LMFDB - Embedded newform 567.2.p.b.404.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(80,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.80"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,3,0,1,3,0,1,0,0,9,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			404.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	567.404
Dual form			567.2.p.b.80.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.73205i q^{8} +(4.50000 - 2.59808i) q^{10} +(1.50000 - 0.866025i) q^{11} -1.73205i q^{13} +(-1.50000 + 4.33013i) q^{14} +(2.50000 - 4.33013i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-4.50000 - 2.59808i) q^{19} +3.00000 q^{20} +3.00000 q^{22} +(4.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(1.50000 - 2.59808i) q^{26} +(-2.00000 + 1.73205i) q^{28} +5.19615i q^{29} +(3.00000 - 1.73205i) q^{31} +(4.50000 - 2.59808i) q^{32} +5.19615i q^{34} +(7.50000 + 2.59808i) q^{35} +(-3.50000 + 6.06218i) q^{37} +(-4.50000 - 7.79423i) q^{38} +(-4.50000 - 2.59808i) q^{40} -3.00000 q^{41} +1.00000 q^{43} +(1.50000 + 0.866025i) q^{44} +(4.50000 + 7.79423i) q^{46} +(-6.50000 + 2.59808i) q^{49} -6.92820i q^{50} +(1.50000 - 0.866025i) q^{52} +(-7.50000 + 4.33013i) q^{53} -5.19615i q^{55} +(4.50000 - 0.866025i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(-12.0000 - 6.92820i) q^{61} +6.00000 q^{62} -1.00000 q^{64} +(-4.50000 - 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(9.00000 + 10.3923i) q^{70} +3.46410i q^{71} +(-4.50000 + 2.59808i) q^{73} +(-10.5000 + 6.06218i) q^{74} -5.19615i q^{76} +(3.00000 + 3.46410i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-7.50000 - 12.9904i) q^{80} +(-4.50000 - 2.59808i) q^{82} +15.0000 q^{83} +9.00000 q^{85} +(1.50000 + 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(1.50000 - 2.59808i) q^{89} +(4.50000 - 0.866025i) q^{91} +5.19615i q^{92} +(-13.5000 + 7.79423i) q^{95} +1.73205i q^{97} +(-12.0000 - 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + q^{4} + 3 q^{5} + q^{7} + 9 q^{10} + 3 q^{11} - 3 q^{14} + 5 q^{16} + 3 q^{17} - 9 q^{19} + 6 q^{20} + 6 q^{22} + 9 q^{23} - 4 q^{25} + 3 q^{26} - 4 q^{28} + 6 q^{31} + 9 q^{32} + 15 q^{35}+ \cdots - 24 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 + q^4 + 3 * q^5 + q^7 + 9 * q^10 + 3 * q^11 - 3 * q^14 + 5 * q^16 + 3 * q^17 - 9 * q^19 + 6 * q^20 + 6 * q^22 + 9 * q^23 - 4 * q^25 + 3 * q^26 - 4 * q^28 + 6 * q^31 + 9 * q^32 + 15 * q^35 - 7 * q^37 - 9 * q^38 - 9 * q^40 - 6 * q^41 + 2 * q^43 + 3 * q^44 + 9 * q^46 - 13 * q^49 + 3 * q^52 - 15 * q^53 + 9 * q^56 - 9 * q^58 - 24 * q^61 + 12 * q^62 - 2 * q^64 - 9 * q^65 + 4 * q^67 - 3 * q^68 + 18 * q^70 - 9 * q^73 - 21 * q^74 + 6 * q^77 - 8 * q^79 - 15 * q^80 - 9 * q^82 + 30 * q^83 + 18 * q^85 + 3 * q^86 - 3 * q^88 + 3 * q^89 + 9 * q^91 - 27 * q^95 - 24 * q^98

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		−	1.73205i		−	0.612372i
$9$		0			0
$10$	4.50000	−	2.59808i	1.42302	−	0.821584i
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$		0			0
$13$		−	1.73205i		−	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$		−	1.73205i		−	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$	−1.50000	+	4.33013i	−0.400892	+	1.15728i
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−4.50000	−	2.59808i	−1.03237	−	0.596040i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−4.50000	−	2.59808i	−1.03237	−	0.596040i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	3.00000			0.670820
$21$		0			0
$22$	3.00000			0.639602
$23$	4.50000	+	2.59808i	0.938315	+	0.541736i	0.889432	−	0.457068i	$-0.151100\pi$
$23$	4.50000	+	2.59808i	0.938315	+	0.541736i	0.0488832	+	0.998805i	$0.484434\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	1.50000	−	2.59808i	0.294174	−	0.509525i
$27$		0			0
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$			5.19615i			0.964901i	0.875923	+	0.482451i	$0.160253\pi$
$29$			5.19615i			0.964901i	−0.875923	+	0.482451i	$0.839747\pi$
$30$		0			0
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	−0.205783	−	0.978598i	$-0.565974\pi$
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	0.744599	+	0.667512i	$0.232641\pi$
$32$	4.50000	−	2.59808i	0.795495	−	0.459279i
$33$		0			0
$34$			5.19615i			0.891133i
$35$	7.50000	+	2.59808i	1.26773	+	0.439155i
$36$		0			0
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	−4.50000	−	7.79423i	−0.729996	−	1.26439i
$39$		0			0
$40$	−4.50000	−	2.59808i	−0.711512	−	0.410792i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	1.50000	+	0.866025i	0.226134	+	0.130558i
$45$		0			0
$46$	4.50000	+	7.79423i	0.663489	+	1.14920i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		−	6.92820i		−	0.979796i
$51$		0			0
$52$	1.50000	−	0.866025i	0.208013	−	0.120096i
$53$	−7.50000	+	4.33013i	−1.03020	+	0.594789i	−0.917043	−	0.398788i	$-0.869431\pi$
$53$	−7.50000	+	4.33013i	−1.03020	+	0.594789i	−0.113161	+	0.993577i	$0.536098\pi$
$54$		0			0
$55$		−	5.19615i		−	0.700649i
$56$	4.50000	−	0.866025i	0.601338	−	0.115728i
$57$		0			0
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−12.0000	−	6.92820i	−1.53644	−	0.887066i	−0.999043	−	0.0437377i	$-0.986073\pi$
$61$	−12.0000	−	6.92820i	−1.53644	−	0.887066i	−0.537400	−	0.843328i	$-0.680593\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.50000	−	2.59808i	−0.558156	−	0.322252i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$		0			0
$70$	9.00000	+	10.3923i	1.07571	+	1.24212i
$71$			3.46410i			0.411113i	0.978645	+	0.205557i	$0.0659005\pi$
$71$			3.46410i			0.411113i	−0.978645	+	0.205557i	$0.934100\pi$
$72$		0			0
$73$	−4.50000	+	2.59808i	−0.526685	+	0.304082i	−0.739666	−	0.672975i	$-0.765016\pi$
$73$	−4.50000	+	2.59808i	−0.526685	+	0.304082i	0.212980	+	0.977056i	$0.431683\pi$
$74$	−10.5000	+	6.06218i	−1.22060	+	0.704714i
$75$		0			0
$76$		−	5.19615i		−	0.596040i
$77$	3.00000	+	3.46410i	0.341882	+	0.394771i
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−7.50000	−	12.9904i	−0.838525	−	1.45237i
$81$		0			0
$82$	−4.50000	−	2.59808i	−0.496942	−	0.286910i
$83$	15.0000			1.64646			0.823232	−	0.567705i	$-0.192169\pi$
$83$	15.0000			1.64646			0.823232	+	0.567705i	$0.192169\pi$
$84$		0			0
$85$	9.00000			0.976187
$86$	1.50000	+	0.866025i	0.161749	+	0.0933859i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$		0			0
$91$	4.50000	−	0.866025i	0.471728	−	0.0907841i
$92$			5.19615i			0.541736i
$93$		0			0
$94$		0			0
$95$	−13.5000	+	7.79423i	−1.38507	+	0.799671i
$96$		0			0
$97$			1.73205i			0.175863i	0.996127	+	0.0879316i	$0.0280257\pi$
$97$			1.73205i			0.175863i	−0.996127	+	0.0879316i	$0.971974\pi$
$98$	−12.0000	−	1.73205i	−1.21218	−	0.174964i
$99$		0			0
