LMFDB - Embedded newform 126.3.r.a.23.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(11,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.11"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.r (of order $6$, degree $2$, 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:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.13
Character	$\chi$	$=$	126.23
Dual form			126.3.r.a.11.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41421i q^{2} +(0.146807 - 2.99641i) q^{3} -2.00000 q^{4} +(2.36201 - 1.36371i) q^{5} +(4.23756 + 0.207617i) q^{6} +(-2.54299 - 6.52175i) q^{7} -2.82843i q^{8} +(-8.95690 - 0.879787i) q^{9} +(1.92857 + 3.34039i) q^{10} +(-2.52158 - 1.45583i) q^{11} +(-0.293614 + 5.99281i) q^{12} +(10.4745 - 18.1424i) q^{13} +(9.22314 - 3.59634i) q^{14} +(-3.73946 - 7.27775i) q^{15} +4.00000 q^{16} +(24.7647 - 14.2979i) q^{17} +(1.24421 - 12.6670i) q^{18} +(-17.7418 + 30.7298i) q^{19} +(-4.72402 + 2.72742i) q^{20} +(-19.9151 + 6.66240i) q^{21} +(2.05886 - 3.56605i) q^{22} +(13.6186 - 7.86269i) q^{23} +(-8.47512 - 0.415233i) q^{24} +(-8.78060 + 15.2084i) q^{25} +(25.6572 + 14.8132i) q^{26} +(-3.95113 + 26.7093i) q^{27} +(5.08599 + 13.0435i) q^{28} +(18.1582 - 10.4836i) q^{29} +(10.2923 - 5.28840i) q^{30} -12.4651 q^{31} +5.65685i q^{32} +(-4.73245 + 7.34194i) q^{33} +(20.2203 + 35.0226i) q^{34} +(-14.9003 - 11.9365i) q^{35} +(17.9138 + 1.75957i) q^{36} +(-5.80585 + 10.0560i) q^{37} +(-43.4585 - 25.0908i) q^{38} +(-52.8242 - 34.0493i) q^{39} +(-3.85715 - 6.68078i) q^{40} +(26.4059 + 15.2455i) q^{41} +(-9.42206 - 28.1642i) q^{42} +(-12.6505 - 21.9113i) q^{43} +(5.04315 + 2.91167i) q^{44} +(-22.3561 + 10.1365i) q^{45} +(11.1195 + 19.2596i) q^{46} +84.6070i q^{47} +(0.587228 - 11.9856i) q^{48} +(-36.0664 + 33.1695i) q^{49} +(-21.5080 - 12.4176i) q^{50} +(-39.2067 - 76.3041i) q^{51} +(-20.9490 + 36.2847i) q^{52} +(15.1905 - 8.77025i) q^{53} +(-37.7727 - 5.58775i) q^{54} -7.94133 q^{55} +(-18.4463 + 7.19267i) q^{56} +(89.4743 + 57.6731i) q^{57} +(14.8261 + 25.6795i) q^{58} -43.1446i q^{59} +(7.47893 + 14.5555i) q^{60} +30.2949 q^{61} -17.6283i q^{62} +(17.0396 + 60.6519i) q^{63} -8.00000 q^{64} -57.1367i q^{65} +(-10.3831 - 6.69270i) q^{66} +86.4501 q^{67} +(-49.5294 + 28.5958i) q^{68} +(-21.5605 - 41.9611i) q^{69} +(16.8808 - 21.0723i) q^{70} -1.24828i q^{71} +(-2.48841 + 25.3339i) q^{72} +(-6.48414 - 11.2309i) q^{73} +(-14.2214 - 8.21071i) q^{74} +(44.2816 + 28.5429i) q^{75} +(35.4837 - 61.4596i) q^{76} +(-3.08222 + 20.1473i) q^{77} +(48.1530 - 74.7047i) q^{78} +103.529 q^{79} +(9.44805 - 5.45483i) q^{80} +(79.4519 + 15.7603i) q^{81} +(-21.5604 + 37.3436i) q^{82} +(35.2944 - 20.3772i) q^{83} +(39.8303 - 13.3248i) q^{84} +(38.9964 - 67.5437i) q^{85} +(30.9872 - 17.8905i) q^{86} +(-28.7475 - 55.9484i) q^{87} +(-4.11772 + 7.13210i) q^{88} +(15.5031 + 8.95074i) q^{89} +(-14.3352 - 31.6163i) q^{90} +(-144.957 - 22.1761i) q^{91} +(-27.2372 + 15.7254i) q^{92} +(-1.82997 + 37.3505i) q^{93} -119.652 q^{94} +96.7788i q^{95} +(16.9502 + 0.830466i) q^{96} +(-2.62198 - 4.54141i) q^{97} +(-46.9088 - 51.0055i) q^{98} +(21.3047 + 15.2582i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27}+ \cdots + 394 q^{99}+O(q^{100}) $ 32 * q - 64 * q^4 + 8 * q^6 + 2 * q^7 - 20 * q^9 - 36 * q^11 + 10 * q^13 + 36 * q^14 + 10 * q^15 + 128 * q^16 - 54 * q^17 + 28 * q^19 + 28 * q^21 - 126 * q^23 - 16 * q^24 + 80 * q^25 - 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 + 76 * q^30 + 16 * q^31 - 40 * q^33 - 90 * q^35 + 40 * q^36 + 22 * q^37 + 46 * q^39 + 72 * q^41 + 120 * q^42 + 16 * q^43 + 72 * q^44 + 464 * q^45 - 12 * q^46 + 2 * q^49 - 288 * q^50 - 286 * q^51 - 20 * q^52 - 72 * q^53 - 160 * q^54 - 24 * q^55 - 72 * q^56 - 282 * q^57 - 24 * q^58 - 20 * q^60 + 124 * q^61 + 66 * q^63 - 256 * q^64 - 16 * q^66 - 140 * q^67 + 108 * q^68 + 218 * q^69 + 72 * q^70 + 196 * q^73 + 216 * q^74 + 658 * q^75 - 56 * q^76 + 486 * q^77 + 32 * q^78 + 76 * q^79 - 380 * q^81 - 56 * q^84 + 60 * q^85 - 144 * q^86 - 740 * q^87 - 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 + 238 * q^93 - 336 * q^94 + 32 * q^96 - 38 * q^97 + 288 * q^98 + 394 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	0.146807	−	2.99641i	0.0489357	−	0.998802i
$3$	0.146807	−	2.99641i	0.0489357	−	0.998802i
$4$	−2.00000			−0.500000
$5$	2.36201	−	1.36371i	0.472402	−	0.272742i	−0.244842	−	0.969563i	$-0.578736\pi$
$5$	2.36201	−	1.36371i	0.472402	−	0.272742i	0.717245	+	0.696821i	$0.245403\pi$
$6$	4.23756	+	0.207617i	0.706260	+	0.0346028i
$7$	−2.54299	−	6.52175i	−0.363285	−	0.931678i
$7$	−2.54299	−	6.52175i	−0.363285	−	0.931678i
$8$		−	2.82843i		−	0.353553i
$9$	−8.95690	−	0.879787i	−0.995211	−	0.0977541i
$10$	1.92857	+	3.34039i	0.192857	+	0.334039i
$11$	−2.52158	−	1.45583i	−0.229234	−	0.132348i	0.380984	−	0.924581i	$-0.375585\pi$
$11$	−2.52158	−	1.45583i	−0.229234	−	0.132348i	−0.610219	+	0.792233i	$0.708918\pi$
$12$	−0.293614	+	5.99281i	−0.0244678	+	0.499401i
$13$	10.4745	−	18.1424i	0.805731	−	1.39557i	−0.110065	−	0.993924i	$-0.535106\pi$
$13$	10.4745	−	18.1424i	0.805731	−	1.39557i	0.915796	−	0.401643i	$-0.131561\pi$
$14$	9.22314	−	3.59634i	0.658796	−	0.256881i
$15$	−3.73946	−	7.27775i	−0.249298	−	0.485183i
$16$	4.00000			0.250000
$17$	24.7647	−	14.2979i	1.45675	−	0.841053i	0.457898	−	0.889005i	$-0.348603\pi$
$17$	24.7647	−	14.2979i	1.45675	−	0.841053i	0.998850	+	0.0479514i	$0.0152693\pi$
$18$	1.24421	−	12.6670i	0.0691226	−	0.703720i
$19$	−17.7418	+	30.7298i	−0.933782	+	1.61736i	−0.156989	+	0.987600i	$0.550179\pi$
$19$	−17.7418	+	30.7298i	−0.933782	+	1.61736i	−0.776792	+	0.629757i	$0.783155\pi$
$20$	−4.72402	+	2.72742i	−0.236201	+	0.136371i
$21$	−19.9151	+	6.66240i	−0.948339	+	0.317257i
$22$	2.05886	−	3.56605i	0.0935845	−	0.162093i
$23$	13.6186	−	7.86269i	0.592112	−	0.341856i	−0.173820	−	0.984777i	$-0.555611\pi$
$23$	13.6186	−	7.86269i	0.592112	−	0.341856i	0.765932	+	0.642921i	$0.222278\pi$
$24$	−8.47512	−	0.415233i	−0.353130	−	0.0173014i
$25$	−8.78060	+	15.2084i	−0.351224	+	0.608338i
$26$	25.6572	+	14.8132i	0.986815	+	0.569738i
$27$	−3.95113	+	26.7093i	−0.146338	+	0.989235i
$28$	5.08599	+	13.0435i	0.181642	+	0.465839i
$29$	18.1582	−	10.4836i	0.626144	−	0.361505i	−0.153113	−	0.988209i	$-0.548930\pi$
$29$	18.1582	−	10.4836i	0.626144	−	0.361505i	0.779257	+	0.626704i	$0.215597\pi$
$30$	10.2923	−	5.28840i	0.343076	−	0.176280i
$31$	−12.4651			−0.402101			−0.201050	−	0.979581i	$-0.564435\pi$
$31$	−12.4651			−0.402101			−0.201050	+	0.979581i	$0.564435\pi$
$32$			5.65685i			0.176777i
$33$	−4.73245	+	7.34194i	−0.143408	+	0.222483i
$34$	20.2203	+	35.0226i	0.594715	+	1.03008i
$35$	−14.9003	−	11.9365i	−0.425724	−	0.341044i
$36$	17.9138	+	1.75957i	0.497605	+	0.0488771i
$37$	−5.80585	+	10.0560i	−0.156915	+	0.271785i	−0.933755	−	0.357914i	$-0.883488\pi$
$37$	−5.80585	+	10.0560i	−0.156915	+	0.271785i	0.776840	+	0.629698i	$0.216821\pi$
$38$	−43.4585	−	25.0908i	−1.14364	−	0.660283i
$39$	−52.8242	−	34.0493i	−1.35447	−	0.873059i
$40$	−3.85715	−	6.68078i	−0.0964287	−	0.167019i
$41$	26.4059	+	15.2455i	0.644047	+	0.371841i	0.786172	−	0.618008i	$-0.212060\pi$
$41$	26.4059	+	15.2455i	0.644047	+	0.371841i	−0.142125	+	0.989849i	$0.545393\pi$
$42$	−9.42206	−	28.1642i	−0.224335	−	0.670577i
$43$	−12.6505	−	21.9113i	−0.294197	−	0.509564i	0.680601	−	0.732655i	$-0.261719\pi$
$43$	−12.6505	−	21.9113i	−0.294197	−	0.509564i	−0.974798	+	0.223090i	$0.928386\pi$
$44$	5.04315	+	2.91167i	0.114617	+	0.0661742i
$45$	−22.3561	+	10.1365i	−0.496802	+	0.225256i
$46$	11.1195	+	19.2596i	0.241729	+	0.418687i
$47$			84.6070i			1.80015i	0.435736	+	0.900075i	$0.356488\pi$
$47$			84.6070i			1.80015i	−0.435736	+	0.900075i	$0.643512\pi$
$48$	0.587228	−	11.9856i	0.0122339	−	0.249700i
$49$	−36.0664	+	33.1695i	−0.736048	+	0.676929i
$50$	−21.5080	−	12.4176i	−0.430160	−	0.248353i
$51$	−39.2067	−	76.3041i	−0.768759	−	1.49616i
$52$	−20.9490	+	36.2847i	−0.402866	+	0.697784i
$53$	15.1905	−	8.77025i	0.286614	−	0.165476i	−0.349800	−	0.936824i	$-0.613750\pi$
$53$	15.1905	−	8.77025i	0.286614	−	0.165476i	0.636414	+	0.771348i	$0.280417\pi$
$54$	−37.7727	−	5.58775i	−0.699494	−	0.103477i
$55$	−7.94133			−0.144388
$56$	−18.4463	+	7.19267i	−0.329398	+	0.128441i
$57$	89.4743	+	57.6731i	1.56972	+	1.01181i
$58$	14.8261	+	25.6795i	0.255622	+	0.442751i
$59$		−	43.1446i		−	0.731264i	−0.930760	−	0.365632i	$-0.880853\pi$
$59$		−	43.1446i		−	0.731264i	0.930760	−	0.365632i	$-0.119147\pi$
$60$	7.47893	+	14.5555i	0.124649	+	0.242592i
$61$	30.2949			0.496637			0.248319	−	0.968678i	$-0.420122\pi$
$61$	30.2949			0.496637			0.248319	+	0.968678i	$0.420122\pi$
$62$		−	17.6283i		−	0.284328i
$63$	17.0396	+	60.6519i	0.270470	+	0.962729i
$64$	−8.00000			−0.125000
$65$		−	57.1367i		−	0.879026i
$66$	−10.3831	−	6.69270i	−0.157319	−	0.101405i
$67$	86.4501			1.29030			0.645150	−	0.764056i	$-0.276795\pi$
$67$	86.4501			1.29030			0.645150	+	0.764056i	$0.276795\pi$
$68$	−49.5294	+	28.5958i	−0.728374	+	0.420527i
$69$	−21.5605	−	41.9611i	−0.312471	−	0.608132i
