LMFDB - Embedded newform 126.3.o.a.97.13

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			97.13
Character	$\chi$	$=$	126.97
Dual form			126.3.o.a.13.13

$q$-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} +(3.39779 + 6.12005i) 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} +(9.89810 + 0.166104i) 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} +(19.0253 - 8.89038i) 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} +(2.56445 - 29.5876i) 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} +(-25.9100 + 41.5893i) 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} +(-9.61040 - 17.3101i) 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} +(-22.6328 - 58.7942i) 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} +(67.8447 - 37.6667i) 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} +(-14.7529 - 0.247575i) 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} +(-34.4239 - 24.0624i) 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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

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

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	$-0.379908\pi$
$5$	6.78854	−	3.91937i	1.35771	−	0.783874i	0.989315	+	0.145796i	$0.0465744\pi$
$6$	−3.51763	−	2.37198i	−0.586272	−	0.395329i
$7$	3.39779	+	6.12005i	0.485399	+	0.874293i
$7$	3.39779	+	6.12005i	0.485399	+	0.874293i
$8$	−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	−0.909947	−	0.414724i	$-0.863878\pi$
$11$	−1.05393	+	1.82546i	−0.0958116	+	0.165951i	0.814135	+	0.580675i	$0.197211\pi$
$12$	−5.39241	+	2.63096i	−0.449367	+	0.219247i
$13$	−8.95661	+	5.17110i	−0.688970	+	0.397777i	−0.803226	−	0.595674i	$-0.796885\pi$
$13$	−8.95661	+	5.17110i	−0.688970	+	0.397777i	0.114256	+	0.993451i	$0.463552\pi$
$14$	9.89810	+	0.166104i	0.707007	+	0.0118646i
$15$	−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
$21$	19.0253	−	8.89038i	0.905965	−	0.423352i
$22$	1.49048	+	2.58159i	0.0677490	+	0.117345i
$23$	22.7785	+	39.4534i	0.990367	+	1.71537i	0.615097	+	0.788451i	$0.289117\pi$
$23$	22.7785	+	39.4534i	0.990367	+	1.71537i	0.375270	+	0.926915i	$0.377550\pi$
$24$	−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	−0.984895	−	0.173154i	$-0.944604\pi$
$29$	−9.93225	+	17.2032i	−0.342491	+	0.593213i	0.642403	+	0.766367i	$0.277937\pi$
$30$	−33.1762	−	2.31538i	−1.10587	−	0.0771794i
$31$	5.21387	−	3.01023i	0.168189	−	0.0971042i	−0.413542	−	0.910485i	$-0.635709\pi$
$31$	5.21387	−	3.01023i	0.168189	−	0.0971042i	0.581732	+	0.813381i	$0.302375\pi$
$32$	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	$-0.398502\pi$
$41$	52.9968	−	30.5977i	1.29260	−	0.746285i	0.979115	+	0.203307i	$0.0651688\pi$
$42$	2.56445	−	29.5876i	0.0610583	−	0.704466i
$43$	34.3646	−	59.5213i	0.799178	−	1.38422i	−0.120974	−	0.992656i	$-0.538602\pi$
$43$	34.3646	−	59.5213i	0.799178	−	1.38422i	0.920152	−	0.391561i	$-0.128065\pi$
$44$	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	$-0.0721162\pi$
$47$	59.5554	+	34.3843i	1.26714	+	0.731581i	0.292690	+	0.956207i	$0.405450\pi$
$48$	9.94936	+	6.70896i	0.207278	+	0.139770i
$49$	−25.9100	+	41.5893i	−0.528777	+	0.848761i
$50$	−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
$56$	−9.61040	−	17.3101i	−0.171614	−	0.309109i
$57$	−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	$-0.783950\pi$
$59$	−36.8068	+	21.2504i	−0.623844	+	0.360177i	0.154520	+	0.987990i	$0.450617\pi$
$60$	−26.2949	+	38.9952i	−0.438248	+	0.649920i
$61$	−9.89468	−	5.71270i	−0.162208	−	0.0936508i	0.416699	−	0.909045i	$-0.363187\pi$
$61$	−9.89468	−	5.71270i	−0.162208	−	0.0936508i	−0.578907	+	0.815394i	$0.696520\pi$
$62$		−	8.51422i		−	0.137326i
$63$	−22.6328	−	58.7942i	−0.359250	−	0.933241i
$64$	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	0.896519	−	0.443005i	$-0.146088\pi$
$67$	4.32856	+	7.49729i	0.0646054	+	0.111900i	−0.831913	+	0.554905i	$0.812754\pi$
$68$	−16.3543	+	9.44215i	−0.240504	+	0.138855i
$69$	122.831	−	59.9292i	1.78015	−	0.868539i
$70$	67.8447	−	37.6667i	0.969210	−	0.538096i
$71$	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
$77$	−14.7529	−	0.247575i	−0.191596	−	0.00321525i
$78$	43.7718	+	3.05485i	0.561177	+	0.0391647i
