LMFDB - Embedded newform 126.3.o.a.13.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(13,126)] 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([2, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.13"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.o (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			13.12
Character	$\chi$	$=$	126.13
Dual form			126.3.o.a.97.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(-0.208863 - 2.99272i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-6.78854 - 3.91937i) q^{5} +(3.51763 - 2.37198i) q^{6} +(-6.99901 - 0.117453i) q^{7} -2.82843 q^{8} +(-8.91275 + 1.25014i) q^{9} -11.0856i q^{10} +(-1.05393 - 1.82546i) q^{11} +(5.39241 + 2.63096i) q^{12} +(8.95661 + 5.17110i) q^{13} +(-4.80520 - 8.65506i) q^{14} +(-10.3117 + 21.1348i) q^{15} +(-2.00000 - 3.46410i) q^{16} -9.44215i q^{17} +(-7.83337 - 10.0319i) q^{18} -7.01239i q^{19} +(13.5771 - 7.83874i) q^{20} +(1.11033 + 20.9706i) q^{21} +(1.49048 - 2.58159i) q^{22} +(22.7785 - 39.4534i) q^{23} +(0.590754 + 8.46469i) q^{24} +(18.2229 + 31.5630i) q^{25} +14.6261i q^{26} +(5.60286 + 26.4123i) q^{27} +(7.20245 - 12.0052i) q^{28} +(-9.93225 - 17.2032i) q^{29} +(-33.1762 + 2.31538i) q^{30} +(-5.21387 - 3.01023i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-5.24295 + 3.53538i) q^{33} +(11.5642 - 6.67661i) q^{34} +(47.0528 + 28.2290i) q^{35} +(6.74745 - 16.6875i) q^{36} -40.4151 q^{37} +(8.58839 - 4.95851i) q^{38} +(13.6050 - 27.8847i) q^{39} +(19.2009 + 11.0856i) q^{40} +(-52.9968 - 30.5977i) q^{41} +(-24.8985 + 16.1883i) q^{42} +(34.3646 + 59.5213i) q^{43} +4.21571 q^{44} +(65.4044 + 26.4457i) q^{45} +64.4272 q^{46} +(-59.5554 + 34.3843i) q^{47} +(-9.94936 + 6.70896i) q^{48} +(48.9724 + 1.64411i) q^{49} +(-25.7710 + 44.6368i) q^{50} +(-28.2577 + 1.97212i) q^{51} +(-17.9132 + 10.3422i) q^{52} -64.4077 q^{53} +(-28.3865 + 25.5384i) q^{54} +16.5229i q^{55} +(19.7962 + 0.332208i) q^{56} +(-20.9861 + 1.46463i) q^{57} +(14.0463 - 24.3290i) q^{58} +(36.8068 + 21.2504i) q^{59} +(-26.2949 - 38.9952i) q^{60} +(9.89468 - 5.71270i) q^{61} -8.51422i q^{62} +(62.5273 - 7.70290i) q^{63} +8.00000 q^{64} +(-40.5349 - 70.2085i) q^{65} +(-8.03727 - 3.92139i) q^{66} +(4.32856 - 7.49729i) q^{67} +(16.3543 + 9.44215i) q^{68} +(-122.831 - 59.9292i) q^{69} +(-1.30205 + 77.5886i) q^{70} +56.4985 q^{71} +(25.2091 - 3.53592i) q^{72} -64.7908i q^{73} +(-28.5778 - 49.4982i) q^{74} +(90.6530 - 61.1283i) q^{75} +(12.1458 + 7.01239i) q^{76} +(7.16205 + 12.9002i) q^{77} +(43.7718 - 3.05485i) q^{78} +(-57.0864 - 98.8765i) q^{79} +31.3549i q^{80} +(77.8743 - 22.2843i) q^{81} -86.5433i q^{82} +(86.5846 - 49.9896i) q^{83} +(-37.4325 - 19.0475i) q^{84} +(-37.0073 + 64.0985i) q^{85} +(-48.5989 + 84.1758i) q^{86} +(-49.4098 + 33.3176i) q^{87} +(2.98096 + 5.16317i) q^{88} -90.9556i q^{89} +(13.8586 + 98.8036i) q^{90} +(-62.0801 - 37.2446i) q^{91} +(45.5569 + 78.9069i) q^{92} +(-7.91980 + 16.2324i) q^{93} +(-84.2240 - 48.6267i) q^{94} +(-27.4841 + 47.6039i) q^{95} +(-15.2520 - 7.44148i) q^{96} +(39.5328 - 22.8243i) q^{97} +(32.6151 + 61.1413i) q^{98} +(11.6755 + 14.9523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	−0.208863	−	2.99272i	−0.0696210	−	0.997574i
$3$	−0.208863	−	2.99272i	−0.0696210	−	0.997574i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−6.78854	−	3.91937i	−1.35771	−	0.783874i	−0.368394	−	0.929670i	$-0.620092\pi$
$5$	−6.78854	−	3.91937i	−1.35771	−	0.783874i	−0.989315	+	0.145796i	$0.953426\pi$
$6$	3.51763	−	2.37198i	0.586272	−	0.395329i
$7$	−6.99901	−	0.117453i	−0.999859	−	0.0167790i
$7$	−6.99901	−	0.117453i	−0.999859	−	0.0167790i
$8$	−2.82843			−0.353553
$9$	−8.91275	+	1.25014i	−0.990306	+	0.138904i
$10$		−	11.0856i		−	1.10856i
$11$	−1.05393	−	1.82546i	−0.0958116	−	0.165951i	0.814135	−	0.580675i	$-0.197211\pi$
$11$	−1.05393	−	1.82546i	−0.0958116	−	0.165951i	−0.909947	+	0.414724i	$0.863878\pi$
$12$	5.39241	+	2.63096i	0.449367	+	0.219247i
$13$	8.95661	+	5.17110i	0.688970	+	0.397777i	0.803226	−	0.595674i	$-0.203115\pi$
$13$	8.95661	+	5.17110i	0.688970	+	0.397777i	−0.114256	+	0.993451i	$0.536448\pi$
$14$	−4.80520	−	8.65506i	−0.343229	−	0.618219i
$15$	−10.3117	+	21.1348i	−0.687446	+	1.40899i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	9.44215i		−	0.555421i	−0.960665	−	0.277710i	$-0.910424\pi$
$17$		−	9.44215i		−	0.555421i	0.960665	−	0.277710i	$-0.0895755\pi$
$18$	−7.83337	−	10.0319i	−0.435187	−	0.557326i
$19$		−	7.01239i		−	0.369073i	−0.982826	−	0.184537i	$-0.940922\pi$
$19$		−	7.01239i		−	0.369073i	0.982826	−	0.184537i	$-0.0590784\pi$
$20$	13.5771	−	7.83874i	0.678854	−	0.391937i
$21$	1.11033	+	20.9706i	0.0528729	+	0.998601i
$22$	1.49048	−	2.58159i	0.0677490	−	0.117345i
$23$	22.7785	−	39.4534i	0.990367	−	1.71537i	0.375270	−	0.926915i	$-0.377550\pi$
$23$	22.7785	−	39.4534i	0.990367	−	1.71537i	0.615097	−	0.788451i	$-0.289117\pi$
$24$	0.590754	+	8.46469i	0.0246147	+	0.352695i
$25$	18.2229	+	31.5630i	0.728915	+	1.26252i
$26$			14.6261i			0.562542i
$27$	5.60286	+	26.4123i	0.207513	+	0.978232i
$28$	7.20245	−	12.0052i	0.257230	−	0.428757i
$29$	−9.93225	−	17.2032i	−0.342491	−	0.593213i	0.642403	−	0.766367i	$-0.277937\pi$
$29$	−9.93225	−	17.2032i	−0.342491	−	0.593213i	−0.984895	+	0.173154i	$0.944604\pi$
$30$	−33.1762	+	2.31538i	−1.10587	+	0.0771794i
$31$	−5.21387	−	3.01023i	−0.168189	−	0.0971042i	0.413542	−	0.910485i	$-0.364291\pi$
$31$	−5.21387	−	3.01023i	−0.168189	−	0.0971042i	−0.581732	+	0.813381i	$0.697625\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	−5.24295	+	3.53538i	−0.158877	+	0.107133i
$34$	11.5642	−	6.67661i	0.340124	−	0.196371i
$35$	47.0528	+	28.2290i	1.34436	+	0.806544i
$36$	6.74745	−	16.6875i	0.187429	−	0.463541i
$37$	−40.4151			−1.09230			−0.546151	−	0.837687i	$-0.683907\pi$
$37$	−40.4151			−1.09230			−0.546151	+	0.837687i	$0.683907\pi$
$38$	8.58839	−	4.95851i	0.226010	−	0.130487i
$39$	13.6050	−	27.8847i	0.348845	−	0.714992i
$40$	19.2009	+	11.0856i	0.480023	+	0.277141i
$41$	−52.9968	−	30.5977i	−1.29260	−	0.746285i	−0.313489	−	0.949592i	$-0.601498\pi$
$41$	−52.9968	−	30.5977i	−1.29260	−	0.746285i	−0.979115	+	0.203307i	$0.934831\pi$
$42$	−24.8985	+	16.1883i	−0.592822	+	0.385437i
$43$	34.3646	+	59.5213i	0.799178	+	1.38422i	0.920152	+	0.391561i	$0.128065\pi$
$43$	34.3646	+	59.5213i	0.799178	+	1.38422i	−0.120974	+	0.992656i	$0.538602\pi$
$44$	4.21571			0.0958116
$45$	65.4044	+	26.4457i	1.45343	+	0.587683i
$46$	64.4272			1.40059
$47$	−59.5554	+	34.3843i	−1.26714	+	0.731581i	−0.974445	−	0.224626i	$-0.927884\pi$
$47$	−59.5554	+	34.3843i	−1.26714	+	0.731581i	−0.292690	+	0.956207i	$0.594550\pi$
$48$	−9.94936	+	6.70896i	−0.207278	+	0.139770i
$49$	48.9724	+	1.64411i	0.999437	+	0.0335534i
$50$	−25.7710	+	44.6368i	−0.515421	+	0.892735i
$51$	−28.2577	+	1.97212i	−0.554073	+	0.0386690i
$52$	−17.9132	+	10.3422i	−0.344485	+	0.198889i
$53$	−64.4077			−1.21524			−0.607620	−	0.794228i	$-0.707875\pi$
$53$	−64.4077			−1.21524			−0.607620	+	0.794228i	$0.707875\pi$
$54$	−28.3865	+	25.5384i	−0.525675	+	0.472933i
$55$			16.5229i			0.300417i
$56$	19.7962	+	0.332208i	0.353504	+	0.00593229i
$57$	−20.9861	+	1.46463i	−0.368178	+	0.0256952i
$58$	14.0463	−	24.3290i	0.242178	−	0.419465i
$59$	36.8068	+	21.2504i	0.623844	+	0.360177i	0.778364	−	0.627813i	$-0.216050\pi$
$59$	36.8068	+	21.2504i	0.623844	+	0.360177i	−0.154520	+	0.987990i	$0.549383\pi$
$60$	−26.2949	−	38.9952i	−0.438248	−	0.649920i
$61$	9.89468	−	5.71270i	0.162208	−	0.0936508i	−0.416699	−	0.909045i	$-0.636813\pi$
$61$	9.89468	−	5.71270i	0.162208	−	0.0936508i	0.578907	+	0.815394i	$0.303480\pi$
$62$		−	8.51422i		−	0.137326i
$63$	62.5273	−	7.70290i	0.992497	−	0.122268i
$64$	8.00000			0.125000
$65$	−40.5349	−	70.2085i	−0.623614	−	1.08013i
$66$	−8.03727	−	3.92139i	−0.121777	−	0.0594150i
$67$	4.32856	−	7.49729i	0.0646054	−	0.111900i	−0.831913	−	0.554905i	$-0.812754\pi$
$67$	4.32856	−	7.49729i	0.0646054	−	0.111900i	0.896519	+	0.443005i	$0.146088\pi$
$68$	16.3543	+	9.44215i	0.240504	+	0.138855i
$69$	−122.831	−	59.9292i	−1.78015	−	0.868539i
$70$	−1.30205	+	77.5886i	−0.0186006	+	1.10841i
$71$	56.4985			0.795753			0.397876	−	0.917439i	$-0.369747\pi$
$71$	56.4985			0.795753			0.397876	+	0.917439i	$0.369747\pi$
$72$	25.2091	−	3.53592i	0.350126	−	0.0491100i
$73$		−	64.7908i		−	0.887545i	−0.896139	−	0.443773i	$-0.853640\pi$
$73$		−	64.7908i		−	0.887545i	0.896139	−	0.443773i	$-0.146360\pi$
$74$	−28.5778	−	49.4982i	−0.386187	−	0.668895i
$75$	90.6530	−	61.1283i	1.20871	−	0.815044i
$76$	12.1458	+	7.01239i	0.159813	+	0.0922683i
$77$	7.16205	+	12.9002i	0.0930136	+	0.167535i
$78$	43.7718	−	3.05485i	0.561177	−	0.0391647i
$79$	−57.0864	−	98.8765i	−0.722612	−	1.25160i	−0.959949	−	0.280174i	$-0.909608\pi$
$79$	−57.0864	−	98.8765i	−0.722612	−	1.25160i	0.237337	−	0.971427i	$-0.423725\pi$
