LMFDB - Embedded newform 567.2.f.k.190.2

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)

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);

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")

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 = [4,0,0,-2,0,0,-2,0,0,12] 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			190.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	567.190
Dual form			567.2.f.k.379.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.73205 q^{8} +3.00000 q^{10} +(-0.866025 - 1.50000i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(0.866025 - 1.50000i) q^{14} +(2.50000 + 4.33013i) q^{16} +6.92820 q^{17} +5.00000 q^{19} +(0.866025 + 1.50000i) q^{20} +(1.50000 - 2.59808i) q^{22} +(0.866025 - 1.50000i) q^{23} +(1.00000 + 1.73205i) q^{25} -3.46410 q^{26} +1.00000 q^{28} +(-5.19615 - 9.00000i) q^{29} +(-2.50000 + 4.33013i) q^{31} +(-2.59808 + 4.50000i) q^{32} +(6.00000 + 10.3923i) q^{34} -1.73205 q^{35} -7.00000 q^{37} +(4.33013 + 7.50000i) q^{38} +(1.50000 - 2.59808i) q^{40} +(2.59808 - 4.50000i) q^{41} +(2.00000 + 3.46410i) q^{43} +1.73205 q^{44} +3.00000 q^{46} +(3.46410 + 6.00000i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-1.73205 + 3.00000i) q^{50} +(-1.00000 - 1.73205i) q^{52} -13.8564 q^{53} -3.00000 q^{55} +(-0.866025 - 1.50000i) q^{56} +(9.00000 - 15.5885i) q^{58} +(-3.46410 + 6.00000i) q^{59} +(-4.00000 - 6.92820i) q^{61} -8.66025 q^{62} +1.00000 q^{64} +(1.73205 + 3.00000i) q^{65} +(-7.00000 + 12.1244i) q^{67} +(-3.46410 + 6.00000i) q^{68} +(-1.50000 - 2.59808i) q^{70} -5.19615 q^{71} -4.00000 q^{73} +(-6.06218 - 10.5000i) q^{74} +(-2.50000 + 4.33013i) q^{76} +(-0.866025 + 1.50000i) q^{77} +(-4.00000 - 6.92820i) q^{79} +8.66025 q^{80} +9.00000 q^{82} +(-5.19615 - 9.00000i) q^{83} +(6.00000 - 10.3923i) q^{85} +(-3.46410 + 6.00000i) q^{86} +(-1.50000 - 2.59808i) q^{88} +8.66025 q^{89} +2.00000 q^{91} +(0.866025 + 1.50000i) q^{92} +(-6.00000 + 10.3923i) q^{94} +(4.33013 - 7.50000i) q^{95} +(2.00000 + 3.46410i) q^{97} -1.73205 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} + 10 q^{16} + 20 q^{19} + 6 q^{22} + 4 q^{25} + 4 q^{28} - 10 q^{31} + 24 q^{34} - 28 q^{37} + 6 q^{40} + 8 q^{43} + 12 q^{46} - 2 q^{49} - 4 q^{52} - 12 q^{55}+ \cdots + 8 q^{97}+O(q^{100}) $ 4 * q - 2 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 + 10 * q^16 + 20 * q^19 + 6 * q^22 + 4 * q^25 + 4 * q^28 - 10 * q^31 + 24 * q^34 - 28 * q^37 + 6 * q^40 + 8 * q^43 + 12 * q^46 - 2 * q^49 - 4 * q^52 - 12 * q^55 + 36 * q^58 - 16 * q^61 + 4 * q^64 - 28 * q^67 - 6 * q^70 - 16 * q^73 - 10 * q^76 - 16 * q^79 + 36 * q^82 + 24 * q^85 - 6 * q^88 + 8 * q^91 - 24 * q^94 + 8 * q^97

Character values

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

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

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 $

$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	0.990839	+	0.135045i	$0.0431180\pi$
$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	−0.378467	+	0.925615i	$0.623549\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	−0.604787	−	0.796387i	$-0.706742\pi$
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	0.992085	+	0.125567i	$0.0400750\pi$
$6$		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
$10$	3.00000			0.948683
$11$	−0.866025	−	1.50000i	−0.261116	−	0.452267i	0.705422	−	0.708787i	$-0.250757\pi$
$11$	−0.866025	−	1.50000i	−0.261116	−	0.452267i	−0.966539	+	0.256520i	$0.917424\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	0.866025	−	1.50000i	0.231455	−	0.400892i
$15$		0			0
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	6.92820			1.68034			0.840168	−	0.542326i	$-0.182456\pi$
$17$	6.92820			1.68034			0.840168	+	0.542326i	$0.182456\pi$
$18$		0			0
$19$	5.00000			1.14708			0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000			1.14708			0.573539	+	0.819178i	$0.305570\pi$
$20$	0.866025	+	1.50000i	0.193649	+	0.335410i
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	0.866025	−	1.50000i	0.180579	−	0.312772i	−0.761499	−	0.648166i	$-0.775536\pi$
$23$	0.866025	−	1.50000i	0.180579	−	0.312772i	0.942078	+	0.335394i	$0.108870\pi$
$24$		0			0
$25$	1.00000	+	1.73205i	0.200000	+	0.346410i
$26$	−3.46410			−0.679366
$27$		0			0
$28$	1.00000			0.188982
$29$	−5.19615	−	9.00000i	−0.964901	−	1.67126i	−0.709880	−	0.704323i	$-0.751251\pi$
$29$	−5.19615	−	9.00000i	−0.964901	−	1.67126i	−0.255021	−	0.966935i	$-0.582082\pi$
$30$		0			0
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$	−2.59808	+	4.50000i	−0.459279	+	0.795495i
$33$		0			0
$34$	6.00000	+	10.3923i	1.02899	+	1.78227i
$35$	−1.73205			−0.292770
$36$		0			0
$37$	−7.00000			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$38$	4.33013	+	7.50000i	0.702439	+	1.21666i
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	2.59808	−	4.50000i	0.405751	−	0.702782i	−0.588657	−	0.808383i	$-0.700343\pi$
$41$	2.59808	−	4.50000i	0.405751	−	0.702782i	0.994409	+	0.105601i	$0.0336766\pi$
$42$		0			0
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$	1.73205			0.261116
$45$		0			0
$46$	3.00000			0.442326
$47$	3.46410	+	6.00000i	0.505291	+	0.875190i	0.999981	+	0.00612051i	$0.00194823\pi$
$47$	3.46410	+	6.00000i	0.505291	+	0.875190i	−0.494690	+	0.869069i	$0.664718\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−1.73205	+	3.00000i	−0.244949	+	0.424264i
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−13.8564			−1.90332			−0.951662	−	0.307148i	$-0.900625\pi$
$53$	−13.8564			−1.90332			−0.951662	+	0.307148i	$0.900625\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$	−0.866025	−	1.50000i	−0.115728	−	0.200446i
$57$		0			0
$58$	9.00000	−	15.5885i	1.18176	−	2.04686i
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	−0.998448	−	0.0556984i	$-0.982261\pi$
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	0.547460	+	0.836832i	$0.315595\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	−8.66025			−1.09985
$63$		0			0
$64$	1.00000			0.125000
$65$	1.73205	+	3.00000i	0.214834	+	0.372104i
$66$		0			0
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	0.0212861	+	0.999773i	$0.493224\pi$
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	−0.876472	+	0.481452i	$0.840109\pi$
$68$	−3.46410	+	6.00000i	−0.420084	+	0.727607i
$69$		0			0
$70$	−1.50000	−	2.59808i	−0.179284	−	0.310530i
$71$	−5.19615			−0.616670			−0.308335	−	0.951278i	$-0.599772\pi$
$71$	−5.19615			−0.616670			−0.308335	+	0.951278i	$0.599772\pi$
$72$		0			0