$79$	−57.0864	+	98.8765i	−0.722612	+	1.25160i	0.237337	+	0.971427i	$0.423725\pi$
$79$	−57.0864	+	98.8765i	−0.722612	+	1.25160i	−0.959949	+	0.280174i	$0.909608\pi$
$80$			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	$-0.539076\pi$
$83$	−86.5846	−	49.9896i	−1.04319	−	0.602285i	−0.920735	+	0.390190i	$0.872409\pi$
$84$	−34.4239	−	24.0624i	−0.409808	−	0.286457i
$85$	−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	$-0.408941\pi$
$97$	−39.5328	−	22.8243i	−0.407555	−	0.235302i	−0.689738	+	0.724059i	$0.742274\pi$
$98$	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	$-0.334292\pi$
$101$	−0.526801	−	0.304149i	−0.00521585	−	0.00301137i	−0.502606	+	0.864516i	$0.667625\pi$
$102$	−22.3966	+	33.2140i	−0.219574	+	0.325627i
$103$	−84.7729	+	48.9437i	−0.823038	+	0.475181i	−0.851463	−	0.524415i	$-0.824284\pi$
$103$	−84.7729	+	48.9437i	−0.823038	+	0.475181i	0.0284251	+	0.999596i	$0.490951\pi$
$104$	25.3331	−	14.6261i	0.243588	−	0.140635i
$105$	94.3092	−	134.920i	0.898183	−	1.28495i
$106$	−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
$112$	−27.9961	−	0.469813i	−0.249965	−	0.00419476i
$113$	25.1877	+	43.6264i	0.222900	+	0.386074i	0.955687	−	0.294384i	$-0.0951143\pi$
$113$	25.1877	+	43.6264i	0.222900	+	0.386074i	−0.732787	+	0.680458i	$0.761781\pi$
$114$	−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
$119$	57.7865	−	32.0824i	0.485600	−	0.269600i
$120$	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
$126$	−88.0117	−	13.8544i	−0.698505	−	0.109956i
$127$	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	$-0.829403\pi$
$131$	−111.014	+	64.0941i	−0.847438	+	0.489268i	0.0123479	+	0.999924i	$0.496069\pi$
$132$	0.880506	−	12.6164i	0.00667050	−	0.0955791i
$133$	42.9162	−	23.8266i	0.322678	−	0.179148i
$134$	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	−0.102757	−	0.994706i	$-0.532766\pi$
$137$	110.979	−	192.221i	0.810063	−	1.40307i	0.912820	−	0.408363i	$-0.133900\pi$
$138$	13.4565	−	192.813i	0.0975106	−	1.39719i
$139$	−206.757	+	119.371i	−1.48746	+	0.858788i	−0.999898	−	0.0142986i	$-0.995448\pi$
$139$	−206.757	+	119.371i	−1.48746	+	0.858788i	−0.487566	+	0.873086i	$0.662115\pi$
$140$	1.84137	−	109.727i	0.0131526	−	0.783763i
$141$	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
$147$	119.053	+	86.2280i	0.809888	+	0.586585i
$148$	40.4151	+	70.0011i	0.273075	+	0.472980i
$149$	51.5809	+	89.3407i	0.346180	+	0.599602i	0.985567	−	0.169283i	$-0.0541452\pi$
$149$	51.5809	+	89.3407i	0.346180	+	0.599602i	−0.639387	+	0.768885i	$0.720812\pi$
$150$	−138.968	+	67.8026i	−0.926453	+	0.452017i
$151$	−100.671	+	174.368i	−0.666697	+	1.15475i	0.312126	+	0.950041i	$0.398959\pi$
$151$	−100.671	+	174.368i	−0.666697	+	1.15475i	−0.978822	+	0.204712i	$0.934374\pi$
$152$			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	$-0.569736\pi$
$157$	81.5336	−	47.0735i	0.519322	−	0.299831i	0.736657	+	0.676266i	$0.236403\pi$
$158$	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	$-0.546222\pi$
$167$	106.856	−	61.6935i	0.639858	−	0.369422i	0.784560	+	0.620053i	$0.212889\pi$
$168$	−53.8116	+	25.1458i	−0.320307	+	0.149677i
$169$	−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	$-0.0640481\pi$
$173$	224.321	+	129.512i	1.29666	+	0.748624i	0.316830	+	0.948482i	$0.397381\pi$
$174$	75.7435	−	36.9553i	0.435308	−	0.212387i
$175$	255.084	+	4.28067i	1.45763	+	0.0244610i
$176$	−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	$-0.159237\pi$
$182$	−89.5124	+	49.6964i	−0.491826	+	0.273057i
$183$	−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
$189$	−180.682	+	55.4536i	−0.955988	+	0.293405i
$190$	−77.7369			−0.409141
$191$	121.207	−	209.936i	0.634590	−	1.09914i	−0.352011	−	0.935996i	$-0.614502\pi$
$191$	121.207	−	209.936i	0.634590	−	1.09914i	0.986602	−	0.163147i	$-0.0521645\pi$
$192$	1.67090	−	23.9418i	0.00870263	−	0.124697i
$193$	−124.323	−	215.333i	−0.644159	−	1.11572i	−0.984495	−	0.175412i	$-0.943874\pi$
$193$	−124.323	−	215.333i	−0.644159	−	1.11572i	0.340336	−	0.940304i	$-0.389459\pi$
$194$	−55.9078	+	32.2784i	−0.288185	+	0.166383i
$195$	201.648	+	135.974i	1.03409	+	0.697300i
$196$	97.9448	+	3.28823i	0.499718	+	0.0167767i
$197$	−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
$203$	−139.032	−	2.33315i	−0.684887	−	0.0114934i
