LMFDB - Embedded newform 169.3.j.a.5.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,3,Mod(5,169)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("169.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	169.j (of order $52$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.60491646769$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$30$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.10
Character	$\chi$	$=$	169.5
Dual form			169.3.j.a.34.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.19267 - 0.401821i) q^{2} +(-1.90733 - 1.00104i) q^{3} +(0.906258 + 0.343698i) q^{4} +(-0.00411255 + 0.0679886i) q^{5} +(3.77990 + 2.96136i) q^{6} +(8.11874 + 4.90795i) q^{7} +(5.78175 + 3.49519i) q^{8} +(-2.47676 - 3.58821i) q^{9} +(0.0363367 - 0.147424i) q^{10} +(5.16153 - 0.945885i) q^{11} +(-1.38448 - 1.56275i) q^{12} +(-10.2816 - 7.95545i) q^{13} +(-15.8296 - 14.0238i) q^{14} +(0.0759036 - 0.125560i) q^{15} +(-14.1750 - 12.5579i) q^{16} +(-2.34053 - 9.49590i) q^{17} +(3.98890 + 8.86297i) q^{18} +(-10.4218 + 10.4218i) q^{19} +(-0.0270946 + 0.0602018i) q^{20} +(-10.5720 - 17.4883i) q^{21} -11.6976 q^{22} -44.9730i q^{23} +(-7.52886 - 12.4543i) q^{24} +(24.8131 + 3.01286i) q^{25} +(19.3474 + 21.5750i) q^{26} +(3.46884 + 28.5685i) q^{27} +(5.67082 + 7.23827i) q^{28} +(-22.8298 - 33.0747i) q^{29} +(-0.216884 + 0.244811i) q^{30} +(-20.4841 - 16.0482i) q^{31} +(9.36844 + 11.9579i) q^{32} +(-10.7916 - 3.36280i) q^{33} +(1.31635 + 21.7618i) q^{34} +(-0.367074 + 0.531798i) q^{35} +(-1.01133 - 4.10311i) q^{36} +(2.28915 - 2.92189i) q^{37} +(27.0393 - 18.6639i) q^{38} +(11.6466 + 25.4660i) q^{39} +(-0.261411 + 0.378719i) q^{40} +(36.6302 - 11.4144i) q^{41} +(16.1538 + 42.5941i) q^{42} +(-22.8592 - 2.77561i) q^{43} +(5.00277 + 0.916792i) q^{44} +(0.254144 - 0.153635i) q^{45} +(-18.0711 + 98.6108i) q^{46} +(31.7684 - 70.5866i) q^{47} +(14.4653 + 38.1418i) q^{48} +(19.0546 + 36.3054i) q^{49} +(-53.1962 - 16.5766i) q^{50} +(-5.04165 + 20.4548i) q^{51} +(-6.58348 - 10.7435i) q^{52} +(-90.3065 + 22.2585i) q^{53} +(3.87340 - 64.0350i) q^{54} +(0.0430824 + 0.354815i) q^{55} +(29.7863 + 56.7530i) q^{56} +(30.3106 - 9.44517i) q^{57} +(36.7680 + 81.6952i) q^{58} +(96.6370 + 5.84546i) q^{59} +(0.111943 - 0.0877017i) q^{60} +(84.2333 + 20.7616i) q^{61} +(38.4662 + 43.4193i) q^{62} +(-2.49744 - 41.2876i) q^{63} +(19.4659 + 37.0893i) q^{64} +(0.583164 - 0.666313i) q^{65} +(22.3111 + 11.7098i) q^{66} +(-43.3979 - 19.5318i) q^{67} +(1.14260 - 9.41017i) q^{68} +(-45.0200 + 85.7784i) q^{69} +(1.01856 - 1.01856i) q^{70} +(-49.4707 + 