LMFDB - Embedded newform 126.3.r.a.11.9

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			11.9
Character	$\chi$	$=$	126.11
Dual form			126.3.r.a.23.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41421i q^{2} +(-2.92348 + 0.673248i) q^{3} -2.00000 q^{4} +(-1.51694 - 0.875808i) q^{5} +(-0.952117 - 4.13443i) q^{6} +(-1.24611 - 6.88819i) q^{7} -2.82843i q^{8} +(8.09347 - 3.93646i) q^{9} +(1.23858 - 2.14528i) q^{10} +(3.90930 - 2.25703i) q^{11} +(5.84696 - 1.34650i) q^{12} +(-4.80730 - 8.32649i) q^{13} +(9.74138 - 1.76226i) q^{14} +(5.02439 + 1.53913i) q^{15} +4.00000 q^{16} +(0.491183 + 0.283585i) q^{17} +(5.56699 + 11.4459i) q^{18} +(-10.8517 - 18.7956i) q^{19} +(3.03389 + 1.75162i) q^{20} +(8.28044 + 19.2986i) q^{21} +(3.19193 + 5.52858i) q^{22} +(-23.7816 - 13.7303i) q^{23} +(1.90423 + 8.26885i) q^{24} +(-10.9659 - 18.9935i) 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} +(-2.17666 + 7.10556i) q^{30} -39.9896 q^{31} +5.65685i q^{32} +(-9.90921 + 9.23032i) 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} +(26.5810 - 15.3466i) q^{38} +(19.6598 + 21.1058i) q^{39} +(-2.47716 + 4.29057i) q^{40} +(-28.0456 + 16.1921i) q^{41} +(-27.2923 + 11.7103i) q^{42} +(-1.47486 + 2.55453i) q^{43} +(-7.81860 + 4.51407i) q^{44} +(-15.7249 - 1.11695i) q^{45} +(19.4176 - 33.6323i) q^{46} -55.1749i q^{47} +(-11.6939 + 2.69299i) q^{48} +(-45.8944 + 17.1669i) q^{49} +(26.8609 - 15.5082i) q^{50} +(-1.62689 - 0.498366i) q^{51} +(9.61460 + 16.6530i) q^{52} +(48.3659 + 27.9241i) q^{53} +(-23.9809 - 29.7139i) q^{54} -7.90692 q^{55} +(-19.4828 + 3.52453i) q^{56} +(44.3788 + 47.6428i) q^{57} +(-39.9956 + 69.2744i) q^{58} +12.4226i q^{59} +(-10.0488 - 3.07826i) q^{60} +79.5276 q^{61} -56.5538i q^{62} +(-37.2004 - 50.8442i) q^{63} -8.00000 q^{64} +16.8411i q^{65} +(-13.0537 - 14.0137i) q^{66} +0.284475 q^{67} +(-0.982367 - 0.567170i) q^{68} +(78.7691 + 24.1294i) q^{69} +(-16.3205 - 5.85832i) q^{70} -8.92640i q^{71} +(-11.1340 - 22.8918i) q^{72} +(4.02599 - 6.97323i) q^{73} +(18.2246 - 10.5220i) q^{74} +(44.8460 + 48.1444i) q^{75} +(21.7033 + 37.5913i) q^{76} +(-20.4183 - 24.1155i) q^{77} +(-29.8481 + 27.8032i) q^{78} +97.6526 q^{79} +(-6.06778 - 3.50323i) q^{80} +(50.0086 - 63.7192i) q^{81} +(-22.8992 - 39.6625i) q^{82} +(-19.5749 - 11.3016i) q^{83} +(-16.5609 - 38.5971i) q^{84} +(-0.496732 - 0.860365i) q^{85} +(-3.61265 - 2.08577i) q^{86} +(-162.245 - 49.7008i) q^{87} +(-6.38386 - 11.0572i) 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} +(116.909 - 26.9229i) q^{93} +78.0291 q^{94} +38.0159i q^{95} +(-3.80847 - 16.5377i) 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 - 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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−2.92348	+	0.673248i	−0.974493	+	0.224416i
$3$	−2.92348	+	0.673248i	−0.974493	+	0.224416i
$4$	−2.00000			−0.500000
$5$	−1.51694	−	0.875808i	−0.303389	−	0.175162i	0.340575	−	0.940217i	$-0.389378\pi$
$5$	−1.51694	−	0.875808i	−0.303389	−	0.175162i	−0.643964	+	0.765056i	$0.722711\pi$
$6$	−0.952117	−	4.13443i	−0.158686	−	0.689071i
$7$	−1.24611	−	6.88819i	−0.178016	−	0.984028i
$7$	−1.24611	−	6.88819i	−0.178016	−	0.984028i
$8$		−	2.82843i		−	0.353553i
$9$	8.09347	−	3.93646i	0.899275	−	0.437384i
$10$	1.23858	−	2.14528i	0.123858	−	0.214528i
$11$	3.90930	−	2.25703i	0.355391	−	0.205185i	−0.311666	−	0.950192i	$-0.600887\pi$
$11$	3.90930	−	2.25703i	0.355391	−	0.205185i	0.667057	+	0.745007i	$0.267554\pi$
$12$	5.84696	−	1.34650i	0.487247	−	0.112208i
$13$	−4.80730	−	8.32649i	−0.369792	−	0.640499i	0.619741	−	0.784807i	$-0.287238\pi$
$13$	−4.80730	−	8.32649i	−0.369792	−	0.640499i	−0.989533	+	0.144308i	$0.953904\pi$
$14$	9.74138	−	1.76226i	0.695813	−	0.125876i
$15$	5.02439	+	1.53913i	0.334959	+	0.102609i
$16$	4.00000			0.250000
$17$	0.491183	+	0.283585i	0.0288931	+	0.0166815i	0.514377	−	0.857564i	$-0.328023\pi$
$17$	0.491183	+	0.283585i	0.0288931	+	0.0166815i	−0.485484	+	0.874246i	$0.661357\pi$
$18$	5.56699	+	11.4459i	0.309277	+	0.635883i
$19$	−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
$21$	8.28044	+	19.2986i	0.394307	+	0.918979i
$22$	3.19193	+	5.52858i	0.145088	+	0.251299i
$23$	−23.7816	−	13.7303i	−1.03398	−	0.596971i	−0.115861	−	0.993265i	$-0.536963\pi$
$23$	−23.7816	−	13.7303i	−1.03398	−	0.596971i	−0.918123	+	0.396294i	$0.870296\pi$
$24$	1.90423	+	8.26885i	0.0793431	+	0.344535i
$25$	−10.9659	−	18.9935i	−0.438637	−	0.759741i
$26$	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	0.955193	+	0.295982i	$0.0956469\pi$
$29$	48.9844	+	28.2812i	1.68912	+	0.975213i	0.733925	+	0.679231i	$0.237686\pi$
$30$	−2.17666	+	7.10556i	−0.0725552	+	0.236852i
$31$	−39.9896			−1.28999			−0.644993	−	0.764188i	$-0.723140\pi$
$31$	−39.9896			−1.28999			−0.644993	+	0.764188i	$0.723140\pi$
$32$			5.65685i			0.176777i
$33$	−9.90921	+	9.23032i	−0.300279	+	0.279707i
$34$	−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	$0.897780\pi$
$38$	26.5810	−	15.3466i	0.699501	−	0.403857i
$39$	19.6598	+	21.1058i	0.504098	+	0.541175i
$40$	−2.47716	+	4.29057i	−0.0619290	+	0.107264i
$41$	−28.0456	+	16.1921i	−0.684040	+	0.394930i	−0.801375	−	0.598162i	$-0.795898\pi$
$41$	−28.0456	+	16.1921i	−0.684040	+	0.394930i	0.117336	+	0.993092i	$0.462565\pi$
$42$	−27.2923	+	11.7103i	−0.649816	+	0.278817i
$43$	−1.47486	+	2.55453i	−0.0342991	+	0.0594077i	−0.882665	−	0.470002i	$-0.844253\pi$
$43$	−1.47486	+	2.55453i	−0.0342991	+	0.0594077i	0.848366	+	0.529410i	$0.177587\pi$
$44$	−7.81860	+	4.51407i	−0.177695	+	0.102592i
$45$	−15.7249	−	1.11695i	−0.349443	−	0.0248210i
$46$	19.4176	−	33.6323i	0.422122	−	0.731137i
$47$		−	55.1749i		−	1.17393i	−0.809611	−	0.586967i	$-0.800322\pi$
$47$		−	55.1749i		−	1.17393i	0.809611	−	0.586967i	$-0.199678\pi$
$48$	−11.6939	+	2.69299i	−0.243623	+	0.0561040i
$49$	−45.8944	+	17.1669i	−0.936621	+	0.350345i
$50$	26.8609	−	15.5082i	0.537218	−	0.310163i
$51$	−1.62689	−	0.498366i	−0.0318998	−	0.00977189i
$52$	9.61460	+	16.6530i	0.184896	+	0.320249i
$53$	48.3659	+	27.9241i	0.912565	+	0.526870i	0.881256	−	0.472640i	$-0.156699\pi$
$53$	48.3659	+	27.9241i	0.912565	+	0.526870i	0.0313093	+	0.999510i	$0.490032\pi$
$54$	−23.9809	−	29.7139i	−0.444091	−	0.550257i
$55$	−7.90692			−0.143762
$56$	−19.4828	+	3.52453i	−0.347906	+	0.0629380i
$57$	44.3788	+	47.6428i	0.778575	+	0.835839i
$58$	−39.9956	+	69.2744i	−0.689580	+	1.19439i
$59$			12.4226i			0.210553i	0.994443	+	0.105277i	$0.0335728\pi$
$59$			12.4226i			0.210553i	−0.994443	+	0.105277i	$0.966427\pi$
$60$	−10.0488	−	3.07826i	−0.167480	−	0.0513043i
$61$	79.5276			1.30373			0.651866	−	0.758334i	$-0.273986\pi$
$61$	79.5276			1.30373			0.651866	+	0.758334i	$0.273986\pi$
$62$		−	56.5538i		−	0.912158i
$63$	−37.2004	−	50.8442i	−0.590483	−	0.807050i
$64$	−8.00000			−0.125000
$65$			16.8411i			0.259094i
$66$	−13.0537	−	14.0137i	−0.197783	−	0.212329i
$67$	0.284475			0.00424590			0.00212295	−	0.999998i	$-0.499324\pi$
$67$	0.284475			0.00424590			0.00212295	+	0.999998i	$0.499324\pi$
$68$	−0.982367	−	0.567170i	−0.0144466	−	0.00834073i
$69$	78.7691	+	24.1294i	1.14158	+	0.349702i
$70$	−16.3205	−	5.85832i	−0.233150	−	0.0836903i
$71$		−	8.92640i		−	0.125724i	−0.998022	−	0.0628619i	$-0.979977\pi$
$71$		−	8.92640i		−	0.125724i	0.998022	−	0.0628619i	$-0.0200228\pi$
$72$	−11.1340	−	22.8918i	−0.154639	−	0.317942i
$73$	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	$0.149103\pi$
$74$	18.2246	−	10.5220i	0.246279	−	0.142189i
$75$	44.8460	+	48.1444i	0.597947	+	0.641926i
$76$	21.7033	+	37.5913i	0.285570	+	0.494622i
$77$	−20.4183	−	24.1155i	−0.265173	−	0.313188i
$78$	−29.8481	+	27.8032i	−0.382668	+	0.356451i
$79$	97.6526			1.23611			0.618055	−	0.786135i	$-0.287921\pi$
$79$	97.6526			1.23611			0.618055	+	0.786135i	$0.287921\pi$
$80$	−6.06778	−	3.50323i	−0.0758472	−	0.0437904i
$81$	50.0086	−	63.7192i	0.617391	−	0.786657i
$82$	−22.8992	−	39.6625i	−0.279258	−	0.483689i
$83$	−19.5749	−	11.3016i	−0.235842	−	0.136163i	0.377422	−	0.926041i	$-0.376811\pi$
