LMFDB - Embedded newform 161.4.i.b.8.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [161,4,Mod(8,161)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("161.8"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [190] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$190$
Relative dimension:	$19$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			8.16
Character	$\chi$	$=$	161.8
Dual form			161.4.i.b.141.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.425855 - 2.96189i) q^{2} +(-1.87521 - 4.10613i) q^{3} +(-0.915470 - 0.268806i) q^{4} +(12.1922 + 14.0705i) q^{5} +(-12.9605 + 3.80554i) q^{6} +(-5.88877 - 3.78449i) q^{7} +(8.75848 - 19.1784i) q^{8} +(4.33731 - 5.00552i) q^{9} +(46.8674 - 30.1199i) q^{10} +(-2.19356 - 15.2566i) q^{11} +(0.612943 + 4.26311i) q^{12} +(8.96917 - 5.76413i) q^{13} +(-13.7170 + 15.8302i) q^{14} +(34.9126 - 76.4480i) q^{15} +(-59.4956 - 38.2355i) q^{16} +(125.816 - 36.9430i) q^{17} +(-12.9787 - 14.9782i) q^{18} +(-15.5805 - 4.57484i) q^{19} +(-7.37934 - 16.1585i) q^{20} +(-4.49693 + 31.2768i) q^{21} -46.1223 q^{22} +(-87.7155 - 66.8804i) q^{23} -95.1731 q^{24} +(-31.5411 + 219.374i) q^{25} +(-13.2531 - 29.0203i) q^{26} +(-145.629 - 42.7606i) q^{27} +(4.37370 + 5.04752i) q^{28} +(-19.4178 + 5.70157i) q^{29} +(-211.562 - 135.963i) q^{30} +(-42.7561 + 93.6228i) q^{31} +(-28.1307 + 32.4645i) q^{32} +(-58.5321 + 37.6163i) q^{33} +(-55.8414 - 388.386i) q^{34} +(-18.5473 - 128.999i) q^{35} +(-5.31619 + 3.41651i) q^{36} +(16.1910 - 18.6855i) q^{37} +(-20.1852 + 44.1993i) q^{38} +(-40.4874 - 26.0197i) q^{39} +(376.635 - 110.590i) q^{40} +(14.2592 + 16.4560i) q^{41} +(90.7233 + 26.6388i) q^{42} +(144.113 + 315.563i) q^{43} +(-2.09292 + 14.5566i) q^{44} +123.312 q^{45} +(-235.446 + 231.322i) q^{46} +181.130 q^{47} +(-45.4335 + 315.997i) q^{48} +(20.3553 + 44.5720i) q^{49} +(636.327 + 186.843i) q^{50} +(-387.625 - 447.343i) q^{51} +(-9.76044 + 2.86592i) q^{52} +(281.543 + 180.937i) q^{53} +(-188.669 + 413.128i) q^{54} +(187.924 - 216.876i) q^{55} +(-124.157 + 79.7909i) q^{56} +(10.4317 + 72.5542i) q^{57} +(8.61825 + 59.9413i) q^{58} +(7.98180 - 5.12959i) q^{59} +(-52.5111 + 60.6011i) q^{60} +(216.991 - 475.143i) q^{61} +(259.092 + 166.508i) q^{62} +(-44.4847 + 13.0619i) q^{63} +(-286.331 - 330.444i) q^{64} +(190.458 + 55.9236i) q^{65} +(86.4890 + 189.385i) q^{66} +(83.1092 - 578.037i) q^{67} -125.112 q^{68} +(-110.135 + 485.586i) q^{69} -389.980 q^{70} +(-76.1552 + 529.671i) q^{71} +(-58.0096 - 127.023i) q^{72} +(-217.509 - 63.8664i) q^{73} +(-48.4492 - 55.9133i) q^{74} +(959.923 - 281.859i) q^{75} +(13.0337 + 8.37625i) q^{76} +(-44.8209 + 98.1440i) q^{77} +(-94.3090 + 108.838i) q^{78} +(-981.067 + 630.494i) q^{79} +(-187.388 - 1303.31i) q^{80} +(72.0547 + 501.151i) q^{81} +(54.8130 - 35.2262i) q^{82} +(-394.222 + 454.956i) q^{83} +(12.5242 - 27.4242i) q^{84} +(2053.78 + 1319.89i) q^{85} +(996.034 - 292.462i) q^{86} +(59.8238 + 69.0403i) q^{87} +(-311.809 - 91.5554i) q^{88} +(-24.7740 - 54.2475i) q^{89} +(52.5129 - 365.235i) q^{90} -74.6317 q^{91} +(62.3230 + 84.8055i) q^{92} +464.604 q^{93} +(77.1351 - 536.486i) q^{94} +(-125.589 - 275.003i) q^{95} +(186.055 + 54.6306i) q^{96} +(1196.48 + 1380.81i) q^{97} +(140.685 - 41.3090i) q^{98} +(-85.8812 - 55.1925i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 190 q + 2 q^{2} - 2 q^{3} - 58 q^{4} - 26 q^{5} - 9 q^{6} + 133 q^{7} - 27 q^{8} - 589 q^{9} + 12 q^{10} + 122 q^{11} - 117 q^{12} + 64 q^{13} - 14 q^{14} + 582 q^{15} - 626 q^{16} + 104 q^{17} + 33 q^{18}+ \cdots + 1926 q^{99}+O(q^{100}) $ 190 * q + 2 * q^2 - 2 * q^3 - 58 * q^4 - 26 * q^5 - 9 * q^6 + 133 * q^7 - 27 * q^8 - 589 * q^9 + 12 * q^10 + 122 * q^11 - 117 * q^12 + 64 * q^13 - 14 * q^14 + 582 * q^15 - 626 * q^16 + 104 * q^17 + 33 * q^18 + 82 * q^19 + 945 * q^20 + 14 * q^21 - 280 * q^22 - 267 * q^23 - 84 * q^24 - 793 * q^25 + 27 * q^26 - 302 * q^27 + 868 * q^28 + 342 * q^29 + 1020 * q^30 - 1440 * q^31 + 242 * q^32 + 648 * q^33 + 2860 * q^34 - 280 * q^35 - 1612 * q^36 + 1018 * q^37 - 48 * q^38 + 1164 * q^39 - 5858 * q^40 - 228 * q^41 + 63 * q^42 - 124 * q^43 - 1400 * q^44 + 164 * q^45 - 3912 * q^46 + 3084 * q^47 - 4329 * q^48 - 931 * q^49 - 6141 * q^50 + 3858 * q^51 + 1987 * q^52 + 1202 * q^53 - 295 * q^54 + 7494 * q^55 + 189 * q^56 + 5126 * q^57 + 249 * q^58 - 1116 * q^59 + 3140 * q^60 + 1180 * q^61 - 293 * q^62 + 1197 * q^63 - 2933 * q^64 + 1152 * q^65 + 9861 * q^66 - 4930 * q^67 + 100 * q^68 - 7394 * q^69 - 84 * q^70 - 15114 * q^71 + 1271 * q^72 - 6944 * q^73 + 7528 * q^74 + 10798 * q^75 + 5821 * q^76 + 1379 * q^77 + 3217 * q^78 + 1432 * q^79 + 8074 * q^80 + 2175 * q^81 + 1801 * q^82 + 4210 * q^83 - 1876 * q^84 + 10028 * q^85 - 4476 * q^86 + 2582 * q^87 - 5609 * q^88 - 1996 * q^89 - 33389 * q^90 - 4452 * q^91 - 13192 * q^92 + 3984 * q^93 - 11373 * q^94 - 740 * q^95 - 18056 * q^96 + 7238 * q^97 - 1519 * q^98 + 1926 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	0.425855	−	2.96189i	0.150562	−	1.04718i	−0.764717	−	0.644366i	$-0.777121\pi$
$2$	0.425855	−	2.96189i	0.150562	−	1.04718i	0.915280	−	0.402819i	$-0.131970\pi$
$3$	−1.87521	−	4.10613i	−0.360884	−	0.790226i	−0.999781	−	0.0209335i	$-0.993336\pi$
$3$	−1.87521	−	4.10613i	−0.360884	−	0.790226i	0.638897	−	0.769292i	$-0.279391\pi$
$4$	−0.915470	−	0.268806i	−0.114434	−	0.0336008i
$5$	12.1922	+	14.0705i	1.09050	+	1.25851i	0.963817	+	0.266564i	$0.0858883\pi$
$5$	12.1922	+	14.0705i	1.09050	+	1.25851i	0.126685	+	0.991943i	$0.459566\pi$
$6$	−12.9605	+	3.80554i	−0.881848	+	0.258934i
$7$	−5.88877	−	3.78449i	−0.317964	−	0.204343i
$7$	−5.88877	−	3.78449i	−0.317964	−	0.204343i
$8$	8.75848	−	19.1784i	0.387074	−	0.847574i
$9$	4.33731	−	5.00552i	0.160641	−	0.185390i
$10$	46.8674	−	30.1199i	1.48208	−	0.952474i
$11$	−2.19356	−	15.2566i	−0.0601258	−	0.418184i	−0.997548	−	0.0699889i	$-0.977704\pi$
$11$	−2.19356	−	15.2566i	−0.0601258	−	0.418184i	0.937422	−	0.348196i	$-0.113205\pi$
$12$	0.612943	+	4.26311i	0.0147451	+	0.102555i
$13$	8.96917	−	5.76413i	0.191354	−	0.122976i	−0.441456	−	0.897283i	$-0.645538\pi$
$13$	8.96917	−	5.76413i	0.191354	−	0.122976i	0.632810	+	0.774307i	$0.281902\pi$
$14$	−13.7170	+	15.8302i	−0.261858	+	0.302201i
$15$	34.9126	−	76.4480i	0.600960	−	1.31592i
$16$	−59.4956	−	38.2355i	−0.929619	−	0.597430i
$17$	125.816	−	36.9430i	1.79500	−	0.527058i	0.797870	−	0.602830i	$-0.205960\pi$
$17$	125.816	−	36.9430i	1.79500	−	0.527058i	0.997125	+	0.0757716i	$0.0241420\pi$
$18$	−12.9787	−	14.9782i	−0.169951	−	0.196134i
$19$	−15.5805	−	4.57484i	−0.188126	−	0.0552389i	0.186312	−	0.982491i	$-0.440346\pi$
$19$	−15.5805	−	4.57484i	−0.188126	−	0.0552389i	−0.374439	+	0.927252i	$0.622165\pi$
$20$	−7.37934	−	16.1585i	−0.0825035	−	0.180657i
$21$	−4.49693	+	31.2768i	−0.0467290	+	0.325008i
$22$	−46.1223			−0.446969
$23$	−87.7155	−	66.8804i	−0.795215	−	0.606328i
$23$	−87.7155	−	66.8804i	−0.795215	−	0.606328i
$24$	−95.1731			−0.809464
$25$	−31.5411	+	219.374i	−0.252329	+	1.75499i
$26$	−13.2531	−	29.0203i	−0.0999675	−	0.218898i
$27$	−145.629	−	42.7606i	−1.03801	−	0.304788i
$28$	4.37370	+	5.04752i	0.0295197	+	0.0340676i
$29$	−19.4178	+	5.70157i	−0.124338	+	0.0365088i	−0.343309	−	0.939222i	$-0.611548\pi$
$29$	−19.4178	+	5.70157i	−0.124338	+	0.0365088i	0.218972	+	0.975731i	$0.429730\pi$
$30$	−211.562	−	135.963i	−1.28753	−	0.827444i
$31$	−42.7561	+	93.6228i	−0.247717	+	0.542424i	−0.992118	−	0.125309i	$-0.960008\pi$
$31$	−42.7561	+	93.6228i	−0.247717	+	0.542424i	0.744401	+	0.667733i	$0.232735\pi$
$32$	−28.1307	+	32.4645i	−0.155402	+	0.179343i
$33$	−58.5321	+	37.6163i	−0.308762	+	0.198429i
$34$	−55.8414	−	388.386i	−0.281668	−	1.95905i
$35$	−18.5473	−	128.999i	−0.0895734	−	0.622996i
$36$	−5.31619	+	3.41651i	−0.0246120	+	0.0158172i
$37$	16.1910	−	18.6855i	0.0719403	−	0.0830235i	−0.718638	−	0.695384i	$-0.755234\pi$
$37$	16.1910	−	18.6855i	0.0719403	−	0.0830235i	0.790579	+	0.612360i	$0.209780\pi$
$38$	−20.1852	+	44.1993i	−0.0861701	+	0.188686i
$39$	−40.4874	−	26.0197i	−0.166235	−	0.106833i
$40$	376.635	−	110.590i	1.48878	−	0.437146i
$41$	14.2592	+	16.4560i	0.0543148	+	0.0626827i	0.782257	−	0.622956i	$-0.214068\pi$
$41$	14.2592	+	16.4560i	0.0543148	+	0.0626827i	−0.727942	+	0.685639i	$0.759523\pi$
$42$	90.7233	+	26.6388i	0.333307	+	0.0978678i
$43$	144.113	+	315.563i	0.511093	+	1.11914i	0.972703	+	0.232055i	$0.0745450\pi$
$43$	144.113	+	315.563i	0.511093	+	1.11914i	−0.461609	+	0.887083i	$0.652728\pi$
$44$	−2.09292	+	14.5566i	−0.00717090	+	0.0498747i
$45$	123.312			0.408494
$46$	−235.446	+	231.322i	−0.754666	+	0.741447i
$47$	181.130			0.562139			0.281069	−	0.959687i	$-0.409311\pi$
$47$	181.130			0.562139			0.281069	+	0.959687i	$0.409311\pi$
$48$	−45.4335	+	315.997i	−0.136620	+	0.950212i
$49$	20.3553	+	44.5720i	0.0593450	+	0.129947i
$50$	636.327	+	186.843i	1.79981	+	0.528471i
$51$	−387.625	−	447.343i	−1.06428	−	1.22824i
$52$	−9.76044	+	2.86592i	−0.0260294	+	0.00764293i
$53$	281.543	+	180.937i	0.729678	+	0.468936i	0.851991	−	0.523556i	$-0.175395\pi$
$53$	281.543	+	180.937i	0.729678	+	0.468936i	−0.122313	+	0.992492i	$0.539031\pi$
$54$	−188.669	+	413.128i	−0.475456	+	1.04110i
$55$	187.924	−	216.876i	0.460721	−	0.531700i
$56$	−124.157	+	79.7909i	−0.296271	+	0.190402i
$57$	10.4317	+	72.5542i	0.0242406	+	0.168597i
$58$	8.61825	+	59.9413i	0.0195109	+	0.135701i
$59$	7.98180	−	5.12959i	0.0176126	−	0.0113189i	−0.531805	−	0.846867i	$-0.678486\pi$
$59$	7.98180	−	5.12959i	0.0176126	−	0.0113189i	0.549417	+	0.835548i	$0.314850\pi$
