LMFDB - Embedded newform 567.2.f.n.379.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(190,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.190"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-2,0,0,4,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
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:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			379.4
Root			$1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	567.379
Dual form			567.2.f.n.190.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.09445 - 1.89564i) q^{2} +(-1.39564 - 2.41733i) q^{4} +(0.456850 + 0.791288i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.73205 q^{8} +2.00000 q^{10} +(1.32288 - 2.29129i) q^{11} +(-2.00000 - 3.46410i) q^{13} +(-1.09445 - 1.89564i) q^{14} +(0.895644 - 1.55130i) q^{16} -3.46410 q^{17} +5.58258 q^{19} +(1.27520 - 2.20871i) q^{20} +(-2.89564 - 5.01540i) q^{22} +(-1.73205 - 3.00000i) q^{23} +(2.08258 - 3.60713i) q^{25} -8.75560 q^{26} -2.79129 q^{28} +(-4.37780 + 7.58258i) q^{29} +(4.58258 + 7.93725i) q^{31} +(-3.69253 - 6.39564i) q^{32} +(-3.79129 + 6.56670i) q^{34} +0.913701 q^{35} +3.00000 q^{37} +(6.10985 - 10.5826i) q^{38} +(-0.791288 - 1.37055i) q^{40} +(-0.456850 - 0.791288i) q^{41} +(-0.291288 + 0.504525i) q^{43} -7.38505 q^{44} -7.58258 q^{46} +(-6.56670 + 11.3739i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-4.55855 - 7.89564i) q^{50} +(-5.58258 + 9.66930i) q^{52} +8.66025 q^{53} +2.41742 q^{55} +(-0.866025 + 1.50000i) q^{56} +(9.58258 + 16.5975i) q^{58} +(1.73205 + 3.00000i) q^{59} +(-5.79129 + 10.0308i) q^{61} +20.0616 q^{62} -12.5826 q^{64} +(1.82740 - 3.16515i) q^{65} +(-4.29129 - 7.43273i) q^{67} +(4.83465 + 8.37386i) q^{68} +(1.00000 - 1.73205i) q^{70} +4.47315 q^{71} +15.1652 q^{73} +(3.28335 - 5.68693i) q^{74} +(-7.79129 - 13.4949i) q^{76} +(-1.32288 - 2.29129i) q^{77} +(-0.291288 + 0.504525i) q^{79} +1.63670 q^{80} -2.00000 q^{82} +(-4.83465 + 8.37386i) q^{83} +(-1.58258 - 2.74110i) q^{85} +(0.637600 + 1.10436i) q^{86} +(-2.29129 + 3.96863i) q^{88} +1.82740 q^{89} -4.00000 q^{91} +(-4.83465 + 8.37386i) q^{92} +(14.3739 + 24.8963i) q^{94} +(2.55040 + 4.41742i) q^{95} +(0.791288 - 1.37055i) q^{97} -2.18890 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 4 q^{7} + 16 q^{10} - 16 q^{13} - 2 q^{16} + 8 q^{19} - 14 q^{22} - 20 q^{25} - 4 q^{28} - 12 q^{34} + 24 q^{37} + 12 q^{40} + 16 q^{43} - 24 q^{46} - 4 q^{49} - 8 q^{52} + 56 q^{55} + 40 q^{58}+ \cdots - 12 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 + 4 * q^7 + 16 * q^10 - 16 * q^13 - 2 * q^16 + 8 * q^19 - 14 * q^22 - 20 * q^25 - 4 * q^28 - 12 * q^34 + 24 * q^37 + 12 * q^40 + 16 * q^43 - 24 * q^46 - 4 * q^49 - 8 * q^52 + 56 * q^55 + 40 * q^58 - 28 * q^61 - 64 * q^64 - 16 * q^67 + 8 * q^70 + 48 * q^73 - 44 * q^76 + 16 * q^79 - 16 * q^82 + 24 * q^85 - 32 * q^91 + 60 * q^94 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.09445	−	1.89564i	0.773893	−	1.34042i	−0.161521	−	0.986869i	$-0.551640\pi$
$2$	1.09445	−	1.89564i	0.773893	−	1.34042i	0.935414	−	0.353553i	$-0.115027\pi$
$3$		0			0
$3$		0			0
$4$	−1.39564	−	2.41733i	−0.697822	−	1.20866i
$5$	0.456850	+	0.791288i	0.204310	+	0.353875i	0.949913	−	0.312516i	$-0.101172\pi$
$5$	0.456850	+	0.791288i	0.204310	+	0.353875i	−0.745603	+	0.666390i	$0.767838\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−1.73205			−0.612372
$9$		0			0
$10$	2.00000			0.632456
$11$	1.32288	−	2.29129i	0.398862	−	0.690849i	−0.594724	−	0.803930i	$-0.702739\pi$
$11$	1.32288	−	2.29129i	0.398862	−	0.690849i	0.993586	+	0.113081i	$0.0360719\pi$
$12$		0			0
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$	−1.09445	−	1.89564i	−0.292504	−	0.506632i
$15$		0			0
$16$	0.895644	−	1.55130i	0.223911	−	0.387825i
$17$	−3.46410			−0.840168			−0.420084	−	0.907485i	$-0.637999\pi$
$17$	−3.46410			−0.840168			−0.420084	+	0.907485i	$0.637999\pi$
$18$		0			0
$19$	5.58258			1.28073			0.640365	−	0.768070i	$-0.278783\pi$
$19$	5.58258			1.28073			0.640365	+	0.768070i	$0.278783\pi$
$20$	1.27520	−	2.20871i	0.285144	−	0.493883i
$21$		0			0
$22$	−2.89564	−	5.01540i	−0.617353	−	1.06929i
$23$	−1.73205	−	3.00000i	−0.361158	−	0.625543i	0.626994	−	0.779024i	$-0.284285\pi$
$23$	−1.73205	−	3.00000i	−0.361158	−	0.625543i	−0.988152	+	0.153481i	$0.950952\pi$
$24$		0			0
$25$	2.08258	−	3.60713i	0.416515	−	0.721425i
$26$	−8.75560			−1.71712
$27$		0			0
$28$	−2.79129			−0.527504
$29$	−4.37780	+	7.58258i	−0.812937	+	1.40805i	0.0978621	+	0.995200i	$0.468800\pi$
$29$	−4.37780	+	7.58258i	−0.812937	+	1.40805i	−0.910799	+	0.412849i	$0.864534\pi$
$30$		0			0
$31$	4.58258	+	7.93725i	0.823055	+	1.42557i	0.903397	+	0.428806i	$0.141065\pi$
$31$	4.58258	+	7.93725i	0.823055	+	1.42557i	−0.0803419	+	0.996767i	$0.525601\pi$
$32$	−3.69253	−	6.39564i	−0.652753	−	1.13060i
$33$		0			0
$34$	−3.79129	+	6.56670i	−0.650201	+	1.12618i
$35$	0.913701			0.154444
$36$		0			0
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	6.10985	−	10.5826i	0.991149	−	1.71672i
$39$		0			0
$40$	−0.791288	−	1.37055i	−0.125114	−	0.216703i
$41$	−0.456850	−	0.791288i	−0.0713480	−	0.123578i	0.828144	−	0.560515i	$-0.189397\pi$
$41$	−0.456850	−	0.791288i	−0.0713480	−	0.123578i	−0.899492	+	0.436937i	$0.856063\pi$
$42$		0			0
$43$	−0.291288	+	0.504525i	−0.0444210	+	0.0769394i	−0.887381	−	0.461037i	$-0.847478\pi$
$43$	−0.291288	+	0.504525i	−0.0444210	+	0.0769394i	0.842960	+	0.537976i	$0.180811\pi$
$44$	−7.38505			−1.11334
$45$		0			0
$46$	−7.58258			−1.11799
$47$	−6.56670	+	11.3739i	−0.957852	+	1.65905i	−0.230150	+	0.973155i	$0.573922\pi$
$47$	−6.56670	+	11.3739i	−0.957852	+	1.65905i	−0.727702	+	0.685893i	$0.759412\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−4.55855	−	7.89564i	−0.644677	−	1.11661i
$51$		0			0
$52$	−5.58258	+	9.66930i	−0.774164	+	1.34089i
$53$	8.66025			1.18958			0.594789	−	0.803882i	$-0.297236\pi$
$53$	8.66025			1.18958			0.594789	+	0.803882i	$0.297236\pi$
$54$		0			0
$55$	2.41742			0.325965
$56$	−0.866025	+	1.50000i	−0.115728	+	0.200446i
$57$		0			0
$58$	9.58258	+	16.5975i	1.25825	+	2.17936i
$59$	1.73205	+	3.00000i	0.225494	+	0.390567i	0.956467	−	0.291839i	$-0.0942671\pi$
$59$	1.73205	+	3.00000i	0.225494	+	0.390567i	−0.730974	+	0.682406i	$0.760934\pi$
$60$		0			0
$61$	−5.79129	+	10.0308i	−0.741498	+	1.28431i	0.210315	+	0.977634i	$0.432551\pi$
$61$	−5.79129	+	10.0308i	−0.741498	+	1.28431i	−0.951813	+	0.306679i	$0.900782\pi$
$62$	20.0616			2.54783
$63$		0			0
$64$	−12.5826			−1.57282
$65$	1.82740	−	3.16515i	0.226661	−	0.392589i
$66$		0			0
$67$	−4.29129	−	7.43273i	−0.524264	−	0.908052i	−0.999601	−	0.0282483i	$-0.991007\pi$
$67$	−4.29129	−	7.43273i	−0.524264	−	0.908052i	0.475337	−	0.879804i	$-0.342326\pi$
$68$	4.83465	+	8.37386i	0.586288	+	1.01548i
$69$		0			0
$70$	1.00000	−	1.73205i	0.119523	−	0.207020i
$71$	4.47315			0.530866			0.265433	−	0.964129i	$-0.414485\pi$
$71$	4.47315			0.530866			0.265433	+	0.964129i	$0.414485\pi$
$72$		0			0
$73$	15.1652			1.77495			0.887473	−	0.460859i	$-0.152459\pi$