$83$	−19.5749	−	11.3016i	−0.235842	−	0.136163i	−0.613264	+	0.789878i	$0.710144\pi$
$84$	−16.5609	−	38.5971i	−0.197153	−	0.459489i
$85$	−0.496732	−	0.860365i	−0.00584390	−	0.0101219i
$86$	−3.61265	−	2.08577i	−0.0420076	−	0.0242531i
$87$	−162.245	−	49.7008i	−1.86489	−	0.571273i
$88$	−6.38386	−	11.0572i	−0.0725438	−	0.125650i
$89$	47.1301	−	27.2106i	0.529552	−	0.305737i	−0.211282	−	0.977425i	$-0.567764\pi$
$89$	47.1301	−	27.2106i	0.529552	−	0.305737i	0.740834	+	0.671688i	$0.234430\pi$
$90$	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
$93$	116.909	−	26.9229i	1.25708	−	0.289494i
$94$	78.0291			0.830097
$95$			38.0159i			0.400167i
$96$	−3.80847	−	16.5377i	−0.0396715	−	0.172268i
$97$	38.0319	−	65.8731i	0.392081	−	0.679104i	−0.600643	−	0.799517i	$-0.705089\pi$
$97$	38.0319	−	65.8731i	0.392081	−	0.679104i	0.992724	+	0.120413i	$0.0384220\pi$
$98$	−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
$101$	−168.803	+	97.4586i	−1.67132	+	0.964937i	−0.704419	+	0.709785i	$0.748792\pi$
$101$	−168.803	+	97.4586i	−1.67132	+	0.964937i	−0.966901	+	0.255152i	$0.917874\pi$
$102$	0.704797	−	2.30077i	0.00690977	−	0.0225565i
$103$	58.2628	−	100.914i	0.565658	−	0.979748i	−0.431330	−	0.902194i	$-0.641956\pi$
$103$	58.2628	−	100.914i	0.565658	−	0.979748i	0.996988	−	0.0775540i	$-0.0247110\pi$
$104$	−23.5509	+	13.5971i	−0.226451	+	0.130741i
$105$	4.34087	−	36.5269i	0.0413416	−	0.347875i
$106$	−39.4906	+	68.3998i	−0.372553	+	0.645281i
$107$	−65.8789	+	38.0352i	−0.615691	+	0.355469i	−0.775189	−	0.631729i	$-0.782346\pi$
$107$	−65.8789	+	38.0352i	−0.615691	+	0.355469i	0.159498	+	0.987198i	$0.449012\pi$
$108$	42.0218	−	33.9141i	0.389091	−	0.314020i
$109$	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	$-0.0939561\pi$
$110$		−	11.1821i		−	0.101655i
$111$	30.4272	+	32.6651i	0.274119	+	0.294280i
$112$	−4.98444	−	27.5528i	−0.0445039	−	0.246007i
$113$	88.3982	−	51.0367i	0.782285	−	0.451652i	−0.0549546	−	0.998489i	$-0.517501\pi$
$113$	88.3982	−	51.0367i	0.782285	−	0.451652i	0.837239	+	0.546837i	$0.184168\pi$
$114$	−67.3771	+	62.7611i	−0.591027	+	0.550536i
$115$	24.0503	+	41.6563i	0.209133	+	0.362229i
$116$	−97.9689	−	56.5623i	−0.844559	−	0.487606i
$117$	−71.6846	−	48.4665i	−0.612689	−	0.414243i
$118$	−17.5683			−0.148883
$119$	1.34132	−	3.73674i	0.0112716	−	0.0314012i
$120$	4.35331	−	14.2111i	0.0362776	−	0.118426i
$121$	−50.3116	+	87.1422i	−0.415798	+	0.720184i
$122$			112.469i			0.921878i
$123$	71.0895	−	66.2191i	0.577963	−	0.538367i
$124$	79.9791			0.644993
$125$			82.2066i			0.657652i
$126$	71.9045	−	52.6093i	0.570671	−	0.417534i
$127$	−221.800			−1.74646			−0.873228	−	0.487313i	$-0.837977\pi$
$127$	−221.800			−1.74646			−0.873228	+	0.487313i	$0.837977\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	2.59189	−	8.46107i	0.0200922	−	0.0655897i
$130$	−23.8169			−0.183207
$131$	−2.09587	−	1.21005i	−0.0159990	−	0.00923703i	0.491979	−	0.870607i	$-0.336274\pi$
$131$	−2.09587	−	1.21005i	−0.0159990	−	0.00923703i	−0.507978	+	0.861370i	$0.669607\pi$
$132$	19.8184	−	18.4606i	0.150140	−	0.139853i
$133$	−115.946	+	98.1698i	−0.871772	+	0.738119i
$134$			0.402309i			0.00300230i
$135$	46.7235	−	7.32141i	0.346100	−	0.0542326i
$136$	0.802099	−	1.38928i	0.00589779	−	0.0102153i
$137$	−205.101	+	118.415i	−1.49709	+	0.864344i	−0.999994	−	0.00335292i	$-0.998933\pi$
$137$	−205.101	+	118.415i	−1.49709	+	0.864344i	−0.497093	+	0.867697i	$0.665599\pi$
$138$	−34.1241	+	111.396i	−0.247276	+	0.807219i
$139$	112.225	+	194.379i	0.807373	+	1.39841i	0.914677	+	0.404185i	$0.132445\pi$
$139$	112.225	+	194.379i	0.807373	+	1.39841i	−0.107304	+	0.994226i	$0.534222\pi$
$140$	8.28491	−	23.0807i	0.0591780	−	0.164862i
$141$	37.1464	+	161.303i	0.263450	+	1.14399i
$142$	12.6238			0.0889002
$143$	−37.5863	−	21.7005i	−0.262841	−	0.151752i
$144$	32.3739	−	15.7458i	0.224819	−	0.109346i
$145$	−49.5378	−	85.8019i	−0.341640	−	0.591737i
$146$	9.86163	+	5.69362i	0.0675454	+	0.0389974i
$147$	122.614	−	81.0854i	0.834108	−	0.551601i
$148$	14.8803	+	25.7735i	0.100543	+	0.174145i
$149$	−71.5236	−	41.2942i	−0.480024	−	0.277142i	0.240402	−	0.970673i	$-0.422721\pi$
$149$	−71.5236	−	41.2942i	−0.480024	−	0.277142i	−0.720427	+	0.693531i	$0.756054\pi$
$150$	−68.0865	+	63.4218i	−0.453910	+	0.422812i
$151$	106.866	+	185.098i	0.707724	+	1.22581i	0.965700	+	0.259662i	$0.0836111\pi$
$151$	106.866	+	185.098i	0.707724	+	1.22581i	−0.257976	+	0.966151i	$0.583056\pi$
$152$	−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
$156$	−39.3197	−	42.2116i	−0.252049	−	0.270587i
$157$	161.794			1.03054			0.515268	−	0.857029i	$-0.327693\pi$
$157$	161.794			1.03054			0.515268	+	0.857029i	$0.327693\pi$
$158$			138.102i			0.874061i
$159$	−160.197	−	49.0732i	−1.00753	−	0.308637i
$160$	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	$0.886050\pi$
$164$	56.0912	−	32.3843i	0.342020	−	0.197465i
$165$	23.1157	−	5.32332i	0.140095	−	0.0322625i
$166$	15.9828	−	27.6831i	0.0962821	−	0.166765i
$167$	−41.1006	+	23.7295i	−0.246112	+	0.142093i	−0.617982	−	0.786192i	$-0.712050\pi$
$167$	−41.1006	+	23.7295i	−0.246112	+	0.142093i	0.371871	+	0.928284i	$0.378716\pi$
$168$	54.5846	−	23.4206i	0.324908	−	0.139408i
$169$	38.2798	−	66.3025i	0.226507	−	0.392322i
$170$	1.21674	−	0.702485i	0.00715729	−	0.00413226i
$171$	−161.816	−	109.405i	−0.946292	−	0.639795i
$172$	2.94972	−	5.10906i	0.0171495	−	0.0297039i
$173$		−	91.9101i		−	0.531272i	−0.964073	−	0.265636i	$-0.914418\pi$
$173$		−	91.9101i		−	0.531272i	0.964073	−	0.265636i	$-0.0855819\pi$
$174$	70.2875	−	229.449i	0.403951	−	1.31867i
$175$	−117.166	+	99.2034i	−0.669522	+	0.566877i
$176$	15.6372	−	9.02814i	0.0888477	−	0.0512962i
$177$	−8.36351	−	36.3173i	−0.0472515	−	0.205183i
$178$	38.4816	+	66.6521i	0.216189	+	0.374450i
$179$	143.122	+	82.6317i	0.799566	+	0.461629i	0.843319	−	0.537413i	$-0.180598\pi$
$179$	143.122	+	82.6317i	0.799566	+	0.461629i	−0.0437536	+	0.999042i	$0.513932\pi$
$180$	31.4498	+	2.23389i	0.174721	+	0.0124105i
$181$	244.607			1.35142			0.675709	−	0.737169i	$-0.263838\pi$
$181$	244.607			1.35142			0.675709	+	0.737169i	$0.263838\pi$
$182$	−61.5032	−	72.6397i	−0.337930	−	0.399119i
$183$	−232.497	+	53.5418i	−1.27048	+	0.292578i
$184$	−38.8352	+	67.2646i	−0.211061	+	0.365569i
$185$			26.0647i			0.140890i
$186$	38.0747	+	165.334i	0.204703	+	0.888892i
$187$	2.56024			0.0136911
$188$			110.350i			0.586967i
$189$	142.985	+	123.597i	0.756537	+	0.653951i
$190$	−53.7626			−0.282961
$191$		−	146.941i		−	0.769324i	−0.923057	−	0.384662i	$-0.874318\pi$
$191$		−	146.941i		−	0.769324i	0.923057	−	0.384662i	$-0.125682\pi$
$192$	23.3878	−	5.38599i	0.121812	−	0.0280520i
$193$	−253.782			−1.31493			−0.657466	−	0.753484i	$-0.728372\pi$
$193$	−253.782			−1.31493			−0.657466	+	0.753484i	$0.728372\pi$
$194$	93.1586	+	53.7852i	0.480199	+	0.277243i
$195$	−11.3382	−	49.2346i	−0.0581448	−	0.252485i
$196$	91.7888	−	34.3338i	0.468310	−	0.175172i
$197$		−	318.129i		−	1.61487i	−0.589958	−	0.807434i	$-0.700856\pi$
$197$		−	318.129i		−	1.61487i	0.589958	−	0.807434i	$-0.299144\pi$
$198$	47.5968	+	32.1806i	0.240388	+	0.162528i
$199$	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	$-0.0464803\pi$
$200$	−53.7218	+	31.0163i	−0.268609	+	0.155082i
$201$	−0.831658	+	0.191522i	−0.00413760	+	0.000952848i
$202$	−137.827	−	238.724i	−0.682313	−	1.18180i
$203$	133.766	−	372.656i	0.658947	−	1.83574i
$204$	3.25378	+	0.996733i	0.0159499	+	0.00488595i
$205$	56.7248			0.276707
$206$	142.714	+	82.3960i	0.692786	+	0.399980i
$207$	−246.525	−	17.5107i	−1.19094	−	0.0845930i
$208$	−19.2292	−	33.3059i	−0.0924481	−	0.160125i
$209$	−84.8448	−	48.9852i	−0.405956	−	0.234379i
$210$	51.6568	+	6.13891i	0.245985	+	0.0292329i
$211$	−107.527	−	186.242i	−0.509605	−	0.882661i	−0.999938	−	0.0111265i	$-0.996458\pi$
$211$	−107.527	−	186.242i	−0.509605	−	0.882661i	0.490333	−	0.871535i	$-0.336875\pi$
$212$	−96.7319	−	55.8482i	−0.456282	−	0.263435i
$213$	6.00968	+	26.0961i	0.0282145	+	0.122517i
