LMFDB - Embedded newform 66.3.g.a.47.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [66,3,Mod(5,66)] 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("66.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(66, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	66.g (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.79836974478$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			47.2
Character	$\chi$	$=$	66.47
Dual form			66.3.g.a.59.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.831254 - 1.14412i) q^{2} +(-2.26295 + 1.96953i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(4.67695 - 6.43727i) q^{5} +(4.13447 + 0.951916i) q^{6} +(3.16174 - 9.73084i) q^{7} +(2.68999 - 0.874032i) q^{8} +(1.24191 - 8.91390i) q^{9} -11.2528 q^{10} +(-1.09041 + 10.9458i) q^{11} +(-2.34769 - 5.52163i) q^{12} +(0.714210 - 0.518904i) q^{13} +(-13.7615 + 4.47138i) q^{14} +(2.09468 + 23.7786i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(6.95364 - 9.57087i) q^{17} +(-11.2309 + 5.98882i) q^{18} +(-2.07750 - 6.39389i) q^{19} +(9.35390 + 12.8745i) q^{20} +(12.0103 + 28.2476i) q^{21} +(13.4298 - 7.85119i) q^{22} +15.1865i q^{23} +(-4.36590 + 7.27592i) q^{24} +(-11.8391 - 36.4371i) q^{25} +(-1.18738 - 0.385803i) q^{26} +(14.7458 + 22.6177i) q^{27} +(16.5551 + 12.0280i) q^{28} +(8.13630 + 2.64364i) q^{29} +(25.4644 - 22.1626i) q^{30} +(-39.3890 + 28.6178i) q^{31} +5.65685i q^{32} +(-19.0906 - 26.9175i) q^{33} -16.7305 q^{34} +(-47.8527 - 65.8636i) q^{35} +(16.1877 + 7.87134i) q^{36} +(-13.1618 + 40.5080i) q^{37} +(-5.58847 + 7.69186i) q^{38} +(-0.594227 + 2.58091i) q^{39} +(6.95458 - 21.4040i) q^{40} +(8.28079 - 2.69059i) q^{41} +(22.3351 - 37.2222i) q^{42} +77.4014 q^{43} +(-20.1463 - 8.83897i) q^{44} +(-51.5728 - 49.6843i) q^{45} +(17.3752 - 12.6238i) q^{46} +(58.6782 - 19.0657i) q^{47} +(11.9537 - 1.05301i) q^{48} +(-45.0509 - 32.7314i) q^{49} +(-31.8472 + 43.8339i) q^{50} +(3.11435 + 35.3538i) q^{51} +(0.545608 + 1.67921i) q^{52} +(7.86527 + 10.8256i) q^{53} +(13.6199 - 35.6721i) q^{54} +(65.3614 + 58.2123i) q^{55} -28.9394i q^{56} +(17.2942 + 10.3774i) q^{57} +(-3.73868 - 11.5065i) q^{58} +(-43.1725 - 14.0276i) q^{59} +(-46.5242 - 10.7117i) q^{60} +(46.7325 + 33.9531i) q^{61} +(65.4846 + 21.2772i) q^{62} +(-82.8132 - 40.2683i) q^{63} +(6.47214 - 4.70228i) q^{64} -7.02445i q^{65} +(-14.9278 + 44.2172i) q^{66} -28.4340 q^{67} +(13.9073 + 19.1417i) q^{68} +(-29.9103 - 34.3664i) q^{69} +(-35.5783 + 109.499i) q^{70} +(-24.4556 + 33.6602i) q^{71} +(-4.45032 - 25.0638i) q^{72} +(-1.05367 + 3.24287i) q^{73} +(57.2869 - 18.6137i) q^{74} +(98.5553 + 59.1379i) q^{75} +13.4459 q^{76} +(103.064 + 45.2185i) q^{77} +(3.44683 - 1.46553i) q^{78} +(-68.9341 + 50.0835i) q^{79} +(-30.2698 + 9.83527i) q^{80} +(-77.9153 - 22.1405i) q^{81} +(-9.96180 - 7.23767i) q^{82} +(-6.20265 + 8.53722i) q^{83} +(-61.1529 + 5.38700i) q^{84} +(-29.0884 - 89.5249i) q^{85} +(-64.3402 - 88.5567i) q^{86} +(-23.6188 + 10.0422i) q^{87} +(6.63380 + 30.3972i) q^{88} +86.3091i q^{89} +(-13.9749 + 100.306i) q^{90} +(-2.79122 - 8.59051i) q^{91} +(-28.8865 - 9.38578i) q^{92} +(32.7719 - 142.339i) q^{93} +(-70.5900 - 51.2867i) q^{94} +(-50.8755 - 16.5305i) q^{95} +(-11.1413 - 12.8012i) q^{96} +(52.4764 - 38.1263i) q^{97} +78.7518i q^{98} +(96.2158 + 23.3135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 12 q^{6} - 8 q^{7} + 26 q^{9} + 16 q^{10} - 24 q^{12} + 8 q^{13} - 82 q^{15} - 32 q^{16} - 8 q^{18} - 4 q^{19} - 100 q^{21} - 24 q^{24} - 88 q^{25} - 106 q^{27} - 24 q^{28} - 36 q^{30}+ \cdots + 470 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 12 * q^6 - 8 * q^7 + 26 * q^9 + 16 * q^10 - 24 * q^12 + 8 * q^13 - 82 * q^15 - 32 * q^16 - 8 * q^18 - 4 * q^19 - 100 * q^21 - 24 * q^24 - 88 * q^25 - 106 * q^27 - 24 * q^28 - 36 * q^30 - 148 * q^31 + 78 * q^33 - 32 * q^34 + 8 * q^36 + 96 * q^37 + 362 * q^39 + 48 * q^40 + 152 * q^42 + 560 * q^43 - 20 * q^45 + 176 * q^46 + 8 * q^48 + 208 * q^49 - 82 * q^51 + 24 * q^52 - 176 * q^54 - 108 * q^55 - 142 * q^57 - 144 * q^58 - 36 * q^60 - 384 * q^61 + 506 * q^63 + 64 * q^64 + 400 * q^66 - 680 * q^67 + 136 * q^69 - 400 * q^70 + 16 * q^72 - 92 * q^73 + 90 * q^75 + 128 * q^76 + 152 * q^78 + 320 * q^79 - 198 * q^81 - 328 * q^82 - 240 * q^84 - 1024 * q^85 - 1332 * q^87 - 736 * q^90 - 264 * q^91 - 226 * q^93 - 64 * q^94 - 32 * q^96 - 248 * q^97 + 470 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.831254	−	1.14412i	−0.415627	−	0.572061i
$2$	−0.831254	−	1.14412i	−0.415627	−	0.572061i
$3$	−2.26295	+	1.96953i	−0.754317	+	0.656510i
$3$	−2.26295	+	1.96953i	−0.754317	+	0.656510i
$4$	−0.618034	+	1.90211i	−0.154508	+	0.475528i
$5$	4.67695	−	6.43727i	0.935390	−	1.28745i	−0.0223303	−	0.999751i	$-0.507109\pi$
$5$	4.67695	−	6.43727i	0.935390	−	1.28745i	0.957720	−	0.287703i	$-0.0928915\pi$
$6$	4.13447	+	0.951916i	0.689079	+	0.158653i
$7$	3.16174	−	9.73084i	0.451677	−	1.39012i	−0.423314	−	0.905983i	$-0.639133\pi$
$7$	3.16174	−	9.73084i	0.451677	−	1.39012i	0.874992	−	0.484138i	$-0.160867\pi$
$8$	2.68999	−	0.874032i	0.336249	−	0.109254i
$9$	1.24191	−	8.91390i	0.137990	−	0.990434i
$10$	−11.2528			−1.12528
$11$	−1.09041	+	10.9458i	−0.0991281	+	0.995075i
$11$	−1.09041	+	10.9458i	−0.0991281	+	0.995075i
$12$	−2.34769	−	5.52163i	−0.195641	−	0.460136i
$13$	0.714210	−	0.518904i	0.0549392	−	0.0399157i	−0.559977	−	0.828508i	$-0.689190\pi$
$13$	0.714210	−	0.518904i	0.0549392	−	0.0399157i	0.614916	+	0.788593i	$0.289190\pi$
$14$	−13.7615	+	4.47138i	−0.982964	+	0.319384i
$15$	2.09468	+	23.7786i	0.139645	+	1.58524i
$16$	−3.23607	−	2.35114i	−0.202254	−	0.146946i
$17$	6.95364	−	9.57087i	0.409038	−	0.562992i	−0.553946	−	0.832553i	$-0.686878\pi$
$17$	6.95364	−	9.57087i	0.409038	−	0.562992i	0.962983	+	0.269561i	$0.0868785\pi$
$18$	−11.2309	+	5.98882i	−0.623941	+	0.332712i
$19$	−2.07750	−	6.39389i	−0.109342	−	0.336521i	0.881383	−	0.472403i	$-0.156613\pi$
$19$	−2.07750	−	6.39389i	−0.109342	−	0.336521i	−0.990725	+	0.135882i	$0.956613\pi$
$20$	9.35390	+	12.8745i	0.467695	+	0.643727i
$21$	12.0103	+	28.2476i	0.571920	+	1.34512i
$22$	13.4298	−	7.85119i	0.610444	−	0.356872i
$23$			15.1865i			0.660283i	0.943931	+	0.330142i	$0.107096\pi$
$23$			15.1865i			0.660283i	−0.943931	+	0.330142i	$0.892904\pi$
$24$	−4.36590	+	7.27592i	−0.181912	+	0.303163i
$25$	−11.8391	−	36.4371i	−0.473565	−	1.45748i
$26$	−1.18738	−	0.385803i	−0.0456684	−	0.0148386i
$27$	14.7458	+	22.6177i	0.546142	+	0.837693i
$28$	16.5551	+	12.0280i	0.591254	+	0.429571i
$29$	8.13630	+	2.64364i	0.280562	+	0.0911601i	0.445918	−	0.895074i	$-0.352877\pi$
$29$	8.13630	+	2.64364i	0.280562	+	0.0911601i	−0.165356	+	0.986234i	$0.552877\pi$
$30$	25.4644	−	22.1626i	0.848815	−	0.738754i
$31$	−39.3890	+	28.6178i	−1.27061	+	0.923155i	−0.999227	−	0.0393150i	$-0.987482\pi$
$31$	−39.3890	+	28.6178i	−1.27061	+	0.923155i	−0.271387	+	0.962470i	$0.587482\pi$
$32$			5.65685i			0.176777i
$33$	−19.0906	−	26.9175i	−0.578502	−	0.815681i
$34$	−16.7305			−0.492073
$35$	−47.8527	−	65.8636i	−1.36722	−	1.88182i
$36$	16.1877	+	7.87134i	0.449659	+	0.218648i
$37$	−13.1618	+	40.5080i	−0.355725	+	1.09481i	0.599862	+	0.800103i	$0.295222\pi$
$37$	−13.1618	+	40.5080i	−0.355725	+	1.09481i	−0.955588	+	0.294707i	$0.904778\pi$
$38$	−5.58847	+	7.69186i	−0.147065	+	0.202417i
$39$	−0.594227	+	2.58091i	−0.0152366	+	0.0661772i
$40$	6.95458	−	21.4040i	0.173865	−	0.535100i
$41$	8.28079	−	2.69059i	0.201970	−	0.0656242i	−0.206285	−	0.978492i	$-0.566137\pi$
$41$	8.28079	−	2.69059i	0.201970	−	0.0656242i	0.408255	+	0.912868i	$0.366137\pi$
$42$	22.3351	−	37.2222i	0.531788	−	0.886242i
$43$	77.4014			1.80003			0.900016	−	0.435857i	$-0.143555\pi$
$43$	77.4014			1.80003			0.900016	+	0.435857i	$0.143555\pi$
$44$	−20.1463	−	8.83897i	−0.457870	−	0.200886i
$45$	−51.5728	−	49.6843i	−1.14606	−	1.10410i
$46$	17.3752	−	12.6238i	0.377722	−	0.274431i
$47$	58.6782	−	19.0657i	1.24847	−	0.405654i	0.391100	−	0.920348i	$-0.372095\pi$
$47$	58.6782	−	19.0657i	1.24847	−	0.405654i	0.857374	+	0.514695i	$0.172095\pi$
$48$	11.9537	−	1.05301i	0.249036	−	0.0219377i
$49$	−45.0509	−	32.7314i	−0.919405	−	0.667987i
$50$	−31.8472	+	43.8339i	−0.636944	+	0.876678i
$51$	3.11435	+	35.3538i	0.0610656	+	0.693212i
$52$	0.545608	+	1.67921i	0.0104925	+	0.0322925i
$53$	7.86527	+	10.8256i	0.148401	+	0.204257i	0.876746	−	0.480955i	$-0.159710\pi$
$53$	7.86527	+	10.8256i	0.148401	+	0.204257i	−0.728344	+	0.685211i	$0.759710\pi$
$54$	13.6199	−	35.6721i	0.252221	−	0.660594i
$55$	65.3614	+	58.2123i	1.18839	+	1.05841i
$56$		−	28.9394i		−	0.516775i
$57$	17.2942	+	10.3774i	0.303408	+	0.182059i
$58$	−3.73868	−	11.5065i	−0.0644599	−	0.198387i
$59$	−43.1725	−	14.0276i	−0.731737	−	0.237756i	−0.0806323	−	0.996744i	$-0.525694\pi$
$59$	−43.1725	−	14.0276i	−0.731737	−	0.237756i	−0.651104	+	0.758988i	$0.725694\pi$
$60$	−46.5242	−	10.7117i	−0.775403	−	0.178528i
$61$	46.7325	+	33.9531i	0.766106	+	0.556609i	0.900777	−	0.434282i	$-0.142998\pi$
$61$	46.7325	+	33.9531i	0.766106	+	0.556609i	−0.134671	+	0.990890i	$0.542998\pi$
$62$	65.4846	+	21.2772i	1.05620	+	0.343181i
$63$	−82.8132	−	40.2683i	−1.31450	−	0.639179i
$64$	6.47214	−	4.70228i	0.101127	−	0.0734732i
$65$		−	7.02445i		−	0.108068i
$66$	−14.9278	+	44.2172i	−0.226178	+	0.669958i
