LMFDB - Embedded newform 585.2.bf.a.199.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(199,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.199"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	585.199
Dual form			585.2.bf.a.244.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09445 + 1.89564i) q^{2} +(-1.39564 - 2.41733i) q^{4} +(0.456850 - 2.18890i) q^{5} +(0.866025 + 1.50000i) q^{7} +1.73205 q^{8} +(3.64938 + 3.26167i) q^{10} +(-2.29129 - 1.32288i) q^{11} +(-3.46410 - 1.00000i) q^{13} -3.79129 q^{14} +(0.895644 - 1.55130i) q^{16} +(3.96863 - 2.29129i) q^{17} +(-1.50000 + 0.866025i) q^{19} +(-5.92889 + 1.95057i) q^{20} +(5.01540 - 2.89564i) q^{22} +(-3.96863 - 2.29129i) q^{23} +(-4.58258 - 2.00000i) q^{25} +(5.68693 - 5.47225i) q^{26} +(2.41733 - 4.18693i) q^{28} +(2.29129 - 3.96863i) q^{29} -9.66930i q^{31} +(3.69253 + 6.39564i) q^{32} +10.0308i q^{34} +(3.67900 - 1.21037i) q^{35} +(3.96863 - 6.87386i) q^{37} -3.79129i q^{38} +(0.791288 - 3.79129i) q^{40} +(2.29129 + 1.32288i) q^{41} +(1.22753 - 0.708712i) q^{43} +7.38505i q^{44} +(8.68693 - 5.01540i) q^{46} -8.75560 q^{47} +(2.00000 - 3.46410i) q^{49} +(8.80669 - 6.49803i) q^{50} +(2.41733 + 9.76951i) q^{52} +1.58258i q^{53} +(-3.94242 + 4.41105i) q^{55} +(1.50000 + 2.59808i) q^{56} +(5.01540 + 8.68693i) q^{58} +(2.91742 - 1.68438i) q^{59} +(5.29129 + 9.16478i) q^{61} +(18.3296 + 10.5826i) q^{62} -12.5826 q^{64} +(-3.77148 + 7.12573i) q^{65} +(-7.43273 + 12.8739i) q^{67} +(-11.0776 - 6.39564i) q^{68} +(-1.73205 + 8.29875i) q^{70} +(3.08258 - 1.77973i) q^{71} +(8.68693 + 15.0462i) q^{74} +(4.18693 + 2.41733i) q^{76} -4.58258i q^{77} +6.00000 q^{79} +(-2.98647 - 2.66919i) q^{80} +(-5.01540 + 2.89564i) q^{82} -11.3060 q^{83} +(-3.20233 - 9.73371i) q^{85} +3.10260i q^{86} +(-3.96863 - 2.29129i) q^{88} +(-3.70871 - 2.14123i) q^{89} +(-1.50000 - 6.06218i) q^{91} +12.7913i q^{92} +(9.58258 - 16.5975i) q^{94} +(1.21037 + 3.67900i) q^{95} +(-2.23658 - 3.87386i) q^{97} +(4.37780 + 7.58258i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 4 q^{10} - 12 q^{14} - 2 q^{16} - 12 q^{19} - 24 q^{20} + 18 q^{26} - 6 q^{35} - 12 q^{40} + 42 q^{46} + 16 q^{49} + 12 q^{50} - 14 q^{55} + 12 q^{56} + 60 q^{59} + 24 q^{61} - 64 q^{64}+ \cdots + 6 q^{95}+O(q^{100}) $ 8 * q - 2 * q^4 - 4 * q^10 - 12 * q^14 - 2 * q^16 - 12 * q^19 - 24 * q^20 + 18 * q^26 - 6 * q^35 - 12 * q^40 + 42 * q^46 + 16 * q^49 + 12 * q^50 - 14 * q^55 + 12 * q^56 + 60 * q^59 + 24 * q^61 - 64 * q^64 + 24 * q^65 - 12 * q^71 + 42 * q^74 + 6 * q^76 + 48 * q^79 - 18 * q^80 + 42 * q^85 - 48 * q^89 - 12 * q^91 + 40 * q^94 + 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.09445	+	1.89564i	−0.773893	+	1.34042i	0.161521	+	0.986869i	$0.448360\pi$
$2$	−1.09445	+	1.89564i	−0.773893	+	1.34042i	−0.935414	+	0.353553i	$0.884973\pi$
$3$		0			0
$3$		0			0
$4$	−1.39564	−	2.41733i	−0.697822	−	1.20866i
$5$	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	$-0.0605189\pi$
$7$	0.866025	+	1.50000i	0.327327	+	0.566947i	−0.654654	+	0.755929i	$0.727186\pi$
$8$	1.73205			0.612372
$9$		0			0
$10$	3.64938	+	3.26167i	1.15403	+	1.03143i
$11$	−2.29129	−	1.32288i	−0.690849	−	0.398862i	0.113081	−	0.993586i	$-0.463928\pi$
$11$	−2.29129	−	1.32288i	−0.690849	−	0.398862i	−0.803930	+	0.594724i	$0.797261\pi$
$12$		0			0
$13$	−3.46410	−	1.00000i	−0.960769	−	0.277350i
$13$	−3.46410	−	1.00000i	−0.960769	−	0.277350i
$14$	−3.79129			−1.01326
$15$		0			0
$16$	0.895644	−	1.55130i	0.223911	−	0.387825i
$17$	3.96863	−	2.29129i	0.962533	−	0.555719i	0.0655816	−	0.997847i	$-0.479110\pi$
$17$	3.96863	−	2.29129i	0.962533	−	0.555719i	0.896952	+	0.442128i	$0.145776\pi$
$18$		0			0
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	−0.662094	−	0.749421i	$-0.730332\pi$
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	0.317970	+	0.948101i	$0.396999\pi$
$20$	−5.92889	+	1.95057i	−1.32574	+	0.436161i
$21$		0			0
$22$	5.01540	−	2.89564i	1.06929	−	0.617353i
$23$	−3.96863	−	2.29129i	−0.827516	−	0.477767i	0.0254855	−	0.999675i	$-0.491887\pi$
$23$	−3.96863	−	2.29129i	−0.827516	−	0.477767i	−0.853001	+	0.521909i	$0.825220\pi$
$24$		0			0
$25$	−4.58258	−	2.00000i	−0.916515	−	0.400000i
$26$	5.68693	−	5.47225i	1.11530	−	1.07320i
$27$		0			0
$28$	2.41733	−	4.18693i	0.456832	−	0.791256i
$29$	2.29129	−	3.96863i	0.425481	−	0.736956i	−0.570984	−	0.820961i	$-0.693438\pi$
$29$	2.29129	−	3.96863i	0.425481	−	0.736956i	0.996465	+	0.0840058i	$0.0267714\pi$
$30$		0			0
$31$		−	9.66930i		−	1.73666i	−0.495988	−	0.868329i	$-0.665194\pi$
$31$		−	9.66930i		−	1.73666i	0.495988	−	0.868329i	$-0.334806\pi$
$32$	3.69253	+	6.39564i	0.652753	+	1.13060i
$33$		0			0
$34$			10.0308i			1.72027i
$35$	3.67900	−	1.21037i	0.621864	−	0.204590i
$36$		0			0
$37$	3.96863	−	6.87386i	0.652438	−	1.13006i	−0.330091	−	0.943949i	$-0.607080\pi$
$37$	3.96863	−	6.87386i	0.652438	−	1.13006i	0.982529	−	0.186107i	$-0.0595872\pi$
$38$		−	3.79129i		−	0.615028i
$39$		0			0
$40$	0.791288	−	3.79129i	0.125114	−	0.599455i
$41$	2.29129	+	1.32288i	0.357839	+	0.206598i	0.668132	−	0.744042i	$-0.267094\pi$
$41$	2.29129	+	1.32288i	0.357839	+	0.206598i	−0.310293	+	0.950641i	$0.600427\pi$
$42$		0			0
$43$	1.22753	−	0.708712i	0.187196	−	0.108078i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$	1.22753	−	0.708712i	0.187196	−	0.108078i	0.590669	+	0.806914i	$0.298864\pi$
$44$			7.38505i			1.11334i
$45$		0			0
$46$	8.68693	−	5.01540i	1.28082	−	0.739481i
$47$	−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
$50$	8.80669	−	6.49803i	1.24545	−	0.918960i
$51$		0			0
$52$	2.41733	+	9.76951i	0.335223	+	1.35479i
$53$			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
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$		0			0
$58$	5.01540	+	8.68693i	0.658555	+	1.14065i
$59$	2.91742	−	1.68438i	0.379816	−	0.219287i	−0.297922	−	0.954590i	$-0.596294\pi$
$59$	2.91742	−	1.68438i	0.379816	−	0.219287i	0.677738	+	0.735303i	$0.262960\pi$
$60$		0			0
$61$	5.29129	+	9.16478i	0.677480	+	1.17343i	0.975737	+	0.218944i	$0.0702613\pi$
$61$	5.29129	+	9.16478i	0.677480	+	1.17343i	−0.298257	+	0.954485i	$0.596405\pi$
$62$	18.3296	+	10.5826i	2.32786	+	1.34399i
$63$		0			0
$64$	−12.5826			−1.57282
$65$	−3.77148	+	7.12573i	−0.467794	+	0.883837i
$66$		0			0
$67$	−7.43273	+	12.8739i	−0.908052	+	1.57279i	−0.0912856	+	0.995825i	$0.529098\pi$
$67$	−7.43273	+	12.8739i	−0.908052	+	1.57279i	−0.816767	+	0.576968i	$0.804236\pi$
$68$	−11.0776	−	6.39564i	−1.34335	−	0.775586i
$69$		0			0
$70$	−1.73205	+	8.29875i	−0.207020	+	0.991891i
$71$	3.08258	−	1.77973i	0.365834	−	0.211215i	−0.305803	−	0.952095i	$-0.598925\pi$
$71$	3.08258	−	1.77973i	0.365834	−	0.211215i	0.671637	+	0.740880i	$0.265591\pi$
$72$		0			0
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	8.68693	+	15.0462i	1.00984	+	1.74909i
$75$		0			0
$76$	4.18693	+	2.41733i	0.480274	+	0.277286i
$77$		−	4.58258i		−	0.522233i
$78$		0			0
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$	−2.98647	−	2.66919i	−0.333897	−	0.298424i
$81$		0			0
$82$	−5.01540	+	2.89564i	−0.553859	+	0.319770i
