0.409175	+	0.708712i	−0.0271579	+	0.0470389i	0.852127	+	0.523335i	$0.175312\pi$
$228$		0			0
$229$		−	26.2668i		−	1.73576i	−0.496774	−	0.867880i	$-0.665482\pi$
$229$		−	26.2668i		−	1.73576i	0.496774	−	0.867880i	$-0.334518\pi$
$230$		0			0
$231$	2.29129	+	3.96863i	0.150756	+	0.261116i
$232$		0			0
$233$			2.83485i			0.185717i	0.995679	+	0.0928586i	$0.0296004\pi$
$233$			2.83485i			0.185717i	−0.995679	+	0.0928586i	$0.970400\pi$
$234$		0			0
$235$	4.00000	−	0.834849i	0.260931	−	0.0544595i
$236$		0			0
$237$	5.19615	−	3.00000i	0.337526	−	0.194871i
$238$		0			0
$239$			0.190700i			0.0123354i	0.999981	+	0.00616769i	$0.00196325\pi$
$239$			0.190700i			0.0123354i	−0.999981	+	0.00616769i	$0.998037\pi$
$240$		0			0
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	0.450910	−	0.892570i	$-0.351100\pi$
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	−0.547533	+	0.836784i	$0.684433\pi$
$242$		0			0
$243$	13.8564	+	8.00000i	0.888889	+	0.513200i
$244$		0			0
$245$	−5.96038	−	6.66888i	−0.380795	−	0.426059i
$246$		0			0
$247$	6.06218	+	1.50000i	0.385727	+	0.0954427i
$248$		0			0
$249$	−5.20871	+	3.00725i	−0.330089	+	0.190577i
$250$		0			0
$251$	−0.0825757	+	0.143025i	−0.00521213	+	0.00902768i	−0.868620	−	0.495479i	$-0.834992\pi$
$251$	−0.0825757	+	0.143025i	−0.00521213	+	0.00902768i	0.863408	+	0.504507i	$0.168326\pi$
$252$		0			0
$253$	−6.06218	+	10.5000i	−0.381126	+	0.660129i
$254$		0			0
$255$	−10.0308	+	2.09355i	−0.628153	+	0.131103i
$256$		0			0
$257$	15.7315	−	9.08258i	0.981303	−	0.566556i	0.0786397	−	0.996903i	$-0.474942\pi$
$257$	15.7315	−	9.08258i	0.981303	−	0.566556i	0.902663	+	0.430348i	$0.141609\pi$
$258$		0			0
$259$	13.7477			0.854242
$260$		0			0
$261$	−9.16515			−0.567309
$262$		0			0
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	−0.720672	−	0.693276i	$-0.756167\pi$
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	0.240059	+	0.970758i	$0.422833\pi$
$264$		0			0
$265$	−3.46410	−	16.5975i	−0.212798	−	1.01958i
$266$		0			0
$267$	−4.78698	+	8.29129i	−0.292958	+	0.507419i
$268$		0			0
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	−0.998816	−	0.0486418i	$-0.984511\pi$
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	0.541533	+	0.840679i	$0.317844\pi$
$270$		0			0
$271$	−7.50000	+	4.33013i	−0.455593	+	0.263036i	−0.710189	−	0.704011i	$-0.751391\pi$
$271$	−7.50000	+	4.33013i	−0.455593	+	0.263036i	0.254597	+	0.967047i	$0.418057\pi$
$272$		0			0
$273$	1.73205	+	6.00000i	0.104828	+	0.363137i
$274$		0			0
$275$	7.85425	−	10.6448i	0.473629	−	0.641903i
$276$		0			0
$277$	−6.42368	−	3.70871i	−0.385961	−	0.222835i	0.294447	−	0.955668i	$-0.404864\pi$
$277$	−6.42368	−	3.70871i	−0.385961	−	0.222835i	−0.680409	+	0.732833i	$0.738198\pi$
$278$		0			0
$279$	−10.7477	−	6.20520i	−0.643450	−	0.371496i
$280$		0			0
$281$		−	3.65480i		−	0.218027i	−0.994040	−	0.109014i	$-0.965231\pi$
$281$		−	3.65480i		−	0.218027i	0.994040	−	0.109014i	$-0.0347692\pi$
$282$		0			0
$283$	24.0302	−	13.8739i	1.42845	−	0.824716i	0.431451	−	0.902136i	$-0.358002\pi$
$283$	24.0302	−	13.8739i	1.42845	−	0.824716i	0.996998	+	0.0774209i	$0.0246685\pi$
$284$		0			0
$285$	3.79129	−	0.791288i	0.224577	−	0.0468718i
$286$		0			0
$287$		−	4.58258i		−	0.270501i
$288$		0			0
$289$	2.00000	+	3.46410i	0.117647	+	0.203771i
$290$		0			0
$291$		−	11.4014i		−	0.668359i
$292$		0			0
$293$	−9.06943	+	15.7087i	−0.529842	+	0.917713i	0.469552	+	0.882905i	$0.344415\pi$
$293$	−9.06943	+	15.7087i	−0.529842	+	0.917713i	−0.999394	+	0.0348081i	$0.988918\pi$
$294$		0			0
$295$	−29.6345	−	9.74958i	−1.72539	−	0.567642i
$296$		0			0
$297$	−6.61438	−	11.4564i	−0.383805	−	0.664770i
$298$		0			0
$299$	−11.4564	+	11.9059i	−0.662543	+	0.688535i
$300$		0			0
$301$	15.8739	−	9.16478i	0.914954	−	0.528249i
$302$		0			0
$303$	7.79423	+	4.50000i	0.447767	+	0.258518i
$304$		0			0
$305$	−0.990505	+	3.01071i	−0.0567162	+	0.172393i
$306$		0			0
$307$	−24.2487			−1.38395			−0.691974	−	0.721923i	$-0.743259\pi$
$307$	−24.2487			−1.38395			−0.691974	+	0.721923i	$0.743259\pi$
$308$		0			0
$309$	1.58258	+	2.74110i	0.0900296	+	0.155936i
$310$		0			0
$311$	−7.58258			−0.429968			−0.214984	−	0.976618i	$-0.568970\pi$
$311$	−7.58258			−0.429968			−0.214984	+	0.976618i	$0.568970\pi$
$312$		0			0
$313$		−	3.25227i		−	0.183829i	−0.995767	−	0.0919147i	$-0.970701\pi$
$313$		−	3.25227i		−	0.183829i	0.995767	−	0.0919147i	$-0.0292987\pi$
$314$		0			0
$315$	−5.16184	−	5.77542i	−0.290837	−	0.325408i
$316$		0			0
$317$	−0.190700			−0.0107108			−0.00535540	−	0.999986i	$-0.501705\pi$
$317$	−0.190700			−0.0107108			−0.00535540	+	0.999986i	$0.501705\pi$
$318$		0			0
$319$	10.5000	+	6.06218i	0.587887	+	0.339417i
$320$		0			0
$321$	5.29129	−	9.16478i	0.295331	−	0.511528i
$322$		0			0
$323$	−3.96863	−	6.87386i	−0.220820	−	0.382472i
$324$		0			0
$325$	13.8745	−	11.5108i	0.769619	−	0.638503i
$326$		0			0
$327$	−6.56670	−	11.3739i	−0.363140	−	0.628976i
$328$		0			0
$329$	−1.58258	+	2.74110i	−0.0872502	+	0.151122i
$330$		0			0