$80$			31.3549i			0.391937i
$81$	77.8743	−	22.2843i	0.961411	−	0.275115i
$82$		−	86.5433i		−	1.05541i
$83$	86.5846	−	49.9896i	1.04319	−	0.602285i	0.122453	−	0.992474i	$-0.460924\pi$
$83$	86.5846	−	49.9896i	1.04319	−	0.602285i	0.920735	+	0.390190i	$0.127591\pi$
$84$	−37.4325	−	19.0475i	−0.445625	−	0.226756i
$85$	−37.0073	+	64.0985i	−0.435380	+	0.754100i
$86$	−48.5989	+	84.1758i	−0.565104	+	0.978789i
$87$	−49.4098	+	33.3176i	−0.567929	+	0.382961i
$88$	2.98096	+	5.16317i	0.0338745	+	0.0586724i
$89$		−	90.9556i		−	1.02197i	−0.859589	−	0.510986i	$-0.829280\pi$
$89$		−	90.9556i		−	1.02197i	0.859589	−	0.510986i	$-0.170720\pi$
$90$	13.8586	+	98.8036i	0.153984	+	1.09782i
$91$	−62.0801	−	37.2446i	−0.682199	−	0.409281i
$92$	45.5569	+	78.9069i	0.495184	+	0.857683i
$93$	−7.91980	+	16.2324i	−0.0851591	+	0.174542i
$94$	−84.2240	−	48.6267i	−0.896000	−	0.517306i
$95$	−27.4841	+	47.6039i	−0.289307	+	0.501094i
$96$	−15.2520	−	7.44148i	−0.158875	−	0.0775154i
$97$	39.5328	−	22.8243i	0.407555	−	0.235302i	−0.282184	−	0.959360i	$-0.591059\pi$
$97$	39.5328	−	22.8243i	0.407555	−	0.235302i	0.689738	+	0.724059i	$0.257726\pi$
$98$	32.6151	+	61.1413i	0.332807	+	0.623891i
$99$	11.6755	+	14.9523i	0.117934	+	0.151033i
$100$	−72.8915			−0.728915
$101$	0.526801	−	0.304149i	0.00521585	−	0.00301137i	−0.497390	−	0.867527i	$-0.665708\pi$
$101$	0.526801	−	0.304149i	0.00521585	−	0.00301137i	0.502606	+	0.864516i	$0.332375\pi$
$102$	−22.3966	−	33.2140i	−0.219574	−	0.325627i
$103$	84.7729	+	48.9437i	0.823038	+	0.475181i	0.851463	−	0.524415i	$-0.175716\pi$
$103$	84.7729	+	48.9437i	0.823038	+	0.475181i	−0.0284251	+	0.999596i	$0.509049\pi$
$104$	−25.3331	−	14.6261i	−0.243588	−	0.140635i
$105$	74.6541	−	146.712i	0.710991	−	1.39726i
$106$	−45.5431	−	78.8830i	−0.429652	−	0.744179i
$107$	−65.2642			−0.609946			−0.304973	−	0.952361i	$-0.598647\pi$
$107$	−65.2642			−0.609946			−0.304973	+	0.952361i	$0.598647\pi$
$108$	−51.3502	−	16.7078i	−0.475465	−	0.154702i
$109$	−197.677			−1.81355			−0.906776	−	0.421612i	$-0.861464\pi$
$109$	−197.677			−1.81355			−0.906776	+	0.421612i	$0.861464\pi$
$110$	−20.2364	+	11.6835i	−0.183967	+	0.106213i
$111$	8.44123	+	120.951i	0.0760471	+	1.08965i
$112$	13.5912	+	24.4802i	0.121350	+	0.218573i
$113$	25.1877	−	43.6264i	0.222900	−	0.386074i	−0.732787	−	0.680458i	$-0.761781\pi$
$113$	25.1877	−	43.6264i	0.222900	−	0.386074i	0.955687	+	0.294384i	$0.0951143\pi$
$114$	−16.6332	−	24.6670i	−0.145905	−	0.216377i
$115$	−309.265	+	178.554i	−2.68926	+	1.55265i
$116$	39.7290			0.342491
$117$	−86.2927	−	34.8918i	−0.737544	−	0.298220i
$118$			60.1053i			0.509367i
$119$	−1.10901	+	66.0858i	−0.00931943	+	0.555342i
$120$	29.1659	−	59.7783i	0.243049	−	0.498153i
$121$	58.2785	−	100.941i	0.481640	−	0.834225i
$122$	13.9932	+	8.07898i	0.114698	+	0.0662211i
$123$	−80.5013	+	164.995i	−0.654482	+	1.34142i
$124$	10.4277	−	6.02046i	0.0840947	−	0.0485521i
$125$		−	89.7203i		−	0.717763i
$126$	53.6476	+	71.1332i	0.425774	+	0.564550i
$127$	118.295			0.931457			0.465729	−	0.884928i	$-0.345792\pi$
$127$	118.295			0.931457			0.465729	+	0.884928i	$0.345792\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	170.953	−	115.276i	1.32522	−	0.893609i
$130$	57.3250	−	99.2898i	0.440962	−	0.763768i
$131$	111.014	+	64.0941i	0.847438	+	0.489268i	0.859785	−	0.510655i	$-0.170597\pi$
$131$	111.014	+	64.0941i	0.847438	+	0.489268i	−0.0123479	+	0.999924i	$0.503931\pi$
$132$	−0.880506	−	12.6164i	−0.00667050	−	0.0955791i
$133$	−0.823628	+	49.0798i	−0.00619269	+	0.369021i
$134$	12.2430			0.0913659
$135$	65.4842	−	201.261i	0.485068	−	1.49082i
$136$			26.7064i			0.196371i
$137$	110.979	+	192.221i	0.810063	+	1.40307i	0.912820	+	0.408363i	$0.133900\pi$
$137$	110.979	+	192.221i	0.810063	+	1.40307i	−0.102757	+	0.994706i	$0.532766\pi$
$138$	−13.4565	−	192.813i	−0.0975106	−	1.39719i
$139$	206.757	+	119.371i	1.48746	+	0.858788i	0.999898	−	0.0142986i	$-0.00455153\pi$
$139$	206.757	+	119.371i	1.48746	+	0.858788i	0.487566	+	0.873086i	$0.337885\pi$
$140$	−95.9469	+	53.2687i	−0.685335	+	0.380491i
$141$	115.342	+	171.051i	0.818025	+	1.21313i
$142$	39.9504	+	69.1962i	0.281341	+	0.487297i
$143$		−	21.7999i		−	0.152447i
$144$	22.1561	+	28.3744i	0.153862	+	0.197044i
$145$			155.713i			1.07388i
$146$	79.3522	−	45.8140i	0.543508	−	0.313795i
$147$	−5.30815	−	146.904i	−0.0361099	−	0.999348i
$148$	40.4151	−	70.0011i	0.273075	−	0.472980i
$149$	51.5809	−	89.3407i	0.346180	−	0.599602i	−0.639387	−	0.768885i	$-0.720812\pi$
$149$	51.5809	−	89.3407i	0.346180	−	0.599602i	0.985567	+	0.169283i	$0.0541452\pi$
$150$	138.968	+	67.8026i	0.926453	+	0.452017i
$151$	−100.671	−	174.368i	−0.666697	−	1.15475i	−0.978822	−	0.204712i	$-0.934374\pi$
$151$	−100.671	−	174.368i	−0.666697	−	1.15475i	0.312126	−	0.950041i	$-0.398959\pi$
$152$			19.8340i			0.130487i
$153$	11.8040	+	84.1556i	0.0771502	+	0.550036i
$154$	−10.7351	+	17.8935i	−0.0697084	+	0.116191i
$155$	23.5964	+	40.8702i	0.152235	+	0.263679i
$156$	34.6927	+	51.4492i	0.222389	+	0.329802i
$157$	−81.5336	−	47.0735i	−0.519322	−	0.299831i	0.217335	−	0.976097i	$-0.430264\pi$
$157$	−81.5336	−	47.0735i	−0.519322	−	0.299831i	−0.736657	+	0.676266i	$0.763597\pi$
$158$	80.7323	−	139.832i	0.510964	−	0.885016i
$159$	13.4524	+	192.754i	0.0846062	+	1.21229i
$160$	−38.4018	+	22.1713i	−0.240011	+	0.138571i
$161$	−164.061	+	273.460i	−1.01901	+	1.69851i
$162$	82.3581	+	79.6188i	0.508383	+	0.491474i
$163$	9.85556			0.0604636			0.0302318	−	0.999543i	$-0.490375\pi$
$163$	9.85556			0.0604636			0.0302318	+	0.999543i	$0.490375\pi$
$164$	105.994	−	61.1954i	0.646302	−	0.373143i
$165$	49.4485	−	3.45103i	0.299688	−	0.0209153i
$166$	122.449	+	70.6960i	0.737645	+	0.425880i
$167$	−106.856	−	61.6935i	−0.639858	−	0.369422i	0.144702	−	0.989475i	$-0.453778\pi$
$167$	−106.856	−	61.6935i	−0.639858	−	0.369422i	−0.784560	+	0.620053i	$0.787111\pi$
$168$	−3.14049	−	59.3139i	−0.0186934	−	0.353059i
$169$	−31.0194	−	53.7272i	−0.183547	−	0.317912i
$170$	−104.672			−0.615720
$171$	8.76645	+	62.4997i	0.0512658	+	0.365495i
$172$	−137.459			−0.799178
$173$	−224.321	+	129.512i	−1.29666	+	0.748624i	−0.979825	−	0.199858i	$-0.935952\pi$
$173$	−224.321	+	129.512i	−1.29666	+	0.748624i	−0.316830	+	0.948482i	$0.602619\pi$
$174$	−75.7435	−	36.9553i	−0.435308	−	0.212387i
$175$	−123.835	−	223.050i	−0.707629	−	1.27457i
$176$	−4.21571	+	7.30183i	−0.0239529	+	0.0414876i
$177$	55.9090	−	114.591i	0.315870	−	0.647406i
$178$	111.397	−	64.3153i	0.625828	−	0.361322i
$179$	23.4639			0.131083			0.0655416	−	0.997850i	$-0.479122\pi$
$179$	23.4639			0.131083			0.0655416	+	0.997850i	$0.479122\pi$
$180$	−111.210	+	86.8379i	−0.617832	+	0.482433i
$181$		−	173.634i		−	0.959304i	−0.877459	−	0.479652i	$-0.840763\pi$
$181$		−	173.634i		−	0.959304i	0.877459	−	0.479652i	$-0.159237\pi$
$182$	1.71788	−	102.368i	0.00943891	−	0.562463i
$183$	−19.1631	−	28.4189i	−0.104717	−	0.155294i
$184$	−64.4272	+	111.591i	−0.350148	+	0.606474i
$185$	274.360	+	158.402i	1.48303	+	0.856226i
$186$	−25.4807	+	1.77831i	−0.136993	+	0.00956078i
$187$	−17.2362	+	9.95135i	−0.0921724	+	0.0532157i
$188$		−	137.537i		−	0.731581i
$189$	−36.1123	−	185.518i	−0.191070	−	0.981576i
$190$	−77.7369			−0.409141
$191$	121.207	+	209.936i	0.634590	+	1.09914i	0.986602	+	0.163147i	$0.0521645\pi$
$191$	121.207	+	209.936i	0.634590	+	1.09914i	−0.352011	+	0.935996i	$0.614502\pi$
$192$	−1.67090	−	23.9418i	−0.00870263	−	0.124697i
$193$	−124.323	+	215.333i	−0.644159	+	1.11572i	0.340336	+	0.940304i	$0.389459\pi$
$193$	−124.323	+	215.333i	−0.644159	+	1.11572i	−0.984495	+	0.175412i	$0.943874\pi$
$194$	55.9078	+	32.2784i	0.288185	+	0.166383i
$195$	−201.648	+	135.974i	−1.03409	+	0.697300i
$196$	−51.8201	+	83.1786i	−0.264388	+	0.424381i
$197$	−6.15551			−0.0312462			−0.0156231	−	0.999878i	$-0.504973\pi$
$197$	−6.15551			−0.0312462			−0.0156231	+	0.999878i	$0.504973\pi$
$198$	−10.0569	+	24.8723i	−0.0507926	+	0.125618i
$199$		−	293.738i		−	1.47607i	−0.674761	−	0.738036i	$-0.735753\pi$
$199$		−	293.738i		−	1.47607i	0.674761	−	0.738036i	$-0.264247\pi$
$200$	−51.5421	−	89.2735i	−0.257710	−	0.446368i
$201$	−23.3414	−	11.3883i	−0.116126	−	0.0566581i
$202$	0.745009	+	0.430131i	0.00368817	+	0.00212936i
$203$	67.4954	+	121.572i	0.332490	+	0.598876i
$204$	24.8419	−	50.9159i	0.121774	−	0.249588i
$205$	239.847	+	415.428i	1.16999	+	2.02648i
$206$			138.434i			0.672008i
$207$	−153.696	+	380.115i	−0.742495	+	1.83630i
$208$		−	41.3688i		−	0.198889i
$209$	−12.8008	+	7.39055i	−0.0612479	+	0.0353615i
$210$	232.473	−	12.3087i	1.10701	−	0.0586130i
$211$	37.0792	−	64.2230i	0.175731	−	0.304374i	−0.764683	−	0.644406i	$-0.777105\pi$
$211$	37.0792	−	64.2230i	0.175731	−	0.304374i	0.940414	+	0.340032i	$0.110438\pi$
$212$	64.4077	−	111.557i	0.303810	−	0.526214i
