LMFDB - Embedded newform 1040.2.df.b.49.3

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			49.3
Root			$0.228425 - 1.39564i$ of defining polynomial
Character	$\chi$	$=$	1040.49
Dual form			1040.2.df.b.849.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{3} +(-0.456850 - 2.18890i) q^{5} +(-0.866025 + 1.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-2.29129 + 1.32288i) q^{11} +(-3.46410 + 1.00000i) q^{13} +(-1.49009 - 1.66722i) q^{15} +(-3.96863 - 2.29129i) q^{17} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(-3.96863 + 2.29129i) q^{23} +(-4.58258 + 2.00000i) q^{25} +5.00000i q^{27} +(-2.29129 - 3.96863i) q^{29} -9.66930i q^{31} +(-1.32288 + 2.29129i) q^{33} +(3.67900 + 1.21037i) q^{35} +(3.96863 + 6.87386i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(-2.29129 + 1.32288i) q^{41} +(-1.22753 - 0.708712i) q^{43} +(4.24814 + 1.39761i) q^{45} -8.75560 q^{47} +(2.00000 + 3.46410i) q^{49} -4.58258 q^{51} +1.58258i q^{53} +(3.94242 + 4.41105i) q^{55} +1.73205 q^{57} +(2.91742 + 1.68438i) q^{59} +(5.29129 - 9.16478i) q^{61} +(-1.73205 - 3.00000i) q^{63} +(3.77148 + 7.12573i) q^{65} +(7.43273 + 12.8739i) q^{67} +(-2.29129 + 3.96863i) q^{69} +(3.08258 + 1.77973i) q^{71} +(-2.96863 + 4.02334i) q^{75} -4.58258i q^{77} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} -11.3060 q^{83} +(-3.20233 + 9.73371i) q^{85} +(-3.96863 - 2.29129i) q^{87} +(3.70871 - 2.14123i) q^{89} +(1.50000 - 6.06218i) q^{91} +(-4.83465 - 8.37386i) q^{93} +(1.21037 - 3.67900i) q^{95} +(-2.23658 + 3.87386i) q^{97} -5.29150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.228714	−	0.973494i	$-0.573452\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i	0.728714	+	0.684819i	$0.240119\pi$
$4$		0			0
$5$	−0.456850	−	2.18890i	−0.204310	−	0.978906i
$5$	−0.456850	−	2.18890i	−0.204310	−	0.978906i
$6$		0			0
$7$	−0.866025	+	1.50000i	−0.327327	+	0.566947i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	−0.866025	+	1.50000i	−0.327327	+	0.566947i	0.654654	+	0.755929i	$0.272814\pi$
$8$		0			0
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$		0			0
$11$	−2.29129	+	1.32288i	−0.690849	+	0.398862i	−0.803930	−	0.594724i	$-0.797261\pi$
$11$	−2.29129	+	1.32288i	−0.690849	+	0.398862i	0.113081	+	0.993586i	$0.463928\pi$
$12$		0			0
$13$	−3.46410	+	1.00000i	−0.960769	+	0.277350i
$13$	−3.46410	+	1.00000i	−0.960769	+	0.277350i
$14$		0			0
$15$	−1.49009	−	1.66722i	−0.384741	−	0.430474i
$16$		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	0.570984	−	0.820961i	$-0.306562\pi$
$29$	−2.29129	−	3.96863i	−0.425481	−	0.736956i	−0.996465	+	0.0840058i	$0.973229\pi$
$30$		0			0
$31$		−	9.66930i		−	1.73666i	−0.495988	−	0.868329i	$-0.665194\pi$
$31$		−	9.66930i		−	1.73666i	0.495988	−	0.868329i	$-0.334806\pi$
$32$		0			0
$33$	−1.32288	+	2.29129i	−0.230283	+	0.398862i
$34$		0			0
$35$	3.67900	+	1.21037i	0.621864	+	0.204590i
$36$		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	−0.668132	−	0.744042i	$-0.732906\pi$
$41$	−2.29129	+	1.32288i	−0.357839	+	0.206598i	0.310293	+	0.950641i	$0.399573\pi$
$42$		0			0
$43$	−1.22753	−	0.708712i	−0.187196	−	0.108078i	0.403473	−	0.914991i	$-0.367803\pi$
$43$	−1.22753	−	0.708712i	−0.187196	−	0.108078i	−0.590669	+	0.806914i	$0.701136\pi$
$44$		0			0
$45$	4.24814	+	1.39761i	0.633275	+	0.208344i
$46$		0			0
$47$	−8.75560			−1.27714			−0.638568	−	0.769565i	$-0.720473\pi$
$47$	−8.75560			−1.27714			−0.638568	+	0.769565i	$0.720473\pi$
$48$		0			0
$49$	2.00000	+	3.46410i	0.285714	+	0.494872i
$50$		0			0
$51$	−4.58258			−0.641689
$52$		0			0
$53$			1.58258i			0.217383i	0.994076	+	0.108692i	$0.0346661\pi$
$53$			1.58258i			0.217383i	−0.994076	+	0.108692i	$0.965334\pi$
$54$		0			0
$55$	3.94242	+	4.41105i	0.531596	+	0.594785i
$56$		0			0
$57$	1.73205			0.229416
$58$		0			0
$59$	2.91742	+	1.68438i	0.379816	+	0.219287i	0.677738	−	0.735303i	$-0.262960\pi$
$59$	2.91742	+	1.68438i	0.379816	+	0.219287i	−0.297922	+	0.954590i	$0.596294\pi$
$60$		0			0
$61$	5.29129	−	9.16478i	0.677480	−	1.17343i	−0.298257	−	0.954485i	$-0.596405\pi$
$61$	5.29129	−	9.16478i	0.677480	−	1.17343i	0.975737	−	0.218944i	$-0.0702613\pi$
$62$		0			0
$63$	−1.73205	−	3.00000i	−0.218218	−	0.377964i
$64$		0			0
$65$	3.77148	+	7.12573i	0.467794	+	0.883837i
$66$		0			0
$67$	7.43273	+	12.8739i	0.908052	+	1.57279i	0.816767	+	0.576968i	$0.195764\pi$
$67$	7.43273	+	12.8739i	0.908052	+	1.57279i	0.0912856	+	0.995825i	$0.470902\pi$
$68$		0			0
$69$	−2.29129	+	3.96863i	−0.275839	+	0.477767i
$70$		0			0
$71$	3.08258	+	1.77973i	0.365834	+	0.211215i	0.671637	−	0.740880i	$-0.265591\pi$
$71$	3.08258	+	1.77973i	0.365834	+	0.211215i	−0.305803	+	0.952095i	$0.598925\pi$
$72$		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
$83$	−11.3060			−1.24100			−0.620498	−	0.784208i	$-0.713069\pi$
$83$	−11.3060			−1.24100			−0.620498	+	0.784208i	$0.713069\pi$
$84$		0			0
$85$	−3.20233	+	9.73371i	−0.347342	+	1.05577i
$86$		0			0
$87$	−3.96863	−	2.29129i	−0.425481	−	0.245652i
$88$		0			0
$89$	3.70871	−	2.14123i	0.393123	−	0.226969i	−0.290390	−	0.956909i	$-0.593785\pi$
$89$	3.70871	−	2.14123i	0.393123	−	0.226969i	0.683512	+	0.729939i	$0.260452\pi$
$90$		0			0
$91$	1.50000	−	6.06218i	0.157243	−	0.635489i
$92$		0			0
$93$	−4.83465	−	8.37386i	−0.501330	−	0.868329i
$94$		0			0
$95$	1.21037	−	3.67900i	0.124181	−	0.377457i
$96$		0			0
$97$	−2.23658	+	3.87386i	−0.227090	+	0.393331i	−0.956944	−	0.290271i	$-0.906254\pi$
$97$	−2.23658	+	3.87386i	−0.227090	+	0.393331i	0.729854	+	0.683603i	$0.239588\pi$
$98$		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
$103$		−	15.1652i		−	1.49427i	−0.664674	−	0.747133i	$-0.731430\pi$
$103$		−	15.1652i		−	1.49427i	0.664674	−	0.747133i	$-0.268570\pi$
$104$		0			0
$105$	3.79129	−	0.791288i	0.369992	−	0.0772218i
$106$		0			0
$107$	1.22753	−	0.708712i	0.118669	−	0.0685138i	−0.439490	−	0.898247i	$-0.644841\pi$
$107$	1.22753	−	0.708712i	0.118669	−	0.0685138i	0.558160	+	0.829733i	$0.311508\pi$
$108$		0			0
$109$		−	2.74110i		−	0.262550i	−0.991346	−	0.131275i	$-0.958093\pi$
$109$		−	2.74110i		−	0.262550i	0.991346	−	0.131275i	$-0.0419071\pi$