$331$	3.87386	+	2.23658i	0.212927	+	0.122933i	0.602671	−	0.797990i	$-0.294103\pi$
$331$	3.87386	+	2.23658i	0.212927	+	0.122933i	−0.389744	+	0.920923i	$0.627437\pi$
$332$		0			0
$333$	−15.8745			−0.869918
$334$		0			0
$335$	−1.50358	−	1.68231i	−0.0821494	−	0.0919143i
$336$		0			0
$337$		−	30.7477i		−	1.67494i	−0.546487	−	0.837468i	$-0.684035\pi$
$337$		−	30.7477i		−	1.67494i	0.546487	−	0.837468i	$-0.315965\pi$
$338$		0			0
$339$	−7.41742			−0.402859
$340$		0			0
$341$	8.20871	+	14.2179i	0.444527	+	0.769943i
$342$		0			0
$343$	19.0526			1.02874
$344$		0			0
$345$	−3.20233	+	9.73371i	−0.172408	+	0.524045i
$346$		0			0
$347$	18.4726	+	10.6652i	0.991660	+	0.572535i	0.905770	−	0.423769i	$-0.139293\pi$
$347$	18.4726	+	10.6652i	0.991660	+	0.572535i	0.0858901	+	0.996305i	$0.472627\pi$
$348$		0			0
$349$	2.12614	−	1.22753i	0.113809	−	0.0657079i	−0.442015	−	0.897008i	$-0.645736\pi$
$349$	2.12614	−	1.22753i	0.113809	−	0.0657079i	0.555824	+	0.831300i	$0.312403\pi$
$350$		0			0
$351$	−5.00000	−	17.3205i	−0.266880	−	0.924500i
$352$		0			0
$353$	3.41643	+	5.91742i	0.181838	+	0.314953i	0.942506	−	0.334188i	$-0.108462\pi$
$353$	3.41643	+	5.91742i	0.181838	+	0.314953i	−0.760668	+	0.649141i	$0.775129\pi$
$354$		0			0
$355$	14.9185	+	4.90811i	0.791792	+	0.260495i
$356$		0			0
$357$	3.96863	−	6.87386i	0.210042	−	0.363803i
$358$		0			0
$359$		−	19.5293i		−	1.03072i	−0.856975	−	0.515359i	$-0.827659\pi$
$359$		−	19.5293i		−	1.03072i	0.856975	−	0.515359i	$-0.172341\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$		0			0
$363$		−	4.00000i		−	0.209946i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−1.51358	+	0.873864i	−0.0790080	+	0.0456153i	−0.538984	−	0.842316i	$-0.681192\pi$
$367$	−1.51358	+	0.873864i	−0.0790080	+	0.0456153i	0.459976	+	0.887932i	$0.347858\pi$
$368$		0			0
$369$			5.29150i			0.275465i
$370$		0			0
$371$	11.3739	+	6.56670i	0.590502	+	0.340926i
$372$		0			0
$373$	11.2583	+	6.50000i	0.582934	+	0.336557i	0.762299	−	0.647225i	$-0.224071\pi$
$373$	11.2583	+	6.50000i	0.582934	+	0.336557i	−0.179364	+	0.983783i	$0.557404\pi$
$374$		0			0
$375$	4.65997	−	10.1629i	0.240640	−	0.524810i
$376$		0			0
$377$	11.9059	+	11.4564i	0.613184	+	0.590037i
$378$		0			0
$379$	9.24773	−	5.33918i	0.475024	−	0.274255i	−0.243317	−	0.969947i	$-0.578235\pi$
$379$	9.24773	−	5.33918i	0.475024	−	0.274255i	0.718340	+	0.695692i	$0.244902\pi$
$380$		0			0
$381$	−8.87386	+	15.3700i	−0.454622	+	0.787428i
$382$		0			0
$383$	−11.8105	+	20.4564i	−0.603490	+	1.04528i	0.388798	+	0.921323i	$0.372890\pi$
$383$	−11.8105	+	20.4564i	−0.603490	+	1.04528i	−0.992288	+	0.123952i	$0.960443\pi$
$384$		0			0
$385$	2.09355	+	10.0308i	0.106697	+	0.511217i
$386$		0			0
$387$	−18.3296	+	10.5826i	−0.931744	+	0.537943i
$388$		0			0
$389$	3.16515			0.160480			0.0802398	−	0.996776i	$-0.474431\pi$
$389$	3.16515			0.160480			0.0802398	+	0.996776i	$0.474431\pi$
$390$		0			0
$391$	21.0000			1.06202
$392$		0			0
$393$	−6.56670	+	3.79129i	−0.331246	+	0.191245i
$394$		0			0
$395$	13.1334	−	2.74110i	0.660813	−	0.137920i
$396$		0			0
$397$	−10.1738	+	17.6216i	−0.510610	+	0.884402i	0.489315	+	0.872107i	$0.337247\pi$
$397$	−10.1738	+	17.6216i	−0.510610	+	0.884402i	−0.999924	+	0.0122949i	$0.996086\pi$
$398$		0			0
$399$	−1.50000	+	2.59808i	−0.0750939	+	0.130066i
$400$		0			0
$401$	−25.8303	+	14.9131i	−1.28990	+	0.744726i	−0.978637	−	0.205596i	$-0.934087\pi$
$401$	−25.8303	+	14.9131i	−1.28990	+	0.744726i	−0.311267	+	0.950323i	$0.600753\pi$
$402$		0			0
$403$	6.20520	+	21.4955i	0.309103	+	1.07076i
$404$		0			0
$405$	1.49009	+	1.66722i	0.0740434	+	0.0828448i
$406$		0			0
$407$	18.1865	+	10.5000i	0.901473	+	0.520466i
$408$		0			0
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	0.673830	−	0.738886i	$-0.264648\pi$
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	−0.302979	+	0.952997i	$0.597981\pi$
$410$		0			0
$411$			10.4877i			0.517318i
$412$		0			0
$413$	20.9276	−	12.0826i	1.02978	−	0.594545i
$414$		0			0
$415$	−13.1652	+	2.74773i	−0.646252	+	0.134881i
$416$		0			0
$417$			21.7477i			1.06499i
$418$		0			0
$419$	2.91742	+	5.05313i	0.142526	+	0.246861i	0.928447	−	0.371465i	$-0.121144\pi$
$419$	2.91742	+	5.05313i	0.142526	+	0.246861i	−0.785922	+	0.618326i	$0.787811\pi$
$420$		0			0
$421$		−	5.48220i		−	0.267186i	−0.991036	−	0.133593i	$-0.957348\pi$
$421$		−	5.48220i		−	0.267186i	0.991036	−	0.133593i	$-0.0426515\pi$
$422$		0			0
$423$	1.82740	−	3.16515i	0.0888513	−	0.153895i
$424$		0			0
$425$	−22.7691	−	2.56275i	−1.10446	−	0.124311i
$426$		0			0
$427$	−1.22753	−	2.12614i	−0.0594041	−	0.102891i
$428$		0			0
$429$	−2.29129	+	9.26013i	−0.110624	+	0.447083i
$430$		0			0
$431$	−7.33485	+	4.23478i	−0.353307	+	0.203982i	−0.666141	−	0.745826i	$-0.732055\pi$
$431$	−7.33485	+	4.23478i	−0.353307	+	0.203982i	0.312834	+	0.949808i	$0.398722\pi$
$432$		0			0
$433$	−8.44178	−	4.87386i	−0.405686	−	0.234223i	0.283248	−	0.959047i	$-0.408588\pi$
$433$	−8.44178	−	4.87386i	−0.405686	−	0.234223i	−0.688934	+	0.724824i	$0.741921\pi$
$434$		0			0
$435$	9.73371	+	3.20233i	0.466696	+	0.153540i