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	−10.5000	−	6.06218i	−1.03460	−	0.597324i	−0.116298	−	0.993214i	$-0.537103\pi$
$103$	−10.5000	−	6.06218i	−1.03460	−	0.597324i	−0.918298	+	0.395890i	$0.870436\pi$
$104$	−3.00000			−0.294174
$105$		0			0
$106$	−15.0000			−1.45693
$107$	−7.50000	−	4.33013i	−0.725052	−	0.418609i	0.0915571	−	0.995800i	$-0.470816\pi$
$107$	−7.50000	−	4.33013i	−0.725052	−	0.418609i	−0.816609	+	0.577191i	$0.804149\pi$
$108$		0			0
$109$	−9.50000	−	16.4545i	−0.909935	−	1.57605i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	−9.50000	−	16.4545i	−0.909935	−	1.57605i	−0.0957826	−	0.995402i	$-0.530535\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$		0			0
$112$	12.5000	+	4.33013i	1.18114	+	0.409159i
$113$			1.73205i			0.162938i	0.996676	+	0.0814688i	$0.0259611\pi$
$113$			1.73205i			0.162938i	−0.996676	+	0.0814688i	$0.974039\pi$
$114$		0			0
$115$	13.5000	−	7.79423i	1.25888	−	0.726816i
$116$	−4.50000	+	2.59808i	−0.417815	+	0.241225i
$117$		0			0
$118$		0			0
$119$	−6.00000	+	5.19615i	−0.550019	+	0.476331i
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$	−12.0000	−	20.7846i	−1.08643	−	1.88175i
$123$		0			0
$124$	3.00000	+	1.73205i	0.269408	+	0.155543i
$125$	3.00000			0.268328
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$	−10.5000	−	6.06218i	−0.928078	−	0.535826i
$129$		0			0
$130$	−4.50000	−	7.79423i	−0.394676	−	0.683599i
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	−0.599699	−	0.800226i	$-0.704713\pi$
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	0.992865	+	0.119241i	$0.0380462\pi$
$132$		0			0
$133$	4.50000	−	12.9904i	0.390199	−	1.12641i
$134$			6.92820i			0.598506i
$135$		0			0
$136$	4.50000	−	2.59808i	0.385872	−	0.222783i
$137$	−10.5000	+	6.06218i	−0.897076	+	0.517927i	−0.876250	−	0.481856i	$-0.839963\pi$
$137$	−10.5000	+	6.06218i	−0.897076	+	0.517927i	−0.0208253	+	0.999783i	$0.506629\pi$
$138$		0			0
$139$		−	8.66025i		−	0.734553i	−0.930112	−	0.367277i	$-0.880290\pi$
$139$		−	8.66025i		−	0.734553i	0.930112	−	0.367277i	$-0.119710\pi$
$140$	1.50000	+	7.79423i	0.126773	+	0.658733i
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−1.50000	−	2.59808i	−0.125436	−	0.217262i
$144$		0			0
$145$	13.5000	+	7.79423i	1.12111	+	0.647275i
$146$	−9.00000			−0.744845
$147$		0			0
$148$	−7.00000			−0.575396
$149$	1.50000	+	0.866025i	0.122885	+	0.0709476i	0.560182	−	0.828369i	$-0.310731\pi$
$149$	1.50000	+	0.866025i	0.122885	+	0.0709476i	−0.437298	+	0.899317i	$0.644064\pi$
$150$		0			0
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	0.971274	+	0.237964i	$0.0764802\pi$
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	−0.279554	+	0.960130i	$0.590186\pi$
$152$	−4.50000	+	7.79423i	−0.364998	+	0.632195i
$153$		0			0
$154$	1.50000	+	7.79423i	0.120873	+	0.628077i
$155$		−	10.3923i		−	0.834730i
$156$		0			0
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$	−12.0000	+	6.92820i	−0.954669	+	0.551178i
$159$		0			0
$160$		−	15.5885i		−	1.23238i
$161$	−4.50000	+	12.9904i	−0.354650	+	1.02379i
$162$		0			0
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	−0.996942	−	0.0781474i	$-0.975100\pi$
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	0.566149	+	0.824303i	$0.308433\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	22.5000	+	12.9904i	1.74634	+	1.00825i
$167$	9.00000			0.696441			0.348220	−	0.937413i	$-0.386786\pi$
$167$	9.00000			0.696441			0.348220	+	0.937413i	$0.386786\pi$
$168$		0			0
$169$	10.0000			0.769231
$170$	13.5000	+	7.79423i	1.03540	+	0.597790i
$171$		0			0
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	8.00000	−	6.92820i	0.604743	−	0.523723i
$176$		−	8.66025i		−	0.652791i
$177$		0			0
$178$	4.50000	−	2.59808i	0.337289	−	0.194734i
$179$	13.5000	−	7.79423i	1.00904	−	0.582568i	0.0981277	−	0.995174i	$-0.468715\pi$
$179$	13.5000	−	7.79423i	1.00904	−	0.582568i	0.910910	+	0.412606i	$0.135381\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	7.50000	+	2.59808i	0.555937	+	0.192582i
$183$		0			0
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	10.5000	+	18.1865i	0.771975	+	1.33710i
$186$		0			0
$187$	4.50000	+	2.59808i	0.329073	+	0.189990i
$188$		0			0
$189$		0			0
$190$	−27.0000			−1.95879
$191$	15.0000	+	8.66025i	1.08536	+	0.626634i	0.932338	−	0.361588i	$-0.117765\pi$
$191$	15.0000	+	8.66025i	1.08536	+	0.626634i	0.153024	+	0.988222i	$0.451099\pi$
$192$		0			0
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	−1.50000	+	2.59808i	−0.107694	+	0.186531i
$195$		0			0
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$		−	13.8564i		−	0.987228i	−0.869681	−	0.493614i	$-0.835676\pi$
$197$		−	13.8564i		−	0.987228i	0.869681	−	0.493614i	$-0.164324\pi$
$198$		0			0
$199$	−7.50000	+	4.33013i	−0.531661	+	0.306955i	−0.741693	−	0.670740i	$-0.765977\pi$
$199$	−7.50000	+	4.33013i	−0.531661	+	0.306955i	0.210032	+	0.977695i	$0.432643\pi$
$200$	−6.00000	+	3.46410i	−0.424264	+	0.244949i
$201$		0			0
$202$			5.19615i			0.365600i
$203$	−13.5000	+	2.59808i	−0.947514	+	0.182349i
$204$		0			0
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	−10.5000	−	18.1865i	−0.731570	−	1.26712i
$207$		0			0
$208$	−7.50000	−	4.33013i	−0.520031	−	0.300240i
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−5.00000			−0.344214			−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000			−0.344214			−0.172107	+	0.985078i	$0.555058\pi$
$212$	−7.50000	−	4.33013i	−0.515102	−	0.297394i
$213$		0			0
$214$	−7.50000	−	12.9904i	−0.512689	−	0.888004i
$215$	1.50000	−	2.59808i	0.102299	−	0.177187i
$216$		0			0
$217$	6.00000	+	6.92820i	0.407307	+	0.470317i
$218$		−	32.9090i		−	2.22888i
$219$		0			0
$220$	4.50000	−	2.59808i	0.303390	−	0.175162i
$221$	4.50000	−	2.59808i	0.302703	−	0.174766i
$222$		0			0
$223$			5.19615i			0.347960i	0.984749	+	0.173980i	$0.0556628\pi$
$223$			5.19615i			0.347960i	−0.984749	+	0.173980i	$0.944337\pi$
$224$	9.00000	+	10.3923i	0.601338	+	0.694365i
$225$		0			0
$226$	−1.50000	+	2.59808i	−0.0997785	+	0.172821i
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	−0.969533	−	0.244962i	$-0.921225\pi$
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	0.272623	−	0.962121i	$-0.412109\pi$
$228$		0			0
$229$	−7.50000	−	4.33013i	−0.495614	−	0.286143i	0.231287	−	0.972886i	$-0.425707\pi$
$229$	−7.50000	−	4.33013i	−0.495614	−	0.286143i	−0.726900	+	0.686743i	$0.759040\pi$
$230$	27.0000			1.78033
$231$		0			0
$232$	9.00000			0.590879
$233$	4.50000	+	2.59808i	0.294805	+	0.170206i	0.640107	−	0.768286i	$-0.278890\pi$
$233$	4.50000	+	2.59808i	0.294805	+	0.170206i	−0.345302	+	0.938492i	$0.612223\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	−13.5000	+	2.59808i	−0.875075	+	0.168408i
$239$			1.73205i			0.112037i	0.998430	+	0.0560185i	$0.0178406\pi$