$213$	−11.8004	−	169.084i	−0.0554011	−	0.793822i
$214$	−46.1488	−	79.9320i	−0.215649	−	0.373514i
$215$		−	538.751i		−	2.50582i
$216$	−15.8473	−	74.7052i	−0.0733670	−	0.345857i
$217$	36.1384	+	21.6810i	0.166536	+	0.0999126i
$218$	−139.779	−	242.104i	−0.641188	−	1.11057i
$219$	−193.901	+	13.5324i	−0.885391	+	0.0617918i
$220$	−28.6185	−	16.5229i	−0.130084	−	0.0751042i
$221$	48.8263	−	84.5697i	0.220934	−	0.382668i
$222$	−142.166	+	95.8638i	−0.640385	+	0.431819i
$223$	240.774	−	139.011i	1.07970	−	0.623366i	0.148886	−	0.988854i	$-0.452431\pi$
$223$	240.774	−	139.011i	1.07970	−	0.623366i	0.930816	+	0.365488i	$0.119098\pi$
$224$	−20.3716	+	33.9558i	−0.0909447	+	0.151588i
$225$	−201.874	−	258.532i	−0.897218	−	1.14903i
$226$	71.2416			0.315228
$227$	−87.4980	+	50.5170i	−0.385454	+	0.222542i	−0.680188	−	0.733037i	$-0.738102\pi$
$227$	−87.4980	+	50.5170i	−0.385454	+	0.222542i	0.294735	+	0.955579i	$0.404769\pi$
$228$	18.4493	−	37.8137i	0.0809180	−	0.165849i
$229$	−51.0727	−	29.4869i	−0.223025	−	0.128764i	0.384325	−	0.923198i	$-0.374434\pi$
$229$	−51.0727	−	29.4869i	−0.223025	−	0.128764i	−0.607350	+	0.794434i	$0.707767\pi$
$230$	−437.367	−	252.514i	−1.90159	−	1.09789i
$231$	37.1108	−	24.1284i	0.160653	−	0.104452i
$232$	28.0927	+	48.6579i	0.121089	+	0.209732i
$233$	−179.497			−0.770374			−0.385187	−	0.922839i	$-0.625863\pi$
$233$	−179.497			−0.770374			−0.385187	+	0.922839i	$0.625863\pi$
$234$	−18.2846	−	130.359i	−0.0781394	−	0.557088i
$235$	539.059			2.29387
$236$	−73.6136	+	42.5008i	−0.311922	+	0.180088i
$237$	−283.986	+	191.495i	−1.19826	+	0.807997i
$238$	−81.7224	+	45.3714i	−0.343371	+	0.190636i
$239$	−91.2575	+	158.063i	−0.381831	+	0.661350i	−0.991324	−	0.131441i	$-0.958040\pi$
$239$	−91.2575	+	158.063i	−0.381831	+	0.661350i	0.609493	+	0.792791i	$0.291373\pi$
$240$	93.8366	−	6.54889i	0.390986	−	0.0272870i
$241$	4.89842	−	2.82810i	0.0203254	−	0.0117349i	−0.489803	−	0.871833i	$-0.662931\pi$
$241$	4.89842	−	2.82810i	0.0203254	−	0.0117349i	0.510128	+	0.860098i	$0.329598\pi$
$242$	164.836			0.681142
$243$	−82.9558	−	228.402i	−0.341382	−	0.939925i
$244$			22.8508i			0.0936508i
$245$	−326.007	−	203.102i	−1.33064	−	0.828988i
$246$	−259.000	+	18.0757i	−1.05285	+	0.0734785i
$247$	36.2618	−	62.8072i	0.146809	−	0.254280i
$248$	14.7471	+	8.51422i	0.0594640	+	0.0343315i
$249$	−167.689	−	248.682i	−0.673451	−	0.998725i
$250$	109.885	−	63.4419i	0.439538	−	0.253767i
$251$		−	150.523i		−	0.599693i	−0.953987	−	0.299847i	$-0.903064\pi$
$251$		−	150.523i		−	0.599693i	0.953987	−	0.299847i	$-0.0969355\pi$
$252$	−49.1855	+	116.003i	−0.195181	+	0.460331i
$253$	−96.0274			−0.379555
$254$	83.6472	+	144.881i	0.329320	+	0.570399i
$255$	199.558	+	97.3646i	0.782581	+	0.381822i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−88.3013	−	50.9808i	−0.343585	−	0.198369i	0.318271	−	0.948000i	$-0.396898\pi$
$257$	−88.3013	−	50.9808i	−0.343585	−	0.198369i	−0.661856	+	0.749631i	$0.730231\pi$
$258$	262.065	+	127.862i	1.01576	+	0.495589i
$259$	282.866	+	4.74689i	1.09215	+	0.0183278i
$260$	162.140			0.623614
$261$	110.030	+	140.911i	0.421571	+	0.539888i
$262$			181.286i			0.691930i
$263$	−56.3682	−	97.6325i	−0.214328	−	0.371226i	0.738737	−	0.673994i	$-0.235423\pi$
$263$	−56.3682	−	97.6325i	−0.214328	−	0.371226i	−0.953064	+	0.302768i	$0.902089\pi$
$264$	14.8293	−	9.99957i	0.0561716	−	0.0378772i
$265$	437.234	+	252.437i	1.64994	+	0.952594i
$266$	−60.6926	+	33.6959i	−0.228168	+	0.126676i
$267$	−272.205	+	18.9973i	−1.01949	+	0.0711508i
$268$	8.65713	+	14.9946i	0.0323027	+	0.0559499i
$269$		−	67.6480i		−	0.251479i	−0.992063	−	0.125740i	$-0.959870\pi$
$269$		−	67.6480i		−	0.251479i	0.992063	−	0.125740i	$-0.0401304\pi$
$270$	292.797	−	62.1113i	1.08443	−	0.230042i
$271$			144.406i			0.532863i	0.963854	+	0.266431i	$0.0858446\pi$
$271$			144.406i			0.532863i	−0.963854	+	0.266431i	$0.914155\pi$
$272$	−32.7086	+	18.8843i	−0.120252	+	0.0694276i
$273$	−98.4965	+	193.567i	−0.360793	+	0.709038i
$274$	−156.947	+	271.841i	−0.572801	+	0.992120i
$275$	38.4112	−	66.5302i	0.139677	−	0.241928i
$276$	226.631	−	152.820i	0.821127	−	0.553695i
$277$	128.720	+	222.949i	0.464692	+	0.804871i	0.999188	−	0.0403008i	$-0.0128316\pi$
$277$	128.720	+	222.949i	0.464692	+	0.804871i	−0.534495	+	0.845171i	$0.679498\pi$
$278$			337.634i			1.21451i
$279$	50.2332	+	20.3114i	0.180047	+	0.0728007i
$280$	−133.085	−	79.8438i	−0.475305	−	0.285156i
$281$	−146.075	−	253.010i	−0.519840	−	0.900390i	−0.999734	−	0.0230634i	$-0.992658\pi$
$281$	−146.075	−	253.010i	−0.519840	−	0.900390i	0.479894	−	0.877327i	$-0.340675\pi$
$282$	−127.935	+	262.215i	−0.453670	+	0.929841i
$283$	−287.137	−	165.778i	−1.01462	−	0.585790i	−0.102077	−	0.994776i	$-0.532549\pi$
$283$	−287.137	−	165.778i	−1.01462	−	0.585790i	−0.912540	+	0.408987i	$0.865882\pi$
$284$	−56.4985	+	97.8582i	−0.198938	+	0.344571i
$285$	148.206	+	72.3096i	0.520020	+	0.253718i
$286$	26.6993	−	15.4148i	0.0933541	−	0.0538980i
$287$	367.331	+	220.378i	1.27990	+	0.767869i
$288$	−19.0847	+	47.1993i	−0.0662662	+	0.163887i
$289$	199.846			0.691508
$290$	−190.708	+	110.105i	−0.657615	+	0.379674i
$291$	−76.5636	−	113.543i	−0.263105	−	0.390184i
$292$	112.221	+	64.7908i	0.384318	+	0.221886i
$293$	128.607	+	74.2511i	0.438931	+	0.253417i	0.703144	−	0.711047i	$-0.251779\pi$
$293$	128.607	+	74.2511i	0.438931	+	0.253417i	−0.264213	+	0.964464i	$0.585112\pi$
$294$	176.167	−	110.378i	0.599206	−	0.375436i
$295$	−166.576	−	288.519i	−0.564666	−	0.978030i
$296$	114.311			0.386187
$297$	42.3094	−	38.0644i	0.142456	−	0.128163i
$298$	145.893			0.489573
$299$	408.036	−	235.579i	1.36467	−	0.787891i
$300$	15.2243	+	218.144i	0.0507478	+	0.727147i
$301$	−233.528	−	420.627i	−0.775839	−	1.39743i
$302$	142.371	−	246.593i	0.471426	−	0.816533i
$303$	−1.02026	−	1.51304i	−0.00336720	−	0.00499354i
$304$	−24.2916	+	14.0248i	−0.0799067	+	0.0461341i
$305$	−89.5607			−0.293642
$306$	−94.7224	+	73.9638i	−0.309550	+	0.241712i
$307$			47.5917i			0.155022i	0.996992	+	0.0775109i	$0.0246973\pi$
$307$			47.5917i			0.155022i	−0.996992	+	0.0775109i	$0.975303\pi$
$308$	−29.5058	−	0.495149i	−0.0957981	−	0.00160763i
$309$	128.769	−	263.924i	0.416727	−	0.854123i
$310$	−33.3704	+	57.7992i	−0.107646	+	0.186449i
$311$	−13.1863	−	7.61311i	−0.0423996	−	0.0244794i	0.478650	−	0.878006i	$-0.341126\pi$
$311$	−13.1863	−	7.61311i	−0.0423996	−	0.0244794i	−0.521050	+	0.853526i	$0.674459\pi$
$312$	−38.4806	+	78.8698i	−0.123335	+	0.252788i
$313$	135.158	−	78.0334i	0.431814	−	0.249308i	−0.268305	−	0.963334i	$-0.586464\pi$
$313$	135.158	−	78.0334i	0.431814	−	0.249308i	0.700119	+	0.714026i	$0.253130\pi$
$314$		−	133.144i		−	0.424025i
$315$	−454.660	−	192.776i	−1.44336	−	0.611988i
$316$	228.345			0.722612
$317$	148.788	+	257.709i	0.469363	+	0.812961i	0.999387	−	0.0350219i	$-0.0111501\pi$
$317$	148.788	+	257.709i	0.469363	+	0.812961i	−0.530023	+	0.847983i	$0.677817\pi$
$318$	−226.562	+	152.774i	−0.712461	+	0.480420i
$319$	−20.9358	+	36.2618i	−0.0656293	+	0.113673i
$320$	−54.3083	−	31.3549i	−0.169714	−	0.0979842i
$321$	13.6313	+	195.318i	0.0424651	+	0.608466i
$322$	−450.927	−	7.56718i	−1.40039	−	0.0235006i
$323$	−66.2120			−0.204991
$324$	−39.2767	+	157.167i	−0.121224	+	0.485082i
$325$			376.930i			1.15978i
$326$	6.96893	+	12.0705i	0.0213771	+	0.0370262i
$327$	41.2875	+	591.593i	0.126261	+	1.80915i
$328$	149.897	+	86.5433i	0.457005	+	0.263852i
$329$	420.867	−	233.661i	1.27923	−	0.710217i
$330$	39.1920	+	58.1215i	0.118764	+	0.176126i
$331$	−151.889	−	263.079i	−0.458878	−	0.794800i	0.540024	−	0.841650i	$-0.318415\pi$
$331$	−151.889	−	263.079i	−0.458878	−	0.794800i	−0.998902	+	0.0468498i	$0.985082\pi$
$332$			199.959i			0.602285i
$333$	360.210	−	50.5245i	1.08171	−	0.151725i
$334$		−	174.496i		−	0.522442i
$335$	−58.7693	+	33.9305i	−0.175431	+	0.101285i
$336$	70.4237	−	45.7876i	0.209594	−	0.136272i
$337$	−150.144	+	260.057i	−0.445531	+	0.771682i	−0.998089	−	0.0617925i	$-0.980318\pi$
$337$	−150.144	+	260.057i	−0.445531	+	0.771682i	0.552558	+	0.833474i	$0.313652\pi$
$338$	43.8681	−	75.9817i	0.129787	−	0.224798i
$339$	−135.822	−	66.2678i	−0.400656	−	0.195480i
$340$	−74.0145	−	128.197i	−0.217690	−	0.377050i
$341$			12.6903i			0.0372148i
$342$	−70.3473	+	54.9306i	−0.205694	+	0.160616i
$343$	−342.565	−	17.2591i	−0.998733	−	0.0503182i
$344$	−97.1979	−	168.352i	−0.282552	−	0.489394i
$345$	598.957	+	888.250i	1.73611	+	2.57464i
$346$	−317.238	−	183.158i	−0.916874	−	0.529357i
$347$	19.6093	−	33.9643i	0.0565110	−	0.0978799i	−0.836386	−	0.548141i	$-0.815336\pi$
$347$	19.6093	−	33.9643i	0.0565110	−	0.0978799i	0.892897	+	0.450261i	$0.148669\pi$
$348$	−8.29792	−	118.898i	−0.0238446	−	0.341660i
$349$	391.985	−	226.313i	1.12317	−	0.648460i	0.180959	−	0.983491i	$-0.442080\pi$
$349$	391.985	−	226.313i	1.12317	−	0.648460i	0.942207	+	0.335030i	$0.108747\pi$
