LMFDB - Embedded newform 576.3.o.a.511.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [576,3,Mod(319,576)] 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("576.319"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(576, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	576.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$15.6948632272$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			511.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	576.511
Dual form			576.3.o.a.319.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{5} +(3.00000 + 1.73205i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-10.5000 - 6.06218i) q^{11} +(-11.0000 - 19.0526i) q^{13} -12.0000 q^{15} -11.0000 q^{17} +15.5885i q^{19} +(-9.00000 + 5.19615i) q^{21} +(-21.0000 + 12.1244i) q^{23} +(4.50000 - 7.79423i) q^{25} +27.0000 q^{27} +(17.0000 - 29.4449i) q^{29} +(-6.00000 + 3.46410i) q^{31} +(31.5000 - 18.1865i) q^{33} +13.8564i q^{35} +16.0000 q^{37} +66.0000 q^{39} +(-6.50000 - 11.2583i) q^{41} +(-43.5000 - 25.1147i) q^{43} +(18.0000 - 31.1769i) q^{45} +(-3.00000 - 1.73205i) q^{47} +(-18.5000 - 32.0429i) q^{49} +(16.5000 - 28.5788i) q^{51} -52.0000 q^{53} -48.4974i q^{55} +(-40.5000 - 23.3827i) q^{57} +(-46.5000 + 26.8468i) q^{59} +(-8.00000 + 13.8564i) q^{61} -31.1769i q^{63} +(44.0000 - 76.2102i) q^{65} +(100.500 - 58.0237i) q^{67} -72.7461i q^{69} -25.0000 q^{73} +(13.5000 + 23.3827i) q^{75} +(-21.0000 - 36.3731i) q^{77} +(-24.0000 - 13.8564i) q^{79} +(-40.5000 + 70.1481i) q^{81} +(30.0000 + 17.3205i) q^{83} +(-22.0000 - 38.1051i) q^{85} +(51.0000 + 88.3346i) q^{87} -2.00000 q^{89} -76.2102i q^{91} -20.7846i q^{93} +(-54.0000 + 31.1769i) q^{95} +(21.5000 - 37.2391i) q^{97} +109.119i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 4 q^{5} + 6 q^{7} - 9 q^{9} - 21 q^{11} - 22 q^{13} - 24 q^{15} - 22 q^{17} - 18 q^{21} - 42 q^{23} + 9 q^{25} + 54 q^{27} + 34 q^{29} - 12 q^{31} + 63 q^{33} + 32 q^{37} + 132 q^{39} - 13 q^{41}+ \cdots + 43 q^{97}+O(q^{100}) $ 2 * q - 3 * q^3 + 4 * q^5 + 6 * q^7 - 9 * q^9 - 21 * q^11 - 22 * q^13 - 24 * q^15 - 22 * q^17 - 18 * q^21 - 42 * q^23 + 9 * q^25 + 54 * q^27 + 34 * q^29 - 12 * q^31 + 63 * q^33 + 32 * q^37 + 132 * q^39 - 13 * q^41 - 87 * q^43 + 36 * q^45 - 6 * q^47 - 37 * q^49 + 33 * q^51 - 104 * q^53 - 81 * q^57 - 93 * q^59 - 16 * q^61 + 88 * q^65 + 201 * q^67 - 50 * q^73 + 27 * q^75 - 42 * q^77 - 48 * q^79 - 81 * q^81 + 60 * q^83 - 44 * q^85 + 102 * q^87 - 4 * q^89 - 108 * q^95 + 43 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$3$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$4$		0			0
$5$	2.00000	+	3.46410i	0.400000	+	0.692820i	0.993725	−	0.111847i	$-0.0356768\pi$
$5$	2.00000	+	3.46410i	0.400000	+	0.692820i	−0.593725	+	0.804668i	$0.702343\pi$
$6$		0			0
$7$	3.00000	+	1.73205i	0.428571	+	0.247436i	0.698738	−	0.715378i	$-0.253745\pi$
$7$	3.00000	+	1.73205i	0.428571	+	0.247436i	−0.270166	+	0.962814i	$0.587079\pi$
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$10$		0			0
$11$	−10.5000	−	6.06218i	−0.954545	−	0.551107i	−0.0600555	−	0.998195i	$-0.519128\pi$
$11$	−10.5000	−	6.06218i	−0.954545	−	0.551107i	−0.894490	+	0.447088i	$0.852461\pi$
$12$		0			0
$13$	−11.0000	−	19.0526i	−0.846154	−	1.46558i	−0.884615	−	0.466321i	$-0.845579\pi$
$13$	−11.0000	−	19.0526i	−0.846154	−	1.46558i	0.0384615	−	0.999260i	$-0.487754\pi$
$14$		0			0
$15$	−12.0000			−0.800000
$16$		0			0
$17$	−11.0000			−0.647059			−0.323529	−	0.946218i	$-0.604869\pi$
$17$	−11.0000			−0.647059			−0.323529	+	0.946218i	$0.604869\pi$
$18$		0			0
$19$			15.5885i			0.820445i	0.911985	+	0.410223i	$0.134549\pi$
$19$			15.5885i			0.820445i	−0.911985	+	0.410223i	$0.865451\pi$
$20$		0			0
$21$	−9.00000	+	5.19615i	−0.428571	+	0.247436i
$22$		0			0
$23$	−21.0000	+	12.1244i	−0.913043	+	0.527146i	−0.881409	−	0.472354i	$-0.843405\pi$
$23$	−21.0000	+	12.1244i	−0.913043	+	0.527146i	−0.0316343	+	0.999500i	$0.510071\pi$
$24$		0			0
$25$	4.50000	−	7.79423i	0.180000	−	0.311769i
$26$		0			0
$27$	27.0000			1.00000
$28$		0			0
$29$	17.0000	−	29.4449i	0.586207	−	1.01534i	−0.408517	−	0.912751i	$-0.633954\pi$
$29$	17.0000	−	29.4449i	0.586207	−	1.01534i	0.994724	−	0.102589i	$-0.0327128\pi$
$30$		0			0
$31$	−6.00000	+	3.46410i	−0.193548	+	0.111745i	−0.593643	−	0.804729i	$-0.702311\pi$
$31$	−6.00000	+	3.46410i	−0.193548	+	0.111745i	0.400094	+	0.916474i	$0.368977\pi$
$32$		0			0
$33$	31.5000	−	18.1865i	0.954545	−	0.551107i
$34$		0			0
$35$			13.8564i			0.395897i
$36$		0			0
$37$	16.0000			0.432432			0.216216	−	0.976346i	$-0.430628\pi$
$37$	16.0000			0.432432			0.216216	+	0.976346i	$0.430628\pi$
$38$		0			0
$39$	66.0000			1.69231
$40$		0			0
$41$	−6.50000	−	11.2583i	−0.158537	−	0.274593i	0.775805	−	0.630973i	$-0.217344\pi$
$41$	−6.50000	−	11.2583i	−0.158537	−	0.274593i	−0.934341	+	0.356380i	$0.884011\pi$
$42$		0			0
$43$	−43.5000	−	25.1147i	−1.01163	−	0.584064i	−0.0999600	−	0.994991i	$-0.531871\pi$
$43$	−43.5000	−	25.1147i	−1.01163	−	0.584064i	−0.911668	+	0.410928i	$0.865205\pi$
$44$		0			0
$45$	18.0000	−	31.1769i	0.400000	−	0.692820i
$46$		0			0
$47$	−3.00000	−	1.73205i	−0.0638298	−	0.0368521i	0.467745	−	0.883863i	$-0.345066\pi$
$47$	−3.00000	−	1.73205i	−0.0638298	−	0.0368521i	−0.531575	+	0.847011i	$0.678400\pi$
$48$		0			0
$49$	−18.5000	−	32.0429i	−0.377551	−	0.653938i
$50$		0			0
$51$	16.5000	−	28.5788i	0.323529	−	0.560369i
$52$		0			0
$53$	−52.0000			−0.981132			−0.490566	−	0.871404i	$-0.663210\pi$
$53$	−52.0000			−0.981132			−0.490566	+	0.871404i	$0.663210\pi$
$54$		0			0
$55$		−	48.4974i		−	0.881771i
$56$		0			0
$57$	−40.5000	−	23.3827i	−0.710526	−	0.410223i
$58$		0			0
$59$	−46.5000	+	26.8468i	−0.788136	+	0.455030i	−0.839306	−	0.543660i	$-0.817038\pi$
$59$	−46.5000	+	26.8468i	−0.788136	+	0.455030i	0.0511702	+	0.998690i	$0.483705\pi$
$60$		0			0
$61$	−8.00000	+	13.8564i	−0.131148	+	0.227154i	−0.924119	−	0.382104i	$-0.875199\pi$
$61$	−8.00000	+	13.8564i	−0.131148	+	0.227154i	0.792972	+	0.609259i	$0.208533\pi$
$62$		0			0
$63$		−	31.1769i		−	0.494872i
$64$		0			0
$65$	44.0000	−	76.2102i	0.676923	−	1.17247i
$66$		0			0
$67$	100.500	−	58.0237i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$67$	100.500	−	58.0237i	1.50000	−	0.866025i	1.00000			$0$
$68$		0			0
$69$		−	72.7461i		−	1.05429i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	−25.0000			−0.342466			−0.171233	−	0.985231i	$-0.554775\pi$
$73$	−25.0000			−0.342466			−0.171233	+	0.985231i	$0.554775\pi$
$74$		0			0
