LMFDB - Embedded newform 126.3.i.a.95.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(65,126)] 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, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.65"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.i (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			95.12
Character	$\chi$	$=$	126.95
Dual form			126.3.i.a.65.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 + 0.707107i) q^{2} +(0.878690 + 2.86843i) q^{3} +(1.00000 + 1.73205i) q^{4} -1.75162i q^{5} +(-0.952117 + 4.13443i) q^{6} +(6.58841 + 2.36493i) q^{7} +2.82843i q^{8} +(-7.45581 + 5.04093i) q^{9} +(1.23858 - 2.14528i) q^{10} -4.51407i q^{11} +(-4.08958 + 4.39037i) q^{12} +(-4.80730 + 8.32649i) q^{13} +(6.39685 + 7.55515i) q^{14} +(5.02439 - 1.53913i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-0.491183 - 0.283585i) q^{17} +(-12.6959 + 0.901796i) q^{18} +(-10.8517 - 18.7956i) q^{19} +(3.03389 - 1.75162i) q^{20} +(-0.994487 + 20.9764i) q^{21} +(3.19193 - 5.52858i) q^{22} -27.4607i q^{23} +(-8.11315 + 2.48531i) q^{24} +21.9318 q^{25} +(-11.7754 + 6.79855i) q^{26} +(-21.0109 - 16.9571i) q^{27} +(2.49222 + 13.7764i) q^{28} +(48.9844 - 28.2812i) q^{29} +(7.24193 + 1.66774i) q^{30} +(19.9948 + 34.6320i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(12.9483 - 3.96647i) q^{33} +(-0.401050 - 0.694638i) q^{34} +(4.14246 - 11.5404i) q^{35} +(-16.1869 - 7.87291i) q^{36} +(-7.44017 - 12.8868i) q^{37} -30.6932i q^{38} +(-28.1081 - 6.47301i) q^{39} +4.95432 q^{40} +(-28.0456 - 16.1921i) q^{41} +(-16.0506 + 24.9876i) q^{42} +(-1.47486 - 2.55453i) q^{43} +(7.81860 - 4.51407i) q^{44} +(8.82977 + 13.0597i) q^{45} +(19.4176 - 33.6323i) q^{46} +(-47.7829 - 27.5875i) q^{47} +(-11.6939 - 2.69299i) q^{48} +(37.8142 + 31.1623i) q^{49} +(26.8609 + 15.5082i) q^{50} +(0.381846 - 1.65811i) q^{51} -19.2292 q^{52} +(-48.3659 - 27.9241i) q^{53} +(-13.7425 - 35.6250i) q^{54} -7.90692 q^{55} +(-6.68904 + 18.6348i) q^{56} +(44.3788 - 47.6428i) q^{57} +79.9912 q^{58} +(-10.7583 + 6.21132i) q^{59} +(7.69024 + 7.16337i) q^{60} +(-39.7638 + 68.8730i) q^{61} +56.5538i q^{62} +(-61.0433 + 15.5792i) q^{63} -8.00000 q^{64} +(14.5848 + 8.42054i) q^{65} +(18.6631 + 4.29792i) q^{66} +(-0.142238 - 0.246363i) q^{67} -1.13434i q^{68} +(78.7691 - 24.1294i) q^{69} +(13.2337 - 11.2048i) q^{70} +8.92640i q^{71} +(-14.2579 - 21.0882i) q^{72} +(4.02599 - 6.97323i) q^{73} -21.0440i q^{74} +(19.2713 + 62.9100i) q^{75} +(21.7033 - 37.5913i) q^{76} +(10.6755 - 29.7405i) q^{77} +(-29.8481 - 27.8032i) q^{78} +(-48.8263 + 84.5697i) q^{79} +(6.06778 + 3.50323i) q^{80} +(30.1781 - 75.1683i) q^{81} +(-22.8992 - 39.6625i) q^{82} +(-19.5749 + 11.3016i) q^{83} +(-37.3267 + 19.2539i) q^{84} +(-0.496732 + 0.860365i) q^{85} -4.17153i q^{86} +(124.165 + 115.658i) q^{87} +12.7677 q^{88} +(-47.1301 + 27.2106i) q^{89} +(1.57960 + 22.2384i) q^{90} +(-51.3640 + 43.4893i) q^{91} +(47.5633 - 27.4607i) q^{92} +(-81.7703 + 87.7845i) q^{93} +(-39.0146 - 67.5752i) q^{94} +(-32.9227 + 19.0080i) q^{95} +(-12.4178 - 11.5671i) q^{96} +(38.0319 + 65.8731i) q^{97} +(24.2776 + 64.9045i) q^{98} +(22.7551 + 33.6560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 8 q^{6} + 2 q^{7} + 4 q^{9} + 10 q^{13} + 36 q^{14} + 10 q^{15} - 64 q^{16} + 54 q^{17} + 24 q^{18} + 28 q^{19} + 16 q^{21} + 8 q^{24} - 160 q^{25} + 72 q^{26} - 126 q^{27} - 4 q^{28}+ \cdots + 394 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 + 8 * q^6 + 2 * q^7 + 4 * q^9 + 10 * q^13 + 36 * q^14 + 10 * q^15 - 64 * q^16 + 54 * q^17 + 24 * q^18 + 28 * q^19 + 16 * q^21 + 8 * q^24 - 160 * q^25 + 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 - 80 * q^30 - 8 * q^31 - 106 * q^33 + 90 * q^35 + 40 * q^36 + 22 * q^37 - 170 * q^39 + 72 * q^41 + 72 * q^42 + 16 * q^43 - 72 * q^44 - 250 * q^45 - 12 * q^46 - 108 * q^47 + 74 * q^49 - 288 * q^50 + 122 * q^51 + 40 * q^52 + 72 * q^53 + 8 * q^54 - 24 * q^55 - 282 * q^57 + 48 * q^58 - 90 * q^59 + 52 * q^60 - 62 * q^61 - 438 * q^63 - 256 * q^64 + 378 * q^65 + 224 * q^66 + 70 * q^67 + 218 * q^69 - 108 * q^70 + 48 * q^72 + 196 * q^73 + 166 * q^75 - 56 * q^76 + 630 * q^77 + 32 * q^78 - 38 * q^79 + 400 * q^81 + 184 * q^84 + 60 * q^85 - 98 * q^87 + 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 - 182 * q^93 + 168 * q^94 - 72 * q^95 - 16 * q^96 - 38 * q^97 - 288 * q^98 + 394 * q^99

Character values

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

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$	0.878690	+	2.86843i	0.292897	+	0.956144i
$3$	0.878690	+	2.86843i	0.292897	+	0.956144i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$		−	1.75162i		−	0.350323i	−0.984540	−	0.175162i	$-0.943955\pi$
$5$		−	1.75162i		−	0.350323i	0.984540	−	0.175162i	$-0.0560448\pi$
$6$	−0.952117	+	4.13443i	−0.158686	+	0.689071i
$7$	6.58841	+	2.36493i	0.941201	+	0.337848i
$7$	6.58841	+	2.36493i	0.941201	+	0.337848i
$8$			2.82843i			0.353553i
$9$	−7.45581	+	5.04093i	−0.828423	+	0.560103i
$10$	1.23858	−	2.14528i	0.123858	−	0.214528i
$11$		−	4.51407i		−	0.410370i	−0.978723	−	0.205185i	$-0.934220\pi$
$11$		−	4.51407i		−	0.410370i	0.978723	−	0.205185i	$-0.0657796\pi$
$12$	−4.08958	+	4.39037i	−0.340798	+	0.365864i
$13$	−4.80730	+	8.32649i	−0.369792	+	0.640499i	−0.989533	−	0.144308i	$-0.953904\pi$
$13$	−4.80730	+	8.32649i	−0.369792	+	0.640499i	0.619741	+	0.784807i	$0.287238\pi$
$14$	6.39685	+	7.55515i	0.456918	+	0.539653i
$15$	5.02439	−	1.53913i	0.334959	−	0.102609i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−0.491183	−	0.283585i	−0.0288931	−	0.0166815i	0.485484	−	0.874246i	$-0.338643\pi$
$17$	−0.491183	−	0.283585i	−0.0288931	−	0.0166815i	−0.514377	+	0.857564i	$0.671977\pi$
$18$	−12.6959	+	0.901796i	−0.705330	+	0.0500998i
$19$	−10.8517	−	18.7956i	−0.571140	−	0.989244i	−0.996449	−	0.0841959i	$-0.973168\pi$
$19$	−10.8517	−	18.7956i	−0.571140	−	0.989244i	0.425309	−	0.905048i	$-0.360165\pi$
$20$	3.03389	−	1.75162i	0.151694	−	0.0875808i
$21$	−0.994487	+	20.9764i	−0.0473565	+	0.998878i
$22$	3.19193	−	5.52858i	0.145088	−	0.251299i
$23$		−	27.4607i		−	1.19394i	−0.802263	−	0.596971i	$-0.796371\pi$
$23$		−	27.4607i		−	1.19394i	0.802263	−	0.596971i	$-0.203629\pi$
$24$	−8.11315	+	2.48531i	−0.338048	+	0.103555i
$25$	21.9318			0.877274
$26$	−11.7754	+	6.79855i	−0.452901	+	0.261483i
$27$	−21.0109	−	16.9571i	−0.778181	−	0.628040i
$28$	2.49222	+	13.7764i	0.0890078	+	0.492014i
$29$	48.9844	−	28.2812i	1.68912	−	0.975213i	0.733925	−	0.679231i	$-0.237686\pi$
$29$	48.9844	−	28.2812i	1.68912	−	0.975213i	0.955193	−	0.295982i	$-0.0956469\pi$
$30$	7.24193	+	1.66774i	0.241398	+	0.0555914i
$31$	19.9948	+	34.6320i	0.644993	+	1.11716i	0.984303	+	0.176486i	$0.0564731\pi$
$31$	19.9948	+	34.6320i	0.644993	+	1.11716i	−0.339310	+	0.940675i	$0.610194\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	12.9483	−	3.96647i	0.392373	−	0.120196i
$34$	−0.401050	−	0.694638i	−0.0117956	−	0.0204305i
$35$	4.14246	−	11.5404i	0.118356	−	0.329724i
$36$	−16.1869	−	7.87291i	−0.449637	−	0.218692i
$37$	−7.44017	−	12.8868i	−0.201086	−	0.348291i	0.747793	−	0.663932i	$-0.231114\pi$
$37$	−7.44017	−	12.8868i	−0.201086	−	0.348291i	−0.948879	+	0.315641i	$0.897780\pi$
$38$		−	30.6932i		−	0.807715i
$39$	−28.1081	−	6.47301i	−0.720720	−	0.165975i
$40$	4.95432			0.123858
$41$	−28.0456	−	16.1921i	−0.684040	−	0.394930i	0.117336	−	0.993092i	$-0.462565\pi$
$41$	−28.0456	−	16.1921i	−0.684040	−	0.394930i	−0.801375	+	0.598162i	$0.795898\pi$
$42$	−16.0506	+	24.9876i	−0.382157	+	0.594942i
$43$	−1.47486	−	2.55453i	−0.0342991	−	0.0594077i	0.848366	−	0.529410i	$-0.177587\pi$
$43$	−1.47486	−	2.55453i	−0.0342991	−	0.0594077i	−0.882665	+	0.470002i	$0.844253\pi$
$44$	7.81860	−	4.51407i	0.177695	−	0.102592i
$45$	8.82977	+	13.0597i	0.196217	+	0.290216i
$46$	19.4176	−	33.6323i	0.422122	−	0.731137i
$47$	−47.7829	−	27.5875i	−1.01666	−	0.586967i	−0.103523	−	0.994627i	$-0.533012\pi$
$47$	−47.7829	−	27.5875i	−1.01666	−	0.586967i	−0.913134	+	0.407660i	$0.866345\pi$
$48$	−11.6939	−	2.69299i	−0.243623	−	0.0561040i
$49$	37.8142	+	31.1623i	0.771718	+	0.635965i
$50$	26.8609	+	15.5082i	0.537218	+	0.310163i
$51$	0.381846	−	1.65811i	0.00748718	−	0.0325120i
$52$	−19.2292			−0.369792
$53$	−48.3659	−	27.9241i	−0.912565	−	0.526870i	−0.0313093	−	0.999510i	$-0.509968\pi$
$53$	−48.3659	−	27.9241i	−0.912565	−	0.526870i	−0.881256	+	0.472640i	$0.843301\pi$
$54$	−13.7425	−	35.6250i	−0.254491	−	0.659723i
$55$	−7.90692			−0.143762
$56$	−6.68904	+	18.6348i	−0.119447	+	0.332765i
$57$	44.3788	−	47.6428i	0.778575	−	0.835839i
$58$	79.9912			1.37916
$59$	−10.7583	+	6.21132i	−0.182344	+	0.105277i	−0.588394	−	0.808575i	$-0.700239\pi$
$59$	−10.7583	+	6.21132i	−0.182344	+	0.105277i	0.406049	+	0.913851i	$0.366906\pi$
$60$	7.69024	+	7.16337i	0.128171	+	0.119390i
$61$	−39.7638	+	68.8730i	−0.651866	+	1.12906i	0.330804	+	0.943700i	$0.392680\pi$
$61$	−39.7638	+	68.8730i	−0.651866	+	1.12906i	−0.982670	+	0.185365i	$0.940653\pi$
$62$			56.5538i			0.912158i
$63$	−61.0433	+	15.5792i	−0.968942	+	0.247288i
$64$	−8.00000			−0.125000