$110$		0			0
$111$	6.87386	+	3.96863i	0.652438	+	0.376685i
$112$		0			0
$113$	−14.3609	−	8.29129i	−1.35096	−	0.779979i	−0.362578	−	0.931953i	$-0.618103\pi$
$113$	−14.3609	−	8.29129i	−1.35096	−	0.779979i	−0.988384	+	0.151975i	$0.951437\pi$
$114$		0			0
$115$	6.82847	+	7.64016i	0.636758	+	0.712448i
$116$		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
$125$	6.47135	+	9.11710i	0.578815	+	0.815459i
$126$		0			0
$127$	8.44178	−	4.87386i	0.749087	−	0.432485i	−0.0762771	−	0.997087i	$-0.524303\pi$
$127$	8.44178	−	4.87386i	0.749087	−	0.432485i	0.825364	+	0.564601i	$0.190970\pi$
$128$		0			0
$129$	−1.41742			−0.124797
$130$		0			0
$131$	−1.58258			−0.138270			−0.0691351	−	0.997607i	$-0.522024\pi$
$131$	−1.58258			−0.138270			−0.0691351	+	0.997607i	$0.522024\pi$
$132$		0			0
$133$	−2.59808	+	1.50000i	−0.225282	+	0.130066i
$134$		0			0
$135$	10.9445	−	2.28425i	0.941953	−	0.196597i
$136$		0			0
$137$	0.0476751	−	0.0825757i	0.00407316	−	0.00705492i	−0.863982	−	0.503523i	$-0.832037\pi$
$137$	0.0476751	−	0.0825757i	0.00407316	−	0.00705492i	0.868055	+	0.496468i	$0.165370\pi$
$138$		0			0
$139$	−2.87386	+	4.97768i	−0.243758	+	0.422201i	−0.961782	−	0.273817i	$-0.911714\pi$
$139$	−2.87386	+	4.97768i	−0.243758	+	0.422201i	0.718024	+	0.696019i	$0.245047\pi$
$140$		0			0
$141$	−7.58258	+	4.37780i	−0.638568	+	0.368677i
$142$		0			0
$143$	6.61438	−	6.87386i	0.553122	−	0.574821i
$144$		0			0
$145$	−7.64016	+	6.82847i	−0.634480	+	0.567074i
$146$		0			0
$147$	3.46410	+	2.00000i	0.285714	+	0.164957i
$148$		0			0
$149$	8.45644	+	4.88233i	0.692778	+	0.399976i	0.804652	−	0.593747i	$-0.202352\pi$
$149$	8.45644	+	4.88233i	0.692778	+	0.399976i	−0.111874	+	0.993722i	$0.535685\pi$
$150$		0			0
$151$			6.20520i			0.504972i	0.967601	+	0.252486i	$0.0812482\pi$
$151$			6.20520i			0.504972i	−0.967601	+	0.252486i	$0.918752\pi$
$152$		0			0
$153$	7.93725	−	4.58258i	0.641689	−	0.370479i
$154$		0			0
$155$	−21.1652	+	4.41742i	−1.70003	+	0.354816i
$156$		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
$159$	0.791288	+	1.37055i	0.0627532	+	0.108692i
$160$		0			0
$161$		−	7.93725i		−	0.625543i
$162$		0			0
$163$	−5.33918	+	9.24773i	−0.418197	+	0.724338i	−0.995758	−	0.0920093i	$-0.970671\pi$
$163$	−5.33918	+	9.24773i	−0.418197	+	0.724338i	0.577561	+	0.816347i	$0.304004\pi$
$164$		0			0
$165$	5.61976	+	1.84887i	0.437498	+	0.143934i
$166$		0			0
$167$	−2.14123	−	3.70871i	−0.165693	−	0.286989i	0.771208	−	0.636583i	$-0.219653\pi$
$167$	−2.14123	−	3.70871i	−0.165693	−	0.286989i	−0.936901	+	0.349594i	$0.886319\pi$
$168$		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
$173$	−6.42368	−	3.70871i	−0.488383	−	0.281968i	0.235520	−	0.971869i	$-0.424321\pi$
$173$	−6.42368	−	3.70871i	−0.488383	−	0.281968i	−0.723903	+	0.689901i	$0.757654\pi$
$174$		0			0
$175$	0.968627	−	8.60591i	0.0732213	−	0.650546i
$176$		0			0
$177$	3.36875			0.253211
$178$		0			0
$179$	0.0825757	+	0.143025i	0.00617200	+	0.0106902i	0.869095	−	0.494645i	$-0.164702\pi$
$179$	0.0825757	+	0.143025i	0.00617200	+	0.0106902i	−0.862923	+	0.505336i	$0.831369\pi$
$180$		0			0
$181$	−18.7477			−1.39351			−0.696754	−	0.717310i	$-0.745373\pi$
$181$	−18.7477			−1.39351			−0.696754	+	0.717310i	$0.745373\pi$
$182$		0			0
$183$		−	10.5826i		−	0.782287i
$184$		0			0
$185$	13.2331	−	11.8273i	0.972920	−	0.869557i
$186$		0			0
$187$	12.1244			0.886621
$188$		0			0
$189$	−7.50000	−	4.33013i	−0.545545	−	0.314970i
$190$		0			0
$191$	−3.70871	+	6.42368i	−0.268353	+	0.464801i	−0.968437	−	0.249260i	$-0.919813\pi$
$191$	−3.70871	+	6.42368i	−0.268353	+	0.464801i	0.700084	+	0.714061i	$0.253146\pi$
$192$		0			0
$193$	0.504525	+	0.873864i	0.0363165	+	0.0629021i	0.883612	−	0.468219i	$-0.155104\pi$
$193$	0.504525	+	0.873864i	0.0363165	+	0.0629021i	−0.847296	+	0.531121i	$0.821771\pi$
$194$		0			0
$195$	6.82906	+	4.28532i	0.489039	+	0.306878i
$196$		0			0
$197$	9.98313	+	17.2913i	0.711269	+	1.23195i	0.964381	+	0.264516i	$0.0852123\pi$
$197$	9.98313	+	17.2913i	0.711269	+	1.23195i	−0.253113	+	0.967437i	$0.581454\pi$
$198$		0			0
$199$	−0.708712	+	1.22753i	−0.0502393	+	0.0870170i	−0.890051	−	0.455860i	$-0.849332\pi$
$199$	−0.708712	+	1.22753i	−0.0502393	+	0.0870170i	0.839812	+	0.542877i	$0.182665\pi$
$200$		0			0
$201$	12.8739	+	7.43273i	0.908052	+	0.524264i
$202$		0			0
$203$	7.93725			0.557086
$204$		0			0
$205$	3.94242	+	4.41105i	0.275351	+	0.308081i
$206$		0			0
$207$		−	9.16515i		−	0.637022i
$208$		0			0
$209$	−4.58258			−0.316983
$210$		0			0
$211$	9.08258	+	15.7315i	0.625270	+	1.08300i	0.988489	+	0.151296i	$0.0483446\pi$
$211$	9.08258	+	15.7315i	0.625270	+	1.08300i	−0.363218	+	0.931704i	$0.618322\pi$
$212$		0			0
$213$	3.55945			0.243890
$214$		0			0
$215$	−0.990505	+	3.01071i	−0.0675519	+	0.205329i
$216$		0			0
$217$	14.5040	+	8.37386i	0.984593	+	0.568455i
$218$		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	0.683835	−	0.729637i	$-0.260311\pi$
$223$	−4.33013	−	7.50000i	−0.289967	−	0.502237i	−0.973801	+	0.227400i	$0.926978\pi$
$224$		0			0
$225$	1.11847	−	9.93725i	0.0745649	−	0.662484i
$226$		0			0
$227$	3.05493	−	5.29129i	0.202763	−	0.351195i	−0.746655	−	0.665212i	$-0.768341\pi$
$227$	3.05493	−	5.29129i	0.202763	−	0.351195i	0.949418	+	0.314016i	$0.101675\pi$
$228$		0			0
$229$			5.48220i			0.362274i	0.983458	+	0.181137i	$0.0579778\pi$
$229$			5.48220i			0.362274i	−0.983458	+	0.181137i	$0.942022\pi$
$230$		0			0
$231$	−2.29129	−	3.96863i	−0.150756	−	0.261116i
$232$		0			0
$233$		−	21.1652i		−	1.38658i	−0.720661	−	0.693288i	$-0.756162\pi$
$233$		−	21.1652i		−	1.38658i	0.720661	−	0.693288i	$-0.243838\pi$
$234$		0			0
$235$	4.00000	+	19.1652i	0.260931	+	1.25020i
$236$		0			0
$237$	−5.19615	+	3.00000i	−0.337526	+	0.194871i
$238$		0			0
$239$		−	20.9753i		−	1.35678i	−0.734702	−	0.678390i	$-0.762678\pi$
$239$		−	20.9753i		−	1.35678i	0.734702	−	0.678390i	$-0.237322\pi$
$240$		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
$245$	6.66888	−	5.96038i	0.426059	−	0.380795i
$246$		0			0
$247$	−6.06218	−	1.50000i	−0.385727	−	0.0954427i
$248$		0			0
$249$	−9.79129	+	5.65300i	−0.620498	+	0.358244i