$83$	−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
$86$			3.10260i			0.334562i
$87$		0			0
$88$	−3.96863	−	2.29129i	−0.423057	−	0.244252i
$89$	−3.70871	−	2.14123i	−0.393123	−	0.226969i	0.290390	−	0.956909i	$-0.406215\pi$
$89$	−3.70871	−	2.14123i	−0.393123	−	0.226969i	−0.683512	+	0.729939i	$0.739548\pi$
$90$		0			0
$91$	−1.50000	−	6.06218i	−0.157243	−	0.635489i
$92$			12.7913i			1.33358i
$93$		0			0
$94$	9.58258	−	16.5975i	0.988367	−	1.71190i
$95$	1.21037	+	3.67900i	0.124181	+	0.377457i
$96$		0			0
$97$	−2.23658	−	3.87386i	−0.227090	−	0.393331i	0.729854	−	0.683603i	$-0.239588\pi$
$97$	−2.23658	−	3.87386i	−0.227090	−	0.393331i	−0.956944	+	0.290271i	$0.906254\pi$
$98$	4.37780	+	7.58258i	0.442225	+	0.765956i
$99$		0			0
$100$	1.56099	+	13.8689i	0.156099	+	1.38689i
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$		0			0
$103$		−	15.1652i		−	1.49427i	−0.664674	−	0.747133i	$-0.731430\pi$
$103$		−	15.1652i		−	1.49427i	0.664674	−	0.747133i	$-0.268570\pi$
$104$	−6.00000	−	1.73205i	−0.588348	−	0.169842i
$105$		0			0
$106$	−3.00000	−	1.73205i	−0.291386	−	0.168232i
$107$	1.22753	+	0.708712i	0.118669	+	0.0685138i	0.558160	−	0.829733i	$-0.311508\pi$
$107$	1.22753	+	0.708712i	0.118669	+	0.0685138i	−0.439490	+	0.898247i	$0.644841\pi$
$108$		0			0
$109$			2.74110i			0.262550i	0.991346	+	0.131275i	$0.0419071\pi$
$109$			2.74110i			0.262550i	−0.991346	+	0.131275i	$0.958093\pi$
$110$	−4.04699	−	12.3011i	−0.385865	−	1.17286i
$111$		0			0
$112$	3.10260			0.293168
$113$	14.3609	−	8.29129i	1.35096	−	0.779979i	0.362578	−	0.931953i	$-0.381897\pi$
$113$	14.3609	−	8.29129i	1.35096	−	0.779979i	0.988384	+	0.151975i	$0.0485632\pi$
$114$		0			0
$115$	−6.82847	+	7.64016i	−0.636758	+	0.712448i
$116$	−12.7913			−1.18764
$117$		0			0
$118$			7.37386i			0.678819i
$119$	6.87386	+	3.96863i	0.630126	+	0.363803i
$120$		0			0
$121$	−2.00000	−	3.46410i	−0.181818	−	0.314918i
$122$	−23.1642			−2.09719
$123$		0			0
$124$	−23.3739	+	13.4949i	−2.09903	+	1.21188i
$125$	−6.47135	+	9.11710i	−0.578815	+	0.815459i
$126$		0			0
$127$	−8.44178	−	4.87386i	−0.749087	−	0.432485i	0.0762771	−	0.997087i	$-0.475697\pi$
$127$	−8.44178	−	4.87386i	−0.749087	−	0.432485i	−0.825364	+	0.564601i	$0.809030\pi$
$128$	6.38595	−	11.0608i	0.564444	−	0.977645i
$129$		0			0
$130$	−9.38014	−	14.9481i	−0.822693	−	1.31104i
$131$	−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
$134$	−16.2695	−	28.1796i	−1.40547	−	2.43435i
$135$		0			0
$136$	6.87386	−	3.96863i	0.589429	−	0.340307i
$137$	−0.0476751	−	0.0825757i	−0.00407316	−	0.00705492i	0.863982	−	0.503523i	$-0.167963\pi$
$137$	−0.0476751	−	0.0825757i	−0.00407316	−	0.00705492i	−0.868055	+	0.496468i	$0.834630\pi$
$138$		0			0
$139$	2.87386	+	4.97768i	0.243758	+	0.422201i	0.961782	−	0.273817i	$-0.0882864\pi$
$139$	2.87386	+	4.97768i	0.243758	+	0.422201i	−0.718024	+	0.696019i	$0.754953\pi$
$140$	−8.06042	−	7.20409i	−0.681230	−	0.608857i
$141$		0			0
$142$			7.79129i			0.653830i
$143$	6.61438	+	6.87386i	0.553122	+	0.574821i
$144$		0			0
$145$	−7.64016	−	6.82847i	−0.634480	−	0.567074i
$146$		0			0
$147$		0			0
$148$	−22.1552			−1.82114
$149$	−8.45644	+	4.88233i	−0.692778	+	0.399976i	−0.804652	−	0.593747i	$-0.797648\pi$
$149$	−8.45644	+	4.88233i	−0.692778	+	0.399976i	0.111874	+	0.993722i	$0.464315\pi$
$150$		0			0
$151$			6.20520i			0.504972i	0.967601	+	0.252486i	$0.0812482\pi$
$151$			6.20520i			0.504972i	−0.967601	+	0.252486i	$0.918752\pi$
$152$	−2.59808	+	1.50000i	−0.210732	+	0.121666i
$153$		0			0
$154$	8.68693	+	5.01540i	0.700013	+	0.404153i
$155$	−21.1652	−	4.41742i	−1.70003	−	0.354816i
$156$		0			0
$157$			9.16515i			0.731459i	0.930721	+	0.365729i	$0.119180\pi$
$157$			9.16515i			0.731459i	−0.930721	+	0.365729i	$0.880820\pi$
$158$	−6.56670	+	11.3739i	−0.522419	+	0.904856i
$159$		0			0
$160$	15.6864	−	5.16072i	1.24012	−	0.407991i
$161$		−	7.93725i		−	0.625543i
$162$		0			0
$163$	5.33918	+	9.24773i	0.418197	+	0.724338i	0.995758	−	0.0920093i	$-0.0293290\pi$
$163$	5.33918	+	9.24773i	0.418197	+	0.724338i	−0.577561	+	0.816347i	$0.695996\pi$
$164$		−	7.38505i		−	0.576676i
$165$		0			0
$166$	12.3739	−	21.4322i	0.960398	−	1.66346i
$167$	−2.14123	+	3.70871i	−0.165693	+	0.286989i	−0.936901	−	0.349594i	$-0.886319\pi$
$167$	−2.14123	+	3.70871i	−0.165693	+	0.286989i	0.771208	+	0.636583i	$0.219653\pi$
$168$		0			0
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$	21.9564	+	4.58258i	1.68398	+	0.351468i
$171$		0			0
$172$	−3.42638	−	1.97822i	−0.261259	−	0.150838i
$173$	6.42368	−	3.70871i	0.488383	−	0.281968i	−0.235520	−	0.971869i	$-0.575679\pi$
$173$	6.42368	−	3.70871i	0.488383	−	0.281968i	0.723903	+	0.689901i	$0.242346\pi$
$174$		0			0
$175$	−0.968627	−	8.60591i	−0.0732213	−	0.650546i
$176$	−4.10436	+	2.36965i	−0.309377	+	0.178619i
$177$		0			0
$178$	8.11800	−	4.68693i	0.608470	−	0.351300i
$179$	0.0825757	−	0.143025i	0.00617200	−	0.0106902i	−0.862923	−	0.505336i	$-0.831369\pi$
$179$	0.0825757	−	0.143025i	0.00617200	−	0.0106902i	0.869095	+	0.494645i	$0.164702\pi$
$180$		0			0
$181$	−18.7477			−1.39351			−0.696754	−	0.717310i	$-0.745373\pi$
$181$	−18.7477			−1.39351			−0.696754	+	0.717310i	$0.745373\pi$
$182$	13.1334	+	3.79129i	0.973513	+	0.281029i
$183$		0			0
$184$	−6.87386	−	3.96863i	−0.506748	−	0.292571i
$185$	−13.2331	−	11.8273i	−0.972920	−	0.869557i
$186$		0			0
$187$	−12.1244			−0.886621
$188$	12.2197	+	21.1652i	0.891214	+	1.54363i
$189$		0			0
$190$	−8.29875	−	1.73205i	−0.602055	−	0.125656i
$191$	−3.70871	−	6.42368i	−0.268353	−	0.464801i	0.700084	−	0.714061i	$-0.253146\pi$
$191$	−3.70871	−	6.42368i	−0.268353	−	0.464801i	−0.968437	+	0.249260i	$0.919813\pi$
$192$		0			0
$193$	0.504525	−	0.873864i	0.0363165	−	0.0629021i	−0.847296	−	0.531121i	$-0.821771\pi$
$193$	0.504525	−	0.873864i	0.0363165	−	0.0629021i	0.883612	+	0.468219i	$0.155104\pi$
$194$	9.79129			0.702973
$195$		0			0
$196$	−11.1652			−0.797511
$197$	−9.98313	+	17.2913i	−0.711269	+	1.23195i	0.253113	+	0.967437i	$0.418546\pi$
$197$	−9.98313	+	17.2913i	−0.711269	+	1.23195i	−0.964381	+	0.264516i	$0.914788\pi$
$198$		0			0
$199$	0.708712	+	1.22753i	0.0502393	+	0.0870170i	0.890051	−	0.455860i	$-0.150668\pi$
$199$	0.708712	+	1.22753i	0.0502393	+	0.0870170i	−0.839812	+	0.542877i	$0.817335\pi$
$200$	−7.93725	−	3.46410i	−0.561249	−	0.244949i
$201$		0			0
$202$	9.85005	+	17.0608i	0.693047	+	1.20039i
$203$	7.93725			0.557086
$204$		0			0
$205$	3.94242	−	4.41105i	0.275351	−	0.308081i
$206$	28.7477	+	16.5975i	2.00295	+	1.15640i
$207$		0			0
$208$	−4.65390	+	4.47822i	−0.322690	+	0.310509i
$209$	4.58258			0.316983
$210$		0			0
$211$	−9.08258	+	15.7315i	−0.625270	+	1.08300i	0.363218	+	0.931704i	$0.381678\pi$
$211$	−9.08258	+	15.7315i	−0.625270	+	1.08300i	−0.988489	+	0.151296i	$0.951655\pi$
$212$	3.82560	−	2.20871i	0.262743	−	0.151695i
$213$		0			0
$214$	−2.68693	+	1.55130i	−0.183675	+	0.106045i
$215$	−0.990505	−	3.01071i	−0.0675519	−	0.205329i
$216$		0			0
$217$	14.5040	−	8.37386i	0.984593	−	0.568455i
$218$	−5.19615	−	3.00000i	−0.351928	−	0.203186i
$219$		0			0
$220$	16.1652	+	3.37386i	1.08985	+	0.227466i