$75$	13.5000	+	23.3827i	0.180000	+	0.311769i
$76$		0			0
$77$	−21.0000	−	36.3731i	−0.272727	−	0.472377i
$78$		0			0
$79$	−24.0000	−	13.8564i	−0.303797	−	0.175398i	0.340350	−	0.940299i	$-0.389454\pi$
$79$	−24.0000	−	13.8564i	−0.303797	−	0.175398i	−0.644148	+	0.764901i	$0.722788\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.500000	+	0.866025i
$82$		0			0
$83$	30.0000	+	17.3205i	0.361446	+	0.208681i	0.669715	−	0.742618i	$-0.266416\pi$
$83$	30.0000	+	17.3205i	0.361446	+	0.208681i	−0.308269	+	0.951299i	$0.599750\pi$
$84$		0			0
$85$	−22.0000	−	38.1051i	−0.258824	−	0.448296i
$86$		0			0
$87$	51.0000	+	88.3346i	0.586207	+	1.01534i
$88$		0			0
$89$	−2.00000			−0.0224719			−0.0112360	−	0.999937i	$-0.503577\pi$
$89$	−2.00000			−0.0224719			−0.0112360	+	0.999937i	$0.503577\pi$
$90$		0			0
$91$		−	76.2102i		−	0.837475i
$92$		0			0
$93$		−	20.7846i		−	0.223490i
$94$		0			0
$95$	−54.0000	+	31.1769i	−0.568421	+	0.328178i
$96$		0			0
$97$	21.5000	−	37.2391i	0.221649	−	0.383908i	−0.733659	−	0.679517i	$-0.762189\pi$
$97$	21.5000	−	37.2391i	0.221649	−	0.383908i	0.955309	+	0.295609i	$0.0955226\pi$
$98$		0			0
$99$			109.119i			1.10221i
$100$		0			0
$101$	−10.0000	+	17.3205i	−0.0990099	+	0.171490i	−0.911275	−	0.411798i	$-0.864901\pi$
$101$	−10.0000	+	17.3205i	−0.0990099	+	0.171490i	0.812265	+	0.583288i	$0.198234\pi$
$102$		0			0
$103$	21.0000	−	12.1244i	0.203883	−	0.117712i	−0.394582	−	0.918861i	$-0.629111\pi$
$103$	21.0000	−	12.1244i	0.203883	−	0.117712i	0.598466	+	0.801148i	$0.295777\pi$
$104$		0			0
$105$	−36.0000	−	20.7846i	−0.342857	−	0.197949i
$106$		0			0
$107$			15.5885i			0.145687i	0.997343	+	0.0728433i	$0.0232073\pi$
$107$			15.5885i			0.145687i	−0.997343	+	0.0728433i	$0.976793\pi$
$108$		0			0
$109$	88.0000			0.807339			0.403670	−	0.914905i	$-0.367734\pi$
$109$	88.0000			0.807339			0.403670	+	0.914905i	$0.367734\pi$
$110$		0			0
$111$	−24.0000	+	41.5692i	−0.216216	+	0.374497i
$112$		0			0
$113$	25.0000	+	43.3013i	0.221239	+	0.383197i	0.955184	−	0.296011i	$-0.0956566\pi$
$113$	25.0000	+	43.3013i	0.221239	+	0.383197i	−0.733946	+	0.679208i	$0.762323\pi$
$114$		0			0
$115$	−84.0000	−	48.4974i	−0.730435	−	0.421717i
$116$		0			0
$117$	−99.0000	+	171.473i	−0.846154	+	1.46558i
$118$		0			0
$119$	−33.0000	−	19.0526i	−0.277311	−	0.160106i
$120$		0			0
$121$	13.0000	+	22.5167i	0.107438	+	0.186088i
$122$		0			0
$123$	39.0000			0.317073
$124$		0			0
$125$	136.000			1.08800
$126$		0			0
$127$		−	218.238i		−	1.71841i	−0.511629	−	0.859206i	$-0.670958\pi$
$127$		−	218.238i		−	1.71841i	0.511629	−	0.859206i	$-0.329042\pi$
$128$		0			0
$129$	130.500	−	75.3442i	1.01163	−	0.584064i
$130$		0			0
$131$	−168.000	+	96.9948i	−1.28244	+	0.740419i	−0.977294	−	0.211886i	$-0.932039\pi$
$131$	−168.000	+	96.9948i	−1.28244	+	0.740419i	−0.305148	+	0.952305i	$0.598706\pi$
$132$		0			0
$133$	−27.0000	+	46.7654i	−0.203008	+	0.351619i
$134$		0			0
$135$	54.0000	+	93.5307i	0.400000	+	0.692820i
$136$		0			0
$137$	−84.5000	+	146.358i	−0.616788	+	1.06831i	0.373280	+	0.927719i	$0.378233\pi$
$137$	−84.5000	+	146.358i	−0.616788	+	1.06831i	−0.990068	+	0.140590i	$0.955100\pi$
$138$		0			0
$139$	−169.500	+	97.8609i	−1.21942	+	0.704035i	−0.964795	−	0.263004i	$-0.915287\pi$
$139$	−169.500	+	97.8609i	−1.21942	+	0.704035i	−0.254630	+	0.967039i	$0.581954\pi$
$140$		0			0
$141$	9.00000	−	5.19615i	0.0638298	−	0.0368521i
$142$		0			0
$143$			266.736i			1.86529i
$144$		0			0
$145$	136.000			0.937931
$146$		0			0
$147$	111.000			0.755102
$148$		0			0
$149$	65.0000	+	112.583i	0.436242	+	0.755593i	0.997396	−	0.0721185i	$-0.0229760\pi$
$149$	65.0000	+	112.583i	0.436242	+	0.755593i	−0.561154	+	0.827711i	$0.689643\pi$
$150$		0			0
$151$	−105.000	−	60.6218i	−0.695364	−	0.401469i	0.110254	−	0.993903i	$-0.464833\pi$
$151$	−105.000	−	60.6218i	−0.695364	−	0.401469i	−0.805618	+	0.592435i	$0.798167\pi$
$152$		0			0
$153$	49.5000	+	85.7365i	0.323529	+	0.560369i
$154$		0			0
$155$	−24.0000	−	13.8564i	−0.154839	−	0.0893962i
$156$		0			0
$157$	−2.00000	−	3.46410i	−0.0127389	−	0.0220643i	0.859586	−	0.510992i	$-0.170722\pi$
$157$	−2.00000	−	3.46410i	−0.0127389	−	0.0220643i	−0.872325	+	0.488927i	$0.837388\pi$
$158$		0			0
$159$	78.0000	−	135.100i	0.490566	−	0.849685i
$160$		0			0
$161$	−84.0000			−0.521739
$162$		0			0
$163$		−	311.769i		−	1.91269i	−0.292233	−	0.956347i	$-0.594398\pi$
$163$		−	311.769i		−	1.91269i	0.292233	−	0.956347i	$-0.405602\pi$
$164$		0			0
$165$	126.000	+	72.7461i	0.763636	+	0.440886i
$166$		0			0
$167$	−156.000	+	90.0666i	−0.934132	+	0.539321i	−0.888116	−	0.459620i	$-0.847986\pi$
$167$	−156.000	+	90.0666i	−0.934132	+	0.539321i	−0.0460158	+	0.998941i	$0.514652\pi$
$168$		0			0
$169$	−157.500	+	272.798i	−0.931953	+	1.61419i
$170$		0			0
$171$	121.500	−	70.1481i	0.710526	−	0.410223i
$172$		0			0
$173$	−1.00000	+	1.73205i	−0.00578035	+	0.0100119i	−0.868901	−	0.494986i	$-0.835173\pi$
$173$	−1.00000	+	1.73205i	−0.00578035	+	0.0100119i	0.863121	+	0.504998i	$0.168507\pi$
$174$		0			0
$175$	27.0000	−	15.5885i	0.154286	−	0.0890769i
$176$		0			0
$177$		−	161.081i		−	0.910061i
$178$		0			0
$179$			187.061i			1.04504i	0.852628	+	0.522518i	$0.175007\pi$
$179$			187.061i			1.04504i	−0.852628	+	0.522518i	$0.824993\pi$
$180$		0			0
$181$	−254.000			−1.40331			−0.701657	−	0.712514i	$-0.747556\pi$
$181$	−254.000			−1.40331			−0.701657	+	0.712514i	$0.747556\pi$
$182$		0			0
$183$	−24.0000	−	41.5692i	−0.131148	−	0.227154i
$184$		0			0
$185$	32.0000	+	55.4256i	0.172973	+	0.299598i
$186$		0			0
$187$	115.500	+	66.6840i	0.617647	+	0.356599i
$188$		0			0
$189$	81.0000	+	46.7654i	0.428571	+	0.247436i
$190$		0			0
$191$	−3.00000	−	1.73205i	−0.0157068	−	0.00906833i	0.492126	−	0.870524i	$-0.336220\pi$
$191$	−3.00000	−	1.73205i	−0.0157068	−	0.00906833i	−0.507833	+	0.861456i	$0.669553\pi$
$192$		0			0
$193$	33.5000	+	58.0237i	0.173575	+	0.300641i	0.939667	−	0.342090i	$-0.111135\pi$
$193$	33.5000	+	58.0237i	0.173575	+	0.300641i	−0.766092	+	0.642731i	$0.777801\pi$
$194$		0			0
$195$	132.000	+	228.631i	0.676923	+	1.17247i
$196$		0			0
$197$	−268.000			−1.36041			−0.680203	−	0.733024i	$-0.738108\pi$
$197$	−268.000			−1.36041			−0.680203	+	0.733024i	$0.738108\pi$
$198$		0			0
$199$			31.1769i			0.156668i	0.996927	+	0.0783340i	$0.0249600\pi$
$199$			31.1769i			0.156668i	−0.996927	+	0.0783340i	$0.975040\pi$
$200$		0			0
$201$			348.142i			1.73205i
$202$		0			0
$203$	102.000	−	58.8897i	0.502463	−	0.290097i
$204$		0			0
$205$	26.0000	−	45.0333i	0.126829	−	0.219675i