$70$	16.8808	−	21.0723i	0.241155	−	0.301032i
$71$		−	1.24828i		−	0.0175814i	−0.999961	−	0.00879071i	$-0.997202\pi$
$71$		−	1.24828i		−	0.0175814i	0.999961	−	0.00879071i	$-0.00279821\pi$
$72$	−2.48841	+	25.3339i	−0.0345613	+	0.351860i
$73$	−6.48414	−	11.2309i	−0.0888239	−	0.153848i	0.818190	−	0.574947i	$-0.194978\pi$
$73$	−6.48414	−	11.2309i	−0.0888239	−	0.153848i	−0.907014	+	0.421100i	$0.861644\pi$
$74$	−14.2214	−	8.21071i	−0.192181	−	0.110956i
$75$	44.2816	+	28.5429i	0.590422	+	0.380573i
$76$	35.4837	−	61.4596i	0.466891	−	0.808679i
$77$	−3.08222	+	20.1473i	−0.0400288	+	0.261653i
$78$	48.1530	−	74.7047i	0.617346	−	0.957752i
$79$	103.529			1.31049			0.655247	−	0.755415i	$-0.272565\pi$
$79$	103.529			1.31049			0.655247	+	0.755415i	$0.272565\pi$
$80$	9.44805	−	5.45483i	0.118101	−	0.0681854i
$81$	79.4519	+	15.7603i	0.980888	+	0.194572i
$82$	−21.5604	+	37.3436i	−0.262931	+	0.455410i
$83$	35.2944	−	20.3772i	0.425234	−	0.245509i	−0.272080	−	0.962275i	$-0.587712\pi$
$83$	35.2944	−	20.3772i	0.425234	−	0.245509i	0.697314	+	0.716766i	$0.254378\pi$
$84$	39.8303	−	13.3248i	0.474170	−	0.158629i
$85$	38.9964	−	67.5437i	0.458781	−	0.794631i
$86$	30.9872	−	17.8905i	0.360316	−	0.208029i
$87$	−28.7475	−	55.9484i	−0.330431	−	0.643085i
$88$	−4.11772	+	7.13210i	−0.0467923	+	0.0810466i
$89$	15.5031	+	8.95074i	0.174193	+	0.100570i	0.584561	−	0.811350i	$-0.301267\pi$
$89$	15.5031	+	8.95074i	0.174193	+	0.100570i	−0.410369	+	0.911920i	$0.634600\pi$
$90$	−14.3352	−	31.6163i	−0.159280	−	0.351292i
$91$	−144.957	−	22.1761i	−1.59293	−	0.243693i
$92$	−27.2372	+	15.7254i	−0.296056	+	0.170928i
$93$	−1.82997	+	37.3505i	−0.0196771	+	0.401619i
$94$	−119.652			−1.27290
$95$			96.7788i			1.01872i
$96$	16.9502	+	0.830466i	0.176565	+	0.00865069i
$97$	−2.62198	−	4.54141i	−0.0270307	−	0.0468186i	0.852194	−	0.523227i	$-0.175272\pi$
$97$	−2.62198	−	4.54141i	−0.0270307	−	0.0468186i	−0.879224	+	0.476408i	$0.841939\pi$
$98$	−46.9088	−	51.0055i	−0.478661	−	0.520465i
$99$	21.3047	+	15.2582i	0.215199	+	0.154123i
$100$	17.5612	−	30.4169i	0.175612	−	0.304169i
$101$	155.079	+	89.5347i	1.53543	+	0.886482i	0.999097	+	0.0424762i	$0.0135247\pi$
$101$	155.079	+	89.5347i	1.53543	+	0.886482i	0.536334	+	0.844006i	$0.319809\pi$
$102$	107.910	−	55.4467i	1.05794	−	0.543595i
$103$	−76.1322	−	131.865i	−0.739148	−	1.28024i	−0.952880	−	0.303349i	$-0.901895\pi$
$103$	−76.1322	−	131.865i	−0.739148	−	1.28024i	0.213732	−	0.976892i	$-0.431438\pi$
$104$	−51.3144	−	29.6264i	−0.493407	−	0.284869i
$105$	−37.9542	+	42.8951i	−0.361469	+	0.408525i
$106$	12.4030	+	21.4826i	0.117010	+	0.202666i
$107$	−129.207	−	74.5978i	−1.20754	−	0.697175i	−0.245321	−	0.969442i	$-0.578893\pi$
$107$	−129.207	−	74.5978i	−1.20754	−	0.697175i	−0.962222	+	0.272267i	$0.912227\pi$
$108$	7.90227	−	53.4187i	0.0731692	−	0.494617i
$109$	−11.0071	−	19.0649i	−0.100983	−	0.174907i	0.811107	−	0.584898i	$-0.198865\pi$
$109$	−11.0071	−	19.0649i	−0.100983	−	0.174907i	−0.912090	+	0.409990i	$0.865532\pi$
$110$		−	11.2307i		−	0.102098i
$111$	29.2796	+	18.8730i	0.263780	+	0.170027i
$112$	−10.1720	−	26.0870i	−0.0908212	−	0.232920i
$113$	13.7209	+	7.92175i	0.121424	+	0.0701040i	0.559482	−	0.828843i	$-0.311000\pi$
$113$	13.7209	+	7.92175i	0.121424	+	0.0701040i	−0.438058	+	0.898947i	$0.644334\pi$
$114$	−81.5621	+	126.536i	−0.715457	+	1.10996i
$115$	21.4448	−	37.1436i	0.186477	−	0.322987i
$116$	−36.3164	+	20.9673i	−0.313072	+	0.180752i
$117$	−109.780	+	153.284i	−0.938294	+	1.31012i
$118$	61.0156			0.517082
$119$	−156.224	−	125.150i	−1.31281	−	1.05168i
$120$	−20.5846	+	10.5768i	−0.171538	+	0.0881400i
$121$	−56.2611	−	97.4471i	−0.464968	−	0.805348i
$122$			42.8434i			0.351176i
$123$	49.5582	−	76.8848i	0.402912	−	0.625079i
$124$	24.9302			0.201050
$125$			116.082i			0.928657i
$126$	−85.7747	+	24.0976i	−0.680752	+	0.191251i
$127$	−86.5080			−0.681166			−0.340583	−	0.940215i	$-0.610624\pi$
$127$	−86.5080			−0.681166			−0.340583	+	0.940215i	$0.610624\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−67.5122	+	34.6892i	−0.523350	+	0.268909i
$130$	80.8035			0.621565
$131$	87.6284	−	50.5923i	0.668919	−	0.386200i	−0.126748	−	0.991935i	$-0.540454\pi$
$131$	87.6284	−	50.5923i	0.668919	−	0.386200i	0.795667	+	0.605734i	$0.207121\pi$
$132$	9.46490	−	14.6839i	0.0717038	−	0.111242i
$133$	245.529	+	37.5622i	1.84608	+	0.282422i
$134$			122.259i			0.912380i
$135$	27.0911	+	68.4760i	0.200675	+	0.507229i
$136$	−40.4406	−	70.0452i	−0.297357	−	0.515038i
$137$	35.2605	+	20.3576i	0.257376	+	0.148596i	0.623137	−	0.782113i	$-0.285858\pi$
$137$	35.2605	+	20.3576i	0.257376	+	0.148596i	−0.365761	+	0.930709i	$0.619191\pi$
$138$	59.3420	−	30.4912i	0.430014	−	0.220951i
$139$	−22.3342	+	38.6840i	−0.160678	+	0.278302i	−0.935112	−	0.354352i	$-0.884701\pi$
$139$	−22.3342	+	38.6840i	−0.160678	+	0.278302i	0.774434	+	0.632655i	$0.218035\pi$
$140$	29.8007	+	23.8731i	0.212862	+	0.170522i
$141$	253.517	+	12.4209i	1.79799	+	0.0880915i
$142$	1.76534			0.0124319
$143$	−52.8245	+	30.4983i	−0.369402	+	0.213275i
$144$	−35.8276	−	3.51915i	−0.248803	−	0.0244385i
$145$	28.5932	−	49.5249i	0.197195	−	0.341551i
$146$	15.8828	−	9.16996i	0.108787	−	0.0628080i
$147$	94.0946	+	112.939i	0.640099	+	0.768292i
$148$	11.6117	−	20.1121i	0.0784574	−	0.135892i
$149$	−54.3567	+	31.3829i	−0.364810	+	0.210623i	−0.671189	−	0.741286i	$-0.734216\pi$
$149$	−54.3567	+	31.3829i	−0.364810	+	0.210623i	0.306379	+	0.951910i	$0.400883\pi$
$150$	−40.3658	+	62.6237i	−0.269105	+	0.417491i
$151$	−94.8677	+	164.316i	−0.628263	+	1.08818i	0.359637	+	0.933092i	$0.382900\pi$
$151$	−94.8677	+	164.316i	−0.628263	+	1.08818i	−0.987900	+	0.155091i	$0.950433\pi$
$152$	86.9170	+	50.1815i	0.571822	+	0.330142i
$153$	−234.394	+	106.277i	−1.53199	+	0.694622i
$154$	−28.4925	−	4.35892i	−0.185016	−	0.0283047i
$155$	−29.4428	+	16.9988i	−0.189953	+	0.109670i
$156$	105.648	+	68.0986i	0.677233	+	0.436529i
$157$	−86.0225			−0.547914			−0.273957	−	0.961742i	$-0.588333\pi$
$157$	−86.0225			−0.547914			−0.273957	+	0.961742i	$0.588333\pi$
$158$			146.412i			0.926659i
$159$	−24.0492	−	46.8045i	−0.151253	−	0.294368i
$160$	7.71430	+	13.3616i	0.0482144	+	0.0835097i
$161$	−85.9105	−	68.8222i	−0.533606	−	0.427467i
$162$	−22.2885	+	112.362i	−0.137583	+	0.693593i
$163$	36.5758	−	63.3511i	0.224391	−	0.388657i	−0.731745	−	0.681578i	$-0.761294\pi$
$163$	36.5758	−	63.3511i	0.224391	−	0.388657i	0.956137	+	0.292921i	$0.0946273\pi$
$164$	−52.8119	−	30.4909i	−0.322024	−	0.185920i
$165$	−1.16584	+	23.7954i	−0.00706571	+	0.144215i
$166$	28.8177	+	49.9138i	0.173601	+	0.300686i
$167$	−72.8922	−	42.0843i	−0.436480	−	0.252002i	0.265623	−	0.964077i	$-0.414422\pi$
$167$	−72.8922	−	42.0843i	−0.436480	−	0.252002i	−0.702103	+	0.712075i	$0.747756\pi$
$168$	18.8441	+	56.3285i	0.112167	+	0.335289i
$169$	−134.930	−	233.706i	−0.798405	−	1.38288i
$170$	95.5212	+	55.1492i	0.561889	+	0.324407i
$171$	185.948	−	259.634i	1.08741	−	1.51833i
$172$	25.3009	+	43.8225i	0.147099	+	0.254782i
$173$			236.832i			1.36897i	0.729026	+	0.684486i	$0.239973\pi$
$173$			236.832i			1.36897i	−0.729026	+	0.684486i	$0.760027\pi$
$174$	79.1229	−	40.6551i	0.454729	−	0.233650i
$175$	121.515	+	18.5899i	0.694369	+	0.106228i
$176$	−10.0863	−	5.82333i	−0.0573086	−	0.0330871i
$177$	−129.279	−	6.33393i	−0.730388	−	0.0357849i
$178$	−12.6583	+	21.9247i	−0.0711138	+	0.123173i
$179$	−166.309	+	96.0186i	−0.929101	+	0.536417i	−0.886527	−	0.462677i	$-0.846889\pi$
$179$	−166.309	+	96.0186i	−0.929101	+	0.536417i	−0.0425737	+	0.999093i	$0.513556\pi$
$180$	44.7121	−	20.2731i	0.248401	−	0.112628i
$181$	−45.1148			−0.249253			−0.124626	−	0.992204i	$-0.539773\pi$
$181$	−45.1148			−0.249253			−0.124626	+	0.992204i	$0.539773\pi$
$182$	31.3618	−	205.000i	0.172317	−	1.12637i
$183$	4.44750	−	90.7758i	0.0243033	−	0.496042i
$184$	−22.2391	−	38.5192i	−0.120864	−	0.209343i
$185$			31.6699i			0.171189i
$186$	−52.8217	−	2.58796i	−0.283987	−	0.0139138i
$187$	−83.2615			−0.445249
$188$		−	169.214i		−	0.900075i
$189$	184.239	−	42.1534i	0.974811	−	0.223034i
$190$	−136.866			−0.720347
$191$		−	87.2707i		−	0.456915i	−0.973554	−	0.228457i	$-0.926632\pi$
$191$		−	87.2707i		−	0.456915i	0.973554	−	0.228457i	$-0.0733681\pi$
$192$	−1.17446	+	23.9712i	−0.00611696	+	0.124850i
$193$	−158.035			−0.818832			−0.409416	−	0.912348i	$-0.634268\pi$
$193$	−158.035			−0.818832			−0.409416	+	0.912348i	$0.634268\pi$
$194$	6.42252	−	3.70804i	0.0331058	−	0.0191136i
$195$	−171.205	−	8.38807i	−0.877973	−	0.0430157i
$196$	72.1327	−	66.3391i	0.368024	−	0.338465i
$197$			72.5385i			0.368216i	0.982906	+	0.184108i	$0.0589396\pi$
$197$			72.5385i			0.368216i	−0.982906	+	0.184108i	$0.941060\pi$
$198$	−21.5783	+	30.1294i	−0.108982	+	0.152169i
$199$	156.303	+	270.725i	0.785442	+	1.36043i	0.928735	+	0.370745i	$0.120898\pi$
$199$	156.303	+	270.725i	0.785442	+	1.36043i	−0.143292	+	0.989680i	$0.545769\pi$
$200$	43.0160	+	24.8353i	0.215080	+	0.124176i
$201$	12.6915	−	259.040i	0.0631417	−	1.28875i
$202$	−126.621	+	219.314i	−0.626837	+	1.08571i
