LMFDB - Embedded newform 126.3.r.a.11.8

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			11.8
Character	$\chi$	$=$	126.11
Dual form			126.3.r.a.23.16

$q$-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} +(2.81732 - 1.03088i) q^{3} -2.00000 q^{4} +(6.63902 + 3.83304i) q^{5} +(-1.45789 - 3.98429i) q^{6} +(2.93662 + 6.35423i) q^{7} +2.82843i q^{8} +(6.87456 - 5.80865i) q^{9} +(5.42073 - 9.38899i) q^{10} +(-8.62843 + 4.98162i) q^{11} +(-5.63464 + 2.06177i) q^{12} +(-5.46176 - 9.46004i) q^{13} +(8.98624 - 4.15301i) q^{14} +(22.6556 + 3.95484i) q^{15} +4.00000 q^{16} +(-24.5539 - 14.1762i) q^{17} +(-8.21467 - 9.72210i) q^{18} +(-5.29575 - 9.17250i) q^{19} +(-13.2780 - 7.66608i) q^{20} +(14.8239 + 14.8746i) q^{21} +(7.04508 + 12.2024i) q^{22} +(-0.643871 - 0.371739i) q^{23} +(2.91578 + 7.96858i) q^{24} +(16.8844 + 29.2446i) q^{25} +(-13.3785 + 7.72409i) q^{26} +(13.3798 - 23.4517i) q^{27} +(-5.87324 - 12.7085i) q^{28} +(-39.7806 - 22.9673i) q^{29} +(5.59299 - 32.0399i) q^{30} +47.6494 q^{31} -5.65685i q^{32} +(-19.1735 + 22.9297i) q^{33} +(-20.0482 + 34.7245i) q^{34} +(-4.85975 + 53.4420i) q^{35} +(-13.7491 + 11.6173i) q^{36} +(12.6993 + 21.9958i) q^{37} +(-12.9719 + 7.48932i) q^{38} +(-25.1397 - 21.0215i) q^{39} +(-10.8415 + 18.7780i) q^{40} +(-32.2267 + 18.6061i) q^{41} +(21.0358 - 20.9641i) q^{42} +(11.0473 - 19.1345i) q^{43} +(17.2569 - 9.96325i) q^{44} +(67.9051 - 12.2133i) q^{45} +(-0.525718 + 0.910571i) q^{46} +29.8032i q^{47} +(11.2693 - 4.12353i) q^{48} +(-31.7525 + 37.3199i) q^{49} +(41.3581 - 23.8781i) q^{50} +(-83.7902 - 14.6267i) q^{51} +(10.9235 + 18.9201i) q^{52} +(26.8405 + 15.4964i) q^{53} +(-33.1657 - 18.9219i) q^{54} -76.3790 q^{55} +(-17.9725 + 8.30601i) q^{56} +(-24.3756 - 20.3826i) q^{57} +(-32.4807 + 56.2583i) q^{58} +58.4538i q^{59} +(-45.3113 - 7.90968i) q^{60} -25.6194 q^{61} -67.3864i q^{62} +(57.0975 + 26.6248i) q^{63} -8.00000 q^{64} -83.7405i q^{65} +(32.4275 + 27.1155i) q^{66} +1.60882 q^{67} +(49.1078 + 28.3524i) q^{68} +(-2.19721 - 0.383552i) q^{69} +(75.5784 + 6.87272i) q^{70} -98.6493i q^{71} +(16.4293 + 19.4442i) q^{72} +(43.7317 - 75.7455i) q^{73} +(31.1067 - 17.9595i) q^{74} +(77.7164 + 64.9855i) q^{75} +(10.5915 + 18.3450i) q^{76} +(-56.9928 - 40.1979i) q^{77} +(-29.7289 + 35.5529i) q^{78} +107.397 q^{79} +(26.5561 + 15.3322i) q^{80} +(13.5192 - 79.8638i) q^{81} +(26.3130 + 45.5755i) q^{82} +(135.329 + 78.1320i) q^{83} +(-29.6477 - 29.7492i) q^{84} +(-108.676 - 188.232i) q^{85} +(-27.0602 - 15.6232i) q^{86} +(-135.751 - 23.6972i) q^{87} +(-14.0902 - 24.4049i) q^{88} +(-54.2036 + 31.2945i) q^{89} +(-17.2722 - 96.0323i) q^{90} +(44.0722 - 62.4858i) q^{91} +(1.28774 + 0.743478i) q^{92} +(134.244 - 49.1209i) q^{93} +42.1481 q^{94} -81.1952i q^{95} +(-5.83155 - 15.9372i) q^{96} +(30.3830 - 52.6249i) q^{97} +(52.7783 + 44.9049i) q^{98} +(-30.3801 + 84.3660i) 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
$3$	2.81732	−	1.03088i	0.939106	−	0.343628i
$3$	2.81732	−	1.03088i	0.939106	−	0.343628i
$4$	−2.00000			−0.500000
$5$	6.63902	+	3.83304i	1.32780	+	0.766608i	0.984960	−	0.172785i	$-0.0552765\pi$
$5$	6.63902	+	3.83304i	1.32780	+	0.766608i	0.342844	+	0.939392i	$0.388610\pi$
$6$	−1.45789	−	3.98429i	−0.242981	−	0.664048i
$7$	2.93662	+	6.35423i	0.419517	+	0.907747i
$7$	2.93662	+	6.35423i	0.419517	+	0.907747i
$8$			2.82843i			0.353553i
$9$	6.87456	−	5.80865i	0.763840	−	0.645405i
$10$	5.42073	−	9.38899i	0.542073	−	0.938899i
$11$	−8.62843	+	4.98162i	−0.784402	+	0.452875i	−0.837988	−	0.545688i	$-0.816268\pi$
$11$	−8.62843	+	4.98162i	−0.784402	+	0.452875i	0.0535859	+	0.998563i	$0.482935\pi$
$12$	−5.63464	+	2.06177i	−0.469553	+	0.171814i
$13$	−5.46176	−	9.46004i	−0.420135	−	0.727695i	0.575817	−	0.817578i	$-0.304684\pi$
$13$	−5.46176	−	9.46004i	−0.420135	−	0.727695i	−0.995952	+	0.0898831i	$0.971351\pi$
$14$	8.98624	−	4.15301i	0.641874	−	0.296643i
$15$	22.6556	+	3.95484i	1.51038	+	0.263656i
$16$	4.00000			0.250000
$17$	−24.5539	−	14.1762i	−1.44435	−	0.833895i	−0.446212	−	0.894927i	$-0.647227\pi$
$17$	−24.5539	−	14.1762i	−1.44435	−	0.833895i	−0.998136	+	0.0610326i	$0.980561\pi$
$18$	−8.21467	−	9.72210i	−0.456371	−	0.540117i
$19$	−5.29575	−	9.17250i	−0.278723	−	0.482763i	0.692344	−	0.721567i	$-0.256578\pi$
$19$	−5.29575	−	9.17250i	−0.278723	−	0.482763i	−0.971068	+	0.238804i	$0.923245\pi$
$20$	−13.2780	−	7.66608i	−0.663902	−	0.383304i
$21$	14.8239	+	14.8746i	0.705898	+	0.708313i
$22$	7.04508	+	12.2024i	0.320231	+	0.554656i
$23$	−0.643871	−	0.371739i	−0.0279944	−	0.0161626i	0.485938	−	0.873994i	$-0.338478\pi$
$23$	−0.643871	−	0.371739i	−0.0279944	−	0.0161626i	−0.513932	+	0.857831i	$0.671812\pi$
$24$	2.91578	+	7.96858i	0.121491	+	0.332024i
$25$	16.8844	+	29.2446i	0.675375	+	1.16978i
$26$	−13.3785	+	7.72409i	−0.514558	+	0.297080i
$27$	13.3798	−	23.4517i	0.495548	−	0.868581i
$28$	−5.87324	−	12.7085i	−0.209759	−	0.453874i
$29$	−39.7806	−	22.9673i	−1.37175	−	0.791977i	−0.380597	−	0.924741i	$-0.624282\pi$
$29$	−39.7806	−	22.9673i	−1.37175	−	0.791977i	−0.991148	+	0.132763i	$0.957615\pi$
$30$	5.59299	−	32.0399i	0.186433	−	1.06800i
$31$	47.6494			1.53708			0.768539	−	0.639803i	$-0.220984\pi$
$31$	47.6494			1.53708			0.768539	+	0.639803i	$0.220984\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−19.1735	+	22.9297i	−0.581017	+	0.694840i
$34$	−20.0482	+	34.7245i	−0.589653	+	1.02131i
$35$	−4.85975	+	53.4420i	−0.138850	+	1.52692i
$36$	−13.7491	+	11.6173i	−0.381920	+	0.322703i
$37$	12.6993	+	21.9958i	0.343223	+	0.594480i	0.985029	−	0.172387i	$-0.0551479\pi$
$37$	12.6993	+	21.9958i	0.343223	+	0.594480i	−0.641806	+	0.766867i	$0.721815\pi$
$38$	−12.9719	+	7.48932i	−0.341365	+	0.197087i
$39$	−25.1397	−	21.0215i	−0.644608	−	0.539013i
$40$	−10.8415	+	18.7780i	−0.271037	+	0.469449i
$41$	−32.2267	+	18.6061i	−0.786017	+	0.453807i	−0.838559	−	0.544811i	$-0.816601\pi$
$41$	−32.2267	+	18.6061i	−0.786017	+	0.453807i	0.0525412	+	0.998619i	$0.483268\pi$
$42$	21.0358	−	20.9641i	0.500853	−	0.499145i
$43$	11.0473	−	19.1345i	0.256914	−	0.444988i	−0.708500	−	0.705711i	$-0.750628\pi$
$43$	11.0473	−	19.1345i	0.256914	−	0.444988i	0.965414	+	0.260723i	$0.0839610\pi$
$44$	17.2569	−	9.96325i	0.392201	−	0.226437i
$45$	67.9051	−	12.2133i	1.50900	−	0.271406i
$46$	−0.525718	+	0.910571i	−0.0114287	+	0.0197950i
$47$			29.8032i			0.634112i	0.948407	+	0.317056i	$0.102694\pi$
$47$			29.8032i			0.634112i	−0.948407	+	0.317056i	$0.897306\pi$
$48$	11.2693	−	4.12353i	0.234777	−	0.0859069i
$49$	−31.7525	+	37.3199i	−0.648011	+	0.761631i
$50$	41.3581	−	23.8781i	0.827162	−	0.477562i
$51$	−83.7902	−	14.6267i	−1.64295	−	0.286798i
$52$	10.9235	+	18.9201i	0.210068	+	0.363848i
$53$	26.8405	+	15.4964i	0.506425	+	0.292385i	0.731363	−	0.681988i	$-0.238885\pi$
$53$	26.8405	+	15.4964i	0.506425	+	0.292385i	−0.224938	+	0.974373i	$0.572218\pi$
$54$	−33.1657	−	18.9219i	−0.614179	−	0.350405i
$55$	−76.3790			−1.38871
$56$	−17.9725	+	8.30601i	−0.320937	+	0.148322i
$57$	−24.3756	−	20.3826i	−0.427642	−	0.357589i
$58$	−32.4807	+	56.2583i	−0.560013	+	0.969970i
$59$			58.4538i			0.990742i	0.868681	+	0.495371i	$0.164968\pi$
$59$			58.4538i			0.990742i	−0.868681	+	0.495371i	$0.835032\pi$
$60$	−45.3113	−	7.90968i	−0.755188	−	0.131828i
$61$	−25.6194			−0.419991			−0.209995	−	0.977702i	$-0.567345\pi$
$61$	−25.6194			−0.419991			−0.209995	+	0.977702i	$0.567345\pi$
$62$		−	67.3864i		−	1.08688i
$63$	57.0975	+	26.6248i	0.906309	+	0.422615i
$64$	−8.00000			−0.125000
$65$		−	83.7405i		−	1.28832i
$66$	32.4275	+	27.1155i	0.491326	+	0.410841i
$67$	1.60882			0.0240122			0.0120061	−	0.999928i	$-0.496178\pi$
$67$	1.60882			0.0240122			0.0120061	+	0.999928i	$0.496178\pi$
$68$	49.1078	+	28.3524i	0.722174	+	0.416947i
$69$	−2.19721	−	0.383552i	−0.0318436	−	0.00555872i
$70$	75.5784	+	6.87272i	1.07969	+	0.0981817i
$71$		−	98.6493i		−	1.38943i	−0.719287	−	0.694713i	$-0.755531\pi$
$71$		−	98.6493i		−	1.38943i	0.719287	−	0.694713i	$-0.244469\pi$
$72$	16.4293	+	19.4442i	0.228185	+	0.270058i
$73$	43.7317	−	75.7455i	0.599064	−	1.03761i	−0.393895	−	0.919155i	$-0.628873\pi$
$73$	43.7317	−	75.7455i	0.599064	−	1.03761i	0.992959	−	0.118455i	$-0.0377940\pi$
$74$	31.1067	−	17.9595i	0.420361	−	0.242695i
$75$	77.7164	+	64.9855i	1.03622	+	0.866473i
$76$	10.5915	+	18.3450i	0.139362	+	0.241382i
$77$	−56.9928	−	40.1979i	−0.740166	−	0.522050i
$78$	−29.7289	+	35.5529i	−0.381140	+	0.455806i
$79$	107.397			1.35945			0.679727	−	0.733465i	$-0.262098\pi$
$79$	107.397			1.35945			0.679727	+	0.733465i	$0.262098\pi$
$80$	26.5561	+	15.3322i	0.331951	+	0.191652i
$81$	13.5192	−	79.8638i	0.166904	−	0.985973i
$82$	26.3130	+	45.5755i	0.320890	+	0.555798i
$83$	135.329	+	78.1320i	1.63047	+	0.941350i	0.983949	+	0.178450i	$0.0571084\pi$
$83$	135.329	+	78.1320i	1.63047	+	0.941350i	0.646517	+	0.762900i	$0.276225\pi$
