LMFDB - Embedded newform 289.3.e.i.249.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,3,Mod(40,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([15])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.40"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,-8,0,-16] 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:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			249.1
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.249
Dual form			289.3.e.i.65.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23044 - 0.509666i) q^{2} +(0.523336 + 2.63099i) q^{3} +(-1.57420 - 1.57420i) q^{4} +(-1.35115 - 0.902812i) q^{5} +(0.696990 - 3.50400i) q^{6} +(-7.37170 + 4.92562i) q^{7} +(3.17331 + 7.66104i) q^{8} +(1.66671 - 0.690373i) q^{9} +(1.20238 + 1.79949i) q^{10} +(-8.12279 - 1.61572i) q^{11} +(3.31786 - 4.96553i) q^{12} +(16.1480 - 16.1480i) q^{13} +(11.5809 - 2.30358i) q^{14} +(1.66818 - 4.02734i) q^{15} -2.13880i q^{16} -2.40265 q^{18} +(1.20778 + 0.500280i) q^{19} +(0.705778 + 3.54819i) q^{20} +(-16.8171 - 16.8171i) q^{21} +(9.17115 + 6.12797i) q^{22} +(5.21946 - 26.2400i) q^{23} +(-18.4954 + 12.3582i) q^{24} +(-8.55654 - 20.6573i) q^{25} +(-28.0993 + 11.6391i) q^{26} +(16.1016 + 24.0978i) q^{27} +(19.3584 + 3.85063i) q^{28} +(9.19303 - 13.7583i) q^{29} +(-4.10520 + 4.10520i) q^{30} +(13.4734 - 2.68003i) q^{31} +(11.6032 - 28.0125i) q^{32} -22.2165i q^{33} +14.4072 q^{35} +(-3.71051 - 1.53694i) q^{36} +(-3.77234 - 18.9648i) q^{37} +(-1.23113 - 1.23113i) q^{38} +(50.9361 + 34.0344i) q^{39} +(2.62885 - 13.2161i) q^{40} +(21.9781 - 14.6853i) q^{41} +(12.1214 + 29.2636i) q^{42} +(21.8944 - 9.06895i) q^{43} +(10.2434 + 15.3303i) q^{44} +(-2.87525 - 0.571923i) q^{45} +(-19.7959 + 29.6266i) q^{46} +(26.8680 - 26.8680i) q^{47} +(5.62714 - 1.11931i) q^{48} +(11.3288 - 27.3503i) q^{49} +29.7786i q^{50} -50.8404 q^{52} +(-26.1557 - 10.8340i) q^{53} +(-7.53030 - 37.8574i) q^{54} +(9.51644 + 9.51644i) q^{55} +(-61.1281 - 40.8445i) q^{56} +(-0.684154 + 3.43947i) q^{57} +(-18.3236 + 12.2435i) q^{58} +(-9.12070 - 22.0193i) q^{59} +(-8.96587 + 3.71379i) q^{60} +(-28.6898 - 42.9373i) q^{61} +(-17.9442 - 3.56932i) q^{62} +(-8.88596 + 13.2988i) q^{63} +(-34.6035 + 34.6035i) q^{64} +(-36.3971 + 7.23983i) q^{65} +(-11.3230 + 27.3362i) q^{66} -70.4415i q^{67} +71.7687 q^{69} +(-17.7272 - 7.34286i) q^{70} +(20.4612 + 102.865i) q^{71} +(10.5780 + 10.5780i) q^{72} +(-29.5868 - 19.7693i) q^{73} +(-5.02408 + 25.2578i) q^{74} +(49.8712 - 33.3228i) q^{75} +(-1.11375 - 2.68883i) q^{76} +(67.8373 - 28.0991i) q^{77} +(-45.3277 - 67.8377i) q^{78} +(-7.11865 - 1.41599i) q^{79} +(-1.93093 + 2.88984i) q^{80} +(-43.4936 + 43.4936i) q^{81} +(-34.5274 + 6.86792i) q^{82} +(-51.5218 + 124.385i) q^{83} +52.9469i q^{84} -31.5619 q^{86} +(41.0090 + 16.9865i) q^{87} +(-13.3980 - 67.3563i) q^{88} +(38.6522 + 38.6522i) q^{89} +(3.24634 + 2.16914i) q^{90} +(-39.4995 + 198.577i) q^{91} +(-49.5234 + 33.0905i) q^{92} +(14.1023 + 34.0458i) q^{93} +(-46.7533 + 19.3658i) q^{94} +(-1.18024 - 1.76635i) q^{95} +(79.7729 + 15.8678i) q^{96} +(44.0470 - 65.9209i) q^{97} +(-27.8790 + 27.8790i) q^{98} +(-14.6538 + 2.91482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 8 q^{3} - 16 q^{5} - 24 q^{6} + 8 q^{7} + 24 q^{8} + 16 q^{9} - 48 q^{10} - 48 q^{11} - 40 q^{12} + 16 q^{13} + 8 q^{14} + 16 q^{15} + 56 q^{18} - 32 q^{20} - 64 q^{21} - 56 q^{22} - 40 q^{23}+ \cdots - 272 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 8 * q^3 - 16 * q^5 - 24 * q^6 + 8 * q^7 + 24 * q^8 + 16 * q^9 - 48 * q^10 - 48 * q^11 - 40 * q^12 + 16 * q^13 + 8 * q^14 + 16 * q^15 + 56 * q^18 - 32 * q^20 - 64 * q^21 - 56 * q^22 - 40 * q^23 - 104 * q^24 - 64 * q^25 - 176 * q^26 + 16 * q^27 - 56 * q^28 + 64 * q^29 + 16 * q^30 + 40 * q^31 - 88 * q^32 - 160 * q^35 + 128 * q^36 + 128 * q^37 - 120 * q^38 + 176 * q^39 - 16 * q^40 + 112 * q^41 - 16 * q^42 + 232 * q^43 + 24 * q^44 + 160 * q^45 - 136 * q^46 + 192 * q^47 - 8 * q^48 - 16 * q^49 - 384 * q^52 + 32 * q^53 + 224 * q^55 - 136 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 64 * q^60 - 64 * q^61 + 56 * q^62 + 168 * q^63 - 64 * q^64 - 96 * q^65 + 8 * q^66 + 240 * q^69 - 224 * q^70 + 88 * q^71 + 40 * q^72 + 48 * q^73 + 192 * q^74 - 80 * q^76 + 48 * q^77 + 304 * q^78 - 168 * q^79 - 112 * q^80 - 424 * q^81 + 136 * q^82 + 264 * q^83 + 832 * q^86 - 208 * q^87 - 320 * q^88 + 160 * q^89 + 144 * q^90 - 224 * q^91 - 184 * q^92 + 64 * q^93 - 32 * q^94 - 16 * q^95 + 232 * q^96 + 104 * q^97 - 120 * q^98 - 272 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{16}\right)$

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 $

$2$	−1.23044	−	0.509666i	−0.615221	−	0.254833i	0.0532379	−	0.998582i	$-0.483046\pi$
$2$	−1.23044	−	0.509666i	−0.615221	−	0.254833i	−0.668459	+	0.743749i	$0.733046\pi$
$3$	0.523336	+	2.63099i	0.174445	+	0.876995i	0.964525	+	0.263991i	$0.0850391\pi$
$3$	0.523336	+	2.63099i	0.174445	+	0.876995i	−0.790080	+	0.613004i	$0.789961\pi$
$4$	−1.57420	−	1.57420i	−0.393549	−	0.393549i
$5$	−1.35115	−	0.902812i	−0.270231	−	0.180562i	0.413070	−	0.910699i	$-0.364456\pi$
$5$	−1.35115	−	0.902812i	−0.270231	−	0.180562i	−0.683301	+	0.730137i	$0.739456\pi$
$6$	0.696990	−	3.50400i	0.116165	−	0.584001i
$7$	−7.37170	+	4.92562i	−1.05310	+	0.703659i	−0.956520	−	0.291666i	$-0.905790\pi$
$7$	−7.37170	+	4.92562i	−1.05310	+	0.703659i	−0.0965803	+	0.995325i	$0.530790\pi$
$8$	3.17331	+	7.66104i	0.396664	+	0.957631i
$9$	1.66671	−	0.690373i	0.185190	−	0.0767081i
$10$	1.20238	+	1.79949i	0.120238	+	0.179949i
$11$	−8.12279	−	1.61572i	−0.738436	−	0.146884i	−0.188479	−	0.982077i	$-0.560356\pi$
$11$	−8.12279	−	1.61572i	−0.738436	−	0.146884i	−0.549957	+	0.835193i	$0.685356\pi$
$12$	3.31786	−	4.96553i	0.276488	−	0.413794i
$13$	16.1480	−	16.1480i	1.24216	−	1.24216i	0.283051	−	0.959105i	$-0.408654\pi$
$13$	16.1480	−	16.1480i	1.24216	−	1.24216i	0.959105	−	0.283051i	$-0.0913464\pi$
$14$	11.5809	−	2.30358i	0.827205	−	0.164541i
$15$	1.66818	−	4.02734i	0.111212	−	0.268489i
$16$		−	2.13880i		−	0.133675i
$17$		0			0
$17$		0			0
$18$	−2.40265			−0.133480
$19$	1.20778	+	0.500280i	0.0635675	+	0.0263305i	0.414241	−	0.910167i	$-0.364047\pi$
$19$	1.20778	+	0.500280i	0.0635675	+	0.0263305i	−0.350673	+	0.936498i	$0.614047\pi$
$20$	0.705778	+	3.54819i	0.0352889	+	0.177409i
$21$	−16.8171	−	16.8171i	−0.800814	−	0.800814i
$22$	9.17115	+	6.12797i	0.416870	+	0.278544i
$23$	5.21946	−	26.2400i	0.226933	−	1.14087i	−0.684370	−	0.729135i	$-0.739923\pi$
$23$	5.21946	−	26.2400i	0.226933	−	1.14087i	0.911303	−	0.411735i	$-0.135077\pi$
$24$	−18.4954	+	12.3582i	−0.770642	+	0.514926i
$25$	−8.55654	−	20.6573i	−0.342262	−	0.826293i
$26$	−28.0993	+	11.6391i	−1.08074	+	0.447658i
$27$	16.1016	+	24.0978i	0.596356	+	0.892510i
$28$	19.3584	+	3.85063i	0.691372	+	0.137522i
$29$	9.19303	−	13.7583i	0.317001	−	0.474425i	−0.638414	−	0.769694i	$-0.720409\pi$
$29$	9.19303	−	13.7583i	0.317001	−	0.474425i	0.955414	+	0.295268i	$0.0954090\pi$
$30$	−4.10520	+	4.10520i	−0.136840	+	0.136840i
$31$	13.4734	−	2.68003i	0.434627	−	0.0864526i	0.0270721	−	0.999633i	$-0.491382\pi$
$31$	13.4734	−	2.68003i	0.434627	−	0.0864526i	0.407555	+	0.913181i	$0.366382\pi$
$32$	11.6032	−	28.0125i	0.362599	−	0.875391i
$33$		−	22.2165i		−	0.673228i
$34$		0			0
$35$	14.4072			0.411634
$36$	−3.71051	−	1.53694i	−0.103070	−	0.0426929i
$37$	−3.77234	−	18.9648i	−0.101955	−	0.512563i	−0.997687	−	0.0679693i	$-0.978348\pi$
$37$	−3.77234	−	18.9648i	−0.101955	−	0.512563i	0.895732	−	0.444594i	$-0.146652\pi$
$38$	−1.23113	−	1.23113i	−0.0323982	−	0.0323982i
$39$	50.9361	+	34.0344i	1.30605	+	0.872677i
$40$	2.62885	−	13.2161i	0.0657214	−	0.330404i
$41$	21.9781	−	14.6853i	0.536051	−	0.358178i	−0.257888	−	0.966175i	$-0.583027\pi$
$41$	21.9781	−	14.6853i	0.536051	−	0.358178i	0.793939	+	0.607997i	$0.208027\pi$
$42$	12.1214	+	29.2636i	0.288604	+	0.696752i
$43$	21.8944	−	9.06895i	0.509172	−	0.210906i	−0.113281	−	0.993563i	$-0.536136\pi$
$43$	21.8944	−	9.06895i	0.509172	−	0.210906i	0.622453	+	0.782657i	$0.286136\pi$
$44$	10.2434	+	15.3303i	0.232805	+	0.348417i
$45$	−2.87525	−	0.571923i	−0.0638945	−	0.0127094i
$46$	−19.7959	+	29.6266i	−0.430345	+	0.644058i
$47$	26.8680	−	26.8680i	0.571660	−	0.571660i	−0.360932	−	0.932592i	$-0.617541\pi$
$47$	26.8680	−	26.8680i	0.571660	−	0.571660i	0.932592	+	0.360932i	$0.117541\pi$
$48$	5.62714	−	1.11931i	0.117232	−	0.0233189i
$49$	11.3288	−	27.3503i	0.231201	−	0.558169i
$50$			29.7786i			0.595572i
$51$		0			0
$52$	−50.8404			−0.977699
$53$	−26.1557	−	10.8340i	−0.493503	−	0.204416i	0.122031	−	0.992526i	$-0.461059\pi$
$53$	−26.1557	−	10.8340i	−0.493503	−	0.204416i	−0.615533	+	0.788111i	$0.711059\pi$
$54$	−7.53030	−	37.8574i	−0.139450	−	0.701062i
$55$	9.51644	+	9.51644i	0.173026	+	0.173026i
$56$	−61.1281	−	40.8445i	−1.09157	−	0.729365i
$57$	−0.684154	+	3.43947i	−0.0120027	+	0.0603416i
$58$	−18.3236	+	12.2435i	−0.315925	+	0.211094i
$59$	−9.12070	−	22.0193i	−0.154588	−	0.373209i	0.827544	−	0.561401i	$-0.189737\pi$
$59$	−9.12070	−	22.0193i	−0.154588	−	0.373209i	−0.982132	+	0.188192i	$0.939737\pi$
$60$	−8.96587	+	3.71379i	−0.149431	+	0.0618964i
$61$	−28.6898	−	42.9373i	−0.470324	−	0.703890i	0.518148	−	0.855291i	$-0.326622\pi$