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	−6.06218	−	10.5000i	−0.704714	−	1.22060i
$75$		0			0
$76$	−2.50000	+	4.33013i	−0.286770	+	0.496700i
$77$	−0.866025	+	1.50000i	−0.0986928	+	0.170941i
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	8.66025			0.968246
$81$		0			0
$82$	9.00000			0.993884
$83$	−5.19615	−	9.00000i	−0.570352	−	0.987878i	−0.996530	−	0.0832389i	$-0.973474\pi$
$83$	−5.19615	−	9.00000i	−0.570352	−	0.987878i	0.426178	−	0.904639i	$-0.359860\pi$
$84$		0			0
$85$	6.00000	−	10.3923i	0.650791	−	1.12720i
$86$	−3.46410	+	6.00000i	−0.373544	+	0.646997i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	8.66025			0.917985			0.458993	−	0.888440i	$-0.348210\pi$
$89$	8.66025			0.917985			0.458993	+	0.888440i	$0.348210\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$	0.866025	+	1.50000i	0.0902894	+	0.156386i
$93$		0			0
$94$	−6.00000	+	10.3923i	−0.618853	+	1.07188i
$95$	4.33013	−	7.50000i	0.444262	−	0.769484i
$96$		0			0
$97$	2.00000	+	3.46410i	0.203069	+	0.351726i	0.949516	−	0.313719i	$-0.101575\pi$
$97$	2.00000	+	3.46410i	0.203069	+	0.351726i	−0.746447	+	0.665445i	$0.768242\pi$
$98$	−1.73205			−0.174964
$99$		0			0
$100$	−2.00000			−0.200000
$101$	6.92820	+	12.0000i	0.689382	+	1.19404i	0.972038	+	0.234823i	$0.0754512\pi$
$101$	6.92820	+	12.0000i	0.689382	+	1.19404i	−0.282656	+	0.959221i	$0.591216\pi$
$102$		0			0
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$		0			0
$106$	−12.0000	−	20.7846i	−1.16554	−	2.01878i
$107$	3.46410			0.334887			0.167444	−	0.985882i	$-0.446449\pi$
$107$	3.46410			0.334887			0.167444	+	0.985882i	$0.446449\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$	−2.59808	−	4.50000i	−0.247717	−	0.429058i
$111$		0			0
$112$	2.50000	−	4.33013i	0.236228	−	0.409159i
$113$	5.19615	−	9.00000i	0.488813	−	0.846649i	−0.511104	−	0.859519i	$-0.670763\pi$
$113$	5.19615	−	9.00000i	0.488813	−	0.846649i	0.999917	+	0.0128699i	$0.00409674\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$	10.3923			0.964901
$117$		0			0
$118$	−12.0000			−1.10469
$119$	−3.46410	−	6.00000i	−0.317554	−	0.550019i
$120$		0			0
$121$	4.00000	−	6.92820i	0.363636	−	0.629837i
$122$	6.92820	−	12.0000i	0.627250	−	1.08643i
$123$		0			0
$124$	−2.50000	−	4.33013i	−0.224507	−	0.388857i
$125$	12.1244			1.08444
$126$		0			0
$127$	−10.0000			−0.887357			−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000			−0.887357			−0.443678	+	0.896186i	$0.646327\pi$
$128$	6.06218	+	10.5000i	0.535826	+	0.928078i
$129$		0			0
$130$	−3.00000	+	5.19615i	−0.263117	+	0.455733i
$131$	3.46410	−	6.00000i	0.302660	−	0.524222i	−0.674078	−	0.738661i	$-0.735459\pi$
$131$	3.46410	−	6.00000i	0.302660	−	0.524222i	0.976738	+	0.214438i	$0.0687920\pi$
$132$		0			0
$133$	−2.50000	−	4.33013i	−0.216777	−	0.375470i
$134$	−24.2487			−2.09477
$135$		0			0
$136$	12.0000			1.02899
$137$	1.73205	+	3.00000i	0.147979	+	0.256307i	0.930480	−	0.366342i	$-0.119390\pi$
$137$	1.73205	+	3.00000i	0.147979	+	0.256307i	−0.782501	+	0.622649i	$0.786057\pi$
$138$		0			0
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	0.0346338	+	0.999400i	$0.488974\pi$
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	−0.882823	+	0.469706i	$0.844360\pi$
$140$	0.866025	−	1.50000i	0.0731925	−	0.126773i
$141$		0			0
$142$	−4.50000	−	7.79423i	−0.377632	−	0.654077i
$143$	3.46410			0.289683
$144$		0			0
$145$	−18.0000			−1.49482
$146$	−3.46410	−	6.00000i	−0.286691	−	0.496564i
$147$		0			0
$148$	3.50000	−	6.06218i	0.287698	−	0.498308i
$149$	−1.73205	+	3.00000i	−0.141895	+	0.245770i	−0.928210	−	0.372056i	$-0.878653\pi$
$149$	−1.73205	+	3.00000i	−0.141895	+	0.245770i	0.786315	+	0.617826i	$0.211986\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$	8.66025			0.702439
$153$		0			0
$154$	−3.00000			−0.241747
$155$	4.33013	+	7.50000i	0.347804	+	0.602414i
$156$		0			0
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	−0.594565	−	0.804048i	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$	6.92820	−	12.0000i	0.551178	−	0.954669i
$159$		0			0
$160$	4.50000	+	7.79423i	0.355756	+	0.616188i
$161$	−1.73205			−0.136505
$162$		0			0
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	2.59808	+	4.50000i	0.202876	+	0.351391i
$165$		0			0
$166$	9.00000	−	15.5885i	0.698535	−	1.20990i
$167$	−5.19615	+	9.00000i	−0.402090	+	0.696441i	−0.993978	−	0.109580i	$-0.965050\pi$
$167$	−5.19615	+	9.00000i	−0.402090	+	0.696441i	0.591888	+	0.806020i	$0.298383\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	20.7846			1.59411
$171$		0			0
$172$	−4.00000			−0.304997
$173$	0.866025	+	1.50000i	0.0658427	+	0.114043i	0.897067	−	0.441894i	$-0.145693\pi$
$173$	0.866025	+	1.50000i	0.0658427	+	0.114043i	−0.831225	+	0.555936i	$0.812360\pi$
$174$		0			0
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$	4.33013	−	7.50000i	0.326396	−	0.565334i
$177$		0			0
$178$	7.50000	+	12.9904i	0.562149	+	0.973670i
$179$	−3.46410			−0.258919			−0.129460	−	0.991585i	$-0.541324\pi$
$179$	−3.46410			−0.258919			−0.129460	+	0.991585i	$0.541324\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	1.73205	+	3.00000i	0.128388	+	0.222375i
$183$		0			0
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	−6.06218	+	10.5000i	−0.445700	+	0.771975i
$186$		0			0
$187$	−6.00000	−	10.3923i	−0.438763	−	0.759961i
$188$	−6.92820			−0.505291
$189$		0			0
$190$	15.0000			1.08821
$191$	−4.33013	−	7.50000i	−0.313317	−	0.542681i	0.665761	−	0.746165i	$-0.268107\pi$
$191$	−4.33013	−	7.50000i	−0.313317	−	0.542681i	−0.979078	+	0.203484i	$0.934774\pi$
$192$		0			0
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	−0.133056	−	0.991109i	$-0.542479\pi$
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	0.924853	−	0.380325i	$-0.124188\pi$
$194$	−3.46410	+	6.00000i	−0.248708	+	0.430775i
$195$		0			0
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	10.3923			0.740421			0.370211	−	0.928948i	$-0.379286\pi$
$197$	10.3923			0.740421			0.370211	+	0.928948i	$0.379286\pi$
$198$		0			0
$199$	−25.0000			−1.77220			−0.886102	−	0.463491i	$-0.846597\pi$
$199$	−25.0000			−1.77220			−0.886102	+	0.463491i	$0.846597\pi$
$200$	1.73205	+	3.00000i	0.122474	+	0.212132i
$201$		0			0
$202$	−12.0000	+	20.7846i	−0.844317	+	1.46240i
$203$	−5.19615	+	9.00000i	−0.364698	+	0.631676i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	−8.66025			−0.603388
$207$		0			0
$208$	−10.0000			−0.693375
$209$	−4.33013	−	7.50000i	−0.299521	−	0.518786i
$210$		0			0
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	−0.898392	−	0.439194i	$-0.855264\pi$