$84$	−29.6477	−	29.7492i	−0.352949	−	0.354157i
$85$	−108.676	−	188.232i	−1.27854	−	2.21450i
$86$	−27.0602	−	15.6232i	−0.314654	−	0.181666i
$87$	−135.751	−	23.6972i	−1.56036	−	0.272381i
$88$	−14.0902	−	24.4049i	−0.160115	−	0.277328i
$89$	−54.2036	+	31.2945i	−0.609029	+	0.351623i	−0.772586	−	0.634911i	$-0.781037\pi$
$89$	−54.2036	+	31.2945i	−0.609029	+	0.351623i	0.163556	+	0.986534i	$0.447704\pi$
$90$	−17.2722	−	96.0323i	−0.191913	−	1.06703i
$91$	44.0722	−	62.4858i	0.484310	−	0.686657i
$92$	1.28774	+	0.743478i	0.0139972	+	0.00808128i
$93$	134.244	−	49.1209i	1.44348	−	0.528182i
$94$	42.1481			0.448385
$95$		−	81.1952i		−	0.854686i
$96$	−5.83155	−	15.9372i	−0.0607453	−	0.166012i
$97$	30.3830	−	52.6249i	0.313227	−	0.542525i	−0.665832	−	0.746102i	$-0.731923\pi$
$97$	30.3830	−	52.6249i	0.313227	−	0.542525i	0.979059	+	0.203577i	$0.0652566\pi$
$98$	52.7783	+	44.9049i	0.538555	+	0.458213i
$99$	−30.3801	+	84.3660i	−0.306870	+	0.852182i
$100$	−33.7687	−	58.4892i	−0.337687	−	0.584892i
$101$	−14.6186	+	8.44005i	−0.144739	+	0.0835648i	−0.570620	−	0.821214i	$-0.693297\pi$
$101$	−14.6186	+	8.44005i	−0.144739	+	0.0835648i	0.425882	+	0.904779i	$0.359964\pi$
$102$	−20.6853	+	118.497i	−0.202797	+	1.16174i
$103$	−78.6740	+	136.267i	−0.763825	+	1.32298i	0.177040	+	0.984204i	$0.443348\pi$
$103$	−78.6740	+	136.267i	−0.763825	+	1.32298i	−0.940865	+	0.338781i	$0.889986\pi$
$104$	26.7570	−	15.4482i	0.257279	−	0.148540i
$105$	41.4010	+	155.573i	0.394295	+	1.48165i
$106$	21.9152	−	37.9583i	0.206747	−	0.358097i
$107$	−71.7631	+	41.4325i	−0.670683	+	0.387219i	−0.796336	−	0.604855i	$-0.793231\pi$
$107$	−71.7631	+	41.4325i	−0.670683	+	0.387219i	0.125652	+	0.992074i	$0.459898\pi$
$108$	−26.7596	+	46.9034i	−0.247774	+	0.434290i
$109$	0.587347	−	1.01731i	0.00538850	−	0.00933316i	−0.863319	−	0.504659i	$-0.831618\pi$
$109$	0.587347	−	1.01731i	0.00538850	−	0.00933316i	0.868707	+	0.495326i	$0.164951\pi$
$110$			108.016i			0.981966i
$111$	58.4529	+	48.8776i	0.526603	+	0.440339i
$112$	11.7465	+	25.4169i	0.104879	+	0.226937i
$113$	−34.0786	+	19.6753i	−0.301580	+	0.174118i	−0.643153	−	0.765738i	$-0.722374\pi$
$113$	−34.0786	+	19.6753i	−0.301580	+	0.174118i	0.341572	+	0.939856i	$0.389041\pi$
$114$	−28.8253	+	34.4723i	−0.252853	+	0.302388i
$115$	−2.84978	−	4.93596i	−0.0247807	−	0.0429214i
$116$	79.5612	+	45.9347i	0.685873	+	0.395989i
$117$	−92.4972	−	33.3082i	−0.790575	−	0.284686i
$118$	82.6662			0.700561
$119$	17.9734	−	197.651i	0.151037	−	1.66094i
$120$	−11.1860	+	64.0798i	−0.0932165	+	0.533998i
$121$	−10.8669	+	18.8219i	−0.0898087	+	0.155553i
$122$			36.2314i			0.296978i
$123$	−71.6122	+	85.6413i	−0.582213	+	0.696271i
$124$	−95.2988			−0.768539
$125$			67.2217i			0.537774i
$126$	37.6531	−	80.7480i	0.298834	−	0.640857i
$127$	−86.8989			−0.684243			−0.342122	−	0.939656i	$-0.611146\pi$
$127$	−86.8989			−0.684243			−0.342122	+	0.939656i	$0.611146\pi$
$128$			11.3137i			0.0883883i
$129$	11.3983	−	65.2964i	0.0883593	−	0.506174i
$130$	−118.427			−0.910976
$131$	78.7600	+	45.4721i	0.601221	+	0.347115i	0.769522	−	0.638620i	$-0.220495\pi$
$131$	78.7600	+	45.4721i	0.601221	+	0.347115i	−0.168301	+	0.985736i	$0.553828\pi$
$132$	38.3471	−	45.8594i	0.290508	−	0.347420i
$133$	42.7326	−	60.5865i	0.321298	−	0.455538i
$134$		−	2.27521i		−	0.0169792i
$135$	178.720	−	104.411i	1.32385	−	0.773414i
$136$	40.0964	−	69.4490i	0.294826	−	0.510654i
$137$	−58.5106	+	33.7811i	−0.427085	+	0.246578i	−0.698104	−	0.715996i	$-0.745973\pi$
$137$	−58.5106	+	33.7811i	−0.427085	+	0.246578i	0.271019	+	0.962574i	$0.412639\pi$
$138$	−0.542424	+	3.10732i	−0.00393061	+	0.0225168i
$139$	41.8849	+	72.5467i	0.301330	+	0.521919i	0.976437	−	0.215801i	$-0.0692361\pi$
$139$	41.8849	+	72.5467i	0.301330	+	0.521919i	−0.675108	+	0.737719i	$0.735903\pi$
$140$	9.71949	−	106.884i	0.0694249	−	0.763458i
$141$	30.7236	+	83.9652i	0.217898	+	0.595498i
$142$	−139.511			−0.982473
$143$	94.2527	+	54.4168i	0.659110	+	0.380537i
$144$	27.4982	−	23.2346i	0.190960	−	0.161351i
$145$	−176.069	−	304.961i	−1.21427	−	2.10318i
$146$	−107.120	−	61.8460i	−0.733701	−	0.423602i
$147$	−50.9845	+	137.875i	−0.346833	+	0.937927i
$148$	−25.3985	−	43.9915i	−0.171612	−	0.297240i
$149$	87.0552	+	50.2613i	0.584263	+	0.337324i	0.762826	−	0.646604i	$-0.223811\pi$
$149$	87.0552	+	50.2613i	0.584263	+	0.337324i	−0.178563	+	0.983929i	$0.557145\pi$
$150$	91.9033	−	109.908i	0.612689	−	0.732717i
$151$	39.1366	+	67.7866i	0.259183	+	0.448918i	0.966023	−	0.258455i	$-0.0832134\pi$
$151$	39.1366	+	67.7866i	0.259183	+	0.448918i	−0.706840	+	0.707373i	$0.749880\pi$
$152$	25.9437	−	14.9786i	0.170683	−	0.0985436i
$153$	−251.142	+	45.1698i	−1.64145	+	0.295228i
$154$	−56.8484	+	80.6000i	−0.369145	+	0.523377i
$155$	316.345	+	182.642i	2.04094	+	1.17834i
$156$	50.2794	+	42.0430i	0.322304	+	0.269507i
$157$	−238.344			−1.51812			−0.759058	−	0.651023i	$-0.774340\pi$
$157$	−238.344			−1.51812			−0.759058	+	0.651023i	$0.774340\pi$
$158$		−	151.882i		−	0.961279i
$159$	91.5933	+	15.9888i	0.576059	+	0.100559i
$160$	21.6829	−	37.5560i	0.135518	−	0.234725i
$161$	0.471312	−	5.18296i	0.00292740	−	0.0321923i
$162$	−112.945	−	19.1190i	−0.697188	−	0.118019i
$163$	40.6681	+	70.4391i	0.249497	+	0.432142i	0.963386	−	0.268117i	$-0.0864013\pi$
$163$	40.6681	+	70.4391i	0.249497	+	0.432142i	−0.713889	+	0.700259i	$0.753068\pi$
$164$	64.4534	−	37.2122i	0.393009	−	0.226904i
$165$	−215.184	+	78.7378i	−1.30415	+	0.477199i
$166$	110.495	−	191.384i	0.665635	−	1.15291i
$167$	−166.402	+	96.0720i	−0.996417	+	0.575281i	−0.907186	−	0.420730i	$-0.861774\pi$
$167$	−166.402	+	96.0720i	−0.996417	+	0.575281i	−0.0892305	+	0.996011i	$0.528441\pi$
$168$	−42.0717	+	41.9282i	−0.250427	+	0.249573i
$169$	24.8384	−	43.0214i	0.146973	−	0.254565i
$170$	−266.201	+	153.691i	−1.56589	+	0.904064i
$171$	−89.6858	−	32.2958i	−0.524478	−	0.188864i
$172$	−22.0946	+	38.2690i	−0.128457	+	0.222494i
$173$			62.4034i			0.360713i	0.983601	+	0.180357i	$0.0577252\pi$
$173$			62.4034i			0.360713i	−0.983601	+	0.180357i	$0.942275\pi$
$174$	−33.5129	+	191.981i	−0.192603	+	1.10334i
$175$	−136.244	+	193.167i	−0.778536	+	1.10381i
$176$	−34.5137	+	19.9265i	−0.196101	+	0.113219i
$177$	60.2590	+	164.683i	0.340446	+	0.930412i
$178$	44.2571	+	76.6555i	0.248635	+	0.430649i
$179$	−105.048	−	60.6496i	−0.586861	−	0.338824i	0.176994	−	0.984212i	$-0.443363\pi$
$179$	−105.048	−	60.6496i	−0.586861	−	0.338824i	−0.763855	+	0.645387i	$0.776696\pi$
$180$	−135.810	+	24.4265i	−0.754501	+	0.135703i
$181$	227.780			1.25845			0.629227	−	0.777222i	$-0.283372\pi$
$181$	227.780			1.25845			0.629227	+	0.777222i	$0.283372\pi$
$182$	−88.3683	−	62.3275i	−0.485540	−	0.342459i
$183$	−72.1781	+	26.4106i	−0.394416	+	0.144320i
$184$	1.05144	−	1.82114i	0.00571433	−	0.00989751i
$185$			194.707i			1.05247i
$186$	−69.4675	−	189.849i	−0.373481	−	1.02069i
$187$	282.482			1.51060
$188$		−	59.6065i		−	0.317056i
$189$	188.309	+	16.1496i	0.996343	+	0.0854479i
$190$	−114.827			−0.604354
$191$		−	150.487i		−	0.787889i	−0.919134	−	0.393945i	$-0.871110\pi$
$191$		−	150.487i		−	0.787889i	0.919134	−	0.393945i	$-0.128890\pi$
$192$	−22.5385	+	8.24706i	−0.117388	+	0.0429534i
$193$	377.717			1.95708			0.978540	−	0.206055i	$-0.0660625\pi$
$193$	377.717			1.95708			0.978540	+	0.206055i	$0.0660625\pi$
$194$	−74.4229	−	42.9681i	−0.383623	−	0.221485i
$195$	−86.3266	−	235.924i	−0.442701	−	1.20986i
$196$	63.5051	−	74.6399i	0.324005	−	0.380816i
$197$		−	316.391i		−	1.60604i	−0.595949	−	0.803022i	$-0.703224\pi$
$197$		−	316.391i		−	1.60604i	0.595949	−	0.803022i	$-0.296776\pi$
$198$	119.311	+	42.9640i	0.602583	+	0.216990i
$199$	43.8716	−	75.9878i	0.220460	−	0.381848i	−0.734488	−	0.678622i	$-0.762577\pi$
$199$	43.8716	−	75.9878i	0.220460	−	0.381848i	0.954948	+	0.296774i	$0.0959107\pi$
$200$	−82.7162	+	47.7562i	−0.413581	+	0.238781i
$201$	4.53256	−	1.65850i	0.0225500	−	0.00825127i
$202$	11.9360	+	20.6738i	0.0590892	+	0.102346i
$203$	29.1193	−	320.222i	0.143445	−	1.57745i
$204$	167.580	+	29.2534i	0.821473	+	0.143399i
$205$	−285.272			−1.39157
$206$	192.711	+	111.262i	0.935491	+	0.540106i
$207$	−6.58563	+	1.18448i	−0.0318146	+	0.00572211i
$208$	−21.8470	−	37.8402i	−0.105034	−	0.181924i
$209$	91.3879	+	52.7628i	0.437263	+	0.252454i
$210$	220.013	−	58.5499i	1.04768	−	0.278809i
$211$	−48.5679	−	84.1221i	−0.230180	−	0.398683i	0.727681	−	0.685915i	$-0.240598\pi$
$211$	−48.5679	−	84.1221i	−0.230180	−	0.398683i	−0.957861	+	0.287233i	$0.907265\pi$
$212$	−53.6811	−	30.9928i	−0.253213	−	0.146192i
$213$	−101.696	−	277.926i	−0.477445	−	1.30482i
$214$	58.5943	+	101.488i	0.273805	+	0.474245i
$215$	146.686	−	84.6894i	0.682262	−	0.393904i
$216$	66.3314	+	37.8438i	0.307090	+	0.175203i
$217$	139.928	+	302.775i	0.644830	+	1.39528i
$218$	−1.43870	−	0.830634i	−0.00659954	−	0.00381025i
$219$	45.1214	−	258.481i	0.206034	−	1.18028i