$239$			1.73205i			0.112037i	−0.998430	+	0.0560185i	$0.982159\pi$
$240$		0			0
$241$	−19.5000	+	11.2583i	−1.25611	+	0.725213i	−0.972315	−	0.233674i	$-0.924925\pi$
$241$	−19.5000	+	11.2583i	−1.25611	+	0.725213i	−0.283790	+	0.958886i	$0.591592\pi$
$242$	−12.0000	+	6.92820i	−0.771389	+	0.445362i
$243$		0			0
$244$		−	13.8564i		−	0.887066i
$245$	−3.00000	+	20.7846i	−0.191663	+	1.32788i
$246$		0			0
$247$	−4.50000	+	7.79423i	−0.286328	+	0.495935i
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$		0			0
$250$	4.50000	+	2.59808i	0.284605	+	0.164317i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$	30.0000	+	17.3205i	1.88237	+	1.08679i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	−0.815442	−	0.578838i	$-0.803506\pi$
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	0.909010	+	0.416775i	$0.136840\pi$
$258$		0			0
$259$	−17.5000	−	6.06218i	−1.08740	−	0.376685i
$260$		−	5.19615i		−	0.322252i
$261$		0			0
$262$	13.5000	−	7.79423i	0.834033	−	0.481529i
$263$	19.5000	−	11.2583i	1.20242	−	0.694218i	0.241329	−	0.970443i	$-0.422417\pi$
$263$	19.5000	−	11.2583i	1.20242	−	0.694218i	0.961093	+	0.276225i	$0.0890835\pi$
$264$		0			0
$265$			25.9808i			1.59599i
$266$	18.0000	−	15.5885i	1.10365	−	0.955790i
$267$		0			0
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	0.998816	−	0.0486418i	$-0.0154893\pi$
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	−0.541533	+	0.840679i	$0.682156\pi$
$270$		0			0
$271$	−10.5000	−	6.06218i	−0.637830	−	0.368251i	0.145948	−	0.989292i	$-0.453377\pi$
$271$	−10.5000	−	6.06218i	−0.637830	−	0.368251i	−0.783778	+	0.621041i	$0.786710\pi$
$272$	15.0000			0.909509
$273$		0			0
$274$	−21.0000			−1.26866
$275$	−6.00000	−	3.46410i	−0.361814	−	0.208893i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	7.50000	−	12.9904i	0.449820	−	0.779111i
$279$		0			0
$280$	4.50000	−	12.9904i	0.268926	−	0.776324i
$281$			19.0526i			1.13658i	0.822828	+	0.568290i	$0.192395\pi$
$281$			19.0526i			1.13658i	−0.822828	+	0.568290i	$0.807605\pi$
$282$		0			0
$283$	−3.00000	+	1.73205i	−0.178331	+	0.102960i	−0.586509	−	0.809943i	$-0.699498\pi$
$283$	−3.00000	+	1.73205i	−0.178331	+	0.102960i	0.408177	+	0.912903i	$0.366165\pi$
$284$	−3.00000	+	1.73205i	−0.178017	+	0.102778i
$285$		0			0
$286$		−	5.19615i		−	0.307255i
$287$	−1.50000	−	7.79423i	−0.0885422	−	0.460079i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	13.5000	+	23.3827i	0.792747	+	1.37308i
$291$		0			0
$292$	−4.50000	−	2.59808i	−0.263343	−	0.152041i
$293$	9.00000			0.525786			0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000			0.525786			0.262893	+	0.964825i	$0.415323\pi$
$294$		0			0
$295$		0			0
$296$	10.5000	+	6.06218i	0.610300	+	0.352357i
$297$		0			0
$298$	1.50000	+	2.59808i	0.0868927	+	0.150503i
$299$	4.50000	−	7.79423i	0.260242	−	0.450752i
$300$		0			0
$301$	0.500000	+	2.59808i	0.0288195	+	0.149751i
$302$			29.4449i			1.69436i
$303$		0			0
$304$	−22.5000	+	12.9904i	−1.29046	+	0.745049i
$305$	−36.0000	+	20.7846i	−2.06135	+	1.19012i
$306$		0			0
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$	−1.50000	+	4.33013i	−0.0854704	+	0.246732i
$309$		0			0
$310$	9.00000	−	15.5885i	0.511166	−	0.885365i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	18.0000	+	10.3923i	1.01742	+	0.587408i	0.913356	−	0.407163i	$-0.133482\pi$
$313$	18.0000	+	10.3923i	1.01742	+	0.587408i	0.104065	+	0.994571i	$0.466815\pi$
$314$		0			0
$315$		0			0
$316$	−8.00000			−0.450035
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$		0			0
$322$	−18.0000	+	15.5885i	−1.00310	+	0.868711i
$323$		−	15.5885i		−	0.867365i
$324$		0			0
$325$	−6.00000	+	3.46410i	−0.332820	+	0.192154i
$326$	−16.5000	+	9.52628i	−0.913850	+	0.527612i
$327$		0			0
$328$			5.19615i			0.286910i
$329$		0			0
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	7.50000	+	12.9904i	0.411616	+	0.712940i
$333$		0			0
$334$	13.5000	+	7.79423i	0.738687	+	0.426481i
$335$	12.0000			0.655630
$336$		0			0
$337$	19.0000			1.03500			0.517498	−	0.855684i	$-0.326864\pi$
$337$	19.0000			1.03500			0.517498	+	0.855684i	$0.326864\pi$
$338$	15.0000	+	8.66025i	0.815892	+	0.471056i
$339$		0			0
$340$	4.50000	+	7.79423i	0.244047	+	0.422701i
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		−	1.73205i		−	0.0933859i
$345$		0			0
$346$	−9.00000	+	5.19615i	−0.483843	+	0.279347i
$347$	3.00000	−	1.73205i	0.161048	−	0.0929814i	−0.417310	−	0.908764i	$-0.637027\pi$
$347$	3.00000	−	1.73205i	0.161048	−	0.0929814i	0.578358	+	0.815783i	$0.303694\pi$
$348$		0			0
$349$		−	12.1244i		−	0.649002i	−0.945885	−	0.324501i	$-0.894804\pi$
$349$		−	12.1244i		−	0.649002i	0.945885	−	0.324501i	$-0.105196\pi$
$350$	18.0000	−	3.46410i	0.962140	−	0.185164i
$351$		0			0
$352$	4.50000	−	7.79423i	0.239851	−	0.415434i
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	−0.997592	−	0.0693543i	$-0.977906\pi$
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	0.438733	−	0.898617i	$-0.355427\pi$
$354$		0			0
$355$	9.00000	+	5.19615i	0.477670	+	0.275783i
$356$	3.00000			0.159000
$357$		0			0
$358$	27.0000			1.42699
$359$	−19.5000	−	11.2583i	−1.02917	−	0.594192i	−0.112424	−	0.993660i	$-0.535861\pi$
$359$	−19.5000	−	11.2583i	−1.02917	−	0.594192i	−0.916747	+	0.399468i	$0.869195\pi$
$360$		0			0
$361$	4.00000	+	6.92820i	0.210526	+	0.364642i
$362$		0			0
$363$		0			0
$364$	3.00000	+	3.46410i	0.157243	+	0.181568i
$365$			15.5885i			0.815937i
$366$		0			0
$367$	4.50000	−	2.59808i	0.234898	−	0.135618i	−0.377932	−	0.925834i	$-0.623365\pi$
$367$	4.50000	−	2.59808i	0.234898	−	0.135618i	0.612830	+	0.790215i	$0.290031\pi$
$368$	22.5000	−	12.9904i	1.17289	−	0.677170i
$369$		0			0
$370$			36.3731i			1.89095i
$371$	−15.0000	−	17.3205i	−0.778761	−	0.899236i
$372$		0			0
$373$	18.5000	−	32.0429i	0.957894	−	1.65912i	0.230291	−	0.973122i	$-0.426032\pi$
$373$	18.5000	−	32.0429i	0.957894	−	1.65912i	0.727603	−	0.685999i	$-0.240634\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$		0			0
$376$		0			0
$377$	9.00000			0.463524
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−13.5000	−	7.79423i	−0.692535	−	0.399835i
$381$		0			0
$382$	15.0000	+	25.9808i	0.767467	+	1.32929i
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	−0.727851	−	0.685736i	$-0.759481\pi$
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	0.957790	+	0.287469i	$0.0928139\pi$
$384$		0			0
$385$	13.5000	−	2.59808i	0.688024	−	0.132410i
$386$			3.46410i			0.176318i
$387$		0			0
$388$	−1.50000	+	0.866025i	−0.0761510	+	0.0439658i
$389$	31.5000	−	18.1865i	1.59711	−	0.922094i	0.605074	−	0.796170i	$-0.293144\pi$
$389$	31.5000	−	18.1865i	1.59711	−	0.922094i	0.992040	−	0.125924i	$-0.0401896\pi$
$390$		0			0