$60$	−52.5111	+	60.6011i	−0.112986	+	0.130393i
$61$	216.991	−	475.143i	0.455456	−	0.997309i	−0.533044	−	0.846088i	$-0.678952\pi$
$61$	216.991	−	475.143i	0.455456	−	0.997309i	0.988500	−	0.151222i	$-0.0483208\pi$
$62$	259.092	+	166.508i	0.530722	+	0.341074i
$63$	−44.4847	+	13.0619i	−0.0889611	+	0.0261213i
$64$	−286.331	−	330.444i	−0.559240	−	0.645398i
$65$	190.458	+	55.9236i	0.363437	+	0.106715i
$66$	86.4890	+	189.385i	0.161304	+	0.353206i
$67$	83.1092	−	578.037i	0.151543	−	1.05401i	−0.762091	−	0.647470i	$-0.775827\pi$
$67$	83.1092	−	578.037i	0.151543	−	1.05401i	0.913634	−	0.406537i	$-0.133264\pi$
$68$	−125.112			−0.223118
$69$	−110.135	+	485.586i	−0.192155	+	0.847213i
$70$	−389.980			−0.665879
$71$	−76.1552	+	529.671i	−0.127295	+	0.885358i	0.821667	+	0.569968i	$0.193044\pi$
$71$	−76.1552	+	529.671i	−0.127295	+	0.885358i	−0.948962	+	0.315390i	$0.897865\pi$
$72$	−58.0096	−	127.023i	−0.0949514	−	0.207915i
$73$	−217.509	−	63.8664i	−0.348733	−	0.102397i	0.102675	−	0.994715i	$-0.467260\pi$
$73$	−217.509	−	63.8664i	−0.348733	−	0.102397i	−0.451408	+	0.892318i	$0.649078\pi$
$74$	−48.4492	−	55.9133i	−0.0761095	−	0.0878350i
$75$	959.923	−	281.859i	1.47790	−	0.433950i
$76$	13.0337	+	8.37625i	0.0196719	+	0.0126424i
$77$	−44.8209	+	98.1440i	−0.0663352	+	0.145254i
$78$	−94.3090	+	108.838i	−0.136902	+	0.157994i
$79$	−981.067	+	630.494i	−1.39720	+	0.897925i	−0.999805	−	0.0197232i	$-0.993722\pi$
$79$	−981.067	+	630.494i	−1.39720	+	0.897925i	−0.397393	+	0.917648i	$0.630085\pi$
$80$	−187.388	−	1303.31i	−0.261882	−	1.82143i
$81$	72.0547	+	501.151i	0.0988404	+	0.687450i
$82$	54.8130	−	35.2262i	0.0738181	−	0.0474400i
$83$	−394.222	+	454.956i	−0.521343	+	0.601662i	−0.953967	−	0.299913i	$-0.903042\pi$
$83$	−394.222	+	454.956i	−0.521343	+	0.601662i	0.432624	+	0.901575i	$0.357588\pi$
$84$	12.5242	−	27.4242i	0.0162679	−	0.0356217i
$85$	2053.78	+	1319.89i	2.62075	+	1.68426i
$86$	996.034	−	292.462i	1.24890	−	0.366709i
$87$	59.8238	+	69.0403i	0.0737216	+	0.0850793i
$88$	−311.809	−	91.5554i	−0.377715	−	0.110907i
$89$	−24.7740	−	54.2475i	−0.0295061	−	0.0646093i	0.894305	−	0.447458i	$-0.147670\pi$
$89$	−24.7740	−	54.2475i	−0.0295061	−	0.0646093i	−0.923811	+	0.382848i	$0.874943\pi$
$90$	52.5129	−	365.235i	0.0615038	−	0.427768i
$91$	−74.6317			−0.0859728
$92$	62.3230	+	84.8055i	0.0706264	+	0.0961042i
$93$	464.604			0.518035
$94$	77.1351	−	536.486i	0.0846370	−	0.588663i
$95$	−125.589	−	275.003i	−0.135634	−	0.296997i
$96$	186.055	+	54.6306i	0.197803	+	0.0580803i
$97$	1196.48	+	1380.81i	1.25242	+	1.44536i	0.847314	+	0.531093i	$0.178219\pi$
$97$	1196.48	+	1380.81i	1.25242	+	1.44536i	0.405102	+	0.914272i	$0.367236\pi$
$98$	140.685	−	41.3090i	0.145014	−	0.0425800i
$99$	−85.8812	−	55.1925i	−0.0871857	−	0.0560309i
$100$	87.8440	−	192.351i	0.0878440	−	0.192351i
$101$	−1059.63	+	1222.88i	−1.04393	+	1.20476i	−0.0655738	+	0.997848i	$0.520888\pi$
$101$	−1059.63	+	1222.88i	−1.04393	+	1.20476i	−0.978359	+	0.206915i	$0.933658\pi$
$102$	−1490.05	+	957.596i	−1.44644	+	0.929570i
$103$	−157.392	−	1094.69i	−0.150566	−	1.04721i	−0.915273	−	0.402833i	$-0.868025\pi$
$103$	−157.392	−	1094.69i	−0.150566	−	1.04721i	0.764707	−	0.644378i	$-0.222884\pi$
$104$	−31.9906	−	222.499i	−0.0301628	−	0.209787i
$105$	−494.909	+	318.058i	−0.459982	+	0.295613i
$106$	655.811	−	756.846i	0.600925	−	0.693504i
$107$	−654.246	+	1432.60i	−0.591106	+	1.29434i	0.343665	+	0.939092i	$0.388331\pi$
$107$	−654.246	+	1432.60i	−0.591106	+	1.29434i	−0.934771	+	0.355250i	$0.884396\pi$
$108$	121.825	+	78.2922i	0.108543	+	0.0697562i
$109$	627.755	−	184.325i	0.551633	−	0.161974i	0.00597510	−	0.999982i	$-0.498098\pi$
$109$	627.755	−	184.325i	0.551633	−	0.161974i	0.545658	+	0.838008i	$0.316280\pi$
$110$	−562.332	−	648.966i	−0.487421	−	0.562514i
$111$	−107.087	−	31.4435i	−0.0915694	−	0.0268872i
$112$	205.655	+	450.321i	0.173505	+	0.379922i
$113$	−150.885	+	1049.43i	−0.125611	+	0.873647i	0.825413	+	0.564530i	$0.190942\pi$
$113$	−150.885	+	1049.43i	−0.125611	+	0.873647i	−0.951024	+	0.309117i	$0.899967\pi$
$114$	219.340			0.180202
$115$	−128.400	−	2049.62i	−0.104116	−	1.66199i
$116$	19.3090			0.0154551
$117$	10.0496	−	69.8962i	0.00794087	−	0.0552299i
$118$	−11.7942	−	25.8256i	−0.00920120	−	0.0201478i
$119$	−880.714	−	258.601i	−0.678444	−	0.199209i
$120$	−1160.37	−	1339.14i	−0.882722	−	1.01872i
$121$	1049.13	−	308.054i	0.788230	−	0.231445i
$122$	−1314.91	−	845.044i	−0.975793	−	0.627104i
$123$	40.8315	−	89.4084i	0.0299321	−	0.0655422i
$124$	64.3083	−	74.2158i	0.0465731	−	0.0537482i
$125$	−1513.45	+	972.637i	−1.08294	+	0.695962i
$126$	19.7438	+	137.321i	0.0139597	+	0.0970916i
$127$	238.044	+	1655.63i	0.166323	+	1.15680i	0.886405	+	0.462911i	$0.153195\pi$
$127$	238.044	+	1655.63i	0.166323	+	1.15680i	−0.720082	+	0.693889i	$0.755896\pi$
$128$	−1389.77	+	893.152i	−0.959685	+	0.616752i
$129$	1025.50	−	1183.49i	0.699927	−	0.807759i
$130$	246.747	−	540.300i	0.166470	−	0.364519i
$131$	879.113	+	564.972i	0.586324	+	0.376808i	0.799913	−	0.600116i	$-0.204879\pi$
$131$	879.113	+	564.972i	0.586324	+	0.376808i	−0.213589	+	0.976924i	$0.568515\pi$
$132$	63.6959	−	18.7028i	0.0420001	−	0.0123324i
$133$	74.4364	+	85.9042i	0.0485297	+	0.0560063i
$134$	−1676.69	−	492.320i	−1.08092	−	0.317388i
$135$	−1173.88	−	2570.43i	−0.748379	−	1.63872i
$136$	393.452	−	2736.52i	0.248075	−	1.72540i
$137$	−2346.68			−1.46344			−0.731718	−	0.681608i	$-0.761281\pi$
$137$	−2346.68			−1.46344			−0.731718	+	0.681608i	$0.761281\pi$
$138$	1391.35	+	532.997i	0.858258	+	0.328781i
$139$	2065.78			1.26056			0.630278	−	0.776370i	$-0.282941\pi$
$139$	2065.78			1.26056			0.630278	+	0.776370i	$0.282941\pi$
$140$	−17.6963	+	123.081i	−0.0106830	+	0.0743016i
$141$	−339.656	−	743.744i	−0.202867	−	0.444217i
$142$	1536.39	+	451.126i	0.907967	+	0.266603i
$143$	−107.615	−	124.195i	−0.0629318	−	0.0726272i
$144$	−449.440	+	131.967i	−0.260092	+	0.0763700i
$145$	−316.969	−	203.704i	−0.181537	−	0.116667i
$146$	−281.792	+	617.039i	−0.159735	+	0.349771i
$147$	144.848	−	167.163i	0.0812712	−	0.0937919i
$148$	−19.8452	+	12.7537i	−0.0110221	+	0.00708344i
$149$	−93.3843	−	649.502i	−0.0513445	−	0.357109i	−0.999256	−	0.0385744i	$-0.987718\pi$
$149$	−93.3843	−	649.502i	−0.0513445	−	0.357109i	0.947911	−	0.318535i	$-0.103191\pi$
$150$	−426.046	−	2963.21i	−0.231910	−	1.61297i
$151$	−1870.00	+	1201.77i	−1.00780	+	0.647676i	−0.936824	−	0.349802i	$-0.886249\pi$
$151$	−1870.00	+	1201.77i	−1.00780	+	0.647676i	−0.0709793	+	0.997478i	$0.522612\pi$
$152$	−224.199	+	258.740i	−0.119638	+	0.138069i
$153$	360.785	−	790.009i	0.190639	−	0.417441i
$154$	271.604	+	174.549i	0.142120	+	0.0913350i
$155$	−1838.61	+	539.866i	−0.952781	+	0.279762i
$156$	30.0707	+	34.7035i	0.0154332	+	0.0178109i
$157$	1826.64	+	536.349i	0.928544	+	0.272645i	0.710827	−	0.703367i	$-0.248321\pi$
$157$	1826.64	+	536.349i	0.928544	+	0.272645i	0.217717	+	0.976012i	$0.430139\pi$
$158$	1449.66	+	3174.31i	0.729928	+	1.59832i
$159$	214.999	−	1495.35i	0.107236	−	0.745842i
$160$	−799.768			−0.395170
$161$	263.429	+	725.802i	0.128951	+	0.355287i
$162$	1515.04			0.734769
$163$	−2.16996	+	15.0924i	−0.00104273	+	0.00725233i	−0.990336	−	0.138688i	$-0.955712\pi$
$163$	−2.16996	+	15.0924i	−0.00104273	+	0.00725233i	0.989293	+	0.145940i	$0.0466207\pi$
$164$	−8.63038	−	18.8979i	−0.00410926	−	0.00899803i
$165$	−1242.92	−	364.953i	−0.586430	−	0.172191i
$166$	1179.65	+	1361.38i	0.551556	+	0.636530i
$167$	711.975	−	209.055i	0.329906	−	0.0968692i	−0.112585	−	0.993642i	$-0.535913\pi$
$167$	711.975	−	209.055i	0.329906	−	0.0968692i	0.442491	+	0.896773i	$0.354095\pi$
$168$	560.453	+	360.181i	0.257380	+	0.165408i
$169$	−865.446	+	1895.06i	−0.393922	+	0.862568i
$170$	4783.96	−	5520.99i	2.15831	−	2.49083i
$171$	−90.4767	+	58.1458i	−0.0404615	+	0.0260031i
$172$	−47.1057	−	327.627i	−0.0208824	−	0.145240i
$173$	164.999	+	1147.59i	0.0725122	+	0.504334i	0.993418	+	0.114548i	$0.0365419\pi$
$173$	164.999	+	1147.59i	0.0725122	+	0.504334i	−0.920905	+	0.389786i	$0.872549\pi$
$174$	229.966	−	147.790i	0.100193	−	0.0643904i
$175$	1015.95	−	1172.47i	0.438851	−	0.506461i
$176$	−452.835	+	991.571i	−0.193942	+	0.424673i
$177$	−36.0303	−	23.1553i	−0.0153006	−	0.00983310i
$178$	−171.225	+	50.2762i	−0.0721004	+	0.0211706i
$179$	1888.22	+	2179.12i	0.788449	+	0.909918i	0.997689	−	0.0679461i	$-0.0216446\pi$
$179$	1888.22	+	2179.12i	0.788449	+	0.909918i	−0.209240	+	0.977864i	$0.567099\pi$
$180$	−112.888	−	33.1469i	−0.0467455	−	0.0137257i
$181$	−1999.59	−	4378.48i	−0.821150	−	1.79807i	−0.549028	−	0.835804i	$-0.685002\pi$
$181$	−1999.59	−	4378.48i	−0.821150	−	1.79807i	−0.272122	−	0.962263i	$-0.587725\pi$
$182$	−31.7823	+	221.051i	−0.0129443	+	0.0900294i
$183$	−2357.91			−0.952467
$184$	−2050.91	+	1096.47i	−0.821714	+	0.439310i
$185$	460.319			0.182937
$186$	197.854	−	1376.11i	0.0779966	−	0.542478i
$187$	−839.609	−	1838.49i	−0.328333	−	0.718949i
$188$	−165.819	−	48.6889i	−0.0643276	−	0.0188883i
$189$	695.751	+	802.940i	0.267770	+	0.309023i
$190$	−868.009	+	254.870i	−0.331432	+	0.0973171i
$191$	−3934.04	−	2528.25i	−1.49035	−	0.957791i	−0.996078	−	0.0884848i	$-0.971798\pi$
$191$	−3934.04	−	2528.25i	−1.49035	−	0.957791i	−0.494274	−	0.869306i	$-0.664566\pi$
$192$	−819.915	+	1795.36i	−0.308189	+	0.674840i
$193$	70.0096	−	80.7954i	0.0261109	−	0.0301336i	−0.742544	−	0.669797i	$-0.766381\pi$
$193$	70.0096	−	80.7954i	0.0261109	−	0.0301336i	0.768655	+	0.639664i	$0.220926\pi$
$194$	4599.34	−	2955.82i	1.70213	−	1.09389i
$195$	−127.519	−	886.915i	−0.0468299	−	0.325709i