$204$	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
$210$	−98.5556	−	210.907i	−0.469313	−	1.00432i
$211$	37.0792	+	64.2230i	0.175731	+	0.304374i	0.940414	−	0.340032i	$-0.110438\pi$
$211$	37.0792	+	64.2230i	0.175731	+	0.304374i	−0.764683	+	0.644406i	$0.777105\pi$
$212$	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	$-0.547569\pi$
$223$	−240.774	−	139.011i	−1.07970	−	0.623366i	−0.930816	+	0.365488i	$0.880902\pi$
$224$	−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	$-0.261898\pi$
$227$	87.4980	+	50.5170i	0.385454	+	0.222542i	−0.294735	+	0.955579i	$0.595231\pi$
$228$	18.4493	+	37.8137i	0.0809180	+	0.165849i
$229$	51.0727	−	29.4869i	0.223025	−	0.128764i	−0.384325	−	0.923198i	$-0.625566\pi$
$229$	51.0727	−	29.4869i	0.223025	−	0.128764i	0.607350	+	0.794434i	$0.292233\pi$
$230$	437.367	−	252.514i	1.90159	−	1.09789i
$231$	−3.82226	+	44.0996i	−0.0165466	+	0.190907i
$232$	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
$238$	1.56838	−	93.4594i	0.00658983	−	0.392686i
$239$	−91.2575	−	158.063i	−0.381831	−	0.661350i	0.609493	−	0.792791i	$-0.291373\pi$
$239$	−91.2575	−	158.063i	−0.381831	−	0.661350i	−0.991324	+	0.131441i	$0.958040\pi$
$240$	93.8366	+	6.54889i	0.390986	+	0.0272870i
$241$	−4.89842	−	2.82810i	−0.0203254	−	0.0117349i	0.489803	−	0.871833i	$-0.337069\pi$
$241$	−4.89842	−	2.82810i	−0.0203254	−	0.0117349i	−0.510128	+	0.860098i	$0.670402\pi$
$242$	164.836			0.681142
$243$	82.9558	−	228.402i	0.341382	−	0.939925i
$244$			22.8508i			0.0936508i
$245$	−12.8878	+	383.882i	−0.0526032	+	1.56686i
$246$	−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	$-0.0969355\pi$
$252$	−79.2018	+	97.9953i	−0.314293	+	0.388870i
$253$	−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	$-0.603102\pi$
$257$	88.3013	−	50.9808i	0.343585	−	0.198369i	0.661856	+	0.749631i	$0.269769\pi$
$258$	−262.065	+	127.862i	−1.01576	+	0.495589i
$259$	−137.322	−	247.343i	−0.530201	−	0.954991i
$260$	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	−0.953064	−	0.302768i	$-0.902089\pi$
$263$	−56.3682	+	97.6325i	−0.214328	+	0.371226i	0.738737	+	0.673994i	$0.235423\pi$
$264$	−14.8293	−	9.99957i	−0.0561716	−	0.0378772i
$265$	−437.234	+	252.437i	−1.64994	+	0.952594i
$266$	1.16479	−	69.4093i	0.00437889	−	0.260937i
$267$	−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
$273$	−124.429	+	178.009i	−0.455784	+	0.652049i
$274$	−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	−0.534495	−	0.845171i	$-0.679498\pi$
$277$	128.720	−	222.949i	0.464692	−	0.804871i	0.999188	+	0.0403008i	$0.0128316\pi$
$278$			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	0.479894	+	0.877327i	$0.340675\pi$
$281$	−146.075	+	253.010i	−0.519840	+	0.900390i	−0.999734	+	0.0230634i	$0.992658\pi$
$282$	−127.935	−	262.215i	−0.453670	−	0.929841i
$283$	287.137	−	165.778i	1.01462	−	0.585790i	0.102077	−	0.994776i	$-0.467451\pi$
$283$	287.137	−	165.778i	1.01462	−	0.585790i	0.912540	+	0.408987i	$0.134118\pi$
$284$	−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	$-0.748221\pi$
$293$	−128.607	+	74.2511i	−0.438931	+	0.253417i	0.264213	+	0.964464i	$0.414888\pi$
$294$	189.791	−	84.8377i	0.645547	−	0.288564i
$295$	−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
$301$	481.037	+	8.07248i	1.59813	+	0.0268189i
$302$	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	$0.975303\pi$
$308$	14.3241	+	25.8004i	0.0465068	+	0.0837674i
$309$	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	$-0.658874\pi$
$311$	13.1863	−	7.61311i	0.0423996	−	0.0244794i	0.521050	+	0.853526i	$0.325541\pi$
$312$	−38.4806	−	78.8698i	−0.123335	−	0.252788i
$313$	−135.158	−	78.0334i	−0.431814	−	0.249308i	0.268305	−	0.963334i	$-0.413536\pi$
$313$	−135.158	−	78.0334i	−0.431814	−	0.249308i	−0.700119	+	0.714026i	$0.746870\pi$
$314$		−	133.144i		−	0.424025i
$315$	−384.080	−	310.421i	−1.21930	−	0.985463i
$316$	228.345			0.722612
$317$	148.788	−	257.709i	0.469363	−	0.812961i	−0.530023	−	0.847983i	$-0.677817\pi$
$317$	148.788	−	257.709i	0.469363	−	0.812961i	0.999387	+	0.0350219i	$0.0111501\pi$
$318$	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
$322$	218.910	+	394.298i	0.679845	+	1.22453i
$323$	−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