$391$			15.5885i			0.788342i
$392$	4.50000	+	11.2583i	0.227284	+	0.568632i
$393$		0			0
$394$	12.0000	−	20.7846i	0.604551	−	1.04711i
$395$	12.0000	+	20.7846i	0.603786	+	1.04579i
$396$		0			0
$397$	7.50000	+	4.33013i	0.376414	+	0.217323i	0.676257	−	0.736666i	$-0.263601\pi$
$397$	7.50000	+	4.33013i	0.376414	+	0.217323i	−0.299843	+	0.953989i	$0.596934\pi$
$398$	−15.0000			−0.751882
$399$		0			0
$400$	−20.0000			−1.00000
$401$	−28.5000	−	16.4545i	−1.42322	−	0.821698i	−0.426649	−	0.904417i	$-0.640306\pi$
$401$	−28.5000	−	16.4545i	−1.42322	−	0.821698i	−0.996573	+	0.0827195i	$0.973639\pi$
$402$		0			0
$403$	−3.00000	−	5.19615i	−0.149441	−	0.258839i
$404$	−1.50000	+	2.59808i	−0.0746278	+	0.129259i
$405$		0			0
$406$	−22.5000	−	7.79423i	−1.11666	−	0.386821i
$407$			12.1244i			0.600982i
$408$		0			0
$409$	6.00000	−	3.46410i	0.296681	−	0.171289i	−0.344270	−	0.938871i	$-0.611874\pi$
$409$	6.00000	−	3.46410i	0.296681	−	0.171289i	0.640951	+	0.767582i	$0.278540\pi$
$410$	−13.5000	+	7.79423i	−0.666717	+	0.384930i
$411$		0			0
$412$		−	12.1244i		−	0.597324i
$413$		0			0
$414$		0			0
$415$	22.5000	−	38.9711i	1.10448	−	1.91302i
$416$	−4.50000	−	7.79423i	−0.220631	−	0.382143i
$417$		0			0
$418$	−13.5000	−	7.79423i	−0.660307	−	0.381228i
$419$	33.0000			1.61216			0.806078	−	0.591810i	$-0.201586\pi$
$419$	33.0000			1.61216			0.806078	+	0.591810i	$0.201586\pi$
$420$		0			0
$421$	11.0000			0.536107			0.268054	−	0.963404i	$-0.413620\pi$
$421$	11.0000			0.536107			0.268054	+	0.963404i	$0.413620\pi$
$422$	−7.50000	−	4.33013i	−0.365094	−	0.210787i
$423$		0			0
$424$	7.50000	+	12.9904i	0.364232	+	0.630869i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	12.0000	−	34.6410i	0.580721	−	1.67640i
$428$		−	8.66025i		−	0.418609i
$429$		0			0
$430$	4.50000	−	2.59808i	0.217009	−	0.125290i
$431$	13.5000	−	7.79423i	0.650272	−	0.375435i	−0.138288	−	0.990392i	$-0.544160\pi$
$431$	13.5000	−	7.79423i	0.650272	−	0.375435i	0.788560	+	0.614957i	$0.210827\pi$
$432$		0			0
$433$		−	13.8564i		−	0.665896i	−0.942945	−	0.332948i	$-0.891957\pi$
$433$		−	13.8564i		−	0.665896i	0.942945	−	0.332948i	$-0.108043\pi$
$434$	3.00000	+	15.5885i	0.144005	+	0.748270i
$435$		0			0
$436$	9.50000	−	16.4545i	0.454967	−	0.788027i
$437$	−13.5000	−	23.3827i	−0.645793	−	1.11855i
$438$		0			0
$439$	−27.0000	−	15.5885i	−1.28864	−	0.743996i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	−27.0000	−	15.5885i	−1.28864	−	0.743996i	−0.978412	+	0.206666i	$0.933739\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	9.00000			0.428086
$443$	−27.0000	−	15.5885i	−1.28281	−	0.740630i	−0.305448	−	0.952209i	$-0.598806\pi$
$443$	−27.0000	−	15.5885i	−1.28281	−	0.740630i	−0.977361	+	0.211579i	$0.932139\pi$
$444$		0			0
$445$	−4.50000	−	7.79423i	−0.213320	−	0.369482i
$446$	−4.50000	+	7.79423i	−0.213081	+	0.369067i
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$			34.6410i			1.63481i	0.576063	+	0.817405i	$0.304588\pi$
$449$			34.6410i			1.63481i	−0.576063	+	0.817405i	$0.695412\pi$
$450$		0			0
$451$	−4.50000	+	2.59808i	−0.211897	+	0.122339i
$452$	−1.50000	+	0.866025i	−0.0705541	+	0.0407344i
$453$		0			0
$454$		−	36.3731i		−	1.70707i
$455$	4.50000	−	12.9904i	0.210963	−	0.608998i
$456$		0			0
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	−0.383437	−	0.923567i	$-0.625260\pi$
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	0.991551	−	0.129718i	$-0.0414071\pi$
$458$	−7.50000	−	12.9904i	−0.350452	−	0.607001i
$459$		0			0
$460$	13.5000	+	7.79423i	0.629441	+	0.363408i
$461$	−15.0000			−0.698620			−0.349310	−	0.937007i	$-0.613584\pi$
$461$	−15.0000			−0.698620			−0.349310	+	0.937007i	$0.613584\pi$
$462$		0			0
$463$	−1.00000			−0.0464739			−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000			−0.0464739			−0.0232370	+	0.999730i	$0.507397\pi$
$464$	22.5000	+	12.9904i	1.04454	+	0.603063i
$465$		0			0
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	1.50000	−	2.59808i	0.0694117	−	0.120225i	−0.829231	−	0.558906i	$-0.811221\pi$
$467$	1.50000	−	2.59808i	0.0694117	−	0.120225i	0.898642	+	0.438682i	$0.144554\pi$
$468$		0			0
$469$	−8.00000	+	6.92820i	−0.369406	+	0.319915i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.50000	−	0.866025i	0.0689701	−	0.0398199i
$474$		0			0
$475$			20.7846i			0.953663i
$476$	−7.50000	−	2.59808i	−0.343762	−	0.119083i
$477$		0			0
$478$	−1.50000	+	2.59808i	−0.0686084	+	0.118833i
$479$	13.5000	+	23.3827i	0.616831	+	1.06838i	0.990060	+	0.140643i	$0.0449170\pi$
$479$	13.5000	+	23.3827i	0.616831	+	1.06838i	−0.373230	+	0.927739i	$0.621750\pi$
$480$		0			0
$481$	10.5000	+	6.06218i	0.478759	+	0.276412i
$482$	−39.0000			−1.77640
$483$		0			0
$484$	−8.00000			−0.363636
$485$	4.50000	+	2.59808i	0.204334	+	0.117973i
$486$		0			0
$487$	11.5000	+	19.9186i	0.521115	+	0.902597i	0.999698	+	0.0245553i	$0.00781698\pi$
$487$	11.5000	+	19.9186i	0.521115	+	0.902597i	−0.478584	+	0.878042i	$0.658850\pi$
$488$	−12.0000	+	20.7846i	−0.543214	+	0.940875i
$489$		0			0
$490$	−22.5000	+	28.5788i	−1.01645	+	1.29106i
$491$		−	25.9808i		−	1.17250i	−0.810132	−	0.586248i	$-0.800605\pi$
$491$		−	25.9808i		−	1.17250i	0.810132	−	0.586248i	$-0.199395\pi$
$492$		0			0
$493$	−13.5000	+	7.79423i	−0.608009	+	0.351034i
$494$	−13.5000	+	7.79423i	−0.607394	+	0.350679i
$495$		0			0
$496$		−	17.3205i		−	0.777714i
$497$	−9.00000	+	1.73205i	−0.403705	+	0.0776931i
$498$		0			0
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	0.437955	+	0.898997i	$0.355703\pi$
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	−0.997532	+	0.0702185i	$0.977630\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$		0			0
$502$	18.0000	+	10.3923i	0.803379	+	0.463831i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	13.5000	+	7.79423i	0.600148	+	0.346496i
$507$		0			0
$508$	10.0000	+	17.3205i	0.443678	+	0.768473i
$509$	−16.5000	+	28.5788i	−0.731350	+	1.26673i	0.224957	+	0.974369i	$0.427776\pi$
$509$	−16.5000	+	28.5788i	−0.731350	+	1.26673i	−0.956306	+	0.292366i	$0.905557\pi$
$510$		0			0
$511$	−9.00000	−	10.3923i	−0.398137	−	0.459728i
$512$		−	8.66025i		−	0.382733i
$513$		0			0
$514$	4.50000	−	2.59808i	0.198486	−	0.114596i
$515$	−31.5000	+	18.1865i	−1.38806	+	0.801394i
$516$		0			0
$517$		0			0
$518$	−21.0000	−	24.2487i	−0.922687	−	1.06543i
$519$		0			0
$520$	−4.50000	+	7.79423i	−0.197338	+	0.341800i
$521$	−22.5000	−	38.9711i	−0.985743	−	1.70736i	−0.638588	−	0.769549i	$-0.720481\pi$
$521$	−22.5000	−	38.9711i	−0.985743	−	1.70736i	−0.347155	−	0.937808i	$-0.612852\pi$
$522$		0			0
$523$	−16.5000	−	9.52628i	−0.721495	−	0.416555i	0.0938079	−	0.995590i	$-0.470096\pi$
$523$	−16.5000	−	9.52628i	−0.721495	−	0.416555i	−0.815303	+	0.579035i	$0.803429\pi$
$524$	9.00000			0.393167