$67$	−28.4340			−0.424389			−0.212194	−	0.977227i	$-0.568061\pi$
$67$	−28.4340			−0.424389			−0.212194	+	0.977227i	$0.568061\pi$
$68$	13.9073	+	19.1417i	0.204519	+	0.281496i
$69$	−29.9103	−	34.3664i	−0.433482	−	0.498063i
$70$	−35.5783	+	109.499i	−0.508262	+	1.56427i
$71$	−24.4556	+	33.6602i	−0.344445	+	0.474087i	−0.945733	−	0.324945i	$-0.894654\pi$
$71$	−24.4556	+	33.6602i	−0.344445	+	0.474087i	0.601288	+	0.799032i	$0.294654\pi$
$72$	−4.45032	−	25.0638i	−0.0618099	−	0.348109i
$73$	−1.05367	+	3.24287i	−0.0144339	+	0.0444229i	−0.958014	−	0.286721i	$-0.907435\pi$
$73$	−1.05367	+	3.24287i	−0.0144339	+	0.0444229i	0.943580	+	0.331144i	$0.107435\pi$
$74$	57.2869	−	18.6137i	0.774148	−	0.251536i
$75$	98.5553	+	59.1379i	1.31407	+	0.788505i
$76$	13.4459			0.176919
$77$	103.064	+	45.2185i	1.33850	+	0.587253i
$78$	3.44683	−	1.46553i	0.0441902	−	0.0187888i
$79$	−68.9341	+	50.0835i	−0.872583	+	0.633969i	−0.931279	−	0.364307i	$-0.881306\pi$
$79$	−68.9341	+	50.0835i	−0.872583	+	0.633969i	0.0586957	+	0.998276i	$0.481306\pi$
$80$	−30.2698	+	9.83527i	−0.378373	+	0.122941i
$81$	−77.9153	−	22.1405i	−0.961918	−	0.273339i
$82$	−9.96180	−	7.23767i	−0.121485	−	0.0882643i
$83$	−6.20265	+	8.53722i	−0.0747308	+	0.102858i	−0.844746	−	0.535167i	$-0.820249\pi$
$83$	−6.20265	+	8.53722i	−0.0747308	+	0.102858i	0.770015	+	0.638025i	$0.220249\pi$
$84$	−61.1529	+	5.38700i	−0.728010	+	0.0641310i
$85$	−29.0884	−	89.5249i	−0.342216	−	1.05323i
$86$	−64.3402	−	88.5567i	−0.748142	−	1.02973i
$87$	−23.6188	+	10.0422i	−0.271480	+	0.115428i
$88$	6.63380	+	30.3972i	0.0753841	+	0.345423i
$89$			86.3091i			0.969766i	0.874579	+	0.484883i	$0.161138\pi$
$89$			86.3091i			0.969766i	−0.874579	+	0.484883i	$0.838862\pi$
$90$	−13.9749	+	100.306i	−0.155276	+	1.11451i
$91$	−2.79122	−	8.59051i	−0.0306728	−	0.0944012i
$92$	−28.8865	−	9.38578i	−0.313983	−	0.102019i
$93$	32.7719	−	142.339i	0.352386	−	1.53052i
$94$	−70.5900	−	51.2867i	−0.750958	−	0.545603i
$95$	−50.8755	−	16.5305i	−0.535532	−	0.174005i
$96$	−11.1413	−	12.8012i	−0.116056	−	0.133346i
$97$	52.4764	−	38.1263i	0.540993	−	0.393055i	−0.283460	−	0.958984i	$-0.591482\pi$
$97$	52.4764	−	38.1263i	0.540993	−	0.393055i	0.824454	+	0.565929i	$0.191482\pi$
$98$			78.7518i			0.803590i
$99$	96.2158	+	23.3135i	0.971877	+	0.235490i
$100$	76.6245			0.766245
$101$	28.4131	+	39.1073i	0.281318	+	0.387201i	0.926170	−	0.377106i	$-0.123081\pi$
$101$	28.4131	+	39.1073i	0.281318	+	0.387201i	−0.644852	+	0.764308i	$0.723081\pi$
$102$	37.8603	−	32.9512i	0.371179	−	0.323051i
$103$	4.54013	−	13.9731i	0.0440790	−	0.135661i	−0.926595	−	0.376061i	$-0.877278\pi$
$103$	4.54013	−	13.9731i	0.0440790	−	0.135661i	0.970674	+	0.240400i	$0.0772784\pi$
$104$	1.46768	−	2.02009i	0.0141123	−	0.0194240i
$105$	238.009	+	54.7989i	2.26675	+	0.521894i
$106$	5.84780	−	17.9977i	0.0551679	−	0.169789i
$107$	53.6980	−	17.4475i	0.501850	−	0.163061i	−0.0471424	−	0.998888i	$-0.515011\pi$
$107$	53.6980	−	17.4475i	0.501850	−	0.163061i	0.548993	+	0.835827i	$0.315011\pi$
$108$	−52.1349	+	14.0697i	−0.482730	+	0.130275i
$109$	125.293			1.14947			0.574737	−	0.818338i	$-0.305105\pi$
$109$	125.293			1.14947			0.574737	+	0.818338i	$0.305105\pi$
$110$	12.2701	−	123.171i	0.111546	−	1.11973i
$111$	−49.9971	−	117.590i	−0.450424	−	1.05937i
$112$	−33.1102	+	24.0560i	−0.295627	+	0.214785i
$113$	−117.276	+	38.1051i	−1.03784	+	0.337214i	−0.777884	−	0.628408i	$-0.783707\pi$
$113$	−117.276	+	38.1051i	−1.03784	+	0.337214i	−0.259953	+	0.965621i	$0.583707\pi$
$114$	−2.50292	−	28.4130i	−0.0219554	−	0.249237i
$115$	97.7596	+	71.0265i	0.850084	+	0.617622i
$116$	−10.0570	+	13.8423i	−0.0866984	+	0.119330i
$117$	−3.73848	−	7.01083i	−0.0319528	−	0.0599216i
$118$	19.8380	+	61.0551i	0.168119	+	0.517416i
$119$	−71.1470	−	97.9254i	−0.597874	−	0.822903i
$120$	26.4179	+	62.1335i	0.220149	+	0.517779i
$121$	−118.622	−	23.8709i	−0.980347	−	0.197280i
$122$		−	81.6914i		−	0.669601i
$123$	−13.4398	+	22.3979i	−0.109267	+	0.182097i
$124$	−30.0905	−	92.6092i	−0.242666	−	0.746848i
$125$	−100.740	−	32.7323i	−0.805918	−	0.261859i
$126$	22.7670	+	128.222i	0.180690	+	1.01763i
$127$	−129.087	−	93.7869i	−1.01643	−	0.738479i	−0.0508815	−	0.998705i	$-0.516203\pi$
$127$	−129.087	−	93.7869i	−1.01643	−	0.738479i	−0.965548	+	0.260226i	$0.916203\pi$
$128$	−10.7600	−	3.49613i	−0.0840623	−	0.0273135i
$129$	−175.156	+	152.444i	−1.35780	+	1.18174i
$130$	−8.03683	+	5.83910i	−0.0618218	+	0.0449161i
$131$		−	70.2061i		−	0.535924i	−0.963429	−	0.267962i	$-0.913650\pi$
$131$		−	70.2061i		−	0.535924i	0.963429	−	0.267962i	$-0.0863502\pi$
$132$	62.9987	−	19.6765i	0.477263	−	0.149065i
$133$	−68.7865			−0.517192
$134$	23.6359	+	32.5320i	0.176387	+	0.242776i
$135$	214.562	+	10.8591i	1.58935	+	0.0804375i
$136$	10.3400	−	31.8233i	0.0760295	−	0.233995i
$137$	131.184	−	180.560i	0.957551	−	1.31796i	0.00945990	−	0.999955i	$-0.496989\pi$
$137$	131.184	−	180.560i	0.957551	−	1.31796i	0.948091	−	0.318000i	$-0.103011\pi$
$138$	−14.4563	+	62.7882i	−0.104756	+	0.454987i
$139$	25.1413	−	77.3769i	0.180873	−	0.556669i	−0.818980	−	0.573822i	$-0.805460\pi$
$139$	25.1413	−	77.3769i	0.180873	−	0.556669i	0.999853	+	0.0171530i	$0.00546025\pi$
$140$	154.855	−	50.3153i	1.10610	−	0.359395i
$141$	−95.2356	+	158.713i	−0.675430	+	1.12563i
$142$	58.8402			0.414367
$143$	4.90105	+	8.38343i	0.0342731	+	0.0586254i
$144$	−24.9767	+	25.9261i	−0.173450	+	0.180042i
$145$	55.0709	−	40.0113i	0.379799	−	0.275940i
$146$	4.58611	−	1.49012i	0.0314117	−	0.0102063i
$147$	166.413	−	14.6595i	1.13206	−	0.0997243i
$148$	−68.9163	−	50.0706i	−0.465651	−	0.338315i
$149$	−133.091	+	183.184i	−0.893228	+	1.22942i	0.0793501	+	0.996847i	$0.474716\pi$
$149$	−133.091	+	183.184i	−0.893228	+	1.22942i	−0.972578	+	0.232576i	$0.925284\pi$
$150$	−14.2635	−	161.918i	−0.0950899	−	1.07945i
$151$	−62.5799	−	192.601i	−0.414436	−	1.27550i	−0.912754	−	0.408509i	$-0.866049\pi$
$151$	−62.5799	−	192.601i	−0.414436	−	1.27550i	0.498318	−	0.866994i	$-0.333951\pi$
$152$	−11.1769	−	15.3837i	−0.0735325	−	0.101209i
$153$	−76.6780	−	73.8702i	−0.501163	−	0.482812i
$154$	−33.9373	−	155.506i	−0.220372	−	1.00978i
$155$			387.402i			2.49937i
$156$	−4.54194	−	2.72538i	−0.0291150	−	0.0174704i
$157$	47.7416	+	146.933i	0.304086	+	0.935882i	0.980017	+	0.198916i	$0.0637421\pi$
$157$	47.7416	+	146.933i	0.304086	+	0.935882i	−0.675930	+	0.736966i	$0.736258\pi$
$158$	114.603	+	37.2369i	0.725338	+	0.235677i
$159$	−39.1201	−	9.00697i	−0.246038	−	0.0566476i
$160$	36.4147	+	26.4568i	0.227592	+	0.165355i
$161$	147.778	+	48.0158i	0.917873	+	0.298235i
$162$	39.4360	+	107.549i	0.243432	+	0.663883i
$163$	−16.8185	+	12.2193i	−0.103181	+	0.0749652i	−0.638179	−	0.769888i	$-0.720312\pi$
$163$	−16.8185	+	12.2193i	−0.103181	+	0.0749652i	0.534999	+	0.844853i	$0.320312\pi$
$164$			17.4139i			0.106182i
$165$	−262.561	−	3.00047i	−1.59128	−	0.0181847i
$166$	14.9236			0.0899013
$167$	−121.390	−	167.079i	−0.726884	−	1.00047i	−0.999267	−	0.0382816i	$-0.987812\pi$
$167$	−121.390	−	167.079i	−0.726884	−	1.00047i	0.272383	−	0.962189i	$-0.412188\pi$
$168$	56.9970	+	65.4884i	0.339268	+	0.389812i
$169$	−51.9830	+	159.987i	−0.307592	+	0.946671i
$170$	−78.2476	+	107.699i	−0.460280	+	0.633521i
$171$	−59.5746	+	10.5780i	−0.348389	+	0.0618598i
$172$	−47.8367	+	147.226i	−0.278120	+	0.855966i
$173$	16.2620	−	5.28385i	0.0940002	−	0.0305425i	−0.261639	−	0.965166i	$-0.584263\pi$
$173$	16.2620	−	5.28385i	0.0940002	−	0.0305425i	0.355640	+	0.934623i	$0.384263\pi$
$174$	31.1228	+	18.6751i	0.178866	+	0.107328i
$175$	−391.996			−2.23998
$176$	29.2638	−	32.8577i	0.166272	−	0.186692i
$177$	125.325	−	53.2857i	0.708051	−	0.301049i
$178$	98.7483	−	71.7448i	0.554765	−	0.403061i
$179$	−96.7507	+	31.4362i	−0.540507	+	0.175621i	−0.566532	−	0.824040i	$-0.691715\pi$
$179$	−96.7507	+	31.4362i	−0.540507	+	0.175621i	0.0260249	+	0.999661i	$0.491715\pi$
$180$	126.379	−	67.3907i	0.702106	−	0.374393i
$181$	252.821	+	183.685i	1.39680	+	1.01484i	0.995080	+	0.0990739i	$0.0315880\pi$
$181$	252.821	+	183.685i	1.39680	+	1.01484i	0.401722	+	0.915762i	$0.368412\pi$
$182$	−7.50838	+	10.3344i	−0.0412548	+	0.0567824i
$183$	−172.625	+	15.2067i	−0.943306	+	0.0830966i
$184$	13.2735	+	40.8516i	0.0721386	+	0.222020i
$185$	199.203	+	274.180i	1.07678	+	1.48205i
$186$	−190.095	+	80.8245i	−1.02201	+	0.434540i
$187$	97.1787	+	86.5495i	0.519672	+	0.462831i
$188$			123.396i			0.656361i
$189$	266.712	−	71.9779i	1.41117	−	0.380835i
$190$	23.3776	+	71.9489i	0.123040	+	0.378678i
$191$	−53.4332	−	17.3615i	−0.279755	−	0.0908980i	0.165779	−	0.986163i	$-0.446986\pi$
$191$	−53.4332	−	17.3615i	−0.279755	−	0.0908980i	−0.445534	+	0.895265i	$0.646986\pi$
$192$	−5.38485	+	23.3881i	−0.0280461	+	0.121813i
$193$	−283.272	−	205.809i	−1.46773	−	1.06637i	−0.981264	−	0.192667i	$-0.938286\pi$
$193$	−283.272	−	205.809i	−1.46773	−	1.06637i	−0.486465	−	0.873700i	$-0.661714\pi$
$194$	−87.2423	−	28.3468i	−0.449703	−	0.146117i
$195$	13.8349	+	15.8960i	0.0709480	+	0.0815179i
$196$	90.1017	−	65.4627i	0.459703	−	0.333993i
$197$		−	140.232i		−	0.711840i	−0.934517	−	0.355920i	$-0.884168\pi$
$197$		−	140.232i		−	0.711840i	0.934517	−	0.355920i	$-0.115832\pi$
$198$	−53.3063	−	129.462i	−0.269224	−	0.653849i
$199$	152.464			0.766152			0.383076	−	0.923717i	$-0.374865\pi$
$199$	152.464			0.766152			0.383076	+	0.923717i	$0.374865\pi$