$329$	−8.07710	+	481.312i	−0.0245504	+	1.46296i
$330$	39.1920	−	58.1215i	0.118764	−	0.176126i
$331$	−151.889	+	263.079i	−0.458878	+	0.794800i	−0.998902	−	0.0468498i	$-0.985082\pi$
$331$	−151.889	+	263.079i	−0.458878	+	0.794800i	0.540024	+	0.841650i	$0.318415\pi$
$332$			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
$336$	−7.25336	+	83.6863i	−0.0215874	+	0.249066i
$337$	−150.144	−	260.057i	−0.445531	−	0.771682i	0.552558	−	0.833474i	$-0.313652\pi$
$337$	−150.144	−	260.057i	−0.445531	−	0.771682i	−0.998089	+	0.0617925i	$0.980318\pi$
$338$	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	0.892897	−	0.450261i	$-0.148669\pi$
$347$	19.6093	+	33.9643i	0.0565110	+	0.0978799i	−0.836386	+	0.548141i	$0.815336\pi$
$348$	8.29792	−	118.898i	0.0238446	−	0.341660i
$349$	−391.985	−	226.313i	−1.12317	−	0.648460i	−0.180959	−	0.983491i	$-0.557920\pi$
$349$	−391.985	−	226.313i	−1.12317	−	0.648460i	−0.942207	+	0.335030i	$0.891253\pi$
$350$	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	$-0.130080\pi$
$353$	364.417	+	210.396i	1.03234	+	0.596024i	0.114688	+	0.993402i	$0.463413\pi$
$354$	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
$357$	−83.9443	−	179.640i	−0.235138	−	0.503192i
$358$	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
$364$	−2.42945	+	144.770i	−0.00667432	+	0.397721i
$365$	−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	$-0.321238\pi$
$367$	24.1481	+	13.9419i	0.0657986	+	0.0379889i	−0.466740	+	0.884395i	$0.654572\pi$
$368$	−182.228			−0.495184
$369$	−510.598	+	206.456i	−1.38374	+	0.559503i
$370$			448.028i			1.21089i
$371$	−218.844	−	394.178i	−0.589875	−	1.06248i
$372$	−20.1955	+	29.9499i	−0.0542891	+	0.0805104i
$373$	62.6374	+	108.491i	0.167929	+	0.290861i	0.937691	−	0.347469i	$-0.112959\pi$
$373$	62.6374	+	108.491i	0.167929	+	0.290861i	−0.769763	+	0.638330i	$0.779625\pi$
$374$	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
$378$	−59.8448	+	260.501i	−0.158320	+	0.689155i
$379$	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	$-0.400750\pi$
$383$	491.936	−	284.020i	1.28443	−	0.741565i	0.977655	+	0.210217i	$0.0674170\pi$
$384$	−28.1410	−	18.9758i	−0.0732840	−	0.0494162i
$385$	−101.121	+	56.1414i	−0.262652	+	0.145822i
$386$	−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	−0.613911	−	0.789376i	$-0.710404\pi$
$389$	146.522	−	253.784i	0.376664	−	0.652401i	0.990575	+	0.136974i	$0.0437378\pi$
$390$	309.120	−	150.820i	0.792615	−	0.386717i
$391$	372.525	−	215.078i	0.952750	−	0.550071i
$392$	73.2847	−	117.632i	0.186951	−	0.300082i
$393$	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
$399$	−62.3428	−	133.413i	−0.156248	−	0.334367i
$400$	72.8915	+	126.252i	0.182229	+	0.315630i
$401$	69.4682	+	120.322i	0.173237	+	0.300056i	0.939550	−	0.342412i	$-0.111244\pi$
$401$	69.4682	+	120.322i	0.173237	+	0.300056i	−0.766313	+	0.642468i	$0.777911\pi$
$402$	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	$-0.866477\pi$
$409$	−416.051	+	240.207i	−1.01724	+	0.587303i	−0.103936	+	0.994584i	$0.533144\pi$
$410$	−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	$-0.488449\pi$
$419$	385.429	−	222.527i	0.919878	−	0.531092i	0.883596	+	0.468250i	$0.155115\pi$
$420$	−327.997	−	28.4286i	−0.780946	−	0.0676871i
$421$	−283.010	+	490.188i	−0.672233	+	1.16434i	0.305036	+	0.952341i	$0.401331\pi$
$421$	−283.010	+	490.188i	−0.672233	+	1.16434i	−0.977269	+	0.212001i	$0.932002\pi$
$422$	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
$427$	1.34195	−	79.9665i	0.00314274	−	0.187275i
$428$	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	$-0.000599115\pi$
$434$	52.1075	−	28.9295i	0.120063	−	0.0666579i
$435$	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	$-0.0809861\pi$
$439$	541.613	+	312.700i	1.23374	+	0.712302i	0.265935	+	0.963991i	$0.414319\pi$
$440$		−	46.7339i		−	0.106213i
$441$	282.922	−	338.284i	0.641547	−	0.767084i
$442$	138.102			0.312447
$443$	148.901	−	257.904i	0.336119	−	0.582175i	−0.647580	−	0.761997i	$-0.724219\pi$
$443$	148.901	−	257.904i	0.336119	−	0.582175i	0.983699	+	0.179822i	$0.0575522\pi$
$444$	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
$448$	27.1823	+	48.9604i	0.0606748	+	0.109287i
$449$	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
