LMFDB - Embedded newform 567.2.f.n.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(190,567)]

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

lf = mfeigenbasis(mf)

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")

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

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			379.1
Root			$-1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	567.379
Dual form			567.2.f.n.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09445 + 1.89564i) q^{2} +(-1.39564 - 2.41733i) q^{4} +(-0.456850 - 0.791288i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.73205 q^{8} +2.00000 q^{10} +(-1.32288 + 2.29129i) q^{11} +(-2.00000 - 3.46410i) q^{13} +(1.09445 + 1.89564i) q^{14} +(0.895644 - 1.55130i) q^{16} +3.46410 q^{17} +5.58258 q^{19} +(-1.27520 + 2.20871i) q^{20} +(-2.89564 - 5.01540i) q^{22} +(1.73205 + 3.00000i) q^{23} +(2.08258 - 3.60713i) q^{25} +8.75560 q^{26} -2.79129 q^{28} +(4.37780 - 7.58258i) q^{29} +(4.58258 + 7.93725i) q^{31} +(3.69253 + 6.39564i) q^{32} +(-3.79129 + 6.56670i) q^{34} -0.913701 q^{35} +3.00000 q^{37} +(-6.10985 + 10.5826i) q^{38} +(-0.791288 - 1.37055i) q^{40} +(0.456850 + 0.791288i) q^{41} +(-0.291288 + 0.504525i) q^{43} +7.38505 q^{44} -7.58258 q^{46} +(6.56670 - 11.3739i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(4.55855 + 7.89564i) q^{50} +(-5.58258 + 9.66930i) q^{52} -8.66025 q^{53} +2.41742 q^{55} +(0.866025 - 1.50000i) q^{56} +(9.58258 + 16.5975i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(-5.79129 + 10.0308i) q^{61} -20.0616 q^{62} -12.5826 q^{64} +(-1.82740 + 3.16515i) q^{65} +(-4.29129 - 7.43273i) q^{67} +(-4.83465 - 8.37386i) q^{68} +(1.00000 - 1.73205i) q^{70} -4.47315 q^{71} +15.1652 q^{73} +(-3.28335 + 5.68693i) q^{74} +(-7.79129 - 13.4949i) q^{76} +(1.32288 + 2.29129i) q^{77} +(-0.291288 + 0.504525i) q^{79} -1.63670 q^{80} -2.00000 q^{82} +(4.83465 - 8.37386i) q^{83} +(-1.58258 - 2.74110i) q^{85} +(-0.637600 - 1.10436i) q^{86} +(-2.29129 + 3.96863i) q^{88} -1.82740 q^{89} -4.00000 q^{91} +(4.83465 - 8.37386i) q^{92} +(14.3739 + 24.8963i) q^{94} +(-2.55040 - 4.41742i) q^{95} +(0.791288 - 1.37055i) q^{97} +2.18890 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.448360\pi$
$2$	−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	−	0.791288i	−0.204310	−	0.353875i	0.745603	−	0.666390i	$-0.232162\pi$
$5$	−0.456850	−	0.791288i	−0.204310	−	0.353875i	−0.949913	+	0.312516i	$0.898828\pi$
$6$		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	−0.993586	−	0.113081i	$-0.963928\pi$
$11$	−1.32288	+	2.29129i	−0.398862	+	0.690849i	0.594724	+	0.803930i	$0.297261\pi$
$12$		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	$-0.362001\pi$
$17$	3.46410			0.840168			0.420084	+	0.907485i	$0.362001\pi$
$18$		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	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$		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	$-0.531200\pi$
$29$	4.37780	−	7.58258i	0.812937	−	1.40805i	0.910799	−	0.412849i	$-0.135466\pi$
$30$		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	0.899492	−	0.436937i	$-0.143937\pi$
$41$	0.456850	+	0.791288i	0.0713480	+	0.123578i	−0.828144	+	0.560515i	$0.810603\pi$
$42$		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	$-0.426078\pi$
$47$	6.56670	−	11.3739i	0.957852	−	1.65905i	0.727702	−	0.685893i	$-0.240588\pi$
$48$		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	$-0.702764\pi$
$53$	−8.66025			−1.18958			−0.594789	+	0.803882i	$0.702764\pi$
$54$		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	0.730974	−	0.682406i	$-0.239066\pi$
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	−0.956467	+	0.291839i	$0.905733\pi$
$60$		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	$-0.585515\pi$
$71$	−4.47315			−0.530866			−0.265433	+	0.964129i	$0.585515\pi$
$72$		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	$-0.655273\pi$
$83$	4.83465	−	8.37386i	0.530672	−	0.919151i	0.999359	−	0.0357868i	$-0.0113937\pi$
$84$		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	$-0.530877\pi$