$350$	185.615	−	309.386i	0.530328	−	0.883961i
$351$	−86.3979	+	265.537i	−0.246148	+	0.756517i
$352$	−11.9238			−0.0338745
$353$	−364.417	+	210.396i	−1.03234	+	0.596024i	−0.917655	−	0.397378i	$-0.869920\pi$
$353$	−364.417	+	210.396i	−1.03234	+	0.596024i	−0.114688	+	0.993402i	$0.536587\pi$
$354$	179.878	−	12.5538i	0.508131	−	0.0354626i
$355$	−383.542	−	221.438i	−1.08040	−	0.623770i
$356$	157.540	+	90.9556i	0.442527	+	0.255493i
$357$	198.008	−	10.4839i	0.554644	−	0.0293667i
$358$	16.5915	+	28.7373i	0.0463449	+	0.0802718i
$359$	268.070			0.746714			0.373357	−	0.927688i	$-0.378207\pi$
$359$	268.070			0.746714			0.373357	+	0.927688i	$0.378207\pi$
$360$	−184.991	−	74.7998i	−0.513865	−	0.207777i
$361$	311.826			0.863785
$362$	212.657	−	122.778i	0.587451	−	0.339165i
$363$	−314.261	−	153.328i	−0.865733	−	0.422392i
$364$	126.590	−	70.2813i	0.347774	−	0.193080i
$365$	−253.939	+	439.835i	−0.695723	+	1.20503i
$366$	21.2555	−	43.5651i	0.0580750	−	0.119030i
$367$	−24.1481	+	13.9419i	−0.0657986	+	0.0379889i	−0.532538	−	0.846406i	$-0.678762\pi$
$367$	−24.1481	+	13.9419i	−0.0657986	+	0.0379889i	0.466740	+	0.884395i	$0.345428\pi$
$368$	−182.228			−0.495184
$369$	510.598	+	206.456i	1.38374	+	0.559503i
$370$			448.028i			1.21089i
$371$	450.790	+	7.56489i	1.21507	+	0.0203905i
$372$	−20.1955	−	29.9499i	−0.0542891	−	0.0805104i
$373$	62.6374	−	108.491i	0.167929	−	0.290861i	−0.769763	−	0.638330i	$-0.779625\pi$
$373$	62.6374	−	108.491i	0.167929	−	0.290861i	0.937691	+	0.347469i	$0.112959\pi$
$374$	−24.3757	−	14.0733i	−0.0651757	−	0.0376292i
$375$	−268.508	+	18.7393i	−0.716021	+	0.0499714i
$376$	168.448	−	97.2535i	0.448000	−	0.258653i
$377$		−	205.443i		−	0.544941i
$378$	201.677	−	175.409i	0.533537	−	0.464046i
$379$	56.1639			0.148190			0.0740949	−	0.997251i	$-0.476393\pi$
$379$	56.1639			0.148190			0.0740949	+	0.997251i	$0.476393\pi$
$380$	−54.9683	−	95.2078i	−0.144653	−	0.250547i
$381$	−24.7075	−	354.024i	−0.0648490	−	0.929197i
$382$	−171.412	+	296.895i	−0.448723	+	0.777211i
$383$	−491.936	−	284.020i	−1.28443	−	0.741565i	−0.306774	−	0.951782i	$-0.599250\pi$
$383$	−491.936	−	284.020i	−1.28443	−	0.741565i	−0.977655	+	0.210217i	$0.932583\pi$
$384$	28.1410	−	18.9758i	0.0732840	−	0.0494162i
$385$	1.94067	−	115.644i	0.00504070	−	0.300374i
$386$	−351.638			−0.910979
$387$	−380.693	−	487.538i	−0.983704	−	1.25979i
$388$			91.2971i			0.235302i
$389$	146.522	+	253.784i	0.376664	+	0.652401i	0.990575	−	0.136974i	$-0.0437378\pi$
$389$	146.522	+	253.784i	0.376664	+	0.652401i	−0.613911	+	0.789376i	$0.710404\pi$
$390$	−309.120	−	150.820i	−0.792615	−	0.386717i
$391$	−372.525	−	215.078i	−0.952750	−	0.550071i
$392$	−138.515	−	4.65026i	−0.353354	−	0.0118629i
$393$	168.629	−	345.622i	0.429082	−	0.879445i
$394$	−4.35260	−	7.53893i	−0.0110472	−	0.0191343i
$395$			894.970i			2.26575i
$396$	−37.5736	+	5.27022i	−0.0948828	+	0.0133086i
$397$			507.654i			1.27873i	0.768905	+	0.639363i	$0.220802\pi$
$397$			507.654i			1.27873i	−0.768905	+	0.639363i	$0.779198\pi$
$398$	359.755	−	207.704i	0.903906	−	0.521870i
$399$	147.054	−	7.78607i	0.368557	−	0.0195140i
$400$	72.8915	−	126.252i	0.182229	−	0.315630i
$401$	69.4682	−	120.322i	0.173237	−	0.300056i	−0.766313	−	0.642468i	$-0.777911\pi$
$401$	69.4682	−	120.322i	0.173237	−	0.300056i	0.939550	+	0.342412i	$0.111244\pi$
$402$	−2.55712	−	36.6400i	−0.00636098	−	0.0911442i
$403$	−31.1324	−	53.9229i	−0.0772517	−	0.133804i
$404$			1.21660i			0.00301137i
$405$	−615.994	−	153.940i	−1.52097	−	0.380099i
$406$	−101.168	+	168.629i	−0.249182	+	0.415342i
$407$	42.5946	+	73.7761i	0.104655	+	0.181268i
$408$	79.9249	−	5.57799i	0.195894	−	0.0136715i
$409$	416.051	+	240.207i	1.01724	+	0.587303i	0.913303	−	0.407281i	$-0.133523\pi$
$409$	416.051	+	240.207i	1.01724	+	0.587303i	0.103936	+	0.994584i	$0.466856\pi$
$410$	−339.195	+	587.503i	−0.827305	+	1.43293i
$411$	552.083	−	372.276i	1.34327	−	0.905780i
$412$	−169.546	+	97.8873i	−0.411519	+	0.237591i
$413$	−255.115	−	153.055i	−0.617713	−	0.370593i
$414$	−574.224	+	80.5428i	−1.38701	+	0.194548i
$415$	−783.711			−1.88846
$416$	50.6662	−	29.2522i	0.121794	−	0.0703177i
$417$	314.061	−	643.700i	0.753145	−	1.54364i
$418$	−18.1031	−	10.4518i	−0.0433088	−	0.0250043i
$419$	−385.429	−	222.527i	−0.919878	−	0.531092i	−0.0362816	−	0.999342i	$-0.511551\pi$
$419$	−385.429	−	222.527i	−0.919878	−	0.531092i	−0.883596	+	0.468250i	$0.844885\pi$
$420$	179.458	+	276.016i	0.427282	+	0.657182i
$421$	−283.010	−	490.188i	−0.672233	−	1.16434i	−0.977269	−	0.212001i	$-0.932002\pi$
$421$	−283.010	−	490.188i	−0.672233	−	1.16434i	0.305036	−	0.952341i	$-0.401331\pi$
$422$	104.876			0.248521
$423$	487.817	−	380.911i	1.15323	−	0.900499i
$424$	182.172			0.429652
$425$	298.022	−	172.063i	0.701229	−	0.404855i
$426$	198.741	−	134.013i	0.466528	−	0.314585i
$427$	−69.9240	+	38.8211i	−0.163756	+	0.0909159i
$428$	65.2642	−	113.041i	0.152487	−	0.264114i
$429$	−65.2409	+	4.55319i	−0.152077	+	0.0106135i
$430$	659.832	−	380.954i	1.53449	−	0.885940i
$431$	−474.624			−1.10121			−0.550607	−	0.834764i	$-0.685604\pi$
$431$	−474.624			−1.10121			−0.550607	+	0.834764i	$0.685604\pi$
$432$	80.2891	−	72.2334i	0.185854	−	0.167207i
$433$		−	1.62996i		−	0.00376435i	−0.999998	−	0.00188217i	$-0.999401\pi$
$433$		−	1.62996i		−	0.00376435i	0.999998	−	0.00188217i	$-0.000599115\pi$
$434$	−1.00002	+	59.5911i	−0.00230420	+	0.137307i
$435$	466.004	−	32.5226i	1.07127	−	0.0747646i
$436$	197.677	−	342.387i	0.453388	−	0.785291i
$437$	−276.663	−	159.731i	−0.633096	−	0.365518i
$438$	−153.682	−	227.910i	−0.350873	−	0.520343i
$439$	−541.613	+	312.700i	−1.23374	+	0.712302i	−0.967808	−	0.251689i	$-0.919014\pi$
$439$	−541.613	+	312.700i	−1.23374	+	0.712302i	−0.265935	+	0.963991i	$0.585681\pi$
$440$		−	46.7339i		−	0.106213i
$441$	−438.534	+	46.5687i	−0.994409	+	0.105598i
$442$	138.102			0.312447
$443$	148.901	+	257.904i	0.336119	+	0.582175i	0.983699	−	0.179822i	$-0.0575522\pi$
$443$	148.901	+	257.904i	0.336119	+	0.582175i	−0.647580	+	0.761997i	$0.724219\pi$
$444$	−217.935	−	106.331i	−0.490844	−	0.239483i
$445$	−356.488	+	617.456i	−0.801097	+	1.38754i
$446$	340.505	+	196.591i	0.763465	+	0.440787i
$447$	−278.145	−	135.707i	−0.622249	−	0.303596i
$448$	−55.9921	−	0.939626i	−0.124982	−	0.00209738i
$449$	191.361			0.426194			0.213097	−	0.977031i	$-0.431645\pi$
$449$	191.361			0.426194			0.213097	+	0.977031i	$0.431645\pi$
$450$	173.889	−	430.054i	0.386420	−	0.955675i
$451$			128.991i			0.286011i
$452$	50.3754	+	87.2528i	0.111450	+	0.193037i
$453$	−500.807	+	337.700i	−1.10553	+	0.745474i
$454$	−123.741	−	71.4418i	−0.272557	−	0.157361i
$455$	275.458	+	496.151i	0.605403	+	1.09044i
$456$	59.3577	−	4.14260i	0.130170	−	0.00908464i
$457$	106.962	+	185.264i	0.234053	+	0.405392i	0.958997	−	0.283416i	$-0.0914676\pi$
$457$	106.962	+	185.264i	0.234053	+	0.405392i	−0.724944	+	0.688808i	$0.758134\pi$
$458$		−	83.4014i		−	0.182099i
$459$	249.389	−	52.9030i	0.543330	−	0.115257i
$460$		−	714.217i		−	1.55265i
$461$	−268.859	+	155.226i	−0.583207	+	0.336715i	−0.762407	−	0.647098i	$-0.775983\pi$
$461$	−268.859	+	155.226i	−0.583207	+	0.336715i	0.179200	+	0.983813i	$0.442649\pi$
$462$	55.7924	+	28.3899i	0.120763	+	0.0614499i
$463$	83.7628	−	145.081i	0.180913	−	0.313351i	−0.761279	−	0.648425i	$-0.775428\pi$
$463$	83.7628	−	145.081i	0.180913	−	0.313351i	0.942192	+	0.335074i	$0.108761\pi$
$464$	−39.7290	+	68.8127i	−0.0856229	+	0.148303i
$465$	117.385	−	79.1537i	0.252440	−	0.170223i
$466$	−126.924	−	219.838i	−0.272368	−	0.471756i
$467$			315.106i			0.674744i	0.941371	+	0.337372i	$0.109538\pi$
$467$			315.106i			0.674744i	−0.941371	+	0.337372i	$0.890462\pi$
$468$	146.727	−	114.572i	0.313519	−	0.244811i
$469$	−31.1763	+	51.9653i	−0.0664739	+	0.110800i
$470$	381.172	+	660.210i	0.811005	+	1.40470i
$471$	−123.848	+	253.839i	−0.262948	+	0.538937i
$472$	−104.105	−	60.1053i	−0.220562	−	0.127342i
$473$	72.4357	−	125.462i	0.153141	−	0.265248i
$474$	−435.342	−	212.403i	−0.918442	−	0.448108i
$475$	221.332	−	127.786i	0.465962	−	0.269023i
$476$	−113.355	−	68.0066i	−0.238140	−	0.142871i
$477$	574.050	−	80.5185i	1.20346	−	0.168802i
$478$	−258.115			−0.539990
$479$	778.130	−	449.253i	1.62449	−	0.937898i	0.638789	−	0.769382i	$-0.279436\pi$
$479$	778.130	−	449.253i	1.62449	−	0.937898i	0.985699	−	0.168516i	$-0.0538976\pi$
$480$	74.3732	+	110.295i	0.154944	+	0.229781i
$481$	−361.983	−	208.991i	−0.752563	−	0.434492i
$482$	6.92741	+	3.99954i	0.0143722	+	0.00829780i
$483$	852.655	+	433.872i	1.76533	+	0.898286i
$484$	116.557	+	201.883i	0.240820	+	0.417113i
$485$	−357.827			−0.737787
$486$	221.075	−	263.104i	0.454887	−	0.541366i
$487$	328.435			0.674404			0.337202	−	0.941432i	$-0.390519\pi$
$487$	328.435			0.674404			0.337202	+	0.941432i	$0.390519\pi$