$214$	−53.7899	−	93.1669i	−0.251355	−	0.435359i
$215$	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
$219$	−7.07520	+	23.0966i	−0.0323069	+	0.105464i
$220$	15.8138			0.0718811
$221$		−	5.45311i		−	0.0246747i
$222$	−46.1954	+	43.0305i	−0.208088	+	0.193831i
$223$	−40.9462	+	70.9208i	−0.183615	+	0.318031i	−0.943109	−	0.332484i	$-0.892113\pi$
$223$	−40.9462	+	70.9208i	−0.183615	+	0.318031i	0.759494	+	0.650514i	$0.225447\pi$
$224$	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
$227$	−20.4484	+	11.8059i	−0.0900811	+	0.0520084i	−0.544364	−	0.838849i	$-0.683229\pi$
$227$	−20.4484	+	11.8059i	−0.0900811	+	0.0520084i	0.454283	+	0.890858i	$0.349896\pi$
$228$	−88.7575	−	95.2856i	−0.389287	−	0.417919i
$229$	−19.1123	+	33.1035i	−0.0834598	+	0.144557i	−0.904734	−	0.425977i	$-0.859930\pi$
$229$	−19.1123	+	33.1035i	−0.0834598	+	0.144557i	0.821274	+	0.570534i	$0.193264\pi$
$230$	−58.9109	+	34.0122i	−0.256134	+	0.147879i
$231$	75.9282	+	56.7546i	0.328694	+	0.245691i
$232$	79.9912	−	138.549i	0.344790	−	0.597193i
$233$	118.984	−	68.6952i	0.510659	−	0.294829i	−0.222445	−	0.974945i	$-0.571404\pi$
$233$	118.984	−	68.6952i	0.510659	−	0.294829i	0.733105	+	0.680116i	$0.238071\pi$
$234$	68.5419	−	101.377i	0.292914	−	0.433236i
$235$	−48.3226	+	83.6973i	−0.205628	+	0.356159i
$236$		−	24.8453i		−	0.105277i
$237$	−285.486	+	65.7445i	−1.20458	+	0.277403i
$238$	5.28455	+	1.89691i	0.0222040	+	0.00797022i
$239$	348.038	−	200.940i	1.45623	−	0.840753i	0.457404	−	0.889259i	$-0.348779\pi$
$239$	348.038	−	200.940i	1.45623	−	0.840753i	0.998823	+	0.0485057i	$0.0154459\pi$
$240$	20.0976	+	6.15651i	0.0837399	+	0.0256521i
$241$	−219.749	−	380.616i	−0.911821	−	1.57932i	−0.811490	−	0.584366i	$-0.801343\pi$
$241$	−219.749	−	380.616i	−0.911821	−	1.57932i	−0.100330	−	0.994954i	$-0.531990\pi$
$242$	−123.238	−	71.1513i	−0.509247	−	0.294014i
$243$	−103.300	+	219.950i	−0.425105	+	0.905144i
$244$	−159.055			−0.651866
$245$	84.6542	+	14.1535i	0.345527	+	0.0577694i
$246$	93.6479	+	100.536i	0.380683	+	0.408682i
$247$	−104.334	+	180.713i	−0.422407	+	0.731630i
$248$			113.108i			0.456079i
$249$	64.8355	+	19.8611i	0.260384	+	0.0797636i
$250$	−116.258			−0.465031
$251$		−	114.101i		−	0.454587i	−0.973826	−	0.227294i	$-0.927012\pi$
$251$		−	114.101i		−	0.454587i	0.973826	−	0.227294i	$-0.0729877\pi$
$252$	74.4008	+	101.688i	0.295241	+	0.403525i
$253$	−123.959			−0.489958
$254$		−	313.672i		−	1.23493i
$255$	2.03142	+	2.18084i	0.00796637	+	0.00855230i
$256$	16.0000			0.0625000
$257$	260.101	+	150.169i	1.01207	+	0.584317i	0.911796	−	0.410644i	$-0.134696\pi$
$257$	260.101	+	150.169i	1.01207	+	0.584317i	0.100270	+	0.994960i	$0.468029\pi$
$258$	11.9658	+	3.66549i	0.0463789	+	0.0142073i
$259$	−79.4952	+	67.3077i	−0.306931	+	0.259875i
$260$		−	33.6822i		−	0.129547i
$261$	507.782	+	36.0679i	1.94552	+	0.138191i
$262$	1.71127	−	2.96401i	0.00653157	−	0.0113130i
$263$	365.056	−	210.765i	1.38804	−	0.801388i	0.394949	−	0.918703i	$-0.370762\pi$
$263$	365.056	−	210.765i	1.38804	−	0.801388i	0.993095	+	0.117315i	$0.0374288\pi$
$264$	26.1073	+	28.0275i	0.0988913	+	0.106165i
$265$	−48.9123	−	84.7185i	−0.184575	−	0.319693i
$266$	−138.833	−	163.972i	−0.521929	−	0.616436i
$267$	−119.465	+	111.280i	−0.447433	+	0.416779i
$268$	−0.568950			−0.00212295
$269$	445.841	+	257.406i	1.65740	+	0.956901i	0.973908	+	0.226943i	$0.0728730\pi$
$269$	445.841	+	257.406i	1.65740	+	0.956901i	0.683492	+	0.729958i	$0.260460\pi$
$270$	10.3540	+	66.0770i	0.0383483	+	0.244730i
$271$	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
$273$	120.883	−	161.721i	0.442793	−	0.592384i
$274$	−167.464	−	290.057i	−0.611184	−	1.05860i
$275$	−85.7381	−	49.5009i	−0.311775	−	0.180003i
$276$	−157.538	−	48.2588i	−0.570790	−	0.174851i
$277$	−74.7657	−	129.498i	−0.269912	−	0.467501i	0.698927	−	0.715193i	$-0.253661\pi$
$277$	−74.7657	−	129.498i	−0.269912	−	0.467501i	−0.968839	+	0.247692i	$0.920328\pi$
$278$	−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	0.469221	−	0.883081i	$-0.344535\pi$
$281$	−17.1238	−	9.88641i	−0.0609387	−	0.0351830i	−0.530160	+	0.847898i	$0.677868\pi$
$282$	−228.117	+	52.5330i	−0.808924	+	0.186287i
$283$	549.954			1.94330			0.971650	−	0.236425i	$-0.0759756\pi$
$283$	549.954			1.94330			0.971650	+	0.236425i	$0.0759756\pi$
$284$			17.8528i			0.0628619i
$285$	−25.5941	−	111.139i	−0.0898040	−	0.389961i
$286$	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
$290$	121.342	−	70.0570i	0.418421	−	0.241576i
$291$	−66.8364	+	218.184i	−0.229678	+	0.749772i
$292$	−8.05199	+	13.9465i	−0.0275753	+	0.0477618i
$293$	−113.883	+	65.7505i	−0.388680	+	0.224404i	−0.681588	−	0.731736i	$-0.738710\pi$
$293$	−113.883	+	65.7505i	−0.388680	+	0.224404i	0.292908	+	0.956141i	$0.405377\pi$
$294$	114.672	+	173.402i	0.390041	+	0.589803i
$295$	10.8798	−	18.8444i	0.0368808	−	0.0638794i
$296$	−36.4493	+	21.0440i	−0.123139	+	0.0710946i
$297$	−43.8652	+	113.713i	−0.147694	+	0.382871i
$298$	58.3988	−	101.150i	0.195969	−	0.339429i
$299$			264.023i			0.883021i
$300$	−89.6920	−	96.2889i	−0.298973	−	0.320963i
$301$	19.4339	+	6.97589i	0.0645646	+	0.0231757i
$302$	−261.768	+	151.132i	−0.866781	+	0.500436i
$303$	427.879	−	398.565i	1.41214	−	1.31540i
$304$	−43.4067	−	75.1826i	−0.142785	−	0.247311i
$305$	−120.639	−	69.6509i	−0.395538	−	0.228364i
$306$	−0.511472	+	7.20075i	−0.00167148	+	0.0235319i
$307$	252.488			0.822437			0.411218	−	0.911537i	$-0.365103\pi$
$307$	252.488			0.822437			0.411218	+	0.911537i	$0.365103\pi$
$308$	40.8366	+	48.2310i	0.132586	+	0.156594i
$309$	−102.390	+	334.246i	−0.331359	+	1.08170i
$310$	−49.5303	+	85.7889i	−0.159775	+	0.276738i
$311$		−	206.921i		−	0.665341i	−0.943043	−	0.332671i	$-0.892050\pi$
$311$		−	206.921i		−	0.665341i	0.943043	−	0.332671i	$-0.107950\pi$
$312$	59.6962	−	55.6064i	0.191334	−	0.178226i
$313$	−339.941			−1.08607			−0.543037	−	0.839709i	$-0.682726\pi$
$313$	−339.941			−1.08607			−0.543037	+	0.839709i	$0.682726\pi$
$314$			228.811i			0.728698i
$315$	11.9012	+	109.708i	0.0377817	+	0.348280i
$316$	−195.305			−0.618055
$317$			274.716i			0.866611i	0.901247	+	0.433306i	$0.142653\pi$
$317$			274.716i			0.866611i	−0.901247	+	0.433306i	$0.857347\pi$
$318$	69.4000	−	226.552i	0.218239	−	0.712429i
$319$	255.326			0.800396
$320$	12.1356	+	7.00646i	0.0379236	+	0.0218952i
$321$	166.989	−	155.548i	0.520214	−	0.484573i
$322$	−255.862	−	91.8428i	−0.794604	−	0.285226i
$323$		−	12.3095i		−	0.0381098i
$324$	−100.017	+	127.438i	−0.308695	+	0.393328i
$325$	−105.433	+	182.615i	−0.324409	+	0.561893i
$326$	65.8230	−	38.0029i	0.201911	−	0.116573i
$327$	−139.893	+	456.674i	−0.427809	+	1.39656i
$328$	45.7983	+	79.3250i	0.139629	+	0.241844i
$329$	−380.056	+	68.7540i	−1.15518	+	0.208979i
$330$	7.52831	+	32.6906i	0.0228130	+	0.0990623i
$331$	−197.017			−0.595217			−0.297609	−	0.954688i	$-0.596189\pi$
$331$	−197.017			−0.595217			−0.297609	+	0.954688i	$0.596189\pi$
$332$	39.1498	+	22.6031i	0.117921	+	0.0680817i
$333$	−110.945	−	75.0107i	−0.333168	−	0.225257i
$334$	−33.5585	−	58.1251i	−0.100475	−	0.174027i
$335$	−0.431533	−	0.249146i	−0.00128816	−	0.000743718i
$336$	33.1218	+	77.1942i	0.0985767	+	0.229745i
$337$	−162.571	−	281.581i	−0.482405	−	0.835551i	0.517391	−	0.855749i	$-0.326903\pi$
$337$	−162.571	−	281.581i	−0.482405	−	0.835551i	−0.999796	+	0.0201987i	$0.993570\pi$
$338$	93.7659	+	54.1358i	0.277414	+	0.160165i
$339$	−224.070	+	208.719i	−0.660973	+	0.615689i
$340$	0.993464	+	1.72073i	0.00292195	+	0.00506097i
$341$	−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
$345$	−98.3555	−	105.590i	−0.285088	−	0.306057i
$346$	129.980			0.375666
$347$		−	97.4654i		−	0.280880i	−0.990089	−	0.140440i	$-0.955148\pi$
$347$		−	97.4654i		−	0.280880i	0.990089	−	0.140440i	$-0.0448517\pi$
$348$	324.491	+	99.4015i	0.932444	+	0.285637i
$349$	−106.817	+	185.012i	−0.306065	+	0.530121i	−0.977498	−	0.210945i	$-0.932346\pi$
$349$	−106.817	+	185.012i	−0.306065	+	0.530121i	0.671433	+	0.741066i	$0.265679\pi$
$350$	−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