15.4157i) q^{71} +(-1.77855 - 29.4029i) q^{72} +(-50.7956 + 9.30864i) q^{73} +(-6.19342 + 5.48689i) q^{74} +(-44.3108 - 30.5855i) q^{75} +(-13.0269 + 5.86291i) q^{76} +(46.5475 + 17.6531i) q^{77} +(-15.3043 - 60.5182i) q^{78} +(-22.4214 - 59.1204i) q^{79} +(0.912091 - 0.912091i) q^{80} +(8.06738 - 21.2719i) q^{81} +(-84.9044 + 10.3093i) q^{82} +(46.5080 - 149.249i) q^{83} +(-3.57030 - 19.4825i) q^{84} +(0.655239 - 0.120077i) q^{85} +(49.0074 + 15.2713i) q^{86} +(10.4348 + 85.9379i) q^{87} +(33.1487 + 12.5716i) q^{88} +(-35.4701 - 35.4701i) q^{89} +(-0.618986 + 0.234750i) q^{90} +(-44.4285 - 115.050i) q^{91} +(15.4571 - 40.7572i) q^{92} +(23.0049 + 51.1147i) q^{93} +(-98.0208 + 142.008i) q^{94} +(-0.665707 - 0.751427i) q^{95} +(-5.89829 - 32.1859i) q^{96} +(-118.374 + 7.16032i) q^{97} +(-27.1920 - 87.2622i) q^{98} +(-16.1779 - 16.1779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 22 q^{2} - 22 q^{3} - 26 q^{4} - 34 q^{5} - 10 q^{6} - 14 q^{7} - 62 q^{8} - 202 q^{9} - 26 q^{10} - 22 q^{11} - 26 q^{12} - 34 q^{13} - 38 q^{14} + 2 q^{15} + 242 q^{16} - 26 q^{17} - 58 q^{18}+ \cdots - 178 q^{99}+O(q^{100}) $ 720 * q - 22 * q^2 - 22 * q^3 - 26 * q^4 - 34 * q^5 - 10 * q^6 - 14 * q^7 - 62 * q^8 - 202 * q^9 - 26 * q^10 - 22 * q^11 - 26 * q^12 - 34 * q^13 - 38 * q^14 + 2 * q^15 + 242 * q^16 - 26 * q^17 - 58 * q^18 - 26 * q^19 - 42 * q^20 - 58 * q^21 - 108 * q^22 + 262 * q^24 - 26 * q^25 + 62 * q^26 + 2 * q^27 - 30 * q^28 - 54 * q^29 - 858 * q^30 - 66 * q^31 - 696 * q^32 + 50 * q^33 + 82 * q^34 - 2 * q^35 - 26 * q^36 - 66 * q^37 + 884 * q^38 + 922 * q^39 - 522 * q^40 - 58 * q^41 - 106 * q^42 - 26 * q^43 + 42 * q^44 - 212 * q^45 - 54 * q^46 + 368 * q^47 + 94 * q^48 - 26 * q^49 + 102 * q^50 - 26 * q^51 - 1276 * q^52 + 620 * q^53 - 178 * q^54 - 834 * q^55 - 26 * q^56 + 14 * q^57 + 114 * q^58 - 82 * q^59 + 1338 * q^60 + 254 * q^61 + 1404 * q^62 - 1392 * q^63 - 26 * q^64 - 82 * q^65 - 304 * q^66 - 358 * q^67 - 434 * q^68 + 208 * q^69 + 838 * q^70 - 310 * q^71 + 22 * q^72 - 26 * q^73 - 1308 * q^74 + 1664 * q^75 - 106 * q^76 - 26 * q^77 - 574 * q^78 - 78 * q^79 + 62 * q^80 - 262 * q^81 + 1274 * q^82 + 26 * q^83 + 158 * q^84 + 1522 * q^85 - 1562 * q^86 - 122 * q^87 - 442 * q^88 - 616 * q^89 - 26 * q^90 - 182 * q^91 + 646 * q^92 + 544 * q^93 - 2394 * q^94 - 26 * q^95 - 4064 * q^96 + 1914 * q^97 - 250 * q^98 - 178 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{52}\right)$

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 $

$2$	−2.19267	−	0.401821i	−1.09633	−	0.200910i	−0.398498	−	0.917169i	$-0.630468\pi$