$203$	−114.548	−	91.7632i	−0.564275	−	0.452036i
$204$	78.4134	+	152.608i	0.384379	+	0.748080i
$205$	83.1615			0.405666
$206$	186.485	−	107.667i	0.905267	−	0.522656i
$207$	−128.898	+	58.4439i	−0.622694	+	0.282338i
$208$	41.8980	−	72.5695i	0.201433	−	0.348892i
$209$	89.4749	−	51.6583i	0.428109	−	0.247169i
$210$	−60.6628	−	53.6753i	−0.288871	−	0.255597i
$211$	91.2819	−	158.105i	0.432616	−	0.749312i	−0.564482	−	0.825445i	$-0.690924\pi$
$211$	91.2819	−	158.105i	0.432616	−	0.749312i	0.997098	+	0.0761331i	$0.0242574\pi$
$212$	−30.3810	+	17.5405i	−0.143307	+	0.0827382i
$213$	−3.74035	−	0.183256i	−0.0175604	−	0.000860359i
$214$	105.497	−	182.726i	0.492977	−	0.853862i
$215$	−59.7611	−	34.5031i	−0.277959	−	0.160480i
$216$	75.5454	+	11.1755i	0.349747	+	0.0517384i
$217$	31.6987	+	81.2943i	0.146077	+	0.374628i
$218$	26.9619	−	15.5664i	0.123678	−	0.0714057i
$219$	−34.6042	+	17.7804i	−0.158010	+	0.0811888i
$220$	15.8827			0.0721939
$221$		−	599.054i		−	2.71065i
$222$	−26.6904	+	41.4076i	−0.120227	+	0.186521i
$223$	125.388	+	217.179i	0.562279	+	0.973896i	0.997297	+	0.0734742i	$0.0234087\pi$
$223$	125.388	+	217.179i	0.562279	+	0.973896i	−0.435018	+	0.900422i	$0.643258\pi$
$224$	36.8926	−	14.3853i	0.164699	−	0.0642203i
$225$	92.0271	−	128.495i	0.409009	−	0.571091i
$226$	−11.2030	+	19.4042i	−0.0495710	+	0.0858595i
$227$	351.333	+	202.842i	1.54772	+	0.893578i	0.998315	+	0.0580230i	$0.0184797\pi$
$227$	351.333	+	202.842i	1.54772	+	0.893578i	0.549407	+	0.835555i	$0.314854\pi$
$228$	−178.949	−	115.346i	−0.784862	−	0.505905i
$229$	−54.8376	−	94.9815i	−0.239465	−	0.414766i	0.721096	−	0.692836i	$-0.243639\pi$
$229$	−54.8376	−	94.9815i	−0.239465	−	0.414766i	−0.960561	+	0.278069i	$0.910306\pi$
$230$	52.5289	+	30.3276i	0.228387	+	0.131859i
$231$	59.9169	+	12.1933i	0.259380	+	0.0527850i
$232$	−29.6522	−	51.3591i	−0.127811	−	0.221375i
$233$	−59.9074	−	34.5876i	−0.257113	−	0.148445i	0.365904	−	0.930653i	$-0.380760\pi$
$233$	−59.9074	−	34.5876i	−0.257113	−	0.148445i	−0.623017	+	0.782208i	$0.714093\pi$
$234$	−216.776	−	155.253i	−0.926394	−	0.663474i
$235$	115.379	+	199.843i	0.490976	+	0.850395i
$236$			86.2891i			0.365632i
$237$	15.1988	−	310.215i	0.0641299	−	1.30892i
$238$	176.988	−	220.934i	0.743648	−	0.928294i
$239$	−206.558	−	119.256i	−0.864260	−	0.498981i	0.00117636	−	0.999999i	$-0.499626\pi$
$239$	−206.558	−	119.256i	−0.864260	−	0.498981i	−0.865437	+	0.501018i	$0.832959\pi$
$240$	−14.9579	−	29.1110i	−0.0623244	−	0.121296i
$241$	−140.911	+	244.065i	−0.584693	+	1.01272i	0.410220	+	0.911987i	$0.365452\pi$
$241$	−140.911	+	244.065i	−0.584693	+	1.01272i	−0.994914	+	0.100732i	$0.967881\pi$
$242$	137.811	−	79.5652i	0.569467	−	0.328782i
$243$	58.8884	−	235.757i	0.242339	−	0.970192i
$244$	−60.5898			−0.248319
$245$	−39.9556	+	127.531i	−0.163084	+	0.520534i
$246$	108.731	+	70.0859i	0.441998	+	0.284902i
$247$	371.674	+	643.758i	1.50475	+	2.60631i
$248$			35.2567i			0.142164i
$249$	−55.8770	−	108.748i	−0.224405	−	0.436738i
$250$	−164.165			−0.656660
$251$			222.540i			0.886615i	0.896370	+	0.443308i	$0.146195\pi$
$251$			222.540i			0.886615i	−0.896370	+	0.443308i	$0.853805\pi$
$252$	−34.0792	−	121.304i	−0.135235	−	0.481364i
$253$	−45.7871			−0.180977
$254$		−	122.341i		−	0.481657i
$255$	−196.663	−	126.765i	−0.771229	−	0.497117i
$256$	16.0000			0.0625000
$257$	291.865	−	168.508i	1.13566	−	0.655674i	0.190309	−	0.981724i	$-0.439051\pi$
$257$	291.865	−	168.508i	1.13566	−	0.655674i	0.945353	+	0.326050i	$0.105718\pi$
$258$	−49.0580	−	95.4767i	−0.190147	−	0.370065i
$259$	80.3471	+	12.2919i	0.310220	+	0.0474589i
$260$			114.273i			0.439513i
$261$	−171.864	+	77.9255i	−0.658484	+	0.298565i
$262$	71.5483	+	123.925i	0.273085	+	0.472997i
$263$	−141.259	−	81.5557i	−0.537105	−	0.310098i	0.206800	−	0.978383i	$-0.433695\pi$
$263$	−141.259	−	81.5557i	−0.537105	−	0.310098i	−0.743905	+	0.668285i	$0.767029\pi$
$264$	20.7661	+	13.3854i	0.0786596	+	0.0507023i
$265$	23.9201	−	41.4309i	0.0902646	−	0.156343i
$266$	−53.1209	+	347.231i	−0.199703	+	1.30538i
$267$	29.0960	−	45.1396i	0.108974	−	0.169062i
$268$	−172.900			−0.645150
$269$	430.483	−	248.539i	1.60031	−	0.923938i	0.608882	−	0.793261i	$-0.291618\pi$
$269$	430.483	−	248.539i	1.60031	−	0.923938i	0.991425	−	0.130677i	$-0.0417152\pi$
$270$	−96.8396	+	38.3126i	−0.358665	+	0.141899i
$271$	−86.2128	+	149.325i	−0.318129	+	0.551015i	−0.980098	−	0.198516i	$-0.936388\pi$
$271$	−86.2128	+	149.325i	−0.318129	+	0.551015i	0.661969	+	0.749531i	$0.269721\pi$
$272$	99.0588	−	57.1916i	0.364187	−	0.210263i
$273$	−87.7293	+	431.093i	−0.321353	+	1.57910i
$274$	−28.7901	+	49.8659i	−0.105073	+	0.181992i
$275$	44.2819	−	25.5662i	0.161025	−	0.0929679i
$276$	43.1210	+	83.9222i	0.156236	+	0.304066i
$277$	−44.6018	+	77.2526i	−0.161017	+	0.278890i	−0.935234	−	0.354031i	$-0.884811\pi$
$277$	−44.6018	+	77.2526i	−0.161017	+	0.278890i	0.774216	+	0.632921i	$0.218144\pi$
$278$	−54.7075	−	31.5854i	−0.196790	−	0.113616i
$279$	111.649	+	10.9666i	0.400175	+	0.0393070i
$280$	−33.7616	+	42.1445i	−0.120577	+	0.150516i
$281$	−406.825	+	234.881i	−1.44778	+	0.835874i	−0.998349	−	0.0574426i	$-0.981705\pi$
$281$	−406.825	+	234.881i	−1.44778	+	0.835874i	−0.449428	+	0.893317i	$0.648372\pi$
$282$	−17.5658	+	358.527i	−0.0622901	+	1.27137i
$283$	−47.4160			−0.167548			−0.0837738	−	0.996485i	$-0.526697\pi$
$283$	−47.4160			−0.167548			−0.0837738	+	0.996485i	$0.526697\pi$
$284$			2.49656i			0.00879071i
$285$	289.989	+	14.2078i	1.01750	+	0.0498520i
$286$	−43.1311	−	74.7052i	−0.150808	−	0.261207i
$287$	32.2770	−	210.982i	0.112463	−	0.735129i
$288$	4.97683	−	50.6679i	0.0172806	−	0.175930i
$289$	264.360	−	457.886i	0.914742	−	1.58438i
$290$	70.0388	+	40.4369i	0.241513	+	0.139438i
$291$	−13.9928	+	7.18981i	−0.0480853	+	0.0247073i
$292$	12.9683	+	22.4617i	0.0444119	+	0.0769238i
$293$	80.5230	+	46.4900i	0.274823	+	0.158669i	0.631077	−	0.775720i	$-0.282613\pi$
$293$	80.5230	+	46.4900i	0.274823	+	0.158669i	−0.356255	+	0.934389i	$0.615946\pi$
$294$	−159.720	+	133.070i	−0.543265	+	0.452618i
$295$	−58.8366	−	101.908i	−0.199446	−	0.345451i
$296$	28.4427	+	16.4214i	0.0960903	+	0.0554778i
$297$	48.8474	−	61.5975i	0.164469	−	0.207399i
$298$	−44.3821	−	76.8720i	−0.148933	−	0.257960i
$299$		−	329.431i		−	1.10178i
$300$	−88.5632	−	57.0859i	−0.295211	−	0.190286i
$301$	−110.730	+	138.223i	−0.367872	+	0.459214i
$302$	−232.378	−	134.163i	−0.769462	−	0.444249i
$303$	291.049	−	451.534i	0.960557	−	1.49021i
$304$	−70.9674	+	122.919i	−0.233445	+	0.404339i
$305$	71.5569	−	41.3134i	0.234613	−	0.135454i
$306$	−150.299	−	331.483i	−0.491172	−	1.08328i
$307$	202.315			0.659008			0.329504	−	0.944154i	$-0.393119\pi$
$307$	202.315			0.659008			0.329504	+	0.944154i	$0.393119\pi$
$308$	6.16444	−	40.2945i	0.0200144	−	0.130826i
$309$	−406.297	+	208.764i	−1.31488	+	0.675613i
$310$	−24.0399	−	41.6383i	−0.0775481	−	0.134317i
$311$			297.017i			0.955037i	0.878622	+	0.477519i	$0.158464\pi$
$311$			297.017i			0.955037i	−0.878622	+	0.477519i	$0.841536\pi$
$312$	−96.3059	+	149.409i	−0.308673	+	0.478876i
$313$	−378.321			−1.20869			−0.604347	−	0.796721i	$-0.706566\pi$
$313$	−378.321			−1.20869			−0.604347	+	0.796721i	$0.706566\pi$
$314$		−	121.654i		−	0.387434i
$315$	122.959	+	120.023i	0.390347	+	0.381027i
$316$	−207.058			−0.655247
$317$			258.230i			0.814607i	0.913293	+	0.407304i	$0.133531\pi$
$317$			258.230i			0.814607i	−0.913293	+	0.407304i	$0.866469\pi$
$318$	66.1916	−	34.0106i	0.208150	−	0.106952i
$319$	−61.0497			−0.191378
$320$	−18.8961	+	10.9097i	−0.0590503	+	0.0340927i
$321$	−242.494	+	376.205i	−0.755432	+	1.17198i
$322$	97.3293	−	121.496i	0.302265	−	0.377316i
$323$			1014.69i			3.14144i
$324$	−158.904	−	31.5206i	−0.490444	−	0.0972859i
$325$	183.945	+	318.602i	0.565984	+	0.980313i
$326$	89.5920	+	51.7260i	0.274822	+	0.158669i
$327$	−58.7421	+	30.1830i	−0.179640	+	0.0923026i
$328$	43.1207	−	74.6873i	0.131466	−	0.227705i
$329$	551.785	−	215.155i	1.67716	−	0.653967i
$330$	−33.6518	−	1.64875i	−0.101975	−	0.00499621i
$331$	−381.770			−1.15338			−0.576692	−	0.816961i	$-0.695657\pi$
$331$	−381.770			−1.15338			−0.576692	+	0.816961i	$0.695657\pi$
$332$	−70.5888	+	40.7544i	−0.212617	+	0.122754i
$333$	60.8496	−	84.9629i	0.182731	−	0.255144i
$334$	59.5162	−	103.085i	0.178192	−	0.308638i
$335$	204.196	−	117.893i	0.609541	−	0.351919i
$336$	−79.6605	+	26.6496i	−0.237085	+	0.0793143i
$337$	−121.433	+	210.329i	−0.360337	+	0.624122i	−0.988016	−	0.154350i	$-0.950672\pi$
$337$	−121.433	+	210.329i	−0.360337	+	0.624122i	0.627679	+	0.778472i	$0.284005\pi$
$338$	330.511	−	190.820i	0.977842	−	0.564558i
$339$	25.7511	−	39.9503i	0.0759619	−	0.117848i
$340$	−77.9927	+	135.087i	−0.229390	+	0.397316i
$341$	31.4318	+	18.1471i	0.0921752	+	0.0532174i
$342$	367.179	+	262.970i	1.07362	+	0.768917i
$343$	308.040	+	150.866i	0.898075	+	0.439842i
$344$	−61.9744	+	35.7809i	−0.180158	+	0.104014i
$345$	−108.149	−	69.7104i	−0.313475	−	0.202059i
$346$	−334.931			−0.968009
$347$			242.378i			0.698495i	0.937031	+	0.349247i	$0.113563\pi$