$353$	−555.729	+	320.850i	−1.57430	+	0.908924i	−0.578670	+	0.815562i	$0.696428\pi$
$353$	−555.729	+	320.850i	−1.57430	+	0.908924i	−0.995632	+	0.0933624i	$0.970238\pi$
$354$	51.3604	−	11.8278i	0.145086	−	0.0334118i
$355$	−7.81781	+	13.5408i	−0.0220220	+	0.0381432i
$356$	−94.2603	+	54.4212i	−0.264776	+	0.152869i
$357$	−1.40556	+	11.8273i	−0.00393715	+	0.0331298i
$358$	−116.859	+	202.405i	−0.326421	+	0.565378i
$359$	−263.839	+	152.328i	−0.734928	+	0.424311i	−0.820222	−	0.572045i	$-0.806150\pi$
$359$	−263.839	+	152.328i	−0.734928	+	0.424311i	0.0852941	+	0.996356i	$0.472817\pi$
$360$	−3.15920	+	44.4768i	−0.00877556	+	0.123547i
$361$	−55.0174	+	95.2929i	−0.152403	+	0.263969i
$362$			345.926i			0.955596i
$363$	88.4166	−	288.631i	0.243572	−	0.795126i
$364$	102.728	−	86.9786i	0.282220	−	0.238952i
$365$	−12.2144	+	7.05200i	−0.0334641	+	0.0193205i
$366$	−75.7196	−	328.801i	−0.206884	−	0.898364i
$367$	−62.6630	−	108.536i	−0.170744	−	0.295737i	0.767936	−	0.640526i	$-0.221284\pi$
$367$	−62.6630	−	108.536i	−0.170744	−	0.295737i	−0.938680	+	0.344789i	$0.887950\pi$
$368$	−95.1265	−	54.9213i	−0.258496	−	0.149243i
$369$	−163.247	+	241.451i	−0.442403	+	0.654339i
$370$	−36.8610			−0.0996243
$371$	132.077	−	367.950i	0.356003	−	0.991780i
$372$	−233.817	+	53.8458i	−0.628542	+	0.144747i
$373$	132.413	−	229.345i	0.354993	−	0.614867i	−0.632123	−	0.774868i	$-0.717816\pi$
$373$	132.413	−	229.345i	0.354993	−	0.614867i	0.987117	+	0.160001i	$0.0511498\pi$
$374$			3.62073i			0.00968110i
$375$	−55.3454	−	240.329i	−0.147588	−	0.640878i
$376$	−156.058			−0.415049
$377$		−	543.824i		−	1.44250i
$378$	−174.792	+	202.212i	−0.462413	+	0.534952i
$379$	−190.773			−0.503359			−0.251679	−	0.967811i	$-0.580983\pi$
$379$	−190.773			−0.503359			−0.251679	+	0.967811i	$0.580983\pi$
$380$		−	76.0318i		−	0.200084i
$381$	648.427	−	149.326i	1.70191	−	0.391933i
$382$	207.806			0.543994
$383$	519.145	+	299.729i	1.35547	+	0.782582i	0.989010	−	0.147852i	$-0.0472358\pi$
$383$	519.145	+	299.729i	1.35547	+	0.782582i	0.366461	+	0.930433i	$0.380569\pi$
$384$	7.61693	+	33.0754i	0.0198358	+	0.0861339i
$385$	9.85288	+	54.4644i	0.0255919	+	0.141466i
$386$		−	358.902i		−	0.929797i
$387$	−1.88094	+	26.4808i	−0.00486030	+	0.0684257i
$388$	−76.0637	+	131.746i	−0.196040	+	0.339552i
$389$	87.4253	−	50.4750i	0.224744	−	0.129756i	−0.383401	−	0.923582i	$-0.625247\pi$
$389$	87.4253	−	50.4750i	0.224744	−	0.129756i	0.608145	+	0.793826i	$0.291914\pi$
$390$	69.6282	−	16.0347i	0.178534	−	0.0411146i
$391$	−7.78743	−	13.4882i	−0.0199167	−	0.0344967i
$392$	48.5553	+	129.809i	0.123866	+	0.331145i
$393$	6.94190	+	2.12652i	0.0176639	+	0.00541099i
$394$	449.902			1.14188
$395$	−148.134	−	85.5250i	−0.375022	−	0.216519i
$396$	−45.5102	+	67.3121i	−0.114925	+	0.169980i
$397$	−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
$399$	272.872	−	365.058i	0.683890	−	0.914932i
$400$	−43.8637	−	75.9741i	−0.109659	−	0.189935i
$401$	−522.234	−	301.512i	−1.30233	−	0.751901i	−0.321527	−	0.946900i	$-0.604196\pi$
$401$	−522.234	−	301.512i	−1.30233	−	0.751901i	−0.980803	+	0.195000i	$0.937529\pi$
$402$	−0.270854	−	1.17614i	−0.000673765	−	0.00292572i
$403$	192.242	+	332.973i	0.477027	+	0.826235i
$404$	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
$408$	−1.40959	+	4.60153i	−0.00345489	+	0.0112783i
$409$	439.430			1.07440			0.537201	−	0.843454i	$-0.319482\pi$
$409$	439.430			1.07440			0.537201	+	0.843454i	$0.319482\pi$
$410$			80.2210i			0.195661i
$411$	519.886	−	484.268i	1.26493	−	1.17827i
$412$	−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
$416$	47.1017	−	27.1942i	0.113225	−	0.0653706i
$417$	−458.952	−	492.708i	−1.10061	−	1.18155i
$418$	69.2755	−	119.989i	0.165731	−	0.287054i
$419$	−49.5525	+	28.6092i	−0.118264	+	0.0682796i	−0.557965	−	0.829864i	$-0.688418\pi$
$419$	−49.5525	+	28.6092i	−0.118264	+	0.0682796i	0.439701	+	0.898144i	$0.355084\pi$
$420$	−8.68173	+	73.0538i	−0.0206708	+	0.173938i
$421$	163.713	−	283.558i	0.388866	−	0.673536i	−0.603431	−	0.797415i	$-0.706200\pi$
$421$	163.713	−	283.558i	0.388866	−	0.673536i	0.992297	+	0.123879i	$0.0395336\pi$
$422$	263.385	−	152.066i	0.624136	−	0.360345i
$423$	−217.194	−	446.557i	−0.513460	−	1.05569i
$424$	78.9812	−	136.800i	0.186277	−	0.322640i
$425$		−	12.4391i		−	0.0292684i
$426$	−36.9055	+	8.49897i	−0.0866327	+	0.0199506i
$427$	−99.1001	−	547.802i	−0.232085	−	1.28291i
$428$	131.758	−	76.0704i	0.307845	−	0.177735i
$429$	124.493	+	38.1360i	0.290193	+	0.0888951i
$430$	3.65346	+	6.32798i	0.00849642	+	0.0147162i
$431$	90.4104	+	52.1985i	0.209769	+	0.121110i	0.601204	−	0.799096i	$-0.294688\pi$
$431$	90.4104	+	52.1985i	0.209769	+	0.121110i	−0.391435	+	0.920206i	$0.628021\pi$
$432$	−84.0436	+	67.8283i	−0.194545	+	0.157010i
$433$	426.363			0.984673			0.492337	−	0.870405i	$-0.336143\pi$
$433$	426.363			0.984673			0.492337	+	0.870405i	$0.336143\pi$
$434$	−389.553	+	70.4722i	−0.897589	+	0.162378i
$435$	202.589	+	217.489i	0.465721	+	0.499975i
$436$	−159.207	+	275.754i	−0.365153	+	0.632464i
$437$			595.988i			1.36382i
$438$	−32.6635	−	10.0058i	−0.0745742	−	0.0228444i
$439$	284.606			0.648306			0.324153	−	0.946005i	$-0.394921\pi$
$439$	284.606			0.648306			0.324153	+	0.946005i	$0.394921\pi$
$440$			22.3641i			0.0508276i
$441$	−303.869	+	319.601i	−0.689044	+	0.724719i
$442$	7.71186			0.0174476
$443$			460.919i			1.04045i	0.854030	+	0.520224i	$0.174152\pi$
$443$			460.919i			1.04045i	−0.854030	+	0.520224i	$0.825848\pi$
$444$	−60.8544	−	65.3302i	−0.137059	−	0.147140i
$445$	−95.3250			−0.214214
$446$	−100.297	−	57.9066i	−0.224882	−	0.129835i
$447$	236.899	+	72.5696i	0.529976	+	0.162348i
$448$	9.96888	+	55.1055i	0.0222520	+	0.123003i
$449$		−	184.454i		−	0.410811i	−0.978677	−	0.205406i	$-0.934149\pi$
$449$		−	184.454i		−	0.410811i	0.978677	−	0.205406i	$-0.0658514\pi$
$450$	156.351	−	231.252i	0.347446	−	0.513892i
$451$	−73.0925	+	126.600i	−0.162068	+	0.280709i
$452$	−176.796	+	102.073i	−0.391142	+	0.225826i
$453$	−437.038	−	469.182i	−0.964764	−	1.03572i
$454$	−16.6961	−	28.9184i	−0.0367755	−	0.0636970i
$455$	116.005	−	20.9858i	0.254955	−	0.0461227i
$456$	134.754	−	125.522i	0.295514	−	0.275268i
$457$	−158.091			−0.345933			−0.172967	−	0.984928i	$-0.555335\pi$
$457$	−158.091			−0.345933			−0.172967	+	0.984928i	$0.555335\pi$
$458$	−46.8154	−	27.0289i	−0.102217	−	0.0590150i
$459$	−15.1290	+	2.37066i	−0.0329607	+	0.00516483i
$460$	−48.1005	−	83.3126i	−0.104566	−	0.181114i
$461$	−301.115	−	173.849i	−0.653179	−	0.377113i	0.136494	−	0.990641i	$-0.456416\pi$
$461$	−301.115	−	173.849i	−0.653179	−	0.377113i	−0.789673	+	0.613528i	$0.789750\pi$
$462$	−80.2631	+	107.379i	−0.173730	+	0.232421i
$463$	170.634	+	295.547i	0.368541	+	0.638331i	0.989338	−	0.145640i	$-0.0465242\pi$
$463$	170.634	+	295.547i	0.368541	+	0.638331i	−0.620797	+	0.783971i	$0.713191\pi$
$464$	195.938	+	113.125i	0.422280	+	0.243803i
$465$	−200.923	−	61.5491i	−0.432093	−	0.132364i
$466$	97.1497	+	168.268i	0.208476	+	0.361091i
$467$	−222.692	+	128.571i	−0.476856	+	0.275313i	−0.719105	−	0.694901i	$-0.755448\pi$
$467$	−222.692	+	128.571i	−0.476856	+	0.275313i	0.242249	+	0.970214i	$0.422115\pi$
$468$	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
$471$	−473.002	+	108.928i	−1.00425	+	0.231269i
$472$	35.1365			0.0744417
$473$			13.3152i			0.0281506i
$474$	−92.9767	−	403.738i	−0.196153	−	0.851767i
$475$	−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
$479$	172.286	−	99.4696i	0.359680	−	0.207661i	−0.309261	−	0.950977i	$-0.600082\pi$
$479$	172.286	−	99.4696i	0.359680	−	0.207661i	0.668940	+	0.743316i	$0.266748\pi$
$480$	−8.70662	+	28.4223i	−0.0181388	+	0.0592130i
$481$	−71.5343	+	123.901i	−0.148720	+	0.257590i
$482$	538.272	−	310.772i	1.11675	−	0.644755i
$483$	68.0532	−	572.644i	0.140897	−	1.18560i
$484$	100.623	−	174.284i	0.207899	−	0.360092i
$485$	−115.384	+	66.6172i	−0.237906	+	0.137355i
$486$	−311.056	−	146.089i	−0.640034	−	0.300594i
$487$	−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	$0.324472\pi$