$455$	−567.409	−	9.52191i	−1.24705	−	0.0209273i
$456$	59.3577	+	4.14260i	0.130170	+	0.00908464i
$457$	106.962	−	185.264i	0.234053	−	0.405392i	−0.724944	−	0.688808i	$-0.758134\pi$
$457$	106.962	−	185.264i	0.234053	−	0.405392i	0.958997	+	0.283416i	$0.0914676\pi$
$458$		−	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	$-0.224017\pi$
$461$	268.859	+	155.226i	0.583207	+	0.336715i	−0.179200	+	0.983813i	$0.557351\pi$
$462$	51.3080	+	35.8644i	0.111056	+	0.0776287i
$463$	83.7628	+	145.081i	0.180913	+	0.313351i	0.942192	−	0.335074i	$-0.108761\pi$
$463$	83.7628	+	145.081i	0.180913	+	0.313351i	−0.761279	+	0.648425i	$0.775428\pi$
$464$	−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	−0.985699	−	0.168516i	$-0.946102\pi$
$479$	−778.130	−	449.253i	−1.62449	−	0.937898i	−0.638789	−	0.769382i	$-0.720564\pi$
$480$	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
$483$	784.122	+	548.103i	1.62344	+	1.13479i
$484$	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
$490$	461.044	+	287.230i	0.940906	+	0.586183i
$491$	−165.906	−	287.358i	−0.337894	−	0.585250i	0.646142	−	0.763217i	$-0.276381\pi$
$491$	−165.906	−	287.358i	−0.337894	−	0.585250i	−0.984036	+	0.177967i	$0.943048\pi$
$492$	−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
$497$	191.970	+	345.773i	0.386257	+	0.695721i
$498$	185.998	+	381.222i	0.373491	+	0.765505i
$499$	−63.7291	−	110.382i	−0.127714	−	0.221206i	0.795077	−	0.606509i	$-0.207430\pi$
$499$	−63.7291	−	110.382i	−0.127714	−	0.221206i	−0.922790	+	0.385302i	$0.874097\pi$
$500$	−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	$0.953063\pi$
$504$	64.0151	+	166.295i	0.127014	+	0.329951i
$505$	−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	$-0.589604\pi$
$509$	211.358	−	122.028i	0.415242	−	0.239740i	0.693039	+	0.720900i	$0.256271\pi$
$510$	−21.8622	+	313.255i	−0.0428670	+	0.614226i
$511$	396.523	−	220.145i	0.775974	−	0.430813i
$512$	−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
$518$	−400.033	−	6.71312i	−0.772265	−	0.0129597i
$519$	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
$525$	66.0886	−	762.502i	0.125883	−	1.45239i
$526$	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
$546$	130.032	+	278.265i	0.238153	+	0.509643i
$547$	394.904	−	683.994i	0.721945	−	1.25045i	−0.238274	−	0.971198i	$-0.576582\pi$
$547$	394.904	−	683.994i	0.721945	−	1.25045i	0.960219	−	0.279247i	$-0.0900849\pi$
$548$	−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
$553$	−799.097	−	13.4100i	−1.44502	−	0.0242495i
$554$	−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
$560$	−191.894	+	106.537i	−0.342668	+	0.190246i
$561$	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	$-0.561077\pi$
$563$	317.573	−	183.351i	0.564074	−	0.325668i	0.754779	+	0.655979i	$0.227744\pi$
$564$	−411.610	−	28.7264i	−0.729806	−	0.0509334i
$565$	341.976	+	197.440i	0.605267	+	0.349451i
$566$		−	468.892i		−	0.828432i
$567$	128.219	+	552.312i	0.226136	+	0.974096i
$568$	−159.802			−0.281341
$569$	−111.553	+	193.216i	−0.196051	+	0.339570i	−0.947245	−	0.320512i	$-0.896145\pi$
$569$	−111.553	+	193.216i	−0.196051	+	0.339570i	0.751193	+	0.660082i	$0.229479\pi$
$570$	−16.2364	+	232.645i	−0.0284848	+	0.408149i
$571$	191.237	+	331.233i	0.334917	+	0.580093i	0.983469	−	0.181077i	$-0.0579585\pi$
$571$	191.237	+	331.233i	0.334917	+	0.580093i	−0.648552	+	0.761170i	$0.724625\pi$
$572$	−37.7585	+	21.7999i	−0.0660113	+	0.0381117i
$573$	−602.965	−	406.586i	−1.05229	−	0.709574i
$574$	529.650	−	294.056i	0.922735	−	0.512293i
$575$	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
$581$	11.7429	−	699.756i	0.0202115	−	1.20440i
$582$	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	$-0.234918\pi$
$587$	309.364	+	178.611i	0.527025	+	0.304278i	−0.212779	+	0.977100i	$0.568251\pi$
$588$	30.2978	−	292.435i	0.0515269	−	0.497338i
$589$	−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	0.898389	+	0.439200i	$0.144738\pi$
$599$	496.902	+	860.660i	0.829553	+	1.43683i	−0.0688358	+	0.997628i	$0.521928\pi$
$600$	256.405	+	172.897i	0.427342	+	0.288162i
$601$	203.743	+	117.631i	0.339006	+	0.195725i	0.659832	−	0.751413i	$-0.270627\pi$
$601$	203.743	+	117.631i	0.339006	+	0.195725i	−0.320826	+	0.947138i	$0.603961\pi$
