LMFDB - Embedded newform 1014.3.f.l.577.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1014,3,Mod(577,1014)] 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("1014.577"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1014, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1014.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,24,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$27.6294988061$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.10
Character	$\chi$	$=$	1014.577
Dual form			1014.3.f.l.775.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-3.76999 + 3.76999i) q^{5} +(1.73205 - 1.73205i) q^{6} +(-3.86894 - 3.86894i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +7.53998i q^{10} +(3.48592 + 3.48592i) q^{11} -3.46410i q^{12} -7.73788 q^{14} +(-6.52981 + 6.52981i) q^{15} -4.00000 q^{16} +26.1246i q^{17} +(3.00000 - 3.00000i) q^{18} +(21.7198 - 21.7198i) q^{19} +(7.53998 + 7.53998i) q^{20} +(-6.70120 - 6.70120i) q^{21} +6.97184 q^{22} +37.2382i q^{23} +(-3.46410 - 3.46410i) q^{24} -3.42563i q^{25} +5.19615 q^{27} +(-7.73788 + 7.73788i) q^{28} +36.3770 q^{29} +13.0596i q^{30} +(-3.56835 + 3.56835i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(6.03779 + 6.03779i) q^{33} +(26.1246 + 26.1246i) q^{34} +29.1717 q^{35} -6.00000i q^{36} +(-10.3200 - 10.3200i) q^{37} -43.4397i q^{38} +15.0800 q^{40} +(7.79177 - 7.79177i) q^{41} -13.4024 q^{42} +38.2640i q^{43} +(6.97184 - 6.97184i) q^{44} +(-11.3100 + 11.3100i) q^{45} +(37.2382 + 37.2382i) q^{46} +(27.8611 + 27.8611i) q^{47} -6.92820 q^{48} -19.0626i q^{49} +(-3.42563 - 3.42563i) q^{50} +45.2491i q^{51} +49.9991 q^{53} +(5.19615 - 5.19615i) q^{54} -26.2838 q^{55} +15.4758i q^{56} +(37.6199 - 37.6199i) q^{57} +(36.3770 - 36.3770i) q^{58} +(-19.1413 - 19.1413i) q^{59} +(13.0596 + 13.0596i) q^{60} +83.7923 q^{61} +7.13670i q^{62} +(-11.6068 - 11.6068i) q^{63} +8.00000i q^{64} +12.0756 q^{66} +(-83.7289 + 83.7289i) q^{67} +52.2492 q^{68} +64.4984i q^{69} +(29.1717 - 29.1717i) q^{70} +(27.7368 - 27.7368i) q^{71} +(-6.00000 - 6.00000i) q^{72} +(76.1331 + 76.1331i) q^{73} -20.6400 q^{74} -5.93337i q^{75} +(-43.4397 - 43.4397i) q^{76} -26.9736i q^{77} +103.672 q^{79} +(15.0800 - 15.0800i) q^{80} +9.00000 q^{81} -15.5835i q^{82} +(-49.8772 + 49.8772i) q^{83} +(-13.4024 + 13.4024i) q^{84} +(-98.4894 - 98.4894i) q^{85} +(38.2640 + 38.2640i) q^{86} +63.0069 q^{87} -13.9437i q^{88} +(31.2373 + 31.2373i) q^{89} +22.6199i q^{90} +74.4764 q^{92} +(-6.18056 + 6.18056i) q^{93} +55.7222 q^{94} +163.767i q^{95} +(-6.92820 + 6.92820i) q^{96} +(-99.3124 + 99.3124i) q^{97} +(-19.0626 - 19.0626i) q^{98} +(10.4578 + 10.4578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 8 q^{5} + 24 q^{7} - 48 q^{8} + 72 q^{9} + 64 q^{11} + 48 q^{14} + 24 q^{15} - 96 q^{16} + 72 q^{18} + 160 q^{19} - 16 q^{20} + 128 q^{22} + 48 q^{28} + 8 q^{29} - 176 q^{31} - 96 q^{32}+ \cdots + 192 q^{99}+O(q^{100}) $ 24 * q + 24 * q^2 + 8 * q^5 + 24 * q^7 - 48 * q^8 + 72 * q^9 + 64 * q^11 + 48 * q^14 + 24 * q^15 - 96 * q^16 + 72 * q^18 + 160 * q^19 - 16 * q^20 + 128 * q^22 + 48 * q^28 + 8 * q^29 - 176 * q^31 - 96 * q^32 + 24 * q^33 - 32 * q^34 - 376 * q^35 - 48 * q^37 - 32 * q^40 + 176 * q^41 + 128 * q^44 + 24 * q^45 - 24 * q^46 + 128 * q^47 + 56 * q^50 - 520 * q^53 + 264 * q^55 + 216 * q^57 + 8 * q^58 + 128 * q^59 - 48 * q^60 - 40 * q^61 + 72 * q^63 + 48 * q^66 - 448 * q^67 - 64 * q^68 - 376 * q^70 - 24 * q^71 - 144 * q^72 - 208 * q^73 - 96 * q^74 - 320 * q^76 + 392 * q^79 - 32 * q^80 + 216 * q^81 + 200 * q^83 - 256 * q^85 + 424 * q^86 + 408 * q^87 - 240 * q^89 - 48 * q^92 + 144 * q^93 + 256 * q^94 - 736 * q^97 + 104 * q^98 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$		−	2.00000i		−	0.500000i
$5$	−3.76999	+	3.76999i	−0.753998	+	0.753998i	−0.975223	−	0.221225i	$-0.928994\pi$
$5$	−3.76999	+	3.76999i	−0.753998	+	0.753998i	0.221225	+	0.975223i	$0.428994\pi$
$6$	1.73205	−	1.73205i	0.288675	−	0.288675i
$7$	−3.86894	−	3.86894i	−0.552706	−	0.552706i	0.374515	−	0.927221i	$-0.377809\pi$
$7$	−3.86894	−	3.86894i	−0.552706	−	0.552706i	−0.927221	+	0.374515i	$0.877809\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	3.00000			0.333333
$10$			7.53998i			0.753998i
$11$	3.48592	+	3.48592i	0.316902	+	0.316902i	0.847576	−	0.530674i	$-0.178061\pi$
$11$	3.48592	+	3.48592i	0.316902	+	0.316902i	−0.530674	+	0.847576i	$0.678061\pi$
$12$		−	3.46410i		−	0.288675i
$13$		0			0
$13$		0			0
$14$	−7.73788			−0.552706
$15$	−6.52981	+	6.52981i	−0.435321	+	0.435321i
$16$	−4.00000			−0.250000
$17$			26.1246i			1.53674i	0.640005	+	0.768371i	$0.278932\pi$
$17$			26.1246i			1.53674i	−0.640005	+	0.768371i	$0.721068\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$	21.7198	−	21.7198i	1.14315	−	1.14315i	0.155279	−	0.987871i	$-0.450372\pi$
$19$	21.7198	−	21.7198i	1.14315	−	1.14315i	0.987871	−	0.155279i	$-0.0496277\pi$
$20$	7.53998	+	7.53998i	0.376999	+	0.376999i
$21$	−6.70120	−	6.70120i	−0.319105	−	0.319105i
$22$	6.97184			0.316902
$23$			37.2382i			1.61905i	0.587084	+	0.809526i	$0.300276\pi$
$23$			37.2382i			1.61905i	−0.587084	+	0.809526i	$0.699724\pi$
$24$	−3.46410	−	3.46410i	−0.144338	−	0.144338i
$25$		−	3.42563i		−	0.137025i
$26$		0			0
$27$	5.19615			0.192450
$28$	−7.73788	+	7.73788i	−0.276353	+	0.276353i
$29$	36.3770			1.25438			0.627190	−	0.778866i	$-0.284205\pi$
$29$	36.3770			1.25438			0.627190	+	0.778866i	$0.284205\pi$
$30$			13.0596i			0.435321i
$31$	−3.56835	+	3.56835i	−0.115108	+	0.115108i	−0.762315	−	0.647207i	$-0.775937\pi$
$31$	−3.56835	+	3.56835i	−0.115108	+	0.115108i	0.647207	+	0.762315i	$0.275937\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	6.03779	+	6.03779i	0.182963	+	0.182963i
$34$	26.1246	+	26.1246i	0.768371	+	0.768371i
$35$	29.1717			0.833478
$36$		−	6.00000i		−	0.166667i
$37$	−10.3200	−	10.3200i	−0.278919	−	0.278919i	0.553758	−	0.832677i	$-0.313193\pi$
$37$	−10.3200	−	10.3200i	−0.278919	−	0.278919i	−0.832677	+	0.553758i	$0.813193\pi$
$38$		−	43.4397i		−	1.14315i
$39$		0			0
$40$	15.0800			0.376999
$41$	7.79177	−	7.79177i	0.190043	−	0.190043i	−0.605672	−	0.795715i	$-0.707095\pi$
$41$	7.79177	−	7.79177i	0.190043	−	0.190043i	0.795715	+	0.605672i	$0.207095\pi$
$42$	−13.4024			−0.319105
$43$			38.2640i			0.889860i	0.895565	+	0.444930i	$0.146772\pi$
$43$			38.2640i			0.889860i	−0.895565	+	0.444930i	$0.853228\pi$
$44$	6.97184	−	6.97184i	0.158451	−	0.158451i
$45$	−11.3100	+	11.3100i	−0.251333	+	0.251333i
$46$	37.2382	+	37.2382i	0.809526	+	0.809526i
$47$	27.8611	+	27.8611i	0.592789	+	0.592789i	0.938384	−	0.345595i	$-0.112323\pi$
$47$	27.8611	+	27.8611i	0.592789	+	0.592789i	−0.345595	+	0.938384i	$0.612323\pi$
$48$	−6.92820			−0.144338
$49$		−	19.0626i		−	0.389032i
$50$	−3.42563	−	3.42563i	−0.0685127	−	0.0685127i
$51$			45.2491i			0.887238i
$52$		0			0
$53$	49.9991			0.943378			0.471689	−	0.881765i	$-0.343644\pi$
$53$	49.9991			0.943378			0.471689	+	0.881765i	$0.343644\pi$
$54$	5.19615	−	5.19615i	0.0962250	−	0.0962250i
$55$	−26.2838			−0.477886
$56$			15.4758i			0.276353i
$57$	37.6199	−	37.6199i	0.659998	−	0.659998i
$58$	36.3770	−	36.3770i	0.627190	−	0.627190i
$59$	−19.1413	−	19.1413i	−0.324429	−	0.324429i	0.526034	−	0.850463i	$-0.323678\pi$
$59$	−19.1413	−	19.1413i	−0.324429	−	0.324429i	−0.850463	+	0.526034i	$0.823678\pi$
$60$	13.0596	+	13.0596i	0.217660	+	0.217660i
$61$	83.7923			1.37364			0.686822	−	0.726826i	$-0.259005\pi$
$61$	83.7923			1.37364			0.686822	+	0.726826i	$0.259005\pi$
$62$			7.13670i			0.115108i
$63$	−11.6068	−	11.6068i	−0.184235	−	0.184235i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	12.0756			0.182963
$67$	−83.7289	+	83.7289i	−1.24968	+	1.24968i	−0.293826	+	0.955859i	$0.594929\pi$
$67$	−83.7289	+	83.7289i	−1.24968	+	1.24968i	−0.955859	+	0.293826i	$0.905071\pi$