$525$		0			0
$526$	39.0000			1.70048
$527$	9.00000	+	5.19615i	0.392046	+	0.226348i
$528$		0			0
$529$	2.00000	+	3.46410i	0.0869565	+	0.150613i
$530$	−22.5000	+	38.9711i	−0.977338	+	1.69280i
$531$		0			0
$532$	13.5000	−	2.59808i	0.585299	−	0.112641i
$533$			5.19615i			0.225070i
$534$		0			0
$535$	−22.5000	+	12.9904i	−0.972760	+	0.561623i
$536$	6.00000	−	3.46410i	0.259161	−	0.149626i
$537$		0			0
$538$			25.9808i			1.12011i
$539$	−7.50000	+	9.52628i	−0.323048	+	0.410326i
$540$		0			0
$541$	6.50000	−	11.2583i	0.279457	−	0.484033i	−0.691793	−	0.722096i	$-0.743179\pi$
$541$	6.50000	−	11.2583i	0.279457	−	0.484033i	0.971250	+	0.238062i	$0.0765123\pi$
$542$	−10.5000	−	18.1865i	−0.451014	−	0.781179i
$543$		0			0
$544$	13.5000	+	7.79423i	0.578808	+	0.334175i
$545$	−57.0000			−2.44161
$546$		0			0
$547$	−19.0000			−0.812381			−0.406191	−	0.913788i	$-0.633143\pi$
$547$	−19.0000			−0.812381			−0.406191	+	0.913788i	$0.633143\pi$
$548$	−10.5000	−	6.06218i	−0.448538	−	0.258963i
$549$		0			0
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	13.5000	−	23.3827i	0.575119	−	0.996136i
$552$		0			0
$553$	−20.0000	−	6.92820i	−0.850487	−	0.294617i
$554$			1.73205i			0.0735878i
$555$		0			0
$556$	7.50000	−	4.33013i	0.318071	−	0.183638i
$557$	10.5000	−	6.06218i	0.444899	−	0.256863i	−0.260774	−	0.965400i	$-0.583978\pi$
$557$	10.5000	−	6.06218i	0.444899	−	0.256863i	0.705674	+	0.708537i	$0.250645\pi$
$558$		0			0
$559$		−	1.73205i		−	0.0732579i
$560$	30.0000	−	25.9808i	1.26773	−	1.09789i
$561$		0			0
$562$	−16.5000	+	28.5788i	−0.696010	+	1.20553i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$		0			0
$565$	4.50000	+	2.59808i	0.189316	+	0.109302i
$566$	−6.00000			−0.252199
$567$		0			0
$568$	6.00000			0.251754
$569$	−6.00000	−	3.46410i	−0.251533	−	0.145223i	0.368933	−	0.929456i	$-0.379723\pi$
$569$	−6.00000	−	3.46410i	−0.251533	−	0.145223i	−0.620466	+	0.784233i	$0.713057\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	1.50000	−	2.59808i	0.0627182	−	0.108631i
$573$		0			0
$574$	4.50000	−	12.9904i	0.187826	−	0.542208i
$575$		−	20.7846i		−	0.866778i
$576$		0			0
$577$	−34.5000	+	19.9186i	−1.43625	+	0.829222i	−0.997587	−	0.0694283i	$-0.977883\pi$
$577$	−34.5000	+	19.9186i	−1.43625	+	0.829222i	−0.438667	+	0.898650i	$0.644549\pi$
$578$	12.0000	−	6.92820i	0.499134	−	0.288175i
$579$		0			0
$580$			15.5885i			0.647275i
$581$	7.50000	+	38.9711i	0.311152	+	1.61680i
$582$		0			0
$583$	−7.50000	+	12.9904i	−0.310618	+	0.538007i
$584$	4.50000	+	7.79423i	0.186211	+	0.322527i
$585$		0			0
$586$	13.5000	+	7.79423i	0.557680	+	0.321977i
$587$	−21.0000			−0.866763			−0.433381	−	0.901211i	$-0.642680\pi$
$587$	−21.0000			−0.866763			−0.433381	+	0.901211i	$0.642680\pi$
$588$		0			0
$589$	−18.0000			−0.741677
$590$		0			0
$591$		0			0
$592$	17.5000	+	30.3109i	0.719246	+	1.24577i
$593$	19.5000	−	33.7750i	0.800769	−	1.38697i	−0.118342	−	0.992973i	$-0.537758\pi$
$593$	19.5000	−	33.7750i	0.800769	−	1.38697i	0.919111	−	0.394000i	$-0.128909\pi$
$594$		0			0
$595$	4.50000	+	23.3827i	0.184482	+	0.958597i
$596$			1.73205i			0.0709476i
$597$		0			0
$598$	13.5000	−	7.79423i	0.552056	−	0.318730i
$599$	21.0000	−	12.1244i	0.858037	−	0.495388i	−0.00531761	−	0.999986i	$-0.501693\pi$
$599$	21.0000	−	12.1244i	0.858037	−	0.495388i	0.863354	+	0.504598i	$0.168359\pi$
$600$		0			0
$601$			29.4449i			1.20108i	0.799594	+	0.600541i	$0.205048\pi$
$601$			29.4449i			1.20108i	−0.799594	+	0.600541i	$0.794952\pi$
$602$	−1.50000	+	4.33013i	−0.0611354	+	0.176483i
$603$		0			0
$604$	−8.50000	+	14.7224i	−0.345860	+	0.599047i
$605$	12.0000	+	20.7846i	0.487869	+	0.845015i
$606$		0			0
$607$	13.5000	+	7.79423i	0.547948	+	0.316358i	0.748294	−	0.663367i	$-0.230873\pi$
$607$	13.5000	+	7.79423i	0.547948	+	0.316358i	−0.200346	+	0.979725i	$0.564207\pi$
$608$	−27.0000			−1.09499
$609$		0			0
$610$	−72.0000			−2.91519
$611$		0			0
$612$		0			0
$613$	−23.5000	−	40.7032i	−0.949156	−	1.64399i	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	−23.5000	−	40.7032i	−0.949156	−	1.64399i	−0.201948	−	0.979396i	$-0.564727\pi$
$614$	−21.0000	+	36.3731i	−0.847491	+	1.46790i
$615$		0			0
$616$	6.00000	−	5.19615i	0.241747	−	0.209359i
$617$		−	5.19615i		−	0.209189i	−0.994515	−	0.104595i	$-0.966645\pi$
$617$		−	5.19615i		−	0.209189i	0.994515	−	0.104595i	$-0.0333545\pi$
$618$		0			0
$619$	16.5000	−	9.52628i	0.663191	−	0.382893i	−0.130301	−	0.991475i	$-0.541594\pi$
$619$	16.5000	−	9.52628i	0.663191	−	0.382893i	0.793492	+	0.608581i	$0.208261\pi$
$620$	9.00000	−	5.19615i	0.361449	−	0.208683i
$621$		0			0
$622$		−	41.5692i		−	1.66677i
$623$	7.50000	+	2.59808i	0.300481	+	0.104090i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	18.0000	+	31.1769i	0.719425	+	1.24608i
$627$		0			0
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	12.0000	+	6.92820i	0.477334	+	0.275589i
$633$		0			0
$634$		0			0
$635$	30.0000	−	51.9615i	1.19051	−	2.06203i
$636$		0			0
$637$	4.50000	+	11.2583i	0.178296	+	0.446071i
$638$			15.5885i			0.617153i
$639$		0			0
$640$	−31.5000	+	18.1865i	−1.24515	+	0.718886i
$641$	−10.5000	+	6.06218i	−0.414725	+	0.239442i	−0.692818	−	0.721113i	$-0.743631\pi$
$641$	−10.5000	+	6.06218i	−0.414725	+	0.239442i	0.278093	+	0.960554i	$0.410298\pi$
$642$		0			0
$643$			12.1244i			0.478138i	0.971003	+	0.239069i	$0.0768422\pi$
$643$			12.1244i			0.478138i	−0.971003	+	0.239069i	$0.923158\pi$
$644$	−13.5000	+	2.59808i	−0.531975	+	0.102379i
$645$		0			0
$646$	13.5000	−	23.3827i	0.531150	−	0.919979i
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	0.835033	−	0.550200i	$-0.185449\pi$
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	−0.894004	+	0.448059i	$0.852115\pi$
$648$		0			0
$649$		0			0
$650$	−12.0000			−0.470679
$651$		0			0
$652$	−11.0000			−0.430793
$653$	−34.5000	−	19.9186i	−1.35009	−	0.779474i	−0.361828	−	0.932245i	$-0.617847\pi$
$653$	−34.5000	−	19.9186i	−1.35009	−	0.779474i	−0.988262	+	0.152771i	$0.951180\pi$
$654$		0			0
$655$	−13.5000	−	23.3827i	−0.527489	−	0.913637i
$656$	−7.50000	+	12.9904i	−0.292826	+	0.507189i
$657$		0			0
$658$		0			0
$659$		−	12.1244i		−	0.472298i	−0.971717	−	0.236149i	$-0.924115\pi$
$659$		−	12.1244i		−	0.472298i	0.971717	−	0.236149i	$-0.0758853\pi$
$660$		0			0
$661$	−36.0000	+	20.7846i	−1.40024	+	0.808428i	−0.994417	−	0.105525i	$-0.966348\pi$
$661$	−36.0000	+	20.7846i	−1.40024	+	0.808428i	−0.405821	+	0.913953i	$0.633014\pi$
$662$	12.0000	−	6.92820i	0.466393	−	0.269272i
$663$		0			0
$664$		−	25.9808i		−	1.00825i
$665$	−27.0000	−	31.1769i	−1.04702	−	1.20899i
$666$		0			0
$667$	−13.5000	+	23.3827i	−0.522722	+	0.905381i
$668$	4.50000	+	7.79423i	0.174110	+	0.301568i
$669$		0			0
$670$	18.0000	+	10.3923i	0.695401	+	0.401490i