$196$	−6.65348	−	46.2759i	−0.00242474	−	0.0168644i
$197$	−786.728	+	505.600i	−0.284528	+	0.182855i	−0.675118	−	0.737710i	$-0.735907\pi$
$197$	−786.728	+	505.600i	−0.284528	+	0.182855i	0.390590	+	0.920565i	$0.372271\pi$
$198$	−200.047	+	230.866i	−0.0718016	+	0.0828634i
$199$	1422.11	−	3113.99i	0.506587	−	1.10927i	−0.467685	−	0.883895i	$-0.654912\pi$
$199$	1422.11	−	3113.99i	0.506587	−	1.10927i	0.974272	−	0.225376i	$-0.0723609\pi$
$200$	3930.98	+	2526.29i	1.38981	+	0.893178i
$201$	−2529.35	+	742.683i	−0.887593	+	0.260621i
$202$	3170.78	+	3659.27i	1.10443	+	1.27458i
$203$	135.924	+	39.9110i	0.0469952	+	0.0137990i
$204$	234.610	+	513.725i	0.0805196	+	0.176313i
$205$	−57.6937	+	401.268i	−0.0196561	+	0.136711i
$206$	−3309.36			−1.11929
$207$	−715.220	+	148.981i	−0.240151	+	0.0500235i
$208$	−754.021			−0.251356
$209$	−35.6196	+	247.739i	−0.0117888	+	0.0819928i
$210$	731.294	+	1601.31i	0.240305	+	0.526195i
$211$	−384.118	−	112.787i	−0.125326	−	0.0367990i	0.218468	−	0.975844i	$-0.429894\pi$
$211$	−384.118	−	112.787i	−0.125326	−	0.0367990i	−0.343794	+	0.939045i	$0.611712\pi$
$212$	−209.108	−	241.323i	−0.0677432	−	0.0781799i
$213$	2317.71	−	680.541i	0.745572	−	0.218920i
$214$	3964.58	+	2547.88i	1.26642	+	0.813877i
$215$	−2683.09	+	5875.15i	−0.851095	+	1.86364i
$216$	−2095.57	+	2418.42i	−0.660119	+	0.761818i
$217$	606.095	−	389.514i	0.189606	−	0.121852i
$218$	−278.618	−	1937.83i	−0.0865615	−	0.602049i
$219$	145.631	+	1012.88i	0.0449352	+	0.312531i
$220$	−230.336	+	148.028i	−0.0705875	+	0.0453638i
$221$	915.523	−	1056.57i	0.278664	−	0.321595i
$222$	−138.735	+	303.788i	−0.0419428	+	0.0918419i
$223$	4286.88	+	2755.01i	1.28731	+	0.827306i	0.991771	−	0.128023i	$-0.0408631\pi$
$223$	4286.88	+	2755.01i	1.28731	+	0.827306i	0.295543	+	0.955329i	$0.404499\pi$
$224$	288.517	−	84.7162i	0.0860596	−	0.0252694i
$225$	961.275	+	1109.37i	0.284822	+	0.328702i
$226$	3044.04	+	893.810i	0.895957	+	0.263077i
$227$	1900.97	+	4162.55i	0.555823	+	1.21708i	0.954009	+	0.299778i	$0.0969128\pi$
$227$	1900.97	+	4162.55i	0.555823	+	1.21708i	−0.398185	+	0.917305i	$0.630360\pi$
$228$	9.95310	−	69.2253i	0.00289105	−	0.0201077i
$229$	−5060.79			−1.46038			−0.730188	−	0.683246i	$-0.760568\pi$
$229$	−5060.79			−1.46038			−0.730188	+	0.683246i	$0.760568\pi$
$230$	−6125.43	−	492.535i	−1.75608	−	0.141203i
$231$	487.041			0.138723
$232$	−60.7232	+	422.339i	−0.0171839	+	0.119517i
$233$	−1369.36	−	2998.47i	−0.385019	−	0.843075i	−0.998572	−	0.0534209i	$-0.982988\pi$
$233$	−1369.36	−	2998.47i	−0.385019	−	0.843075i	0.613553	−	0.789654i	$-0.289740\pi$
$234$	−202.745	−	59.5313i	−0.0566404	−	0.0166311i
$235$	2208.37	+	2548.60i	0.613014	+	0.707455i
$236$	−8.68597	+	2.55043i	−0.00239580	+	0.000703470i
$237$	4428.60	+	2846.09i	1.21379	+	0.780056i
$238$	−1141.00	+	2498.45i	−0.310757	+	0.680463i
$239$	3842.95	−	4435.00i	1.04008	−	1.20032i	0.0607300	−	0.998154i	$-0.480657\pi$
$239$	3842.95	−	4435.00i	1.04008	−	1.20032i	0.979352	−	0.202164i	$-0.0647974\pi$
$240$	−5000.18	+	3213.42i	−1.34483	+	0.864272i
$241$	214.785	+	1493.87i	0.0574089	+	0.399288i	0.998183	+	0.0602539i	$0.0191910\pi$
$241$	214.785	+	1493.87i	0.0574089	+	0.399288i	−0.940774	+	0.339034i	$0.889900\pi$
$242$	−465.641	−	3238.60i	−0.123688	−	0.860269i
$243$	−1524.77	+	979.911i	−0.402527	+	0.258689i
$244$	−326.370	+	376.651i	−0.0856299	+	0.0988222i
$245$	−378.975	+	829.840i	−0.0988239	+	0.216394i
$246$	−247.429	−	159.013i	−0.0641281	−	0.0412126i
$247$	−166.114	+	48.7754i	−0.0427917	+	0.0125648i
$248$	1421.06	+	1639.99i	0.363860	+	0.419917i
$249$	2607.36	+	765.590i	0.663593	+	0.194848i
$250$	2236.33	+	4896.88i	0.565751	+	1.23882i
$251$	−432.717	+	3009.61i	−0.108816	+	0.756833i	0.860221	+	0.509921i	$0.170325\pi$
$251$	−432.717	+	3009.61i	−0.108816	+	0.756833i	−0.969038	+	0.246913i	$0.920584\pi$
$252$	44.2356			0.0110579
$253$	−827.956	+	1484.94i	−0.205744	+	0.369002i
$254$	5005.17			1.23643
$255$	1568.36	−	10908.2i	0.385154	−	2.67881i
$256$	600.486	+	1314.88i	0.146603	+	0.321016i
$257$	−3431.13	−	1007.47i	−0.832794	−	0.244530i	−0.162577	−	0.986696i	$-0.551981\pi$
$257$	−3431.13	−	1007.47i	−0.832794	−	0.244530i	−0.670217	+	0.742165i	$0.733799\pi$
$258$	−3068.66	−	3541.42i	−0.740490	−	0.854571i
$259$	−166.060	+	48.7597i	−0.0398397	+	0.0116980i
$260$	−159.326	−	102.393i	−0.0380038	−	0.0244236i
$261$	−55.6815	+	121.925i	−0.0132054	+	0.0289157i
$262$	2047.76	−	2363.24i	0.482866	−	0.557257i
$263$	2481.49	−	1594.76i	0.581806	−	0.373904i	−0.216385	−	0.976308i	$-0.569427\pi$
$263$	2481.49	−	1594.76i	0.581806	−	0.373904i	0.798191	+	0.602404i	$0.205790\pi$
$264$	208.768	+	1452.01i	0.0486697	+	0.338505i
$265$	886.750	+	6167.48i	0.205557	+	1.42968i
$266$	286.138	−	183.889i	0.0659557	−	0.0423872i
$267$	−176.291	+	203.451i	−0.0404077	+	0.0466329i
$268$	−231.464	+	506.835i	−0.0527571	+	0.115522i
$269$	−3019.24	−	1940.35i	−0.684337	−	0.439796i	0.151732	−	0.988422i	$-0.451515\pi$
$269$	−3019.24	−	1940.35i	−0.684337	−	0.439796i	−0.836068	+	0.548625i	$0.815151\pi$
$270$	−8113.22	+	2382.26i	−1.82872	+	0.536961i
$271$	−4213.30	−	4862.41i	−0.944428	−	1.08993i	−0.995828	−	0.0912494i	$-0.970914\pi$
$271$	−4213.30	−	4862.41i	−0.944428	−	1.08993i	0.0514005	−	0.998678i	$-0.483632\pi$
$272$	−8898.05	−	2612.70i	−1.98354	−	0.582421i
$273$	139.950	+	306.448i	0.0310262	+	0.0679380i
$274$	−999.346	+	6950.61i	−0.220338	+	1.53249i
$275$	3416.07			0.749080
$276$	231.354	−	414.935i	0.0504561	−	0.0904933i
$277$	−6485.27			−1.40672			−0.703362	−	0.710832i	$-0.748319\pi$
$277$	−6485.27			−1.40672			−0.703362	+	0.710832i	$0.748319\pi$
$278$	879.722	−	6118.60i	0.189792	−	1.32003i
$279$	283.184	+	620.088i	0.0607664	+	0.133060i
$280$	−2636.45	−	774.131i	−0.562707	−	0.165226i
$281$	−1558.23	−	1798.30i	−0.330806	−	0.381770i	0.565843	−	0.824513i	$-0.308551\pi$
$281$	−1558.23	−	1798.30i	−0.330806	−	0.381770i	−0.896649	+	0.442743i	$0.854005\pi$
$282$	−2347.53	+	689.297i	−0.495721	+	0.145557i
$283$	6700.19	+	4305.95i	1.40737	+	0.904460i	0.999961	−	0.00878776i	$-0.00279727\pi$
$283$	6700.19	+	4305.95i	1.40737	+	0.904460i	0.407405	+	0.913247i	$0.366434\pi$
$284$	212.097	−	464.427i	0.0443156	−	0.0970376i
$285$	−893.691	+	1031.37i	−0.185746	+	0.214363i
$286$	−413.679	+	265.855i	−0.0855292	+	0.0549663i
$287$	−21.6917	−	150.869i	−0.00446140	−	0.0310297i
$288$	40.4905	+	281.617i	0.00828446	+	0.0576197i
$289$	10331.9	−	6639.88i	2.10296	−	1.35149i
$290$	−738.330	+	852.078i	−0.149504	+	0.172537i
$291$	3426.15	−	7502.23i	0.690188	−	1.51130i
$292$	181.955	+	116.936i	0.0364662	+	0.0234354i
$293$	−4533.58	+	1331.18i	−0.903940	+	0.265421i	−0.700488	−	0.713664i	$-0.747034\pi$
$293$	−4533.58	+	1331.18i	−0.903940	+	0.265421i	−0.203452	+	0.979085i	$0.565216\pi$
$294$	−433.435	−	500.211i	−0.0859811	−	0.0992275i
$295$	169.492	+	49.7673i	0.0334515	+	0.00982224i
$296$	−216.548	−	474.175i	−0.0425223	−	0.0931109i
$297$	−332.933	+	2315.60i	−0.0650463	+	0.452407i
$298$	−1963.52			−0.381690
$299$	−1172.24	−	94.2580i	−0.226731	−	0.0182310i
$300$	−954.547			−0.183703
$301$	345.596	−	2403.67i	0.0661789	−	0.460284i
$302$	2763.17	+	6050.50i	0.526499	+	1.15287i
$303$	7008.34	+	2057.83i	1.32877	+	0.390163i
$304$	752.048	+	867.910i	0.141885	+	0.163744i
$305$	9331.11	−	2739.86i	1.75180	−	0.514374i
$306$	−2186.27	−	1405.03i	−0.408434	−	0.262485i
$307$	1232.54	−	2698.88i	0.229136	−	0.501737i	−0.759786	−	0.650173i	$-0.774697\pi$
$307$	1232.54	−	2698.88i	0.229136	−	0.501737i	0.988922	+	0.148436i	$0.0474238\pi$
$308$	67.4139	−	77.7998i	0.0124716	−	0.0143930i
$309$	−4199.79	+	2699.04i	−0.773196	+	0.496903i
$310$	816.038	+	5675.67i	0.149509	+	1.03986i
$311$	−823.659	−	5728.67i	−0.150178	−	1.04451i	−0.915919	−	0.401363i	$-0.868537\pi$
$311$	−823.659	−	5728.67i	−0.150178	−	1.04451i	0.765741	−	0.643149i	$-0.222372\pi$
$312$	−853.623	+	548.590i	−0.154894	+	0.0995443i
$313$	4976.43	−	5743.11i	0.898673	−	1.03712i	−0.100437	−	0.994943i	$-0.532024\pi$
$313$	4976.43	−	5743.11i	0.898673	−	1.03712i	0.999110	−	0.0421802i	$-0.0134304\pi$
$314$	2366.49	−	5181.88i	0.425314	−	0.931307i
$315$	−726.154	−	466.671i	−0.129886	−	0.0834728i
$316$	1067.62	−	313.481i	0.190058	−	0.0558060i
$317$	−4226.38	−	4877.50i	−0.748824	−	0.864189i	0.245630	−	0.969364i	$-0.421005\pi$
$317$	−4226.38	−	4877.50i	−0.748824	−	0.864189i	−0.994454	+	0.105175i	$0.966460\pi$
$318$	−4337.50	−	1273.60i	−0.764889	−	0.224592i
$319$	129.581	+	283.742i	0.0227433	+	0.0498009i
$320$	1158.52	−	8057.66i	0.202385	−	1.40762i
$321$	7109.29			1.23614
$322$	2261.92	−	471.159i	0.391466	−	0.0815425i
$323$	−2129.28			−0.366800
$324$	68.7487	−	478.158i	0.0117882	−	0.0819886i
$325$	981.601	+	2149.41i	0.167537	+	0.366854i
$326$	43.7779	+	12.8544i	0.00743753	+	0.00218386i
$327$	−1934.04	−	2232.00i	−0.327072	−	0.377461i
$328$	440.488	−	129.339i	0.0741520	−	0.0217730i
$329$	−1066.63	−	685.484i	−0.178740	−	0.114869i
$330$	−1610.25	+	3525.96i	−0.268610	+	0.588175i
$331$	3775.40	−	4357.04i	0.626932	−	0.723519i	−0.350075	−	0.936721i	$-0.613844\pi$
$331$	3775.40	−	4357.04i	0.626932	−	0.723519i	0.977008	+	0.213203i	$0.0683895\pi$
$332$	483.193	−	310.529i	0.0798755	−	0.0513329i
$333$	−23.3049	−	162.089i	−0.00383514	−	0.0266740i
$334$	−315.998	−	2197.82i	−0.0517684	−	0.360057i
$335$	9146.57	−	5878.15i	1.49173	−	0.958679i
$336$	1463.43	−	1688.89i	0.237609	−	0.274216i
$337$	−2358.20	+	5163.74i	−0.381185	+	0.834679i	0.617651	+	0.786452i	$0.288084\pi$
$337$	−2358.20	+	5163.74i	−0.381185	+	0.834679i	−0.998836	+	0.0482269i	$0.984643\pi$
$338$	5244.40	+	3370.37i	0.843958	+	0.542379i