$220$	152.758			0.694355
$221$			309.708i			1.40139i
$222$	69.1234	−	82.6649i	0.311367	−	0.372364i
$223$	−140.617	+	243.556i	−0.630569	+	1.09218i	0.356867	+	0.934155i	$0.383845\pi$
$223$	−140.617	+	243.556i	−0.630569	+	1.09218i	−0.987436	+	0.158022i	$0.949488\pi$
$224$	35.9450	−	16.6120i	0.160469	−	0.0741608i
$225$	285.944	+	102.968i	1.27086	+	0.457637i
$226$	27.8250	+	48.1944i	0.123120	+	0.213250i
$227$	−110.285	+	63.6730i	−0.485836	+	0.280498i	−0.722846	−	0.691010i	$-0.757166\pi$
$227$	−110.285	+	63.6730i	−0.485836	+	0.280498i	0.237009	+	0.971507i	$0.423833\pi$
$228$	48.7511	+	40.7651i	0.213821	+	0.178794i
$229$	60.5220	−	104.827i	0.264288	−	0.457761i	−0.703089	−	0.711102i	$-0.748196\pi$
$229$	60.5220	−	104.827i	0.264288	−	0.457761i	0.967377	+	0.253341i	$0.0815296\pi$
$230$	−6.98050	+	4.03020i	−0.0303500	+	0.0175226i
$231$	−202.006	−	54.4973i	−0.874485	−	0.235919i
$232$	64.9615	−	112.517i	0.280006	−	0.484985i
$233$	230.397	−	133.020i	0.988830	−	0.570901i	0.0839058	−	0.996474i	$-0.473261\pi$
$233$	230.397	−	133.020i	0.988830	−	0.570901i	0.904924	+	0.425572i	$0.139927\pi$
$234$	−47.1049	+	130.811i	−0.201303	+	0.559021i
$235$	−114.237	+	197.864i	−0.486115	+	0.841975i
$236$		−	116.908i		−	0.495371i
$237$	302.571	−	110.714i	1.27667	−	0.467146i
$238$	−279.521	−	25.4182i	−1.17446	−	0.106799i
$239$	96.5968	−	55.7702i	0.404171	−	0.233348i	−0.284111	−	0.958791i	$-0.591699\pi$
$239$	96.5968	−	55.7702i	0.404171	−	0.233348i	0.688282	+	0.725443i	$0.258365\pi$
$240$	90.6225	+	15.8194i	0.377594	+	0.0659140i
$241$	160.550	+	278.081i	0.666183	+	1.15386i	0.978963	+	0.204037i	$0.0654062\pi$
$241$	160.550	+	278.081i	0.666183	+	1.15386i	−0.312781	+	0.949825i	$0.601260\pi$
$242$	26.6182	+	15.3681i	0.109993	+	0.0635043i
$243$	−44.2423	−	238.939i	−0.182067	−	0.983286i
$244$	51.2389			0.209995
$245$	−353.854	+	126.059i	−1.44430	+	0.514526i
$246$	121.115	+	101.275i	0.492338	+	0.411687i
$247$	−57.8481	+	100.196i	−0.234203	+	0.405652i
$248$			134.773i			0.543439i
$249$	461.809	+	80.6148i	1.85465	+	0.323754i
$250$	95.0659			0.380264
$251$		−	323.335i		−	1.28819i	−0.764947	−	0.644093i	$-0.777235\pi$
$251$		−	323.335i		−	1.28819i	0.764947	−	0.644093i	$-0.222765\pi$
$252$	−114.195	−	53.2495i	−0.453155	−	0.211308i
$253$	7.40745			0.0292785
$254$			122.894i			0.483833i
$255$	−500.220	−	418.278i	−1.96165	−	1.64031i
$256$	16.0000			0.0625000
$257$	204.239	+	117.917i	0.794703	+	0.458822i	0.841616	−	0.540077i	$-0.181605\pi$
$257$	204.239	+	117.917i	0.794703	+	0.458822i	−0.0469126	+	0.998899i	$0.514938\pi$
$258$	−92.3430	−	16.1197i	−0.357919	−	0.0624794i
$259$	−102.473	+	145.287i	−0.395650	+	0.560955i
$260$			167.481i			0.644158i
$261$	−406.884	+	73.1811i	−1.55894	+	0.280388i
$262$	64.3073	−	111.383i	0.245448	−	0.425128i
$263$	145.689	−	84.1133i	0.553949	−	0.319823i	−0.196764	−	0.980451i	$-0.563043\pi$
$263$	145.689	−	84.1133i	0.553949	−	0.319823i	0.750713	+	0.660628i	$0.229710\pi$
$264$	−64.8550	−	54.2310i	−0.245663	−	0.205420i
$265$	118.797	+	205.762i	0.448289	+	0.776459i
$266$	−85.6823	−	60.4330i	−0.322114	−	0.227192i
$267$	−120.448	+	144.044i	−0.451116	+	0.539491i
$268$	−3.21764			−0.0120061
$269$	−290.003	−	167.433i	−1.07808	−	0.622428i	−0.147700	−	0.989032i	$-0.547187\pi$
$269$	−290.003	−	167.433i	−1.07808	−	0.622428i	−0.930377	+	0.366604i	$0.880520\pi$
$270$	−147.659	−	252.748i	−0.546886	−	0.936104i
$271$	−3.54968	−	6.14822i	−0.0130984	−	0.0226872i	0.859402	−	0.511301i	$-0.170836\pi$
$271$	−3.54968	−	6.14822i	−0.0130984	−	0.0226872i	−0.872500	+	0.488614i	$0.837503\pi$
$272$	−98.2157	−	56.7048i	−0.361087	−	0.208474i
$273$	59.7498	−	221.476i	0.218864	−	0.811266i
$274$	47.7737	+	82.7466i	0.174357	+	0.301995i
$275$	−291.371	−	168.223i	−1.05953	−	0.611720i
$276$	4.39442	+	0.767103i	0.0159218	+	0.00277936i
$277$	−261.435	−	452.819i	−0.943810	−	1.63473i	−0.758116	−	0.652120i	$-0.773880\pi$
$277$	−261.435	−	452.819i	−0.943810	−	1.63473i	−0.185694	−	0.982608i	$-0.559453\pi$
$278$	102.597	−	59.2341i	0.369052	−	0.213072i
$279$	327.569	−	276.779i	1.17408	−	0.992038i
$280$	−151.157	−	13.7454i	−0.539846	−	0.0490908i
$281$	270.951	+	156.433i	0.964237	+	0.556703i	0.897475	−	0.441066i	$-0.145400\pi$
$281$	270.951	+	156.433i	0.964237	+	0.556703i	0.0667628	+	0.997769i	$0.478733\pi$
$282$	118.745	−	43.4498i	0.421081	−	0.154077i
$283$	202.707			0.716280			0.358140	−	0.933668i	$-0.383411\pi$
$283$	202.707			0.716280			0.358140	+	0.933668i	$0.383411\pi$
$284$			197.299i			0.694713i
$285$	−83.7027	−	228.753i	−0.293694	−	0.802641i
$286$	76.9570	−	133.293i	0.269080	−	0.466061i
$287$	−212.865	−	150.137i	−0.741690	−	0.523125i
$288$	−32.8587	−	38.8884i	−0.114093	−	0.135029i
$289$	257.430	+	445.882i	0.890761	+	1.54284i
$290$	−431.280	+	249.000i	−1.48717	+	0.858620i
$291$	31.3485	−	179.582i	0.107727	−	0.617122i
$292$	−87.4634	+	151.491i	−0.299532	+	0.518805i
$293$	−268.759	+	155.168i	−0.917267	+	0.529584i	−0.882762	−	0.469820i	$-0.844319\pi$
$293$	−268.759	+	155.168i	−0.917267	+	0.529584i	−0.0345046	+	0.999405i	$0.510985\pi$
$294$	194.985	+	72.1030i	0.663214	+	0.245248i
$295$	−224.056	+	388.076i	−0.759511	+	1.31551i
$296$	−62.2134	+	35.9189i	−0.210180	+	0.121348i
$297$	1.38089	+	269.004i	0.00464948	+	0.905738i
$298$	71.0803	−	123.115i	0.238524	−	0.413136i
$299$			8.12139i			0.0271618i
$300$	−155.433	−	129.971i	−0.518109	−	0.433237i
$301$	154.027	+	14.0064i	0.511716	+	0.0465329i
$302$	95.8647	−	55.3475i	0.317433	−	0.183270i
$303$	−32.4845	+	38.8483i	−0.107210	+	0.128212i
$304$	−21.1830	−	36.6900i	−0.0696809	−	0.120691i
$305$	−170.088	−	98.2003i	−0.557665	−	0.321968i
$306$	63.8798	+	355.168i	0.208757	+	1.16068i
$307$	−517.470			−1.68557			−0.842786	−	0.538249i	$-0.819086\pi$
$307$	−517.470			−1.68557			−0.842786	+	0.538249i	$0.819086\pi$
$308$	113.986	+	80.3958i	0.370083	+	0.261025i
$309$	−81.1740	+	465.012i	−0.262699	+	1.50489i
$310$	258.295	−	447.380i	0.833209	−	1.44316i
$311$			41.7071i			0.134106i	0.997749	+	0.0670532i	$0.0213597\pi$
$311$			41.7071i			0.134106i	−0.997749	+	0.0670532i	$0.978640\pi$
$312$	59.4578	−	71.1058i	0.190570	−	0.227903i
$313$	−236.404			−0.755283			−0.377642	−	0.925952i	$-0.623265\pi$
$313$	−236.404			−0.755283			−0.377642	+	0.925952i	$0.623265\pi$
$314$			337.070i			1.07347i
$315$	277.017	+	395.619i	0.879420	+	1.25593i
$316$	−214.794			−0.679727
$317$		−	363.141i		−	1.14555i	−0.819711	−	0.572777i	$-0.805866\pi$
$317$		−	363.141i		−	1.14555i	0.819711	−	0.572777i	$-0.194134\pi$
$318$	22.6116	−	129.533i	0.0711057	−	0.407335i
$319$	457.659			1.43467
$320$	−53.1121	−	30.6643i	−0.165975	−	0.0958260i
$321$	−159.468	+	190.708i	−0.496784	+	0.594105i
$322$	−7.32981	−	0.666536i	−0.0227634	−	0.00206999i
$323$			300.294i			0.929704i
$324$	−27.0384	+	159.728i	−0.0834519	+	0.492987i
$325$	184.437	−	319.454i	0.567497	−	0.982934i
$326$	99.6160	−	57.5133i	0.305571	−	0.176421i
$327$	0.606011	−	3.47159i	0.00185324	−	0.0106165i
$328$	−52.6260	−	91.1509i	−0.160445	−	0.277899i
$329$	−189.377	+	87.5208i	−0.575613	+	0.266021i
$330$	111.352	+	304.316i	0.337431	+	0.922170i
$331$	−54.3080			−0.164073			−0.0820363	−	0.996629i	$-0.526142\pi$
$331$	−54.3080			−0.164073			−0.0820363	+	0.996629i	$0.526142\pi$
$332$	−270.657	−	156.264i	−0.815233	−	0.470675i
$333$	215.068	+	77.4457i	0.645848	+	0.232570i
$334$	135.866	+	235.327i	0.406785	+	0.704573i
$335$	10.6810	+	6.16667i	0.0318835	+	0.0184080i
$336$	59.2954	+	59.4983i	0.176475	+	0.177078i
$337$	−88.0335	−	152.479i	−0.261227	−	0.452459i	0.705341	−	0.708868i	$-0.250794\pi$
$337$	−88.0335	−	152.479i	−0.261227	−	0.452459i	−0.966568	+	0.256409i	$0.917460\pi$
$338$	−60.8415	−	35.1268i	−0.180004	−	0.103926i
$339$	−75.7273	+	90.5625i	−0.223384	+	0.267146i
$340$	217.352	+	376.464i	0.639270	+	1.10725i
$341$	−411.139	+	237.371i	−1.20569	+	0.696104i
$342$	−45.6732	+	126.835i	−0.133547	+	0.370862i
$343$	−330.385	−	92.1685i	−0.963220	−	0.268713i
$344$	54.1205	+	31.2465i	0.157327	+	0.0908328i
$345$	−13.1171	−	10.9684i	−0.0380207	−	0.0317924i
$346$	88.2517			0.255063
$347$		−	173.047i		−	0.498695i	−0.968414	−	0.249348i	$-0.919784\pi$
$347$		−	173.047i		−	0.498695i	0.968414	−	0.249348i	$-0.0802161\pi$
$348$	271.503	+	47.3944i	0.780180	+	0.136191i
$349$	59.2604	−	102.642i	0.169801	−	0.294103i	−0.768549	−	0.639791i	$-0.779021\pi$
$349$	59.2604	−	102.642i	0.169801	−	0.294103i	0.938350	+	0.345688i	$0.112354\pi$
$350$	273.180	+	192.678i	0.780514	+	0.550508i
$351$	−294.931	+	1.51399i	−0.840259	+	0.00431335i
$352$	28.1803	+	48.8097i	0.0800577	+	0.138664i
$353$	−329.840	+	190.433i	−0.934391	+	0.539471i	−0.888198	−	0.459462i	$-0.848042\pi$
$353$	−329.840	+	190.433i	−0.934391	+	0.539471i	−0.0461931	+	0.998933i	$0.514709\pi$
$354$	232.897	−	85.2191i	0.657901	−	0.240732i
$355$	378.126	−	654.934i	1.06514	−	1.84488i
$356$	108.407	−	62.5890i	0.304515	−	0.175812i