$68$	52.2492			0.768371
$69$			64.4984i			0.934760i
$70$	29.1717	−	29.1717i	0.416739	−	0.416739i
$71$	27.7368	−	27.7368i	0.390659	−	0.390659i	−0.484263	−	0.874922i	$-0.660912\pi$
$71$	27.7368	−	27.7368i	0.390659	−	0.390659i	0.874922	+	0.484263i	$0.160912\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	76.1331	+	76.1331i	1.04292	+	1.04292i	0.999037	+	0.0438822i	$0.0139726\pi$
$73$	76.1331	+	76.1331i	1.04292	+	1.04292i	0.0438822	+	0.999037i	$0.486027\pi$
$74$	−20.6400			−0.278919
$75$		−	5.93337i		−	0.0791116i
$76$	−43.4397	−	43.4397i	−0.571575	−	0.571575i
$77$		−	26.9736i		−	0.350307i
$78$		0			0
$79$	103.672			1.31230			0.656149	−	0.754631i	$-0.272184\pi$
$79$	103.672			1.31230			0.656149	+	0.754631i	$0.272184\pi$
$80$	15.0800	−	15.0800i	0.188499	−	0.188499i
$81$	9.00000			0.111111
$82$		−	15.5835i		−	0.190043i
$83$	−49.8772	+	49.8772i	−0.600930	+	0.600930i	−0.940559	−	0.339629i	$-0.889698\pi$
$83$	−49.8772	+	49.8772i	−0.600930	+	0.600930i	0.339629	+	0.940559i	$0.389698\pi$
$84$	−13.4024	+	13.4024i	−0.159552	+	0.159552i
$85$	−98.4894	−	98.4894i	−1.15870	−	1.15870i
$86$	38.2640	+	38.2640i	0.444930	+	0.444930i
$87$	63.0069			0.724217
$88$		−	13.9437i		−	0.158451i
$89$	31.2373	+	31.2373i	0.350980	+	0.350980i	0.860474	−	0.509494i	$-0.170167\pi$
$89$	31.2373	+	31.2373i	0.350980	+	0.350980i	−0.509494	+	0.860474i	$0.670167\pi$
$90$			22.6199i			0.251333i
$91$		0			0
$92$	74.4764			0.809526
$93$	−6.18056	+	6.18056i	−0.0664577	+	0.0664577i
$94$	55.7222			0.592789
$95$			163.767i			1.72386i
$96$	−6.92820	+	6.92820i	−0.0721688	+	0.0721688i
$97$	−99.3124	+	99.3124i	−1.02384	+	1.02384i	−0.0241301	+	0.999709i	$0.507682\pi$
$97$	−99.3124	+	99.3124i	−1.02384	+	1.02384i	−0.999709	+	0.0241301i	$0.992318\pi$
$98$	−19.0626	−	19.0626i	−0.194516	−	0.194516i
$99$	10.4578	+	10.4578i	0.105634	+	0.105634i
$100$	−6.85127			−0.0685127
$101$			173.923i			1.72201i	0.508599	+	0.861003i	$0.330163\pi$
$101$			173.923i			1.72201i	−0.508599	+	0.861003i	$0.669837\pi$
$102$	45.2491	+	45.2491i	0.443619	+	0.443619i
$103$		−	155.027i		−	1.50512i	−0.658524	−	0.752560i	$-0.728819\pi$
$103$		−	155.027i		−	1.50512i	0.658524	−	0.752560i	$-0.271181\pi$
$104$		0			0
$105$	50.5269			0.481209
$106$	49.9991	−	49.9991i	0.471689	−	0.471689i
$107$	−182.242			−1.70319			−0.851596	−	0.524199i	$-0.824365\pi$
$107$	−182.242			−1.70319			−0.851596	+	0.524199i	$0.824365\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	57.3652	−	57.3652i	0.526287	−	0.526287i	−0.393176	−	0.919463i	$-0.628624\pi$
$109$	57.3652	−	57.3652i	0.526287	−	0.526287i	0.919463	+	0.393176i	$0.128624\pi$
$110$	−26.2838	+	26.2838i	−0.238943	+	0.238943i
$111$	−17.8748	−	17.8748i	−0.161034	−	0.161034i
$112$	15.4758	+	15.4758i	0.138176	+	0.138176i
$113$	52.6082			0.465559			0.232780	−	0.972530i	$-0.425218\pi$
$113$	52.6082			0.465559			0.232780	+	0.972530i	$0.425218\pi$
$114$		−	75.2398i		−	0.659998i
$115$	−140.388	−	140.388i	−1.22076	−	1.22076i
$116$		−	72.7541i		−	0.627190i
$117$		0			0
$118$	−38.2826			−0.324429
$119$	101.075	−	101.075i	0.849366	−	0.849366i
$120$	26.1192			0.217660
$121$		−	96.6967i		−	0.799147i
$122$	83.7923	−	83.7923i	0.686822	−	0.686822i
$123$	13.4957	−	13.4957i	0.109721	−	0.109721i
$124$	7.13670	+	7.13670i	0.0575540	+	0.0575540i
$125$	−81.3351	−	81.3351i	−0.650681	−	0.650681i
$126$	−23.2136			−0.184235
$127$			190.997i			1.50391i	0.659212	+	0.751957i	$0.270890\pi$
$127$			190.997i			1.50391i	−0.659212	+	0.751957i	$0.729110\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$			66.2752i			0.513761i
$130$		0			0
$131$	−59.2049			−0.451946			−0.225973	−	0.974134i	$-0.572556\pi$
$131$	−59.2049			−0.451946			−0.225973	+	0.974134i	$0.572556\pi$
$132$	12.0756	−	12.0756i	0.0914817	−	0.0914817i
$133$	−168.066			−1.26365
$134$			167.458i			1.24968i
$135$	−19.5894	+	19.5894i	−0.145107	+	0.145107i
$136$	52.2492	−	52.2492i	0.384185	−	0.384185i
$137$	−171.924	−	171.924i	−1.25492	−	1.25492i	−0.953487	−	0.301436i	$-0.902534\pi$
$137$	−171.924	−	171.924i	−1.25492	−	1.25492i	−0.301436	−	0.953487i	$-0.597466\pi$
$138$	64.4984	+	64.4984i	0.467380	+	0.467380i
$139$	−219.773			−1.58110			−0.790549	−	0.612399i	$-0.790205\pi$
$139$	−219.773			−1.58110			−0.790549	+	0.612399i	$0.790205\pi$
$140$		−	58.3435i		−	0.416739i
$141$	48.2568	+	48.2568i	0.342247	+	0.342247i
$142$		−	55.4736i		−	0.390659i
$143$		0			0
$144$	−12.0000			−0.0833333
$145$	−137.141	+	137.141i	−0.945800	+	0.945800i
$146$	152.266			1.04292
$147$		−	33.0174i		−	0.224608i
$148$	−20.6400	+	20.6400i	−0.139460	+	0.139460i
$149$	152.728	−	152.728i	1.02502	−	1.02502i	0.0253424	−	0.999679i	$-0.491932\pi$
$149$	152.728	−	152.728i	1.02502	−	1.02502i	0.999679	−	0.0253424i	$-0.00806760\pi$
$150$	−5.93337	−	5.93337i	−0.0395558	−	0.0395558i
$151$	82.7928	+	82.7928i	0.548296	+	0.548296i	0.925948	−	0.377651i	$-0.123268\pi$
$151$	82.7928	+	82.7928i	0.548296	+	0.548296i	−0.377651	+	0.925948i	$0.623268\pi$
$152$	−86.8794			−0.571575
$153$			78.3738i			0.512247i
$154$	−26.9736	−	26.9736i	−0.175153	−	0.175153i
$155$		−	26.9053i		−	0.173582i
$156$		0			0
$157$	27.5664			0.175582			0.0877911	−	0.996139i	$-0.472019\pi$
$157$	27.5664			0.175582			0.0877911	+	0.996139i	$0.472019\pi$
$158$	103.672	−	103.672i	0.656149	−	0.656149i
$159$	86.6009			0.544660
$160$		−	30.1599i		−	0.188499i
$161$	144.072	−	144.072i	0.894859	−	0.894859i
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	70.1303	+	70.1303i	0.430247	+	0.430247i	0.888712	−	0.458465i	$-0.151601\pi$
$163$	70.1303	+	70.1303i	0.430247	+	0.430247i	−0.458465	+	0.888712i	$0.651601\pi$
$164$	−15.5835	−	15.5835i	−0.0950216	−	0.0950216i
$165$	−45.5248			−0.275908
$166$			99.7544i			0.600930i
$167$	46.3471	+	46.3471i	0.277527	+	0.277527i	0.832121	−	0.554594i	$-0.187126\pi$
$167$	46.3471	+	46.3471i	0.277527	+	0.277527i	−0.554594	+	0.832121i	$0.687126\pi$
$168$			26.8048i			0.159552i
$169$		0			0
$170$	−196.979			−1.15870
$171$	65.1595	−	65.1595i	0.381050	−	0.381050i
$172$	76.5280			0.444930
$173$		−	128.629i		−	0.743518i	−0.928329	−	0.371759i	$-0.878755\pi$
$173$		−	128.629i		−	0.743518i	0.928329	−	0.371759i	$-0.121245\pi$
$174$	63.0069	−	63.0069i	0.362108	−	0.362108i
$175$	−13.2536	+	13.2536i	−0.0757347	+	0.0757347i
$176$	−13.9437	−	13.9437i	−0.0792254	−	0.0792254i
$177$	−33.1537	−	33.1537i	−0.187309	−	0.187309i
$178$	62.4745			0.350980
$179$		−	79.6484i		−	0.444963i	−0.974937	−	0.222482i	$-0.928584\pi$
$179$		−	79.6484i		−	0.444963i	0.974937	−	0.222482i	$-0.0714158\pi$
$180$	22.6199	+	22.6199i	0.125666	+	0.125666i
$181$		−	66.6961i		−	0.368487i	−0.982881	−	0.184243i	$-0.941017\pi$
$181$		−	66.6961i		−	0.368487i	0.982881	−	0.184243i	$-0.0589834\pi$
$182$		0			0
$183$	145.132			0.793074
$184$	74.4764	−	74.4764i	0.404763	−	0.404763i
$185$	77.8126			0.420609
$186$			12.3611i			0.0664577i
$187$	−91.0682	+	91.0682i	−0.486996	+	0.486996i
$188$	55.7222	−	55.7222i	0.296395	−	0.296395i
$189$	−20.1036	−	20.1036i	−0.106368	−	0.106368i
$190$	163.767	+	163.767i	0.861932	+	0.861932i
$191$	89.4356			0.468249			0.234125	−	0.972207i	$-0.424778\pi$
$191$	89.4356			0.468249			0.234125	+	0.972207i	$0.424778\pi$
$192$			13.8564i			0.0721688i
$193$	−94.9756	−	94.9756i	−0.492102	−	0.492102i	0.416866	−	0.908968i	$-0.363128\pi$
$193$	−94.9756	−	94.9756i	−0.492102	−	0.492102i	−0.908968	+	0.416866i	$0.863128\pi$
$194$			198.625i			1.02384i
$195$		0			0
$196$	−38.1252			−0.194516
$197$	−26.0190	+	26.0190i	−0.132076	+	0.132076i	−0.770054	−	0.637978i	$-0.779771\pi$
$197$	−26.0190	+	26.0190i	−0.132076	+	0.132076i	0.637978	+	0.770054i	$0.279771\pi$
$198$	20.9155			0.105634
$199$		−	90.5342i		−	0.454946i	−0.973784	−	0.227473i	$-0.926954\pi$
$199$		−	90.5342i		−	0.454946i	0.973784	−	0.227473i	$-0.0730463\pi$