$200$	−63.6944	−	87.6678i	−0.318472	−	0.438339i
$201$	64.3449	−	56.0017i	0.320124	−	0.278615i
$202$	21.1251	−	65.0162i	0.104579	−	0.321862i
$203$	51.4498	−	70.8145i	0.253447	−	0.348840i
$204$	−69.1717	−	15.9260i	−0.339077	−	0.0780687i
$205$	21.4088	−	65.8894i	0.104433	−	0.321412i
$206$	−19.7609	+	6.42072i	−0.0959269	+	0.0311685i
$207$	135.371	+	18.8602i	0.653967	+	0.0911122i
$208$	−3.53125			−0.0169772
$209$	72.2517	−	15.7680i	0.345702	−	0.0754450i
$210$	−135.149	−	317.863i	−0.643567	−	1.51363i
$211$	160.272	−	116.444i	0.759581	−	0.551868i	−0.139201	−	0.990264i	$-0.544453\pi$
$211$	160.272	−	116.444i	0.759581	−	0.551868i	0.898782	+	0.438396i	$0.144453\pi$
$212$	−25.4525	+	8.27003i	−0.120059	+	0.0390096i
$213$	−10.9530	−	124.337i	−0.0514224	−	0.583743i
$214$	−64.5988	−	46.9338i	−0.301864	−	0.219317i
$215$	362.002	−	498.253i	1.68373	−	2.31746i
$216$	59.4348	+	47.9532i	0.275161	+	0.222005i
$217$	153.937	+	473.771i	0.709389	+	2.18328i
$218$	−104.150	−	143.350i	−0.477752	−	0.657569i
$219$	−4.00252	−	9.41370i	−0.0182763	−	0.0429850i
$220$	−151.122	+	88.3476i	−0.686918	+	0.401580i
$221$		−	10.4439i		−	0.0472574i
$222$	−92.9775	+	154.950i	−0.418817	+	0.697974i
$223$	8.38343	+	25.8016i	0.0375939	+	0.115702i	0.968092	−	0.250594i	$-0.0806258\pi$
$223$	8.38343	+	25.8016i	0.0375939	+	0.115702i	−0.930498	+	0.366296i	$0.880626\pi$
$224$	55.0460	+	17.8855i	0.245741	+	0.0798461i
$225$	−339.500	+	60.2814i	−1.50889	+	0.267917i
$226$	141.083	+	102.503i	0.624260	+	0.453551i
$227$	127.298	+	41.3617i	0.560786	+	0.182210i	0.575675	−	0.817679i	$-0.304739\pi$
$227$	127.298	+	41.3617i	0.560786	+	0.182210i	−0.0148890	+	0.999889i	$0.504739\pi$
$228$	−30.4274	+	26.4820i	−0.133453	+	0.116149i
$229$	−18.9062	+	13.7361i	−0.0825597	+	0.0599831i	−0.628299	−	0.777972i	$-0.716249\pi$
$229$	−18.9062	+	13.7361i	−0.0825597	+	0.0599831i	0.545740	+	0.837955i	$0.316249\pi$
$230$		−	170.890i		−	0.743000i
$231$	−322.289	+	100.661i	−1.39519	+	0.435763i
$232$	24.1972			0.104298
$233$	−148.044	−	203.765i	−0.635382	−	0.874528i	0.362977	−	0.931798i	$-0.381760\pi$
$233$	−148.044	−	203.765i	−0.635382	−	0.874528i	−0.998359	+	0.0572698i	$0.981760\pi$
$234$	−4.91363	+	10.1051i	−0.0209984	+	0.0431840i
$235$	151.704	−	466.897i	0.645549	−	1.98680i
$236$	53.3641	−	73.4494i	0.226119	−	0.311226i
$237$	57.3535	−	249.104i	0.241998	−	1.05107i
$238$	−52.8975	+	162.802i	−0.222258	+	0.684041i
$239$	−287.357	+	93.3679i	−1.20233	+	0.390661i	−0.840618	−	0.541629i	$-0.817808\pi$
$239$	−287.357	+	93.3679i	−1.20233	+	0.390661i	−0.361712	+	0.932290i	$0.617808\pi$
$240$	49.1284	−	81.8741i	0.204701	−	0.341142i
$241$	140.768			0.584100			0.292050	−	0.956403i	$-0.405663\pi$
$241$	140.768			0.584100			0.292050	+	0.956403i	$0.405663\pi$
$242$	71.2938	+	155.561i	0.294603	+	0.642814i
$243$	219.925	−	103.354i	0.905041	−	0.425324i
$244$	−93.4649	+	67.9063i	−0.383053	+	0.278304i
$245$	−421.401	+	136.921i	−1.72000	+	0.558863i
$246$	36.7979	−	3.24155i	0.149585	−	0.0131771i
$247$	−4.80159	−	3.48856i	−0.0194396	−	0.0141237i
$248$	−80.9434	+	111.409i	−0.326385	+	0.449230i
$249$	−2.77800	−	31.5356i	−0.0111566	−	0.126649i
$250$	46.2905	+	142.468i	0.185162	+	0.569870i
$251$	−271.220	−	373.303i	−1.08056	−	1.48726i	−0.858905	−	0.512136i	$-0.828855\pi$
$251$	−271.220	−	373.303i	−1.08056	−	1.48726i	−0.221654	−	0.975125i	$-0.571145\pi$
$252$	127.776	−	132.633i	0.507048	−	0.526321i
$253$	−166.229	−	16.5595i	−0.657031	−	0.0654526i
$254$			225.652i			0.888392i
$255$	242.148	+	145.300i	0.949598	+	0.569804i
$256$	4.94427	+	15.2169i	0.0193136	+	0.0594410i
$257$	268.565	+	87.2620i	1.04500	+	0.339541i	0.780704	−	0.624901i	$-0.214861\pi$
$257$	268.565	+	87.2620i	1.04500	+	0.339541i	0.264295	+	0.964442i	$0.414861\pi$
$258$	320.014	+	73.6796i	1.24036	+	0.285580i
$259$	352.562	+	256.152i	1.36125	+	0.989002i
$260$	13.3613	+	4.34135i	0.0513896	+	0.0166975i
$261$	33.6697	−	69.2430i	0.129003	−	0.265299i
$262$	−80.3244	+	58.3591i	−0.306582	+	0.222745i
$263$			394.231i			1.49898i	0.662017	+	0.749489i	$0.269701\pi$
$263$			394.231i			1.49898i	−0.662017	+	0.749489i	$0.730299\pi$
$264$	−74.8803	−	55.7220i	−0.283637	−	0.211068i
$265$	106.473			0.401784
$266$	57.1790	+	78.7002i	0.214959	+	0.295865i
$267$	−169.988	−	195.313i	−0.636661	−	0.731511i
$268$	17.5732	−	54.0847i	0.0655716	−	0.201809i
$269$	−119.852	+	164.962i	−0.445547	+	0.613242i	−0.971433	−	0.237312i	$-0.923734\pi$
$269$	−119.852	+	164.962i	−0.445547	+	0.613242i	0.525887	+	0.850555i	$0.323734\pi$
$270$	−165.931	−	254.512i	−0.614560	−	0.942635i
$271$	−1.60423	+	4.93732i	−0.00591967	+	0.0182189i	−0.953973	−	0.299893i	$-0.903049\pi$
$271$	−1.60423	+	4.93732i	−0.00591967	+	0.0182189i	0.948053	+	0.318112i	$0.103049\pi$
$272$	−45.0049	+	14.6230i	−0.165459	+	0.0537610i
$273$	23.2357	+	13.9425i	0.0851123	+	0.0510714i
$274$	−315.630			−1.15194
$275$	411.743	−	89.8577i	1.49725	−	0.326755i
$276$	83.8543	−	35.6532i	0.303820	−	0.129178i
$277$	−325.827	+	236.727i	−1.17627	+	0.854612i	−0.991746	−	0.128216i	$-0.959075\pi$
$277$	−325.827	+	236.727i	−1.17627	+	0.854612i	−0.184526	+	0.982828i	$0.559075\pi$
$278$	−109.428	+	35.5552i	−0.393624	+	0.127896i
$279$	206.179	+	386.651i	0.738992	+	1.38584i
$280$	−186.290	−	135.348i	−0.665323	−	0.483385i
$281$	−126.850	+	174.594i	−0.451424	+	0.621332i	−0.972703	−	0.232055i	$-0.925455\pi$
$281$	−126.850	+	174.594i	−0.451424	+	0.621332i	0.521279	+	0.853386i	$0.325455\pi$
$282$	260.753	−	22.9699i	0.924654	−	0.0814535i
$283$	47.9188	+	147.479i	0.169324	+	0.521127i	0.999329	−	0.0366298i	$-0.0116622\pi$
$283$	47.9188	+	147.479i	0.169324	+	0.521127i	−0.830005	+	0.557757i	$0.811662\pi$
$284$	−48.9111	−	67.3204i	−0.172222	−	0.237044i
$285$	147.686	−	62.7932i	0.518197	−	0.220327i
$286$	5.51766	−	12.5762i	0.0192925	−	0.0439726i
$287$		−	89.0860i		−	0.310404i
$288$	50.4247	+	7.02528i	0.175086	+	0.0243933i
$289$	46.0576	+	141.751i	0.159369	+	0.490486i
$290$	−91.5557	−	29.7483i	−0.315709	−	0.102580i
$291$	−43.6606	+	189.632i	−0.150036	+	0.651655i
$292$	−5.51710	−	4.00841i	−0.0188942	−	0.0137274i
$293$	264.801	+	86.0391i	0.903758	+	0.293649i	0.723787	−	0.690023i	$-0.242400\pi$
$293$	264.801	+	86.0391i	0.903758	+	0.293649i	0.179971	+	0.983672i	$0.442400\pi$
$294$	−155.104	−	178.212i	−0.527564	−	0.606162i
$295$	−292.215	+	212.306i	−0.990558	+	0.719683i
$296$			120.470i			0.406994i
$297$	−263.648	+	136.743i	−0.887705	+	0.460413i
$298$	320.217			1.07456
$299$	7.88034	+	10.8464i	0.0263557	+	0.0362754i
$300$	−173.398	+	150.914i	−0.577992	+	0.503047i
$301$	244.723	−	753.181i	0.813034	−	2.50226i
$302$	−168.339	+	231.699i	−0.557415	+	0.767216i
$303$	−141.321	−	32.5375i	−0.466405	−	0.107384i
$304$	−8.31001	+	25.5756i	−0.0273355	+	0.0841302i
$305$	437.131	−	142.032i	1.43322	−	0.465680i
$306$	−20.7777	+	149.134i	−0.0679010	+	0.487366i
$307$	−272.606			−0.887967			−0.443984	−	0.896035i	$-0.646435\pi$
$307$	−272.606			−0.887967			−0.443984	+	0.896035i	$0.646435\pi$
$308$	−149.708	+	168.094i	−0.486065	+	0.545759i
$309$	17.2463	+	40.5624i	0.0558133	+	0.131270i
$310$	443.235	−	322.029i	1.42979	−	1.03880i
$311$	223.774	−	72.7087i	0.719531	−	0.233790i	0.0737113	−	0.997280i	$-0.476516\pi$
$311$	223.774	−	72.7087i	0.719531	−	0.233790i	0.645820	+	0.763490i	$0.276516\pi$
$312$	0.657334	+	7.46201i	0.00210684	+	0.0239167i
$313$	−192.976	−	140.205i	−0.616536	−	0.447940i	0.235174	−	0.971953i	$-0.424434\pi$
$313$	−192.976	−	140.205i	−0.616536	−	0.447940i	−0.851710	+	0.524014i	$0.824434\pi$
$314$	128.425	−	176.761i	0.408995	−	0.562934i
$315$	−646.531	+	344.758i	−2.05248	+	1.09447i
$316$	−52.6609	−	162.074i	−0.166649	−	0.512892i
$317$	6.44025	+	8.86425i	0.0203163	+	0.0279629i	0.819054	−	0.573716i	$-0.194499\pi$
$317$	6.44025	+	8.86425i	0.0203163	+	0.0279629i	−0.798738	+	0.601679i	$0.794499\pi$
$318$	22.2136	+	52.2453i	0.0698542	+	0.164293i
$319$	−37.8087	+	86.1758i	−0.118523	+	0.270144i
$320$		−	63.6552i		−	0.198922i
$321$	−87.1526	+	145.243i	−0.271503	+	0.452470i
$322$	−67.9046	−	208.989i	−0.210884	−	0.649034i
$323$	−75.6413	−	24.5773i	−0.234184	−	0.0760908i
$324$	90.2680	−	134.520i	0.278605	−	0.415186i
$325$	−27.3630	−	19.8804i	−0.0841938	−	0.0611704i
$326$	27.9608	+	9.08503i	0.0857694	+	0.0278682i
$327$	−283.531	+	246.767i	−0.867068	+	0.754640i
$328$	19.9236	−	14.4753i	0.0607427	−	0.0441321i
$329$		−	631.270i		−	1.91875i
$330$	214.822	+	302.896i	0.650974	+	0.917865i
$331$	−240.991			−0.728069			−0.364034	−	0.931386i	$-0.618601\pi$
$331$	−240.991			−0.728069			−0.364034	+	0.931386i	$0.618601\pi$
$332$	−12.4053	−	17.0744i	−0.0373654	−	0.0514290i
$333$	344.738	+	167.631i	1.03525	+	0.503395i
$334$	−90.2528	+	277.769i	−0.270218	+	0.831645i
$335$	−132.984	+	183.037i	−0.396969	+	0.546380i
$336$	27.5479	−	119.649i	0.0819877	−	0.356098i
$337$	13.6049	−	41.8715i	0.0403705	−	0.124248i	−0.928840	−	0.370481i	$-0.879193\pi$
$337$	13.6049	−	41.8715i	0.0403705	−	0.124248i	0.969211	+	0.246233i	$0.0791929\pi$
$338$	226.256	−	73.5151i	0.669397	−	0.217500i
$339$	190.340	−	317.208i	0.561474	−	0.935716i
$340$	188.264			0.553718
$341$	−270.295	−	462.351i	−0.792655	−	1.35587i
$342$	61.6242	+	59.3676i	0.180188	+	0.173590i
$343$	−55.3430	+	40.2090i	−0.161350	+	0.117227i
$344$	208.209	−	67.6513i	0.605260	−	0.196661i
$345$	−361.114	+	31.8108i	−1.04671	+	0.0922053i