$347$			242.378i			0.698495i	−0.937031	+	0.349247i	$0.886437\pi$
$348$	57.4949	+	111.897i	0.165215	+	0.321542i
$349$	−2.46388	−	4.26756i	−0.00705982	−	0.0122280i	0.862474	−	0.506102i	$-0.168914\pi$
$349$	−2.46388	−	4.26756i	−0.00705982	−	0.0122280i	−0.869534	+	0.493874i	$0.835581\pi$
$350$	−26.2900	+	171.848i	−0.0751144	+	0.490993i
$351$	443.185	+	351.450i	1.26263	+	1.00128i
$352$	8.23544	−	14.2642i	0.0233961	−	0.0405233i
$353$	−530.683	−	306.390i	−1.50335	−	0.867960i	−0.999992	−	0.00388263i	$-0.998764\pi$
$353$	−530.683	−	306.390i	−1.50335	−	0.867960i	−0.503359	−	0.864078i	$-0.667903\pi$
$354$	8.95753	−	182.828i	0.0253037	−	0.516462i
$355$	−1.70229	−	2.94845i	−0.00479518	−	0.00830550i
$356$	−31.0063	−	17.9015i	−0.0870963	−	0.0502850i
$357$	−397.934	+	449.737i	−1.11466	+	1.25977i
$358$	−135.791	−	235.196i	−0.379304	−	0.656973i
$359$	−461.352	−	266.362i	−1.28510	−	0.741955i	−0.307327	−	0.951604i	$-0.599435\pi$
$359$	−461.352	−	266.362i	−1.28510	−	0.741955i	−0.977777	+	0.209649i	$0.932768\pi$
$360$	28.6704	+	63.2325i	0.0796401	+	0.175646i
$361$	−449.046	−	777.771i	−1.24390	−	2.15449i
$362$		−	63.8019i		−	0.176248i
$363$	−300.251	+	154.275i	−0.827136	+	0.425000i
$364$	289.913	+	44.3522i	0.796465	+	0.121847i
$365$	−30.6313	−	17.6850i	−0.0839212	−	0.0484520i
$366$	128.376	+	6.28972i	0.350755	+	0.0171850i
$367$	185.198	−	320.773i	0.504628	−	0.874041i	−0.495358	−	0.868689i	$-0.664963\pi$
$367$	185.198	−	320.773i	0.504628	−	0.874041i	0.999986	−	0.00535178i	$-0.00170353\pi$
$368$	54.4743	−	31.4508i	0.148028	−	0.0854641i
$369$	−223.102	−	159.784i	−0.604614	−	0.433018i
$370$	−44.7881			−0.121049
$371$	−95.8268	−	76.7660i	−0.258293	−	0.206917i
$372$	3.65993	−	74.7011i	0.00983853	−	0.200809i
$373$	209.212	+	362.366i	0.560891	+	0.971492i	0.997419	+	0.0718011i	$0.0228747\pi$
$373$	209.212	+	362.366i	0.560891	+	0.971492i	−0.436528	+	0.899691i	$0.643792\pi$
$374$		−	117.750i		−	0.314838i
$375$	347.829	+	17.0417i	0.927544	+	0.0454445i
$376$	239.305			0.636449
$377$		−	439.243i		−	1.16510i
$378$	59.6139	+	260.554i	0.157709	+	0.689295i
$379$	241.600			0.637468			0.318734	−	0.947844i	$-0.396742\pi$
$379$	241.600			0.637468			0.318734	+	0.947844i	$0.396742\pi$
$380$		−	193.558i		−	0.509362i
$381$	−12.7000	+	259.213i	−0.0333333	+	0.680350i
$382$	123.419			0.323087
$383$	−145.452	+	83.9766i	−0.379770	+	0.219260i	−0.677718	−	0.735322i	$-0.737031\pi$
$383$	−145.452	+	83.9766i	−0.379770	+	0.219260i	0.297948	+	0.954582i	$0.403698\pi$
$384$	−33.9005	−	1.66093i	−0.0882825	−	0.00432534i
$385$	20.1948	+	51.7913i	0.0524539	+	0.134523i
$386$		−	223.495i		−	0.579002i
$387$	94.0317	+	207.387i	0.242976	+	0.535883i
$388$	5.24396	+	9.08281i	0.0135154	+	0.0234093i
$389$	436.463	+	251.992i	1.12201	+	0.647795i	0.941914	−	0.335854i	$-0.109025\pi$
$389$	436.463	+	251.992i	1.12201	+	0.647795i	0.180099	+	0.983648i	$0.442358\pi$
$390$	11.8625	−	242.120i	0.0304167	−	0.620820i
$391$	224.840	−	389.435i	0.575039	−	0.995997i
$392$	93.8176	+	102.011i	0.239331	+	0.260232i
$393$	−138.730	−	269.997i	−0.353004	−	0.687016i
$394$	−102.585			−0.260368
$395$	244.537	−	141.183i	0.619080	−	0.357426i
$396$	−42.6094	−	30.5164i	−0.107599	−	0.0770616i
$397$	170.757	−	295.760i	0.430118	−	0.744986i	−0.566765	−	0.823879i	$-0.691805\pi$
$397$	170.757	−	295.760i	0.430118	−	0.744986i	0.996883	+	0.0788933i	$0.0251386\pi$
$398$	−382.863	+	221.046i	−0.961966	+	0.555391i
$399$	148.597	−	730.191i	0.372423	−	1.83005i
$400$	−35.1224	+	60.8338i	−0.0878060	+	0.152084i
$401$	−589.296	+	340.230i	−1.46957	+	0.848455i	−0.999417	−	0.0341316i	$-0.989133\pi$
$401$	−589.296	+	340.230i	−1.46957	+	0.848455i	−0.470150	+	0.882587i	$0.655800\pi$
$402$	366.337	+	17.9485i	0.911287	+	0.0446479i
$403$	−130.566	+	226.147i	−0.323985	+	0.561158i
$404$	−310.157	−	179.069i	−0.767716	−	0.443241i
$405$	209.159	−	71.1232i	0.516442	−	0.175613i
$406$	129.773	−	161.995i	0.319638	−	0.399002i
$407$	29.2798	−	16.9047i	0.0719405	−	0.0415349i
$408$	−215.821	+	110.893i	−0.528972	+	0.271797i
$409$	−257.554			−0.629717			−0.314858	−	0.949139i	$-0.601957\pi$
$409$	−257.554			−0.629717			−0.314858	+	0.949139i	$0.601957\pi$
$410$			117.608i			0.286849i
$411$	66.1763	−	102.666i	0.161013	−	0.249796i
$412$	152.264	+	263.730i	0.369574	+	0.640121i
$413$	−281.378	+	109.716i	−0.681303	+	0.265657i
$414$	−82.6521	−	182.289i	−0.199643	−	0.440311i
$415$	55.5772	−	96.2625i	0.133921	−	0.231958i
$416$	102.629	+	59.2527i	0.246704	+	0.142434i
$417$	112.634	+	72.6015i	0.270106	+	0.174104i
$418$	73.0559	+	126.537i	0.174775	+	0.302719i
$419$	187.674	+	108.354i	0.447909	+	0.258600i	0.706947	−	0.707267i	$-0.250072\pi$
$419$	187.674	+	108.354i	0.447909	+	0.258600i	−0.259038	+	0.965867i	$0.583405\pi$
$420$	75.9084	−	85.7902i	0.180734	−	0.204262i
$421$	−395.045	−	684.238i	−0.938349	−	1.62527i	−0.768550	−	0.639790i	$-0.779021\pi$
$421$	−395.045	−	684.238i	−0.938349	−	1.62527i	−0.169799	−	0.985479i	$-0.554312\pi$
$422$	223.594	+	129.092i	0.529844	+	0.305905i
$423$	74.4361	−	757.816i	0.175972	−	1.79153i
$424$	−24.8060	−	42.9653i	−0.0585048	−	0.101333i
$425$			502.177i			1.18159i
$426$	0.259164	−	5.28966i	0.000608365	−	0.0124170i
$427$	−77.0397	−	197.576i	−0.180421	−	0.462706i
$428$	258.414	+	149.196i	0.603771	+	0.348588i
$429$	83.6301	+	162.761i	0.194942	+	0.379397i
$430$	48.7948	−	84.5150i	0.113476	−	0.196547i
$431$	478.460	−	276.239i	1.11012	−	0.640925i	0.171256	−	0.985227i	$-0.445218\pi$
$431$	478.460	−	276.239i	1.11012	−	0.640925i	0.938859	+	0.344301i	$0.111884\pi$
$432$	−15.8045	+	106.837i	−0.0365846	+	0.247309i
$433$	−351.734			−0.812319			−0.406160	−	0.913802i	$-0.633132\pi$
$433$	−351.734			−0.812319			−0.406160	+	0.913802i	$0.633132\pi$
$434$	−114.968	+	44.8288i	−0.264902	+	0.103292i
$435$	−144.199	−	92.9475i	−0.331492	−	0.213672i
$436$	22.0143	+	38.1298i	0.0504914	+	0.0874537i
$437$			557.995i			1.27688i
$438$	−25.1452	−	48.9377i	−0.0574092	−	0.111730i
$439$	47.2343			0.107595			0.0537976	−	0.998552i	$-0.482867\pi$
$439$	47.2343			0.107595			0.0537976	+	0.998552i	$0.482867\pi$
$440$			22.4615i			0.0510488i
$441$	352.225	−	265.365i	0.798696	−	0.601735i
$442$	847.190			1.91672
$443$		−	512.244i		−	1.15631i	−0.815928	−	0.578154i	$-0.803773\pi$
$443$		−	512.244i		−	1.15631i	0.815928	−	0.578154i	$-0.196227\pi$
$444$	−58.5592	−	37.7460i	−0.131890	−	0.0850134i
$445$	48.8248			0.109719
$446$	−307.137	+	177.326i	−0.688648	+	0.397591i
$447$	86.0559	+	167.482i	0.192519	+	0.374680i
$448$	20.3440	+	52.1740i	0.0454106	+	0.116460i
$449$		−	560.296i		−	1.24787i	−0.781475	−	0.623937i	$-0.785532\pi$
$449$		−	560.296i		−	1.24787i	0.781475	−	0.623937i	$-0.214468\pi$
$450$	181.720	+	130.146i	0.403822	+	0.289213i
$451$	−44.3897	−	76.8853i	−0.0984251	−	0.170477i
$452$	−27.4417	−	15.8435i	−0.0607118	−	0.0350520i
$453$	478.429	+	308.385i	1.05614	+	0.680761i
$454$	−286.862	+	496.860i	−0.631855	+	1.09440i
$455$	−372.631	+	145.298i	−0.818969	+	0.319337i
$456$	163.124	−	253.071i	0.357729	−	0.554981i
$457$	669.482			1.46495			0.732475	−	0.680794i	$-0.238365\pi$
$457$	669.482			1.46495			0.732475	+	0.680794i	$0.238365\pi$
$458$	134.324	−	77.5520i	0.293284	−	0.169328i
$459$	284.039	+	717.942i	0.618821	+	1.56414i
$460$	−42.8897	+	74.2871i	−0.0932385	+	0.161494i
$461$	80.8290	−	46.6667i	0.175334	−	0.101229i	−0.409765	−	0.912191i	$-0.634389\pi$
$461$	80.8290	−	46.6667i	0.175334	−	0.101229i	0.585099	+	0.810962i	$0.301056\pi$
$462$	−17.2440	+	84.7353i	−0.0373246	+	0.183410i
$463$	−208.033	+	360.324i	−0.449316	+	0.778238i	−0.998342	−	0.0575676i	$-0.981666\pi$
$463$	−208.033	+	360.324i	−0.449316	+	0.778238i	0.549026	+	0.835805i	$0.314999\pi$
$464$	72.6327	−	41.9345i	0.156536	−	0.0903761i
$465$	46.6129	+	90.7180i	0.100243	+	0.195092i
$466$	48.9142	−	84.7219i	0.104966	−	0.181807i
$467$	−646.848	−	373.458i	−1.38511	−	0.799696i	−0.392354	−	0.919814i	$-0.628339\pi$
$467$	−646.848	−	373.458i	−1.38511	−	0.799696i	−0.992760	+	0.120119i	$0.961672\pi$
$468$	219.561	−	306.568i	0.469147	−	0.655060i
$469$	−219.842	−	563.806i	−0.468746	−	1.20214i
$470$	−282.620	+	163.171i	−0.601320	+	0.347172i
$471$	−12.6287	+	257.758i	−0.0268126	+	0.547258i
$472$	−122.031			−0.258541
$473$			73.6679i			0.155746i
$474$	438.710	+	21.4943i	0.925549	+	0.0453467i
$475$	−311.568	−	539.652i	−0.655933	−	1.13611i
$476$	312.448	+	250.299i	0.656403	+	0.525839i
$477$	−143.776	+	65.1898i	−0.301417	+	0.136666i
$478$	168.654	−	292.117i	0.352833	−	0.611124i
$479$	−9.52571	−	5.49967i	−0.0198867	−	0.0114816i	0.490024	−	0.871709i	$-0.336988\pi$
$479$	−9.52571	−	5.49967i	−0.0198867	−	0.0114816i	−0.509910	+	0.860228i	$0.670321\pi$
$480$	41.1692	−	21.1536i	0.0857691	−	0.0440700i
$481$	121.627	+	210.664i	0.252862	+	0.437970i
$482$	−345.160	−	199.278i	−0.716100	−	0.413441i
$483$	−218.831	+	247.319i	−0.453067	+	0.512048i
$484$	112.522	+	194.894i	0.232484	+	0.402674i
$485$	−12.3863	−	7.15124i	−0.0255388	−	0.0147448i
$486$	333.410	+	83.2808i	0.686029	+	0.171360i
$487$	−207.376	−	359.187i	−0.425824	−	0.737549i	0.570673	−	0.821178i	$-0.306683\pi$