$200$	−6.85127	+	6.85127i	−0.0342563	+	0.0342563i
$201$	−145.023	+	145.023i	−0.721506	+	0.721506i
$202$	173.923	+	173.923i	0.861003	+	0.861003i
$203$	−140.741	−	140.741i	−0.693303	−	0.693303i
$204$	90.4983			0.443619
$205$			58.7498i			0.286584i
$206$	−155.027	−	155.027i	−0.752560	−	0.752560i
$207$			111.715i			0.539684i
$208$		0			0
$209$	151.427			0.724532
$210$	50.5269	−	50.5269i	0.240604	−	0.240604i
$211$	−310.627			−1.47217			−0.736084	−	0.676890i	$-0.763327\pi$
$211$	−310.627			−1.47217			−0.736084	+	0.676890i	$0.763327\pi$
$212$		−	99.9981i		−	0.471689i
$213$	48.0416	−	48.0416i	0.225547	−	0.225547i
$214$	−182.242	+	182.242i	−0.851596	+	0.851596i
$215$	−144.255	−	144.255i	−0.670953	−	0.670953i
$216$	−10.3923	−	10.3923i	−0.0481125	−	0.0481125i
$217$	27.6115			0.127242
$218$		−	114.730i		−	0.526287i
$219$	131.866	+	131.866i	0.602130	+	0.602130i
$220$			52.5675i			0.238943i
$221$		0			0
$222$	−35.7495			−0.161034
$223$	−153.225	+	153.225i	−0.687107	+	0.687107i	−0.961592	−	0.274484i	$-0.911493\pi$
$223$	−153.225	+	153.225i	−0.687107	+	0.687107i	0.274484	+	0.961592i	$0.411493\pi$
$224$	30.9515			0.138176
$225$		−	10.2769i		−	0.0456751i
$226$	52.6082	−	52.6082i	0.232780	−	0.232780i
$227$	190.324	−	190.324i	0.838430	−	0.838430i	−0.150223	−	0.988652i	$-0.547999\pi$
$227$	190.324	−	190.324i	0.838430	−	0.838430i	0.988652	+	0.150223i	$0.0479990\pi$
$228$	−75.2398	−	75.2398i	−0.329999	−	0.329999i
$229$	−176.747	−	176.747i	−0.771822	−	0.771822i	0.206603	−	0.978425i	$-0.433759\pi$
$229$	−176.747	−	176.747i	−0.771822	−	0.771822i	−0.978425	+	0.206603i	$0.933759\pi$
$230$	−280.775			−1.22076
$231$		−	46.7197i		−	0.202250i
$232$	−72.7541	−	72.7541i	−0.313595	−	0.313595i
$233$			412.535i			1.77054i	0.465080	+	0.885269i	$0.346025\pi$
$233$			412.535i			1.77054i	−0.465080	+	0.885269i	$0.653975\pi$
$234$		0			0
$235$	−210.072			−0.893923
$236$	−38.2826	+	38.2826i	−0.162215	+	0.162215i
$237$	179.564			0.757656
$238$		−	202.149i		−	0.849366i
$239$	11.6678	−	11.6678i	0.0488194	−	0.0488194i	−0.682276	−	0.731095i	$-0.739010\pi$
$239$	11.6678	−	11.6678i	0.0488194	−	0.0488194i	0.731095	+	0.682276i	$0.239010\pi$
$240$	26.1192	−	26.1192i	0.108830	−	0.108830i
$241$	171.252	+	171.252i	0.710589	+	0.710589i	0.966658	−	0.256070i	$-0.0824276\pi$
$241$	171.252	+	171.252i	0.710589	+	0.710589i	−0.256070	+	0.966658i	$0.582428\pi$
$242$	−96.6967	−	96.6967i	−0.399573	−	0.399573i
$243$	15.5885			0.0641500
$244$		−	167.585i		−	0.686822i
$245$	71.8658	+	71.8658i	0.293330	+	0.293330i
$246$		−	26.9915i		−	0.109721i
$247$		0			0
$248$	14.2734			0.0575540
$249$	−86.3898	+	86.3898i	−0.346947	+	0.346947i
$250$	−162.670			−0.650681
$251$			40.4473i			0.161144i	0.996749	+	0.0805722i	$0.0256748\pi$
$251$			40.4473i			0.161144i	−0.996749	+	0.0805722i	$0.974325\pi$
$252$	−23.2136	+	23.2136i	−0.0921176	+	0.0921176i
$253$	−129.809	+	129.809i	−0.513080	+	0.513080i
$254$	190.997	+	190.997i	0.751957	+	0.751957i
$255$	−170.589	−	170.589i	−0.668975	−	0.668975i
$256$	16.0000			0.0625000
$257$		−	163.494i		−	0.636164i	−0.948063	−	0.318082i	$-0.896961\pi$
$257$		−	163.494i		−	0.636164i	0.948063	−	0.318082i	$-0.103039\pi$
$258$	66.2752	+	66.2752i	0.256881	+	0.256881i
$259$			79.8550i			0.308320i
$260$		0			0
$261$	109.131			0.418127
$262$	−59.2049	+	59.2049i	−0.225973	+	0.225973i
$263$	4.14190			0.0157487			0.00787433	−	0.999969i	$-0.497493\pi$
$263$	4.14190			0.0157487			0.00787433	+	0.999969i	$0.497493\pi$
$264$		−	24.1512i		−	0.0914817i
$265$	−188.496	+	188.496i	−0.711305	+	0.711305i
$266$	−168.066	+	168.066i	−0.631826	+	0.631826i
$267$	54.1045	+	54.1045i	0.202639	+	0.202639i
$268$	167.458	+	167.458i	0.624842	+	0.624842i
$269$	270.955			1.00727			0.503634	−	0.863917i	$-0.331996\pi$
$269$	270.955			1.00727			0.503634	+	0.863917i	$0.331996\pi$
$270$			39.1789i			0.145107i
$271$	124.334	+	124.334i	0.458796	+	0.458796i	0.898260	−	0.439464i	$-0.144832\pi$
$271$	124.334	+	124.334i	0.458796	+	0.458796i	−0.439464	+	0.898260i	$0.644832\pi$
$272$		−	104.498i		−	0.384185i
$273$		0			0
$274$	−343.849			−1.25492
$275$	11.9415	−	11.9415i	0.0434236	−	0.0434236i
$276$	128.997			0.467380
$277$		−	553.304i		−	1.99749i	−0.0501154	−	0.998743i	$-0.515959\pi$
$277$		−	553.304i		−	1.99749i	0.0501154	−	0.998743i	$-0.484041\pi$
$278$	−219.773	+	219.773i	−0.790549	+	0.790549i
$279$	−10.7050	+	10.7050i	−0.0383693	+	0.0383693i
$280$	−58.3435	−	58.3435i	−0.208369	−	0.208369i
$281$	−62.7814	−	62.7814i	−0.223422	−	0.223422i	0.586516	−	0.809938i	$-0.300499\pi$
$281$	−62.7814	−	62.7814i	−0.223422	−	0.223422i	−0.809938	+	0.586516i	$0.800499\pi$
$282$	96.5136			0.342247
$283$			341.345i			1.20617i	0.797679	+	0.603083i	$0.206061\pi$
$283$			341.345i			1.20617i	−0.797679	+	0.603083i	$0.793939\pi$
$284$	−55.4736	−	55.4736i	−0.195330	−	0.195330i
$285$			283.653i			0.995274i
$286$		0			0
$287$	−60.2918			−0.210076
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$	−393.495			−1.36157
$290$			274.282i			0.945800i
$291$	−172.014	+	172.014i	−0.591114	+	0.591114i
$292$	152.266	−	152.266i	0.521459	−	0.521459i
$293$	275.307	+	275.307i	0.939613	+	0.939613i	0.998278	−	0.0586650i	$-0.0186844\pi$
$293$	275.307	+	275.307i	0.939613	+	0.939613i	−0.0586650	+	0.998278i	$0.518684\pi$
$294$	−33.0174	−	33.0174i	−0.112304	−	0.112304i
$295$	144.325			0.489238
$296$			41.2800i			0.139460i
$297$	18.1134	+	18.1134i	0.0609878	+	0.0609878i
$298$		−	305.456i		−	1.02502i
$299$		0			0
$300$	−11.8667			−0.0395558
$301$	148.041	−	148.041i	0.491831	−	0.491831i
$302$	165.586			0.548296
$303$			301.243i			0.994201i
$304$	−86.8794	+	86.8794i	−0.285787	+	0.285787i
$305$	−315.896	+	315.896i	−1.03572	+	1.03572i
$306$	78.3738	+	78.3738i	0.256124	+	0.256124i
$307$	−151.708	−	151.708i	−0.494164	−	0.494164i	0.415451	−	0.909615i	$-0.363624\pi$
$307$	−151.708	−	151.708i	−0.494164	−	0.494164i	−0.909615	+	0.415451i	$0.863624\pi$
$308$	−53.9473			−0.175153
$309$		−	268.515i		−	0.868981i
$310$	−26.9053	−	26.9053i	−0.0867912	−	0.0867912i
$311$		−	242.225i		−	0.778859i	−0.921056	−	0.389429i	$-0.872672\pi$
$311$		−	242.225i		−	0.778859i	0.921056	−	0.389429i	$-0.127328\pi$
$312$		0			0
$313$	49.4596			0.158018			0.0790089	−	0.996874i	$-0.474824\pi$
$313$	49.4596			0.158018			0.0790089	+	0.996874i	$0.474824\pi$
$314$	27.5664	−	27.5664i	0.0877911	−	0.0877911i
$315$	87.5152			0.277826
$316$		−	207.343i		−	0.656149i
$317$	−66.1813	+	66.1813i	−0.208774	+	0.208774i	−0.803746	−	0.594972i	$-0.797163\pi$
$317$	−66.1813	+	66.1813i	−0.208774	+	0.208774i	0.594972	+	0.803746i	$0.297163\pi$
$318$	86.6009	−	86.6009i	0.272330	−	0.272330i
$319$	126.807	+	126.807i	0.397515	+	0.397515i
$320$	−30.1599	−	30.1599i	−0.0942497	−	0.0942497i
$321$	−315.652			−0.983338
$322$		−	288.145i		−	0.894859i
$323$	567.422	+	567.422i	1.75673	+	1.75673i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	140.261			0.430247
$327$	99.3595	−	99.3595i	0.303852	−	0.303852i
$328$	−31.1671			−0.0950216
$329$		−	215.586i		−	0.655276i
$330$	−45.5248	+	45.5248i	−0.137954	+	0.137954i
$331$	152.672	−	152.672i	0.461246	−	0.461246i	−0.437818	−	0.899064i	$-0.644248\pi$
$331$	152.672	−	152.672i	0.461246	−	0.461246i	0.899064	+	0.437818i	$0.144248\pi$
$332$	99.7544	+	99.7544i	0.300465	+	0.300465i
$333$	−30.9600	−	30.9600i	−0.0929730	−	0.0929730i
$334$	92.6942			0.277527
$335$		−	631.314i		−	1.88452i
$336$	26.8048	+	26.8048i	0.0797762	+	0.0797762i
$337$		−	440.101i		−	1.30594i	−0.757385	−	0.652969i	$-0.773523\pi$
$337$		−	440.101i		−	1.30594i	0.757385	−	0.652969i	$-0.226477\pi$
$338$		0			0
$339$	91.1201			0.268791
$340$	−196.979	+	196.979i	−0.579350	+	0.579350i
$341$	−24.8780			−0.0729559
$342$		−	130.319i		−	0.381050i
$343$	−263.330	+	263.330i	−0.767726	+	0.767726i