$357$	−153.119	−	575.375i	−0.428904	−	1.61170i
$358$	−85.7715	+	148.561i	−0.239585	+	0.414974i
$359$	168.395	−	97.2227i	0.469066	−	0.270815i	−0.246783	−	0.969071i	$-0.579373\pi$
$359$	168.395	−	97.2227i	0.469066	−	0.270815i	0.715849	+	0.698255i	$0.246040\pi$
$360$	34.5443	+	192.065i	0.0959564	+	0.533513i
$361$	124.410	−	215.485i	0.344626	−	0.596911i
$362$		−	322.130i		−	0.889861i
$363$	−11.2122	+	64.2298i	−0.0308875	+	0.176942i
$364$	−88.1444	+	124.972i	−0.242155	+	0.343329i
$365$	580.671	−	335.251i	1.59088	−	0.918495i
$366$	37.3503	+	102.075i	0.102050	+	0.278894i
$367$	−138.936	−	240.644i	−0.378571	−	0.655705i	0.612283	−	0.790638i	$-0.290251\pi$
$367$	−138.936	−	240.644i	−0.378571	−	0.655705i	−0.990855	+	0.134934i	$0.956918\pi$
$368$	−2.57548	−	1.48696i	−0.00699859	−	0.00404064i
$369$	−113.468	+	315.102i	−0.307502	+	0.853936i
$370$	275.357			0.744209
$371$	−19.6472	+	216.058i	−0.0529575	+	0.582367i
$372$	−268.487	+	98.2419i	−0.721739	+	0.264091i
$373$	−172.015	+	297.938i	−0.461165	+	0.798761i	−0.999019	−	0.0442764i	$-0.985902\pi$
$373$	−172.015	+	297.938i	−0.461165	+	0.798761i	0.537854	+	0.843038i	$0.319235\pi$
$374$		−	399.490i		−	1.06816i
$375$	69.2977	+	189.385i	0.184794	+	0.505027i
$376$	−84.2963			−0.224192
$377$			501.768i			1.33095i
$378$	22.8390	−	266.309i	0.0604208	−	0.704521i
$379$	0.490343			0.00129378			0.000646891	−	1.00000i	$-0.499794\pi$
$379$	0.490343			0.00129378			0.000646891		1.00000i	$0.499794\pi$
$380$			162.390i			0.427343i
$381$	−244.822	+	89.5826i	−0.642577	+	0.235125i
$382$	−212.821			−0.557122
$383$	433.397	+	250.222i	1.13158	+	0.653320i	0.944333	−	0.328992i	$-0.106709\pi$
$383$	433.397	+	250.222i	1.13158	+	0.653320i	0.187251	+	0.982312i	$0.440042\pi$
$384$	11.6631	+	31.8743i	0.0303727	+	0.0830060i
$385$	−224.296	−	485.330i	−0.582587	−	1.26060i
$386$		−	534.172i		−	1.38387i
$387$	−35.2001	−	195.711i	−0.0909564	−	0.505713i
$388$	−60.7660	+	105.250i	−0.156613	+	0.271262i
$389$	235.361	−	135.885i	0.605040	−	0.349320i	−0.165982	−	0.986129i	$-0.553079\pi$
$389$	235.361	−	135.885i	0.605040	−	0.349320i	0.771022	+	0.636809i	$0.219746\pi$
$390$	−333.646	+	122.084i	−0.855503	+	0.313037i
$391$	10.5397	+	18.2553i	0.0269557	+	0.0466887i
$392$	−105.557	−	89.8097i	−0.269277	−	0.229106i
$393$	268.768	+	46.9171i	0.683889	+	0.119382i
$394$	−447.444			−1.13564
$395$	713.009	+	411.656i	1.80509	+	1.04217i
$396$	60.7603	−	168.732i	0.153435	−	0.426091i
$397$	228.047	+	394.988i	0.574424	+	0.994932i	0.996104	+	0.0881874i	$0.0281074\pi$
$397$	228.047	+	394.988i	0.574424	+	0.994932i	−0.421679	+	0.906745i	$0.638559\pi$
$398$	−107.463	−	62.0438i	−0.270008	−	0.155889i
$399$	57.9337	−	214.744i	0.145197	−	0.538205i
$400$	67.5375	+	116.978i	0.168844	+	0.292446i
$401$	105.114	+	60.6873i	0.262129	+	0.151340i	0.625305	−	0.780380i	$-0.284975\pi$
$401$	105.114	+	60.6873i	0.262129	+	0.151340i	−0.363177	+	0.931720i	$0.618308\pi$
$402$	−2.34548	−	6.41000i	−0.00583453	−	0.0159453i
$403$	−260.249	−	450.765i	−0.645780	−	1.11852i
$404$	29.2372	−	16.8801i	0.0723693	−	0.0417824i
$405$	395.875	−	478.398i	0.977470	−	1.18123i
$406$	−452.862	−	41.1809i	−1.11542	−	0.101431i
$407$	−219.149	−	126.526i	−0.538450	−	0.310874i
$408$	41.3705	−	236.994i	0.101398	−	0.580869i
$409$	−182.969			−0.447357			−0.223678	−	0.974663i	$-0.571807\pi$
$409$	−182.969			−0.447357			−0.223678	+	0.974663i	$0.571807\pi$
$410$			403.435i			0.983988i
$411$	−130.019	+	155.490i	−0.316347	+	0.378321i
$412$	157.348	−	272.535i	0.381913	−	0.661492i
$413$	−371.429	+	171.657i	−0.899344	+	0.415633i
$414$	1.67510	+	9.31349i	0.00404614	+	0.0224963i
$415$	598.966	+	1037.44i	1.44329	+	2.49986i
$416$	−53.5141	+	30.8964i	−0.128640	+	0.0742701i
$417$	192.790	+	161.209i	0.462326	+	0.386592i
$418$	74.6179	−	129.242i	0.178512	−	0.309191i
$419$	45.2341	−	26.1159i	0.107957	−	0.0623292i	−0.445049	−	0.895506i	$-0.646814\pi$
$419$	45.2341	−	26.1159i	0.107957	−	0.0623292i	0.553006	+	0.833177i	$0.313480\pi$
$420$	−82.8020	−	311.146i	−0.197148	−	0.740824i
$421$	227.122	−	393.386i	0.539481	−	0.934409i	−0.459450	−	0.888203i	$-0.651954\pi$
$421$	227.122	−	393.386i	0.539481	−	0.934409i	0.998932	−	0.0462059i	$-0.0147130\pi$
$422$	−118.967	+	68.6854i	−0.281911	+	0.162762i
$423$	173.117	+	204.884i	0.409259	+	0.484360i
$424$	−43.8304	+	75.9165i	−0.103374	+	0.179048i
$425$		−	957.425i		−	2.25277i
$426$	−393.047	+	143.820i	−0.922646	+	0.337605i
$427$	−75.2346	−	162.792i	−0.176193	−	0.381246i
$428$	143.526	−	82.8649i	0.335342	−	0.193610i
$429$	321.637	+	56.1460i	0.749737	+	0.130877i
$430$	−119.769	−	207.446i	−0.278532	−	0.482432i
$431$	304.768	+	175.958i	0.707118	+	0.408255i	0.809993	−	0.586439i	$-0.199471\pi$
$431$	304.768	+	175.958i	0.707118	+	0.408255i	−0.102875	+	0.994694i	$0.532804\pi$
$432$	53.5192	−	93.8067i	0.123887	−	0.217145i
$433$	−400.013			−0.923817			−0.461908	−	0.886928i	$-0.652835\pi$
$433$	−400.013			−0.923817			−0.461908	+	0.886928i	$0.652835\pi$
$434$	428.189	−	197.888i	0.986611	−	0.455964i
$435$	−810.423	−	677.666i	−1.86304	−	1.55785i
$436$	−1.17469	+	2.03463i	−0.00269425	+	0.00466658i
$437$			7.87454i			0.0180195i
$438$	−365.548	−	63.8112i	−0.834585	−	0.145688i
$439$	194.883			0.443925			0.221963	−	0.975055i	$-0.428754\pi$
$439$	194.883			0.443925			0.221963	+	0.975055i	$0.428754\pi$
$440$		−	216.032i		−	0.490983i
$441$	−1.50638	+	440.997i	−0.00341584	+	0.999994i
$442$	437.993			0.990935
$443$			299.032i			0.675015i	0.941323	+	0.337508i	$0.109584\pi$
$443$			299.032i			0.675015i	−0.941323	+	0.337508i	$0.890416\pi$
$444$	−116.906	−	97.7552i	−0.263301	−	0.220169i
$445$	−479.812			−1.07823
$446$	344.440	+	198.862i	0.772286	+	0.445879i
$447$	297.076	+	51.8585i	0.664599	+	0.116015i
$448$	−23.4930	−	50.8339i	−0.0524396	−	0.113468i
$449$			176.698i			0.393537i	0.980450	+	0.196769i	$0.0630448\pi$
$449$			176.698i			0.393537i	−0.980450	+	0.196769i	$0.936955\pi$
$450$	145.619	−	404.386i	0.323598	−	0.898636i
$451$	185.377	−	321.083i	0.411036	−	0.711935i
$452$	68.1572	−	39.3506i	0.150790	−	0.0870588i
$453$	180.140	+	150.631i	0.397661	+	0.332519i
$454$	90.0472	+	155.966i	0.198342	+	0.343538i
$455$	532.106	−	245.914i	1.16946	−	0.540470i
$456$	57.6506	−	68.9445i	0.126427	−	0.151194i
$457$	−46.0458			−0.100757			−0.0503784	−	0.998730i	$-0.516043\pi$
$457$	−46.0458			−0.100757			−0.0503784	+	0.998730i	$0.516043\pi$
$458$	−148.248	−	85.5911i	−0.323686	−	0.186880i
$459$	−660.982	+	386.156i	−1.44005	+	0.841298i
$460$	5.69956	+	9.87192i	0.0123903	+	0.0214607i
$461$	−105.387	−	60.8451i	−0.228605	−	0.131985i	0.381323	−	0.924442i	$-0.375468\pi$
$461$	−105.387	−	60.8451i	−0.228605	−	0.131985i	−0.609928	+	0.792457i	$0.708802\pi$
$462$	−77.0709	+	285.680i	−0.166820	+	0.618355i
$463$	−212.622	−	368.272i	−0.459227	−	0.795404i	0.539693	−	0.841862i	$-0.318540\pi$
$463$	−212.622	−	368.272i	−0.459227	−	0.795404i	−0.998920	+	0.0464574i	$0.985207\pi$
$464$	−159.122	−	91.8694i	−0.342936	−	0.197994i
$465$	1079.53	+	188.446i	2.32156	+	0.405260i
$466$	−188.119	−	325.831i	−0.403688	−	0.699209i
$467$	−140.848	+	81.3184i	−0.301601	+	0.174129i	−0.643162	−	0.765730i	$-0.722378\pi$
$467$	−140.848	+	81.3184i	−0.301601	+	0.174129i	0.341561	+	0.939860i	$0.389044\pi$
$468$	184.994	+	66.6164i	0.395287	+	0.142343i
$469$	4.72449	+	10.2228i	0.0100735	+	0.0217970i
$470$	279.822	+	161.555i	0.595367	+	0.343735i
$471$	−671.492	+	245.705i	−1.42567	+	0.521667i
$472$	−165.332			−0.350280
$473$			220.134i			0.465399i
$474$	−156.573	−	427.900i	−0.330322	−	0.902743i
$475$	178.831	−	309.744i	0.376485	−	0.652092i
$476$	−35.9468	+	395.303i	−0.0755185	+	0.830468i
$477$	274.530	−	49.3764i	0.575535	−	0.103514i
$478$	−78.8709	−	136.608i	−0.165002	−	0.285792i
$479$	664.047	−	383.388i	1.38632	−	0.800392i	0.393421	−	0.919359i	$-0.371292\pi$
$479$	664.047	−	383.388i	1.38632	−	0.800392i	0.992898	+	0.118967i	$0.0379583\pi$
$480$	22.3720	−	128.160i	0.0466082	−	0.266999i
$481$	138.721	−	240.271i	0.288400	−	0.499524i
$482$	393.266	−	227.052i	0.815904	−	0.471062i
$483$	−4.01519	−	15.0879i	−0.00831302	−	0.0312379i
$484$	21.7337	−	37.6439i	0.0449043	−	0.0777766i
$485$	403.427	−	232.919i	0.831808	−	0.480244i
$486$	−337.910	+	62.5681i	−0.695288	+	0.128741i
$487$	−76.0499	+	131.722i	−0.156160	+	0.270477i	−0.933481	−	0.358627i	$-0.883245\pi$
$487$	−76.0499	+	131.722i	−0.156160	+	0.270477i	0.777321	+	0.629104i	$0.216578\pi$
$488$		−	72.4627i		−	0.148489i
$489$	187.189	+	156.525i	0.382800	+	0.320093i
$490$	178.274	+	500.426i	0.363825	+	1.02128i
$491$	−350.834	+	202.554i	−0.714529	+	0.412533i	−0.812736	−	0.582633i	$-0.802023\pi$
$491$	−350.834	+	202.554i	−0.714529	+	0.412533i	0.0982070	+	0.995166i	$0.468689\pi$
$492$	143.224	−	171.283i	0.291106	−	0.348135i
$493$	651.180	+	1127.88i	1.32085	+	2.28778i
$494$	141.698	+	81.8096i	0.286839	+	0.165607i
$495$	−525.072	+	443.659i	−1.06075	+	0.896281i