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	0.829549	+	0.558433i	$0.188597\pi$
$212$	6.92820	−	12.0000i	0.475831	−	0.824163i
$213$		0			0
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$	6.92820			0.472500
$216$		0			0
$217$	5.00000			0.339422
$218$	−6.06218	−	10.5000i	−0.410582	−	0.711150i
$219$		0			0
$220$	1.50000	−	2.59808i	0.101130	−	0.175162i
$221$	−6.92820	+	12.0000i	−0.466041	+	0.807207i
$222$		0			0
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$	5.19615			0.347183
$225$		0			0
$226$	18.0000			1.19734
$227$	1.73205	+	3.00000i	0.114960	+	0.199117i	0.917764	−	0.397127i	$-0.129993\pi$
$227$	1.73205	+	3.00000i	0.114960	+	0.199117i	−0.802804	+	0.596244i	$0.796659\pi$
$228$		0			0
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	0.924510	+	0.381157i	$0.124474\pi$
$230$	2.59808	−	4.50000i	0.171312	−	0.296721i
$231$		0			0
$232$	−9.00000	−	15.5885i	−0.590879	−	1.02343i
$233$	−17.3205			−1.13470			−0.567352	−	0.823475i	$-0.692032\pi$
$233$	−17.3205			−1.13470			−0.567352	+	0.823475i	$0.692032\pi$
$234$		0			0
$235$	12.0000			0.782794
$236$	−3.46410	−	6.00000i	−0.225494	−	0.390567i
$237$		0			0
$238$	6.00000	−	10.3923i	0.388922	−	0.673633i
$239$	−5.19615	+	9.00000i	−0.336111	+	0.582162i	−0.983698	−	0.179830i	$-0.942445\pi$
$239$	−5.19615	+	9.00000i	−0.336111	+	0.582162i	0.647586	+	0.761992i	$0.275778\pi$
$240$		0			0
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$	13.8564			0.890724
$243$		0			0
$244$	8.00000			0.512148
$245$	0.866025	+	1.50000i	0.0553283	+	0.0958315i
$246$		0			0
$247$	−5.00000	+	8.66025i	−0.318142	+	0.551039i
$248$	−4.33013	+	7.50000i	−0.274963	+	0.476250i
$249$		0			0
$250$	10.5000	+	18.1865i	0.664078	+	1.15022i
$251$	−20.7846			−1.31191			−0.655956	−	0.754799i	$-0.727735\pi$
$251$	−20.7846			−1.31191			−0.655956	+	0.754799i	$0.727735\pi$
$252$		0			0
$253$	−3.00000			−0.188608
$254$	−8.66025	−	15.0000i	−0.543393	−	0.941184i
$255$		0			0
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	0.866025	−	1.50000i	0.0540212	−	0.0935674i	−0.837750	−	0.546054i	$-0.816129\pi$
$257$	0.866025	−	1.50000i	0.0540212	−	0.0935674i	0.891771	+	0.452486i	$0.149463\pi$
$258$		0			0
$259$	3.50000	+	6.06218i	0.217479	+	0.376685i
$260$	−3.46410			−0.214834
$261$		0			0
$262$	12.0000			0.741362
$263$	4.33013	+	7.50000i	0.267007	+	0.462470i	0.968088	−	0.250612i	$-0.0806320\pi$
$263$	4.33013	+	7.50000i	0.267007	+	0.462470i	−0.701080	+	0.713082i	$0.747299\pi$
$264$		0			0
$265$	−12.0000	+	20.7846i	−0.737154	+	1.27679i
$266$	4.33013	−	7.50000i	0.265497	−	0.459855i
$267$		0			0
$268$	−7.00000	−	12.1244i	−0.427593	−	0.740613i
$269$	−19.0526			−1.16166			−0.580828	−	0.814027i	$-0.697271\pi$
$269$	−19.0526			−1.16166			−0.580828	+	0.814027i	$0.697271\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	17.3205	+	30.0000i	1.05021	+	1.81902i
$273$		0			0
$274$	−3.00000	+	5.19615i	−0.181237	+	0.313911i
$275$	1.73205	−	3.00000i	0.104447	−	0.180907i
$276$		0			0
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$	−34.6410			−2.07763
$279$		0			0
$280$	−3.00000			−0.179284
$281$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$281$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	2.59808	−	4.50000i	0.154167	−	0.267026i
$285$		0			0
$286$	3.00000	+	5.19615i	0.177394	+	0.307255i
$287$	−5.19615			−0.306719
$288$		0			0
$289$	31.0000			1.82353
$290$	−15.5885	−	27.0000i	−0.915386	−	1.58549i
$291$		0			0
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$293$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$294$		0			0
$295$	6.00000	+	10.3923i	0.349334	+	0.605063i
$296$	−12.1244			−0.704714
$297$		0			0
$298$	−6.00000			−0.347571
$299$	1.73205	+	3.00000i	0.100167	+	0.173494i
$300$		0			0
$301$	2.00000	−	3.46410i	0.115278	−	0.199667i
$302$	−8.66025	+	15.0000i	−0.498342	+	0.863153i
$303$		0			0
$304$	12.5000	+	21.6506i	0.716924	+	1.24175i
$305$	−13.8564			−0.793416
$306$		0			0
$307$	17.0000			0.970241			0.485121	−	0.874447i	$-0.338776\pi$
$307$	17.0000			0.970241			0.485121	+	0.874447i	$0.338776\pi$
$308$	−0.866025	−	1.50000i	−0.0493464	−	0.0854704i
$309$		0			0
$310$	−7.50000	+	12.9904i	−0.425971	+	0.737804i
$311$	1.73205	−	3.00000i	0.0982156	−	0.170114i	−0.812731	−	0.582640i	$-0.802020\pi$
$311$	1.73205	−	3.00000i	0.0982156	−	0.170114i	0.910946	+	0.412525i	$0.135353\pi$
$312$		0			0
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	0.836379	−	0.548151i	$-0.184668\pi$
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	−0.892903	+	0.450250i	$0.851335\pi$
$314$	17.3205			0.977453
$315$		0			0
$316$	8.00000			0.450035
$317$	3.46410	+	6.00000i	0.194563	+	0.336994i	0.946757	−	0.321948i	$-0.104338\pi$
$317$	3.46410	+	6.00000i	0.194563	+	0.336994i	−0.752194	+	0.658942i	$0.771004\pi$
$318$		0			0
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$	0.866025	−	1.50000i	0.0484123	−	0.0838525i
$321$		0			0
$322$	−1.50000	−	2.59808i	−0.0835917	−	0.144785i
$323$	34.6410			1.92748
$324$		0			0
$325$	−4.00000			−0.221880
$326$	1.73205	+	3.00000i	0.0959294	+	0.166155i
$327$		0			0
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	3.46410	−	6.00000i	0.190982	−	0.330791i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	10.3923			0.570352
$333$		0			0
$334$	−18.0000			−0.984916
$335$	12.1244	+	21.0000i	0.662424	+	1.14735i
$336$		0			0
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	−0.632882	−	0.774248i	$-0.718128\pi$
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	0.986960	+	0.160968i	$0.0514616\pi$
$338$	−7.79423	+	13.5000i	−0.423950	+	0.734303i
$339$		0			0
$340$	6.00000	+	10.3923i	0.325396	+	0.563602i
$341$	8.66025			0.468979
$342$		0			0
$343$	1.00000			0.0539949
$344$	3.46410	+	6.00000i	0.186772	+	0.323498i
$345$		0			0
$346$	−1.50000	+	2.59808i	−0.0806405	+	0.139673i
$347$	−16.4545	+	28.5000i	−0.883323	+	1.52996i	−0.0356990	+	0.999363i	$0.511366\pi$
$347$	−16.4545	+	28.5000i	−0.883323	+	1.52996i	−0.847624	+	0.530598i	$0.821968\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$	3.46410			0.185164
$351$		0			0
$352$	9.00000			0.479702
$353$	−16.4545	−	28.5000i	−0.875784	−	1.51690i	−0.855926	−	0.517099i	$-0.827012\pi$
$353$	−16.4545	−	28.5000i	−0.875784	−	1.51690i	−0.0198582	−	0.999803i	$-0.506321\pi$
$354$		0			0
$355$	−4.50000	+	7.79423i	−0.238835	+	0.413675i
$356$	−4.33013	+	7.50000i	−0.229496	+	0.397499i
$357$		0			0
$358$	−3.00000	−	5.19615i	−0.158555	−	0.274625i
$359$	−17.3205			−0.914141			−0.457071	−	0.889430i	$-0.651101\pi$