$344$	76.5280	−	76.5280i	0.222465	−	0.222465i
$345$	−243.158	−	243.158i	−0.704807	−	0.704807i
$346$	−128.629	−	128.629i	−0.371759	−	0.371759i
$347$	−124.893			−0.359922			−0.179961	−	0.983674i	$-0.557597\pi$
$347$	−124.893			−0.359922			−0.179961	+	0.983674i	$0.557597\pi$
$348$		−	126.014i		−	0.362108i
$349$	−357.385	−	357.385i	−1.02402	−	1.02402i	−0.999704	−	0.0243202i	$-0.992258\pi$
$349$	−357.385	−	357.385i	−1.02402	−	1.02402i	−0.0243202	−	0.999704i	$-0.507742\pi$
$350$			26.5071i			0.0757347i
$351$		0			0
$352$	−27.8874			−0.0792254
$353$	82.3626	−	82.3626i	0.233322	−	0.233322i	−0.580756	−	0.814078i	$-0.697243\pi$
$353$	82.3626	−	82.3626i	0.233322	−	0.233322i	0.814078	+	0.580756i	$0.197243\pi$
$354$	−66.3075			−0.187309
$355$			209.135i			0.589112i
$356$	62.4745	−	62.4745i	0.175490	−	0.175490i
$357$	175.066	−	175.066i	0.490382	−	0.490382i
$358$	−79.6484	−	79.6484i	−0.222482	−	0.222482i
$359$	−390.725	−	390.725i	−1.08837	−	1.08837i	−0.995696	−	0.0926747i	$-0.970458\pi$
$359$	−390.725	−	390.725i	−1.08837	−	1.08837i	−0.0926747	−	0.995696i	$-0.529542\pi$
$360$	45.2399			0.125666
$361$		−	582.504i		−	1.61358i
$362$	−66.6961	−	66.6961i	−0.184243	−	0.184243i
$363$		−	167.484i		−	0.461387i
$364$		0			0
$365$	−574.042			−1.57272
$366$	145.132	−	145.132i	0.396537	−	0.396537i
$367$	368.677			1.00457			0.502285	−	0.864702i	$-0.332493\pi$
$367$	368.677			1.00457			0.502285	+	0.864702i	$0.332493\pi$
$368$		−	148.953i		−	0.404763i
$369$	23.3753	−	23.3753i	0.0633477	−	0.0633477i
$370$	77.8126	−	77.8126i	0.210304	−	0.210304i
$371$	−193.443	−	193.443i	−0.521411	−	0.521411i
$372$	12.3611	+	12.3611i	0.0332288	+	0.0332288i
$373$	−174.888			−0.468869			−0.234435	−	0.972132i	$-0.575324\pi$
$373$	−174.888			−0.468869			−0.234435	+	0.972132i	$0.575324\pi$
$374$			182.136i			0.486996i
$375$	−140.877	−	140.877i	−0.375671	−	0.375671i
$376$		−	111.444i		−	0.296395i
$377$		0			0
$378$	−40.2072			−0.106368
$379$	−270.602	+	270.602i	−0.713990	+	0.713990i	−0.967368	−	0.253377i	$-0.918459\pi$
$379$	−270.602	+	270.602i	−0.713990	+	0.713990i	0.253377	+	0.967368i	$0.418459\pi$
$380$	327.534			0.861932
$381$			330.817i			0.868285i
$382$	89.4356	−	89.4356i	0.234125	−	0.234125i
$383$	49.7751	−	49.7751i	0.129961	−	0.129961i	−0.639134	−	0.769095i	$-0.720707\pi$
$383$	49.7751	−	49.7751i	0.129961	−	0.129961i	0.769095	+	0.639134i	$0.220707\pi$
$384$	13.8564	+	13.8564i	0.0360844	+	0.0360844i
$385$	101.690	+	101.690i	0.264131	+	0.264131i
$386$	−189.951			−0.492102
$387$			114.792i			0.296620i
$388$	198.625	+	198.625i	0.511919	+	0.511919i
$389$			359.190i			0.923368i	0.887044	+	0.461684i	$0.152755\pi$
$389$			359.190i			0.923368i	−0.887044	+	0.461684i	$0.847245\pi$
$390$		0			0
$391$	−972.833			−2.48806
$392$	−38.1252	+	38.1252i	−0.0972581	+	0.0972581i
$393$	−102.546			−0.260931
$394$			52.0381i			0.132076i
$395$	−390.841	+	390.841i	−0.989470	+	0.989470i
$396$	20.9155	−	20.9155i	0.0528170	−	0.0528170i
$397$	462.559	+	462.559i	1.16514	+	1.16514i	0.983335	+	0.181802i	$0.0581929\pi$
$397$	462.559	+	462.559i	1.16514	+	1.16514i	0.181802	+	0.983335i	$0.441807\pi$
$398$	−90.5342	−	90.5342i	−0.227473	−	0.227473i
$399$	−291.098			−0.729569
$400$			13.7025i			0.0342563i
$401$	532.299	+	532.299i	1.32743	+	1.32743i	0.907606	+	0.419822i	$0.137908\pi$
$401$	532.299	+	532.299i	1.32743	+	1.32743i	0.419822	+	0.907606i	$0.362092\pi$
$402$			290.045i			0.721506i
$403$		0			0
$404$	347.845			0.861003
$405$	−33.9299	+	33.9299i	−0.0837775	+	0.0837775i
$406$	−281.481			−0.693303
$407$		−	71.9494i		−	0.176780i
$408$	90.4983	−	90.4983i	0.221809	−	0.221809i
$409$	−106.915	+	106.915i	−0.261406	+	0.261406i	−0.825625	−	0.564219i	$-0.809177\pi$
$409$	−106.915	+	106.915i	−0.261406	+	0.261406i	0.564219	+	0.825625i	$0.309177\pi$
$410$	58.7498	+	58.7498i	0.143292	+	0.143292i
$411$	−297.782	−	297.782i	−0.724530	−	0.724530i
$412$	−310.055			−0.752560
$413$			148.113i			0.358628i
$414$	111.715	+	111.715i	0.269842	+	0.269842i
$415$		−	376.073i		−	0.906200i
$416$		0			0
$417$	−380.657			−0.912847
$418$	151.427	−	151.427i	0.362266	−	0.362266i
$419$	210.680			0.502816			0.251408	−	0.967881i	$-0.419106\pi$
$419$	210.680			0.502816			0.251408	+	0.967881i	$0.419106\pi$
$420$		−	101.054i		−	0.240604i
$421$	62.4036	−	62.4036i	0.148227	−	0.148227i	−0.629099	−	0.777326i	$-0.716576\pi$
$421$	62.4036	−	62.4036i	0.148227	−	0.148227i	0.777326	+	0.629099i	$0.216576\pi$
$422$	−310.627	+	310.627i	−0.736084	+	0.736084i
$423$	83.5833	+	83.5833i	0.197596	+	0.197596i
$424$	−99.9981	−	99.9981i	−0.235845	−	0.235845i
$425$	89.4933			0.210572
$426$		−	96.0831i		−	0.225547i
$427$	−324.187	−	324.187i	−0.759221	−	0.759221i
$428$			364.483i			0.851596i
$429$		0			0
$430$	−288.510			−0.670953
$431$	44.3693	−	44.3693i	0.102945	−	0.102945i	−0.653758	−	0.756703i	$-0.726809\pi$
$431$	44.3693	−	44.3693i	0.102945	−	0.102945i	0.756703	+	0.653758i	$0.226809\pi$
$432$	−20.7846			−0.0481125
$433$			80.6942i			0.186361i	0.995649	+	0.0931804i	$0.0297033\pi$
$433$			80.6942i			0.186361i	−0.995649	+	0.0931804i	$0.970297\pi$
$434$	27.6115	−	27.6115i	0.0636209	−	0.0636209i
$435$	−237.535	+	237.535i	−0.546058	+	0.546058i
$436$	−114.730	−	114.730i	−0.263143	−	0.263143i
$437$	808.808	+	808.808i	1.85082	+	1.85082i
$438$	263.733			0.602130
$439$			32.6159i			0.0742959i	0.999310	+	0.0371480i	$0.0118273\pi$
$439$			32.6159i			0.0742959i	−0.999310	+	0.0371480i	$0.988173\pi$
$440$	52.5675	+	52.5675i	0.119472	+	0.119472i
$441$		−	57.1878i		−	0.129677i
$442$		0			0
$443$	228.810			0.516502			0.258251	−	0.966078i	$-0.416854\pi$
$443$	228.810			0.516502			0.258251	+	0.966078i	$0.416854\pi$
$444$	−35.7495	+	35.7495i	−0.0805170	+	0.0805170i
$445$	−235.528			−0.529277
$446$			306.450i			0.687107i
$447$	264.533	−	264.533i	0.591796	−	0.591796i
$448$	30.9515	−	30.9515i	0.0690882	−	0.0690882i
$449$	−38.0255	−	38.0255i	−0.0846893	−	0.0846893i	0.663493	−	0.748182i	$-0.269073\pi$
$449$	−38.0255	−	38.0255i	−0.0846893	−	0.0846893i	−0.748182	+	0.663493i	$0.769073\pi$
$450$	−10.2769	−	10.2769i	−0.0228376	−	0.0228376i
$451$	54.3230			0.120450
$452$		−	105.216i		−	0.232780i
$453$	143.401	+	143.401i	0.316559	+	0.316559i
$454$		−	380.647i		−	0.838430i
$455$		0			0
$456$	−150.480			−0.329999
$457$	−558.092	+	558.092i	−1.22121	+	1.22121i	−0.254004	+	0.967203i	$0.581748\pi$
$457$	−558.092	+	558.092i	−1.22121	+	1.22121i	−0.967203	+	0.254004i	$0.918252\pi$
$458$	−353.495			−0.771822
$459$			135.747i			0.295746i
$460$	−280.775	+	280.775i	−0.610381	+	0.610381i
$461$	−157.751	+	157.751i	−0.342194	+	0.342194i	−0.857192	−	0.514998i	$-0.827793\pi$
$461$	−157.751	+	157.751i	−0.342194	+	0.342194i	0.514998	+	0.857192i	$0.327793\pi$
$462$	−46.7197	−	46.7197i	−0.101125	−	0.101125i
$463$	−320.752	−	320.752i	−0.692769	−	0.692769i	0.270071	−	0.962840i	$-0.412953\pi$
$463$	−320.752	−	320.752i	−0.692769	−	0.692769i	−0.962840	+	0.270071i	$0.912953\pi$
$464$	−145.508			−0.313595
$465$		−	46.6013i		−	0.100218i
$466$	412.535	+	412.535i	0.885269	+	0.885269i
$467$		−	46.9561i		−	0.100548i	−0.998735	−	0.0502742i	$-0.983990\pi$
$467$		−	46.9561i		−	0.100548i	0.998735	−	0.0502742i	$-0.0160095\pi$
$468$		0			0
$469$	647.884			1.38142
$470$	−210.072	+	210.072i	−0.446962	+	0.446962i
$471$	47.7464			0.101372
$472$			76.5653i			0.162215i
$473$	−133.385	+	133.385i	−0.281998	+	0.281998i
$474$	179.564	−	179.564i	0.378828	−	0.378828i
$475$	−74.4042	−	74.4042i	−0.156640	−	0.156640i
$476$	−202.149	−	202.149i	−0.424683	−	0.424683i
$477$	149.997			0.314459
$478$		−	23.3357i		−	0.0488194i
$479$	−341.797	−	341.797i	−0.713563	−	0.713563i	0.253716	−	0.967279i	$-0.418347\pi$
$479$	−341.797	−	341.797i	−0.713563	−	0.713563i	−0.967279	+	0.253716i	$0.918347\pi$
$480$		−	52.2385i		−	0.108830i