$346$	−19.5633	−	14.2135i	−0.0565412	−	0.0410796i
$347$	−344.693	+	474.429i	−0.993352	+	1.36723i	−0.0640349	+	0.997948i	$0.520397\pi$
$347$	−344.693	+	474.429i	−0.993352	+	1.36723i	−0.929317	+	0.369284i	$0.879603\pi$
$348$	−4.50426	−	51.1320i	−0.0129433	−	0.146931i
$349$	−153.775	−	473.271i	−0.440617	−	1.35608i	−0.887220	−	0.461347i	$-0.847366\pi$
$349$	−153.775	−	473.271i	−0.440617	−	1.35608i	0.446603	−	0.894732i	$-0.352634\pi$
$350$	325.848	+	448.492i	0.930995	+	1.28140i
$351$	22.2680	+	8.50213i	0.0634417	+	0.0242226i
$352$	−61.9189	−	6.16829i	−0.175906	−	0.0175235i
$353$		−	106.906i		−	0.302851i	−0.988469	−	0.151425i	$-0.951614\pi$
$353$		−	106.906i		−	0.302851i	0.988469	−	0.151425i	$-0.0483863\pi$
$354$	−165.142	−	99.0932i	−0.466503	−	0.279924i
$355$	102.302	+	314.854i	0.288175	+	0.886912i
$356$	−164.170	−	53.3420i	−0.461151	−	0.149837i
$357$	353.869	+	81.4745i	0.991230	+	0.228220i
$358$	116.391	+	84.5632i	0.325115	+	0.236210i
$359$	52.8249	+	17.1638i	0.147145	+	0.0478102i	0.381663	−	0.924301i	$-0.375351\pi$
$359$	52.8249	+	17.1638i	0.147145	+	0.0478102i	−0.234519	+	0.972112i	$0.575351\pi$
$360$	−182.156	−	88.5743i	−0.505990	−	0.246040i
$361$	255.489	−	185.624i	0.707727	−	0.514193i
$362$		−	441.947i		−	1.22085i
$363$	315.450	−	179.611i	0.869009	−	0.494796i
$364$	18.0652			0.0496296
$365$	15.9473	+	21.9495i	0.0436911	+	0.0601357i
$366$	160.894	+	184.864i	0.439600	+	0.505092i
$367$	−98.5960	+	303.447i	−0.268654	+	0.826832i	0.722175	+	0.691710i	$0.243142\pi$
$367$	−98.5960	+	303.447i	−0.268654	+	0.826832i	−0.990829	+	0.135122i	$0.956858\pi$
$368$	35.7056	−	49.1446i	0.0970262	−	0.133545i
$369$	−13.6997	−	77.1556i	−0.0371266	−	0.209094i
$370$	148.107	−	455.826i	0.400289	−	1.23196i
$371$	130.210	−	42.3079i	0.350971	−	0.114037i
$372$	250.490	+	150.306i	0.673360	+	0.404048i
$373$	−178.809			−0.479380			−0.239690	−	0.970849i	$-0.577046\pi$
$373$	−178.809			−0.479380			−0.239690	+	0.970849i	$0.577046\pi$
$374$	18.2431	−	183.129i	0.0487783	−	0.489650i
$375$	292.437	−	124.338i	0.779831	−	0.331569i
$376$	141.180	−	102.573i	0.375479	−	0.272801i
$377$	7.18282	−	2.33384i	0.0190526	−	0.00619056i
$378$	−304.057	−	245.319i	−0.804383	−	0.648993i
$379$	−142.840	−	103.779i	−0.376887	−	0.273824i	0.383174	−	0.923676i	$-0.374831\pi$
$379$	−142.840	−	103.779i	−0.376887	−	0.273824i	−0.760061	+	0.649852i	$0.774831\pi$
$380$	62.8856	−	86.5546i	0.165489	−	0.227775i
$381$	476.833	−	42.0046i	1.25153	−	0.110248i
$382$	24.5529	+	75.5660i	0.0642746	+	0.197817i
$383$	−136.523	−	187.908i	−0.356457	−	0.490620i	0.592701	−	0.805423i	$-0.298062\pi$
$383$	−136.523	−	187.908i	−0.356457	−	0.490620i	−0.949157	+	0.314802i	$0.898062\pi$
$384$	31.2350	−	13.2805i	0.0813413	−	0.0345847i
$385$	773.110	−	451.969i	2.00808	−	1.17395i
$386$			495.177i			1.28284i
$387$	96.1253	−	689.948i	0.248386	−	1.78281i
$388$	40.0884	+	123.379i	0.103321	+	0.317988i
$389$	129.104	+	41.9484i	0.331887	+	0.107836i	0.470220	−	0.882549i	$-0.344175\pi$
$389$	129.104	+	41.9484i	0.331887	+	0.107836i	−0.138333	+	0.990386i	$0.544175\pi$
$390$	6.68668	−	29.0424i	0.0171453	−	0.0744676i
$391$	145.348	+	105.602i	0.371734	+	0.270081i
$392$	−149.795	−	48.6713i	−0.382130	−	0.124161i
$393$	138.273	+	158.873i	0.351840	+	0.404257i
$394$	−160.443	+	116.569i	−0.407216	+	0.295860i
$395$			677.985i			1.71642i
$396$	−103.810	+	168.605i	−0.262145	+	0.425770i
$397$	−618.121			−1.55698			−0.778489	−	0.627658i	$-0.784014\pi$
$397$	−618.121			−1.55698			−0.778489	+	0.627658i	$0.784014\pi$
$398$	−126.737	−	174.438i	−0.318433	−	0.438286i
$399$	155.661	−	135.477i	0.390127	−	0.339541i
$400$	−47.3565	+	145.748i	−0.118391	+	0.364371i
$401$	164.977	−	227.071i	0.411413	−	0.566262i	−0.552149	−	0.833745i	$-0.686192\pi$
$401$	164.977	−	227.071i	0.411413	−	0.566262i	0.963562	+	0.267483i	$0.0861921\pi$
$402$	−117.560	−	27.0668i	−0.292437	−	0.0673304i
$403$	−13.2821	+	40.8783i	−0.0329582	+	0.101435i
$404$	−91.9468	+	29.8753i	−0.227591	+	0.0739488i
$405$	−506.930	+	398.012i	−1.25168	+	0.982746i
$406$	−123.788			−0.304897
$407$	−429.041	−	188.237i	−1.05416	−	0.462500i
$408$	39.2779	+	92.3795i	0.0962695	+	0.226420i
$409$	−588.189	+	427.344i	−1.43811	+	1.04485i	−0.449682	+	0.893189i	$0.648463\pi$
$409$	−588.189	+	427.344i	−1.43811	+	1.04485i	−0.988432	+	0.151662i	$0.951537\pi$
$410$	−93.1816	+	30.2765i	−0.227272	+	0.0738452i
$411$	58.7539	+	666.970i	0.142954	+	1.62280i
$412$	23.7724	+	17.2717i	0.0577001	+	0.0419216i
$413$	−273.000	+	375.753i	−0.661018	+	0.909813i
$414$	−90.9493	−	170.559i	−0.219684	−	0.411978i
$415$	25.9469	+	79.8563i	0.0625226	+	0.192425i
$416$	2.93536	+	4.04018i	0.00705616	+	0.00971198i
$417$	95.5026	+	224.617i	0.229023	+	0.538650i
$418$	−78.1001	−	69.5576i	−0.186842	−	0.166406i
$419$			62.5690i			0.149329i	0.997209	+	0.0746647i	$0.0237886\pi$
$419$			62.5690i			0.149329i	−0.997209	+	0.0746647i	$0.976211\pi$
$420$	−251.331	+	418.852i	−0.598408	+	0.997267i
$421$	−150.518	−	463.247i	−0.357525	−	1.10035i	−0.954531	−	0.298113i	$-0.903643\pi$
$421$	−150.518	−	463.247i	−0.357525	−	1.10035i	0.597005	−	0.802237i	$-0.296357\pi$
$422$	−266.453	−	86.5758i	−0.631405	−	0.205156i
$423$	−97.0771	−	546.730i	−0.229497	−	1.29251i
$424$	30.6195	+	22.2463i	0.0722157	+	0.0524678i
$425$	−431.060	−	140.060i	−1.01426	−	0.329552i
$426$	−133.153	+	115.887i	−0.312565	+	0.272036i
$427$	478.149	−	347.395i	1.11979	−	0.813572i
$428$			112.923i			0.263838i
$429$	−27.6023	−	9.31855i	−0.0643409	−	0.0217216i
$430$	−870.979			−2.02553
$431$	318.787	+	438.772i	0.739644	+	1.01803i	0.998639	+	0.0521544i	$0.0166088\pi$
$431$	318.787	+	438.772i	0.739644	+	1.01803i	−0.258995	+	0.965879i	$0.583391\pi$
$432$	5.45895	−	107.862i	0.0126364	−	0.249680i
$433$	28.4927	−	87.6914i	0.0658029	−	0.202520i	−0.912749	−	0.408521i	$-0.866045\pi$
$433$	28.4927	−	87.6914i	0.0658029	−	0.202520i	0.978552	+	0.206000i	$0.0660448\pi$
$434$	414.091	−	569.947i	0.954126	−	1.31324i
$435$	−45.8193	+	199.007i	−0.105332	+	0.457488i
$436$	−77.4351	+	238.321i	−0.177603	+	0.546607i
$437$	97.1009	−	31.5500i	0.222199	−	0.0721968i
$438$	−7.44332	+	12.4046i	−0.0169939	+	0.0283209i
$439$	846.447			1.92813			0.964063	−	0.265675i	$-0.0855948\pi$
$439$	846.447			1.92813			0.964063	+	0.265675i	$0.0855948\pi$
$440$	226.701	+	99.4628i	0.515230	+	0.226052i
$441$	−347.713	+	360.930i	−0.788465	+	0.818435i
$442$	−11.9491	+	8.68152i	−0.0270341	+	0.0196414i
$443$	552.137	−	179.400i	1.24636	−	0.404967i	0.389745	−	0.920923i	$-0.372563\pi$
$443$	552.137	−	179.400i	1.24636	−	0.404967i	0.856615	+	0.515956i	$0.172563\pi$
$444$	254.570	−	22.4253i	0.573356	−	0.0505073i
$445$	555.595	+	403.663i	1.24853	+	0.907109i
$446$	22.5514	−	31.0393i	0.0505637	−	0.0695949i
$447$	−59.6078	−	676.663i	−0.133351	−	1.51379i
$448$	−25.2939	−	77.8467i	−0.0564597	−	0.173765i
$449$	110.028	+	151.441i	0.245051	+	0.337284i	0.913770	−	0.406231i	$-0.133157\pi$
$449$	110.028	+	151.441i	0.245051	+	0.337284i	−0.668719	+	0.743515i	$0.733157\pi$
$450$	351.180	+	338.320i	0.780400	+	0.751823i
$451$	20.4213	+	93.5738i	0.0452800	+	0.207481i
$452$		−	246.622i		−	0.545623i
$453$	520.949	+	312.594i	1.15000	+	0.690053i
$454$	−58.4943	−	180.027i	−0.128842	−	0.396535i
$455$	−68.3538	−	22.2095i	−0.150228	−	0.0488121i
$456$	55.5916	+	12.7993i	0.121911	+	0.0280687i
$457$	−335.315	−	243.620i	−0.733730	−	0.533086i	0.157011	−	0.987597i	$-0.449814\pi$
$457$	−335.315	−	243.620i	−0.733730	−	0.533086i	−0.890741	+	0.454511i	$0.849814\pi$
$458$	31.4316	+	10.2128i	0.0686280	+	0.0222986i
$459$	319.008	+	16.1452i	0.695007	+	0.0351746i
$460$	−195.519	+	142.053i	−0.425042	+	0.308811i
$461$			178.501i			0.387204i	0.981080	+	0.193602i	$0.0620171\pi$
$461$			178.501i			0.387204i	−0.981080	+	0.193602i	$0.937983\pi$
$462$	383.073	+	285.063i	0.829162	+	0.617020i
$463$	217.484			0.469727			0.234864	−	0.972028i	$-0.424536\pi$
$463$	217.484			0.469727			0.234864	+	0.972028i	$0.424536\pi$
$464$	−20.1140	−	27.6846i	−0.0433492	−	0.0596651i
$465$	−762.999	−	876.672i	−1.64086	−	1.88532i
$466$	−110.070	+	338.761i	−0.236202	+	0.726955i
$467$	−133.815	+	184.181i	−0.286542	+	0.394391i	−0.927887	−	0.372861i	$-0.878377\pi$
$467$	−133.815	+	184.181i	−0.286542	+	0.394391i	0.641345	+	0.767253i	$0.278377\pi$
$468$	15.6459	−	2.77808i	0.0334314	−	0.00593606i
$469$	−89.9011	+	276.687i	−0.191687	+	0.589951i
$470$	−660.292	+	214.542i	−1.40488	+	0.456472i
$471$	−397.427	−	238.475i	−0.843793	−	0.506316i
$472$	−128.394			−0.272022
$473$	−84.3992	+	847.222i	−0.178434	+	1.79117i
$474$	−332.681	+	141.449i	−0.701859	+	0.298417i
$475$	−208.379	+	151.396i	−0.438693	+	0.318729i
$476$	230.236	−	74.8084i	0.483690	−	0.157160i
$477$	106.266	−	56.6658i	0.222781	−	0.118796i
$478$	345.691	+	251.159i	0.723203	+	0.525438i
$479$	21.2478	−	29.2451i	0.0443587	−	0.0610545i	−0.786261	−	0.617894i	$-0.787986\pi$
$479$	21.2478	−	29.2451i	0.0443587	−	0.0610545i	0.830620	+	0.556839i	$0.187986\pi$
$480$	−134.512	+	11.8493i	−0.280234	+	0.0246860i
$481$	11.6194	+	35.7609i	0.0241568	+	0.0743471i
$482$	−117.014	−	161.056i	−0.242768	−	0.334141i
$483$	−428.982	+	182.395i	−0.888162	+	0.377629i
$484$	118.718	−	210.879i	0.245284	−	0.435701i
$485$		−	516.119i		−	1.06416i
$486$	−301.063	−	165.708i	−0.619471	−	0.340963i