$206$		0			0
$207$	189.000	+	109.119i	0.913043	+	0.527146i
$208$		0			0
$209$	94.5000	−	163.679i	0.452153	−	0.783152i
$210$		0			0
$211$	114.000	−	65.8179i	0.540284	−	0.311933i	−0.204910	−	0.978781i	$-0.565690\pi$
$211$	114.000	−	65.8179i	0.540284	−	0.311933i	0.745194	+	0.666848i	$0.232357\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	200.918i		−	0.934502i
$216$		0			0
$217$	−24.0000			−0.110599
$218$		0			0
$219$	37.5000	−	64.9519i	0.171233	−	0.296584i
$220$		0			0
$221$	121.000	+	209.578i	0.547511	+	0.948317i
$222$		0			0
$223$	−51.0000	−	29.4449i	−0.228700	−	0.132040i	0.381272	−	0.924463i	$-0.375486\pi$
$223$	−51.0000	−	29.4449i	−0.228700	−	0.132040i	−0.609972	+	0.792423i	$0.708819\pi$
$224$		0			0
$225$	−81.0000			−0.360000
$226$		0			0
$227$	−388.500	−	224.301i	−1.71145	−	0.988108i	−0.932607	−	0.360894i	$-0.882471\pi$
$227$	−388.500	−	224.301i	−1.71145	−	0.988108i	−0.778847	−	0.627214i	$-0.784195\pi$
$228$		0			0
$229$	205.000	+	355.070i	0.895197	+	1.55053i	0.833561	+	0.552427i	$0.186298\pi$
$229$	205.000	+	355.070i	0.895197	+	1.55053i	0.0616353	+	0.998099i	$0.480368\pi$
$230$		0			0
$231$	126.000			0.545455
$232$		0			0
$233$	−65.0000			−0.278970			−0.139485	−	0.990224i	$-0.544545\pi$
$233$	−65.0000			−0.278970			−0.139485	+	0.990224i	$0.544545\pi$
$234$		0			0
$235$		−	13.8564i		−	0.0589634i
$236$		0			0
$237$	72.0000	−	41.5692i	0.303797	−	0.175398i
$238$		0			0
$239$	33.0000	−	19.0526i	0.138075	−	0.0797178i	−0.429371	−	0.903128i	$-0.641265\pi$
$239$	33.0000	−	19.0526i	0.138075	−	0.0797178i	0.567446	+	0.823410i	$0.307931\pi$
$240$		0			0
$241$	111.500	−	193.124i	0.462656	−	0.801343i	−0.536437	−	0.843941i	$-0.680230\pi$
$241$	111.500	−	193.124i	0.462656	−	0.801343i	0.999092	+	0.0425975i	$0.0135633\pi$
$242$		0			0
$243$	−121.500	−	210.444i	−0.500000	−	0.866025i
$244$		0			0
$245$	74.0000	−	128.172i	0.302041	−	0.523150i
$246$		0			0
$247$	297.000	−	171.473i	1.20243	−	0.694223i
$248$		0			0
$249$	−90.0000	+	51.9615i	−0.361446	+	0.208681i
$250$		0			0
$251$			109.119i			0.434738i	0.976090	+	0.217369i	$0.0697475\pi$
$251$			109.119i			0.434738i	−0.976090	+	0.217369i	$0.930253\pi$
$252$		0			0
$253$	294.000			1.16206
$254$		0			0
$255$	132.000			0.517647
$256$		0			0
$257$	218.500	+	378.453i	0.850195	+	1.47258i	0.881032	+	0.473056i	$0.156849\pi$
$257$	218.500	+	378.453i	0.850195	+	1.47258i	−0.0308379	+	0.999524i	$0.509818\pi$
$258$		0			0
$259$	48.0000	+	27.7128i	0.185328	+	0.106999i
$260$		0			0
$261$	−306.000			−1.17241
$262$		0			0
$263$	−273.000	−	157.617i	−1.03802	−	0.599303i	−0.118750	−	0.992924i	$-0.537889\pi$
$263$	−273.000	−	157.617i	−1.03802	−	0.599303i	−0.919273	+	0.393621i	$0.871222\pi$
$264$		0			0
$265$	−104.000	−	180.133i	−0.392453	−	0.679748i
$266$		0			0
$267$	3.00000	−	5.19615i	0.0112360	−	0.0194612i
$268$		0			0
$269$	−304.000			−1.13011			−0.565056	−	0.825053i	$-0.691145\pi$
$269$	−304.000			−1.13011			−0.565056	+	0.825053i	$0.691145\pi$
$270$		0			0
$271$			311.769i			1.15044i	0.817999	+	0.575220i	$0.195083\pi$
$271$			311.769i			1.15044i	−0.817999	+	0.575220i	$0.804917\pi$
$272$		0			0
$273$	198.000	+	114.315i	0.725275	+	0.418738i
$274$		0			0
$275$	−94.5000	+	54.5596i	−0.343636	+	0.198399i
$276$		0			0
$277$	−17.0000	+	29.4449i	−0.0613718	+	0.106299i	−0.895079	−	0.445908i	$-0.852881\pi$
$277$	−17.0000	+	29.4449i	−0.0613718	+	0.106299i	0.833707	+	0.552207i	$0.186214\pi$
$278$		0			0
$279$	54.0000	+	31.1769i	0.193548	+	0.111745i
$280$		0			0
$281$	109.000	−	188.794i	0.387900	−	0.671863i	−0.604267	−	0.796782i	$-0.706534\pi$
$281$	109.000	−	188.794i	0.387900	−	0.671863i	0.992167	+	0.124919i	$0.0398671\pi$
$282$		0			0
$283$	6.00000	−	3.46410i	0.0212014	−	0.0122406i	−0.489362	−	0.872081i	$-0.662770\pi$
$283$	6.00000	−	3.46410i	0.0212014	−	0.0122406i	0.510563	+	0.859840i	$0.329437\pi$
$284$		0			0
$285$		−	187.061i		−	0.656356i
$286$		0			0
$287$		−	45.0333i		−	0.156911i
$288$		0			0
$289$	−168.000			−0.581315
$290$		0			0
$291$	64.5000	+	111.717i	0.221649	+	0.383908i
$292$		0			0
$293$	101.000	+	174.937i	0.344710	+	0.597055i	0.985301	−	0.170827i	$-0.0546440\pi$
$293$	101.000	+	174.937i	0.344710	+	0.597055i	−0.640591	+	0.767882i	$0.721311\pi$
$294$		0			0
$295$	−186.000	−	107.387i	−0.630508	−	0.364024i
$296$		0			0
$297$	−283.500	−	163.679i	−0.954545	−	0.551107i
$298$		0			0
$299$	462.000	+	266.736i	1.54515	+	0.892093i
$300$		0			0
$301$	−87.0000	−	150.688i	−0.289037	−	0.500626i
$302$		0			0
$303$	−30.0000	−	51.9615i	−0.0990099	−	0.171490i
$304$		0			0
$305$	−64.0000			−0.209836
$306$		0			0
$307$			109.119i			0.355437i	0.984081	+	0.177719i	$0.0568717\pi$
$307$			109.119i			0.355437i	−0.984081	+	0.177719i	$0.943128\pi$
$308$		0			0
$309$			72.7461i			0.235424i
$310$		0			0
$311$	−237.000	+	136.832i	−0.762058	+	0.439974i	−0.830034	−	0.557713i	$-0.811679\pi$
$311$	−237.000	+	136.832i	−0.762058	+	0.439974i	0.0679762	+	0.997687i	$0.478346\pi$
$312$		0			0
$313$	39.5000	−	68.4160i	0.126198	−	0.218581i	−0.796003	−	0.605293i	$-0.793056\pi$
$313$	39.5000	−	68.4160i	0.126198	−	0.218581i	0.922201	+	0.386712i	$0.126389\pi$
$314$		0			0
$315$	108.000	−	62.3538i	0.342857	−	0.197949i
$316$		0			0
$317$	251.000	−	434.745i	0.791798	−	1.37143i	−0.133054	−	0.991109i	$-0.542479\pi$
$317$	251.000	−	434.745i	0.791798	−	1.37143i	0.924853	−	0.380326i	$-0.124188\pi$
$318$		0			0
$319$	−357.000	+	206.114i	−1.11912	+	0.646126i
$320$		0			0
$321$	−40.5000	−	23.3827i	−0.126168	−	0.0728433i
$322$		0			0
$323$		−	171.473i		−	0.530876i
$324$		0			0
$325$	−198.000			−0.609231
$326$		0			0
$327$	−132.000	+	228.631i	−0.403670	+	0.699176i
$328$		0			0
$329$	−6.00000	−	10.3923i	−0.0182371	−	0.0315876i
$330$		0			0
$331$	−354.000	−	204.382i	−1.06949	−	0.617468i	−0.141445	−	0.989946i	$-0.545175\pi$
$331$	−354.000	−	204.382i	−1.06949	−	0.617468i	−0.928041	+	0.372478i	$0.878508\pi$
$332$		0			0
$333$	−72.0000	−	124.708i	−0.216216	−	0.374497i
$334$		0			0
$335$	402.000	+	232.095i	1.20000	+	0.692820i
$336$		0			0
$337$	168.500	+	291.851i	0.500000	+	0.866025i	1.00000			$0$
$337$	168.500	+	291.851i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$338$		0			0
$339$	−150.000			−0.442478
$340$		0			0
$341$	84.0000			0.246334
$342$		0			0
$343$		−	297.913i		−	0.868550i
$344$		0			0
$345$	252.000	−	145.492i	0.730435	−	0.421717i
$346$		0			0
$347$	−235.500	+	135.966i	−0.678674	+	0.391833i	−0.799355	−	0.600859i	$-0.794826\pi$
$347$	−235.500	+	135.966i	−0.678674	+	0.391833i	0.120681	+	0.992691i	$0.461492\pi$