$496$	190.598			0.384269
$497$	626.840	−	289.695i	1.26125	−	0.582888i
$498$	114.007	−	653.096i	0.228929	−	1.31144i
$499$	182.907	−	316.804i	0.366547	−	0.634878i	−0.622476	−	0.782639i	$-0.713873\pi$
$499$	182.907	−	316.804i	0.366547	−	0.634878i	0.989023	+	0.147761i	$0.0472066\pi$
$500$		−	134.443i		−	0.268887i
$501$	−369.767	+	442.206i	−0.738058	+	0.882646i
$502$	−457.264			−0.910885
$503$			239.788i			0.476717i	0.971177	+	0.238358i	$0.0766093\pi$
$503$			239.788i			0.476717i	−0.971177	+	0.238358i	$0.923391\pi$
$504$	−75.3062	+	161.496i	−0.149417	+	0.320429i
$505$	−129.404			−0.256246
$506$		−	10.4757i		−	0.0207030i
$507$	25.6277	−	146.811i	0.0505478	−	0.289567i
$508$	173.798			0.342122
$509$	−296.395	−	171.124i	−0.582308	−	0.336196i	0.179742	−	0.983714i	$-0.442474\pi$
$509$	−296.395	−	171.124i	−0.582308	−	0.336196i	−0.762050	+	0.647518i	$0.775807\pi$
$510$	−591.534	+	707.418i	−1.15987	+	1.38709i
$511$	609.728	+	55.4456i	1.19321	+	0.108504i
$512$		−	22.6274i		−	0.0441942i
$513$	−285.966	+	1.46797i	−0.557440	+	0.00286154i
$514$	166.760	−	288.837i	0.324436	−	0.561940i
$515$	−1044.64	+	603.121i	−2.02842	+	1.17111i
$516$	−22.7967	+	130.593i	−0.0441796	+	0.253087i
$517$	−148.469	−	257.155i	−0.287173	−	0.497399i
$518$	205.467	+	144.919i	0.396655	+	0.279767i
$519$	64.3305	+	175.810i	0.123951	+	0.338748i
$520$	236.854			0.455488
$521$	203.560	+	117.525i	0.390710	+	0.225577i	0.682468	−	0.730916i	$-0.260907\pi$
$521$	203.560	+	117.525i	0.390710	+	0.225577i	−0.291758	+	0.956492i	$0.594240\pi$
$522$	103.494	+	575.420i	0.198264	+	1.10234i
$523$	−18.2473	−	31.6052i	−0.0348896	−	0.0604306i	0.848053	−	0.529911i	$-0.177775\pi$
$523$	−18.2473	−	31.6052i	−0.0348896	−	0.0604306i	−0.882943	+	0.469480i	$0.844441\pi$
$524$	−157.520	−	90.9442i	−0.300611	−	0.173558i
$525$	−184.709	+	684.665i	−0.351827	+	1.30412i
$526$	−118.954	−	206.035i	−0.226149	−	0.391701i
$527$	−1169.98	−	675.488i	−2.22007	−	1.28176i
$528$	−76.6942	+	91.7188i	−0.145254	+	0.173710i
$529$	−264.224	−	457.649i	−0.499478	−	0.865120i
$530$	290.991	−	168.004i	0.549040	−	0.316988i
$531$	339.538	+	401.844i	0.639430	+	0.756769i
$532$	−85.4652	+	121.173i	−0.160649	+	0.227769i
$533$	352.029	+	203.244i	0.660467	+	0.381321i
$534$	203.709	+	170.339i	0.381478	+	0.318987i
$535$	−635.249			−1.18738
$536$			4.55043i			0.00848961i
$537$	−358.477	−	62.5768i	−0.667554	−	0.116530i
$538$	−236.786	+	410.126i	−0.440123	+	0.762316i
$539$	88.0605	−	480.191i	0.163378	−	0.890893i
$540$	−357.440	+	208.822i	−0.661925	+	0.386707i
$541$	−437.424	−	757.641i	−0.808548	−	1.40045i	−0.913870	−	0.406008i	$-0.866921\pi$
$541$	−437.424	−	757.641i	−0.808548	−	1.40045i	0.105322	−	0.994438i	$-0.466413\pi$
$542$	−8.69489	+	5.02000i	−0.0160422	+	0.00926199i
$543$	641.729	−	234.815i	1.18182	−	0.432439i
$544$	−80.1927	+	138.898i	−0.147413	+	0.255327i
$545$	7.79881	−	4.50265i	0.0143097	−	0.00826174i
$546$	−313.214	−	84.4990i	−0.573652	−	0.154760i
$547$	−508.530	+	880.800i	−0.929671	+	1.61024i	−0.145801	+	0.989314i	$0.546576\pi$
$547$	−508.530	+	880.800i	−0.929671	+	1.61024i	−0.783871	+	0.620924i	$0.786758\pi$
$548$	117.021	−	67.5623i	0.213543	−	0.123289i
$549$	−176.122	+	148.814i	−0.320806	+	0.271064i
$550$	−237.903	+	412.061i	−0.432552	+	0.749201i
$551$			486.517i			0.882971i
$552$	1.08485	−	6.21464i	0.00196530	−	0.0112584i
$553$	315.384	+	682.424i	0.570314	+	1.23404i
$554$	−640.383	+	369.726i	−1.15593	+	0.667375i
$555$	200.720	+	548.552i	0.361658	+	0.988381i
$556$	−83.7697	−	145.093i	−0.150665	−	0.260959i
$557$	−506.945	−	292.685i	−0.910134	−	0.525466i	−0.0296598	−	0.999560i	$-0.509442\pi$
$557$	−506.945	−	292.685i	−0.910134	−	0.525466i	−0.880474	+	0.474094i	$0.842776\pi$
$558$	−391.424	−	463.252i	−0.701477	−	0.830201i
$559$	−241.351			−0.431754
$560$	−19.4390	+	213.768i	−0.0347125	+	0.381729i
$561$	795.842	−	291.206i	1.41861	−	0.519084i
$562$	221.230	−	383.182i	0.393648	−	0.681819i
$563$		−	847.497i		−	1.50532i	−0.658407	−	0.752662i	$-0.728770\pi$
$563$		−	847.497i		−	1.50532i	0.658407	−	0.752662i	$-0.271230\pi$
$564$	−61.4473	−	167.930i	−0.108949	−	0.297749i
$565$	−301.664			−0.533919
$566$		−	286.671i		−	0.506486i
$567$	547.174	−	148.626i	0.965034	−	0.262126i
$568$	279.022			0.491236
$569$			493.737i			0.867727i	0.900979	+	0.433864i	$0.142850\pi$
$569$			493.737i			0.867727i	−0.900979	+	0.433864i	$0.857150\pi$
$570$	−323.505	+	118.373i	−0.567553	+	0.207673i
$571$	7.73344			0.0135437			0.00677184	−	0.999977i	$-0.497844\pi$
$571$	7.73344			0.0135437			0.00677184	+	0.999977i	$0.497844\pi$
$572$	−188.505	−	108.834i	−0.329555	−	0.190269i
$573$	−155.134	−	423.969i	−0.270740	−	0.739912i
$574$	−212.326	+	301.037i	−0.369905	+	0.524454i
$575$		−	25.1063i		−	0.0436631i
$576$	−54.9965	+	46.4692i	−0.0954800	+	0.0806757i
$577$	−445.351	+	771.370i	−0.771839	+	1.33686i	0.164716	+	0.986341i	$0.447329\pi$
$577$	−445.351	+	771.370i	−0.771839	+	1.33686i	−0.936554	+	0.350523i	$0.886004\pi$
$578$	630.572	−	364.061i	1.09095	−	0.629863i
$579$	1064.15	−	389.382i	1.83791	−	0.672507i
$580$	352.139	+	609.922i	0.607136	+	1.05159i
$581$	−99.0603	+	1089.35i	−0.170500	+	1.87496i
$582$	−253.968	−	44.3335i	−0.436371	−	0.0761743i
$583$	−308.789			−0.529655
$584$	214.241	+	123.692i	0.366851	+	0.211801i
$585$	−486.419	−	575.679i	−0.831486	−	0.984067i
$586$	219.441	+	380.083i	0.374473	+	0.648605i
$587$	187.116	+	108.031i	0.318766	+	0.184040i	0.650843	−	0.759213i	$-0.274416\pi$
$587$	187.116	+	108.031i	0.318766	+	0.184040i	−0.332076	+	0.943253i	$0.607749\pi$
$588$	101.969	−	275.750i	0.173417	−	0.468963i
$589$	−252.339	−	437.064i	−0.428419	−	0.742044i
$590$	548.822	+	316.863i	0.930207	+	0.537055i
$591$	−326.162	−	891.373i	−0.551881	−	1.50825i
$592$	50.7970	+	87.9831i	0.0858058	+	0.148620i
$593$	−896.355	+	517.511i	−1.51156	+	0.872699i	−0.511650	+	0.859194i	$0.670966\pi$
$593$	−896.355	+	517.511i	−1.51156	+	0.872699i	−0.999909	+	0.0135054i	$0.995701\pi$
$594$	380.429	−	1.95288i	0.640453	−	0.00328768i
$595$	876.931	−	1243.32i	1.47383	−	2.08961i
$596$	−174.110	−	100.523i	−0.292131	−	0.168662i
$597$	45.2657	−	259.308i	0.0758219	−	0.434352i
$598$	11.4854			0.0192063
$599$			398.933i			0.665999i	0.942927	+	0.332999i	$0.108061\pi$
$599$			398.933i			0.665999i	−0.942927	+	0.332999i	$0.891939\pi$
$600$	−183.807	+	219.815i	−0.306344	+	0.366358i
$601$	459.343	−	795.605i	0.764297	−	1.32380i	−0.176320	−	0.984333i	$-0.556419\pi$
$601$	459.343	−	795.605i	0.764297	−	1.32380i	0.940617	−	0.339469i	$-0.110247\pi$
$602$	19.8080	−	217.827i	0.0329037	−	0.361838i
$603$	11.0599	−	9.34507i	0.0183415	−	0.0154976i
$604$	−78.2732	−	135.573i	−0.129591	−	0.224459i
$605$	−144.290	+	83.3061i	−0.238497	+	0.137696i
$606$	54.9399	+	45.9400i	0.0906598	+	0.0758087i
$607$	−475.551	+	823.678i	−0.783444	+	1.35697i	0.146480	+	0.989214i	$0.453206\pi$
$607$	−475.551	+	823.678i	−0.783444	+	1.35697i	−0.929924	+	0.367752i	$0.880128\pi$
$608$	−51.8875	+	29.9573i	−0.0853413	+	0.0492718i
$609$	−248.073	−	932.185i	−0.407344	−	1.53068i
$610$	−138.876	+	240.541i	−0.227666	+	0.394329i
$611$	281.940	−	162.778i	0.461440	−	0.266413i
$612$	502.284	−	90.3397i	0.820726	−	0.147614i
$613$	292.779	−	507.109i	0.477617	−	0.827257i	−0.522054	−	0.852913i	$-0.674834\pi$
$613$	292.779	−	507.109i	0.477617	−	0.827257i	0.999671	+	0.0256553i	$0.00816723\pi$
$614$			731.814i			1.19188i
$615$	−803.701	+	294.082i	−1.30683	+	0.478181i
$616$	113.697	−	161.200i	0.184573	−	0.261688i
$617$	−774.449	+	447.129i	−1.25519	+	0.724682i	−0.972135	−	0.234423i	$-0.924680\pi$
$617$	−774.449	+	447.129i	−1.25519	+	0.724682i	−0.283051	+	0.959105i	$0.591347\pi$
$618$	657.627	+	114.797i	1.06412	+	0.185756i
$619$	41.7252	+	72.2702i	0.0674074	+	0.116753i	0.897759	−	0.440486i	$-0.145194\pi$
$619$	41.7252	+	72.2702i	0.0674074	+	0.116753i	−0.830352	+	0.557239i	$0.811861\pi$
$620$	−632.690	−	365.284i	−1.02047	−	0.589168i
$621$	−17.3328	+	10.1261i	−0.0279110	+	0.0163061i
$622$	58.9827			0.0948275
$623$	−358.028	−	252.522i	−0.574683	−	0.405333i
$624$	−100.559	−	84.0860i	−0.161152	−	0.134753i
$625$	164.446	−	284.828i	0.263113	−	0.455725i
$626$			334.325i			0.534066i
$627$	311.861	+	54.4395i	0.497386	+	0.0868253i
$628$	476.689			0.759058
$629$		−	720.110i		−	1.14485i
$630$	559.490	−	391.762i	0.888079	−	0.621844i
$631$	237.722			0.376738			0.188369	−	0.982098i	$-0.439680\pi$
$631$	237.722			0.376738			0.188369	+	0.982098i	$0.439680\pi$
$632$			303.764i			0.480639i
$633$	−223.551	−	186.931i	−0.353161	−	0.295309i
$634$	−513.558			−0.810029
$635$	−576.923	−	333.087i	−0.908541	−	0.524546i
$636$	−183.187	−	31.9777i	−0.288029	−	0.0502793i
$637$	526.473	+	96.5478i	0.826488	+	0.151566i
$638$		−	647.227i		−	1.01446i
$639$	−573.019	−	678.170i	−0.896743	−	1.06130i
$640$	−43.3659	+	75.1119i	−0.0677592	+	0.117362i