$61$	−28.6898	−	42.9373i	−0.470324	−	0.703890i	−0.988472	+	0.151401i	$0.951622\pi$
$62$	−17.9442	−	3.56932i	−0.289423	−	0.0575697i
$63$	−8.88596	+	13.2988i	−0.141047	+	0.211092i
$64$	−34.6035	+	34.6035i	−0.540679	+	0.540679i
$65$	−36.3971	+	7.23983i	−0.559955	+	0.111382i
$66$	−11.3230	+	27.3362i	−0.171561	+	0.414184i
$67$		−	70.4415i		−	1.05137i	−0.850681	−	0.525683i	$-0.823810\pi$
$67$		−	70.4415i		−	1.05137i	0.850681	−	0.525683i	$-0.176190\pi$
$68$		0			0
$69$	71.7687			1.04013
$70$	−17.7272	−	7.34286i	−0.253246	−	0.104898i
$71$	20.4612	+	102.865i	0.288185	+	1.44881i	0.805289	+	0.592883i	$0.202010\pi$
$71$	20.4612	+	102.865i	0.288185	+	1.44881i	−0.517104	+	0.855923i	$0.672990\pi$
$72$	10.5780	+	10.5780i	0.146916	+	0.146916i
$73$	−29.5868	−	19.7693i	−0.405299	−	0.270812i	0.336167	−	0.941802i	$-0.390869\pi$
$73$	−29.5868	−	19.7693i	−0.405299	−	0.270812i	−0.741466	+	0.670990i	$0.765869\pi$
$74$	−5.02408	+	25.2578i	−0.0678930	+	0.341321i
$75$	49.8712	−	33.3228i	0.664949	−	0.444305i
$76$	−1.11375	−	2.68883i	−0.0146546	−	0.0353793i
$77$	67.8373	−	28.0991i	0.881003	−	0.364924i
$78$	−45.3277	−	67.8377i	−0.581125	−	0.869715i
$79$	−7.11865	−	1.41599i	−0.0901095	−	0.0179239i	0.149830	−	0.988712i	$-0.452127\pi$
$79$	−7.11865	−	1.41599i	−0.0901095	−	0.0179239i	−0.239939	+	0.970788i	$0.577127\pi$
$80$	−1.93093	+	2.88984i	−0.0241366	+	0.0361230i
$81$	−43.4936	+	43.4936i	−0.536958	+	0.536958i
$82$	−34.5274	+	6.86792i	−0.421066	+	0.0837551i
$83$	−51.5218	+	124.385i	−0.620745	+	1.49861i	0.230085	+	0.973170i	$0.426099\pi$
$83$	−51.5218	+	124.385i	−0.620745	+	1.49861i	−0.850830	+	0.525441i	$0.823901\pi$
$84$			52.9469i			0.630320i
$85$		0			0
$86$	−31.5619			−0.366999
$87$	41.0090	+	16.9865i	0.471368	+	0.195247i
$88$	−13.3980	−	67.3563i	−0.152250	−	0.765412i
$89$	38.6522	+	38.6522i	0.434294	+	0.434294i	0.890086	−	0.455792i	$-0.150644\pi$
$89$	38.6522	+	38.6522i	0.434294	+	0.434294i	−0.455792	+	0.890086i	$0.650644\pi$
$90$	3.24634	+	2.16914i	0.0360705	+	0.0241015i
$91$	−39.4995	+	198.577i	−0.434060	+	2.18217i
$92$	−49.5234	+	33.0905i	−0.538298	+	0.359679i
$93$	14.1023	+	34.0458i	0.151637	+	0.366084i
$94$	−46.7533	+	19.3658i	−0.497375	+	0.206020i
$95$	−1.18024	−	1.76635i	−0.0124236	−	0.0185932i
$96$	79.7729	+	15.8678i	0.830968	+	0.165290i
$97$	44.0470	−	65.9209i	0.454092	−	0.679597i	−0.531820	−	0.846857i	$-0.678492\pi$
$97$	44.0470	−	65.9209i	0.454092	−	0.679597i	0.985913	+	0.167260i	$0.0534919\pi$
$98$	−27.8790	+	27.8790i	−0.284480	+	0.284480i
$99$	−14.6538	+	2.91482i	−0.148018	+	0.0294426i
$100$	−19.0490	+	45.9884i	−0.190490	+	0.459884i
$101$			140.647i			1.39254i	0.717779	+	0.696271i	$0.245159\pi$
$101$			140.647i			1.39254i	−0.717779	+	0.696271i	$0.754841\pi$
$102$		0			0
$103$	−42.3283			−0.410954			−0.205477	−	0.978662i	$-0.565875\pi$
$103$	−42.3283			−0.410954			−0.205477	+	0.978662i	$0.565875\pi$
$104$	174.953	+	72.4681i	1.68224	+	0.696808i
$105$	7.53981	+	37.9052i	0.0718077	+	0.361002i
$106$	26.6613	+	26.6613i	0.251522	+	0.251522i
$107$	−61.3221	−	40.9741i	−0.573104	−	0.382936i	0.234983	−	0.972000i	$-0.424497\pi$
$107$	−61.3221	−	40.9741i	−0.573104	−	0.382936i	−0.808086	+	0.589064i	$0.799497\pi$
$108$	12.5875	−	63.2818i	0.116551	−	0.585942i
$109$	174.800	−	116.798i	1.60367	−	1.07154i	0.654837	−	0.755770i	$-0.272737\pi$
$109$	174.800	−	116.798i	1.60367	−	1.07154i	0.948836	−	0.315770i	$-0.102263\pi$
$110$	−6.85923	−	16.5596i	−0.0623566	−	0.150542i
$111$	47.9220	−	19.8500i	0.431730	−	0.178828i
$112$	10.5349	+	15.7666i	0.0940615	+	0.140773i
$113$	−140.877	−	28.0222i	−1.24670	−	0.247984i	−0.472729	−	0.881208i	$-0.656731\pi$
$113$	−140.877	−	28.0222i	−1.24670	−	0.247984i	−0.773969	+	0.633224i	$0.781731\pi$
$114$	2.59479	−	3.88338i	0.0227613	−	0.0340648i
$115$	−30.7421	+	30.7421i	−0.267323	+	0.267323i
$116$	−36.1300	+	7.18670i	−0.311465	+	0.0619543i
$117$	15.7659	−	38.0622i	0.134751	−	0.325318i
$118$			31.7420i			0.269000i
$119$		0			0
$120$	36.1473			0.301227
$121$	−48.4202	−	20.0563i	−0.400167	−	0.165755i
$122$	13.4175	+	67.4541i	0.109979	+	0.552902i
$123$	50.1387	+	50.1387i	0.407632	+	0.407632i
$124$	−25.4287	−	16.9909i	−0.205070	−	0.137024i
$125$	−15.0141	+	75.4810i	−0.120113	+	0.603848i
$126$	17.7116	−	11.8345i	0.140568	−	0.0939247i
$127$	−41.4251	−	100.009i	−0.326182	−	0.787472i	−0.998869	−	0.0475454i	$-0.984860\pi$
$127$	−41.4251	−	100.009i	−0.326182	−	0.787472i	0.672687	−	0.739927i	$-0.265140\pi$
$128$	−51.8363	+	21.4713i	−0.404971	+	0.167744i
$129$	35.3184	+	52.8577i	0.273786	+	0.409750i
$130$	48.4744	+	9.64216i	0.372880	+	0.0741705i
$131$	−51.4936	+	77.0656i	−0.393081	+	0.588287i	−0.974243	−	0.225501i	$-0.927598\pi$
$131$	−51.4936	+	77.0656i	−0.393081	+	0.588287i	0.581162	+	0.813788i	$0.302598\pi$
$132$	−34.9732	+	34.9732i	−0.264948	+	0.264948i
$133$	−11.3676	+	2.26116i	−0.0854707	+	0.0170012i
$134$	−35.9016	+	86.6742i	−0.267923	+	0.646822i
$135$		−	47.0965i		−	0.348863i
$136$		0			0
$137$	102.046			0.744863			0.372431	−	0.928060i	$-0.378524\pi$
$137$	102.046			0.744863			0.372431	+	0.928060i	$0.378524\pi$
$138$	−88.3072	−	36.5780i	−0.639907	−	0.265058i
$139$	−6.01550	−	30.2420i	−0.0432770	−	0.217568i	0.953095	−	0.302671i	$-0.0978782\pi$
$139$	−6.01550	−	30.2420i	−0.0432770	−	0.217568i	−0.996372	+	0.0851025i	$0.972878\pi$
$140$	−22.6798	−	22.6798i	−0.161999	−	0.161999i
$141$	84.7504	+	56.6284i	0.601067	+	0.401620i
$142$	27.2506	−	136.998i	0.191906	−	0.964775i
$143$	−157.258	+	105.076i	−1.09970	+	0.734799i
$144$	−1.47657	−	3.56475i	−0.0102539	−	0.0247552i
$145$	−24.8424	+	10.2900i	−0.171327	+	0.0709659i
$146$	26.3292	+	39.4044i	0.180337	+	0.269893i
$147$	77.8870	+	15.4927i	0.529843	+	0.105392i
$148$	−23.9160	+	35.7928i	−0.161595	+	0.241843i
$149$	23.3099	−	23.3099i	0.156443	−	0.156443i	−0.624546	−	0.780988i	$-0.714716\pi$
$149$	23.3099	−	23.3099i	0.156443	−	0.156443i	0.780988	+	0.624546i	$0.214716\pi$
$150$	−78.3471	+	15.5842i	−0.522314	+	0.103895i
$151$	53.9466	−	130.239i	0.357262	−	0.862507i	−0.638421	−	0.769688i	$-0.720412\pi$
$151$	53.9466	−	130.239i	0.357262	−	0.862507i	0.995683	−	0.0928198i	$-0.0295880\pi$
$152$			10.8404i			0.0713185i
$153$		0			0
$154$	−97.7910			−0.635006
$155$	−20.6242	−	8.54284i	−0.133060	−	0.0551151i
$156$	−26.6066	−	133.760i	−0.170555	−	0.857438i
$157$	−78.3942	−	78.3942i	−0.499326	−	0.499326i	0.411902	−	0.911228i	$-0.364865\pi$
$157$	−78.3942	−	78.3942i	−0.499326	−	0.499326i	−0.911228	+	0.411902i	$0.864865\pi$
$158$	8.03741	+	5.37042i	0.0508697	+	0.0339900i
$159$	14.8160	−	74.4850i	0.0931823	−	0.468459i
$160$	−40.9677	+	27.3737i	−0.256048	+	0.171086i
$161$	90.7719	+	219.143i	0.563800	+	1.36113i
$162$	75.6835	−	31.3491i	0.467182	−	0.193513i
$163$	−90.7416	−	135.804i	−0.556697	−	0.833156i	0.441238	−	0.897390i	$-0.354539\pi$
$163$	−90.7416	−	135.804i	−0.556697	−	0.833156i	−0.997935	+	0.0642345i	$0.979539\pi$
$164$	−57.7154	−	11.4803i	−0.351923	−	0.0700019i
$165$	−20.0573	+	30.0179i	−0.121560	+	0.181927i
$166$	126.789	−	126.789i	0.763791	−	0.763791i
$167$	163.517	−	32.5256i	0.979145	−	0.194764i	0.320525	−	0.947240i	$-0.396141\pi$
$167$	163.517	−	32.5256i	0.979145	−	0.194764i	0.658620	+	0.752476i	$0.271141\pi$
$168$	75.4707	−	182.202i	0.449230	−	1.08454i
$169$		−	352.517i		−	2.08590i
$170$		0			0
$171$	2.35840			0.0137918
$172$	−48.7424	−	20.1898i	−0.283386	−	0.117382i
$173$	−3.26113	−	16.3948i	−0.0188504	−	0.0947676i	0.970215	−	0.242246i	$-0.0778842\pi$
$173$	−3.26113	−	16.3948i	−0.0188504	−	0.0947676i	−0.989065	+	0.147479i	$0.952884\pi$
$174$	−41.8018	−	41.8018i	−0.240240	−	0.240240i
$175$	164.826	+	110.133i	0.941864	+	0.629334i
$176$	−3.45570	+	17.3730i	−0.0196347	+	0.0987102i
$177$	53.1594	−	35.5199i	0.300335	−	0.200678i
$178$	−27.8596	−	67.2590i	−0.156514	−	0.377859i
$179$	35.7824	−	14.8215i	0.199901	−	0.0828019i	−0.280487	−	0.959858i	$-0.590496\pi$
$179$	35.7824	−	14.8215i	0.199901	−	0.0828019i	0.480388	+	0.877056i	$0.340496\pi$
$180$	3.62590	+	5.42654i	0.0201439	+	0.0301474i
$181$	42.3641	+	8.42674i	0.234056	+	0.0465566i	0.310724	−	0.950500i	$-0.399428\pi$
$181$	42.3641	+	8.42674i	0.234056	+	0.0465566i	−0.0766687	+	0.997057i	$0.524428\pi$
$182$	149.810	−	224.207i	0.823132	−	1.23190i
$183$	97.9531	−	97.9531i	0.535263	−	0.535263i
$184$	217.589	−	43.2811i	1.18255	−	0.235223i
$185$	−12.0247	+	29.0301i	−0.0649982	+	0.156920i
$186$		−	49.0789i		−	0.263865i
$187$		0			0
$188$	−84.5912			−0.449953
$189$	−237.393	−	98.3313i	−1.25605	−	0.520271i
$190$	0.551967	+	2.77493i	0.00290509	+	0.0146049i
$191$	−107.196	−	107.196i	−0.561234	−	0.561234i	0.368424	−	0.929658i	$-0.379898\pi$
$191$	−107.196	−	107.196i	−0.561234	−	0.561234i	−0.929658	+	0.368424i	$0.879898\pi$
$192$	−109.151	−	72.9320i	−0.568492	−	0.379854i
$193$	40.1233	−	201.713i	0.207893	−	1.04515i	−0.726028	−	0.687666i	$-0.758636\pi$
$193$	40.1233	−	201.713i	0.207893	−	1.04515i	0.933920	−	0.357482i	$-0.116364\pi$
$194$	−87.7949	+	58.6627i	−0.452551	+	0.302385i
$195$	−38.0958	−	91.9714i	−0.195363	−	0.471648i
$196$	−60.8886	+	25.2209i	−0.310656	+	0.128678i
$197$	77.7868	+	116.416i	0.394857	+	0.590945i	0.974627	−	0.223835i	$-0.0718578\pi$
$197$	77.7868	+	116.416i	0.394857	+	0.590945i	−0.579770	+	0.814780i	$0.696858\pi$
$198$	19.5162	+	3.88201i	0.0985667	+	0.0196061i
$199$	−82.3749	+	123.283i	−0.413944	+	0.619511i	−0.978589	−	0.205823i	$-0.934013\pi$