$671$	−24.0000			−0.926510
$672$		0			0
$673$	−29.0000			−1.11787			−0.558934	−	0.829212i	$-0.688789\pi$
$673$	−29.0000			−1.11787			−0.558934	+	0.829212i	$0.688789\pi$
$674$	28.5000	+	16.4545i	1.09778	+	0.633803i
$675$		0			0
$676$	5.00000	+	8.66025i	0.192308	+	0.333087i
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$		0			0
$679$	−4.50000	+	0.866025i	−0.172694	+	0.0332350i
$680$		−	15.5885i		−	0.597790i
$681$		0			0
$682$	9.00000	−	5.19615i	0.344628	−	0.198971i
$683$	7.50000	−	4.33013i	0.286980	−	0.165688i	−0.349599	−	0.936899i	$-0.613682\pi$
$683$	7.50000	−	4.33013i	0.286980	−	0.165688i	0.636579	+	0.771212i	$0.280349\pi$
$684$		0			0
$685$			36.3731i			1.38974i
$686$	−1.50000	−	32.0429i	−0.0572703	−	1.22341i
$687$		0			0
$688$	2.50000	−	4.33013i	0.0953116	−	0.165085i
$689$	7.50000	+	12.9904i	0.285727	+	0.494894i
$690$		0			0
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	0.555976	−	0.831198i	$-0.312345\pi$
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	−0.441851	+	0.897089i	$0.645678\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	6.00000			0.227757
$695$	−22.5000	−	12.9904i	−0.853474	−	0.492753i
$696$		0			0
$697$	−4.50000	−	7.79423i	−0.170450	−	0.295227i
$698$	10.5000	−	18.1865i	0.397431	−	0.688370i
$699$		0			0
$700$	10.0000	+	3.46410i	0.377964	+	0.130931i
$701$			34.6410i			1.30837i	0.756333	+	0.654187i	$0.226989\pi$
$701$			34.6410i			1.30837i	−0.756333	+	0.654187i	$0.773011\pi$
$702$		0			0
$703$	31.5000	−	18.1865i	1.18805	−	0.685918i
$704$	−1.50000	+	0.866025i	−0.0565334	+	0.0326396i
$705$		0			0
$706$		−	36.3731i		−	1.36892i
$707$	−6.00000	+	5.19615i	−0.225653	+	0.195421i
$708$		0			0
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$	9.00000	+	15.5885i	0.337764	+	0.585024i
$711$		0			0
$712$	−4.50000	−	2.59808i	−0.168645	−	0.0973670i
$713$	18.0000			0.674105
$714$		0			0
$715$	−9.00000			−0.336581
$716$	13.5000	+	7.79423i	0.504519	+	0.291284i
$717$		0			0
$718$	−19.5000	−	33.7750i	−0.727734	−	1.26047i
$719$	−4.50000	+	7.79423i	−0.167822	+	0.290676i	−0.937654	−	0.347571i	$-0.887007\pi$
$719$	−4.50000	+	7.79423i	−0.167822	+	0.290676i	0.769832	+	0.638247i	$0.220340\pi$
$720$		0			0
$721$	10.5000	−	30.3109i	0.391040	−	1.12884i
$722$			13.8564i			0.515682i
$723$		0			0
$724$		0			0
$725$	18.0000	−	10.3923i	0.668503	−	0.385961i
$726$		0			0
$727$			12.1244i			0.449667i	0.974397	+	0.224834i	$0.0721839\pi$
$727$			12.1244i			0.449667i	−0.974397	+	0.224834i	$0.927816\pi$
$728$	−1.50000	−	7.79423i	−0.0555937	−	0.288873i
$729$		0			0
$730$	−13.5000	+	23.3827i	−0.499657	+	0.865432i
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$		0			0
$733$	−37.5000	−	21.6506i	−1.38509	−	0.799684i	−0.392337	−	0.919822i	$-0.628333\pi$
$733$	−37.5000	−	21.6506i	−1.38509	−	0.799684i	−0.992757	+	0.120137i	$0.961667\pi$
$734$	9.00000			0.332196
$735$		0			0
$736$	27.0000			0.995233
$737$	6.00000	+	3.46410i	0.221013	+	0.127602i
$738$		0			0
$739$	3.50000	+	6.06218i	0.128750	+	0.223001i	0.923192	−	0.384338i	$-0.125570\pi$
$739$	3.50000	+	6.06218i	0.128750	+	0.223001i	−0.794443	+	0.607339i	$0.792237\pi$
$740$	−10.5000	+	18.1865i	−0.385988	+	0.668550i
$741$		0			0
$742$	−7.50000	−	38.9711i	−0.275334	−	1.43068i
$743$		−	12.1244i		−	0.444799i	−0.974956	−	0.222400i	$-0.928611\pi$
$743$		−	12.1244i		−	0.444799i	0.974956	−	0.222400i	$-0.0713890\pi$
$744$		0			0
$745$	4.50000	−	2.59808i	0.164867	−	0.0951861i
$746$	55.5000	−	32.0429i	2.03200	−	1.17318i
$747$		0			0
$748$			5.19615i			0.189990i
$749$	7.50000	−	21.6506i	0.274044	−	0.791097i
$750$		0			0
$751$	−18.5000	+	32.0429i	−0.675075	+	1.16926i	0.301373	+	0.953506i	$0.402555\pi$
$751$	−18.5000	+	32.0429i	−0.675075	+	1.16926i	−0.976447	+	0.215757i	$0.930778\pi$
$752$		0			0
$753$		0			0
$754$	13.5000	+	7.79423i	0.491641	+	0.283849i
$755$	51.0000			1.85608
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	−30.0000	−	17.3205i	−1.08965	−	0.629109i
$759$		0			0
$760$	13.5000	+	23.3827i	0.489696	+	0.848179i
$761$	−22.5000	+	38.9711i	−0.815624	+	1.41270i	0.0932544	+	0.995642i	$0.470273\pi$
$761$	−22.5000	+	38.9711i	−0.815624	+	1.41270i	−0.908879	+	0.417061i	$0.863060\pi$
$762$		0			0
$763$	38.0000	−	32.9090i	1.37569	−	1.19138i
$764$			17.3205i			0.626634i
$765$		0			0
$766$	13.5000	−	7.79423i	0.487775	−	0.281617i
$767$		0			0
$768$		0			0
$769$		−	15.5885i		−	0.562134i	−0.959688	−	0.281067i	$-0.909312\pi$
$769$		−	15.5885i		−	0.562134i	0.959688	−	0.281067i	$-0.0906883\pi$
$770$	22.5000	+	7.79423i	0.810844	+	0.280885i
$771$		0			0
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	25.5000	+	44.1673i	0.917171	+	1.58859i	0.803691	+	0.595047i	$0.202867\pi$
$773$	25.5000	+	44.1673i	0.917171	+	1.58859i	0.113480	+	0.993540i	$0.463800\pi$
$774$		0			0
$775$	−12.0000	−	6.92820i	−0.431053	−	0.248868i
$776$	3.00000			0.107694
$777$		0			0
$778$	63.0000			2.25866
$779$	13.5000	+	7.79423i	0.483688	+	0.279257i
$780$		0			0
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	−13.5000	+	23.3827i	−0.482759	+	0.836163i
$783$		0			0
$784$	−5.00000	+	34.6410i	−0.178571	+	1.23718i
$785$		0			0
$786$		0			0
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.221162	−	0.975237i	$-0.429015\pi$
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.955161	+	0.296087i	$0.0956817\pi$
$788$	12.0000	−	6.92820i	0.427482	−	0.246807i
$789$		0			0
$790$			41.5692i			1.47897i
$791$	−4.50000	+	0.866025i	−0.160002	+	0.0307923i
$792$		0			0
$793$	−12.0000	+	20.7846i	−0.426132	+	0.738083i
$794$	7.50000	+	12.9904i	0.266165	+	0.461011i
$795$		0			0
$796$	−7.50000	−	4.33013i	−0.265830	−	0.153477i
$797$	45.0000			1.59398			0.796991	−	0.603991i	$-0.206424\pi$
$797$	45.0000			1.59398			0.796991	+	0.603991i	$0.206424\pi$
$798$		0			0
$799$		0			0
$800$	−18.0000	−	10.3923i	−0.636396	−	0.367423i
$801$		0			0
$802$	−28.5000	−	49.3634i	−1.00637	−	1.74308i
$803$	−4.50000	+	7.79423i	−0.158802	+	0.275052i
$804$		0			0
$805$	27.0000	+	31.1769i	0.951625	+	1.09884i
$806$		−	10.3923i		−	0.366053i
$807$		0			0
$808$	4.50000	−	2.59808i	0.158309	−	0.0914000i
$809$	−1.50000	+	0.866025i	−0.0527372	+	0.0304478i	−0.526137	−	0.850400i	$-0.676360\pi$
$809$	−1.50000	+	0.866025i	−0.0527372	+	0.0304478i	0.473400	+	0.880848i	$0.343027\pi$
$810$		0			0
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$	−9.00000	−	10.3923i	−0.315838	−	0.364698i
$813$		0			0
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$	16.5000	+	28.5788i	0.577970	+	1.00107i
$816$		0			0
$817$	−4.50000	−	2.59808i	−0.157435	−	0.0908952i
$818$	12.0000			0.419570
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−6.00000	−	3.46410i	−0.209401	−	0.120898i	0.391632	−	0.920122i	$-0.371911\pi$