$339$	4592.04	−	1348.35i	0.735709	−	0.216024i
$340$	−1525.38	−	1760.39i	−0.243310	−	0.280795i
$341$	1522.15	+	446.944i	0.241728	+	0.0709776i
$342$	133.691	+	292.743i	0.0211380	+	0.0462858i
$343$	48.8140	−	339.509i	0.00768428	−	0.0534453i
$344$	7314.21			1.14638
$345$	−8175.25	+	4370.70i	−1.27577	+	0.682059i
$346$	3469.30			0.539048
$347$	160.269	−	1114.70i	0.0247946	−	0.172450i	−0.973661	−	0.227999i	$-0.926782\pi$
$347$	160.269	−	1114.70i	0.0247946	−	0.172450i	0.998456	+	0.0555489i	$0.0176909\pi$
$348$	−36.2084	−	79.2854i	−0.00557751	−	0.0122131i
$349$	−2106.88	−	618.635i	−0.323148	−	0.0948847i	0.116135	−	0.993233i	$-0.462949\pi$
$349$	−2106.88	−	618.635i	−0.323148	−	0.0948847i	−0.439283	+	0.898349i	$0.644768\pi$
$350$	−3040.09	−	3508.45i	−0.464284	−	0.535812i
$351$	−1552.65	+	455.900i	−0.236110	+	0.0693280i
$352$	557.004	+	357.965i	0.0843421	+	0.0542034i
$353$	−5388.09	+	11798.3i	−0.812406	+	1.77892i	−0.215701	+	0.976459i	$0.569204\pi$
$353$	−5388.09	+	11798.3i	−0.812406	+	1.77892i	−0.596704	+	0.802461i	$0.703524\pi$
$354$	−83.9270	+	96.8570i	−0.0126008	+	0.0145421i
$355$	−8381.26	+	5386.31i	−1.25304	+	0.805283i
$356$	8.09780	+	56.3214i	0.00120557	+	0.00838491i
$357$	589.672	+	4101.26i	0.0874195	+	0.608016i
$358$	7258.42	−	4664.71i	1.07156	−	0.688652i
$359$	−183.235	+	211.465i	−0.0269381	+	0.0310882i	−0.769059	−	0.639178i	$-0.779275\pi$
$359$	−183.235	+	211.465i	−0.0269381	+	0.0310882i	0.742121	+	0.670266i	$0.233820\pi$
$360$	1080.02	−	2364.92i	0.158117	−	0.346228i
$361$	−5548.34	−	3565.70i	−0.808913	−	0.519857i
$362$	−13820.1	+	4057.95i	−2.00654	+	0.589174i
$363$	−3232.25	−	3730.22i	−0.467354	−	0.539355i
$364$	68.3231	+	20.0615i	0.00983819	+	0.00288875i
$365$	−1753.28	−	3839.14i	−0.251427	−	0.550547i
$366$	−1004.13	+	6983.85i	−0.143406	+	0.997408i
$367$	−8670.89			−1.23329			−0.616644	−	0.787242i	$-0.711508\pi$
$367$	−8670.89			−1.23329			−0.616644	+	0.787242i	$0.711508\pi$
$368$	2661.48	+	7332.94i	0.377009	+	1.03874i
$369$	144.217			0.0203459
$370$	196.029	−	1363.41i	0.0275434	−	0.191569i
$371$	−973.192	−	2130.99i	−0.136188	−	0.298209i
$372$	−425.332	−	124.889i	−0.0592807	−	0.0174064i
$373$	−2336.89	−	2696.92i	−0.324396	−	0.374373i	0.570003	−	0.821642i	$-0.306942\pi$
$373$	−2336.89	−	2696.92i	−0.324396	−	0.374373i	−0.894399	+	0.447270i	$0.852396\pi$
$374$	−5802.94	+	1703.90i	−0.802307	+	0.235579i
$375$	6831.82	+	4390.54i	0.940783	+	0.604604i
$376$	1586.42	−	3473.78i	0.217589	−	0.476454i
$377$	−141.297	+	163.065i	−0.0193028	+	0.0222766i
$378$	2674.51	−	1718.80i	0.363920	−	0.233877i
$379$	−1708.88	−	11885.5i	−0.231607	−	1.61086i	−0.691153	−	0.722708i	$-0.742897\pi$
$379$	−1708.88	−	11885.5i	−0.231607	−	1.61086i	0.459546	−	0.888154i	$-0.348012\pi$
$380$	41.0510	+	285.516i	0.00554177	+	0.0385438i
$381$	6351.87	−	4082.10i	0.854111	−	0.548904i
$382$	−9163.73	+	10575.5i	−1.22737	+	1.41647i
$383$	2592.76	−	5677.34i	0.345910	−	0.757438i	−0.654089	−	0.756417i	$-0.726948\pi$
$383$	2592.76	−	5677.34i	0.345910	−	0.757438i	0.999999	−	0.00102051i	$-0.000324839\pi$
$384$	6273.51	+	4031.74i	0.833708	+	0.535792i
$385$	−1927.40	+	565.937i	−0.255142	+	0.0749164i
$386$	−209.493	−	241.768i	−0.0276241	−	0.0318799i
$387$	2204.62	+	647.335i	0.289579	+	0.0850281i
$388$	−724.172	−	1585.72i	−0.0947532	−	0.207481i
$389$	1724.07	−	11991.2i	0.224715	−	1.56292i	−0.495148	−	0.868808i	$-0.664886\pi$
$389$	1724.07	−	11991.2i	0.224715	−	1.56292i	0.719863	−	0.694116i	$-0.244205\pi$
$390$	−2681.25			−0.348129
$391$	−13506.8	−	5174.17i	−1.74698	−	0.669231i
$392$	1033.10			0.133111
$393$	671.329	−	4669.20i	0.0861681	−	0.599313i
$394$	1162.50	+	2545.51i	0.148644	+	0.325485i
$395$	−20832.7	−	6117.05i	−2.65369	−	0.779195i
$396$	63.7856	+	73.6125i	0.00809431	+	0.00934133i
$397$	−2601.89	+	763.985i	−0.328930	+	0.0965827i	−0.442028	−	0.897001i	$-0.645741\pi$
$397$	−2601.89	+	763.985i	−0.328930	+	0.0965827i	0.113098	+	0.993584i	$0.463923\pi$
$398$	−8617.67	−	5538.24i	−1.08534	−	0.697505i
$399$	213.150	−	466.734i	0.0267440	−	0.0585612i
$400$	10264.4	−	11845.8i	1.28305	−	1.48072i
$401$	−10852.3	+	6974.34i	−1.35146	+	0.868534i	−0.997765	−	0.0668254i	$-0.978713\pi$
$401$	−10852.3	+	6974.34i	−1.35146	+	0.868534i	−0.353700	+	0.935359i	$0.615077\pi$
$402$	1122.61	+	7807.91i	0.139280	+	0.968714i
$403$	156.168	+	1086.17i	0.0193034	+	0.134258i
$404$	1298.78	−	834.674i	0.159942	−	0.102789i
$405$	−6172.96	+	7123.98i	−0.757375	+	0.874058i
$406$	176.096	−	385.596i	0.0215258	−	0.0471350i
$407$	−320.592	−	206.032i	−0.0390446	−	0.0250924i
$408$	−11974.3	+	3515.98i	−1.45298	+	0.426634i
$409$	4476.59	+	5166.25i	0.541205	+	0.624584i	0.958811	−	0.284044i	$-0.0916762\pi$
$409$	4476.59	+	5166.25i	0.541205	+	0.624584i	−0.417606	+	0.908628i	$0.637131\pi$
$410$	1163.94	+	341.764i	0.140202	+	0.0411671i
$411$	4400.52	+	9635.80i	0.528131	+	1.15644i
$412$	−150.171	+	1044.46i	−0.0179573	+	0.124895i
$413$	−66.4159			−0.00791311
$414$	136.683	+	2181.85i	0.0162261	+	0.259014i
$415$	−11207.9			−1.32572
$416$	−65.1789	+	453.329i	−0.00768187	+	0.0534286i
$417$	−3873.77	−	8482.37i	−0.454914	−	0.996123i
$418$	718.607	+	211.002i	0.0840867	+	0.0246901i
$419$	7410.18	+	8551.81i	0.863988	+	0.997096i	0.999980	+	0.00638571i	$0.00203265\pi$
$419$	7410.18	+	8551.81i	0.863988	+	0.997096i	−0.135991	+	0.990710i	$0.543422\pi$
$420$	538.570	−	158.138i	0.0625703	−	0.0183723i
$421$	11601.9	+	7456.10i	1.34309	+	0.863155i	0.997175	−	0.0751095i	$-0.0239306\pi$
$421$	11601.9	+	7456.10i	1.34309	+	0.863155i	0.345920	+	0.938264i	$0.387567\pi$
$422$	−497.642	+	1089.68i	−0.0574048	+	0.125699i
$423$	785.616	−	906.650i	0.0903025	−	0.104215i
$424$	5935.97	−	3814.82i	0.679897	−	0.436943i
$425$	4135.92	+	28766.0i	0.472051	+	3.28319i
$426$	−1028.68	−	7154.60i	−0.116994	−	0.813712i
$427$	−3075.98	+	1976.81i	−0.348612	+	0.224039i
$428$	984.034	−	1135.64i	0.111133	−	0.128255i
$429$	−308.159	+	674.774i	−0.0346808	+	0.0759403i
$430$	16258.9	+	10449.0i	1.82343	+	1.17185i
$431$	−3910.27	+	1148.16i	−0.437010	+	0.128318i	−0.492835	−	0.870123i	$-0.664039\pi$
$431$	−3910.27	+	1148.16i	−0.437010	+	0.128318i	0.0558249	+	0.998441i	$0.482221\pi$
$432$	7029.34	+	8112.29i	0.782868	+	0.903478i
$433$	13074.5	+	3839.02i	1.45109	+	0.426077i	0.909901	−	0.414826i	$-0.136158\pi$
$433$	13074.5	+	3839.02i	1.45109	+	0.426077i	0.541185	+	0.840903i	$0.317976\pi$
$434$	−895.587	−	1961.06i	−0.0990542	−	0.216899i
$435$	−242.052	+	1683.51i	−0.0266793	+	0.185558i
$436$	−624.238			−0.0685679
$437$	1060.68	+	1443.31i	0.116108	+	0.157993i
$438$	3062.07			0.334044
$439$	−1094.97	+	7615.69i	−0.119044	+	0.827966i	0.839569	+	0.543253i	$0.182807\pi$
$439$	−1094.97	+	7615.69i	−0.119044	+	0.827966i	−0.958613	+	0.284713i	$0.908102\pi$
$440$	−2513.40	−	5503.58i	−0.272322	−	0.596302i
$441$	311.393	+	91.4333i	0.0336241	+	0.00987294i
$442$	−2739.56	−	3161.62i	−0.294813	−	0.340233i
$443$	10657.6	−	3129.36i	1.14302	−	0.335621i	0.345208	−	0.938526i	$-0.387808\pi$
$443$	10657.6	−	3129.36i	1.14302	−	0.335621i	0.797813	+	0.602905i	$0.205990\pi$
$444$	89.5824	+	57.5711i	0.00957520	+	0.00615361i
$445$	461.242	−	1009.98i	0.0491348	−	0.107590i
$446$	9985.63	−	11524.0i	1.06016	−	1.22349i
$447$	−2491.83	+	1601.40i	−0.263667	+	0.169449i
$448$	435.580	+	3029.52i	0.0459357	+	0.319490i
$449$	−528.053	−	3672.69i	−0.0555020	−	0.386025i	−0.998572	−	0.0534294i	$-0.982985\pi$
$449$	−528.053	−	3672.69i	−0.0555020	−	0.386025i	0.943070	−	0.332595i	$-0.107924\pi$
$450$	3695.19	−	2374.76i	0.387096	−	0.248771i
$451$	219.783	−	253.643i	0.0229472	−	0.0264825i
$452$	420.224	−	920.163i	0.0437294	−	0.0957540i
$453$	8441.28	+	5424.88i	0.875510	+	0.562656i
$454$	13138.5	−	3857.82i	1.35820	−	0.398803i
$455$	−909.924	−	1050.11i	−0.0937536	−	0.108197i
$456$	1482.84	+	435.401i	0.152281	+	0.0447139i
$457$	−5506.66	−	12057.9i	−0.563656	−	1.23423i	−0.950107	−	0.311924i	$-0.899026\pi$
$457$	−5506.66	−	12057.9i	−0.563656	−	1.23423i	0.386451	−	0.922310i	$-0.373701\pi$
$458$	−2155.16	+	14989.5i	−0.219878	+	1.52928i
$459$	−19902.2			−2.02387
$460$	−433.405	+	1910.88i	−0.0439296	+	0.193686i
$461$	6476.37			0.654305			0.327152	−	0.944972i	$-0.393911\pi$
$461$	6476.37			0.654305			0.327152	+	0.944972i	$0.393911\pi$
$462$	207.409	−	1442.56i	0.0208864	−	0.145268i
$463$	−1835.21	−	4018.55i	−0.184210	−	0.403365i	0.794887	−	0.606758i	$-0.207530\pi$
$463$	−1835.21	−	4018.55i	−0.184210	−	0.403365i	−0.979097	+	0.203393i	$0.934803\pi$
$464$	1373.28	+	403.230i	0.137398	+	0.0403437i
$465$	5664.55	+	6537.23i	0.564918	+	0.651950i
$466$	−9464.27	+	2778.96i	−0.940824	+	0.276251i
$467$	15554.7	+	9996.40i	1.54130	+	0.990532i	0.987453	+	0.157911i	$0.0504759\pi$
$467$	15554.7	+	9996.40i	1.54130	+	0.990532i	0.553844	+	0.832621i	$0.313160\pi$
$468$	−27.9886	+	61.2865i	−0.00276447	+	0.00605335i
$469$	−2676.98	+	3089.41i	−0.263564	+	0.304169i
$470$	8489.09	−	5455.61i	0.833133	−	0.535422i
$471$	−1223.00	−	8506.18i	−0.119646	−	0.832153i
$472$	−28.4689	−	198.006i	−0.00277625	−	0.0193092i
$473$	4498.29	−	2890.88i	0.437276	−	0.281020i
$474$	10315.7	−	11905.0i	0.999614	−	1.15362i
$475$	1495.02	−	3273.64i	0.144413	−	0.316221i
$476$	736.753	+	473.483i	0.0709434	+	0.0455925i
$477$	2126.82	−	624.492i	0.204152	−	0.0599445i
$478$	−11499.4	−	13271.0i	−1.10036	−	1.26988i
$479$	1689.44	+	496.065i	0.161154	+	0.0473190i	0.361314	−	0.932444i	$-0.382328\pi$
$479$	1689.44	+	496.065i	0.161154	+	0.0473190i	−0.200161	+	0.979763i	$0.564146\pi$
$480$	1499.73	+	3283.96i	0.142611	+	0.312274i