$221$	−16.0390	+	3.96863i	−1.07890	+	0.266959i
$222$		0			0
$223$	4.33013	−	7.50000i	0.289967	−	0.502237i	−0.683835	−	0.729637i	$-0.739689\pi$
$223$	4.33013	−	7.50000i	0.289967	−	0.502237i	0.973801	+	0.227400i	$0.0730224\pi$
$224$	−6.39564	+	11.0776i	−0.427327	+	0.740152i
$225$		0			0
$226$			36.2976i			2.41448i
$227$	3.05493	+	5.29129i	0.202763	+	0.351195i	0.949418	−	0.314016i	$-0.101675\pi$
$227$	3.05493	+	5.29129i	0.202763	+	0.351195i	−0.746655	+	0.665212i	$0.768341\pi$
$228$		0			0
$229$		−	5.48220i		−	0.362274i	−0.983458	−	0.181137i	$-0.942022\pi$
$229$		−	5.48220i		−	0.362274i	0.983458	−	0.181137i	$-0.0579778\pi$
$230$	−7.00959	−	21.3061i	−0.462199	−	1.40488i
$231$		0			0
$232$	3.96863	−	6.87386i	0.260553	−	0.451291i
$233$		−	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
$236$	−8.14337	−	4.70158i	−0.530088	−	0.306047i
$237$		0			0
$238$	−15.0462	+	8.68693i	−0.975301	+	0.563090i
$239$			20.9753i			1.35678i	0.734702	+	0.678390i	$0.237322\pi$
$239$			20.9753i			1.35678i	−0.734702	+	0.678390i	$0.762678\pi$
$240$		0			0
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	0.450910	+	0.892570i	$0.351100\pi$
$242$	8.75560			0.562832
$243$		0			0
$244$	14.7695	−	25.5815i	0.945521	−	1.63769i
$245$	−6.66888	−	5.96038i	−0.426059	−	0.380795i
$246$		0			0
$247$	6.06218	−	1.50000i	0.385727	−	0.0954427i
$248$		−	16.7477i		−	1.06348i
$249$		0			0
$250$	−10.2002	−	22.2456i	−0.645118	−	1.40694i
$251$	9.08258	+	15.7315i	0.573287	+	0.992962i	0.996225	+	0.0868039i	$0.0276654\pi$
$251$	9.08258	+	15.7315i	0.573287	+	0.992962i	−0.422938	+	0.906158i	$0.639001\pi$
$252$		0			0
$253$	6.06218	+	10.5000i	0.381126	+	0.660129i
$254$	18.4782	−	10.6684i	1.15943	−	0.669395i
$255$		0			0
$256$	1.39564	+	2.41733i	0.0872277	+	0.151083i
$257$	−0.143025	−	0.0825757i	−0.00892167	−	0.00515093i	0.495533	−	0.868589i	$-0.334973\pi$
$257$	−0.143025	−	0.0825757i	−0.00892167	−	0.00515093i	−0.504454	+	0.863438i	$0.668306\pi$
$258$		0			0
$259$	13.7477			0.854242
$260$	22.4888	−	0.828086i	1.39470	−	0.0513557i
$261$		0			0
$262$	1.73205	−	3.00000i	0.107006	−	0.185341i
$263$	7.79423	+	4.50000i	0.480613	+	0.277482i	0.720672	−	0.693276i	$-0.243833\pi$
$263$	7.79423	+	4.50000i	0.480613	+	0.277482i	−0.240059	+	0.970758i	$0.577167\pi$
$264$		0			0
$265$	3.46410	+	0.723000i	0.212798	+	0.0444135i
$266$	5.68693	−	3.28335i	0.348688	−	0.201315i
$267$		0			0
$268$	41.4938			2.53464
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	0.998816	−	0.0486418i	$-0.0154893\pi$
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	−0.541533	+	0.840679i	$0.682156\pi$
$270$		0			0
$271$	7.50000	+	4.33013i	0.455593	+	0.263036i	0.710189	−	0.704011i	$-0.248609\pi$
$271$	7.50000	+	4.33013i	0.455593	+	0.263036i	−0.254597	+	0.967047i	$0.581943\pi$
$272$		−	8.20871i		−	0.497726i
$273$		0			0
$274$	0.208712			0.0126088
$275$	7.85425	+	10.6448i	0.473629	+	0.641903i
$276$		0			0
$277$	14.3609	−	8.29129i	0.862865	−	0.498175i	−0.00210581	−	0.999998i	$-0.500670\pi$
$277$	14.3609	−	8.29129i	0.862865	−	0.498175i	0.864971	+	0.501823i	$0.167337\pi$
$278$	−12.5812			−0.754571
$279$		0			0
$280$	6.37221	−	2.09642i	0.380812	−	0.125285i
$281$			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	$-0.330947\pi$
$283$	0.218475	+	0.126136i	0.0129870	+	0.00749803i	−0.493492	+	0.869750i	$0.664280\pi$
$284$	−8.60436	−	4.96773i	−0.510575	−	0.294780i
$285$		0			0
$286$	−20.2695	+	5.01540i	−1.19856	+	0.296567i
$287$			4.58258i			0.270501i
$288$		0			0
$289$	2.00000	−	3.46410i	0.117647	−	0.203771i
$290$	21.3061	−	7.00959i	1.25114	−	0.411617i
$291$		0			0
$292$		0			0
$293$	−11.7152	−	20.2913i	−0.684408	−	1.18543i	−0.973622	−	0.228165i	$-0.926727\pi$
$293$	−11.7152	−	20.2913i	−0.684408	−	1.18543i	0.289214	−	0.957264i	$-0.406606\pi$
$294$		0			0
$295$	−2.35411	−	7.15546i	−0.137061	−	0.416607i
$296$	6.87386	−	11.9059i	0.399535	−	0.692015i
$297$		0			0
$298$		−	21.3739i		−	1.23815i
$299$	11.4564	+	11.9059i	0.662543	+	0.688535i
$300$		0			0
$301$	2.12614	+	1.22753i	0.122548	+	0.0707534i
$302$	−11.7629	−	6.79129i	−0.676876	−	0.390795i
$303$		0			0
$304$			3.10260i			0.177946i
$305$	22.4781	−	7.39517i	1.28709	−	0.423446i
$306$		0			0
$307$	−24.2487			−1.38395			−0.691974	−	0.721923i	$-0.743259\pi$
$307$	−24.2487			−1.38395			−0.691974	+	0.721923i	$0.743259\pi$
$308$	−11.0776	+	6.39564i	−0.631204	+	0.364426i
$309$		0			0
$310$	31.5381	−	35.2869i	1.79124	−	2.00416i
$311$	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	$-0.664775\pi$
$313$		−	30.7477i		−	1.73796i	0.494843	−	0.868982i	$-0.335225\pi$
$314$	−17.3739	−	10.0308i	−0.980464	−	0.566071i
$315$		0			0
$316$	−8.37386	−	14.5040i	−0.471067	−	0.815911i
$317$	20.9753			1.17809			0.589045	−	0.808100i	$-0.299504\pi$
$317$	20.9753			1.17809			0.589045	+	0.808100i	$0.299504\pi$
$318$		0			0
$319$	−10.5000	+	6.06218i	−0.587887	+	0.339417i
$320$	−5.74835	+	27.5420i	−0.321343	+	1.53965i
$321$		0			0
$322$	15.0462	+	8.68693i	0.838492	+	0.484104i
$323$	−3.96863	+	6.87386i	−0.220820	+	0.382472i
$324$		0			0
$325$	13.8745	+	11.5108i	0.769619	+	0.638503i
$326$	−23.3739			−1.29456
$327$		0			0
$328$	3.96863	+	2.29129i	0.219131	+	0.126515i
$329$	−7.58258	−	13.1334i	−0.418041	−	0.724068i
$330$		0			0
$331$	9.87386	−	5.70068i	0.542717	−	0.313338i	−0.203463	−	0.979083i	$-0.565220\pi$
$331$	9.87386	−	5.70068i	0.542717	−	0.313338i	0.746179	+	0.665745i	$0.231886\pi$
$332$	15.7792	+	27.3303i	0.865994	+	1.49995i
$333$		0			0
$334$	−4.68693	−	8.11800i	−0.256457	−	0.444197i
$335$	24.7840	+	22.1509i	1.35409	+	1.21023i
$336$		0			0
$337$		−	3.25227i		−	0.177163i	−0.996069	−	0.0885813i	$-0.971767\pi$
$337$		−	3.25227i		−	0.177163i	0.996069	−	0.0885813i	$-0.0282333\pi$
$338$	−25.1724	+	13.2695i	−1.36920	+	0.721766i
$339$		0			0
$340$	−19.0602	+	21.3259i	−1.03369	+	1.15656i
$341$	−12.7913	+	22.1552i	−0.692687	+	1.19977i
$342$		0			0
$343$	19.0526			1.02874
$344$	2.12614	−	1.22753i	0.114634	−	0.0661837i
$345$		0			0
$346$			16.2360i			0.872853i
$347$	13.2764	−	7.66515i	0.712716	−	0.411487i	−0.0993497	−	0.995053i	$-0.531676\pi$
$347$	13.2764	−	7.66515i	0.712716	−	0.411487i	0.812066	+	0.583566i	$0.198343\pi$
$348$		0			0
$349$	15.8739	+	9.16478i	0.849708	+	0.490579i	0.860552	−	0.509362i	$-0.170118\pi$
$349$	15.8739	+	9.16478i	0.849708	+	0.490579i	−0.0108440	+	0.999941i	$0.503452\pi$
$350$	17.3739	+	7.58258i	0.928672	+	0.405306i
$351$		0			0
$352$		−	19.5390i		−	1.04143i
$353$	8.70793	−	15.0826i	0.463476	−	0.802765i	−0.535655	−	0.844437i	$-0.679935\pi$
$353$	8.70793	−	15.0826i	0.463476	−	0.802765i	0.999131	+	0.0416724i	$0.0132686\pi$
$354$		0			0
$355$	−2.48737	−	7.56052i	−0.132016	−	0.401271i
$356$			11.9536i			0.633537i
$357$		0			0
$358$	0.180750	+	0.313068i	0.00955294	+	0.0165462i
$359$		−	33.3857i		−	1.76203i	−0.473088	−	0.881015i	$-0.656861\pi$
$359$		−	33.3857i		−	1.76203i	0.473088	−	0.881015i	$-0.343139\pi$
$360$		0			0
$361$	−8.00000	+	13.8564i	−0.421053	+	0.729285i
$362$	20.5185	−	35.5390i	1.07843	−	1.86789i
$363$		0			0
$364$	−12.5608	+	12.0866i	−0.658365	+	0.633512i
$365$		0			0