$602$	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	$-0.813294\pi$
$607$	−467.352	+	269.826i	−0.769937	+	0.444523i	0.0629152	+	0.998019i	$0.479960\pi$
$608$	34.3535	−	19.8340i	0.0565025	−	0.0326218i
$609$	−36.0211	+	415.597i	−0.0591480	+	0.682424i
$610$	−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
$616$	41.7275	+	0.700246i	0.0677395	+	0.00113676i
$617$	333.055	+	576.868i	0.539797	+	0.934956i	0.998915	+	0.0465807i	$0.0148325\pi$
$617$	333.055	+	576.868i	0.539797	+	0.934956i	−0.459117	+	0.888376i	$0.651834\pi$
$618$	414.293	+	28.9137i	0.670377	+	0.0467858i
$619$	−581.338	−	335.636i	−0.939157	−	0.542223i	−0.0494614	−	0.998776i	$-0.515750\pi$
$619$	−581.338	−	335.636i	−0.939157	−	0.542223i	−0.889696	+	0.456553i	$0.849084\pi$
$620$	−94.3856			−0.152235
$621$	−1169.68	+	380.579i	−1.88354	+	0.612848i
$622$		−	21.5331i		−	0.0346192i
$623$	556.653	−	309.048i	0.893504	−	0.496064i
$624$	−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
$630$	−651.772	+	250.899i	−1.03456	+	0.398252i
$631$	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
$637$	17.0038	−	506.483i	0.0266935	−	0.795106i
$638$	−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	−0.550130	−	0.835079i	$-0.685422\pi$
$641$	287.254	−	497.539i	0.448135	−	0.776192i	0.998265	+	0.0588868i	$0.0187551\pi$
$642$	229.575	+	154.805i	0.357594	+	0.241130i
$643$	−128.360	+	74.1086i	−0.199626	+	0.115254i	−0.596481	−	0.802627i	$-0.703435\pi$
$643$	−128.360	+	74.1086i	−0.199626	+	0.115254i	0.396855	+	0.917881i	$0.370102\pi$
$644$	637.707	+	10.7016i	0.990228	+	0.0166174i
$645$	−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
$651$	72.4333	−	103.624i	0.111265	−	0.159176i
$652$	−9.85556	−	17.0703i	−0.0151159	−	0.0261815i
$653$	43.6173	+	75.5473i	0.0667952	+	0.115693i	0.897489	−	0.441037i	$-0.145389\pi$
$653$	43.6173	+	75.5473i	0.0667952	+	0.115693i	−0.830694	+	0.556730i	$0.812056\pi$
$654$	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	−0.984842	−	0.173457i	$-0.944506\pi$
$659$	−225.512	+	390.598i	−0.342203	+	0.592713i	0.642639	+	0.766170i	$0.277840\pi$
$660$	−43.4711	−	89.0983i	−0.0658653	−	0.134997i
$661$	227.522	−	131.360i	0.344209	−	0.198729i	−0.317923	−	0.948117i	$-0.602985\pi$
$661$	227.522	−	131.360i	0.344209	−	0.198729i	0.662132	+	0.749388i	$0.269652\pi$
$662$	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
$672$	97.3654	+	68.0586i	0.144889	+	0.101278i
$673$	294.210	−	509.587i	0.437162	−	0.757187i	−0.560307	−	0.828285i	$-0.689317\pi$
$673$	294.210	−	509.587i	0.437162	−	0.757187i	0.997469	+	0.0710979i	$0.0226503\pi$
$674$	−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	$-0.622099\pi$
$677$	−923.740	−	533.321i	−1.36446	−	0.787772i	−0.990214	+	0.139557i	$0.955432\pi$
$678$	14.8797	−	213.206i	0.0219465	−	0.314463i
$679$	5.36157	−	319.495i	0.00789627	−	0.470537i
$680$	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
$686$	−263.368	+	407.351i	−0.383919	+	0.593807i
$687$	−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	$-0.328593\pi$
$691$	17.8222	+	10.2897i	0.0257920	+	0.0148910i	−0.487049	+	0.873375i	$0.661927\pi$
$692$		−	518.048i		−	0.748624i
$693$	131.180	+	20.6497i	0.189292	+	0.0297976i
$694$	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
$700$	−247.670	−	446.100i	−0.353814	−	0.637286i
$701$	−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
$707$	0.0714465	−	4.25748i	0.000101056	−	0.00602190i
$708$	142.568	−	211.428i	0.201368	−	0.298627i
$709$	596.846	−	1033.77i	0.841814	−	1.45806i	−0.0465457	−	0.998916i	$-0.514821\pi$
$709$	596.846	−	1033.77i	0.841814	−	1.45806i	0.888360	−	0.459148i	$-0.151845\pi$
$710$		−	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
$714$	−279.370	−	24.2139i	−0.391275	−	0.0339131i
$715$	−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	$-0.300978\pi$
$727$	127.774	+	73.7701i	0.175754	+	0.101472i	−0.409542	+	0.912291i	$0.634311\pi$
$728$	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	$-0.510676\pi$
$733$	597.569	−	345.006i	0.815237	−	0.470677i	0.848771	+	0.528760i	$0.177343\pi$
$734$	34.1506	−	19.7168i	0.0465267	−	0.0268622i
$735$	1146.16	+	118.748i	1.55940	+	0.161562i
$736$	−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
$742$	−637.514	−	10.6984i	−0.859183	−	0.0144183i