$821$	−6.00000	−	3.46410i	−0.209401	−	0.120898i	−0.601033	+	0.799224i	$0.705244\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	−10.5000	+	18.1865i	−0.365785	+	0.633558i
$825$		0			0
$826$		0			0
$827$		−	24.2487i		−	0.843210i	−0.906780	−	0.421605i	$-0.861467\pi$
$827$		−	24.2487i		−	0.843210i	0.906780	−	0.421605i	$-0.138533\pi$
$828$		0			0
$829$	31.5000	−	18.1865i	1.09404	−	0.631644i	0.159391	−	0.987216i	$-0.449047\pi$
$829$	31.5000	−	18.1865i	1.09404	−	0.631644i	0.934649	+	0.355571i	$0.115714\pi$
$830$	67.5000	−	38.9711i	2.34296	−	1.35271i
$831$		0			0
$832$			1.73205i			0.0600481i
$833$	−16.5000	−	12.9904i	−0.571691	−	0.450090i
$834$		0			0
$835$	13.5000	−	23.3827i	0.467187	−	0.809191i
$836$	−4.50000	−	7.79423i	−0.155636	−	0.269569i
$837$		0			0
$838$	49.5000	+	28.5788i	1.70995	+	0.987240i
$839$	39.0000			1.34643			0.673215	−	0.739447i	$-0.264913\pi$
$839$	39.0000			1.34643			0.673215	+	0.739447i	$0.264913\pi$
$840$		0			0
$841$	2.00000			0.0689655
$842$	16.5000	+	9.52628i	0.568628	+	0.328297i
$843$		0			0
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	15.0000	−	25.9808i	0.516016	−	0.893765i
$846$		0			0
$847$	−20.0000	−	6.92820i	−0.687208	−	0.238056i
$848$			43.3013i			1.48697i
$849$		0			0
$850$	18.0000	−	10.3923i	0.617395	−	0.356453i
$851$	−31.5000	+	18.1865i	−1.07981	+	0.623426i
$852$		0			0
$853$		−	25.9808i		−	0.889564i	−0.895639	−	0.444782i	$-0.853281\pi$
$853$		−	25.9808i		−	0.889564i	0.895639	−	0.444782i	$-0.146719\pi$
$854$	48.0000	−	41.5692i	1.64253	−	1.42247i
$855$		0			0
$856$	−7.50000	+	12.9904i	−0.256345	+	0.444002i
$857$	13.5000	+	23.3827i	0.461151	+	0.798737i	0.999019	−	0.0442921i	$-0.0141032\pi$
$857$	13.5000	+	23.3827i	0.461151	+	0.798737i	−0.537867	+	0.843029i	$0.680770\pi$
$858$		0			0
$859$	43.5000	+	25.1147i	1.48420	+	0.856904i	0.999839	−	0.0179638i	$-0.00571836\pi$
$859$	43.5000	+	25.1147i	1.48420	+	0.856904i	0.484362	+	0.874868i	$0.339052\pi$
$860$	3.00000			0.102299
$861$		0			0
$862$	27.0000			0.919624
$863$	−37.5000	−	21.6506i	−1.27651	−	0.736996i	−0.300309	−	0.953842i	$-0.597090\pi$
$863$	−37.5000	−	21.6506i	−1.27651	−	0.736996i	−0.976206	+	0.216846i	$0.930423\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	12.0000	−	20.7846i	0.407777	−	0.706290i
$867$		0			0
$868$	−3.00000	+	8.66025i	−0.101827	+	0.293948i
$869$			13.8564i			0.470046i
$870$		0			0
$871$	6.00000	−	3.46410i	0.203302	−	0.117377i
$872$	−28.5000	+	16.4545i	−0.965132	+	0.557219i
$873$		0			0
$874$		−	46.7654i		−	1.58186i
$875$	1.50000	+	7.79423i	0.0507093	+	0.263493i
$876$		0			0
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	−0.992225	−	0.124459i	$-0.960280\pi$
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	0.603897	+	0.797062i	$0.293614\pi$
$878$	−27.0000	−	46.7654i	−0.911206	−	1.57825i
$879$		0			0
$880$	−22.5000	−	12.9904i	−0.758475	−	0.437906i
$881$	−54.0000			−1.81931			−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000			−1.81931			−0.909653	+	0.415369i	$0.863653\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	4.50000	+	2.59808i	0.151351	+	0.0873828i
$885$		0			0
$886$	−27.0000	−	46.7654i	−0.907083	−	1.57111i
$887$	−7.50000	+	12.9904i	−0.251825	+	0.436174i	−0.964028	−	0.265799i	$-0.914364\pi$
$887$	−7.50000	+	12.9904i	−0.251825	+	0.436174i	0.712203	+	0.701974i	$0.247698\pi$
$888$		0			0
$889$	10.0000	+	51.9615i	0.335389	+	1.74273i
$890$		−	15.5885i		−	0.522526i
$891$		0			0
$892$	−4.50000	+	2.59808i	−0.150671	+	0.0869900i
$893$		0			0
$894$		0			0
$895$		−	46.7654i		−	1.56319i
$896$	10.5000	−	30.3109i	0.350780	−	1.01262i
$897$		0			0
$898$	−30.0000	+	51.9615i	−1.00111	+	1.73398i
$899$	9.00000	+	15.5885i	0.300167	+	0.519904i
$900$		0			0
$901$	−22.5000	−	12.9904i	−0.749584	−	0.432772i
$902$	−9.00000			−0.299667
$903$		0			0
$904$	3.00000			0.0997785
$905$		0			0
$906$		0			0
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	0.664089	−	0.747653i	$-0.268820\pi$
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	−0.979531	+	0.201291i	$0.935486\pi$
$908$	10.5000	−	18.1865i	0.348455	−	0.603541i
$909$		0			0
$910$	18.0000	−	15.5885i	0.596694	−	0.516752i
$911$		−	5.19615i		−	0.172156i	−0.996288	−	0.0860781i	$-0.972567\pi$
$911$		−	5.19615i		−	0.172156i	0.996288	−	0.0860781i	$-0.0274335\pi$
$912$		0			0
$913$	22.5000	−	12.9904i	0.744641	−	0.429919i
$914$	39.0000	−	22.5167i	1.29001	−	0.744785i
$915$		0			0
$916$		−	8.66025i		−	0.286143i
$917$	22.5000	+	7.79423i	0.743015	+	0.257388i
$918$		0			0
$919$	14.5000	−	25.1147i	0.478311	−	0.828459i	−0.521380	−	0.853325i	$-0.674583\pi$
$919$	14.5000	−	25.1147i	0.478311	−	0.828459i	0.999691	+	0.0248659i	$0.00791589\pi$
$920$	−13.5000	−	23.3827i	−0.445082	−	0.770904i
$921$		0			0
$922$	−22.5000	−	12.9904i	−0.740998	−	0.427815i
$923$	6.00000			0.197492
$924$		0			0
$925$	28.0000			0.920634
$926$	−1.50000	−	0.866025i	−0.0492931	−	0.0284594i
$927$		0			0
$928$	13.5000	+	23.3827i	0.443159	+	0.767574i
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$		0			0
$931$	36.0000	+	5.19615i	1.17985	+	0.170297i
$932$			5.19615i			0.170206i
$933$		0			0
$934$	4.50000	−	2.59808i	0.147244	−	0.0850117i
$935$	13.5000	−	7.79423i	0.441497	−	0.254899i
$936$		0			0
$937$		−	13.8564i		−	0.452669i	−0.974050	−	0.226335i	$-0.927326\pi$
$937$		−	13.8564i		−	0.452669i	0.974050	−	0.226335i	$-0.0726743\pi$
$938$	−18.0000	+	3.46410i	−0.587721	+	0.113107i
$939$		0			0
$940$		0			0
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	0.974609	−	0.223912i	$-0.0718827\pi$
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	−0.681218	+	0.732081i	$0.738549\pi$
$942$		0			0
$943$	−13.5000	−	7.79423i	−0.439620	−	0.253815i
$944$		0			0
$945$		0			0
$946$	3.00000			0.0975384
$947$	45.0000	+	25.9808i	1.46230	+	0.844261i	0.999118	−	0.0419998i	$-0.0133729\pi$
$947$	45.0000	+	25.9808i	1.46230	+	0.844261i	0.463186	+	0.886261i	$0.346706\pi$
$948$		0			0
$949$	4.50000	+	7.79423i	0.146076	+	0.253011i
$950$	−18.0000	+	31.1769i	−0.583997	+	1.01151i
$951$		0			0
$952$	9.00000	+	10.3923i	0.291692	+	0.336817i
$953$			20.7846i			0.673280i	0.941634	+	0.336640i	$0.109290\pi$
$953$			20.7846i			0.673280i	−0.941634	+	0.336640i	$0.890710\pi$
$954$		0			0
$955$	45.0000	−	25.9808i	1.45617	−	0.840718i
$956$	−1.50000	+	0.866025i	−0.0485135	+	0.0280093i
$957$		0			0
$958$			46.7654i			1.51092i
$959$	−21.0000	−	24.2487i	−0.678125	−	0.783032i
$960$		0			0
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	10.5000	+	18.1865i	0.338534	+	0.586357i
$963$		0			0
$964$	−19.5000	−	11.2583i	−0.628053	−	0.362606i
$965$	6.00000			0.193147
$966$		0			0
$967$	−25.0000			−0.803946			−0.401973	−	0.915652i	$-0.631675\pi$