$366$		0			0
$367$	22.2982	+	12.8739i	1.16396	+	0.672010i	0.952249	−	0.305323i	$-0.0987644\pi$
$367$	22.2982	+	12.8739i	1.16396	+	0.672010i	0.211707	+	0.977333i	$0.432098\pi$
$368$	−7.10895	+	4.10436i	−0.370580	+	0.213954i
$369$		0			0
$370$	36.9033	−	12.1410i	1.91851	−	0.631179i
$371$	−2.37386	+	1.37055i	−0.123245	+	0.0711554i
$372$		0			0
$373$	−11.2583	+	6.50000i	−0.582934	+	0.336557i	−0.762299	−	0.647225i	$-0.775929\pi$
$373$	−11.2583	+	6.50000i	−0.582934	+	0.336557i	0.179364	+	0.983783i	$0.442596\pi$
$374$	13.2695	−	22.9835i	0.686150	−	1.18845i
$375$		0			0
$376$	−15.1652			−0.782083
$377$	−11.9059	+	11.4564i	−0.613184	+	0.590037i
$378$		0			0
$379$	18.2477	+	10.5353i	0.937323	+	0.541164i	0.889120	−	0.457674i	$-0.151317\pi$
$379$	18.2477	+	10.5353i	0.937323	+	0.541164i	0.0482027	+	0.998838i	$0.484651\pi$
$380$	7.20409	−	8.06042i	0.369562	−	0.413491i
$381$		0			0
$382$	16.2360			0.830706
$383$	−1.41823	−	2.45644i	−0.0724680	−	0.125518i	0.827514	−	0.561444i	$-0.189754\pi$
$383$	−1.41823	−	2.45644i	−0.0724680	−	0.125518i	−0.899982	+	0.435926i	$0.856421\pi$
$384$		0			0
$385$	−10.0308	−	2.09355i	−0.511217	−	0.106697i
$386$	1.10436	+	1.91280i	0.0562102	+	0.0973590i
$387$		0			0
$388$	−6.24293	+	10.8131i	−0.316937	+	0.548950i
$389$	15.1652			0.768904			0.384452	−	0.923145i	$-0.374390\pi$
$389$	15.1652			0.768904			0.384452	+	0.923145i	$0.374390\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$	3.46410	−	6.00000i	0.174964	−	0.303046i
$393$		0			0
$394$	−21.8521	−	37.8489i	−1.10089	−	1.90680i
$395$	2.74110	−	13.1334i	0.137920	−	0.660813i
$396$		0			0
$397$	−13.6379	−	23.6216i	−0.684468	−	1.18553i	−0.973604	−	0.228245i	$-0.926701\pi$
$397$	−13.6379	−	23.6216i	−0.684468	−	1.18553i	0.289135	−	0.957288i	$-0.406632\pi$
$398$	−3.10260			−0.155519
$399$		0			0
$400$	−7.20696	+	5.31767i	−0.360348	+	0.265883i
$401$	−10.8303	−	6.25288i	−0.540840	−	0.312254i	0.204580	−	0.978850i	$-0.434417\pi$
$401$	−10.8303	−	6.25288i	−0.540840	−	0.312254i	−0.745419	+	0.666596i	$0.767751\pi$
$402$		0			0
$403$	−9.66930	+	33.4955i	−0.481662	+	1.66853i
$404$	−25.1216			−1.24985
$405$		0			0
$406$	−8.68693	+	15.0462i	−0.431125	+	0.746731i
$407$	−18.1865	+	10.5000i	−0.901473	+	0.520466i
$408$		0			0
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	−0.302979	−	0.952997i	$-0.597981\pi$
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	0.673830	+	0.738886i	$0.264648\pi$
$410$	4.04699	+	12.3011i	0.199867	+	0.607508i
$411$		0			0
$412$	−36.6591	+	21.1652i	−1.80607	+	1.04273i
$413$	5.05313	+	2.91742i	0.248648	+	0.143557i
$414$		0			0
$415$	−5.16515	+	24.7477i	−0.253547	+	1.21482i
$416$	−6.39564	−	25.8477i	−0.313572	−	1.26729i
$417$		0			0
$418$	−5.01540	+	8.68693i	−0.245311	+	0.424892i
$419$	12.0826	−	20.9276i	0.590272	−	1.02238i	−0.403923	−	0.914793i	$-0.632354\pi$
$419$	12.0826	−	20.9276i	0.590272	−	1.02238i	0.994195	−	0.107589i	$-0.0343130\pi$
$420$		0			0
$421$		−	26.2668i		−	1.28017i	−0.768306	−	0.640083i	$-0.778900\pi$
$421$		−	26.2668i		−	1.28017i	0.768306	−	0.640083i	$-0.221100\pi$
$422$	−19.8809	−	34.4347i	−0.967785	−	1.67625i
$423$		0			0
$424$			2.74110i			0.133120i
$425$	−22.7691	+	2.56275i	−1.10446	+	0.124311i
$426$		0			0
$427$	−9.16478	+	15.8739i	−0.443515	+	0.768190i
$428$		−	3.95644i		−	0.191242i
$429$		0			0
$430$	6.79129	+	1.41742i	0.327505	+	0.0683543i
$431$	−25.6652	−	14.8178i	−1.23625	−	0.713747i	−0.267922	−	0.963441i	$-0.586337\pi$
$431$	−25.6652	−	14.8178i	−1.23625	−	0.713747i	−0.968325	+	0.249693i	$0.919670\pi$
$432$		0			0
$433$	−15.3700	+	8.87386i	−0.738634	+	0.426451i	−0.821573	−	0.570104i	$-0.806903\pi$
$433$	−15.3700	+	8.87386i	−0.738634	+	0.426451i	0.0829383	+	0.996555i	$0.473570\pi$
$434$			36.6591i			1.75969i
$435$		0			0
$436$	6.62614	−	3.82560i	0.317334	−	0.183213i
$437$	7.93725			0.379690
$438$		0			0
$439$	20.2477	−	35.0701i	0.966371	−	1.67380i	0.260487	−	0.965477i	$-0.416117\pi$
$439$	20.2477	−	35.0701i	0.966371	−	1.67380i	0.705885	−	0.708327i	$-0.250550\pi$
$440$	−6.82847	+	7.64016i	−0.325535	+	0.364230i
$441$		0			0
$442$	10.0308	−	34.7477i	0.477117	−	1.65278i
$443$			25.9129i			1.23116i	0.788075	+	0.615579i	$0.211078\pi$
$443$			25.9129i			1.23116i	−0.788075	+	0.615579i	$0.788922\pi$
$444$		0			0
$445$	−6.38126	+	7.13978i	−0.302501	+	0.338458i
$446$	9.47822	+	16.4168i	0.448807	+	0.777356i
$447$		0			0
$448$	−10.8968	−	18.8739i	−0.514827	−	0.891706i
$449$	−32.4564	+	18.7387i	−1.53171	+	0.884336i	−0.532431	+	0.846473i	$0.678721\pi$
$449$	−32.4564	+	18.7387i	−1.53171	+	0.884336i	−0.999283	+	0.0378622i	$0.987945\pi$
$450$		0			0
$451$	−3.50000	−	6.06218i	−0.164809	−	0.285457i
$452$	−40.0855	−	23.1434i	−1.88546	−	1.08857i
$453$		0			0
$454$	−13.3739			−0.627667
$455$	−13.9548	+	0.513844i	−0.654210	+	0.0240894i
$456$		0			0
$457$	−0.866025	+	1.50000i	−0.0405110	+	0.0701670i	−0.885570	−	0.464506i	$-0.846232\pi$
$457$	−0.866025	+	1.50000i	−0.0405110	+	0.0701670i	0.845059	+	0.534673i	$0.179565\pi$
$458$	10.3923	+	6.00000i	0.485601	+	0.280362i
$459$		0			0
$460$	27.9989	+	5.84370i	1.30545	+	0.272464i
$461$	1.03901	−	0.599876i	0.0483917	−	0.0279390i	−0.475609	−	0.879657i	$-0.657772\pi$
$461$	1.03901	−	0.599876i	0.0483917	−	0.0279390i	0.524001	+	0.851718i	$0.324439\pi$
$462$		0			0
$463$	8.22330			0.382169			0.191085	−	0.981574i	$-0.438799\pi$
$463$	8.22330			0.382169			0.191085	+	0.981574i	$0.438799\pi$
$464$	−4.10436	−	7.10895i	−0.190540	−	0.330025i
$465$		0			0
$466$	40.1216	+	23.1642i	1.85860	+	1.07306i
$467$			12.3303i			0.570578i	0.958441	+	0.285289i	$0.0920896\pi$
$467$			12.3303i			0.570578i	−0.958441	+	0.285289i	$0.907910\pi$
$468$		0			0
$469$	−25.7477			−1.18892
$470$	−31.9525	−	28.5579i	−1.47386	−	1.31728i
$471$		0			0
$472$	5.05313	−	2.91742i	0.232589	−	0.134285i
$473$	−3.75015			−0.172432
$474$		0			0
$475$	8.60591	−	0.968627i	0.394866	−	0.0444437i
$476$		−	22.1552i		−	1.01548i
$477$		0			0
$478$	−39.7617	−	22.9564i	−1.81866	−	1.05000i
$479$	28.0390	+	16.1883i	1.28114	+	0.739664i	0.977056	−	0.212983i	$-0.0683179\pi$
$479$	28.0390	+	16.1883i	1.28114	+	0.739664i	0.304079	+	0.952647i	$0.401651\pi$
$480$		0			0
$481$	−20.6216	+	19.8431i	−0.940264	+	0.904769i
$482$		−	3.79129i		−	0.172688i
$483$		0			0
$484$	−5.58258	+	9.66930i	−0.253753	+	0.439514i
$485$	−9.50128	+	3.12587i	−0.431431	+	0.141938i
$486$		0			0
$487$	10.5353	+	18.2477i	0.477401	+	0.826883i	0.999665	−	0.0259009i	$-0.00824545\pi$
$487$	10.5353	+	18.2477i	0.477401	+	0.826883i	−0.522263	+	0.852784i	$0.674912\pi$
$488$	9.16478	+	15.8739i	0.414870	+	0.718576i
$489$		0			0
$490$	18.5975	−	6.11847i	0.840150	−	0.276404i
$491$	14.2913	−	24.7532i	0.644957	−	1.11710i	−0.339355	−	0.940658i	$-0.610209\pi$
$491$	14.2913	−	24.7532i	0.644957	−	1.11710i	0.984311	−	0.176439i	$-0.0564580\pi$
$492$		0			0
$493$		−	21.0000i		−	0.945792i
$494$	−3.79129	+	13.1334i	−0.170578	+	0.590900i
$495$		0			0
$496$	−15.0000	−	8.66025i	−0.673520	−	0.388857i
$497$	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	$0.878842\pi$
$500$	31.0707	+	2.91914i	1.38952	+	0.130548i
$501$		0			0