$250$		0			0
$251$	9.08258	−	15.7315i	0.573287	−	0.992962i	−0.422938	−	0.906158i	$-0.639001\pi$
$251$	9.08258	−	15.7315i	0.573287	−	0.992962i	0.996225	−	0.0868039i	$-0.0276654\pi$
$252$		0			0
$253$	6.06218	−	10.5000i	0.381126	−	0.660129i
$254$		0			0
$255$	2.09355	+	10.0308i	0.131103	+	0.628153i
$256$		0			0
$257$	0.143025	−	0.0825757i	0.00892167	−	0.00515093i	−0.495533	−	0.868589i	$-0.665027\pi$
$257$	0.143025	−	0.0825757i	0.00892167	−	0.00515093i	0.504454	+	0.863438i	$0.331694\pi$
$258$		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	−0.240059	−	0.970758i	$-0.577167\pi$
$263$	7.79423	−	4.50000i	0.480613	−	0.277482i	0.720672	+	0.693276i	$0.243833\pi$
$264$		0			0
$265$	3.46410	−	0.723000i	0.212798	−	0.0444135i
$266$		0			0
$267$	2.14123	−	3.70871i	0.131041	−	0.226969i
$268$		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
$277$	14.3609	+	8.29129i	0.862865	+	0.498175i	0.864971	−	0.501823i	$-0.167337\pi$
$277$	14.3609	+	8.29129i	0.862865	+	0.498175i	−0.00210581	+	0.999998i	$0.500670\pi$
$278$		0			0
$279$	16.7477	+	9.66930i	1.00266	+	0.578886i
$280$		0			0
$281$			17.5112i			1.04463i	0.852752	+	0.522316i	$0.174932\pi$
$281$			17.5112i			1.04463i	−0.852752	+	0.522316i	$0.825068\pi$
$282$		0			0
$283$	−0.218475	+	0.126136i	−0.0129870	+	0.00749803i	−0.506479	−	0.862252i	$-0.669053\pi$
$283$	−0.218475	+	0.126136i	−0.0129870	+	0.00749803i	0.493492	+	0.869750i	$0.335720\pi$
$284$		0			0
$285$	−0.791288	−	3.79129i	−0.0468718	−	0.224577i
$286$		0			0
$287$		−	4.58258i		−	0.270501i
$288$		0			0
$289$	2.00000	+	3.46410i	0.117647	+	0.203771i
$290$		0			0
$291$			4.47315i			0.262221i
$292$		0			0
$293$	11.7152	−	20.2913i	0.684408	−	1.18543i	−0.289214	−	0.957264i	$-0.593394\pi$
$293$	11.7152	−	20.2913i	0.684408	−	1.18543i	0.973622	−	0.228165i	$-0.0732727\pi$
$294$		0			0
$295$	2.35411	−	7.15546i	0.137061	−	0.416607i
$296$		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
$301$	2.12614	−	1.22753i	0.122548	−	0.0707534i
$302$		0			0
$303$	−7.79423	−	4.50000i	−0.447767	−	0.258518i
$304$		0			0
$305$	−22.4781	−	7.39517i	−1.28709	−	0.423446i
$306$		0			0
$307$	24.2487			1.38395			0.691974	−	0.721923i	$-0.256741\pi$
$307$	24.2487			1.38395			0.691974	+	0.721923i	$0.256741\pi$
$308$		0			0
$309$	−7.58258	−	13.1334i	−0.431358	−	0.747133i
$310$		0			0
$311$	1.58258			0.0897396			0.0448698	−	0.998993i	$-0.485713\pi$
$311$	1.58258			0.0897396			0.0448698	+	0.998993i	$0.485713\pi$
$312$		0			0
$313$			30.7477i			1.73796i	0.494843	+	0.868982i	$0.335225\pi$
$313$			30.7477i			1.73796i	−0.494843	+	0.868982i	$0.664775\pi$
$314$		0			0
$315$	−5.77542	+	5.16184i	−0.325408	+	0.290837i
$316$		0			0
$317$	−20.9753			−1.17809			−0.589045	−	0.808100i	$-0.700496\pi$
$317$	−20.9753			−1.17809			−0.589045	+	0.808100i	$0.700496\pi$
$318$		0			0
$319$	10.5000	+	6.06218i	0.587887	+	0.339417i
$320$		0			0
$321$	0.708712	−	1.22753i	0.0395565	−	0.0685138i
$322$		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
$327$	−1.37055	−	2.37386i	−0.0757916	−	0.131275i
$328$		0			0
$329$	7.58258	−	13.1334i	0.418041	−	0.724068i
$330$		0			0
$331$	−9.87386	−	5.70068i	−0.542717	−	0.313338i	0.203463	−	0.979083i	$-0.434780\pi$
$331$	−9.87386	−	5.70068i	−0.542717	−	0.313338i	−0.746179	+	0.665745i	$0.768114\pi$
$332$		0			0
$333$	−15.8745			−0.869918
$334$		0			0
$335$	24.7840	−	22.1509i	1.35409	−	1.21023i
$336$		0			0
$337$			3.25227i			0.177163i	0.996069	+	0.0885813i	$0.0282333\pi$
$337$			3.25227i			0.177163i	−0.996069	+	0.0885813i	$0.971767\pi$
$338$		0			0
$339$	−16.5826			−0.900642
$340$		0			0
$341$	12.7913	+	22.1552i	0.692687	+	1.19977i
$342$		0			0
$343$	−19.0526			−1.02874
$344$		0			0
$345$	9.73371	+	3.20233i	0.524045	+	0.172408i
$346$		0			0
$347$	13.2764	+	7.66515i	0.712716	+	0.411487i	0.812066	−	0.583566i	$-0.198343\pi$
$347$	13.2764	+	7.66515i	0.712716	+	0.411487i	−0.0993497	+	0.995053i	$0.531676\pi$
$348$		0			0
$349$	15.8739	−	9.16478i	0.849708	−	0.490579i	−0.0108440	−	0.999941i	$-0.503452\pi$
$349$	15.8739	−	9.16478i	0.849708	−	0.490579i	0.860552	+	0.509362i	$0.170118\pi$
$350$		0			0
$351$	−5.00000	−	17.3205i	−0.266880	−	0.924500i
$352$		0			0
$353$	−8.70793	−	15.0826i	−0.463476	−	0.802765i	0.535655	−	0.844437i	$-0.320065\pi$
$353$	−8.70793	−	15.0826i	−0.463476	−	0.802765i	−0.999131	+	0.0416724i	$0.986731\pi$
$354$		0			0
$355$	2.48737	−	7.56052i	0.132016	−	0.401271i
$356$		0			0
$357$	3.96863	−	6.87386i	0.210042	−	0.363803i
$358$		0			0
$359$			33.3857i			1.76203i	0.473088	+	0.881015i	$0.343139\pi$
$359$			33.3857i			1.76203i	−0.473088	+	0.881015i	$0.656861\pi$
$360$		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
$367$	−22.2982	+	12.8739i	−1.16396	+	0.672010i	−0.952249	−	0.305323i	$-0.901236\pi$
$367$	−22.2982	+	12.8739i	−1.16396	+	0.672010i	−0.211707	+	0.977333i	$0.567902\pi$
$368$		0			0
$369$		−	5.29150i		−	0.275465i
$370$		0			0
$371$	−2.37386	−	1.37055i	−0.123245	−	0.0711554i
$372$		0			0
$373$	−11.2583	−	6.50000i	−0.582934	−	0.336557i	0.179364	−	0.983783i	$-0.442596\pi$
$373$	−11.2583	−	6.50000i	−0.582934	−	0.336557i	−0.762299	+	0.647225i	$0.775929\pi$
$374$		0			0
$375$	10.1629	+	4.65997i	0.524810	+	0.240640i
$376$		0			0
$377$	11.9059	+	11.4564i	0.613184	+	0.590037i
$378$		0			0
$379$	−18.2477	+	10.5353i	−0.937323	+	0.541164i	−0.889120	−	0.457674i	$-0.848683\pi$
$379$	−18.2477	+	10.5353i	−0.937323	+	0.541164i	−0.0482027	+	0.998838i	$0.515349\pi$
$380$		0			0
$381$	4.87386	−	8.44178i	0.249696	−	0.432485i
$382$		0			0
$383$	−1.41823	+	2.45644i	−0.0724680	+	0.125518i	−0.899982	−	0.435926i	$-0.856421\pi$
$383$	−1.41823	+	2.45644i	−0.0724680	+	0.125518i	0.827514	+	0.561444i	$0.189754\pi$
$384$		0			0
$385$	−10.0308	+	2.09355i	−0.511217	+	0.106697i
$386$		0			0
$387$	2.45505	−	1.41742i	0.124797	−	0.0720517i
$388$		0			0
$389$	−15.1652			−0.768904			−0.384452	−	0.923145i	$-0.625610\pi$
$389$	−15.1652			−0.768904			−0.384452	+	0.923145i	$0.625610\pi$
$390$		0			0
$391$	21.0000			1.06202
$392$		0			0
$393$	−1.37055	+	0.791288i	−0.0691351	+	0.0399152i
$394$		0			0
$395$	2.74110	+	13.1334i	0.137920	+	0.660813i