$488$		−	224.938i		−	0.460939i
$489$	109.896	+	117.979i	0.224736	+	0.241265i
$490$	−20.0161	+	119.719i	−0.0408491	+	0.244325i
$491$	−824.496	+	476.023i	−1.67922	+	0.969497i	−0.717056	+	0.697015i	$0.754511\pi$
$491$	−824.496	+	476.023i	−1.67922	+	0.969497i	−0.962161	+	0.272482i	$0.912156\pi$
$492$	−142.179	+	132.438i	−0.288982	+	0.269183i
$493$	16.0402	+	27.7825i	0.0325360	+	0.0563539i
$494$	−255.566	−	147.551i	−0.517340	−	0.298687i
$495$	−63.9944	+	31.1252i	−0.129282	+	0.0628792i
$496$	−159.958			−0.322497
$497$	−61.4867	+	11.1233i	−0.123716	+	0.0223808i
$498$	−28.0879	+	91.6913i	−0.0564014	+	0.184119i
$499$	−7.59991	+	13.1634i	−0.0152303	+	0.0263796i	−0.873540	−	0.486752i	$-0.838181\pi$
$499$	−7.59991	+	13.1634i	−0.0152303	+	0.0263796i	0.858310	+	0.513132i	$0.171515\pi$
$500$		−	164.413i		−	0.328826i
$501$	104.181	−	97.0435i	0.207946	−	0.193700i
$502$	161.364			0.321442
$503$		−	247.471i		−	0.491989i	−0.969271	−	0.245995i	$-0.920885\pi$
$503$		−	247.471i		−	0.491989i	0.969271	−	0.245995i	$-0.0791146\pi$
$504$	−143.809	+	105.219i	−0.285335	+	0.208767i
$505$	341.420			0.676080
$506$		−	175.305i		−	0.346453i
$507$	−67.2721	+	219.606i	−0.132687	+	0.433148i
$508$	443.600			0.873228
$509$	−173.870	−	100.384i	−0.341591	−	0.197217i	0.319385	−	0.947625i	$-0.396524\pi$
$509$	−173.870	−	100.384i	−0.341591	−	0.197217i	−0.660975	+	0.750408i	$0.729857\pi$
$510$	−3.08417	+	2.87287i	−0.00604739	+	0.00563307i
$511$	−53.0498	−	19.0424i	−0.103816	−	0.0372650i
$512$			22.6274i			0.0441942i
$513$	546.722	+	210.901i	1.06574	+	0.411113i
$514$	−212.372	+	367.838i	−0.413174	+	0.715639i
$515$	−176.763	+	102.054i	−0.343228	+	0.198163i
$516$	−5.18378	+	16.9221i	−0.0100461	+	0.0327948i
$517$	−124.532	−	215.695i	−0.240874	−	0.417206i
$518$	−95.1874	−	112.423i	−0.183760	−	0.217033i
$519$	61.8783	+	268.697i	0.119226	+	0.517721i
$520$	47.6338			0.0916034
$521$	−248.569	−	143.512i	−0.477101	−	0.275454i	0.242107	−	0.970250i	$-0.422162\pi$
$521$	−248.569	−	143.512i	−0.477101	−	0.275454i	−0.719207	+	0.694795i	$0.755495\pi$
$522$	−51.0077	+	718.112i	−0.0977159	+	1.37569i
$523$	−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
$525$	275.745	−	368.901i	0.525229	−	0.702669i
$526$	298.067	+	516.267i	0.566667	+	0.981495i
$527$	−19.6422	−	11.3404i	−0.0372718	−	0.0215189i
$528$	−39.6369	+	36.9213i	−0.0750698	+	0.0699267i
$529$	112.544	+	194.932i	0.212749	+	0.368492i
$530$	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
$534$	−157.374	−	168.948i	−0.294707	−	0.316383i
$535$	133.246			0.249058
$536$		−	0.804617i		−	0.00150115i
$537$	−474.047	−	145.215i	−0.882768	−	0.270419i
$538$	−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	$0.867692\pi$
$542$	−591.295	+	341.385i	−1.09095	+	0.629861i
$543$	−715.102	+	164.681i	−1.31695	+	0.303280i
$544$	−1.60420	+	2.77855i	−0.00294889	+	0.00510763i
$545$	−241.508	+	139.435i	−0.443134	+	0.255843i
$546$	228.708	+	170.954i	0.418879	+	0.313102i
$547$	22.9108	−	39.6827i	0.0418845	−	0.0725461i	−0.844323	−	0.535834i	$-0.819997\pi$
$547$	22.9108	−	39.6827i	0.0418845	−	0.0725461i	0.886208	+	0.463288i	$0.153331\pi$
$548$	410.202	−	236.830i	0.748544	−	0.432172i
$549$	643.655	−	313.057i	1.17241	−	0.570231i
$550$	70.0049	−	121.252i	0.127282	−	0.220458i
$551$		−	1227.59i		−	2.22793i
$552$	68.2483	−	222.793i	0.123638	−	0.403610i
$553$	−121.686	−	672.650i	−0.220047	−	1.21637i
$554$	183.138	−	105.735i	0.330573	−	0.190857i
$555$	−17.5480	−	76.1995i	−0.0316180	−	0.137296i
$556$	−224.450	−	388.758i	−0.403686	−	0.699205i
$557$	772.053	+	445.745i	1.38609	+	0.800260i	0.992872	−	0.119185i	$-0.0380280\pi$
$557$	772.053	+	445.745i	1.38609	+	0.800260i	0.393219	+	0.919445i	$0.371361\pi$
$558$	−222.621	−	457.717i	−0.398963	−	0.820281i
$559$	28.3604			0.0507341
$560$	−16.5698	+	46.1614i	−0.0295890	+	0.0824311i
$561$	−7.48482	+	1.72368i	−0.0133419	+	0.00307251i
$562$	13.9815	−	24.2167i	0.0248781	−	0.0430901i
$563$		−	335.625i		−	0.596137i	−0.954544	−	0.298069i	$-0.903658\pi$
$563$		−	335.625i		−	0.596137i	0.954544	−	0.298069i	$-0.0963424\pi$
$564$	−74.2928	−	322.606i	−0.131725	−	0.571996i
$565$	−178.793			−0.316449
$566$			777.752i			1.37412i
$567$	−501.226	−	265.068i	−0.883997	−	0.467492i
$568$	−25.2477			−0.0444501
$569$			945.483i			1.66166i	0.556529	+	0.830828i	$0.312133\pi$
$569$			945.483i			1.66166i	−0.556529	+	0.830828i	$0.687867\pi$
$570$	157.174	−	36.1956i	0.275744	−	0.0635010i
$571$	−516.310			−0.904221			−0.452111	−	0.891962i	$-0.649329\pi$
$571$	−516.310			−0.904221			−0.452111	+	0.891962i	$0.649329\pi$
$572$	75.1727	+	43.4010i	0.131421	+	0.0758758i
$573$	98.9277	+	429.579i	0.172649	+	0.749701i
$574$	−244.668	+	207.158i	−0.426251	+	0.360902i
$575$			602.263i			1.04741i
$576$	−64.7478	+	31.4916i	−0.112409	+	0.0546730i
$577$	−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	$0.292478\pi$
$578$	353.557	−	204.126i	0.611691	−	0.353160i
$579$	741.926	−	170.858i	1.28139	−	0.295092i
$580$	99.0755	+	171.604i	0.170820	+	0.295869i
$581$	−53.4549	+	148.919i	−0.0920050	+	0.256314i
$582$	−308.558	−	94.5210i	−0.530169	−	0.162407i
$583$	252.103			0.432423
$584$	−19.7233	−	11.3872i	−0.0337727	−	0.0194987i
$585$	66.2942	+	136.303i	0.113323	+	0.232996i
$586$	−92.9853	−	161.055i	−0.158678	−	0.274838i
$587$	333.063	+	192.294i	0.567398	+	0.327588i	0.756110	−	0.654445i	$-0.227098\pi$
$587$	333.063	+	192.294i	0.567398	+	0.327588i	−0.188711	+	0.982033i	$0.560431\pi$
$588$	−245.228	+	162.171i	−0.417054	+	0.275801i
$589$	433.954	+	751.630i	0.736763	+	1.27611i
$590$	26.6501	+	15.3864i	0.0451696	+	0.0260787i
$591$	214.180	+	930.044i	0.362402	+	1.57368i
$592$	−29.7607	−	51.5470i	−0.0502714	−	0.0870727i
$593$	−234.426	+	135.346i	−0.395321	+	0.228239i	−0.684463	−	0.729047i	$-0.739963\pi$
$593$	−234.426	+	135.346i	−0.395321	+	0.228239i	0.289142	+	0.957286i	$0.406630\pi$
$594$	−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
$597$	−217.066	+	708.601i	−0.363595	+	1.18694i
$598$	−373.385			−0.624390
$599$			290.145i			0.484383i	0.970228	+	0.242191i	$0.0778662\pi$
$599$			290.145i			0.484383i	−0.970228	+	0.242191i	$0.922134\pi$
$600$	136.173	−	126.844i	0.226955	−	0.211406i
$601$	332.538	−	575.974i	0.553309	−	0.958359i	−0.444724	−	0.895667i	$-0.646698\pi$
$601$	332.538	−	575.974i	0.553309	−	0.958359i	0.998033	−	0.0626911i	$-0.0199683\pi$
$602$	−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
$605$	152.640	−	88.1266i	0.252297	−	0.145664i
$606$	563.656	+	605.113i	0.930125	+	0.998536i
$607$	137.803	−	238.683i	0.227024	−	0.393217i	−0.729901	−	0.683553i	$-0.760434\pi$
$607$	137.803	−	238.683i	0.227024	−	0.393217i	0.956925	+	0.290336i	$0.0937672\pi$
$608$	106.324	−	61.3863i	0.174875	−	0.100964i
$609$	−140.173	+	1179.51i	−0.230169	+	1.93680i
$610$	98.5013	−	170.609i	0.161478	−	0.279687i
$611$	−459.413	+	265.242i	−0.751904	+	0.434112i
$612$	−10.1834	−	0.723330i	−0.0166395	−	0.00118191i
$613$	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	$0.150392\pi$
$614$			357.072i			0.581551i
$615$	−165.834	+	38.1899i	−0.269649	+	0.0620974i
$616$	−68.2089	+	57.7517i	−0.110729	+	0.0937527i
$617$	446.057	−	257.531i	0.722945	−	0.417392i	−0.0928908	−	0.995676i	$-0.529611\pi$
$617$	446.057	−	257.531i	0.722945	−	0.417392i	0.815836	+	0.578284i	$0.196277\pi$
$618$	−472.695	−	144.801i	−0.764878	−	0.234306i
$619$	−539.269	−	934.042i	−0.871194	−	1.50895i	−0.860762	−	0.509007i	$-0.830013\pi$
$619$	−539.269	−	934.042i	−0.871194	−	1.50895i	−0.0104316	−	0.999946i	$-0.503321\pi$
$620$	−121.324	−	70.0464i	−0.195684	−	0.112978i
$621$	732.500	−	114.780i	1.17955	−	0.184831i
$622$	292.631			0.470467
$623$	−246.161	−	290.734i	−0.395122	−	0.466668i
$624$	78.6393	+	84.4232i	0.126025	+	0.135294i
$625$	−202.151	+	350.136i	−0.323441	+	0.560217i
$626$		−	480.749i		−	0.767970i
$627$	281.021	+	86.0856i	0.448200	+	0.137298i
$628$	−323.588			−0.515268
$629$		−	8.43968i		−	0.0134176i
$630$	−155.151	+	16.8309i	−0.246271	+	0.0267157i