$348$		0			0
$349$	136.000	−	235.559i	0.389685	−	0.674954i	−0.602722	−	0.797951i	$-0.705917\pi$
$349$	136.000	−	235.559i	0.389685	−	0.674954i	0.992407	+	0.122997i	$0.0392506\pi$
$350$		0			0
$351$	−297.000	−	514.419i	−0.846154	−	1.46558i
$352$		0			0
$353$	230.500	−	399.238i	0.652975	−	1.13099i	−0.329423	−	0.944182i	$-0.606854\pi$
$353$	230.500	−	399.238i	0.652975	−	1.13099i	0.982397	−	0.186803i	$-0.0598125\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	99.0000	−	57.1577i	0.277311	−	0.160106i
$358$		0			0
$359$			530.008i			1.47634i	0.674612	+	0.738172i	$0.264311\pi$
$359$			530.008i			1.47634i	−0.674612	+	0.738172i	$0.735689\pi$
$360$		0			0
$361$	118.000			0.326870
$362$		0			0
$363$	−78.0000			−0.214876
$364$		0			0
$365$	−50.0000	−	86.6025i	−0.136986	−	0.237267i
$366$		0			0
$367$	84.0000	+	48.4974i	0.228883	+	0.132146i	0.610057	−	0.792358i	$-0.291147\pi$
$367$	84.0000	+	48.4974i	0.228883	+	0.132146i	−0.381174	+	0.924503i	$0.624480\pi$
$368$		0			0
$369$	−58.5000	+	101.325i	−0.158537	+	0.274593i
$370$		0			0
$371$	−156.000	−	90.0666i	−0.420485	−	0.242767i
$372$		0			0
$373$	−173.000	−	299.645i	−0.463807	−	0.803337i	0.535340	−	0.844637i	$-0.320184\pi$
$373$	−173.000	−	299.645i	−0.463807	−	0.803337i	−0.999147	+	0.0412995i	$0.986850\pi$
$374$		0			0
$375$	−204.000	+	353.338i	−0.544000	+	0.942236i
$376$		0			0
$377$	−748.000			−1.98408
$378$		0			0
$379$			327.358i			0.863740i	0.901936	+	0.431870i	$0.142146\pi$
$379$			327.358i			0.863740i	−0.901936	+	0.431870i	$0.857854\pi$
$380$		0			0
$381$	567.000	+	327.358i	1.48819	+	0.859206i
$382$		0			0
$383$	546.000	−	315.233i	1.42559	−	0.823063i	0.428819	−	0.903390i	$-0.358930\pi$
$383$	546.000	−	315.233i	1.42559	−	0.823063i	0.996769	+	0.0803272i	$0.0255965\pi$
$384$		0			0
$385$	84.0000	−	145.492i	0.218182	−	0.377902i
$386$		0			0
$387$			452.065i			1.16813i
$388$		0			0
$389$	−73.0000	+	126.440i	−0.187661	+	0.325038i	−0.944470	−	0.328598i	$-0.893424\pi$
$389$	−73.0000	+	126.440i	−0.187661	+	0.325038i	0.756809	+	0.653636i	$0.226757\pi$
$390$		0			0
$391$	231.000	−	133.368i	0.590793	−	0.341094i
$392$		0			0
$393$		−	581.969i		−	1.48084i
$394$		0			0
$395$		−	110.851i		−	0.280636i
$396$		0			0
$397$	−488.000			−1.22922			−0.614610	−	0.788831i	$-0.710686\pi$
$397$	−488.000			−1.22922			−0.614610	+	0.788831i	$0.710686\pi$
$398$		0			0
$399$	−81.0000	−	140.296i	−0.203008	−	0.351619i
$400$		0			0
$401$	−222.500	−	385.381i	−0.554863	−	0.961051i	−0.997914	−	0.0645544i	$-0.979437\pi$
$401$	−222.500	−	385.381i	−0.554863	−	0.961051i	0.443051	−	0.896496i	$-0.353896\pi$
$402$		0			0
$403$	132.000	+	76.2102i	0.327543	+	0.189107i
$404$		0			0
$405$	−324.000			−0.800000
$406$		0			0
$407$	−168.000	−	96.9948i	−0.412776	−	0.238317i
$408$		0			0
$409$	33.5000	+	58.0237i	0.0819071	+	0.141867i	0.904069	−	0.427386i	$-0.140566\pi$
$409$	33.5000	+	58.0237i	0.0819071	+	0.141867i	−0.822162	+	0.569254i	$0.807232\pi$
$410$		0			0
$411$	−253.500	−	439.075i	−0.616788	−	1.06831i
$412$		0			0
$413$	−186.000			−0.450363
$414$		0			0
$415$			138.564i			0.333889i
$416$		0			0
$417$		−	587.165i		−	1.40807i
$418$		0			0
$419$	534.000	−	308.305i	1.27446	−	0.735812i	0.298638	−	0.954366i	$-0.403468\pi$
$419$	534.000	−	308.305i	1.27446	−	0.735812i	0.975825	+	0.218555i	$0.0701342\pi$
$420$		0			0
$421$	136.000	−	235.559i	0.323040	−	0.559522i	−0.658073	−	0.752954i	$-0.728628\pi$
$421$	136.000	−	235.559i	0.323040	−	0.559522i	0.981114	+	0.193431i	$0.0619617\pi$
$422$		0			0
$423$			31.1769i			0.0737043i
$424$		0			0
$425$	−49.5000	+	85.7365i	−0.116471	+	0.201733i
$426$		0			0
$427$	−48.0000	+	27.7128i	−0.112412	+	0.0649012i
$428$		0			0
$429$	−693.000	−	400.104i	−1.61538	−	0.932643i
$430$		0			0
$431$		−	405.300i		−	0.940371i	−0.882568	−	0.470185i	$-0.844187\pi$
$431$		−	405.300i		−	0.940371i	0.882568	−	0.470185i	$-0.155813\pi$
$432$		0			0
$433$	−439.000			−1.01386			−0.506928	−	0.861988i	$-0.669219\pi$
$433$	−439.000			−1.01386			−0.506928	+	0.861988i	$0.669219\pi$
$434$		0			0
$435$	−204.000	+	353.338i	−0.468966	+	0.812272i
$436$		0			0
$437$	−189.000	−	327.358i	−0.432494	−	0.749102i
$438$		0			0
$439$	732.000	+	422.620i	1.66743	+	0.962689i	0.969018	+	0.246989i	$0.0794410\pi$
$439$	732.000	+	422.620i	1.66743	+	0.962689i	0.698408	+	0.715700i	$0.253892\pi$
$440$		0			0
$441$	−166.500	+	288.386i	−0.377551	+	0.653938i
$442$		0			0
$443$	286.500	+	165.411i	0.646727	+	0.373388i	0.787201	−	0.616696i	$-0.211529\pi$
$443$	286.500	+	165.411i	0.646727	+	0.373388i	−0.140474	+	0.990084i	$0.544863\pi$
$444$		0			0
$445$	−4.00000	−	6.92820i	−0.00898876	−	0.0155690i
$446$		0			0
$447$	−390.000			−0.872483
$448$		0			0
$449$	−47.0000			−0.104677			−0.0523385	−	0.998629i	$-0.516667\pi$
$449$	−47.0000			−0.104677			−0.0523385	+	0.998629i	$0.516667\pi$
$450$		0			0
$451$			157.617i			0.349483i
$452$		0			0
$453$	315.000	−	181.865i	0.695364	−	0.401469i
$454$		0			0
$455$	264.000	−	152.420i	0.580220	−	0.334990i
$456$		0			0
$457$	165.500	−	286.654i	0.362144	−	0.627253i	−0.626169	−	0.779687i	$-0.715378\pi$
$457$	165.500	−	286.654i	0.362144	−	0.627253i	0.988314	+	0.152435i	$0.0487114\pi$
$458$		0			0
$459$	−297.000			−0.647059
$460$		0			0
$461$	269.000	−	465.922i	0.583514	−	1.01068i	−0.411545	−	0.911390i	$-0.635011\pi$
$461$	269.000	−	465.922i	0.583514	−	1.01068i	0.995059	−	0.0992865i	$-0.0316560\pi$
$462$		0			0
$463$	−492.000	+	284.056i	−1.06263	+	0.613513i	−0.926160	−	0.377131i	$-0.876911\pi$
$463$	−492.000	+	284.056i	−1.06263	+	0.613513i	−0.136475	+	0.990644i	$0.543577\pi$
$464$		0			0
$465$	72.0000	−	41.5692i	0.154839	−	0.0893962i
$466$		0			0
$467$		−	639.127i		−	1.36858i	−0.729210	−	0.684290i	$-0.760112\pi$
$467$		−	639.127i		−	1.36858i	0.729210	−	0.684290i	$-0.239888\pi$
$468$		0			0
$469$	402.000			0.857143
$470$		0			0
$471$	12.0000			0.0254777
$472$		0			0
$473$	304.500	+	527.409i	0.643763	+	1.11503i
$474$		0			0
$475$	121.500	+	70.1481i	0.255789	+	0.147680i
$476$		0			0
$477$	234.000	+	405.300i	0.490566	+	0.849685i
$478$		0			0
$479$	105.000	+	60.6218i	0.219207	+	0.126559i	0.605583	−	0.795782i	$-0.292940\pi$
$479$	105.000	+	60.6218i	0.219207	+	0.126559i	−0.386376	+	0.922341i	$0.626273\pi$
$480$		0			0
$481$	−176.000	−	304.841i	−0.365904	−	0.633765i
$482$		0			0
$483$	126.000	−	218.238i	0.260870	−	0.451839i
$484$		0			0
$485$	172.000			0.354639
$486$		0			0
$487$		−	405.300i		−	0.832238i	−0.909310	−	0.416119i	$-0.863390\pi$