$396$		0			0
$397$	−13.6379	+	23.6216i	−0.684468	+	1.18553i	0.289135	+	0.957288i	$0.406632\pi$
$397$	−13.6379	+	23.6216i	−0.684468	+	1.18553i	−0.973604	+	0.228245i	$0.926701\pi$
$398$		0			0
$399$	−1.50000	+	2.59808i	−0.0750939	+	0.130066i
$400$		0			0
$401$	10.8303	−	6.25288i	0.540840	−	0.312254i	−0.204580	−	0.978850i	$-0.565583\pi$
$401$	10.8303	−	6.25288i	0.540840	−	0.312254i	0.745419	+	0.666596i	$0.232249\pi$
$402$		0			0
$403$	9.66930	+	33.4955i	0.481662	+	1.66853i
$404$		0			0
$405$	−1.66722	+	1.49009i	−0.0828448	+	0.0740434i
$406$		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
$411$		−	0.0953502i		−	0.00470328i
$412$		0			0
$413$	−5.05313	+	2.91742i	−0.248648	+	0.143557i
$414$		0			0
$415$	5.16515	+	24.7477i	0.253547	+	1.21482i
$416$		0			0
$417$			5.74773i			0.281467i
$418$		0			0
$419$	12.0826	+	20.9276i	0.590272	+	1.02238i	0.994195	+	0.107589i	$0.0343130\pi$
$419$	12.0826	+	20.9276i	0.590272	+	1.02238i	−0.403923	+	0.914793i	$0.632354\pi$
$420$		0			0
$421$			26.2668i			1.28017i	0.768306	+	0.640083i	$0.221100\pi$
$421$			26.2668i			1.28017i	−0.768306	+	0.640083i	$0.778900\pi$
$422$		0			0
$423$	8.75560	−	15.1652i	0.425712	−	0.737355i
$424$		0			0
$425$	22.7691	+	2.56275i	1.10446	+	0.124311i
$426$		0			0
$427$	9.16478	+	15.8739i	0.443515	+	0.768190i
$428$		0			0
$429$	2.29129	−	9.26013i	0.110624	−	0.447083i
$430$		0			0
$431$	−25.6652	+	14.8178i	−1.23625	+	0.713747i	−0.968325	−	0.249693i	$-0.919670\pi$
$431$	−25.6652	+	14.8178i	−1.23625	+	0.713747i	−0.267922	+	0.963441i	$0.586337\pi$
$432$		0			0
$433$	−15.3700	−	8.87386i	−0.738634	−	0.426451i	0.0829383	−	0.996555i	$-0.473570\pi$
$433$	−15.3700	−	8.87386i	−0.738634	−	0.426451i	−0.821573	+	0.570104i	$0.806903\pi$
$434$		0			0
$435$	−3.20233	+	9.73371i	−0.153540	+	0.466696i
$436$		0			0
$437$	−7.93725			−0.379690
$438$		0			0
$439$	−20.2477	−	35.0701i	−0.966371	−	1.67380i	−0.705885	−	0.708327i	$-0.749450\pi$
$439$	−20.2477	−	35.0701i	−0.966371	−	1.67380i	−0.260487	−	0.965477i	$-0.583883\pi$
$440$		0			0
$441$	−8.00000			−0.380952
$442$		0			0
$443$		−	25.9129i		−	1.23116i	−0.788075	−	0.615579i	$-0.788922\pi$
$443$		−	25.9129i		−	1.23116i	0.788075	−	0.615579i	$-0.211078\pi$
$444$		0			0
$445$	−6.38126	−	7.13978i	−0.302501	−	0.338458i
$446$		0			0
$447$	9.76465			0.461852
$448$		0			0
$449$	32.4564	+	18.7387i	1.53171	+	0.884336i	0.999283	+	0.0378622i	$0.0120548\pi$
$449$	32.4564	+	18.7387i	1.53171	+	0.884336i	0.532431	+	0.846473i	$0.321279\pi$
$450$		0			0
$451$	3.50000	−	6.06218i	0.164809	−	0.285457i
$452$		0			0
$453$	3.10260	+	5.37386i	0.145773	+	0.252486i
$454$		0			0
$455$	−13.9548	−	0.513844i	−0.654210	−	0.0240894i
$456$		0			0
$457$	−0.866025	−	1.50000i	−0.0405110	−	0.0701670i	0.845059	−	0.534673i	$-0.179565\pi$
$457$	−0.866025	−	1.50000i	−0.0405110	−	0.0701670i	−0.885570	+	0.464506i	$0.846232\pi$
$458$		0			0
$459$	11.4564	−	19.8431i	0.534741	−	0.926198i
$460$		0			0
$461$	−1.03901	−	0.599876i	−0.0483917	−	0.0279390i	0.475609	−	0.879657i	$-0.342228\pi$
$461$	−1.03901	−	0.599876i	−0.0483917	−	0.0279390i	−0.524001	+	0.851718i	$0.675561\pi$
$462$		0			0
$463$	−8.22330			−0.382169			−0.191085	−	0.981574i	$-0.561201\pi$
$463$	−8.22330			−0.382169			−0.191085	+	0.981574i	$0.561201\pi$
$464$		0			0
$465$	−16.1208	+	14.4082i	−0.747586	+	0.668163i
$466$		0			0
$467$		−	12.3303i		−	0.570578i	−0.958441	−	0.285289i	$-0.907910\pi$
$467$		−	12.3303i		−	0.570578i	0.958441	−	0.285289i	$-0.0920896\pi$
$468$		0			0
$469$	−25.7477			−1.18892
$470$		0			0
$471$	−4.58258	−	7.93725i	−0.211154	−	0.365729i
$472$		0			0
$473$	3.75015			0.172432
$474$		0			0
$475$	−8.60591	−	0.968627i	−0.394866	−	0.0444437i
$476$		0			0
$477$	−2.74110	−	1.58258i	−0.125506	−	0.0724612i
$478$		0			0
$479$	28.0390	−	16.1883i	1.28114	−	0.739664i	0.304079	−	0.952647i	$-0.401651\pi$
$479$	28.0390	−	16.1883i	1.28114	−	0.739664i	0.977056	+	0.212983i	$0.0683179\pi$
$480$		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
$485$	9.50128	+	3.12587i	0.431431	+	0.141938i
$486$		0			0
$487$	−10.5353	+	18.2477i	−0.477401	+	0.826883i	−0.999665	−	0.0259009i	$-0.991755\pi$
$487$	−10.5353	+	18.2477i	−0.477401	+	0.826883i	0.522263	+	0.852784i	$0.325088\pi$
$488$		0			0
$489$			10.6784i			0.482892i
$490$		0			0
$491$	14.2913	+	24.7532i	0.644957	+	1.11710i	0.984311	+	0.176439i	$0.0564580\pi$
$491$	14.2913	+	24.7532i	0.644957	+	1.11710i	−0.339355	+	0.940658i	$0.610209\pi$
$492$		0			0
$493$			21.0000i			0.945792i
$494$		0			0
$495$	−11.5826	+	2.41742i	−0.520598	+	0.108655i
$496$		0			0
$497$	−5.33918	+	3.08258i	−0.239495	+	0.138272i
$498$		0			0
$499$			16.5975i			0.743006i	0.928432	+	0.371503i	$0.121158\pi$
$499$			16.5975i			0.743006i	−0.928432	+	0.371503i	$0.878842\pi$
$500$		0			0
$501$	−3.70871	−	2.14123i	−0.165693	−	0.0956629i
$502$		0			0
$503$	15.7315	+	9.08258i	0.701432	+	0.404972i	0.807881	−	0.589346i	$-0.200615\pi$
$503$	15.7315	+	9.08258i	0.701432	+	0.404972i	−0.106448	+	0.994318i	$0.533948\pi$
$504$		0			0
$505$	−15.0050	+	13.4109i	−0.667712	+	0.596775i
$506$		0			0
$507$	6.06218	−	11.5000i	0.269231	−	0.510733i
$508$		0			0
$509$	−25.6652	+	14.8178i	−1.13759	+	0.656787i	−0.945832	−	0.324656i	$-0.894751\pi$
$509$	−25.6652	+	14.8178i	−1.13759	+	0.656787i	−0.191756	+	0.981443i	$0.561418\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−4.33013	+	7.50000i	−0.191180	+	0.331133i
$514$		0			0
$515$	−33.1950	+	6.92820i	−1.46275	+	0.305293i
$516$		0			0
$517$	20.0616	−	11.5826i	0.882309	−	0.509401i
$518$		0			0
$519$	−7.41742			−0.325589
$520$		0			0
$521$	−27.4955			−1.20460			−0.602299	−	0.798271i	$-0.705748\pi$
$521$	−27.4955			−1.20460			−0.602299	+	0.798271i	$0.705748\pi$
$522$		0			0
$523$	−15.7315	+	9.08258i	−0.687890	+	0.397153i	−0.802821	−	0.596220i	$-0.796669\pi$
$523$	−15.7315	+	9.08258i	−0.687890	+	0.397153i	0.114931	+	0.993373i	$0.463335\pi$
$524$		0			0
$525$	−3.46410	−	7.93725i	−0.151186	−	0.346410i
$526$		0			0
$527$	−22.1552	+	38.3739i	−0.965094	+	1.67159i
$528$		0			0
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$		0			0