$199$	−82.3749	+	123.283i	−0.413944	+	0.619511i	0.564645	+	0.825334i	$0.309013\pi$
$200$	131.104	−	131.104i	0.655520	−	0.655520i
$201$	185.331	−	36.8645i	0.922043	−	0.183406i
$202$	71.6828	−	173.058i	0.354865	−	0.856721i
$203$			146.704i			0.722678i
$204$		0			0
$205$	−42.9538			−0.209531
$206$	52.0825	+	21.5733i	0.252828	+	0.104725i
$207$	−9.41607	−	47.3378i	−0.0454883	−	0.228685i
$208$	−34.5373	−	34.5373i	−0.166045	−	0.166045i
$209$	−9.00225	−	6.01511i	−0.0430730	−	0.0287804i
$210$	10.0417	−	50.4829i	0.0478175	−	0.240395i
$211$	−170.184	+	113.713i	−0.806559	+	0.538925i	−0.889127	−	0.457660i	$-0.848688\pi$
$211$	−170.184	+	113.713i	−0.806559	+	0.538925i	0.0825683	+	0.996585i	$0.473688\pi$
$212$	24.1193	+	58.2291i	0.113770	+	0.274665i
$213$	−259.929	+	107.666i	−1.22032	+	0.505474i
$214$	54.5702	+	81.6701i	0.255001	+	0.381636i
$215$	−37.7702	−	7.51296i	−0.175675	−	0.0349440i
$216$	−133.519	+	199.825i	−0.618142	+	0.925115i
$217$	−86.1213	+	86.1213i	−0.396872	+	0.396872i
$218$	−274.610	+	54.6233i	−1.25968	+	0.250565i
$219$	36.5289	−	88.1885i	0.166799	−	0.402687i
$220$		−	29.9615i		−	0.136189i
$221$		0			0
$222$	−69.0821			−0.311181
$223$	107.408	+	44.4897i	0.481649	+	0.199506i	0.610278	−	0.792187i	$-0.291058\pi$
$223$	107.408	+	44.4897i	0.481649	+	0.199506i	−0.128629	+	0.991693i	$0.541058\pi$
$224$	52.4438	+	263.653i	0.234124	+	1.17702i
$225$	−28.5225	−	28.5225i	−0.126767	−	0.126767i
$226$	159.059	+	106.280i	0.703801	+	0.470265i
$227$	29.9302	−	150.469i	0.131851	−	0.662859i	−0.857164	−	0.515044i	$-0.827776\pi$
$227$	29.9302	−	150.469i	0.131851	−	0.662859i	0.989015	−	0.147816i	$-0.0472243\pi$
$228$	6.49140	−	4.33742i	0.0284711	−	0.0190238i
$229$	−3.69064	−	8.91000i	−0.0161164	−	0.0389083i	0.915617	−	0.402053i	$-0.131703\pi$
$229$	−3.69064	−	8.91000i	−0.0161164	−	0.0389083i	−0.931733	+	0.363144i	$0.881703\pi$
$230$	53.4946	−	22.1582i	0.232585	−	0.0963399i
$231$	109.430	+	163.774i	0.473723	+	0.708977i
$232$	134.576	+	26.7687i	0.580067	+	0.115382i
$233$	216.700	−	324.315i	0.930044	−	1.39191i	0.0100614	−	0.999949i	$-0.496797\pi$
$233$	216.700	−	324.315i	0.930044	−	1.39191i	0.919982	−	0.391960i	$-0.128203\pi$
$234$	−38.7980	+	38.7980i	−0.165803	+	0.165803i
$235$	−60.5596	+	12.0461i	−0.257700	+	0.0512598i
$236$	−20.3050	+	49.0206i	−0.0860381	+	0.207714i
$237$		−	19.4701i		−	0.0821523i
$238$		0			0
$239$	372.281			1.55766			0.778831	−	0.627233i	$-0.215813\pi$
$239$	372.281			1.55766			0.778831	+	0.627233i	$0.215813\pi$
$240$	−8.61365	−	3.56789i	−0.0358902	−	0.0148662i
$241$	−27.1147	−	136.315i	−0.112509	−	0.565621i	−0.995381	−	0.0960065i	$-0.969393\pi$
$241$	−27.1147	−	136.315i	−0.112509	−	0.565621i	0.882872	−	0.469614i	$-0.155607\pi$
$242$	49.3563	+	49.3563i	0.203952	+	0.203952i
$243$	79.6872	+	53.2453i	0.327931	+	0.219116i
$244$	−22.4284	+	112.755i	−0.0919197	+	0.462111i
$245$	−39.9992	+	26.7266i	−0.163262	+	0.109088i
$246$	−36.1388	−	87.2468i	−0.146906	−	0.354662i
$247$	27.5818	−	11.4248i	0.111667	−	0.0462541i
$248$	63.2872	+	94.7160i	0.255190	+	0.381919i
$249$	−354.218	−	70.4583i	−1.42256	−	0.282965i
$250$	56.9441	−	85.2228i	0.227776	−	0.340891i
$251$	154.052	−	154.052i	0.613754	−	0.613754i	−0.330168	−	0.943922i	$-0.607106\pi$
$251$	154.052	−	154.052i	0.613754	−	0.613754i	0.943922	+	0.330168i	$0.107106\pi$
$252$	34.9232	−	6.94665i	0.138584	−	0.0275661i
$253$	−84.7932	+	204.709i	−0.335151	+	0.809126i
$254$			144.168i			0.567591i
$255$		0			0
$256$	270.472			1.05653
$257$	391.977	+	162.362i	1.52520	+	0.631760i	0.978626	−	0.205648i	$-0.0659301\pi$
$257$	391.977	+	162.362i	1.52520	+	0.631760i	0.546578	+	0.837408i	$0.315930\pi$
$258$	−16.5175	−	83.0389i	−0.0640212	−	0.321856i
$259$	121.222	+	121.222i	0.468039	+	0.468039i
$260$	68.6931	+	45.8993i	0.264204	+	0.176536i
$261$	5.82370	−	29.2777i	0.0223130	−	0.112175i
$262$	102.638	−	68.5803i	0.391747	−	0.261757i
$263$	54.7003	+	132.058i	0.207986	+	0.502122i	0.993106	−	0.117221i	$-0.0373987\pi$
$263$	54.7003	+	132.058i	0.207986	+	0.502122i	−0.785120	+	0.619344i	$0.787399\pi$
$264$	170.202	−	70.4999i	0.644704	−	0.267045i
$265$	25.5592	+	38.2521i	0.0964499	+	0.144347i
$266$	15.1396	+	3.01146i	0.0569158	+	0.0113213i
$267$	−81.4652	+	121.921i	−0.305113	+	0.456634i
$268$	−110.889	+	110.889i	−0.413764	+	0.413764i
$269$	44.9250	−	8.93614i	0.167008	−	0.0332199i	−0.110878	−	0.993834i	$-0.535366\pi$
$269$	44.9250	−	8.93614i	0.167008	−	0.0332199i	0.277886	+	0.960614i	$0.410366\pi$
$270$	−24.0035	+	57.9495i	−0.0889018	+	0.214628i
$271$			329.809i			1.21701i	0.793550	+	0.608504i	$0.208230\pi$
$271$			329.809i			1.21701i	−0.793550	+	0.608504i	$0.791770\pi$
$272$		0			0
$273$	−543.126			−1.98947
$274$	−125.562	−	52.0095i	−0.458255	−	0.189816i
$275$	36.1265	+	181.620i	0.131369	+	0.660437i
$276$	−112.978	−	112.978i	−0.409341	−	0.409341i
$277$	−234.642	−	156.783i	−0.847082	−	0.566002i	0.0545479	−	0.998511i	$-0.482628\pi$
$277$	−234.642	−	156.783i	−0.847082	−	0.566002i	−0.901629	+	0.432509i	$0.857628\pi$
$278$	−8.01157	+	40.2769i	−0.0288186	+	0.144881i
$279$	20.6060	−	13.7685i	0.0738568	−	0.0493495i
$280$	45.7185	+	110.374i	0.163280	+	0.394194i
$281$	−141.231	+	58.4999i	−0.502603	+	0.208185i	−0.619556	−	0.784953i	$-0.712687\pi$
$281$	−141.231	+	58.4999i	−0.502603	+	0.208185i	0.116953	+	0.993137i	$0.462687\pi$
$282$	−75.4189	−	112.872i	−0.267443	−	0.400257i
$283$	311.786	+	62.0182i	1.10172	+	0.219145i	0.712272	−	0.701904i	$-0.247666\pi$
$283$	311.786	+	62.0182i	1.10172	+	0.219145i	0.389447	+	0.921049i	$0.372666\pi$
$284$	129.720	−	194.140i	0.456761	−	0.683592i
$285$	4.02959	−	4.02959i	0.0141389	−	0.0141389i
$286$	247.050	−	49.1414i	0.863813	−	0.171823i
$287$	−89.6819	+	216.511i	−0.312480	+	0.754395i
$288$		−	54.6992i		−	0.189928i
$289$		0			0
$290$	35.8116			0.123488
$291$	196.488	+	81.3882i	0.675218	+	0.279684i
$292$	15.4548	+	77.6963i	0.0529272	+	0.266083i
$293$	−27.2633	−	27.2633i	−0.0930488	−	0.0930488i	0.659050	−	0.752099i	$-0.270958\pi$
$293$	−27.2633	−	27.2633i	−0.0930488	−	0.0930488i	−0.752099	+	0.659050i	$0.770958\pi$
$294$	−87.9393	−	58.7592i	−0.299113	−	0.199861i
$295$	−7.55584	+	37.9858i	−0.0256130	+	0.128765i
$296$	133.320	−	89.0814i	0.450404	−	0.300951i
$297$	−91.8547	−	221.757i	−0.309275	−	0.746656i
$298$	−40.5618	+	16.8013i	−0.136114	+	0.0563801i
$299$	−339.440	−	508.008i	−1.13525	−	1.69902i
$300$	−130.964	−	26.0503i	−0.436546	−	0.0868344i
$301$	−116.729	+	174.697i	−0.387803	+	0.580388i
$302$	−132.756	+	132.756i	−0.439591	+	0.439591i
$303$	−370.039	+	73.6054i	−1.22125	+	0.242922i
$304$	1.07000	−	2.58320i	0.00351972	−	0.00849736i
$305$			83.9164i			0.275136i
$306$		0			0
$307$	−4.80965			−0.0156666			−0.00783330	−	0.999969i	$-0.502493\pi$
$307$	−4.80965			−0.0156666			−0.00783330	+	0.999969i	$0.502493\pi$
$308$	−151.023	−	62.5557i	−0.490334	−	0.203103i
$309$	−22.1519	−	111.365i	−0.0716890	−	0.360405i
$310$	21.0229	+	21.0229i	0.0678159	+	0.0678159i
$311$	−399.630	−	267.024i	−1.28498	−	0.858598i	−0.289843	−	0.957074i	$-0.593603\pi$
$311$	−399.630	−	267.024i	−1.28498	−	0.858598i	−0.995139	+	0.0984763i	$0.968603\pi$
$312$	−99.1031	+	498.225i	−0.317638	+	1.59688i
$313$	73.7441	−	49.2742i	0.235604	−	0.157426i	−0.432164	−	0.901795i	$-0.642250\pi$
$313$	73.7441	−	49.2742i	0.235604	−	0.157426i	0.667768	+	0.744369i	$0.267250\pi$
$314$	56.5047	+	136.414i	0.179951	+	0.434441i
$315$	24.0126	−	9.94634i	0.0762305	−	0.0315757i
$316$	8.97712	+	13.4352i	0.0284086	+	0.0425165i
$317$	−117.988	−	23.4692i	−0.372201	−	0.0740353i	0.00544574	−	0.999985i	$-0.498267\pi$
$317$	−117.988	−	23.4692i	−0.372201	−	0.0740353i	−0.377647	+	0.925950i	$0.623267\pi$
$318$	−56.1927	+	84.0983i	−0.176707	+	0.264460i
$319$	−96.9027	+	96.9027i	−0.303770	+	0.303770i
$320$	77.9950	−	15.5142i	0.243734	−	0.0484818i
$321$	75.7103	−	182.781i	0.235858	−	0.569411i
$322$		−	315.906i		−	0.981074i
$323$		0			0
$324$	136.935			0.422639
$325$	−471.746	−	195.404i	−1.45153	−	0.601242i
$326$	42.4374	+	213.347i	0.130176	+	0.654440i
$327$	398.773	+	398.773i	1.21949	+	1.21949i
$328$	182.248	+	121.774i	0.555634	+	0.371263i
$329$	−65.7216	+	330.405i	−0.199762	+	1.00427i
$330$	39.9785	−	26.7128i	0.121147	−	0.0809478i
$331$	−38.9023	−	93.9184i	−0.117530	−	0.283741i	0.854157	−	0.520015i	$-0.174074\pi$
$331$	−38.9023	−	93.9184i	−0.117530	−	0.283741i	−0.971687	+	0.236274i	$0.924074\pi$
$332$	276.912	−	114.701i	0.834071	−	0.345484i
$333$	−19.3802	−	29.0045i	−0.0581988	−	0.0871006i
$334$	−217.776	−	43.3183i	−0.652023	−	0.129695i
$335$	−63.5954	+	95.1772i	−0.189837	+	0.284111i
$336$	−35.9683	+	35.9683i	−0.107049	+	0.107049i
$337$	−539.044	+	107.223i	−1.59954	+	0.318168i	−0.912696	−	0.408639i	$-0.866004\pi$
$337$	−539.044	+	107.223i	−1.59954	+	0.318168i	−0.686842	+	0.726807i	$0.741004\pi$
$338$	−179.666	+	433.752i	−0.531556	+	1.28329i
$339$		−	385.310i		−	1.13661i
$340$		0			0
$341$	−113.772			−0.333642
$342$	−2.90187	−	1.20200i	−0.00848501	−	0.00351461i
$343$	−33.5487	−	168.661i	−0.0978097	−	0.491722i
$344$	138.955	+	138.955i	0.403940	+	0.403940i
$345$	−96.9704	−	64.7936i	−0.281074	−	0.187807i
$346$	−4.34324	+	21.8349i	−0.0125527	+	0.0631067i
$347$	−212.258	+	141.826i	−0.611695	+	0.408722i	−0.822466	−	0.568814i	$-0.807403\pi$