$73$	15.1652			1.77495			0.887473	+	0.460859i	$0.152459\pi$
$74$	3.28335	−	5.68693i	0.381682	−	0.661092i
$75$		0			0
$76$	−7.79129	−	13.4949i	−0.893722	−	1.54797i
$77$	−1.32288	−	2.29129i	−0.150756	−	0.261116i
$78$		0			0
$79$	−0.291288	+	0.504525i	−0.0327724	+	0.0567635i	−0.881946	−	0.471350i	$-0.843767\pi$
$79$	−0.291288	+	0.504525i	−0.0327724	+	0.0567635i	0.849174	+	0.528113i	$0.177100\pi$
$80$	1.63670			0.182989
$81$		0			0
$82$	−2.00000			−0.220863
$83$	−4.83465	+	8.37386i	−0.530672	+	0.919151i	0.468687	+	0.883364i	$0.344727\pi$
$83$	−4.83465	+	8.37386i	−0.530672	+	0.919151i	−0.999359	+	0.0357868i	$0.988606\pi$
$84$		0			0
$85$	−1.58258	−	2.74110i	−0.171654	−	0.297314i
$86$	0.637600	+	1.10436i	0.0687542	+	0.119086i
$87$		0			0
$88$	−2.29129	+	3.96863i	−0.244252	+	0.423057i
$89$	1.82740			0.193704			0.0968521	−	0.995299i	$-0.469123\pi$
$89$	1.82740			0.193704			0.0968521	+	0.995299i	$0.469123\pi$
$90$		0			0
$91$	−4.00000			−0.419314
$92$	−4.83465	+	8.37386i	−0.504047	+	0.873036i
$93$		0			0
$94$	14.3739	+	24.8963i	1.48255	+	2.56785i
$95$	2.55040	+	4.41742i	0.261666	+	0.453218i
$96$		0			0
$97$	0.791288	−	1.37055i	0.0803431	−	0.139158i	−0.823054	−	0.567963i	$-0.807732\pi$
$97$	0.791288	−	1.37055i	0.0803431	−	0.139158i	0.903397	+	0.428804i	$0.141065\pi$
$98$	−2.18890			−0.221112
$99$		0			0
$100$	−11.6261			−1.16261
$101$	4.37780	−	7.58258i	0.435608	−	0.754494i	−0.561737	−	0.827316i	$-0.689867\pi$
$101$	4.37780	−	7.58258i	0.435608	−	0.754494i	0.997345	+	0.0728211i	$0.0232002\pi$
$102$		0			0
$103$	2.79129	+	4.83465i	0.275034	+	0.476372i	0.970144	−	0.242531i	$-0.0779776\pi$
$103$	2.79129	+	4.83465i	0.275034	+	0.476372i	−0.695110	+	0.718904i	$0.744644\pi$
$104$	3.46410	+	6.00000i	0.339683	+	0.588348i
$105$		0			0
$106$	9.47822	−	16.4168i	0.920606	−	1.59454i
$107$	−16.5022			−1.59532			−0.797662	−	0.603105i	$-0.793930\pi$
$107$	−16.5022			−1.59532			−0.797662	+	0.603105i	$0.793930\pi$
$108$		0			0
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$	2.64575	−	4.58258i	0.252262	−	0.436931i
$111$		0			0
$112$	−0.895644	−	1.55130i	−0.0846304	−	0.146584i
$113$	1.68438	+	2.91742i	0.158453	+	0.274448i	0.934311	−	0.356459i	$-0.116016\pi$
$113$	1.68438	+	2.91742i	0.158453	+	0.274448i	−0.775858	+	0.630907i	$0.782683\pi$
$114$		0			0
$115$	1.58258	−	2.74110i	0.147576	−	0.255609i
$116$	24.4394			2.26914
$117$		0			0
$118$	7.58258			0.698033
$119$	−1.73205	+	3.00000i	−0.158777	+	0.275010i
$120$		0			0
$121$	2.00000	+	3.46410i	0.181818	+	0.314918i
$122$	12.6766	+	21.9564i	1.14768	+	1.98784i
$123$		0			0
$124$	12.7913	−	22.1552i	1.14869	−	1.98959i
$125$	8.37420			0.749012
$126$		0			0
$127$	−16.5826			−1.47147			−0.735733	−	0.677272i	$-0.763162\pi$
$127$	−16.5826			−1.47147			−0.735733	+	0.677272i	$0.763162\pi$
$128$	−6.38595	+	11.0608i	−0.564444	+	0.977645i
$129$		0			0
$130$	−4.00000	−	6.92820i	−0.350823	−	0.607644i
$131$	−4.01630	−	6.95644i	−0.350906	−	0.607787i	0.635502	−	0.772099i	$-0.280793\pi$
$131$	−4.01630	−	6.95644i	−0.350906	−	0.607787i	−0.986408	+	0.164312i	$0.947460\pi$
$132$		0			0
$133$	2.79129	−	4.83465i	0.242035	−	0.419218i
$134$	−18.7864			−1.62290
$135$		0			0
$136$	6.00000			0.514496
$137$	−7.07123	+	12.2477i	−0.604136	+	1.04639i	0.388052	+	0.921638i	$0.373148\pi$
$137$	−7.07123	+	12.2477i	−0.604136	+	1.04639i	−0.992187	+	0.124756i	$0.960185\pi$
$138$		0			0
$139$	−0.791288	−	1.37055i	−0.0671162	−	0.116249i	0.830515	−	0.556997i	$-0.188046\pi$
$139$	−0.791288	−	1.37055i	−0.0671162	−	0.116249i	−0.897631	+	0.440748i	$0.854713\pi$
$140$	−1.27520	−	2.20871i	−0.107774	−	0.186670i
$141$		0			0
$142$	4.89564	−	8.47950i	0.410833	−	0.711584i
$143$	−10.5830			−0.884995
$144$		0			0
$145$	−8.00000			−0.664364
$146$	16.5975	−	28.7477i	1.37362	−	2.37918i
$147$		0			0
$148$	−4.18693	−	7.25198i	−0.344164	−	0.596109i
$149$	10.5353	+	18.2477i	0.863088	+	1.49491i	0.868933	+	0.494929i	$0.164806\pi$
$149$	10.5353	+	18.2477i	0.863088	+	1.49491i	−0.00584547	+	0.999983i	$0.501861\pi$
$150$		0			0
$151$	5.70871	−	9.88778i	0.464568	−	0.804656i	−0.534614	−	0.845097i	$-0.679543\pi$
$151$	5.70871	−	9.88778i	0.464568	−	0.804656i	0.999182	+	0.0404406i	$0.0128761\pi$
$152$	−9.66930			−0.784284
$153$		0			0
$154$	−5.79129			−0.466675
$155$	−4.18710	+	7.25227i	−0.336316	+	0.582517i
$156$		0			0
$157$	−9.58258	−	16.5975i	−0.764773	−	1.32463i	−0.940367	−	0.340163i	$-0.889518\pi$
$157$	−9.58258	−	16.5975i	−0.764773	−	1.32463i	0.175594	−	0.984463i	$-0.443815\pi$
$158$	0.637600	+	1.10436i	0.0507248	+	0.0878579i
$159$		0			0
$160$	3.37386	−	5.84370i	0.266727	−	0.461985i
$161$	−3.46410			−0.273009
$162$		0			0
$163$	5.41742			0.424325			0.212163	−	0.977234i	$-0.431949\pi$
$163$	5.41742			0.424325			0.212163	+	0.977234i	$0.431949\pi$
$164$	−1.27520	+	2.20871i	−0.0995764	+	0.172471i
$165$		0			0
$166$	10.5826	+	18.3296i	0.821367	+	1.42265i
$167$	3.92095	+	6.79129i	0.303412	+	0.525526i	0.976907	−	0.213667i	$-0.0685407\pi$
$167$	3.92095	+	6.79129i	0.303412	+	0.525526i	−0.673494	+	0.739192i	$0.735207\pi$
$168$		0			0
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	−6.92820			−0.531369
$171$		0			0
$172$	1.62614			0.123992
$173$	7.48040	−	12.9564i	0.568725	−	0.985060i	−0.427968	−	0.903794i	$-0.640770\pi$
$173$	7.48040	−	12.9564i	0.568725	−	0.985060i	0.996692	−	0.0812659i	$-0.0258963\pi$
$174$		0			0
$175$	−2.08258	−	3.60713i	−0.157428	−	0.272673i
$176$	−2.36965	−	4.10436i	−0.178619	−	0.309377i
$177$		0			0
$178$	2.00000	−	3.46410i	0.149906	−	0.259645i
$179$	−12.2197			−0.913344			−0.456672	−	0.889635i	$-0.650959\pi$
$179$	−12.2197			−0.913344			−0.456672	+	0.889635i	$0.650959\pi$
$180$		0			0
$181$	−5.16515			−0.383923			−0.191961	−	0.981402i	$-0.561485\pi$
$181$	−5.16515			−0.383923			−0.191961	+	0.981402i	$0.561485\pi$
$182$	−4.37780	+	7.58258i	−0.324504	+	0.562058i
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	1.37055	+	2.37386i	0.100765	+	0.174530i
$186$		0			0
$187$	−4.58258	+	7.93725i	−0.335111	+	0.580429i
$188$	36.6591			2.67364
$189$		0			0
$190$	11.1652			0.810005
$191$	−0.409175	+	0.708712i	−0.0296069	+	0.0512806i	−0.880449	−	0.474141i	$-0.842759\pi$
$191$	−0.409175	+	0.708712i	−0.0296069	+	0.0512806i	0.850842	+	0.525421i	$0.176092\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	−1.73205	−	3.00000i	−0.124354	−	0.215387i
$195$		0			0
$196$	−1.39564	+	2.41733i	−0.0996889	+	0.172666i
$197$	10.4877			0.747214			0.373607	−	0.927587i	$-0.378121\pi$
$197$	10.4877			0.747214			0.373607	+	0.927587i	$0.378121\pi$
$198$		0			0
$199$	10.7477			0.761886			0.380943	−	0.924598i	$-0.375599\pi$
$199$	10.7477			0.761886			0.380943	+	0.924598i	$0.375599\pi$
$200$	−3.60713	+	6.24773i	−0.255062	+	0.441781i
$201$		0			0
$202$	−9.58258	−	16.5975i	−0.674228	−	1.16780i
$203$	4.37780	+	7.58258i	0.307261	+	0.532192i
$204$		0			0
$205$	0.417424	−	0.723000i	0.0291542	−	0.0504965i
$206$	12.2197			0.851387
$207$		0			0
$208$	−7.16515			−0.496814