$436$		0			0
$437$	−7.93725			−0.379690
$438$		0			0
$439$	7.24773	+	12.5534i	0.345915	+	0.599143i	0.985520	−	0.169562i	$-0.0542352\pi$
$439$	7.24773	+	12.5534i	0.345915	+	0.599143i	−0.639604	+	0.768704i	$0.720902\pi$
$440$		0			0
$441$	−8.00000			−0.380952
$442$		0			0
$443$		−	19.9129i		−	0.946089i	−0.881038	−	0.473045i	$-0.843155\pi$
$443$		−	19.9129i		−	0.946089i	0.881038	−	0.473045i	$-0.156845\pi$
$444$		0			0
$445$	−15.9619	+	14.2661i	−0.756666	+	0.676278i
$446$		0			0
$447$	16.6929			0.789545
$448$		0			0
$449$	9.54356	+	5.50998i	0.450388	+	0.260032i	0.707994	−	0.706218i	$-0.249600\pi$
$449$	9.54356	+	5.50998i	0.450388	+	0.260032i	−0.257606	+	0.966250i	$0.582934\pi$
$450$		0			0
$451$	3.50000	−	6.06218i	0.164809	−	0.285457i
$452$		0			0
$453$	4.83465	+	8.37386i	0.227152	+	0.393438i
$454$		0			0
$455$	−0.513844	+	13.9548i	−0.0240894	+	0.654210i
$456$		0			0
$457$	0.866025	+	1.50000i	0.0405110	+	0.0701670i	0.885570	−	0.464506i	$-0.153768\pi$
$457$	0.866025	+	1.50000i	0.0405110	+	0.0701670i	−0.845059	+	0.534673i	$0.820435\pi$
$458$		0			0
$459$	−11.4564	+	19.8431i	−0.534741	+	0.926198i
$460$		0			0
$461$	31.0390	+	17.9204i	1.44563	+	0.834635i	0.998217	−	0.0596914i	$-0.0190117\pi$
$461$	31.0390	+	17.9204i	1.44563	+	0.834635i	0.447414	+	0.894327i	$0.352345\pi$
$462$		0			0
$463$	−39.4002			−1.83108			−0.915542	−	0.402223i	$-0.868238\pi$
$463$	−39.4002			−1.83108			−0.915542	+	0.402223i	$0.868238\pi$
$464$		0			0
$465$	9.24634	+	10.3454i	0.428789	+	0.479758i
$466$		0			0
$467$		−	24.3303i		−	1.12587i	−0.826500	−	0.562936i	$-0.809672\pi$
$467$		−	24.3303i		−	1.12587i	0.826500	−	0.562936i	$-0.190328\pi$
$468$		0			0
$469$	1.74773			0.0807025
$470$		0			0
$471$	4.58258	+	7.93725i	0.211154	+	0.365729i
$472$		0			0
$473$	27.9989			1.28739
$474$		0			0
$475$	8.60591	+	0.968627i	0.394866	+	0.0444437i
$476$		0			0
$477$	−13.1334	−	7.58258i	−0.601337	−	0.347182i
$478$		0			0
$479$	−4.03901	+	2.33193i	−0.184547	+	0.106548i	−0.589427	−	0.807821i	$-0.700647\pi$
$479$	−4.03901	+	2.33193i	−0.184547	+	0.106548i	0.404880	+	0.914370i	$0.367313\pi$
$480$		0			0
$481$	20.6216	+	19.8431i	0.940264	+	0.904769i
$482$		0			0
$483$	−3.96863	−	6.87386i	−0.180579	−	0.312772i
$484$		0			0
$485$	7.96734	−	24.2173i	0.361778	−	1.09965i
$486$		0			0
$487$	−5.33918	+	9.24773i	−0.241941	+	0.419055i	−0.961267	−	0.275618i	$-0.911117\pi$
$487$	−5.33918	+	9.24773i	−0.241941	+	0.419055i	0.719326	+	0.694673i	$0.244451\pi$
$488$		0			0
$489$		−	21.0707i		−	0.952848i
$490$		0			0
$491$	9.70871	+	16.8160i	0.438148	+	0.758895i	0.997547	−	0.0700041i	$-0.0223012\pi$
$491$	9.70871	+	16.8160i	0.438148	+	0.758895i	−0.559399	+	0.828899i	$0.688968\pi$
$492$		0			0
$493$		−	21.0000i		−	0.945792i
$494$		0			0
$495$	−2.41742	−	11.5826i	−0.108655	−	0.520598i
$496$		0			0
$497$	−10.5353	+	6.08258i	−0.472574	+	0.272841i
$498$		0			0
$499$			0.723000i			0.0323659i	0.999869	+	0.0161830i	$0.00515142\pi$
$499$			0.723000i			0.0323659i	−0.999869	+	0.0161830i	$0.994849\pi$
$500$		0			0
$501$	−8.29129	−	4.78698i	−0.370427	−	0.213866i
$502$		0			0
$503$	0.143025	+	0.0825757i	0.00637718	+	0.00368187i	0.503185	−	0.864179i	$-0.332161\pi$
$503$	0.143025	+	0.0825757i	0.00637718	+	0.00368187i	−0.496808	+	0.867860i	$0.665495\pi$
$504$		0			0
$505$	13.4109	+	15.0050i	0.596775	+	0.667712i
$506$		0			0
$507$	−6.06218	+	11.5000i	−0.269231	+	0.510733i
$508$		0			0
$509$	−7.33485	+	4.23478i	−0.325111	+	0.187703i	−0.653669	−	0.756781i	$-0.726771\pi$
$509$	−7.33485	+	4.23478i	−0.325111	+	0.187703i	0.328557	+	0.944484i	$0.393438\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	4.33013	−	7.50000i	0.191180	−	0.331133i
$514$		0			0
$515$	1.44600	+	6.92820i	0.0637184	+	0.305293i
$516$		0			0
$517$	−4.18710	+	2.41742i	−0.184149	+	0.106318i
$518$		0			0
$519$	−16.5826			−0.727894
$520$		0			0
$521$	27.4955			1.20460			0.602299	−	0.798271i	$-0.294252\pi$
$521$	27.4955			1.20460			0.602299	+	0.798271i	$0.294252\pi$
$522$		0			0
$523$	−0.143025	+	0.0825757i	−0.00625406	+	0.00361078i	−0.503124	−	0.864214i	$-0.667816\pi$
$523$	−0.143025	+	0.0825757i	−0.00625406	+	0.00361078i	0.496870	+	0.867825i	$0.334483\pi$
$524$		0			0
$525$	3.46410	+	7.93725i	0.151186	+	0.346410i
$526$		0			0
$527$	14.2179	−	24.6261i	0.619342	−	1.07273i
$528$		0			0
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$		0			0
$531$	−24.1652	+	13.9518i	−1.04868	+	0.605455i
$532$		0			0
$533$	6.61438	−	6.87386i	0.286501	−	0.297740i
$534$		0			0
$535$	17.6435	−	15.7690i	0.762794	−	0.681755i
$536$		0			0
$537$	15.7315	+	9.08258i	0.678864	+	0.391942i
$538$		0			0
$539$	9.16515	+	5.29150i	0.394771	+	0.227921i
$540$		0			0
$541$			10.3923i			0.446800i	0.974727	+	0.223400i	$0.0717156\pi$
$541$			10.3923i			0.446800i	−0.974727	+	0.223400i	$0.928284\pi$
$542$		0			0
$543$	−7.57575	+	4.37386i	−0.325107	+	0.187700i
$544$		0			0
$545$	−6.00000	−	28.7477i	−0.257012	−	1.23142i
$546$		0			0
$547$			28.7477i			1.22916i	0.788853	+	0.614582i	$0.210675\pi$
$547$			28.7477i			1.22916i	−0.788853	+	0.614582i	$0.789325\pi$