$347$	−212.258	+	141.826i	−0.611695	+	0.408722i	0.210771	+	0.977535i	$0.432403\pi$
$348$	−37.8162	−	91.2964i	−0.108667	−	0.262346i
$349$	513.215	−	212.580i	1.47053	−	0.609113i	0.503549	−	0.863967i	$-0.332027\pi$
$349$	513.215	−	212.580i	1.47053	−	0.609113i	0.966980	+	0.254854i	$0.0820273\pi$
$350$	−146.678	−	219.519i	−0.419080	−	0.627198i
$351$	649.141	+	129.122i	1.84940	+	0.367869i
$352$	−139.511	+	208.792i	−0.396337	+	0.593160i
$353$	−408.644	+	408.644i	−1.15763	+	1.15763i	−0.172648	+	0.984984i	$0.555232\pi$
$353$	−408.644	+	408.644i	−1.15763	+	1.15763i	−0.984984	+	0.172648i	$0.944768\pi$
$354$	−83.5128	+	16.6117i	−0.235912	+	0.0469258i
$355$	65.2217	−	157.459i	0.183723	−	0.443547i
$356$		−	121.692i		−	0.341832i
$357$		0			0
$358$	−51.5822			−0.144084
$359$	159.526	+	66.0778i	0.444362	+	0.184061i	0.593634	−	0.804735i	$-0.297693\pi$
$359$	159.526	+	66.0778i	0.444362	+	0.184061i	−0.149272	+	0.988796i	$0.547693\pi$
$360$	−4.74254	−	23.8423i	−0.0131737	−	0.0662287i
$361$	−254.057	−	254.057i	−0.703759	−	0.703759i
$362$	−47.8317	−	31.9602i	−0.132132	−	0.0882877i
$363$	27.4279	−	137.889i	0.0755588	−	0.379860i
$364$	374.780	−	250.420i	1.02962	−	0.687967i
$365$	22.1284	+	53.4227i	0.0606257	+	0.146363i
$366$	−170.449	+	70.6023i	−0.465708	+	0.192902i
$367$	−11.3429	−	16.9759i	−0.0309071	−	0.0462558i	0.815694	−	0.578483i	$-0.196355\pi$
$367$	−11.3429	−	16.9759i	−0.0309071	−	0.0462558i	−0.846601	+	0.532227i	$0.821355\pi$
$368$	−56.1220	−	11.1634i	−0.152505	−	0.0303352i
$369$	26.4927	−	39.6492i	0.0717960	−	0.107450i
$370$	29.5913	−	29.5913i	0.0799766	−	0.0799766i
$371$	246.176	−	48.9675i	0.663547	−	0.131988i
$372$	31.3952	−	75.7946i	0.0843956	−	0.203749i
$373$			690.960i			1.85244i	0.376983	+	0.926220i	$0.376961\pi$
$373$			690.960i			1.85244i	−0.376983	+	0.926220i	$0.623039\pi$
$374$		0			0
$375$	−206.447			−0.550525
$376$	291.098	+	120.577i	0.774196	+	0.320682i
$377$	−73.7207	−	370.619i	−0.195546	−	0.983075i
$378$	241.982	+	241.982i	0.640164	+	0.640164i
$379$	145.381	+	97.1405i	0.383591	+	0.256308i	0.732383	−	0.680893i	$-0.238408\pi$
$379$	145.381	+	97.1405i	0.383591	+	0.256308i	−0.348792	+	0.937200i	$0.613408\pi$
$380$	−0.922659	+	4.63852i	−0.00242805	+	0.0122066i
$381$	241.443	−	161.327i	0.633709	−	0.423431i
$382$	77.2642	+	186.532i	0.202262	+	0.488304i
$383$	−440.512	+	182.466i	−1.15016	+	0.476412i	−0.874588	−	0.484868i	$-0.838868\pi$
$383$	−440.512	+	182.466i	−1.15016	+	0.476412i	−0.275574	+	0.961280i	$0.588868\pi$
$384$	−83.6184	−	125.144i	−0.217756	−	0.325895i
$385$	−117.027	−	23.2781i	−0.303966	−	0.0604625i
$386$	−152.176	+	227.747i	−0.394238	+	0.590019i
$387$	30.2306	−	30.2306i	0.0781151	−	0.0781151i
$388$	−173.111	+	34.4340i	−0.446163	+	0.0887473i
$389$	−84.5808	+	204.196i	−0.217431	+	0.524926i	−0.994530	−	0.104453i	$-0.966691\pi$
$389$	−84.5808	+	204.196i	−0.217431	+	0.524926i	0.777098	+	0.629379i	$0.216691\pi$
$390$			132.582i			0.339953i
$391$		0			0
$392$	245.482			0.626228
$393$	−229.707	−	95.1478i	−0.584496	−	0.242106i
$394$	−36.3788	−	182.889i	−0.0923320	−	0.464184i
$395$	8.34002	+	8.34002i	0.0211140	+	0.0211140i
$396$	27.6564	+	18.4794i	0.0698395	+	0.0466652i
$397$	23.6042	−	118.666i	0.0594565	−	0.298908i	−0.939603	−	0.342266i	$-0.888806\pi$
$397$	23.6042	−	118.666i	0.0594565	−	0.298908i	0.999060	+	0.0433581i	$0.0138056\pi$
$398$	164.191	−	109.709i	0.412539	−	0.275650i
$399$	−11.8981	−	28.7246i	−0.0298199	−	0.0719916i
$400$	−44.1818	+	18.3007i	−0.110454	+	0.0457517i
$401$	290.087	+	434.146i	0.723409	+	1.08266i	0.992818	+	0.119633i	$0.0381718\pi$
$401$	290.087	+	434.146i	0.723409	+	1.08266i	−0.269409	+	0.963026i	$0.586828\pi$
$402$	−246.827	−	49.0970i	−0.613998	−	0.122132i
$403$	174.292	−	260.846i	0.432486	−	0.647262i
$404$	221.406	−	221.406i	0.548034	−	0.548034i
$405$	98.0330	−	19.5000i	0.242057	−	0.0481481i
$406$	74.7699	−	180.510i	0.184162	−	0.444607i
$407$			160.142i			0.393471i
$408$		0			0
$409$	136.013			0.332550			0.166275	−	0.986079i	$-0.446826\pi$
$409$	136.013			0.332550			0.166275	+	0.986079i	$0.446826\pi$
$410$	52.8522	+	21.8921i	0.128908	+	0.0533954i
$411$	53.4044	+	268.482i	0.129938	+	0.653241i
$412$	66.6331	+	66.6331i	0.161731	+	0.161731i
$413$	175.694	+	117.395i	0.425409	+	0.284249i
$414$	−12.5405	+	63.0455i	−0.0302911	+	0.152284i
$415$	181.910	−	121.548i	0.438337	−	0.292887i
$416$	−264.979	−	639.715i	−0.636968	−	1.53778i
$417$	76.4181	−	31.6534i	0.183257	−	0.0759074i
$418$	8.01105	+	11.9894i	0.0191652	+	0.0286827i
$419$	367.332	+	73.0669i	0.876687	+	0.174384i	0.612865	−	0.790187i	$-0.290017\pi$
$419$	367.332	+	73.0669i	0.876687	+	0.174384i	0.263822	+	0.964571i	$0.415017\pi$
$420$	47.8011	−	71.5394i	0.113812	−	0.170332i
$421$	−273.997	+	273.997i	−0.650824	+	0.650824i	−0.953192	−	0.302367i	$-0.902223\pi$
$421$	−273.997	+	273.997i	−0.650824	+	0.650824i	0.302367	+	0.953192i	$0.402223\pi$
$422$	267.357	−	53.1807i	0.633548	−	0.126021i
$423$	26.2322	−	63.3301i	0.0620146	−	0.149716i
$424$		−	234.759i		−	0.553678i
$425$		0			0
$426$	374.701			0.879580
$427$	422.985	+	175.206i	0.990598	+	0.410319i
$428$	32.0318	+	161.034i	0.0748405	+	0.376249i
$429$	−358.753	−	358.753i	−0.836254	−	0.836254i
$430$	42.6450	+	28.4945i	0.0991744	+	0.0662662i
$431$	−13.4283	+	67.5084i	−0.0311561	+	0.156632i	−0.993232	−	0.116151i	$-0.962944\pi$
$431$	−13.4283	+	67.5084i	−0.0311561	+	0.156632i	0.962075	+	0.272783i	$0.0879442\pi$
$432$	51.5402	−	34.4381i	0.119306	−	0.0797177i
$433$	104.262	+	251.710i	0.240790	+	0.581317i	0.997362	−	0.0725929i	$-0.0231274\pi$
$433$	104.262	+	251.710i	0.240790	+	0.581317i	−0.756572	+	0.653910i	$0.773127\pi$
$434$	149.860	−	62.0742i	0.345301	−	0.143028i
$435$	−40.0739	−	59.9748i	−0.0921239	−	0.137873i
$436$	−459.033	−	91.3074i	−1.05283	−	0.209421i
$437$	19.4313	−	29.0810i	0.0444653	−	0.0665470i
$438$	−89.8934	+	89.8934i	−0.205236	+	0.205236i
$439$	−144.392	+	28.7213i	−0.328910	+	0.0654244i	−0.356783	−	0.934187i	$-0.616127\pi$
$439$	−144.392	+	28.7213i	−0.328910	+	0.0654244i	0.0278730	+	0.999611i	$0.491127\pi$
$440$	−42.7073	+	103.105i	−0.0970620	+	0.234328i
$441$		−	53.4060i		−	0.121102i
$442$		0			0
$443$	−619.331			−1.39804			−0.699019	−	0.715103i	$-0.746380\pi$
$443$	−619.331			−1.39804			−0.699019	+	0.715103i	$0.746380\pi$
$444$	−106.687	−	44.1910i	−0.240285	−	0.0995293i
$445$	−17.3294	−	87.1206i	−0.0389424	−	0.195777i
$446$	−109.484	−	109.484i	−0.245480	−	0.245480i
$447$	73.5271	+	49.1292i	0.164490	+	0.109909i
$448$	84.6432	−	425.530i	0.188936	−	0.949844i
$449$	−521.681	+	348.576i	−1.16187	+	0.776339i	−0.978407	−	0.206687i	$-0.933732\pi$
$449$	−521.681	+	348.576i	−1.16187	+	0.776339i	−0.183466	+	0.983026i	$0.558732\pi$
$450$	20.5583	+	49.6322i	0.0456852	+	0.110294i
$451$	−202.251	+	83.7750i	−0.448450	+	0.185754i
$452$	177.656	+	265.880i	0.393043	+	0.588231i
$453$	370.888	+	73.7743i	0.818738	+	0.162857i
$454$	−113.516	+	169.889i	−0.250036	+	0.374205i
$455$	232.648	−	232.648i	0.511314	−	0.511314i
$456$	−28.5210	+	5.67318i	−0.0625460	+	0.0124412i
$457$	52.9634	−	127.865i	0.115894	−	0.279792i	−0.855280	−	0.518167i	$-0.826615\pi$
$457$	52.9634	−	127.865i	0.115894	−	0.279792i	0.971173	+	0.238375i	$0.0766147\pi$
$458$			12.8442i			0.0280442i
$459$		0			0
$460$	96.7883			0.210409
$461$	135.609	+	56.1709i	0.294162	+	0.121846i	0.524884	−	0.851174i	$-0.324109\pi$
$461$	135.609	+	56.1709i	0.294162	+	0.121846i	−0.230722	+	0.973020i	$0.574109\pi$
$462$	−51.1775	−	257.287i	−0.110774	−	0.556898i
$463$	522.332	+	522.332i	1.12815	+	1.12815i	0.990478	+	0.137669i	$0.0439609\pi$
$463$	522.332	+	522.332i	1.12815	+	1.12815i	0.137669	+	0.990478i	$0.456039\pi$
$464$	−29.4263	−	19.6620i	−0.0634187	−	0.0423750i
$465$	11.6827	−	58.7328i	0.0251241	−	0.126307i
$466$	−431.929	+	288.606i	−0.926887	+	0.619326i
$467$	2.92741	+	7.06740i	0.00626855	+	0.0151336i	0.926983	−	0.375104i	$-0.122393\pi$
$467$	2.92741	+	7.06740i	0.00626855	+	0.0151336i	−0.920714	+	0.390237i	$0.872393\pi$
$468$	−84.7360	+	35.0988i	−0.181060	+	0.0749974i
$469$	346.968	+	519.274i	0.739803	+	1.10719i
$470$	80.6546	+	16.0432i	0.171605	+	0.0341344i
$471$	165.228	−	247.281i	0.350802	−	0.525012i
$472$	139.748	−	139.748i	0.296077	−	0.296077i
$473$	−192.496	+	38.2899i	−0.406969	+	0.0809512i
$474$	−9.92325	+	23.9568i	−0.0209351	+	0.0505419i
$475$		−	29.2302i		−	0.0615372i
$476$		0			0
$477$	−51.0733			−0.107072
$478$	−458.071	−	189.739i	−0.958307	−	0.396944i
$479$	147.664	+	742.358i	0.308276	+	1.54981i	0.755357	+	0.655314i	$0.227464\pi$
$479$	147.664	+	742.358i	0.308276	+	1.54981i	−0.447081	+	0.894493i	$0.647536\pi$
$480$	−93.4598	−	93.4598i	−0.194708	−	0.194708i
$481$	−367.160	−	245.329i	−0.763327	−	0.510039i
$482$	−36.1119	+	181.547i	−0.0749209	+	0.376653i
$483$	−529.057	+	353.505i	−1.09536	+	0.731894i
$484$	44.6504	+	107.796i	0.0922529	+	0.222718i
$485$	−119.028	+	49.3032i	−0.245419	+	0.101656i
$486$	−70.9132	−	106.129i	−0.145912	−	0.218373i
$487$	8.66318	+	1.72321i	0.0177889	+	0.00353843i	0.203977	−	0.978976i	$-0.434613\pi$
$487$	8.66318	+	1.72321i	0.0177889	+	0.00353843i	−0.186188	+	0.982514i	$0.559613\pi$
$488$	237.903	−	356.047i	0.487506	−	0.729605i
$489$	309.811	−	309.811i	0.633561	−	0.633561i
$490$	62.8383	−	12.4993i	0.128241	−	0.0255088i
$491$	224.608	−	542.252i	0.457450	−	1.10438i	−0.511976	−	0.859000i	$-0.671086\pi$