$65$	14.5848	+	8.42054i	0.224382	+	0.129547i
$66$	18.6631	+	4.29792i	0.282774	+	0.0651200i
$67$	−0.142238	−	0.246363i	−0.00212295	−	0.00367706i	0.864962	−	0.501837i	$-0.167342\pi$
$67$	−0.142238	−	0.246363i	−0.00212295	−	0.00367706i	−0.867085	+	0.498160i	$0.834009\pi$
$68$		−	1.13434i		−	0.0166815i
$69$	78.7691	−	24.1294i	1.14158	−	0.349702i
$70$	13.2337	−	11.2048i	0.189053	−	0.160069i
$71$			8.92640i			0.125724i	0.998022	+	0.0628619i	$0.0200228\pi$
$71$			8.92640i			0.125724i	−0.998022	+	0.0628619i	$0.979977\pi$
$72$	−14.2579	−	21.0882i	−0.198026	−	0.292892i
$73$	4.02599	−	6.97323i	0.0551506	−	0.0955237i	−0.837132	−	0.547001i	$-0.815769\pi$
$73$	4.02599	−	6.97323i	0.0551506	−	0.0955237i	0.892283	+	0.451477i	$0.149103\pi$
$74$		−	21.0440i		−	0.284378i
$75$	19.2713	+	62.9100i	0.256951	+	0.838800i
$76$	21.7033	−	37.5913i	0.285570	−	0.494622i
$77$	10.6755	−	29.7405i	0.138643	−	0.386241i
$78$	−29.8481	−	27.8032i	−0.382668	−	0.356451i
$79$	−48.8263	+	84.5697i	−0.618055	+	1.07050i	0.371786	+	0.928319i	$0.378746\pi$
$79$	−48.8263	+	84.5697i	−0.618055	+	1.07050i	−0.989840	+	0.142184i	$0.954588\pi$
$80$	6.06778	+	3.50323i	0.0758472	+	0.0437904i
$81$	30.1781	−	75.1683i	0.372569	−	0.928004i
$82$	−22.8992	−	39.6625i	−0.279258	−	0.483689i
$83$	−19.5749	+	11.3016i	−0.235842	+	0.136163i	−0.613264	−	0.789878i	$-0.710144\pi$
$83$	−19.5749	+	11.3016i	−0.235842	+	0.136163i	0.377422	+	0.926041i	$0.376811\pi$
$84$	−37.3267	+	19.2539i	−0.444366	+	0.229214i
$85$	−0.496732	+	0.860365i	−0.00584390	+	0.0101219i
$86$		−	4.17153i		−	0.0485062i
$87$	124.165	+	115.658i	1.42718	+	1.32940i
$88$	12.7677			0.145088
$89$	−47.1301	+	27.2106i	−0.529552	+	0.305737i	−0.740834	−	0.671688i	$-0.765570\pi$
$89$	−47.1301	+	27.2106i	−0.529552	+	0.305737i	0.211282	+	0.977425i	$0.432236\pi$
$90$	1.57960	+	22.2384i	0.0175511	+	0.247093i
$91$	−51.3640	+	43.4893i	−0.564440	+	0.477905i
$92$	47.5633	−	27.4607i	0.516992	−	0.298486i
$93$	−81.7703	+	87.7845i	−0.879250	+	0.943919i
$94$	−39.0146	−	67.5752i	−0.415049	−	0.718885i
$95$	−32.9227	+	19.0080i	−0.346555	+	0.200084i
$96$	−12.4178	−	11.5671i	−0.129352	−	0.120490i
$97$	38.0319	+	65.8731i	0.392081	+	0.679104i	0.992724	−	0.120413i	$-0.0384220\pi$
$97$	38.0319	+	65.8731i	0.392081	+	0.679104i	−0.600643	+	0.799517i	$0.705089\pi$
$98$	24.2776	+	64.9045i	0.247731	+	0.662291i
$99$	22.7551	+	33.6560i	0.229849	+	0.339960i
$100$	21.9318	+	37.9871i	0.219318	+	0.379871i
$101$			194.917i			1.92987i	0.262482	+	0.964937i	$0.415459\pi$
$101$			194.917i			1.92987i	−0.262482	+	0.964937i	$0.584541\pi$
$102$	1.64012	−	1.76076i	0.0160797	−	0.0172623i
$103$	−116.526			−1.13132			−0.565658	−	0.824640i	$-0.691378\pi$
$103$	−116.526			−1.13132			−0.565658	+	0.824640i	$0.691378\pi$
$104$	−23.5509	−	13.5971i	−0.226451	−	0.130741i
$105$	36.7427	+	1.74196i	0.349930	+	0.0165901i
$106$	−39.4906	−	68.3998i	−0.372553	−	0.645281i
$107$	65.8789	−	38.0352i	0.615691	−	0.355469i	−0.159498	−	0.987198i	$-0.550988\pi$
$107$	65.8789	−	38.0352i	0.615691	−	0.355469i	0.775189	+	0.631729i	$0.217654\pi$
$108$	8.35960	−	53.3490i	0.0774037	−	0.493972i
$109$	79.6034	−	137.877i	0.730307	−	1.26493i	−0.226446	−	0.974024i	$-0.572711\pi$
$109$	79.6034	−	137.877i	0.730307	−	1.26493i	0.956752	−	0.290904i	$-0.0939561\pi$
$110$	−9.68395	−	5.59103i	−0.0880359	−	0.0508276i
$111$	30.4272	−	32.6651i	0.274119	−	0.294280i
$112$	−21.3692	+	18.0930i	−0.190796	+	0.161545i
$113$	88.3982	+	51.0367i	0.782285	+	0.451652i	0.837239	−	0.546837i	$-0.184168\pi$
$113$	88.3982	+	51.0367i	0.782285	+	0.451652i	−0.0549546	+	0.998489i	$0.517501\pi$
$114$	88.0412	−	26.9698i	0.772291	−	0.236577i
$115$	−48.1005			−0.418266
$116$	97.9689	+	56.5623i	0.844559	+	0.487606i
$117$	−6.13091	−	86.3139i	−0.0524009	−	0.737726i
$118$	−17.5683			−0.148883
$119$	−2.56546	−	3.02999i	−0.0215585	−	0.0254621i
$120$	4.35331	+	14.2111i	0.0362776	+	0.118426i
$121$	100.623			0.831597
$122$	−97.4011	+	56.2345i	−0.798369	+	0.460939i
$123$	21.8027	−	94.6748i	0.177257	−	0.769714i
$124$	−39.9896	+	69.2640i	−0.322497	+	0.558580i
$125$		−	82.2066i		−	0.657652i
$126$	−85.7787	−	24.0837i	−0.680783	−	0.191140i
$127$	−221.800			−1.74646			−0.873228	−	0.487313i	$-0.837977\pi$
$127$	−221.800			−1.74646			−0.873228	+	0.487313i	$0.837977\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	6.03156	−	6.47518i	0.0467563	−	0.0501952i
$130$	11.9084	+	20.6260i	0.0916034	+	0.158662i
$131$		−	2.42010i		−	0.0184741i	−0.999957	−	0.00923703i	$-0.997060\pi$
$131$		−	2.42010i		−	0.0184741i	0.999957	−	0.00923703i	$-0.00294028\pi$
$132$	19.8184	+	18.4606i	0.150140	+	0.139853i
$133$	−27.0447	−	149.497i	−0.203344	−	1.12404i
$134$		−	0.402309i		−	0.00300230i
$135$	−29.7023	+	36.8030i	−0.220017	+	0.272615i
$136$	0.802099	−	1.38928i	0.00589779	−	0.0102153i
$137$			236.830i			1.72869i	0.502901	+	0.864344i	$0.332266\pi$
$137$			236.830i			1.72869i	−0.502901	+	0.864344i	$0.667734\pi$
$138$	113.534	+	26.1458i	0.822711	+	0.189462i
$139$	112.225	−	194.379i	0.807373	−	1.39841i	−0.107304	−	0.994226i	$-0.534222\pi$
$139$	112.225	−	194.379i	0.807373	−	1.39841i	0.914677	−	0.404185i	$-0.132445\pi$
$140$	24.1309	−	4.36541i	0.172364	−	0.0311815i
$141$	37.1464	−	161.303i	0.263450	−	1.14399i
$142$	−6.31192	+	10.9326i	−0.0444501	+	0.0769899i
$143$	37.5863	+	21.7005i	0.262841	+	0.151752i
$144$	−2.55067	−	35.9095i	−0.0177130	−	0.249372i
$145$	−49.5378	−	85.8019i	−0.341640	−	0.591737i
$146$	9.86163	−	5.69362i	0.0675454	−	0.0389974i
$147$	−56.1600	+	135.849i	−0.382041	+	0.924145i
$148$	14.8803	−	25.7735i	0.100543	−	0.174145i
$149$		−	82.5884i		−	0.554284i	−0.960829	−	0.277142i	$-0.910613\pi$
$149$		−	82.5884i		−	0.554284i	0.960829	−	0.277142i	$-0.0893873\pi$
$150$	−20.8817	+	90.6756i	−0.139211	+	0.604504i
$151$	−213.733			−1.41545			−0.707724	−	0.706489i	$-0.750278\pi$
$151$	−213.733			−1.41545			−0.707724	+	0.706489i	$0.750278\pi$
$152$	53.1621	−	30.6932i	0.349751	−	0.201929i
$153$	5.09170	−	0.361665i	0.0332791	−	0.00236382i
$154$	34.1045	−	28.8758i	0.221458	−	0.187505i
$155$	60.6619	−	35.0232i	0.391367	−	0.225956i
$156$	−16.8965	−	55.1576i	−0.108311	−	0.353575i
$157$	−80.8970	−	140.118i	−0.515268	−	0.892470i	−0.999843	−	0.0177201i	$-0.994359\pi$
$157$	−80.8970	−	140.118i	−0.515268	−	0.892470i	0.484575	−	0.874749i	$-0.338974\pi$
$158$	−119.600	+	69.0508i	−0.756959	+	0.437031i
$159$	37.5997	−	163.271i	0.236476	−	1.02686i
$160$	4.95432	+	8.58113i	0.0309645	+	0.0536321i
$161$	64.9427	−	180.922i	0.403371	−	1.12374i
$162$	90.1126	−	70.7229i	0.556250	−	0.436561i
$163$	−26.8721	−	46.5439i	−0.164860	−	0.285545i	0.771746	−	0.635931i	$-0.219384\pi$
$163$	−26.8721	−	46.5439i	−0.164860	−	0.285545i	−0.936605	+	0.350386i	$0.886050\pi$
$164$		−	64.7686i		−	0.394930i
$165$	−6.94773	−	22.6805i	−0.0421074	−	0.137457i
$166$	−31.9656			−0.192564
$167$	−41.1006	−	23.7295i	−0.246112	−	0.142093i	0.371871	−	0.928284i	$-0.378716\pi$
$167$	−41.1006	−	23.7295i	−0.246112	−	0.142093i	−0.617982	+	0.786192i	$0.712050\pi$
$168$	−59.3303	−	2.81284i	−0.353157	−	0.0167431i
$169$	38.2798	+	66.3025i	0.226507	+	0.392322i
$170$	−1.21674	+	0.702485i	−0.00715729	+	0.00413226i
$171$	175.655	+	85.4342i	1.02722	+	0.499615i
$172$	2.94972	−	5.10906i	0.0171495	−	0.0297039i
$173$	−79.5964	−	45.9550i	−0.460095	−	0.265636i	0.251989	−	0.967730i	$-0.418915\pi$
$173$	−79.5964	−	45.9550i	−0.460095	−	0.265636i	−0.712084	+	0.702094i	$0.752249\pi$
$174$	70.2875	+	229.449i	0.403951	+	1.31867i
$175$	144.496	+	51.8674i	0.825691	+	0.296385i
$176$	15.6372	+	9.02814i	0.0888477	+	0.0512962i
$177$	−27.2700	−	25.4017i	−0.154068	−	0.143512i
$178$	−76.9632			−0.432378
$179$	−143.122	−	82.6317i	−0.799566	−	0.461629i	0.0437536	−	0.999042i	$-0.486068\pi$
$179$	−143.122	−	82.6317i	−0.799566	−	0.461629i	−0.843319	+	0.537413i	$0.819402\pi$
$180$	−13.7903	+	28.3533i	−0.0766129	+	0.157518i
$181$	244.607			1.35142			0.675709	−	0.737169i	$-0.263838\pi$
$181$	244.607			1.35142			0.675709	+	0.737169i	$0.263838\pi$
$182$	−93.6594	+	16.9435i	−0.514612	+	0.0930960i
$183$	−232.497	−	53.5418i	−1.27048	−	0.292578i
$184$	77.6705			0.422122
$185$	−22.5727	+	13.0323i	−0.122014	+	0.0704450i
$186$	−162.221	+	49.6933i	−0.872154	+	0.267168i
$187$	−1.28012	+	2.21724i	−0.00684557	+	0.0118569i
$188$		−	110.350i		−	0.586967i
$189$	−98.3260	−	161.409i	−0.520243	−	0.854018i
$190$	−53.7626			−0.282961
$191$	−127.255	−	73.4705i	−0.666254	−	0.384662i	0.128402	−	0.991722i	$-0.459015\pi$
$191$	−127.255	−	73.4705i	−0.666254	−	0.384662i	−0.794656	+	0.607060i	$0.792349\pi$
$192$	−7.02952	−	22.9475i	−0.0366121	−	0.119518i
$193$	126.891	+	219.782i	0.657466	+	1.13876i	0.981269	+	0.192640i	$0.0617050\pi$
$193$	126.891	+	219.782i	0.657466	+	1.13876i	−0.323803	+	0.946124i	$0.604962\pi$
$194$			107.570i			0.554486i
$195$	−11.3382	+	49.2346i	−0.0581448	+	0.252485i
$196$	−16.1605	+	96.6584i	−0.0824515	+	0.493155i
$197$			318.129i			1.61487i	0.589958	+	0.807434i	$0.299144\pi$
$197$			318.129i			1.61487i	−0.589958	+	0.807434i	$0.700856\pi$
$198$	4.07077	+	57.3103i	0.0205595	+	0.289446i
$199$	123.517	−	213.938i	0.620689	−	1.07506i	−0.368669	−	0.929561i	$-0.620186\pi$