$209$	7.38505	−	12.7913i	0.510835	−	0.884792i
$210$		0			0
$211$	7.87386	+	13.6379i	0.542059	+	0.938874i	0.998786	+	0.0492668i	$0.0156885\pi$
$211$	7.87386	+	13.6379i	0.542059	+	0.938874i	−0.456727	+	0.889607i	$0.650978\pi$
$212$	−12.0866	−	20.9347i	−0.830113	−	1.43780i
$213$		0			0
$214$	−18.0608	+	31.2822i	−1.23461	+	2.13841i
$215$	−0.532300			−0.0363025
$216$		0			0
$217$	9.16515			0.622171
$218$	6.56670	−	11.3739i	0.444753	−	0.770335i
$219$		0			0
$220$	−3.37386	−	5.84370i	−0.227466	−	0.393982i
$221$	6.92820	+	12.0000i	0.466041	+	0.807207i
$222$		0			0
$223$	−11.0000	+	19.0526i	−0.736614	+	1.27585i	0.217397	+	0.976083i	$0.430243\pi$
$223$	−11.0000	+	19.0526i	−0.736614	+	1.27585i	−0.954011	+	0.299770i	$0.903090\pi$
$224$	−7.38505			−0.493435
$225$		0			0
$226$	7.37386			0.490502
$227$	−1.37055	+	2.37386i	−0.0909666	+	0.157559i	−0.907918	−	0.419148i	$-0.862329\pi$
$227$	−1.37055	+	2.37386i	−0.0909666	+	0.157559i	0.816951	+	0.576706i	$0.195662\pi$
$228$		0			0
$229$	11.9564	+	20.7092i	0.790104	+	1.36850i	0.925902	+	0.377763i	$0.123307\pi$
$229$	11.9564	+	20.7092i	0.790104	+	1.36850i	−0.135798	+	0.990736i	$0.543360\pi$
$230$	−3.46410	−	6.00000i	−0.228416	−	0.395628i
$231$		0			0
$232$	7.58258	−	13.1334i	0.497820	−	0.862250i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	−12.0000			−0.782794
$236$	4.83465	−	8.37386i	0.314709	−	0.545092i
$237$		0			0
$238$	3.79129	+	6.56670i	0.245753	+	0.425656i
$239$	−4.69163	−	8.12614i	−0.303476	−	0.525636i	0.673445	−	0.739238i	$-0.264814\pi$
$239$	−4.69163	−	8.12614i	−0.303476	−	0.525636i	−0.976921	+	0.213601i	$0.931481\pi$
$240$		0			0
$241$	−13.7913	+	23.8872i	−0.888375	+	1.53871i	−0.0465790	+	0.998915i	$0.514832\pi$
$241$	−13.7913	+	23.8872i	−0.888375	+	1.53871i	−0.841796	+	0.539796i	$0.818501\pi$
$242$	8.75560			0.562832
$243$		0			0
$244$	32.3303			2.06974
$245$	0.456850	−	0.791288i	0.0291871	−	0.0505535i
$246$		0			0
$247$	−11.1652	−	19.3386i	−0.710422	−	1.23049i
$248$	−7.93725	−	13.7477i	−0.504016	−	0.872982i
$249$		0			0
$250$	9.16515	−	15.8745i	0.579655	−	1.00399i
$251$	2.55040			0.160980			0.0804899	−	0.996755i	$-0.474352\pi$
$251$	2.55040			0.160980			0.0804899	+	0.996755i	$0.474352\pi$
$252$		0			0
$253$	−9.16515			−0.576208
$254$	−18.1488	+	31.4347i	−1.13876	+	1.97239i
$255$		0			0
$256$	1.39564	+	2.41733i	0.0872277	+	0.151083i
$257$	−15.6838	−	27.1652i	−0.978329	−	1.69452i	−0.668481	−	0.743730i	$-0.733055\pi$
$257$	−15.6838	−	27.1652i	−0.978329	−	1.69452i	−0.309849	−	0.950786i	$-0.600278\pi$
$258$		0			0
$259$	1.50000	−	2.59808i	0.0932055	−	0.161437i
$260$	−10.2016			−0.632677
$261$		0			0
$262$	−17.5826			−1.08626
$263$	4.78698	−	8.29129i	0.295178	−	0.511263i	−0.679849	−	0.733353i	$-0.737954\pi$
$263$	4.78698	−	8.29129i	0.295178	−	0.511263i	0.975026	+	0.222090i	$0.0712878\pi$
$264$		0			0
$265$	3.95644	+	6.85275i	0.243042	+	0.420961i
$266$	−6.10985	−	10.5826i	−0.374619	−	0.648859i
$267$		0			0
$268$	−11.9782	+	20.7469i	−0.731686	+	1.26732i
$269$	−6.92820			−0.422420			−0.211210	−	0.977441i	$-0.567740\pi$
$269$	−6.92820			−0.422420			−0.211210	+	0.977441i	$0.567740\pi$
$270$		0			0
$271$	−18.7477			−1.13884			−0.569422	−	0.822046i	$-0.692833\pi$
$271$	−18.7477			−1.13884			−0.569422	+	0.822046i	$0.692833\pi$
$272$	−3.10260	+	5.37386i	−0.188123	+	0.325838i
$273$		0			0
$274$	15.4782	+	26.8091i	0.935073	+	1.61959i
$275$	−5.50998	−	9.54356i	−0.332264	−	0.575498i
$276$		0			0
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	−0.951807	−	0.306699i	$-0.900776\pi$
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	0.741512	+	0.670940i	$0.234109\pi$
$278$	−3.46410			−0.207763
$279$		0			0
$280$	−1.58258			−0.0945770
$281$	4.23478	−	7.33485i	0.252626	−	0.437560i	−0.711622	−	0.702562i	$-0.752039\pi$
$281$	4.23478	−	7.33485i	0.252626	−	0.437560i	0.964248	+	0.265002i	$0.0853726\pi$
$282$		0			0
$283$	−4.20871	−	7.28970i	−0.250182	−	0.433328i	0.713394	−	0.700763i	$-0.247157\pi$
$283$	−4.20871	−	7.28970i	−0.250182	−	0.433328i	−0.963576	+	0.267435i	$0.913824\pi$
$284$	−6.24293	−	10.8131i	−0.370450	−	0.641638i
$285$		0			0
$286$	−11.5826	+	20.0616i	−0.684892	+	1.18627i
$287$	−0.913701			−0.0539340
$288$		0			0
$289$	−5.00000			−0.294118
$290$	−8.75560	+	15.1652i	−0.514147	+	0.890528i
$291$		0			0
$292$	−21.1652	−	36.6591i	−1.23860	−	2.14531i
$293$	8.20340	+	14.2087i	0.479248	+	0.830082i	0.999717	−	0.0237989i	$-0.00757613\pi$
$293$	8.20340	+	14.2087i	0.479248	+	0.830082i	−0.520469	+	0.853881i	$0.674243\pi$
$294$		0			0
$295$	−1.58258	+	2.74110i	−0.0921411	+	0.159593i
$296$	−5.19615			−0.302020
$297$		0			0
$298$	46.1216			2.67175
$299$	−6.92820	+	12.0000i	−0.400668	+	0.693978i
$300$		0			0
$301$	0.291288	+	0.504525i	0.0167896	+	0.0290804i
$302$	−12.4958	−	21.6434i	−0.719053	−	1.24544i
$303$		0			0
$304$	5.00000	−	8.66025i	0.286770	−	0.496700i
$305$	−10.5830			−0.605981
$306$		0			0
$307$	−20.3303			−1.16031			−0.580156	−	0.814505i	$-0.697008\pi$
$307$	−20.3303			−1.16031			−0.580156	+	0.814505i	$0.697008\pi$
$308$	−3.69253	+	6.39564i	−0.210401	+	0.364426i
$309$		0			0
$310$	9.16515	+	15.8745i	0.520546	+	0.901611i
$311$	−16.9590	−	29.3739i	−0.961657	−	1.66564i	−0.718340	−	0.695692i	$-0.755098\pi$
$311$	−16.9590	−	29.3739i	−0.961657	−	1.66564i	−0.243317	−	0.969947i	$-0.578236\pi$
$312$		0			0
$313$	−8.58258	+	14.8655i	−0.485116	+	0.840245i	−0.999854	−	0.0171023i	$-0.994556\pi$
$313$	−8.58258	+	14.8655i	−0.485116	+	0.840245i	0.514738	+	0.857348i	$0.327889\pi$
$314$	−41.9506			−2.36741
$315$		0			0
$316$	1.62614			0.0914773
$317$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$317$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$318$		0			0
$319$	11.5826	+	20.0616i	0.648500	+	1.12323i
$320$	−5.74835	−	9.95644i	−0.321343	−	0.556582i
$321$		0			0
$322$	−3.79129	+	6.56670i	−0.211280	+	0.365948i
$323$	−19.3386			−1.07603
$324$		0			0
$325$	−16.6606			−0.924164
$326$	5.92910	−	10.2695i	0.328383	−	0.568775i
$327$		0			0
$328$	0.791288	+	1.37055i	0.0436916	+	0.0756760i
$329$	6.56670	+	11.3739i	0.362034	+	0.627061i
$330$		0			0
$331$	11.1652	−	19.3386i	0.613692	−	1.06295i	−0.376920	−	0.926246i	$-0.623017\pi$
$331$	11.1652	−	19.3386i	0.613692	−	1.06295i	0.990612	−	0.136700i	$-0.0436498\pi$
$332$	26.9898			1.48126
$333$		0			0
$334$	17.1652			0.939235
$335$	3.92095	−	6.79129i	0.214224	−	0.371048i
$336$		0			0
$337$	0.917424	+	1.58903i	0.0499753	+	0.0865597i	0.889931	−	0.456095i	$-0.150752\pi$
$337$	0.917424	+	1.58903i	0.0499753	+	0.0865597i	−0.839956	+	0.542655i	$0.817419\pi$
$338$	3.28335	+	5.68693i	0.178591	+	0.309328i
$339$		0			0
$340$	−4.41742	+	7.65120i	−0.239568	+	0.414945i
$341$	24.2487			1.31314
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	0.504525	−	0.873864i	0.0272022	−	0.0471156i
$345$		0			0
$346$	−16.3739	−	28.3604i	−0.880264	−	1.52466i
$347$	11.0875	+	19.2042i	0.595210	+	1.03093i	0.993517	+	0.113682i	$0.0362644\pi$
$347$	11.0875	+	19.2042i	0.595210	+	1.03093i	−0.398307	+	0.917252i	$0.630402\pi$
$348$		0			0