$488$	−27.9864	+	16.1580i	−0.0573492	+	0.0331106i
$489$	−2.05846	−	29.4949i	−0.00420953	−	0.0603168i
$490$	18.2261	−	542.891i	0.0371961	−	1.10794i
$491$	−165.906	+	287.358i	−0.337894	+	0.585250i	−0.984036	−	0.177967i	$-0.943048\pi$
$491$	−165.906	+	287.358i	−0.337894	+	0.585250i	0.646142	+	0.763217i	$0.276381\pi$
$492$	−205.279	−	304.428i	−0.417233	−	0.618755i
$493$	−162.435	+	93.7818i	−0.329483	+	0.190227i
$494$	102.564			0.207619
$495$	−20.6559	−	147.265i	−0.0417291	−	0.297504i
$496$			24.0818i			0.0485521i
$497$	−395.434	−	6.63593i	−0.795641	−	0.0133520i
$498$	185.998	−	381.222i	0.373491	−	0.765505i
$499$	−63.7291	+	110.382i	−0.127714	+	0.221206i	−0.922790	−	0.385302i	$-0.874097\pi$
$499$	−63.7291	+	110.382i	−0.127714	+	0.221206i	0.795077	+	0.606509i	$0.207430\pi$
$500$	155.400	+	89.7203i	0.310800	+	0.179441i
$501$	−162.313	+	332.676i	−0.323978	+	0.664025i
$502$	184.352	−	106.436i	0.367236	−	0.212024i
$503$			147.803i			0.293844i	0.989148	+	0.146922i	$0.0469366\pi$
$503$			147.803i			0.293844i	−0.989148	+	0.146922i	$0.953063\pi$
$504$	−176.854	+	21.7871i	−0.350901	+	0.0432283i
$505$	−4.76828			−0.00944215
$506$	−67.9016	−	117.609i	−0.134193	−	0.232429i
$507$	−154.312	+	104.054i	−0.304362	+	0.205235i
$508$	−118.295	+	204.893i	−0.232864	+	0.403333i
$509$	−211.358	−	122.028i	−0.415242	−	0.239740i	0.277798	−	0.960640i	$-0.410396\pi$
$509$	−211.358	−	122.028i	−0.415242	−	0.239740i	−0.693039	+	0.720900i	$0.743729\pi$
$510$	21.8622	+	313.255i	0.0428670	+	0.614226i
$511$	−7.60989	+	453.472i	−0.0148922	+	0.887420i
$512$	−22.6274			−0.0441942
$513$	185.213	−	39.2894i	0.361039	−	0.0765875i
$514$		−	144.195i		−	0.280536i
$515$	−383.656	−	664.512i	−0.744964	−	1.29032i
$516$	28.7100	+	411.375i	0.0556396	+	0.797239i
$517$	125.534	+	72.4771i	0.242813	+	0.140188i
$518$	194.203	+	349.795i	0.374909	+	0.675281i
$519$	434.446	+	644.281i	0.837082	+	1.24139i
$520$	114.650	+	198.580i	0.220481	+	0.381884i
$521$		−	147.106i		−	0.282354i	−0.989984	−	0.141177i	$-0.954911\pi$
$521$		−	147.106i		−	0.282354i	0.989984	−	0.141177i	$-0.0450886\pi$
$522$	−94.7769	+	234.398i	−0.181565	+	0.449038i
$523$			62.8703i			0.120211i	0.998192	+	0.0601055i	$0.0191437\pi$
$523$			62.8703i			0.120211i	−0.998192	+	0.0601055i	$0.980856\pi$
$524$	−222.029	+	128.188i	−0.423719	+	0.244634i
$525$	−641.662	+	417.191i	−1.22221	+	0.794649i
$526$	79.7166	−	138.073i	0.151553	−	0.262497i
$527$	−28.4231	+	49.2302i	−0.0539337	+	0.0934159i
$528$	22.7328	+	11.0914i	0.0430546	+	0.0210064i
$529$	−773.216	−	1339.25i	−1.46166	−	2.53166i
$530$			714.001i			1.34717i
$531$	−354.616	−	143.386i	−0.667827	−	0.270030i
$532$	−84.1851	−	50.5064i	−0.158243	−	0.0949368i
$533$	−316.448	−	548.103i	−0.593710	−	1.02834i
$534$	−215.744	−	319.948i	−0.404016	−	0.599154i
$535$	443.049	+	255.795i	0.828129	+	0.478121i
$536$	−12.2430	+	21.2055i	−0.0228415	+	0.0395626i
$537$	−4.90074	−	70.2209i	−0.00912615	−	0.130765i
$538$	82.8515	−	47.8343i	0.153999	−	0.0889114i
$539$	−48.6121	−	91.1298i	−0.0901895	−	0.169072i
$540$	283.109	+	314.682i	0.524276	+	0.582745i
$541$	9.15847			0.0169288			0.00846439	−	0.999964i	$-0.497306\pi$
$541$	9.15847			0.0169288			0.00846439	+	0.999964i	$0.497306\pi$
$542$	−176.860	+	102.110i	−0.326311	+	0.188395i
$543$	−519.638	+	36.2657i	−0.956976	+	0.0667877i
$544$	−46.2569	−	26.7064i	−0.0850311	−	0.0490927i
$545$	1341.94	+	774.770i	2.46228	+	1.42160i
$546$	−306.718	+	16.2398i	−0.561755	+	0.0297432i
$547$	394.904	+	683.994i	0.721945	+	1.25045i	0.960219	+	0.279247i	$0.0900849\pi$
$547$	394.904	+	683.994i	0.721945	+	1.25045i	−0.238274	+	0.971198i	$0.576582\pi$
$548$	−443.914			−0.810063
$549$	−81.0472	+	63.2856i	−0.147627	+	0.115274i
$550$	108.643			0.197533
$551$	−120.635	+	69.6488i	−0.218939	+	0.126404i
$552$	347.418	+	169.505i	0.629380	+	0.307075i
$553$	387.935	+	698.743i	0.701510	+	1.26355i
$554$	−182.037	+	315.298i	−0.328587	+	0.569129i
$555$	416.749	−	854.167i	0.750898	−	1.53904i
$556$	−413.515	+	238.743i	−0.743732	+	0.429394i
$557$	676.050			1.21373			0.606867	−	0.794803i	$-0.292426\pi$
$557$	676.050			1.21373			0.606867	+	0.794803i	$0.292426\pi$
$558$	10.6439	+	75.8851i	0.0190752	+	0.135995i
$559$			710.812i			1.27158i
$560$	3.68274	−	219.454i	0.00657632	−	0.391882i
$561$	33.3816	+	49.5048i	0.0595038	+	0.0882438i
$562$	206.581	−	357.810i	0.367583	−	0.636672i
$563$	−317.573	−	183.351i	−0.564074	−	0.325668i	0.190705	−	0.981647i	$-0.438923\pi$
$563$	−317.573	−	183.351i	−0.564074	−	0.325668i	−0.754779	+	0.655979i	$0.772256\pi$
$564$	−411.610	+	28.7264i	−0.729806	+	0.0509334i
$565$	−341.976	+	197.440i	−0.605267	+	0.349451i
$566$		−	468.892i		−	0.828432i
$567$	−547.661	+	146.822i	−0.965892	+	0.258945i
$568$	−159.802			−0.281341
$569$	−111.553	−	193.216i	−0.196051	−	0.339570i	0.751193	−	0.660082i	$-0.229479\pi$
$569$	−111.553	−	193.216i	−0.196051	−	0.339570i	−0.947245	+	0.320512i	$0.896145\pi$
$570$	16.2364	+	232.645i	0.0284848	+	0.408149i
$571$	191.237	−	331.233i	0.334917	−	0.580093i	−0.648552	−	0.761170i	$-0.724625\pi$
$571$	191.237	−	331.233i	0.334917	−	0.580093i	0.983469	+	0.181077i	$0.0579585\pi$
$572$	37.7585	+	21.7999i	0.0660113	+	0.0381117i
$573$	602.965	−	406.586i	1.05229	−	0.709574i
$574$	−10.1648	+	605.718i	−0.0177087	+	1.05526i
$575$	1660.36			2.88758
$576$	−71.3020	+	10.0011i	−0.123788	+	0.0173630i
$577$		−	591.373i		−	1.02491i	−0.858714	−	0.512455i	$-0.828736\pi$
$577$		−	591.373i		−	1.02491i	0.858714	−	0.512455i	$-0.171264\pi$
$578$	141.312	+	244.760i	0.244485	+	0.423460i
$579$	670.399	+	327.088i	1.15786	+	0.564919i
$580$	−269.702	−	155.713i	−0.465004	−	0.268470i
$581$	−611.878	+	339.708i	−1.05315	+	0.584696i
$582$	84.9231	−	174.058i	0.145916	−	0.299069i
$583$	67.8810	+	117.573i	0.116434	+	0.201670i
$584$			183.256i			0.313795i
$585$	449.048	+	575.077i	0.767603	+	0.983037i
$586$			210.014i			0.358386i
$587$	−309.364	+	178.611i	−0.527025	+	0.304278i	−0.739804	−	0.672822i	$-0.765082\pi$
$587$	−309.364	+	178.611i	−0.527025	+	0.304278i	0.212779	+	0.977100i	$0.431749\pi$
$588$	259.754	+	137.710i	0.441758	+	0.234201i
$589$	−21.1089	+	36.5617i	−0.0358386	+	0.0620742i
$590$	235.575	−	408.027i	0.399279	−	0.691572i
$591$	1.28566	+	18.4217i	0.00217539	+	0.0311704i
$592$	80.8303	+	140.002i	0.136538	+	0.236490i
$593$		−	755.558i		−	1.27413i	−0.770811	−	0.637064i	$-0.780149\pi$
$593$		−	755.558i		−	1.27413i	0.770811	−	0.637064i	$-0.219851\pi$
$594$	76.5365	+	24.9027i	0.128849	+	0.0419237i
$595$	266.543	−	444.279i	0.447971	−	0.746688i
$596$	103.162	+	178.681i	0.173090	+	0.299801i
$597$	−879.077	+	61.3511i	−1.47249	+	0.102766i
$598$	577.049	+	333.160i	0.964965	+	0.557123i
$599$	496.902	−	860.660i	0.829553	−	1.43683i	−0.0688358	−	0.997628i	$-0.521928\pi$
$599$	496.902	−	860.660i	0.829553	−	1.43683i	0.898389	−	0.439200i	$-0.144738\pi$
$600$	−256.405	+	172.897i	−0.427342	+	0.288162i
$601$	−203.743	+	117.631i	−0.339006	+	0.195725i	−0.659832	−	0.751413i	$-0.729373\pi$
$601$	−203.743	+	117.631i	−0.339006	+	0.195725i	0.320826	+	0.947138i	$0.396039\pi$
$602$	350.031	−	583.440i	0.581448	−	0.969169i
$603$	−29.2068	+	72.2328i	−0.0484358	+	0.119789i
$604$	402.685			0.666697
$605$	−791.252	+	456.830i	−1.30785	+	0.755090i
$606$	1.13166	−	2.31944i	0.00186742	−	0.00382746i
$607$	467.352	+	269.826i	0.769937	+	0.444523i	0.832852	−	0.553496i	$-0.186706\pi$
$607$	467.352	+	269.826i	0.769937	+	0.444523i	−0.0629152	+	0.998019i	$0.520040\pi$
$608$	−34.3535	−	19.8340i	−0.0565025	−	0.0326218i
$609$	349.733	−	227.387i	0.574274	−	0.373377i
$610$	−63.3289	−	109.689i	−0.103818	−	0.179818i
$611$	−711.219			−1.16402
$612$	−157.566	−	63.7105i	−0.257460	−	0.104102i
$613$	−261.237			−0.426161			−0.213081	−	0.977035i	$-0.568350\pi$
$613$	−261.237			−0.426161			−0.213081	+	0.977035i	$0.568350\pi$
$614$	−58.2877	+	33.6524i	−0.0949311	+	0.0548085i
$615$	1193.16	−	804.563i	1.94010	−	1.30823i
$616$	−20.2573	−	36.4872i	−0.0328853	−	0.0592325i
$617$	333.055	−	576.868i	0.539797	−	0.934956i	−0.459117	−	0.888376i	$-0.651834\pi$
$617$	333.055	−	576.868i	0.539797	−	0.934956i	0.998915	−	0.0465807i	$-0.0148325\pi$
$618$	414.293	−	28.9137i	0.670377	−	0.0467858i
$619$	581.338	−	335.636i	0.939157	−	0.542223i	0.0494614	−	0.998776i	$-0.484250\pi$
$619$	581.338	−	335.636i	0.939157	−	0.542223i	0.889696	+	0.456553i	$0.150916\pi$
$620$	−94.3856			−0.152235
$621$	1169.68	+	380.579i	1.88354	+	0.612848i
$622$		−	21.5331i		−	0.0346192i
$623$	−10.6830	+	636.599i	−0.0171477	+	1.02183i
$624$	−123.805	+	8.64042i	−0.198406	+	0.0138468i
$625$	103.925	−	180.004i	0.166280	−	0.288006i
$626$	191.142	+	110.356i	0.305339	+	0.176287i
$627$	24.7915	+	36.7656i	0.0395398	+	0.0586374i
$628$	163.067	−	94.1469i	0.259661	−	0.149915i
$629$			381.606i			0.606687i
$630$	−85.3916	−	693.156i	−0.135542	−	1.10025i