$481$	37.5147	−	260.920i	0.00355618	−	0.0247338i
$482$	4516.13			0.426772
$483$	2486.26	−	2442.70i	0.234221	−	0.230118i
$484$	−1043.26			−0.0979769
$485$	−4841.05	+	33670.3i	−0.453239	+	3.15235i
$486$	2253.05	+	4933.50i	0.210289	+	0.460469i
$487$	17233.4	+	5060.18i	1.60353	+	0.470839i	0.956526	−	0.291646i	$-0.0942029\pi$
$487$	17233.4	+	5060.18i	1.60353	+	0.470839i	0.647006	+	0.762485i	$0.276021\pi$
$488$	−7211.98	−	8323.07i	−0.668998	−	0.772065i
$489$	66.0407	−	19.3913i	0.00610728	−	0.00179326i
$490$	2296.50	+	1475.87i	0.211725	+	0.136068i
$491$	1490.69	−	3264.15i	0.137014	−	0.300018i	−0.828671	−	0.559736i	$-0.810902\pi$
$491$	1490.69	−	3264.15i	0.137014	−	0.300018i	0.965684	+	0.259718i	$0.0836296\pi$
$492$	−61.4135	+	70.8750i	−0.00562751	+	0.00649450i
$493$	−2232.44	+	1434.70i	−0.203943	+	0.131066i
$494$	73.7268	+	512.781i	0.00671483	+	0.0467026i
$495$	−270.492	−	1881.31i	−0.0245610	−	0.170826i
$496$	6123.52	−	3935.35i	0.554343	−	0.356255i
$497$	2452.99	−	2830.91i	0.221392	−	0.255500i
$498$	3377.95	−	7396.67i	0.303955	−	0.665568i
$499$	6572.57	+	4223.93i	0.589636	+	0.378936i	0.801172	−	0.598434i	$-0.204210\pi$
$499$	6572.57	+	4223.93i	0.589636	+	0.378936i	−0.211536	+	0.977370i	$0.567846\pi$
$500$	1646.97	−	483.594i	0.147310	−	0.0432540i
$501$	−2193.51	−	2531.45i	−0.195606	−	0.225742i
$502$	8729.86	+	2563.32i	0.776161	+	0.227901i
$503$	−2423.86	−	5307.52i	−0.214860	−	0.470478i	0.771258	−	0.636523i	$-0.219628\pi$
$503$	−2423.86	−	5307.52i	−0.214860	−	0.470478i	−0.986118	+	0.166044i	$0.946901\pi$
$504$	−139.113	+	967.549i	−0.0122948	+	0.0855120i
$505$	−30125.8			−2.65461
$506$	4045.64	+	3084.68i	0.355436	+	0.271010i
$507$	9404.27			0.823784
$508$	227.122	−	1579.67i	0.0198365	−	0.137966i
$509$	−3283.82	−	7190.56i	−0.285958	−	0.626161i	0.711077	−	0.703115i	$-0.248208\pi$
$509$	−3283.82	−	7190.56i	−0.285958	−	0.626161i	−0.997035	+	0.0769537i	$0.975481\pi$
$510$	−31640.9	−	9290.59i	−2.74722	−	0.806656i
$511$	1039.16	+	1199.26i	0.0899604	+	0.103820i
$512$	−8530.60	+	2504.81i	−0.736334	+	0.216207i
$513$	2073.35	+	1332.46i	0.178442	+	0.114678i
$514$	−4445.18	+	9733.58i	−0.381456	+	0.835272i
$515$	13483.9	−	15561.2i	1.15373	−	1.33147i
$516$	−1256.95	+	807.792i	−0.107237	+	0.0689168i
$517$	−397.320	−	2763.42i	−0.0337991	−	0.235078i
$518$	73.7030	+	512.616i	0.00625159	+	0.0434808i
$519$	4402.76	−	2829.48i	0.372369	−	0.239307i
$520$	2740.65	−	3162.88i	0.231126	−	0.266734i
$521$	−6324.49	+	13848.7i	−0.531825	+	1.16453i	0.432940	+	0.901423i	$0.357476\pi$
$521$	−6324.49	+	13848.7i	−0.531825	+	1.16453i	−0.964765	+	0.263112i	$0.915251\pi$
$522$	337.417	+	216.845i	0.0282919	+	0.0181821i
$523$	18493.6	−	5430.22i	1.54622	−	0.454010i	0.606248	−	0.795275i	$-0.292674\pi$
$523$	18493.6	−	5430.22i	1.54622	−	0.454010i	0.939967	+	0.341266i	$0.110856\pi$
$524$	−652.934	−	753.526i	−0.0544343	−	0.0628205i
$525$	−6719.46	−	1973.01i	−0.558593	−	0.164018i
$526$	−3666.73	−	8029.02i	−0.303949	−	0.665555i
$527$	−1920.71	+	13358.8i	−0.158761	+	1.10421i
$528$	4920.69			0.405578
$529$	3221.01	+	11732.9i	0.264734	+	0.964322i
$530$	18645.0			1.52809
$531$	8.94325	−	62.2017i	0.000730893	−	0.00508347i
$532$	−45.0527	−	98.6517i	−0.00367159	−	0.00803965i
$533$	222.747	+	65.4045i	0.0181018	+	0.00531517i
$534$	527.524	+	608.795i	0.0427494	+	0.0493355i
$535$	−28134.1	+	8260.93i	−2.27354	+	0.667572i
$536$	−10357.9	−	6656.63i	−0.834690	−	0.536423i
$537$	5406.97	−	11839.6i	0.434502	−	0.951428i
$538$	−7032.85	+	8116.35i	−0.563583	+	0.650410i
$539$	635.364	−	408.324i	0.0507738	−	0.0326303i
$540$	383.701	+	2668.70i	0.0305775	+	0.212671i
$541$	−2867.29	−	19942.4i	−0.227864	−	1.58483i	−0.707082	−	0.707132i	$-0.749989\pi$
$541$	−2867.29	−	19942.4i	−0.227864	−	1.58483i	0.479218	−	0.877696i	$-0.340920\pi$
$542$	−16196.2	+	10408.6i	−1.28355	+	0.824888i
$543$	−14229.0	+	16421.1i	−1.12454	+	1.29779i
$544$	−2339.96	+	5123.80i	−0.184421	+	0.403825i
$545$	10247.3	+	6585.51i	0.805402	+	0.517601i
$546$	967.262	−	284.014i	0.0758150	−	0.0222613i
$547$	415.839	+	479.904i	0.0325046	+	0.0375123i	0.771769	−	0.635903i	$-0.219372\pi$
$547$	415.839	+	479.904i	0.0325046	+	0.0375123i	−0.739265	+	0.673415i	$0.764827\pi$
$548$	2148.32	+	630.803i	0.167466	+	0.0491726i
$549$	−1437.18	−	3146.99i	−0.111726	−	0.244646i
$550$	1454.75	−	10118.0i	0.112783	−	0.784425i
$551$	328.621			0.0254079
$552$	8348.15	+	6365.22i	0.643698	+	0.490800i
$553$	8163.38			0.627744
$554$	−2761.79	+	19208.6i	−0.211800	+	1.47310i
$555$	−863.193	−	1890.13i	−0.0660190	−	0.144561i
$556$	−1891.16	−	555.295i	−0.144250	−	0.0423556i
$557$	−1534.92	−	1771.39i	−0.116762	−	0.134751i	0.694359	−	0.719628i	$-0.255688\pi$
$557$	−1534.92	−	1771.39i	−0.116762	−	0.134751i	−0.811121	+	0.584878i	$0.801142\pi$
$558$	1957.22	−	574.693i	0.148487	−	0.0435998i
$559$	3111.52	+	1999.65i	0.235426	+	0.151299i
$560$	−3828.87	+	8384.07i	−0.288928	+	0.632663i
$561$	−5974.63	+	6895.09i	−0.449642	+	0.518915i
$562$	−5989.94	+	3849.50i	−0.449591	+	0.288935i
$563$	−869.260	−	6045.84i	−0.0650710	−	0.452578i	−0.996143	−	0.0877434i	$-0.972034\pi$
$563$	−869.260	−	6045.84i	−0.0650710	−	0.452578i	0.931072	−	0.364835i	$-0.118875\pi$
$564$	111.022	+	772.177i	0.00828880	+	0.0576499i
$565$	−16605.7	+	10671.8i	−1.23647	+	0.794631i
$566$	15607.0	−	18011.5i	1.15903	−	1.33760i
$567$	1472.29	−	3223.86i	0.109048	−	0.238782i
$568$	9491.25	+	6099.65i	0.701133	+	0.450591i
$569$	6775.08	−	1989.34i	0.499167	−	0.146569i	−0.0224508	−	0.999748i	$-0.507147\pi$
$569$	6775.08	−	1989.34i	0.499167	−	0.146569i	0.521618	+	0.853179i	$0.325329\pi$
$570$	2674.23	+	3086.23i	0.196511	+	0.226786i
$571$	−14243.4	−	4182.24i	−1.04390	−	0.306517i	−0.285550	−	0.958364i	$-0.592176\pi$
$571$	−14243.4	−	4182.24i	−1.04390	−	0.306517i	−0.758351	+	0.651847i	$0.773994\pi$
$572$	65.1343	+	142.624i	0.00476119	+	0.0104256i
$573$	−3004.20	+	20894.7i	−0.219027	+	1.52337i
$574$	−456.094			−0.0331655
$575$	17438.4	−	17133.0i	1.26475	−	1.24260i
$576$	−2895.95			−0.209487
$577$	242.434	−	1686.17i	0.0174916	−	0.121657i	−0.979205	−	0.202874i	$-0.934972\pi$
$577$	242.434	−	1686.17i	0.0174916	−	0.121657i	0.996696	+	0.0812174i	$0.0258808\pi$
$578$	−15266.7	−	33429.4i	−1.09864	−	2.40568i
$579$	−463.039	−	135.961i	−0.0332353	−	0.00975878i
$580$	235.419	+	271.688i	0.0168539	+	0.0194504i
$581$	4043.26	−	1187.21i	0.288714	−	0.0847740i
$582$	−20761.7	−	13342.7i	−1.47869	−	0.950299i
$583$	2142.89	−	4692.28i	0.152229	−	0.333335i
$584$	−3129.91	+	3612.10i	−0.221775	+	0.255942i
$585$	1106.00	−	710.785i	0.0781668	−	0.0502348i
$586$	2012.15	+	13994.8i	0.141845	+	0.986555i
$587$	−1845.19	−	12833.6i	−0.129743	−	0.902383i	−0.945878	−	0.324522i	$-0.894797\pi$
$587$	−1845.19	−	12833.6i	−0.129743	−	0.902383i	0.816135	−	0.577861i	$-0.196113\pi$
$588$	−177.539	+	114.097i	−0.0124516	+	0.00800219i
$589$	1094.47	−	1263.08i	0.0765650	−	0.0883607i
$590$	219.584	−	480.821i	0.0153222	−	0.0335510i
$591$	3551.34	+	2282.31i	0.247179	+	0.158852i
$592$	−1677.74	+	492.630i	−0.116478	+	0.0342010i
$593$	2554.61	+	2948.18i	0.176906	+	0.204160i	0.837277	−	0.546779i	$-0.184146\pi$
$593$	2554.61	+	2948.18i	0.176906	+	0.204160i	−0.660371	+	0.750940i	$0.729601\pi$
$594$	6716.77	+	1972.22i	0.463960	+	0.136231i
$595$	−7099.17	−	15545.0i	−0.489139	−	1.07107i
$596$	−89.0997	+	619.702i	−0.00612360	+	0.0425906i
$597$	−15453.2			−1.05939
$598$	−778.387	+	3431.91i	−0.0532284	+	0.234684i
$599$	−6628.35			−0.452132			−0.226066	−	0.974112i	$-0.572586\pi$
$599$	−6628.35			−0.452132			−0.226066	+	0.974112i	$0.572586\pi$
$600$	3001.87	−	20878.5i	0.204251	−	1.42060i
$601$	5545.51	+	12143.0i	0.376383	+	0.824164i	0.999129	+	0.0417395i	$0.0132899\pi$
$601$	5545.51	+	12143.0i	0.376383	+	0.824164i	−0.622745	+	0.782424i	$0.713983\pi$
$602$	−6972.24	−	2047.23i	−0.472038	−	0.138603i
$603$	−2532.91	−	2923.13i	−0.171058	−	0.197411i
$604$	2034.97	−	597.522i	0.137089	−	0.0402530i
$605$	17125.7	+	11006.0i	1.15084	+	0.739601i
$606$	9079.60	−	19881.5i	0.608636	−	1.33273i
$607$	−7393.50	+	8532.56i	−0.494387	+	0.570553i	−0.947033	−	0.321137i	$-0.895935\pi$
$607$	−7393.50	+	8532.56i	−0.494387	+	0.570553i	0.452646	+	0.891691i	$0.350480\pi$
$608$	586.809	−	377.119i	0.0391419	−	0.0251549i
$609$	−91.0067	−	632.965i	−0.00605546	−	0.0421167i
$610$	−4141.46	−	28804.5i	−0.274890	−	1.91190i
$611$	1624.58	−	1044.06i	0.107567	−	0.0691294i
$612$	−542.647	+	626.248i	−0.0358418	+	0.0413637i
$613$	9922.98	−	21728.3i	0.653809	−	1.43164i	−0.234371	−	0.972147i	$-0.575303\pi$
$613$	9922.98	−	21728.3i	0.653809	−	1.43164i	0.888180	−	0.459496i	$-0.151970\pi$
$614$	−7468.89	−	4799.97i	−0.490912	−	0.315490i
$615$	1755.85	−	515.564i	0.115126	−	0.0338041i
$616$	1489.68	+	1719.19i	0.0974367	+	0.112448i
$617$	−9712.92	−	2851.97i	−0.633756	−	0.186088i	−0.0509531	−	0.998701i	$-0.516226\pi$
$617$	−9712.92	−	2851.97i	−0.633756	−	0.186088i	−0.582803	+	0.812613i	$0.698044\pi$
$618$	6205.75	+	13588.7i	0.403935	+	0.884494i
$619$	1543.12	−	10732.6i	0.100199	−	0.696898i	−0.876362	−	0.481654i	$-0.840036\pi$
$619$	1543.12	−	10732.6i	0.100199	−	0.696898i	0.976560	−	0.215244i	$-0.0690547\pi$
$620$	1828.32			0.118430
$621$	9914.10	+	13490.5i	0.640643	+	0.871749i
$622$	−17318.4			−1.11641
$623$	−59.4104	+	413.208i	−0.00382059	+	0.0265728i
$624$	1413.95	+	3096.11i	0.0907102	+	0.198628i
$625$	−5556.34	−	1631.49i	−0.355606	−	0.104415i
$626$	−14891.2	−	17185.4i	−0.950754	−	1.09723i
$627$	1084.05	−	318.305i	0.0690472	−	0.0202741i
$628$	−1528.06	−	982.023i	−0.0970957	−	0.0623996i
$629$	1346.80	−	2949.08i	0.0853742	−	0.186944i