$359$	−17.3205			−0.914141			−0.457071	+	0.889430i	$0.651101\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$	1.73205	+	3.00000i	0.0910346	+	0.157676i
$363$		0			0
$364$	−1.00000	+	1.73205i	−0.0524142	+	0.0907841i
$365$	−3.46410	+	6.00000i	−0.181319	+	0.314054i
$366$		0			0
$367$	12.5000	+	21.6506i	0.652495	+	1.13015i	0.982516	+	0.186180i	$0.0596109\pi$
$367$	12.5000	+	21.6506i	0.652495	+	1.13015i	−0.330021	+	0.943974i	$0.607056\pi$
$368$	8.66025			0.451447
$369$		0			0
$370$	−21.0000			−1.09174
$371$	6.92820	+	12.0000i	0.359694	+	0.623009i
$372$		0			0
$373$	9.50000	−	16.4545i	0.491891	−	0.851981i	−0.508065	−	0.861319i	$-0.669639\pi$
$373$	9.50000	−	16.4545i	0.491891	−	0.851981i	0.999956	+	0.00933789i	$0.00297238\pi$
$374$	10.3923	−	18.0000i	0.537373	−	0.930758i
$375$		0			0
$376$	6.00000	+	10.3923i	0.309426	+	0.535942i
$377$	20.7846			1.07046
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$	4.33013	+	7.50000i	0.222131	+	0.384742i
$381$		0			0
$382$	7.50000	−	12.9904i	0.383733	−	0.664646i
$383$	19.0526	−	33.0000i	0.973540	−	1.68622i	0.288870	−	0.957368i	$-0.406720\pi$
$383$	19.0526	−	33.0000i	0.973540	−	1.68622i	0.684670	−	0.728853i	$-0.259946\pi$
$384$		0			0
$385$	1.50000	+	2.59808i	0.0764471	+	0.132410i
$386$	38.1051			1.93950
$387$		0			0
$388$	−4.00000			−0.203069
$389$	−3.46410	−	6.00000i	−0.175637	−	0.304212i	0.764745	−	0.644334i	$-0.222865\pi$
$389$	−3.46410	−	6.00000i	−0.175637	−	0.304212i	−0.940382	+	0.340121i	$0.889532\pi$
$390$		0			0
$391$	6.00000	−	10.3923i	0.303433	−	0.525561i
$392$	−0.866025	+	1.50000i	−0.0437409	+	0.0757614i
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	−13.8564			−0.697191
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	−21.6506	−	37.5000i	−1.08525	−	1.87971i
$399$		0			0
$400$	−5.00000	+	8.66025i	−0.250000	+	0.433013i
$401$	−1.73205	+	3.00000i	−0.0864945	+	0.149813i	−0.906027	−	0.423220i	$-0.860900\pi$
$401$	−1.73205	+	3.00000i	−0.0864945	+	0.149813i	0.819533	+	0.573033i	$0.194233\pi$
$402$		0			0
$403$	−5.00000	−	8.66025i	−0.249068	−	0.431398i
$404$	−13.8564			−0.689382
$405$		0			0
$406$	−18.0000			−0.893325
$407$	6.06218	+	10.5000i	0.300491	+	0.520466i
$408$		0			0
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	−0.812333	−	0.583193i	$-0.801803\pi$
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	0.911227	+	0.411905i	$0.135136\pi$
$410$	7.79423	−	13.5000i	0.384930	−	0.666717i
$411$		0			0
$412$	−2.50000	−	4.33013i	−0.123166	−	0.213330i
$413$	6.92820			0.340915
$414$		0			0
$415$	−18.0000			−0.883585
$416$	−5.19615	−	9.00000i	−0.254762	−	0.441261i
$417$		0			0
$418$	7.50000	−	12.9904i	0.366837	−	0.635380i
$419$	15.5885	−	27.0000i	0.761546	−	1.31904i	−0.180508	−	0.983574i	$-0.557774\pi$
$419$	15.5885	−	27.0000i	0.761546	−	1.31904i	0.942053	−	0.335463i	$-0.108893\pi$
$420$		0			0
$421$	−8.50000	−	14.7224i	−0.414265	−	0.717527i	0.581086	−	0.813842i	$-0.302628\pi$
$421$	−8.50000	−	14.7224i	−0.414265	−	0.717527i	−0.995351	+	0.0963145i	$0.969295\pi$
$422$	−3.46410			−0.168630
$423$		0			0
$424$	−24.0000			−1.16554
$425$	6.92820	+	12.0000i	0.336067	+	0.582086i
$426$		0			0
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$	−1.73205	+	3.00000i	−0.0837218	+	0.145010i
$429$		0			0
$430$	6.00000	+	10.3923i	0.289346	+	0.501161i
$431$	22.5167			1.08459			0.542295	−	0.840188i	$-0.317556\pi$
$431$	22.5167			1.08459			0.542295	+	0.840188i	$0.317556\pi$
$432$		0			0
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$	4.33013	+	7.50000i	0.207853	+	0.360012i
$435$		0			0
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	4.33013	−	7.50000i	0.207138	−	0.358774i
$438$		0			0
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	−5.19615			−0.247717
$441$		0			0
$442$	−24.0000			−1.14156
$443$	−9.52628	−	16.5000i	−0.452607	−	0.783939i	0.545940	−	0.837824i	$-0.316173\pi$
$443$	−9.52628	−	16.5000i	−0.452607	−	0.783939i	−0.998547	+	0.0538857i	$0.982839\pi$
$444$		0			0
$445$	7.50000	−	12.9904i	0.355534	−	0.615803i
$446$	−16.4545	+	28.5000i	−0.779142	+	1.34951i
$447$		0			0
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−10.3923			−0.490443			−0.245222	−	0.969467i	$-0.578861\pi$
$449$	−10.3923			−0.490443			−0.245222	+	0.969467i	$0.578861\pi$
$450$		0			0
$451$	−9.00000			−0.423793
$452$	5.19615	+	9.00000i	0.244406	+	0.423324i
$453$		0			0
$454$	−3.00000	+	5.19615i	−0.140797	+	0.243868i
$455$	1.73205	−	3.00000i	0.0811998	−	0.140642i
$456$		0			0
$457$	−8.50000	−	14.7224i	−0.397613	−	0.688686i	0.595818	−	0.803120i	$-0.296828\pi$
$457$	−8.50000	−	14.7224i	−0.397613	−	0.688686i	−0.993431	+	0.114433i	$0.963495\pi$
$458$	6.92820			0.323734
$459$		0			0
$460$	3.00000			0.139876
$461$	18.1865	+	31.5000i	0.847031	+	1.46710i	0.883845	+	0.467779i	$0.154946\pi$
$461$	18.1865	+	31.5000i	0.847031	+	1.46710i	−0.0368141	+	0.999322i	$0.511721\pi$
$462$		0			0
$463$	11.0000	−	19.0526i	0.511213	−	0.885448i	−0.488702	−	0.872451i	$-0.662530\pi$
$463$	11.0000	−	19.0526i	0.511213	−	0.885448i	0.999916	−	0.0129968i	$-0.00413714\pi$
$464$	25.9808	−	45.0000i	1.20613	−	2.08907i
$465$		0			0
$466$	−15.0000	−	25.9808i	−0.694862	−	1.20354i
$467$	13.8564			0.641198			0.320599	−	0.947215i	$-0.396116\pi$
$467$	13.8564			0.641198			0.320599	+	0.947215i	$0.396116\pi$
$468$		0			0
$469$	14.0000			0.646460
$470$	10.3923	+	18.0000i	0.479361	+	0.830278i
$471$		0			0
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	3.46410	−	6.00000i	0.159280	−	0.275880i
$474$		0			0
$475$	5.00000	+	8.66025i	0.229416	+	0.397360i
$476$	6.92820			0.317554
$477$		0			0
$478$	−18.0000			−0.823301
$479$	−13.8564	−	24.0000i	−0.633115	−	1.09659i	−0.986911	−	0.161265i	$-0.948443\pi$
$479$	−13.8564	−	24.0000i	−0.633115	−	1.09659i	0.353796	−	0.935323i	$-0.384891\pi$
$480$		0			0
$481$	7.00000	−	12.1244i	0.319173	−	0.552823i
$482$	6.92820	−	12.0000i	0.315571	−	0.546585i
$483$		0			0
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$	6.92820			0.314594
$486$		0			0
$487$	−4.00000			−0.181257			−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000			−0.181257			−0.0906287	+	0.995885i	$0.528888\pi$
$488$	−6.92820	−	12.0000i	−0.313625	−	0.543214i
$489$		0			0
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	18.1865	−	31.5000i	0.820747	−	1.42158i	−0.0843802	−	0.996434i	$-0.526891\pi$
$491$	18.1865	−	31.5000i	0.820747	−	1.42158i	0.905127	−	0.425141i	$-0.139776\pi$
$492$		0			0
$493$	−36.0000	−	62.3538i	−1.62136	−	2.80828i
$494$	−17.3205			−0.779287
$495$		0			0
$496$	−25.0000			−1.12253
$497$	2.59808	+	4.50000i	0.116540	+	0.201853i
$498$		0			0