$743$	35.6377	+	61.7263i	0.0479646	+	0.0830772i	0.889011	−	0.457886i	$-0.151393\pi$
$743$	35.6377	+	61.7263i	0.0479646	+	0.0830772i	−0.841046	+	0.540963i	$0.818060\pi$
$744$	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
$749$	−221.754	−	399.420i	−0.296067	−	0.533272i
$750$	−212.815	+	315.603i	−0.283753	+	0.420804i
$751$	678.540	+	1175.27i	0.903515	+	1.56493i	0.822898	+	0.568189i	$0.192356\pi$
$751$	678.540	+	1175.27i	0.903515	+	1.56493i	0.0806166	+	0.996745i	$0.474311\pi$
$752$	−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
$756$	276.730	+	257.496i	0.366045	+	0.340604i
$757$	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	$-0.722975\pi$
$761$	−231.955	+	133.919i	−0.304803	+	0.175978i	0.339795	+	0.940499i	$0.389642\pi$
$762$	−416.118	−	280.593i	−0.546087	−	0.368232i
$763$	−671.666	−	1209.79i	−0.880296	−	1.58558i
$764$	−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	$-0.388629\pi$
$769$	1021.03	−	589.492i	1.32774	−	0.766569i	0.984949	+	0.172844i	$0.0552956\pi$
$770$	−2.74452	+	163.546i	−0.00356432	+	0.212397i
$771$	−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
$777$	−768.909	+	359.306i	−0.989587	+	0.462427i
$778$	−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	$-0.792739\pi$
$787$	−525.886	+	303.620i	−0.668216	+	0.385795i	0.127184	+	0.991879i	$0.459406\pi$
$788$	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	$-0.634615\pi$
$797$	138.769	−	80.1182i	0.174114	−	0.100525i	0.584524	+	0.811376i	$0.301281\pi$
$798$	−207.479	−	17.9829i	−0.259999	−	0.0225350i
$799$	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
$805$	−41.9436	+	2499.41i	−0.0521038	+	3.10485i
$806$	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	$-0.00377248\pi$
$812$	134.991	+	243.144i	0.166245	+	0.299438i
$813$	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
$819$	506.744	+	409.561i	0.618735	+	0.500074i
$820$	−959.389			−1.16999
$821$	712.768	−	1234.55i	0.868171	−	1.50372i	0.00430682	−	0.999991i	$-0.498629\pi$
$821$	712.768	−	1234.55i	0.868171	−	1.50372i	0.863864	−	0.503725i	$-0.168038\pi$
$822$	−846.324	+	412.922i	−1.02959	+	0.502338i
$823$	−307.257	−	532.185i	−0.373338	−	0.646641i	0.616739	−	0.787168i	$-0.288454\pi$
$823$	−307.257	−	532.185i	−0.373338	−	0.646641i	−0.990077	+	0.140527i	$0.955120\pi$
$824$	239.774	−	138.434i	0.290988	−	0.168002i
$825$	207.129	−	101.058i	0.251065	−	0.122495i
$826$	−367.847	+	204.225i	−0.445336	+	0.247246i
$827$	−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
$833$	392.692	+	244.647i	0.471419	+	0.293693i
$834$	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	$-0.438360\pi$
$839$	−470.831	−	271.834i	−0.561181	−	0.323998i	−0.753619	+	0.657311i	$0.771694\pi$
$840$	−266.747	+	381.611i	−0.317556	+	0.454299i
$841$	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	0.947777	+	0.318935i	$0.103325\pi$
$853$	1448.28	+	836.167i	1.69787	+	0.980266i	0.750094	+	0.661331i	$0.230008\pi$
$854$	−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	$-0.521878\pi$
$857$	−828.715	−	478.459i	−0.966996	−	0.558295i	−0.898319	+	0.439344i	$0.855211\pi$
$858$	−51.7088	+	76.6839i	−0.0602667	+	0.0893752i
$859$	−1415.32	+	817.134i	−1.64763	+	0.951262i	−0.669624	+	0.742700i	$0.733545\pi$
$859$	−1415.32	+	817.134i	−1.64763	+	0.951262i	−0.978009	+	0.208561i	$0.933122\pi$
$860$	−933.144	+	538.751i	−1.08505	+	0.626454i
$861$	736.253	−	1053.29i	0.855114	−	1.22333i
$862$	−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
$868$	1.41425	−	84.2746i	0.00162932	−	0.0970906i
$869$	−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
$875$	549.093	−	304.851i	0.627535	−	0.348401i
$876$	170.462	+	349.378i	0.194591	+	0.398834i
$877$	−157.796	−	273.311i	−0.179927	−	0.311643i	0.761928	−	0.647661i	$-0.224253\pi$
$877$	−157.796	−	273.311i	−0.179927	−	0.311643i	−0.941855	+	0.336019i	$0.890919\pi$
$878$	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	$0.729083\pi$
$882$	−214.255	−	585.710i	−0.242920	−	0.664071i
$883$	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	$-0.787498\pi$
$887$	−569.288	+	328.679i	−0.641813	+	0.370551i	0.143499	+	0.989650i	$0.454165\pi$
$888$	23.8754	−	342.102i	0.0268867	−	0.385250i
$889$	401.942	+	723.972i	0.452128	+	0.814366i