$531$	−5.83485	+	3.36875i	−0.253211	+	0.146191i
$532$		0			0
$533$	6.61438	−	6.87386i	0.286501	−	0.297740i
$534$		0			0
$535$	−2.11210	−	2.36316i	−0.0913139	−	0.102168i
$536$		0			0
$537$	0.143025	+	0.0825757i	0.00617200	+	0.00356340i
$538$		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
$543$	−16.2360	+	9.37386i	−0.696754	+	0.402271i
$544$		0			0
$545$	−6.00000	+	1.25227i	−0.257012	+	0.0536415i
$546$		0			0
$547$		−	1.25227i		−	0.0535433i	−0.999642	−	0.0267717i	$-0.991477\pi$
$547$		−	1.25227i		−	0.0535433i	0.999642	−	0.0267717i	$-0.00852270\pi$
$548$		0			0
$549$	10.5826	+	18.3296i	0.451653	+	0.782287i
$550$		0			0
$551$		−	7.93725i		−	0.338138i
$552$		0			0
$553$	5.19615	−	9.00000i	0.220963	−	0.382719i
$554$		0			0
$555$	5.54661	−	16.8593i	0.235440	−	0.715636i
$556$		0			0
$557$	−6.51903	−	11.2913i	−0.276220	−	0.478427i	0.694222	−	0.719761i	$-0.255749\pi$
$557$	−6.51903	−	11.2913i	−0.276220	−	0.478427i	−0.970442	+	0.241334i	$0.922415\pi$
$558$		0			0
$559$	4.96099	+	1.22753i	0.209827	+	0.0519188i
$560$		0			0
$561$	10.5000	−	6.06218i	0.443310	−	0.255945i
$562$		0			0
$563$	7.79423	+	4.50000i	0.328488	+	0.189652i	0.655169	−	0.755482i	$-0.272597\pi$
$563$	7.79423	+	4.50000i	0.328488	+	0.189652i	−0.326682	+	0.945134i	$0.605931\pi$
$564$		0			0
$565$	−11.5880	+	35.2225i	−0.487511	+	1.48182i
$566$		0			0
$567$	1.73205			0.0727393
$568$		0			0
$569$	−9.87386	−	17.1020i	−0.413934	−	0.716955i	0.581382	−	0.813631i	$-0.302512\pi$
$569$	−9.87386	−	17.1020i	−0.413934	−	0.716955i	−0.995316	+	0.0966762i	$0.969179\pi$
$570$		0			0
$571$	−29.0780			−1.21688			−0.608439	−	0.793601i	$-0.708204\pi$
$571$	−29.0780			−1.21688			−0.608439	+	0.793601i	$0.708204\pi$
$572$		0			0
$573$			7.41742i			0.309867i
$574$		0			0
$575$	13.6040	−	18.4373i	0.567324	−	0.768887i
$576$		0			0
$577$	6.92820			0.288425			0.144212	−	0.989547i	$-0.453935\pi$
$577$	6.92820			0.288425			0.144212	+	0.989547i	$0.453935\pi$
$578$		0			0
$579$	0.873864	+	0.504525i	0.0363165	+	0.0209674i
$580$		0			0
$581$	9.79129	−	16.9590i	0.406211	−	0.703578i
$582$		0			0
$583$	−2.09355	−	3.62614i	−0.0867060	−	0.150179i
$584$		0			0
$585$	−16.1136	−	0.593336i	−0.666215	−	0.0245314i
$586$		0			0
$587$	−9.35548	−	16.2042i	−0.386142	−	0.668818i	0.605785	−	0.795628i	$-0.292859\pi$
$587$	−9.35548	−	16.2042i	−0.386142	−	0.668818i	−0.991927	+	0.126811i	$0.959526\pi$
$588$		0			0
$589$	8.37386	−	14.5040i	0.345039	−	0.597625i
$590$		0			0
$591$	17.2913	+	9.98313i	0.711269	+	0.410651i
$592$		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
$595$	−11.8273	−	13.2331i	−0.484870	−	0.542506i
$596$		0			0
$597$			1.41742i			0.0580113i
$598$		0			0
$599$	−39.4955			−1.61374			−0.806870	−	0.590729i	$-0.798840\pi$
$599$	−39.4955			−1.61374			−0.806870	+	0.590729i	$0.798840\pi$
$600$		0			0
$601$	14.4564	+	25.0393i	0.589690	+	1.02137i	0.994273	+	0.106872i	$0.0340836\pi$
$601$	14.4564	+	25.0393i	0.589690	+	1.02137i	−0.404582	+	0.914502i	$0.632583\pi$
$602$		0			0
$603$	−29.7309			−1.21074
$604$		0			0
$605$	8.49628	+	2.79523i	0.345423	+	0.113642i
$606$		0			0
$607$	−17.1020	−	9.87386i	−0.694150	−	0.400768i	0.111015	−	0.993819i	$-0.464590\pi$
$607$	−17.1020	−	9.87386i	−0.694150	−	0.400768i	−0.805165	+	0.593051i	$0.797923\pi$
$608$		0			0
$609$	6.87386	−	3.96863i	0.278543	−	0.160817i
$610$		0			0
$611$	30.3303	−	8.75560i	1.22703	−	0.354214i
$612$		0			0
$613$	10.8968	+	18.8739i	0.440119	+	0.762308i	0.997698	−	0.0678157i	$-0.0216030\pi$
$613$	10.8968	+	18.8739i	0.440119	+	0.762308i	−0.557579	+	0.830124i	$0.688270\pi$
$614$		0			0
$615$	5.61976	+	1.84887i	0.226611	+	0.0745536i
$616$		0			0
$617$	1.68438	−	2.91742i	0.0678104	−	0.117451i	−0.830127	−	0.557575i	$-0.811732\pi$
$617$	1.68438	−	2.91742i	0.0678104	−	0.117451i	0.897937	+	0.440124i	$0.145065\pi$
$618$		0			0
$619$			2.01810i			0.0811143i	0.999177	+	0.0405572i	$0.0129133\pi$
$619$			2.01810i			0.0811143i	−0.999177	+	0.0405572i	$0.987087\pi$
$620$		0			0
$621$	−11.4564	−	19.8431i	−0.459731	−	0.796278i
$622$		0			0
$623$			7.41742i			0.297173i
$624$		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
$631$	18.8739	+	10.8968i	0.751357	+	0.433796i	0.826184	−	0.563401i	$-0.190507\pi$
$631$	18.8739	+	10.8968i	0.751357	+	0.433796i	−0.0748272	+	0.997197i	$0.523841\pi$
$632$		0			0
$633$	15.7315	+	9.08258i	0.625270	+	0.361000i
$634$		0			0
$635$	−14.5250	−	16.2516i	−0.576408	−	0.644925i
$636$		0			0
$637$	−10.3923	−	10.0000i	−0.411758	−	0.396214i
$638$		0			0
$639$	−6.16515	+	3.55945i	−0.243890	+	0.140810i
$640$		0			0
$641$	0.0825757	−	0.143025i	0.00326154	−	0.00564916i	−0.864390	−	0.502822i	$-0.832295\pi$
$641$	0.0825757	−	0.143025i	0.00326154	−	0.00564916i	0.867652	+	0.497173i	$0.165628\pi$
$642$		0			0
$643$	−2.95958	+	5.12614i	−0.116714	+	0.202155i	−0.918464	−	0.395505i	$-0.870570\pi$
$643$	−2.95958	+	5.12614i	−0.116714	+	0.202155i	0.801749	+	0.597660i	$0.203903\pi$
$644$		0			0
$645$	0.647551	+	3.10260i	0.0254973	+	0.122165i
$646$		0			0
$647$	−23.3827	+	13.5000i	−0.919268	+	0.530740i	−0.883402	−	0.468617i	$-0.844753\pi$
$647$	−23.3827	+	13.5000i	−0.919268	+	0.530740i	−0.0358667	+	0.999357i	$0.511419\pi$
$648$		0			0
$649$	−8.91288			−0.349861
$650$		0			0
$651$	16.7477			0.656395
$652$		0			0
$653$	−42.2843	+	24.4129i	−1.65471	+	0.955350i	−0.679619	+	0.733566i	$0.737855\pi$
$653$	−42.2843	+	24.4129i	−1.65471	+	0.955350i	−0.975096	+	0.221784i	$0.928812\pi$
$654$		0			0
$655$	0.723000	+	3.46410i	0.0282500	+	0.135354i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.2477	−	21.2137i	0.477104	−	0.826368i	−0.522552	−	0.852607i	$-0.675020\pi$
$659$	12.2477	−	21.2137i	0.477104	−	0.826368i	0.999656	+	0.0262396i	$0.00835327\pi$
$660$		0			0
$661$	2.12614	−	1.22753i	0.0826971	−	0.0477452i	−0.458081	−	0.888910i	$-0.651463\pi$
$661$	2.12614	−	1.22753i	0.0826971	−	0.0477452i	0.540778	+	0.841165i	$0.318130\pi$
$662$		0			0
$663$	15.8745	−	4.58258i	0.616515	−	0.177972i
$664$		0			0
$665$	4.47028	+	5.00166i	0.173350	+	0.193956i
$666$		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
$671$			27.9989i			1.08088i
$672$		0			0