$199$	123.517	−	213.938i	0.620689	−	1.07506i	0.989358	−	0.145504i	$-0.0464803\pi$
$200$			62.0326i			0.310163i
$201$	0.581692	−	0.624475i	0.00289399	−	0.00310684i
$202$	−137.827	+	238.724i	−0.682313	+	1.18180i
$203$	389.612	−	70.4829i	1.91927	−	0.347206i
$204$	3.25378	−	0.996733i	0.0159499	−	0.00488595i
$205$	−28.3624	+	49.1252i	−0.138353	+	0.239635i
$206$	−142.714	−	82.3960i	−0.692786	−	0.399980i
$207$	138.427	+	204.741i	0.668730	+	0.989089i
$208$	−19.2292	−	33.3059i	−0.0924481	−	0.160125i
$209$	−84.8448	+	48.9852i	−0.405956	+	0.234379i
$210$	43.7686	+	28.1144i	0.208422	+	0.133878i
$211$	−107.527	+	186.242i	−0.509605	+	0.882661i	0.490333	+	0.871535i	$0.336875\pi$
$211$	−107.527	+	186.242i	−0.509605	+	0.882661i	−0.999938	+	0.0111265i	$0.996458\pi$
$212$		−	111.696i		−	0.526870i
$213$	−25.6048	+	7.84354i	−0.120210	+	0.0368241i
$214$	107.580			0.502710
$215$	−4.47456	+	2.58339i	−0.0208119	+	0.0120158i
$216$	47.9618	−	59.4278i	0.222045	−	0.275129i
$217$	49.8314	+	275.456i	0.229638	+	1.26938i
$218$	194.988	−	112.576i	0.894439	−	0.516405i
$219$	23.5398	+	5.42099i	0.107488	+	0.0247534i
$220$	−7.90692	−	13.6952i	−0.0359405	−	0.0622508i
$221$	4.72253	−	2.72655i	0.0213689	−	0.0123374i
$222$	60.3633	−	18.4911i	0.271907	−	0.0832935i
$223$	−40.9462	−	70.9208i	−0.183615	−	0.318031i	0.759494	−	0.650514i	$-0.225447\pi$
$223$	−40.9462	−	70.9208i	−0.183615	−	0.318031i	−0.943109	+	0.332484i	$0.892113\pi$
$224$	−38.9655	+	7.04906i	−0.173953	+	0.0314690i
$225$	−163.520	+	110.557i	−0.726754	+	0.491364i
$226$	72.1768	+	125.014i	0.319366	+	0.553159i
$227$			23.6118i			0.104017i	0.998647	+	0.0520084i	$0.0165622\pi$
$227$			23.6118i			0.104017i	−0.998647	+	0.0520084i	$0.983438\pi$
$228$	126.899	+	29.2235i	0.556573	+	0.128173i
$229$	38.2246			0.166920			0.0834598	−	0.996511i	$-0.473403\pi$
$229$	38.2246			0.166920			0.0834598	+	0.996511i	$0.473403\pi$
$230$	−58.9109	−	34.0122i	−0.256134	−	0.147879i
$231$	94.6891	+	4.48919i	0.409910	+	0.0194337i
$232$	79.9912	+	138.549i	0.344790	+	0.597193i
$233$	−118.984	+	68.6952i	−0.510659	+	0.294829i	−0.733105	−	0.680116i	$-0.761929\pi$
$233$	−118.984	+	68.6952i	−0.510659	+	0.294829i	0.222445	+	0.974945i	$0.428596\pi$
$234$	53.5244	−	110.048i	0.228737	−	0.470289i
$235$	−48.3226	+	83.6973i	−0.205628	+	0.356159i
$236$	−21.5166	−	12.4226i	−0.0911721	−	0.0526383i
$237$	−285.486	−	65.7445i	−1.20458	−	0.277403i
$238$	−0.999503	−	5.52501i	−0.00419959	−	0.0232143i
$239$	348.038	+	200.940i	1.45623	+	0.840753i	0.998823	−	0.0485057i	$-0.0154459\pi$
$239$	348.038	+	200.940i	1.45623	+	0.840753i	0.457404	+	0.889259i	$0.348779\pi$
$240$	−4.71709	+	20.4833i	−0.0196545	+	0.0853469i
$241$	439.498			1.82364			0.911821	−	0.410588i	$-0.134677\pi$
$241$	439.498			1.82364			0.911821	+	0.410588i	$0.134677\pi$
$242$	123.238	+	71.1513i	0.509247	+	0.294014i
$243$	242.133	+	20.5142i	0.996430	+	0.0844207i
$244$	−159.055			−0.651866
$245$	54.5844	−	66.2359i	0.222793	−	0.270351i
$246$	93.6479	−	100.536i	0.380683	−	0.408682i
$247$	208.669			0.844813
$248$	−97.9540	+	56.5538i	−0.394976	+	0.228039i
$249$	−49.6180	−	46.2186i	−0.199269	−	0.185617i
$250$	58.1288	−	100.682i	0.232515	−	0.402728i
$251$			114.101i			0.454587i	0.973826	+	0.227294i	$0.0729877\pi$
$251$			114.101i			0.454587i	−0.973826	+	0.227294i	$0.927012\pi$
$252$	−88.0273	−	90.1510i	−0.349315	−	0.357742i
$253$	−123.959			−0.489958
$254$	−271.648	−	156.836i	−1.06948	−	0.617465i
$255$	−2.90437	−	0.668848i	−0.0113897	−	0.00262293i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$			300.339i			1.16863i	0.811526	+	0.584317i	$0.198637\pi$
$257$			300.339i			1.16863i	−0.811526	+	0.584317i	$0.801363\pi$
$258$	11.9658	−	3.66549i	0.0463789	−	0.0142073i
$259$	−18.5425	−	102.499i	−0.0715928	−	0.395748i
$260$			33.6822i			0.129547i
$261$	−222.655	+	457.786i	−0.853085	+	1.75397i
$262$	1.71127	−	2.96401i	0.00653157	−	0.0113130i
$263$		−	421.530i		−	1.60278i	−0.598145	−	0.801388i	$-0.704096\pi$
$263$		−	421.530i		−	1.60278i	0.598145	−	0.801388i	$-0.295904\pi$
$264$	11.2189	+	36.6233i	0.0424957	+	0.138725i
$265$	−48.9123	+	84.7185i	−0.184575	+	0.319693i
$266$	72.5873	−	202.219i	0.272885	−	0.760222i
$267$	−119.465	−	111.280i	−0.447433	−	0.416779i
$268$	0.284475	−	0.492725i	0.00106147	−	0.00183853i
$269$	−445.841	−	257.406i	−1.65740	−	0.956901i	−0.973908	−	0.226943i	$-0.927127\pi$
$269$	−445.841	−	257.406i	−1.65740	−	0.956901i	−0.683492	−	0.729958i	$-0.739540\pi$
$270$	−62.4014	+	24.0716i	−0.231116	+	0.0891542i
$271$	241.395	+	418.109i	0.890758	+	1.54284i	0.838969	+	0.544179i	$0.183159\pi$
$271$	241.395	+	418.109i	0.890758	+	1.54284i	0.0517888	+	0.998658i	$0.483508\pi$
$272$	1.96473	−	1.13434i	0.00722329	−	0.00417037i
$273$	−169.879	−	109.121i	−0.622268	−	0.399709i
$274$	−167.464	+	290.057i	−0.611184	+	1.05860i
$275$		−	99.0019i		−	0.360007i
$276$	120.562	+	112.303i	0.436820	+	0.406893i
$277$	149.531			0.539824			0.269912	−	0.962885i	$-0.413005\pi$
$277$	149.531			0.539824			0.269912	+	0.962885i	$0.413005\pi$
$278$	274.894	−	158.710i	0.988826	−	0.570899i
$279$	−323.655	−	157.417i	−1.16005	−	0.564219i
$280$	32.6411	+	11.7166i	0.116575	+	0.0418451i
$281$	−17.1238	+	9.88641i	−0.0609387	+	0.0351830i	−0.530160	−	0.847898i	$-0.677868\pi$
$281$	−17.1238	+	9.88641i	−0.0609387	+	0.0351830i	0.469221	+	0.883081i	$0.344535\pi$
$282$	159.553	−	171.288i	0.565792	−	0.607405i
$283$	−274.977	−	476.274i	−0.971650	−	1.68295i	−0.690575	−	0.723261i	$-0.742642\pi$
$283$	−274.977	−	476.274i	−0.971650	−	1.68295i	−0.281075	−	0.959686i	$-0.590691\pi$
$284$	−15.4610	+	8.92640i	−0.0544400	+	0.0314310i
$285$	−83.4519	−	77.7346i	−0.292814	−	0.272753i
$286$	30.6891	+	53.1551i	0.107305	+	0.185857i
$287$	−146.483	−	173.006i	−0.510392	−	0.602810i
$288$	22.2680	−	45.7836i	0.0773193	−	0.158971i
$289$	−144.339	−	250.003i	−0.499443	−	0.865061i
$290$		−	140.114i		−	0.483151i
$291$	−155.534	+	166.974i	−0.534482	+	0.573793i
$292$	16.1040			0.0551506
$293$	−113.883	−	65.7505i	−0.388680	−	0.224404i	0.292908	−	0.956141i	$-0.405377\pi$
$293$	−113.883	−	65.7505i	−0.388680	−	0.224404i	−0.681588	+	0.731736i	$0.738710\pi$
$294$	−164.842	+	126.670i	−0.560686	+	0.430849i
$295$	10.8798	+	18.8444i	0.0368808	+	0.0638794i
$296$	36.4493	−	21.0440i	0.123139	−	0.0710946i
$297$	−76.5454	+	94.8447i	−0.257729	+	0.319342i
$298$	58.3988	−	101.150i	0.195969	−	0.339429i
$299$	228.651	+	132.012i	0.764719	+	0.441510i
$300$	−89.6920	+	96.2889i	−0.298973	+	0.320963i
$301$	−3.67567	−	20.3182i	−0.0122115	−	0.0675025i
$302$	−261.768	−	151.132i	−0.866781	−	0.500436i
$303$	−559.107	+	171.272i	−1.84524	+	0.565254i
$304$	86.8133			0.285570
$305$	120.639	+	69.6509i	0.395538	+	0.228364i
$306$	6.49177	+	3.15743i	0.0212149	+	0.0103184i
$307$	252.488			0.822437			0.411218	−	0.911537i	$-0.365103\pi$
$307$	252.488			0.822437			0.411218	+	0.911537i	$0.365103\pi$
$308$	62.1876	−	11.2500i	0.201908	−	0.0365261i
$309$	−102.390	−	334.246i	−0.331359	−	1.08170i
$310$	99.0605			0.319550
$311$	179.199	−	103.461i	0.576202	−	0.332671i	−0.183420	−	0.983035i	$-0.558717\pi$
$311$	179.199	−	103.461i	0.576202	−	0.332671i	0.759623	+	0.650364i	$0.225384\pi$
$312$	18.3084	−	79.5017i	0.0586809	−	0.254813i
$313$	169.971	−	294.398i	0.543037	−	0.940568i	−0.455691	−	0.890138i	$-0.650608\pi$
$313$	169.971	−	294.398i	0.543037	−	0.940568i	0.998728	−	0.0504294i	$-0.0160590\pi$
$314$		−	228.811i		−	0.728698i
$315$	27.2887	+	106.924i	0.0866309	+	0.339443i
$316$	−195.305			−0.618055
$317$	237.911	+	137.358i	0.750507	+	0.433306i	0.825877	−	0.563850i	$-0.190680\pi$
$317$	237.911	+	137.358i	0.750507	+	0.433306i	−0.0753699	+	0.997156i	$0.524014\pi$
$318$	161.500	−	173.378i	0.507862	−	0.545215i
$319$	−127.663	−	221.119i	−0.400198	−	0.693163i
$320$			14.0129i			0.0437904i
$321$	166.989	+	155.548i	0.520214	+	0.484573i
$322$	207.469	−	175.662i	0.644315	−	0.545534i
$323$			12.3095i			0.0381098i
$324$	160.374	−	22.8983i	0.494980	−	0.0706738i
$325$	−105.433	+	182.615i	−0.324409	+	0.561893i
$326$		−	76.0059i		−	0.233147i
$327$	465.438	+	107.186i	1.42336	+	0.327785i
$328$	45.7983	−	79.3250i	0.139629	−	0.241844i
$329$	−249.571	−	294.761i	−0.758573	−	0.895930i
$330$	7.52831	−	32.6906i	0.0228130	−	0.0990623i
$331$	98.5084	−	170.622i	0.297609	−	0.515473i	−0.677980	−	0.735081i	$-0.737144\pi$
$331$	98.5084	−	170.622i	0.297609	−	0.515473i	0.975588	+	0.219607i	$0.0704776\pi$
$332$	−39.1498	−	22.6031i	−0.117921	−	0.0680817i
$333$	120.434	+	58.5758i	0.361663	+	0.175903i
$334$	−33.5585	−	58.1251i	−0.100475	−	0.174027i
$335$	−0.431533	+	0.249146i	−0.00128816	+	0.000743718i
$336$	−70.6755	−	45.3979i	−0.210344	−	0.135113i
$337$	−162.571	+	281.581i	−0.482405	+	0.835551i	−0.999796	−	0.0201987i	$-0.993570\pi$
$337$	−162.571	+	281.581i	−0.482405	+	0.835551i	0.517391	+	0.855749i	$0.326903\pi$
$338$			108.272i			0.320330i
$339$	−68.7207	+	298.410i	−0.202716	+	0.880264i
$340$	−1.98693			−0.00584390
$341$	156.331	−	90.2578i	0.458449	−	0.264686i
$342$	154.722	+	228.842i	0.452403	+	0.669129i
$343$	175.438	+	294.738i	0.511482	+	0.859294i
$344$	7.22531	−	4.17153i	0.0210038	−	0.0121266i