$2$	−2.19267	−	0.401821i	−1.09633	−	0.200910i	−0.697835	+	0.716259i	$0.745853\pi$
$3$	−1.90733	−	1.00104i	−0.635777	−	0.333681i	0.115853	−	0.993266i	$-0.463040\pi$
$3$	−1.90733	−	1.00104i	−0.635777	−	0.333681i	−0.751630	+	0.659585i	$0.770732\pi$
$4$	0.906258	+	0.343698i	0.226565	+	0.0859246i
$5$	−0.00411255	+	0.0679886i	−0.000822511	+	0.0135977i	−0.998564	−	0.0535782i	$-0.982937\pi$
$5$	−0.00411255	+	0.0679886i	−0.000822511	+	0.0135977i	0.997741	+	0.0671760i	$0.0213989\pi$
$6$	3.77990	+	2.96136i	0.629983	+	0.493560i
$7$	8.11874	+	4.90795i	1.15982	+	0.701136i	0.960358	−	0.278770i	$-0.0899266\pi$
$7$	8.11874	+	4.90795i	1.15982	+	0.701136i	0.199462	+	0.979905i	$0.436080\pi$
$8$	5.78175	+	3.49519i	0.722718	+	0.436898i
$9$	−2.47676	−	3.58821i	−0.275196	−	0.398690i
$10$	0.0363367	−	0.147424i	0.00363367	−	0.0147424i
$11$	5.16153	−	0.945885i	0.469230	−	0.0859895i	0.0595624	−	0.998225i	$-0.481029\pi$
$11$	5.16153	−	0.945885i	0.469230	−	0.0859895i	0.409667	+	0.912235i	$0.365645\pi$
$12$	−1.38448	−	1.56275i	−0.115373	−	0.130229i
$13$	−10.2816	−	7.95545i	−0.790890	−	0.611958i
$13$	−10.2816	−	7.95545i	−0.790890	−	0.611958i
$14$	−15.8296	−	14.0238i	−1.13068	−	1.00170i
$15$	0.0759036	−	0.125560i	0.00506024	−	0.00837066i
$16$	−14.1750	−	12.5579i	−0.885935	−	0.784870i
$17$	−2.34053	−	9.49590i	−0.137678	−	0.558582i	−0.998745	−	0.0500901i	$-0.984049\pi$
$17$	−2.34053	−	9.49590i	−0.137678	−	0.558582i	0.861066	−	0.508492i	$-0.169797\pi$
$18$	3.98890	+	8.86297i	0.221605	+	0.492387i
$19$	−10.4218	+	10.4218i	−0.548518	+	0.548518i	−0.926012	−	0.377494i	$-0.876786\pi$
$19$	−10.4218	+	10.4218i	−0.548518	+	0.548518i	0.377494	+	0.926012i	$0.376786\pi$
$20$	−0.0270946	+	0.0602018i	−0.00135473	+	0.00301009i
$21$	−10.5720	−	17.4883i	−0.503431	−	0.832776i
$22$	−11.6976			−0.531708
$23$		−	44.9730i		−	1.95535i	−0.210127	−	0.977674i	$-0.567388\pi$
$23$		−	44.9730i		−	1.95535i	0.210127	−	0.977674i	$-0.432612\pi$
$24$	−7.52886	−	12.4543i	−0.313703	−	0.518927i
$25$	24.8131	+	3.01286i	0.992525	+	0.120514i
$26$	19.3474	+	21.5750i	0.744130	+	0.829808i
$27$	3.46884	+	28.5685i	0.128476	+	1.05809i
$28$	5.67082	+	7.23827i	0.202529	+	0.258510i
$29$	−22.8298	−	33.0747i	−0.787234	−	1.14051i	−0.987009	−	0.160664i	$-0.948637\pi$
$29$	−22.8298	−	33.0747i	−0.787234	−	1.14051i	0.199775	−	0.979842i	$-0.435979\pi$
$30$	−0.216884	+	0.244811i	−0.00722946	+	0.00816038i
$31$	−20.4841	−	16.0482i	−0.660776	−	0.517685i	0.229382	−	0.973336i	$-0.426329\pi$
$31$	−20.4841	−	16.0482i	−0.660776	−	0.517685i	−0.890158	+	0.455652i	$0.849406\pi$
$32$	9.36844	+	11.9579i	0.292764	+	0.373685i