$349$	−1.37386	+	2.37960i	−0.0735412	+	0.127377i	−0.900451	−	0.434958i	$-0.856763\pi$
$349$	−1.37386	+	2.37960i	−0.0735412	+	0.127377i	0.826910	+	0.562335i	$0.190097\pi$
$350$	−9.11710			−0.487330
$351$		0			0
$352$	−19.5390			−1.04143
$353$	4.64395	−	8.04356i	0.247173	−	0.428116i	−0.715568	−	0.698544i	$-0.753832\pi$
$353$	4.64395	−	8.04356i	0.247173	−	0.428116i	0.962740	+	0.270428i	$0.0871652\pi$
$354$		0			0
$355$	2.04356	+	3.53955i	0.108461	+	0.187860i
$356$	−2.55040	−	4.41742i	−0.135171	−	0.234123i
$357$		0			0
$358$	−13.3739	+	23.1642i	−0.706831	+	1.22427i
$359$	−25.0671			−1.32299			−0.661494	−	0.749950i	$-0.730077\pi$
$359$	−25.0671			−1.32299			−0.661494	+	0.749950i	$0.730077\pi$
$360$		0			0
$361$	12.1652			0.640271
$362$	−5.65300	+	9.79129i	−0.297115	+	0.514619i
$363$		0			0
$364$	5.58258	+	9.66930i	0.292606	+	0.506809i
$365$	6.92820	+	12.0000i	0.362639	+	0.628109i
$366$		0			0
$367$	13.5826	−	23.5257i	0.709005	−	1.22803i	−0.256222	−	0.966618i	$-0.582478\pi$
$367$	13.5826	−	23.5257i	0.709005	−	1.22803i	0.965227	−	0.261414i	$-0.0841888\pi$
$368$	−6.20520			−0.323469
$369$		0			0
$370$	6.00000			0.311925
$371$	4.33013	−	7.50000i	0.224809	−	0.389381i
$372$		0			0
$373$	−14.6652	−	25.4008i	−0.759333	−	1.31520i	−0.943191	−	0.332250i	$-0.892192\pi$
$373$	−14.6652	−	25.4008i	−0.759333	−	1.31520i	0.183859	−	0.982953i	$-0.441141\pi$
$374$	10.0308	+	17.3739i	0.518681	+	0.898381i
$375$		0			0
$376$	11.3739	−	19.7001i	0.586562	−	1.01596i
$377$	35.0224			1.80375
$378$		0			0
$379$	16.9129			0.868756			0.434378	−	0.900731i	$-0.356968\pi$
$379$	16.9129			0.868756			0.434378	+	0.900731i	$0.356968\pi$
$380$	7.11890	−	12.3303i	0.365192	−	0.632531i
$381$		0			0
$382$	0.895644	+	1.55130i	0.0458251	+	0.0793715i
$383$	6.20520	+	10.7477i	0.317071	+	0.549183i	0.979876	−	0.199609i	$-0.0639673\pi$
$383$	6.20520	+	10.7477i	0.317071	+	0.549183i	−0.662805	+	0.748792i	$0.730634\pi$
$384$		0			0
$385$	1.20871	−	2.09355i	0.0616017	−	0.106697i
$386$	−30.6446			−1.55977
$387$		0			0
$388$	−4.41742			−0.224261
$389$	15.8745	−	27.4955i	0.804869	−	1.39407i	−0.111510	−	0.993763i	$-0.535569\pi$
$389$	15.8745	−	27.4955i	0.804869	−	1.39407i	0.916379	−	0.400312i	$-0.131098\pi$
$390$		0			0
$391$	6.00000	+	10.3923i	0.303433	+	0.525561i
$392$	0.866025	+	1.50000i	0.0437409	+	0.0757614i
$393$		0			0
$394$	11.4782	−	19.8809i	0.578264	−	1.00158i
$395$	−0.532300			−0.0267829
$396$		0			0
$397$	7.58258			0.380559			0.190279	−	0.981730i	$-0.439061\pi$
$397$	7.58258			0.380559			0.190279	+	0.981730i	$0.439061\pi$
$398$	11.7629	−	20.3739i	0.589619	−	1.02125i
$399$		0			0
$400$	−3.73049	−	6.46140i	−0.186525	−	0.323070i
$401$	−8.80328	−	15.2477i	−0.439615	−	0.761435i	0.558045	−	0.829811i	$-0.311552\pi$
$401$	−8.80328	−	15.2477i	−0.439615	−	0.761435i	−0.997660	+	0.0683756i	$0.978218\pi$
$402$		0			0
$403$	18.3303	−	31.7490i	0.913097	−	1.58153i
$404$	−24.4394			−1.21591
$405$		0			0
$406$	19.1652			0.951150
$407$	3.96863	−	6.87386i	0.196718	−	0.340725i
$408$		0			0
$409$	−18.3739	−	31.8245i	−0.908529	−	1.57362i	−0.816109	−	0.577898i	$-0.803873\pi$
$409$	−18.3739	−	31.8245i	−0.908529	−	1.57362i	−0.0924204	−	0.995720i	$-0.529460\pi$
$410$	−0.913701	−	1.58258i	−0.0451245	−	0.0781578i
$411$		0			0
$412$	7.79129	−	13.4949i	0.383849	−	0.664846i
$413$	3.46410			0.170457
$414$		0			0
$415$	−8.83485			−0.433686
$416$	−14.7701	+	25.5826i	−0.724164	+	1.25429i
$417$		0			0
$418$	−16.1652	−	27.9989i	−0.790663	−	1.36947i
$419$	−14.5040	−	25.1216i	−0.708565	−	1.22727i	−0.965390	−	0.260812i	$-0.916010\pi$
$419$	−14.5040	−	25.1216i	−0.708565	−	1.22727i	0.256825	−	0.966458i	$-0.417324\pi$
$420$		0			0
$421$	−1.08258	+	1.87508i	−0.0527615	+	0.0913856i	−0.891200	−	0.453611i	$-0.850136\pi$
$421$	−1.08258	+	1.87508i	−0.0527615	+	0.0913856i	0.838438	+	0.544996i	$0.183469\pi$
$422$	34.4702			1.67798
$423$		0			0
$424$	−15.0000			−0.728464
$425$	−7.21425	+	12.4955i	−0.349943	+	0.606119i
$426$		0			0
$427$	5.79129	+	10.0308i	0.280260	+	0.485425i
$428$	23.0311	+	39.8911i	1.11325	+	1.92821i
$429$		0			0
$430$	−0.582576	+	1.00905i	−0.0280943	+	0.0486607i
$431$	4.91010			0.236511			0.118256	−	0.992983i	$-0.462270\pi$
$431$	4.91010			0.236511			0.118256	+	0.992983i	$0.462270\pi$
$432$		0			0
$433$	23.9129			1.14918			0.574590	−	0.818442i	$-0.305162\pi$
$433$	23.9129			1.14918			0.574590	+	0.818442i	$0.305162\pi$
$434$	10.0308	−	17.3739i	0.481494	−	0.833972i
$435$		0			0
$436$	−8.37386	−	14.5040i	−0.401035	−	0.694614i
$437$	−9.66930	−	16.7477i	−0.462546	−	0.801152i
$438$		0			0
$439$	−8.20871	+	14.2179i	−0.391780	+	0.678584i	−0.992684	−	0.120738i	$-0.961474\pi$
$439$	−8.20871	+	14.2179i	−0.391780	+	0.678584i	0.600904	+	0.799321i	$0.294807\pi$
$440$	−4.18710			−0.199612
$441$		0			0
$442$	30.3303			1.44267
$443$	8.66025	−	15.0000i	0.411461	−	0.712672i	−0.583589	−	0.812049i	$-0.698352\pi$
$443$	8.66025	−	15.0000i	0.411461	−	0.712672i	0.995050	+	0.0993779i	$0.0316853\pi$
$444$		0			0
$445$	0.834849	+	1.44600i	0.0395756	+	0.0685470i
$446$	24.0779	+	41.7042i	1.14012	+	1.97475i
$447$		0			0
$448$	−6.29129	+	10.8968i	−0.297235	+	0.514827i
$449$	36.9452			1.74355			0.871775	−	0.489906i	$-0.162969\pi$
$449$	36.9452			1.74355			0.871775	+	0.489906i	$0.162969\pi$
$450$		0			0
$451$	−2.41742			−0.113832
$452$	4.70158	−	8.14337i	0.221144	−	0.383032i
$453$		0			0
$454$	3.00000	+	5.19615i	0.140797	+	0.243868i
$455$	−1.82740	−	3.16515i	−0.0856699	−	0.148385i
$456$		0			0
$457$	2.66515	−	4.61618i	0.124671	−	0.215936i	−0.796934	−	0.604067i	$-0.793546\pi$
$457$	2.66515	−	4.61618i	0.124671	−	0.215936i	0.921604	+	0.388131i	$0.126879\pi$
$458$	52.3429			2.44582
$459$		0			0
$460$	−8.83485			−0.411927
$461$	−11.8582	+	20.5390i	−0.552292	+	0.956597i	0.445817	+	0.895124i	$0.352913\pi$
$461$	−11.8582	+	20.5390i	−0.552292	+	0.956597i	−0.998109	+	0.0614732i	$0.980420\pi$
$462$		0			0
$463$	12.4564	+	21.5752i	0.578900	+	1.00268i	0.995606	+	0.0936426i	$0.0298511\pi$
$463$	12.4564	+	21.5752i	0.578900	+	1.00268i	−0.416706	+	0.909041i	$0.636816\pi$
$464$	7.84190	+	13.5826i	0.364051	+	0.630555i
$465$		0			0
$466$		0			0
$467$	−9.66930			−0.447442			−0.223721	−	0.974653i	$-0.571820\pi$
$467$	−9.66930			−0.447442			−0.223721	+	0.974653i	$0.571820\pi$
$468$		0			0
$469$	−8.58258			−0.396307
$470$	−13.1334	+	22.7477i	−0.605799	+	1.04927i
$471$		0			0
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	0.770675	+	1.33485i	0.0354357	+	0.0613764i
$474$		0			0
$475$	11.6261	−	20.1371i	0.533444	−	0.923952i
$476$	9.66930			0.443192
$477$		0			0
$478$	−20.5390			−0.939433
$479$	8.85095	−	15.3303i	0.404410	−	0.700459i	−0.589842	−	0.807519i	$-0.700810\pi$
$479$	8.85095	−	15.3303i	0.404410	−	0.700459i	0.994253	+	0.107059i	$0.0341434\pi$
$480$		0			0
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	30.1878	+	52.2867i	1.37501	+	2.38160i
$483$		0			0
$484$	5.58258	−	9.66930i	0.253753	−	0.439514i
$485$	1.44600			0.0656595
$486$		0			0
$487$	2.58258			0.117028			0.0585138	−	0.998287i	$-0.481364\pi$