$487$	−97.6415	−	300.510i	−0.200496	−	0.617063i	−0.999868	−	0.0162271i	$-0.994835\pi$
$487$	−97.6415	−	300.510i	−0.200496	−	0.617063i	0.799372	−	0.600836i	$-0.205165\pi$
$488$	155.386	+	50.4880i	0.318414	+	0.103459i
$489$	13.9931	−	60.7762i	0.0286157	−	0.124287i
$490$	506.946	+	368.318i	1.03458	+	0.751669i
$491$	−129.137	−	41.9591i	−0.263008	−	0.0854565i	0.174545	−	0.984649i	$-0.444155\pi$
$491$	−129.137	−	41.9591i	−0.263008	−	0.0854565i	−0.437553	+	0.899193i	$0.644155\pi$
$492$	−34.2971	−	39.4067i	−0.0697096	−	0.0800950i
$493$	81.8788	−	59.4885i	0.166083	−	0.120666i
$494$			8.39348i			0.0169909i
$495$	600.071	−	510.331i	1.21227	−	1.03097i
$496$	194.750			0.392641
$497$	250.220	+	344.398i	0.503460	+	0.692954i
$498$	−33.7714	+	29.3925i	−0.0678141	+	0.0590211i
$499$	−257.602	+	792.818i	−0.516237	+	1.58881i	0.264783	+	0.964308i	$0.414700\pi$
$499$	−257.602	+	792.818i	−0.516237	+	1.58881i	−0.781020	+	0.624506i	$0.785300\pi$
$500$	124.521	−	171.389i	0.249042	−	0.342778i
$501$	603.765	+	139.010i	1.20512	+	0.277466i
$502$	−201.651	+	620.618i	−0.401695	+	1.23629i
$503$	204.979	−	66.6017i	0.407513	−	0.132409i	−0.0980854	−	0.995178i	$-0.531272\pi$
$503$	204.979	−	66.6017i	0.407513	−	0.132409i	0.505598	+	0.862769i	$0.331272\pi$
$504$	−257.963	−	35.9400i	−0.511831	−	0.0713095i
$505$	384.631			0.761645
$506$	119.232	+	203.951i	0.235637	+	0.403066i
$507$	−197.465	−	464.426i	−0.389477	−	0.916027i
$508$	258.173	−	187.574i	0.508215	−	0.369240i
$509$	−509.188	+	165.445i	−1.00037	+	0.325040i	−0.763013	−	0.646383i	$-0.776281\pi$
$509$	−509.188	+	165.445i	−1.00037	+	0.325040i	−0.237357	+	0.971423i	$0.576281\pi$
$510$	−35.0450	−	397.828i	−0.0687156	−	0.780055i
$511$	28.2244	+	20.5063i	0.0552337	+	0.0401296i
$512$	13.3001	−	18.3060i	0.0259767	−	0.0357538i
$513$	113.981	−	141.272i	0.222185	−	0.275383i
$514$	−123.407	−	379.808i	−0.240092	−	0.738926i
$515$	−68.7146	−	94.5775i	−0.133426	−	0.183646i
$516$	−181.714	−	427.382i	−0.352159	−	0.828259i
$517$	144.707	+	663.071i	0.279897	+	1.28254i
$518$		−	616.302i		−	1.18977i
$519$	−26.3935	+	43.9857i	−0.0508545	+	0.0847508i
$520$	−6.13959	−	18.8957i	−0.0118069	−	0.0363379i
$521$	−843.510	−	274.073i	−1.61902	−	0.526052i	−0.647311	−	0.762226i	$-0.724107\pi$
$521$	−843.510	−	274.073i	−1.61902	−	0.526052i	−0.971711	+	0.236174i	$0.924107\pi$
$522$	−107.211	+	19.0362i	−0.205384	+	0.0364679i
$523$	−252.074	−	183.142i	−0.481976	−	0.350176i	0.320114	−	0.947379i	$-0.396279\pi$
$523$	−252.074	−	183.142i	−0.481976	−	0.350176i	−0.802090	+	0.597203i	$0.796279\pi$
$524$	133.540	+	43.3897i	0.254847	+	0.0828048i
$525$	887.068	−	772.048i	1.68965	−	1.47057i
$526$	451.049	−	327.706i	0.857507	−	0.623016i
$527$			575.985i			1.09295i
$528$	−1.50836	+	131.991i	−0.00285674	+	0.249984i
$529$	298.370			0.564026
$530$	−88.5059	−	121.818i	−0.166992	−	0.229845i
$531$	−178.657	+	367.414i	−0.336453	+	0.691929i
$532$	42.5124	−	130.840i	0.0799105	−	0.245939i
$533$	4.51806	−	6.21858i	0.00847666	−	0.0116671i
$534$	−82.1591	+	356.843i	−0.153856	+	0.668245i
$535$	138.828	−	427.269i	0.259492	−	0.798635i
$536$	−76.4874	+	24.8523i	−0.142700	+	0.0463662i
$537$	157.028	−	261.692i	0.292417	−	0.487322i
$538$	288.364			0.535993
$539$	407.395	−	457.428i	0.755836	−	0.848660i
$540$	−153.262	+	401.409i	−0.283818	+	0.743350i
$541$	−262.375	+	190.627i	−0.484982	+	0.352360i	−0.803251	−	0.595640i	$-0.796898\pi$
$541$	−262.375	+	190.627i	−0.484982	+	0.352360i	0.318269	+	0.948000i	$0.396898\pi$
$542$	6.98242	−	2.26873i	0.0128827	−	0.00418584i
$543$	−933.896	+	82.2676i	−1.71988	+	0.151506i
$544$	54.1410	+	39.3357i	0.0995239	+	0.0723083i
$545$	585.987	−	806.542i	1.07521	−	1.47989i
$546$	−3.36280	−	38.1742i	−0.00615897	−	0.0699161i
$547$	−319.940	−	984.674i	−0.584899	−	1.80014i	−0.599674	−	0.800245i	$-0.704703\pi$
$547$	−319.940	−	984.674i	−0.584899	−	1.80014i	0.0147744	−	0.999891i	$-0.495297\pi$
$548$	262.369	+	361.120i	0.478775	+	0.658978i
$549$	360.692	−	374.402i	0.656999	−	0.681971i
$550$	−445.072	−	396.391i	−0.809221	−	0.720710i
$551$		−	57.5148i		−	0.104383i
$552$	−110.496	−	66.3027i	−0.200174	−	0.120114i
$553$	269.403	+	829.138i	0.487167	+	1.49935i
$554$	541.690	+	176.006i	0.977781	+	0.317700i
$555$	−990.794	−	228.119i	−1.78521	−	0.411026i
$556$	131.642	+	95.6432i	0.236765	+	0.172020i
$557$	−829.951	−	269.668i	−1.49004	−	0.484143i	−0.552944	−	0.833219i	$-0.686496\pi$
$557$	−829.951	−	269.668i	−1.49004	−	0.484143i	−0.937094	+	0.349076i	$0.886496\pi$
$558$	270.989	−	557.299i	0.485643	−	0.998744i
$559$	55.2808	−	40.1639i	0.0988924	−	0.0718495i
$560$			325.648i			0.581514i
$561$	−390.372	−	4.46107i	−0.695851	−	0.00795199i
$562$	305.202			0.543064
$563$	−140.362	−	193.192i	−0.249311	−	0.343147i	0.665959	−	0.745988i	$-0.268023\pi$
$563$	−140.362	−	193.192i	−0.249311	−	0.343147i	−0.915270	+	0.402842i	$0.868023\pi$
$564$	−243.032	−	279.239i	−0.430908	−	0.495105i
$565$	−303.199	+	933.150i	−0.536635	+	1.65159i
$566$	128.901	−	177.417i	0.227741	−	0.313458i
$567$	−461.794	+	688.179i	−0.814451	+	1.21372i
$568$	−36.3652	+	111.921i	−0.0640233	+	0.197043i
$569$	422.079	−	137.142i	0.741790	−	0.241022i	0.0863452	−	0.996265i	$-0.472481\pi$
$569$	422.079	−	137.142i	0.741790	−	0.241022i	0.655445	+	0.755243i	$0.272481\pi$
$570$	−194.608	−	116.774i	−0.341417	−	0.204867i
$571$	−247.835			−0.434038			−0.217019	−	0.976167i	$-0.569633\pi$
$571$	−247.835			−0.434038			−0.217019	+	0.976167i	$0.569633\pi$
$572$	−18.9753	+	4.14110i	−0.0331735	+	0.00723969i
$573$	155.111	−	65.9501i	0.270700	−	0.115096i
$574$	−101.925	+	74.0531i	−0.177570	+	0.129012i
$575$	553.352	−	179.795i	0.962352	−	0.312687i
$576$	−33.8779	−	63.5318i	−0.0588158	−	0.110298i
$577$	−432.508	−	314.235i	−0.749580	−	0.544602i	0.146117	−	0.989267i	$-0.453322\pi$
$577$	−432.508	−	314.235i	−0.749580	−	0.544602i	−0.895697	+	0.444666i	$0.853322\pi$
$578$	123.895	−	170.526i	0.214350	−	0.295028i
$579$	1046.38	−	92.1762i	1.80721	−	0.159199i
$580$	42.0704	+	129.479i	0.0725352	+	0.223240i
$581$	63.4632	+	87.3495i	0.109231	+	0.150343i
$582$	253.255	−	107.679i	0.435146	−	0.185015i
$583$	−127.072	+	74.2875i	−0.217962	+	0.127423i
$584$			9.64425i			0.0165141i
$585$	−62.6152	−	8.72370i	−0.107035	−	0.0149123i
$586$	−121.678	−	374.485i	−0.207641	−	0.639054i
$587$	861.450	+	279.902i	1.46755	+	0.476835i	0.930366	−	0.366632i	$-0.119489\pi$
$587$	861.450	+	279.902i	1.46755	+	0.476835i	0.537181	+	0.843467i	$0.319489\pi$
$588$	−74.9651	+	325.597i	−0.127492	+	0.553736i
$589$	264.810	+	192.396i	0.449592	+	0.326648i
$590$	485.809	+	157.849i	0.823405	+	0.267541i
$591$	276.192	+	317.339i	0.467330	+	0.536953i
$592$	137.833	−	100.141i	0.232825	−	0.169158i
$593$		−	1093.69i		−	1.84433i	−0.386794	−	0.922166i	$-0.626417\pi$
$593$		−	1093.69i		−	1.84433i	0.386794	−	0.922166i	$-0.373583\pi$
$594$	375.609	+	187.978i	0.632338	+	0.316462i
$595$	−963.123			−1.61869
$596$	−266.182	−	366.368i	−0.446614	−	0.614712i
$597$	−345.019	+	300.283i	−0.577922	+	0.502986i
$598$	5.85900	−	18.0322i	0.00979766	−	0.0301541i
$599$	−402.440	+	553.911i	−0.671853	+	0.924727i	−0.999801	−	0.0199694i	$-0.993643\pi$
$599$	−402.440	+	553.911i	−0.671853	+	0.924727i	0.327947	+	0.944696i	$0.393643\pi$
$600$	316.802	+	72.9401i	0.528003	+	0.121567i
$601$	1.46593	−	4.51166i	0.00243915	−	0.00750692i	−0.949830	−	0.312768i	$-0.898744\pi$
$601$	1.46593	−	4.51166i	0.00243915	−	0.00750692i	0.952269	+	0.305261i	$0.0987437\pi$
$602$	−1065.16	+	346.091i	−1.76937	+	0.574902i
$603$	−35.3124	+	253.458i	−0.0585612	+	0.420329i
$604$	405.025			0.670572
$605$	−708.452	+	651.959i	−1.17100	+	1.07762i
$606$	80.2464	+	188.735i	0.132420	+	0.311444i
$607$	562.329	−	408.556i	0.926407	−	0.673074i	−0.0187035	−	0.999825i	$-0.505954\pi$
$607$	562.329	−	408.556i	0.926407	−	0.673074i	0.945110	+	0.326751i	$0.105954\pi$
$608$	36.1693	−	11.7521i	0.0594890	−	0.0193291i
$609$	23.0429	+	261.582i	0.0378373	+	0.429527i
$610$	−525.869	−	382.066i	−0.862080	−	0.626338i
$611$	32.0153	−	44.0653i	0.0523982	−	0.0721200i
$612$	187.899	−	100.196i	0.307025	−	0.163719i
$613$	102.166	+	314.434i	0.166665	+	0.512943i	0.999155	−	0.0410973i	$-0.0130853\pi$
$613$	102.166	+	314.434i	0.166665	+	0.512943i	−0.832490	+	0.554040i	$0.813085\pi$
$614$	226.605	+	311.895i	0.369063	+	0.507972i
$615$	81.3241	+	191.270i	0.132234	+	0.311008i
$616$	316.765	+	31.5558i	0.514229	+	0.0512269i
$617$		−	16.4953i		−	0.0267346i	−0.999911	−	0.0133673i	$-0.995745\pi$
$617$		−	16.4953i		−	0.0267346i	0.999911	−	0.0133673i	$-0.00425508\pi$
$618$	32.0723	−	53.4495i	0.0518969	−	0.0864879i
$619$	105.519	+	324.753i	0.170466	+	0.524641i	0.999397	−	0.0347097i	$-0.0110507\pi$
$619$	105.519	+	324.753i	0.170466	+	0.524641i	−0.828931	+	0.559350i	$0.811051\pi$
$620$	−736.882	−	239.427i	−1.18852	−	0.386173i
$621$	−343.484	+	223.938i	−0.553114	+	0.360608i
$622$	−269.201	−	195.586i	−0.432799	−	0.314447i
$623$	839.861	+	272.887i	1.34809	+	0.438021i
$624$	7.99105	−	6.95490i	0.0128062	−	0.0111457i
$625$	93.0197	−	67.5828i	0.148832	−	0.108132i
$626$			337.334i			0.538872i
$627$	−132.447	+	177.984i	−0.211239	+	0.283866i
$628$	−308.990			−0.492022
$629$	296.174	+	407.648i	0.470865	+	0.648089i
$630$	931.877	+	453.129i	1.47917	+	0.719252i
$631$	182.208	−	560.778i	0.288761	−	0.888714i	−0.696486	−	0.717571i	$-0.745254\pi$
$631$	182.208	−	560.778i	0.288761	−	0.888714i	0.985246	−	0.171143i	$-0.0547460\pi$