$481$		0			0
$482$	342.504			0.710589
$483$	249.541	−	249.541i	0.516647	−	0.516647i
$484$	−193.393			−0.399573
$485$		−	748.813i		−	1.54394i
$486$	15.5885	−	15.5885i	0.0320750	−	0.0320750i
$487$	195.401	−	195.401i	0.401234	−	0.401234i	−0.477434	−	0.878668i	$-0.658433\pi$
$487$	195.401	−	195.401i	0.401234	−	0.401234i	0.878668	+	0.477434i	$0.158433\pi$
$488$	−167.585	−	167.585i	−0.343411	−	0.343411i
$489$	121.469	+	121.469i	0.248403	+	0.248403i
$490$	143.732			0.293330
$491$		−	34.9120i		−	0.0711038i	−0.999368	−	0.0355519i	$-0.988681\pi$
$491$		−	34.9120i		−	0.0711038i	0.999368	−	0.0355519i	$-0.0113189\pi$
$492$	−26.9915	−	26.9915i	−0.0548607	−	0.0548607i
$493$			950.335i			1.92766i
$494$		0			0
$495$	−78.8513			−0.159295
$496$	14.2734	−	14.2734i	0.0287770	−	0.0287770i
$497$	−214.624			−0.431839
$498$			172.780i			0.346947i
$499$	266.311	−	266.311i	0.533689	−	0.533689i	−0.387979	−	0.921668i	$-0.626827\pi$
$499$	266.311	−	266.311i	0.533689	−	0.533689i	0.921668	+	0.387979i	$0.126827\pi$
$500$	−162.670	+	162.670i	−0.325340	+	0.325340i
$501$	80.2755	+	80.2755i	0.160231	+	0.160231i
$502$	40.4473	+	40.4473i	0.0805722	+	0.0805722i
$503$	473.341			0.941035			0.470518	−	0.882391i	$-0.344067\pi$
$503$	473.341			0.941035			0.470518	+	0.882391i	$0.344067\pi$
$504$			46.4273i			0.0921176i
$505$	−655.687	−	655.687i	−1.29839	−	1.29839i
$506$			259.619i			0.513080i
$507$		0			0
$508$	381.994			0.751957
$509$	−356.092	+	356.092i	−0.699591	+	0.699591i	−0.964322	−	0.264731i	$-0.914717\pi$
$509$	−356.092	+	356.092i	−0.699591	+	0.699591i	0.264731	+	0.964322i	$0.414717\pi$
$510$	−341.177			−0.668975
$511$		−	589.109i		−	1.15285i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	112.860	−	112.860i	0.219999	−	0.219999i
$514$	−163.494	−	163.494i	−0.318082	−	0.318082i
$515$	584.451	+	584.451i	1.13486	+	1.13486i
$516$	132.550			0.256881
$517$			194.243i			0.375712i
$518$	79.8550	+	79.8550i	0.154160	+	0.154160i
$519$		−	222.791i		−	0.429270i
$520$		0			0
$521$	164.557			0.315849			0.157924	−	0.987451i	$-0.449520\pi$
$521$	164.557			0.315849			0.157924	+	0.987451i	$0.449520\pi$
$522$	109.131	−	109.131i	0.209063	−	0.209063i
$523$	269.222			0.514765			0.257382	−	0.966310i	$-0.417140\pi$
$523$	269.222			0.514765			0.257382	+	0.966310i	$0.417140\pi$
$524$			118.410i			0.225973i
$525$	−22.9559	+	22.9559i	−0.0437255	+	0.0437255i
$526$	4.14190	−	4.14190i	0.00787433	−	0.00787433i
$527$	−93.2217	−	93.2217i	−0.176891	−	0.176891i
$528$	−24.1512	−	24.1512i	−0.0457408	−	0.0457408i
$529$	−857.683			−1.62133
$530$			376.992i			0.711305i
$531$	−57.4239	−	57.4239i	−0.108143	−	0.108143i
$532$			336.131i			0.631826i
$533$		0			0
$534$	108.209			0.202639
$535$	687.049	−	687.049i	1.28420	−	1.28420i
$536$	334.916			0.624842
$537$		−	137.955i		−	0.256900i
$538$	270.955	−	270.955i	0.503634	−	0.503634i
$539$	66.4507	−	66.4507i	0.123285	−	0.123285i
$540$	39.1789	+	39.1789i	0.0725535	+	0.0725535i
$541$	233.134	+	233.134i	0.430931	+	0.430931i	0.888945	−	0.458014i	$-0.151439\pi$
$541$	233.134	+	233.134i	0.430931	+	0.430931i	−0.458014	+	0.888945i	$0.651439\pi$
$542$	248.667			0.458796
$543$		−	115.521i		−	0.212746i
$544$	−104.498	−	104.498i	−0.192093	−	0.192093i
$545$			432.533i			0.793638i
$546$		0			0
$547$	−5.40285			−0.00987723			−0.00493862	−	0.999988i	$-0.501572\pi$
$547$	−5.40285			−0.00987723			−0.00493862	+	0.999988i	$0.501572\pi$
$548$	−343.849	+	343.849i	−0.627461	+	0.627461i
$549$	251.377			0.457881
$550$		−	23.8830i		−	0.0434236i
$551$	790.103	−	790.103i	1.43394	−	1.43394i
$552$	128.997	−	128.997i	0.233690	−	0.233690i
$553$	−401.099	−	401.099i	−0.725315	−	0.725315i
$554$	−553.304	−	553.304i	−0.998743	−	0.998743i
$555$	134.775			0.242839
$556$			439.545i			0.790549i
$557$	265.762	+	265.762i	0.477131	+	0.477131i	0.904213	−	0.427082i	$-0.140458\pi$
$557$	265.762	+	265.762i	0.477131	+	0.477131i	−0.427082	+	0.904213i	$0.640458\pi$
$558$			21.4101i			0.0383693i
$559$		0			0
$560$	−116.687			−0.208369
$561$	−157.735	+	157.735i	−0.281167	+	0.281167i
$562$	−125.563			−0.223422
$563$		−	202.971i		−	0.360517i	−0.983619	−	0.180258i	$-0.942307\pi$
$563$		−	202.971i		−	0.360517i	0.983619	−	0.180258i	$-0.0576934\pi$
$564$	96.5136	−	96.5136i	0.171123	−	0.171123i
$565$	−198.332	+	198.332i	−0.351031	+	0.351031i
$566$	341.345	+	341.345i	0.603083	+	0.603083i
$567$	−34.8205	−	34.8205i	−0.0614118	−	0.0614118i
$568$	−110.947			−0.195330
$569$			213.041i			0.374413i	0.982321	+	0.187207i	$0.0599434\pi$
$569$			213.041i			0.374413i	−0.982321	+	0.187207i	$0.940057\pi$
$570$	283.653	+	283.653i	0.497637	+	0.497637i
$571$		−	681.429i		−	1.19340i	−0.802466	−	0.596698i	$-0.796479\pi$
$571$		−	681.429i		−	1.19340i	0.802466	−	0.596698i	$-0.203521\pi$
$572$		0			0
$573$	154.907			0.270344
$574$	−60.2918	+	60.2918i	−0.105038	+	0.105038i
$575$	127.564			0.221851
$576$			24.0000i			0.0416667i
$577$	−193.569	+	193.569i	−0.335476	+	0.335476i	−0.854661	−	0.519186i	$-0.826235\pi$
$577$	−193.569	+	193.569i	−0.335476	+	0.335476i	0.519186	+	0.854661i	$0.326235\pi$
$578$	−393.495	+	393.495i	−0.680787	+	0.680787i
$579$	−164.503	−	164.503i	−0.284115	−	0.284115i
$580$	274.282	+	274.282i	0.472900	+	0.472900i
$581$	385.944			0.664275
$582$			344.028i			0.591114i
$583$	174.293	+	174.293i	0.298958	+	0.298958i
$584$		−	304.532i		−	0.521459i
$585$		0			0
$586$	550.613			0.939613
$587$	638.458	−	638.458i	1.08766	−	1.08766i	0.0918940	−	0.995769i	$-0.470708\pi$
$587$	638.458	−	638.458i	1.08766	−	1.08766i	0.995769	−	0.0918940i	$-0.0292921\pi$
$588$	−66.0348			−0.112304
$589$			155.008i			0.263171i
$590$	144.325	−	144.325i	0.244619	−	0.244619i
$591$	−45.0663	+	45.0663i	−0.0762543	+	0.0762543i
$592$	41.2800	+	41.2800i	0.0697298	+	0.0697298i
$593$	573.894	+	573.894i	0.967780	+	0.967780i	0.999497	−	0.0317166i	$-0.0100974\pi$
$593$	573.894	+	573.894i	0.967780	+	0.967780i	−0.0317166	+	0.999497i	$0.510097\pi$
$594$	36.2267			0.0609878
$595$			762.100i			1.28084i
$596$	−305.456	−	305.456i	−0.512511	−	0.512511i
$597$		−	156.810i		−	0.262663i
$598$		0			0
$599$	−525.606			−0.877472			−0.438736	−	0.898616i	$-0.644574\pi$
$599$	−525.606			−0.877472			−0.438736	+	0.898616i	$0.644574\pi$
$600$	−11.8667	+	11.8667i	−0.0197779	+	0.0197779i
$601$	960.818			1.59870			0.799349	−	0.600867i	$-0.205178\pi$
$601$	960.818			1.59870			0.799349	+	0.600867i	$0.205178\pi$
$602$		−	296.082i		−	0.491831i
$603$	−251.187	+	251.187i	−0.416562	+	0.416562i
$604$	165.586	−	165.586i	0.274148	−	0.274148i
$605$	364.546	+	364.546i	0.602555	+	0.602555i
$606$	301.243	+	301.243i	0.497100	+	0.497100i
$607$	−619.758			−1.02102			−0.510509	−	0.859872i	$-0.670543\pi$
$607$	−619.758			−1.02102			−0.510509	+	0.859872i	$0.670543\pi$
$608$			173.759i			0.285787i
$609$	−243.770	−	243.770i	−0.400279	−	0.400279i
$610$			631.792i			1.03572i
$611$		0			0
$612$	156.748			0.256124
$613$	444.841	−	444.841i	0.725679	−	0.725679i	−0.244077	−	0.969756i	$-0.578485\pi$
$613$	444.841	−	444.841i	0.725679	−	0.725679i	0.969756	+	0.244077i	$0.0784849\pi$
$614$	−303.417			−0.494164
$615$			101.758i			0.165459i
$616$	−53.9473	+	53.9473i	−0.0875767	+	0.0875767i
$617$	−24.2555	+	24.2555i	−0.0393121	+	0.0393121i	−0.726490	−	0.687178i	$-0.758849\pi$
$617$	−24.2555	+	24.2555i	−0.0393121	+	0.0393121i	0.687178	+	0.726490i	$0.258849\pi$
$618$	−268.515	−	268.515i	−0.434491	−	0.434491i
$619$	99.9062	+	99.9062i	0.161399	+	0.161399i	0.783186	−	0.621787i	$-0.213593\pi$
$619$	99.9062	+	99.9062i	0.161399	+	0.161399i	−0.621787	+	0.783186i	$0.713593\pi$
$620$	−53.8105			−0.0867912
$621$			193.495i			0.311587i
$622$	−242.225	−	242.225i	−0.389429	−	0.389429i
$623$		−	241.710i		−	0.387978i
$624$		0			0
$625$	698.906			1.11825
$626$	49.4596	−	49.4596i	0.0790089	−	0.0790089i
$627$	262.280			0.418309