$631$	252.355			0.399929			0.199965	−	0.979803i	$-0.435917\pi$
$631$	252.355			0.399929			0.199965	+	0.979803i	$0.435917\pi$
$632$	161.465	+	279.665i	0.255482	+	0.442508i
$633$	−199.946	−	97.5538i	−0.315870	−	0.154113i
$634$	−210.418	+	364.455i	−0.331890	+	0.574850i
$635$	−803.051	−	463.642i	−1.26465	−	0.730145i
$636$	−347.312	−	169.454i	−0.546089	−	0.266437i
$637$	430.125	+	267.967i	0.675235	+	0.420670i
$638$	−59.2153			−0.0928139
$639$	−503.557	+	70.6308i	−0.788039	+	0.110533i
$640$		−	88.6852i		−	0.138571i
$641$	287.254	+	497.539i	0.448135	+	0.776192i	0.998265	−	0.0588868i	$-0.0187551\pi$
$641$	287.254	+	497.539i	0.448135	+	0.776192i	−0.550130	+	0.835079i	$0.685422\pi$
$642$	−229.575	+	154.805i	−0.357594	+	0.241130i
$643$	128.360	+	74.1086i	0.199626	+	0.115254i	0.596481	−	0.802627i	$-0.296565\pi$
$643$	128.360	+	74.1086i	0.199626	+	0.115254i	−0.396855	+	0.917881i	$0.629898\pi$
$644$	−309.586	−	557.621i	−0.480723	−	0.865871i
$645$	−1612.33	+	112.525i	−2.49974	+	0.174458i
$646$	−46.8190	−	81.0929i	−0.0724752	−	0.125531i
$647$		−	904.316i		−	1.39771i	−0.715265	−	0.698853i	$-0.753694\pi$
$647$		−	904.316i		−	1.39771i	0.715265	−	0.698853i	$-0.246306\pi$
$648$	−220.262	+	63.0296i	−0.339910	+	0.0972679i
$649$		−	89.5856i		−	0.138036i
$650$	−461.643	+	266.529i	−0.710219	+	0.410045i
$651$	57.3373	−	112.681i	0.0880757	−	0.173088i
$652$	−9.85556	+	17.0703i	−0.0151159	+	0.0261815i
$653$	43.6173	−	75.5473i	0.0667952	−	0.115693i	−0.830694	−	0.556730i	$-0.812056\pi$
$653$	43.6173	−	75.5473i	0.0667952	−	0.115693i	0.897489	+	0.441037i	$0.145389\pi$
$654$	−695.355	+	468.886i	−1.06323	+	0.716951i
$655$	−502.417	−	870.212i	−0.767049	−	1.32857i
$656$			244.782i			0.373143i
$657$	80.9974	+	577.464i	0.123284	+	0.878941i
$658$	583.774	+	350.232i	0.887194	+	0.532267i
$659$	−225.512	−	390.598i	−0.342203	−	0.592713i	0.642639	−	0.766170i	$-0.277840\pi$
$659$	−225.512	−	390.598i	−0.342203	−	0.592713i	−0.984842	+	0.173457i	$0.944506\pi$
$660$	−43.4711	+	89.0983i	−0.0658653	+	0.134997i
$661$	−227.522	−	131.360i	−0.344209	−	0.198729i	0.317923	−	0.948117i	$-0.397015\pi$
$661$	−227.522	−	131.360i	−0.344209	−	0.198729i	−0.662132	+	0.749388i	$0.730348\pi$
$662$	214.803	−	372.050i	0.324476	−	0.562008i
$663$	−263.291	−	128.460i	−0.397121	−	0.193756i
$664$	−244.898	+	141.392i	−0.368823	+	0.212940i
$665$	197.953	−	329.952i	0.297674	−	0.496169i
$666$	316.587	+	405.439i	0.475355	+	0.608768i
$667$	−904.965			−1.35677
$668$	213.713	−	123.387i	0.319929	−	0.184711i
$669$	−466.309	−	691.534i	−0.697024	−	1.03368i
$670$	−83.1123	−	47.9849i	−0.124048	−	0.0716193i
$671$	−20.8566	−	12.0415i	−0.0310828	−	0.0179457i
$672$	105.875	+	53.8744i	0.157552	+	0.0801702i
$673$	294.210	+	509.587i	0.437162	+	0.757187i	0.997469	−	0.0710979i	$-0.0226503\pi$
$673$	294.210	+	509.587i	0.437162	+	0.757187i	−0.560307	+	0.828285i	$0.689317\pi$
$674$	−424.671			−0.630075
$675$	−731.549	+	658.150i	−1.08378	+	0.975038i
$676$	124.078			0.183547
$677$	923.740	−	533.321i	1.36446	−	0.787772i	0.374247	−	0.927329i	$-0.377901\pi$
$677$	923.740	−	533.321i	1.36446	−	0.787772i	0.990214	+	0.139557i	$0.0445680\pi$
$678$	−14.8797	−	213.206i	−0.0219465	−	0.314463i
$679$	−279.371	+	155.104i	−0.411445	+	0.228430i
$680$	104.672	−	181.298i	0.153930	−	0.266614i
$681$	169.458	+	251.306i	0.248837	+	0.369025i
$682$	−15.5423	+	8.97337i	−0.0227893	+	0.0131574i
$683$	−91.4075			−0.133832			−0.0669162	−	0.997759i	$-0.521316\pi$
$683$	−91.4075			−0.133832			−0.0669162	+	0.997759i	$0.521316\pi$
$684$	−117.019	−	47.3157i	−0.171081	−	0.0691751i
$685$		−	1739.86i		−	2.53995i
$686$	−221.092	−	431.759i	−0.322292	−	0.629387i
$687$	−77.5787	+	159.005i	−0.112924	+	0.231449i
$688$	137.459	−	238.085i	0.199794	−	0.346054i
$689$	−576.875	−	333.059i	−0.837264	−	0.483394i
$690$	−664.354	+	1361.66i	−0.962831	+	1.97342i
$691$	−17.8222	+	10.2897i	−0.0257920	+	0.0148910i	−0.512841	−	0.858484i	$-0.671407\pi$
$691$	−17.8222	+	10.2897i	−0.0257920	+	0.0148910i	0.487049	+	0.873375i	$0.338073\pi$
$692$		−	518.048i		−	0.748624i
$693$	−79.9606	−	106.023i	−0.115383	−	0.152991i
$694$	55.4635			0.0799186
$695$	−935.721	−	1620.72i	−1.34636	−	2.33197i
$696$	139.752	−	94.2363i	0.200793	−	0.135397i
$697$	−288.908	+	500.403i	−0.414502	+	0.717939i
$698$	554.351	+	320.054i	0.794199	+	0.458531i
$699$	37.4903	+	537.185i	0.0536342	+	0.768504i
$700$	510.169	+	8.56135i	0.728813	+	0.0122305i
$701$	−509.822			−0.727278			−0.363639	−	0.931540i	$-0.618466\pi$
$701$	−509.822			−0.727278			−0.363639	+	0.931540i	$0.618466\pi$
$702$	−386.308	+	81.9479i	−0.550296	+	0.116735i
$703$			283.407i			0.403139i
$704$	−8.43142	−	14.6037i	−0.0119765	−	0.0207438i
$705$	−112.589	−	1613.25i	−0.159701	−	2.28830i
$706$	−515.364	−	297.545i	−0.729977	−	0.421452i
$707$	−3.72281	+	2.06687i	−0.00526565	+	0.00292343i
$708$	142.568	+	211.428i	0.201368	+	0.298627i
$709$	596.846	+	1033.77i	0.841814	+	1.45806i	0.888360	+	0.459148i	$0.151845\pi$
$709$	596.846	+	1033.77i	0.841814	+	1.45806i	−0.0465457	+	0.998916i	$0.514821\pi$
$710$		−	626.322i		−	0.882144i
$711$	632.406	+	809.896i	0.889460	+	1.13909i
$712$			257.261i			0.361322i
$713$	−237.528	+	137.137i	−0.333139	+	0.192338i
$714$	152.853	+	235.096i	0.214080	+	0.329266i
$715$	−85.4417	+	147.989i	−0.119499	+	0.206978i
$716$	−23.4639	+	40.6407i	−0.0327708	+	0.0567607i
$717$	492.098	+	240.095i	0.686329	+	0.334860i
$718$	189.554	+	328.318i	0.264003	+	0.457267i
$719$			721.258i			1.00314i	0.865117	+	0.501571i	$0.167244\pi$
$719$			721.258i			1.00314i	−0.865117	+	0.501571i	$0.832756\pi$
$720$	−39.1980	−	279.459i	−0.0544416	−	0.388137i
$721$	−587.578	−	352.514i	−0.814949	−	0.488924i
$722$	220.495	+	381.908i	0.305394	+	0.528958i
$723$	−9.48682	−	14.0689i	−0.0131215	−	0.0194591i
$724$	300.743	+	173.634i	0.415391	+	0.239826i
$725$	361.989	−	626.983i	0.499295	−	0.864804i
$726$	−34.4282	−	493.309i	−0.0474218	−	0.679489i
$727$	−127.774	+	73.7701i	−0.175754	+	0.101472i	−0.585296	−	0.810819i	$-0.699022\pi$
$727$	−127.774	+	73.7701i	−0.175754	+	0.101472i	0.409542	+	0.912291i	$0.365689\pi$
$728$	175.589	+	105.344i	0.241194	+	0.144703i
$729$	−666.216	+	295.968i	−0.913877	+	0.405992i
$730$	−718.248			−0.983901
$731$	562.009	−	324.476i	0.768822	−	0.443880i
$732$	68.3860	−	4.77269i	0.0934236	−	0.00652006i
$733$	−597.569	−	345.006i	−0.815237	−	0.470677i	0.0335343	−	0.999438i	$-0.489324\pi$
$733$	−597.569	−	345.006i	−0.815237	−	0.470677i	−0.848771	+	0.528760i	$0.822657\pi$
$734$	−34.1506	−	19.7168i	−0.0465267	−	0.0268622i
$735$	−539.737	+	1018.07i	−0.734336	+	1.38513i
$736$	−128.854	−	223.182i	−0.175074	−	0.303237i
$737$	−18.2480			−0.0247598
$738$	108.191	+	771.339i	0.146600	+	1.04518i
$739$	456.471			0.617687			0.308844	−	0.951113i	$-0.400058\pi$
$739$	456.471			0.617687			0.308844	+	0.951113i	$0.400058\pi$
$740$	−548.720	+	316.804i	−0.741513	+	0.428113i
$741$	−195.538	−	95.4033i	−0.263884	−	0.128749i
$742$	309.492	+	557.452i	0.417105	+	0.751283i
$743$	35.6377	−	61.7263i	0.0479646	−	0.0830772i	−0.841046	−	0.540963i	$-0.818060\pi$
$743$	35.6377	−	61.7263i	0.0479646	−	0.0830772i	0.889011	+	0.457886i	$0.151393\pi$
$744$	22.4006	−	45.9121i	0.0301083	−	0.0617099i
$745$	−700.318	+	404.329i	−0.940024	+	0.542723i
$746$	177.165			0.237487
$747$	−709.213	+	553.788i	−0.949415	+	0.741349i
$748$		−	39.8054i		−	0.0532157i
$749$	456.785	+	7.66550i	0.609860	+	0.0102343i
$750$	−212.815	−	315.603i	−0.283753	−	0.420804i
$751$	678.540	−	1175.27i	0.903515	−	1.56493i	0.0806166	−	0.996745i	$-0.474311\pi$
$751$	678.540	−	1175.27i	0.903515	−	1.56493i	0.822898	−	0.568189i	$-0.192356\pi$
$752$	238.221	+	137.537i	0.316784	+	0.182895i
$753$	−450.473	+	31.4387i	−0.598238	+	0.0417513i
$754$	251.615	−	145.270i	0.333707	−	0.192666i
$755$			1578.27i			2.09042i
$756$	357.439	+	122.970i	0.472803	+	0.162658i
$757$	310.769			0.410527			0.205264	−	0.978707i	$-0.434195\pi$
$757$	310.769			0.410527			0.205264	+	0.978707i	$0.434195\pi$
$758$	39.7139	+	68.7865i	0.0523930	+	0.0907473i
$759$	20.0566	+	287.383i	0.0264250	+	0.378634i
$760$	77.7369	−	134.644i	0.102285	−	0.177163i
$761$	231.955	+	133.919i	0.304803	+	0.175978i	0.644599	−	0.764521i	$-0.277025\pi$
$761$	231.955	+	133.919i	0.304803	+	0.175978i	−0.339795	+	0.940499i	$0.610358\pi$
$762$	416.118	−	280.593i	0.546087	−	0.368232i
$763$	1383.55	+	23.2178i	1.81330	+	0.0304297i
$764$	−484.827			−0.634590
$765$	249.705	−	617.558i	0.326411	−	0.807265i
$766$		−	803.329i		−	1.04873i
$767$	219.776	+	380.664i	0.286540	+	0.496302i
$768$	43.1393	+	21.0477i	0.0561709	+	0.0274058i
$769$	−1021.03	−	589.492i	−1.32774	−	0.766569i	−0.342788	−	0.939413i	$-0.611371\pi$
$769$	−1021.03	−	589.492i	−1.32774	−	0.766569i	−0.984949	+	0.172844i	$0.944704\pi$
$770$	143.007	−	79.3959i	0.185723	−	0.103112i
$771$	−134.128	+	274.909i	−0.173967	+	0.356562i