$345$	−42.2655	−	137.973i	−0.122509	−	0.399922i
$346$	−64.9902	−	112.566i	−0.187833	−	0.325336i
$347$	84.4075	−	48.7327i	0.243249	−	0.140440i	−0.373420	−	0.927662i	$-0.621815\pi$
$347$	84.4075	−	48.7327i	0.243249	−	0.140440i	0.616669	+	0.787222i	$0.288482\pi$
$348$	−76.1610	+	330.718i	−0.218853	+	0.950339i
$349$	−106.817	−	185.012i	−0.306065	−	0.530121i	0.671433	−	0.741066i	$-0.265679\pi$
$349$	−106.817	−	185.012i	−0.306065	−	0.530121i	−0.977498	+	0.210945i	$0.932346\pi$
$350$	140.295	+	165.698i	0.400842	+	0.473424i
$351$	242.198	−	93.4293i	0.690024	−	0.266180i
$352$	12.7677	+	22.1143i	0.0362719	+	0.0628248i
$353$			641.700i			1.81785i	0.416962	+	0.908924i	$0.363095\pi$
$353$			641.700i			1.81785i	−0.416962	+	0.908924i	$0.636905\pi$
$354$	−15.4370	−	50.3933i	−0.0436075	−	0.142354i
$355$	15.6356			0.0440440
$356$	−94.2603	−	54.4212i	−0.264776	−	0.152869i
$357$	6.43708	−	10.0213i	0.0180310	−	0.0280707i
$358$	−116.859	−	202.405i	−0.326421	−	0.565378i
$359$	263.839	−	152.328i	0.734928	−	0.424311i	−0.0852941	−	0.996356i	$-0.527183\pi$
$359$	263.839	−	152.328i	0.734928	−	0.424311i	0.820222	+	0.572045i	$0.193850\pi$
$360$	−36.9384	+	24.9744i	−0.102607	+	0.0693732i
$361$	−55.0174	+	95.2929i	−0.152403	+	0.263969i
$362$	299.581	+	172.963i	0.827571	+	0.477798i
$363$	88.4166	+	288.631i	0.243572	+	0.795126i
$364$	−126.690	−	45.4758i	−0.348049	−	0.124933i
$365$	−12.2144	−	7.05200i	−0.0334641	−	0.0193205i
$366$	−246.890	−	229.976i	−0.674564	−	0.628349i
$367$	125.326			0.341488			0.170744	−	0.985315i	$-0.445383\pi$
$367$	125.326			0.341488			0.170744	+	0.985315i	$0.445383\pi$
$368$	95.1265	+	54.9213i	0.258496	+	0.149243i
$369$	290.726	−	20.6504i	0.787876	−	0.0559631i
$370$	−36.8610			−0.0996243
$371$	−252.616	−	298.357i	−0.680905	−	0.804198i
$372$	−233.817	−	53.8458i	−0.628542	−	0.144747i
$373$	−264.825			−0.709987			−0.354993	−	0.934869i	$-0.615517\pi$
$373$	−264.825			−0.709987			−0.354993	+	0.934869i	$0.615517\pi$
$374$	−3.13565	+	1.81037i	−0.00838408	+	0.00484055i
$375$	235.804	−	72.2341i	0.628811	−	0.192624i
$376$	78.0291	−	135.150i	0.207524	−	0.359443i
$377$			543.824i			1.44250i
$378$	−6.29053	−	267.212i	−0.0166416	−	0.706911i
$379$	−190.773			−0.503359			−0.251679	−	0.967811i	$-0.580983\pi$
$379$	−190.773			−0.503359			−0.251679	+	0.967811i	$0.580983\pi$
$380$	−65.8455	−	38.0159i	−0.173278	−	0.100042i
$381$	−194.893	−	636.218i	−0.511531	−	1.66986i
$382$	−103.903	−	179.965i	−0.271997	−	0.471113i
$383$			599.457i			1.56516i	0.622548	+	0.782582i	$0.286098\pi$
$383$			599.457i			1.56516i	−0.622548	+	0.782582i	$0.713902\pi$
$384$	7.61693	−	33.0754i	0.0198358	−	0.0861339i
$385$	−52.0940	−	18.6993i	−0.135309	−	0.0485697i
$386$			358.902i			0.929797i
$387$	23.8735	+	11.6114i	0.0616886	+	0.0300037i
$388$	−76.0637	+	131.746i	−0.196040	+	0.339552i
$389$		−	100.950i		−	0.259512i	−0.991546	−	0.129756i	$-0.958581\pi$
$389$		−	100.950i		−	0.259512i	0.991546	−	0.129756i	$-0.0414193\pi$
$390$	−48.7005	+	52.2824i	−0.124873	+	0.134058i
$391$	−7.78743	+	13.4882i	−0.0199167	+	0.0344967i
$392$	−88.1403	+	106.955i	−0.224848	+	0.272843i
$393$	6.94190	−	2.12652i	0.0176639	−	0.00541099i
$394$	−224.951	+	389.627i	−0.570942	+	0.988900i
$395$	148.134	+	85.5250i	0.375022	+	0.216519i
$396$	−35.5389	+	73.0690i	−0.0897446	+	0.184518i
$397$	−154.534	−	267.661i	−0.389255	−	0.674210i	0.603094	−	0.797670i	$-0.293934\pi$
$397$	−154.534	−	267.661i	−0.389255	−	0.674210i	−0.992350	+	0.123460i	$0.960601\pi$
$398$	302.554	−	174.680i	0.760185	−	0.438893i
$399$	405.057	−	208.937i	1.01518	−	0.523652i
$400$	−43.8637	+	75.9741i	−0.109659	+	0.189935i
$401$		−	603.024i		−	1.50380i	−0.659276	−	0.751901i	$-0.729137\pi$
$401$		−	603.024i		−	1.50380i	0.659276	−	0.751901i	$-0.270863\pi$
$402$	1.15400	−	0.353505i	0.00287063	−	0.000879365i
$403$	−384.484			−0.954054
$404$	−337.607	+	194.917i	−0.835660	+	0.482468i
$405$	−131.666	−	52.8605i	−0.325101	−	0.130520i
$406$	527.015	+	189.174i	1.29807	+	0.465946i
$407$	−58.1717	+	33.5855i	−0.142928	+	0.0825196i
$408$	4.68984	+	1.08002i	0.0114947	+	0.00264712i
$409$	−219.715	−	380.558i	−0.537201	−	0.930459i	−0.999053	−	0.0435023i	$-0.986148\pi$
$409$	−219.715	−	380.558i	−0.537201	−	0.930459i	0.461853	−	0.886957i	$-0.347185\pi$
$410$	−69.4735	+	40.1105i	−0.169447	+	0.0978305i
$411$	−679.332	+	208.100i	−1.65287	+	0.506327i
$412$	−116.526	−	201.828i	−0.282829	−	0.489874i
$413$	−85.5695	+	15.4800i	−0.207190	+	0.0374817i
$414$	24.7639	+	348.639i	0.0598163	+	0.842123i
$415$	19.7960	+	34.2877i	0.0477012	+	0.0826209i
$416$		−	54.3884i		−	0.130741i
$417$	656.174	+	151.110i	1.57356	+	0.362375i
$418$	−138.551			−0.331462
$419$	−49.5525	−	28.6092i	−0.118264	−	0.0682796i	0.439701	−	0.898144i	$-0.355084\pi$
$419$	−49.5525	−	28.6092i	−0.118264	−	0.0682796i	−0.557965	+	0.829864i	$0.688418\pi$
$420$	33.7255	+	65.3821i	0.0802988	+	0.155672i
$421$	163.713	+	283.558i	0.388866	+	0.673536i	0.992297	−	0.123879i	$-0.0395336\pi$
$421$	163.713	+	283.558i	0.388866	+	0.673536i	−0.603431	+	0.797415i	$0.706200\pi$
$422$	−263.385	+	152.066i	−0.624136	+	0.360345i
$423$	495.326	−	35.1832i	1.17098	−	0.0831754i
$424$	78.9812	−	136.800i	0.186277	−	0.322640i
$425$	−10.7726	−	6.21954i	−0.0253472	−	0.0146342i
$426$	−36.9055	−	8.49897i	−0.0866327	−	0.0199506i
$427$	−424.860	+	359.724i	−0.994989	+	0.842445i
$428$	131.758	+	76.0704i	0.307845	+	0.177735i
$429$	−29.2196	+	126.882i	−0.0681110	+	0.295762i
$430$	−7.30692			−0.0169928
$431$	−90.4104	−	52.1985i	−0.209769	−	0.121110i	0.391435	−	0.920206i	$-0.371979\pi$
$431$	−90.4104	−	52.1985i	−0.209769	−	0.121110i	−0.601204	+	0.799096i	$0.705312\pi$
$432$	100.763	−	38.8698i	0.233247	−	0.0899763i
$433$	426.363			0.984673			0.492337	−	0.870405i	$-0.336143\pi$
$433$	426.363			0.984673			0.492337	+	0.870405i	$0.336143\pi$
$434$	−133.746	+	372.599i	−0.308171	+	0.858524i
$435$	202.589	−	217.489i	0.465721	−	0.499975i
$436$	318.414			0.730307
$437$	−516.141	+	297.994i	−1.18110	+	0.681909i
$438$	24.9971	+	23.2845i	0.0570709	+	0.0531610i
$439$	−142.303	+	246.476i	−0.324153	+	0.561449i	−0.981341	−	0.192278i	$-0.938413\pi$
$439$	−142.303	+	246.476i	−0.324153	+	0.561449i	0.657188	+	0.753727i	$0.271746\pi$
$440$		−	22.3641i		−	0.0508276i
$441$	−439.022	−	41.7216i	−0.995515	−	0.0946068i
$442$	7.71186			0.0174476
$443$	399.167	+	230.459i	0.901055	+	0.520224i	0.877542	−	0.479499i	$-0.159182\pi$
$443$	399.167	+	230.459i	0.901055	+	0.520224i	0.0235125	+	0.999724i	$0.492515\pi$
$444$	87.0048	+	20.0363i	0.195957	+	0.0451269i
$445$	47.6625	+	82.5539i	0.107107	+	0.185514i
$446$		−	115.813i		−	0.259671i
$447$	236.899	−	72.5696i	0.529976	−	0.162348i
$448$	−52.7072	−	18.9195i	−0.117650	−	0.0422310i
$449$			184.454i			0.410811i	0.978677	+	0.205406i	$0.0658514\pi$
$449$			184.454i			0.410811i	−0.978677	+	0.205406i	$0.934149\pi$
$450$	−278.445	+	19.7781i	−0.618767	+	0.0439512i
$451$	−73.0925	+	126.600i	−0.162068	+	0.280709i
$452$			204.147i			0.451652i
$453$	−187.805	−	613.077i	−0.414580	−	1.35337i
$454$	−16.6961	+	28.9184i	−0.0367755	+	0.0636970i
$455$	76.1766	+	89.9700i	0.167421	+	0.197736i
$456$	134.754	+	125.522i	0.295514	+	0.275268i
$457$	79.0457	−	136.911i	0.172967	−	0.299587i	−0.766489	−	0.642257i	$-0.777998\pi$
$457$	79.0457	−	136.911i	0.172967	−	0.299587i	0.939456	+	0.342670i	$0.111331\pi$
$458$	46.8154	+	27.0289i	0.102217	+	0.0590150i
$459$	5.51144	+	14.2874i	0.0120075	+	0.0311272i
$460$	−48.1005	−	83.3126i	−0.104566	−	0.181114i
$461$	−301.115	+	173.849i	−0.653179	+	0.377113i	−0.789673	−	0.613528i	$-0.789750\pi$
$461$	−301.115	+	173.849i	−0.653179	+	0.377113i	0.136494	+	0.990641i	$0.456416\pi$
$462$	112.796	+	72.4534i	0.244146	+	0.156826i
$463$	170.634	−	295.547i	0.368541	−	0.638331i	−0.620797	−	0.783971i	$-0.713191\pi$
$463$	170.634	−	295.547i	0.368541	−	0.638331i	0.989338	+	0.145640i	$0.0465242\pi$
$464$			226.249i			0.487606i
$465$	153.765	+	143.230i	0.330677	+	0.308022i
$466$	−194.299			−0.416951
$467$	222.692	−	128.571i	0.476856	−	0.275313i	−0.242249	−	0.970214i	$-0.577885\pi$
$467$	222.692	−	128.571i	0.476856	−	0.275313i	0.719105	+	0.694901i	$0.244552\pi$
$468$	143.369	−	96.9329i	0.306344	−	0.207122i
$469$	−0.354487	−	1.95952i	−0.000755836	−	0.00417808i
$470$	−118.366	+	68.3385i	−0.251842	+	0.145401i
$471$	330.835	−	355.168i	0.702409	−	0.754071i
$472$	−17.5683	−	30.4291i	−0.0372209	−	0.0644684i
$473$	−11.5313	+	6.65762i	−0.0243791	+	0.0140753i
$474$	−303.159	−	282.389i	−0.639575	−	0.595757i
$475$	−237.997	−	412.223i	−0.501046	−	0.867838i
$476$	2.68264	−	7.47349i	0.00563580	−	0.0157006i
$477$	501.370	−	35.6125i	1.05109	−	0.0746593i
$478$	284.172	+	492.200i	0.594502	+	1.02971i
$479$		−	198.939i		−	0.415322i	−0.978201	−	0.207661i	$-0.933415\pi$
$479$		−	198.939i		−	0.415322i	0.978201	−	0.207661i	$-0.0665851\pi$
$480$	−20.2611	+	21.7513i	−0.0422106	+	0.0453152i
$481$	143.069			0.297440
$482$	538.272	+	310.772i	1.11675	+	0.644755i
$483$	576.027	+	27.3093i	1.19260	+	0.0565410i
$484$	100.623	+	174.284i	0.207899	+	0.360092i
$485$	115.384	−	66.6172i	0.237906	−	0.137355i
$486$	282.045	+	196.338i	0.580339	+	0.403988i