$491$	224.608	−	542.252i	0.457450	−	1.10438i	0.969426	−	0.245383i	$-0.0789137\pi$
$492$		−	157.857i		−	0.320847i
$493$		0			0
$494$	−39.7607			−0.0804871
$495$	22.4310	+	9.29123i	0.0453152	+	0.0187702i
$496$	−5.73204	−	28.8169i	−0.0115565	−	0.0580986i
$497$	−657.508	−	657.508i	−1.32295	−	1.32295i
$498$	399.934	+	267.228i	0.803081	+	0.536602i
$499$	21.8676	−	109.936i	0.0438229	−	0.220312i	−0.952668	−	0.304012i	$-0.901674\pi$
$499$	21.8676	−	109.936i	0.0438229	−	0.220312i	0.996491	+	0.0836997i	$0.0266736\pi$
$500$	142.457	−	95.1868i	0.284914	−	0.190374i
$501$	171.149	+	413.190i	0.341614	+	0.824730i
$502$	−268.067	+	111.037i	−0.533999	+	0.221190i
$503$	−265.535	−	397.401i	−0.527902	−	0.790061i	0.467686	−	0.883895i	$-0.345088\pi$
$503$	−265.535	−	397.401i	−0.527902	−	0.790061i	−0.995588	+	0.0938335i	$0.970088\pi$
$504$	−130.080	−	25.8746i	−0.258096	−	0.0513385i
$505$	126.977	−	190.035i	0.251441	−	0.376307i
$506$	208.666	−	208.666i	0.412384	−	0.412384i
$507$	927.468	−	184.485i	1.82933	−	0.363875i
$508$	−92.2226	+	222.645i	−0.181541	+	0.438278i
$509$		−	235.103i		−	0.461891i	−0.972967	−	0.230946i	$-0.925818\pi$
$509$		−	235.103i		−	0.461891i	0.972967	−	0.230946i	$-0.0741820\pi$
$510$		0			0
$511$	315.481			0.617380
$512$	−125.455	−	51.9650i	−0.245029	−	0.101494i
$513$	7.39162	+	37.1602i	0.0144086	+	0.0724370i
$514$	−399.555	−	399.555i	−0.777345	−	0.777345i
$515$	57.1920	+	38.2145i	0.111052	+	0.0742029i
$516$	27.6104	−	138.807i	0.0535084	−	0.269005i
$517$	−261.655	+	174.832i	−0.506102	+	0.338166i
$518$	−87.3740	−	210.940i	−0.168676	−	0.407219i
$519$	41.4278	−	17.1600i	0.0798223	−	0.0330635i
$520$	−170.964	−	255.865i	−0.328777	−	0.492049i
$521$	−593.308	−	118.016i	−1.13879	−	0.226519i	−0.410546	−	0.911840i	$-0.634662\pi$
$521$	−593.308	−	118.016i	−1.13879	−	0.226519i	−0.728241	+	0.685321i	$0.759662\pi$
$522$	−22.0876	+	33.0564i	−0.0423134	+	0.0633265i
$523$	721.650	−	721.650i	1.37983	−	1.37983i	0.534934	−	0.844894i	$-0.320336\pi$
$523$	721.650	−	721.650i	1.37983	−	1.37983i	0.844894	−	0.534934i	$-0.179664\pi$
$524$	202.378	−	40.2554i	0.386217	−	0.0768233i
$525$	−203.500	+	491.292i	−0.387619	+	0.935795i
$526$		−	190.369i		−	0.361918i
$527$		0			0
$528$	−47.5166			−0.0899935
$529$	−172.563	−	71.4781i	−0.326207	−	0.135119i
$530$	−11.9534	−	60.0936i	−0.0225535	−	0.113384i
$531$	−30.4031	−	30.4031i	−0.0572563	−	0.0572563i
$532$	21.4544	+	14.3353i	0.0403277	+	0.0269461i
$533$	117.764	−	592.041i	0.220946	−	1.11077i
$534$	162.377	−	108.497i	0.304078	−	0.203178i
$535$	45.8636	+	110.725i	0.0857264	+	0.206962i
$536$	539.655	−	223.533i	1.00682	−	0.417038i
$537$	57.7215	+	86.3863i	0.107489	+	0.160868i
$538$	−59.8321	−	11.9013i	−0.111212	−	0.0221215i
$539$	−136.212	+	203.856i	−0.252713	+	0.378212i
$540$	−74.1392	+	74.1392i	−0.137295	+	0.137295i
$541$	557.546	−	110.903i	1.03058	−	0.204996i	0.349297	−	0.937012i	$-0.386420\pi$
$541$	557.546	−	110.903i	1.03058	−	0.204996i	0.681288	+	0.732016i	$0.261420\pi$
$542$	168.093	−	405.812i	0.310134	−	0.748730i
$543$			115.869i			0.213387i
$544$		0			0
$545$	−341.629			−0.626841
$546$	668.285	+	276.813i	1.22397	+	0.506983i
$547$	71.5805	+	359.860i	0.130860	+	0.657879i	0.989410	+	0.145148i	$0.0463659\pi$
$547$	71.5805	+	359.860i	0.130860	+	0.657879i	−0.858550	+	0.512730i	$0.828634\pi$
$548$	−160.641	−	160.641i	−0.293140	−	0.293140i
$549$	−77.4602	−	51.7573i	−0.141093	−	0.0942755i
$550$	48.1140	−	241.885i	0.0874800	−	0.439792i
$551$	17.9862	−	12.0180i	0.0326428	−	0.0218112i
$552$	227.744	+	549.823i	0.412580	+	0.996056i
$553$	59.4512	−	24.6255i	0.107507	−	0.0445307i
$554$	208.806	+	312.501i	0.376907	+	0.564081i
$555$	−82.6708	−	16.4442i	−0.148956	−	0.0296293i
$556$	−38.1372	+	57.0764i	−0.0685922	+	0.102655i
$557$	−146.512	+	146.512i	−0.263038	+	0.263038i	−0.826287	−	0.563249i	$-0.809551\pi$
$557$	−146.512	+	146.512i	−0.263038	+	0.263038i	0.563249	+	0.826287i	$0.309551\pi$
$558$	−32.3719	+	6.43917i	−0.0580141	+	0.0115397i
$559$	207.105	−	499.996i	0.370493	−	0.894448i
$560$		−	30.8141i		−	0.0550251i
$561$		0			0
$562$	203.593			0.362264
$563$	−793.273	−	328.584i	−1.40901	−	0.583631i	−0.456936	−	0.889499i	$-0.651053\pi$
$563$	−793.273	−	328.584i	−1.40901	−	0.583631i	−0.952074	+	0.305868i	$0.901053\pi$
$564$	−44.2696	−	222.558i	−0.0784922	−	0.394607i
$565$	165.048	+	165.048i	0.292120	+	0.292120i
$566$	−352.027	−	235.217i	−0.621955	−	0.415577i
$567$	106.389	−	534.854i	0.187635	−	0.943306i
$568$	−723.125	+	483.177i	−1.27311	+	0.850663i
$569$	−120.952	−	292.003i	−0.212569	−	0.513187i	0.781248	−	0.624221i	$-0.214584\pi$
$569$	−120.952	−	292.003i	−0.212569	−	0.513187i	−0.993817	+	0.111034i	$0.964584\pi$
$570$	−7.01193	+	2.90444i	−0.0123016	+	0.00509550i
$571$	150.213	+	224.810i	0.263071	+	0.393713i	0.939365	−	0.342918i	$-0.111415\pi$
$571$	150.213	+	224.810i	0.263071	+	0.393713i	−0.676294	+	0.736631i	$0.736415\pi$
$572$	412.966	+	82.1440i	0.721968	+	0.143608i
$573$	225.931	−	338.130i	0.394295	−	0.590105i
$574$	220.697	−	220.697i	0.384489	−	0.384489i
$575$	−586.709	+	116.704i	−1.02036	+	0.202963i
$576$	−33.7846	+	81.5632i	−0.0586538	+	0.141603i
$577$			63.2031i			0.109537i	0.998499	+	0.0547687i	$0.0174421\pi$
$577$			63.2031i			0.109537i	−0.998499	+	0.0547687i	$0.982558\pi$
$578$		0			0
$579$	551.703			0.952855
$580$	55.3054	+	22.9082i	0.0953541	+	0.0394970i
$581$	−232.868	−	1170.70i	−0.400805	−	2.01498i
$582$	−200.287	−	200.287i	−0.344136	−	0.344136i
$583$	194.952	+	130.263i	0.334395	+	0.223435i
$584$	57.5653	−	289.400i	0.0985706	−	0.495548i
$585$	−55.6651	+	37.1942i	−0.0951540	+	0.0635799i
$586$	19.6507	+	47.4411i	0.0335337	+	0.0809575i
$587$	−685.040	+	283.753i	−1.16702	+	0.483395i	−0.880206	−	0.474592i	$-0.842596\pi$
$587$	−685.040	+	283.753i	−1.16702	+	0.483395i	−0.286812	+	0.957987i	$0.592596\pi$
$588$	−98.2209	−	146.998i	−0.167042	−	0.249997i
$589$	17.6137	+	3.50359i	0.0299045	+	0.00594837i
$590$	28.6571	−	42.8883i	0.0485713	−	0.0726921i
$591$	−265.581	+	265.581i	−0.449375	+	0.449375i
$592$	−40.5619	+	8.06826i	−0.0685167	+	0.0136288i
$593$	76.8977	−	185.647i	0.129676	−	0.313065i	−0.845685	−	0.533683i	$-0.820808\pi$
$593$	76.8977	−	185.647i	0.129676	−	0.313065i	0.975360	+	0.220618i	$0.0708075\pi$
$594$			319.674i			0.538172i
$595$		0			0
$596$	−73.3889			−0.123136
$597$	−367.465	−	152.209i	−0.615519	−	0.254956i
$598$	158.747	+	798.076i	0.265464	+	1.33458i
$599$	457.825	+	457.825i	0.764316	+	0.764316i	0.977099	−	0.212784i	$-0.0682529\pi$
$599$	457.825	+	457.825i	0.764316	+	0.764316i	−0.212784	+	0.977099i	$0.568253\pi$
$600$	413.544	+	276.322i	0.689241	+	0.460536i
$601$	−139.911	+	703.378i	−0.232796	+	1.17035i	0.670693	+	0.741735i	$0.265997\pi$
$601$	−139.911	+	703.378i	−0.232796	+	1.17035i	−0.903489	+	0.428611i	$0.859003\pi$
$602$	232.665	−	155.462i	0.386487	−	0.258242i
$603$	−48.6309	−	117.405i	−0.0806482	−	0.194702i
$604$	−289.944	+	120.099i	−0.480040	+	0.198839i
$605$	47.3161	+	70.8135i	0.0782084	+	0.117047i
$606$	492.826	+	98.0293i	0.813245	+	0.161764i
$607$	−577.021	+	863.573i	−0.950612	+	1.42269i	−0.0448067	+	0.998996i	$0.514267\pi$
$607$	−577.021	+	863.573i	−0.950612	+	1.42269i	−0.905805	+	0.423695i	$0.860733\pi$
$608$	28.0282	−	28.0282i	0.0460990	−	0.0460990i
$609$	−385.975	+	76.7753i	−0.633786	+	0.126068i
$610$	42.7693	−	103.254i	0.0701136	−	0.169269i
$611$		−	867.731i		−	1.42018i
$612$		0			0
$613$	−626.391			−1.02185			−0.510923	−	0.859627i	$-0.670696\pi$
$613$	−626.391			−1.02185			−0.510923	+	0.859627i	$0.670696\pi$
$614$	5.91799	+	2.45131i	0.00963842	+	0.00399237i
$615$	−22.4793	−	113.011i	−0.0365517	−	0.183758i
$616$	430.537	+	430.537i	0.698924	+	0.698924i
$617$	557.109	+	372.249i	0.902933	+	0.603320i	0.918006	−	0.396566i	$-0.129798\pi$
$617$	557.109	+	372.249i	0.902933	+	0.603320i	−0.0150736	+	0.999886i	$0.504798\pi$
$618$	−29.5024	+	148.319i	−0.0477385	+	0.239998i
$619$	654.389	−	437.249i	1.05717	−	0.706379i	0.0997323	−	0.995014i	$-0.468201\pi$
$619$	654.389	−	437.249i	1.05717	−	0.706379i	0.957439	+	0.288635i	$0.0932013\pi$
$620$	19.0185	+	45.9147i	0.0306750	+	0.0740560i
$621$	716.368	−	296.729i	1.15357	−	0.477825i
$622$	355.628	+	532.235i	0.571749	+	0.855684i
$623$	−475.318	−	94.5466i	−0.762950	−	0.151760i
$624$	72.7926	−	108.942i	0.116655	−	0.174586i
$625$	−306.829	+	306.829i	−0.490927	+	0.490927i
$626$	−115.851	+	23.0442i	−0.185066	+	0.0368119i
$627$	11.1145	−	26.8327i	0.0177264	−	0.0427954i
$628$			246.816i			0.393019i
$629$		0			0
$630$	−34.6154			−0.0549451
$631$	767.465	+	317.894i	1.21627	+	0.503794i	0.896221	−	0.443608i	$-0.146302\pi$
$631$	767.465	+	317.894i	1.21627	+	0.503794i	0.320046	+	0.947402i	$0.396302\pi$
$632$	−11.7417	−	59.0297i	−0.0185787	−	0.0934013i
$633$	−388.241	−	388.241i	−0.613336	−	0.613336i
$634$	133.216	+	89.0118i	0.210119	+	0.140397i
$635$	−34.3176	+	172.526i	−0.0540435	+	0.271695i
$636$	−140.577	+	93.9308i	−0.221034	+	0.147690i
$637$	−258.714	−	624.591i	−0.406145	−	0.980520i
$638$	168.621	−	69.8452i	0.264297	−	0.109475i
$639$	105.118	+	157.320i	0.164504	+	0.246198i
$640$	89.4233	+	17.7874i	0.139724	+	0.0277928i
$641$	−469.870	+	703.209i	−0.733026	+	1.09705i	0.258357	+	0.966050i	$0.416819\pi$
$641$	−469.870	+	703.209i	−0.733026	+	1.09705i	−0.991382	+	0.131001i	$0.958181\pi$