$632$	−141.658	+	194.975i	−0.224142	+	0.308505i
$633$	−133.347	+	579.167i	−0.210659	+	0.914956i
$634$	4.78830	−	14.7369i	0.00755253	−	0.0232443i
$635$	−1207.46	+	392.328i	−1.90151	+	0.617840i
$636$	41.3098	−	68.8442i	0.0649525	−	0.108246i
$637$	−49.1602			−0.0771746
$638$	130.024	−	28.3761i	0.203800	−	0.0444767i
$639$	269.672	+	259.797i	0.422022	+	0.406569i
$640$	−72.8294	+	52.9136i	−0.113796	+	0.0826775i
$641$	429.182	−	139.450i	0.669551	−	0.217550i	0.0455361	−	0.998963i	$-0.485500\pi$
$641$	429.182	−	139.450i	0.669551	−	0.217550i	0.624015	+	0.781412i	$0.285500\pi$
$642$	238.621	−	21.0203i	0.371684	−	0.0327420i
$643$	−275.123	−	199.888i	−0.427874	−	0.310868i	0.352924	−	0.935652i	$-0.385187\pi$
$643$	−275.123	−	199.888i	−0.427874	−	0.310868i	−0.780798	+	0.624783i	$0.785187\pi$
$644$	−182.663	+	251.414i	−0.283638	+	0.390395i
$645$	162.131	+	1840.50i	0.251366	+	2.85348i
$646$	34.7576	+	106.973i	0.0538044	+	0.165593i
$647$	380.135	+	523.211i	0.587534	+	0.808672i	0.994496	−	0.104774i	$-0.0334118\pi$
$647$	380.135	+	523.211i	0.587534	+	0.808672i	−0.406962	+	0.913445i	$0.633412\pi$
$648$	−228.943	+	8.54277i	−0.353308	+	0.0131833i
$649$	200.619	−	457.262i	0.309120	−	0.704564i
$650$			47.8322i			0.0735881i
$651$	−1281.46	−	768.936i	−1.96845	−	1.18116i
$652$	−12.8482	−	39.5426i	−0.0197058	−	0.0606482i
$653$	−347.582	−	112.936i	−0.532284	−	0.172950i	0.0305287	−	0.999534i	$-0.490281\pi$
$653$	−347.582	−	112.936i	−0.532284	−	0.172950i	−0.562813	+	0.826584i	$0.690281\pi$
$654$	518.019	+	119.268i	0.792077	+	0.182367i
$655$	−451.935	−	328.350i	−0.689977	−	0.501298i
$656$	−33.1231	−	10.7624i	−0.0504926	−	0.0164060i
$657$	27.5981	+	13.4197i	0.0420062	+	0.0204257i
$658$	−722.250	+	524.745i	−1.09764	+	0.797485i
$659$		−	371.868i		−	0.564291i	−0.959372	−	0.282145i	$-0.908954\pi$
$659$		−	371.868i		−	0.564291i	0.959372	−	0.282145i	$-0.0910461\pi$
$660$	167.979	−	497.565i	0.254513	−	0.753887i
$661$	1177.75			1.78177			0.890883	−	0.454233i	$-0.150087\pi$
$661$	1177.75			1.78177			0.890883	+	0.454233i	$0.150087\pi$
$662$	200.324	+	275.723i	0.302605	+	0.416500i
$663$	20.5695	+	23.6340i	0.0310249	+	0.0356471i
$664$	−9.22330	+	28.3864i	−0.0138905	+	0.0427506i
$665$	−321.711	+	442.797i	−0.483776	+	0.665860i
$666$	−94.7753	−	533.767i	−0.142305	−	0.801452i
$667$	−40.1477	+	123.562i	−0.0601915	+	0.185250i
$668$	392.825	−	127.637i	0.588062	−	0.191073i
$669$	−69.7882	−	41.8763i	−0.104317	−	0.0625953i
$670$	319.961			0.477554
$671$	−422.602	+	474.502i	−0.629810	+	0.707157i
$672$	−159.792	+	67.9406i	−0.237786	+	0.101102i
$673$	−227.771	+	165.486i	−0.338442	+	0.245892i	−0.744004	−	0.668175i	$-0.767076\pi$
$673$	−227.771	+	165.486i	−0.338442	+	0.245892i	0.405562	+	0.914067i	$0.367076\pi$
$674$	−59.2152	+	19.2402i	−0.0878564	+	0.0285463i
$675$	649.546	−	805.069i	0.962290	−	1.19269i
$676$	−272.187	−	197.755i	−0.402643	−	0.292537i
$677$	−315.539	+	434.303i	−0.466085	+	0.641511i	−0.975757	−	0.218858i	$-0.929767\pi$
$677$	−315.539	+	434.303i	−0.466085	+	0.641511i	0.509672	+	0.860369i	$0.329767\pi$
$678$	−521.145	+	45.9081i	−0.768651	+	0.0677111i
$679$	−205.084	−	631.185i	−0.302039	−	0.929580i
$680$	−156.495	−	215.397i	−0.230140	−	0.316761i
$681$	−369.533	+	157.118i	−0.542633	+	0.230717i
$682$	−304.302	+	693.582i	−0.446190	+	1.01698i
$683$		−	1196.04i		−	1.75116i	−0.483072	−	0.875580i	$-0.660479\pi$
$683$		−	1196.04i		−	1.75116i	0.483072	−	0.875580i	$-0.339521\pi$
$684$	16.6985	−	119.855i	0.0244130	−	0.175227i
$685$	−548.769	−	1688.94i	−0.801123	−	2.46560i
$686$	92.0081	+	29.8953i	0.134123	+	0.0435791i
$687$	15.7300	−	68.3205i	0.0228967	−	0.0994475i
$688$	−250.476	−	181.982i	−0.364064	−	0.264508i
$689$	11.2349	+	3.65044i	0.0163061	+	0.00529817i
$690$	336.573	+	386.716i	0.487787	+	0.560458i
$691$	−102.993	+	74.8287i	−0.149049	+	0.108290i	−0.659811	−	0.751432i	$-0.729363\pi$
$691$	−102.993	+	74.8287i	−0.149049	+	0.108290i	0.510762	+	0.859722i	$0.329363\pi$
$692$			34.1978i			0.0494188i
$693$	531.070	−	862.550i	0.766334	−	1.24466i
$694$	829.333			1.19500
$695$	−380.511	−	523.729i	−0.547498	−	0.753567i
$696$	−54.7572	+	47.6571i	−0.0786741	+	0.0684729i
$697$	31.8303	−	97.9637i	0.0456676	−	0.140550i
$698$	−413.654	+	569.346i	−0.592628	+	0.815683i
$699$	736.338	+	169.534i	1.05342	+	0.242537i
$700$	242.267	−	745.621i	0.346095	−	1.06517i
$701$	436.943	−	141.972i	0.623314	−	0.202527i	0.0197031	−	0.999806i	$-0.493728\pi$
$701$	436.943	−	141.972i	0.623314	−	0.202527i	0.603611	+	0.797279i	$0.293728\pi$
$702$	−8.78291	−	32.5448i	−0.0125113	−	0.0463601i
$703$	286.347			0.407322
$704$	44.4131	+	75.9703i	0.0630867	+	0.107912i
$705$	576.268	+	1355.35i	0.817402	+	1.92248i
$706$	−122.314	+	88.8663i	−0.173249	+	0.125873i
$707$	470.382	−	152.836i	0.665321	−	0.216176i
$708$	23.9003	+	271.315i	0.0337575	+	0.383213i
$709$	−88.6401	−	64.4008i	−0.125021	−	0.0908333i	0.523517	−	0.852015i	$-0.324620\pi$
$709$	−88.6401	−	64.4008i	−0.125021	−	0.0908333i	−0.648539	+	0.761182i	$0.724620\pi$
$710$	275.192	−	378.770i	0.387595	−	0.533479i
$711$	360.830	+	676.671i	0.507497	+	0.951717i
$712$	75.4370	+	232.171i	0.105951	+	0.326083i
$713$	−434.605	−	598.182i	−0.609544	−	0.838965i
$714$	−200.938	−	472.596i	−0.281426	−	0.661899i
$715$	76.8883	+	7.65952i	0.107536	+	0.0107126i
$716$		−	203.459i		−	0.284161i
$717$	466.384	−	777.245i	0.650466	−	1.08402i
$718$	−24.2733	−	74.7057i	−0.0338069	−	0.104047i
$719$	966.606	+	314.069i	1.34438	+	0.436814i	0.890797	−	0.454402i	$-0.150147\pi$
$719$	966.606	+	314.069i	1.34438	+	0.436814i	0.453578	+	0.891216i	$0.350147\pi$
$720$	50.0783	+	282.037i	0.0695532	+	0.391718i
$721$	−121.615	−	88.3586i	−0.168676	−	0.122550i
$722$	−424.753	−	138.011i	−0.588300	−	0.191150i
$723$	−318.552	+	277.247i	−0.440597	+	0.383468i
$724$	−505.642	+	367.371i	−0.698401	+	0.507418i
$725$		−	327.761i		−	0.452085i
$726$	−467.716	−	211.612i	−0.644237	−	0.291476i
$727$	−334.801			−0.460524			−0.230262	−	0.973129i	$-0.573958\pi$
$727$	−334.801			−0.460524			−0.230262	+	0.973129i	$0.573958\pi$
$728$	−15.0168	−	20.6688i	−0.0206274	−	0.0283912i
$729$	−294.122	+	667.033i	−0.403459	+	0.914998i
$730$	11.8567	−	36.4912i	0.0162421	−	0.0499880i
$731$	538.221	−	740.798i	0.736281	−	1.01340i
$732$	77.7633	−	337.751i	0.106234	−	0.461408i
$733$	229.066	−	704.991i	0.312504	−	0.961789i	−0.664265	−	0.747497i	$-0.731256\pi$
$733$	229.066	−	704.991i	0.312504	−	0.961789i	0.976770	−	0.214292i	$-0.0687445\pi$
$734$	429.139	−	139.436i	0.584658	−	0.189967i
$735$	683.939	−	1139.81i	0.930530	−	1.55076i
$736$	−85.9079			−0.116723
$737$	31.0047	−	311.234i	0.0420688	−	0.422298i
$738$	−76.8875	+	79.8100i	−0.104184	+	0.108144i
$739$	−78.4855	+	57.0230i	−0.106205	+	0.0771624i	−0.639620	−	0.768691i	$-0.720908\pi$
$739$	−78.4855	+	57.0230i	−0.106205	+	0.0771624i	0.533415	+	0.845854i	$0.320908\pi$
$740$	−644.636	+	209.455i	−0.871130	+	0.283047i
$741$	17.7366	−	1.56243i	0.0239360	−	0.00210854i
$742$	−156.643	−	113.808i	−0.211109	−	0.153380i
$743$	673.183	−	926.556i	0.906033	−	1.24705i	−0.0624701	−	0.998047i	$-0.519898\pi$
$743$	673.183	−	926.556i	0.906033	−	1.24705i	0.968503	−	0.249001i	$-0.0801022\pi$
$744$	−36.2523	−	411.534i	−0.0487262	−	0.553137i
$745$	556.745	+	1713.48i	0.747308	+	2.29998i
$746$	148.635	+	204.579i	0.199243	+	0.274235i
$747$	68.3968	+	65.8923i	0.0915620	+	0.0882092i
$748$	−224.687	+	131.354i	−0.300383	+	0.175607i
$749$		−	577.691i		−	0.771284i
$750$	−385.347	−	231.227i	−0.513796	−	0.308302i
$751$	347.052	+	1068.12i	0.462120	+	1.42226i	0.862568	+	0.505941i	$0.168855\pi$
$751$	347.052	+	1068.12i	0.462120	+	1.42226i	−0.400448	+	0.916320i	$0.631145\pi$
$752$	−234.713	−	76.2629i	−0.312118	−	0.101413i
$753$	1348.99	+	310.590i	1.79149	+	0.412470i
$754$	−8.64095	−	6.27802i	−0.0114601	−	0.00832628i
$755$	−1532.51	−	497.942i	−2.02981	−	0.659525i
$756$	−27.9269	+	551.801i	−0.0369404	+	0.729895i
$757$	−874.744	+	635.539i	−1.15554	+	0.839549i	−0.989208	−	0.146520i	$-0.953193\pi$
$757$	−874.744	+	635.539i	−1.15554	+	0.839549i	−0.166333	+	0.986070i	$0.553193\pi$
$758$			249.694i			0.329411i
$759$	408.782	−	289.919i	0.538580	−	0.381975i
$760$	−151.303			−0.199083
$761$	747.275	+	1028.54i	0.981964	+	1.35156i	0.935764	+	0.352626i	$0.114711\pi$
$761$	747.275	+	1028.54i	0.981964	+	1.35156i	0.0462001	+	0.998932i	$0.485289\pi$
$762$	−444.427	−	510.639i	−0.583238	−	0.670129i
$763$	396.143	−	1219.20i	0.519191	−	1.59791i
$764$	66.0471	−	90.9060i	0.0864491	−	0.118987i
$765$	−834.141	+	148.110i	−1.09038	+	0.193607i
$766$	−101.504	+	312.398i	−0.132512	+	0.407830i
$767$	−38.1132	+	12.3837i	−0.0496912	+	0.0161457i
$768$	−41.1588	−	24.6972i	−0.0535922	−	0.0321579i
$769$	−829.280			−1.07839			−0.539193	−	0.842182i	$-0.681271\pi$
$769$	−829.280			−1.07839			−0.539193	+	0.842182i	$0.681271\pi$
$770$	−1159.76	−	508.832i	−1.50618	−	0.660821i
$771$	−779.614	+	331.477i	−1.01117	+	0.429931i
$772$	566.543	−	411.618i	0.733864	−	0.533184i
$773$	−897.497	+	291.615i	−1.16106	+	0.377250i	−0.825298	−	0.564697i	$-0.808993\pi$
$773$	−897.497	+	291.615i	−1.16106	+	0.377250i	−0.335759	+	0.941948i	$0.608993\pi$
$774$	−869.290	+	463.543i	−1.12311	+	0.598893i
$775$	1509.08	+	1096.41i	1.94720	+	1.41473i
$776$	107.837	−	148.426i	0.138966	−	0.191270i