$487$	−231.666	+	401.257i	−0.475700	+	0.823937i	−0.999613	−	0.0278350i	$-0.991139\pi$
$487$	−231.666	+	401.257i	−0.475700	+	0.823937i	0.523912	+	0.851772i	$0.324472\pi$
$488$	−194.802	−	112.469i	−0.399185	−	0.230469i
$489$	109.896	−	117.979i	0.224736	−	0.241265i
$490$	113.688	−	42.5251i	0.232016	−	0.0867859i
$491$	−824.496	−	476.023i	−1.67922	−	0.969497i	−0.962161	−	0.272482i	$-0.912156\pi$
$491$	−824.496	−	476.023i	−1.67922	−	0.969497i	−0.717056	−	0.697015i	$-0.754511\pi$
$492$	185.784	−	56.9115i	0.377610	−	0.115674i
$493$	−32.0805			−0.0650719
$494$	255.566	+	147.551i	0.517340	+	0.298687i
$495$	58.9524	−	39.8582i	0.119096	−	0.0805216i
$496$	−159.958			−0.322497
$497$	−21.1103	+	58.8107i	−0.0424755	+	0.118331i
$498$	−28.0879	−	91.6913i	−0.0564014	−	0.184119i
$499$	15.1998			0.0304606			0.0152303	−	0.999884i	$-0.495152\pi$
$499$	15.1998			0.0304606			0.0152303	+	0.999884i	$0.495152\pi$
$500$	142.386	−	82.2066i	0.284772	−	0.164413i
$501$	31.9516	−	138.745i	0.0637757	−	0.276937i
$502$	−80.6818	+	139.745i	−0.160721	+	0.278377i
$503$			247.471i			0.491989i	0.969271	+	0.245995i	$0.0791146\pi$
$503$			247.471i			0.491989i	−0.969271	+	0.245995i	$0.920885\pi$
$504$	−44.0645	−	172.657i	−0.0874297	−	0.342573i
$505$	341.420			0.676080
$506$	−151.819	−	87.6525i	−0.300037	−	0.173226i
$507$	−156.548	+	168.062i	−0.308773	+	0.331484i
$508$	−221.800	−	384.169i	−0.436614	−	0.756237i
$509$		−	200.767i		−	0.394435i	−0.980360	−	0.197217i	$-0.936810\pi$
$509$		−	200.767i		−	0.394435i	0.980360	−	0.197217i	$-0.0631905\pi$
$510$	−3.08417	−	2.87287i	−0.00604739	−	0.00563307i
$511$	43.0161	−	36.4212i	0.0841802	−	0.0712744i
$512$		−	22.6274i		−	0.0441942i
$513$	−90.7156	+	578.926i	−0.176834	+	1.12851i
$514$	−212.372	+	367.838i	−0.413174	+	0.715639i
$515$			204.108i			0.396326i
$516$	17.2469	+	3.97179i	0.0334242	+	0.00769726i
$517$	−124.532	+	215.695i	−0.240874	+	0.417206i
$518$	49.7677	−	138.646i	0.0960766	−	0.267657i
$519$	61.8783	−	268.697i	0.119226	−	0.517721i
$520$	−23.8169	+	41.2521i	−0.0458017	+	0.0793309i
$521$	248.569	+	143.512i	0.477101	+	0.275454i	0.719207	−	0.694795i	$-0.244505\pi$
$521$	248.569	+	143.512i	0.477101	+	0.275454i	−0.242107	+	0.970250i	$0.577838\pi$
$522$	−596.399	+	403.230i	−1.14253	+	0.772471i
$523$	−280.624	−	486.054i	−0.536565	−	0.929358i	−0.999086	−	0.0427498i	$-0.986388\pi$
$523$	−280.624	−	486.054i	−0.536565	−	0.929358i	0.462520	−	0.886609i	$-0.346945\pi$
$524$	4.19174	−	2.42010i	0.00799951	−	0.00461852i
$525$	−21.8109	+	460.052i	−0.0415447	+	0.876289i
$526$	298.067	−	516.267i	0.566667	−	0.981495i
$527$		−	22.6809i		−	0.0430377i
$528$	−12.1564	+	52.7872i	−0.0230234	+	0.0999757i
$529$	−225.088			−0.425498
$530$	−119.810	+	69.1724i	−0.226057	+	0.130514i
$531$	48.9011	−	100.542i	0.0920925	−	0.189345i
$532$	231.891	−	196.340i	0.435886	−	0.369059i
$533$	269.647	−	155.681i	0.505905	−	0.292084i
$534$	−67.6268	−	220.764i	−0.126642	−	0.413415i
$535$	−66.6231	−	115.395i	−0.124529	−	0.215691i
$536$	0.696819	−	0.402309i	0.00130004	−	0.000750576i
$537$	111.263	−	483.144i	0.207194	−	0.899710i
$538$	−364.027	−	630.514i	−0.676631	−	1.17196i
$539$	140.669	−	170.696i	0.260981	−	0.316690i
$540$	−93.4470	−	14.6428i	−0.173050	−	0.0271163i
$541$	−58.2830	−	100.949i	−0.107732	−	0.186597i	0.807119	−	0.590389i	$-0.201026\pi$
$541$	−58.2830	−	100.949i	−0.107732	−	0.186597i	−0.914851	+	0.403791i	$0.867692\pi$
$542$			682.769i			1.25972i
$543$	214.933	+	701.637i	0.395826	+	1.29215i
$544$	3.20840			0.00589779
$545$	−241.508	−	139.435i	−0.443134	−	0.255843i
$546$	−130.899	−	253.768i	−0.239741	−	0.464776i
$547$	22.9108	+	39.6827i	0.0418845	+	0.0725461i	0.886208	−	0.463288i	$-0.153331\pi$
$547$	22.9108	+	39.6827i	0.0418845	+	0.0725461i	−0.844323	+	0.535834i	$0.819997\pi$
$548$	−410.202	+	236.830i	−0.748544	+	0.432172i
$549$	−50.7121	−	713.950i	−0.0923718	−	1.30046i
$550$	70.0049	−	121.252i	0.127282	−	0.220458i
$551$	−1063.13	−	613.796i	−1.92945	−	1.11397i
$552$	68.2483	+	222.793i	0.123638	+	0.403610i
$553$	−521.689	+	441.708i	−0.943380	+	0.798749i
$554$	183.138	+	105.735i	0.330573	+	0.190857i
$555$	−57.2167	−	53.2967i	−0.103093	−	0.0960302i
$556$	448.899			0.807373
$557$	−772.053	−	445.745i	−1.38609	−	0.800260i	−0.393219	−	0.919445i	$-0.628639\pi$
$557$	−772.053	−	445.745i	−1.38609	−	0.800260i	−0.992872	+	0.119185i	$0.961972\pi$
$558$	−285.084	−	421.654i	−0.510902	−	0.755653i
$559$	28.3604			0.0507341
$560$	31.6921	+	37.4306i	0.0565929	+	0.0668404i
$561$	−7.48482	−	1.72368i	−0.0133419	−	0.00307251i
$562$	−27.9630			−0.0497562
$563$	290.660	−	167.813i	0.516270	−	0.298069i	−0.219137	−	0.975694i	$-0.570324\pi$
$563$	290.660	−	167.813i	0.516270	−	0.298069i	0.735407	+	0.677625i	$0.236991\pi$
$564$	316.531	−	96.9633i	0.561225	−	0.171921i
$565$	89.3967	−	154.840i	0.158224	−	0.274052i
$566$		−	777.752i		−	1.37412i
$567$	376.594	−	423.870i	0.664187	−	0.747567i
$568$	−25.2477			−0.0444501
$569$	818.812	+	472.741i	1.43904	+	0.830828i	0.997783	−	0.0665539i	$-0.0212004\pi$
$569$	818.812	+	472.741i	1.43904	+	0.830828i	0.441254	+	0.897382i	$0.354534\pi$
$570$	−47.2407	−	154.214i	−0.0828784	−	0.270552i
$571$	258.155	+	447.138i	0.452111	+	0.783079i	0.998517	−	0.0544416i	$-0.0173379\pi$
$571$	258.155	+	447.138i	0.452111	+	0.783079i	−0.546406	+	0.837520i	$0.684005\pi$
$572$			86.8019i			0.151752i
$573$	98.9277	−	429.579i	0.172649	−	0.749701i
$574$	−57.0697	−	315.468i	−0.0994246	−	0.549595i
$575$		−	602.263i		−	1.04741i
$576$	59.6465	−	40.3274i	0.103553	−	0.0700129i
$577$	−222.167	+	384.804i	−0.385038	+	0.666905i	−0.991774	−	0.127998i	$-0.959145\pi$
$577$	−222.167	+	384.804i	−0.385038	+	0.666905i	0.606737	+	0.794903i	$0.292478\pi$
$578$		−	408.253i		−	0.706320i
$579$	−518.931	+	557.098i	−0.896253	+	0.962173i
$580$	99.0755	−	171.604i	0.170820	−	0.295869i
$581$	−155.695	+	28.1660i	−0.267977	+	0.0484784i
$582$	−308.558	+	94.5210i	−0.530169	+	0.162407i
$583$	−126.051	+	218.327i	−0.216211	+	0.374489i
$584$	19.7233	+	11.3872i	0.0337727	+	0.0194987i
$585$	−151.189	+	10.7390i	−0.258442	+	0.0183573i
$586$	−92.9853	−	161.055i	−0.158678	−	0.274838i
$587$	333.063	−	192.294i	0.567398	−	0.327588i	−0.188711	−	0.982033i	$-0.560431\pi$
$587$	333.063	−	192.294i	0.567398	−	0.327588i	0.756110	+	0.654445i	$0.227098\pi$
$588$	−291.458	+	38.5774i	−0.495677	+	0.0656079i
$589$	433.954	−	751.630i	0.736763	−	1.27611i
$590$			30.7728i			0.0521573i
$591$	−912.531	+	279.537i	−1.54405	+	0.472989i
$592$	59.5214			0.100543
$593$	234.426	−	135.346i	0.395321	−	0.228239i	−0.289142	−	0.957286i	$-0.593370\pi$
$593$	234.426	−	135.346i	0.395321	−	0.228239i	0.684463	+	0.729047i	$0.260037\pi$
$594$	−160.814	+	62.0348i	−0.270730	+	0.104436i
$595$	−5.30738	+	4.49369i	−0.00891996	+	0.00755243i
$596$	143.047	−	82.5884i	0.240012	−	0.138571i
$597$	722.199	+	166.315i	1.20971	+	0.278585i
$598$	186.693	+	323.361i	0.312195	+	0.540738i
$599$	−251.273	+	145.073i	−0.419488	+	0.242191i	−0.694858	−	0.719147i	$-0.744533\pi$
$599$	−251.273	+	145.073i	−0.419488	+	0.242191i	0.275370	+	0.961338i	$0.411200\pi$
$600$	−177.936	+	54.5074i	−0.296561	+	0.0908457i
$601$	332.538	+	575.974i	0.553309	+	0.958359i	0.998033	+	0.0626911i	$0.0199683\pi$
$601$	332.538	+	575.974i	0.553309	+	0.958359i	−0.444724	+	0.895667i	$0.646698\pi$
$602$	9.86540	−	27.4838i	0.0163877	−	0.0456541i
$603$	2.30239	+	1.11982i	0.00381823	+	0.00185709i
$604$	−213.733	−	370.196i	−0.353862	−	0.612907i
$605$		−	176.253i		−	0.291328i
$606$	−805.871	−	185.584i	−1.32982	−	0.306244i
$607$	−275.607			−0.454048			−0.227024	−	0.973889i	$-0.572900\pi$
$607$	−275.607			−0.454048			−0.227024	+	0.973889i	$0.572900\pi$
$608$	106.324	+	61.3863i	0.174875	+	0.100964i
$609$	544.524	+	1055.64i	0.894128	+	1.73341i
$610$	98.5013	+	170.609i	0.161478	+	0.279687i
$611$	459.413	−	265.242i	0.751904	−	0.434112i
$612$	5.71812	+	8.45742i	0.00934334	+	0.0138193i
$613$	31.3289	−	54.2633i	0.0511075	−	0.0885209i	−0.839340	−	0.543607i	$-0.817058\pi$
$613$	31.3289	−	54.2633i	0.0511075	−	0.0885209i	0.890447	+	0.455086i	$0.150392\pi$
$614$	309.233	+	178.536i	0.503638	+	0.290775i
$615$	−165.834	−	38.1899i	−0.269649	−	0.0620974i
$616$	84.1189	+	30.1948i	0.136557	+	0.0490176i
$617$	446.057	+	257.531i	0.722945	+	0.417392i	0.815836	−	0.578284i	$-0.196277\pi$
$617$	446.057	+	257.531i	0.722945	+	0.417392i	−0.0928908	+	0.995676i	$0.529611\pi$
$618$	110.946	−	481.766i	0.179524	−	0.779557i
$619$	1078.54			1.74239			0.871194	−	0.490939i	$-0.163346\pi$
$619$	1078.54			1.74239			0.871194	+	0.490939i	$0.163346\pi$
$620$	121.324	+	70.0464i	0.195684	+	0.112978i
$621$	−465.652	+	576.973i	−0.749843	+	0.929104i
$622$	292.631			0.470467
$623$	−374.864	+	67.8148i	−0.601708	+	0.108852i
$624$	78.6393	−	84.4232i	0.126025	−	0.135294i
$625$	404.302			0.646883
$626$	416.341	−	240.375i	0.665082	−	0.383985i
$627$	−215.063	−	200.329i	−0.343003	−	0.319504i
$628$	161.794	−	280.235i	0.257634	−	0.446235i
$629$			8.43968i			0.0134176i
$630$	−42.1853	+	150.251i	−0.0669608	+	0.238494i
$631$	65.5284			0.103848			0.0519242	−	0.998651i	$-0.483465\pi$
$631$	65.5284			0.103848			0.0519242	+	0.998651i	$0.483465\pi$