$33$	−10.7916	−	3.36280i	−0.327018	−	0.101903i
$34$	1.31635	+	21.7618i	0.0387161	+	0.640053i
$35$	−0.367074	+	0.531798i	−0.0104878	+	0.0151942i
$36$	−1.01133	−	4.10311i	−0.0280924	−	0.113975i
$37$	2.28915	−	2.92189i	0.0618690	−	0.0789699i	−0.755258	−	0.655428i	$-0.772488\pi$
$37$	2.28915	−	2.92189i	0.0618690	−	0.0789699i	0.817127	+	0.576458i	$0.195565\pi$
$38$	27.0393	−	18.6639i	0.711561	−	0.491155i
$39$	11.6466	+	25.4660i	0.298631	+	0.652974i
$40$	−0.261411	+	0.378719i	−0.00653527	+	0.00946797i
$41$	36.6302	−	11.4144i	0.893420	−	0.278401i	0.183782	−	0.982967i	$-0.441166\pi$
$41$	36.6302	−	11.4144i	0.893420	−	0.278401i	0.709638	+	0.704566i	$0.248858\pi$
$42$	16.1538	+	42.5941i	0.384614	+	1.01414i
$43$	−22.8592	−	2.77561i	−0.531610	−	0.0645491i	−0.149670	−	0.988736i	$-0.547821\pi$
$43$	−22.8592	−	2.77561i	−0.531610	−	0.0645491i	−0.381940	+	0.924187i	$0.624744\pi$
$44$	5.00277	+	0.916792i	0.113699	+	0.0208362i
$45$	0.254144	−	0.153635i	0.00564763	−	0.00341411i
$46$	−18.0711	+	98.6108i	−0.392850	+	2.14371i
$47$	31.7684	−	70.5866i	0.675924	−	1.50184i	−0.179415	−	0.983774i	$-0.557420\pi$
$47$	31.7684	−	70.5866i	0.675924	−	1.50184i	0.855339	−	0.518069i	$-0.173349\pi$
$48$	14.4653	+	38.1418i	0.301360	+	0.794621i
$49$	19.0546	+	36.3054i	0.388869	+	0.740927i
$50$	−53.1962	−	16.5766i	−1.06392	−	0.331532i
$51$	−5.04165	+	20.4548i	−0.0988559	+	0.401074i
$52$	−6.58348	−	10.7435i	−0.126605	−	0.206605i
$53$	−90.3065	+	22.2585i	−1.70390	+	0.419973i	−0.966742	−	0.255753i	$-0.917677\pi$
$53$	−90.3065	+	22.2585i	−1.70390	+	0.419973i	−0.737153	+	0.675725i	$0.763831\pi$
$54$	3.87340	−	64.0350i	0.0717297	−	1.18583i
$55$	0.0430824	+	0.354815i	0.000783315	+	0.00645118i
$56$	29.7863	+	56.7530i	0.531898	+	1.01345i
$57$	30.3106	−	9.44517i	0.531765	−	0.165705i
$58$	36.7680	+	81.6952i	0.633931	+	1.40854i
$59$	96.6370	+	5.84546i	1.63792	+	0.0990757i	0.853477	−	0.521131i	$-0.174490\pi$
$59$	96.6370	+	5.84546i	1.63792	+	0.0990757i	0.784439	+	0.620206i	$0.212951\pi$
$60$	0.111943	−	0.0877017i	0.00186572	−	0.00146170i
$61$	84.2333	+	20.7616i	1.38087	+	0.340355i	0.858698	−	0.512483i	$-0.171274\pi$
$61$	84.2333	+	20.7616i	1.38087	+	0.340355i	0.522176	+	0.852838i	$0.325120\pi$
$62$	38.4662	+	43.4193i	0.620422	+	0.700312i
$63$	−2.49744	−	41.2876i	−0.0396419	−	0.655359i
$64$	19.4659	+	37.0893i	0.304155	+	0.579520i
$65$	0.583164	−	0.666313i	0.00897175	−	0.0102510i
$66$	22.3111	+	11.7098i	0.338048	+	0.177421i
$67$	−43.3979	−	19.5318i	−0.647730	−	0.291520i	0.0597920	−	0.998211i	$-0.480956\pi$
$67$	−43.3979	−	19.5318i	−0.647730	−	0.291520i	−0.707522	+	0.706691i	$0.750187\pi$