$628$		−	55.1328i		−	0.0877911i
$629$	269.606	−	269.606i	0.428626	−	0.428626i
$630$	87.5152	−	87.5152i	0.138913	−	0.138913i
$631$	170.213	+	170.213i	0.269751	+	0.269751i	0.829000	−	0.559249i	$-0.188910\pi$
$631$	170.213	+	170.213i	0.269751	+	0.269751i	−0.559249	+	0.829000i	$0.688910\pi$
$632$	−207.343	−	207.343i	−0.328075	−	0.328075i
$633$	−538.023			−0.849957
$634$			132.363i			0.208774i
$635$	−720.057	−	720.057i	−1.13395	−	1.13395i
$636$		−	173.202i		−	0.272330i
$637$		0			0
$638$	253.615			0.397515
$639$	83.2104	−	83.2104i	0.130220	−	0.130220i
$640$	−60.3198			−0.0942497
$641$			706.615i			1.10236i	0.834385	+	0.551182i	$0.185823\pi$
$641$			706.615i			1.10236i	−0.834385	+	0.551182i	$0.814177\pi$
$642$	−315.652	+	315.652i	−0.491669	+	0.491669i
$643$	742.784	−	742.784i	1.15519	−	1.15519i	0.169688	−	0.985498i	$-0.445724\pi$
$643$	742.784	−	742.784i	1.15519	−	1.15519i	0.985498	−	0.169688i	$-0.0542760\pi$
$644$	−288.145	−	288.145i	−0.447430	−	0.447430i
$645$	−249.857	−	249.857i	−0.387375	−	0.387375i
$646$	1134.84			1.75673
$647$		−	461.398i		−	0.713134i	−0.934270	−	0.356567i	$-0.883947\pi$
$647$		−	461.398i		−	0.713134i	0.934270	−	0.356567i	$-0.116053\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	133.450i		−	0.205624i
$650$		0			0
$651$	47.8245			0.0734631
$652$	140.261	−	140.261i	0.215124	−	0.215124i
$653$	−313.633			−0.480295			−0.240148	−	0.970736i	$-0.577196\pi$
$653$	−313.633			−0.480295			−0.240148	+	0.970736i	$0.577196\pi$
$654$		−	198.719i		−	0.303852i
$655$	223.202	−	223.202i	0.340766	−	0.340766i
$656$	−31.1671	+	31.1671i	−0.0475108	+	0.0475108i
$657$	228.399	+	228.399i	0.347640	+	0.347640i
$658$	−215.586	−	215.586i	−0.327638	−	0.327638i
$659$	415.245			0.630115			0.315057	−	0.949073i	$-0.397976\pi$
$659$	415.245			0.630115			0.315057	+	0.949073i	$0.397976\pi$
$660$			91.0496i			0.137954i
$661$	31.9625	+	31.9625i	0.0483547	+	0.0483547i	0.730871	−	0.682516i	$-0.239114\pi$
$661$	31.9625	+	31.9625i	0.0483547	+	0.0483547i	−0.682516	+	0.730871i	$0.739114\pi$
$662$		−	305.345i		−	0.461246i
$663$		0			0
$664$	199.509			0.300465
$665$	633.605	−	633.605i	0.952790	−	0.952790i
$666$	−61.9200			−0.0929730
$667$			1354.61i			2.03091i
$668$	92.6942	−	92.6942i	0.138764	−	0.138764i
$669$	−265.393	+	265.393i	−0.396702	+	0.396702i
$670$	−631.314	−	631.314i	−0.942260	−	0.942260i
$671$	292.093	+	292.093i	0.435310	+	0.435310i
$672$	53.6096			0.0797762
$673$		−	341.508i		−	0.507441i	−0.967278	−	0.253720i	$-0.918346\pi$
$673$		−	341.508i		−	0.507441i	0.967278	−	0.253720i	$-0.0816543\pi$
$674$	−440.101	−	440.101i	−0.652969	−	0.652969i
$675$		−	17.8001i		−	0.0263705i
$676$		0			0
$677$	1060.95			1.56714			0.783568	−	0.621306i	$-0.213398\pi$
$677$	1060.95			1.56714			0.783568	+	0.621306i	$0.213398\pi$
$678$	91.1201	−	91.1201i	0.134395	−	0.134395i
$679$	768.467			1.13176
$680$			393.958i			0.579350i
$681$	329.650	−	329.650i	0.484068	−	0.484068i
$682$	−24.8780	+	24.8780i	−0.0364779	+	0.0364779i
$683$	−137.929	−	137.929i	−0.201945	−	0.201945i	0.598888	−	0.800833i	$-0.295610\pi$
$683$	−137.929	−	137.929i	−0.201945	−	0.201945i	−0.800833	+	0.598888i	$0.795610\pi$
$684$	−130.319	−	130.319i	−0.190525	−	0.190525i
$685$	1296.31			1.89242
$686$			526.660i			0.767726i
$687$	−306.135	−	306.135i	−0.445612	−	0.445612i
$688$		−	153.056i		−	0.222465i
$689$		0			0
$690$	−486.317			−0.704807
$691$	398.988	−	398.988i	0.577407	−	0.577407i	−0.356781	−	0.934188i	$-0.616126\pi$
$691$	398.988	−	398.988i	0.577407	−	0.577407i	0.934188	+	0.356781i	$0.116126\pi$
$692$	−257.257			−0.371759
$693$		−	80.9209i		−	0.116769i
$694$	−124.893	+	124.893i	−0.179961	+	0.179961i
$695$	828.540	−	828.540i	1.19214	−	1.19214i
$696$	−126.014	−	126.014i	−0.181054	−	0.181054i
$697$	203.557	+	203.557i	0.292047	+	0.292047i
$698$	−714.769			−1.02402
$699$			714.532i			1.02222i
$700$	26.5071	+	26.5071i	0.0378674	+	0.0378674i
$701$			589.971i			0.841613i	0.907150	+	0.420807i	$0.138253\pi$
$701$			589.971i			0.841613i	−0.907150	+	0.420807i	$0.861747\pi$
$702$		0			0
$703$	−448.298			−0.637692
$704$	−27.8874	+	27.8874i	−0.0396127	+	0.0396127i
$705$	−363.855			−0.516107
$706$		−	164.725i		−	0.233322i
$707$	672.897	−	672.897i	0.951763	−	0.951763i
$708$	−66.3075	+	66.3075i	−0.0936546	+	0.0936546i
$709$	−98.7332	−	98.7332i	−0.139257	−	0.139257i	0.634042	−	0.773299i	$-0.281395\pi$
$709$	−98.7332	−	98.7332i	−0.139257	−	0.139257i	−0.773299	+	0.634042i	$0.781395\pi$
$710$	209.135	+	209.135i	0.294556	+	0.294556i
$711$	311.015			0.437433
$712$		−	124.949i		−	0.175490i
$713$	−132.879	−	132.879i	−0.186366	−	0.186366i
$714$		−	350.132i		−	0.490382i
$715$		0			0
$716$	−159.297			−0.222482
$717$	20.2093	−	20.2093i	0.0281859	−	0.0281859i
$718$	−781.450			−1.08837
$719$			708.385i			0.985236i	0.870246	+	0.492618i	$0.163960\pi$
$719$			708.385i			0.985236i	−0.870246	+	0.492618i	$0.836040\pi$
$720$	45.2399	−	45.2399i	0.0628331	−	0.0628331i
$721$	−599.791	+	599.791i	−0.831888	+	0.831888i
$722$	−582.504	−	582.504i	−0.806792	−	0.806792i
$723$	296.617	+	296.617i	0.410259	+	0.410259i
$724$	−133.392			−0.184243
$725$		−	124.614i		−	0.171882i
$726$	−167.484	−	167.484i	−0.230694	−	0.230694i
$727$		−	970.555i		−	1.33501i	−0.744603	−	0.667507i	$-0.767361\pi$
$727$		−	970.555i		−	1.33501i	0.744603	−	0.667507i	$-0.232639\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	−574.042	+	574.042i	−0.786359	+	0.786359i
$731$	−999.632			−1.36748
$732$		−	290.265i		−	0.396537i
$733$	523.682	−	523.682i	0.714437	−	0.714437i	−0.253023	−	0.967460i	$-0.581425\pi$
$733$	523.682	−	523.682i	0.714437	−	0.714437i	0.967460	+	0.253023i	$0.0814250\pi$
$734$	368.677	−	368.677i	0.502285	−	0.502285i
$735$	124.475	+	124.475i	0.169354	+	0.169354i
$736$	−148.953	−	148.953i	−0.202381	−	0.202381i
$737$	−583.744			−0.792055
$738$		−	46.7506i		−	0.0633477i
$739$	630.840	+	630.840i	0.853640	+	0.853640i	0.990579	−	0.136939i	$-0.0437266\pi$
$739$	630.840	+	630.840i	0.853640	+	0.853640i	−0.136939	+	0.990579i	$0.543727\pi$
$740$		−	155.625i		−	0.210304i
$741$		0			0
$742$	−386.887			−0.521411
$743$	50.2030	−	50.2030i	0.0675680	−	0.0675680i	−0.672515	−	0.740083i	$-0.734786\pi$
$743$	50.2030	−	50.2030i	0.0675680	−	0.0675680i	0.740083	+	0.672515i	$0.234786\pi$
$744$	24.7222			0.0332288
$745$			1151.57i			1.54573i
$746$	−174.888	+	174.888i	−0.234435	+	0.234435i
$747$	−149.632	+	149.632i	−0.200310	+	0.200310i
$748$	182.136	+	182.136i	0.243498	+	0.243498i
$749$	705.082	+	705.082i	0.941364	+	0.941364i
$750$	−281.753			−0.375671
$751$			794.498i			1.05792i	0.848647	+	0.528960i	$0.177418\pi$
$751$			794.498i			1.05792i	−0.848647	+	0.528960i	$0.822582\pi$
$752$	−111.444	−	111.444i	−0.148197	−	0.148197i
$753$			70.0567i			0.0930368i
$754$		0			0
$755$	−624.256			−0.826829
$756$	−40.2072	+	40.2072i	−0.0531841	+	0.0531841i
$757$	545.450			0.720541			0.360271	−	0.932848i	$-0.382684\pi$
$757$	545.450			0.720541			0.360271	+	0.932848i	$0.382684\pi$
$758$			541.205i			0.713990i
$759$	−224.836	+	224.836i	−0.296227	+	0.296227i
$760$	327.534	−	327.534i	0.430966	−	0.430966i
$761$	88.4825	+	88.4825i	0.116271	+	0.116271i	0.762849	−	0.646577i	$-0.223800\pi$
$761$	88.4825	+	88.4825i	0.116271	+	0.116271i	−0.646577	+	0.762849i	$0.723800\pi$
$762$	330.817	+	330.817i	0.434143	+	0.434143i
$763$	−443.886			−0.581763
$764$		−	178.871i		−	0.234125i
$765$	−295.468	−	295.468i	−0.386233	−	0.386233i
$766$		−	99.5502i		−	0.129961i
$767$		0			0
$768$	27.7128			0.0360844
$769$	200.890	−	200.890i	0.261235	−	0.261235i	−0.564321	−	0.825556i	$-0.690862\pi$
$769$	200.890	−	200.890i	0.261235	−	0.261235i	0.825556	+	0.564321i	$0.190862\pi$
$770$	203.381			0.264131
$771$		−	283.180i		−	0.367290i
$772$	−189.951	+	189.951i	−0.246051	+	0.246051i