$632$	−239.199	−	138.102i	−0.378480	−	0.218515i
$633$	−628.704	−	144.784i	−0.993213	−	0.228727i
$634$	194.253	+	336.457i	0.306393	+	0.530689i
$635$			388.508i			0.611824i
$636$	320.393	−	98.1465i	0.503763	−	0.154318i
$637$	−441.256	+	165.053i	−0.692710	+	0.259109i
$638$		−	361.086i		−	0.565966i
$639$	−44.9973	−	66.5535i	−0.0704183	−	0.104153i
$640$	−9.90864	+	17.1623i	−0.0154822	+	0.0268160i
$641$		−	791.031i		−	1.23406i	−0.786940	−	0.617029i	$-0.788336\pi$
$641$		−	791.031i		−	1.23406i	0.786940	−	0.617029i	$-0.211664\pi$
$642$	94.5294	+	308.586i	0.147242	+	0.480663i
$643$	−414.293	+	717.577i	−0.644313	+	1.11598i	0.340147	+	0.940372i	$0.389523\pi$
$643$	−414.293	+	717.577i	−0.644313	+	1.11598i	−0.984460	+	0.175610i	$0.943810\pi$
$644$	378.309	−	68.4380i	0.587436	−	0.106270i
$645$	−11.3420	−	10.5650i	−0.0175845	−	0.0163798i
$646$	−8.70411	+	15.0760i	−0.0134739	+	0.0233374i
$647$	−54.8043	−	31.6413i	−0.0847053	−	0.0489046i	0.457049	−	0.889441i	$-0.348906\pi$
$647$	−54.8043	−	31.6413i	−0.0847053	−	0.0489046i	−0.541754	+	0.840537i	$0.682240\pi$
$648$	212.608	+	85.3566i	0.328099	+	0.131723i
$649$	28.0383	+	48.5638i	0.0432023	+	0.0748286i
$650$	−258.257	+	149.105i	−0.397318	+	0.229392i
$651$	−746.340	+	384.978i	−1.14645	+	0.591365i
$652$	53.7443	−	93.0878i	0.0824298	−	0.142773i
$653$			651.734i			0.998062i	0.866584	+	0.499031i	$0.166311\pi$
$653$			651.734i			0.998062i	−0.866584	+	0.499031i	$0.833689\pi$
$654$	494.251	+	460.390i	0.755736	+	0.703959i
$655$	−4.23909			−0.00647189
$656$	112.182	−	64.7686i	0.171010	−	0.0987326i
$657$	5.13448	+	72.2858i	0.00781504	+	0.110024i
$658$	−97.2328	−	537.480i	−0.147770	−	0.816839i
$659$	−58.2921	+	33.6550i	−0.0884554	+	0.0510698i	−0.543575	−	0.839360i	$-0.682930\pi$
$659$	−58.2921	+	33.6550i	−0.0884554	+	0.0510698i	0.455120	+	0.890430i	$0.349596\pi$
$660$	32.3360	−	34.7143i	0.0489939	−	0.0525974i
$661$	243.282	+	421.376i	0.368051	+	0.637483i	0.989261	−	0.146161i	$-0.0466918\pi$
$661$	243.282	+	421.376i	0.368051	+	0.637483i	−0.621210	+	0.783644i	$0.713358\pi$
$662$	241.295	−	139.312i	0.364495	−	0.210441i
$663$	11.9706	+	11.1505i	0.0180552	+	0.0168182i
$664$	−31.9656	−	55.3661i	−0.0481410	−	0.0833827i
$665$	−261.861	+	47.3720i	−0.393776	+	0.0712361i
$666$	106.081	+	156.900i	0.159281	+	0.235585i
$667$	−776.620	−	1345.15i	−1.16435	−	2.01671i
$668$		−	94.9178i		−	0.142093i
$669$	167.453	−	179.769i	0.250303	−	0.268713i
$670$	−0.704690			−0.00105178
$671$	310.897	+	179.497i	0.463334	+	0.267506i
$672$	−54.4584	−	105.576i	−0.0810392	−	0.157107i
$673$	135.979	+	235.523i	0.202050	+	0.349960i	0.949189	−	0.314707i	$-0.101906\pi$
$673$	135.979	+	235.523i	0.202050	+	0.349960i	−0.747139	+	0.664668i	$0.768573\pi$
$674$	−398.215	+	229.910i	−0.590824	+	0.341112i
$675$	−460.808	−	371.900i	−0.682678	−	0.550963i
$676$	−76.5595	+	132.605i	−0.113254	+	0.196161i
$677$	−513.950	−	296.729i	−0.759158	−	0.438300i	0.0698351	−	0.997559i	$-0.477753\pi$
$677$	−513.950	−	296.729i	−0.759158	−	0.438300i	−0.828994	+	0.559258i	$0.811086\pi$
$678$	−295.173	+	316.883i	−0.435358	+	0.467379i
$679$	94.7837	+	523.942i	0.139593	+	0.771637i
$680$	−2.43348	−	1.40497i	−0.00357865	−	0.00206613i
$681$	−67.7288	+	20.7475i	−0.0994550	+	0.0304662i
$682$	255.288			0.374322
$683$	763.359	+	440.725i	1.11766	+	0.645279i	0.940801	−	0.338958i	$-0.110075\pi$
$683$	763.359	+	440.725i	1.11766	+	0.645279i	0.176854	+	0.984237i	$0.443408\pi$
$684$	27.6790	+	389.678i	0.0404663	+	0.569705i
$685$	414.836			0.605600
$686$	6.45604	+	485.032i	0.00941113	+	0.707044i
$687$	33.5876	+	109.645i	0.0488902	+	0.159599i
$688$	11.7989			0.0171495
$689$	465.019	−	268.479i	0.674919	−	0.389665i
$690$	45.7973	−	198.868i	0.0663729	−	0.288215i
$691$	−438.204	+	758.992i	−0.634159	+	1.09840i	0.352533	+	0.935799i	$0.385320\pi$
$691$	−438.204	+	758.992i	−0.634159	+	1.09840i	−0.986693	+	0.162597i	$0.948013\pi$
$692$		−	183.820i		−	0.265636i
$693$	70.3255	+	275.554i	0.101480	+	0.397625i
$694$	137.837			0.198612
$695$	−340.478	−	196.575i	−0.489896	−	0.282841i
$696$	−327.131	+	351.191i	−0.470015	+	0.504585i
$697$	9.18370	+	15.9066i	0.0131760	+	0.0228216i
$698$		−	302.124i		−	0.432842i
$699$	−301.597	−	280.935i	−0.431470	−	0.401909i
$700$	54.6589	+	302.142i	0.0780842	+	0.431631i
$701$			286.681i			0.408961i	0.978871	+	0.204480i	$0.0655504\pi$
$701$			286.681i			0.408961i	−0.978871	+	0.204480i	$0.934450\pi$
$702$	362.696	+	56.8331i	0.516661	+	0.0809589i
$703$	−161.477	+	279.686i	−0.229696	+	0.397846i
$704$			36.1126i			0.0512962i
$705$	−282.541	−	65.0663i	−0.400767	−	0.0922926i
$706$	−453.751	+	785.919i	−0.642706	+	1.11320i
$707$	−460.967	+	1284.19i	−0.652004	+	1.81640i
$708$	16.7270	−	72.6346i	0.0236257	−	0.102591i
$709$	−328.602	+	569.156i	−0.463473	+	0.802758i	−0.999131	−	0.0416765i	$-0.986730\pi$
$709$	−328.602	+	569.156i	−0.463473	+	0.802758i	0.535659	+	0.844435i	$0.320063\pi$
$710$	19.1496	+	11.0561i	0.0269713	+	0.0155719i
$711$	−62.2698	−	876.665i	−0.0875806	−	1.23300i
$712$	−76.9632	−	133.304i	−0.108094	−	0.187225i
$713$	951.017	−	549.070i	1.33383	−	0.770084i
$714$	14.9699	−	7.72178i	0.0209662	−	0.0108148i
$715$	38.0109	−	65.8368i	0.0531621	−	0.0920795i
$716$		−	330.527i		−	0.461629i
$717$	−270.565	+	1174.89i	−0.377357	+	1.63862i
$718$	430.848			0.600066
$719$	−404.412	+	233.488i	−0.562465	+	0.324739i	−0.754134	−	0.656720i	$-0.771943\pi$
$719$	−404.412	+	233.488i	−0.562465	+	0.324739i	0.191669	+	0.981460i	$0.438610\pi$
$720$	−62.8997	+	4.46779i	−0.0873607	+	0.00620526i
$721$	−767.717	−	275.575i	−1.06480	−	0.382212i
$722$	−134.765	+	77.8064i	−0.186655	+	0.107765i
$723$	386.182	+	1260.67i	0.534139	+	1.74366i
$724$	244.607	+	423.671i	0.337854	+	0.585181i
$725$	1074.32	−	620.258i	1.48182	−	0.855529i
$726$	−95.8050	+	416.019i	−0.131963	+	0.573029i
$727$	−21.8124	−	37.7802i	−0.0300033	−	0.0519673i	0.850634	−	0.525759i	$-0.176218\pi$
$727$	−21.8124	−	37.7802i	−0.0300033	−	0.0519673i	−0.880637	+	0.473791i	$0.842885\pi$
$728$	−123.006	−	145.279i	−0.168965	−	0.199560i
$729$	153.916	+	712.566i	0.211133	+	0.977457i
$730$	−9.97303	−	17.2738i	−0.0136617	−	0.0236627i
$731$			1.67299i			0.00228863i
$732$	−139.760	−	456.239i	−0.190929	−	0.623278i
$733$	1118.07			1.52533			0.762665	−	0.646794i	$-0.223891\pi$
$733$	1118.07			1.52533			0.762665	+	0.646794i	$0.223891\pi$
$734$	153.492	+	88.6189i	0.209118	+	0.120734i
$735$	237.956	+	98.3707i	0.323750	+	0.133838i
$736$	77.6705	+	134.529i	0.105531	+	0.182784i
$737$	−1.11210	+	0.642070i	−0.00150895	+	0.000871194i
$738$	370.667	+	180.283i	0.502259	+	0.244286i
$739$	414.623	−	718.148i	0.561060	−	0.971784i	−0.436345	−	0.899780i	$-0.643727\pi$
$739$	414.623	−	718.148i	0.561060	−	0.971784i	0.997404	−	0.0720041i	$-0.0229395\pi$
$740$	−45.1453	−	26.0647i	−0.0610072	−	0.0352225i
$741$	183.355	+	598.552i	0.247443	+	0.807763i
$742$	−98.4193	−	544.038i	−0.132641	−	0.733205i
$743$	−1010.16	−	583.214i	−1.35957	−	0.784945i	−0.370000	−	0.929032i	$-0.620642\pi$
$743$	−1010.16	−	583.214i	−1.35957	−	0.784945i	−0.989565	+	0.144086i	$0.953976\pi$
$744$	−248.292	−	231.281i	−0.333726	−	0.310862i
$745$	−144.663			−0.194179
$746$	−324.343	−	187.260i	−0.434776	−	0.251018i
$747$	88.9762	−	182.938i	0.119111	−	0.244897i
$748$	−5.12049			−0.00684557
$749$	523.988	−	94.7921i	0.699583	−	0.126558i
$750$	339.877	+	78.2702i	0.453169	+	0.104360i
$751$	1217.73			1.62147			0.810737	−	0.585411i	$-0.199067\pi$
$751$	1217.73			1.62147			0.810737	+	0.585411i	$0.199067\pi$
$752$	191.132	−	110.350i	0.254164	−	0.146742i
$753$	−327.292	+	100.260i	−0.434651	+	0.133147i
$754$	−384.542	+	666.046i	−0.510002	+	0.883350i
$755$			374.377i			0.495864i
$756$	181.243	−	331.715i	0.239740	−	0.438776i
$757$	212.121			0.280213			0.140106	−	0.990136i	$-0.455256\pi$
$757$	212.121			0.280213			0.140106	+	0.990136i	$0.455256\pi$
$758$	−233.648	−	134.897i	−0.308243	−	0.177964i
$759$	−108.922	−	355.569i	−0.143507	−	0.468470i
$760$	−53.7626	−	93.1196i	−0.0707403	−	0.122526i
$761$		−	1021.32i		−	1.34208i	−0.741423	−	0.671038i	$-0.765849\pi$
$761$		−	1021.32i		−	1.34208i	0.741423	−	0.671038i	$-0.234151\pi$
$762$	211.179	−	917.015i	0.277138	−	1.20343i
$763$	850.530	−	720.134i	1.11472	−	0.943819i
$764$		−	293.882i		−	0.384662i
$765$	−0.633498	−	8.91870i	−0.000828102	−	0.0116584i
$766$	−423.880	+	734.182i	−0.553369	+	0.958463i
$767$		−	119.439i		−	0.155722i
$768$	32.7166	−	35.1229i	0.0425998	−	0.0457330i
$769$	−19.1405	+	33.1524i	−0.0248902	+	0.0431110i	−0.878202	−	0.478290i	$-0.841257\pi$
$769$	−19.1405	+	33.1524i	−0.0248902	+	0.0431110i	0.853312	+	0.521401i	$0.174590\pi$
$770$	−50.5794	−	59.7379i	−0.0656875	−	0.0775817i
$771$	−861.501	+	263.905i	−1.11738	+	0.342289i
$772$	−253.782	+	439.563i	−0.328733	+	0.569382i
$773$	−329.696	−	190.350i	−0.426515	−	0.246249i	0.271346	−	0.962482i	$-0.412531\pi$
$773$	−329.696	−	190.350i	−0.426515	−	0.246249i	−0.697861	+	0.716233i	$0.745865\pi$
$774$	21.0284	+	31.1021i	0.0271685	+	0.0401837i
$775$	438.522	+	759.543i	0.565835	+	0.980056i
$776$	−186.317	+	107.570i	−0.240100	+	0.138622i
$777$	277.717	−	143.253i	0.357423	−	0.184366i