$967$	−25.0000			−0.803946			−0.401973	+	0.915652i	$0.631675\pi$
$968$	12.0000	+	6.92820i	0.385695	+	0.222681i
$969$		0			0
$970$	4.50000	+	7.79423i	0.144486	+	0.250258i
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.107135	+	0.994244i	$0.534168\pi$
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.807473	+	0.589904i	$0.799166\pi$
$972$		0			0
$973$	22.5000	−	4.33013i	0.721317	−	0.138817i
$974$			39.8372i			1.27647i
$975$		0			0
$976$	−60.0000	+	34.6410i	−1.92055	+	1.10883i
$977$	36.0000	−	20.7846i	1.15174	−	0.664959i	0.202431	−	0.979297i	$-0.435116\pi$
$977$	36.0000	−	20.7846i	1.15174	−	0.664959i	0.949311	+	0.314338i	$0.101783\pi$
$978$		0			0
$979$		−	5.19615i		−	0.166070i
$980$	−19.5000	+	7.79423i	−0.622905	+	0.248978i
$981$		0			0
$982$	22.5000	−	38.9711i	0.718004	−	1.24362i
$983$	19.5000	+	33.7750i	0.621953	+	1.07725i	0.989122	+	0.147100i	$0.0469940\pi$
$983$	19.5000	+	33.7750i	0.621953	+	1.07725i	−0.367168	+	0.930155i	$0.619673\pi$
$984$		0			0
$985$	−36.0000	−	20.7846i	−1.14706	−	0.662253i
$986$	−27.0000			−0.859855
$987$		0			0
$988$	−9.00000			−0.286328
$989$	4.50000	+	2.59808i	0.143092	+	0.0826140i
$990$		0			0
$991$	23.5000	+	40.7032i	0.746502	+	1.29298i	0.949490	+	0.313798i	$0.101602\pi$
$991$	23.5000	+	40.7032i	0.746502	+	1.29298i	−0.202988	+	0.979181i	$0.565065\pi$
$992$	9.00000	−	15.5885i	0.285750	−	0.494934i
$993$		0			0
$994$	−15.0000	−	5.19615i	−0.475771	−	0.164812i
$995$			25.9808i			0.823646i
$996$		0			0
$997$	−7.50000	+	4.33013i	−0.237527	+	0.137136i	−0.614040	−	0.789275i	$-0.710457\pi$
$997$	−7.50000	+	4.33013i	−0.237527	+	0.137136i	0.376512	+	0.926412i	$0.377123\pi$
$998$	−37.5000	+	21.6506i	−1.18704	+	0.685339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.p.b.404.1		2
3.2	odd	2		567.2.p.a.404.1		2
7.3	odd	6		567.2.p.a.80.1		2
9.2	odd	6		63.2.i.a.5.1	✓	2
9.4	even	3		63.2.s.a.47.1	yes	2
9.5	odd	6		189.2.s.a.89.1		2
9.7	even	3		189.2.i.a.152.1		2
21.17	even	6	inner	567.2.p.b.80.1		2
36.7	odd	6		3024.2.ca.a.2609.1		2
36.11	even	6		1008.2.ca.a.257.1		2
36.23	even	6		3024.2.df.a.1601.1		2
36.31	odd	6		1008.2.df.a.929.1		2
63.2	odd	6		441.2.o.a.293.1		2
63.4	even	3		441.2.i.a.227.1		2
63.5	even	6		1323.2.o.b.440.1		2
63.11	odd	6		441.2.s.a.374.1		2
63.13	odd	6		441.2.s.a.362.1		2
63.16	even	3		1323.2.o.b.881.1		2
63.20	even	6		441.2.i.a.68.1		2
63.23	odd	6		1323.2.o.a.440.1		2
63.25	even	3		1323.2.s.a.962.1		2
63.31	odd	6		63.2.i.a.38.1	yes	2
63.32	odd	6		1323.2.i.a.521.1		2
63.34	odd	6		1323.2.i.a.1097.1		2
63.38	even	6		63.2.s.a.59.1	yes	2
63.40	odd	6		441.2.o.a.146.1		2
63.41	even	6		1323.2.s.a.656.1		2
63.47	even	6		441.2.o.b.293.1		2
63.52	odd	6		189.2.s.a.17.1		2
63.58	even	3		441.2.o.b.146.1		2
63.59	even	6		189.2.i.a.143.1		2
63.61	odd	6		1323.2.o.a.881.1		2
252.31	even	6		1008.2.ca.a.353.1		2
252.59	odd	6		3024.2.ca.a.2033.1		2
252.115	even	6		3024.2.df.a.17.1		2
252.227	odd	6		1008.2.df.a.689.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.a.5.1	✓	2	9.2	odd	6
63.2.i.a.38.1	yes	2	63.31	odd	6
63.2.s.a.47.1	yes	2	9.4	even	3
63.2.s.a.59.1	yes	2	63.38	even	6
189.2.i.a.143.1		2	63.59	even	6
189.2.i.a.152.1		2	9.7	even	3
189.2.s.a.17.1		2	63.52	odd	6
189.2.s.a.89.1		2	9.5	odd	6
441.2.i.a.68.1		2	63.20	even	6
441.2.i.a.227.1		2	63.4	even	3
441.2.o.a.146.1		2	63.40	odd	6
441.2.o.a.293.1		2	63.2	odd	6
441.2.o.b.146.1		2	63.58	even	3
441.2.o.b.293.1		2	63.47	even	6
441.2.s.a.362.1		2	63.13	odd	6
441.2.s.a.374.1		2	63.11	odd	6
567.2.p.a.80.1		2	7.3	odd	6
567.2.p.a.404.1		2	3.2	odd	2
567.2.p.b.80.1		2	21.17	even	6	inner
567.2.p.b.404.1		2	1.1	even	1	trivial
1008.2.ca.a.257.1		2	36.11	even	6
1008.2.ca.a.353.1		2	252.31	even	6
1008.2.df.a.689.1		2	252.227	odd	6
1008.2.df.a.929.1		2	36.31	odd	6
1323.2.i.a.521.1		2	63.32	odd	6
1323.2.i.a.1097.1		2	63.34	odd	6
1323.2.o.a.440.1		2	63.23	odd	6
1323.2.o.a.881.1		2	63.61	odd	6
1323.2.o.b.440.1		2	63.5	even	6
1323.2.o.b.881.1		2	63.16	even	3
1323.2.s.a.656.1		2	63.41	even	6
1323.2.s.a.962.1		2	63.25	even	3
3024.2.ca.a.2033.1		2	252.59	odd	6
3024.2.ca.a.2609.1		2	36.7	odd	6
3024.2.df.a.17.1		2	252.115	even	6
3024.2.df.a.1601.1		2	36.23	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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.73205i q^{8} +(4.50000 - 2.59808i) q^{10} +(1.50000 - 0.866025i) q^{11} -1.73205i q^{13} +(-1.50000 + 4.33013i) q^{14} +(2.50000 - 4.33013i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-4.50000 - 2.59808i) q^{19} +3.00000 q^{20} +3.00000 q^{22} +(4.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(1.50000 - 2.59808i) q^{26} +(-2.00000 + 1.73205i) q^{28} +5.19615i q^{29} +(3.00000 - 1.73205i) q^{31} +(4.50000 - 2.59808i) q^{32} +5.19615i q^{34} +(7.50000 + 2.59808i) q^{35} +(-3.50000 + 6.06218i) q^{37} +(-4.50000 - 7.79423i) q^{38} +(-4.50000 - 2.59808i) q^{40} -3.00000 q^{41} +1.00000 q^{43} +(1.50000 + 0.866025i) q^{44} +(4.50000 + 7.79423i) q^{46} +(-6.50000 + 2.59808i) q^{49} -6.92820i q^{50} +(1.50000 - 0.866025i) q^{52} +(-7.50000 + 4.33013i) q^{53} -5.19615i q^{55} +(4.50000 - 0.866025i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(-12.0000 - 6.92820i) q^{61} +6.00000 q^{62} -1.00000 q^{64} +(-4.50000 - 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(9.00000 + 10.3923i) q^{70} +3.46410i q^{71} +(-4.50000 + 2.59808i) q^{73} +(-10.5000 + 6.06218i) q^{74} -5.19615i q^{76} +(3.00000 + 3.46410i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-7.50000 - 12.9904i) q^{80} +(-4.50000 - 2.59808i) q^{82} +15.0000 q^{83} +9.00000 q^{85} +(1.50000 + 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(1.50000 - 2.59808i) q^{89} +(4.50000 - 0.866025i) q^{91} +5.19615i q^{92} +(-13.5000 + 7.79423i) q^{95} +1.73205i q^{97} +(-12.0000 - 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + q^{4} + 3 q^{5} + q^{7} + 9 q^{10} + 3 q^{11} - 3 q^{14} + 5 q^{16} + 3 q^{17} - 9 q^{19} + 6 q^{20} + 6 q^{22} + 9 q^{23} - 4 q^{25} + 3 q^{26} - 4 q^{28} + 6 q^{31} + 9 q^{32} + 15 q^{35}+ \cdots - 24 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 + q^4 + 3 * q^5 + q^7 + 9 * q^10 + 3 * q^11 - 3 * q^14 + 5 * q^16 + 3 * q^17 - 9 * q^19 + 6 * q^20 + 6 * q^22 + 9 * q^23 - 4 * q^25 + 3 * q^26 - 4 * q^28 + 6 * q^31 + 9 * q^32 + 15 * q^35 - 7 * q^37 - 9 * q^38 - 9 * q^40 - 6 * q^41 + 2 * q^43 + 3 * q^44 + 9 * q^46 - 13 * q^49 + 3 * q^52 - 15 * q^53 + 9 * q^56 - 9 * q^58 - 24 * q^61 + 12 * q^62 - 2 * q^64 - 9 * q^65 + 4 * q^67 - 3 * q^68 + 18 * q^70 - 9 * q^73 - 21 * q^74 + 6 * q^77 - 8 * q^79 - 15 * q^80 - 9 * q^82 + 30 * q^83 + 18 * q^85 + 3 * q^86 - 3 * q^88 + 3 * q^89 + 9 * q^91 - 27 * q^95 - 24 * q^98

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