$487$	2.58258			0.117028			0.0585138	+	0.998287i	$0.481364\pi$
$488$	10.0308	−	17.3739i	0.454073	−	0.786478i
$489$		0			0
$490$	−1.00000	−	1.73205i	−0.0451754	−	0.0782461i
$491$	16.5022	+	28.5826i	0.744732	+	1.28991i	0.950320	+	0.311275i	$0.100756\pi$
$491$	16.5022	+	28.5826i	0.744732	+	1.28991i	−0.205588	+	0.978639i	$0.565911\pi$
$492$		0			0
$493$	15.1652	−	26.2668i	0.683004	−	1.18300i
$494$	−48.8788			−2.19916
$495$		0			0
$496$	16.4174			0.737164
$497$	2.23658	−	3.87386i	0.100324	−	0.173767i
$498$		0			0
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	0.998233	−	0.0594153i	$-0.0189236\pi$
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	−0.550572	+	0.834788i	$0.685590\pi$
$500$	−11.6874	−	20.2432i	−0.522677	−	0.905303i
$501$		0			0
$502$	2.79129	−	4.83465i	0.124581	−	0.215781i
$503$	−26.2668			−1.17118			−0.585590	−	0.810608i	$-0.699137\pi$
$503$	−26.2668			−1.17118			−0.585590	+	0.810608i	$0.699137\pi$
$504$		0			0
$505$	8.00000			0.355995
$506$	−10.0308	+	17.3739i	−0.445924	+	0.772362i
$507$		0			0
$508$	23.1434	+	40.0855i	1.02682	+	1.77851i
$509$	−4.28245	−	7.41742i	−0.189816	−	0.328772i	0.755373	−	0.655296i	$-0.227456\pi$
$509$	−4.28245	−	7.41742i	−0.189816	−	0.328772i	−0.945189	+	0.326524i	$0.894123\pi$
$510$		0			0
$511$	7.58258	−	13.1334i	0.335433	−	0.580988i
$512$	−19.4340			−0.858868
$513$		0			0
$514$	−68.6606			−3.02849
$515$	−2.55040	+	4.41742i	−0.112384	+	0.194655i
$516$		0			0
$517$	17.3739	+	30.0924i	0.764102	+	1.32346i
$518$	−3.28335	−	5.68693i	−0.144262	−	0.249869i
$519$		0			0
$520$	−3.16515	+	5.48220i	−0.138801	+	0.240411i
$521$	−3.46410			−0.151765			−0.0758825	−	0.997117i	$-0.524177\pi$
$521$	−3.46410			−0.151765			−0.0758825	+	0.997117i	$0.524177\pi$
$522$		0			0
$523$	−15.5826			−0.681378			−0.340689	−	0.940176i	$-0.610660\pi$
$523$	−15.5826			−0.681378			−0.340689	+	0.940176i	$0.610660\pi$
$524$	−11.2107	+	19.4174i	−0.489740	+	0.848254i
$525$		0			0
$526$	−10.4782	−	18.1488i	−0.456872	−	0.791326i
$527$	−15.8745	−	27.4955i	−0.691504	−	1.19772i
$528$		0			0
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	17.3205			0.752355
$531$		0			0
$532$	−15.5826			−0.675590
$533$	−1.82740	+	3.16515i	−0.0791535	+	0.137098i
$534$		0			0
$535$	−7.53901	−	13.0580i	−0.325940	−	0.564545i
$536$	7.43273	+	12.8739i	0.321045	+	0.556066i
$537$		0			0
$538$	−7.58258	+	13.1334i	−0.326908	+	0.566221i
$539$	−2.64575			−0.113961
$540$		0			0
$541$	11.0000			0.472927			0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000			0.472927			0.236463	+	0.971640i	$0.424012\pi$
$542$	−20.5185	+	35.5390i	−0.881343	+	1.52653i
$543$		0			0
$544$	12.7913	+	22.1552i	0.548422	+	0.949895i
$545$	2.74110	+	4.74773i	0.117416	+	0.203370i
$546$		0			0
$547$	−16.4564	+	28.5034i	−0.703627	+	1.21872i	0.263558	+	0.964643i	$0.415104\pi$
$547$	−16.4564	+	28.5034i	−0.703627	+	1.21872i	−0.967185	+	0.254073i	$0.918229\pi$
$548$	39.4757			1.68632
$549$		0			0
$550$	−24.1216			−1.02855
$551$	−24.4394	+	42.3303i	−1.04115	+	1.80333i
$552$		0			0
$553$	0.291288	+	0.504525i	0.0123868	+	0.0214546i
$554$	7.66115	+	13.2695i	0.325491	+	0.563767i
$555$		0			0
$556$	−2.20871	+	3.82560i	−0.0936703	+	0.162242i
$557$	29.8263			1.26378			0.631890	−	0.775058i	$-0.282280\pi$
$557$	29.8263			1.26378			0.631890	+	0.775058i	$0.282280\pi$
$558$		0			0
$559$	2.33030			0.0985613
$560$	0.818350	−	1.41742i	0.0345816	−	0.0598971i
$561$		0			0
$562$	−9.26951	−	16.0553i	−0.391011	−	0.677250i
$563$	−10.2970	−	17.8348i	−0.433965	−	0.751649i	0.563246	−	0.826290i	$-0.309552\pi$
$563$	−10.2970	−	17.8348i	−0.433965	−	0.751649i	−0.997211	+	0.0746403i	$0.976219\pi$
$564$		0			0
$565$	−1.53901	+	2.66565i	−0.0647468	+	0.112145i
$566$	−18.4249			−0.774457
$567$		0			0
$568$	−7.74773			−0.325087
$569$	16.5498	−	28.6652i	0.693805	−	1.20171i	−0.276777	−	0.960934i	$-0.589266\pi$
$569$	16.5498	−	28.6652i	0.693805	−	1.20171i	0.970582	−	0.240771i	$-0.0774004\pi$
$570$		0			0
$571$	9.58258	+	16.5975i	0.401018	+	0.694584i	0.993849	−	0.110743i	$-0.0353230\pi$
$571$	9.58258	+	16.5975i	0.401018	+	0.694584i	−0.592831	+	0.805327i	$0.701990\pi$
$572$	14.7701	+	25.5826i	0.617569	+	1.06966i
$573$		0			0
$574$	−1.00000	+	1.73205i	−0.0417392	+	0.0722944i
$575$	−14.4285			−0.601710
$576$		0			0
$577$	5.25227			0.218655			0.109327	−	0.994006i	$-0.465130\pi$
$577$	5.25227			0.218655			0.109327	+	0.994006i	$0.465130\pi$
$578$	−5.47225	+	9.47822i	−0.227616	+	0.394242i
$579$		0			0
$580$	11.1652	+	19.3386i	0.463608	+	0.802992i
$581$	4.83465	+	8.37386i	0.200575	+	0.347406i
$582$		0			0
$583$	11.4564	−	19.8431i	0.474477	−	0.821819i
$584$	−26.2668			−1.08693
$585$		0			0
$586$	35.9129			1.48355
$587$	−9.57395	+	16.5826i	−0.395159	+	0.684436i	−0.993122	−	0.117088i	$-0.962644\pi$
$587$	−9.57395	+	16.5826i	−0.395159	+	0.684436i	0.597962	+	0.801524i	$0.295977\pi$
$588$		0			0
$589$	25.5826	+	44.3103i	1.05411	+	1.82577i
$590$	3.46410	+	6.00000i	0.142615	+	0.247016i
$591$		0			0
$592$	2.68693	−	4.65390i	0.110432	−	0.191274i
$593$	11.8383			0.486141			0.243070	−	0.970009i	$-0.421845\pi$
$593$	11.8383			0.486141			0.243070	+	0.970009i	$0.421845\pi$
$594$		0			0
$595$	−3.16515			−0.129759
$596$	29.4071	−	50.9347i	1.20456	−	2.08636i
$597$		0			0
$598$	15.1652	+	26.2668i	0.620149	+	1.07413i
$599$	−5.70068	−	9.87386i	−0.232923	−	0.403435i	0.725744	−	0.687965i	$-0.241496\pi$
$599$	−5.70068	−	9.87386i	−0.232923	−	0.403435i	−0.958667	+	0.284530i	$0.908162\pi$
$600$		0			0
$601$	−6.79129	+	11.7629i	−0.277022	+	0.479817i	−0.970643	−	0.240523i	$-0.922681\pi$
$601$	−6.79129	+	11.7629i	−0.277022	+	0.479817i	0.693621	+	0.720340i	$0.256014\pi$
$602$	1.27520			0.0519733
$603$		0			0
$604$	−31.8693			−1.29674
$605$	−1.82740	+	3.16515i	−0.0742944	+	0.128682i
$606$		0			0
$607$	−6.20871	−	10.7538i	−0.252004	−	0.436483i	0.712074	−	0.702105i	$-0.247756\pi$
$607$	−6.20871	−	10.7538i	−0.252004	−	0.436483i	−0.964077	+	0.265621i	$0.914423\pi$
$608$	−20.6138	−	35.7042i	−0.836000	−	1.44800i
$609$		0			0
$610$	−11.5826	+	20.0616i	−0.468965	+	0.812271i
$611$	52.5336			2.12528
$612$		0			0
$613$	1.00000			0.0403896			0.0201948	−	0.999796i	$-0.493571\pi$
$613$	1.00000			0.0403896			0.0201948	+	0.999796i	$0.493571\pi$
$614$	−22.2505	+	38.5390i	−0.897958	+	1.55531i
$615$		0			0
$616$	2.29129	+	3.96863i	0.0923186	+	0.159901i
$617$	−19.3386	−	33.4955i	−0.778543	−	1.34848i	−0.932781	−	0.360443i	$-0.882626\pi$
$617$	−19.3386	−	33.4955i	−0.778543	−	1.34848i	0.154238	−	0.988034i	$-0.450708\pi$
$618$		0			0
$619$	−8.95644	+	15.5130i	−0.359990	+	0.623520i	−0.987959	−	0.154718i	$-0.950553\pi$
$619$	−8.95644	+	15.5130i	−0.359990	+	0.623520i	0.627969	+	0.778238i	$0.283886\pi$
$620$	23.3748			0.938755
$621$		0			0
$622$	−74.2432			−2.97688
$623$	0.913701	−	1.58258i	0.0366066	−	0.0634046i
$624$		0			0
$625$	−6.58712	−	11.4092i	−0.263485	−	0.456369i
$626$	18.7864	+	32.5390i	0.750856	+	1.30052i
$627$		0			0
$628$	−26.7477	+	46.3284i	−1.06735	+	1.84871i