$773$	714.337	−	714.337i	0.924110	−	0.924110i	−0.0732069	−	0.997317i	$-0.523323\pi$
$773$	714.337	−	714.337i	0.924110	−	0.924110i	0.997317	+	0.0732069i	$0.0233233\pi$
$774$	114.792	+	114.792i	0.148310	+	0.148310i
$775$	12.2239	+	12.2239i	0.0157727	+	0.0157727i
$776$	397.250			0.511919
$777$			138.313i			0.178009i
$778$	359.190	+	359.190i	0.461684	+	0.461684i
$779$		−	338.472i		−	0.434496i
$780$		0			0
$781$	193.377			0.247601
$782$	−972.833	+	972.833i	−1.24403	+	1.24403i
$783$	189.021			0.241406
$784$			76.2504i			0.0972581i
$785$	−103.925	+	103.925i	−0.132389	+	0.132389i
$786$	−102.546	+	102.546i	−0.130466	+	0.130466i
$787$	−1057.22	−	1057.22i	−1.34336	−	1.34336i	−0.892690	−	0.450670i	$-0.851185\pi$
$787$	−1057.22	−	1057.22i	−1.34336	−	1.34336i	−0.450670	−	0.892690i	$-0.648815\pi$
$788$	52.0381	+	52.0381i	0.0660382	+	0.0660382i
$789$	7.17398			0.00909250
$790$			781.681i			0.989470i
$791$	−203.538	−	203.538i	−0.257317	−	0.257317i
$792$		−	41.8310i		−	0.0528170i
$793$		0			0
$794$	925.119			1.16514
$795$	−326.484	+	326.484i	−0.410672	+	0.410672i
$796$	−181.068			−0.227473
$797$		−	1039.27i		−	1.30397i	−0.758231	−	0.651986i	$-0.773936\pi$
$797$		−	1039.27i		−	1.30397i	0.758231	−	0.651986i	$-0.226064\pi$
$798$	−291.098	+	291.098i	−0.364785	+	0.364785i
$799$	−727.860	+	727.860i	−0.910963	+	0.910963i
$800$	13.7025	+	13.7025i	0.0171282	+	0.0171282i
$801$	93.7118	+	93.7118i	0.116993	+	0.116993i
$802$	1064.60			1.32743
$803$			530.788i			0.661006i
$804$	290.045	+	290.045i	0.360753	+	0.360753i
$805$			1086.30i			1.34944i
$806$		0			0
$807$	469.308			0.581546
$808$	347.845	−	347.845i	0.430502	−	0.430502i
$809$	1420.18			1.75548			0.877738	−	0.479141i	$-0.159052\pi$
$809$	1420.18			1.75548			0.877738	+	0.479141i	$0.159052\pi$
$810$			67.8598i			0.0837775i
$811$	519.737	−	519.737i	0.640859	−	0.640859i	−0.309908	−	0.950767i	$-0.600298\pi$
$811$	519.737	−	519.737i	0.640859	−	0.640859i	0.950767	+	0.309908i	$0.100298\pi$
$812$	−281.481	+	281.481i	−0.346652	+	0.346652i
$813$	215.352	+	215.352i	0.264886	+	0.264886i
$814$	−71.9494	−	71.9494i	−0.0883899	−	0.0883899i
$815$	−528.781			−0.648811
$816$		−	180.997i		−	0.221809i
$817$	831.088	+	831.088i	1.01724	+	1.01724i
$818$			213.830i			0.261406i
$819$		0			0
$820$	117.500			0.143292
$821$	−862.830	+	862.830i	−1.05095	+	1.05095i	−0.0523199	+	0.998630i	$0.516662\pi$
$821$	−862.830	+	862.830i	−1.05095	+	1.05095i	−0.998630	+	0.0523199i	$0.983338\pi$
$822$	−595.563			−0.724530
$823$		−	252.703i		−	0.307051i	−0.988145	−	0.153525i	$-0.950937\pi$
$823$		−	252.703i		−	0.307051i	0.988145	−	0.153525i	$-0.0490627\pi$
$824$	−310.055	+	310.055i	−0.376280	+	0.376280i
$825$	20.6833	−	20.6833i	0.0250706	−	0.0250706i
$826$	148.113	+	148.113i	0.179314	+	0.179314i
$827$	−1148.09	−	1148.09i	−1.38826	−	1.38826i	−0.828980	−	0.559278i	$-0.811078\pi$
$827$	−1148.09	−	1148.09i	−1.38826	−	1.38826i	−0.559278	−	0.828980i	$-0.688922\pi$
$828$	223.429			0.269842
$829$		−	1345.34i		−	1.62285i	−0.584455	−	0.811426i	$-0.698692\pi$
$829$		−	1345.34i		−	1.62285i	0.584455	−	0.811426i	$-0.301308\pi$
$830$	−376.073	−	376.073i	−0.453100	−	0.453100i
$831$		−	958.350i		−	1.15325i
$832$		0			0
$833$	498.003			0.597842
$834$	−380.657	+	380.657i	−0.456424	+	0.456424i
$835$	−349.456			−0.418510
$836$		−	302.855i		−	0.362266i
$837$	−18.5417	+	18.5417i	−0.0221526	+	0.0221526i
$838$	210.680	−	210.680i	0.251408	−	0.251408i
$839$	60.7079	+	60.7079i	0.0723574	+	0.0723574i	0.742359	−	0.670002i	$-0.233707\pi$
$839$	60.7079	+	60.7079i	0.0723574	+	0.0723574i	−0.670002	+	0.742359i	$0.733707\pi$
$840$	−101.054	−	101.054i	−0.120302	−	0.120302i
$841$	482.288			0.573470
$842$		−	124.807i		−	0.148227i
$843$	−108.741	−	108.741i	−0.128992	−	0.128992i
$844$			621.255i			0.736084i
$845$		0			0
$846$	167.167			0.197596
$847$	−374.114	+	374.114i	−0.441693	+	0.441693i
$848$	−199.996			−0.235845
$849$			591.227i			0.696380i
$850$	89.4933	−	89.4933i	0.105286	−	0.105286i
$851$	384.298	−	384.298i	0.451584	−	0.451584i
$852$	−96.0831	−	96.0831i	−0.112774	−	0.112774i
$853$	995.685	+	995.685i	1.16727	+	1.16727i	0.982846	+	0.184428i	$0.0590434\pi$
$853$	995.685	+	995.685i	1.16727	+	1.16727i	0.184428	+	0.982846i	$0.440957\pi$
$854$	−648.375			−0.759221
$855$			491.302i			0.574622i
$856$	364.483	+	364.483i	0.425798	+	0.425798i
$857$		−	1713.66i		−	1.99961i	−0.0197851	−	0.999804i	$-0.506298\pi$
$857$		−	1713.66i		−	1.99961i	0.0197851	−	0.999804i	$-0.493702\pi$
$858$		0			0
$859$	1251.13			1.45650			0.728249	−	0.685313i	$-0.240334\pi$
$859$	1251.13			1.45650			0.728249	+	0.685313i	$0.240334\pi$
$860$	−288.510	+	288.510i	−0.335476	+	0.335476i
$861$	−104.428			−0.121287
$862$		−	88.7386i		−	0.102945i
$863$	−468.627	+	468.627i	−0.543021	+	0.543021i	−0.924413	−	0.381392i	$-0.875445\pi$
$863$	−468.627	+	468.627i	−0.543021	+	0.543021i	0.381392	+	0.924413i	$0.375445\pi$
$864$	−20.7846	+	20.7846i	−0.0240563	+	0.0240563i
$865$	484.928	+	484.928i	0.560611	+	0.560611i
$866$	80.6942	+	80.6942i	0.0931804	+	0.0931804i
$867$	−681.553			−0.786105
$868$		−	55.2229i		−	0.0636209i
$869$	361.391	+	361.391i	0.415870	+	0.415870i
$870$			475.070i			0.546058i
$871$		0			0
$872$	−229.461			−0.263143
$873$	−297.937	+	297.937i	−0.341280	+	0.341280i
$874$	1617.62			1.85082
$875$			629.362i			0.719270i
$876$	263.733	−	263.733i	0.301065	−	0.301065i
$877$	27.1349	−	27.1349i	0.0309406	−	0.0309406i	−0.691467	−	0.722408i	$-0.743035\pi$
$877$	27.1349	−	27.1349i	0.0309406	−	0.0309406i	0.722408	+	0.691467i	$0.243035\pi$
$878$	32.6159	+	32.6159i	0.0371480	+	0.0371480i
$879$	476.845	+	476.845i	0.542486	+	0.542486i
$880$	105.135			0.119472
$881$		−	1347.93i		−	1.53001i	−0.644027	−	0.765003i	$-0.722738\pi$
$881$		−	1347.93i		−	1.53001i	0.644027	−	0.765003i	$-0.277262\pi$
$882$	−57.1878	−	57.1878i	−0.0648387	−	0.0648387i
$883$			762.177i			0.863168i	0.902073	+	0.431584i	$0.142045\pi$
$883$			762.177i			0.863168i	−0.902073	+	0.431584i	$0.857955\pi$
$884$		0			0
$885$	249.978			0.282461
$886$	228.810	−	228.810i	0.258251	−	0.258251i
$887$	−665.668			−0.750471			−0.375236	−	0.926929i	$-0.622438\pi$
$887$	−665.668			−0.750471			−0.375236	+	0.926929i	$0.622438\pi$
$888$			71.4991i			0.0805170i
$889$	738.957	−	738.957i	0.831222	−	0.831222i
$890$	−235.528	+	235.528i	−0.264638	+	0.264638i
$891$	31.3733	+	31.3733i	0.0352113	+	0.0352113i
$892$	306.450	+	306.450i	0.343554	+	0.343554i
$893$	1210.28			1.35529
$894$		−	529.066i		−	0.591796i
$895$	300.274	+	300.274i	0.335501	+	0.335501i
$896$		−	61.9031i		−	0.0690882i
$897$		0			0
$898$	−76.0510			−0.0846893
$899$	−129.806	+	129.806i	−0.144389	+	0.144389i
$900$	−20.5538			−0.0228376
$901$			1306.21i			1.44973i
$902$	54.3230	−	54.3230i	0.0602250	−	0.0602250i
$903$	256.415	−	256.415i	0.283959	−	0.283959i
$904$	−105.216	−	105.216i	−0.116390	−	0.116390i
$905$	251.443	+	251.443i	0.277838	+	0.277838i
$906$	286.803			0.316559
$907$		−	1284.18i		−	1.41586i	−0.706284	−	0.707929i	$-0.749630\pi$
$907$		−	1284.18i		−	1.41586i	0.706284	−	0.707929i	$-0.250370\pi$
$908$	−380.647	−	380.647i	−0.419215	−	0.419215i
$909$			521.768i			0.574002i
$910$		0			0
$911$	−1105.31			−1.21329			−0.606644	−	0.794973i	$-0.707485\pi$
$911$	−1105.31			−1.21329			−0.606644	+	0.794973i	$0.707485\pi$
$912$	−150.480	+	150.480i	−0.164999	+	0.164999i
$913$	−347.736			−0.380872
$914$			1116.18i			1.22121i
$915$	−547.148	+	547.148i	−0.597976	+	0.597976i
$916$	−353.495	+	353.495i	−0.385911	+	0.385911i
$917$	229.060	+	229.060i	0.249793	+	0.249793i
$918$	135.747	+	135.747i	0.147873	+	0.147873i
$919$	−1527.45			−1.66208			−0.831040	−	0.556212i	$-0.812254\pi$
$919$	−1527.45			−1.66208			−0.831040	+	0.556212i	$0.812254\pi$
$920$			561.550i			0.610381i
$921$	−262.767	−	262.767i	−0.285306	−	0.285306i
$922$			315.503i			0.342194i