$772$	−248.645	−	430.667i	−0.322080	−	0.557858i
$773$		−	586.849i		−	0.759184i	−0.925154	−	0.379592i	$-0.876064\pi$
$773$		−	586.849i		−	0.759184i	0.925154	−	0.379592i	$-0.123936\pi$
$774$	327.919	−	810.994i	0.423668	−	1.04780i
$775$		−	219.420i		−	0.283123i
$776$	−111.816	+	64.5568i	−0.144092	+	0.0831917i
$777$	−44.8742	−	847.531i	−0.0577531	−	1.09077i
$778$	−207.214	+	358.905i	−0.266342	+	0.461317i
$779$	−214.563	+	371.634i	−0.275434	+	0.477065i
$780$	−33.8650	−	485.239i	−0.0434166	−	0.622101i
$781$	−59.5453	−	103.135i	−0.0762424	−	0.132056i
$782$		−	608.331i		−	0.777917i
$783$	398.726	−	358.720i	0.509228	−	0.458136i
$784$	−92.2494	−	172.934i	−0.117665	−	0.220579i
$785$	368.996	+	639.120i	0.470059	+	0.814166i
$786$	542.537	−	37.8639i	0.690251	−	0.0481729i
$787$	525.886	+	303.620i	0.668216	+	0.385795i	0.795400	−	0.606084i	$-0.207261\pi$
$787$	525.886	+	303.620i	0.668216	+	0.385795i	−0.127184	+	0.991879i	$0.540594\pi$
$788$	6.15551	−	10.6617i	0.00781156	−	0.0135300i
$789$	−280.414	+	189.086i	−0.355404	+	0.239653i
$790$	−1096.11	+	632.839i	−1.38748	+	0.801062i
$791$	−181.413	+	302.383i	−0.229347	+	0.382280i
$792$	−33.0232	−	42.2914i	−0.0416960	−	0.0533983i
$793$	118.164			0.149009
$794$	−621.747	+	358.966i	−0.783056	+	0.452098i
$795$	664.152	−	1361.25i	0.835412	−	1.71226i
$796$	508.770	+	293.738i	0.639158	+	0.369018i
$797$	−138.769	−	80.1182i	−0.174114	−	0.100525i	0.410410	−	0.911901i	$-0.365385\pi$
$797$	−138.769	−	80.1182i	−0.174114	−	0.100525i	−0.584524	+	0.811376i	$0.698719\pi$
$798$	113.519	+	174.598i	0.142254	+	0.218795i
$799$	324.662	+	562.331i	0.406335	+	0.703793i
$800$	206.168			0.257710
$801$	113.707	+	810.664i	0.141956	+	1.01207i
$802$	196.486			0.244995
$803$	−118.273	+	68.2848i	−0.147289	+	0.0850371i
$804$	43.0664	−	29.0402i	0.0535652	−	0.0361196i
$805$	2185.52	−	1213.38i	2.71493	−	1.50730i
$806$	44.0279	−	76.2586i	0.0546252	−	0.0946136i
$807$	−202.452	+	14.1292i	−0.250869	+	0.0175083i
$808$	−1.49002	+	0.860263i	−0.00184408	+	0.00106468i
$809$	−806.158			−0.996487			−0.498244	−	0.867037i	$-0.666022\pi$
$809$	−806.158			−0.996487			−0.498244	+	0.867037i	$0.666022\pi$
$810$	−247.036	−	863.287i	−0.304983	−	1.06579i
$811$		−	19.2228i		−	0.0237026i	−0.999930	−	0.0118513i	$-0.996228\pi$
$811$		−	19.2228i		−	0.0237026i	0.999930	−	0.0118513i	$-0.00377248\pi$
$812$	−278.064	−	4.66630i	−0.342443	−	0.00574668i
$813$	432.166	−	30.1610i	0.531570	−	0.0370985i
$814$	−60.2379	+	104.335i	−0.0740023	+	0.128176i
$815$	−66.9049	−	38.6276i	−0.0820919	−	0.0473958i
$816$	63.3471	+	93.9434i	0.0776312	+	0.115127i
$817$	417.387	−	240.978i	0.510877	−	0.294955i
$818$			679.408i			0.830572i
$819$	599.865	+	254.343i	0.732436	+	0.310553i
$820$	−959.389			−1.16999
$821$	712.768	+	1234.55i	0.868171	+	1.50372i	0.863864	+	0.503725i	$0.168038\pi$
$821$	712.768	+	1234.55i	0.868171	+	1.50372i	0.00430682	+	0.999991i	$0.498629\pi$
$822$	846.324	+	412.922i	1.02959	+	0.502338i
$823$	−307.257	+	532.185i	−0.373338	+	0.646641i	−0.990077	−	0.140527i	$-0.955120\pi$
$823$	−307.257	+	532.185i	−0.373338	+	0.646641i	0.616739	+	0.787168i	$0.288454\pi$
$824$	−239.774	−	138.434i	−0.290988	−	0.168002i
$825$	−207.129	−	101.058i	−0.251065	−	0.122495i
$826$	7.05956	−	420.678i	0.00854668	−	0.509295i
$827$	−681.029			−0.823494			−0.411747	−	0.911298i	$-0.635081\pi$
$827$	−681.029			−0.823494			−0.411747	+	0.911298i	$0.635081\pi$
$828$	−504.682	−	646.325i	−0.609519	−	0.780586i
$829$			1137.71i			1.37239i	0.727419	+	0.686194i	$0.240720\pi$
$829$			1137.71i			1.37239i	−0.727419	+	0.686194i	$0.759280\pi$
$830$	−554.167	−	959.846i	−0.667671	−	1.15644i
$831$	640.340	−	431.788i	0.770565	−	0.519601i
$832$	71.6529	+	41.3688i	0.0861213	+	0.0497221i
$833$	15.5240	−	462.405i	0.0186362	−	0.555108i
$834$	1010.44	−	70.5192i	1.21156	−	0.0845553i
$835$	483.599	+	837.618i	0.579160	+	1.00314i
$836$		−	29.5622i		−	0.0353615i
$837$	50.2945	−	154.576i	0.0600890	−	0.184679i
$838$		−	629.402i		−	0.751077i
$839$	470.831	−	271.834i	0.561181	−	0.323998i	−0.192438	−	0.981309i	$-0.561640\pi$
$839$	470.831	−	271.834i	0.561181	−	0.323998i	0.753619	+	0.657311i	$0.228306\pi$
$840$	−211.154	+	414.964i	−0.251373	+	0.494004i
$841$	223.201	−	386.595i	0.265399	−	0.459685i
$842$	400.237	−	693.230i	0.475341	−	0.823314i
$843$	−726.677	+	490.007i	−0.862014	+	0.581265i
$844$	74.1583	+	128.446i	0.0878653	+	0.152187i
$845$			486.306i			0.575510i
$846$	811.458	+	328.107i	0.959170	+	0.387833i
$847$	−419.748	+	699.644i	−0.495570	+	0.826027i
$848$	128.815	+	223.115i	0.151905	+	0.263107i
$849$	−436.156	+	893.945i	−0.513729	+	1.05294i
$850$	421.467	+	243.334i	0.495844	+	0.286275i
$851$	−920.594	+	1594.52i	−1.08178	+	1.87370i
$852$	304.663	+	148.645i	0.357585	+	0.174466i
$853$	−1448.28	+	836.167i	−1.69787	+	0.980266i	−0.750094	+	0.661331i	$0.769992\pi$
$853$	−1448.28	+	836.167i	−1.69787	+	0.980266i	−0.947777	+	0.318935i	$0.896675\pi$
$854$	−96.9897	−	58.1884i	−0.113571	−	0.0681363i
$855$	185.448	−	458.641i	0.216898	−	0.536422i
$856$	184.595			0.215649
$857$	828.715	−	478.459i	0.966996	−	0.558295i	0.0686767	−	0.997639i	$-0.478122\pi$
$857$	828.715	−	478.459i	0.966996	−	0.558295i	0.898319	+	0.439344i	$0.144789\pi$
$858$	−51.7088	−	76.6839i	−0.0602667	−	0.0893752i
$859$	1415.32	+	817.134i	1.64763	+	0.951262i	0.978009	+	0.208561i	$0.0668781\pi$
$859$	1415.32	+	817.134i	1.64763	+	0.951262i	0.669624	+	0.742700i	$0.266455\pi$
$860$	933.144	+	538.751i	1.08505	+	0.626454i
$861$	582.809	−	1145.35i	0.676898	−	1.33025i
$862$	−335.610	−	581.293i	−0.389338	−	0.674354i
$863$	1264.39			1.46511			0.732555	−	0.680708i	$-0.238328\pi$
$863$	1264.39			1.46511			0.732555	+	0.680708i	$0.238328\pi$
$864$	145.240	+	47.2569i	0.168102	+	0.0546955i
$865$	2030.42			2.34731
$866$	1.99629	−	1.15256i	0.00230518	−	0.00133090i
$867$	−41.7404	−	598.083i	−0.0481435	−	0.689830i
$868$	−73.6911	+	40.9125i	−0.0848976	+	0.0471343i
$869$	−120.330	+	208.417i	−0.138469	+	0.239836i
$870$	369.347	+	547.739i	0.424536	+	0.629586i
$871$	77.5385	−	44.7669i	0.0890224	−	0.0513971i
$872$	559.116			0.641188
$873$	−323.813	+	252.848i	−0.370919	+	0.289632i
$874$		−	451.788i		−	0.516920i
$875$	−10.5379	+	627.954i	−0.0120434	+	0.717662i
$876$	170.462	−	349.378i	0.194591	−	0.398834i
$877$	−157.796	+	273.311i	−0.179927	+	0.311643i	−0.941855	−	0.336019i	$-0.890919\pi$
$877$	−157.796	+	273.311i	−0.179927	+	0.311643i	0.761928	+	0.647661i	$0.224253\pi$
$878$	−765.957	−	442.225i	−0.872388	−	0.503673i
$879$	195.352	−	400.392i	0.222243	−	0.455509i
$880$	57.2371	−	33.0458i	0.0650421	−	0.0375521i
$881$			1325.05i			1.50403i	0.659148	+	0.752013i	$0.270917\pi$
$881$			1325.05i			1.50403i	−0.659148	+	0.752013i	$0.729083\pi$
$882$	−367.125	−	504.164i	−0.416242	−	0.571614i
$883$	53.0789			0.0601120			0.0300560	−	0.999548i	$-0.490431\pi$
$883$	53.0789			0.0601120			0.0300560	+	0.999548i	$0.490431\pi$
$884$	97.6527	+	169.139i	0.110467	+	0.191334i
$885$	−828.665	+	558.778i	−0.936344	+	0.631387i
$886$	−210.577	+	364.731i	−0.237672	+	0.411660i
$887$	569.288	+	328.679i	0.641813	+	0.370551i	0.785313	−	0.619099i	$-0.212502\pi$
$887$	569.288	+	328.679i	0.641813	+	0.370551i	−0.143499	+	0.989650i	$0.545835\pi$
$888$	−23.8754	−	342.102i	−0.0268867	−	0.385250i
$889$	−827.949	−	13.8941i	−0.931326	−	0.0156290i
$890$	−1008.30			−1.13292
$891$	−122.753	−	118.670i	−0.137770	−	0.133188i
$892$			556.043i			0.623366i
$893$	241.116	+	417.625i	0.270007	+	0.467665i
$894$	−30.4716	−	436.616i	−0.0340846	−	0.488385i
$895$	−159.286	−	91.9636i	−0.177973	−	0.102753i
$896$	−38.4416	−	69.2405i	−0.0429036	−	0.0772773i
$897$	−790.247	−	1171.93i	−0.880989	−	1.30650i
$898$	135.313	+	234.369i	0.150682	+	0.260990i
$899$			119.594i			0.133029i
$900$	649.664	−	91.1244i	0.721849	−	0.101249i
$901$			608.147i			0.674969i
$902$	−157.981	+	91.2104i	−0.175145	+	0.101120i
$903$	−1210.04	+	786.736i	−1.34003	+	0.871247i
$904$	−71.2416	+	123.394i	−0.0788071	+	0.136498i
$905$	−680.536	+	1178.72i	−0.751973	+	1.30246i
$906$	−767.720	−	374.571i	−0.847373	−	0.413434i
$907$	254.110	+	440.131i	0.280165	+	0.485260i	0.971425	−	0.237346i	$-0.0762774\pi$
$907$	254.110	+	440.131i	0.280165	+	0.485260i	−0.691260	+	0.722606i	$0.742944\pi$
$908$		−	202.068i		−	0.222542i
$909$	−4.31502	+	3.36938i	−0.00474700	+	0.00370669i
$910$	−412.880	+	688.198i	−0.453715	+	0.756261i
$911$	−615.535	−	1066.14i	−0.675670	−	1.17029i	−0.976273	−	0.216545i	$-0.930521\pi$
$911$	−615.535	−	1066.14i	−0.675670	−	1.17029i	0.300603	−	0.953749i	$-0.402812\pi$
$912$	47.0459	+	69.7688i	0.0515854	+	0.0765009i
$913$	−182.508	−	105.371i	−0.199899	−	0.115412i
$914$	−151.268	+	262.003i	−0.165501	+	0.286656i
$915$	18.7059	+	268.030i	0.0204436	+	0.292929i
$916$	102.145	−	58.9737i	0.111513	−	0.0643818i
$917$	−769.463	−	461.635i	−0.839109	−	0.503419i