$487$		−	405.300i		−	0.832238i	0.909310	−	0.416119i	$-0.136610\pi$
$488$		0			0
$489$	810.000	+	467.654i	1.65644	+	0.956347i
$490$		0			0
$491$	628.500	−	362.865i	1.28004	−	0.739032i	0.303185	−	0.952932i	$-0.401950\pi$
$491$	628.500	−	362.865i	1.28004	−	0.739032i	0.976856	+	0.213900i	$0.0686166\pi$
$492$		0			0
$493$	−187.000	+	323.894i	−0.379310	+	0.656985i
$494$		0			0
$495$	−378.000	+	218.238i	−0.763636	+	0.440886i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	451.500	−	260.674i	0.904810	−	0.522392i	0.0260521	−	0.999661i	$-0.491706\pi$
$499$	451.500	−	260.674i	0.904810	−	0.522392i	0.878758	+	0.477269i	$0.158373\pi$
$500$		0			0
$501$		−	540.400i		−	1.07864i
$502$		0			0
$503$		−	872.954i		−	1.73549i	−0.497006	−	0.867747i	$-0.665567\pi$
$503$		−	872.954i		−	1.73549i	0.497006	−	0.867747i	$-0.334433\pi$
$504$		0			0
$505$	−80.0000			−0.158416
$506$		0			0
$507$	−472.500	−	818.394i	−0.931953	−	1.61419i
$508$		0			0
$509$	380.000	+	658.179i	0.746562	+	1.29308i	0.949461	+	0.313884i	$0.101630\pi$
$509$	380.000	+	658.179i	0.746562	+	1.29308i	−0.202900	+	0.979200i	$0.565037\pi$
$510$		0			0
$511$	−75.0000	−	43.3013i	−0.146771	−	0.0847383i
$512$		0			0
$513$			420.888i			0.820445i
$514$		0			0
$515$	84.0000	+	48.4974i	0.163107	+	0.0941698i
$516$		0			0
$517$	21.0000	+	36.3731i	0.0406190	+	0.0703541i
$518$		0			0
$519$	−3.00000	−	5.19615i	−0.00578035	−	0.0100119i
$520$		0			0
$521$	745.000			1.42994			0.714971	−	0.699154i	$-0.246440\pi$
$521$	745.000			1.42994			0.714971	+	0.699154i	$0.246440\pi$
$522$		0			0
$523$			561.184i			1.07301i	0.843897	+	0.536505i	$0.180256\pi$
$523$			561.184i			1.07301i	−0.843897	+	0.536505i	$0.819744\pi$
$524$		0			0
$525$			93.5307i			0.178154i
$526$		0			0
$527$	66.0000	−	38.1051i	0.125237	−	0.0723057i
$528$		0			0
$529$	29.5000	−	51.0955i	0.0557656	−	0.0965888i
$530$		0			0
$531$	418.500	+	241.621i	0.788136	+	0.455030i
$532$		0			0
$533$	−143.000	+	247.683i	−0.268293	+	0.464697i
$534$		0			0
$535$	−54.0000	+	31.1769i	−0.100935	+	0.0582746i
$536$		0			0
$537$	−486.000	−	280.592i	−0.905028	−	0.522518i
$538$		0			0
$539$			448.601i			0.832284i
$540$		0			0
$541$	520.000			0.961183			0.480591	−	0.876945i	$-0.340422\pi$
$541$	520.000			0.961183			0.480591	+	0.876945i	$0.340422\pi$
$542$		0			0
$543$	381.000	−	659.911i	0.701657	−	1.21531i
$544$		0			0
$545$	176.000	+	304.841i	0.322936	+	0.559341i
$546$		0			0
$547$	334.500	+	193.124i	0.611517	+	0.353060i	0.773559	−	0.633724i	$-0.218475\pi$
$547$	334.500	+	193.124i	0.611517	+	0.353060i	−0.162042	+	0.986784i	$0.551808\pi$
$548$		0			0
$549$	144.000			0.262295
$550$		0			0
$551$	459.000	+	265.004i	0.833031	+	0.480951i
$552$		0			0
$553$	−48.0000	−	83.1384i	−0.0867993	−	0.150341i
$554$		0			0
$555$	−192.000			−0.345946
$556$		0			0
$557$	−934.000			−1.67684			−0.838420	−	0.545025i	$-0.816520\pi$
$557$	−934.000			−1.67684			−0.838420	+	0.545025i	$0.816520\pi$
$558$		0			0
$559$			1105.05i			1.97683i
$560$		0			0
$561$	−346.500	+	200.052i	−0.617647	+	0.356599i
$562$		0			0
$563$	−613.500	+	354.204i	−1.08970	+	0.629137i	−0.933496	−	0.358588i	$-0.883258\pi$
$563$	−613.500	+	354.204i	−1.08970	+	0.629137i	−0.156202	+	0.987725i	$0.549925\pi$
$564$		0			0
$565$	−100.000	+	173.205i	−0.176991	+	0.306558i
$566$		0			0
$567$	−243.000	+	140.296i	−0.428571	+	0.247436i
$568$		0			0
$569$	347.500	−	601.888i	0.610721	−	1.05780i	−0.380399	−	0.924823i	$-0.624213\pi$
$569$	347.500	−	601.888i	0.610721	−	1.05780i	0.991119	−	0.132976i	$-0.0424535\pi$
$570$		0			0
$571$	−466.500	+	269.334i	−0.816988	+	0.471688i	−0.849377	−	0.527787i	$-0.823022\pi$
$571$	−466.500	+	269.334i	−0.816988	+	0.471688i	0.0323889	+	0.999475i	$0.489689\pi$
$572$		0			0
$573$	9.00000	−	5.19615i	0.0157068	−	0.00906833i
$574$		0			0
$575$			218.238i			0.379545i
$576$		0			0
$577$	227.000			0.393414			0.196707	−	0.980462i	$-0.436975\pi$
$577$	227.000			0.393414			0.196707	+	0.980462i	$0.436975\pi$
$578$		0			0
$579$	−201.000			−0.347150
$580$		0			0
$581$	60.0000	+	103.923i	0.103270	+	0.178869i
$582$		0			0
$583$	546.000	+	315.233i	0.936535	+	0.540709i
$584$		0			0
$585$	−792.000			−1.35385
$586$		0			0
$587$	124.500	+	71.8801i	0.212095	+	0.122453i	0.602285	−	0.798281i	$-0.294257\pi$
$587$	124.500	+	71.8801i	0.212095	+	0.122453i	−0.390189	+	0.920735i	$0.627590\pi$
$588$		0			0
$589$	−54.0000	−	93.5307i	−0.0916808	−	0.158796i
$590$		0			0
$591$	402.000	−	696.284i	0.680203	−	1.17815i
$592$		0			0
$593$	−506.000			−0.853288			−0.426644	−	0.904420i	$-0.640304\pi$
$593$	−506.000			−0.853288			−0.426644	+	0.904420i	$0.640304\pi$
$594$		0			0
$595$		−	152.420i		−	0.256169i
$596$		0			0
$597$	−81.0000	−	46.7654i	−0.135678	−	0.0783340i
$598$		0			0
$599$	−48.0000	+	27.7128i	−0.0801336	+	0.0462651i	−0.539531	−	0.841965i	$-0.681399\pi$
$599$	−48.0000	+	27.7128i	−0.0801336	+	0.0462651i	0.459398	+	0.888231i	$0.348065\pi$
$600$		0			0
$601$	−167.500	+	290.119i	−0.278702	+	0.482726i	−0.971062	−	0.238826i	$-0.923238\pi$
$601$	−167.500	+	290.119i	−0.278702	+	0.482726i	0.692360	+	0.721552i	$0.256571\pi$
$602$		0			0
$603$	−904.500	−	522.213i	−1.50000	−	0.866025i
$604$		0			0
$605$	−52.0000	+	90.0666i	−0.0859504	+	0.148870i
$606$		0			0
$607$	−546.000	+	315.233i	−0.899506	+	0.519330i	−0.877040	−	0.480418i	$-0.840485\pi$
$607$	−546.000	+	315.233i	−0.899506	+	0.519330i	−0.0224660	+	0.999748i	$0.507152\pi$
$608$		0			0
$609$			353.338i			0.580194i
$610$		0			0
$611$			76.2102i			0.124730i
$612$		0			0
$613$	340.000			0.554649			0.277325	−	0.960776i	$-0.410552\pi$
$613$	340.000			0.554649			0.277325	+	0.960776i	$0.410552\pi$
$614$		0			0
$615$	78.0000	+	135.100i	0.126829	+	0.219675i
$616$		0			0
$617$	−195.500	−	338.616i	−0.316856	−	0.548810i	0.662974	−	0.748642i	$-0.269294\pi$
$617$	−195.500	−	338.616i	−0.316856	−	0.548810i	−0.979830	+	0.199832i	$0.935960\pi$
$618$		0			0
$619$	10.5000	+	6.06218i	0.0169628	+	0.00979350i	0.508457	−	0.861087i	$-0.330216\pi$
$619$	10.5000	+	6.06218i	0.0169628	+	0.00979350i	−0.491495	+	0.870881i	$0.663549\pi$
$620$		0			0
$621$	−567.000	+	327.358i	−0.913043	+	0.527146i
$622$		0			0
$623$	−6.00000	−	3.46410i	−0.00963082	−	0.00556036i
$624$		0			0
$625$	159.500	+	276.262i	0.255200	+	0.442019i
$626$		0			0
$627$	283.500	+	491.036i	0.452153	+	0.783152i
$628$		0			0
$629$	−176.000			−0.279809
$630$		0			0
$631$			436.477i			0.691722i	0.938286	+	0.345861i	$0.112413\pi$
$631$			436.477i			0.691722i	−0.938286	+	0.345861i	$0.887587\pi$
$632$		0			0
$633$			394.908i			0.623867i