$923$		0			0
$924$	−93.4394			−0.101125
$925$	−35.3525	+	35.3525i	−0.0382190	+	0.0382190i
$926$	−641.504			−0.692769
$927$		−	465.082i		−	0.501706i
$928$	−145.508	+	145.508i	−0.156798	+	0.156798i
$929$	−1288.66	+	1288.66i	−1.38714	+	1.38714i	−0.555886	+	0.831259i	$0.687621\pi$
$929$	−1288.66	+	1288.66i	−1.38714	+	1.38714i	−0.831259	+	0.555886i	$0.812379\pi$
$930$	−46.6013	−	46.6013i	−0.0501089	−	0.0501089i
$931$	−414.037	−	414.037i	−0.444722	−	0.444722i
$932$	825.070			0.885269
$933$		−	419.546i		−	0.449674i
$934$	−46.9561	−	46.9561i	−0.0502742	−	0.0502742i
$935$		−	686.653i		−	0.734388i
$936$		0			0
$937$	−182.294			−0.194551			−0.0972755	−	0.995257i	$-0.531013\pi$
$937$	−182.294			−0.194551			−0.0972755	+	0.995257i	$0.531013\pi$
$938$	647.884	−	647.884i	0.690708	−	0.690708i
$939$	85.6665			0.0912316
$940$			420.144i			0.446962i
$941$	−358.362	+	358.362i	−0.380831	+	0.380831i	−0.871401	−	0.490571i	$-0.836788\pi$
$941$	−358.362	+	358.362i	−0.380831	+	0.380831i	0.490571	+	0.871401i	$0.336788\pi$
$942$	47.7464	−	47.7464i	0.0506862	−	0.0506862i
$943$	290.151	+	290.151i	0.307690	+	0.307690i
$944$	76.5653	+	76.5653i	0.0811073	+	0.0811073i
$945$	151.581			0.160403
$946$			266.770i			0.281998i
$947$	−95.6115	−	95.6115i	−0.100963	−	0.100963i	0.654821	−	0.755784i	$-0.272744\pi$
$947$	−95.6115	−	95.6115i	−0.100963	−	0.100963i	−0.755784	+	0.654821i	$0.772744\pi$
$948$		−	359.129i		−	0.378828i
$949$		0			0
$950$	−148.808			−0.156640
$951$	−114.629	+	114.629i	−0.120536	+	0.120536i
$952$	−404.298			−0.424683
$953$		−	679.051i		−	0.712541i	−0.934383	−	0.356270i	$-0.884048\pi$
$953$		−	679.051i		−	0.712541i	0.934383	−	0.356270i	$-0.115952\pi$
$954$	149.997	−	149.997i	0.157230	−	0.157230i
$955$	−337.171	+	337.171i	−0.353059	+	0.353059i
$956$	−23.3357	−	23.3357i	−0.0244097	−	0.0244097i
$957$	219.637	+	219.637i	0.229506	+	0.229506i
$958$	−683.594			−0.713563
$959$			1330.33i			1.38721i
$960$	−52.2385	−	52.2385i	−0.0544151	−	0.0544151i
$961$			935.534i			0.973500i
$962$		0			0
$963$	−546.725			−0.567731
$964$	342.504	−	342.504i	0.355294	−	0.355294i
$965$	716.114			0.742087
$966$		−	499.081i		−	0.516647i
$967$	−814.203	+	814.203i	−0.841989	+	0.841989i	−0.989117	−	0.147129i	$-0.952997\pi$
$967$	−814.203	+	814.203i	−0.841989	+	0.841989i	0.147129	+	0.989117i	$0.452997\pi$
$968$	−193.393	+	193.393i	−0.199787	+	0.199787i
$969$	982.804	+	982.804i	1.01425	+	1.01425i
$970$	−748.813	−	748.813i	−0.771972	−	0.771972i
$971$	283.673			0.292145			0.146073	−	0.989274i	$-0.453337\pi$
$971$	283.673			0.292145			0.146073	+	0.989274i	$0.453337\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	850.287	+	850.287i	0.873882	+	0.873882i
$974$		−	390.801i		−	0.401234i
$975$		0			0
$976$	−335.169			−0.343411
$977$	−663.701	+	663.701i	−0.679326	+	0.679326i	−0.959848	−	0.280522i	$-0.909493\pi$
$977$	−663.701	+	663.701i	−0.679326	+	0.679326i	0.280522	+	0.959848i	$0.409493\pi$
$978$	242.939			0.248403
$979$			217.781i			0.222453i
$980$	143.732	−	143.732i	0.146665	−	0.146665i
$981$	172.096	−	172.096i	0.175429	−	0.175429i
$982$	−34.9120	−	34.9120i	−0.0355519	−	0.0355519i
$983$	1288.44	+	1288.44i	1.31073	+	1.31073i	0.920880	+	0.389845i	$0.127471\pi$
$983$	1288.44	+	1288.44i	1.31073	+	1.31073i	0.389845	+	0.920880i	$0.372529\pi$
$984$	−53.9830			−0.0548607
$985$		−	196.183i		−	0.199171i
$986$	950.335	+	950.335i	0.963829	+	0.963829i
$987$		−	373.406i		−	0.378324i
$988$		0			0
$989$	−1424.88			−1.44073
$990$	−78.8513	+	78.8513i	−0.0796477	+	0.0796477i
$991$	1044.65			1.05414			0.527069	−	0.849822i	$-0.323291\pi$
$991$	1044.65			1.05414			0.527069	+	0.849822i	$0.323291\pi$
$992$		−	28.5468i		−	0.0287770i
$993$	264.437	−	264.437i	0.266301	−	0.266301i
$994$	−214.624	+	214.624i	−0.215920	+	0.215920i
$995$	341.313	+	341.313i	0.343028	+	0.343028i
$996$	172.780	+	172.780i	0.173474	+	0.173474i
$997$	834.569			0.837080			0.418540	−	0.908198i	$-0.362542\pi$
$997$	834.569			0.837080			0.418540	+	0.908198i	$0.362542\pi$
$998$		−	532.622i		−	0.533689i
$999$	−53.6243	−	53.6243i	−0.0536780	−	0.0536780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.3.f.l.577.10	yes	24
13.5	odd	4		1014.3.f.k.775.10	yes	24
13.8	odd	4	inner	1014.3.f.l.775.10	yes	24
13.12	even	2		1014.3.f.k.577.10	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.3.f.k.577.10	✓	24	13.12	even	2
1014.3.f.k.775.10	yes	24	13.5	odd	4
1014.3.f.l.577.10	yes	24	1.1	even	1	trivial
1014.3.f.l.775.10	yes	24	13.8	odd	4	inner

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1014.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-3.76999 + 3.76999i) q^{5} +(1.73205 - 1.73205i) q^{6} +(-3.86894 - 3.86894i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +7.53998i q^{10} +(3.48592 + 3.48592i) q^{11} -3.46410i q^{12} -7.73788 q^{14} +(-6.52981 + 6.52981i) q^{15} -4.00000 q^{16} +26.1246i q^{17} +(3.00000 - 3.00000i) q^{18} +(21.7198 - 21.7198i) q^{19} +(7.53998 + 7.53998i) q^{20} +(-6.70120 - 6.70120i) q^{21} +6.97184 q^{22} +37.2382i q^{23} +(-3.46410 - 3.46410i) q^{24} -3.42563i q^{25} +5.19615 q^{27} +(-7.73788 + 7.73788i) q^{28} +36.3770 q^{29} +13.0596i q^{30} +(-3.56835 + 3.56835i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(6.03779 + 6.03779i) q^{33} +(26.1246 + 26.1246i) q^{34} +29.1717 q^{35} -6.00000i q^{36} +(-10.3200 - 10.3200i) q^{37} -43.4397i q^{38} +15.0800 q^{40} +(7.79177 - 7.79177i) q^{41} -13.4024 q^{42} +38.2640i q^{43} +(6.97184 - 6.97184i) q^{44} +(-11.3100 + 11.3100i) q^{45} +(37.2382 + 37.2382i) q^{46} +(27.8611 + 27.8611i) q^{47} -6.92820 q^{48} -19.0626i q^{49} +(-3.42563 - 3.42563i) q^{50} +45.2491i q^{51} +49.9991 q^{53} +(5.19615 - 5.19615i) q^{54} -26.2838 q^{55} +15.4758i q^{56} +(37.6199 - 37.6199i) q^{57} +(36.3770 - 36.3770i) q^{58} +(-19.1413 - 19.1413i) q^{59} +(13.0596 + 13.0596i) q^{60} +83.7923 q^{61} +7.13670i q^{62} +(-11.6068 - 11.6068i) q^{63} +8.00000i q^{64} +12.0756 q^{66} +(-83.7289 + 83.7289i) q^{67} +52.2492 q^{68} +64.4984i q^{69} +(29.1717 - 29.1717i) q^{70} +(27.7368 - 27.7368i) q^{71} +(-6.00000 - 6.00000i) q^{72} +(76.1331 + 76.1331i) q^{73} -20.6400 q^{74} -5.93337i q^{75} +(-43.4397 - 43.4397i) q^{76} -26.9736i q^{77} +103.672 q^{79} +(15.0800 - 15.0800i) q^{80} +9.00000 q^{81} -15.5835i q^{82} +(-49.8772 + 49.8772i) q^{83} +(-13.4024 + 13.4024i) q^{84} +(-98.4894 - 98.4894i) q^{85} +(38.2640 + 38.2640i) q^{86} +63.0069 q^{87} -13.9437i q^{88} +(31.2373 + 31.2373i) q^{89} +22.6199i q^{90} +74.4764 q^{92} +(-6.18056 + 6.18056i) q^{93} +55.7222 q^{94} +163.767i q^{95} +(-6.92820 + 6.92820i) q^{96} +(-99.3124 + 99.3124i) q^{97} +(-19.0626 - 19.0626i) q^{98} +(10.4578 + 10.4578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{5} + 24 q^{7} - 48 q^{8} + 72 q^{9} + 64 q^{11} + 48 q^{14} + 24 q^{15} - 96 q^{16} + 72 q^{18} + 160 q^{19} - 16 q^{20} + 128 q^{22} + 48 q^{28} + 8 q^{29} - 176 q^{31} - 96 q^{32}+ \cdots + 192 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^5 + 24 * q^7 - 48 * q^8 + 72 * q^9 + 64 * q^11 + 48 * q^14 + 24 * q^15 - 96 * q^16 + 72 * q^18 + 160 * q^19 - 16 * q^20 + 128 * q^22 + 48 * q^28 + 8 * q^29 - 176 * q^31 - 96 * q^32 + 24 * q^33 - 32 * q^34 - 376 * q^35 - 48 * q^37 - 32 * q^40 + 176 * q^41 + 128 * q^44 + 24 * q^45 - 24 * q^46 + 128 * q^47 + 56 * q^50 - 520 * q^53 + 264 * q^55 + 216 * q^57 + 8 * q^58 + 128 * q^59 - 48 * q^60 - 40 * q^61 + 72 * q^63 + 48 * q^66 - 448 * q^67 - 64 * q^68 - 376 * q^70 - 24 * q^71 - 144 * q^72 - 208 * q^73 - 96 * q^74 - 320 * q^76 + 392 * q^79 - 32 * q^80 + 216 * q^81 + 200 * q^83 - 256 * q^85 + 424 * q^86 + 408 * q^87 - 240 * q^89 - 48 * q^92 + 144 * q^93 + 256 * q^94 - 736 * q^97 + 104 * q^98 + 192 * q^99

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