$68$	1.14260	−	9.41017i	0.0168030	−	0.138385i
$69$	−45.0200	+	85.7784i	−0.652463	+	1.24316i
$70$	1.01856	−	1.01856i	0.0145508	−	0.0145508i
$71$	−49.4707	+	15.4157i	−0.696770	+	0.217122i	−0.625373	−	0.780326i	$-0.715053\pi$
$71$	−49.4707	+	15.4157i	−0.696770	+	0.217122i	−0.0713968	+	0.997448i	$0.522746\pi$
$72$	−1.77855	−	29.4029i	−0.0247020	−	0.408373i
$73$	−50.7956	+	9.30864i	−0.695830	+	0.127516i	−0.516518	−	0.856277i	$-0.672772\pi$
$73$	−50.7956	+	9.30864i	−0.695830	+	0.127516i	−0.179312	+	0.983792i	$0.557387\pi$
$74$	−6.19342	+	5.48689i	−0.0836949	+	0.0741472i
$75$	−44.3108	−	30.5855i	−0.590811	−	0.407807i
$76$	−13.0269	+	5.86291i	−0.171406	+	0.0771436i
$77$	46.5475	+	17.6531i	0.604512	+	0.229261i
$78$	−15.3043	−	60.5182i	−0.196209	−	0.775875i
$79$	−22.4214	−	59.1204i	−0.283815	−	0.748359i	−0.998789	−	0.0492076i	$-0.984330\pi$
$79$	−22.4214	−	59.1204i	−0.283815	−	0.748359i	0.714973	−	0.699152i	$-0.246439\pi$
$80$	0.912091	−	0.912091i	0.0114011	−	0.0114011i
$81$	8.06738	−	21.2719i	0.0995973	−	0.262616i
$82$	−84.9044	+	10.3093i	−1.03542	+	0.125723i
$83$	46.5080	−	149.249i	0.560337	−	1.79818i	−0.0409630	−	0.999161i	$-0.513043\pi$
$83$	46.5080	−	149.249i	0.560337	−	1.79818i	0.601300	−	0.799023i	$-0.294650\pi$
$84$	−3.57030	−	19.4825i	−0.0425036	−	0.231935i
$85$	0.655239	−	0.120077i	0.00770869	−	0.00141267i
$86$	49.0074	+	15.2713i	0.569853	+	0.177573i
$87$	10.4348	+	85.9379i	0.119940	+	0.987792i
$88$	33.1487	+	12.5716i	0.376689	+	0.142859i
$89$	−35.4701	−	35.4701i	−0.398540	−	0.398540i	0.479178	−	0.877718i	$-0.340935\pi$
$89$	−35.4701	−	35.4701i	−0.398540	−	0.398540i	−0.877718	+	0.479178i	$0.840935\pi$
$90$	−0.618986	+	0.234750i	−0.00687762	+	0.00260834i
$91$	−44.4285	−	115.050i	−0.488225	−	1.26428i
$92$	15.4571	−	40.7572i	0.168012	−	0.443013i
$93$	23.0049	+	51.1147i	0.247364	+	0.549621i
$94$	−98.0208	+	142.008i	−1.04277	+	1.51072i
$95$	−0.665707	−	0.751427i	−0.00700744	−	0.00790976i
$96$	−5.89829	−	32.1859i	−0.0614405	−	0.335270i
$97$	−118.374	+	7.16032i	−1.22035	+	0.0738177i	−0.657960	−	0.753053i	$-0.728580\pi$
$97$	−118.374	+	7.16032i	−1.22035	+	0.0738177i	−0.562392	+	0.826871i	$0.690119\pi$
$98$	−27.1920	−	87.2622i	−0.277469	−	0.890430i
$99$	−16.1779	−	16.1779i	−0.163413	−	0.163413i
$100$	21.4516	+	11.2587i	0.214516	+	0.112587i
$101$	33.6276	+	4.08313i	0.332946	+	0.0404270i	0.285303	−	0.958437i	$-0.407906\pi$
$101$	33.6276	+	4.08313i	0.332946	+	0.0404270i	0.0476435	+	0.998864i	$0.484829\pi$
$102$	19.2738	−	42.8247i	0.188959	−	0.419850i
$103$	22.0642	−	42.0398i	0.214215	−	0.408153i	−0.754510	−	0.656288i	$-0.772125\pi$