$890$	−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
$896$	79.1848	+	1.32883i	0.0883759	+	0.00148307i
$897$	−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
$903$	124.630	−	1437.92i	0.138017	−	1.59239i
$904$	−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	−0.691260	−	0.722606i	$-0.742944\pi$
$907$	254.110	−	440.131i	0.280165	−	0.485260i	0.971425	+	0.237346i	$0.0762774\pi$
$908$		−	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	0.300603	+	0.953749i	$0.402812\pi$
$911$	−615.535	+	1066.14i	−0.675670	+	1.17029i	−0.976273	+	0.216545i	$0.930521\pi$
$912$	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
$924$	80.2051	−	37.4793i	0.0868020	−	0.0405620i
$925$	−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	$-0.0765901\pi$
$929$	1161.63	+	670.670i	1.25041	+	0.721927i	0.279222	+	0.960227i	$0.409923\pi$
$930$	−179.947	+	87.7960i	−0.193491	+	0.0944043i
$931$	291.640	+	181.691i	0.313255	+	0.195157i
$932$	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	$-0.286672\pi$
$938$	41.5992	+	74.9280i	0.0443489	+	0.0798805i
$939$	−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	$-0.759111\pi$
$941$	−466.720	+	269.461i	−0.495983	+	0.286356i	0.231070	+	0.972937i	$0.425777\pi$
$942$	−398.462	−	27.8088i	−0.422996	−	0.0295210i
$943$	2414.37	+	1393.94i	2.56031	+	1.47819i
$944$		−	170.003i		−	0.180088i
$945$	−1009.22	+	1084.61i	−1.06796	+	1.14773i
$946$	204.879			0.216574
$947$	−233.960	+	405.231i	−0.247054	+	0.427910i	−0.962707	−	0.270546i	$-0.912796\pi$
$947$	−233.960	+	405.231i	−0.247054	+	0.427910i	0.715653	+	0.698456i	$0.246129\pi$
$948$	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
$952$	−163.445	+	90.7429i	−0.171686	+	0.0953181i
$953$	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
$959$	1553.48	+	26.0696i	1.61990	+	0.0271841i
$960$	−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
$966$	1225.75	−	572.782i	1.26889	−	0.592942i
$967$	−231.563	−	401.080i	−0.239466	−	0.414767i	0.721095	−	0.692836i	$-0.243639\pi$
$967$	−231.563	−	401.080i	−0.239466	−	0.414767i	−0.960561	+	0.278069i	$0.910306\pi$
$968$	−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	−0.996420	−	0.0845376i	$-0.973059\pi$
$977$	−558.279	−	966.968i	−0.571422	−	0.989732i	0.424998	−	0.905194i	$-0.360275\pi$
$978$	−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	$-0.447050\pi$
$983$	−595.403	−	343.756i	−0.605700	−	0.349701i	−0.771281	+	0.636495i	$0.780383\pi$
$984$	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
$987$	1438.75	+	124.701i	1.45770	+	0.126343i
$988$	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
$994$	559.228	+	9.38462i	0.562603	+	0.00944127i
$995$	−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	−0.966494	−	0.256688i	$-0.917369\pi$
$997$	−1667.02	−	962.456i	−1.67204	−	0.965353i	−0.705545	−	0.708665i	$-0.749298\pi$
$998$	−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.97.13	yes	32
3.2	odd	2		378.3.o.a.181.1		32
7.6	odd	2	inner	126.3.o.a.97.12	yes	32
9.2	odd	6		1134.3.c.d.811.9		16
9.4	even	3	inner	126.3.o.a.13.12	✓	32
9.5	odd	6		378.3.o.a.307.8		32
9.7	even	3		1134.3.c.e.811.8		16
21.20	even	2		378.3.o.a.181.8		32
63.13	odd	6	inner	126.3.o.a.13.13	yes	32
63.20	even	6		1134.3.c.d.811.16		16
63.34	odd	6		1134.3.c.e.811.1		16
63.41	even	6		378.3.o.a.307.1		32

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.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} +(3.39779 + 6.12005i) 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} +(9.89810 + 0.166104i) 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} +(19.0253 - 8.89038i) 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} +(2.56445 - 29.5876i) 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} +(-25.9100 + 41.5893i) 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} +(-9.61040 - 17.3101i) 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} +(-22.6328 - 58.7942i) 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} +(67.8447 - 37.6667i) 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} +(-14.7529 - 0.247575i) 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} +(-34.4239 - 24.0624i) 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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