$641$	−548.667	+	316.773i	−0.855956	+	0.494186i	−0.862656	−	0.505791i	$-0.831201\pi$
$641$	−548.667	+	316.773i	−0.855956	+	0.494186i	0.00670030	+	0.999978i	$0.497867\pi$
$642$	269.702	+	225.521i	0.420096	+	0.351279i
$643$	148.120	+	256.551i	0.230357	+	0.398990i	0.957913	−	0.287058i	$-0.0926772\pi$
$643$	148.120	+	256.551i	0.230357	+	0.398990i	−0.727556	+	0.686048i	$0.759344\pi$
$644$	−0.942624	+	10.3659i	−0.00146370	+	0.0160961i
$645$	325.957	−	389.814i	0.505360	−	0.604362i
$646$	424.680			0.657400
$647$	853.776	+	492.928i	1.31959	+	0.761867i	0.983663	−	0.180021i	$-0.0576165\pi$
$647$	853.776	+	492.928i	1.31959	+	0.761867i	0.335929	+	0.941887i	$0.390950\pi$
$648$	225.889	+	38.2381i	0.348594	+	0.0590094i
$649$	−291.195	−	504.364i	−0.448682	−	0.777141i
$650$	−451.776	−	260.833i	−0.695039	−	0.401281i
$651$	706.348	+	708.765i	1.08502	+	1.08873i
$652$	−81.3361	−	140.878i	−0.124749	−	0.216071i
$653$	477.521	+	275.697i	0.731272	+	0.422200i	0.818887	−	0.573954i	$-0.194591\pi$
$653$	477.521	+	275.697i	0.731272	+	0.422200i	−0.0876152	+	0.996154i	$0.527925\pi$
$654$	−4.90956	−	0.857029i	−0.00750698	−	0.00131044i
$655$	348.593	+	603.780i	0.532202	+	0.921802i
$656$	−128.907	+	74.4244i	−0.196504	+	0.113452i
$657$	−139.343	−	774.739i	−0.212090	−	1.17921i
$658$	123.773	+	267.819i	0.188105	+	0.407020i
$659$	−342.424	−	197.699i	−0.519612	−	0.299998i	0.217164	−	0.976135i	$-0.430319\pi$
$659$	−342.424	−	197.699i	−0.519612	−	0.299998i	−0.736776	+	0.676137i	$0.763653\pi$
$660$	430.368	−	157.476i	0.652073	−	0.238599i
$661$	133.642			0.202182			0.101091	−	0.994877i	$-0.467767\pi$
$661$	133.642			0.202182			0.101091	+	0.994877i	$0.467767\pi$
$662$			76.8032i			0.116017i
$663$	319.273	+	872.546i	0.481558	+	1.31606i
$664$	−220.991	+	382.767i	−0.332817	+	0.576457i
$665$	515.933	−	238.439i	0.775839	−	0.358555i
$666$	109.525	−	304.151i	0.164452	−	0.456684i
$667$	17.0757	+	29.5760i	0.0256008	+	0.0443418i
$668$	332.803	−	192.144i	0.498208	−	0.287641i
$669$	−145.085	+	831.133i	−0.216869	+	1.24235i
$670$	8.72099	−	15.1052i	0.0130164	−	0.0225451i
$671$	221.055	−	127.626i	0.329442	−	0.190203i
$672$	84.1433	−	83.8564i	0.125213	−	0.124786i
$673$	−158.325	+	274.227i	−0.235253	+	0.407469i	−0.959346	−	0.282232i	$-0.908925\pi$
$673$	−158.325	+	274.227i	−0.235253	+	0.407469i	0.724093	+	0.689702i	$0.242258\pi$
$674$	−215.637	+	124.498i	−0.319936	+	0.184715i
$675$	911.744	−	4.68031i	1.35073	−	0.00693379i
$676$	−49.6769	+	86.0428i	−0.0734865	+	0.127282i
$677$		−	307.871i		−	0.454758i	−0.973806	−	0.227379i	$-0.926984\pi$
$677$		−	307.871i		−	0.454758i	0.973806	−	0.227379i	$-0.0730157\pi$
$678$	128.075	+	107.095i	0.188901	+	0.157957i
$679$	423.614	+	38.5213i	0.623880	+	0.0567324i
$680$	532.401	−	307.382i	0.782943	−	0.452032i
$681$	−245.068	+	293.078i	−0.359865	+	0.430364i
$682$	335.694	+	581.439i	0.492220	+	0.852549i
$683$	−760.049	−	438.815i	−1.11281	−	0.642481i	−0.173254	−	0.984877i	$-0.555428\pi$
$683$	−760.049	−	438.815i	−1.11281	−	0.642481i	−0.939556	+	0.342396i	$0.888762\pi$
$684$	179.372	+	64.5916i	0.262239	+	0.0944322i
$685$	−517.938			−0.756113
$686$	−130.346	+	467.234i	−0.190009	+	0.681100i
$687$	62.4452	−	357.723i	0.0908955	−	0.520703i
$688$	44.1892	−	76.5379i	0.0642285	−	0.111247i
$689$		−	338.550i		−	0.491365i
$690$	−15.5116	+	18.5504i	−0.0224806	+	0.0268847i
$691$	−592.012			−0.856746			−0.428373	−	0.903602i	$-0.640913\pi$
$691$	−592.012			−0.856746			−0.428373	+	0.903602i	$0.640913\pi$
$692$		−	124.807i		−	0.180357i
$693$	−625.296	+	54.7083i	−0.902303	+	0.0789442i
$694$	−244.726			−0.352631
$695$			642.185i			0.924007i
$696$	67.0257	−	383.963i	0.0963013	−	0.551670i
$697$	1055.06			1.51371
$698$	−145.158	−	83.8069i	−0.207963	−	0.120067i
$699$	511.975	−	612.272i	0.732439	−	0.875926i
$700$	272.488	−	386.335i	0.389268	−	0.551907i
$701$			47.5192i			0.0677877i	0.999425	+	0.0338938i	$0.0107908\pi$
$701$			47.5192i			0.0677877i	−0.999425	+	0.0338938i	$0.989209\pi$
$702$	2.14110	+	417.095i	0.00305000	+	0.594153i
$703$	134.504	−	232.968i	0.191329	−	0.331391i
$704$	69.0274	−	39.8530i	0.0980503	−	0.0566094i
$705$	−117.867	+	675.211i	−0.167187	+	0.957747i
$706$	269.313	+	466.464i	0.381463	+	0.660714i
$707$	−96.5592	−	68.1047i	−0.136576	−	0.0963291i
$708$	−120.518	−	329.366i	−0.170223	−	0.465206i
$709$	502.058			0.708121			0.354061	−	0.935222i	$-0.384801\pi$
$709$	502.058			0.708121			0.354061	+	0.935222i	$0.384801\pi$
$710$	−926.217	−	534.751i	−1.30453	−	0.753171i
$711$	738.306	−	623.831i	1.03841	−	0.877399i
$712$	−88.5141	−	153.311i	−0.124318	−	0.215324i
$713$	−30.6800	−	17.7131i	−0.0430295	−	0.0248431i
$714$	−813.704	+	216.542i	−1.13964	+	0.303281i
$715$	417.164	+	722.549i	0.583446	+	1.01056i
$716$	210.096	+	121.299i	0.293431	+	0.169412i
$717$	214.651	−	256.702i	0.299374	−	0.358023i
$718$	−137.494	−	238.146i	−0.191495	−	0.331680i
$719$	−152.732	+	88.1797i	−0.212423	+	0.122642i	−0.602437	−	0.798167i	$-0.705803\pi$
$719$	−152.732	+	88.1797i	−0.212423	+	0.122642i	0.390014	+	0.920809i	$0.372470\pi$
$720$	271.620	−	48.8530i	0.377251	−	0.0678514i
$721$	−1096.91	−	99.7474i	−1.52137	−	0.138346i
$722$	−304.741	−	175.943i	−0.422080	−	0.243688i
$723$	738.989	+	617.934i	1.02211	+	0.854680i
$724$	−455.560			−0.629227
$725$		−	1551.16i		−	2.13953i
$726$	90.8347	+	15.8564i	0.125117	+	0.0218408i
$727$	448.280	−	776.443i	0.616616	−	1.06801i	−0.373483	−	0.927637i	$-0.621837\pi$
$727$	448.280	−	776.443i	0.616616	−	1.06801i	0.990099	−	0.140373i	$-0.0448300\pi$
$728$	176.737	+	124.655i	0.242770	+	0.171229i
$729$	−370.962	−	627.557i	−0.508865	−	0.860847i
$730$	−474.116	−	821.193i	−0.649474	−	1.12492i
$731$	−542.509	+	313.218i	−0.742146	+	0.428478i
$732$	144.356	−	52.8213i	0.197208	−	0.0721602i
$733$	−268.922	+	465.786i	−0.366878	+	0.635452i	−0.989076	−	0.147408i	$-0.952907\pi$
$733$	−268.922	+	465.786i	−0.366878	+	0.635452i	0.622197	+	0.782860i	$0.286240\pi$
$734$	−340.322	+	196.485i	−0.463653	+	0.267690i
$735$	−866.968	+	719.930i	−1.17955	+	0.979497i
$736$	−2.10287	+	3.64228i	−0.00285716	+	0.00494875i
$737$	−13.8816	+	8.01453i	−0.0188353	+	0.0108745i
$738$	445.622	+	160.468i	0.603824	+	0.217437i
$739$	−176.304	+	305.367i	−0.238571	+	0.413217i	−0.960304	−	0.278954i	$-0.910012\pi$
$739$	−176.304	+	305.367i	−0.238571	+	0.413217i	0.721733	+	0.692171i	$0.243346\pi$
$740$		−	389.414i		−	0.526235i
$741$	−59.6864	+	341.918i	−0.0805484	+	0.461428i
$742$	305.552	+	27.7854i	0.411796	+	0.0374466i
$743$	192.004	−	110.854i	0.258418	−	0.149198i	−0.365195	−	0.930931i	$-0.618998\pi$
$743$	192.004	−	110.854i	0.258418	−	0.149198i	0.623613	+	0.781734i	$0.285664\pi$
$744$	138.935	+	379.698i	0.186741	+	0.510347i
$745$	385.307	+	667.372i	0.517191	+	0.895801i
$746$	421.348	+	243.265i	0.564810	+	0.326093i
$747$	1384.17	−	248.953i	1.85297	−	0.333271i
$748$	−564.964			−0.755300
$749$	−474.012	−	334.328i	−0.632860	−	0.446366i
$750$	267.831	−	98.0018i	0.357108	−	0.130669i
$751$	535.616	−	927.714i	0.713203	−	1.23530i	−0.250445	−	0.968131i	$-0.580577\pi$
$751$	535.616	−	927.714i	0.713203	−	1.23530i	0.963648	−	0.267174i	$-0.0860898\pi$
$752$			119.213i			0.158528i
$753$	−333.320	−	910.937i	−0.442656	−	1.20974i
$754$	709.607			0.941124
$755$			600.049i			0.794766i
$756$	−376.618	−	32.2993i	−0.498171	−	0.0427239i
$757$	724.845			0.957524			0.478762	−	0.877945i	$-0.341086\pi$
$757$	724.845			0.957524			0.478762	+	0.877945i	$0.341086\pi$
$758$		−	0.693450i		−	0.000914842i
$759$	20.8692	−	7.63621i	0.0274956	−	0.0100609i
$760$	229.655			0.302177
$761$	814.116	+	470.030i	1.06980	+	0.617648i	0.928126	−	0.372266i	$-0.121419\pi$
$761$	814.116	+	470.030i	1.06980	+	0.617648i	0.141671	+	0.989914i	$0.454752\pi$
$762$	126.689	+	346.230i	0.166258	+	0.454371i
$763$	8.18907	+	0.744672i	0.0107327	+	0.000975979i
$764$			300.974i			0.393945i
$765$	−1840.47	−	662.754i	−2.40585	−	0.866345i
$766$	353.867	−	612.916i	0.461967	−	0.800151i
$767$	552.975	−	319.260i	0.720959	−	0.416246i
$768$	45.0771	−	16.4941i	0.0586941	−	0.0214767i
$769$	127.113	+	220.165i	0.165296	+	0.286301i	0.936760	−	0.349972i	$-0.113809\pi$
$769$	127.113	+	220.165i	0.165296	+	0.286301i	−0.771464	+	0.636272i	$0.780475\pi$
$770$	−686.360	+	317.203i	−0.891377	+	0.411951i
$771$	696.964	+	121.664i	0.903974	+	0.157801i
$772$	−755.433			−0.978540
$773$	388.501	+	224.301i	0.502588	+	0.290169i	0.729782	−	0.683680i	$-0.239622\pi$
$773$	388.501	+	224.301i	0.502588	+	0.290169i	−0.227194	+	0.973850i	$0.572955\pi$
$774$	−276.777	+	49.7805i	−0.357593	+	0.0643159i
$775$	804.530	+	1393.49i	1.03810	+	1.79805i
$776$	148.846	+	85.9361i	0.191812	+	0.110742i
$777$	−138.926	+	514.958i	−0.178798	+	0.662752i
$778$	−192.171	−	332.850i	−0.247006	−	0.427828i
$779$	341.329	+	197.066i	0.438163	+	0.252974i
$780$	172.653	+	471.847i	0.221350	+	0.604932i
$781$	491.433	+	851.188i	0.629236	+	1.08987i
$782$	25.8169	−	14.9054i	0.0330139	−	0.0190606i