$630$	−1691.46	+	1952.05i	−0.106967	+	0.123447i
$631$	−15977.1	+	10267.8i	−1.00798	+	0.647792i	−0.936871	−	0.349676i	$-0.886292\pi$
$631$	−15977.1	+	10267.8i	−1.00798	+	0.647792i	−0.0711132	+	0.997468i	$0.522655\pi$
$632$	3499.20	+	24337.5i	0.220239	+	1.53179i
$633$	257.182	+	1788.74i	0.0161486	+	0.112316i
$634$	−16246.4	+	10441.0i	−1.01771	+	0.654043i
$635$	−20393.4	+	23535.2i	−1.27447	+	1.47081i
$636$	−598.784	+	1311.15i	−0.0373323	+	0.0817463i
$637$	439.489	+	282.443i	0.0273363	+	0.0175679i
$638$	895.593	−	262.970i	0.0555750	−	0.0163183i
$639$	2320.97	+	2678.54i	0.143687	+	0.165824i
$640$	−29511.5	−	8665.35i	−1.82272	−	0.535200i
$641$	8730.39	+	19116.9i	0.537956	+	1.17796i	0.962183	+	0.272403i	$0.0878185\pi$
$641$	8730.39	+	19116.9i	0.537956	+	1.17796i	−0.424227	+	0.905556i	$0.639454\pi$
$642$	3027.53	−	21056.9i	0.186117	−	1.29447i
$643$	13049.2			0.800324			0.400162	−	0.916444i	$-0.368954\pi$
$643$	13049.2			0.800324			0.400162	+	0.916444i	$0.368954\pi$
$644$	−46.0610	−	735.261i	−0.00281841	−	0.0449897i
$645$	29155.5			1.77984
$646$	−906.765	+	6306.69i	−0.0552263	+	0.384107i
$647$	−1407.58	−	3082.18i	−0.0855298	−	0.187284i	0.862034	−	0.506850i	$-0.169190\pi$
$647$	−1407.58	−	3082.18i	−0.0855298	−	0.187284i	−0.947564	+	0.319566i	$0.896463\pi$
$648$	10242.4	+	3007.43i	0.620923	+	0.182320i
$649$	−95.7686	−	110.523i	−0.00579236	−	0.00668475i
$650$	6784.31	−	1992.05i	0.409389	−	0.120207i
$651$	−2735.95	−	1758.29i	−0.164716	−	0.105857i
$652$	6.04348	−	13.2334i	0.000363007	−	0.000794875i
$653$	−5888.82	+	6796.06i	−0.352906	+	0.407275i	−0.904250	−	0.427003i	$-0.859569\pi$
$653$	−5888.82	+	6796.06i	−0.352906	+	0.407275i	0.551345	+	0.834278i	$0.314115\pi$
$654$	−7434.54	+	4777.89i	−0.444516	+	0.285673i
$655$	2768.86	+	19257.8i	0.165173	+	1.14880i
$656$	−219.156	−	1524.26i	−0.0130436	−	0.0907203i
$657$	−1263.09	+	811.738i	−0.0750042	+	0.0482023i
$658$	−2484.56	+	2867.33i	−0.147201	+	0.169879i
$659$	719.159	−	1574.74i	0.0425106	−	0.0930852i	−0.887185	−	0.461413i	$-0.847342\pi$
$659$	719.159	−	1574.74i	0.0425106	−	0.0930852i	0.929696	+	0.368328i	$0.120070\pi$
$660$	1039.75	+	668.207i	0.0613216	+	0.0394090i
$661$	21656.3	−	6358.86i	1.27433	−	0.374177i	0.426521	−	0.904478i	$-0.359739\pi$
$661$	21656.3	−	6358.86i	1.27433	−	0.374177i	0.847810	+	0.530301i	$0.177921\pi$
$662$	−11297.3	−	13037.8i	−0.663265	−	0.765449i
$663$	−6055.21	−	1777.97i	−0.354698	−	0.104149i
$664$	5272.55	+	11545.3i	0.308154	+	0.674764i
$665$	−301.175	+	2094.72i	−0.0175625	+	0.122150i
$666$	−490.014			−0.0285100
$667$	2084.56	+	798.553i	0.121011	+	0.0463569i
$668$	−707.987			−0.0410073
$669$	3273.65	−	22768.8i	0.189188	−	1.31583i
$670$	−13515.3	−	29594.3i	−0.779315	−	1.70646i
$671$	−7725.04	−	2268.28i	−0.444444	−	0.130500i
$672$	−888.886	−	1025.83i	−0.0510261	−	0.0588872i
$673$	−20191.2	+	5928.67i	−1.15648	+	0.339574i	−0.803065	−	0.595891i	$-0.796799\pi$
$673$	−20191.2	+	5928.67i	−1.15648	+	0.339574i	−0.353418	+	0.935465i	$0.614981\pi$
$674$	14290.2	+	9183.72i	0.816671	+	0.524843i
$675$	13973.9	−	30598.5i	0.796821	−	1.74480i
$676$	1301.69	−	1502.24i	0.0740609	−	0.0854709i
$677$	−17274.7	+	11101.8i	−0.980683	+	0.630247i	−0.929648	−	0.368450i	$-0.879889\pi$
$677$	−17274.7	+	11101.8i	−0.980683	+	0.630247i	−0.0510357	+	0.998697i	$0.516252\pi$
$678$	−2038.10	−	14175.3i	−0.115447	−	0.802949i
$679$	−1820.14	−	12659.4i	−0.102873	−	0.715496i
$680$	43301.3	−	27828.1i	2.44196	−	1.56935i
$681$	13527.3	−	15611.3i	0.761183	−	0.878452i
$682$	1972.01	−	4318.10i	0.110722	−	0.242447i
$683$	13983.9	+	8986.93i	0.783427	+	0.503478i	0.870169	−	0.492753i	$-0.164009\pi$
$683$	13983.9	+	8986.93i	0.783427	+	0.503478i	−0.0867426	+	0.996231i	$0.527646\pi$
$684$	98.4587	−	28.9101i	0.00550389	−	0.00161609i
$685$	−28611.2	−	33019.1i	−1.59588	−	1.84174i
$686$	−984.798	−	289.163i	−0.0548102	−	0.0160937i
$687$	9490.03	+	20780.3i	0.527027	+	1.15403i
$688$	3491.64	−	24284.9i	0.193485	−	1.34572i
$689$	3568.15			0.197294
$690$	9464.04	+	26075.4i	0.522159	+	1.43866i
$691$	−15957.7			−0.878521			−0.439261	−	0.898360i	$-0.644759\pi$
$691$	−15957.7			−0.878521			−0.439261	+	0.898360i	$0.644759\pi$
$692$	157.428	−	1094.94i	0.00864816	−	0.0601493i
$693$	296.860	+	650.032i	0.0162724	+	0.0356316i
$694$	−3233.36	−	949.399i	−0.176854	−	0.0519290i
$695$	25186.4	+	29066.6i	1.37464	+	1.58642i
$696$	1848.05	−	542.636i	0.100647	−	0.0295525i
$697$	2401.97	+	1543.65i	0.130532	+	0.0838880i
$698$	−2729.55	+	5976.88i	−0.148016	+	0.324109i
$699$	−9744.30	+	11245.5i	−0.527272	+	0.608504i
$700$	−1245.24	+	800.270i	−0.0672369	+	0.0432105i
$701$	−2433.85	−	16927.8i	−0.131135	−	0.912062i	−0.944079	−	0.329720i	$-0.893046\pi$
$701$	−2433.85	−	16927.8i	−0.131135	−	0.912062i	0.812944	−	0.582342i	$-0.197863\pi$
$702$	689.119	+	4792.93i	0.0370500	+	0.257688i
$703$	−337.747	+	217.057i	−0.0181200	+	0.0116450i
$704$	−4413.35	+	5093.28i	−0.236270	+	0.272671i
$705$	6323.72	−	13847.0i	0.337823	−	0.739729i
$706$	32650.6	+	20983.3i	1.74054	+	1.11858i
$707$	10867.9	−	3191.10i	0.578118	−	0.169751i
$708$	26.7604	+	30.8832i	0.00142051	+	0.00163935i
$709$	18813.7	+	5524.21i	0.996565	+	0.292618i	0.739046	−	0.673655i	$-0.235277\pi$
$709$	18813.7	+	5524.21i	0.996565	+	0.292618i	0.257519	+	0.966273i	$0.417095\pi$
$710$	12384.4	+	27118.1i	0.654619	+	1.43341i
$711$	−1099.24	+	7645.40i	−0.0579814	+	0.403270i
$712$	−1257.36			−0.0661822
$713$	10011.9	−	5352.62i	0.525875	−	0.281146i
$714$	12398.6			0.649867
$715$	435.420	−	3028.41i	0.0227745	−	0.158400i
$716$	−1142.85	−	2502.49i	−0.0596512	−	0.130618i
$717$	−25417.0	−	7463.11i	−1.32387	−	0.388724i
$718$	548.302	+	632.775i	0.0284992	+	0.0328899i
$719$	17109.8	−	5023.88i	0.887463	−	0.260583i	0.193937	−	0.981014i	$-0.437874\pi$
$719$	17109.8	−	5023.88i	0.887463	−	0.260583i	0.693526	+	0.720431i	$0.256056\pi$
$720$	−7336.50	−	4714.88i	−0.379744	−	0.244046i
$721$	−3215.98	+	7042.02i	−0.166116	+	0.363743i
$722$	−12924.0	+	14915.1i	−0.666178	+	0.768811i
$723$	5731.25	−	3683.25i	0.294810	−	0.189463i
$724$	653.598	+	4545.87i	0.0335508	+	0.233351i
$725$	−638.315	−	4439.58i	−0.0326985	−	0.227423i
$726$	−12425.0	+	7985.04i	−0.635170	+	0.408199i
$727$	7077.01	−	8167.30i	0.361034	−	0.416656i	−0.545952	−	0.837817i	$-0.683832\pi$
$727$	7077.01	−	8167.30i	0.361034	−	0.416656i	0.906986	+	0.421161i	$0.138377\pi$
$728$	−653.660	+	1431.32i	−0.0332778	+	0.0728683i
$729$	18383.0	+	11814.1i	0.933955	+	0.600217i
$730$	−12117.7	+	3558.09i	−0.614380	+	0.180398i
$731$	29789.6	+	34379.0i	1.50726	+	1.73947i
$732$	2158.59	+	633.820i	0.108994	+	0.0320036i
$733$	−13568.4	−	29710.7i	−0.683713	−	1.49712i	−0.858661	−	0.512544i	$-0.828703\pi$
$733$	−13568.4	−	29710.7i	−0.683713	−	1.49712i	0.174948	−	0.984578i	$-0.444024\pi$
$734$	−3692.54	+	25682.2i	−0.185687	+	1.29148i
$735$	4118.09			0.206664
$736$	4638.74	−	966.251i	0.232318	−	0.0483920i
$737$	−9001.17			−0.449881
$738$	61.4155	−	427.154i	0.00306333	−	0.0213059i
$739$	−5009.96	−	10970.3i	−0.249384	−	0.546074i	0.742996	−	0.669296i	$-0.233404\pi$
$739$	−5009.96	−	10970.3i	−0.249384	−	0.546074i	−0.992379	+	0.123223i	$0.960677\pi$
$740$	−421.408	−	123.737i	−0.0209341	−	0.00614682i
$741$	511.776	+	590.621i	0.0253719	+	0.0292807i
$742$	−6726.20	+	1974.99i	−0.332785	+	0.0977145i
$743$	8390.39	+	5392.17i	0.414285	+	0.266245i	0.731137	−	0.682230i	$-0.238990\pi$
$743$	8390.39	+	5392.17i	0.414285	+	0.266245i	−0.316853	+	0.948475i	$0.602626\pi$
$744$	4069.23	−	8910.37i	0.200518	−	0.439073i
$745$	8000.28	−	9232.81i	0.393433	−	0.454046i
$746$	−8983.13	+	5773.11i	−0.440879	+	0.283336i
$747$	567.431	+	3946.57i	0.0277928	+	0.193303i
$748$	274.440	+	1908.77i	0.0134151	+	0.0933043i
$749$	9274.36	−	5960.27i	0.452440	−	0.290766i
$750$	15913.6	−	18365.3i	0.774779	−	0.894143i
$751$	−3085.40	+	6756.07i	−0.149917	+	0.328273i	−0.969659	−	0.244460i	$-0.921389\pi$
$751$	−3085.40	+	6756.07i	−0.149917	+	0.328273i	0.819742	+	0.572732i	$0.194117\pi$
$752$	−10776.4	−	6925.60i	−0.522575	−	0.335839i
$753$	13169.3	−	3866.86i	0.637339	−	0.187140i
$754$	422.808	+	487.946i	0.0204214	+	0.0235676i
$755$	−39709.0	−	11659.6i	−1.91412	−	0.562035i
$756$	−421.104	−	922.090i	−0.0202585	−	0.0443599i
$757$	−2075.61	+	14436.2i	−0.0996558	+	0.693121i	0.877341	+	0.479867i	$0.159315\pi$
$757$	−2075.61	+	14436.2i	−0.0996558	+	0.693121i	−0.976997	+	0.213254i	$0.931594\pi$
$758$	−35931.2			−1.72174
$759$	7649.97	+	615.121i	0.365845	+	0.0294170i
$760$	−6374.08			−0.304227
$761$	−5092.13	+	35416.5i	−0.242562	+	1.68705i	0.396607	+	0.917988i	$0.370188\pi$
$761$	−5092.13	+	35416.5i	−0.242562	+	1.68705i	−0.639169	+	0.769066i	$0.720722\pi$
$762$	−9385.74	−	20551.9i	−0.446206	−	0.977056i
$763$	−4394.28	−	1290.28i	−0.208498	−	0.0612204i
$764$	2921.89	+	3372.04i	0.138364	+	0.159681i
$765$	15514.6	−	4555.50i	0.733244	−	0.215300i
$766$	−15711.5	−	10097.2i	−0.741096	−	0.476274i
$767$	42.0225	−	92.0164i	0.00197828	−	0.00433184i
$768$	4273.04	−	4931.35i	0.200768	−	0.231699i
$769$	−3081.33	+	1980.25i	−0.144494	+	0.0928603i	−0.610890	−	0.791715i	$-0.709188\pi$
$769$	−3081.33	+	1980.25i	−0.144494	+	0.0928603i	0.466397	+	0.884576i	$0.345552\pi$
$770$	855.445	+	5949.75i	0.0400365	+	0.278460i
$771$	2297.28	+	15977.9i	0.107308	+	0.746343i
$772$	−85.8100	+	55.1467i	−0.00400048	+	0.00257095i
$773$	9325.74	−	10762.5i	0.433924	−	0.500775i	−0.496104	−	0.868263i	$-0.665237\pi$
$773$	9325.74	−	10762.5i	0.433924	−	0.500775i	0.930028	+	0.367488i	$0.119782\pi$
$774$	2856.18	−	6254.16i	0.132640	−	0.290441i