$918$	241.137	+	268.029i	0.262677	+	0.291971i
$919$	−953.211			−1.03723			−0.518613	−	0.855009i	$-0.673552\pi$
$919$	−953.211			−1.03723			−0.518613	+	0.855009i	$0.673552\pi$
$920$	874.734	−	505.028i	0.950797	−	0.548943i
$921$	142.429	−	9.94015i	0.154646	−	0.0107928i
$922$	−380.223	−	219.522i	−0.412390	−	0.238093i
$923$	506.035	+	292.159i	0.548250	+	0.316532i
$924$	4.68083	+	88.4061i	0.00506584	+	0.0956776i
$925$	−736.480	−	1275.62i	−0.796195	−	1.37905i
$926$	236.917			0.255850
$927$	−816.746	−	330.245i	−0.881064	−	0.356251i
$928$	−112.371			−0.121089
$929$	−1161.63	+	670.670i	−1.25041	+	0.721927i	−0.971192	−	0.238300i	$-0.923410\pi$
$929$	−1161.63	+	670.670i	−1.25041	+	0.721927i	−0.279222	+	0.960227i	$0.590077\pi$
$930$	179.947	+	87.7960i	0.193491	+	0.0944043i
$931$	11.5292	−	343.414i	0.0123836	−	0.368865i
$932$	179.497	−	310.898i	0.192593	−	0.333582i
$933$	−20.0298	+	41.0530i	−0.0214681	+	0.0440010i
$934$	−385.924	+	222.813i	−0.413195	+	0.238558i
$935$	156.012			0.166858
$936$	244.072	+	98.6888i	0.260761	+	0.105437i
$937$		−	1468.66i		−	1.56741i	−0.621136	−	0.783703i	$-0.713328\pi$
$937$		−	1468.66i		−	1.56741i	0.621136	−	0.783703i	$-0.286672\pi$
$938$	−85.6891	−	1.43798i	−0.0913530	−	0.00153303i
$939$	−261.762	−	388.191i	−0.278766	−	0.413409i
$940$	−539.059	+	933.677i	−0.573467	+	0.993274i
$941$	466.720	+	269.461i	0.495983	+	0.286356i	0.727053	−	0.686581i	$-0.240889\pi$
$941$	466.720	+	269.461i	0.495983	+	0.286356i	−0.231070	+	0.972937i	$0.574223\pi$
$942$	−398.462	+	27.8088i	−0.422996	+	0.0295210i
$943$	−2414.37	+	1393.94i	−2.56031	+	1.47819i
$944$		−	170.003i		−	0.180088i
$945$	−481.963	+	1400.93i	−0.510014	+	1.48247i
$946$	204.879			0.216574
$947$	−233.960	−	405.231i	−0.247054	−	0.427910i	0.715653	−	0.698456i	$-0.246129\pi$
$947$	−233.960	−	405.231i	−0.247054	−	0.427910i	−0.962707	+	0.270546i	$0.912796\pi$
$948$	−47.6929	−	683.374i	−0.0503090	−	0.720859i
$949$	335.040	−	580.306i	0.353045	−	0.611492i
$950$	313.010	+	180.717i	0.329485	+	0.190228i
$951$	740.174	−	499.107i	0.778311	−	0.524824i
$952$	3.13676	−	186.919i	0.00329491	−	0.196343i
$953$	209.542			0.219876			0.109938	−	0.993938i	$-0.464935\pi$
$953$	209.542			0.219876			0.109938	+	0.993938i	$0.464935\pi$
$954$	504.529	+	646.129i	0.528856	+	0.677284i
$955$		−	1900.22i		−	1.98975i
$956$	−182.515	−	316.125i	−0.190915	−	0.330675i
$957$	112.894	+	55.0811i	0.117967	+	0.0575560i
$958$	1100.44	+	635.340i	1.14869	+	0.663194i
$959$	−754.164	−	1358.39i	−0.786406	−	1.41646i
$960$	−82.4936	+	169.079i	−0.0859308	+	0.176124i
$961$	−462.377	−	800.860i	−0.481142	−	0.833362i
$962$		−	591.115i		−	0.614465i
$963$	581.684	−	81.5893i	0.604033	−	0.0847240i
$964$			11.3124i			0.0117349i
$965$	1687.94	−	974.533i	1.74916	−	1.00988i
$966$	71.5355	+	1351.08i	0.0740533	+	1.39863i
$967$	−231.563	+	401.080i	−0.239466	+	0.414767i	−0.960561	−	0.278069i	$-0.910306\pi$
$967$	−231.563	+	401.080i	−0.239466	+	0.414767i	0.721095	+	0.692836i	$0.243639\pi$
$968$	−164.836	+	285.505i	−0.170286	+	0.294943i
$969$	13.8292	+	198.154i	0.0142717	+	0.204493i
$970$	−253.022	−	438.247i	−0.260847	−	0.451801i
$971$			20.0008i			0.0205981i	0.999947	+	0.0102991i	$0.00327835\pi$
$971$			20.0008i			0.0205981i	−0.999947	+	0.0102991i	$0.996722\pi$
$972$	478.559	+	84.7180i	0.492345	+	0.0871584i
$973$	−1433.08	−	859.767i	−1.47284	−	0.883625i
$974$	232.238	+	402.249i	0.238438	+	0.412986i
$975$	1128.04	−	78.7267i	1.15697	−	0.0807453i
$976$	−39.5787	−	22.8508i	−0.0405520	−	0.0234127i
$977$	−558.279	+	966.968i	−0.571422	+	0.989732i	0.424998	+	0.905194i	$0.360275\pi$
$977$	−558.279	+	966.968i	−0.571422	+	0.989732i	−0.996420	+	0.0845376i	$0.973059\pi$
$978$	34.6682	−	23.3772i	0.0354481	−	0.0239030i
$979$	−166.035	+	95.8606i	−0.169597	+	0.0979168i
$980$	677.790	−	361.559i	0.691623	−	0.368938i
$981$	1761.85	−	247.124i	1.79597	−	0.251910i
$982$	−469.253			−0.477855
$983$	595.403	−	343.756i	0.605700	−	0.349701i	−0.165581	−	0.986196i	$-0.552950\pi$
$983$	595.403	−	343.756i	0.605700	−	0.349701i	0.771281	+	0.636495i	$0.219617\pi$
$984$	227.692	−	466.677i	0.231394	−	0.474265i
$985$	41.7869	+	24.1257i	0.0424233	+	0.0244931i
$986$	−229.718	−	132.628i	−0.232979	−	0.134511i
$987$	−787.186	−	1210.74i	−0.797555	−	1.22668i
$988$	72.5236	+	125.614i	0.0734044	+	0.127140i
$989$	3131.09			3.16592
$990$	165.756	−	129.430i	0.167430	−	0.130737i
$991$	−470.055			−0.474324			−0.237162	−	0.971470i	$-0.576217\pi$
$991$	−470.055			−0.474324			−0.237162	+	0.971470i	$0.576217\pi$
$992$	−29.4941	+	17.0284i	−0.0297320	+	0.0171658i
$993$	−755.597	+	509.507i	−0.760924	+	0.513099i
$994$	−271.486	−	488.998i	−0.273125	−	0.491949i
$995$	−1151.27	+	1994.06i	−1.15705	+	2.00408i
$996$	598.420	−	41.7639i	0.600823	−	0.0419317i
$997$	1667.02	−	962.456i	1.67204	−	0.965353i	0.705545	−	0.708665i	$-0.250702\pi$
$997$	1667.02	−	962.456i	1.67204	−	0.965353i	0.966494	−	0.256688i	$-0.0826312\pi$
$998$	−180.253			−0.180614
$999$	−226.440	−	1067.46i	−0.226667	−	1.06852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.o.a.13.12	✓	32
3.2	odd	2		378.3.o.a.307.8		32
7.6	odd	2	inner	126.3.o.a.13.13	yes	32
9.2	odd	6		378.3.o.a.181.1		32
9.4	even	3		1134.3.c.e.811.8		16
9.5	odd	6		1134.3.c.d.811.9		16
9.7	even	3	inner	126.3.o.a.97.13	yes	32
21.20	even	2		378.3.o.a.307.1		32
63.13	odd	6		1134.3.c.e.811.1		16
63.20	even	6		378.3.o.a.181.8		32
63.34	odd	6	inner	126.3.o.a.97.12	yes	32
63.41	even	6		1134.3.c.d.811.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.o.a.13.12	✓	32	1.1	even	1	trivial
126.3.o.a.13.13	yes	32	7.6	odd	2	inner
126.3.o.a.97.12	yes	32	63.34	odd	6	inner
126.3.o.a.97.13	yes	32	9.7	even	3	inner
378.3.o.a.181.1		32	9.2	odd	6
378.3.o.a.181.8		32	63.20	even	6
378.3.o.a.307.1		32	21.20	even	2
378.3.o.a.307.8		32	3.2	odd	2
1134.3.c.d.811.9		16	9.5	odd	6
1134.3.c.d.811.16		16	63.41	even	6
1134.3.c.e.811.1		16	63.13	odd	6
1134.3.c.e.811.8		16	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-0.208863 - 2.99272i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-6.78854 - 3.91937i) q^{5} +(3.51763 - 2.37198i) q^{6} +(-6.99901 - 0.117453i) q^{7} -2.82843 q^{8} +(-8.91275 + 1.25014i) q^{9} -11.0856i q^{10} +(-1.05393 - 1.82546i) q^{11} +(5.39241 + 2.63096i) q^{12} +(8.95661 + 5.17110i) q^{13} +(-4.80520 - 8.65506i) q^{14} +(-10.3117 + 21.1348i) q^{15} +(-2.00000 - 3.46410i) q^{16} -9.44215i q^{17} +(-7.83337 - 10.0319i) q^{18} -7.01239i q^{19} +(13.5771 - 7.83874i) q^{20} +(1.11033 + 20.9706i) q^{21} +(1.49048 - 2.58159i) q^{22} +(22.7785 - 39.4534i) q^{23} +(0.590754 + 8.46469i) q^{24} +(18.2229 + 31.5630i) q^{25} +14.6261i q^{26} +(5.60286 + 26.4123i) q^{27} +(7.20245 - 12.0052i) q^{28} +(-9.93225 - 17.2032i) q^{29} +(-33.1762 + 2.31538i) q^{30} +(-5.21387 - 3.01023i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-5.24295 + 3.53538i) q^{33} +(11.5642 - 6.67661i) q^{34} +(47.0528 + 28.2290i) q^{35} +(6.74745 - 16.6875i) q^{36} -40.4151 q^{37} +(8.58839 - 4.95851i) q^{38} +(13.6050 - 27.8847i) q^{39} +(19.2009 + 11.0856i) q^{40} +(-52.9968 - 30.5977i) q^{41} +(-24.8985 + 16.1883i) q^{42} +(34.3646 + 59.5213i) q^{43} +4.21571 q^{44} +(65.4044 + 26.4457i) q^{45} +64.4272 q^{46} +(-59.5554 + 34.3843i) q^{47} +(-9.94936 + 6.70896i) q^{48} +(48.9724 + 1.64411i) q^{49} +(-25.7710 + 44.6368i) q^{50} +(-28.2577 + 1.97212i) q^{51} +(-17.9132 + 10.3422i) q^{52} -64.4077 q^{53} +(-28.3865 + 25.5384i) q^{54} +16.5229i q^{55} +(19.7962 + 0.332208i) q^{56} +(-20.9861 + 1.46463i) q^{57} +(14.0463 - 24.3290i) q^{58} +(36.8068 + 21.2504i) q^{59} +(-26.2949 - 38.9952i) q^{60} +(9.89468 - 5.71270i) q^{61} -8.51422i q^{62} +(62.5273 - 7.70290i) q^{63} +8.00000 q^{64} +(-40.5349 - 70.2085i) q^{65} +(-8.03727 - 3.92139i) q^{66} +(4.32856 - 7.49729i) q^{67} +(16.3543 + 9.44215i) q^{68} +(-122.831 - 59.9292i) q^{69} +(-1.30205 + 77.5886i) q^{70} +56.4985 q^{71} +(25.2091 - 3.53592i) q^{72} -64.7908i q^{73} +(-28.5778 - 49.4982i) q^{74} +(90.6530 - 61.1283i) q^{75} +(12.1458 + 7.01239i) q^{76} +(7.16205 + 12.9002i) q^{77} +(43.7718 - 3.05485i) q^{78} +(-57.0864 - 98.8765i) q^{79} +31.3549i q^{80} +(77.8743 - 22.2843i) q^{81} -86.5433i q^{82} +(86.5846 - 49.9896i) q^{83} +(-37.4325 - 19.0475i) q^{84} +(-37.0073 + 64.0985i) q^{85} +(-48.5989 + 84.1758i) q^{86} +(-49.4098 + 33.3176i) q^{87} +(2.98096 + 5.16317i) q^{88} -90.9556i q^{89} +(13.8586 + 98.8036i) q^{90} +(-62.0801 - 37.2446i) q^{91} +(45.5569 + 78.9069i) q^{92} +(-7.91980 + 16.2324i) q^{93} +(-84.2240 - 48.6267i) q^{94} +(-27.4841 + 47.6039i) q^{95} +(-15.2520 - 7.44148i) q^{96} +(39.5328 - 22.8243i) q^{97} +(32.6151 + 61.1413i) q^{98} +(11.6755 + 14.9523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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