$631$	65.5284			0.103848			0.0519242	−	0.998651i	$-0.483465\pi$
$631$	65.5284			0.103848			0.0519242	+	0.998651i	$0.483465\pi$
$632$		−	276.203i		−	0.437031i
$633$	439.739	+	472.081i	0.694690	+	0.745784i
$634$	−388.507			−0.612787
$635$	336.458	+	194.254i	0.529855	+	0.305912i
$636$	320.393	+	98.1465i	0.503763	+	0.154318i
$637$	363.568	+	299.613i	0.570750	+	0.470350i
$638$			361.086i			0.565966i
$639$	−35.1384	−	72.2456i	−0.0549896	−	0.113060i
$640$	−9.90864	+	17.1623i	−0.0154822	+	0.0268160i
$641$	685.053	−	395.516i	1.06873	−	0.617029i	0.140893	−	0.990025i	$-0.455003\pi$
$641$	685.053	−	395.516i	1.06873	−	0.617029i	0.927833	+	0.372996i	$0.121669\pi$
$642$	219.978	+	236.158i	0.342645	+	0.367847i
$643$	−414.293	−	717.577i	−0.644313	−	1.11598i	−0.984460	−	0.175610i	$-0.943810\pi$
$643$	−414.293	−	717.577i	−0.644313	−	1.11598i	0.340147	−	0.940372i	$-0.389523\pi$
$644$	129.885	−	361.844i	0.201685	−	0.561870i
$645$	−11.3420	+	10.5650i	−0.0175845	+	0.0163798i
$646$	17.4082			0.0269477
$647$	54.8043	+	31.6413i	0.0847053	+	0.0489046i	0.541754	−	0.840537i	$-0.317760\pi$
$647$	54.8043	+	31.6413i	0.0847053	+	0.0489046i	−0.457049	+	0.889441i	$0.651094\pi$
$648$	−180.225	−	141.446i	−0.278125	−	0.218281i
$649$	28.0383	+	48.5638i	0.0432023	+	0.0748286i
$650$	−258.257	−	149.105i	−0.397318	−	0.229392i
$651$	−331.131	−	771.741i	−0.508650	−	1.18547i
$652$	53.7443	+	93.0878i	0.0824298	+	0.142773i
$653$	564.419	+	325.867i	0.864347	+	0.499031i	0.865466	−	0.500968i	$-0.167023\pi$
$653$	564.419	+	325.867i	0.864347	+	0.499031i	−0.00111857	+	0.999999i	$0.500356\pi$
$654$	−645.835	−	197.839i	−0.987515	−	0.302506i
$655$	2.11955	+	3.67116i	0.00323595	+	0.00560482i
$656$	−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	0.455120	−	0.890430i	$-0.349596\pi$
$659$	−58.2921	−	33.6550i	−0.0884554	−	0.0510698i	−0.543575	+	0.839360i	$0.682930\pi$
$660$	−46.2314	+	10.6466i	−0.0700476	+	0.0161313i
$661$	−486.564			−0.736102			−0.368051	−	0.929806i	$-0.619975\pi$
$661$	−486.564			−0.736102			−0.368051	+	0.929806i	$0.619975\pi$
$662$		−	278.624i		−	0.420882i
$663$	3.67130	+	15.9421i	0.00553740	+	0.0240453i
$664$	−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
$668$	82.2012	−	47.4589i	0.123056	−	0.0710463i
$669$	71.9580	−	234.903i	0.107561	−	0.351125i
$670$	0.352345	−	0.610280i	0.000525888	−	0.000910865i
$671$	310.897	−	179.497i	0.463334	−	0.267506i
$672$	−109.169	+	46.8412i	−0.162454	+	0.0697042i
$673$	135.979	−	235.523i	0.202050	−	0.349960i	−0.747139	−	0.664668i	$-0.768573\pi$
$673$	135.979	−	235.523i	0.202050	−	0.349960i	0.949189	+	0.314707i	$0.101906\pi$
$674$	398.215	−	229.910i	0.590824	−	0.341112i
$675$	552.478	+	213.121i	0.818487	+	0.315735i
$676$	−76.5595	+	132.605i	−0.113254	+	0.196161i
$677$		−	593.459i		−	0.876601i	−0.898829	−	0.438300i	$-0.855581\pi$
$677$		−	593.459i		−	0.876601i	0.898829	−	0.438300i	$-0.144419\pi$
$678$	−295.173	−	316.883i	−0.435358	−	0.467379i
$679$	−501.139	−	179.886i	−0.738054	−	0.264927i
$680$	−2.43348	+	1.40497i	−0.00357865	+	0.00206613i
$681$	51.8322	−	48.2812i	0.0761120	−	0.0708975i
$682$	−127.644	−	221.086i	−0.187161	−	0.324173i
$683$	−763.359	−	440.725i	−1.11766	−	0.645279i	−0.176854	−	0.984237i	$-0.556592\pi$
$683$	−763.359	−	440.725i	−1.11766	−	0.645279i	−0.940801	+	0.338958i	$0.889925\pi$
$684$	323.632	+	218.810i	0.473146	+	0.319897i
$685$	414.836			0.605600
$686$	−416.822	+	248.107i	−0.607613	+	0.361672i
$687$	33.5876	−	109.645i	0.0488902	−	0.159599i
$688$	−5.89944	+	10.2181i	−0.00857477	+	0.0148519i
$689$		−	536.958i		−	0.779329i
$690$	149.326	−	139.096i	0.216415	−	0.201588i
$691$	876.408			1.26832			0.634159	−	0.773203i	$-0.281346\pi$
$691$	876.408			1.26832			0.634159	+	0.773203i	$0.281346\pi$
$692$			183.820i			0.265636i
$693$	−260.185	−	114.802i	−0.375447	−	0.165660i
$694$	137.837			0.198612
$695$		−	393.150i		−	0.565683i
$696$	−140.575	+	458.899i	−0.201976	+	0.659337i
$697$	−18.3674			−0.0263521
$698$	−261.647	−	151.062i	−0.374852	−	0.216421i
$699$	−301.597	+	280.935i	−0.431470	+	0.401909i
$700$	234.333	−	198.407i	0.334761	−	0.283438i
$701$		−	286.681i		−	0.408961i	−0.978871	−	0.204480i	$-0.934450\pi$
$701$		−	286.681i		−	0.408961i	0.978871	−	0.204480i	$-0.0655504\pi$
$702$	−132.129	+	342.520i	−0.188218	+	0.487921i
$703$	−161.477	+	279.686i	−0.229696	+	0.397846i
$704$	−31.2744	+	18.0563i	−0.0444238	+	0.0256481i
$705$	84.9213	−	277.220i	0.120456	−	0.393221i
$706$	−453.751	−	785.919i	−0.642706	−	1.11320i
$707$	881.661	+	1041.31i	1.24705	+	1.47285i
$708$	16.7270	+	72.6346i	0.0236257	+	0.102591i
$709$	657.204			0.926945			0.463473	−	0.886111i	$-0.346603\pi$
$709$	657.204			0.926945			0.463473	+	0.886111i	$0.346603\pi$
$710$	−19.1496	−	11.0561i	−0.0269713	−	0.0155719i
$711$	790.349	−	384.405i	1.11160	−	0.540654i
$712$	−76.9632	−	133.304i	−0.108094	−	0.187225i
$713$	951.017	+	549.070i	1.33383	+	0.770084i
$714$	−16.7264	−	1.98777i	−0.0234263	−	0.00278399i
$715$	38.0109	+	65.8368i	0.0531621	+	0.0920795i
$716$	−286.244	−	165.263i	−0.399783	−	0.230815i
$717$	−882.201	+	821.760i	−1.23041	+	1.14611i
$718$	−215.424	−	373.125i	−0.300033	−	0.519673i
$719$	404.412	−	233.488i	0.562465	−	0.324739i	−0.191669	−	0.981460i	$-0.561390\pi$
$719$	404.412	−	233.488i	0.562465	−	0.324739i	0.754134	+	0.656720i	$0.228057\pi$
$720$	−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
$723$	898.680	+	964.778i	1.24299	+	1.33441i
$724$	−489.213			−0.675709
$725$		−	1240.52i		−	1.71106i
$726$	408.186	+	125.040i	0.562239	+	0.172231i
$727$	−21.8124	+	37.7802i	−0.0300033	+	0.0519673i	−0.880637	−	0.473791i	$-0.842885\pi$
$727$	−21.8124	+	37.7802i	−0.0300033	+	0.0519673i	0.850634	+	0.525759i	$0.176218\pi$
$728$	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
$731$	−1.44885	+	0.836496i	−0.00198202	+	0.00114432i
$732$	464.995	−	107.084i	0.635239	−	0.146289i
$733$	−559.033	+	968.274i	−0.762665	+	1.32097i	0.178808	+	0.983884i	$0.442776\pi$
$733$	−559.033	+	968.274i	−0.762665	+	1.32097i	−0.941472	+	0.337090i	$0.890557\pi$
$734$	153.492	−	88.6189i	0.209118	−	0.120734i
$735$	−257.014	+	15.6158i	−0.349678	+	0.0212460i
$736$	77.6705	−	134.529i	0.105531	−	0.182784i
$737$	1.11210	−	0.642070i	0.00150895	−	0.000871194i
$738$	−341.463	−	230.866i	−0.462687	−	0.312826i
$739$	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	$-0.0229395\pi$
$740$		−	52.1293i		−	0.0704450i
$741$	183.355	−	598.552i	0.247443	−	0.807763i
$742$	520.360	+	186.785i	0.701294	+	0.251732i
$743$	−1010.16	+	583.214i	−1.35957	+	0.784945i	−0.989565	−	0.144086i	$-0.953976\pi$
$743$	−1010.16	+	583.214i	−1.35957	+	0.784945i	−0.370000	+	0.929032i	$0.620642\pi$
$744$	−76.1495	−	330.668i	−0.102351	−	0.444446i
$745$	72.3316	+	125.282i	0.0970893	+	0.168164i
$746$	324.343	+	187.260i	0.434776	+	0.251018i
$747$	−202.917	−	14.4133i	−0.271642	−	0.0192948i
$748$	−5.12049			−0.00684557
$749$	344.086	+	406.391i	0.459394	+	0.542578i
$750$	339.877	−	78.2702i	0.453169	−	0.104360i
$751$	−608.863	+	1054.58i	−0.810737	+	1.40424i	0.101612	+	0.994824i	$0.467600\pi$
$751$	−608.863	+	1054.58i	−0.810737	+	1.40424i	−0.912349	+	0.409413i	$0.865733\pi$
$752$		−	220.700i		−	0.293484i
$753$	76.8185	+	333.573i	0.102017	+	0.442992i
$754$	769.084			1.02000
$755$		−	374.377i		−	0.495864i
$756$	−285.971	−	247.194i	−0.378268	−	0.326976i
$757$	212.121			0.280213			0.140106	−	0.990136i	$-0.455256\pi$
$757$	212.121			0.280213			0.140106	+	0.990136i	$0.455256\pi$
$758$		−	269.794i		−	0.355928i
$759$	362.393	−	83.4554i	0.477461	−	0.109954i
$760$	107.525			0.141481
$761$	−884.489	−	510.660i	−1.16227	−	0.671038i	−0.210425	−	0.977610i	$-0.567485\pi$
$761$	−884.489	−	510.660i	−1.16227	−	0.671038i	−0.951848	+	0.306572i	$0.900818\pi$
$762$	211.179	+	917.015i	0.277138	+	1.20343i
$763$	−1048.92	−	376.514i	−1.37473	−	0.493465i
$764$			293.882i			0.384662i
$765$	−7.40707	−	5.00798i	−0.00968245	−	0.00654637i
$766$	−423.880	+	734.182i	−0.553369	+	0.958463i
$767$	103.437	−	59.7193i	0.134859	−	0.0778609i
$768$	−46.7757	+	10.7720i	−0.0609058	+	0.0140260i