$775$	−19189.8	−	12332.5i	−0.889442	−	0.571610i
$776$	36961.2	−	10852.8i	1.70983	−	0.502052i
$777$	511.611	+	590.431i	0.0236216	+	0.0272607i
$778$	−34782.3	−	10213.0i	−1.60284	−	0.470635i
$779$	−146.881	−	321.625i	−0.00675553	−	0.0147926i
$780$	−121.668	+	846.223i	−0.00558517	+	0.0388457i
$781$	8248.02			0.377897
$782$	−21077.2	+	37802.1i	−0.963837	+	1.72865i
$783$	3071.60			0.140192
$784$	493.179	−	3430.13i	0.0224662	−	0.156256i
$785$	14724.0	+	32241.0i	0.669454	+	1.46590i
$786$	−13543.7	−	3976.80i	−0.614617	−	0.180468i
$787$	−19975.1	−	23052.5i	−0.904746	−	1.04413i	−0.998820	−	0.0485675i	$-0.984534\pi$
$787$	−19975.1	−	23052.5i	−0.904746	−	1.04413i	0.0940737	−	0.995565i	$-0.470011\pi$
$788$	856.135	−	251.384i	0.0387037	−	0.0113644i
$789$	−11201.6	−	7198.82i	−0.505433	−	0.324822i
$790$	−26989.7	+	59099.2i	−1.21551	+	2.66159i
$791$	4860.08	−	5608.83i	0.218463	−	0.252120i
$792$	−1810.69	+	1163.66i	−0.0812376	+	0.0522082i
$793$	−792.564	−	5512.40i	−0.0354915	−	0.246849i
$794$	1154.81	+	8031.86i	0.0516153	+	0.358993i
$795$	23661.7	−	15206.4i	1.05559	−	0.678386i
$796$	−2138.96	+	2468.49i	−0.0952430	+	0.109916i
$797$	6476.32	−	14181.2i	0.287833	−	0.630267i	−0.709384	−	0.704823i	$-0.751027\pi$
$797$	6476.32	−	14181.2i	0.287833	−	0.630267i	0.997217	+	0.0745556i	$0.0237538\pi$
$798$	−1291.64	−	830.088i	−0.0572978	−	0.0368231i
$799$	22789.1	−	6691.48i	1.00904	−	0.296280i
$800$	−6234.59	−	7195.10i	−0.275532	−	0.317981i
$801$	−378.990	−	111.281i	−0.0167178	−	0.00490878i
$802$	16035.7	+	35113.3i	0.706035	+	1.54600i
$803$	−497.263	+	3458.54i	−0.0218531	+	0.151991i
$804$	2515.18			0.110328
$805$	−7000.65	+	12555.7i	−0.306510	+	0.549727i
$806$	3283.62			0.143499
$807$	−2305.63	+	16036.0i	−0.100572	+	0.699496i
$808$	14172.1	+	31032.6i	0.617046	+	1.35114i
$809$	11126.0	+	3266.89i	0.483523	+	0.141975i	0.514404	−	0.857548i	$-0.328013\pi$
$809$	11126.0	+	3266.89i	0.483523	+	0.141975i	−0.0308811	+	0.999523i	$0.509831\pi$
$810$	18471.6	+	21317.4i	0.801267	+	0.924712i
$811$	−11766.5	+	3454.95i	−0.509465	+	0.149593i	−0.526355	−	0.850265i	$-0.676442\pi$
$811$	−11766.5	+	3454.95i	−0.509465	+	0.149593i	0.0168897	+	0.999857i	$0.494624\pi$
$812$	−113.706	−	73.0747i	−0.00491418	−	0.00315815i
$813$	−12064.9	+	26418.4i	−0.520460	+	1.13965i
$814$	−746.769	+	861.817i	−0.0321551	+	0.0371089i
$815$	−238.815	+	153.477i	−0.0102642	+	0.00659640i
$816$	5957.59	+	41436.0i	0.255585	+	1.77763i
$817$	−801.695	−	5575.91i	−0.0343302	−	0.238772i
$818$	17208.2	−	11059.1i	0.735540	−	0.472703i
$819$	−323.701	+	373.570i	−0.0138108	+	0.0159385i
$820$	160.680	−	351.841i	0.00684293	−	0.0149839i
$821$	−32130.5	−	20649.0i	−1.36585	−	0.877778i	−0.367221	−	0.930134i	$-0.619691\pi$
$821$	−32130.5	−	20649.0i	−1.36585	−	0.877778i	−0.998629	+	0.0523552i	$0.983327\pi$
$822$	30414.1	−	8930.39i	1.29053	−	0.378933i
$823$	2785.91	+	3215.11i	0.117996	+	0.136175i	0.811674	−	0.584110i	$-0.198556\pi$
$823$	2785.91	+	3215.11i	0.117996	+	0.136175i	−0.693678	+	0.720285i	$0.744011\pi$
$824$	−22372.9	−	6569.27i	−0.945869	−	0.277732i
$825$	−6405.85	−	14026.9i	−0.270331	−	0.591943i
$826$	−28.2835	+	196.716i	−0.00119142	+	0.00828648i
$827$	−27678.8			−1.16383			−0.581915	−	0.813249i	$-0.697696\pi$
$827$	−27678.8			−1.16383			−0.581915	+	0.813249i	$0.697696\pi$
$828$	694.810	+	55.8684i	0.0291622	+	0.00234488i
$829$	−8447.89			−0.353929			−0.176965	−	0.984217i	$-0.556628\pi$
$829$	−8447.89			−0.353929			−0.176965	+	0.984217i	$0.556628\pi$
$830$	−4772.94	+	33196.5i	−0.199604	+	1.38827i
$831$	12161.2	+	26629.4i	0.507664	+	1.11163i
$832$	−4472.87	−	1313.35i	−0.186381	−	0.0547264i
$833$	4207.65	+	4855.89i	0.175014	+	0.201977i
$834$	−26773.5	+	7861.40i	−1.11162	+	0.326401i
$835$	11622.1	+	7469.04i	0.481674	+	0.309553i
$836$	99.2026	−	217.223i	0.00410406	−	0.00898663i
$837$	10229.9	−	11806.0i	0.422458	−	0.487543i
$838$	28485.1	−	18306.3i	1.17423	−	0.754630i
$839$	2373.02	+	16504.7i	0.0976468	+	0.679148i	0.978574	+	0.205896i	$0.0660109\pi$
$839$	2373.02	+	16504.7i	0.0976468	+	0.679148i	−0.880927	+	0.473252i	$0.843080\pi$
$840$	1765.20	+	12277.3i	0.0725064	+	0.504293i
$841$	−20172.8	+	12964.3i	−0.827127	+	0.531562i
$842$	27024.9	−	31188.3i	1.10610	−	1.27651i
$843$	−4462.04	+	9770.51i	−0.182302	+	0.399186i
$844$	321.331	+	206.507i	0.0131051	+	0.00842211i
$845$	−37216.2	+	10927.7i	−1.51512	+	0.444880i
$846$	−2350.83	−	2713.01i	−0.0955358	−	0.110254i
$847$	−7343.94	−	2156.37i	−0.297923	−	0.0874781i
$848$	−9832.38	−	21529.9i	−0.398167	−	0.871864i
$849$	5116.56	−	35586.4i	0.206831	−	1.43854i
$850$	86962.8			3.50918
$851$	−2669.90	+	556.140i	−0.107547	+	0.0224022i
$852$	−2304.73			−0.0926744
$853$	−564.106	+	3923.44i	−0.0226432	+	0.157487i	−0.998006	−	0.0631204i	$-0.979895\pi$
$853$	−564.106	+	3923.44i	−0.0226432	+	0.157487i	0.975363	+	0.220607i	$0.0708039\pi$
$854$	4545.17	+	9952.54i	0.182123	+	0.398793i
$855$	−1921.25	−	564.130i	−0.0768484	−	0.0225647i
$856$	21744.8	+	25094.8i	0.868248	+	1.00201i
$857$	−15669.9	+	4601.11i	−0.624591	+	0.183397i	−0.578688	−	0.815549i	$-0.696435\pi$
$857$	−15669.9	+	4601.11i	−0.624591	+	0.183397i	−0.0459038	+	0.998946i	$0.514617\pi$
$858$	1867.37	+	1200.09i	0.0743019	+	0.0477509i
$859$	11918.4	−	26097.8i	0.473402	−	1.03661i	−0.510823	−	0.859686i	$-0.670659\pi$
$859$	11918.4	−	26097.8i	0.473402	−	1.03661i	0.984225	−	0.176920i	$-0.0566134\pi$
$860$	4035.57	−	4657.30i	0.160014	−	0.184666i
$861$	−578.812	+	371.980i	−0.0229104	+	0.0147236i
$862$	1735.51	+	12070.7i	0.0685750	+	0.476950i
$863$	−3224.60	−	22427.6i	−0.127192	−	0.884641i	−0.949090	−	0.315006i	$-0.897994\pi$
$863$	−3224.60	−	22427.6i	−0.127192	−	0.884641i	0.821898	−	0.569635i	$-0.192916\pi$
$864$	5484.86	−	3524.91i	0.215971	−	0.138796i
$865$	−14135.5	+	16313.3i	−0.555633	+	0.641234i
$866$	16938.6	−	37090.3i	0.664661	−	1.45540i
$867$	−46638.6	−	29972.8i	−1.82691	−	1.17408i
$868$	−659.566	+	193.666i	−0.0257916	+	0.00757310i
$869$	11771.2	+	13584.7i	0.459506	+	0.530298i
$870$	4883.27	+	1433.86i	0.190297	+	0.0558762i
$871$	−2586.46	−	5663.56i	−0.100619	−	0.220324i
$872$	1963.11	−	13653.7i	0.0762378	−	0.530245i
$873$	12101.2			0.469145
$874$	4726.62	−	2526.97i	0.182929	−	0.0977988i
$875$	12593.3			0.486550
$876$	138.949	−	966.412i	0.00535919	−	0.0372740i
$877$	−1365.64	−	2990.34i	−0.0525821	−	0.115139i	0.881517	−	0.472152i	$-0.156522\pi$
$877$	−1365.64	−	2990.34i	−0.0525821	−	0.115139i	−0.934099	+	0.357013i	$0.883795\pi$
$878$	22090.5	+	6486.36i	0.849110	+	0.249321i
$879$	13967.4	+	16119.2i	0.535960	+	0.618531i
$880$	−19473.0	+	5717.79i	−0.745948	+	0.219030i
$881$	−36102.9	−	23201.9i	−1.38063	−	0.887280i	−0.381325	−	0.924441i	$-0.624532\pi$
$881$	−36102.9	−	23201.9i	−1.38063	−	0.887280i	−0.999309	+	0.0371614i	$0.988168\pi$
$882$	403.423	−	883.374i	0.0154013	−	0.0337242i
$883$	−2232.15	+	2576.04i	−0.0850711	+	0.0981773i	−0.796689	−	0.604389i	$-0.793417\pi$
$883$	−2232.15	+	2576.04i	−0.0850711	+	0.0981773i	0.711618	+	0.702566i	$0.247963\pi$
$884$	−1122.15	+	721.159i	−0.0426944	+	0.0274380i
$885$	−113.481	−	789.280i	−0.00431032	−	0.0299789i
$886$	−4730.20	−	32899.3i	−0.179361	−	1.24749i
$887$	−2268.69	+	1458.00i	−0.0858795	+	0.0551914i	−0.582876	−	0.812561i	$-0.698073\pi$
$887$	−2268.69	+	1458.00i	−0.0858795	+	0.0551914i	0.496996	+	0.867753i	$0.334436\pi$
$888$	−1540.95	+	1778.35i	−0.0582330	+	0.0672045i
$889$	4863.93	−	10650.5i	0.183499	−	0.401808i
$890$	−2795.02	−	1796.25i	−0.105269	−	0.0676522i
$891$	7487.79	−	2198.61i	0.281538	−	0.0826670i
$892$	−3183.95	−	3674.47i	−0.119514	−	0.137927i
$893$	−2822.09	−	828.640i	−0.105753	−	0.0310519i
$894$	3682.01	+	8062.47i	0.137746	+	0.301621i
$895$	−7639.89	+	53136.6i	−0.285333	+	1.98454i
$896$	11564.2			0.431174
$897$	1811.16	+	4990.14i	0.0674169	+	0.185748i
$898$	−11103.0			−0.412596
$899$	296.431	−	2061.72i	0.0109973	−	0.0764876i
$900$	−581.813	−	1273.99i	−0.0215486	−	0.0471849i
$901$	42107.1	+	12363.8i	1.55693	+	0.457155i
$902$	−657.666	−	758.987i	−0.0242770	−	0.0280172i
$903$	−10517.9	+	3088.33i	−0.387611	+	0.113813i
$904$	18804.9	+	12085.2i	0.691859	+	0.444631i
$905$	37228.3	−	81518.5i	1.36741	−	2.99422i
$906$	19662.6	−	22691.9i	0.721024	−	0.832106i
$907$	6798.71	−	4369.26i	0.248895	−	0.159955i	−0.410245	−	0.911975i	$-0.634557\pi$
$907$	6798.71	−	4369.26i	0.248895	−	0.159955i	0.659140	+	0.752020i	$0.270921\pi$
$908$	−621.364	−	4321.68i	−0.0227100	−	0.157952i
$909$	1525.20	+	10608.0i	0.0556521	+	0.387069i
$910$	−3497.79	+	2247.90i	−0.127418	+	0.0818868i
$911$	−29186.2	+	33682.6i	−1.06145	+	1.22498i	−0.0879891	+	0.996121i	$0.528044\pi$
$911$	−29186.2	+	33682.6i	−1.06145	+	1.22498i	−0.973460	+	0.228856i	$0.926501\pi$
$912$	2153.51	−	4715.52i	0.0781905	−	0.171213i
$913$	7805.82	+	5016.49i	0.282952	+	0.181842i
$914$	−38059.2	+	11175.2i	−1.37734	+	0.404423i
$915$	−28748.0	−	33177.0i	−1.03867	−	1.19869i
$916$	4633.00	+	1360.37i	0.167116	+	0.0490698i
$917$	−3038.77	−	6653.98i	−0.109432	−	0.239623i
$918$	−8475.47	+	58948.2i	−0.304719	+	2.11937i
$919$	−10750.4			−0.385879			−0.192939	−	0.981211i	$-0.561802\pi$
$919$	−10750.4			−0.385879			−0.192939	+	0.981211i	$0.561802\pi$
$920$	−40433.1	−	15489.1i	−1.44896	−	0.555065i
$921$	−13393.2			−0.479177
$922$	2757.99	−	19182.3i	0.0985137	−	0.685178i
$923$	2370.05	+	5189.68i	0.0845190	+	0.185071i
$924$	−445.871	−	130.920i	−0.0158746	−	0.00466119i
$925$	3588.41	+	4141.25i	0.127553	+	0.147204i
$926$	−12684.0	+	3724.36i	−0.450133	+	0.132171i
$927$	−6162.14	−	3960.17i	−0.218329	−	0.140312i
$928$	361.136	−	790.778i	0.0127747	−	0.0279726i