$502$	−39.7617			−1.77465
$503$	15.7315	−	9.08258i	0.701432	−	0.404972i	−0.106448	−	0.994318i	$-0.533948\pi$
$503$	15.7315	−	9.08258i	0.701432	−	0.404972i	0.807881	+	0.589346i	$0.200615\pi$
$504$		0			0
$505$	−15.0050	−	13.4109i	−0.667712	−	0.596775i
$506$	−26.5390			−1.17980
$507$		0			0
$508$			27.2087i			1.20719i
$509$	25.6652	+	14.8178i	1.13759	+	0.656787i	0.945832	−	0.324656i	$-0.105249\pi$
$509$	25.6652	+	14.8178i	1.13759	+	0.656787i	0.191756	+	0.981443i	$0.438582\pi$
$510$		0			0
$511$		0			0
$512$	19.4340			0.858868
$513$		0			0
$514$	0.313068	−	0.180750i	0.0138088	−	0.00797254i
$515$	−33.1950	−	6.92820i	−1.46275	−	0.305293i
$516$		0			0
$517$	20.0616	+	11.5826i	0.882309	+	0.509401i
$518$	−15.0462	+	26.0608i	−0.661092	+	1.14505i
$519$		0			0
$520$	−6.53239	+	12.3421i	−0.286464	+	0.541238i
$521$	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
$523$	15.7315	+	9.08258i	0.687890	+	0.397153i	0.802821	−	0.596220i	$-0.203331\pi$
$523$	15.7315	+	9.08258i	0.687890	+	0.397153i	−0.114931	+	0.993373i	$0.536665\pi$
$524$	2.20871	+	3.82560i	0.0964880	+	0.167122i
$525$		0			0
$526$	−17.0608	+	9.85005i	−0.743886	+	0.429483i
$527$	−22.1552	−	38.3739i	−0.965094	−	1.67159i
$528$		0			0
$529$	−1.00000	−	1.73205i	−0.0434783	−	0.0753066i
$530$	−5.16184	+	5.77542i	−0.224216	+	0.250868i
$531$		0			0
$532$			8.37386i			0.363053i
$533$	−6.61438	−	6.87386i	−0.286501	−	0.297740i
$534$		0			0
$535$	2.11210	−	2.36316i	0.0913139	−	0.102168i
$536$	−12.8739	+	22.2982i	−0.556066	+	0.963135i
$537$		0			0
$538$	−32.8335			−1.41555
$539$	−9.16515	+	5.29150i	−0.394771	+	0.227921i
$540$		0			0
$541$		−	10.3923i		−	0.446800i	−0.974727	−	0.223400i	$-0.928284\pi$
$541$		−	10.3923i		−	0.446800i	0.974727	−	0.223400i	$-0.0717156\pi$
$542$	−16.4168	+	9.47822i	−0.705160	+	0.407124i
$543$		0			0
$544$	29.3085	+	16.9213i	1.25659	+	0.725494i
$545$	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	$-0.00852270\pi$
$548$	−0.133075	+	0.230493i	−0.00568468	+	0.00984615i
$549$		0			0
$550$	−28.7747	+	3.23870i	−1.22696	+	0.138099i
$551$			7.93725i			0.338138i
$552$		0			0
$553$	5.19615	+	9.00000i	0.220963	+	0.382719i
$554$			36.2976i			1.54214i
$555$		0			0
$556$	8.02178	−	13.8941i	0.340199	−	0.589242i
$557$	6.51903	−	11.2913i	0.276220	−	0.478427i	−0.694222	−	0.719761i	$-0.744251\pi$
$557$	6.51903	−	11.2913i	0.276220	−	0.478427i	0.970442	+	0.241334i	$0.0775848\pi$
$558$		0			0
$559$	−4.96099	+	1.22753i	−0.209827	+	0.0519188i
$560$	1.41742	−	6.79129i	0.0598971	−	0.286984i
$561$		0			0
$562$	−33.1950	−	19.1652i	−1.40025	−	0.808433i
$563$	7.79423	−	4.50000i	0.328488	−	0.189652i	−0.326682	−	0.945134i	$-0.605931\pi$
$563$	7.79423	−	4.50000i	0.328488	−	0.189652i	0.655169	+	0.755482i	$0.272597\pi$
$564$		0			0
$565$	−11.5880	−	35.2225i	−0.487511	−	1.48182i
$566$	−0.478220	+	0.276100i	−0.0201011	+	0.0116054i
$567$		0			0
$568$	5.33918	−	3.08258i	0.224027	−	0.129342i
$569$	9.87386	−	17.1020i	0.413934	−	0.716955i	−0.581382	−	0.813631i	$-0.697488\pi$
$569$	9.87386	−	17.1020i	0.413934	−	0.716955i	0.995316	+	0.0966762i	$0.0308211\pi$
$570$		0			0
$571$	29.0780			1.21688			0.608439	−	0.793601i	$-0.291796\pi$
$571$	29.0780			1.21688			0.608439	+	0.793601i	$0.291796\pi$
$572$	7.38505	−	25.5826i	0.308785	−	1.06966i
$573$		0			0
$574$	−8.68693	−	5.01540i	−0.362586	−	0.209339i
$575$	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	$0.453935\pi$
$578$	4.37780	+	7.58258i	0.182093	+	0.315394i
$579$		0			0
$580$	−5.84370	+	27.9989i	−0.242647	+	1.16259i
$581$	−9.79129	−	16.9590i	−0.406211	−	0.703578i
$582$		0			0
$583$	2.09355	−	3.62614i	0.0867060	−	0.150179i
$584$		0			0
$585$		0			0
$586$	51.2867			2.11864
$587$	−9.35548	+	16.2042i	−0.386142	+	0.668818i	−0.991927	−	0.126811i	$-0.959526\pi$
$587$	−9.35548	+	16.2042i	−0.386142	+	0.668818i	0.605785	+	0.795628i	$0.292859\pi$
$588$		0			0
$589$	8.37386	+	14.5040i	0.345039	+	0.597625i
$590$	16.1407	+	3.36875i	0.664500	+	0.138689i
$591$		0			0
$592$	−7.10895	−	12.3131i	−0.292176	−	0.506064i
$593$	21.1660			0.869184			0.434592	−	0.900627i	$-0.356893\pi$
$593$	21.1660			0.869184			0.434592	+	0.900627i	$0.356893\pi$
$594$		0			0
$595$	11.8273	−	13.2331i	0.484870	−	0.542506i
$596$	23.6044	+	13.6280i	0.966872	+	0.558224i
$597$		0			0
$598$	−35.1078	+	8.68693i	−1.43567	+	0.355235i
$599$	−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	−0.404582	−	0.914502i	$-0.632583\pi$
$601$	14.4564	−	25.0393i	0.589690	−	1.02137i	0.994273	−	0.106872i	$-0.0340836\pi$
$602$	−4.65390	+	2.68693i	−0.189679	+	0.109511i
$603$		0			0
$604$	15.0000	−	8.66025i	0.610341	−	0.352381i
$605$	−8.49628	+	2.79523i	−0.345423	+	0.113642i
$606$		0			0
$607$	17.1020	−	9.87386i	0.694150	−	0.400768i	−0.111015	−	0.993819i	$-0.535410\pi$
$607$	17.1020	−	9.87386i	0.694150	−	0.400768i	0.805165	+	0.593051i	$0.202077\pi$
$608$	−11.0776	−	6.39564i	−0.449255	−	0.259378i
$609$		0			0
$610$	−10.5826	+	50.7042i	−0.428476	+	2.05295i
$611$	30.3303	+	8.75560i	1.22703	+	0.354214i
$612$		0			0
$613$	10.8968	−	18.8739i	0.440119	−	0.762308i	−0.557579	−	0.830124i	$-0.688270\pi$
$613$	10.8968	−	18.8739i	0.440119	−	0.762308i	0.997698	+	0.0678157i	$0.0216030\pi$
$614$	26.5390	−	45.9669i	1.07103	−	1.85507i
$615$		0			0
$616$		−	7.93725i		−	0.319801i
$617$	−1.68438	−	2.91742i	−0.0678104	−	0.117451i	0.830127	−	0.557575i	$-0.188268\pi$
$617$	−1.68438	−	2.91742i	−0.0678104	−	0.117451i	−0.897937	+	0.440124i	$0.854935\pi$
$618$		0			0
$619$			2.01810i			0.0811143i	0.999177	+	0.0405572i	$0.0129133\pi$
$619$			2.01810i			0.0811143i	−0.999177	+	0.0405572i	$0.987087\pi$
$620$	18.8607	+	57.3282i	0.757462	+	2.30236i
$621$		0			0
$622$	−1.73205	+	3.00000i	−0.0694489	+	0.120289i
$623$		−	7.41742i		−	0.297173i
$624$		0			0
$625$	17.0000	+	18.3303i	0.680000	+	0.733212i
$626$	58.2867	+	33.6519i	2.32961	+	1.34500i
$627$		0			0
$628$	22.1552	−	12.7913i	0.884087	−	0.510428i
$629$		−	36.3731i		−	1.45029i
$630$		0			0
$631$	−18.8739	+	10.8968i	−0.751357	+	0.433796i	−0.826184	−	0.563401i	$-0.809493\pi$
$631$	−18.8739	+	10.8968i	−0.751357	+	0.433796i	0.0748272	+	0.997197i	$0.476159\pi$
$632$	10.3923			0.413384
$633$		0			0
$634$	−22.9564	+	39.7617i	−0.911717	+	1.57914i
$635$	−14.5250	+	16.2516i	−0.576408	+	0.644925i
$636$		0			0
$637$	−10.3923	+	10.0000i	−0.411758	+	0.396214i
$638$		−	26.5390i		−	1.05069i
$639$		0			0
$640$	−21.2936	−	19.0313i	−0.841702	−	0.752280i
$641$	−0.0825757	−	0.143025i	−0.00326154	−	0.00564916i	0.864390	−	0.502822i	$-0.167705\pi$
$641$	−0.0825757	−	0.143025i	−0.00326154	−	0.00564916i	−0.867652	+	0.497173i	$0.834372\pi$
$642$		0			0
$643$	2.95958	+	5.12614i	0.116714	+	0.202155i	0.918464	−	0.395505i	$-0.129430\pi$
$643$	2.95958	+	5.12614i	0.116714	+	0.202155i	−0.801749	+	0.597660i	$0.796097\pi$
$644$	−19.1869	+	11.0776i	−0.756071	+	0.436518i
$645$		0			0
$646$	−8.68693	−	15.0462i	−0.341783	−	0.591985i
$647$	−23.3827	−	13.5000i	−0.919268	−	0.530740i	−0.0358667	−	0.999357i	$-0.511419\pi$
$647$	−23.3827	−	13.5000i	−0.919268	−	0.530740i	−0.883402	+	0.468617i	$0.844753\pi$
$648$		0			0
$649$	−8.91288			−0.349861