$634$		0			0
$635$	756.000	−	436.477i	1.19055	−	0.687365i
$636$		0			0
$637$	−407.000	+	704.945i	−0.638932	+	1.10666i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−210.500	+	364.597i	−0.328393	+	0.568794i	−0.982193	−	0.187874i	$-0.939840\pi$
$641$	−210.500	+	364.597i	−0.328393	+	0.568794i	0.653800	+	0.756667i	$0.273174\pi$
$642$		0			0
$643$	−358.500	+	206.980i	−0.557543	+	0.321897i	−0.752159	−	0.658982i	$-0.770987\pi$
$643$	−358.500	+	206.980i	−0.557543	+	0.321897i	0.194616	+	0.980880i	$0.437654\pi$
$644$		0			0
$645$	522.000	+	301.377i	0.809302	+	0.467251i
$646$		0			0
$647$		−	405.300i		−	0.626430i	−0.949682	−	0.313215i	$-0.898594\pi$
$647$		−	405.300i		−	0.626430i	0.949682	−	0.313215i	$-0.101406\pi$
$648$		0			0
$649$	651.000			1.00308
$650$		0			0
$651$	36.0000	−	62.3538i	0.0552995	−	0.0957816i
$652$		0			0
$653$	443.000	+	767.299i	0.678407	+	1.17504i	0.975460	+	0.220175i	$0.0706628\pi$
$653$	443.000	+	767.299i	0.678407	+	1.17504i	−0.297053	+	0.954861i	$0.596004\pi$
$654$		0			0
$655$	−672.000	−	387.979i	−1.02595	−	0.592335i
$656$		0			0
$657$	112.500	+	194.856i	0.171233	+	0.296584i
$658$		0			0
$659$	−726.000	−	419.156i	−1.10167	−	0.636049i	−0.165010	−	0.986292i	$-0.552766\pi$
$659$	−726.000	−	419.156i	−1.10167	−	0.636049i	−0.936659	+	0.350243i	$0.886099\pi$
$660$		0			0
$661$	124.000	+	214.774i	0.187595	+	0.324923i	0.944448	−	0.328662i	$-0.106598\pi$
$661$	124.000	+	214.774i	0.187595	+	0.324923i	−0.756853	+	0.653585i	$0.773264\pi$
$662$		0			0
$663$	−726.000			−1.09502
$664$		0			0
$665$	−216.000			−0.324812
$666$		0			0
$667$			824.456i			1.23607i
$668$		0			0
$669$	153.000	−	88.3346i	0.228700	−	0.132040i
$670$		0			0
$671$	168.000	−	96.9948i	0.250373	−	0.144553i
$672$		0			0
$673$	−577.000	+	999.393i	−0.857355	+	1.48498i	0.0170877	+	0.999854i	$0.494561\pi$
$673$	−577.000	+	999.393i	−0.857355	+	1.48498i	−0.874443	+	0.485129i	$0.838773\pi$
$674$		0			0
$675$	121.500	−	210.444i	0.180000	−	0.311769i
$676$		0			0
$677$	566.000	−	980.341i	0.836041	−	1.44807i	−0.0571384	−	0.998366i	$-0.518198\pi$
$677$	566.000	−	980.341i	0.836041	−	1.44807i	0.893180	−	0.449700i	$-0.148469\pi$
$678$		0			0
$679$	129.000	−	74.4782i	0.189985	−	0.109688i
$680$		0			0
$681$	1165.50	−	672.902i	1.71145	−	0.988108i
$682$		0			0
$683$		−	795.011i		−	1.16400i	−0.813189	−	0.582000i	$-0.802271\pi$
$683$		−	795.011i		−	1.16400i	0.813189	−	0.582000i	$-0.197729\pi$
$684$		0			0
$685$	−676.000			−0.986861
$686$		0			0
$687$	−1230.00			−1.79039
$688$		0			0
$689$	572.000	+	990.733i	0.830189	+	1.43793i
$690$		0			0
$691$	780.000	+	450.333i	1.12880	+	0.651712i	0.943633	−	0.330995i	$-0.107384\pi$
$691$	780.000	+	450.333i	1.12880	+	0.651712i	0.185166	+	0.982707i	$0.440718\pi$
$692$		0			0
$693$	−189.000	+	327.358i	−0.272727	+	0.472377i
$694$		0			0
$695$	−678.000	−	391.443i	−0.975540	−	0.563228i
$696$		0			0
$697$	71.5000	+	123.842i	0.102582	+	0.177678i
$698$		0			0
$699$	97.5000	−	168.875i	0.139485	−	0.241595i
$700$		0			0
$701$	−142.000			−0.202568			−0.101284	−	0.994858i	$-0.532295\pi$
$701$	−142.000			−0.202568			−0.101284	+	0.994858i	$0.532295\pi$
$702$		0			0
$703$			249.415i			0.354787i
$704$		0			0
$705$	36.0000	+	20.7846i	0.0510638	+	0.0294817i
$706$		0			0
$707$	−60.0000	+	34.6410i	−0.0848656	+	0.0489972i
$708$		0			0
$709$	370.000	−	640.859i	0.521862	−	0.903891i	−0.477815	−	0.878461i	$-0.658571\pi$
$709$	370.000	−	640.859i	0.521862	−	0.903891i	0.999677	−	0.0254305i	$-0.00809566\pi$
$710$		0			0
$711$			249.415i			0.350795i
$712$		0			0
$713$	84.0000	−	145.492i	0.117812	−	0.204056i
$714$		0			0
$715$	−924.000	+	533.472i	−1.29231	+	0.746114i
$716$		0			0
$717$			114.315i			0.159436i
$718$		0			0
$719$		−	124.708i		−	0.173446i	−0.996232	−	0.0867230i	$-0.972360\pi$
$719$		−	124.708i		−	0.173446i	0.996232	−	0.0867230i	$-0.0276395\pi$
$720$		0			0
$721$	84.0000			0.116505
$722$		0			0
$723$	334.500	+	579.371i	0.462656	+	0.801343i
$724$		0			0
$725$	−153.000	−	265.004i	−0.211034	−	0.365522i
$726$		0			0
$727$	705.000	+	407.032i	0.969739	+	0.559879i	0.899157	−	0.437627i	$-0.144181\pi$
$727$	705.000	+	407.032i	0.969739	+	0.559879i	0.0705821	+	0.997506i	$0.477514\pi$
$728$		0			0
$729$	729.000			1.00000
$730$		0			0
$731$	478.500	+	276.262i	0.654583	+	0.377924i
$732$		0			0
$733$	457.000	+	791.547i	0.623465	+	1.07987i	0.988836	+	0.149011i	$0.0476090\pi$
$733$	457.000	+	791.547i	0.623465	+	1.07987i	−0.365370	+	0.930862i	$0.619058\pi$
$734$		0			0
$735$	222.000	+	384.515i	0.302041	+	0.523150i
$736$		0			0
$737$	−1407.00			−1.90909
$738$		0			0
$739$		−	358.535i		−	0.485162i	−0.970131	−	0.242581i	$-0.922006\pi$
$739$		−	358.535i		−	0.485162i	0.970131	−	0.242581i	$-0.0779940\pi$
$740$		0			0
$741$			1028.84i			1.38845i
$742$		0			0
$743$	−345.000	+	199.186i	−0.464334	+	0.268083i	−0.713865	−	0.700284i	$-0.753057\pi$
$743$	−345.000	+	199.186i	−0.464334	+	0.268083i	0.249531	+	0.968367i	$0.419724\pi$
$744$		0			0
$745$	−260.000	+	450.333i	−0.348993	+	0.604474i
$746$		0			0
$747$		−	311.769i		−	0.417362i
$748$		0			0
$749$	−27.0000	+	46.7654i	−0.0360481	+	0.0624371i
$750$		0			0
$751$	966.000	−	557.720i	1.28628	−	0.742637i	0.308295	−	0.951291i	$-0.400241\pi$
$751$	966.000	−	557.720i	1.28628	−	0.742637i	0.977990	+	0.208654i	$0.0669082\pi$
$752$		0			0
$753$	−283.500	−	163.679i	−0.376494	−	0.217369i
$754$		0			0
$755$		−	484.974i		−	0.642350i
$756$		0			0
$757$	−758.000			−1.00132			−0.500661	−	0.865644i	$-0.666909\pi$
$757$	−758.000			−1.00132			−0.500661	+	0.865644i	$0.666909\pi$
$758$		0			0
$759$	−441.000	+	763.834i	−0.581028	+	1.00637i
$760$		0			0
$761$	187.000	+	323.894i	0.245729	+	0.425616i	0.962336	−	0.271861i	$-0.0876392\pi$
$761$	187.000	+	323.894i	0.245729	+	0.425616i	−0.716607	+	0.697477i	$0.754306\pi$
$762$		0			0
$763$	264.000	+	152.420i	0.346003	+	0.199765i
$764$		0			0
$765$	−198.000	+	342.946i	−0.258824	+	0.448296i
$766$		0			0
$767$	1023.00	+	590.629i	1.33377	+	0.770051i
$768$		0			0
$769$	11.0000	+	19.0526i	0.0143043	+	0.0247758i	0.873089	−	0.487561i	$-0.162113\pi$
$769$	11.0000	+	19.0526i	0.0143043	+	0.0247758i	−0.858785	+	0.512337i	$0.828780\pi$
$770$		0			0
$771$	−1311.00			−1.70039
$772$		0			0
$773$	1334.00			1.72574			0.862872	−	0.505423i	$-0.168663\pi$
$773$	1334.00			1.72574			0.862872	+	0.505423i	$0.168663\pi$
$774$		0			0
$775$			62.3538i			0.0804566i
$776$		0			0
$777$	−144.000	+	83.1384i	−0.185328	+	0.106999i
$778$		0			0