$487$	−207.376	−	359.187i	−0.425824	−	0.737549i	−0.996497	+	0.0836282i	$0.973349\pi$
$488$		−	85.6869i		−	0.175588i
$489$	−184.456	−	118.896i	−0.377211	−	0.243142i
$490$	−180.356	−	56.5058i	−0.368073	−	0.115318i
$491$	49.0458	+	28.3166i	0.0998896	+	0.0576713i	0.549113	−	0.835748i	$-0.314966\pi$
$491$	49.0458	+	28.3166i	0.0998896	+	0.0576713i	−0.449223	+	0.893420i	$0.648299\pi$
$492$	−99.1164	+	153.770i	−0.201456	+	0.312540i
$493$	299.788	−	519.248i	0.608089	−	1.05324i
$494$	−910.412	+	525.627i	−1.84294	+	1.06402i
$495$	71.1296	+	6.98668i	0.143696	+	0.0141145i
$496$	−49.8605			−0.100525
$497$	−8.14097	+	3.17437i	−0.0163802	+	0.00638706i
$498$	153.793	−	79.0220i	0.308821	−	0.158679i
$499$	223.211	+	386.613i	0.447317	+	0.774775i	0.998210	−	0.0598003i	$-0.0190464\pi$
$499$	223.211	+	386.613i	0.447317	+	0.774775i	−0.550894	+	0.834575i	$0.685713\pi$
$500$		−	232.164i		−	0.464328i
$501$	−136.803	+	212.236i	−0.273059	+	0.423625i
$502$	−314.720			−0.626932
$503$			198.013i			0.393663i	0.980437	+	0.196832i	$0.0630652\pi$
$503$			198.013i			0.393663i	−0.980437	+	0.196832i	$0.936935\pi$
$504$	171.549	−	48.1952i	0.340376	−	0.0956255i
$505$	488.397			0.967122
$506$		−	64.7527i		−	0.127970i
$507$	−720.088	+	369.997i	−1.42029	+	0.729776i
$508$	173.016			0.340583
$509$	592.816	−	342.262i	1.16467	−	0.672421i	0.212249	−	0.977216i	$-0.431921\pi$
$509$	592.816	−	342.262i	1.16467	−	0.672421i	0.952418	+	0.304794i	$0.0985878\pi$
$510$	179.272	−	278.124i	0.351515	−	0.545341i
$511$	−56.7557	+	70.8480i	−0.111068	+	0.138646i
$512$			22.6274i			0.0441942i
$513$	−750.672	−	595.290i	−1.46330	−	1.16041i
$514$	238.307	+	412.759i	0.463632	+	0.803034i
$515$	−359.650	−	207.644i	−0.698350	−	0.403193i
$516$	135.024	−	69.3784i	0.261675	−	0.134454i
$517$	123.174	−	213.343i	0.238247	−	0.412656i
$518$	−17.3833	+	113.628i	−0.0335585	+	0.219359i
$519$	709.645	+	34.7686i	1.36733	+	0.0669916i
$520$	−161.607			−0.310783
$521$	−818.004	+	472.275i	−1.57006	+	0.906477i	−0.573905	+	0.818922i	$0.694572\pi$
$521$	−818.004	+	472.275i	−1.57006	+	0.906477i	−0.996160	+	0.0875552i	$0.972095\pi$
$522$	−110.203	−	243.053i	−0.211117	−	0.465618i
$523$	−129.056	+	223.531i	−0.246761	+	0.427402i	−0.962625	−	0.270837i	$-0.912700\pi$
$523$	−129.056	+	223.531i	−0.246761	+	0.427402i	0.715864	+	0.698239i	$0.246033\pi$
$524$	−175.257	+	101.185i	−0.334459	+	0.193100i
$525$	73.5420	−	361.378i	0.140080	−	0.688339i
$526$	115.337	−	199.770i	0.219272	−	0.379791i
$527$	−308.695	+	178.225i	−0.585759	+	0.338188i
$528$	−18.9298	+	29.3678i	−0.0358519	+	0.0556208i
$529$	−140.856	+	243.970i	−0.266269	+	0.461191i
$530$	58.5921	+	33.8282i	0.110551	+	0.0638267i
$531$	−37.9580	+	386.441i	−0.0714841	+	0.727762i
$532$	−491.059	−	75.1244i	−0.923042	−	0.141211i
$533$	553.178	−	319.378i	1.03786	−	0.599207i
$534$	63.8371	+	41.1480i	0.119545	+	0.0770561i
$535$	−406.918			−0.760595
$536$		−	244.518i		−	0.456190i
$537$	263.295	+	512.426i	0.490308	+	0.954238i
$538$	351.488	+	608.794i	0.653323	+	1.13159i
$539$	139.233	−	31.1329i	0.258318	−	0.0577605i
$540$	−54.1822	−	136.952i	−0.100337	−	0.253615i
$541$	−388.642	+	673.147i	−0.718377	+	1.24426i	0.243266	+	0.969960i	$0.421781\pi$
$541$	−388.642	+	673.147i	−0.718377	+	1.24426i	−0.961643	+	0.274305i	$0.911552\pi$
$542$	−211.177	−	121.923i	−0.389626	−	0.224951i
$543$	−6.62317	+	135.182i	−0.0121974	+	0.248954i
$544$	80.8812	+	140.090i	0.148679	+	0.257519i
$545$	−51.9979	−	30.0210i	−0.0954091	−	0.0550845i
$546$	−609.658	−	124.068i	−1.11659	−	0.227231i
$547$	201.360	+	348.766i	0.368118	+	0.637598i	0.989271	−	0.146090i	$-0.0466691\pi$
$547$	201.360	+	348.766i	0.368118	+	0.637598i	−0.621154	+	0.783689i	$0.713336\pi$
$548$	−70.5210	−	40.7153i	−0.128688	−	0.0742980i
$549$	−271.348	−	26.6530i	−0.494259	−	0.0485483i
$550$	36.1560	+	62.6241i	0.0657382	+	0.113862i
$551$			743.996i			1.35026i
$552$	−118.684	+	60.9824i	−0.215007	+	0.110475i
$553$	−263.274	−	675.190i	−0.476083	−	1.22096i
$554$	−109.252	−	63.0765i	−0.197205	−	0.113857i
$555$	94.8960	+	4.64937i	0.170984	+	0.00837725i
$556$	44.6685	−	77.3681i	0.0803390	−	0.139151i
$557$	155.838	−	89.9733i	0.279782	−	0.161532i	−0.353543	−	0.935418i	$-0.615023\pi$
$557$	155.838	−	89.9733i	0.279782	−	0.161532i	0.633325	+	0.773886i	$0.281690\pi$
$558$	−15.5092	+	157.895i	−0.0277942	+	0.282966i
$559$	−530.030			−0.948175
$560$	−59.6014	−	47.7462i	−0.106431	−	0.0852610i
$561$	−12.2234	+	249.485i	−0.0217885	+	0.444715i
$562$	−332.171	−	575.338i	−0.591052	−	1.02373i
$563$		−	9.40822i		−	0.0167109i	−0.999965	−	0.00835544i	$-0.997340\pi$
$563$		−	9.40822i		−	0.0167109i	0.999965	−	0.00835544i	$-0.00265965\pi$
$564$	−507.034	−	24.8418i	−0.898996	−	0.0440458i
$565$	43.2118			0.0764811
$566$		−	67.0563i		−	0.118474i
$567$	−99.2610	−	558.244i	−0.175064	−	0.984557i
$568$	−3.53067			−0.00621597
$569$			33.0375i			0.0580624i	0.999579	+	0.0290312i	$0.00924221\pi$
$569$			33.0375i			0.0580624i	−0.999579	+	0.0290312i	$0.990758\pi$
$570$	−20.0929	+	410.106i	−0.0352507	+	0.719484i
$571$	−410.353			−0.718657			−0.359329	−	0.933211i	$-0.616994\pi$
$571$	−410.353			−0.718657			−0.359329	+	0.933211i	$0.616994\pi$
$572$	105.649	−	60.9965i	0.184701	−	0.106637i
$573$	−261.498	−	12.8120i	−0.456367	−	0.0223594i
$574$	298.374	+	45.6465i	0.519815	+	0.0795236i
$575$			276.157i			0.480272i
$576$	71.6552	+	7.03830i	0.124401	+	0.0122193i
$577$	205.506	+	355.947i	0.356163	+	0.616892i	0.987316	−	0.158766i	$-0.0507516\pi$
$577$	205.506	+	355.947i	0.356163	+	0.616892i	−0.631154	+	0.775658i	$0.717418\pi$
$578$	647.548	+	373.862i	1.12033	+	0.646820i
$579$	−23.2006	+	473.536i	−0.0400701	+	0.817851i
$580$	−57.1865	+	99.0499i	−0.0985973	+	0.170776i
$581$	−222.648	−	178.362i	−0.383216	−	0.306991i
$582$	−10.1679	−	19.7888i	−0.0174707	−	0.0340014i
$583$	−51.0721			−0.0876022
$584$	−31.7657	+	18.3399i	−0.0543933	+	0.0314040i
$585$	−50.2681	+	511.767i	−0.0859284	+	0.874816i
$586$	−65.7468	+	113.877i	−0.112196	+	0.194329i
$587$	474.540	−	273.976i	0.808416	−	0.466739i	−0.0379895	−	0.999278i	$-0.512095\pi$
$587$	474.540	−	273.976i	0.808416	−	0.466739i	0.846406	+	0.532539i	$0.178762\pi$
$588$	−188.189	−	225.878i	−0.320050	−	0.384146i
$589$	221.154	−	383.050i	0.375474	−	0.650340i
$590$	144.120	−	83.2075i	0.244271	−	0.141030i
$591$	217.355	+	10.6492i	0.367775	+	0.0180189i
$592$	−23.2234	+	40.2241i	−0.0392287	+	0.0679461i
$593$	347.401	+	200.572i	0.585837	+	0.338233i	0.763450	−	0.645867i	$-0.223504\pi$
$593$	347.401	+	200.572i	0.585837	+	0.338233i	−0.177613	+	0.984100i	$0.556837\pi$
$594$	87.1120	+	69.0807i	0.146653	+	0.116297i
$595$	−539.670	−	82.5612i	−0.907009	−	0.138758i
$596$	108.713	−	62.7657i	0.182405	−	0.105312i
$597$	834.147	−	428.603i	1.39723	−	0.717928i
$598$	465.886			0.779074
$599$		−	245.708i		−	0.410197i	−0.978741	−	0.205098i	$-0.934249\pi$
$599$		−	245.708i		−	0.410197i	0.978741	−	0.205098i	$-0.0657515\pi$
$600$	80.7316	−	125.247i	0.134553	−	0.208746i
$601$	243.356	+	421.505i	0.404919	+	0.701340i	0.994312	−	0.106507i	$-0.0339665\pi$
$601$	243.356	+	421.505i	0.404919	+	0.701340i	−0.589393	+	0.807846i	$0.700633\pi$
$602$	−195.477	−	156.595i	−0.324713	−	0.260125i
$603$	−774.324	−	76.0577i	−1.28412	−	0.126132i
$604$	189.735	−	328.631i	0.314132	−	0.544092i
$605$	−265.779	−	153.447i	−0.439304	−	0.253632i
$606$	638.566	+	411.605i	1.05374	+	0.679217i
$607$	265.813	+	460.402i	0.437913	+	0.758487i	0.997528	−	0.0702653i	$-0.0223846\pi$
$607$	265.813	+	460.402i	0.437913	+	0.758487i	−0.559616	+	0.828752i	$0.689051\pi$
$608$	−173.834	−	100.363i	−0.285911	−	0.165071i
$609$	−291.776	+	329.760i	−0.479107	+	0.541478i
$610$	58.4259	+	101.197i	0.0957802	+	0.165896i
$611$	1534.97	+	886.216i	2.51223	+	1.45044i
$612$	468.788	−	212.554i	0.765993	−	0.347311i
$613$	417.393	+	722.946i	0.680902	+	1.17936i	0.974706	+	0.223492i	$0.0717456\pi$
$613$	417.393	+	722.946i	0.680902	+	1.17936i	−0.293803	+	0.955866i	$0.594921\pi$
$614$			286.117i			0.465989i
$615$	12.2087	−	249.186i	0.0198515	−	0.405180i
$616$	56.9851	+	8.71783i	0.0925082	+	0.0141523i
$617$	739.602	+	427.009i	1.19871	+	0.692073i	0.960267	−	0.279084i	$-0.0900308\pi$
$617$	739.602	+	427.009i	1.19871	+	0.692073i	0.238439	+	0.971157i	$0.423364\pi$
$618$	−295.237	−	574.591i	−0.477730	−	0.929759i
$619$	383.189	−	663.703i	0.619045	−	1.07222i	−0.370615	−	0.928787i	$-0.620853\pi$
$619$	383.189	−	663.703i	0.619045	−	1.07222i	0.989660	−	0.143431i	$-0.0458136\pi$
$620$	58.8855	−	33.9976i	0.0949766	−	0.0548348i
$621$	156.198	+	394.810i	0.251527	+	0.635765i
$622$	−420.045			−0.675313
$623$	18.9501	−	123.869i	0.0304174	−	0.198827i
$624$	−211.297	−	136.197i	−0.338617	−	0.218265i
$625$	−61.2128	−	106.024i	−0.0979405	−	0.169638i
$626$		−	535.027i		−	0.854676i
$627$	−141.654	−	275.687i	−0.225923	−	0.439692i
$628$	172.045			0.273957
$629$			332.046i			0.527895i
$630$	−169.739	+	173.891i	−0.269427	+	0.276017i
$631$	414.115			0.656283			0.328142	−	0.944629i	$-0.393578\pi$
$631$	414.115			0.656283			0.328142	+	0.944629i	$0.393578\pi$