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	0.246214	+	0.969216i	$0.420813\pi$
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	−6.06218	+	10.5000i	−0.271109	+	0.469574i
$501$		0			0
$502$	−18.0000	−	31.1769i	−0.803379	−	1.39149i
$503$	31.1769			1.39011			0.695055	−	0.718957i	$-0.255380\pi$
$503$	31.1769			1.39011			0.695055	+	0.718957i	$0.255380\pi$
$504$		0			0
$505$	24.0000			1.06799
$506$	−2.59808	−	4.50000i	−0.115499	−	0.200049i
$507$		0			0
$508$	5.00000	−	8.66025i	0.221839	−	0.384237i
$509$	−6.92820	+	12.0000i	−0.307087	+	0.531891i	−0.977724	−	0.209895i	$-0.932688\pi$
$509$	−6.92820	+	12.0000i	−0.307087	+	0.531891i	0.670637	+	0.741786i	$0.266021\pi$
$510$		0			0
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$	−8.66025			−0.382733
$513$		0			0
$514$	3.00000			0.132324
$515$	4.33013	+	7.50000i	0.190808	+	0.330489i
$516$		0			0
$517$	6.00000	−	10.3923i	0.263880	−	0.457053i
$518$	−6.06218	+	10.5000i	−0.266357	+	0.461344i
$519$		0			0
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	−39.8372			−1.74530			−0.872649	−	0.488348i	$-0.837600\pi$
$521$	−39.8372			−1.74530			−0.872649	+	0.488348i	$0.837600\pi$
$522$		0			0
$523$	11.0000			0.480996			0.240498	−	0.970650i	$-0.422689\pi$
$523$	11.0000			0.480996			0.240498	+	0.970650i	$0.422689\pi$
$524$	3.46410	+	6.00000i	0.151330	+	0.262111i
$525$		0			0
$526$	−7.50000	+	12.9904i	−0.327016	+	0.566408i
$527$	−17.3205	+	30.0000i	−0.754493	+	1.30682i
$528$		0			0
$529$	10.0000	+	17.3205i	0.434783	+	0.753066i
$530$	−41.5692			−1.80565
$531$		0			0
$532$	5.00000			0.216777
$533$	5.19615	+	9.00000i	0.225070	+	0.389833i
$534$		0			0
$535$	3.00000	−	5.19615i	0.129701	−	0.224649i
$536$	−12.1244	+	21.0000i	−0.523692	+	0.907062i
$537$		0			0
$538$	−16.5000	−	28.5788i	−0.711366	−	1.23212i
$539$	1.73205			0.0746047
$540$		0			0
$541$	−31.0000			−1.33279			−0.666397	−	0.745597i	$-0.732164\pi$
$541$	−31.0000			−1.33279			−0.666397	+	0.745597i	$0.732164\pi$
$542$	17.3205	+	30.0000i	0.743980	+	1.28861i
$543$		0			0
$544$	−18.0000	+	31.1769i	−0.771744	+	1.33670i
$545$	−6.06218	+	10.5000i	−0.259675	+	0.449771i
$546$		0			0
$547$	20.0000	+	34.6410i	0.855138	+	1.48114i	0.876517	+	0.481371i	$0.159861\pi$
$547$	20.0000	+	34.6410i	0.855138	+	1.48114i	−0.0213785	+	0.999771i	$0.506805\pi$
$548$	−3.46410			−0.147979
$549$		0			0
$550$	6.00000			0.255841
$551$	−25.9808	−	45.0000i	−1.10682	−	1.91706i
$552$		0			0
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$	−16.4545	+	28.5000i	−0.699084	+	1.21085i
$555$		0			0
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	17.3205			0.733893			0.366947	−	0.930242i	$-0.380403\pi$
$557$	17.3205			0.733893			0.366947	+	0.930242i	$0.380403\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$	−4.33013	−	7.50000i	−0.182981	−	0.316933i
$561$		0			0
$562$		0			0
$563$	1.73205	−	3.00000i	0.0729972	−	0.126435i	−0.827216	−	0.561884i	$-0.810077\pi$
$563$	1.73205	−	3.00000i	0.0729972	−	0.126435i	0.900214	+	0.435449i	$0.143410\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	6.92820			0.291214
$567$		0			0
$568$	−9.00000			−0.377632
$569$	−12.1244	−	21.0000i	−0.508279	−	0.880366i	−0.999954	−	0.00958679i	$-0.996948\pi$
$569$	−12.1244	−	21.0000i	−0.508279	−	0.880366i	0.491675	−	0.870779i	$-0.336385\pi$
$570$		0			0
$571$	−13.0000	+	22.5167i	−0.544033	+	0.942293i	0.454634	+	0.890678i	$0.349770\pi$
$571$	−13.0000	+	22.5167i	−0.544033	+	0.942293i	−0.998667	+	0.0516146i	$0.983563\pi$
$572$	−1.73205	+	3.00000i	−0.0724207	+	0.125436i
$573$		0			0
$574$	−4.50000	−	7.79423i	−0.187826	−	0.325325i
$575$	3.46410			0.144463
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	26.8468	+	46.5000i	1.11668	+	1.93415i
$579$		0			0
$580$	9.00000	−	15.5885i	0.373705	−	0.647275i
$581$	−5.19615	+	9.00000i	−0.215573	+	0.373383i
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$	−6.92820			−0.286691
$585$		0			0
$586$		0			0
$587$	−15.5885	−	27.0000i	−0.643404	−	1.11441i	−0.984668	−	0.174441i	$-0.944188\pi$
$587$	−15.5885	−	27.0000i	−0.643404	−	1.11441i	0.341263	−	0.939968i	$-0.389145\pi$
$588$		0			0
$589$	−12.5000	+	21.6506i	−0.515054	+	0.892099i
$590$	−10.3923	+	18.0000i	−0.427844	+	0.741048i
$591$		0			0
$592$	−17.5000	−	30.3109i	−0.719246	−	1.24577i
$593$	29.4449			1.20916			0.604578	−	0.796546i	$-0.293342\pi$
$593$	29.4449			1.20916			0.604578	+	0.796546i	$0.293342\pi$
$594$		0			0
$595$	−12.0000			−0.491952
$596$	−1.73205	−	3.00000i	−0.0709476	−	0.122885i
$597$		0			0
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	−0.866025	+	1.50000i	−0.0353848	+	0.0612883i	−0.883175	−	0.469043i	$-0.844599\pi$
$599$	−0.866025	+	1.50000i	−0.0353848	+	0.0612883i	0.847791	+	0.530331i	$0.177932\pi$
$600$		0			0
$601$	−7.00000	−	12.1244i	−0.285536	−	0.494563i	0.687203	−	0.726465i	$-0.258838\pi$
$601$	−7.00000	−	12.1244i	−0.285536	−	0.494563i	−0.972739	+	0.231903i	$0.925505\pi$
$602$	6.92820			0.282372
$603$		0			0
$604$	−10.0000			−0.406894
$605$	−6.92820	−	12.0000i	−0.281672	−	0.487869i
$606$		0			0
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	−0.428497	−	0.903543i	$-0.640957\pi$
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	0.996740	−	0.0806818i	$-0.0257098\pi$
$608$	−12.9904	+	22.5000i	−0.526830	+	0.912495i
$609$		0			0
$610$	−12.0000	−	20.7846i	−0.485866	−	0.841544i
$611$	−13.8564			−0.560570
$612$		0			0
$613$	11.0000			0.444286			0.222143	−	0.975014i	$-0.428695\pi$
$613$	11.0000			0.444286			0.222143	+	0.975014i	$0.428695\pi$
$614$	14.7224	+	25.5000i	0.594149	+	1.02910i
$615$		0			0
$616$	−1.50000	+	2.59808i	−0.0604367	+	0.104679i
$617$	10.3923	−	18.0000i	0.418378	−	0.724653i	−0.577398	−	0.816463i	$-0.695932\pi$
$617$	10.3923	−	18.0000i	0.418378	−	0.724653i	0.995777	+	0.0918100i	$0.0292653\pi$
$618$		0			0
$619$	−8.50000	−	14.7224i	−0.341644	−	0.591744i	0.643094	−	0.765787i	$-0.277650\pi$
$619$	−8.50000	−	14.7224i	−0.341644	−	0.591744i	−0.984738	+	0.174042i	$0.944317\pi$
$620$	−8.66025			−0.347804
$621$		0			0
$622$	6.00000			0.240578
$623$	−4.33013	−	7.50000i	−0.173483	−	0.300481i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	1.73205	−	3.00000i	0.0692267	−	0.119904i
$627$		0			0
$628$	5.00000	+	8.66025i	0.199522	+	0.345582i
$629$	−48.4974			−1.93372
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−6.92820	−	12.0000i	−0.275589	−	0.477334i
$633$		0			0
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$	−8.66025	+	15.0000i	−0.343672	+	0.595257i
$636$		0			0
$637$	−1.00000	−	1.73205i	−0.0396214	−	0.0686264i
$638$	−31.1769			−1.23431