$777$	−1302.33	+	114.723i	−1.67610	+	0.147649i
$778$	−59.3240	−	182.580i	−0.0762519	−	0.234679i
$779$	−34.4067	−	47.3567i	−0.0441678	−	0.0607917i
$780$	−38.7864	+	16.4912i	−0.0497261	+	0.0211426i
$781$	−341.772	−	304.390i	−0.437608	−	0.389743i
$782$		−	254.078i		−	0.324908i
$783$	60.1832	+	223.007i	0.0768624	+	0.284811i
$784$	68.8316	+	211.842i	0.0877954	+	0.270206i
$785$	1169.13	+	379.875i	1.48934	+	0.483917i
$786$	66.8303	−	290.265i	0.0850258	−	0.369294i
$787$	295.668	+	214.815i	0.375690	+	0.272955i	0.759566	−	0.650430i	$-0.225411\pi$
$787$	295.668	+	214.815i	0.375690	+	0.272955i	−0.383876	+	0.923384i	$0.625411\pi$
$788$	266.738	+	86.6684i	0.338500	+	0.109985i
$789$	−776.450	−	892.126i	−0.984094	−	1.13071i
$790$	775.698	−	563.578i	0.981896	−	0.713389i
$791$			1261.67i			1.59503i
$792$	279.197	−	21.3825i	0.352521	−	0.0269982i
$793$	50.9952			0.0643067
$794$	513.815	+	707.206i	0.647122	+	0.890687i
$795$	−240.943	+	209.701i	−0.303073	+	0.263775i
$796$	−94.2281	+	290.004i	−0.118377	+	0.364327i
$797$	544.586	−	749.559i	0.683295	−	0.940475i	−0.316672	−	0.948535i	$-0.602566\pi$
$797$	544.586	−	749.559i	0.683295	−	0.940475i	0.999968	+	0.00805985i	$0.00256556\pi$
$798$	−284.396	−	65.4790i	−0.356386	−	0.0820538i
$799$	225.552	−	694.178i	0.282293	−	0.868808i
$800$	206.119	−	66.9722i	0.257649	−	0.0837153i
$801$	769.351	+	107.188i	0.960489	+	0.133818i
$802$	−396.935			−0.494931
$803$	−34.3470	−	15.0694i	−0.0427733	−	0.0187663i
$804$	66.7542	+	157.002i	0.0830276	+	0.195276i
$805$	1000.24	−	726.716i	1.24253	−	0.902753i
$806$	57.8106	−	18.7838i	0.0717253	−	0.0233050i
$807$	−53.6784	−	609.354i	−0.0665160	−	0.755085i
$808$	110.612	+	80.3645i	0.136896	+	0.0994610i
$809$	266.633	−	366.989i	0.329584	−	0.453633i	−0.611779	−	0.791029i	$-0.709546\pi$
$809$	266.633	−	366.989i	0.329584	−	0.453633i	0.941363	+	0.337395i	$0.109546\pi$
$810$	876.762	+	249.141i	1.08242	+	0.307582i
$811$	171.626	+	528.211i	0.211623	+	0.651309i	0.999376	+	0.0353176i	$0.0112443\pi$
$811$	171.626	+	528.211i	0.211623	+	0.651309i	−0.787753	+	0.615991i	$0.788756\pi$
$812$	102.900	+	141.629i	0.126724	+	0.174420i
$813$	−6.09389	−	14.3325i	−0.00749556	−	0.0176291i
$814$	141.276	+	647.349i	0.173557	+	0.795269i
$815$			165.414i			0.202962i
$816$	73.0436	−	121.730i	0.0895142	−	0.149178i
$817$	−160.801	−	494.896i	−0.196819	−	0.605748i
$818$	977.868	+	317.729i	1.19544	+	0.388421i
$819$	−80.0414	+	14.2121i	−0.0977306	+	0.0173530i
$820$	112.098	+	81.4437i	0.136704	+	0.0993216i
$821$	201.284	+	65.4011i	0.245169	+	0.0796602i	0.429024	−	0.903293i	$-0.358858\pi$
$821$	201.284	+	65.4011i	0.245169	+	0.0796602i	−0.183855	+	0.982953i	$0.558858\pi$
$822$	714.256	−	621.643i	0.868925	−	0.756257i
$823$	65.9884	−	47.9434i	0.0801803	−	0.0582544i	−0.546973	−	0.837150i	$-0.684220\pi$
$823$	65.9884	−	47.9434i	0.0801803	−	0.0582544i	0.627153	+	0.778896i	$0.284220\pi$
$824$		−	41.5558i		−	0.0504317i
$825$	−754.779	+	1014.28i	−0.914883	+	1.22944i
$826$	656.840			0.795206
$827$	581.921	+	800.946i	0.703653	+	0.968496i	0.999910	+	0.0133876i	$0.00426154\pi$
$827$	581.921	+	800.946i	0.703653	+	0.968496i	−0.296257	+	0.955108i	$0.595738\pi$
$828$	−119.538	+	245.835i	−0.144370	+	0.296902i
$829$	95.4438	−	293.746i	0.115131	−	0.354338i	−0.876843	−	0.480777i	$-0.840355\pi$
$829$	95.4438	−	293.746i	0.115131	−	0.354338i	0.991974	+	0.126439i	$0.0403548\pi$
$830$	69.7969	−	96.0672i	0.0840927	−	0.115744i
$831$	271.090	−	1177.43i	0.326221	−	1.41688i
$832$	2.18243	−	6.71683i	0.00262311	−	0.00807312i
$833$	−626.535	+	203.574i	−0.752143	+	0.244386i
$834$	177.602	−	295.980i	0.212952	−	0.354893i
$835$	−1643.26			−1.96798
$836$	−14.6615	+	147.176i	−0.0175377	+	0.176048i
$837$	−1228.09	−	468.897i	−1.46726	−	0.560211i
$838$	71.5866	−	52.0107i	0.0854256	−	0.0620653i
$839$	−666.979	+	216.715i	−0.794970	+	0.258301i	−0.678219	−	0.734860i	$-0.737248\pi$
$839$	−666.979	+	216.715i	−0.794970	+	0.258301i	−0.116751	+	0.993161i	$0.537248\pi$
$840$	688.138	−	60.6186i	0.819212	−	0.0721650i
$841$	−621.173	−	451.308i	−0.738612	−	0.536633i
$842$	−404.893	+	557.287i	−0.480871	+	0.661862i
$843$	−56.8127	−	644.934i	−0.0673935	−	0.765046i
$844$	122.437	+	376.821i	0.145067	+	0.446471i
$845$	786.759	+	1082.88i	0.931076	+	1.28152i
$846$	−544.831	+	565.540i	−0.644008	+	0.668486i
$847$	−607.336	+	1078.82i	−0.717043	+	1.27369i
$848$		−	53.5248i		−	0.0631188i
$849$	−398.902	−	239.360i	−0.469849	−	0.281932i
$850$	198.074	+	609.610i	0.233029	+	0.717189i
$851$	−615.175	−	199.882i	−0.722885	−	0.234880i
$852$	243.273	+	56.0109i	0.285532	+	0.0657405i
$853$	146.308	+	106.299i	0.171522	+	0.124618i	0.670234	−	0.742150i	$-0.266194\pi$
$853$	146.308	+	106.299i	0.171522	+	0.124618i	−0.498712	+	0.866768i	$0.666194\pi$
$854$	−794.926	−	258.287i	−0.930826	−	0.302444i
$855$	−210.534	+	432.970i	−0.246238	+	0.506398i
$856$	129.198	−	93.8675i	0.150932	−	0.109658i
$857$		−	456.026i		−	0.532119i	−0.963957	−	0.266059i	$-0.914278\pi$
$857$		−	456.026i		−	0.532119i	0.963957	−	0.266059i	$-0.0857217\pi$
$858$	12.2829	+	39.3265i	0.0143158	+	0.0458350i
$859$	−45.2880			−0.0527218			−0.0263609	−	0.999652i	$-0.508392\pi$
$859$	−45.2880			−0.0527218			−0.0263609	+	0.999652i	$0.508392\pi$
$860$	724.004	+	996.507i	0.841866	+	1.15873i
$861$	175.457	+	201.597i	0.203783	+	0.234143i
$862$	237.017	−	729.462i	0.274961	−	0.846244i
$863$	−485.953	+	668.856i	−0.563097	+	0.775036i	−0.991716	−	0.128449i	$-0.959000\pi$
$863$	−485.953	+	668.856i	−0.563097	+	0.775036i	0.428619	+	0.903485i	$0.359000\pi$
$864$	−127.945	+	83.4150i	−0.148085	+	0.0965451i
$865$	42.0431	−	129.395i	0.0486047	−	0.149590i
$866$	−124.014	+	40.2947i	−0.143204	+	0.0465297i
$867$	−383.408	−	230.063i	−0.442224	−	0.265355i
$868$	−996.304			−1.14782
$869$	−473.039	−	809.152i	−0.544349	−	0.931130i
$870$	265.776	−	113.003i	0.305490	−	0.129888i
$871$	−20.3079	+	14.7545i	−0.0233156	+	0.0169398i
$872$	337.036	−	109.510i	0.386509	−	0.125585i
$873$	−274.683	−	515.118i	−0.314643	−	0.590055i
$874$	−116.813	−	84.8693i	−0.133653	−	0.0971045i
$875$	−637.026	+	876.792i	−0.728030	+	1.00205i
$876$	20.3796	−	1.79526i	0.0232644	−	0.00204938i
$877$	313.366	+	964.441i	0.357316	+	1.09970i	0.954655	+	0.297716i	$0.0962247\pi$
$877$	313.366	+	964.441i	0.357316	+	1.09970i	−0.597339	+	0.801989i	$0.703775\pi$
$878$	−703.612	−	968.439i	−0.801381	−	1.10301i
$879$	−768.689	+	326.831i	−0.874504	+	0.371822i
$880$	−74.6486	−	342.053i	−0.0848279	−	0.388696i
$881$			1090.27i			1.23754i	0.785573	+	0.618769i	$0.212368\pi$
$881$			1090.27i			1.23754i	−0.785573	+	0.618769i	$0.787632\pi$
$882$	701.986	+	97.8023i	0.795902	+	0.110887i
$883$	340.544	+	1048.09i	0.385667	+	1.18696i	0.935996	+	0.352012i	$0.114502\pi$
$883$	340.544	+	1048.09i	0.385667	+	1.18696i	−0.550329	+	0.834948i	$0.685498\pi$
$884$	19.8654	+	6.45467i	0.0224722	+	0.00730167i
$885$	243.124	−	1055.96i	0.274717	−	1.19318i
$886$	−664.222	−	482.586i	−0.749686	−	0.544679i
$887$	228.297	+	74.1783i	0.257381	+	0.0836283i	0.434866	−	0.900495i	$-0.356796\pi$
$887$	228.297	+	74.1783i	0.257381	+	0.0836283i	−0.177484	+	0.984124i	$0.556796\pi$
$888$	−237.269	−	272.618i	−0.267195	−	0.307002i
$889$	−1320.76	+	959.591i	−1.48567	+	1.07940i
$890$		−	971.216i		−	1.09125i
$891$	327.305	−	828.705i	0.367346	−	0.930084i
$892$	−54.2587			−0.0608282
$893$	−243.808	−	335.573i	−0.273022	−	0.375782i
$894$	−724.637	+	630.678i	−0.810556	+	0.705456i
$895$	−250.135	+	769.835i	−0.279480	+	0.860151i
$896$	−68.0405	+	93.6498i	−0.0759381	+	0.104520i
$897$	−39.1951	−	9.02423i	−0.0436957	−	0.0100605i
$898$	81.8054	−	251.771i	0.0910974	−	0.280369i
$899$	−396.136	+	128.712i	−0.440641	+	0.143173i
$900$	95.1604	−	683.023i	0.105734	−	0.758914i
$901$	158.303			0.175697
$902$	90.0847	−	101.148i	0.0998722	−	0.112138i
$903$	929.615	+	2186.40i	1.02947	+	2.42126i
$904$	−282.165	+	205.005i	−0.312130	+	0.226776i
$905$	2364.86	−	768.390i	2.61311	−	0.849050i
$906$	−75.3946	−	855.874i	−0.0832170	−	0.944673i
$907$	1289.19	+	936.650i	1.42138	+	1.03269i	0.991543	+	0.129781i	$0.0414276\pi$
$907$	1289.19	+	936.650i	1.42138	+	1.03269i	0.429833	+	0.902908i	$0.358572\pi$
$908$	−157.349	+	216.573i	−0.173292	+	0.238516i
$909$	383.885	−	204.704i	0.422316	−	0.225197i
$910$	31.4090	+	96.6668i	0.0345153	+	0.106227i
$911$	−458.969	−	631.716i	−0.503808	−	0.693432i	0.479052	−	0.877786i	$-0.340981\pi$
$911$	−458.969	−	631.716i	−0.503808	−	0.693432i	−0.982860	+	0.184355i	$0.940981\pi$
$912$	−31.5667	−	74.2431i	−0.0346126	−	0.0814069i
$913$	−86.6835	−	77.2022i	−0.0949435	−	0.0845588i
$914$			586.151i			0.641304i
$915$	−709.469	+	1182.35i	−0.775376	+	1.29219i
$916$	−14.4430	−	44.4511i	−0.0157675	−	0.0485274i
$917$	−683.164	−	221.974i	−0.744999	−	0.242065i
$918$	−246.705	−	378.405i	−0.268742	−	0.412206i
$919$	−504.522	−	366.557i	−0.548990	−	0.398865i	0.278423	−	0.960459i	$-0.410188\pi$
$919$	−504.522	−	366.557i	−0.548990	−	0.398865i	−0.827413	+	0.561594i	$0.810188\pi$
$920$	325.052	+	105.616i	0.353318	+	0.114800i
$921$	616.894	−	536.905i	0.669809	−	0.582959i
$922$	204.227	−	148.380i	0.221505	−	0.160933i
$923$			36.7305i			0.0397947i
$924$	7.71648	−	675.242i	0.00835117	−	0.730782i
$925$	1631.82			1.76413
$926$	−180.784	−	248.828i	−0.195231	−	0.268713i
$927$	−118.916	−	57.8236i	−0.128281	−	0.0623771i
$928$	−14.9547	+	46.0258i	−0.0161150	+	0.0495968i