$89$	−1.82740			−0.193704			−0.0968521	+	0.995299i	$0.530877\pi$
$90$		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	−0.997345	−	0.0728211i	$-0.976800\pi$
$101$	−4.37780	+	7.58258i	−0.435608	+	0.754494i	0.561737	+	0.827316i	$0.310133\pi$
$102$		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	$-0.206070\pi$
$107$	16.5022			1.59532			0.797662	+	0.603105i	$0.206070\pi$
$108$		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	0.775858	−	0.630907i	$-0.217317\pi$
$113$	−1.68438	−	2.91742i	−0.158453	−	0.274448i	−0.934311	+	0.356459i	$0.883984\pi$
$114$		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	0.986408	−	0.164312i	$-0.0525404\pi$
$131$	4.01630	+	6.95644i	0.350906	+	0.607787i	−0.635502	+	0.772099i	$0.719207\pi$
$132$		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	$-0.626852\pi$
$137$	7.07123	−	12.2477i	0.604136	−	1.04639i	0.992187	−	0.124756i	$-0.0398149\pi$
$138$		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	$-0.835194\pi$
$149$	−10.5353	−	18.2477i	−0.863088	−	1.49491i	0.00584547	−	0.999983i	$-0.498139\pi$
$150$		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	0.673494	−	0.739192i	$-0.264793\pi$
$167$	−3.92095	−	6.79129i	−0.303412	−	0.525526i	−0.976907	+	0.213667i	$0.931459\pi$
$168$		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	$0.359230\pi$
$173$	−7.48040	+	12.9564i	−0.568725	+	0.985060i	−0.996692	+	0.0812659i	$0.974104\pi$
$174$		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	$-0.349041\pi$
$179$	12.2197			0.913344			0.456672	+	0.889635i	$0.349041\pi$
$180$		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	−0.850842	−	0.525421i	$-0.823908\pi$
$191$	0.409175	−	0.708712i	0.0296069	−	0.0512806i	0.880449	+	0.474141i	$0.157241\pi$
$192$		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	$-0.621879\pi$
$197$	−10.4877			−0.747214			−0.373607	+	0.927587i	$0.621879\pi$
$198$		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	−0.816951	−	0.576706i	$-0.804338\pi$
$227$	1.37055	−	2.37386i	0.0909666	−	0.157559i	0.907918	+	0.419148i	$0.137671\pi$
$228$		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	0.976921	−	0.213601i	$-0.0685194\pi$
$239$	4.69163	+	8.12614i	0.303476	+	0.525636i	−0.673445	+	0.739238i	$0.735186\pi$
$240$		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	$-0.525648\pi$
$251$	−2.55040			−0.160980			−0.0804899	+	0.996755i	$0.525648\pi$
$252$		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	$0.266945\pi$
$257$	15.6838	+	27.1652i	0.978329	+	1.69452i	0.309849	+	0.950786i	$0.399722\pi$
$258$		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	−0.975026	−	0.222090i	$-0.928712\pi$
$263$	−4.78698	+	8.29129i	−0.295178	+	0.511263i	0.679849	+	0.733353i	$0.262046\pi$
$264$		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	$-0.432260\pi$
$269$	6.92820			0.422420			0.211210	+	0.977441i	$0.432260\pi$
$270$		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	−0.964248	−	0.265002i	$-0.914627\pi$
$281$	−4.23478	+	7.33485i	−0.252626	+	0.437560i	0.711622	+	0.702562i	$0.247961\pi$
$282$		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	0.520469	−	0.853881i	$-0.325757\pi$
$293$	−8.20340	−	14.2087i	−0.479248	−	0.830082i	−0.999717	+	0.0237989i	$0.992424\pi$
$294$		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	$0.244902\pi$
$311$	16.9590	+	29.3739i	0.961657	+	1.66564i	0.243317	+	0.969947i	$0.421764\pi$
$312$		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	$-0.963736\pi$
$347$	−11.0875	−	19.2042i	−0.595210	−	1.03093i	0.398307	−	0.917252i	$-0.369598\pi$
$348$		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	−0.962740	−	0.270428i	$-0.912835\pi$
$353$	−4.64395	+	8.04356i	−0.247173	+	0.428116i	0.715568	+	0.698544i	$0.246168\pi$
$354$		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	$-0.269923\pi$
$359$	25.0671			1.32299			0.661494	+	0.749950i	$0.269923\pi$
$360$		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	0.662805	−	0.748792i	$-0.269366\pi$
$383$	−6.20520	−	10.7477i	−0.317071	−	0.549183i	−0.979876	+	0.199609i	$0.936033\pi$
$384$		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	$0.464431\pi$