$769$	−19.1405	−	33.1524i	−0.0248902	−	0.0431110i	0.853312	−	0.521401i	$-0.174590\pi$
$769$	−19.1405	−	33.1524i	−0.0248902	−	0.0431110i	−0.878202	+	0.478290i	$0.841257\pi$
$770$	−77.0242	+	13.9341i	−0.100031	+	0.0180962i
$771$	−861.501	−	263.905i	−1.11738	−	0.342289i
$772$	507.564			0.657466
$773$	329.696	+	190.350i	0.426515	+	0.246249i	0.697861	−	0.716233i	$-0.254135\pi$
$773$	329.696	+	190.350i	0.426515	+	0.246249i	−0.271346	+	0.962482i	$0.587469\pi$
$774$	−37.4494	−	2.66005i	−0.0483843	−	0.00343675i
$775$	438.522	+	759.543i	0.565835	+	0.980056i
$776$	−186.317	−	107.570i	−0.240100	−	0.138622i
$777$	187.088	−	250.293i	0.240782	−	0.322127i
$778$	71.3824	+	123.638i	0.0917512	+	0.158918i
$779$	608.684	+	351.424i	0.781365	+	0.451121i
$780$	22.6765	+	98.4691i	0.0290724	+	0.126242i
$781$	−20.1472	−	34.8960i	−0.0257967	−	0.0446811i
$782$	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
$786$	−3.00735	+	9.81733i	−0.00382615	+	0.0124902i
$787$	855.666			1.08725			0.543625	−	0.839328i	$-0.317051\pi$
$787$	855.666			1.08725			0.543625	+	0.839328i	$0.317051\pi$
$788$			636.258i			0.807434i
$789$	−925.336	+	861.940i	−1.17280	+	1.09245i
$790$	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
$794$	378.530	−	218.544i	0.476738	−	0.275245i
$795$	200.031	+	214.743i	0.251611	+	0.270117i
$796$	−247.034	+	427.876i	−0.310344	+	0.537532i
$797$	−27.2948	+	15.7587i	−0.0342469	+	0.0197725i	−0.517026	−	0.855970i	$-0.672961\pi$
$797$	−27.2948	+	15.7587i	−0.0342469	+	0.0197725i	0.482779	+	0.875742i	$0.339628\pi$
$798$	516.270	+	385.900i	0.646954	+	0.483583i
$799$	15.6468	−	27.1010i	0.0195829	−	0.0339187i
$800$	107.444	−	62.0326i	0.134305	−	0.0775408i
$801$	274.333	−	405.754i	0.342488	−	0.506559i
$802$	426.403	−	738.551i	0.531674	−	0.920886i
$803$		−	36.3472i		−	0.0452643i
$804$	1.66332	−	0.383045i	0.00206880	−	0.000476424i
$805$	256.967	−	217.571i	0.319214	−	0.270275i
$806$	−470.894	+	271.871i	−0.584236	+	0.337309i
$807$	−1476.70	−	452.361i	−1.82987	−	0.560546i
$808$	275.655	+	477.448i	0.341157	+	0.590901i
$809$	366.440	+	211.564i	0.452955	+	0.261514i	0.709077	−	0.705131i	$-0.249112\pi$
$809$	366.440	+	211.564i	0.452955	+	0.261514i	−0.256123	+	0.966644i	$0.582445\pi$
$810$	−74.7560	−	186.204i	−0.0922914	−	0.229881i
$811$	695.569			0.857668			0.428834	−	0.903383i	$-0.358925\pi$
$811$	695.569			0.857668			0.428834	+	0.903383i	$0.358925\pi$
$812$	−267.532	+	745.311i	−0.329473	+	0.917871i
$813$	−987.206	−	1059.81i	−1.21427	−	1.30358i
$814$	47.4970	−	82.2672i	0.0583501	−	0.101065i
$815$			94.1393i			0.115508i
$816$	−6.50755	−	1.99347i	−0.00797494	−	0.00244297i
$817$	64.0188			0.0783583
$818$			621.448i			0.759717i
$819$	−244.520	+	554.172i	−0.298559	+	0.676644i
$820$	−113.450			−0.138353
$821$			91.3532i			0.111271i	0.998451	+	0.0556353i	$0.0177184\pi$
$821$			91.3532i			0.111271i	−0.998451	+	0.0556353i	$0.982282\pi$
$822$	684.859	+	735.230i	0.833161	+	0.894440i
$823$	−657.997			−0.799511			−0.399755	−	0.916622i	$-0.630905\pi$
$823$	−657.997			−0.799511			−0.399755	+	0.916622i	$0.630905\pi$
$824$	−285.428	−	164.792i	−0.346393	−	0.199990i
$825$	283.980	+	86.9920i	0.344218	+	0.105445i
$826$	21.8920	+	121.014i	0.0265036	+	0.146505i
$827$			1364.30i			1.64969i	0.565355	+	0.824847i	$0.308739\pi$
$827$			1364.30i			1.64969i	−0.565355	+	0.824847i	$0.691261\pi$
$828$	493.050	+	35.0215i	0.595471	+	0.0422965i
$829$	−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	$0.322132\pi$
$830$	−48.4901	+	27.9958i	−0.0584218	+	0.0337298i
$831$	305.760	+	328.249i	0.367942	+	0.395004i
$832$	38.4584	+	66.6119i	0.0462240	+	0.0800624i
$833$	−27.4108	−	4.58287i	−0.0329062	−	0.00550165i
$834$	696.795	−	649.057i	0.835485	−	0.778246i
$835$	83.1298			0.0995566
$836$	169.690	+	97.9704i	0.202978	+	0.117189i
$837$	840.217	−	678.106i	1.00384	−	0.810162i
$838$	−40.4595	−	70.0778i	−0.0482810	−	0.0836251i
$839$	−1355.78	−	782.761i	−1.61595	−	0.932969i	−0.987953	−	0.154752i	$-0.950542\pi$
$839$	−1355.78	−	782.761i	−1.61595	−	0.932969i	−0.627996	−	0.778216i	$-0.716125\pi$
$840$	−103.314	−	12.2778i	−0.122992	−	0.0146165i
$841$	1179.15	+	2042.35i	1.40208	+	2.42847i
$842$	401.012	+	231.525i	0.476262	+	0.274970i
$843$	56.7170	+	17.3742i	0.0672800	+	0.0206099i
$844$	215.053	+	372.483i	0.254802	+	0.441331i
$845$	−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
$849$	−1607.78	+	370.255i	−1.89373	+	0.436108i
$850$	17.5915			0.0206959
$851$			408.624i			0.480170i
$852$	−12.0194	−	52.1923i	−0.0141072	−	0.0612586i
$853$	−484.334	+	838.891i	−0.567801	+	0.983460i	0.428982	+	0.903313i	$0.358872\pi$
$853$	−484.334	+	838.891i	−0.567801	+	0.983460i	−0.996783	+	0.0801471i	$0.974461\pi$
$854$	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
$857$	1149.35	−	663.578i	1.34113	−	0.774304i	0.354160	−	0.935185i	$-0.384767\pi$
$857$	1149.35	−	663.578i	1.34113	−	0.774304i	0.986974	+	0.160881i	$0.0514336\pi$
$858$	−53.9324	+	176.059i	−0.0628583	+	0.205197i
$859$	−181.100	+	313.675i	−0.210827	+	0.365163i	−0.951974	−	0.306180i	$-0.900949\pi$
$859$	−181.100	+	313.675i	−0.210827	+	0.365163i	0.741147	+	0.671343i	$0.234282\pi$
$860$	−8.94912	+	5.16678i	−0.0104060	+	0.00600788i
$861$	−544.715	−	407.162i	−0.632654	−	0.472894i
$862$	−73.8198	+	127.860i	−0.0856378	+	0.148329i
$863$	938.041	−	541.578i	1.08695	−	0.627553i	0.154190	−	0.988041i	$-0.450723\pi$
$863$	938.041	−	541.578i	1.08695	−	0.627553i	0.932764	+	0.360488i	$0.117390\pi$
$864$	−95.9237	−	118.856i	−0.111023	−	0.137564i
$865$	−80.4956	+	139.422i	−0.0930584	+	0.161182i
$866$			602.969i			0.696269i
$867$	590.287	+	633.702i	0.680838	+	0.730914i
$868$	−99.6628	−	550.912i	−0.114819	−	0.634691i
$869$	381.753	−	220.405i	0.439302	−	0.253631i
$870$	−307.576	+	286.504i	−0.353535	+	0.329314i
$871$	−1.36756	−	2.36868i	−0.00157010	−	0.00271949i
$872$	−389.975	−	225.152i	−0.447220	−	0.258202i
$873$	48.5033	−	682.853i	0.0555593	−	0.782191i
$874$	−842.854			−0.964364
$875$	566.255	−	102.438i	0.647148	−	0.117072i
$876$	14.1504	−	46.1932i	0.0161534	−	0.0527319i
$877$	570.778	−	988.617i	0.650830	−	1.12727i	−0.332091	−	0.943247i	$-0.607754\pi$
$877$	570.778	−	988.617i	0.650830	−	1.12727i	0.982922	−	0.184024i	$-0.0589125\pi$
$878$			402.494i			0.458421i
$879$	288.669	−	268.892i	0.328406	−	0.305907i
$880$	−31.6277			−0.0359405
$881$		−	536.022i		−	0.608424i	−0.952604	−	0.304212i	$-0.901607\pi$
$881$		−	536.022i		−	0.608424i	0.952604	−	0.304212i	$-0.0983931\pi$
$882$	−451.984	−	429.735i	−0.512454	−	0.487228i
$883$	−413.964			−0.468816			−0.234408	−	0.972138i	$-0.575315\pi$
$883$	−413.964			−0.468816			−0.234408	+	0.972138i	$0.575315\pi$
$884$			10.9062i			0.0123374i
$885$	−19.1200	+	62.4162i	−0.0216045	+	0.0705267i
$886$	−651.837			−0.735708
$887$	99.9924	+	57.7307i	0.112731	+	0.0650853i	0.555305	−	0.831647i	$-0.312601\pi$
$887$	99.9924	+	57.7307i	0.112731	+	0.0650853i	−0.442574	+	0.896732i	$0.645935\pi$
$888$	92.3909	−	86.0611i	0.104044	−	0.0969156i
$889$	276.387	+	1527.80i	0.310896	+	1.71856i
$890$		−	134.810i		−	0.151472i
$891$	51.6823	−	361.969i	0.0580048	−	0.406250i
$892$	81.8923	−	141.842i	0.0918076	−	0.159015i
$893$	−1037.05	+	598.740i	−1.16131	+	0.670482i
$894$	−102.629	+	335.026i	−0.114797	+	0.374749i
$895$	−144.739	−	250.695i	−0.161719	−	0.280106i
$896$	−77.9310	+	14.0981i	−0.0869766	+	0.0157345i
$897$	−177.753	−	771.867i	−0.198164	−	0.860498i
$898$	260.858			0.290487
$899$	−1958.87	−	1130.95i	−2.17894	−	1.25801i
$900$	327.039	+	221.114i	0.363377	+	0.245682i
$901$	15.8377	+	27.4317i	0.0175779	+	0.0304458i
$902$	−179.039	−	103.368i	−0.198491	−	0.114599i
$903$	−61.5113	−	7.31002i	−0.0681188	−	0.00809526i
$904$	−144.354	−	250.028i	−0.159683	−	0.276579i
$905$	−371.054	−	214.228i	−0.410005	−	0.236716i
$906$	663.524	−	618.065i	0.732366	−	0.682191i
$907$	91.2855	+	158.111i	0.100646	+	0.174323i	0.911951	−	0.410300i	$-0.134576\pi$
$907$	91.2855	+	158.111i	0.100646	+	0.174323i	−0.811305	+	0.584623i	$0.801243\pi$