$639$		0			0
$640$	21.0000			0.830098
$641$	−19.0526	−	33.0000i	−0.752531	−	1.30342i	−0.946593	−	0.322432i	$-0.895500\pi$
$641$	−19.0526	−	33.0000i	−0.752531	−	1.30342i	0.194062	−	0.980989i	$-0.437834\pi$
$642$		0			0
$643$	21.5000	−	37.2391i	0.847877	−	1.46857i	−0.0352216	−	0.999380i	$-0.511214\pi$
$643$	21.5000	−	37.2391i	0.847877	−	1.46857i	0.883099	−	0.469187i	$-0.155453\pi$
$644$	0.866025	−	1.50000i	0.0341262	−	0.0591083i
$645$		0			0
$646$	30.0000	+	51.9615i	1.18033	+	2.04440i
$647$	−13.8564			−0.544752			−0.272376	−	0.962191i	$-0.587809\pi$
$647$	−13.8564			−0.544752			−0.272376	+	0.962191i	$0.587809\pi$
$648$		0			0
$649$	12.0000			0.471041
$650$	−3.46410	−	6.00000i	−0.135873	−	0.235339i
$651$		0			0
$652$	−1.00000	+	1.73205i	−0.0391630	+	0.0678323i
$653$	−6.92820	+	12.0000i	−0.271122	+	0.469596i	−0.969149	−	0.246474i	$-0.920728\pi$
$653$	−6.92820	+	12.0000i	−0.271122	+	0.469596i	0.698028	+	0.716071i	$0.254061\pi$
$654$		0			0
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$	25.9808			1.01438
$657$		0			0
$658$	12.0000			0.467809
$659$	12.9904	+	22.5000i	0.506033	+	0.876476i	0.999976	+	0.00698084i	$0.00222209\pi$
$659$	12.9904	+	22.5000i	0.506033	+	0.876476i	−0.493942	+	0.869495i	$0.664445\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$	17.3205	−	30.0000i	0.673181	−	1.16598i
$663$		0			0
$664$	−9.00000	−	15.5885i	−0.349268	−	0.604949i
$665$	−8.66025			−0.335830
$666$		0			0
$667$	−18.0000			−0.696963
$668$	−5.19615	−	9.00000i	−0.201045	−	0.348220i
$669$		0			0
$670$	−21.0000	+	36.3731i	−0.811301	+	1.40521i
$671$	−6.92820	+	12.0000i	−0.267460	+	0.463255i
$672$		0			0
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	0.946156	−	0.323711i	$-0.104931\pi$
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	−0.753420	+	0.657539i	$0.771597\pi$
$674$	22.5167			0.867309
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−4.33013	−	7.50000i	−0.166420	−	0.288248i	0.770738	−	0.637152i	$-0.219888\pi$
$677$	−4.33013	−	7.50000i	−0.166420	−	0.288248i	−0.937159	+	0.348903i	$0.886554\pi$
$678$		0			0
$679$	2.00000	−	3.46410i	0.0767530	−	0.132940i
$680$	10.3923	−	18.0000i	0.398527	−	0.690268i
$681$		0			0
$682$	7.50000	+	12.9904i	0.287190	+	0.497427i
$683$	−29.4449			−1.12668			−0.563338	−	0.826226i	$-0.690483\pi$
$683$	−29.4449			−1.12668			−0.563338	+	0.826226i	$0.690483\pi$
$684$		0			0
$685$	6.00000			0.229248
$686$	0.866025	+	1.50000i	0.0330650	+	0.0572703i
$687$		0			0
$688$	−10.0000	+	17.3205i	−0.381246	+	0.660338i
$689$	13.8564	−	24.0000i	0.527887	−	0.914327i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	−1.73205			−0.0658427
$693$		0			0
$694$	−57.0000			−2.16369
$695$	17.3205	+	30.0000i	0.657004	+	1.13796i
$696$		0			0
$697$	18.0000	−	31.1769i	0.681799	−	1.18091i
$698$	12.1244	−	21.0000i	0.458914	−	0.794862i
$699$		0			0
$700$	1.00000	+	1.73205i	0.0377964	+	0.0654654i
$701$	−31.1769			−1.17754			−0.588768	−	0.808302i	$-0.700387\pi$
$701$	−31.1769			−1.17754			−0.588768	+	0.808302i	$0.700387\pi$
$702$		0			0
$703$	−35.0000			−1.32005
$704$	−0.866025	−	1.50000i	−0.0326396	−	0.0565334i
$705$		0			0
$706$	28.5000	−	49.3634i	1.07261	−	1.85782i
$707$	6.92820	−	12.0000i	0.260562	−	0.451306i
$708$		0			0
$709$	9.50000	+	16.4545i	0.356780	+	0.617961i	0.987421	−	0.158114i	$-0.0505412\pi$
$709$	9.50000	+	16.4545i	0.356780	+	0.617961i	−0.630641	+	0.776075i	$0.717208\pi$
$710$	−15.5885			−0.585024
$711$		0			0
$712$	15.0000			0.562149
$713$	4.33013	+	7.50000i	0.162165	+	0.280877i
$714$		0			0
$715$	3.00000	−	5.19615i	0.112194	−	0.194325i
$716$	1.73205	−	3.00000i	0.0647298	−	0.112115i
$717$		0			0
$718$	−15.0000	−	25.9808i	−0.559795	−	0.969593i
$719$	−6.92820			−0.258378			−0.129189	−	0.991620i	$-0.541237\pi$
$719$	−6.92820			−0.258378			−0.129189	+	0.991620i	$0.541237\pi$
$720$		0			0
$721$	5.00000			0.186210
$722$	5.19615	+	9.00000i	0.193381	+	0.334945i
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	10.3923	−	18.0000i	0.385961	−	0.668503i
$726$		0			0
$727$	20.0000	+	34.6410i	0.741759	+	1.28476i	0.951694	+	0.307049i	$0.0993415\pi$
$727$	20.0000	+	34.6410i	0.741759	+	1.28476i	−0.209935	+	0.977715i	$0.567325\pi$
$728$	3.46410			0.128388
$729$		0			0
$730$	−12.0000			−0.444140
$731$	13.8564	+	24.0000i	0.512498	+	0.887672i
$732$		0			0
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	0.403128	+	0.915144i	$0.367923\pi$
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	−0.994102	+	0.108453i	$0.965410\pi$
$734$	−21.6506	+	37.5000i	−0.799140	+	1.38415i
$735$		0			0
$736$	4.50000	+	7.79423i	0.165872	+	0.287299i
$737$	24.2487			0.893213
$738$		0			0
$739$	38.0000			1.39785			0.698926	−	0.715194i	$-0.253662\pi$
$739$	38.0000			1.39785			0.698926	+	0.715194i	$0.253662\pi$
$740$	−6.06218	−	10.5000i	−0.222850	−	0.385988i
$741$		0			0
$742$	−12.0000	+	20.7846i	−0.440534	+	0.763027i
$743$	−7.79423	+	13.5000i	−0.285943	+	0.495267i	−0.972837	−	0.231490i	$-0.925640\pi$
$743$	−7.79423	+	13.5000i	−0.285943	+	0.495267i	0.686895	+	0.726757i	$0.258973\pi$
$744$		0			0
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$	32.9090			1.20488
$747$		0			0
$748$	12.0000			0.438763
$749$	−1.73205	−	3.00000i	−0.0632878	−	0.109618i
$750$		0			0
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	−0.489053	−	0.872254i	$-0.662658\pi$
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	0.999921	−	0.0125942i	$-0.00400897\pi$
$752$	−17.3205	+	30.0000i	−0.631614	+	1.09399i
$753$		0			0
$754$	18.0000	+	31.1769i	0.655521	+	1.13540i
$755$	17.3205			0.630358
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	6.92820	+	12.0000i	0.251644	+	0.435860i
$759$		0			0
$760$	7.50000	−	12.9904i	0.272054	−	0.471211i
$761$	13.8564	−	24.0000i	0.502294	−	0.869999i	−0.497702	−	0.867348i	$-0.665823\pi$
$761$	13.8564	−	24.0000i	0.502294	−	0.869999i	0.999996	−	0.00265131i	$-0.000843938\pi$
$762$		0			0
$763$	3.50000	+	6.06218i	0.126709	+	0.219466i
$764$	8.66025			0.313317
$765$		0			0
$766$	66.0000			2.38468
$767$	−6.92820	−	12.0000i	−0.250163	−	0.433295i
$768$		0			0
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	−0.596643	−	0.802507i	$-0.703499\pi$
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	0.993313	+	0.115454i	$0.0368323\pi$
$770$	−2.59808	+	4.50000i	−0.0936282	+	0.162169i
$771$		0			0
$772$	11.0000	+	19.0526i	0.395899	+	0.685717i
$773$	43.3013			1.55744			0.778719	−	0.627373i	$-0.215870\pi$
$773$	43.3013			1.55744			0.778719	+	0.627373i	$0.215870\pi$
$774$		0			0
$775$	−10.0000			−0.359211
$776$	3.46410	+	6.00000i	0.124354	+	0.215387i