$629$	−10.3923			−0.414368
$630$		0			0
$631$	−12.8348			−0.510947			−0.255474	−	0.966816i	$-0.582231\pi$
$631$	−12.8348			−0.510947			−0.255474	+	0.966816i	$0.582231\pi$
$632$	0.504525	−	0.873864i	0.0200689	−	0.0347604i
$633$		0			0
$634$		0			0
$635$	−7.57575	−	13.1216i	−0.300635	−	0.520714i
$636$		0			0
$637$	−2.00000	+	3.46410i	−0.0792429	+	0.137253i
$638$	50.7062			2.00748
$639$		0			0
$640$	−11.6697			−0.461285
$641$	6.06218	−	10.5000i	0.239442	−	0.414725i	−0.721113	−	0.692818i	$-0.756369\pi$
$641$	6.06218	−	10.5000i	0.239442	−	0.414725i	0.960554	+	0.278093i	$0.0897023\pi$
$642$		0			0
$643$	−1.16515	−	2.01810i	−0.0459491	−	0.0795862i	0.842136	−	0.539265i	$-0.181298\pi$
$643$	−1.16515	−	2.01810i	−0.0459491	−	0.0795862i	−0.888085	+	0.459679i	$0.847965\pi$
$644$	4.83465	+	8.37386i	0.190512	+	0.329976i
$645$		0			0
$646$	−21.1652	+	36.6591i	−0.832732	+	1.44233i
$647$	−6.01450			−0.236455			−0.118227	−	0.992987i	$-0.537721\pi$
$647$	−6.01450			−0.236455			−0.118227	+	0.992987i	$0.537721\pi$
$648$		0			0
$649$	9.16515			0.359764
$650$	−18.2342	+	31.5826i	−0.715205	+	1.23877i
$651$		0			0
$652$	−7.56080	−	13.0957i	−0.296104	−	0.512866i
$653$	6.06218	+	10.5000i	0.237231	+	0.410897i	0.959919	−	0.280278i	$-0.0904267\pi$
$653$	6.06218	+	10.5000i	0.237231	+	0.410897i	−0.722687	+	0.691175i	$0.757093\pi$
$654$		0			0
$655$	3.66970	−	6.35610i	0.143387	−	0.248353i
$656$	−1.63670			−0.0639024
$657$		0			0
$658$	28.7477			1.12070
$659$	−20.5661	+	35.6216i	−0.801143	+	1.38762i	0.117722	+	0.993047i	$0.462441\pi$
$659$	−20.5661	+	35.6216i	−0.801143	+	1.38762i	−0.918864	+	0.394574i	$0.870892\pi$
$660$		0			0
$661$	4.00000	+	6.92820i	0.155582	+	0.269476i	0.933271	−	0.359174i	$-0.116941\pi$
$661$	4.00000	+	6.92820i	0.155582	+	0.269476i	−0.777689	+	0.628649i	$0.783608\pi$
$662$	−24.4394	−	42.3303i	−0.949865	−	1.64521i
$663$		0			0
$664$	8.37386	−	14.5040i	0.324969	−	0.562863i
$665$	5.10080			0.197801
$666$		0			0
$667$	30.3303			1.17439
$668$	10.9445	−	18.9564i	0.423456	−	0.733447i
$669$		0			0
$670$	−8.58258	−	14.8655i	−0.331574	−	0.574303i
$671$	15.3223	+	26.5390i	0.591511	+	1.02453i
$672$		0			0
$673$	13.2477	−	22.9457i	0.510662	−	0.884493i	−0.489261	−	0.872137i	$-0.662734\pi$
$673$	13.2477	−	22.9457i	0.510662	−	0.884493i	0.999924	−	0.0123559i	$-0.00393310\pi$
$674$	4.01630			0.154702
$675$		0			0
$676$	8.37386			0.322072
$677$	21.7937	−	37.7477i	0.837598	−	1.45076i	−0.0542988	−	0.998525i	$-0.517292\pi$
$677$	21.7937	−	37.7477i	0.837598	−	1.45076i	0.891897	−	0.452238i	$-0.149374\pi$
$678$		0			0
$679$	−0.791288	−	1.37055i	−0.0303668	−	0.0525969i
$680$	2.74110	+	4.74773i	0.105116	+	0.182067i
$681$		0			0
$682$	26.5390	−	45.9669i	1.01623	−	1.76016i
$683$	11.4014			0.436261			0.218130	−	0.975920i	$-0.430004\pi$
$683$	11.4014			0.436261			0.218130	+	0.975920i	$0.430004\pi$
$684$		0			0
$685$	−12.9220			−0.493723
$686$	−1.09445	+	1.89564i	−0.0417863	+	0.0723760i
$687$		0			0
$688$	0.521780	+	0.903750i	0.0198927	+	0.0344552i
$689$	−17.3205	−	30.0000i	−0.659859	−	1.14291i
$690$		0			0
$691$	−14.5826	+	25.2578i	−0.554747	+	0.960851i	0.443176	+	0.896435i	$0.353852\pi$
$691$	−14.5826	+	25.2578i	−0.554747	+	0.960851i	−0.997923	+	0.0644158i	$0.979482\pi$
$692$	−41.7599			−1.58747
$693$		0			0
$694$	48.5390			1.84252
$695$	0.723000	−	1.25227i	0.0274250	−	0.0475014i
$696$		0			0
$697$	1.58258	+	2.74110i	0.0599443	+	0.103827i
$698$	3.00725	+	5.20871i	0.113826	+	0.197153i
$699$		0			0
$700$	−5.81307	+	10.0685i	−0.219713	+	0.380555i
$701$	29.4449			1.11212			0.556059	−	0.831143i	$-0.312313\pi$
$701$	29.4449			1.11212			0.556059	+	0.831143i	$0.312313\pi$
$702$		0			0
$703$	16.7477			0.631652
$704$	−16.6452	+	28.8303i	−0.627339	+	1.08658i
$705$		0			0
$706$	−10.1652	−	17.6066i	−0.382571	−	0.662632i
$707$	−4.37780	−	7.58258i	−0.164644	−	0.285172i
$708$		0			0
$709$	−7.50000	+	12.9904i	−0.281668	+	0.487864i	−0.971796	−	0.235824i	$-0.924221\pi$
$709$	−7.50000	+	12.9904i	−0.281668	+	0.487864i	0.690127	+	0.723688i	$0.257554\pi$
$710$	8.94630			0.335749
$711$		0			0
$712$	−3.16515			−0.118619
$713$	15.8745	−	27.4955i	0.594505	−	1.02971i
$714$		0			0
$715$	−4.83485	−	8.37420i	−0.180813	−	0.313177i
$716$	17.0544	+	29.5390i	0.637351	+	1.10392i
$717$		0			0
$718$	−27.4347	+	47.5182i	−1.02385	+	1.77336i
$719$	14.4285			0.538093			0.269046	−	0.963127i	$-0.413292\pi$
$719$	14.4285			0.538093			0.269046	+	0.963127i	$0.413292\pi$
$720$		0			0
$721$	5.58258			0.207906
$722$	13.3142	−	23.0608i	0.495502	−	0.858234i
$723$		0			0
$724$	7.20871	+	12.4859i	0.267910	+	0.464033i
$725$	18.2342	+	31.5826i	0.677202	+	1.17295i
$726$		0			0
$727$	18.1216	−	31.3875i	0.672093	−	1.16410i	−0.305217	−	0.952283i	$-0.598729\pi$
$727$	18.1216	−	31.3875i	0.672093	−	1.16410i	0.977310	−	0.211816i	$-0.0679377\pi$
$728$	6.92820			0.256776
$729$		0			0
$730$	30.3303			1.12257
$731$	1.00905	−	1.74773i	0.0373211	−	0.0646420i
$732$		0			0
$733$	8.37386	+	14.5040i	0.309296	+	0.535716i	0.978208	−	0.207625i	$-0.0665734\pi$
$733$	8.37386	+	14.5040i	0.309296	+	0.535716i	−0.668913	+	0.743341i	$0.733240\pi$
$734$	−29.7309	−	51.4955i	−1.09739	−	1.90073i
$735$		0			0
$736$	−12.7913	+	22.1552i	−0.471493	+	0.816650i
$737$	−22.7074			−0.836436
$738$		0			0
$739$	−28.5826			−1.05143			−0.525714	−	0.850662i	$-0.676202\pi$
$739$	−28.5826			−1.05143			−0.525714	+	0.850662i	$0.676202\pi$
$740$	3.82560	−	6.62614i	0.140632	−	0.243582i
$741$		0			0
$742$	−9.47822	−	16.4168i	−0.347956	−	0.602678i
$743$	17.1020	+	29.6216i	0.627413	+	1.08671i	0.988069	+	0.154012i	$0.0492194\pi$
$743$	17.1020	+	29.6216i	0.627413	+	1.08671i	−0.360656	+	0.932699i	$0.617447\pi$
$744$		0			0
$745$	−9.62614	+	16.6730i	−0.352674	+	0.610850i
$746$	−64.2011			−2.35057
$747$		0			0
$748$	25.5826			0.935392
$749$	−8.25108	+	14.2913i	−0.301488	+	0.522192i
$750$		0			0
$751$	9.29129	+	16.0930i	0.339044	+	0.587241i	0.984253	−	0.176765i	$-0.0565631\pi$
$751$	9.29129	+	16.0930i	0.339044	+	0.587241i	−0.645209	+	0.764006i	$0.723230\pi$
$752$	11.7629	+	20.3739i	0.428947	+	0.742958i
$753$		0			0
$754$	38.3303	−	66.3900i	1.39591	−	2.41778i
$755$	10.4321			0.379663
$756$		0			0
$757$	−25.1652			−0.914643			−0.457321	−	0.889301i	$-0.651191\pi$
$757$	−25.1652			−0.914643			−0.457321	+	0.889301i	$0.651191\pi$
$758$	18.5103	−	32.0608i	0.672325	−	1.16450i
$759$		0			0
$760$	−4.41742	−	7.65120i	−0.160237	−	0.277538i
$761$	−7.28970	−	12.6261i	−0.264252	−	0.457697i	0.703116	−	0.711075i	$-0.251792\pi$
$761$	−7.28970	−	12.6261i	−0.264252	−	0.457697i	−0.967367	+	0.253378i	$0.918458\pi$
$762$		0			0
$763$	3.00000	−	5.19615i	0.108607	−	0.188113i
$764$	2.28425			0.0826413
$765$		0			0
$766$	27.1652			0.981517
$767$	6.92820	−	12.0000i	0.250163	−	0.433295i
$768$		0			0
$769$	−9.53901	−	16.5221i	−0.343986	−	0.595801i	0.641183	−	0.767388i	$-0.278444\pi$
$769$	−9.53901	−	16.5221i	−0.343986	−	0.595801i	−0.985169	+	0.171587i	$0.945110\pi$
$770$	−2.64575	−	4.58258i	−0.0953463	−	0.165145i
$771$		0			0