$650$	−37.0053	+	13.7031i	−1.45147	+	0.537482i
$651$		0			0
$652$	14.9032	−	25.8131i	0.583654	−	1.01092i
$653$	42.2843	+	24.4129i	1.65471	+	0.955350i	0.975096	+	0.221784i	$0.0711880\pi$
$653$	42.2843	+	24.4129i	1.65471	+	0.955350i	0.679619	+	0.733566i	$0.262145\pi$
$654$		0			0
$655$	−0.723000	+	3.46410i	−0.0282500	+	0.135354i
$656$	4.10436	−	2.36965i	0.160248	−	0.0925193i
$657$		0			0
$658$	33.1950			1.29408
$659$	12.2477	+	21.2137i	0.477104	+	0.826368i	0.999656	−	0.0262396i	$-0.00835327\pi$
$659$	12.2477	+	21.2137i	0.477104	+	0.826368i	−0.522552	+	0.852607i	$0.675020\pi$
$660$		0			0
$661$	2.12614	+	1.22753i	0.0826971	+	0.0477452i	0.540778	−	0.841165i	$-0.318130\pi$
$661$	2.12614	+	1.22753i	0.0826971	+	0.0477452i	−0.458081	+	0.888910i	$0.651463\pi$
$662$			24.9564i			0.969960i
$663$		0			0
$664$	−19.5826			−0.759951
$665$	−4.47028	+	5.00166i	−0.173350	+	0.193956i
$666$		0			0
$667$	−18.1865	+	10.5000i	−0.704185	+	0.406562i
$668$	11.9536			0.462497
$669$		0			0
$670$	−69.1151	+	22.7385i	−2.67015	+	0.878464i
$671$		−	27.9989i		−	1.08088i
$672$		0			0
$673$	5.05313	+	2.91742i	0.194784	+	0.112458i	0.594220	−	0.804302i	$-0.297461\pi$
$673$	5.05313	+	2.91742i	0.194784	+	0.112458i	−0.399436	+	0.916761i	$0.630794\pi$
$674$	6.16515	+	3.55945i	0.237473	+	0.137105i
$675$		0			0
$676$	1.39564	−	36.2599i	0.0536786	−	1.39461i
$677$		−	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
$680$	−5.54661	−	16.8593i	−0.212703	−	0.646524i
$681$		0			0
$682$	−27.9989	−	48.4955i	−1.07213	−	1.85699i
$683$	5.96683	+	10.3348i	0.228314	+	0.395452i	0.957309	−	0.289068i	$-0.0933453\pi$
$683$	5.96683	+	10.3348i	0.228314	+	0.395452i	−0.728994	+	0.684520i	$0.760012\pi$
$684$		0			0
$685$	−0.202530	+	0.0666313i	−0.00773829	+	0.00254585i
$686$	−20.8521	+	36.1169i	−0.796136	+	1.37895i
$687$		0			0
$688$		−	2.53901i		−	0.0967990i
$689$	1.58258	−	5.48220i	0.0602913	−	0.208855i
$690$		0			0
$691$	30.8739	+	17.8250i	1.17450	+	0.678096i	0.954735	−	0.297457i	$-0.0961386\pi$
$691$	30.8739	+	17.8250i	1.17450	+	0.678096i	0.219762	+	0.975554i	$0.429472\pi$
$692$	−17.9303	−	10.3521i	−0.681609	−	0.393527i
$693$		0			0
$694$			33.5565i			1.27379i
$695$	12.2086	−	4.01655i	0.463097	−	0.152356i
$696$		0			0
$697$	12.1244			0.459243
$698$	−34.7463	+	20.0608i	−1.31517	+	0.759312i
$699$		0			0
$700$	−19.4514	+	14.3523i	−0.735195	+	0.542465i
$701$	2.83485			0.107071			0.0535354	−	0.998566i	$-0.482951\pi$
$701$	2.83485			0.107071			0.0535354	+	0.998566i	$0.482951\pi$
$702$		0			0
$703$			13.7477i			0.518505i
$704$	28.8303	+	16.6452i	1.08658	+	0.627339i
$705$		0			0
$706$	19.0608	+	33.0143i	0.717362	+	1.24251i
$707$	15.5885			0.586264
$708$		0			0
$709$	31.5000	−	18.1865i	1.18301	−	0.683010i	0.226299	−	0.974058i	$-0.427337\pi$
$709$	31.5000	−	18.1865i	1.18301	−	0.683010i	0.956708	+	0.291048i	$0.0940040\pi$
$710$	17.0544	+	3.55945i	0.640039	+	0.133584i
$711$		0			0
$712$	−6.42368	−	3.70871i	−0.240738	−	0.138990i
$713$	−22.1552	+	38.3739i	−0.829717	+	1.43711i
$714$		0			0
$715$	18.0680	−	11.3379i	0.675704	−	0.424013i
$716$	−0.460985			−0.0172278
$717$		0			0
$718$	63.2874	+	36.5390i	2.36187	+	1.36362i
$719$	−15.2477	−	26.4098i	−0.568644	−	0.984921i	−0.996700	−	0.0811686i	$-0.974135\pi$
$719$	−15.2477	−	26.4098i	−0.568644	−	0.984921i	0.428056	−	0.903752i	$-0.359199\pi$
$720$		0			0
$721$	22.7477	−	13.1334i	0.847170	−	0.489114i
$722$	−17.5112	−	30.3303i	−0.651700	−	1.12878i
$723$		0			0
$724$	26.1652	+	45.3194i	0.972420	+	1.68428i
$725$	−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	$0.708668\pi$
$728$	−2.59808	−	10.5000i	−0.0962911	−	0.389156i
$729$		0			0
$730$		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	$0.447167\pi$
$734$	−48.8085	+	28.1796i	−1.80156	+	1.04013i
$735$		0			0
$736$		−	33.8426i		−	1.24745i
$737$	34.0610	−	19.6652i	1.25465	−	0.724375i
$738$		0			0
$739$	−42.2477	−	24.3917i	−1.55411	−	0.897265i	−0.997801	−	0.0662878i	$-0.978884\pi$
$739$	−42.2477	−	24.3917i	−1.55411	−	0.897265i	−0.556307	−	0.830977i	$-0.687782\pi$
$740$	−10.1216	+	48.4955i	−0.372077	+	1.78273i
$741$		0			0
$742$		−	6.00000i		−	0.220267i
$743$	21.3845	−	37.0390i	0.784521	−	1.35883i	−0.144764	−	0.989466i	$-0.546242\pi$
$743$	21.3845	−	37.0390i	0.784521	−	1.35883i	0.929285	−	0.369364i	$-0.120424\pi$
$744$		0			0
$745$	6.82361	+	20.7408i	0.249998	+	0.759884i
$746$		−	28.4557i		−	1.04184i
$747$		0			0
$748$	16.9213	+	29.3085i	0.618703	+	1.07163i
$749$			2.45505i			0.0897056i
$750$		0			0
$751$	7.87386	−	13.6379i	0.287321	−	0.497655i	−0.685848	−	0.727745i	$-0.740569\pi$
$751$	7.87386	−	13.6379i	0.287321	−	0.497655i	0.973169	+	0.230090i	$0.0739019\pi$
$752$	−7.84190	+	13.5826i	−0.285965	+	0.495306i
$753$		0			0
$754$	−8.68693	−	35.1078i	−0.316359	−	1.27855i
$755$	13.5826	+	2.83485i	0.494321	+	0.103171i
$756$		0			0
$757$	−15.3700	−	8.87386i	−0.558632	−	0.322526i	0.193965	−	0.981009i	$-0.437865\pi$
$757$	−15.3700	−	8.87386i	−0.558632	−	0.322526i	−0.752596	+	0.658482i	$0.771199\pi$
$758$	−39.9425	+	23.0608i	−1.45078	+	0.837606i
$759$		0			0
$760$	2.09642	+	6.37221i	0.0760451	+	0.231144i
$761$	35.2913	−	20.3754i	1.27931	−	0.738609i	0.302587	−	0.953122i	$-0.402150\pi$
$761$	35.2913	−	20.3754i	1.27931	−	0.738609i	0.976721	+	0.214513i	$0.0688164\pi$
$762$		0			0
$763$	−4.11165	+	2.37386i	−0.148852	+	0.0859396i
$764$	−10.3521	+	17.9303i	−0.374525	+	0.648697i
$765$		0			0
$766$	6.20871			0.224330
$767$	−11.7906	+	2.91742i	−0.425735	+	0.105342i
$768$		0			0
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	0.236433	−	0.971648i	$-0.424022\pi$
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	−0.723255	+	0.690581i	$0.757355\pi$
$770$	14.9468	−	16.7235i	0.538647	−	0.602675i
$771$		0			0
$772$	−2.81655			−0.101370
$773$	−17.3682	−	30.0826i	−0.624690	−	1.08200i	−0.988601	−	0.150561i	$-0.951892\pi$
$773$	−17.3682	−	30.0826i	−0.624690	−	1.08200i	0.363911	−	0.931434i	$-0.381441\pi$
$774$		0			0
$775$	−19.3386	+	44.3103i	−0.694663	+	1.59167i
$776$	−3.87386	−	6.70973i	−0.139064	−	0.240865i
$777$		0			0
$778$	−16.5975	+	28.7477i	−0.595049	+	1.03066i
$779$	−4.58258			−0.164188
$780$		0			0
$781$	−9.41742			−0.336982
$782$	22.9835	−	39.8085i	0.821887	−	1.42355i
$783$		0			0
$784$	−3.58258	−	6.20520i	−0.127949	−	0.221614i
$785$	20.0616	+	4.18710i	0.716030	+	0.149444i
$786$		0			0
$787$	−16.0930	−	27.8739i	−0.573653	−	0.993596i	−0.996187	−	0.0872487i	$-0.972193\pi$
$787$	−16.0930	−	27.8739i	−0.573653	−	0.993596i	0.422534	−	0.906347i	$-0.361141\pi$
$788$	55.7316			1.98536
$789$		0			0
$790$	21.8963	+	19.5700i	0.779034	+	0.696270i
$791$	24.8739	+	14.3609i	0.884413	+	0.510616i
$792$		0			0
$793$	−9.16478	−	37.0390i	−0.325451	−	1.31529i
$794$	59.7042			2.11882
$795$		0			0
$796$	1.97822	−	3.42638i	0.0701161	−	0.121445i
$797$	−17.3881	+	10.0390i	−0.615918	+	0.355600i	−0.775278	−	0.631620i	$-0.782390\pi$
$797$	−17.3881	+	10.0390i	−0.615918	+	0.355600i	0.159360	+	0.987220i	$0.449057\pi$
$798$		0			0
$799$	−34.7477	+	20.0616i	−1.22929	+	0.709729i
$800$	−4.13000	−	36.6936i	−0.146017	−	1.29731i
$801$		0			0