$673$	5.05313	−	2.91742i	0.194784	−	0.112458i	−0.399436	−	0.916761i	$-0.630794\pi$
$673$	5.05313	−	2.91742i	0.194784	−	0.112458i	0.594220	+	0.804302i	$0.297461\pi$
$674$		0			0
$675$	−10.0000	−	22.9129i	−0.384900	−	0.881917i
$676$		0			0
$677$		−	21.1652i		−	0.813443i	−0.913552	−	0.406721i	$-0.866672\pi$
$677$		−	21.1652i		−	0.813443i	0.913552	−	0.406721i	$-0.133328\pi$
$678$		0			0
$679$	−3.87386	−	6.70973i	−0.148665	−	0.257496i
$680$		0			0
$681$		−	6.10985i		−	0.234130i
$682$		0			0
$683$	5.96683	−	10.3348i	0.228314	−	0.395452i	−0.728994	−	0.684520i	$-0.760012\pi$
$683$	5.96683	−	10.3348i	0.228314	−	0.395452i	0.957309	+	0.289068i	$0.0933453\pi$
$684$		0			0
$685$	−0.202530	−	0.0666313i	−0.00773829	−	0.00254585i
$686$		0			0
$687$	2.74110	+	4.74773i	0.104580	+	0.181137i
$688$		0			0
$689$	−1.58258	−	5.48220i	−0.0602913	−	0.208855i
$690$		0			0
$691$	−30.8739	+	17.8250i	−1.17450	+	0.678096i	−0.954735	−	0.297457i	$-0.903861\pi$
$691$	−30.8739	+	17.8250i	−1.17450	+	0.678096i	−0.219762	+	0.975554i	$0.570528\pi$
$692$		0			0
$693$	7.93725	+	4.58258i	0.301511	+	0.174078i
$694$		0			0
$695$	12.2086	+	4.01655i	0.463097	+	0.152356i
$696$		0			0
$697$	12.1244			0.459243
$698$		0			0
$699$	−10.5826	−	18.3296i	−0.400270	−	0.693288i
$700$		0			0
$701$	−2.83485			−0.107071			−0.0535354	−	0.998566i	$-0.517049\pi$
$701$	−2.83485			−0.107071			−0.0535354	+	0.998566i	$0.517049\pi$
$702$		0			0
$703$			13.7477i			0.518505i
$704$		0			0
$705$	13.0467	+	14.5975i	0.491366	+	0.549774i
$706$		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
$713$	22.1552	+	38.3739i	0.829717	+	1.43711i
$714$		0			0
$715$	−18.0680	−	11.3379i	−0.675704	−	0.424013i
$716$		0			0
$717$	−10.4877	−	18.1652i	−0.391669	−	0.678390i
$718$		0			0
$719$	−15.2477	+	26.4098i	−0.568644	+	0.984921i	0.428056	+	0.903752i	$0.359199\pi$
$719$	−15.2477	+	26.4098i	−0.568644	+	0.984921i	−0.996700	+	0.0811686i	$0.974135\pi$
$720$		0			0
$721$	22.7477	+	13.1334i	0.847170	+	0.489114i
$722$		0			0
$723$	−1.73205			−0.0644157
$724$		0			0
$725$	18.4373	+	13.6040i	0.684742	+	0.505238i
$726$		0			0
$727$			42.7477i			1.58543i	0.609595	+	0.792713i	$0.291332\pi$
$727$			42.7477i			1.58543i	−0.609595	+	0.792713i	$0.708668\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	3.24773	+	5.62523i	0.120122	+	0.208057i
$732$		0			0
$733$	8.94630			0.330439			0.165220	−	0.986257i	$-0.447167\pi$
$733$	8.94630			0.330439			0.165220	+	0.986257i	$0.447167\pi$
$734$		0			0
$735$	2.79523	−	8.49628i	0.103103	−	0.313390i
$736$		0			0
$737$	−34.0610	−	19.6652i	−1.25465	−	0.724375i
$738$		0			0
$739$	42.2477	−	24.3917i	1.55411	−	0.897265i	0.556307	−	0.830977i	$-0.312218\pi$
$739$	42.2477	−	24.3917i	1.55411	−	0.897265i	0.997801	−	0.0662878i	$-0.0211156\pi$
$740$		0			0
$741$	−6.00000	+	1.73205i	−0.220416	+	0.0636285i
$742$		0			0
$743$	21.3845	+	37.0390i	0.784521	+	1.35883i	0.929285	+	0.369364i	$0.120424\pi$
$743$	21.3845	+	37.0390i	0.784521	+	1.35883i	−0.144764	+	0.989466i	$0.546242\pi$
$744$		0			0
$745$	6.82361	−	20.7408i	0.249998	−	0.759884i
$746$		0			0
$747$	11.3060	−	19.5826i	0.413665	−	0.716489i
$748$		0			0
$749$			2.45505i			0.0897056i
$750$		0			0
$751$	−7.87386	−	13.6379i	−0.287321	−	0.497655i	0.685848	−	0.727745i	$-0.259431\pi$
$751$	−7.87386	−	13.6379i	−0.287321	−	0.497655i	−0.973169	+	0.230090i	$0.926098\pi$
$752$		0			0
$753$		−	18.1652i		−	0.661975i
$754$		0			0
$755$	13.5826	−	2.83485i	0.494321	−	0.103171i
$756$		0			0
$757$	−15.3700	+	8.87386i	−0.558632	+	0.322526i	−0.752596	−	0.658482i	$-0.771199\pi$
$757$	−15.3700	+	8.87386i	−0.558632	+	0.322526i	0.193965	+	0.981009i	$0.437865\pi$
$758$		0			0
$759$		−	12.1244i		−	0.440086i
$760$		0			0
$761$	−35.2913	−	20.3754i	−1.27931	−	0.738609i	−0.302587	−	0.953122i	$-0.597850\pi$
$761$	−35.2913	−	20.3754i	−1.27931	−	0.738609i	−0.976721	+	0.214513i	$0.931184\pi$
$762$		0			0
$763$	4.11165	+	2.37386i	0.148852	+	0.0859396i
$764$		0			0
$765$	−13.6569	−	15.2803i	−0.493768	−	0.552461i
$766$		0			0
$767$	−11.7906	−	2.91742i	−0.425735	−	0.105342i
$768$		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
$771$	0.0825757	−	0.143025i	0.00297389	−	0.00515093i
$772$		0			0
$773$	17.3682	−	30.0826i	0.624690	−	1.08200i	−0.363911	−	0.931434i	$-0.618559\pi$
$773$	17.3682	−	30.0826i	0.624690	−	1.08200i	0.988601	−	0.150561i	$-0.0481080\pi$
$774$		0			0
$775$	19.3386	+	44.3103i	0.694663	+	1.59167i
$776$		0			0
$777$	−11.9059	+	6.87386i	−0.427121	+	0.246598i
$778$		0			0
$779$	−4.58258			−0.164188
$780$		0			0
$781$	−9.41742			−0.336982
$782$		0			0
$783$	19.8431	−	11.4564i	0.709136	−	0.409420i
$784$		0			0
$785$	−20.0616	+	4.18710i	−0.716030	+	0.149444i
$786$		0			0
$787$	16.0930	−	27.8739i	0.573653	−	0.993596i	−0.422534	−	0.906347i	$-0.638859\pi$
$787$	16.0930	−	27.8739i	0.573653	−	0.993596i	0.996187	−	0.0872487i	$-0.0278075\pi$
$788$		0			0
$789$	4.50000	−	7.79423i	0.160204	−	0.277482i
$790$		0			0
$791$	24.8739	−	14.3609i	0.884413	−	0.510616i
$792$		0			0
$793$	−9.16478	+	37.0390i	−0.325451	+	1.31529i
$794$		0			0
$795$	2.63850	−	2.35819i	0.0935779	−	0.0836363i
$796$		0			0
$797$	17.3881	+	10.0390i	0.615918	+	0.355600i	0.775278	−	0.631620i	$-0.217610\pi$
$797$	17.3881	+	10.0390i	0.615918	+	0.355600i	−0.159360	+	0.987220i	$0.550943\pi$
$798$		0			0
$799$	34.7477	+	20.0616i	1.22929	+	0.709729i
$800$		0			0
$801$			8.56490i			0.302626i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−17.3739	+	3.62614i	−0.612348	+	0.127805i
$806$		0			0
$807$			15.0000i			0.528025i
$808$		0			0
$809$	18.4129	+	31.8920i	0.647362	+	1.12126i	0.983750	+	0.179541i	$0.0574613\pi$
$809$	18.4129	+	31.8920i	0.647362	+	1.12126i	−0.336388	+	0.941723i	$0.609205\pi$
$810$		0			0
$811$		−	18.7665i		−	0.658981i	−0.944159	−	0.329491i	$-0.893123\pi$
$811$		−	18.7665i		−	0.658981i	0.944159	−	0.329491i	$-0.106877\pi$
$812$		0			0
$813$	−4.33013	+	7.50000i	−0.151864	+	0.263036i
$814$		0			0
$815$	22.6816	+	7.46211i	0.794501	+	0.261386i
$816$		0			0
$817$	−1.22753	−	2.12614i	−0.0429457	−	0.0743841i
$818$		0			0
$819$	9.00000	+	8.66025i	0.314485	+	0.302614i
$820$		0			0