$642$	−186.314	+	186.314i	−0.290209	+	0.290209i
$643$	−724.957	+	144.203i	−1.12746	+	0.224266i	−0.723375	−	0.690456i	$-0.757410\pi$
$643$	−724.957	+	144.203i	−1.12746	+	0.224266i	−0.404085	+	0.914721i	$0.632410\pi$
$644$	202.081	−	487.867i	0.313790	−	0.757557i
$645$		−	103.305i		−	0.160162i
$646$		0			0
$647$	874.070			1.35096			0.675479	−	0.737379i	$-0.263937\pi$
$647$	874.070			1.35096			0.675479	+	0.737379i	$0.263937\pi$
$648$	−471.225	−	195.188i	−0.727199	−	0.301216i
$649$	38.5084	+	193.595i	0.0593350	+	0.298297i
$650$	480.866	+	480.866i	0.739793	+	0.739793i
$651$	−271.654	−	181.514i	−0.417288	−	0.278823i
$652$	−70.9377	+	356.628i	−0.108800	+	0.546976i
$653$	960.997	−	642.117i	1.47166	−	0.983335i	0.477140	−	0.878827i	$-0.341673\pi$
$653$	960.997	−	642.117i	1.47166	−	0.983335i	0.994524	−	0.104507i	$-0.0333266\pi$
$654$	−287.426	−	693.908i	−0.439489	−	1.06102i
$655$	139.151	−	57.6384i	0.212445	−	0.0879976i
$656$	−31.4088	−	47.0066i	−0.0478793	−	0.0716565i
$657$	−62.9607	−	12.5237i	−0.0958307	−	0.0190619i
$658$	249.263	−	373.048i	0.378819	−	0.566942i
$659$	−318.726	+	318.726i	−0.483651	+	0.483651i	−0.906295	−	0.422645i	$-0.861102\pi$
$659$	−318.726	+	318.726i	−0.483651	+	0.483651i	0.422645	+	0.906295i	$0.361102\pi$
$660$	78.8284	−	15.6799i	0.119437	−	0.0237575i
$661$	−191.121	+	461.408i	−0.289140	+	0.698045i	−0.999986	−	0.00530241i	$-0.998312\pi$
$661$	−191.121	+	461.408i	−0.289140	+	0.698045i	0.710846	+	0.703347i	$0.248312\pi$
$662$			135.388i			0.204514i
$663$		0			0
$664$	−1116.41			−1.68134
$665$	17.4008	+	7.20763i	0.0261666	+	0.0108385i
$666$	9.06360	+	45.5658i	0.0136090	+	0.0684171i
$667$	−313.036	−	313.036i	−0.469320	−	0.469320i
$668$	−308.610	−	206.207i	−0.461991	−	0.308693i
$669$	−60.8416	+	305.871i	−0.0909441	+	0.457207i
$670$	126.759	−	84.6977i	0.189193	−	0.126414i
$671$	163.666	+	395.126i	0.243914	+	0.588861i
$672$	−666.221	+	275.958i	−0.991400	+	0.410651i
$673$	−522.061	−	781.320i	−0.775722	−	1.16095i	−0.983168	−	0.182704i	$-0.941515\pi$
$673$	−522.061	−	781.320i	−0.775722	−	1.16095i	0.207446	−	0.978247i	$-0.433485\pi$
$674$	717.911	+	142.801i	1.06515	+	0.211871i
$675$	360.021	−	538.810i	0.533365	−	0.798236i
$676$	−554.932	+	554.932i	−0.820905	+	0.820905i
$677$	1091.43	−	217.100i	1.61216	−	0.320679i	0.694943	−	0.719065i	$-0.255430\pi$
$677$	1091.43	−	217.100i	1.61216	−	0.320679i	0.917218	+	0.398386i	$0.130430\pi$
$678$	−196.379	+	474.102i	−0.289645	+	0.699265i
$679$			702.908i			1.03521i
$680$		0			0
$681$	411.546			0.604325
$682$	139.990	+	57.9857i	0.205264	+	0.0850231i
$683$	−256.456	−	1289.29i	−0.375484	−	1.88769i	−0.454387	−	0.890804i	$-0.650142\pi$
$683$	−256.456	−	1289.29i	−0.375484	−	1.88769i	0.0789027	−	0.996882i	$-0.474858\pi$
$684$	−3.71259	−	3.71259i	−0.00542776	−	0.00542776i
$685$	−137.880	−	92.1285i	−0.201285	−	0.134494i
$686$	−44.6809	+	224.626i	−0.0651325	+	0.327443i
$687$	21.5107	−	14.3730i	0.0313110	−	0.0209213i
$688$	−19.3966	−	46.8276i	−0.0281928	−	0.0680634i
$689$	−597.310	+	247.414i	−0.866923	+	0.359091i
$690$	86.2935	+	129.147i	0.125063	+	0.187170i
$691$	470.003	+	93.4894i	0.680178	+	0.135296i	0.523075	−	0.852286i	$-0.324785\pi$
$691$	470.003	+	93.4894i	0.680178	+	0.135296i	0.157103	+	0.987582i	$0.449785\pi$
$692$	−20.6750	+	30.9423i	−0.0298771	+	0.0447143i
$693$	93.6660	−	93.6660i	0.135160	−	0.135160i
$694$	333.456	−	66.3285i	0.480484	−	0.0955742i
$695$	−19.1749	+	46.2924i	−0.0275898	+	0.0666078i
$696$			368.075i			0.528844i
$697$		0			0
$698$	−739.826			−1.05992
$699$	966.675	+	400.410i	1.38294	+	0.572832i
$700$	−86.0974	−	432.841i	−0.122996	−	0.618344i
$701$	777.458	+	777.458i	1.10907	+	1.10907i	0.993273	+	0.115796i	$0.0369420\pi$
$701$	777.458	+	777.458i	1.10907	+	1.10907i	0.115796	+	0.993273i	$0.463058\pi$
$702$	−732.921	−	489.722i	−1.04405	−	0.697610i
$703$	4.93156	−	24.7926i	0.00701502	−	0.0352669i
$704$	336.987	−	225.167i	0.478674	−	0.319840i
$705$	−63.3860	−	153.027i	−0.0899092	−	0.217060i
$706$	711.085	−	294.541i	1.00720	−	0.417197i
$707$	−692.771	−	1036.81i	−0.979875	−	1.46649i
$708$	−139.599	−	27.7679i	−0.197173	−	0.0392202i
$709$	289.947	−	433.937i	0.408953	−	0.612041i	−0.568630	−	0.822593i	$-0.692526\pi$
$709$	289.947	−	433.937i	0.408953	−	0.612041i	0.977583	+	0.210553i	$0.0675264\pi$
$710$	−160.503	+	160.503i	−0.226061	+	0.226061i
$711$	−12.8423	+	2.55448i	−0.0180623	+	0.00359281i
$712$	−173.461	+	418.771i	−0.243625	+	0.588162i
$713$		−	367.531i		−	0.515472i
$714$		0			0
$715$	307.343			0.429851
$716$	−79.6605	−	32.9965i	−0.111258	−	0.0460845i
$717$	194.828	+	979.467i	0.271727	+	1.36606i
$718$	−162.610	−	162.610i	−0.226476	−	0.226476i
$719$	516.851	+	345.349i	0.718847	+	0.480318i	0.860404	−	0.509612i	$-0.170211\pi$
$719$	516.851	+	345.349i	0.718847	+	0.480318i	−0.141557	+	0.989930i	$0.545211\pi$
$720$	−1.22323	+	6.14958i	−0.00169893	+	0.00854108i
$721$	312.032	−	208.493i	0.432776	−	0.289172i
$722$	183.118	+	442.087i	0.253627	+	0.612309i
$723$	344.452	−	142.677i	0.476420	−	0.197340i
$724$	−53.4241	−	79.9548i	−0.0737902	−	0.110435i
$725$	−362.871	−	72.1795i	−0.500511	−	0.0995579i
$726$	−104.026	+	155.686i	−0.143286	+	0.214443i
$727$	181.405	−	181.405i	0.249526	−	0.249526i	−0.571250	−	0.820776i	$-0.693541\pi$
$727$	181.405	−	181.405i	0.249526	−	0.249526i	0.820776	+	0.571250i	$0.193541\pi$
$728$	−1646.65	+	327.540i	−2.26189	+	0.449917i
$729$	−310.231	+	748.965i	−0.425557	+	1.02739i
$730$		−	77.0116i		−	0.105495i
$731$		0			0
$732$	−308.395			−0.421305
$733$	−204.776	−	84.8211i	−0.279367	−	0.115718i	0.238600	−	0.971118i	$-0.423311\pi$
$733$	−204.776	−	84.8211i	−0.279367	−	0.115718i	−0.517968	+	0.855400i	$0.673311\pi$
$734$	5.30478	+	26.6690i	0.00722723	+	0.0363337i
$735$	−91.2502	−	91.2502i	−0.124150	−	0.124150i
$736$	−674.487	−	450.677i	−0.916422	−	0.612334i
$737$	−113.814	+	572.182i	−0.154429	+	0.776366i
$738$	−52.8056	+	35.2836i	−0.0715523	+	0.0478097i
$739$	−113.071	−	272.978i	−0.153006	−	0.369388i	0.828727	−	0.559653i	$-0.189065\pi$
$739$	−113.071	−	272.978i	−0.153006	−	0.369388i	−0.981733	+	0.190265i	$0.939065\pi$
$740$	64.6284	−	26.7699i	0.0873356	−	0.0361756i
$741$	44.4929	+	66.5884i	0.0600445	+	0.0898629i
$742$	−327.862	−	65.2159i	−0.441863	−	0.0878920i
$743$	−415.988	+	622.570i	−0.559876	+	0.837914i	−0.998142	−	0.0609312i	$-0.980593\pi$
$743$	−415.988	+	622.570i	−0.559876	+	0.837914i	0.438265	+	0.898846i	$0.355593\pi$
$744$	−216.076	+	216.076i	−0.290425	+	0.290425i
$745$	−52.5398	+	10.4508i	−0.0705232	+	0.0140279i
$746$	352.159	−	850.187i	0.472063	−	1.13966i
$747$			242.882i			0.325143i
$748$		0			0
$749$	653.871			0.872992
$750$	254.021	+	105.219i	0.338695	+	0.140292i
$751$	135.892	+	683.178i	0.180949	+	0.909691i	0.959414	+	0.282003i	$0.0909987\pi$
$751$	135.892	+	683.178i	0.180949	+	0.909691i	−0.778465	+	0.627688i	$0.784001\pi$
$752$	−57.4652	−	57.4652i	−0.0764165	−	0.0764165i
$753$	485.930	+	324.688i	0.645326	+	0.431193i
$754$	−98.1828	+	493.598i	−0.130216	+	0.654640i
$755$	−190.471	+	127.269i	−0.252280	+	0.168568i
$756$	218.910	+	528.496i	0.289564	+	0.699069i
$757$	633.525	−	262.415i	0.836889	−	0.346651i	0.0772631	−	0.997011i	$-0.475382\pi$
$757$	633.525	−	262.415i	0.836889	−	0.346651i	0.759626	+	0.650360i	$0.225382\pi$
$758$	−129.374	−	193.622i	−0.170678	−	0.255438i
$759$	−582.962	−	115.958i	−0.768066	−	0.152778i
$760$	9.78685	−	14.6471i	0.0128774	−	0.0192724i
$761$	−305.005	+	305.005i	−0.400795	+	0.400795i	−0.878513	−	0.477718i	$-0.841464\pi$
$761$	−305.005	+	305.005i	−0.400795	+	0.400795i	0.477718	+	0.878513i	$0.341464\pi$
$762$	−379.305	+	75.4484i	−0.497775	+	0.0990136i
$763$	−713.275	+	1722.00i	−0.934830	+	2.25688i
$764$			337.495i			0.441747i
$765$		0			0
$766$	635.021			0.829009
$767$	−502.850	−	208.287i	−0.655606	−	0.271561i
$768$	141.547	+	711.607i	0.184307	+	0.926572i
$769$	303.275	+	303.275i	0.394376	+	0.394376i	0.876244	−	0.481868i	$-0.160041\pi$
$769$	303.275	+	303.275i	0.394376	+	0.394376i	−0.481868	+	0.876244i	$0.660041\pi$
$770$	132.131	+	88.2869i	0.171598	+	0.114658i
$771$	−222.037	+	1116.26i	−0.287986	+	1.44780i
$772$	−380.699	+	254.375i	−0.493133	+	0.329501i
$773$	79.8088	+	192.675i	0.103246	+	0.249257i	0.967058	−	0.254557i	$-0.0819297\pi$
$773$	79.8088	+	192.675i	0.103246	+	0.249257i	−0.863812	+	0.503814i	$0.831930\pi$
$774$	−52.6045	+	21.7895i	−0.0679644	+	0.0281518i
$775$	−170.648	−	255.393i	−0.220191	−	0.329539i
$776$	644.798	+	128.258i	0.830925	+	0.165281i
$777$	−255.494	+	382.373i	−0.328821	+	0.492115i
$778$	208.144	−	208.144i	0.267537	−	0.267537i
$779$	33.8915	−	6.74144i	0.0435064	−	0.00865396i
$780$	−84.8108	+	204.751i	−0.108732	+	0.262502i
$781$		−	868.612i		−	1.11218i
$782$		0			0
$783$	479.568			0.612475
$784$	−58.4966	−	24.2301i	−0.0746130	−	0.0309057i
$785$	35.1474	+	176.698i	0.0447737	+	0.225093i
$786$	234.148	+	234.148i	0.297898	+	0.297898i
$787$	−919.662	−	614.498i	−1.16857	−	0.780811i	−0.189009	−	0.981975i	$-0.560527\pi$
$787$	−919.662	−	614.498i	−1.16857	−	0.780811i	−0.979558	+	0.201164i	$0.935527\pi$
$788$	60.8102	−	305.714i	0.0771703	−	0.387962i
$789$	−318.817	+	213.027i	−0.404077	+	0.269996i
$790$	−6.01129	−	14.5125i	−0.00760922	−	0.0183703i
$791$	1176.53	−	487.334i	1.48739	−	0.616099i
$792$	−68.8315	−	103.014i	−0.0869084	−	0.130068i
$793$	−1156.64	−	230.069i	−1.45856	−	0.290125i