$777$		0			0
$778$	6.00000	−	10.3923i	0.215110	−	0.372582i
$779$	12.9904	−	22.5000i	0.465429	−	0.806146i
$780$		0			0
$781$	4.50000	+	7.79423i	0.161023	+	0.278899i
$782$	20.7846			0.743256
$783$		0			0
$784$	−5.00000			−0.178571
$785$	−8.66025	−	15.0000i	−0.309098	−	0.535373i
$786$		0			0
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	−0.828176	−	0.560469i	$-0.810621\pi$
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	0.899468	+	0.436987i	$0.143954\pi$
$788$	−5.19615	+	9.00000i	−0.185105	+	0.320612i
$789$		0			0
$790$	−12.0000	−	20.7846i	−0.426941	−	0.739483i
$791$	−10.3923			−0.369508
$792$		0			0
$793$	16.0000			0.568177
$794$	1.73205	+	3.00000i	0.0614682	+	0.106466i
$795$		0			0
$796$	12.5000	−	21.6506i	0.443051	−	0.767386i
$797$	12.9904	−	22.5000i	0.460143	−	0.796991i	−0.538825	−	0.842418i	$-0.681132\pi$
$797$	12.9904	−	22.5000i	0.460143	−	0.796991i	0.998968	+	0.0454270i	$0.0144648\pi$
$798$		0			0
$799$	24.0000	+	41.5692i	0.849059	+	1.47061i
$800$	−10.3923			−0.367423
$801$		0			0
$802$	−6.00000			−0.211867
$803$	3.46410	+	6.00000i	0.122245	+	0.211735i
$804$		0			0
$805$	−1.50000	+	2.59808i	−0.0528681	+	0.0915702i
$806$	8.66025	−	15.0000i	0.305044	−	0.528352i
$807$		0			0
$808$	12.0000	+	20.7846i	0.422159	+	0.731200i
$809$	38.1051			1.33970			0.669852	−	0.742494i	$-0.266357\pi$
$809$	38.1051			1.33970			0.669852	+	0.742494i	$0.266357\pi$
$810$		0			0
$811$	−43.0000			−1.50993			−0.754967	−	0.655763i	$-0.772347\pi$
$811$	−43.0000			−1.50993			−0.754967	+	0.655763i	$0.772347\pi$
$812$	−5.19615	−	9.00000i	−0.182349	−	0.315838i
$813$		0			0
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$	1.73205	−	3.00000i	0.0606711	−	0.105085i
$816$		0			0
$817$	10.0000	+	17.3205i	0.349856	+	0.605968i
$818$	6.92820			0.242239
$819$		0			0
$820$	9.00000			0.314294
$821$	3.46410	+	6.00000i	0.120898	+	0.209401i	0.920122	−	0.391632i	$-0.128089\pi$
$821$	3.46410	+	6.00000i	0.120898	+	0.209401i	−0.799224	+	0.601033i	$0.794756\pi$
$822$		0			0
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	−4.33013	+	7.50000i	−0.150847	+	0.261275i
$825$		0			0
$826$	6.00000	+	10.3923i	0.208767	+	0.361595i
$827$	−5.19615			−0.180688			−0.0903440	−	0.995911i	$-0.528797\pi$
$827$	−5.19615			−0.180688			−0.0903440	+	0.995911i	$0.528797\pi$
$828$		0			0
$829$	32.0000			1.11141			0.555703	−	0.831381i	$-0.312449\pi$
$829$	32.0000			1.11141			0.555703	+	0.831381i	$0.312449\pi$
$830$	−15.5885	−	27.0000i	−0.541083	−	0.937184i
$831$		0			0
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	−3.46410	+	6.00000i	−0.120024	+	0.207888i
$834$		0			0
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$	8.66025			0.299521
$837$		0			0
$838$	54.0000			1.86540
$839$	5.19615	+	9.00000i	0.179391	+	0.310715i	0.941672	−	0.336532i	$-0.109254\pi$
$839$	5.19615	+	9.00000i	0.179391	+	0.310715i	−0.762281	+	0.647246i	$0.775921\pi$
$840$		0			0
$841$	−39.5000	+	68.4160i	−1.36207	+	2.35917i
$842$	14.7224	−	25.5000i	0.507369	−	0.878788i
$843$		0			0
$844$	−1.00000	−	1.73205i	−0.0344214	−	0.0596196i
$845$	15.5885			0.536259
$846$		0			0
$847$	−8.00000			−0.274883
$848$	−34.6410	−	60.0000i	−1.18958	−	2.06041i
$849$		0			0
$850$	−12.0000	+	20.7846i	−0.411597	+	0.712906i
$851$	−6.06218	+	10.5000i	−0.207809	+	0.359935i
$852$		0			0
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	−0.946232	−	0.323489i	$-0.895144\pi$
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	0.192966	−	0.981205i	$-0.438189\pi$
$854$	−13.8564			−0.474156
$855$		0			0
$856$	6.00000			0.205076
$857$	19.9186	+	34.5000i	0.680406	+	1.17850i	0.974857	+	0.222831i	$0.0715298\pi$
$857$	19.9186	+	34.5000i	0.680406	+	1.17850i	−0.294451	+	0.955667i	$0.595137\pi$
$858$		0			0
$859$	−20.5000	+	35.5070i	−0.699451	+	1.21148i	0.269206	+	0.963083i	$0.413239\pi$
$859$	−20.5000	+	35.5070i	−0.699451	+	1.21148i	−0.968657	+	0.248402i	$0.920095\pi$
$860$	−3.46410	+	6.00000i	−0.118125	+	0.204598i
$861$		0			0
$862$	19.5000	+	33.7750i	0.664173	+	1.15038i
$863$	−17.3205			−0.589597			−0.294798	−	0.955559i	$-0.595253\pi$
$863$	−17.3205			−0.589597			−0.294798	+	0.955559i	$0.595253\pi$
$864$		0			0
$865$	3.00000			0.102003
$866$	22.5167	+	39.0000i	0.765147	+	1.32527i
$867$		0			0
$868$	−2.50000	+	4.33013i	−0.0848555	+	0.146974i
$869$	−6.92820	+	12.0000i	−0.235023	+	0.407072i
$870$		0			0
$871$	−14.0000	−	24.2487i	−0.474372	−	0.821636i
$872$	−12.1244			−0.410582
$873$		0			0
$874$	15.0000			0.507383
$875$	−6.06218	−	10.5000i	−0.204939	−	0.354965i
$876$		0			0
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	−13.8564	+	24.0000i	−0.467631	+	0.809961i
$879$		0			0
$880$	−7.50000	−	12.9904i	−0.252825	−	0.437906i
$881$	5.19615			0.175063			0.0875314	−	0.996162i	$-0.472102\pi$
$881$	5.19615			0.175063			0.0875314	+	0.996162i	$0.472102\pi$
$882$		0			0
$883$	56.0000			1.88455			0.942275	−	0.334840i	$-0.108682\pi$
$883$	56.0000			1.88455			0.942275	+	0.334840i	$0.108682\pi$
$884$	−6.92820	−	12.0000i	−0.233021	−	0.403604i
$885$		0			0
$886$	16.5000	−	28.5788i	0.554328	−	0.960125i
$887$	−1.73205	+	3.00000i	−0.0581566	+	0.100730i	−0.893638	−	0.448789i	$-0.851856\pi$
$887$	−1.73205	+	3.00000i	−0.0581566	+	0.100730i	0.835481	+	0.549519i	$0.185189\pi$
$888$		0			0
$889$	5.00000	+	8.66025i	0.167695	+	0.290456i
$890$	25.9808			0.870877
$891$		0			0
$892$	−19.0000			−0.636167
$893$	17.3205	+	30.0000i	0.579609	+	1.00391i
$894$		0			0
$895$	−3.00000	+	5.19615i	−0.100279	+	0.173688i
$896$	6.06218	−	10.5000i	0.202523	−	0.350780i
$897$		0			0
$898$	−9.00000	−	15.5885i	−0.300334	−	0.520194i
$899$	51.9615			1.73301
$900$		0			0
$901$	−96.0000			−3.19822
$902$	−7.79423	−	13.5000i	−0.259519	−	0.449501i
$903$		0			0
$904$	9.00000	−	15.5885i	0.299336	−	0.518464i
$905$	1.73205	−	3.00000i	0.0575753	−	0.0997234i
$906$		0			0
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$	−3.46410			−0.114960
$909$		0			0
$910$	6.00000			0.198898
$911$	−5.19615	−	9.00000i	−0.172156	−	0.298183i	0.767017	−	0.641626i	$-0.221740\pi$
$911$	−5.19615	−	9.00000i	−0.172156	−	0.298183i	−0.939173	+	0.343443i	$0.888407\pi$
$912$		0			0
$913$	−9.00000	+	15.5885i	−0.297857	+	0.515903i
$914$	14.7224	−	25.5000i	0.486975	−	0.843465i
$915$		0			0
$916$	2.00000	+	3.46410i	0.0660819	+	0.114457i
$917$	−6.92820			−0.228789
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$	−2.59808	−	4.50000i	−0.0856560	−	0.148361i
$921$		0			0
$922$	−31.5000	+	54.5596i	−1.03740	+	1.79682i
$923$	5.19615	−	9.00000i	0.171033	−	0.296239i
$924$		0			0