$548$		0			0
$549$	1.41742	+	2.45505i	0.0604942	+	0.104779i
$550$		0			0
$551$			7.93725i			0.338138i
$552$		0			0
$553$	−5.19615	+	9.00000i	−0.220963	+	0.382719i
$554$		0			0
$555$	16.8593	+	5.54661i	0.715636	+	0.235440i
$556$		0			0
$557$	3.87328	+	6.70871i	0.164116	+	0.284257i	0.936341	−	0.351092i	$-0.114190\pi$
$557$	3.87328	+	6.70871i	0.164116	+	0.284257i	−0.772225	+	0.635349i	$0.780856\pi$
$558$		0			0
$559$	37.0390	+	9.16478i	1.56658	+	0.387629i
$560$		0			0
$561$	10.5000	−	6.06218i	0.443310	−	0.255945i
$562$		0			0
$563$	−7.79423	−	4.50000i	−0.328488	−	0.189652i	0.326682	−	0.945134i	$-0.394069\pi$
$563$	−7.79423	−	4.50000i	−0.328488	−	0.189652i	−0.655169	+	0.755482i	$0.727403\pi$
$564$		0			0
$565$	−15.7551	−	5.18335i	−0.662823	−	0.218065i
$566$		0			0
$567$	−1.73205			−0.0727393
$568$		0			0
$569$	3.87386	+	6.70973i	0.162401	+	0.281286i	0.935729	−	0.352719i	$-0.114743\pi$
$569$	3.87386	+	6.70973i	0.162401	+	0.281286i	−0.773328	+	0.634006i	$0.781410\pi$
$570$		0			0
$571$	35.0780			1.46797			0.733985	−	0.679166i	$-0.237658\pi$
$571$	35.0780			1.46797			0.733985	+	0.679166i	$0.237658\pi$
$572$		0			0
$573$		−	16.5826i		−	0.692747i
$574$		0			0
$575$	−13.6040	+	18.4373i	−0.567324	+	0.768887i
$576$		0			0
$577$	−6.92820			−0.288425			−0.144212	−	0.989547i	$-0.546065\pi$
$577$	−6.92820			−0.288425			−0.144212	+	0.989547i	$0.546065\pi$
$578$		0			0
$579$	−12.8739	−	7.43273i	−0.535020	−	0.308894i
$580$		0			0
$581$	5.20871	−	9.02175i	0.216094	−	0.374285i
$582$		0			0
$583$	10.0308	+	17.3739i	0.415433	+	0.719552i
$584$		0			0
$585$	0.593336	−	16.1136i	0.0245314	−	0.666215i
$586$		0			0
$587$	−19.7478	−	34.2042i	−0.815078	−	1.41176i	−0.909272	−	0.416203i	$-0.863361\pi$
$587$	−19.7478	−	34.2042i	−0.815078	−	1.41176i	0.0941934	−	0.995554i	$-0.469973\pi$
$588$		0			0
$589$	−5.37386	+	9.30780i	−0.221426	+	0.383521i
$590$		0			0
$591$	12.7087	+	7.33738i	0.522767	+	0.301819i
$592$		0			0
$593$	−21.1660			−0.869184			−0.434592	−	0.900627i	$-0.643107\pi$
$593$	−21.1660			−0.869184			−0.434592	+	0.900627i	$0.643107\pi$
$594$		0			0
$595$	13.2331	−	11.8273i	0.542506	−	0.484870i
$596$		0			0
$597$		−	10.5826i		−	0.433116i
$598$		0			0
$599$	15.4955			0.633127			0.316564	−	0.948571i	$-0.397471\pi$
$599$	15.4955			0.633127			0.316564	+	0.948571i	$0.397471\pi$
$600$		0			0
$601$	−8.45644	−	14.6470i	−0.344945	−	0.597463i	0.640398	−	0.768043i	$-0.278769\pi$
$601$	−8.45644	−	14.6470i	−0.344945	−	0.597463i	−0.985344	+	0.170580i	$0.945436\pi$
$602$		0			0
$603$	−2.01810			−0.0821834
$604$		0			0
$605$	2.79523	−	8.49628i	0.113642	−	0.345423i
$606$		0			0
$607$	−6.70973	−	3.87386i	−0.272339	−	0.157235i	0.357611	−	0.933871i	$-0.383591\pi$
$607$	−6.70973	−	3.87386i	−0.272339	−	0.157235i	−0.629950	+	0.776635i	$0.716925\pi$
$608$		0			0
$609$	−6.87386	+	3.96863i	−0.278543	+	0.160817i
$610$		0			0
$611$	−6.33030	+	1.82740i	−0.256097	+	0.0739287i
$612$		0			0
$613$	−2.95958	−	5.12614i	−0.119536	−	0.207043i	0.800048	−	0.599936i	$-0.204807\pi$
$613$	−2.95958	−	5.12614i	−0.119536	−	0.207043i	−0.919584	+	0.392894i	$0.871474\pi$
$614$		0			0
$615$	1.84887	−	5.61976i	0.0745536	−	0.226611i
$616$		0			0
$617$	−6.97588	+	12.0826i	−0.280838	+	0.486426i	−0.971591	−	0.236664i	$-0.923946\pi$
$617$	−6.97588	+	12.0826i	−0.280838	+	0.486426i	0.690753	+	0.723091i	$0.257279\pi$
$618$		0			0
$619$		−	29.7309i		−	1.19499i	−0.801874	−	0.597493i	$-0.796164\pi$
$619$		−	29.7309i		−	1.19499i	0.801874	−	0.597493i	$-0.203836\pi$
$620$		0			0
$621$	11.4564	+	19.8431i	0.459731	+	0.796278i
$622$		0			0
$623$		−	16.5826i		−	0.664367i
$624$		0			0
$625$	17.0000	−	18.3303i	0.680000	−	0.733212i
$626$		0			0
$627$	−3.96863	+	2.29129i	−0.158492	+	0.0915052i
$628$		0			0
$629$		−	36.3731i		−	1.45029i
$630$		0			0
$631$	5.12614	+	2.95958i	0.204068	+	0.117819i	0.598552	−	0.801084i	$-0.295743\pi$
$631$	5.12614	+	2.95958i	0.204068	+	0.117819i	−0.394483	+	0.918903i	$0.629076\pi$
$632$		0			0
$633$	0.143025	+	0.0825757i	0.00568475	+	0.00328209i
$634$		0			0
$635$	−29.5893	+	26.4458i	−1.17422	+	1.04947i
$636$		0			0
$637$	10.3923	+	10.0000i	0.411758	+	0.396214i
$638$		0			0
$639$	12.1652	−	7.02355i	0.481246	−	0.277847i
$640$		0			0
$641$	−9.08258	+	15.7315i	−0.358740	+	0.621356i	−0.987751	−	0.156041i	$-0.950127\pi$
$641$	−9.08258	+	15.7315i	−0.358740	+	0.621356i	0.629010	+	0.777397i	$0.283460\pi$
$642$		0			0
$643$	10.8968	−	18.8739i	0.429729	−	0.744313i	−0.567120	−	0.823635i	$-0.691942\pi$
$643$	10.8968	−	18.8739i	0.429729	−	0.744313i	0.996849	+	0.0793227i	$0.0252757\pi$
$644$		0			0
$645$	23.1642	−	4.83465i	0.912090	−	0.190364i
$646$		0			0
$647$	23.3827	−	13.5000i	0.919268	−	0.530740i	0.0358667	−	0.999357i	$-0.488581\pi$
$647$	23.3827	−	13.5000i	0.919268	−	0.530740i	0.883402	+	0.468617i	$0.155247\pi$
$648$		0			0
$649$	36.9129			1.44896
$650$		0			0
$651$	−10.7477			−0.421237
$652$		0			0
$653$	−37.0882	+	21.4129i	−1.45137	+	0.837951i	−0.998560	−	0.0536545i	$-0.982913\pi$