$389$	−15.8745	+	27.4955i	−0.804869	+	1.39407i	−0.916379	+	0.400312i	$0.868902\pi$
$390$		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	0.997660	−	0.0683756i	$-0.0217816\pi$
$401$	8.80328	+	15.2477i	0.439615	+	0.761435i	−0.558045	+	0.829811i	$0.688448\pi$
$402$		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	$0.0839903\pi$
$419$	14.5040	+	25.1216i	0.708565	+	1.22727i	−0.256825	+	0.966458i	$0.582676\pi$
$420$		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	$-0.537730\pi$
$431$	−4.91010			−0.236511			−0.118256	+	0.992983i	$0.537730\pi$
$432$		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	−0.995050	−	0.0993779i	$-0.968315\pi$
$443$	−8.66025	+	15.0000i	−0.411461	+	0.712672i	0.583589	+	0.812049i	$0.301648\pi$
$444$		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	$-0.837031\pi$
$449$	−36.9452			−1.74355			−0.871775	+	0.489906i	$0.837031\pi$
$450$		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	$-0.647087\pi$
$461$	11.8582	−	20.5390i	0.552292	−	0.956597i	0.998109	−	0.0614732i	$-0.0195799\pi$
$462$		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	$-0.428180\pi$
$467$	9.66930			0.447442			0.223721	+	0.974653i	$0.428180\pi$
$468$		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	−0.994253	−	0.107059i	$-0.965857\pi$
$479$	−8.85095	+	15.3303i	−0.404410	+	0.700459i	0.589842	+	0.807519i	$0.299190\pi$
$480$		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	$-0.899244\pi$
$491$	−16.5022	−	28.5826i	−0.744732	−	1.28991i	0.205588	−	0.978639i	$-0.434089\pi$
$492$		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	$-0.300863\pi$
$503$	26.2668			1.17118			0.585590	+	0.810608i	$0.300863\pi$
$504$		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	0.945189	−	0.326524i	$-0.105877\pi$
$509$	4.28245	+	7.41742i	0.189816	+	0.328772i	−0.755373	+	0.655296i	$0.772544\pi$
$510$		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	$-0.475823\pi$
$521$	3.46410			0.151765			0.0758825	+	0.997117i	$0.475823\pi$
$522$		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	$-0.717720\pi$
$557$	−29.8263			−1.26378			−0.631890	+	0.775058i	$0.717720\pi$
$558$		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	0.997211	−	0.0746403i	$-0.0237808\pi$
$563$	10.2970	+	17.8348i	0.433965	+	0.751649i	−0.563246	+	0.826290i	$0.690448\pi$
$564$		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	$0.410734\pi$
$569$	−16.5498	+	28.6652i	−0.693805	+	1.20171i	−0.970582	+	0.240771i	$0.922600\pi$
$570$		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	−0.597962	−	0.801524i	$-0.704023\pi$
$587$	9.57395	−	16.5826i	0.395159	−	0.684436i	0.993122	+	0.117088i	$0.0373560\pi$
$588$		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	$-0.578155\pi$
$593$	−11.8383			−0.486141			−0.243070	+	0.970009i	$0.578155\pi$
$594$		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	0.958667	−	0.284530i	$-0.0918375\pi$
$599$	5.70068	+	9.87386i	0.232923	+	0.403435i	−0.725744	+	0.687965i	$0.758504\pi$
$600$		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	$0.117374\pi$
$617$	19.3386	+	33.4955i	0.778543	+	1.34848i	−0.154238	+	0.988034i	$0.549292\pi$
$618$		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	−0.960554	−	0.278093i	$-0.910298\pi$
$641$	−6.06218	+	10.5000i	−0.239442	+	0.414725i	0.721113	+	0.692818i	$0.243631\pi$
$642$		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	$-0.462279\pi$
$647$	6.01450			0.236455			0.118227	+	0.992987i	$0.462279\pi$
$648$		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	0.722687	−	0.691175i	$-0.242907\pi$
$653$	−6.06218	−	10.5000i	−0.237231	−	0.410897i	−0.959919	+	0.280278i	$0.909573\pi$
$654$		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	$-0.537559\pi$
$659$	20.5661	−	35.6216i	0.801143	−	1.38762i	0.918864	−	0.394574i	$-0.129108\pi$
$660$		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	$0.482708\pi$
$677$	−21.7937	+	37.7477i	−0.837598	+	1.45076i	−0.891897	+	0.452238i	$0.850626\pi$
$678$		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	$-0.569996\pi$
$683$	−11.4014			−0.436261			−0.218130	+	0.975920i	$0.569996\pi$