$802$	23.7065	−	13.6869i	0.837104	−	0.483302i
$803$		0			0
$804$		0			0
$805$	−17.3739	−	3.62614i	−0.612348	−	0.127805i
$806$	−52.9129	−	54.9887i	−1.86378	−	1.93689i
$807$		0			0
$808$	7.79423	−	13.5000i	0.274200	−	0.474928i
$809$	−18.4129	+	31.8920i	−0.647362	+	1.12126i	0.336388	+	0.941723i	$0.390795\pi$
$809$	−18.4129	+	31.8920i	−0.647362	+	1.12126i	−0.983750	+	0.179541i	$0.942539\pi$
$810$		0			0
$811$		−	18.7665i		−	0.658981i	−0.944159	−	0.329491i	$-0.893123\pi$
$811$		−	18.7665i		−	0.658981i	0.944159	−	0.329491i	$-0.106877\pi$
$812$	−11.0776	−	19.1869i	−0.388747	−	0.673329i
$813$		0			0
$814$		−	45.9669i		−	1.61114i
$815$	22.6816	−	7.46211i	0.794501	−	0.261386i
$816$		0			0
$817$	−1.22753	+	2.12614i	−0.0429457	+	0.0743841i
$818$			18.9564i			0.662796i
$819$		0			0
$820$	−16.1652	−	3.37386i	−0.564512	−	0.117820i
$821$	−20.2913	−	11.7152i	−0.708171	−	0.408863i	0.102213	−	0.994763i	$-0.467408\pi$
$821$	−20.2913	−	11.7152i	−0.708171	−	0.408863i	−0.810383	+	0.585900i	$0.800741\pi$
$822$		0			0
$823$	−35.1455	+	20.2913i	−1.22510	+	0.707310i	−0.966000	−	0.258542i	$-0.916758\pi$
$823$	−35.1455	+	20.2913i	−1.22510	+	0.707310i	−0.259096	+	0.965851i	$0.583425\pi$
$824$		−	26.2668i		−	0.915048i
$825$		0			0
$826$	−11.0608	+	6.38595i	−0.384854	+	0.222196i
$827$	−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	−0.835659	−	0.549248i	$-0.814914\pi$
$829$	1.66515	−	2.88413i	0.0578331	−	0.100170i	0.893492	+	0.449078i	$0.148248\pi$
$830$	−41.2599	−	36.8765i	−1.43215	−	1.28000i
$831$		0			0
$832$	43.5873	+	12.5826i	1.51112	+	0.436222i
$833$		−	18.3303i		−	0.635107i
$834$		0			0
$835$	7.13978	+	6.38126i	0.247082	+	0.220833i
$836$	−6.39564	−	11.0776i	−0.221198	−	0.383126i
$837$		0			0
$838$	26.4476	+	45.8085i	0.913616	+	1.58243i
$839$	−1.16970	+	0.675325i	−0.0403824	+	0.0233148i	−0.520055	−	0.854133i	$-0.674089\pi$
$839$	−1.16970	+	0.675325i	−0.0403824	+	0.0233148i	0.479673	+	0.877447i	$0.340755\pi$
$840$		0			0
$841$	4.00000	+	6.92820i	0.137931	+	0.238904i
$842$	49.7925	+	28.7477i	1.71596	+	0.990712i
$843$		0			0
$844$	50.7042			1.74531
$845$	20.1905	−	20.9128i	0.694574	−	0.719421i
$846$		0			0
$847$	3.46410	−	6.00000i	0.119028	−	0.206162i
$848$	2.45505	+	1.41742i	0.0843068	+	0.0486746i
$849$		0			0
$850$	20.0616	−	45.9669i	0.688108	−	1.57665i
$851$	−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	$0.134742\pi$
$854$	−20.0608	−	34.7463i	−0.686466	−	1.18899i
$855$		0			0
$856$	2.12614	+	1.22753i	0.0726698	+	0.0419560i
$857$			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	$-0.726246\pi$
$859$	−38.2432			−1.30484			−0.652420	+	0.757857i	$0.726246\pi$
$860$	−5.89547	+	6.59625i	−0.201034	+	0.224930i
$861$		0			0
$862$	56.1785	−	32.4347i	1.91345	−	1.10473i
$863$	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
$866$		−	38.8480i		−	1.32011i
$867$		0			0
$868$	−40.4847	−	23.3739i	−1.37414	−	0.793361i
$869$	−13.7477	−	7.93725i	−0.466360	−	0.269253i
$870$		0			0
$871$	38.6216	−	37.1636i	1.30864	−	1.25924i
$872$			4.74773i			0.160778i
$873$		0			0
$874$	−8.68693	+	15.0462i	−0.293840	+	0.508946i
$875$	−19.2800	−	1.81139i	−0.651783	−	0.0612360i
$876$		0			0
$877$	−3.96863	−	6.87386i	−0.134011	−	0.232114i	0.791208	−	0.611547i	$-0.209452\pi$
$877$	−3.96863	−	6.87386i	−0.134011	−	0.232114i	−0.925219	+	0.379433i	$0.876119\pi$
$878$	44.3203	+	76.7650i	1.49574	+	2.59069i
$879$		0			0
$880$	3.31186	+	10.0666i	0.111643	+	0.339345i
$881$	−9.24773	+	16.0175i	−0.311564	+	0.539644i	−0.978701	−	0.205290i	$-0.934186\pi$
$881$	−9.24773	+	16.0175i	−0.311564	+	0.539644i	0.667137	+	0.744935i	$0.267519\pi$
$882$		0			0
$883$		−	46.2432i		−	1.55621i	−0.628136	−	0.778103i	$-0.716182\pi$
$883$		−	46.2432i		−	1.55621i	0.628136	−	0.778103i	$-0.283818\pi$
$884$	31.9782	+	33.2327i	1.07554	+	1.11774i
$885$		0			0
$886$	−49.1216	−	28.3604i	−1.65027	−	0.952785i
$887$	0.429076	+	0.247727i	0.0144070	+	0.00831786i	0.507186	−	0.861837i	$-0.330686\pi$
$887$	0.429076	+	0.247727i	0.0144070	+	0.00831786i	−0.492779	+	0.870154i	$0.664019\pi$
$888$		0			0
$889$		−	16.8836i		−	0.566256i
$890$	−6.55052	−	19.9107i	−0.219574	−	0.667409i
$891$		0			0
$892$	−24.1733			−0.809381
$893$	13.1334	−	7.58258i	0.439493	−	0.253741i
$894$		0			0
$895$	−0.275344	−	0.246091i	−0.00920372	−	0.00822592i
$896$	22.1216			0.739030
$897$		0			0
$898$		−	82.0345i		−	2.73753i
$899$	−38.3739	−	22.1552i	−1.27984	−	0.738916i
$900$		0			0
$901$	3.62614	+	6.28065i	0.120804	+	0.209239i
$902$	15.3223			0.510177
$903$		0			0
$904$	24.8739	−	14.3609i	0.827292	−	0.477637i
$905$	−8.56490	+	41.0369i	−0.284707	+	1.36411i
$906$		0			0
$907$	−29.2264	−	16.8739i	−0.970446	−	0.560287i	−0.0710740	−	0.997471i	$-0.522643\pi$
$907$	−29.2264	−	16.8739i	−0.970446	−	0.560287i	−0.899372	+	0.437184i	$0.855976\pi$
$908$	8.52718	−	14.7695i	0.282984	−	0.490143i
$909$		0			0
$910$	14.2988	−	27.0157i	0.473999	−	0.895561i
$911$	−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
$914$	−1.89564	−	3.28335i	−0.0627023	−	0.108604i
$915$		0			0
$916$	−13.2523	+	7.65120i	−0.437867	+	0.252803i
$917$	−1.37055	−	2.37386i	−0.0452596	−	0.0783919i
$918$		0			0
$919$	17.9174	+	31.0339i	0.591041	+	1.02371i	0.994093	+	0.108536i	$0.0346163\pi$
$919$	17.9174	+	31.0339i	0.591041	+	1.02371i	−0.403051	+	0.915177i	$0.632050\pi$
$920$	−11.8273	+	13.2331i	−0.389933	+	0.436284i
$921$		0			0
$922$			2.62614i			0.0864872i
$923$	−12.4581	+	3.08258i	−0.410063	+	0.101464i
$924$		0			0
$925$	−31.9343	+	23.5627i	−1.04999	+	0.774738i
$926$	−9.00000	+	15.5885i	−0.295758	+	0.512268i
$927$		0			0
$928$	33.8426			1.11094
$929$	13.8303	−	7.98493i	0.453758	−	0.261977i	−0.255658	−	0.966767i	$-0.582292\pi$
$929$	13.8303	−	7.98493i	0.453758	−	0.261977i	0.709416	+	0.704790i	$0.248959\pi$
$930$		0			0
$931$			6.92820i			0.227063i
$932$	−51.1631	+	29.5390i	−1.67590	+	0.967583i
$933$		0			0
$934$	−23.3739	−	13.4949i	−0.764816	−	0.441567i
$935$	−5.53901	+	26.5390i	−0.181145	+	0.867919i
$936$		0			0
$937$			23.4955i			0.767563i	0.923424	+	0.383782i	$0.125378\pi$
$937$			23.4955i			0.767563i	−0.923424	+	0.383782i	$0.874622\pi$
$938$	28.1796	−	48.8085i	0.920097	−	1.59365i
$939$		0			0
$940$	51.9110	−	17.0784i	1.69315	−	0.557037i
$941$		−	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
$944$		−	6.03440i		−	0.196403i
$945$		0			0
$946$	4.10436	−	7.10895i	0.133444	−	0.231132i
$947$	−19.2909	+	33.4129i	−0.626871	+	1.08577i	0.361305	+	0.932448i	$0.382331\pi$
$947$	−19.2909	+	33.4129i	−0.626871	+	1.08577i	−0.988176	+	0.153325i	$0.951002\pi$
$948$		0			0
$949$		0			0
$950$	−7.58258	+	17.3739i	−0.246011	+	0.563683i
$951$		0			0
$952$	11.9059	+	6.87386i	0.385872	+	0.222783i
$953$	−48.5650	+	28.0390i	−1.57317	+	0.908273i	−0.577398	+	0.816463i	$0.695932\pi$
$953$	−48.5650	+	28.0390i	−1.57317	+	0.908273i	−0.995777	+	0.0918100i	$0.970735\pi$
$954$		0			0
$955$	−15.7551	+	5.18335i	−0.509824	+	0.167729i
$956$	50.7042	−	29.2741i	1.63989	−	0.946791i
$957$		0			0
$958$	−61.3746	+	35.4347i	−1.98292	+	1.14484i
$959$	0.0825757	−	0.143025i	0.00266651	−	0.00461853i
$960$		0			0