$794$	−89.5239	+	133.982i	−0.112750	+	0.168743i
$795$	−87.2646	+	87.2646i	−0.109767	+	0.109767i
$796$	323.746	−	64.3970i	0.406716	−	0.0809008i
$797$	23.4701	−	56.6619i	0.0294481	−	0.0710940i	−0.908471	−	0.417947i	$-0.862750\pi$
$797$	23.4701	−	56.6619i	0.0294481	−	0.0710940i	0.937919	+	0.346853i	$0.112750\pi$
$798$			41.4081i			0.0518899i
$799$		0			0
$800$	−677.946			−0.847433
$801$	91.1062	+	37.7374i	0.113741	+	0.0471129i
$802$	−135.666	−	682.039i	−0.169160	−	0.850423i
$803$	208.386	+	208.386i	0.259509	+	0.259509i
$804$	−349.779	−	233.715i	−0.435049	−	0.290690i
$805$	75.1979	−	378.045i	0.0934135	−	0.469621i
$806$	−347.401	+	232.126i	−0.431018	+	0.287997i
$807$	47.0217	+	113.521i	0.0582673	+	0.140670i
$808$	−1077.50	+	446.315i	−1.33354	+	0.552370i
$809$	451.829	+	676.209i	0.558503	+	0.835858i	0.998054	−	0.0623592i	$-0.0198624\pi$
$809$	451.829	+	676.209i	0.558503	+	0.835858i	−0.439551	+	0.898218i	$0.644862\pi$
$810$	−130.562	−	25.9705i	−0.161188	−	0.0320623i
$811$	642.700	−	961.868i	0.792478	−	1.18603i	−0.186579	−	0.982440i	$-0.559740\pi$
$811$	642.700	−	961.868i	0.792478	−	1.18603i	0.979057	−	0.203587i	$-0.0652601\pi$
$812$	230.941	−	230.941i	0.284410	−	0.284410i
$813$	−867.724	+	172.601i	−1.06731	+	0.212301i
$814$	81.6192	−	197.046i	0.100269	−	0.242071i
$815$			265.415i			0.325663i
$816$		0			0
$817$	30.9806			0.0379200
$818$	−167.356	−	69.3211i	−0.204592	−	0.0847446i
$819$	71.2583	+	358.240i	0.0870065	+	0.437411i
$820$	67.6178	+	67.6178i	0.0824608	+	0.0824608i
$821$	−832.050	−	555.958i	−1.01346	−	0.677172i	−0.0662547	−	0.997803i	$-0.521105\pi$
$821$	−832.050	−	555.958i	−1.01346	−	0.677172i	−0.947204	+	0.320631i	$0.896105\pi$
$822$	71.1252	−	357.570i	0.0865270	−	0.435000i
$823$	−45.0492	+	30.1009i	−0.0547378	+	0.0365746i	−0.582638	−	0.812732i	$-0.697979\pi$
$823$	−45.0492	+	30.1009i	−0.0547378	+	0.0365746i	0.527900	+	0.849306i	$0.322979\pi$
$824$	−134.321	−	324.279i	−0.163011	−	0.393542i
$825$	−458.934	+	190.097i	−0.556283	+	0.230420i
$826$	−156.349	−	233.993i	−0.189285	−	0.283284i
$827$	402.321	+	80.0267i	0.486483	+	0.0967675i	0.432237	−	0.901760i	$-0.357724\pi$
$827$	402.321	+	80.0267i	0.486483	+	0.0967675i	0.0542461	+	0.998528i	$0.482724\pi$
$828$	−59.6963	+	89.3418i	−0.0720970	+	0.107901i
$829$	−153.097	+	153.097i	−0.184677	+	0.184677i	−0.793390	−	0.608713i	$-0.791686\pi$
$829$	−153.097	+	153.097i	−0.184677	+	0.184677i	0.608713	+	0.793390i	$0.291686\pi$
$830$	−285.779	+	56.8449i	−0.344312	+	0.0684878i
$831$	289.696	−	699.389i	0.348612	−	0.841623i
$832$			1117.56i			1.34322i
$833$		0			0
$834$	−110.161			−0.132087
$835$	−250.301	−	103.678i	−0.299762	−	0.124165i
$836$	4.70235	+	23.6403i	0.00562482	+	0.0282779i
$837$	281.527	+	281.527i	0.336352	+	0.336352i
$838$	−414.741	−	277.121i	−0.494918	−	0.330694i
$839$	55.3480	−	278.253i	0.0659690	−	0.331648i	−0.933681	−	0.358106i	$-0.883423\pi$
$839$	55.3480	−	278.253i	0.0659690	−	0.331648i	0.999650	+	0.0264576i	$0.00842268\pi$
$840$	−266.467	+	178.048i	−0.317223	+	0.211961i
$841$	217.057	+	524.021i	0.258094	+	0.623093i
$842$	476.785	−	197.491i	0.566252	−	0.234549i
$843$	−227.824	−	340.963i	−0.270254	−	0.404463i
$844$	446.910	+	88.8960i	0.529515	+	0.105327i
$845$	−318.257	+	476.305i	−0.376635	+	0.563674i
$846$	−64.5544	+	64.5544i	−0.0763054	+	0.0763054i
$847$	455.729	−	90.6502i	0.538051	−	0.107025i
$848$	−23.1718	+	55.9416i	−0.0273252	+	0.0659689i
$849$			852.762i			1.00443i
$850$		0			0
$851$	−517.327			−0.607905
$852$	578.667	+	239.692i	0.679187	+	0.281328i
$853$	111.217	+	559.124i	0.130383	+	0.655479i	0.989598	+	0.143864i	$0.0459527\pi$
$853$	111.217	+	559.124i	0.130383	+	0.655479i	−0.859215	+	0.511615i	$0.829047\pi$
$854$	−431.162	−	431.162i	−0.504874	−	0.504874i
$855$	−3.18656	−	2.12919i	−0.00372697	−	0.00249028i
$856$	119.311	−	599.815i	0.139382	−	0.700718i
$857$	1104.79	−	738.200i	1.28914	−	0.861377i	0.293622	−	0.955922i	$-0.405139\pi$
$857$	1104.79	−	738.200i	1.28914	−	0.861377i	0.995521	+	0.0945445i	$0.0301395\pi$
$858$	258.581	+	624.269i	0.301376	+	0.727586i
$859$	−260.316	+	107.826i	−0.303046	+	0.125526i	−0.529024	−	0.848607i	$-0.677442\pi$
$859$	−260.316	+	107.826i	−0.303046	+	0.125526i	0.225979	+	0.974132i	$0.427442\pi$
$860$	47.6309	+	71.2847i	0.0553848	+	0.0828892i
$861$	−616.572	−	122.644i	−0.716111	−	0.142443i
$862$	50.9295	−	76.2213i	0.0590829	−	0.0884238i
$863$	44.4457	−	44.4457i	0.0515014	−	0.0515014i	−0.680887	−	0.732388i	$-0.738406\pi$
$863$	44.4457	−	44.4457i	0.0515014	−	0.0515014i	0.732388	+	0.680887i	$0.238406\pi$
$864$	861.869	−	171.436i	0.997533	−	0.198422i
$865$	−10.3951	+	25.0961i	−0.0120175	+	0.0290128i
$866$		−	362.854i		−	0.419000i
$867$		0			0
$868$	271.144			0.312378
$869$	55.5355	+	23.0035i	0.0639073	+	0.0264713i
$870$	18.7415	+	94.2198i	0.0215419	+	0.108299i
$871$	−1137.49	−	1137.49i	−1.30596	−	1.30596i
$872$	1449.49	+	968.518i	1.66226	+	1.11069i
$873$	27.9034	−	140.280i	0.0319626	−	0.160687i
$874$	−38.7307	+	25.8790i	−0.0443143	+	0.0296099i
$875$	−261.111	−	630.377i	−0.298412	−	0.720431i
$876$	−196.330	+	81.3225i	−0.224121	+	0.0928339i
$877$	250.521	+	374.931i	0.285657	+	0.427515i	0.946351	−	0.323139i	$-0.104738\pi$
$877$	250.521	+	374.931i	0.285657	+	0.427515i	−0.660695	+	0.750655i	$0.729738\pi$
$878$	192.304	+	38.2516i	0.219025	+	0.0435668i
$879$	57.4615	−	85.9972i	0.0653714	−	0.0978353i
$880$	20.3537	−	20.3537i	0.0231292	−	0.0231292i
$881$	965.483	−	192.046i	1.09589	−	0.217987i	0.386143	−	0.922439i	$-0.373807\pi$
$881$	965.483	−	192.046i	1.09589	−	0.217987i	0.709752	+	0.704452i	$0.248807\pi$
$882$	−27.2192	+	65.7130i	−0.0308608	+	0.0745046i
$883$		−	908.452i		−	1.02882i	−0.857543	−	0.514412i	$-0.828010\pi$
$883$		−	908.452i		−	1.02882i	0.857543	−	0.514412i	$-0.171990\pi$
$884$		0			0
$885$	−103.894			−0.117395
$886$	762.051	+	315.652i	0.860103	+	0.356266i
$887$	−48.8583	−	245.627i	−0.0550827	−	0.276919i	0.943421	−	0.331596i	$-0.107587\pi$
$887$	−48.8583	−	245.627i	−0.0550827	−	0.276919i	−0.998504	+	0.0546769i	$0.982587\pi$
$888$	304.143	+	304.143i	0.342503	+	0.342503i
$889$	797.979	+	533.193i	0.897614	+	0.599767i
$890$	−23.0796	+	116.029i	−0.0259322	+	0.130370i
$891$	423.563	−	283.016i	0.475379	−	0.317638i
$892$	−99.0454	−	239.117i	−0.111037	−	0.268068i
$893$	45.8922	−	19.0092i	0.0513911	−	0.0212869i
$894$	−65.4313	−	97.9249i	−0.0731894	−	0.109536i
$895$	−61.7285	−	12.2786i	−0.0689704	−	0.0137191i
$896$	276.362	−	413.605i	0.308440	−	0.461613i
$897$	1158.92	−	1158.92i	1.29200	−	1.29200i
$898$	819.556	−	163.020i	0.912646	−	0.181537i
$899$	86.9888	−	210.010i	0.0967617	−	0.233604i
$900$			89.8001i			0.0997779i
$901$		0			0
$902$	291.555			0.323232
$903$	−520.713	−	215.687i	−0.576648	−	0.238856i
$904$	−232.367	−	1168.19i	−0.257043	−	1.29224i
$905$	−49.6326	−	49.6326i	−0.0548427	−	0.0548427i
$906$	−418.756	−	279.804i	−0.462204	−	0.308835i
$907$	−338.757	+	1703.05i	−0.373492	+	1.87767i	0.0970321	+	0.995281i	$0.469065\pi$
$907$	−338.757	+	1703.05i	−0.373492	+	1.87767i	−0.470524	+	0.882387i	$0.655935\pi$
$908$	−283.984	+	189.752i	−0.312758	+	0.208978i
$909$	97.0986	+	234.417i	0.106819	+	0.257884i
$910$	−404.833	+	167.687i	−0.444871	+	0.184272i
$911$	997.265	+	1492.51i	1.09469	+	1.63832i	0.689882	+	0.723922i	$0.257663\pi$
$911$	997.265	+	1492.51i	1.09469	+	1.63832i	0.404811	+	0.914401i	$0.367337\pi$
$912$	7.35633	+	1.46326i	0.00806615	+	0.00160446i
$913$	619.472	−	927.106i	0.678502	−	1.01545i
$914$	−130.337	+	130.337i	−0.142600	+	0.142600i
$915$	−220.783	+	43.9164i	−0.241293	+	0.0479961i
$916$	−8.21630	+	19.8359i	−0.00896976	+	0.0216549i
$917$		−	821.743i		−	0.896121i
$918$		0			0
$919$	−506.869			−0.551544			−0.275772	−	0.961223i	$-0.588933\pi$
$919$	−506.869			−0.551544			−0.275772	+	0.961223i	$0.588933\pi$
$920$	−333.071	−	137.962i	−0.362033	−	0.149959i
$921$	−2.51706	−	12.6541i	−0.00273296	−	0.0137395i
$922$	−138.230	−	138.230i	−0.149924	−	0.149924i
$923$	1991.48	+	1330.66i	2.15761	+	1.44167i
$924$	85.5476	−	430.077i	0.0925839	−	0.465451i
$925$	−359.484	+	240.200i	−0.388632	+	0.259675i
$926$	−376.485	−	908.914i	−0.406571	−	0.981549i
$927$	−70.5489	+	29.2223i	−0.0761045	+	0.0315235i
$928$	−278.737	−	417.160i	−0.300364	−	0.449526i
$929$	1367.79	+	272.070i	1.47232	+	0.292863i	0.865073	−	0.501646i	$-0.167272\pi$
$929$	1367.79	+	272.070i	1.47232	+	0.292863i	0.607251	+	0.794510i	$0.292272\pi$
$930$	−44.3090	+	66.3131i	−0.0476441	+	0.0713044i
$931$	27.3656	−	27.3656i	0.0293937	−	0.0293937i
$932$	−851.665	+	169.407i	−0.913803	+	0.181767i
$933$	493.396	−	1191.16i	0.528827	−	1.27670i
$934$		−	10.1880i		−	0.0109080i
$935$		0			0
$936$	341.626			0.364985
$937$	185.233	+	76.7261i	0.197687	+	0.0818848i	0.479331	−	0.877634i	$-0.340879\pi$
$937$	185.233	+	76.7261i	0.197687	+	0.0818848i	−0.281643	+	0.959519i	$0.590879\pi$
$938$	−162.268	−	815.774i	−0.172993	−	0.869695i
$939$	168.233	+	168.233i	0.179162	+	0.179162i
$940$	114.296	+	76.3699i	0.121591	+	0.0812446i
$941$	297.945	−	1497.87i	0.316626	−	1.59179i	−0.414830	−	0.909899i	$-0.636159\pi$
$941$	297.945	−	1497.87i	0.316626	−	1.59179i	0.731456	−	0.681889i	$-0.238841\pi$
$942$	−329.334	+	220.054i	−0.349611	+	0.233603i
$943$	−270.628	−	653.355i	−0.286987	−	0.692847i
$944$	−47.0948	+	19.5073i	−0.0498886	+	0.0206645i