$821$	20.2913	−	11.7152i	0.708171	−	0.408863i	−0.102213	−	0.994763i	$-0.532592\pi$
$821$	20.2913	−	11.7152i	0.708171	−	0.408863i	0.810383	+	0.585900i	$0.199259\pi$
$822$		0			0
$823$	35.1455	+	20.2913i	1.22510	+	0.707310i	0.966000	−	0.258542i	$-0.0832419\pi$
$823$	35.1455	+	20.2913i	1.22510	+	0.707310i	0.259096	+	0.965851i	$0.416575\pi$
$824$		0			0
$825$	1.47960	−	13.1458i	0.0515131	−	0.457676i
$826$		0			0
$827$	−31.5583			−1.09739			−0.548695	−	0.836023i	$-0.684875\pi$
$827$	−31.5583			−1.09739			−0.548695	+	0.836023i	$0.684875\pi$
$828$		0			0
$829$	1.66515	+	2.88413i	0.0578331	+	0.100170i	0.893492	−	0.449078i	$-0.148248\pi$
$829$	1.66515	+	2.88413i	0.0578331	+	0.100170i	−0.835659	+	0.549248i	$0.814914\pi$
$830$		0			0
$831$	16.5826			0.575243
$832$		0			0
$833$		−	18.3303i		−	0.635107i
$834$		0			0
$835$	−7.13978	+	6.38126i	−0.247082	+	0.220833i
$836$		0			0
$837$	48.3465			1.67110
$838$		0			0
$839$	−1.16970	−	0.675325i	−0.0403824	−	0.0233148i	0.479673	−	0.877447i	$-0.340755\pi$
$839$	−1.16970	−	0.675325i	−0.0403824	−	0.0233148i	−0.520055	+	0.854133i	$0.674089\pi$
$840$		0			0
$841$	4.00000	−	6.92820i	0.137931	−	0.238904i
$842$		0			0
$843$	8.75560	+	15.1652i	0.301559	+	0.522316i
$844$		0			0
$845$	−20.1905	−	20.9128i	−0.694574	−	0.719421i
$846$		0			0
$847$	−3.46410	−	6.00000i	−0.119028	−	0.206162i
$848$		0			0
$849$	−0.126136	+	0.218475i	−0.00432899	+	0.00749803i
$850$		0			0
$851$	−31.5000	−	18.1865i	−1.07981	−	0.623426i
$852$		0			0
$853$	53.2566			1.82347			0.911736	−	0.410777i	$-0.134742\pi$
$853$	53.2566			1.82347			0.911736	+	0.410777i	$0.134742\pi$
$854$		0			0
$855$	5.16184	+	5.77542i	0.176531	+	0.197515i
$856$		0			0
$857$			22.7477i			0.777048i	0.921439	+	0.388524i	$0.127015\pi$
$857$			22.7477i			0.777048i	−0.921439	+	0.388524i	$0.872985\pi$
$858$		0			0
$859$	38.2432			1.30484			0.652420	−	0.757857i	$-0.273754\pi$
$859$	38.2432			1.30484			0.652420	+	0.757857i	$0.273754\pi$
$860$		0			0
$861$	−2.29129	−	3.96863i	−0.0780869	−	0.135250i
$862$		0			0
$863$	34.8317			1.18569			0.592843	−	0.805318i	$-0.298006\pi$
$863$	34.8317			1.18569			0.592843	+	0.805318i	$0.298006\pi$
$864$		0			0
$865$	−5.18335	+	15.7551i	−0.176239	+	0.535690i
$866$		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
$871$	−38.6216	−	37.1636i	−1.30864	−	1.25924i
$872$		0			0
$873$	−4.47315	−	7.74773i	−0.151393	−	0.262221i
$874$		0			0
$875$	−19.2800	+	1.81139i	−0.651783	+	0.0612360i
$876$		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
$879$		−	23.4304i		−	0.790286i
$880$		0			0
$881$	9.24773	+	16.0175i	0.311564	+	0.539644i	0.978701	−	0.205290i	$-0.0658139\pi$
$881$	9.24773	+	16.0175i	0.311564	+	0.539644i	−0.667137	+	0.744935i	$0.732481\pi$
$882$		0			0
$883$		−	46.2432i		−	1.55621i	−0.628136	−	0.778103i	$-0.716182\pi$
$883$		−	46.2432i		−	1.55621i	0.628136	−	0.778103i	$-0.283818\pi$
$884$		0			0
$885$	−1.53901	−	7.37386i	−0.0517334	−	0.247870i
$886$		0			0
$887$	0.429076	−	0.247727i	0.0144070	−	0.00831786i	−0.492779	−	0.870154i	$-0.664019\pi$
$887$	0.429076	−	0.247727i	0.0144070	−	0.00831786i	0.507186	+	0.861837i	$0.330686\pi$
$888$		0			0
$889$			16.8836i			0.566256i
$890$		0			0
$891$	2.29129	+	1.32288i	0.0767610	+	0.0443180i
$892$		0			0
$893$	−13.1334	−	7.58258i	−0.439493	−	0.253741i
$894$		0			0
$895$	0.275344	−	0.246091i	0.00920372	−	0.00822592i
$896$		0			0
$897$	3.96863	−	16.0390i	0.132509	−	0.535527i
$898$		0			0
$899$	−38.3739	+	22.1552i	−1.27984	+	0.738916i
$900$		0			0
$901$	3.62614	−	6.28065i	0.120804	−	0.209239i
$902$		0			0
$903$	1.22753	−	2.12614i	0.0408495	−	0.0707534i
$904$		0			0
$905$	8.56490	+	41.0369i	0.284707	+	1.36411i
$906$		0			0
$907$	29.2264	−	16.8739i	0.970446	−	0.560287i	0.0710740	−	0.997471i	$-0.477357\pi$
$907$	29.2264	−	16.8739i	0.970446	−	0.560287i	0.899372	+	0.437184i	$0.144024\pi$
$908$		0			0
$909$	18.0000			0.597022
$910$		0			0
$911$	−37.9129			−1.25611			−0.628055	−	0.778169i	$-0.716149\pi$
$911$	−37.9129			−1.25611			−0.628055	+	0.778169i	$0.716149\pi$
$912$		0			0
$913$	25.9053	−	14.9564i	0.857341	−	0.494986i
$914$		0			0
$915$	−23.1642	+	4.83465i	−0.765785	+	0.159829i
$916$		0			0
$917$	1.37055	−	2.37386i	0.0452596	−	0.0783919i
$918$		0			0
$919$	−17.9174	+	31.0339i	−0.591041	+	1.02371i	0.403051	+	0.915177i	$0.367950\pi$
$919$	−17.9174	+	31.0339i	−0.591041	+	1.02371i	−0.994093	+	0.108536i	$0.965384\pi$
$920$		0			0
$921$	21.0000	−	12.1244i	0.691974	−	0.399511i
$922$		0			0
$923$	−12.4581	−	3.08258i	−0.410063	−	0.101464i
$924$		0			0
$925$	−31.9343	−	23.5627i	−1.04999	−	0.774738i
$926$		0			0
$927$	26.2668	+	15.1652i	0.862715	+	0.498089i
$928$		0			0
$929$	−13.8303	−	7.98493i	−0.453758	−	0.261977i	0.255658	−	0.966767i	$-0.417708\pi$
$929$	−13.8303	−	7.98493i	−0.453758	−	0.261977i	−0.709416	+	0.704790i	$0.751041\pi$
$930$		0			0
$931$			6.92820i			0.227063i
$932$		0			0
$933$	1.37055	−	0.791288i	0.0448698	−	0.0259056i
$934$		0			0
$935$	−5.53901	−	26.5390i	−0.181145	−	0.867919i
$936$		0			0
$937$		−	23.4955i		−	0.767563i	−0.923424	−	0.383782i	$-0.874622\pi$
$937$		−	23.4955i		−	0.767563i	0.923424	−	0.383782i	$-0.125378\pi$
$938$		0			0
$939$	15.3739	+	26.6283i	0.501707	+	0.868982i
$940$		0			0
$941$		−	26.4575i		−	0.862490i	−0.902235	−	0.431245i	$-0.858074\pi$
$941$		−	26.4575i		−	0.862490i	0.902235	−	0.431245i	$-0.141926\pi$
$942$		0			0
$943$	6.06218	−	10.5000i	0.197412	−	0.341927i
$944$		0			0
$945$	−6.05184	+	18.3950i	−0.196866	+	0.598389i
$946$		0			0
$947$	−19.2909	−	33.4129i	−0.626871	−	1.08577i	−0.988176	−	0.153325i	$-0.951002\pi$
$947$	−19.2909	−	33.4129i	−0.626871	−	1.08577i	0.361305	−	0.932448i	$-0.382331\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−18.1652	+	10.4877i	−0.589045	+	0.340086i
$952$		0			0
$953$	48.5650	+	28.0390i	1.57317	+	0.908273i	0.995777	+	0.0918100i	$0.0292652\pi$
$953$	48.5650	+	28.0390i	1.57317	+	0.908273i	0.577398	+	0.816463i	$0.304068\pi$
$954$		0			0
$955$	15.7551	+	5.18335i	0.509824	+	0.167729i
$956$		0			0
$957$	12.1244			0.391925
$958$		0			0
$959$	0.0825757	+	0.143025i	0.00266651	+	0.00461853i