$772$	−19.5390	+	33.8426i	−0.703225	+	1.21802i
$773$	−10.7737			−0.387503			−0.193752	−	0.981051i	$-0.562066\pi$
$773$	−10.7737			−0.387503			−0.193752	+	0.981051i	$0.562066\pi$
$774$		0			0
$775$	38.1742			1.37126
$776$	−1.37055	+	2.37386i	−0.0491999	+	0.0852167i
$777$		0			0
$778$	−34.7477	−	60.1848i	−1.24577	−	2.15773i
$779$	−2.55040	−	4.41742i	−0.0913776	−	0.158271i
$780$		0			0
$781$	5.91742	−	10.2493i	0.211742	−	0.366748i
$782$	26.2668			0.939299
$783$		0			0
$784$	−1.79129			−0.0639746
$785$	8.75560	−	15.1652i	0.312501	−	0.541267i
$786$		0			0
$787$	−4.04356	−	7.00365i	−0.144137	−	0.249653i	0.784913	−	0.619605i	$-0.212707\pi$
$787$	−4.04356	−	7.00365i	−0.144137	−	0.249653i	−0.929051	+	0.369952i	$0.879374\pi$
$788$	−14.6370	−	25.3521i	−0.521423	−	0.903131i
$789$		0			0
$790$	−0.582576	+	1.00905i	−0.0207271	+	0.0359004i
$791$	3.36875			0.119779
$792$		0			0
$793$	46.3303			1.64524
$794$	8.29875	−	14.3739i	0.294512	−	0.510109i
$795$		0			0
$796$	−15.0000	−	25.9808i	−0.531661	−	0.920864i
$797$	1.10440	+	1.91288i	0.0391199	+	0.0677576i	0.884922	−	0.465738i	$-0.154211\pi$
$797$	1.10440	+	1.91288i	0.0391199	+	0.0677576i	−0.845803	+	0.533496i	$0.820878\pi$
$798$		0			0
$799$	22.7477	−	39.4002i	0.804757	−	1.39388i
$800$	−30.7599			−1.08753
$801$		0			0
$802$	−38.5390			−1.36086
$803$	20.0616	−	34.7477i	0.707959	−	1.22622i
$804$		0			0
$805$	−1.58258	−	2.74110i	−0.0557785	−	0.0966111i
$806$	−40.1232	−	69.4955i	−1.41328	−	2.44787i
$807$		0			0
$808$	−7.58258	+	13.1334i	−0.266754	+	0.462032i
$809$	−41.8553			−1.47155			−0.735776	−	0.677224i	$-0.763183\pi$
$809$	−41.8553			−1.47155			−0.735776	+	0.677224i	$0.763183\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	12.2197	−	21.1652i	0.428828	−	0.742751i
$813$		0			0
$814$	−8.68693	−	15.0462i	−0.304477	−	0.527369i
$815$	2.47495	+	4.28674i	0.0866938	+	0.150158i
$816$		0			0
$817$	−1.62614	+	2.81655i	−0.0568913	+	0.0985386i
$818$	−80.4371			−2.81242
$819$		0			0
$820$	−2.33030			−0.0813777
$821$	−25.4961	+	44.1606i	−0.889821	+	1.54122i	−0.0497354	+	0.998762i	$0.515838\pi$
$821$	−25.4961	+	44.1606i	−0.889821	+	1.54122i	−0.840086	+	0.542453i	$0.817496\pi$
$822$		0			0
$823$	−6.00000	−	10.3923i	−0.209147	−	0.362253i	0.742299	−	0.670069i	$-0.233735\pi$
$823$	−6.00000	−	10.3923i	−0.209147	−	0.362253i	−0.951446	+	0.307816i	$0.900402\pi$
$824$	−4.83465	−	8.37386i	−0.168423	−	0.291717i
$825$		0			0
$826$	3.79129	−	6.56670i	0.131916	−	0.228485i
$827$	9.38325			0.326288			0.163144	−	0.986602i	$-0.447837\pi$
$827$	9.38325			0.326288			0.163144	+	0.986602i	$0.447837\pi$
$828$		0			0
$829$	26.3303			0.914489			0.457245	−	0.889341i	$-0.348836\pi$
$829$	26.3303			0.914489			0.457245	+	0.889341i	$0.348836\pi$
$830$	−9.66930	+	16.7477i	−0.335626	+	0.581322i
$831$		0			0
$832$	25.1652	+	43.5873i	0.872445	+	1.51112i
$833$	1.73205	+	3.00000i	0.0600120	+	0.103944i
$834$		0			0
$835$	−3.58258	+	6.20520i	−0.123980	+	0.214740i
$836$	−41.2276			−1.42589
$837$		0			0
$838$	−63.4955			−2.19341
$839$	−16.8637	+	29.2087i	−0.582198	+	1.00840i	0.413020	+	0.910722i	$0.364474\pi$
$839$	−16.8637	+	29.2087i	−0.582198	+	1.00840i	−0.995218	+	0.0976749i	$0.968859\pi$
$840$		0			0
$841$	−23.8303	−	41.2753i	−0.821735	−	1.42329i
$842$	2.36965	+	4.10436i	0.0816636	+	0.141445i
$843$		0			0
$844$	21.9782	−	38.0674i	0.756522	−	1.31033i
$845$	−2.74110			−0.0942968
$846$		0			0
$847$	4.00000			0.137442
$848$	7.75650	−	13.4347i	0.266359	−	0.461348i
$849$		0			0
$850$	15.7913	+	27.3513i	0.541637	+	0.938142i
$851$	−5.19615	−	9.00000i	−0.178122	−	0.308516i
$852$		0			0
$853$	7.37386	−	12.7719i	0.252476	−	0.437302i	−0.711731	−	0.702452i	$-0.752088\pi$
$853$	7.37386	−	12.7719i	0.252476	−	0.437302i	0.964207	+	0.265151i	$0.0854217\pi$
$854$	25.3531			0.867566
$855$		0			0
$856$	28.5826			0.976932
$857$	6.30055	−	10.9129i	0.215223	−	0.372777i	−0.738119	−	0.674671i	$-0.764286\pi$
$857$	6.30055	−	10.9129i	0.215223	−	0.372777i	0.953341	+	0.301894i	$0.0976189\pi$
$858$		0			0
$859$	5.16515	+	8.94630i	0.176233	+	0.305244i	0.940587	−	0.339552i	$-0.110276\pi$
$859$	5.16515	+	8.94630i	0.176233	+	0.305244i	−0.764354	+	0.644796i	$0.776942\pi$
$860$	0.742901	+	1.28674i	0.0253327	+	0.0438775i
$861$		0			0
$862$	5.37386	−	9.30780i	0.183035	−	0.317025i
$863$	−18.3296			−0.623945			−0.311973	−	0.950091i	$-0.600990\pi$
$863$	−18.3296			−0.623945			−0.311973	+	0.950091i	$0.600990\pi$
$864$		0			0
$865$	13.6697			0.464784
$866$	26.1715	−	45.3303i	0.889342	−	1.54039i
$867$		0			0
$868$	−12.7913	−	22.1552i	−0.434165	−	0.751995i
$869$	0.770675	+	1.33485i	0.0261434	+	0.0452816i
$870$		0			0
$871$	−17.1652	+	29.7309i	−0.581619	+	1.00739i
$872$	−10.3923			−0.351928
$873$		0			0
$874$	−42.3303			−1.43184
$875$	4.18710	−	7.25227i	0.141550	−	0.245172i
$876$		0			0
$877$	−6.50000	−	11.2583i	−0.219489	−	0.380167i	0.735163	−	0.677891i	$-0.237106\pi$
$877$	−6.50000	−	11.2583i	−0.219489	−	0.380167i	−0.954652	+	0.297724i	$0.903772\pi$
$878$	17.9681	+	31.1216i	0.606393	+	1.05030i
$879$		0			0
$880$	2.16515	−	3.75015i	0.0729872	−	0.126418i
$881$	−37.3821			−1.25944			−0.629718	−	0.776824i	$-0.716829\pi$
$881$	−37.3821			−1.25944			−0.629718	+	0.776824i	$0.716829\pi$
$882$		0			0
$883$	3.08712			0.103890			0.0519450	−	0.998650i	$-0.483458\pi$
$883$	3.08712			0.103890			0.0519450	+	0.998650i	$0.483458\pi$
$884$	19.3386	−	33.4955i	0.650428	−	1.12657i
$885$		0			0
$886$	−18.9564	−	32.8335i	−0.636854	−	1.10306i
$887$	−14.9608	−	25.9129i	−0.502335	−	0.870069i	−0.999996	−	0.00269804i	$-0.999141\pi$
$887$	−14.9608	−	25.9129i	−0.502335	−	0.870069i	0.497662	−	0.867371i	$-0.334192\pi$
$888$		0			0
$889$	−8.29129	+	14.3609i	−0.278081	+	0.481650i
$890$	3.65480			0.122509
$891$		0			0
$892$	61.4083			2.05610
$893$	−36.6591	+	63.4955i	−1.22675	+	2.12479i
$894$		0			0
$895$	−5.58258	−	9.66930i	−0.186605	−	0.323209i
$896$	6.38595	+	11.0608i	0.213340	+	0.369515i
$897$		0			0
$898$	40.4347	−	70.0349i	1.34932	−	2.33709i
$899$	−80.2464			−2.67637
$900$		0			0
$901$	−30.0000			−0.999445
$902$	−2.64575	+	4.58258i	−0.0880939	+	0.152583i
$903$		0			0
$904$	−2.91742	−	5.05313i	−0.0970321	−	0.168065i
$905$	−2.35970	−	4.08712i	−0.0784391	−	0.135861i
$906$		0			0
$907$	−4.70871	+	8.15573i	−0.156350	+	0.270807i	−0.933550	−	0.358448i	$-0.883306\pi$
$907$	−4.70871	+	8.15573i	−0.156350	+	0.270807i	0.777200	+	0.629254i	$0.216640\pi$
$908$	7.65120			0.253914
$909$		0			0
$910$	−8.00000			−0.265197
$911$	−11.4014	+	19.7477i	−0.377744	+	0.654271i	−0.990734	−	0.135819i	$-0.956633\pi$
$911$	−11.4014	+	19.7477i	−0.377744	+	0.654271i	0.612990	+	0.790091i	$0.289967\pi$
$912$		0			0
$913$	12.7913	+	22.1552i	0.423330	+	0.733229i
$914$	−5.83375	−	10.1044i	−0.192963	−	0.334222i
$915$		0			0
$916$	33.3739	−	57.8052i	1.10270	−	1.90994i
$917$	−8.03260			−0.265260
$918$		0			0
$919$	−48.0780			−1.58595			−0.792974	−	0.609256i	$-0.791468\pi$
$919$	−48.0780			−1.58595			−0.792974	+	0.609256i	$0.791468\pi$
$920$	−2.74110	+	4.74773i	−0.0903714	+	0.156528i