$945$	231.979	+	347.182i	0.245481	+	0.367388i
$946$	256.371	+	50.9953i	0.271005	+	0.0539063i
$947$	−565.096	+	845.726i	−0.596723	+	0.893058i	−0.999755	−	0.0221273i	$-0.992956\pi$
$947$	−565.096	+	845.726i	−0.596723	+	0.893058i	0.403033	+	0.915186i	$0.367956\pi$
$948$	−30.6498	+	30.6498i	−0.0323310	+	0.0323310i
$949$	−797.004	+	158.534i	−0.839835	+	0.167054i
$950$	−14.8976	+	35.9661i	−0.0156817	+	0.0378590i
$951$		−	322.706i		−	0.339334i
$952$		0			0
$953$	297.230			0.311889			0.155945	−	0.987766i	$-0.450158\pi$
$953$	297.230			0.311889			0.155945	+	0.987766i	$0.450158\pi$
$954$	62.8428	+	26.0303i	0.0658730	+	0.0272855i
$955$	48.0603	+	241.616i	0.0503249	+	0.253001i
$956$	−586.045	−	586.045i	−0.613017	−	0.613017i
$957$	−305.662	−	204.237i	−0.319396	−	0.213414i
$958$	196.662	−	988.688i	0.205284	−	1.03203i
$959$	−752.255	+	502.640i	−0.784416	+	0.524130i
$960$	81.6352	+	197.085i	0.0850366	+	0.205297i
$961$	−713.498	+	295.540i	−0.742453	+	0.307534i
$962$	326.734	+	488.992i	0.339640	+	0.508308i
$963$	−130.493	−	25.9567i	−0.135507	−	0.0269540i
$964$	−171.902	+	257.270i	−0.178322	+	0.266878i
$965$	−236.322	+	236.322i	−0.244893	+	0.244893i
$966$	831.144	−	165.325i	0.860397	−	0.171144i
$967$	452.787	−	1093.12i	0.468239	−	1.13043i	−0.496692	−	0.867927i	$-0.665452\pi$
$967$	452.787	−	1093.12i	0.468239	−	1.13043i	0.964931	−	0.262502i	$-0.0845477\pi$
$968$		−	434.595i		−	0.448961i
$969$		0			0
$970$	171.586			0.176893
$971$	−510.211	−	211.336i	−0.525449	−	0.217648i	0.104160	−	0.994561i	$-0.466785\pi$
$971$	−510.211	−	211.336i	−0.525449	−	0.217648i	−0.629608	+	0.776913i	$0.716785\pi$
$972$	−41.6248	−	209.262i	−0.0428239	−	0.215290i
$973$	193.305	+	193.305i	0.198669	+	0.198669i
$974$	−9.78129	−	6.53565i	−0.0100424	−	0.00671011i
$975$	267.223	−	1343.42i	0.274074	−	1.37787i
$976$	−91.8341	+	61.3616i	−0.0940923	+	0.0628705i
$977$	125.177	+	302.204i	0.128124	+	0.309318i	0.974904	−	0.222624i	$-0.0714623\pi$
$977$	125.177	+	302.204i	0.128124	+	0.309318i	−0.846781	+	0.531942i	$0.821462\pi$
$978$	−539.105	+	223.305i	−0.551232	+	0.228328i
$979$	−251.512	−	376.415i	−0.256907	−	0.384489i
$980$	105.039	+	20.8937i	0.107183	+	0.0213201i
$981$	210.707	−	315.345i	0.214788	−	0.321453i
$982$	−552.735	+	552.735i	−0.562866	+	0.562866i
$983$	1004.98	−	199.903i	1.02236	−	0.203360i	0.344683	−	0.938719i	$-0.387986\pi$
$983$	1004.98	−	199.903i	1.02236	−	0.203360i	0.677678	+	0.735359i	$0.262986\pi$
$984$	−225.009	+	543.221i	−0.228668	+	0.552053i
$985$		−	227.523i		−	0.230988i
$986$		0			0
$987$	−903.685			−0.915587
$988$	−61.4041	−	25.4344i	−0.0621499	−	0.0257433i
$989$	−123.692	−	621.844i	−0.125068	−	0.628760i
$990$	−22.8646	−	22.8646i	−0.0230956	−	0.0230956i
$991$	343.118	+	229.264i	0.346234	+	0.231346i	0.716512	−	0.697575i	$-0.245738\pi$
$991$	343.118	+	229.264i	0.346234	+	0.231346i	−0.370278	+	0.928921i	$0.620738\pi$
$992$	81.2600	−	408.521i	0.0819153	−	0.411816i
$993$	226.739	−	151.502i	0.228338	−	0.152570i
$994$	473.916	+	1144.14i	0.476777	+	1.15104i
$995$	222.602	−	92.2048i	0.223721	−	0.0926682i
$996$	446.693	+	668.524i	0.448487	+	0.671209i
$997$	1233.85	+	245.429i	1.23757	+	0.246167i	0.770146	−	0.637867i	$-0.220183\pi$
$997$	1233.85	+	245.429i	1.23757	+	0.246167i	0.467421	+	0.884035i	$0.345183\pi$
$998$	−82.9374	+	124.125i	−0.0831037	+	0.124373i
$999$	396.270	−	396.270i	0.396666	−	0.396666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.i.249.1		8
17.2	even	8		289.3.e.k.214.1		8
17.3	odd	16		289.3.e.m.65.1		8
17.4	even	4		289.3.e.c.40.1		8
17.5	odd	16		17.3.e.a.3.1	✓	8
17.6	odd	16		289.3.e.d.158.1		8
17.7	odd	16		289.3.e.k.131.1		8
17.8	even	8		289.3.e.d.75.1		8
17.9	even	8		289.3.e.b.75.1		8
17.10	odd	16		289.3.e.l.131.1		8
17.11	odd	16		289.3.e.b.158.1		8
17.12	odd	16		289.3.e.c.224.1		8
17.13	even	4		17.3.e.a.6.1	yes	8
17.14	odd	16	inner	289.3.e.i.65.1		8
17.15	even	8		289.3.e.l.214.1		8
17.16	even	2		289.3.e.m.249.1		8
51.5	even	16		153.3.p.b.37.1		8
51.47	odd	4		153.3.p.b.91.1		8
68.39	even	16		272.3.bh.c.241.1		8
68.47	odd	4		272.3.bh.c.193.1		8
85.13	odd	4		425.3.t.c.74.1		8
85.22	even	16		425.3.t.c.224.1		8
85.39	odd	16		425.3.u.b.326.1		8
85.47	odd	4		425.3.t.a.74.1		8
85.64	even	4		425.3.u.b.176.1		8
85.73	even	16		425.3.t.a.224.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.3.1	✓	8	17.5	odd	16
17.3.e.a.6.1	yes	8	17.13	even	4
153.3.p.b.37.1		8	51.5	even	16
153.3.p.b.91.1		8	51.47	odd	4
272.3.bh.c.193.1		8	68.47	odd	4
272.3.bh.c.241.1		8	68.39	even	16
289.3.e.b.75.1		8	17.9	even	8
289.3.e.b.158.1		8	17.11	odd	16
289.3.e.c.40.1		8	17.4	even	4
289.3.e.c.224.1		8	17.12	odd	16
289.3.e.d.75.1		8	17.8	even	8
289.3.e.d.158.1		8	17.6	odd	16
289.3.e.i.65.1		8	17.14	odd	16	inner
289.3.e.i.249.1		8	1.1	even	1	trivial
289.3.e.k.131.1		8	17.7	odd	16
289.3.e.k.214.1		8	17.2	even	8
289.3.e.l.131.1		8	17.10	odd	16
289.3.e.l.214.1		8	17.15	even	8
289.3.e.m.65.1		8	17.3	odd	16
289.3.e.m.249.1		8	17.16	even	2
425.3.t.a.74.1		8	85.47	odd	4
425.3.t.a.224.1		8	85.73	even	16
425.3.t.c.74.1		8	85.13	odd	4
425.3.t.c.224.1		8	85.22	even	16
425.3.u.b.176.1		8	85.64	even	4
425.3.u.b.326.1		8	85.39	odd	16

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23044 - 0.509666i) q^{2} +(0.523336 + 2.63099i) q^{3} +(-1.57420 - 1.57420i) q^{4} +(-1.35115 - 0.902812i) q^{5} +(0.696990 - 3.50400i) q^{6} +(-7.37170 + 4.92562i) q^{7} +(3.17331 + 7.66104i) q^{8} +(1.66671 - 0.690373i) q^{9} +(1.20238 + 1.79949i) q^{10} +(-8.12279 - 1.61572i) q^{11} +(3.31786 - 4.96553i) q^{12} +(16.1480 - 16.1480i) q^{13} +(11.5809 - 2.30358i) q^{14} +(1.66818 - 4.02734i) q^{15} -2.13880i q^{16} -2.40265 q^{18} +(1.20778 + 0.500280i) q^{19} +(0.705778 + 3.54819i) q^{20} +(-16.8171 - 16.8171i) q^{21} +(9.17115 + 6.12797i) q^{22} +(5.21946 - 26.2400i) q^{23} +(-18.4954 + 12.3582i) q^{24} +(-8.55654 - 20.6573i) q^{25} +(-28.0993 + 11.6391i) q^{26} +(16.1016 + 24.0978i) q^{27} +(19.3584 + 3.85063i) q^{28} +(9.19303 - 13.7583i) q^{29} +(-4.10520 + 4.10520i) q^{30} +(13.4734 - 2.68003i) q^{31} +(11.6032 - 28.0125i) q^{32} -22.2165i q^{33} +14.4072 q^{35} +(-3.71051 - 1.53694i) q^{36} +(-3.77234 - 18.9648i) q^{37} +(-1.23113 - 1.23113i) q^{38} +(50.9361 + 34.0344i) q^{39} +(2.62885 - 13.2161i) q^{40} +(21.9781 - 14.6853i) q^{41} +(12.1214 + 29.2636i) q^{42} +(21.8944 - 9.06895i) q^{43} +(10.2434 + 15.3303i) q^{44} +(-2.87525 - 0.571923i) q^{45} +(-19.7959 + 29.6266i) q^{46} +(26.8680 - 26.8680i) q^{47} +(5.62714 - 1.11931i) q^{48} +(11.3288 - 27.3503i) q^{49} +29.7786i q^{50} -50.8404 q^{52} +(-26.1557 - 10.8340i) q^{53} +(-7.53030 - 37.8574i) q^{54} +(9.51644 + 9.51644i) q^{55} +(-61.1281 - 40.8445i) q^{56} +(-0.684154 + 3.43947i) q^{57} +(-18.3236 + 12.2435i) q^{58} +(-9.12070 - 22.0193i) q^{59} +(-8.96587 + 3.71379i) q^{60} +(-28.6898 - 42.9373i) q^{61} +(-17.9442 - 3.56932i) q^{62} +(-8.88596 + 13.2988i) q^{63} +(-34.6035 + 34.6035i) q^{64} +(-36.3971 + 7.23983i) q^{65} +(-11.3230 + 27.3362i) q^{66} -70.4415i q^{67} +71.7687 q^{69} +(-17.7272 - 7.34286i) q^{70} +(20.4612 + 102.865i) q^{71} +(10.5780 + 10.5780i) q^{72} +(-29.5868 - 19.7693i) q^{73} +(-5.02408 + 25.2578i) q^{74} +(49.8712 - 33.3228i) q^{75} +(-1.11375 - 2.68883i) q^{76} +(67.8373 - 28.0991i) q^{77} +(-45.3277 - 67.8377i) q^{78} +(-7.11865 - 1.41599i) q^{79} +(-1.93093 + 2.88984i) q^{80} +(-43.4936 + 43.4936i) q^{81} +(-34.5274 + 6.86792i) q^{82} +(-51.5218 + 124.385i) q^{83} +52.9469i q^{84} -31.5619 q^{86} +(41.0090 + 16.9865i) q^{87} +(-13.3980 - 67.3563i) q^{88} +(38.6522 + 38.6522i) q^{89} +(3.24634 + 2.16914i) q^{90} +(-39.4995 + 198.577i) q^{91} +(-49.5234 + 33.0905i) q^{92} +(14.1023 + 34.0458i) q^{93} +(-46.7533 + 19.3658i) q^{94} +(-1.18024 - 1.76635i) q^{95} +(79.7729 + 15.8678i) q^{96} +(44.0470 - 65.9209i) q^{97} +(-27.8790 + 27.8790i) q^{98} +(-14.6538 + 2.91482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 8 q^{3} - 16 q^{5} - 24 q^{6} + 8 q^{7} + 24 q^{8} + 16 q^{9} - 48 q^{10} - 48 q^{11} - 40 q^{12} + 16 q^{13} + 8 q^{14} + 16 q^{15} + 56 q^{18} - 32 q^{20} - 64 q^{21} - 56 q^{22} - 40 q^{23}+ \cdots - 272 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 8 * q^3 - 16 * q^5 - 24 * q^6 + 8 * q^7 + 24 * q^8 + 16 * q^9 - 48 * q^10 - 48 * q^11 - 40 * q^12 + 16 * q^13 + 8 * q^14 + 16 * q^15 + 56 * q^18 - 32 * q^20 - 64 * q^21 - 56 * q^22 - 40 * q^23 - 104 * q^24 - 64 * q^25 - 176 * q^26 + 16 * q^27 - 56 * q^28 + 64 * q^29 + 16 * q^30 + 40 * q^31 - 88 * q^32 - 160 * q^35 + 128 * q^36 + 128 * q^37 - 120 * q^38 + 176 * q^39 - 16 * q^40 + 112 * q^41 - 16 * q^42 + 232 * q^43 + 24 * q^44 + 160 * q^45 - 136 * q^46 + 192 * q^47 - 8 * q^48 - 16 * q^49 - 384 * q^52 + 32 * q^53 + 224 * q^55 - 136 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 64 * q^60 - 64 * q^61 + 56 * q^62 + 168 * q^63 - 64 * q^64 - 96 * q^65 + 8 * q^66 + 240 * q^69 - 224 * q^70 + 88 * q^71 + 40 * q^72 + 48 * q^73 + 192 * q^74 - 80 * q^76 + 48 * q^77 + 304 * q^78 - 168 * q^79 - 112 * q^80 - 424 * q^81 + 136 * q^82 + 264 * q^83 + 832 * q^86 - 208 * q^87 - 320 * q^88 + 160 * q^89 + 144 * q^90 - 224 * q^91 - 184 * q^92 + 64 * q^93 - 32 * q^94 - 16 * q^95 + 232 * q^96 + 104 * q^97 - 120 * q^98 - 272 * q^99

Introduction

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