$103$	22.0642	−	42.0398i	0.214215	−	0.408153i	0.968725	+	0.248135i	$0.0798178\pi$
$104$	−31.6396	−	81.9324i	−0.304227	−	0.787812i
$105$	1.23248	−	0.646857i	0.0117379	−	0.00616055i
$106$	206.956	−	12.5185i	1.95241	−	0.118099i
$107$	−11.7854	+	10.4409i	−0.110144	+	0.0975788i	−0.716397	−	0.697693i	$-0.754210\pi$
$107$	−11.7854	+	10.4409i	−0.110144	+	0.0975788i	0.606254	+	0.795271i	$0.292672\pi$
$108$	−6.67528	+	27.0827i	−0.0618081	+	0.250765i
$109$	134.285	+	171.402i	1.23197	+	1.57249i	0.654394	+	0.756154i	$0.272924\pi$
$109$	134.285	+	171.402i	1.23197	+	1.57249i	0.577574	+	0.816338i	$0.303999\pi$
$110$	0.0481069	−	0.795302i	0.000437336	−	0.00723002i
$111$	−7.29111	+	3.28146i	−0.0656857	+	0.0295627i
$112$	−53.4492	−	171.524i	−0.477225	−	1.53147i
$113$	93.7826	−	49.2209i	0.829934	−	0.435583i	0.00443763	−	0.999990i	$-0.498587\pi$
$113$	93.7826	−	49.2209i	0.829934	−	0.435583i	0.825497	+	0.564407i	$0.190895\pi$
$114$	−70.2563	+	8.53066i	−0.616284	+	0.0748304i
$115$	3.05765	+	0.184954i	0.0265883	+	0.00160830i
$116$	−9.32198	−	37.8207i	−0.0803619	−	0.326041i
$117$	−3.08082	+	56.5963i	−0.0263318	+	0.483729i
$118$	−209.544	−	51.6479i	−1.77580	−	0.437694i
$119$	27.6033	−	88.5820i	0.231960	−	0.744386i
$120$	0.877711	−	0.460658i	0.00731426	−	0.00383882i
$121$	−87.3903	+	33.1428i	−0.722234	+	0.273907i
$122$	−176.353	−	79.3701i	−1.44552	−	0.650574i
$123$	−81.2923	−	14.8974i	−0.660913	−	0.121117i
$124$	−13.0481	−	21.5842i	−0.105227	−	0.174066i
$125$	−0.613828	+	3.34955i	−0.00491062	+	0.0267964i
$126$	−11.1142	+	91.5335i	−0.0882077	+	0.726456i
$127$	183.649	−	69.6488i	1.44605	−	0.548416i	0.498184	−	0.867071i	$-0.334000\pi$
$127$	183.649	−	69.6488i	1.44605	−	0.548416i	0.947871	+	0.318655i	$0.103231\pi$
$128$	−45.8563	−	147.158i	−0.358252	−	1.14967i
$129$	40.8216	+	28.1771i	0.316446	+	0.218427i
$130$	−1.54642	+	1.22667i	−0.0118956	+	0.00943595i
$131$	14.1630	+	20.5186i	0.108114	+	0.156631i	0.873306	−	0.487172i	$-0.161971\pi$
$131$	14.1630	+	20.5186i	0.108114	+	0.156631i	−0.765192	+	0.643802i	$0.777356\pi$
$132$	−8.62419	−	6.75662i	−0.0653348	−	0.0511865i
$133$	−135.762	+	33.4624i	−1.02077	+	0.251597i
$134$	87.3088	+	60.2649i	0.651559	+	0.449738i
$135$	−1.95660	+	0.118352i	−0.0144933	+	0.000876684i
$136$	19.6576	−	63.0835i	0.144541	−	0.463849i
$137$	−100.815	+	78.9832i	−0.735873	+	0.576519i	−0.913141	−	0.407643i	$-0.866351\pi$
$137$	−100.815	+	78.9832i	−0.735873	+	0.576519i	0.177269	+	0.984162i	$0.443274\pi$
$138$	133.181	−	169.993i	0.965082	−	1.23184i
$139$	62.2473	+	55.1463i	0.447823	+	0.396736i	0.856669	−	0.515867i	$-0.172530\pi$