$653$	−37.0882	+	21.4129i	−1.45137	+	0.837951i	−0.452814	+	0.891605i	$0.649580\pi$
$654$		0			0
$655$	−16.5975	+	3.46410i	−0.648518	+	0.135354i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−15.2477	+	26.4098i	−0.593967	+	1.02878i	0.399725	+	0.916635i	$0.369106\pi$
$659$	−15.2477	+	26.4098i	−0.593967	+	1.02878i	−0.993692	+	0.112146i	$0.964228\pi$
$660$		0			0
$661$	15.8739	−	9.16478i	0.617422	−	0.356469i	−0.158443	−	0.987368i	$-0.550647\pi$
$661$	15.8739	−	9.16478i	0.617422	−	0.356469i	0.775865	+	0.630900i	$0.217314\pi$
$662$		0			0
$663$	15.8745	−	4.58258i	0.616515	−	0.177972i
$664$		0			0
$665$	−5.00166	+	4.47028i	−0.193956	+	0.173350i
$666$		0			0
$667$	−18.1865	−	10.5000i	−0.704185	−	0.406562i
$668$		0			0
$669$	−7.50000	−	4.33013i	−0.289967	−	0.167412i
$670$		0			0
$671$		−	3.75015i		−	0.144773i
$672$		0			0
$673$	−20.9276	+	12.0826i	−0.806701	+	0.465749i	−0.845809	−	0.533486i	$-0.820882\pi$
$673$	−20.9276	+	12.0826i	−0.806701	+	0.465749i	0.0391079	+	0.999235i	$0.487548\pi$
$674$		0			0
$675$	−10.0000	−	22.9129i	−0.384900	−	0.881917i
$676$		0			0
$677$			2.83485i			0.108952i	0.998515	+	0.0544760i	$0.0173489\pi$
$677$			2.83485i			0.108952i	−0.998515	+	0.0544760i	$0.982651\pi$
$678$		0			0
$679$	9.87386	+	17.1020i	0.378924	+	0.656316i
$680$		0			0
$681$		−	0.818350i		−	0.0313593i
$682$		0			0
$683$	−16.5498	+	28.6652i	−0.633262	+	1.09684i	0.353619	+	0.935390i	$0.384951\pi$
$683$	−16.5498	+	28.6652i	−0.633262	+	1.09684i	−0.986881	+	0.161452i	$0.948382\pi$
$684$		0			0
$685$	−7.32884	+	22.2765i	−0.280021	+	0.851141i
$686$		0			0
$687$	13.1334	+	22.7477i	0.501071	+	0.867880i
$688$		0			0
$689$	7.58258	+	26.2668i	0.288873	+	1.00069i
$690$		0			0
$691$	−17.1261	+	9.88778i	−0.651509	+	0.376149i	−0.789034	−	0.614349i	$-0.789419\pi$
$691$	−17.1261	+	9.88778i	−0.651509	+	0.376149i	0.137525	+	0.990498i	$0.456085\pi$
$692$		0			0
$693$	7.93725	+	4.58258i	0.301511	+	0.174078i
$694$		0			0
$695$	−15.1975	+	46.1937i	−0.576472	+	1.75223i
$696$		0			0
$697$	−12.1244			−0.459243
$698$		0			0
$699$	−1.41742	−	2.45505i	−0.0536119	−	0.0928586i
$700$		0			0
$701$	−21.1652			−0.799397			−0.399698	−	0.916647i	$-0.630885\pi$
$701$	−21.1652			−0.799397			−0.399698	+	0.916647i	$0.630885\pi$
$702$		0			0
$703$			13.7477i			0.518505i
$704$		0			0
$705$	−3.04668	+	2.72300i	−0.114745	+	0.102554i
$706$		0			0
$707$	−15.5885			−0.586264
$708$		0			0
$709$	31.5000	+	18.1865i	1.18301	+	0.683010i	0.956708	−	0.291048i	$-0.0940040\pi$
$709$	31.5000	+	18.1865i	1.18301	+	0.683010i	0.226299	+	0.974058i	$0.427337\pi$
$710$		0			0
$711$	6.00000	−	10.3923i	0.225018	−	0.389742i
$712$		0			0
$713$	−14.2179	−	24.6261i	−0.532465	−	0.922256i
$714$		0			0
$715$	−11.3379	+	18.0680i	−0.424013	+	0.675704i
$716$		0			0
$717$	−0.0953502	−	0.165151i	−0.00356092	−	0.00616769i
$718$		0			0
$719$	12.2477	−	21.2137i	0.456763	−	0.791137i	−0.542025	−	0.840363i	$-0.682342\pi$
$719$	12.2477	−	21.2137i	0.456763	−	0.791137i	0.998788	+	0.0492257i	$0.0156754\pi$
$720$		0			0
$721$	−4.74773	−	2.74110i	−0.176815	−	0.102084i
$722$		0			0
$723$	1.73205			0.0644157
$724$		0			0
$725$	18.4373	+	13.6040i	0.684742	+	0.505238i
$726$		0			0
$727$		−	15.2523i		−	0.565675i	−0.959168	−	0.282838i	$-0.908724\pi$
$727$		−	15.2523i		−	0.565675i	0.959168	−	0.282838i	$-0.0912758\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−24.2477	−	41.9983i	−0.896835	−	1.55336i
$732$		0			0
$733$	22.8027			0.842237			0.421119	−	0.907006i	$-0.361638\pi$
$733$	22.8027			0.842237			0.421119	+	0.907006i	$0.361638\pi$
$734$		0			0
$735$	8.49628	+	2.79523i	0.313390	+	0.103103i
$736$		0			0
$737$	2.31203	+	1.33485i	0.0851646	+	0.0491698i
$738$		0			0
$739$	14.7523	−	8.51723i	0.542671	−	0.313311i	−0.203490	−	0.979077i	$-0.565228\pi$
$739$	14.7523	−	8.51723i	0.542671	−	0.313311i	0.746161	+	0.665766i	$0.231895\pi$
$740$		0			0
$741$	−6.00000	+	1.73205i	−0.220416	+	0.0636285i
$742$		0			0
$743$	−2.86423	−	4.96099i	−0.105078	−	0.182001i	0.808692	−	0.588232i	$-0.200176\pi$
$743$	−2.86423	−	4.96099i	−0.105078	−	0.182001i	−0.913770	+	0.406232i	$0.866843\pi$
$744$		0			0
$745$	35.4568	+	11.6651i	1.29904	+	0.427375i
$746$		0			0
$747$	−6.01450	+	10.4174i	−0.220059	+	0.381154i
$748$		0			0
$749$			18.3296i			0.669748i
$750$		0			0
$751$	5.87386	+	10.1738i	0.214340	+	0.371248i	0.953068	−	0.302755i	$-0.0979065\pi$
$751$	5.87386	+	10.1738i	0.214340	+	0.371248i	−0.738728	+	0.674004i	$0.764573\pi$
$752$		0			0
$753$		−	0.165151i		−	0.00601845i
$754$		0			0
$755$	4.41742	+	21.1652i	0.160767	+	0.770279i
$756$		0			0
$757$	−8.44178	+	4.87386i	−0.306822	+	0.177144i	−0.645503	−	0.763757i	$-0.723352\pi$
$757$	−8.44178	+	4.87386i	−0.306822	+	0.177144i	0.338682	+	0.940901i	$0.390019\pi$
$758$		0			0
$759$		−	12.1244i		−	0.440086i
$760$		0			0
$761$	−30.7087	−	17.7297i	−1.11319	−	0.642701i	−0.173536	−	0.984827i	$-0.555519\pi$
$761$	−30.7087	−	17.7297i	−1.11319	−	0.642701i	−0.939654	+	0.342127i	$0.888853\pi$
$762$		0			0
$763$	19.7001	+	11.3739i	0.713192	+	0.411762i
$764$		0			0
$765$	−15.2803	+	13.6569i	−0.552461	+	0.493768i