$908$	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	0.00517457	−	0.999987i	$-0.498353\pi$
$911$	−781.868	−	451.411i	−0.858252	−	0.495512i	−0.863427	+	0.504475i	$0.831686\pi$
$912$	177.515	+	190.571i	0.194644	+	0.208960i
$913$	−102.032			−0.111755
$914$		−	223.575i		−	0.244612i
$915$	399.578	+	122.403i	0.436697	+	0.133774i
$916$	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	$-0.388969\pi$
$920$	117.822	−	68.0244i	0.128067	−	0.0739396i
$921$	−738.144	+	169.987i	−0.801459	+	0.184568i
$922$	245.860	−	425.841i	0.266659	−	0.461867i
$923$	−74.3255	+	42.9119i	−0.0805260	+	0.0464917i
$924$	−151.856	−	113.509i	−0.164347	−	0.122845i
$925$	−163.177	+	282.630i	−0.176407	+	0.305546i
$926$	−417.967	+	241.313i	−0.451368	+	0.260598i
$927$	74.3044	−	1046.09i	0.0801558	−	1.12847i
$928$	−159.982	+	277.098i	−0.172395	+	0.298597i
$929$			877.848i			0.944939i	0.881347	+	0.472469i	$0.156637\pi$
$929$			877.848i			0.944939i	−0.881347	+	0.472469i	$0.843363\pi$
$930$	87.0435	−	284.148i	0.0935952	−	0.305536i
$931$	820.694	+	676.326i	0.881518	+	0.726451i
$932$	−237.967	+	137.390i	−0.255330	+	0.147415i
$933$	139.309	+	604.930i	0.149313	+	0.648371i
$934$	−181.827	−	314.934i	−0.194676	−	0.337188i
$935$	−3.88375	−	2.24228i	−0.00415374	−	0.00239816i
$936$	−137.084	+	202.755i	−0.146457	+	0.216618i
$937$	−618.122			−0.659682			−0.329841	−	0.944037i	$-0.606995\pi$
$937$	−618.122			−0.659682			−0.329841	+	0.944037i	$0.606995\pi$
$938$	2.77118	−	0.501321i	0.00295435	−	0.000534457i
$939$	993.811	−	228.865i	1.05837	−	0.243732i
$940$	96.6453	−	167.395i	0.102814	−	0.178079i
$941$		−	959.816i		−	1.02000i	−0.860176	−	0.509998i	$-0.829646\pi$
$941$		−	959.816i		−	1.02000i	0.860176	−	0.509998i	$-0.170354\pi$
$942$	−154.047	−	668.925i	−0.163532	−	0.710112i
$943$	889.294			0.943048
$944$			49.6905i			0.0526383i
$945$	−108.654	−	312.717i	−0.114978	−	0.330918i
$946$	−18.8306			−0.0199055
$947$			746.630i			0.788416i	0.919021	+	0.394208i	$0.128981\pi$
$947$			746.630i			0.788416i	−0.919021	+	0.394208i	$0.871019\pi$
$948$	570.971	−	131.489i	0.602290	−	0.138701i
$949$	−77.4166			−0.0815771
$950$	−582.971	−	336.579i	−0.613654	−	0.354293i
$951$	−184.952	−	803.126i	−0.194481	−	0.844507i
$952$	−10.5691	−	3.79382i	−0.0111020	−	0.00398511i
$953$		−	1477.27i		−	1.55013i	−0.631881	−	0.775065i	$-0.717717\pi$
$953$		−	1477.27i		−	1.55013i	0.631881	−	0.775065i	$-0.282283\pi$
$954$	−50.3637	+	709.045i	−0.0527921	+	0.743234i
$955$	−128.692	+	222.901i	−0.134756	+	0.233404i
$956$	−696.077	+	401.880i	−0.728114	+	0.420377i
$957$	−746.442	+	171.898i	−0.779981	+	0.179622i
$958$	140.671	+	243.650i	0.146839	+	0.254332i
$959$	1071.24	+	1265.22i	1.11704	+	1.31931i
$960$	−40.1951	−	12.3130i	−0.0418699	−	0.0128261i
$961$	638.166			0.664064
$962$	−175.222	−	101.165i	−0.182144	−	0.105161i
$963$	−383.465	+	567.167i	−0.398199	+	0.588958i
$964$	439.498	+	761.232i	0.455910	+	0.789660i
$965$	384.973	+	222.264i	0.398936	+	0.230326i
$966$	809.842	+	96.2418i	0.838345	+	0.0996292i
$967$	81.0172	+	140.326i	0.0837820	+	0.145115i	0.904872	−	0.425685i	$-0.139967\pi$
$967$	81.0172	+	140.326i	0.0837820	+	0.145115i	−0.821090	+	0.570799i	$0.806633\pi$
$968$	246.475	+	142.303i	0.254623	+	0.147007i
$969$	8.28733	+	35.9865i	0.00855246	+	0.0371378i
$970$	−94.2109	−	163.178i	−0.0971247	−	0.168225i
$971$	−1063.88	+	614.232i	−1.09565	+	0.632577i	−0.935076	−	0.354446i	$-0.884669\pi$
$971$	−1063.88	+	614.232i	−1.09565	+	0.632577i	−0.160579	+	0.987023i	$0.551336\pi$
$972$	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
$975$	185.286	−	604.854i	0.190037	−	0.620363i
$976$	318.111			0.325933
$977$			1042.27i			1.06681i	0.845860	+	0.533405i	$0.179088\pi$
$977$			1042.27i			1.06681i	−0.845860	+	0.533405i	$0.820912\pi$
$978$	−166.847	+	155.416i	−0.170600	+	0.158912i
$979$	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
$983$	679.154	−	392.110i	0.690899	−	0.398891i	−0.113050	−	0.993589i	$-0.536062\pi$
$983$	679.154	−	392.110i	0.690899	−	0.398891i	0.803949	+	0.594698i	$0.202729\pi$
$984$	−187.296	−	201.071i	−0.190341	−	0.204341i
$985$	−278.620	+	482.584i	−0.282863	+	0.489933i
$986$	−39.2904	+	22.6843i	−0.0398482	+	0.0230064i
$987$	1064.80	−	456.873i	1.07882	−	0.462890i
$988$	208.669	−	361.425i	0.211203	−	0.365815i
$989$	70.1492	−	40.5006i	0.0709294	−	0.0409511i
$990$	−44.0177	−	90.5018i	−0.0444623	−	0.0914159i
$991$	−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	$0.192890\pi$
$992$		−	226.215i		−	0.228039i
$993$	575.975	−	132.641i	0.580035	−	0.133576i
$994$	−15.7307	−	86.9554i	−0.0158256	−	0.0874803i
$995$	−374.737	+	216.354i	−0.376620	+	0.217442i
$996$	−129.671	−	39.7223i	−0.130192	−	0.0398818i
$997$	113.216	+	196.096i	0.113557	+	0.196686i	0.917202	−	0.398423i	$-0.130442\pi$
$997$	113.216	+	196.096i	0.113557	+	0.196686i	−0.803645	+	0.595109i	$0.797109\pi$
$998$	−18.6159	−	10.7479i	−0.0186532	−	0.0107694i
$999$	374.846	+	144.599i	0.375222	+	0.144744i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.12	✓	32	7.2	even	3
126.3.i.a.95.12	yes	32	9.5	odd	6
126.3.r.a.11.9	yes	32	1.1	even	1	trivial
126.3.r.a.23.1	yes	32	63.23	odd	6	inner
378.3.i.a.179.5		32	9.4	even	3
378.3.i.a.359.4		32	21.2	odd	6
378.3.r.a.233.13		32	63.58	even	3
378.3.r.a.305.5		32	3.2	odd	2

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} +(-2.92348 + 0.673248i) q^{3} -2.00000 q^{4} +(-1.51694 - 0.875808i) q^{5} +(-0.952117 - 4.13443i) q^{6} +(-1.24611 - 6.88819i) q^{7} -2.82843i q^{8} +(8.09347 - 3.93646i) q^{9} +(1.23858 - 2.14528i) q^{10} +(3.90930 - 2.25703i) q^{11} +(5.84696 - 1.34650i) q^{12} +(-4.80730 - 8.32649i) q^{13} +(9.74138 - 1.76226i) q^{14} +(5.02439 + 1.53913i) q^{15} +4.00000 q^{16} +(0.491183 + 0.283585i) q^{17} +(5.56699 + 11.4459i) q^{18} +(-10.8517 - 18.7956i) q^{19} +(3.03389 + 1.75162i) q^{20} +(8.28044 + 19.2986i) q^{21} +(3.19193 + 5.52858i) q^{22} +(-23.7816 - 13.7303i) q^{23} +(1.90423 + 8.26885i) q^{24} +(-10.9659 - 18.9935i) 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} +(-2.17666 + 7.10556i) q^{30} -39.9896 q^{31} +5.65685i q^{32} +(-9.90921 + 9.23032i) 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} +(26.5810 - 15.3466i) q^{38} +(19.6598 + 21.1058i) q^{39} +(-2.47716 + 4.29057i) q^{40} +(-28.0456 + 16.1921i) q^{41} +(-27.2923 + 11.7103i) q^{42} +(-1.47486 + 2.55453i) q^{43} +(-7.81860 + 4.51407i) q^{44} +(-15.7249 - 1.11695i) q^{45} +(19.4176 - 33.6323i) q^{46} -55.1749i q^{47} +(-11.6939 + 2.69299i) q^{48} +(-45.8944 + 17.1669i) q^{49} +(26.8609 - 15.5082i) q^{50} +(-1.62689 - 0.498366i) q^{51} +(9.61460 + 16.6530i) q^{52} +(48.3659 + 27.9241i) q^{53} +(-23.9809 - 29.7139i) q^{54} -7.90692 q^{55} +(-19.4828 + 3.52453i) q^{56} +(44.3788 + 47.6428i) q^{57} +(-39.9956 + 69.2744i) q^{58} +12.4226i q^{59} +(-10.0488 - 3.07826i) q^{60} +79.5276 q^{61} -56.5538i q^{62} +(-37.2004 - 50.8442i) q^{63} -8.00000 q^{64} +16.8411i q^{65} +(-13.0537 - 14.0137i) q^{66} +0.284475 q^{67} +(-0.982367 - 0.567170i) q^{68} +(78.7691 + 24.1294i) q^{69} +(-16.3205 - 5.85832i) q^{70} -8.92640i q^{71} +(-11.1340 - 22.8918i) q^{72} +(4.02599 - 6.97323i) q^{73} +(18.2246 - 10.5220i) q^{74} +(44.8460 + 48.1444i) q^{75} +(21.7033 + 37.5913i) q^{76} +(-20.4183 - 24.1155i) q^{77} +(-29.8481 + 27.8032i) q^{78} +97.6526 q^{79} +(-6.06778 - 3.50323i) q^{80} +(50.0086 - 63.7192i) q^{81} +(-22.8992 - 39.6625i) q^{82} +(-19.5749 - 11.3016i) q^{83} +(-16.5609 - 38.5971i) q^{84} +(-0.496732 - 0.860365i) q^{85} +(-3.61265 - 2.08577i) q^{86} +(-162.245 - 49.7008i) q^{87} +(-6.38386 - 11.0572i) 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} +(116.909 - 26.9229i) q^{93} +78.0291 q^{94} +38.0159i q^{95} +(-3.80847 - 16.5377i) q^{96} +(38.0319 - 65.8731i) q^{97} +(-24.2776 - 64.9045i) q^{98} +(22.7551 - 33.6560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27}+ \cdots + 394 q^{99}+O(q^{100}) \) 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

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