$779$	175.500	−	101.325i	0.225289	−	0.130071i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	459.000	−	795.011i	0.586207	−	1.01534i
$784$		0			0
$785$	8.00000	−	13.8564i	0.0101911	−	0.0176515i
$786$		0			0
$787$	762.000	−	439.941i	0.968234	−	0.559010i	0.0695365	−	0.997579i	$-0.477848\pi$
$787$	762.000	−	439.941i	0.968234	−	0.559010i	0.898697	+	0.438569i	$0.144515\pi$
$788$		0			0
$789$	819.000	−	472.850i	1.03802	−	0.599303i
$790$		0			0
$791$			173.205i			0.218970i
$792$		0			0
$793$	352.000			0.443884
$794$		0			0
$795$	624.000			0.784906
$796$		0			0
$797$	416.000	+	720.533i	0.521957	+	0.904057i	0.999674	+	0.0255425i	$0.00813132\pi$
$797$	416.000	+	720.533i	0.521957	+	0.904057i	−0.477716	+	0.878514i	$0.658535\pi$
$798$		0			0
$799$	33.0000	+	19.0526i	0.0413016	+	0.0238455i
$800$		0			0
$801$	9.00000	+	15.5885i	0.0112360	+	0.0194612i
$802$		0			0
$803$	262.500	+	151.554i	0.326899	+	0.188735i
$804$		0			0
$805$	−168.000	−	290.985i	−0.208696	−	0.361471i
$806$		0			0
$807$	456.000	−	789.815i	0.565056	−	0.978705i
$808$		0			0
$809$	493.000			0.609394			0.304697	−	0.952449i	$-0.401445\pi$
$809$	493.000			0.609394			0.304697	+	0.952449i	$0.401445\pi$
$810$		0			0
$811$		−	327.358i		−	0.403647i	−0.979422	−	0.201823i	$-0.935313\pi$
$811$		−	327.358i		−	0.403647i	0.979422	−	0.201823i	$-0.0646867\pi$
$812$		0			0
$813$	−810.000	−	467.654i	−0.996310	−	0.575220i
$814$		0			0
$815$	1080.00	−	623.538i	1.32515	−	0.765078i
$816$		0			0
$817$	391.500	−	678.098i	0.479192	−	0.829985i
$818$		0			0
$819$	−594.000	+	342.946i	−0.725275	+	0.418738i
$820$		0			0
$821$	−379.000	+	656.447i	−0.461632	+	0.799570i	−0.999042	−	0.0437505i	$-0.986069\pi$
$821$	−379.000	+	656.447i	−0.461632	+	0.799570i	0.537410	+	0.843321i	$0.319403\pi$
$822$		0			0
$823$	750.000	−	433.013i	0.911300	−	0.526139i	0.0304509	−	0.999536i	$-0.490306\pi$
$823$	750.000	−	433.013i	0.911300	−	0.526139i	0.880849	+	0.473397i	$0.156972\pi$
$824$		0			0
$825$		−	327.358i		−	0.396797i
$826$		0			0
$827$			436.477i			0.527783i	0.964552	+	0.263892i	$0.0850061\pi$
$827$			436.477i			0.527783i	−0.964552	+	0.263892i	$0.914994\pi$
$828$		0			0
$829$	718.000			0.866104			0.433052	−	0.901369i	$-0.357437\pi$
$829$	718.000			0.866104			0.433052	+	0.901369i	$0.357437\pi$
$830$		0			0
$831$	−51.0000	−	88.3346i	−0.0613718	−	0.106299i
$832$		0			0
$833$	203.500	+	352.472i	0.244298	+	0.423136i
$834$		0			0
$835$	−624.000	−	360.267i	−0.747305	−	0.431457i
$836$		0			0
$837$	−162.000	+	93.5307i	−0.193548	+	0.111745i
$838$		0			0
$839$	−786.000	−	453.797i	−0.936830	−	0.540879i	−0.0478645	−	0.998854i	$-0.515242\pi$
$839$	−786.000	−	453.797i	−0.936830	−	0.540879i	−0.888965	+	0.457975i	$0.848575\pi$
$840$		0			0
$841$	−157.500	−	272.798i	−0.187277	−	0.324373i
$842$		0			0
$843$	327.000	+	566.381i	0.387900	+	0.671863i
$844$		0			0
$845$	−1260.00			−1.49112
$846$		0			0
$847$			90.0666i			0.106336i
$848$		0			0
$849$			20.7846i			0.0244813i
$850$		0			0
$851$	−336.000	+	193.990i	−0.394830	+	0.227955i
$852$		0			0
$853$	73.0000	−	126.440i	0.0855803	−	0.148229i	−0.820058	−	0.572280i	$-0.806059\pi$
$853$	73.0000	−	126.440i	0.0855803	−	0.148229i	0.905638	+	0.424051i	$0.139392\pi$
$854$		0			0
$855$	486.000	+	280.592i	0.568421	+	0.328178i
$856$		0			0
$857$	73.0000	−	126.440i	0.0851809	−	0.147538i	−0.820287	−	0.571952i	$-0.806187\pi$
$857$	73.0000	−	126.440i	0.0851809	−	0.147538i	0.905468	+	0.424414i	$0.139520\pi$
$858$		0			0
$859$	73.5000	−	42.4352i	0.0855646	−	0.0494008i	−0.456607	−	0.889668i	$-0.650936\pi$
$859$	73.5000	−	42.4352i	0.0855646	−	0.0494008i	0.542172	+	0.840268i	$0.317602\pi$
$860$		0			0
$861$	117.000	+	67.5500i	0.135889	+	0.0784553i
$862$		0			0
$863$			1184.72i			1.37280i	0.727226	+	0.686398i	$0.240809\pi$
$863$			1184.72i			1.37280i	−0.727226	+	0.686398i	$0.759191\pi$
$864$		0			0
$865$	−8.00000			−0.00924855
$866$		0			0
$867$	252.000	−	436.477i	0.290657	−	0.503433i
$868$		0			0
$869$	168.000	+	290.985i	0.193326	+	0.334850i
$870$		0			0
$871$	−2211.00	−	1276.52i	−2.53846	−	1.46558i
$872$		0			0
$873$	−387.000			−0.443299
$874$		0			0
$875$	408.000	+	235.559i	0.466286	+	0.269210i
$876$		0			0
$877$	−740.000	−	1281.72i	−0.843786	−	1.46148i	−0.886672	−	0.462400i	$-0.846989\pi$
$877$	−740.000	−	1281.72i	−0.843786	−	1.46148i	0.0428860	−	0.999080i	$-0.486345\pi$
$878$		0			0
$879$	−606.000			−0.689420
$880$		0			0
$881$	142.000			0.161180			0.0805902	−	0.996747i	$-0.474319\pi$
$881$	142.000			0.161180			0.0805902	+	0.996747i	$0.474319\pi$
$882$		0			0
$883$		−	1200.31i		−	1.35936i	−0.733511	−	0.679678i	$-0.762120\pi$
$883$		−	1200.31i		−	1.35936i	0.733511	−	0.679678i	$-0.237880\pi$
$884$		0			0
$885$	558.000	−	322.161i	0.630508	−	0.364024i
$886$		0			0
$887$	546.000	−	315.233i	0.615558	−	0.355393i	−0.159580	−	0.987185i	$-0.551014\pi$
$887$	546.000	−	315.233i	0.615558	−	0.355393i	0.775138	+	0.631792i	$0.217681\pi$
$888$		0			0
$889$	378.000	−	654.715i	0.425197	−	0.736463i
$890$		0			0
$891$	850.500	−	491.036i	0.954545	−	0.551107i
$892$		0			0
$893$	27.0000	−	46.7654i	0.0302352	−	0.0523688i
$894$		0			0
$895$	−648.000	+	374.123i	−0.724022	+	0.418014i
$896$		0			0
$897$	−1386.00	+	800.207i	−1.54515	+	0.892093i
$898$		0			0
$899$			235.559i			0.262023i
$900$		0			0
$901$	572.000			0.634850
$902$		0			0
$903$	522.000			0.578073
$904$		0			0
$905$	−508.000	−	879.882i	−0.561326	−	0.972245i
$906$		0			0
$907$	−556.500	−	321.295i	−0.613561	−	0.354240i	0.160797	−	0.986988i	$-0.448594\pi$
$907$	−556.500	−	321.295i	−0.613561	−	0.354240i	−0.774358	+	0.632748i	$0.781927\pi$
$908$		0			0
$909$	180.000			0.198020
$910$		0			0
$911$	348.000	+	200.918i	0.381998	+	0.220547i	0.678687	−	0.734428i	$-0.262549\pi$
$911$	348.000	+	200.918i	0.381998	+	0.220547i	−0.296689	+	0.954974i	$0.595883\pi$
$912$		0			0
$913$	−210.000	−	363.731i	−0.230011	−	0.398391i
$914$		0			0
$915$	96.0000	−	166.277i	0.104918	−	0.181723i
$916$		0			0
$917$	−672.000			−0.732824
$918$		0			0
$919$		−	779.423i		−	0.848121i	−0.905634	−	0.424060i	$-0.860604\pi$
$919$		−	779.423i		−	0.848121i	0.905634	−	0.424060i	$-0.139396\pi$
$920$		0			0
$921$	−283.500	−	163.679i	−0.307818	−	0.177719i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	72.0000	−	124.708i	0.0778378	−	0.134819i
$926$		0			0
$927$	−189.000	−	109.119i	−0.203883	−	0.117712i
$928$		0			0
$929$	379.000	−	656.447i	0.407966	−	0.706617i	−0.586696	−	0.809807i	$-0.699572\pi$
$929$	379.000	−	656.447i	0.407966	−	0.706617i	0.994662	+	0.103190i	$0.0329050\pi$
$930$		0			0