$632$		−	292.824i		−	0.463330i
$633$	−460.346	−	296.729i	−0.727244	−	0.468765i
$634$	−365.193			−0.576014
$635$	−204.333	+	117.972i	−0.321784	+	0.185782i
$636$	48.0983	+	93.6090i	0.0756263	+	0.147184i
$637$	223.997	+	1001.76i	0.351643	+	1.57263i
$638$		−	86.3373i		−	0.135325i
$639$	−1.09822	+	11.1807i	−0.00171866	+	0.0174972i
$640$	−15.4286	−	26.7231i	−0.0241072	−	0.0417549i
$641$	443.256	+	255.914i	0.691507	+	0.399242i	0.804176	−	0.594391i	$-0.202607\pi$
$641$	443.256	+	255.914i	0.691507	+	0.399242i	−0.112669	+	0.993633i	$0.535940\pi$
$642$	−532.035	−	342.938i	−0.828715	−	0.534171i
$643$	474.057	−	821.091i	0.737258	−	1.27697i	−0.216467	−	0.976290i	$-0.569453\pi$
$643$	474.057	−	821.091i	0.737258	−	1.27697i	0.953725	−	0.300679i	$-0.0972132\pi$
$644$	171.821	+	137.644i	0.266803	+	0.213733i
$645$	−112.159	+	174.003i	−0.173889	+	0.269773i
$646$	−1434.98			−2.22133
$647$	−118.963	+	68.6832i	−0.183868	+	0.106156i	−0.589109	−	0.808054i	$-0.700521\pi$
$647$	−118.963	+	68.6832i	−0.183868	+	0.106156i	0.405241	+	0.914210i	$0.367188\pi$
$648$	44.5769	−	224.724i	0.0687915	−	0.346796i
$649$	−62.8113	+	108.792i	−0.0967817	+	0.167631i
$650$	−450.571	+	260.137i	−0.693186	+	0.400211i
$651$	248.244	−	83.0476i	0.381328	−	0.127569i
$652$	−73.1516	+	126.702i	−0.112196	+	0.194329i
$653$	126.996	−	73.3211i	0.194481	−	0.112283i	−0.399598	−	0.916691i	$-0.630850\pi$
$653$	126.996	−	73.3211i	0.194481	−	0.112283i	0.594078	+	0.804407i	$0.297517\pi$
$654$	−42.6852	−	83.0739i	−0.0652678	−	0.127024i
$655$	137.986	−	238.999i	0.210666	−	0.364884i
$656$	105.624	+	60.9819i	0.161012	+	0.0929602i
$657$	48.1970	+	106.298i	0.0733593	+	0.161794i
$658$	304.275	+	780.343i	0.462424	+	1.18593i
$659$	736.802	−	425.393i	1.11806	−	0.645513i	0.177155	−	0.984183i	$-0.443310\pi$
$659$	736.802	−	425.393i	1.11806	−	0.645513i	0.940905	+	0.338670i	$0.109977\pi$
$660$	2.33169	−	47.5909i	0.00353286	−	0.0721074i
$661$	−280.785			−0.424788			−0.212394	−	0.977184i	$-0.568126\pi$
$661$	−280.785			−0.424788			−0.212394	+	0.977184i	$0.568126\pi$
$662$		−	539.905i		−	0.815566i
$663$	−1795.01	−	87.9453i	−2.70740	−	0.132648i
$664$	−57.6355	−	99.8276i	−0.0868004	−	0.150343i
$665$	631.167	−	246.108i	0.949123	−	0.370087i
$666$	120.156	+	86.0543i	0.180414	+	0.129211i
$667$	164.859	−	285.544i	0.247165	−	0.428103i
$668$	145.784	+	84.1686i	0.218240	+	0.126001i
$669$	669.164	−	343.831i	1.00024	−	0.513947i
$670$	166.725	+	288.777i	0.248844	+	0.431010i
$671$	−76.3909	−	44.1043i	−0.113846	−	0.0657292i
$672$	−37.6883	−	112.657i	−0.0560837	−	0.167644i
$673$	−182.652	−	316.362i	−0.271400	−	0.470078i	0.697821	−	0.716272i	$-0.254153\pi$
$673$	−182.652	−	316.362i	−0.271400	−	0.470078i	−0.969220	+	0.246194i	$0.920820\pi$
$674$	−297.450	−	171.733i	−0.441321	−	0.254797i
$675$	−371.514	−	294.615i	−0.550391	−	0.436466i
$676$	269.861	+	467.413i	0.399202	+	0.691439i
$677$		−	942.705i		−	1.39247i	−0.717812	−	0.696237i	$-0.754856\pi$
$677$		−	942.705i		−	1.39247i	0.717812	−	0.696237i	$-0.245144\pi$
$678$	56.4983	+	36.4175i	0.0833308	+	0.0537132i
$679$	−22.9502	+	28.6487i	−0.0338000	+	0.0421925i
$680$	−191.042	−	110.298i	−0.280945	−	0.162203i
$681$	659.376	−	1022.96i	0.968246	−	1.50214i
$682$	−25.6639	+	44.4512i	−0.0376304	+	0.0651777i
$683$	730.079	−	421.511i	1.06893	−	0.617147i	0.141041	−	0.990004i	$-0.454955\pi$
$683$	730.079	−	421.511i	1.06893	−	0.617147i	0.927889	+	0.372857i	$0.121622\pi$
$684$	−371.895	+	519.269i	−0.543706	+	0.759165i
$685$	111.048			0.162113
$686$	−213.356	+	435.634i	−0.311015	+	0.635035i
$687$	−292.654	+	150.372i	−0.425988	+	0.218882i
$688$	−50.6019	−	87.6450i	−0.0735493	−	0.127391i
$689$		−	367.456i		−	0.533318i
$690$	98.5854	−	152.946i	0.142877	−	0.221660i
$691$	−749.201			−1.08423			−0.542113	−	0.840305i	$-0.682376\pi$
$691$	−749.201			−1.08423			−0.542113	+	0.840305i	$0.682376\pi$
$692$		−	473.664i		−	0.684486i
$693$	45.3324	−	177.745i	0.0654147	−	0.256487i
$694$	−342.774			−0.493910
$695$			121.830i			0.175294i
$696$	−158.246	+	81.3101i	−0.227365	+	0.116825i
$697$	871.914			1.25095
$698$	6.03525	−	3.48445i	0.00864648	−	0.00499205i
$699$	−112.433	+	174.429i	−0.160849	+	0.249541i
$700$	−243.029	−	37.1797i	−0.347185	−	0.0531139i
$701$		−	849.790i		−	1.21225i	−0.795368	−	0.606127i	$-0.792722\pi$
$701$		−	849.790i		−	1.21225i	0.795368	−	0.606127i	$-0.207278\pi$
$702$	−497.025	+	626.758i	−0.708013	+	0.892817i
$703$	−206.013	−	356.825i	−0.293048	−	0.507575i
$704$	20.1726	+	11.6467i	0.0286543	+	0.0165436i
$705$	615.749	−	316.385i	0.873402	−	0.448773i
$706$	433.301	−	750.499i	0.613741	−	1.06303i
$707$	189.558	−	1239.07i	0.268117	−	1.75257i
$708$	258.557	+	12.6679i	0.365194	+	0.0178925i
$709$	−875.721			−1.23515			−0.617575	−	0.786512i	$-0.711885\pi$
$709$	−875.721			−1.23515			−0.617575	+	0.786512i	$0.711885\pi$
$710$	4.16974	−	2.40740i	0.00587288	−	0.00339071i
$711$	−927.299	−	91.0835i	−1.30422	−	0.128106i
$712$	25.3165	−	43.8495i	0.0355569	−	0.0615863i
$713$	−169.757	+	98.0094i	−0.238089	+	0.137461i
$714$	−636.024	−	562.763i	−0.890791	−	0.788184i
$715$	−83.1815	+	144.075i	−0.116338	+	0.201503i
$716$	332.618	−	192.037i	0.464550	−	0.268208i
$717$	−387.665	+	601.425i	−0.540676	+	0.838807i
$718$	376.693	−	652.451i	0.524641	−	0.908706i
$719$	32.2621	+	18.6266i	0.0448708	+	0.0259062i	0.522268	−	0.852782i	$-0.325086\pi$
$719$	32.2621	+	18.6266i	0.0448708	+	0.0259062i	−0.477397	+	0.878688i	$0.658420\pi$
$720$	−89.4243	+	40.5461i	−0.124200	+	0.0563140i
$721$	−666.385	+	831.847i	−0.924252	+	1.15374i
$722$	1099.93	−	635.048i	1.52346	−	0.879567i
$723$	710.632	+	458.057i	0.982893	+	0.633551i
$724$	90.2296			0.124626
$725$			368.210i			0.507876i
$726$	−218.178	−	424.618i	−0.300521	−	0.584874i
$727$	92.7399	+	160.630i	0.127565	+	0.220949i	0.922733	−	0.385440i	$-0.125950\pi$
$727$	92.7399	+	160.630i	0.127565	+	0.220949i	−0.795168	+	0.606390i	$0.792617\pi$
$728$	−62.7235	+	409.999i	−0.0861587	+	0.563186i
$729$	−697.777	−	211.064i	−0.957170	−	0.289526i
$730$	25.0103	−	43.3191i	0.0342607	−	0.0593413i
$731$	−626.570	−	361.751i	−0.857142	−	0.494871i
$732$	−8.89500	+	181.552i	−0.0121516	+	0.248021i
$733$	315.666	+	546.749i	0.430649	+	0.745906i	0.996929	−	0.0783065i	$-0.0249513\pi$
$733$	315.666	+	546.749i	0.430649	+	0.745906i	−0.566280	+	0.824213i	$0.691618\pi$
$734$	453.641	+	261.910i	0.618040	+	0.356826i
$735$	376.268	+	138.446i	0.511930	+	0.188361i
$736$	44.4781	+	77.0384i	0.0604322	+	0.104672i
$737$	−217.991	−	125.857i	−0.295781	−	0.170769i
$738$	225.968	−	315.514i	0.306190	−	0.427526i
$739$	245.760	+	425.669i	0.332558	+	0.576007i	0.983013	−	0.183538i	$-0.0587550\pi$
$739$	245.760	+	425.669i	0.332558	+	0.576007i	−0.650455	+	0.759545i	$0.725422\pi$
$740$		−	63.3399i		−	0.0855944i
$741$	1983.53	−	1019.18i	2.67682	−	1.37541i
$742$	108.564	−	135.520i	0.146312	−	0.182641i
$743$	−487.432	−	281.419i	−0.656032	−	0.378760i	0.134731	−	0.990882i	$-0.456983\pi$
$743$	−487.432	−	281.419i	−0.656032	−	0.378760i	−0.790764	+	0.612122i	$0.790316\pi$
$744$	105.643	+	5.17593i	0.141994	+	0.00695689i
$745$	−85.5942	+	148.253i	−0.114891	+	0.198998i
$746$	−512.464	+	295.871i	−0.686948	+	0.396610i
$747$	−334.056	+	151.465i	−0.447196	+	0.202765i
$748$	166.523			0.222624
$749$	−157.935	+	1032.36i	−0.210861	+	1.37831i
$750$	−24.1006	+	491.905i	−0.0321341	+	0.655873i
$751$	32.3457	+	56.0244i	0.0430702	+	0.0745997i	0.886757	−	0.462236i	$-0.152953\pi$
$751$	32.3457	+	56.0244i	0.0430702	+	0.0745997i	−0.843687	+	0.536836i	$0.819619\pi$
$752$			338.428i			0.450037i
$753$	666.821	+	32.6705i	0.885553	+	0.0433871i
$754$	621.184			0.823851
$755$			517.488i			0.685414i
$756$	−368.478	+	84.3068i	−0.487405	+	0.111517i
$757$	−629.889			−0.832086			−0.416043	−	0.909345i	$-0.636583\pi$
$757$	−629.889			−0.832086			−0.416043	+	0.909345i	$0.636583\pi$
$758$			341.674i			0.450758i
$759$	−6.72187	+	137.197i	−0.00885622	+	0.180760i
$760$	273.732			0.360174
$761$	412.140	−	237.949i	0.541577	−	0.312680i	−0.204141	−	0.978942i	$-0.565440\pi$
$761$	412.140	−	237.949i	0.541577	−	0.312680i	0.745718	+	0.666262i	$0.232107\pi$
$762$	−366.583	−	17.9605i	−0.481080	−	0.0235702i
$763$	−96.3454	+	120.268i	−0.126272	+	0.157625i
$764$			174.541i			0.228457i
$765$	−408.710	+	570.673i	−0.534262	+	0.745978i
$766$	−118.761	−	205.700i	−0.155040	−	0.268538i
$767$	−782.745	−	451.918i	−1.02053	−	0.589202i
$768$	2.34891	−	47.9425i	0.00305848	−	0.0624251i
$769$	424.359	−	735.011i	0.551832	−	0.955801i	−0.446311	−	0.894878i	$-0.647262\pi$
$769$	424.359	−	735.011i	0.551832	−	0.955801i	0.998142	−	0.0609226i	$-0.0194043\pi$
$770$	−73.2440	+	28.5597i	−0.0951221	+	0.0370905i
$771$	−462.071	−	899.284i	−0.599314	−	1.16639i
$772$	316.069			0.409416
$773$	−45.6733	+	26.3695i	−0.0590857	+	0.0341132i	−0.529252	−	0.848465i	$-0.677527\pi$
$773$	−45.6733	+	26.3695i	−0.0590857	+	0.0341132i	0.470166	+	0.882578i	$0.344194\pi$
$774$	−293.289	+	132.981i	−0.378926	+	0.171810i
$775$	109.451	−	189.575i	0.141227	−	0.244613i
$776$	−12.8450	+	7.41609i	−0.0165529	+	0.00955681i