$783$	−1070.88	+	625.624i	−1.36766	+	0.799009i
$784$	−127.010	+	149.280i	−0.162003	+	0.190408i
$785$	−1582.37	−	913.583i	−2.01576	−	1.16380i
$786$	66.3508	−	380.096i	0.0844157	−	0.483583i
$787$	−1175.28			−1.49336			−0.746681	−	0.665183i	$-0.768354\pi$
$787$	−1175.28			−1.49336			−0.746681	+	0.665183i	$0.768354\pi$
$788$			632.781i			0.803022i
$789$	323.740	−	387.162i	0.410317	−	0.490699i
$790$	582.170	−	1008.35i	0.736924	−	1.27639i
$791$	−225.097	−	158.764i	−0.284573	−	0.200714i
$792$	−238.623	−	85.9280i	−0.301292	−	0.108495i
$793$	139.927	+	242.361i	0.176453	+	0.305625i
$794$	558.598	−	322.506i	0.703523	−	0.406179i
$795$	546.804	+	457.231i	0.687804	+	0.575133i
$796$	−87.7432	+	151.976i	−0.110230	+	0.190924i
$797$	888.104	−	512.747i	1.11431	−	0.643347i	0.174367	−	0.984681i	$-0.444212\pi$
$797$	888.104	−	512.747i	1.11431	−	0.643347i	0.939942	+	0.341334i	$0.110879\pi$
$798$	−303.694	−	81.9307i	−0.380569	−	0.102670i
$799$	422.497	−	731.786i	0.528782	−	0.915878i
$800$	165.432	−	95.5124i	0.206790	−	0.119390i
$801$	−190.848	+	529.986i	−0.238262	+	0.661655i
$802$	85.8249	−	148.653i	0.107014	−	0.185353i
$803$			871.419i			1.08520i
$804$	−9.06511	+	3.31701i	−0.0112750	+	0.00412563i
$805$	22.9955	−	32.6032i	0.0285659	−	0.0405009i
$806$	−637.478	+	368.048i	−0.790916	+	0.456636i
$807$	−989.634	−	172.754i	−1.22631	−	0.214069i
$808$	−23.8721	−	41.3476i	−0.0295446	−	0.0511728i
$809$	305.477	+	176.367i	0.377598	+	0.218006i	0.676773	−	0.736192i	$-0.263378\pi$
$809$	305.477	+	176.367i	0.377598	+	0.218006i	−0.299175	+	0.954198i	$0.596711\pi$
$810$	−676.557	−	559.852i	−0.835255	−	0.691176i
$811$	−1201.41			−1.48140			−0.740700	−	0.671836i	$-0.765506\pi$
$811$	−1201.41			−1.48140			−0.740700	+	0.671836i	$0.765506\pi$
$812$	−58.2386	+	640.443i	−0.0717225	+	0.788723i
$813$	−16.3387	−	13.6622i	−0.0200967	−	0.0168047i
$814$	−178.935	+	309.924i	−0.219821	+	0.380742i
$815$			623.529i			0.765066i
$816$	−335.161	−	58.5067i	−0.410736	−	0.0716994i
$817$	−234.015			−0.286432
$818$			258.757i			0.316329i
$819$	−59.9811	−	685.562i	−0.0732370	−	0.837073i
$820$	570.543			0.695784
$821$		−	222.937i		−	0.271543i	−0.990740	−	0.135772i	$-0.956649\pi$
$821$		−	222.937i		−	0.271543i	0.990740	−	0.135772i	$-0.0433513\pi$
$822$	219.896	+	183.874i	0.267513	+	0.223691i
$823$	−1231.00			−1.49575			−0.747875	−	0.663839i	$-0.768926\pi$
$823$	−1231.00			−1.49575			−0.747875	+	0.663839i	$0.768926\pi$
$824$	−385.422	−	222.524i	−0.467746	−	0.270053i
$825$	−994.303	−	173.569i	−1.20522	−	0.210386i
$826$	242.759	+	525.280i	0.293897	+	0.635932i
$827$			507.869i			0.614110i	0.951692	+	0.307055i	$0.0993436\pi$
$827$			507.869i			0.614110i	−0.951692	+	0.307055i	$0.900656\pi$
$828$	13.1713	−	2.36895i	0.0159073	−	0.00286105i
$829$	347.420	−	601.749i	0.419083	−	0.725873i	−0.576764	−	0.816911i	$-0.695685\pi$
$829$	347.420	−	601.749i	0.419083	−	0.725873i	0.995847	+	0.0910372i	$0.0290182\pi$
$830$	1467.16	−	847.066i	1.76766	−	1.02056i
$831$	−1203.35	−	1006.23i	−1.44808	−	1.21086i
$832$	43.6941	+	75.6803i	0.0525169	+	0.0909619i
$833$	1308.70	−	466.220i	1.57107	−	0.559688i
$834$	227.984	−	272.646i	0.273362	−	0.326914i
$835$	−1472.99			−1.76406
$836$	−182.776	−	105.526i	−0.218631	−	0.126227i
$837$	637.539	−	1117.46i	0.761695	−	1.33508i
$838$	−36.9335	−	63.9707i	−0.0440734	−	0.0763373i
$839$	195.441	+	112.838i	0.232945	+	0.134491i	0.611930	−	0.790912i	$-0.290393\pi$
$839$	195.441	+	112.838i	0.232945	+	0.134491i	−0.378985	+	0.925403i	$0.623727\pi$
$840$	−440.027	+	117.100i	−0.523842	+	0.139404i
$841$	634.498	+	1098.98i	0.754457	+	1.30676i
$842$	−556.332	−	321.199i	−0.660727	−	0.381471i
$843$	924.619	+	161.404i	1.09682	+	0.191464i
$844$	97.1358	+	168.244i	0.115090	+	0.199341i
$845$	329.806	−	190.413i	0.390302	−	0.225341i
$846$	289.750	−	244.824i	0.342494	−	0.289390i
$847$	−151.511	−	13.7776i	−0.178879	−	0.0162664i
$848$	107.362	+	61.9856i	0.126606	+	0.0730962i
$849$	571.091	−	208.967i	0.672663	−	0.246133i
$850$	−1354.00			−1.59295
$851$		−	18.8832i		−	0.0221895i
$852$	203.392	+	555.853i	0.238723	+	0.652409i
$853$	−490.759	+	850.020i	−0.575333	+	0.996507i	0.420672	+	0.907213i	$0.361794\pi$
$853$	−490.759	+	850.020i	−0.575333	+	0.996507i	−0.996005	+	0.0892939i	$0.971539\pi$
$854$	−230.222	+	106.398i	−0.269581	+	0.124588i
$855$	−471.634	−	558.181i	−0.551619	−	0.652844i
$856$	−117.189	−	202.977i	−0.136903	−	0.237122i
$857$	1359.93	−	785.155i	1.58685	−	0.916167i	0.593026	−	0.805183i	$-0.297933\pi$
$857$	1359.93	−	785.155i	1.58685	−	0.916167i	0.993822	−	0.110984i	$-0.0354001\pi$
$858$	79.4025	−	454.864i	0.0925437	−	0.530144i
$859$	−596.812	+	1033.71i	−0.694775	+	1.20339i	0.275481	+	0.961306i	$0.411163\pi$
$859$	−596.812	+	1033.71i	−0.694775	+	1.20339i	−0.970256	+	0.242080i	$0.922170\pi$
$860$	−293.373	+	169.379i	−0.341131	+	0.196952i
$861$	−754.482	−	203.545i	−0.876286	−	0.236405i
$862$	248.842	−	431.007i	0.288680	−	0.500008i
$863$	1018.88	−	588.251i	1.18063	−	0.681635i	0.224467	−	0.974482i	$-0.427936\pi$
$863$	1018.88	−	588.251i	1.18063	−	0.681635i	0.956159	+	0.292847i	$0.0946026\pi$
$864$	−132.663	−	75.6875i	−0.153545	−	0.0876013i
$865$	−239.194	+	414.297i	−0.276525	+	0.478956i
$866$			565.703i			0.653237i
$867$	1184.91	+	990.810i	1.36668	+	1.14280i
$868$	−279.856	−	605.551i	−0.322415	−	0.697639i
$869$	−926.666	+	535.011i	−1.06636	+	0.615662i
$870$	−958.364	+	1146.11i	−1.10157	+	1.31737i
$871$	−8.78698	−	15.2195i	−0.0100884	−	0.0174736i
$872$	2.87740	+	1.66127i	0.00329977	+	0.00190512i
$873$	−96.8098	−	538.258i	−0.110893	−	0.616561i
$874$	11.1363			0.0127417
$875$	−427.143	+	197.405i	−0.488163	+	0.225605i
$876$	−90.2427	+	516.963i	−0.103017	+	0.590140i
$877$	−358.637	+	621.178i	−0.408937	+	0.708299i	−0.994771	−	0.102132i	$-0.967434\pi$
$877$	−358.637	+	621.178i	−0.408937	+	0.708299i	0.585834	+	0.810431i	$0.300767\pi$
$878$		−	275.606i		−	0.313902i
$879$	−597.220	+	714.217i	−0.679431	+	0.812534i
$880$	−305.516			−0.347177
$881$			255.203i			0.289675i	0.989455	+	0.144837i	$0.0462659\pi$
$881$			255.203i			0.289675i	−0.989455	+	0.144837i	$0.953734\pi$
$882$	623.665	+	2.13035i	0.707103	+	0.00241536i
$883$	1220.34			1.38204			0.691019	−	0.722837i	$-0.257162\pi$
$883$	1220.34			1.38204			0.691019	+	0.722837i	$0.257162\pi$
$884$		−	619.416i		−	0.700697i
$885$	−231.175	+	1324.31i	−0.261215	+	1.49639i
$886$	422.895			0.477308
$887$	300.277	+	173.365i	0.338531	+	0.195451i	0.659622	−	0.751597i	$-0.270716\pi$
$887$	300.277	+	173.365i	0.338531	+	0.195451i	−0.321091	+	0.947048i	$0.604050\pi$
$888$	−138.247	+	165.330i	−0.155683	+	0.186182i
$889$	−255.189	−	552.176i	−0.287052	−	0.621120i
$890$			678.556i			0.762423i
$891$	281.202	+	756.447i	0.315603	+	0.848986i
$892$	281.234	−	487.111i	0.315284	−	0.546089i
$893$	273.370	−	157.830i	0.306126	−	0.176742i
$894$	73.3390	−	420.128i	0.0820346	−	0.469942i
$895$	−464.944	−	805.307i	−0.519491	−	0.899785i
$896$	−71.8899	+	33.2241i	−0.0802343	+	0.0370804i
$897$	8.37220	+	22.8805i	0.00933356	+	0.0255078i
$898$	249.889			0.278273
$899$	−1895.52	−	1094.38i	−2.10848	−	1.21733i
$900$	−571.888	−	205.937i	−0.635431	−	0.228818i
$901$	−439.360	−	760.994i	−0.487636	−	0.844611i
$902$	−454.080	−	262.163i	−0.503414	−	0.290646i
$903$	448.381	−	119.323i	0.496546	−	0.132141i
$904$	−55.6501	−	96.3888i	−0.0615598	−	0.106625i
$905$	1512.24	+	873.090i	1.67098	+	0.964740i
$906$	213.025	−	254.757i	0.235127	−	0.281189i
$907$	476.717	+	825.698i	0.525598	+	0.910362i	0.999555	+	0.0298142i	$0.00949155\pi$
$907$	476.717	+	825.698i	0.525598	+	0.910362i	−0.473958	+	0.880547i	$0.657175\pi$
$908$	220.570	−	127.346i	0.242918	−	0.140249i
$909$	−51.4711	+	142.936i	−0.0566239	+	0.157245i
$910$	−347.775	−	752.512i	−0.382170	−	0.826936i
$911$	−94.3251	−	54.4586i	−0.103540	−	0.0597790i	0.447336	−	0.894366i	$-0.352373\pi$
$911$	−94.3251	−	54.4586i	−0.103540	−	0.0597790i	−0.550876	+	0.834587i	$0.685706\pi$
$912$	−97.5023	−	81.5302i	−0.106910	−	0.0893972i
$913$	−1556.90			−1.70525
$914$			65.1186i			0.0712458i
$915$	−580.425	−	101.321i	−0.634344	−	0.110733i
$916$	−121.044	+	209.654i	−0.132144	+	0.228880i
$917$	−57.6521	+	633.994i	−0.0628704	+	0.691378i
$918$	546.107	+	934.770i	0.594887	+	1.01827i
$919$	240.077	+	415.825i	0.261237	+	0.452475i	0.966571	−	0.256400i	$-0.0825364\pi$
$919$	240.077	+	415.825i	0.261237	+	0.452475i	−0.705334	+	0.708875i	$0.749203\pi$
$920$	13.9610	−	8.06039i	0.0151750	−	0.00876130i
$921$	−1457.88	+	533.451i	−1.58293	+	0.579209i
$922$	−86.0479	+	149.039i	−0.0933275	+	0.161648i
$923$	−933.226	+	538.798i	−1.01108	+	0.583747i
$924$	404.012	+	108.995i	0.437243	+	0.117960i
$925$	−428.838	+	742.769i	−0.463609	+	0.802994i
$926$	−520.815	+	300.693i	−0.562436	+	0.324722i
$927$	250.680	+	1393.77i	0.270421	+	1.50353i
$928$	−129.923	+	225.033i	−0.140003	+	0.242493i