$961$	−62.4955			−2.01598
$962$	−15.0462	−	60.8085i	−0.485109	−	1.96055i
$963$		0			0
$964$	4.18693	+	2.41733i	0.134852	+	0.0778568i
$965$	−1.68231	−	1.50358i	−0.0541554	−	0.0484020i
$966$		0			0
$967$	21.5076			0.691638			0.345819	−	0.938301i	$-0.387601\pi$
$967$	21.5076			0.691638			0.345819	+	0.938301i	$0.387601\pi$
$968$	−3.46410	−	6.00000i	−0.111340	−	0.192847i
$969$		0			0
$970$	4.47315	−	21.4322i	0.143624	−	0.688145i
$971$	18.2477	+	31.6060i	0.585597	+	1.01428i	0.994801	+	0.101841i	$0.0324734\pi$
$971$	18.2477	+	31.6060i	0.585597	+	1.01428i	−0.409203	+	0.912443i	$0.634193\pi$
$972$		0			0
$973$	−4.97768	+	8.62159i	−0.159577	+	0.276396i
$974$	−46.1216			−1.47783
$975$		0			0
$976$	18.9564			0.606781
$977$	19.3863	−	33.5780i	0.620222	−	1.07426i	−0.369222	−	0.929341i	$-0.620376\pi$
$977$	19.3863	−	33.5780i	0.620222	−	1.07426i	0.989444	−	0.144915i	$-0.0462909\pi$
$978$		0			0
$979$	5.66515	+	9.81233i	0.181059	+	0.313603i
$980$	−5.10080	+	24.4394i	−0.162939	+	0.780688i
$981$		0			0
$982$	31.2822	+	54.1824i	0.998256	+	1.72903i
$983$	−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
$986$	39.8085	+	22.9835i	1.26776	+	0.731943i
$987$		0			0
$988$	−12.0866	−	12.5608i	−0.384527	−	0.399612i
$989$	−6.49545			−0.206543
$990$		0			0
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	−0.744124	−	0.668042i	$-0.767133\pi$
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	0.950603	+	0.310409i	$0.100466\pi$
$992$	61.8414	−	35.7042i	1.96347	−	1.13361i
$993$		0			0
$994$	−11.6869	+	6.74745i	−0.370687	+	0.214016i
$995$	3.01071	−	0.990505i	0.0954458	−	0.0314011i
$996$		0			0
$997$	15.7315	−	9.08258i	0.498221	−	0.287648i	−0.229758	−	0.973248i	$-0.573793\pi$
$997$	15.7315	−	9.08258i	0.498221	−	0.287648i	0.727979	+	0.685600i	$0.240460\pi$
$998$	−31.4630	−	18.1652i	−0.995943	−	0.575008i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bf.a.199.1		8
3.2	odd	2		65.2.l.a.4.4	yes	8
5.4	even	2	inner	585.2.bf.a.199.4		8
12.11	even	2		1040.2.df.b.849.3		8
13.10	even	6	inner	585.2.bf.a.244.4		8
15.2	even	4		325.2.n.c.251.2		4
15.8	even	4		325.2.n.b.251.1		4
15.14	odd	2		65.2.l.a.4.1	✓	8
39.2	even	12		845.2.n.d.484.4		8
39.5	even	4		845.2.n.c.529.1		8
39.8	even	4		845.2.n.d.529.3		8
39.11	even	12		845.2.n.c.484.2		8
39.17	odd	6		845.2.d.c.844.8		8
39.20	even	12		845.2.b.f.339.2		8
39.23	odd	6		65.2.l.a.49.1	yes	8
39.29	odd	6		845.2.l.c.699.4		8
39.32	even	12		845.2.b.f.339.8		8
39.35	odd	6		845.2.d.c.844.2		8
39.38	odd	2		845.2.l.c.654.1		8
60.59	even	2		1040.2.df.b.849.2		8
65.49	even	6	inner	585.2.bf.a.244.1		8
156.23	even	6		1040.2.df.b.49.2		8
195.23	even	12		325.2.n.b.101.1		4
195.29	odd	6		845.2.l.c.699.1		8
195.32	odd	12		4225.2.a.bk.1.1		4
195.44	even	4		845.2.n.d.529.4		8
195.59	even	12		845.2.b.f.339.7		8
195.62	even	12		325.2.n.c.101.2		4
195.74	odd	6		845.2.d.c.844.7		8
195.89	even	12		845.2.n.d.484.3		8
195.98	odd	12		4225.2.a.bj.1.1		4
195.119	even	12		845.2.n.c.484.1		8
195.134	odd	6		845.2.d.c.844.1		8
195.137	odd	12		4225.2.a.bk.1.4		4
195.149	even	12		845.2.b.f.339.1		8
195.164	even	4		845.2.n.c.529.2		8
195.179	odd	6		65.2.l.a.49.4	yes	8
195.188	odd	12		4225.2.a.bj.1.4		4
195.194	odd	2		845.2.l.c.654.4		8
780.179	even	6		1040.2.df.b.49.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.1	✓	8	15.14	odd	2
65.2.l.a.4.4	yes	8	3.2	odd	2
65.2.l.a.49.1	yes	8	39.23	odd	6
65.2.l.a.49.4	yes	8	195.179	odd	6
325.2.n.b.101.1		4	195.23	even	12
325.2.n.b.251.1		4	15.8	even	4
325.2.n.c.101.2		4	195.62	even	12
325.2.n.c.251.2		4	15.2	even	4
585.2.bf.a.199.1		8	1.1	even	1	trivial
585.2.bf.a.199.4		8	5.4	even	2	inner
585.2.bf.a.244.1		8	65.49	even	6	inner
585.2.bf.a.244.4		8	13.10	even	6	inner
845.2.b.f.339.1		8	195.149	even	12
845.2.b.f.339.2		8	39.20	even	12
845.2.b.f.339.7		8	195.59	even	12
845.2.b.f.339.8		8	39.32	even	12
845.2.d.c.844.1		8	195.134	odd	6
845.2.d.c.844.2		8	39.35	odd	6
845.2.d.c.844.7		8	195.74	odd	6
845.2.d.c.844.8		8	39.17	odd	6
845.2.l.c.654.1		8	39.38	odd	2
845.2.l.c.654.4		8	195.194	odd	2
845.2.l.c.699.1		8	195.29	odd	6
845.2.l.c.699.4		8	39.29	odd	6
845.2.n.c.484.1		8	195.119	even	12
845.2.n.c.484.2		8	39.11	even	12
845.2.n.c.529.1		8	39.5	even	4
845.2.n.c.529.2		8	195.164	even	4
845.2.n.d.484.3		8	195.89	even	12
845.2.n.d.484.4		8	39.2	even	12
845.2.n.d.529.3		8	39.8	even	4
845.2.n.d.529.4		8	195.44	even	4
1040.2.df.b.49.2		8	156.23	even	6
1040.2.df.b.49.3		8	780.179	even	6
1040.2.df.b.849.2		8	60.59	even	2
1040.2.df.b.849.3		8	12.11	even	2
4225.2.a.bj.1.1		4	195.98	odd	12
4225.2.a.bj.1.4		4	195.188	odd	12
4225.2.a.bk.1.1		4	195.32	odd	12
4225.2.a.bk.1.4		4	195.137	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09445 + 1.89564i) q^{2} +(-1.39564 - 2.41733i) q^{4} +(0.456850 - 2.18890i) q^{5} +(0.866025 + 1.50000i) q^{7} +1.73205 q^{8} +(3.64938 + 3.26167i) q^{10} +(-2.29129 - 1.32288i) q^{11} +(-3.46410 - 1.00000i) q^{13} -3.79129 q^{14} +(0.895644 - 1.55130i) q^{16} +(3.96863 - 2.29129i) q^{17} +(-1.50000 + 0.866025i) q^{19} +(-5.92889 + 1.95057i) q^{20} +(5.01540 - 2.89564i) q^{22} +(-3.96863 - 2.29129i) q^{23} +(-4.58258 - 2.00000i) q^{25} +(5.68693 - 5.47225i) q^{26} +(2.41733 - 4.18693i) q^{28} +(2.29129 - 3.96863i) q^{29} -9.66930i q^{31} +(3.69253 + 6.39564i) q^{32} +10.0308i q^{34} +(3.67900 - 1.21037i) q^{35} +(3.96863 - 6.87386i) q^{37} -3.79129i q^{38} +(0.791288 - 3.79129i) q^{40} +(2.29129 + 1.32288i) q^{41} +(1.22753 - 0.708712i) q^{43} +7.38505i q^{44} +(8.68693 - 5.01540i) q^{46} -8.75560 q^{47} +(2.00000 - 3.46410i) q^{49} +(8.80669 - 6.49803i) q^{50} +(2.41733 + 9.76951i) q^{52} +1.58258i q^{53} +(-3.94242 + 4.41105i) q^{55} +(1.50000 + 2.59808i) q^{56} +(5.01540 + 8.68693i) q^{58} +(2.91742 - 1.68438i) q^{59} +(5.29129 + 9.16478i) q^{61} +(18.3296 + 10.5826i) q^{62} -12.5826 q^{64} +(-3.77148 + 7.12573i) q^{65} +(-7.43273 + 12.8739i) q^{67} +(-11.0776 - 6.39564i) q^{68} +(-1.73205 + 8.29875i) q^{70} +(3.08258 - 1.77973i) q^{71} +(8.68693 + 15.0462i) q^{74} +(4.18693 + 2.41733i) q^{76} -4.58258i q^{77} +6.00000 q^{79} +(-2.98647 - 2.66919i) q^{80} +(-5.01540 + 2.89564i) q^{82} -11.3060 q^{83} +(-3.20233 - 9.73371i) q^{85} +3.10260i q^{86} +(-3.96863 - 2.29129i) q^{88} +(-3.70871 - 2.14123i) q^{89} +(-1.50000 - 6.06218i) q^{91} +12.7913i q^{92} +(9.58258 - 16.5975i) q^{94} +(1.21037 + 3.67900i) q^{95} +(-2.23658 - 3.87386i) q^{97} +(4.37780 + 7.58258i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 4 q^{10} - 12 q^{14} - 2 q^{16} - 12 q^{19} - 24 q^{20} + 18 q^{26} - 6 q^{35} - 12 q^{40} + 42 q^{46} + 16 q^{49} + 12 q^{50} - 14 q^{55} + 12 q^{56} + 60 q^{59} + 24 q^{61} - 64 q^{64}+ \cdots + 6 q^{95}+O(q^{100}) \) 8 * q - 2 * q^4 - 4 * q^10 - 12 * q^14 - 2 * q^16 - 12 * q^19 - 24 * q^20 + 18 * q^26 - 6 * q^35 - 12 * q^40 + 42 * q^46 + 16 * q^49 + 12 * q^50 - 14 * q^55 + 12 * q^56 + 60 * q^59 + 24 * q^61 - 64 * q^64 + 24 * q^65 - 12 * q^71 + 42 * q^74 + 6 * q^76 + 48 * q^79 - 18 * q^80 + 42 * q^85 - 48 * q^89 - 12 * q^91 + 40 * q^94 + 6 * q^95

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