$777$	48.6269	−	238.948i	0.0625829	−	0.307526i
$778$	−356.371	+	617.252i	−0.458060	+	0.793383i
$779$	−936.980	+	540.966i	−1.20280	+	0.694436i
$780$	342.409	+	16.7761i	0.438986	+	0.0215079i
$781$	−1.81729	+	3.14764i	−0.00232687	+	0.00403026i
$782$	550.744	+	317.972i	0.704276	+	0.406614i
$783$	208.265	+	526.415i	0.265984	+	0.672305i
$784$	−144.265	+	132.678i	−0.184012	+	0.169232i
$785$	−203.186	+	117.310i	−0.258836	+	0.149439i
$786$	381.834	−	196.195i	0.485794	−	0.249611i
$787$	−312.691			−0.397320			−0.198660	−	0.980068i	$-0.563659\pi$
$787$	−312.691			−0.397320			−0.198660	+	0.980068i	$0.563659\pi$
$788$		−	145.077i		−	0.184108i
$789$	−265.112	+	411.295i	−0.336010	+	0.521287i
$790$	199.663	+	345.827i	0.252739	+	0.437756i
$791$	16.7715	−	109.629i	0.0212030	−	0.138595i
$792$	43.1567	−	60.2587i	0.0544908	−	0.0760843i
$793$	317.324	−	549.621i	0.400156	−	0.693091i
$794$	418.267	+	241.487i	0.526785	+	0.304139i
$795$	−120.632	−	77.7568i	−0.151738	−	0.0978072i
$796$	−312.606	−	541.449i	−0.392721	−	0.680213i
$797$	406.221	+	234.532i	0.509688	+	0.294269i	0.732705	−	0.680546i	$-0.238257\pi$
$797$	406.221	+	234.532i	0.509688	+	0.294269i	−0.223017	+	0.974814i	$0.571591\pi$
$798$	1032.65	+	210.148i	1.29404	+	0.263343i
$799$	1209.70	+	2095.27i	1.51402	+	2.62236i
$800$	−86.0319	−	49.6706i	−0.107540	−	0.0620882i
$801$	−130.985	−	93.8103i	−0.163527	−	0.117116i
$802$	−481.159	−	833.391i	−0.599948	−	1.03914i
$803$			37.7593i			0.0470228i
$804$	−25.3830	+	518.079i	−0.0315709	+	0.644377i
$805$	−296.775	−	45.4020i	−0.368665	−	0.0564000i
$806$	−319.820	−	184.648i	−0.396799	−	0.229092i
$807$	−681.527	−	1326.39i	−0.844519	−	1.64360i
$808$	253.242	−	438.629i	0.313419	−	0.542857i
$809$	−476.849	+	275.309i	−0.589430	+	0.340308i	−0.764872	−	0.644182i	$-0.777198\pi$
$809$	−476.849	+	275.309i	−0.589430	+	0.340308i	0.175442	+	0.984490i	$0.443865\pi$
$810$	100.583	+	295.795i	0.124177	+	0.365180i
$811$	−848.334			−1.04604			−0.523018	−	0.852322i	$-0.675194\pi$
$811$	−848.334			−1.04604			−0.523018	+	0.852322i	$0.675194\pi$
$812$	229.095	+	183.526i	0.282137	+	0.226018i
$813$	434.782	+	280.251i	0.534787	+	0.344712i
$814$	23.9069	+	41.4079i	0.0293696	+	0.0508696i
$815$		−	199.515i		−	0.244803i
$816$	−156.827	−	305.217i	−0.192190	−	0.374040i
$817$	897.771			1.09886
$818$		−	364.237i		−	0.445277i
$819$	1278.85	+	326.160i	1.56148	+	0.398242i
$820$	−166.323			−0.202833
$821$			1379.51i			1.68028i	0.542373	+	0.840138i	$0.317526\pi$
$821$			1379.51i			1.68028i	−0.542373	+	0.840138i	$0.682474\pi$
$822$	145.192	+	93.5874i	0.176632	+	0.113853i
$823$	−103.993			−0.126359			−0.0631794	−	0.998002i	$-0.520124\pi$
$823$	−103.993			−0.126359			−0.0631794	+	0.998002i	$0.520124\pi$
$824$	−372.970	+	215.334i	−0.452634	+	0.261328i
$825$	−70.1057	−	136.440i	−0.0849767	−	0.165382i
$826$	−155.162	−	397.929i	−0.187848	−	0.481754i
$827$		−	445.099i		−	0.538209i	−0.963111	−	0.269104i	$-0.913272\pi$
$827$		−	445.099i		−	0.538209i	0.963111	−	0.269104i	$-0.0867277\pi$
$828$	257.796	−	116.888i	0.311347	−	0.141169i
$829$	370.808	+	642.258i	0.447295	+	0.774738i	0.998209	−	0.0598243i	$-0.0190541\pi$
$829$	370.808	+	642.258i	0.447295	+	0.774738i	−0.550914	+	0.834562i	$0.685721\pi$
$830$	136.136	+	78.5980i	0.164019	+	0.0946964i
$831$	224.932	+	144.986i	0.270677	+	0.174472i
$832$	−83.7960	+	145.139i	−0.100716	+	0.174446i
$833$	−418.918	+	1337.11i	−0.502903	+	1.60517i
$834$	−102.674	+	159.289i	−0.123110	+	0.190994i
$835$	−229.563			−0.274926
$836$	−178.950	+	103.317i	−0.214055	+	0.123585i
$837$	49.2513	−	332.935i	0.0588427	−	0.397772i
$838$	−153.235	+	265.411i	−0.182858	+	0.316720i
$839$	290.739	−	167.858i	0.346531	−	0.200069i	−0.316626	−	0.948551i	$-0.602550\pi$
$839$	290.739	−	167.858i	0.346531	−	0.200069i	0.663156	+	0.748481i	$0.269217\pi$
$840$	121.326	+	107.351i	0.144435	+	0.127798i
$841$	−200.687	+	347.600i	−0.238629	+	0.413317i
$842$	967.659	−	558.678i	1.14924	−	0.663513i
$843$	644.073	+	1253.50i	0.764025	+	1.48695i
$844$	−182.564	+	316.210i	−0.216308	+	0.374656i
$845$	−637.415	−	368.012i	−0.754337	−	0.435517i
$846$	1071.71	+	105.269i	1.26680	+	0.124431i
$847$	−492.454	+	614.728i	−0.581409	+	0.725771i
$848$	60.7621	−	35.0810i	0.0716534	−	0.0413691i
$849$	−6.96100	+	142.077i	−0.00819905	+	0.167347i
$850$	−710.185			−0.835512
$851$			182.599i			0.214569i
$852$	7.48071	+	0.366513i	0.00878018	+	0.000430179i
$853$	346.509	+	600.172i	0.406224	+	0.703601i	0.994463	−	0.105086i	$-0.0335119\pi$
$853$	346.509	+	600.172i	0.406224	+	0.703601i	−0.588239	+	0.808687i	$0.700179\pi$
$854$	279.414	−	108.951i	0.327183	−	0.127577i
$855$	85.1448	−	866.838i	0.0995845	−	1.01385i
$856$	−210.994	+	365.453i	−0.246489	+	0.426931i
$857$	−735.467	−	424.622i	−0.858188	−	0.495475i	0.00521719	−	0.999986i	$-0.498339\pi$
$857$	−735.467	−	424.622i	−0.858188	−	0.495475i	−0.863405	+	0.504511i	$0.831673\pi$
$858$	−230.179	+	118.271i	−0.268274	+	0.137845i
$859$	−730.939	−	1266.02i	−0.850919	−	1.47383i	−0.880380	−	0.474268i	$-0.842713\pi$
$859$	−730.939	−	1266.02i	−0.850919	−	1.47383i	0.0294619	−	0.999566i	$-0.490621\pi$
$860$	119.522	+	69.0062i	0.138979	+	0.0802398i
$861$	−627.449	−	127.689i	−0.728745	−	0.148303i
$862$	390.661	+	676.644i	0.453203	+	0.784970i
$863$	262.264	+	151.418i	0.303898	+	0.175455i	0.644193	−	0.764863i	$-0.277194\pi$
$863$	262.264	+	151.418i	0.303898	+	0.175455i	−0.340295	+	0.940319i	$0.610527\pi$
$864$	−151.091	−	22.3510i	−0.174874	−	0.0258692i
$865$	322.970	+	559.400i	0.373376	+	0.646706i
$866$		−	497.427i		−	0.574396i
$867$	−1333.20	−	859.352i	−1.53772	−	0.991179i
$868$	−63.3974	−	162.589i	−0.0730385	−	0.187314i
$869$	−261.056	−	150.721i	−0.300410	−	0.173442i
$870$	131.448	−	203.928i	0.151089	−	0.234400i
$871$	905.522	−	1568.41i	1.03963	−	1.80070i
$872$	−53.9237	+	31.1329i	−0.0618391	+	0.0357028i
$873$	19.4893	+	42.9837i	0.0223246	+	0.0492368i
$874$	−789.124			−0.902888
$875$	757.058	−	295.196i	0.865209	−	0.337367i
$876$	69.2083	−	35.5607i	0.0790049	−	0.0405944i
$877$	155.891	+	270.011i	0.177754	+	0.307880i	0.941111	−	0.338098i	$-0.109783\pi$
$877$	155.891	+	270.011i	0.177754	+	0.307880i	−0.763357	+	0.645977i	$0.776450\pi$
$878$			66.7994i			0.0760813i
$879$	151.124	−	234.455i	0.171927	−	0.266729i
$880$	−31.7653			−0.0360969
$881$			1088.82i			1.23589i	0.786220	+	0.617947i	$0.212035\pi$
$881$			1088.82i			1.23589i	−0.786220	+	0.617947i	$0.787965\pi$
$882$	375.283	+	498.121i	0.425491	+	0.564763i
$883$	877.900			0.994224			0.497112	−	0.867686i	$-0.334394\pi$
$883$	877.900			0.994224			0.497112	+	0.867686i	$0.334394\pi$
$884$			1198.11i			1.35533i
$885$	−313.995	+	161.338i	−0.354797	+	0.182302i
$886$	724.422			0.817633
$887$	−1311.60	+	757.255i	−1.47870	+	0.853726i	−0.999710	−	0.0240962i	$-0.992329\pi$
$887$	−1311.60	+	757.255i	−1.47870	+	0.853726i	−0.478987	+	0.877822i	$0.658996\pi$
$888$	53.3808	−	82.8152i	0.0601136	−	0.0932604i
$889$	219.989	+	564.184i	0.247457	+	0.634627i
$890$			69.0487i			0.0775828i
$891$	−177.400	−	155.410i	−0.199102	−	0.174422i
$892$	−250.776	−	434.358i	−0.281140	−	0.486948i
$893$	−2599.96	−	1501.08i	−2.91148	−	1.68095i
$894$	−236.855	+	121.701i	−0.264939	+	0.136131i
$895$	−261.883	+	453.594i	−0.292606	+	0.506809i
$896$	−73.7851	+	28.7707i	−0.0823495	+	0.0321102i
$897$	−987.110	−	48.3628i	−1.10046	−	0.0539162i
$898$	792.378			0.882380
$899$	−226.344	+	130.680i	−0.251773	+	0.145361i
$900$	−184.054	+	256.991i	−0.204505	+	0.285545i
$901$	250.793	−	434.385i	0.278349	−	0.482115i
$902$	108.732	−	62.7766i	0.120546	−	0.0695971i
$903$	397.917	+	352.083i	0.440662	+	0.389904i
$904$	22.4061	−	38.8085i	0.0247855	−	0.0429297i
$905$	−106.562	+	61.5234i	−0.117748	+	0.0679817i
$906$	−436.122	+	676.601i	−0.481371	+	0.746800i
$907$	183.872	−	318.475i	0.202725	−	0.351131i	−0.746680	−	0.665183i	$-0.768353\pi$
$907$	183.872	−	318.475i	0.202725	−	0.351131i	0.949406	+	0.314052i	$0.101687\pi$
$908$	−702.666	−	405.684i	−0.773861	−	0.446789i
$909$	−1310.25	−	938.389i	−1.44142	−	1.03233i
$910$	−205.483	−	526.980i	−0.225805	−	0.579099i
$911$	−742.768	+	428.837i	−0.815333	+	0.470733i	−0.848804	−	0.528707i	$-0.822677\pi$
$911$	−742.768	+	428.837i	−0.815333	+	0.470733i	0.0334717	+	0.999440i	$0.489344\pi$
$912$	357.897	+	230.693i	0.392431	+	0.252952i
$913$	−118.663			−0.129971
$914$			946.791i			1.03588i
$915$	−113.287	−	220.479i	−0.123810	−	0.240960i
$916$	109.675	+	189.963i	0.119733	+	0.207383i
$917$	−552.788	−	442.834i	−0.602823	−	0.482916i
$918$	−1015.32	+	401.692i	−1.10602	+	0.437573i
$919$	−52.7068	+	91.2909i	−0.0573524	+	0.0993372i	−0.893276	−	0.449508i	$-0.851599\pi$
$919$	−52.7068	+	91.2909i	−0.0573524	+	0.0993372i	0.835924	+	0.548846i	$0.184933\pi$
$920$	−105.058	−	60.6552i	−0.114193	−	0.0659295i
$921$	29.7013	−	606.219i	0.0322490	−	0.658218i
$922$	65.9966	+	114.310i	0.0715798	+	0.123980i
$923$	−22.6468	−	13.0751i	−0.0245360	−	0.0141659i
$924$	−119.834	−	24.3867i	−0.129690	−	0.0263925i
$925$	−101.958	−	176.596i	−0.110225	−	0.190914i