$925$	−7.00000	−	12.1244i	−0.230159	−	0.398646i
$926$	38.1051			1.25221
$927$		0			0
$928$	54.0000			1.77264
$929$	24.2487	+	42.0000i	0.795574	+	1.37798i	0.922474	+	0.386060i	$0.126164\pi$
$929$	24.2487	+	42.0000i	0.795574	+	1.37798i	−0.126899	+	0.991916i	$0.540503\pi$
$930$		0			0
$931$	−2.50000	+	4.33013i	−0.0819342	+	0.141914i
$932$	8.66025	−	15.0000i	0.283676	−	0.491341i
$933$		0			0
$934$	12.0000	+	20.7846i	0.392652	+	0.680093i
$935$	−20.7846			−0.679729
$936$		0			0
$937$	44.0000			1.43742			0.718709	−	0.695311i	$-0.244734\pi$
$937$	44.0000			1.43742			0.718709	+	0.695311i	$0.244734\pi$
$938$	12.1244	+	21.0000i	0.395874	+	0.685674i
$939$		0			0
$940$	−6.00000	+	10.3923i	−0.195698	+	0.338960i
$941$	−16.4545	+	28.5000i	−0.536401	+	0.929073i	0.462693	+	0.886518i	$0.346883\pi$
$941$	−16.4545	+	28.5000i	−0.536401	+	0.929073i	−0.999094	+	0.0425550i	$0.986450\pi$
$942$		0			0
$943$	−4.50000	−	7.79423i	−0.146540	−	0.253815i
$944$	−34.6410			−1.12747
$945$		0			0
$946$	12.0000			0.390154
$947$	−4.33013	−	7.50000i	−0.140710	−	0.243717i	0.787054	−	0.616884i	$-0.211605\pi$
$947$	−4.33013	−	7.50000i	−0.140710	−	0.243717i	−0.927764	+	0.373167i	$0.878272\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	−8.66025	+	15.0000i	−0.280976	+	0.486664i
$951$		0			0
$952$	−6.00000	−	10.3923i	−0.194461	−	0.336817i
$953$	10.3923			0.336640			0.168320	−	0.985732i	$-0.446166\pi$
$953$	10.3923			0.336640			0.168320	+	0.985732i	$0.446166\pi$
$954$		0			0
$955$	−15.0000			−0.485389
$956$	−5.19615	−	9.00000i	−0.168056	−	0.291081i
$957$		0			0
$958$	24.0000	−	41.5692i	0.775405	−	1.34304i
$959$	1.73205	−	3.00000i	0.0559308	−	0.0968751i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$	24.2487			0.781810
$963$		0			0
$964$	8.00000			0.257663
$965$	−19.0526	−	33.0000i	−0.613324	−	1.06231i
$966$		0			0
$967$	−1.00000	+	1.73205i	−0.0321578	+	0.0556990i	−0.881656	−	0.471892i	$-0.843571\pi$
$967$	−1.00000	+	1.73205i	−0.0321578	+	0.0556990i	0.849499	+	0.527591i	$0.176905\pi$
$968$	6.92820	−	12.0000i	0.222681	−	0.385695i
$969$		0			0
$970$	6.00000	+	10.3923i	0.192648	+	0.333677i
$971$	−38.1051			−1.22285			−0.611426	−	0.791302i	$-0.709404\pi$
$971$	−38.1051			−1.22285			−0.611426	+	0.791302i	$0.709404\pi$
$972$		0			0
$973$	20.0000			0.641171
$974$	−3.46410	−	6.00000i	−0.110997	−	0.192252i
$975$		0			0
$976$	20.0000	−	34.6410i	0.640184	−	1.10883i
$977$	−13.8564	+	24.0000i	−0.443306	+	0.767828i	−0.997932	−	0.0642712i	$-0.979528\pi$
$977$	−13.8564	+	24.0000i	−0.443306	+	0.767828i	0.554627	+	0.832099i	$0.312861\pi$
$978$		0			0
$979$	−7.50000	−	12.9904i	−0.239701	−	0.415174i
$980$	−1.73205			−0.0553283
$981$		0			0
$982$	63.0000			2.01041
$983$	27.7128	+	48.0000i	0.883901	+	1.53096i	0.846968	+	0.531645i	$0.178426\pi$
$983$	27.7128	+	48.0000i	0.883901	+	1.53096i	0.0369339	+	0.999318i	$0.488241\pi$
$984$		0			0
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$	62.3538	−	108.000i	1.98575	−	3.43942i
$987$		0			0
$988$	−5.00000	−	8.66025i	−0.159071	−	0.275519i
$989$	6.92820			0.220304
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	−12.9904	−	22.5000i	−0.412445	−	0.714376i
$993$		0			0
$994$	−4.50000	+	7.79423i	−0.142731	+	0.247218i
$995$	−21.6506	+	37.5000i	−0.686371	+	1.18883i
$996$		0			0
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	−55.4256			−1.75447
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.k.190.2		4
3.2	odd	2	inner	567.2.f.k.190.1		4
9.2	odd	6	inner	567.2.f.k.379.1		4
9.4	even	3		189.2.a.e.1.1	✓	2
9.5	odd	6		189.2.a.e.1.2	yes	2
9.7	even	3	inner	567.2.f.k.379.2		4
36.23	even	6		3024.2.a.bg.1.2		2
36.31	odd	6		3024.2.a.bg.1.1		2
45.4	even	6		4725.2.a.ba.1.2		2
45.14	odd	6		4725.2.a.ba.1.1		2
63.13	odd	6		1323.2.a.t.1.1		2
63.41	even	6		1323.2.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.a.e.1.1	✓	2	9.4	even	3
189.2.a.e.1.2	yes	2	9.5	odd	6
567.2.f.k.190.1		4	3.2	odd	2	inner
567.2.f.k.190.2		4	1.1	even	1	trivial
567.2.f.k.379.1		4	9.2	odd	6	inner
567.2.f.k.379.2		4	9.7	even	3	inner
1323.2.a.t.1.1		2	63.13	odd	6
1323.2.a.t.1.2		2	63.41	even	6
3024.2.a.bg.1.1		2	36.31	odd	6
3024.2.a.bg.1.2		2	36.23	even	6
4725.2.a.ba.1.1		2	45.14	odd	6
4725.2.a.ba.1.2		2	45.4	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.73205 q^{8} +3.00000 q^{10} +(-0.866025 - 1.50000i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(0.866025 - 1.50000i) q^{14} +(2.50000 + 4.33013i) q^{16} +6.92820 q^{17} +5.00000 q^{19} +(0.866025 + 1.50000i) q^{20} +(1.50000 - 2.59808i) q^{22} +(0.866025 - 1.50000i) q^{23} +(1.00000 + 1.73205i) q^{25} -3.46410 q^{26} +1.00000 q^{28} +(-5.19615 - 9.00000i) q^{29} +(-2.50000 + 4.33013i) q^{31} +(-2.59808 + 4.50000i) q^{32} +(6.00000 + 10.3923i) q^{34} -1.73205 q^{35} -7.00000 q^{37} +(4.33013 + 7.50000i) q^{38} +(1.50000 - 2.59808i) q^{40} +(2.59808 - 4.50000i) q^{41} +(2.00000 + 3.46410i) q^{43} +1.73205 q^{44} +3.00000 q^{46} +(3.46410 + 6.00000i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-1.73205 + 3.00000i) q^{50} +(-1.00000 - 1.73205i) q^{52} -13.8564 q^{53} -3.00000 q^{55} +(-0.866025 - 1.50000i) q^{56} +(9.00000 - 15.5885i) q^{58} +(-3.46410 + 6.00000i) q^{59} +(-4.00000 - 6.92820i) q^{61} -8.66025 q^{62} +1.00000 q^{64} +(1.73205 + 3.00000i) q^{65} +(-7.00000 + 12.1244i) q^{67} +(-3.46410 + 6.00000i) q^{68} +(-1.50000 - 2.59808i) q^{70} -5.19615 q^{71} -4.00000 q^{73} +(-6.06218 - 10.5000i) q^{74} +(-2.50000 + 4.33013i) q^{76} +(-0.866025 + 1.50000i) q^{77} +(-4.00000 - 6.92820i) q^{79} +8.66025 q^{80} +9.00000 q^{82} +(-5.19615 - 9.00000i) q^{83} +(6.00000 - 10.3923i) q^{85} +(-3.46410 + 6.00000i) q^{86} +(-1.50000 - 2.59808i) q^{88} +8.66025 q^{89} +2.00000 q^{91} +(0.866025 + 1.50000i) q^{92} +(-6.00000 + 10.3923i) q^{94} +(4.33013 - 7.50000i) q^{95} +(2.00000 + 3.46410i) q^{97} -1.73205 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} + 10 q^{16} + 20 q^{19} + 6 q^{22} + 4 q^{25} + 4 q^{28} - 10 q^{31} + 24 q^{34} - 28 q^{37} + 6 q^{40} + 8 q^{43} + 12 q^{46} - 2 q^{49} - 4 q^{52} - 12 q^{55}+ \cdots + 8 q^{97}+O(q^{100}) \) 4 * q - 2 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 + 10 * q^16 + 20 * q^19 + 6 * q^22 + 4 * q^25 + 4 * q^28 - 10 * q^31 + 24 * q^34 - 28 * q^37 + 6 * q^40 + 8 * q^43 + 12 * q^46 - 2 * q^49 - 4 * q^52 - 12 * q^55 + 36 * q^58 - 16 * q^61 + 4 * q^64 - 28 * q^67 - 6 * q^70 - 16 * q^73 - 10 * q^76 - 16 * q^79 + 36 * q^82 + 24 * q^85 - 6 * q^88 + 8 * q^91 - 24 * q^94 + 8 * q^97

Introduction

L-functions

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