$960$		0			0
$961$	−62.4955			−2.01598
$962$		0			0
$963$			2.83485i			0.0913517i
$964$		0			0
$965$	1.68231	−	1.50358i	0.0541554	−	0.0484020i
$966$		0			0
$967$	−21.5076			−0.691638			−0.345819	−	0.938301i	$-0.612399\pi$
$967$	−21.5076			−0.691638			−0.345819	+	0.938301i	$0.612399\pi$
$968$		0			0
$969$	−6.87386	−	3.96863i	−0.220820	−	0.127491i
$970$		0			0
$971$	18.2477	−	31.6060i	0.585597	−	1.01428i	−0.409203	−	0.912443i	$-0.634193\pi$
$971$	18.2477	−	31.6060i	0.585597	−	1.01428i	0.994801	−	0.101841i	$-0.0324734\pi$
$972$		0			0
$973$	−4.97768	−	8.62159i	−0.159577	−	0.276396i
$974$		0			0
$975$	6.26029	−	16.9059i	0.200490	−	0.541421i
$976$		0			0
$977$	−19.3863	−	33.5780i	−0.620222	−	1.07426i	−0.989444	−	0.144915i	$-0.953709\pi$
$977$	−19.3863	−	33.5780i	−0.620222	−	1.07426i	0.369222	−	0.929341i	$-0.379624\pi$
$978$		0			0
$979$	−5.66515	+	9.81233i	−0.181059	+	0.313603i
$980$		0			0
$981$	4.74773	+	2.74110i	0.151583	+	0.0875166i
$982$		0			0
$983$	−3.12250			−0.0995924			−0.0497962	−	0.998759i	$-0.515857\pi$
$983$	−3.12250			−0.0995924			−0.0497962	+	0.998759i	$0.515857\pi$
$984$		0			0
$985$	33.2881	−	29.7516i	1.06065	−	0.947965i
$986$		0			0
$987$		−	15.1652i		−	0.482712i
$988$		0			0
$989$	6.49545			0.206543
$990$		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
$993$	−11.4014			−0.361811
$994$		0			0
$995$	3.01071	+	0.990505i	0.0954458	+	0.0314011i
$996$		0			0
$997$	15.7315	+	9.08258i	0.498221	+	0.287648i	0.727979	−	0.685600i	$-0.240460\pi$
$997$	15.7315	+	9.08258i	0.498221	+	0.287648i	−0.229758	+	0.973248i	$0.573793\pi$
$998$		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.49.3		8
4.3	odd	2		65.2.l.a.49.4	yes	8
5.4	even	2	inner	1040.2.df.b.49.2		8
12.11	even	2		585.2.bf.a.244.1		8
13.4	even	6	inner	1040.2.df.b.849.2		8
20.3	even	4		325.2.n.c.101.2		4
20.7	even	4		325.2.n.b.101.1		4
20.19	odd	2		65.2.l.a.49.1	yes	8
52.3	odd	6		845.2.d.c.844.1		8
52.7	even	12		845.2.n.d.529.4		8
52.11	even	12		845.2.b.f.339.1		8
52.15	even	12		845.2.b.f.339.7		8
52.19	even	12		845.2.n.c.529.2		8
52.23	odd	6		845.2.d.c.844.7		8
52.31	even	4		845.2.n.d.484.3		8
52.35	odd	6		845.2.l.c.654.4		8
52.43	odd	6		65.2.l.a.4.1	✓	8
52.47	even	4		845.2.n.c.484.1		8
52.51	odd	2		845.2.l.c.699.1		8
60.59	even	2		585.2.bf.a.244.4		8
65.4	even	6	inner	1040.2.df.b.849.3		8
156.95	even	6		585.2.bf.a.199.4		8
260.19	even	12		845.2.n.d.529.3		8
260.43	even	12		325.2.n.c.251.2		4
260.59	even	12		845.2.n.c.529.1		8
260.63	odd	12		4225.2.a.bk.1.1		4
260.67	odd	12		4225.2.a.bj.1.1		4
260.99	even	4		845.2.n.d.484.4		8
260.119	even	12		845.2.b.f.339.2		8
260.139	odd	6		845.2.l.c.654.1		8
260.147	even	12		325.2.n.b.251.1		4
260.159	odd	6		845.2.d.c.844.8		8
260.167	odd	12		4225.2.a.bj.1.4		4
260.179	odd	6		845.2.d.c.844.2		8
260.199	odd	6		65.2.l.a.4.4	yes	8
260.219	even	12		845.2.b.f.339.8		8
260.223	odd	12		4225.2.a.bk.1.4		4
260.239	even	4		845.2.n.c.484.2		8
260.259	odd	2		845.2.l.c.699.4		8
780.719	even	6		585.2.bf.a.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.1	✓	8	52.43	odd	6
65.2.l.a.4.4	yes	8	260.199	odd	6
65.2.l.a.49.1	yes	8	20.19	odd	2
65.2.l.a.49.4	yes	8	4.3	odd	2
325.2.n.b.101.1		4	20.7	even	4
325.2.n.b.251.1		4	260.147	even	12
325.2.n.c.101.2		4	20.3	even	4
325.2.n.c.251.2		4	260.43	even	12
585.2.bf.a.199.1		8	780.719	even	6
585.2.bf.a.199.4		8	156.95	even	6
585.2.bf.a.244.1		8	12.11	even	2
585.2.bf.a.244.4		8	60.59	even	2
845.2.b.f.339.1		8	52.11	even	12
845.2.b.f.339.2		8	260.119	even	12
845.2.b.f.339.7		8	52.15	even	12
845.2.b.f.339.8		8	260.219	even	12
845.2.d.c.844.1		8	52.3	odd	6
845.2.d.c.844.2		8	260.179	odd	6
845.2.d.c.844.7		8	52.23	odd	6
845.2.d.c.844.8		8	260.159	odd	6
845.2.l.c.654.1		8	260.139	odd	6
845.2.l.c.654.4		8	52.35	odd	6
845.2.l.c.699.1		8	52.51	odd	2
845.2.l.c.699.4		8	260.259	odd	2
845.2.n.c.484.1		8	52.47	even	4
845.2.n.c.484.2		8	260.239	even	4
845.2.n.c.529.1		8	260.59	even	12
845.2.n.c.529.2		8	52.19	even	12
845.2.n.d.484.3		8	52.31	even	4
845.2.n.d.484.4		8	260.99	even	4
845.2.n.d.529.3		8	260.19	even	12
845.2.n.d.529.4		8	52.7	even	12
1040.2.df.b.49.2		8	5.4	even	2	inner
1040.2.df.b.49.3		8	1.1	even	1	trivial
1040.2.df.b.849.2		8	13.4	even	6	inner
1040.2.df.b.849.3		8	65.4	even	6	inner
4225.2.a.bj.1.1		4	260.67	odd	12
4225.2.a.bj.1.4		4	260.167	odd	12
4225.2.a.bk.1.1		4	260.63	odd	12
4225.2.a.bk.1.4		4	260.223	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(-0.456850 - 2.18890i) q^{5} +(-0.866025 + 1.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-2.29129 + 1.32288i) q^{11} +(-3.46410 + 1.00000i) q^{13} +(-1.49009 - 1.66722i) q^{15} +(-3.96863 - 2.29129i) q^{17} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(-3.96863 + 2.29129i) q^{23} +(-4.58258 + 2.00000i) q^{25} +5.00000i q^{27} +(-2.29129 - 3.96863i) q^{29} -9.66930i q^{31} +(-1.32288 + 2.29129i) q^{33} +(3.67900 + 1.21037i) q^{35} +(3.96863 + 6.87386i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(-2.29129 + 1.32288i) q^{41} +(-1.22753 - 0.708712i) q^{43} +(4.24814 + 1.39761i) q^{45} -8.75560 q^{47} +(2.00000 + 3.46410i) q^{49} -4.58258 q^{51} +1.58258i q^{53} +(3.94242 + 4.41105i) q^{55} +1.73205 q^{57} +(2.91742 + 1.68438i) q^{59} +(5.29129 - 9.16478i) q^{61} +(-1.73205 - 3.00000i) q^{63} +(3.77148 + 7.12573i) q^{65} +(7.43273 + 12.8739i) q^{67} +(-2.29129 + 3.96863i) q^{69} +(3.08258 + 1.77973i) q^{71} +(-2.96863 + 4.02334i) q^{75} -4.58258i q^{77} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} -11.3060 q^{83} +(-3.20233 + 9.73371i) q^{85} +(-3.96863 - 2.29129i) q^{87} +(3.70871 - 2.14123i) q^{89} +(1.50000 - 6.06218i) q^{91} +(-4.83465 - 8.37386i) q^{93} +(1.21037 - 3.67900i) q^{95} +(-2.23658 + 3.87386i) q^{97} -5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{9} + 6 q^{15} + 12 q^{19} - 6 q^{35} - 20 q^{39} + 12 q^{45} + 16 q^{49} + 14 q^{55} + 60 q^{59} + 24 q^{61} - 24 q^{65} - 12 q^{71} + 8 q^{75} - 48 q^{79} - 4 q^{81} + 42 q^{85} + 48 q^{89}+ \cdots + 6 q^{95}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

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