$684$		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	$-0.687687\pi$
$701$	−29.4449			−1.11212			−0.556059	+	0.831143i	$0.687687\pi$
$702$		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	$-0.586708\pi$
$719$	−14.4285			−0.538093			−0.269046	+	0.963127i	$0.586708\pi$
$720$		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	$-0.950781\pi$
$743$	−17.1020	−	29.6216i	−0.627413	−	1.08671i	0.360656	−	0.932699i	$-0.382553\pi$
$744$		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	0.967367	−	0.253378i	$-0.0815418\pi$
$761$	7.28970	+	12.6261i	0.264252	+	0.457697i	−0.703116	+	0.711075i	$0.748208\pi$
$762$		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	$-0.437934\pi$
$773$	10.7737			0.387503			0.193752	+	0.981051i	$0.437934\pi$
$774$		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	0.845803	−	0.533496i	$-0.179122\pi$
$797$	−1.10440	−	1.91288i	−0.0391199	−	0.0677576i	−0.884922	+	0.465738i	$0.845789\pi$
$798$		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	$-0.236817\pi$
$809$	41.8553			1.47155			0.735776	+	0.677224i	$0.236817\pi$
$810$		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	$-0.484162\pi$
$821$	25.4961	−	44.1606i	0.889821	−	1.54122i	0.840086	−	0.542453i	$-0.182504\pi$
$822$		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	$-0.552163\pi$
$827$	−9.38325			−0.326288			−0.163144	+	0.986602i	$0.552163\pi$
$828$		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	$-0.635526\pi$
$839$	16.8637	−	29.2087i	0.582198	−	1.00840i	0.995218	−	0.0976749i	$-0.0311405\pi$
$840$		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	−0.953341	−	0.301894i	$-0.902381\pi$
$857$	−6.30055	+	10.9129i	−0.215223	+	0.372777i	0.738119	+	0.674671i	$0.235714\pi$
$858$		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	$-0.399010\pi$
$863$	18.3296			0.623945			0.311973	+	0.950091i	$0.399010\pi$
$864$		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	$-0.283171\pi$
$881$	37.3821			1.25944			0.629718	+	0.776824i	$0.283171\pi$
$882$		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	$0.000858813\pi$
$887$	14.9608	+	25.9129i	0.502335	+	0.870069i	−0.497662	+	0.867371i	$0.665808\pi$
$888$		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	−0.612990	−	0.790091i	$-0.710033\pi$
$911$	11.4014	−	19.7477i	0.377744	−	0.654271i	0.990734	+	0.135819i	$0.0433667\pi$
$912$		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	−0.999513	−	0.0312063i	$-0.990065\pi$
$929$	−14.4086	+	24.9564i	−0.472731	+	0.818794i	0.526782	+	0.850000i	$0.323398\pi$
$930$		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	$-0.916560\pi$
$941$	−21.6983	−	37.5826i	−0.707345	−	1.22516i	0.258494	−	0.966013i	$-0.416774\pi$
$942$		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	−0.983409	−	0.181402i	$-0.941937\pi$
$947$	−10.2970	+	17.8348i	−0.334606	+	0.579555i	0.648803	+	0.760956i	$0.275270\pi$
$948$		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	$-0.591536\pi$
$953$	−17.5112			−0.567244			−0.283622	+	0.958936i	$0.591536\pi$
$954$		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	$-0.350049\pi$
$971$	28.2849			0.907706			0.453853	+	0.891077i	$0.350049\pi$
$972$		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	$-0.954328\pi$
$977$	−19.3386	−	33.4955i	−0.618697	−	1.07161i	0.371027	−	0.928622i	$-0.379006\pi$
$978$		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	−0.998599	−	0.0529071i	$-0.983151\pi$
$983$	−14.2179	+	24.6261i	−0.453481	+	0.785452i	0.545119	+	0.838359i	$0.316485\pi$
$984$		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.379.1		8
3.2	odd	2	inner	567.2.f.n.379.4		8
9.2	odd	6		567.2.a.i.1.1	✓	4
9.4	even	3	inner	567.2.f.n.190.1		8
9.5	odd	6	inner	567.2.f.n.190.4		8
9.7	even	3		567.2.a.i.1.4	yes	4
36.7	odd	6		9072.2.a.ci.1.3		4
36.11	even	6		9072.2.a.ci.1.2		4
63.20	even	6		3969.2.a.u.1.1		4
63.34	odd	6		3969.2.a.u.1.4		4

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

Varieties

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Representations

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Database

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