$778$	71.3824	−	123.638i	0.0917512	−	0.158918i
$779$			702.847i			0.902243i
$780$	−96.6150	+	29.5962i	−0.123865	+	0.0379438i
$781$	40.2944			0.0515933
$782$	−19.0752	+	11.0131i	−0.0243929	+	0.0140832i
$783$	−1508.77	−	236.419i	−1.92691	−	0.301940i
$784$	−183.578	+	68.6675i	−0.234155	+	0.0875862i
$785$	−245.432	+	141.700i	−0.312653	+	0.180510i
$786$	10.0057	+	2.30422i	0.0127299	+	0.00293158i
$787$	−427.833	−	741.028i	−0.543625	−	0.941586i	−0.998692	−	0.0511290i	$-0.983718\pi$
$787$	−427.833	−	741.028i	−0.543625	−	0.941586i	0.455067	−	0.890457i	$-0.349615\pi$
$788$	−551.015	+	318.129i	−0.699258	+	0.403717i
$789$	1209.13	−	370.394i	1.53248	−	0.469448i
$790$	120.951	+	209.493i	0.153102	+	0.265180i
$791$	461.705	+	545.306i	0.583697	+	0.689389i
$792$	−95.1936	+	64.3611i	−0.120194	+	0.0812640i
$793$	−382.313	−	662.186i	−0.482110	−	0.835039i
$794$		−	437.089i		−	0.550490i
$795$	−285.988	−	65.8602i	−0.359734	−	0.0828430i
$796$	494.068			0.620689
$797$	−27.2948	−	15.7587i	−0.0342469	−	0.0197725i	0.482779	−	0.875742i	$-0.339628\pi$
$797$	−27.2948	−	15.7587i	−0.0342469	−	0.0197725i	−0.517026	+	0.855970i	$0.672961\pi$
$798$	643.833	+	30.5240i	0.806808	+	0.0382506i
$799$	15.6468	+	27.1010i	0.0195829	+	0.0339187i
$800$	−107.444	+	62.0326i	−0.134305	+	0.0775408i
$801$	214.227	−	440.457i	0.267449	−	0.549883i
$802$	426.403	−	738.551i	0.531674	−	0.920886i
$803$	−31.4776	−	18.1736i	−0.0392000	−	0.0226322i
$804$	1.66332	+	0.383045i	0.00206880	+	0.000476424i
$805$	−316.906	−	113.755i	−0.393672	−	0.141310i
$806$	−470.894	−	271.871i	−0.584236	−	0.337309i
$807$	346.597	−	1505.04i	0.429488	−	1.86499i
$808$	−551.309			−0.682313
$809$	−366.440	−	211.564i	−0.452955	−	0.261514i	0.256123	−	0.966644i	$-0.417555\pi$
$809$	−366.440	−	211.564i	−0.452955	−	0.261514i	−0.709077	+	0.705131i	$0.750888\pi$
$810$	−123.879	−	157.843i	−0.152937	−	0.194867i
$811$	695.569			0.857668			0.428834	−	0.903383i	$-0.358925\pi$
$811$	695.569			0.857668			0.428834	+	0.903383i	$0.358925\pi$
$812$	511.692	+	604.346i	0.630163	+	0.744268i
$813$	−987.206	+	1059.81i	−1.21427	+	1.30358i
$814$	−94.9940			−0.116700
$815$	−81.5270	+	47.0697i	−0.100033	+	0.0577542i
$816$	4.98017	+	4.63897i	0.00610315	+	0.00568502i
$817$	−32.0094	+	55.4419i	−0.0391792	+	0.0678603i
$818$		−	621.448i		−	0.759717i
$819$	163.734	−	583.170i	0.199919	−	0.712052i
$820$	−113.450			−0.138353
$821$	79.1142	+	45.6766i	0.0963632	+	0.0556353i	0.547407	−	0.836866i	$-0.315615\pi$
$821$	79.1142	+	45.6766i	0.0963632	+	0.0556353i	−0.451044	+	0.892502i	$0.648948\pi$
$822$	−979.157	−	225.490i	−1.19119	−	0.274319i
$823$	328.999	+	569.843i	0.399755	+	0.692397i	0.993696	−	0.112113i	$-0.0357617\pi$
$823$	328.999	+	569.843i	0.399755	+	0.692397i	−0.593940	+	0.804509i	$0.702428\pi$
$824$		−	329.584i		−	0.399980i
$825$	283.980	−	86.9920i	0.344218	−	0.105445i
$826$	−115.747	−	41.5478i	−0.140129	−	0.0503000i
$827$		−	1364.30i		−	1.64969i	−0.565355	−	0.824847i	$-0.691261\pi$
$827$		−	1364.30i		−	1.64969i	0.565355	−	0.824847i	$-0.308739\pi$
$828$	−216.195	+	444.504i	−0.261106	+	0.536841i
$829$	−388.984	+	673.740i	−0.469221	+	0.812715i	−0.999381	−	0.0351831i	$-0.988799\pi$
$829$	−388.984	+	673.740i	−0.469221	+	0.812715i	0.530160	+	0.847898i	$0.322132\pi$
$830$			55.9915i			0.0674597i
$831$	131.392	+	428.920i	0.158113	+	0.516150i
$832$	38.4584	−	66.6119i	0.0462240	−	0.0800624i
$833$	−9.73654	−	26.0299i	−0.0116885	−	0.0312484i
$834$	696.795	+	649.057i	0.835485	+	0.778246i
$835$	−41.5649	+	71.9925i	−0.0497783	+	0.0862186i
$836$	−169.690	−	97.9704i	−0.202978	−	0.117189i
$837$	167.148	−	1066.70i	0.199699	−	1.27443i
$838$	−40.4595	−	70.0778i	−0.0482810	−	0.0836251i
$839$	−1355.78	+	782.761i	−1.61595	+	0.932969i	−0.627996	+	0.778216i	$0.716125\pi$
$839$	−1355.78	+	782.761i	−1.61595	+	0.932969i	−0.987953	+	0.154752i	$0.950542\pi$
$840$	−4.92701	+	103.924i	−0.00586548	+	0.123719i
$841$	1179.15	−	2042.35i	1.40208	−	2.42847i
$842$			463.049i			0.549940i
$843$	−43.4050	−	40.4313i	−0.0514887	−	0.0479612i
$844$	−430.106			−0.509605
$845$	116.136	−	67.0514i	0.137440	−	0.0793508i
$846$	631.527	+	307.158i	0.746486	+	0.363071i
$847$	662.946	+	237.967i	0.782699	+	0.280953i
$848$	193.464	−	111.696i	0.228141	−	0.131717i
$849$	1124.54	−	1207.25i	1.32455	−	1.42197i
$850$	−8.79576	−	15.2347i	−0.0103479	−	0.0179232i
$851$	−353.879	+	204.312i	−0.415839	+	0.240085i
$852$	−39.1902	−	36.5052i	−0.0459979	−	0.0428465i
$853$	−484.334	−	838.891i	−0.567801	−	0.983460i	−0.996783	−	0.0801471i	$-0.974461\pi$
$853$	−484.334	−	838.891i	−0.567801	−	0.983460i	0.428982	−	0.903313i	$-0.358872\pi$
$854$	−774.709	+	140.149i	−0.907153	+	0.164109i
$855$	149.648	−	307.681i	0.175027	−	0.359861i
$856$	107.580	+	186.334i	0.125677	+	0.217680i
$857$		−	1327.16i		−	1.54861i	−0.632814	−	0.774304i	$-0.718100\pi$
$857$		−	1327.16i		−	1.54861i	0.632814	−	0.774304i	$-0.281900\pi$
$858$	−125.506	+	134.737i	−0.146277	+	0.157036i
$859$	362.201			0.421654			0.210827	−	0.977523i	$-0.432384\pi$
$859$	362.201			0.421654			0.210827	+	0.977523i	$0.432384\pi$
$860$	−8.94912	−	5.16678i	−0.0104060	−	0.00600788i
$861$	367.545	−	572.194i	0.426881	−	0.664570i
$862$	−73.8198	−	127.860i	−0.0856378	−	0.148329i
$863$	−938.041	+	541.578i	−1.08695	+	0.627553i	−0.932764	−	0.360488i	$-0.882610\pi$
$863$	−938.041	+	541.578i	−1.08695	+	0.627553i	−0.154190	+	0.988041i	$0.549277\pi$
$864$	150.894	+	23.6445i	0.174646	+	0.0273663i
$865$	−80.4956	+	139.422i	−0.0930584	+	0.161182i
$866$	522.186	+	301.484i	0.602987	+	0.348134i
$867$	590.287	−	633.702i	0.680838	−	0.730914i
$868$	−427.272	+	361.766i	−0.492249	+	0.416782i
$869$	381.753	+	220.405i	0.439302	+	0.253631i
$870$	401.907	−	123.117i	0.461962	−	0.141513i
$871$	2.73511			0.00314020
$872$	389.975	+	225.152i	0.447220	+	0.258202i
$873$	−615.620	−	299.421i	−0.705177	−	0.342980i
$874$	−842.854			−0.964364
$875$	194.413	−	541.610i	0.222186	−	0.618983i
$876$	14.1504	+	46.1932i	0.0161534	+	0.0527319i
$877$	−1141.56			−1.30166			−0.650830	−	0.759223i	$-0.725579\pi$
$877$	−1141.56			−1.30166			−0.650830	+	0.759223i	$0.725579\pi$
$878$	−348.570	+	201.247i	−0.397004	+	0.229211i
$879$	88.5328	−	384.441i	0.100720	−	0.437361i
$880$	15.8138	−	27.3904i	0.0179703	−	0.0311254i
$881$			536.022i			0.608424i	0.952604	+	0.304212i	$0.0983931\pi$
$881$			536.022i			0.608424i	−0.952604	+	0.304212i	$0.901607\pi$
$882$	−508.188	−	361.534i	−0.576177	−	0.409902i
$883$	−413.964			−0.468816			−0.234408	−	0.972138i	$-0.575315\pi$
$883$	−413.964			−0.468816			−0.234408	+	0.972138i	$0.575315\pi$
$884$	9.44506	+	5.45311i	0.0106845	+	0.00616868i
$885$	−44.4940	+	47.7665i	−0.0502757	+	0.0539734i
$886$	325.919	+	564.508i	0.367854	+	0.637142i
$887$			115.461i			0.130171i	0.997880	+	0.0650853i	$0.0207320\pi$
$887$			115.461i			0.130171i	−0.997880	+	0.0650853i	$0.979268\pi$
$888$	92.3909	+	86.0611i	0.104044	+	0.0969156i
$889$	−1461.31	−	524.542i	−1.64377	−	0.590036i
$890$			134.810i			0.151472i
$891$	−339.315	−	136.226i	−0.380825	−	0.152891i
$892$	81.8923	−	141.842i	0.0918076	−	0.159015i
$893$			1197.48i			1.34096i
$894$	341.456	+	78.6338i	0.381941	+	0.0879572i
$895$	−144.739	+	250.695i	−0.161719	+	0.280106i
$896$	−51.1748	−	60.4412i	−0.0571148	−	0.0674567i
$897$	−177.753	+	771.867i	−0.198164	+	0.860498i
$898$	−130.429	+	225.909i	−0.145244	+	0.251570i
$899$	1958.87	+	1130.95i	2.17894	+	1.25801i
$900$	−355.010	−	172.667i	−0.394455	−	0.191853i
$901$	15.8377	+	27.4317i	0.0175779	+	0.0304458i
$902$	−179.039	+	103.368i	−0.198491	+	0.114599i
$903$	55.0517	−	28.3969i	0.0609654	−	0.0314472i
$904$	−144.354	+	250.028i	−0.159683	+	0.276579i
$905$		−	428.457i		−	0.473433i
$906$	203.498	−	883.661i	0.224612	−	0.975343i
$907$	−182.571			−0.201291			−0.100646	−	0.994922i	$-0.532091\pi$
$907$	−182.571			−0.201291			−0.100646	+	0.994922i	$0.532091\pi$
$908$	−40.8968	+	23.6118i	−0.0450406	+	0.0260042i
$909$	−982.563	−	1453.27i	−1.08093	−	1.59875i
$910$	29.6784	+	164.055i	0.0326137	+	0.180281i
$911$	−781.868	+	451.411i	−0.858252	+	0.495512i	−0.863427	−	0.504475i	$-0.831686\pi$
$911$	−781.868	+	451.411i	−0.858252	+	0.495512i	0.00517457	+	0.999987i	$0.498353\pi$
$912$	76.2820	+	249.018i	0.0836426	+	0.273046i
$913$	51.0160	+	88.3624i	0.0558774	+	0.0967824i
$914$	193.622	−	111.788i	0.211840	−	0.122306i
$915$	−93.7847	+	407.246i	−0.102497	+	0.445078i
$916$	38.2246	+	66.2070i	0.0417299	+	0.0722783i
$917$	5.72338	−	15.9446i	0.00624142	−	0.0173878i
$918$	−3.35261	+	21.3956i	−0.00365209	+	0.0233068i
$919$	−590.898	−	1023.47i	−0.642979	−	1.11367i	−0.984764	−	0.173895i	$-0.944365\pi$
$919$	−590.898	−	1023.47i	−0.642979	−	1.11367i	0.341785	−	0.939778i	$-0.388969\pi$
$920$		−	136.049i		−	0.147879i
$921$	221.859	+	724.245i	0.240889	+	0.786368i
$922$	−491.719			−0.533318
$923$	−74.3255	−	42.9119i	−0.0805260	−	0.0464917i
$924$	86.9136	+	168.496i	0.0940623	+	0.182354i
$925$	−163.177	−	282.630i	−0.176407	−	0.305546i
$926$	417.967	−	241.313i	0.451368	−	0.260598i
$927$	868.792	−	587.396i	0.937208	−	0.633653i
$928$	−159.982	+	277.098i	−0.172395	+	0.298597i
$929$	760.239	+	438.924i	0.818341	+	0.472469i	0.849844	−	0.527034i	$-0.176696\pi$