$766$		0			0
$767$	48.8311	+	12.0826i	1.76319	+	0.436277i
$768$		0			0
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	−0.723255	−	0.690581i	$-0.757355\pi$
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	0.236433	+	0.971648i	$0.424022\pi$
$770$		0			0
$771$	−9.08258	+	15.7315i	−0.327101	+	0.566556i
$772$		0			0
$773$	−12.0767	+	20.9174i	−0.434368	+	0.752347i	−0.997244	−	0.0741940i	$-0.976362\pi$
$773$	−12.0767	+	20.9174i	−0.434368	+	0.752347i	0.562876	+	0.826541i	$0.309695\pi$
$774$		0			0
$775$	12.4104	+	28.4358i	0.445795	+	1.02144i
$776$		0			0
$777$	−11.9059	+	6.87386i	−0.427121	+	0.246598i
$778$		0			0
$779$	4.58258			0.164188
$780$		0			0
$781$	−18.5826			−0.664937
$782$		0			0
$783$	19.8431	−	11.4564i	0.709136	−	0.409420i
$784$		0			0
$785$	4.18710	+	20.0616i	0.149444	+	0.716030i
$786$		0			0
$787$	−8.15573	+	14.1261i	−0.290720	+	0.503542i	−0.973980	−	0.226633i	$-0.927228\pi$
$787$	−8.15573	+	14.1261i	−0.290720	+	0.503542i	0.683260	+	0.730175i	$0.260562\pi$
$788$		0			0
$789$	4.50000	−	7.79423i	0.160204	−	0.277482i
$790$		0			0
$791$	11.1261	−	6.42368i	0.395600	−	0.228400i
$792$		0			0
$793$	1.22753	−	4.96099i	0.0435907	−	0.176170i
$794$		0			0
$795$	11.2988	+	12.6418i	0.400726	+	0.448359i
$796$		0			0
$797$	38.1727	+	22.0390i	1.35215	+	0.780662i	0.988550	−	0.150895i	$-0.0482154\pi$
$797$	38.1727	+	22.0390i	1.35215	+	0.780662i	0.363596	+	0.931557i	$0.381549\pi$
$798$		0			0
$799$	7.25227	+	4.18710i	0.256567	+	0.148129i
$800$		0			0
$801$			19.1479i			0.676558i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−3.62614	−	17.3739i	−0.127805	−	0.612348i
$806$		0			0
$807$		−	15.0000i		−	0.528025i
$808$		0			0
$809$	−27.4129	−	47.4805i	−0.963785	−	1.66933i	−0.712843	−	0.701323i	$-0.752593\pi$
$809$	−27.4129	−	47.4805i	−0.963785	−	1.66933i	−0.250942	−	0.968002i	$-0.580740\pi$
$810$		0			0
$811$		−	50.5155i		−	1.77384i	−0.461923	−	0.886920i	$-0.652840\pi$
$811$		−	50.5155i		−	1.77384i	0.461923	−	0.886920i	$-0.347160\pi$
$812$		0			0
$813$	4.33013	−	7.50000i	0.151864	−	0.263036i
$814$		0			0
$815$	14.7243	−	44.7555i	0.515770	−	1.56772i
$816$		0			0
$817$	9.16478	+	15.8739i	0.320635	+	0.555356i
$818$		0			0
$819$	9.00000	+	8.66025i	0.314485	+	0.302614i
$820$		0			0
$821$	15.7087	−	9.06943i	0.548238	−	0.316525i	−0.200173	−	0.979761i	$-0.564150\pi$
$821$	15.7087	−	9.06943i	0.548238	−	0.316525i	0.748411	+	0.663235i	$0.230817\pi$
$822$		0			0
$823$	−27.2083	−	15.7087i	−0.948421	−	0.547571i	−0.0558311	−	0.998440i	$-0.517781\pi$
$823$	−27.2083	−	15.7087i	−0.948421	−	0.547571i	−0.892590	+	0.450869i	$0.851114\pi$
$824$		0			0
$825$	−1.47960	+	13.1458i	−0.0515131	+	0.457676i
$826$		0			0
$827$	−10.7737			−0.374638			−0.187319	−	0.982299i	$-0.559980\pi$
$827$	−10.7737			−0.374638			−0.187319	+	0.982299i	$0.559980\pi$
$828$		0			0
$829$	−16.6652	−	28.8649i	−0.578805	−	1.00252i	−0.995617	−	0.0935264i	$-0.970186\pi$
$829$	−16.6652	−	28.8649i	−0.578805	−	1.00252i	0.416812	−	0.908993i	$-0.363147\pi$
$830$		0			0
$831$	7.41742			0.257308
$832$		0			0
$833$		−	18.3303i		−	0.635107i
$834$		0			0
$835$	−14.2661	−	15.9619i	−0.493699	−	0.552384i
$836$		0			0
$837$	31.0260			1.07242
$838$		0			0
$839$	−37.8303	−	21.8413i	−1.30605	−	0.754047i	−0.324613	−	0.945847i	$-0.605234\pi$
$839$	−37.8303	−	21.8413i	−1.30605	−	0.754047i	−0.981434	+	0.191800i	$0.938567\pi$
$840$		0			0
$841$	4.00000	−	6.92820i	0.137931	−	0.238904i
$842$		0			0
$843$	1.82740	+	3.16515i	0.0629390	+	0.109014i
$844$		0			0
$845$	−20.9128	+	20.1905i	−0.719421	+	0.694574i
$846$		0			0
$847$	3.46410	+	6.00000i	0.119028	+	0.206162i
$848$		0			0
$849$	−13.8739	+	24.0302i	−0.476150	+	0.824716i
$850$		0			0
$851$	−31.5000	−	18.1865i	−1.07981	−	0.623426i
$852$		0			0
$853$	−5.63310			−0.192874			−0.0964369	−	0.995339i	$-0.530745\pi$
$853$	−5.63310			−0.192874			−0.0964369	+	0.995339i	$0.530745\pi$
$854$		0			0
$855$	5.77542	−	5.16184i	0.197515	−	0.176531i
$856$		0			0
$857$			4.74773i			0.162179i	0.996707	+	0.0810896i	$0.0258400\pi$
$857$			4.74773i			0.162179i	−0.996707	+	0.0810896i	$0.974160\pi$
$858$		0			0
$859$	−44.2432			−1.50956			−0.754779	−	0.655979i	$-0.772256\pi$
$859$	−44.2432			−1.50956			−0.754779	+	0.655979i	$0.772256\pi$
$860$		0			0
$861$	2.29129	+	3.96863i	0.0780869	+	0.135250i
$862$		0			0
$863$	−13.6657			−0.465186			−0.232593	−	0.972574i	$-0.574721\pi$
$863$	−13.6657			−0.465186			−0.232593	+	0.972574i	$0.574721\pi$
$864$		0			0
$865$	−35.2225	−	11.5880i	−1.19760	−	0.394004i
$866$		0			0
$867$	−3.46410	−	2.00000i	−0.117647	−	0.0679236i
$868$		0			0
$869$	−13.7477	+	7.93725i	−0.466360	+	0.269253i
$870$		0			0
$871$	2.62159	+	2.52263i	0.0888292	+	0.0854759i
$872$		0			0
$873$	−11.4014	−	19.7477i	−0.385877	−	0.668359i
$874$		0			0
$875$	1.81139	+	19.2800i	0.0612360	+	0.651783i
$876$		0			0
$877$	−3.96863	+	6.87386i	−0.134011	+	0.232114i	−0.925219	−	0.379433i	$-0.876119\pi$
$877$	−3.96863	+	6.87386i	−0.134011	+	0.232114i	0.791208	+	0.611547i	$0.209452\pi$
$878$		0			0
$879$		−	18.1389i		−	0.611809i