$931$	499.500	−	288.386i	0.536520	−	0.309760i
$932$		0			0
$933$		−	820.992i		−	0.879949i
$934$		0			0
$935$			533.472i			0.570558i
$936$		0			0
$937$	−754.000			−0.804696			−0.402348	−	0.915487i	$-0.631806\pi$
$937$	−754.000			−0.804696			−0.402348	+	0.915487i	$0.631806\pi$
$938$		0			0
$939$	118.500	+	205.248i	0.126198	+	0.218581i
$940$		0			0
$941$	−898.000	−	1555.38i	−0.954304	−	1.65290i	−0.735953	−	0.677033i	$-0.763266\pi$
$941$	−898.000	−	1555.38i	−0.954304	−	1.65290i	−0.218351	−	0.975870i	$-0.570068\pi$
$942$		0			0
$943$	273.000	+	157.617i	0.289502	+	0.167144i
$944$		0			0
$945$			374.123i			0.395897i
$946$		0			0
$947$	−91.5000	−	52.8275i	−0.0966209	−	0.0557841i	0.450911	−	0.892569i	$-0.351099\pi$
$947$	−91.5000	−	52.8275i	−0.0966209	−	0.0557841i	−0.547532	+	0.836785i	$0.684433\pi$
$948$		0			0
$949$	275.000	+	476.314i	0.289779	+	0.501911i
$950$		0			0
$951$	753.000	+	1304.23i	0.791798	+	1.37143i
$952$		0			0
$953$	1213.00			1.27282			0.636411	−	0.771350i	$-0.280418\pi$
$953$	1213.00			1.27282			0.636411	+	0.771350i	$0.280418\pi$
$954$		0			0
$955$		−	13.8564i		−	0.0145093i
$956$		0			0
$957$		−	1236.68i		−	1.29225i
$958$		0			0
$959$	−507.000	+	292.717i	−0.528676	+	0.305231i
$960$		0			0
$961$	−456.500	+	790.681i	−0.475026	+	0.822769i
$962$		0			0
$963$	121.500	−	70.1481i	0.126168	−	0.0728433i
$964$		0			0
$965$	−134.000	+	232.095i	−0.138860	+	0.240513i
$966$		0			0
$967$	−303.000	+	174.937i	−0.313340	+	0.180907i	−0.648420	−	0.761283i	$-0.724570\pi$
$967$	−303.000	+	174.937i	−0.313340	+	0.180907i	0.335080	+	0.942190i	$0.391237\pi$
$968$		0			0
$969$	445.500	+	257.210i	0.459752	+	0.265438i
$970$		0			0
$971$			1434.14i			1.47697i	0.674270	+	0.738485i	$0.264458\pi$
$971$			1434.14i			1.47697i	−0.674270	+	0.738485i	$0.735542\pi$
$972$		0			0
$973$	−678.000			−0.696814
$974$		0			0
$975$	297.000	−	514.419i	0.304615	−	0.527609i
$976$		0			0
$977$	−78.5000	−	135.966i	−0.0803480	−	0.139167i	0.823051	−	0.567967i	$-0.192270\pi$
$977$	−78.5000	−	135.966i	−0.0803480	−	0.139167i	−0.903399	+	0.428800i	$0.858936\pi$
$978$		0			0
$979$	21.0000	+	12.1244i	0.0214505	+	0.0123844i
$980$		0			0
$981$	−396.000	−	685.892i	−0.403670	−	0.699176i
$982$		0			0
$983$	−1218.00	−	703.213i	−1.23906	−	0.715374i	−0.270161	−	0.962815i	$-0.587077\pi$
$983$	−1218.00	−	703.213i	−1.23906	−	0.715374i	−0.968903	+	0.247441i	$0.920410\pi$
$984$		0			0
$985$	−536.000	−	928.379i	−0.544162	−	0.942517i
$986$		0			0
$987$	36.0000			0.0364742
$988$		0			0
$989$	1218.00			1.23155
$990$		0			0
$991$			249.415i			0.251680i	0.992051	+	0.125840i	$0.0401627\pi$
$991$			249.415i			0.251680i	−0.992051	+	0.125840i	$0.959837\pi$
$992$		0			0
$993$	1062.00	−	613.146i	1.06949	−	0.617468i
$994$		0			0
$995$	−108.000	+	62.3538i	−0.108543	+	0.0626672i
$996$		0			0
$997$	−206.000	+	356.802i	−0.206620	+	0.357876i	−0.950648	−	0.310273i	$-0.899580\pi$
$997$	−206.000	+	356.802i	−0.206620	+	0.357876i	0.744028	+	0.668149i	$0.232913\pi$
$998$		0			0
$999$	432.000			0.432432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.o.a.511.1		2
3.2	odd	2		1728.3.o.b.127.1		2
4.3	odd	2		576.3.o.b.511.1		2
8.3	odd	2		36.3.f.b.7.1	yes	2
8.5	even	2		36.3.f.a.7.1	✓	2
9.4	even	3		576.3.o.b.319.1		2
9.5	odd	6		1728.3.o.a.1279.1		2
12.11	even	2		1728.3.o.a.127.1		2
24.5	odd	2		108.3.f.b.19.1		2
24.11	even	2		108.3.f.a.19.1		2
36.23	even	6		1728.3.o.b.1279.1		2
36.31	odd	6	inner	576.3.o.a.319.1		2
72.5	odd	6		108.3.f.a.91.1		2
72.11	even	6		324.3.d.c.163.2		2
72.13	even	6		36.3.f.b.31.1	yes	2
72.29	odd	6		324.3.d.c.163.1		2
72.43	odd	6		324.3.d.b.163.1		2
72.59	even	6		108.3.f.b.91.1		2
72.61	even	6		324.3.d.b.163.2		2
72.67	odd	6		36.3.f.a.31.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.a.7.1	✓	2	8.5	even	2
36.3.f.a.31.1	yes	2	72.67	odd	6
36.3.f.b.7.1	yes	2	8.3	odd	2
36.3.f.b.31.1	yes	2	72.13	even	6
108.3.f.a.19.1		2	24.11	even	2
108.3.f.a.91.1		2	72.5	odd	6
108.3.f.b.19.1		2	24.5	odd	2
108.3.f.b.91.1		2	72.59	even	6
324.3.d.b.163.1		2	72.43	odd	6
324.3.d.b.163.2		2	72.61	even	6
324.3.d.c.163.1		2	72.29	odd	6
324.3.d.c.163.2		2	72.11	even	6
576.3.o.a.319.1		2	36.31	odd	6	inner
576.3.o.a.511.1		2	1.1	even	1	trivial
576.3.o.b.319.1		2	9.4	even	3
576.3.o.b.511.1		2	4.3	odd	2
1728.3.o.a.127.1		2	12.11	even	2
1728.3.o.a.1279.1		2	9.5	odd	6
1728.3.o.b.127.1		2	3.2	odd	2
1728.3.o.b.1279.1		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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{5} +(3.00000 + 1.73205i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-10.5000 - 6.06218i) q^{11} +(-11.0000 - 19.0526i) q^{13} -12.0000 q^{15} -11.0000 q^{17} +15.5885i q^{19} +(-9.00000 + 5.19615i) q^{21} +(-21.0000 + 12.1244i) q^{23} +(4.50000 - 7.79423i) q^{25} +27.0000 q^{27} +(17.0000 - 29.4449i) q^{29} +(-6.00000 + 3.46410i) q^{31} +(31.5000 - 18.1865i) q^{33} +13.8564i q^{35} +16.0000 q^{37} +66.0000 q^{39} +(-6.50000 - 11.2583i) q^{41} +(-43.5000 - 25.1147i) q^{43} +(18.0000 - 31.1769i) q^{45} +(-3.00000 - 1.73205i) q^{47} +(-18.5000 - 32.0429i) q^{49} +(16.5000 - 28.5788i) q^{51} -52.0000 q^{53} -48.4974i q^{55} +(-40.5000 - 23.3827i) q^{57} +(-46.5000 + 26.8468i) q^{59} +(-8.00000 + 13.8564i) q^{61} -31.1769i q^{63} +(44.0000 - 76.2102i) q^{65} +(100.500 - 58.0237i) q^{67} -72.7461i q^{69} -25.0000 q^{73} +(13.5000 + 23.3827i) q^{75} +(-21.0000 - 36.3731i) q^{77} +(-24.0000 - 13.8564i) q^{79} +(-40.5000 + 70.1481i) q^{81} +(30.0000 + 17.3205i) q^{83} +(-22.0000 - 38.1051i) q^{85} +(51.0000 + 88.3346i) q^{87} -2.00000 q^{89} -76.2102i q^{91} -20.7846i q^{93} +(-54.0000 + 31.1769i) q^{95} +(21.5000 - 37.2391i) q^{97} +109.119i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 4 q^{5} + 6 q^{7} - 9 q^{9} - 21 q^{11} - 22 q^{13} - 24 q^{15} - 22 q^{17} - 18 q^{21} - 42 q^{23} + 9 q^{25} + 54 q^{27} + 34 q^{29} - 12 q^{31} + 63 q^{33} + 32 q^{37} + 132 q^{39} - 13 q^{41}+ \cdots + 43 q^{97}+O(q^{100}) \) 2 * q - 3 * q^3 + 4 * q^5 + 6 * q^7 - 9 * q^9 - 21 * q^11 - 22 * q^13 - 24 * q^15 - 22 * q^17 - 18 * q^21 - 42 * q^23 + 9 * q^25 + 54 * q^27 + 34 * q^29 - 12 * q^31 + 63 * q^33 + 32 * q^37 + 132 * q^39 - 13 * q^41 - 87 * q^43 + 36 * q^45 - 6 * q^47 - 37 * q^49 + 33 * q^51 - 104 * q^53 - 81 * q^57 - 93 * q^59 - 16 * q^61 + 88 * q^65 + 201 * q^67 - 50 * q^73 + 27 * q^75 - 42 * q^77 - 48 * q^79 - 81 * q^81 + 60 * q^83 - 44 * q^85 + 102 * q^87 - 4 * q^89 - 108 * q^95 + 43 * q^97

Introduction

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