$929$		−	669.821i		−	0.721012i	−0.932757	−	0.360506i	$-0.882604\pi$
$929$		−	669.821i		−	0.721012i	0.932757	−	0.360506i	$-0.117396\pi$
$930$	266.503	−	1526.68i	0.286562	−	1.64159i
$931$	510.470	+	93.6132i	0.548303	+	0.100551i
$932$	−460.795	+	266.040i	−0.494415	+	0.285451i
$933$	42.9951	+	117.502i	0.0460826	+	0.125940i
$934$	115.002	+	199.189i	0.123128	+	0.213264i
$935$	1875.40	+	1082.76i	2.00578	+	1.15804i
$936$	94.2098	−	261.622i	0.100652	−	0.279510i
$937$	145.717			0.155515			0.0777573	−	0.996972i	$-0.475224\pi$
$937$	145.717			0.155515			0.0777573	+	0.996972i	$0.475224\pi$
$938$	14.4572	−	6.68144i	0.0154128	−	0.00712307i
$939$	−666.024	+	243.704i	−0.709291	+	0.259536i
$940$	228.474	−	395.728i	0.243057	−	0.420988i
$941$		−	1468.00i		−	1.56004i	−0.625754	−	0.780021i	$-0.715209\pi$
$941$		−	1468.00i		−	1.56004i	0.625754	−	0.780021i	$-0.284791\pi$
$942$	347.479	+	949.633i	0.368874	+	1.00810i
$943$	27.6664			0.0293388
$944$			233.815i			0.247686i
$945$	1188.28	+	829.012i	1.25744	+	0.877262i
$946$	311.316			0.329087
$947$		−	166.652i		−	0.175979i	−0.996121	−	0.0879895i	$-0.971956\pi$
$947$		−	166.652i		−	0.175979i	0.996121	−	0.0879895i	$-0.0280442\pi$
$948$	−605.142	+	221.427i	−0.638336	+	0.233573i
$949$	−955.408			−1.00675
$950$	−438.044	−	252.905i	−0.461099	−	0.266215i
$951$	−374.355	−	1023.08i	−0.393644	−	1.07580i
$952$	559.043	+	50.8365i	0.587230	+	0.0533997i
$953$			1265.35i			1.32775i	0.747842	+	0.663876i	$0.231090\pi$
$953$			1265.35i			1.32775i	−0.747842	+	0.663876i	$0.768910\pi$
$954$	−69.8287	−	388.244i	−0.0731957	−	0.406965i
$955$	576.822	−	999.085i	0.604002	−	1.04616i
$956$	−193.194	+	111.540i	−0.202085	+	0.116674i
$957$	1289.37	−	471.792i	1.34730	−	0.492991i
$958$	−542.192	−	939.104i	−0.565962	−	0.980275i
$959$	−386.477	−	272.588i	−0.403000	−	0.284242i
$960$	−181.245	−	31.6387i	−0.188797	−	0.0329570i
$961$	1309.47			1.36261
$962$	−339.795	−	196.180i	−0.353217	−	0.203930i
$963$	−252.673	+	701.677i	−0.262382	+	0.728636i
$964$	−321.100	−	556.162i	−0.333091	−	0.576931i
$965$	2507.67	+	1447.80i	2.59862	+	1.50031i
$966$	−21.3375	+	5.67833i	−0.0220885	+	0.00587819i
$967$	839.074	+	1453.32i	0.867708	+	1.50291i	0.864333	+	0.502920i	$0.167741\pi$
$967$	839.074	+	1453.32i	0.867708	+	1.50291i	0.00337523	+	0.999994i	$0.498926\pi$
$968$	−53.2365	−	30.7361i	−0.0549964	−	0.0317522i
$969$	309.568	+	846.025i	0.319472	+	0.873091i
$970$	−329.397	−	570.532i	−0.339584	−	0.588177i
$971$	1476.21	−	852.288i	1.52029	−	0.877742i	0.520581	−	0.853813i	$-0.325716\pi$
$971$	1476.21	−	852.288i	1.52029	−	0.877742i	0.999714	−	0.0239297i	$-0.00761780\pi$
$972$	88.4847	+	477.877i	0.0910336	+	0.491643i
$973$	−337.979	+	479.188i	−0.347357	+	0.492485i
$974$	186.284	+	107.551i	0.191256	+	0.110422i
$975$	190.297	−	1090.13i	0.195177	−	1.11809i
$976$	−102.478			−0.104998
$977$		−	1672.49i		−	1.71187i	−0.517087	−	0.855933i	$-0.672984\pi$
$977$		−	1672.49i		−	1.71187i	0.517087	−	0.855933i	$-0.327016\pi$
$978$	221.360	−	264.726i	0.226340	−	0.270681i
$979$	311.795	−	540.044i	0.318483	−	0.551628i
$980$	707.709	−	252.118i	0.722152	−	0.257263i
$981$	−1.87147	−	10.4053i	−0.00190772	−	0.0106068i
$982$	286.454	+	496.154i	0.291705	+	0.505248i
$983$	−719.402	+	415.347i	−0.731844	+	0.422530i	−0.819096	−	0.573656i	$-0.805525\pi$
$983$	−719.402	+	415.347i	−0.731844	+	0.422530i	0.0872526	+	0.996186i	$0.472191\pi$
$984$	−242.230	−	202.550i	−0.246169	−	0.205843i
$985$	1212.74	−	2100.52i	1.23121	−	2.13251i
$986$	1595.06	−	920.907i	1.61771	−	0.933983i
$987$	−443.311	+	441.799i	−0.449150	+	0.447618i
$988$	115.696	−	200.392i	0.117102	−	0.202826i
$989$	−14.2261	+	8.21342i	−0.0143843	+	0.00830477i
$990$	627.428	+	742.564i	0.633766	+	0.750065i
$991$	807.640	−	1398.87i	0.814974	−	1.41158i	−0.0943719	−	0.995537i	$-0.530084\pi$
$991$	807.640	−	1398.87i	0.814974	−	1.41158i	0.909346	−	0.416040i	$-0.136582\pi$
$992$		−	269.546i		−	0.271719i
$993$	−153.003	+	55.9852i	−0.154082	+	0.0563799i
$994$	−409.691	−	886.486i	−0.412164	−	0.891837i
$995$	582.529	−	336.323i	0.585456	−	0.338013i
$996$	−923.618	−	161.230i	−0.927327	−	0.161877i
$997$	−191.233	−	331.225i	−0.191808	−	0.332221i	0.754041	−	0.656827i	$-0.228102\pi$
$997$	−191.233	−	331.225i	−0.191808	−	0.332221i	−0.945849	+	0.324606i	$0.894768\pi$
$998$	−448.029	−	258.669i	−0.448926	−	0.259188i
$999$	685.751	−	3.52021i	0.686437	−	0.00352373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.r.a.11.8	yes	32
3.2	odd	2		378.3.r.a.305.9		32
7.2	even	3		126.3.i.a.65.4	✓	32
9.4	even	3		378.3.i.a.179.9		32
9.5	odd	6		126.3.i.a.95.4	yes	32
21.2	odd	6		378.3.i.a.359.16		32
63.23	odd	6	inner	126.3.r.a.23.16	yes	32
63.58	even	3		378.3.r.a.233.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.4	✓	32	7.2	even	3
126.3.i.a.95.4	yes	32	9.5	odd	6
126.3.r.a.11.8	yes	32	1.1	even	1	trivial
126.3.r.a.23.16	yes	32	63.23	odd	6	inner
378.3.i.a.179.9		32	9.4	even	3
378.3.i.a.359.16		32	21.2	odd	6
378.3.r.a.233.1		32	63.58	even	3
378.3.r.a.305.9		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} +(2.81732 - 1.03088i) q^{3} -2.00000 q^{4} +(6.63902 + 3.83304i) q^{5} +(-1.45789 - 3.98429i) q^{6} +(2.93662 + 6.35423i) q^{7} +2.82843i q^{8} +(6.87456 - 5.80865i) q^{9} +(5.42073 - 9.38899i) q^{10} +(-8.62843 + 4.98162i) q^{11} +(-5.63464 + 2.06177i) q^{12} +(-5.46176 - 9.46004i) q^{13} +(8.98624 - 4.15301i) q^{14} +(22.6556 + 3.95484i) q^{15} +4.00000 q^{16} +(-24.5539 - 14.1762i) q^{17} +(-8.21467 - 9.72210i) q^{18} +(-5.29575 - 9.17250i) q^{19} +(-13.2780 - 7.66608i) q^{20} +(14.8239 + 14.8746i) q^{21} +(7.04508 + 12.2024i) q^{22} +(-0.643871 - 0.371739i) q^{23} +(2.91578 + 7.96858i) q^{24} +(16.8844 + 29.2446i) q^{25} +(-13.3785 + 7.72409i) q^{26} +(13.3798 - 23.4517i) q^{27} +(-5.87324 - 12.7085i) q^{28} +(-39.7806 - 22.9673i) q^{29} +(5.59299 - 32.0399i) q^{30} +47.6494 q^{31} -5.65685i q^{32} +(-19.1735 + 22.9297i) q^{33} +(-20.0482 + 34.7245i) q^{34} +(-4.85975 + 53.4420i) q^{35} +(-13.7491 + 11.6173i) q^{36} +(12.6993 + 21.9958i) q^{37} +(-12.9719 + 7.48932i) q^{38} +(-25.1397 - 21.0215i) q^{39} +(-10.8415 + 18.7780i) q^{40} +(-32.2267 + 18.6061i) q^{41} +(21.0358 - 20.9641i) q^{42} +(11.0473 - 19.1345i) q^{43} +(17.2569 - 9.96325i) q^{44} +(67.9051 - 12.2133i) q^{45} +(-0.525718 + 0.910571i) q^{46} +29.8032i q^{47} +(11.2693 - 4.12353i) q^{48} +(-31.7525 + 37.3199i) q^{49} +(41.3581 - 23.8781i) q^{50} +(-83.7902 - 14.6267i) q^{51} +(10.9235 + 18.9201i) q^{52} +(26.8405 + 15.4964i) q^{53} +(-33.1657 - 18.9219i) q^{54} -76.3790 q^{55} +(-17.9725 + 8.30601i) q^{56} +(-24.3756 - 20.3826i) q^{57} +(-32.4807 + 56.2583i) q^{58} +58.4538i q^{59} +(-45.3113 - 7.90968i) q^{60} -25.6194 q^{61} -67.3864i q^{62} +(57.0975 + 26.6248i) q^{63} -8.00000 q^{64} -83.7405i q^{65} +(32.4275 + 27.1155i) q^{66} +1.60882 q^{67} +(49.1078 + 28.3524i) q^{68} +(-2.19721 - 0.383552i) q^{69} +(75.5784 + 6.87272i) q^{70} -98.6493i q^{71} +(16.4293 + 19.4442i) q^{72} +(43.7317 - 75.7455i) q^{73} +(31.1067 - 17.9595i) q^{74} +(77.7164 + 64.9855i) q^{75} +(10.5915 + 18.3450i) q^{76} +(-56.9928 - 40.1979i) q^{77} +(-29.7289 + 35.5529i) q^{78} +107.397 q^{79} +(26.5561 + 15.3322i) q^{80} +(13.5192 - 79.8638i) q^{81} +(26.3130 + 45.5755i) q^{82} +(135.329 + 78.1320i) q^{83} +(-29.6477 - 29.7492i) q^{84} +(-108.676 - 188.232i) q^{85} +(-27.0602 - 15.6232i) q^{86} +(-135.751 - 23.6972i) q^{87} +(-14.0902 - 24.4049i) q^{88} +(-54.2036 + 31.2945i) q^{89} +(-17.2722 - 96.0323i) q^{90} +(44.0722 - 62.4858i) q^{91} +(1.28774 + 0.743478i) q^{92} +(134.244 - 49.1209i) q^{93} +42.1481 q^{94} -81.1952i q^{95} +(-5.83155 - 15.9372i) q^{96} +(30.3830 - 52.6249i) q^{97} +(52.7783 + 44.9049i) q^{98} +(-30.3801 + 84.3660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27}+ \cdots + 394 q^{99}+O(q^{100}) \) 32 * q - 64 * q^4 + 8 * q^6 + 2 * q^7 - 20 * q^9 - 36 * q^11 + 10 * q^13 + 36 * q^14 + 10 * q^15 + 128 * q^16 - 54 * q^17 + 28 * q^19 + 28 * q^21 - 126 * q^23 - 16 * q^24 + 80 * q^25 - 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 + 76 * q^30 + 16 * q^31 - 40 * q^33 - 90 * q^35 + 40 * q^36 + 22 * q^37 + 46 * q^39 + 72 * q^41 + 120 * q^42 + 16 * q^43 + 72 * q^44 + 464 * q^45 - 12 * q^46 + 2 * q^49 - 288 * q^50 - 286 * q^51 - 20 * q^52 - 72 * q^53 - 160 * q^54 - 24 * q^55 - 72 * q^56 - 282 * q^57 - 24 * q^58 - 20 * q^60 + 124 * q^61 + 66 * q^63 - 256 * q^64 - 16 * q^66 - 140 * q^67 + 108 * q^68 + 218 * q^69 + 72 * q^70 + 196 * q^73 + 216 * q^74 + 658 * q^75 - 56 * q^76 + 486 * q^77 + 32 * q^78 + 76 * q^79 - 380 * q^81 - 56 * q^84 + 60 * q^85 - 144 * q^86 - 740 * q^87 - 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 + 238 * q^93 - 336 * q^94 + 32 * q^96 - 38 * q^97 + 288 * q^98 + 394 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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