$926$	−509.575	−	294.203i	−0.550297	−	0.317714i
$927$	565.895	+	1248.08i	0.610459	+	1.34636i
$928$	59.3044	+	102.718i	0.0639056	+	0.110688i
$929$		−	515.060i		−	0.554424i	−0.960809	−	0.277212i	$-0.910590\pi$
$929$		−	515.060i		−	0.554424i	0.960809	−	0.277212i	$-0.0894105\pi$
$930$	−128.295	+	65.9205i	−0.137951	+	0.0708823i
$931$	−379.409	−	1696.80i	−0.407528	−	1.82256i
$932$	119.815	+	69.1752i	0.128557	+	0.0742223i
$933$	889.982	+	43.6041i	0.953893	+	0.0467354i
$934$	528.149	−	914.781i	0.565470	−	0.979423i
$935$	−196.665	+	113.544i	−0.210337	+	0.121438i
$936$	433.553	+	310.506i	0.463197	+	0.331737i
$937$	86.9061			0.0927493			0.0463746	−	0.998924i	$-0.485233\pi$
$937$	86.9061			0.0927493			0.0463746	+	0.998924i	$0.485233\pi$
$938$	797.342	−	310.904i	0.850044	−	0.331454i
$939$	−55.5403	+	1133.60i	−0.0591483	+	1.20725i
$940$	−230.759	−	399.686i	−0.245488	−	0.425197i
$941$			677.244i			0.719707i	0.933009	+	0.359853i	$0.117173\pi$
$941$			677.244i			0.719707i	−0.933009	+	0.359853i	$0.882827\pi$
$942$	−364.525	−	17.8597i	−0.386970	−	0.0189593i
$943$	479.482			0.508465
$944$		−	172.578i		−	0.182816i
$945$	377.690	−	350.815i	0.399672	−	0.371233i
$946$	−104.182			−0.110129
$947$		−	947.519i		−	1.00055i	−0.865867	−	0.500274i	$-0.833233\pi$
$947$		−	947.519i		−	1.00055i	0.865867	−	0.500274i	$-0.166767\pi$
$948$	−30.3976	+	620.430i	−0.0320650	+	0.654462i
$949$	−271.673			−0.286273
$950$	763.183	−	440.624i	0.803350	−	0.463815i
$951$	773.763	+	37.9101i	0.813631	+	0.0398634i
$952$	−353.977	+	441.868i	−0.371824	+	0.464147i
$953$		−	1873.88i		−	1.96630i	−0.182805	−	0.983149i	$-0.558518\pi$
$953$		−	1873.88i		−	1.96630i	0.182805	−	0.983149i	$-0.441482\pi$
$954$	−92.1923	−	203.330i	−0.0966376	−	0.213134i
$955$	−119.012	−	206.134i	−0.124620	−	0.215848i
$956$	413.116	+	238.513i	0.432130	+	0.249490i
$957$	−8.96252	+	182.930i	−0.00936523	+	0.191149i
$958$	7.77771	−	13.4714i	0.00811870	−	0.0140620i
$959$	43.1002	−	281.729i	0.0449429	−	0.293774i
$960$	29.9157	+	58.2220i	0.0311622	+	0.0606479i
$961$	−805.621			−0.838315
$962$	−297.924	+	172.006i	−0.309692	+	0.178801i
$963$	1091.66	+	781.839i	1.13361	+	0.811878i
$964$	281.822	−	488.130i	0.292347	−	0.506359i
$965$	−373.280	+	215.513i	−0.386818	+	0.223330i
$966$	−349.762	−	309.474i	−0.362073	−	0.320367i
$967$	−801.055	+	1387.47i	−0.828392	+	1.43482i	0.0709071	+	0.997483i	$0.477411\pi$
$967$	−801.055	+	1387.47i	−0.828392	+	1.43482i	−0.899299	+	0.437334i	$0.855923\pi$
$968$	−275.622	+	159.130i	−0.284733	+	0.164391i
$969$	3040.41	+	148.963i	3.13768	+	0.153729i
$970$	10.1134	−	17.5169i	0.0104262	−	0.0180586i
$971$	1566.15	+	904.219i	1.61293	+	0.931225i	0.988687	+	0.149994i	$0.0479253\pi$
$971$	1566.15	+	904.219i	1.61293	+	0.931225i	0.624242	+	0.781231i	$0.285408\pi$
$972$	−117.777	+	471.513i	−0.121170	+	0.485096i
$973$	309.083	+	47.2850i	0.317660	+	0.0485971i
$974$	507.966	−	293.275i	0.521526	−	0.301103i
$975$	981.665	−	504.400i	1.00684	−	0.517334i
$976$	121.180			0.124159
$977$		−	36.3348i		−	0.0371902i	−0.999827	−	0.0185951i	$-0.994081\pi$
$977$		−	36.3348i		−	0.0371902i	0.999827	−	0.0185951i	$-0.00591934\pi$
$978$	168.145	−	260.860i	0.171927	−	0.266728i
$979$	−26.0616	−	45.1400i	−0.0266206	−	0.0461082i
$980$	79.9112	−	255.062i	0.0815421	−	0.260267i
$981$	81.8167	+	180.446i	0.0834013	+	0.183941i
$982$	−40.0457	+	69.3613i	−0.0407798	+	0.0706326i
$983$	677.386	+	391.089i	0.689101	+	0.397853i	0.803275	−	0.595608i	$-0.203089\pi$
$983$	677.386	+	391.089i	0.689101	+	0.397853i	−0.114174	+	0.993461i	$0.536422\pi$
$984$	−217.463	−	140.172i	−0.220999	−	0.142451i
$985$	98.9214	+	171.337i	0.100428	+	0.173946i
$986$	734.328	+	423.964i	0.744754	+	0.429984i
$987$	−563.686	−	1684.96i	−0.571111	−	1.70715i
$988$	−743.348	−	1287.52i	−0.752377	−	1.30315i
$989$	−344.563	−	198.934i	−0.348395	−	0.201146i
$990$	−9.88065	+	100.593i	−0.00998046	+	0.101609i
$991$	−716.282	−	1240.64i	−0.722787	−	1.25190i	−0.959878	−	0.280417i	$-0.909527\pi$
$991$	−716.282	−	1240.64i	−0.722787	−	1.25190i	0.237091	−	0.971488i	$-0.423806\pi$
$992$		−	70.5133i		−	0.0710820i
$993$	−56.0466	+	1143.94i	−0.0564417	+	1.15200i
$994$	−4.48924	−	11.5131i	−0.00451634	−	0.0115826i
$995$	738.379	+	426.303i	0.742090	+	0.428446i
$996$	111.754	+	217.496i	0.112203	+	0.218369i
$997$	213.563	−	369.901i	0.214205	−	0.371014i	−0.738821	−	0.673902i	$-0.764617\pi$
$997$	213.563	−	369.901i	0.214205	−	0.371014i	0.953026	+	0.302887i	$0.0979505\pi$
$998$	−546.753	+	315.668i	−0.547849	+	0.316301i
$999$	−245.650	−	194.803i	−0.245896	−	0.194998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.r.a.23.13	yes	32
3.2	odd	2		378.3.r.a.233.3		32
7.4	even	3		126.3.i.a.95.2	yes	32
9.2	odd	6		126.3.i.a.65.2	✓	32
9.7	even	3		378.3.i.a.359.14		32
21.11	odd	6		378.3.i.a.179.11		32
63.11	odd	6	inner	126.3.r.a.11.5	yes	32
63.25	even	3		378.3.r.a.305.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.2	✓	32	9.2	odd	6
126.3.i.a.95.2	yes	32	7.4	even	3
126.3.r.a.11.5	yes	32	63.11	odd	6	inner
126.3.r.a.23.13	yes	32	1.1	even	1	trivial
378.3.i.a.179.11		32	21.11	odd	6
378.3.i.a.359.14		32	9.7	even	3
378.3.r.a.233.3		32	3.2	odd	2
378.3.r.a.305.11		32	63.25	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(0.146807 - 2.99641i) q^{3} -2.00000 q^{4} +(2.36201 - 1.36371i) q^{5} +(4.23756 + 0.207617i) q^{6} +(-2.54299 - 6.52175i) q^{7} -2.82843i q^{8} +(-8.95690 - 0.879787i) q^{9} +(1.92857 + 3.34039i) q^{10} +(-2.52158 - 1.45583i) q^{11} +(-0.293614 + 5.99281i) q^{12} +(10.4745 - 18.1424i) q^{13} +(9.22314 - 3.59634i) q^{14} +(-3.73946 - 7.27775i) q^{15} +4.00000 q^{16} +(24.7647 - 14.2979i) q^{17} +(1.24421 - 12.6670i) q^{18} +(-17.7418 + 30.7298i) q^{19} +(-4.72402 + 2.72742i) q^{20} +(-19.9151 + 6.66240i) q^{21} +(2.05886 - 3.56605i) q^{22} +(13.6186 - 7.86269i) q^{23} +(-8.47512 - 0.415233i) q^{24} +(-8.78060 + 15.2084i) q^{25} +(25.6572 + 14.8132i) q^{26} +(-3.95113 + 26.7093i) q^{27} +(5.08599 + 13.0435i) q^{28} +(18.1582 - 10.4836i) q^{29} +(10.2923 - 5.28840i) q^{30} -12.4651 q^{31} +5.65685i q^{32} +(-4.73245 + 7.34194i) q^{33} +(20.2203 + 35.0226i) q^{34} +(-14.9003 - 11.9365i) q^{35} +(17.9138 + 1.75957i) q^{36} +(-5.80585 + 10.0560i) q^{37} +(-43.4585 - 25.0908i) q^{38} +(-52.8242 - 34.0493i) q^{39} +(-3.85715 - 6.68078i) q^{40} +(26.4059 + 15.2455i) q^{41} +(-9.42206 - 28.1642i) q^{42} +(-12.6505 - 21.9113i) q^{43} +(5.04315 + 2.91167i) q^{44} +(-22.3561 + 10.1365i) q^{45} +(11.1195 + 19.2596i) q^{46} +84.6070i q^{47} +(0.587228 - 11.9856i) q^{48} +(-36.0664 + 33.1695i) q^{49} +(-21.5080 - 12.4176i) q^{50} +(-39.2067 - 76.3041i) q^{51} +(-20.9490 + 36.2847i) q^{52} +(15.1905 - 8.77025i) q^{53} +(-37.7727 - 5.58775i) q^{54} -7.94133 q^{55} +(-18.4463 + 7.19267i) q^{56} +(89.4743 + 57.6731i) q^{57} +(14.8261 + 25.6795i) q^{58} -43.1446i q^{59} +(7.47893 + 14.5555i) q^{60} +30.2949 q^{61} -17.6283i q^{62} +(17.0396 + 60.6519i) q^{63} -8.00000 q^{64} -57.1367i q^{65} +(-10.3831 - 6.69270i) q^{66} +86.4501 q^{67} +(-49.5294 + 28.5958i) q^{68} +(-21.5605 - 41.9611i) q^{69} +(16.8808 - 21.0723i) q^{70} -1.24828i q^{71} +(-2.48841 + 25.3339i) q^{72} +(-6.48414 - 11.2309i) q^{73} +(-14.2214 - 8.21071i) q^{74} +(44.2816 + 28.5429i) q^{75} +(35.4837 - 61.4596i) q^{76} +(-3.08222 + 20.1473i) q^{77} +(48.1530 - 74.7047i) q^{78} +103.529 q^{79} +(9.44805 - 5.45483i) q^{80} +(79.4519 + 15.7603i) q^{81} +(-21.5604 + 37.3436i) q^{82} +(35.2944 - 20.3772i) q^{83} +(39.8303 - 13.3248i) q^{84} +(38.9964 - 67.5437i) q^{85} +(30.9872 - 17.8905i) q^{86} +(-28.7475 - 55.9484i) q^{87} +(-4.11772 + 7.13210i) q^{88} +(15.5031 + 8.95074i) q^{89} +(-14.3352 - 31.6163i) q^{90} +(-144.957 - 22.1761i) q^{91} +(-27.2372 + 15.7254i) q^{92} +(-1.82997 + 37.3505i) q^{93} -119.652 q^{94} +96.7788i q^{95} +(16.9502 + 0.830466i) q^{96} +(-2.62198 - 4.54141i) q^{97} +(-46.9088 - 51.0055i) q^{98} +(21.3047 + 15.2582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27}+ \cdots + 394 q^{99}+O(q^{100}) \) 32 * q - 64 * q^4 + 8 * q^6 + 2 * q^7 - 20 * q^9 - 36 * q^11 + 10 * q^13 + 36 * q^14 + 10 * q^15 + 128 * q^16 - 54 * q^17 + 28 * q^19 + 28 * q^21 - 126 * q^23 - 16 * q^24 + 80 * q^25 - 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 + 76 * q^30 + 16 * q^31 - 40 * q^33 - 90 * q^35 + 40 * q^36 + 22 * q^37 + 46 * q^39 + 72 * q^41 + 120 * q^42 + 16 * q^43 + 72 * q^44 + 464 * q^45 - 12 * q^46 + 2 * q^49 - 288 * q^50 - 286 * q^51 - 20 * q^52 - 72 * q^53 - 160 * q^54 - 24 * q^55 - 72 * q^56 - 282 * q^57 - 24 * q^58 - 20 * q^60 + 124 * q^61 + 66 * q^63 - 256 * q^64 - 16 * q^66 - 140 * q^67 + 108 * q^68 + 218 * q^69 + 72 * q^70 + 196 * q^73 + 216 * q^74 + 658 * q^75 - 56 * q^76 + 486 * q^77 + 32 * q^78 + 76 * q^79 - 380 * q^81 - 56 * q^84 + 60 * q^85 - 144 * q^86 - 740 * q^87 - 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 + 238 * q^93 - 336 * q^94 + 32 * q^96 - 38 * q^97 + 288 * q^98 + 394 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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