$929$	760.239	+	438.924i	0.818341	+	0.472469i	−0.0315030	+	0.999504i	$0.510029\pi$
$930$	87.0435	+	284.148i	0.0935952	+	0.305536i
$931$	175.368	−	1048.90i	0.188366	−	1.12664i
$932$	−237.967	−	137.390i	−0.255330	−	0.147415i
$933$	454.230	+	423.110i	0.486849	+	0.453494i
$934$	363.654			0.389351
$935$	3.88375	+	2.24228i	0.00415374	+	0.00239816i
$936$	244.133	−	17.3408i	0.260825	−	0.0185265i
$937$	−618.122			−0.659682			−0.329841	−	0.944037i	$-0.606995\pi$
$937$	−618.122			−0.659682			−0.329841	+	0.944037i	$0.606995\pi$
$938$	0.951433	−	2.65057i	0.00101432	−	0.00282577i
$939$	993.811	+	228.865i	1.05837	+	0.243732i
$940$	−193.291			−0.205628
$941$	831.225	−	479.908i	0.883342	−	0.509998i	0.0115830	−	0.999933i	$-0.496313\pi$
$941$	831.225	−	479.908i	0.883342	−	0.509998i	0.871759	+	0.489935i	$0.162980\pi$
$942$	656.330	−	201.054i	0.696741	−	0.213433i
$943$	−444.647	+	770.151i	−0.471524	+	0.816704i
$944$		−	49.6905i		−	0.0526383i
$945$	−282.727	+	172.229i	−0.299182	+	0.182253i
$946$	−18.8306			−0.0199055
$947$	646.600	+	373.315i	0.682788	+	0.394208i	0.800905	−	0.598792i	$-0.204352\pi$
$947$	646.600	+	373.315i	0.682788	+	0.394208i	−0.118117	+	0.993000i	$0.537686\pi$
$948$	−171.613	−	560.220i	−0.181026	−	0.590949i
$949$	38.7083	+	67.0448i	0.0407885	+	0.0706478i
$950$		−	673.157i		−	0.708587i
$951$	−184.952	+	803.126i	−0.194481	+	0.844507i
$952$	8.57010	−	7.25620i	0.00900221	−	0.00762206i
$953$			1477.27i			1.55013i	0.631881	+	0.775065i	$0.282283\pi$
$953$			1477.27i			1.55013i	−0.631881	+	0.775065i	$0.717717\pi$
$954$	639.233	+	310.906i	0.670055	+	0.325897i
$955$	−128.692	+	222.901i	−0.134756	+	0.233404i
$956$			803.760i			0.840753i
$957$	522.089	−	560.488i	0.545547	−	0.585672i
$958$	140.671	−	243.650i	0.146839	−	0.254332i
$959$	−560.088	+	1560.33i	−0.584033	+	1.62704i
$960$	−40.1951	+	12.3130i	−0.0418699	+	0.0128261i
$961$	−319.083	+	552.668i	−0.332032	+	0.575097i
$962$	175.222	+	101.165i	0.182144	+	0.105161i
$963$	−299.448	+	615.674i	−0.310953	+	0.639329i
$964$	439.498	+	761.232i	0.455910	+	0.789660i
$965$	384.973	−	222.264i	0.398936	−	0.230326i
$966$	686.176	+	440.760i	0.710327	+	0.456273i
$967$	81.0172	−	140.326i	0.0837820	−	0.145115i	−0.821090	−	0.570799i	$-0.806633\pi$
$967$	81.0172	−	140.326i	0.0837820	−	0.145115i	0.904872	+	0.425685i	$0.139967\pi$
$968$			284.605i			0.294014i
$969$	−35.3089	+	10.8162i	−0.0364385	+	0.0111622i
$970$	188.422			0.194249
$971$	1063.88	−	614.232i	1.09565	−	0.632577i	0.160579	−	0.987023i	$-0.448664\pi$
$971$	1063.88	−	614.232i	1.09565	−	0.632577i	0.935076	+	0.354446i	$0.115331\pi$
$972$	206.601	+	439.900i	0.212552	+	0.452572i
$973$	1199.08	−	1015.24i	1.23235	−	1.04342i
$974$	−567.464	+	327.625i	−0.582612	+	0.336371i
$975$	−616.462	−	141.965i	−0.632269	−	0.145605i
$976$	−159.055	−	275.492i	−0.162966	−	0.282266i
$977$	−902.636	+	521.137i	−0.923885	+	0.533405i	−0.884872	−	0.465833i	$-0.845755\pi$
$977$	−902.636	+	521.137i	−0.923885	+	0.533405i	−0.0390127	+	0.999239i	$0.512421\pi$
$978$	218.018	−	66.7856i	0.222922	−	0.0682879i
$979$	122.831	+	212.749i	0.125465	+	0.217312i
$980$	169.308	+	28.3070i	0.172764	+	0.0288847i
$981$	101.521	+	1429.26i	0.103487	+	1.45694i
$982$	−673.198	−	1166.01i	−0.685538	−	1.18739i
$983$		−	784.219i		−	0.797782i	−0.916998	−	0.398891i	$-0.869395\pi$
$983$		−	784.219i		−	0.797782i	0.916998	−	0.398891i	$-0.130605\pi$
$984$	267.781	+	61.6673i	0.272135	+	0.0626700i
$985$	557.240			0.565726
$986$	−39.2904	−	22.6843i	−0.0398482	−	0.0230064i
$987$	626.206	−	974.880i	0.634454	−	0.987720i
$988$	208.669	+	361.425i	0.211203	+	0.365815i
$989$	−70.1492	+	40.5006i	−0.0709294	+	0.0409511i
$990$	100.386	−	7.13043i	0.101400	−	0.00720245i
$991$	−81.5488	+	141.247i	−0.0822894	+	0.142529i	−0.904233	−	0.427040i	$-0.859557\pi$
$991$	−81.5488	+	141.247i	−0.0822894	+	0.142529i	0.821944	+	0.569569i	$0.192890\pi$
$992$	−195.908	−	113.108i	−0.197488	−	0.114020i
$993$	575.975	+	132.641i	0.580035	+	0.133576i
$994$	−67.4402	+	57.1009i	−0.0678473	+	0.0574455i
$995$	−374.737	−	216.354i	−0.376620	−	0.217442i
$996$	30.4350	−	132.160i	0.0305573	−	0.132690i
$997$	−226.432			−0.227113			−0.113557	−	0.993532i	$-0.536224\pi$
$997$	−226.432			−0.227113			−0.113557	+	0.993532i	$0.536224\pi$
$998$	18.6159	+	10.7479i	0.0186532	+	0.0107694i
$999$	−62.1969	+	396.926i	−0.0622592	+	0.397323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.i.a.95.12	yes	32
3.2	odd	2		378.3.i.a.179.5		32
7.2	even	3		126.3.r.a.23.1	yes	32
9.2	odd	6		126.3.r.a.11.9	yes	32
9.7	even	3		378.3.r.a.305.5		32
21.2	odd	6		378.3.r.a.233.13		32
63.2	odd	6	inner	126.3.i.a.65.12	✓	32
63.16	even	3		378.3.i.a.359.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.12	✓	32	63.2	odd	6	inner
126.3.i.a.95.12	yes	32	1.1	even	1	trivial
126.3.r.a.11.9	yes	32	9.2	odd	6
126.3.r.a.23.1	yes	32	7.2	even	3
378.3.i.a.179.5		32	3.2	odd	2
378.3.i.a.359.4		32	63.16	even	3
378.3.r.a.233.13		32	21.2	odd	6
378.3.r.a.305.5		32	9.7	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.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(0.878690 + 2.86843i) q^{3} +(1.00000 + 1.73205i) q^{4} -1.75162i q^{5} +(-0.952117 + 4.13443i) q^{6} +(6.58841 + 2.36493i) q^{7} +2.82843i q^{8} +(-7.45581 + 5.04093i) q^{9} +(1.23858 - 2.14528i) q^{10} -4.51407i q^{11} +(-4.08958 + 4.39037i) q^{12} +(-4.80730 + 8.32649i) q^{13} +(6.39685 + 7.55515i) q^{14} +(5.02439 - 1.53913i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-0.491183 - 0.283585i) q^{17} +(-12.6959 + 0.901796i) q^{18} +(-10.8517 - 18.7956i) q^{19} +(3.03389 - 1.75162i) q^{20} +(-0.994487 + 20.9764i) q^{21} +(3.19193 - 5.52858i) q^{22} -27.4607i q^{23} +(-8.11315 + 2.48531i) q^{24} +21.9318 q^{25} +(-11.7754 + 6.79855i) q^{26} +(-21.0109 - 16.9571i) q^{27} +(2.49222 + 13.7764i) q^{28} +(48.9844 - 28.2812i) q^{29} +(7.24193 + 1.66774i) q^{30} +(19.9948 + 34.6320i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(12.9483 - 3.96647i) q^{33} +(-0.401050 - 0.694638i) q^{34} +(4.14246 - 11.5404i) q^{35} +(-16.1869 - 7.87291i) q^{36} +(-7.44017 - 12.8868i) q^{37} -30.6932i q^{38} +(-28.1081 - 6.47301i) q^{39} +4.95432 q^{40} +(-28.0456 - 16.1921i) q^{41} +(-16.0506 + 24.9876i) q^{42} +(-1.47486 - 2.55453i) q^{43} +(7.81860 - 4.51407i) q^{44} +(8.82977 + 13.0597i) q^{45} +(19.4176 - 33.6323i) q^{46} +(-47.7829 - 27.5875i) q^{47} +(-11.6939 - 2.69299i) q^{48} +(37.8142 + 31.1623i) q^{49} +(26.8609 + 15.5082i) q^{50} +(0.381846 - 1.65811i) q^{51} -19.2292 q^{52} +(-48.3659 - 27.9241i) q^{53} +(-13.7425 - 35.6250i) q^{54} -7.90692 q^{55} +(-6.68904 + 18.6348i) q^{56} +(44.3788 - 47.6428i) q^{57} +79.9912 q^{58} +(-10.7583 + 6.21132i) q^{59} +(7.69024 + 7.16337i) q^{60} +(-39.7638 + 68.8730i) q^{61} +56.5538i q^{62} +(-61.0433 + 15.5792i) q^{63} -8.00000 q^{64} +(14.5848 + 8.42054i) q^{65} +(18.6631 + 4.29792i) q^{66} +(-0.142238 - 0.246363i) q^{67} -1.13434i q^{68} +(78.7691 - 24.1294i) q^{69} +(13.2337 - 11.2048i) q^{70} +8.92640i q^{71} +(-14.2579 - 21.0882i) q^{72} +(4.02599 - 6.97323i) q^{73} -21.0440i q^{74} +(19.2713 + 62.9100i) q^{75} +(21.7033 - 37.5913i) q^{76} +(10.6755 - 29.7405i) q^{77} +(-29.8481 - 27.8032i) q^{78} +(-48.8263 + 84.5697i) q^{79} +(6.06778 + 3.50323i) q^{80} +(30.1781 - 75.1683i) q^{81} +(-22.8992 - 39.6625i) q^{82} +(-19.5749 + 11.3016i) q^{83} +(-37.3267 + 19.2539i) q^{84} +(-0.496732 + 0.860365i) q^{85} -4.17153i q^{86} +(124.165 + 115.658i) q^{87} +12.7677 q^{88} +(-47.1301 + 27.2106i) q^{89} +(1.57960 + 22.2384i) q^{90} +(-51.3640 + 43.4893i) q^{91} +(47.5633 - 27.4607i) q^{92} +(-81.7703 + 87.7845i) q^{93} +(-39.0146 - 67.5752i) q^{94} +(-32.9227 + 19.0080i) q^{95} +(-12.4178 - 11.5671i) q^{96} +(38.0319 + 65.8731i) q^{97} +(24.2776 + 64.9045i) q^{98} +(22.7551 + 33.6560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 8 q^{6} + 2 q^{7} + 4 q^{9} + 10 q^{13} + 36 q^{14} + 10 q^{15} - 64 q^{16} + 54 q^{17} + 24 q^{18} + 28 q^{19} + 16 q^{21} + 8 q^{24} - 160 q^{25} + 72 q^{26} - 126 q^{27} - 4 q^{28}+ \cdots + 394 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 + 8 * q^6 + 2 * q^7 + 4 * q^9 + 10 * q^13 + 36 * q^14 + 10 * q^15 - 64 * q^16 + 54 * q^17 + 24 * q^18 + 28 * q^19 + 16 * q^21 + 8 * q^24 - 160 * q^25 + 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 - 80 * q^30 - 8 * q^31 - 106 * q^33 + 90 * q^35 + 40 * q^36 + 22 * q^37 - 170 * q^39 + 72 * q^41 + 72 * q^42 + 16 * q^43 - 72 * q^44 - 250 * q^45 - 12 * q^46 - 108 * q^47 + 74 * q^49 - 288 * q^50 + 122 * q^51 + 40 * q^52 + 72 * q^53 + 8 * q^54 - 24 * q^55 - 282 * q^57 + 48 * q^58 - 90 * q^59 + 52 * q^60 - 62 * q^61 - 438 * q^63 - 256 * q^64 + 378 * q^65 + 224 * q^66 + 70 * q^67 + 218 * q^69 - 108 * q^70 + 48 * q^72 + 196 * q^73 + 166 * q^75 - 56 * q^76 + 630 * q^77 + 32 * q^78 - 38 * q^79 + 400 * q^81 + 184 * q^84 + 60 * q^85 - 98 * q^87 + 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 - 182 * q^93 + 168 * q^94 - 72 * q^95 - 16 * q^96 - 38 * q^97 - 288 * q^98 + 394 * q^99

Introduction

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