$880$		0			0
$881$	−18.2477	−	31.6060i	−0.614782	−	1.06483i	−0.990423	−	0.138068i	$-0.955911\pi$
$881$	−18.2477	−	31.6060i	−0.614782	−	1.06483i	0.375641	−	0.926765i	$-0.377422\pi$
$882$		0			0
$883$		−	36.2432i		−	1.21968i	−0.792524	−	0.609840i	$-0.791234\pi$
$883$		−	36.2432i		−	1.21968i	0.792524	−	0.609840i	$-0.208766\pi$
$884$		0			0
$885$	30.5390	−	6.37386i	1.02656	−	0.214255i
$886$		0			0
$887$	47.1944	−	27.2477i	1.58463	−	0.914889i	0.590465	−	0.807064i	$-0.298945\pi$
$887$	47.1944	−	27.2477i	1.58463	−	0.914889i	0.994170	−	0.107826i	$-0.0343888\pi$
$888$		0			0
$889$		−	30.7400i		−	1.03099i
$890$		0			0
$891$	−2.29129	−	1.32288i	−0.0767610	−	0.0443180i
$892$		0			0
$893$	−2.74110	−	1.58258i	−0.0917275	−	0.0529589i
$894$		0			0
$895$	27.0678	+	30.2853i	0.904776	+	1.01233i
$896$		0			0
$897$	3.96863	−	16.0390i	0.132509	−	0.535527i
$898$		0			0
$899$	−24.6261	+	14.2179i	−0.821328	+	0.474194i
$900$		0			0
$901$	17.3739	−	30.0924i	0.578807	−	1.00252i
$902$		0			0
$903$	−9.16478	+	15.8739i	−0.304985	+	0.528249i
$904$		0			0
$905$	−19.1479	+	3.99640i	−0.636498	+	0.132845i
$906$		0			0
$907$	−5.41463	+	3.12614i	−0.179790	+	0.103802i	−0.587194	−	0.809446i	$-0.699767\pi$
$907$	−5.41463	+	3.12614i	−0.179790	+	0.103802i	0.407404	+	0.913248i	$0.366434\pi$
$908$		0			0
$909$	18.0000			0.597022
$910$		0			0
$911$	7.91288			0.262165			0.131083	−	0.991371i	$-0.458155\pi$
$911$	7.91288			0.262165			0.131083	+	0.991371i	$0.458155\pi$
$912$		0			0
$913$	13.7810	−	7.95644i	0.456083	−	0.263320i
$914$		0			0
$915$	−0.647551	−	3.10260i	−0.0214074	−	0.102569i
$916$		0			0
$917$	6.56670	−	11.3739i	0.216852	−	0.375598i
$918$		0			0
$919$	−27.0826	+	46.9084i	−0.893372	+	1.54737i	−0.0575648	+	0.998342i	$0.518334\pi$
$919$	−27.0826	+	46.9084i	−0.893372	+	1.54737i	−0.835807	+	0.549023i	$0.815000\pi$
$920$		0			0
$921$	21.0000	−	12.1244i	0.691974	−	0.399511i
$922$		0			0
$923$	−24.5824	−	6.08258i	−0.809141	−	0.200210i
$924$		0			0
$925$	31.9343	+	23.5627i	1.04999	+	0.774738i
$926$		0			0
$927$	5.48220	+	3.16515i	0.180059	+	0.103957i
$928$		0			0
$929$	22.8303	+	13.1811i	0.749038	+	0.432457i	0.825346	−	0.564627i	$-0.190980\pi$
$929$	22.8303	+	13.1811i	0.749038	+	0.432457i	−0.0763082	+	0.997084i	$0.524313\pi$
$930$		0			0
$931$			6.92820i			0.227063i
$932$		0			0
$933$	6.56670	−	3.79129i	0.214984	−	0.124121i
$934$		0			0
$935$	26.5390	−	5.53901i	0.867919	−	0.181145i
$936$		0			0
$937$		−	31.4955i		−	1.02891i	−0.857517	−	0.514456i	$-0.827994\pi$
$937$		−	31.4955i		−	1.02891i	0.857517	−	0.514456i	$-0.172006\pi$
$938$		0			0
$939$	1.62614	+	2.81655i	0.0530670	+	0.0919147i
$940$		0			0
$941$			26.4575i			0.862490i	0.902235	+	0.431245i	$0.141926\pi$
$941$			26.4575i			0.862490i	−0.902235	+	0.431245i	$0.858074\pi$
$942$		0			0
$943$	−6.06218	+	10.5000i	−0.197412	+	0.341927i
$944$		0			0
$945$	18.3950	+	6.05184i	0.598389	+	0.196866i
$946$		0			0
$947$	−7.16658	−	12.4129i	−0.232883	−	0.403364i	0.725773	−	0.687935i	$-0.241482\pi$
$947$	−7.16658	−	12.4129i	−0.232883	−	0.403364i	−0.958655	+	0.284570i	$0.908149\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	0.165151	−	0.0953502i	0.00535540	−	0.00309194i
$952$		0			0
$953$	6.99578	+	4.03901i	0.226616	+	0.130837i	0.609010	−	0.793163i	$-0.291567\pi$
$953$	6.99578	+	4.03901i	0.226616	+	0.130837i	−0.382394	+	0.923999i	$0.624900\pi$
$954$		0			0
$955$	11.5880	−	35.2225i	0.374979	−	1.13977i
$956$		0			0
$957$	−12.1244			−0.391925
$958$		0			0
$959$	−9.08258	−	15.7315i	−0.293292	−	0.507996i
$960$		0			0
$961$	−7.50455			−0.242082
$962$		0			0
$963$		−	21.1652i		−	0.682037i
$964$		0			0
$965$	−22.1509	−	24.7840i	−0.713064	−	0.797824i
$966$		0			0
$967$	37.3821			1.20213			0.601064	−	0.799201i	$-0.294744\pi$
$967$	37.3821			1.20213			0.601064	+	0.799201i	$0.294744\pi$
$968$		0			0
$969$	6.87386	+	3.96863i	0.220820	+	0.127491i
$970$		0			0
$971$	−9.24773	+	16.0175i	−0.296774	+	0.514027i	−0.975396	−	0.220460i	$-0.929244\pi$
$971$	−9.24773	+	16.0175i	−0.296774	+	0.514027i	0.678622	+	0.734487i	$0.262577\pi$
$972$		0			0
$973$	−18.8341	−	32.6216i	−0.603793	−	1.04580i
$974$		0			0
$975$	−6.26029	+	16.9059i	−0.200490	+	0.541421i
$976$		0			0
$977$	−17.6542	−	30.5780i	−0.564809	−	0.978278i	−0.997067	−	0.0765281i	$-0.975617\pi$
$977$	−17.6542	−	30.5780i	−0.564809	−	0.978278i	0.432258	−	0.901750i	$-0.357717\pi$
$978$		0			0
$979$	12.6652	−	21.9367i	0.404780	−	0.701100i
$980$		0			0
$981$	−22.7477	−	13.1334i	−0.726279	−	0.419317i
$982$		0			0
$983$	−55.0840			−1.75691			−0.878454	−	0.477827i	$-0.841424\pi$
$983$	−55.0840			−1.75691			−0.878454	+	0.477827i	$0.841424\pi$
$984$		0			0
$985$	21.8668	+	24.4660i	0.696733	+	0.779553i
$986$		0			0
$987$		−	3.16515i		−	0.100748i
$988$		0			0
$989$	−48.4955			−1.54207
$990$		0			0
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	0.744124	−	0.668042i	$-0.232867\pi$
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	−0.950603	+	0.310409i	$0.899534\pi$
$992$		0			0
$993$	−4.47315			−0.141951
$994$		0			0