$929$	−8948.48	+	10327.1i	−0.316028	+	0.364716i	−0.891433	−	0.453153i	$-0.850299\pi$
$929$	−8948.48	+	10327.1i	−0.316028	+	0.364716i	0.575405	+	0.817869i	$0.304845\pi$
$930$	21774.8	−	13993.8i	0.767768	−	0.493415i
$931$	−113.236	−	787.574i	−0.00398621	−	0.0277247i
$932$	447.597	+	3113.10i	0.0157312	+	0.109413i
$933$	−21978.2	+	14124.5i	−0.771204	+	0.495622i
$934$	36232.2	−	41814.2i	1.26933	−	1.46489i
$935$	15631.8	−	34228.9i	0.546754	−	1.19723i
$936$	−1252.48	−	804.919i	−0.0437377	−	0.0281085i
$937$	15204.1	−	4464.32i	0.530091	−	0.155649i	−0.00572477	−	0.999984i	$-0.501822\pi$
$937$	15204.1	−	4464.32i	0.530091	−	0.155649i	0.535816	+	0.844335i	$0.320004\pi$
$938$	8010.46	+	9244.56i	0.278839	+	0.321797i
$939$	−32913.8	−	9664.37i	−1.14388	−	0.335873i
$940$	−1336.62	−	2926.79i	−0.0463784	−	0.101555i
$941$	−3099.81	+	21559.6i	−0.107387	+	0.746891i	0.862977	+	0.505243i	$0.168597\pi$
$941$	−3099.81	+	21559.6i	−0.107387	+	0.746891i	−0.970364	+	0.241648i	$0.922312\pi$
$942$	−25715.2			−0.889432
$943$	−150.168	−	2397.10i	−0.00518574	−	0.0827788i
$944$	−671.015			−0.0231353
$945$	−2815.06	+	19579.2i	−0.0969037	+	0.673980i
$946$	−6646.83	−	14554.5i	−0.228443	−	0.500220i
$947$	−38716.4	−	11368.2i	−1.32853	−	0.390091i	−0.460965	−	0.887418i	$-0.652497\pi$
$947$	−38716.4	−	11368.2i	−1.32853	−	0.390091i	−0.867563	+	0.497328i	$0.834315\pi$
$948$	−3289.20	−	3795.94i	−0.112688	−	0.130049i
$949$	−2319.01	+	680.923i	−0.0793238	+	0.0232916i
$950$	−9059.50	−	5822.19i	−0.309399	−	0.198839i
$951$	−12102.3	+	26500.4i	−0.412666	+	0.903612i
$952$	−12673.3	+	14625.7i	−0.431453	+	0.497923i
$953$	19328.1	−	12421.4i	0.656976	−	0.422213i	−0.169234	−	0.985576i	$-0.554129\pi$
$953$	19328.1	−	12421.4i	0.656976	−	0.422213i	0.826209	+	0.563363i	$0.190493\pi$
$954$	−943.955	−	6565.35i	−0.0320353	−	0.222810i
$955$	−12390.7	−	86179.0i	−0.419846	−	2.92009i
$956$	−4710.26	+	3027.10i	−0.159352	+	0.102409i
$957$	922.091	−	1064.15i	0.0311463	−	0.0359447i
$958$	2188.75	−	4792.68i	0.0738154	−	0.161633i
$959$	13819.1	+	8880.99i	0.465320	+	0.299043i
$960$	−35258.3	+	10352.8i	−1.18537	+	0.348056i
$961$	12571.8	+	14508.6i	0.422000	+	0.487014i
$962$	−756.840	−	222.228i	−0.0253654	−	0.00744795i
$963$	4333.24	+	9488.47i	0.145002	+	0.317509i
$964$	204.931	−	1425.33i	0.00684686	−	0.0476210i
$965$	1990.40			0.0663973
$966$	−6176.22	−	8404.24i	−0.205711	−	0.279919i
$967$	4436.40			0.147534			0.0737669	−	0.997276i	$-0.476498\pi$
$967$	4436.40			0.147534			0.0737669	+	0.997276i	$0.476498\pi$
$968$	3280.85	−	22818.8i	0.108936	−	0.757669i
$969$	3992.85	+	8743.12i	0.132372	+	0.289855i
$970$	97665.9	+	28677.3i	3.23285	+	0.949250i
$971$	−9535.31	−	11004.3i	−0.315142	−	0.363693i	0.575975	−	0.817467i	$-0.304623\pi$
$971$	−9535.31	−	11004.3i	−0.315142	−	0.363693i	−0.891117	+	0.453775i	$0.850077\pi$
$972$	1659.29	−	487.211i	0.0547549	−	0.0160775i
$973$	−12164.9	−	7817.91i	−0.400811	−	0.257586i
$974$	22326.6	−	48888.5i	0.734488	−	1.60830i
$975$	6985.04	−	8061.17i	0.229436	−	0.264784i
$976$	−31077.4	+	19972.2i	−1.01922	+	0.655015i
$977$	−1620.69	−	11272.1i	−0.0530710	−	0.369117i	−0.998999	−	0.0447394i	$-0.985754\pi$
$977$	−1620.69	−	11272.1i	−0.0530710	−	0.369117i	0.945928	−	0.324378i	$-0.105155\pi$
$978$	−29.3110	−	203.863i	−0.000958347	−	0.00666545i
$979$	−773.288	+	496.962i	−0.0252445	+	0.0162237i
$980$	570.007	−	657.823i	0.0185798	−	0.0214422i
$981$	1800.12	−	3941.71i	0.0585866	−	0.128287i
$982$	−9033.22	−	5805.30i	−0.293545	−	0.188650i
$983$	−15407.1	+	4523.93i	−0.499908	+	0.146786i	−0.521959	−	0.852971i	$-0.674799\pi$
$983$	−15407.1	+	4523.93i	−0.499908	+	0.146786i	0.0220509	+	0.999757i	$0.492980\pi$
$984$	−1357.09	−	1566.16i	−0.0439659	−	0.0507393i
$985$	−16706.0	−	4905.32i	−0.540403	−	0.158677i
$986$	3298.72	+	7223.20i	0.106544	+	0.233300i
$987$	−814.528	+	5665.17i	−0.0262682	+	0.182699i
$988$	165.183			0.00531901
$989$	8464.07	−	37318.1i	0.272135	−	1.19985i
$990$	−5687.42			−0.182584
$991$	−4010.12	+	27891.0i	−0.128542	+	0.894032i	0.818861	+	0.573991i	$0.194606\pi$
$991$	−4010.12	+	27891.0i	−0.128542	+	0.894032i	−0.947404	+	0.320041i	$0.896303\pi$
$992$	−1836.66	−	4021.73i	−0.0587844	−	0.128720i
$993$	−24970.3	−	7331.93i	−0.797993	−	0.234312i
$994$	−7340.20	−	8471.04i	−0.234222	−	0.270307i
$995$	61154.2	−	17956.5i	1.94846	−	0.572119i
$996$	−2181.16	−	1401.75i	−0.0693904	−	0.0445945i
$997$	6867.07	−	15036.8i	0.218137	−	0.477653i	−0.768652	−	0.639668i	$-0.779072\pi$
$997$	6867.07	−	15036.8i	0.218137	−	0.477653i	0.986788	+	0.162015i	$0.0517993\pi$
$998$	15309.8	−	17668.4i	0.485593	−	0.560405i
$999$	−3156.89	+	2028.81i	−0.0999797	+	0.0642530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.i.b.8.16	✓	190
23.3	even	11	inner	161.4.i.b.141.16	yes	190

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.i.b.8.16	✓	190	1.1	even	1	trivial
161.4.i.b.141.16	yes	190	23.3	even	11	inner

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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.425855 - 2.96189i) q^{2} +(-1.87521 - 4.10613i) q^{3} +(-0.915470 - 0.268806i) q^{4} +(12.1922 + 14.0705i) q^{5} +(-12.9605 + 3.80554i) q^{6} +(-5.88877 - 3.78449i) q^{7} +(8.75848 - 19.1784i) q^{8} +(4.33731 - 5.00552i) q^{9} +(46.8674 - 30.1199i) q^{10} +(-2.19356 - 15.2566i) q^{11} +(0.612943 + 4.26311i) q^{12} +(8.96917 - 5.76413i) q^{13} +(-13.7170 + 15.8302i) q^{14} +(34.9126 - 76.4480i) q^{15} +(-59.4956 - 38.2355i) q^{16} +(125.816 - 36.9430i) q^{17} +(-12.9787 - 14.9782i) q^{18} +(-15.5805 - 4.57484i) q^{19} +(-7.37934 - 16.1585i) q^{20} +(-4.49693 + 31.2768i) q^{21} -46.1223 q^{22} +(-87.7155 - 66.8804i) q^{23} -95.1731 q^{24} +(-31.5411 + 219.374i) q^{25} +(-13.2531 - 29.0203i) q^{26} +(-145.629 - 42.7606i) q^{27} +(4.37370 + 5.04752i) q^{28} +(-19.4178 + 5.70157i) q^{29} +(-211.562 - 135.963i) q^{30} +(-42.7561 + 93.6228i) q^{31} +(-28.1307 + 32.4645i) q^{32} +(-58.5321 + 37.6163i) q^{33} +(-55.8414 - 388.386i) q^{34} +(-18.5473 - 128.999i) q^{35} +(-5.31619 + 3.41651i) q^{36} +(16.1910 - 18.6855i) q^{37} +(-20.1852 + 44.1993i) q^{38} +(-40.4874 - 26.0197i) q^{39} +(376.635 - 110.590i) q^{40} +(14.2592 + 16.4560i) q^{41} +(90.7233 + 26.6388i) q^{42} +(144.113 + 315.563i) q^{43} +(-2.09292 + 14.5566i) q^{44} +123.312 q^{45} +(-235.446 + 231.322i) q^{46} +181.130 q^{47} +(-45.4335 + 315.997i) q^{48} +(20.3553 + 44.5720i) q^{49} +(636.327 + 186.843i) q^{50} +(-387.625 - 447.343i) q^{51} +(-9.76044 + 2.86592i) q^{52} +(281.543 + 180.937i) q^{53} +(-188.669 + 413.128i) q^{54} +(187.924 - 216.876i) q^{55} +(-124.157 + 79.7909i) q^{56} +(10.4317 + 72.5542i) q^{57} +(8.61825 + 59.9413i) q^{58} +(7.98180 - 5.12959i) q^{59} +(-52.5111 + 60.6011i) q^{60} +(216.991 - 475.143i) q^{61} +(259.092 + 166.508i) q^{62} +(-44.4847 + 13.0619i) q^{63} +(-286.331 - 330.444i) q^{64} +(190.458 + 55.9236i) q^{65} +(86.4890 + 189.385i) q^{66} +(83.1092 - 578.037i) q^{67} -125.112 q^{68} +(-110.135 + 485.586i) q^{69} -389.980 q^{70} +(-76.1552 + 529.671i) q^{71} +(-58.0096 - 127.023i) q^{72} +(-217.509 - 63.8664i) q^{73} +(-48.4492 - 55.9133i) q^{74} +(959.923 - 281.859i) q^{75} +(13.0337 + 8.37625i) q^{76} +(-44.8209 + 98.1440i) q^{77} +(-94.3090 + 108.838i) q^{78} +(-981.067 + 630.494i) q^{79} +(-187.388 - 1303.31i) q^{80} +(72.0547 + 501.151i) q^{81} +(54.8130 - 35.2262i) q^{82} +(-394.222 + 454.956i) q^{83} +(12.5242 - 27.4242i) q^{84} +(2053.78 + 1319.89i) q^{85} +(996.034 - 292.462i) q^{86} +(59.8238 + 69.0403i) q^{87} +(-311.809 - 91.5554i) q^{88} +(-24.7740 - 54.2475i) q^{89} +(52.5129 - 365.235i) q^{90} -74.6317 q^{91} +(62.3230 + 84.8055i) q^{92} +464.604 q^{93} +(77.1351 - 536.486i) q^{94} +(-125.589 - 275.003i) q^{95} +(186.055 + 54.6306i) q^{96} +(1196.48 + 1380.81i) q^{97} +(140.685 - 41.3090i) q^{98} +(-85.8812 - 55.1925i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 2 q^{2} - 2 q^{3} - 58 q^{4} - 26 q^{5} - 9 q^{6} + 133 q^{7} - 27 q^{8} - 589 q^{9} + 12 q^{10} + 122 q^{11} - 117 q^{12} + 64 q^{13} - 14 q^{14} + 582 q^{15} - 626 q^{16} + 104 q^{17} + 33 q^{18}+ \cdots + 1926 q^{99}+O(q^{100}) \) 190 * q + 2 * q^2 - 2 * q^3 - 58 * q^4 - 26 * q^5 - 9 * q^6 + 133 * q^7 - 27 * q^8 - 589 * q^9 + 12 * q^10 + 122 * q^11 - 117 * q^12 + 64 * q^13 - 14 * q^14 + 582 * q^15 - 626 * q^16 + 104 * q^17 + 33 * q^18 + 82 * q^19 + 945 * q^20 + 14 * q^21 - 280 * q^22 - 267 * q^23 - 84 * q^24 - 793 * q^25 + 27 * q^26 - 302 * q^27 + 868 * q^28 + 342 * q^29 + 1020 * q^30 - 1440 * q^31 + 242 * q^32 + 648 * q^33 + 2860 * q^34 - 280 * q^35 - 1612 * q^36 + 1018 * q^37 - 48 * q^38 + 1164 * q^39 - 5858 * q^40 - 228 * q^41 + 63 * q^42 - 124 * q^43 - 1400 * q^44 + 164 * q^45 - 3912 * q^46 + 3084 * q^47 - 4329 * q^48 - 931 * q^49 - 6141 * q^50 + 3858 * q^51 + 1987 * q^52 + 1202 * q^53 - 295 * q^54 + 7494 * q^55 + 189 * q^56 + 5126 * q^57 + 249 * q^58 - 1116 * q^59 + 3140 * q^60 + 1180 * q^61 - 293 * q^62 + 1197 * q^63 - 2933 * q^64 + 1152 * q^65 + 9861 * q^66 - 4930 * q^67 + 100 * q^68 - 7394 * q^69 - 84 * q^70 - 15114 * q^71 + 1271 * q^72 - 6944 * q^73 + 7528 * q^74 + 10798 * q^75 + 5821 * q^76 + 1379 * q^77 + 3217 * q^78 + 1432 * q^79 + 8074 * q^80 + 2175 * q^81 + 1801 * q^82 + 4210 * q^83 - 1876 * q^84 + 10028 * q^85 - 4476 * q^86 + 2582 * q^87 - 5609 * q^88 - 1996 * q^89 - 33389 * q^90 - 4452 * q^91 - 13192 * q^92 + 3984 * q^93 - 11373 * q^94 - 740 * q^95 - 18056 * q^96 + 7238 * q^97 - 1519 * q^98 + 1926 * q^99

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