$921$		0			0
$922$	25.9564	+	44.9579i	0.854830	+	1.48061i
$923$	−8.94630	−	15.4955i	−0.294471	−	0.510039i
$924$		0			0
$925$	6.24773	−	10.8214i	0.205424	−	0.355805i
$926$	54.5318			1.79203
$927$		0			0
$928$	64.6606			2.12259
$929$	14.4086	−	24.9564i	0.472731	−	0.818794i	−0.526782	−	0.850000i	$-0.676602\pi$
$929$	14.4086	−	24.9564i	0.472731	−	0.818794i	0.999513	+	0.0312063i	$0.00993488\pi$
$930$		0			0
$931$	−2.79129	−	4.83465i	−0.0914808	−	0.158449i
$932$		0			0
$933$		0			0
$934$	−10.5826	+	18.3296i	−0.346272	+	0.599761i
$935$	−8.37420			−0.273866
$936$		0			0
$937$	−21.4955			−0.702226			−0.351113	−	0.936333i	$-0.614197\pi$
$937$	−21.4955			−0.702226			−0.351113	+	0.936333i	$0.614197\pi$
$938$	−9.39320	+	16.2695i	−0.306699	+	0.531218i
$939$		0			0
$940$	16.7477	+	29.0079i	0.546251	+	0.946134i
$941$	21.6983	+	37.5826i	0.707345	+	1.22516i	0.965839	+	0.259144i	$0.0834405\pi$
$941$	21.6983	+	37.5826i	0.707345	+	1.22516i	−0.258494	+	0.966013i	$0.583226\pi$
$942$		0			0
$943$	−1.58258	+	2.74110i	−0.0515358	+	0.0892625i
$944$	6.20520			0.201962
$945$		0			0
$946$	3.37386			0.109694
$947$	10.2970	−	17.8348i	0.334606	−	0.579555i	−0.648803	−	0.760956i	$-0.724730\pi$
$947$	10.2970	−	17.8348i	0.334606	−	0.579555i	0.983409	+	0.181402i	$0.0580634\pi$
$948$		0			0
$949$	−30.3303	−	52.5336i	−0.984563	−	1.70531i
$950$	−25.4485	−	44.0780i	−0.825657	−	1.43008i
$951$		0			0
$952$	3.00000	−	5.19615i	0.0972306	−	0.168408i
$953$	17.5112			0.567244			0.283622	−	0.958936i	$-0.408464\pi$
$953$	17.5112			0.567244			0.283622	+	0.958936i	$0.408464\pi$
$954$		0			0
$955$	−0.747727			−0.0241959
$956$	−13.0957	+	22.6824i	−0.423545	+	0.733601i
$957$		0			0
$958$	−19.3739	−	33.5565i	−0.625941	−	1.08416i
$959$	7.07123	+	12.2477i	0.228342	+	0.395500i
$960$		0			0
$961$	−26.5000	+	45.8993i	−0.854839	+	1.48062i
$962$	−26.2668			−0.846876
$963$		0			0
$964$	76.9909			2.47971
$965$	6.39590	−	11.0780i	0.205891	−	0.356614i
$966$		0			0
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	0.832075	−	0.554664i	$-0.187153\pi$
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	−0.896390	+	0.443266i	$0.853820\pi$
$968$	−3.46410	−	6.00000i	−0.111340	−	0.192847i
$969$		0			0
$970$	1.58258	−	2.74110i	0.0508134	−	0.0880115i
$971$	−28.2849			−0.907706			−0.453853	−	0.891077i	$-0.649951\pi$
$971$	−28.2849			−0.907706			−0.453853	+	0.891077i	$0.649951\pi$
$972$		0			0
$973$	−1.58258			−0.0507350
$974$	2.82650	−	4.89564i	0.0905669	−	0.156867i
$975$		0			0
$976$	10.3739	+	17.9681i	0.332059	+	0.575144i
$977$	19.3386	+	33.4955i	0.618697	+	1.07161i	0.989724	+	0.142992i	$0.0456724\pi$
$977$	19.3386	+	33.4955i	0.618697	+	1.07161i	−0.371027	+	0.928622i	$0.620994\pi$
$978$		0			0
$979$	2.41742	−	4.18710i	0.0772612	−	0.133820i
$980$	−2.55040			−0.0814696
$981$		0			0
$982$	72.2432			2.30537
$983$	14.2179	−	24.6261i	0.453481	−	0.785452i	−0.545119	−	0.838359i	$-0.683515\pi$
$983$	14.2179	−	24.6261i	0.453481	−	0.785452i	0.998599	+	0.0529071i	$0.0168487\pi$
$984$		0			0
$985$	4.79129	+	8.29875i	0.152663	+	0.264420i
$986$	−33.1950	−	57.4955i	−1.05714	−	1.83103i
$987$		0			0
$988$	−31.1652	+	53.9796i	−0.991496	+	1.71732i
$989$	2.01810			0.0641719
$990$		0			0
$991$	−8.25227			−0.262142			−0.131071	−	0.991373i	$-0.541842\pi$
$991$	−8.25227			−0.262142			−0.131071	+	0.991373i	$0.541842\pi$
$992$	33.8426	−	58.6170i	1.07450	−	1.86109i
$993$		0			0
$994$	−4.89564	−	8.47950i	−0.155280	−	0.268954i
$995$	4.91010	+	8.50455i	0.155661	+	0.269612i
$996$		0			0
$997$	−12.5826	+	21.7937i	−0.398494	+	0.690212i	−0.993540	−	0.113479i	$-0.963800\pi$
$997$	−12.5826	+	21.7937i	−0.398494	+	0.690212i	0.595046	+	0.803692i	$0.297134\pi$
$998$	43.7780			1.38577
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.n.379.4		8
3.2	odd	2	inner	567.2.f.n.379.1		8
9.2	odd	6		567.2.a.i.1.4	yes	4
9.4	even	3	inner	567.2.f.n.190.4		8
9.5	odd	6	inner	567.2.f.n.190.1		8
9.7	even	3		567.2.a.i.1.1	✓	4
36.7	odd	6		9072.2.a.ci.1.2		4
36.11	even	6		9072.2.a.ci.1.3		4
63.20	even	6		3969.2.a.u.1.4		4
63.34	odd	6		3969.2.a.u.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.a.i.1.1	✓	4	9.7	even	3
567.2.a.i.1.4	yes	4	9.2	odd	6
567.2.f.n.190.1		8	9.5	odd	6	inner
567.2.f.n.190.4		8	9.4	even	3	inner
567.2.f.n.379.1		8	3.2	odd	2	inner
567.2.f.n.379.4		8	1.1	even	1	trivial
3969.2.a.u.1.1		4	63.34	odd	6
3969.2.a.u.1.4		4	63.20	even	6
9072.2.a.ci.1.2		4	36.7	odd	6
9072.2.a.ci.1.3		4	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.09445 - 1.89564i) q^{2} +(-1.39564 - 2.41733i) q^{4} +(0.456850 + 0.791288i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.73205 q^{8} +2.00000 q^{10} +(1.32288 - 2.29129i) q^{11} +(-2.00000 - 3.46410i) q^{13} +(-1.09445 - 1.89564i) q^{14} +(0.895644 - 1.55130i) q^{16} -3.46410 q^{17} +5.58258 q^{19} +(1.27520 - 2.20871i) q^{20} +(-2.89564 - 5.01540i) q^{22} +(-1.73205 - 3.00000i) q^{23} +(2.08258 - 3.60713i) q^{25} -8.75560 q^{26} -2.79129 q^{28} +(-4.37780 + 7.58258i) q^{29} +(4.58258 + 7.93725i) q^{31} +(-3.69253 - 6.39564i) q^{32} +(-3.79129 + 6.56670i) q^{34} +0.913701 q^{35} +3.00000 q^{37} +(6.10985 - 10.5826i) q^{38} +(-0.791288 - 1.37055i) q^{40} +(-0.456850 - 0.791288i) q^{41} +(-0.291288 + 0.504525i) q^{43} -7.38505 q^{44} -7.58258 q^{46} +(-6.56670 + 11.3739i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-4.55855 - 7.89564i) q^{50} +(-5.58258 + 9.66930i) q^{52} +8.66025 q^{53} +2.41742 q^{55} +(-0.866025 + 1.50000i) q^{56} +(9.58258 + 16.5975i) q^{58} +(1.73205 + 3.00000i) q^{59} +(-5.79129 + 10.0308i) q^{61} +20.0616 q^{62} -12.5826 q^{64} +(1.82740 - 3.16515i) q^{65} +(-4.29129 - 7.43273i) q^{67} +(4.83465 + 8.37386i) q^{68} +(1.00000 - 1.73205i) q^{70} +4.47315 q^{71} +15.1652 q^{73} +(3.28335 - 5.68693i) q^{74} +(-7.79129 - 13.4949i) q^{76} +(-1.32288 - 2.29129i) q^{77} +(-0.291288 + 0.504525i) q^{79} +1.63670 q^{80} -2.00000 q^{82} +(-4.83465 + 8.37386i) q^{83} +(-1.58258 - 2.74110i) q^{85} +(0.637600 + 1.10436i) q^{86} +(-2.29129 + 3.96863i) q^{88} +1.82740 q^{89} -4.00000 q^{91} +(-4.83465 + 8.37386i) q^{92} +(14.3739 + 24.8963i) q^{94} +(2.55040 + 4.41742i) q^{95} +(0.791288 - 1.37055i) q^{97} -2.18890 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 4 q^{7} + 16 q^{10} - 16 q^{13} - 2 q^{16} + 8 q^{19} - 14 q^{22} - 20 q^{25} - 4 q^{28} - 12 q^{34} + 24 q^{37} + 12 q^{40} + 16 q^{43} - 24 q^{46} - 4 q^{49} - 8 q^{52} + 56 q^{55} + 40 q^{58}+ \cdots - 12 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 + 4 * q^7 + 16 * q^10 - 16 * q^13 - 2 * q^16 + 8 * q^19 - 14 * q^22 - 20 * q^25 - 4 * q^28 - 12 * q^34 + 24 * q^37 + 12 * q^40 + 16 * q^43 - 24 * q^46 - 4 * q^49 - 8 * q^52 + 56 * q^55 + 40 * q^58 - 28 * q^61 - 64 * q^64 - 16 * q^67 + 8 * q^70 + 48 * q^73 - 44 * q^76 + 16 * q^79 - 16 * q^82 + 24 * q^85 - 32 * q^91 + 60 * q^94 - 12 * q^97

Introduction

L-functions

Modular forms

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Database

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