$929$	−195.774	+	269.460i	−0.210736	+	0.290054i	−0.901280	−	0.433237i	$-0.857371\pi$
$929$	−195.774	+	269.460i	−0.210736	+	0.290054i	0.690544	+	0.723291i	$0.257371\pi$
$930$	−368.774	+	1601.70i	−0.396531	+	1.72226i
$931$	−115.688	+	356.050i	−0.124262	+	0.382438i
$932$	479.081	−	155.663i	0.514035	−	0.167020i
$933$	−363.189	+	605.266i	−0.389270	+	0.648731i
$934$	321.960			0.344711
$935$	1011.64	−	220.778i	1.08197	−	0.236126i
$936$	−16.1842	−	15.5915i	−0.0172908	−	0.0166576i
$937$	708.264	−	514.584i	0.755885	−	0.549183i	−0.141760	−	0.989901i	$-0.545276\pi$
$937$	708.264	−	514.584i	0.755885	−	0.549183i	0.897645	+	0.440718i	$0.145276\pi$
$938$	391.295	−	127.139i	0.417158	−	0.135543i
$939$	712.833	−	62.7940i	0.759141	−	0.0668733i
$940$	794.332	+	577.116i	0.845034	+	0.613953i
$941$	464.863	−	639.829i	0.494009	−	0.679946i	−0.487112	−	0.873340i	$-0.661950\pi$
$941$	464.863	−	639.829i	0.494009	−	0.679946i	0.981121	+	0.193394i	$0.0619496\pi$
$942$	57.5178	+	652.938i	0.0610593	+	0.693140i
$943$	40.8607	+	125.756i	0.0433305	+	0.133358i
$944$	106.728	+	146.899i	0.113060	+	0.155613i
$945$	784.057	−	2053.53i	0.829689	−	2.17305i
$946$	1039.48	−	607.693i	1.09882	−	0.642382i
$947$		−	905.542i		−	0.956222i	−0.878299	−	0.478111i	$-0.841322\pi$
$947$		−	905.542i		−	0.956222i	0.878299	−	0.478111i	$-0.158678\pi$
$948$	438.378	+	263.048i	0.462424	+	0.277477i
$949$	0.930195	+	2.86285i	0.000980185	+	0.00301670i
$950$	346.432	+	112.563i	0.364665	+	0.118487i
$951$	−32.0324	−	7.37510i	−0.0336828	−	0.00775510i
$952$	−276.975	−	201.234i	−0.290940	−	0.211380i
$953$	−450.763	−	146.462i	−0.472994	−	0.153685i	0.0628133	−	0.998025i	$-0.479993\pi$
$953$	−450.763	−	146.462i	−0.472994	−	0.153685i	−0.535808	+	0.844340i	$0.679993\pi$
$954$	−153.167	−	74.4781i	−0.160552	−	0.0780693i
$955$	−361.665	+	262.765i	−0.378707	+	0.275147i
$956$		−	604.290i		−	0.632102i
$957$	−84.1664	−	269.477i	−0.0879482	−	0.281585i
$958$	−51.1223			−0.0533636
$959$	−1342.23	−	1847.42i	−1.39961	−	1.92640i
$960$	125.371	+	144.049i	0.130595	+	0.150051i
$961$	435.552	−	1340.49i	0.453228	−	1.39489i
$962$	31.2562	−	43.0205i	0.0324909	−	0.0447198i
$963$	−88.8378	−	500.327i	−0.0922510	−	0.519550i
$964$	−86.9995	+	267.757i	−0.0902485	+	0.277756i
$965$	−2649.69	+	860.938i	−2.74580	+	0.892163i
$966$	565.275	+	339.192i	0.585171	+	0.351130i
$967$	1510.40			1.56195			0.780974	−	0.624564i	$-0.214723\pi$
$967$	1510.40			1.56195			0.780974	+	0.624564i	$0.214723\pi$
$968$	−339.956	+	39.4670i	−0.351195	+	0.0407717i
$969$	219.578	−	93.3604i	0.226603	−	0.0963472i
$970$	−590.503	+	429.026i	−0.608766	+	0.442295i
$971$	−145.375	+	47.2352i	−0.149717	+	0.0486459i	−0.382917	−	0.923783i	$-0.625080\pi$
$971$	−145.375	+	47.2352i	−0.149717	+	0.0486459i	0.233200	+	0.972429i	$0.425080\pi$
$972$	60.6694	+	482.198i	0.0624170	+	0.496089i
$973$	−673.453	−	489.292i	−0.692140	−	0.502869i
$974$	−262.655	+	361.514i	−0.269666	+	0.371164i
$975$	101.076	−	8.90387i	0.103668	−	0.00913218i
$976$	−71.4009	−	219.749i	−0.0731566	−	0.225153i
$977$	671.431	+	924.146i	0.687237	+	0.945901i	0.999992	−	0.00393265i	$-0.00125181\pi$
$977$	671.431	+	924.146i	0.687237	+	0.945901i	−0.312755	+	0.949834i	$0.601252\pi$
$978$	−81.1673	+	34.5107i	−0.0829931	+	0.0352870i
$979$	−944.724	−	94.1123i	−0.964989	−	0.0961311i
$980$		−	886.174i		−	0.904260i
$981$	155.602	−	1116.85i	0.158615	−	1.13848i
$982$	59.3392	+	182.627i	0.0604269	+	0.185975i
$983$	−261.520	−	84.9731i	−0.266043	−	0.0864427i	0.172958	−	0.984929i	$-0.444668\pi$
$983$	−261.520	−	84.9731i	−0.266043	−	0.0864427i	−0.439001	+	0.898487i	$0.644668\pi$
$984$	−16.5765	+	71.9971i	−0.0168461	+	0.0731678i
$985$	−902.713	−	655.860i	−0.916460	−	0.665847i
$986$	−136.124	−	44.2294i	−0.138057	−	0.0448574i
$987$	1243.30	+	1428.53i	1.25968	+	1.44735i
$988$	9.60318	−	6.97712i	0.00971981	−	0.00706186i
$989$			1175.46i			1.18853i
$990$	−1082.69	−	262.341i	−1.09363	−	0.264991i
$991$	733.303			0.739963			0.369981	−	0.929039i	$-0.379364\pi$
$991$	733.303			0.739963			0.369981	+	0.929039i	$0.379364\pi$
$992$	−161.887	−	222.818i	−0.163192	−	0.224615i
$993$	545.351	−	474.638i	0.549195	−	0.477984i
$994$	186.037	−	572.564i	0.187160	−	0.576021i
$995$	713.067	−	981.453i	0.716651	−	0.986385i
$996$	61.7012	+	14.2060i	0.0619490	+	0.0142631i
$997$	−442.967	+	1363.31i	−0.444300	+	1.36741i	0.438950	+	0.898511i	$0.355350\pi$
$997$	−442.967	+	1363.31i	−0.444300	+	1.36741i	−0.883250	+	0.468903i	$0.844650\pi$
$998$	1121.21	−	364.305i	1.12346	−	0.365035i
$999$	−1110.28	+	299.633i	−1.11139	+	0.299933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.3.g.a.47.2	✓	32
3.2	odd	2	inner	66.3.g.a.47.8	yes	32
11.2	odd	10		726.3.c.i.485.6		16
11.4	even	5	inner	66.3.g.a.59.8	yes	32
11.9	even	5		726.3.c.h.485.14		16
33.2	even	10		726.3.c.i.485.14		16
33.20	odd	10		726.3.c.h.485.6		16
33.26	odd	10	inner	66.3.g.a.59.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.g.a.47.2	✓	32	1.1	even	1	trivial
66.3.g.a.47.8	yes	32	3.2	odd	2	inner
66.3.g.a.59.2	yes	32	33.26	odd	10	inner
66.3.g.a.59.8	yes	32	11.4	even	5	inner
726.3.c.h.485.6		16	33.20	odd	10
726.3.c.h.485.14		16	11.9	even	5
726.3.c.i.485.6		16	11.2	odd	10
726.3.c.i.485.14		16	33.2	even	10

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	66.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.831254 - 1.14412i) q^{2} +(-2.26295 + 1.96953i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(4.67695 - 6.43727i) q^{5} +(4.13447 + 0.951916i) q^{6} +(3.16174 - 9.73084i) q^{7} +(2.68999 - 0.874032i) q^{8} +(1.24191 - 8.91390i) q^{9} -11.2528 q^{10} +(-1.09041 + 10.9458i) q^{11} +(-2.34769 - 5.52163i) q^{12} +(0.714210 - 0.518904i) q^{13} +(-13.7615 + 4.47138i) q^{14} +(2.09468 + 23.7786i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(6.95364 - 9.57087i) q^{17} +(-11.2309 + 5.98882i) q^{18} +(-2.07750 - 6.39389i) q^{19} +(9.35390 + 12.8745i) q^{20} +(12.0103 + 28.2476i) q^{21} +(13.4298 - 7.85119i) q^{22} +15.1865i q^{23} +(-4.36590 + 7.27592i) q^{24} +(-11.8391 - 36.4371i) q^{25} +(-1.18738 - 0.385803i) q^{26} +(14.7458 + 22.6177i) q^{27} +(16.5551 + 12.0280i) q^{28} +(8.13630 + 2.64364i) q^{29} +(25.4644 - 22.1626i) q^{30} +(-39.3890 + 28.6178i) q^{31} +5.65685i q^{32} +(-19.0906 - 26.9175i) q^{33} -16.7305 q^{34} +(-47.8527 - 65.8636i) q^{35} +(16.1877 + 7.87134i) q^{36} +(-13.1618 + 40.5080i) q^{37} +(-5.58847 + 7.69186i) q^{38} +(-0.594227 + 2.58091i) q^{39} +(6.95458 - 21.4040i) q^{40} +(8.28079 - 2.69059i) q^{41} +(22.3351 - 37.2222i) q^{42} +77.4014 q^{43} +(-20.1463 - 8.83897i) q^{44} +(-51.5728 - 49.6843i) q^{45} +(17.3752 - 12.6238i) q^{46} +(58.6782 - 19.0657i) q^{47} +(11.9537 - 1.05301i) q^{48} +(-45.0509 - 32.7314i) q^{49} +(-31.8472 + 43.8339i) q^{50} +(3.11435 + 35.3538i) q^{51} +(0.545608 + 1.67921i) q^{52} +(7.86527 + 10.8256i) q^{53} +(13.6199 - 35.6721i) q^{54} +(65.3614 + 58.2123i) q^{55} -28.9394i q^{56} +(17.2942 + 10.3774i) q^{57} +(-3.73868 - 11.5065i) q^{58} +(-43.1725 - 14.0276i) q^{59} +(-46.5242 - 10.7117i) q^{60} +(46.7325 + 33.9531i) q^{61} +(65.4846 + 21.2772i) q^{62} +(-82.8132 - 40.2683i) q^{63} +(6.47214 - 4.70228i) q^{64} -7.02445i q^{65} +(-14.9278 + 44.2172i) q^{66} -28.4340 q^{67} +(13.9073 + 19.1417i) q^{68} +(-29.9103 - 34.3664i) q^{69} +(-35.5783 + 109.499i) q^{70} +(-24.4556 + 33.6602i) q^{71} +(-4.45032 - 25.0638i) q^{72} +(-1.05367 + 3.24287i) q^{73} +(57.2869 - 18.6137i) q^{74} +(98.5553 + 59.1379i) q^{75} +13.4459 q^{76} +(103.064 + 45.2185i) q^{77} +(3.44683 - 1.46553i) q^{78} +(-68.9341 + 50.0835i) q^{79} +(-30.2698 + 9.83527i) q^{80} +(-77.9153 - 22.1405i) q^{81} +(-9.96180 - 7.23767i) q^{82} +(-6.20265 + 8.53722i) q^{83} +(-61.1529 + 5.38700i) q^{84} +(-29.0884 - 89.5249i) q^{85} +(-64.3402 - 88.5567i) q^{86} +(-23.6188 + 10.0422i) q^{87} +(6.63380 + 30.3972i) q^{88} +86.3091i q^{89} +(-13.9749 + 100.306i) q^{90} +(-2.79122 - 8.59051i) q^{91} +(-28.8865 - 9.38578i) q^{92} +(32.7719 - 142.339i) q^{93} +(-70.5900 - 51.2867i) q^{94} +(-50.8755 - 16.5305i) q^{95} +(-11.1413 - 12.8012i) q^{96} +(52.4764 - 38.1263i) q^{97} +78.7518i q^{98} +(96.2158 + 23.3135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 12 q^{6} - 8 q^{7} + 26 q^{9} + 16 q^{10} - 24 q^{12} + 8 q^{13} - 82 q^{15} - 32 q^{16} - 8 q^{18} - 4 q^{19} - 100 q^{21} - 24 q^{24} - 88 q^{25} - 106 q^{27} - 24 q^{28} - 36 q^{30}+ \cdots + 470 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 12 * q^6 - 8 * q^7 + 26 * q^9 + 16 * q^10 - 24 * q^12 + 8 * q^13 - 82 * q^15 - 32 * q^16 - 8 * q^18 - 4 * q^19 - 100 * q^21 - 24 * q^24 - 88 * q^25 - 106 * q^27 - 24 * q^28 - 36 * q^30 - 148 * q^31 + 78 * q^33 - 32 * q^34 + 8 * q^36 + 96 * q^37 + 362 * q^39 + 48 * q^40 + 152 * q^42 + 560 * q^43 - 20 * q^45 + 176 * q^46 + 8 * q^48 + 208 * q^49 - 82 * q^51 + 24 * q^52 - 176 * q^54 - 108 * q^55 - 142 * q^57 - 144 * q^58 - 36 * q^60 - 384 * q^61 + 506 * q^63 + 64 * q^64 + 400 * q^66 - 680 * q^67 + 136 * q^69 - 400 * q^70 + 16 * q^72 - 92 * q^73 + 90 * q^75 + 128 * q^76 + 152 * q^78 + 320 * q^79 - 198 * q^81 - 328 * q^82 - 240 * q^84 - 1024 * q^85 - 1332 * q^87 - 736 * q^90 - 264 * q^91 - 226 * q^93 - 64 * q^94 - 32 * q^96 - 248 * q^97 + 470 * q^99

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