$995$	7.39517	−	22.4781i	0.234443	−	0.712604i
$996$		0			0
$997$	0.143025	+	0.0825757i	0.00452966	+	0.00261520i	0.502263	−	0.864715i	$-0.332501\pi$
$997$	0.143025	+	0.0825757i	0.00452966	+	0.00261520i	−0.497733	+	0.867330i	$0.665834\pi$
$998$		0			0
$999$	34.3693	−	19.8431i	1.08740	−	0.627809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.df.b.49.1		8
4.3	odd	2		65.2.l.a.49.3	yes	8
5.4	even	2	inner	1040.2.df.b.49.4		8
12.11	even	2		585.2.bf.a.244.2		8
13.4	even	6	inner	1040.2.df.b.849.4		8
20.3	even	4		325.2.n.b.101.2		4
20.7	even	4		325.2.n.c.101.1		4
20.19	odd	2		65.2.l.a.49.2	yes	8
52.3	odd	6		845.2.d.c.844.4		8
52.7	even	12		845.2.n.c.529.3		8
52.11	even	12		845.2.b.f.339.4		8
52.15	even	12		845.2.b.f.339.6		8
52.19	even	12		845.2.n.d.529.1		8
52.23	odd	6		845.2.d.c.844.6		8
52.31	even	4		845.2.n.c.484.4		8
52.35	odd	6		845.2.l.c.654.3		8
52.43	odd	6		65.2.l.a.4.2	✓	8
52.47	even	4		845.2.n.d.484.2		8
52.51	odd	2		845.2.l.c.699.2		8
60.59	even	2		585.2.bf.a.244.3		8
65.4	even	6	inner	1040.2.df.b.849.1		8
156.95	even	6		585.2.bf.a.199.3		8
260.19	even	12		845.2.n.c.529.4		8
260.43	even	12		325.2.n.b.251.2		4
260.59	even	12		845.2.n.d.529.2		8
260.63	odd	12		4225.2.a.bj.1.2		4
260.67	odd	12		4225.2.a.bk.1.2		4
260.99	even	4		845.2.n.c.484.3		8
260.119	even	12		845.2.b.f.339.3		8
260.139	odd	6		845.2.l.c.654.2		8
260.147	even	12		325.2.n.c.251.1		4
260.159	odd	6		845.2.d.c.844.5		8
260.167	odd	12		4225.2.a.bk.1.3		4
260.179	odd	6		845.2.d.c.844.3		8
260.199	odd	6		65.2.l.a.4.3	yes	8
260.219	even	12		845.2.b.f.339.5		8
260.223	odd	12		4225.2.a.bj.1.3		4
260.239	even	4		845.2.n.d.484.1		8
260.259	odd	2		845.2.l.c.699.3		8
780.719	even	6		585.2.bf.a.199.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.2	✓	8	52.43	odd	6
65.2.l.a.4.3	yes	8	260.199	odd	6
65.2.l.a.49.2	yes	8	20.19	odd	2
65.2.l.a.49.3	yes	8	4.3	odd	2
325.2.n.b.101.2		4	20.3	even	4
325.2.n.b.251.2		4	260.43	even	12
325.2.n.c.101.1		4	20.7	even	4
325.2.n.c.251.1		4	260.147	even	12
585.2.bf.a.199.2		8	780.719	even	6
585.2.bf.a.199.3		8	156.95	even	6
585.2.bf.a.244.2		8	12.11	even	2
585.2.bf.a.244.3		8	60.59	even	2
845.2.b.f.339.3		8	260.119	even	12
845.2.b.f.339.4		8	52.11	even	12
845.2.b.f.339.5		8	260.219	even	12
845.2.b.f.339.6		8	52.15	even	12
845.2.d.c.844.3		8	260.179	odd	6
845.2.d.c.844.4		8	52.3	odd	6
845.2.d.c.844.5		8	260.159	odd	6
845.2.d.c.844.6		8	52.23	odd	6
845.2.l.c.654.2		8	260.139	odd	6
845.2.l.c.654.3		8	52.35	odd	6
845.2.l.c.699.2		8	52.51	odd	2
845.2.l.c.699.3		8	260.259	odd	2
845.2.n.c.484.3		8	260.99	even	4
845.2.n.c.484.4		8	52.31	even	4
845.2.n.c.529.3		8	52.7	even	12
845.2.n.c.529.4		8	260.19	even	12
845.2.n.d.484.1		8	260.239	even	4
845.2.n.d.484.2		8	52.47	even	4
845.2.n.d.529.1		8	52.19	even	12
845.2.n.d.529.2		8	260.59	even	12
1040.2.df.b.49.1		8	1.1	even	1	trivial
1040.2.df.b.49.4		8	5.4	even	2	inner
1040.2.df.b.849.1		8	65.4	even	6	inner
1040.2.df.b.849.4		8	13.4	even	6	inner
4225.2.a.bj.1.2		4	260.63	odd	12
4225.2.a.bj.1.3		4	260.223	odd	12
4225.2.a.bk.1.2		4	260.67	odd	12
4225.2.a.bk.1.3		4	260.167	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(-2.18890 + 0.456850i) q^{5} +(0.866025 - 1.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(2.29129 - 1.32288i) q^{11} +(3.46410 - 1.00000i) q^{13} +(1.66722 - 1.49009i) q^{15} +(-3.96863 - 2.29129i) q^{17} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(-3.96863 + 2.29129i) q^{23} +(4.58258 - 2.00000i) q^{25} -5.00000i q^{27} +(2.29129 + 3.96863i) q^{29} +6.20520i q^{31} +(-1.32288 + 2.29129i) q^{33} +(-1.21037 + 3.67900i) q^{35} +(3.96863 + 6.87386i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(2.29129 - 1.32288i) q^{41} +(9.16478 + 5.29129i) q^{43} +(1.39761 - 4.24814i) q^{45} -1.82740 q^{47} +(2.00000 + 3.46410i) q^{49} +4.58258 q^{51} +7.58258i q^{53} +(-4.41105 + 3.94242i) q^{55} -1.73205 q^{57} +(12.0826 + 6.97588i) q^{59} +(0.708712 - 1.22753i) q^{61} +(1.73205 + 3.00000i) q^{63} +(-7.12573 + 3.77148i) q^{65} +(0.504525 + 0.873864i) q^{67} +(2.29129 - 3.96863i) q^{69} +(-6.08258 - 3.51178i) q^{71} +(-2.96863 + 4.02334i) q^{75} -4.58258i q^{77} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +6.01450 q^{83} +(9.73371 + 3.20233i) q^{85} +(-3.96863 - 2.29129i) q^{87} +(8.29129 - 4.78698i) q^{89} +(1.50000 - 6.06218i) q^{91} +(-3.10260 - 5.37386i) q^{93} +(-3.67900 - 1.21037i) q^{95} +(-5.70068 + 9.87386i) q^{97} +5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{9} + 6 q^{15} + 12 q^{19} - 6 q^{35} - 20 q^{39} + 12 q^{45} + 16 q^{49} + 14 q^{55} + 60 q^{59} + 24 q^{61} - 24 q^{65} - 12 q^{71} + 8 q^{75} - 48 q^{79} - 4 q^{81} + 42 q^{85} + 48 q^{89}+ \cdots + 6 q^{95}+O(q^{100}) \) 8 * q - 8 * q^9 + 6 * q^15 + 12 * q^19 - 6 * q^35 - 20 * q^39 + 12 * q^45 + 16 * q^49 + 14 * q^55 + 60 * q^59 + 24 * q^61 - 24 * q^65 - 12 * q^71 + 8 * q^75 - 48 * q^79 - 4 * q^81 + 42 * q^85 + 48 * q^89 + 12 * q^91 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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