$139$	62.2473	+	55.1463i	0.447823	+	0.396736i	−0.408846	+	0.912603i	$0.634069\pi$
$140$	−0.515442	+	0.355784i	−0.00368173	+	0.00254131i
$141$	−131.253	+	102.830i	−0.930874	+	0.729293i
$142$	114.667	−	13.9231i	0.807514	−	0.0980500i
$143$	−60.5935	−	31.3371i	−0.423731	−	0.219141i
$144$	−9.95244	+	81.9657i	−0.0691142	+	0.569206i
$145$	2.34259	−	1.41614i	0.0161558	−	0.00976652i
$146$	115.118			0.788480
$147$		−	88.3209i		−	0.600822i
$148$	3.07881	−	1.86121i	0.0208028	−	0.0125757i
$149$	151.111	+	68.0095i	1.01417	+	0.456440i	0.848191	−	0.529690i	$-0.177692\pi$
$149$	151.111	+	68.0095i	1.01417	+	0.456440i	0.165976	+	0.986130i	$0.446922\pi$
$150$	84.8689	+	84.8689i	0.565792	+	0.565792i
$151$	−157.190	+	70.7455i	−1.04099	+	0.468513i	−0.857487	−	0.514505i	$-0.827976\pi$
$151$	−157.190	+	70.7455i	−1.04099	+	0.468513i	−0.183507	+	0.983018i	$0.558745\pi$
$152$	−96.6828	+	23.8302i	−0.636071	+	0.156777i
$153$	−28.2764	+	31.9174i	−0.184813	+	0.208611i
$154$	−94.9696	−	57.4111i	−0.616686	−	0.372800i
$155$	1.17534	−	1.32668i	0.00758283	−	0.00855925i
$156$	1.80221	+	27.0817i	0.0115526	+	0.173600i
$157$	−28.7737	+	25.4913i	−0.183272	+	0.162365i	−0.749771	−	0.661698i	$-0.769836\pi$
$157$	−28.7737	+	25.4913i	−0.183272	+	0.162365i	0.566499	+	0.824063i	$0.308298\pi$
$158$	25.4068	+	138.641i	0.160803	+	0.877472i
$159$	194.526	+	47.9464i	1.22343	+	0.301549i
$160$	−0.851531	+	0.587770i	−0.00532207	+	0.00367356i
$161$	220.725	−	365.124i	1.37096	−	2.26785i
$162$	−26.2366	+	43.4006i	−0.161954	+	0.267905i
$163$	−24.9251	+	31.8145i	−0.152914	+	0.195181i	−0.857568	−	0.514371i	$-0.828026\pi$
$163$	−24.9251	+	31.8145i	−0.152914	+	0.195181i	0.704654	+	0.709552i	$0.251102\pi$
$164$	37.1196	+	2.24532i	0.226339	+	0.0136910i
$165$	0.273013	−	0.719877i	0.00165463	−	0.00436289i
$166$	−161.948	+	308.566i	−0.975590	+	1.85883i
$167$	−4.09463	+	22.3437i	−0.0245187	+	0.133794i	−0.993602	−	0.112940i	$-0.963973\pi$
$167$	−4.09463	+	22.3437i	−0.0245187	+	0.133794i	0.969083	+	0.246735i	$0.0793577\pi$
$168$		−	138.064i		−	0.821811i
$169$	42.4215	+	163.589i	0.251015	+	0.967983i
$170$	−1.48497			−0.00873511
$171$	63.2082	+	11.5833i	0.369639	+	0.0677388i
$172$	−19.7624	−	10.3721i	−0.114898	−	0.0603029i
$173$	−16.3556	−	6.20285i	−0.0945409	−	0.0358546i	0.306881	−	0.951748i	$-0.400715\pi$
$173$	−16.3556	−	6.20285i	−0.0945409	−	0.0358546i	−0.401422	+	0.915893i	$0.631484\pi$
$174$	11.6517	−	192.626i	0.0669640	−	1.10705i
$175$	186.664	+	146.242i	1.06665	+	0.835670i
$176$	−85.0427	−	51.4101i	−0.483197	−	0.292103i
$177$	−178.467	−	107.887i	−1.00829	−	0.609532i
$178$	63.5214	+	92.0266i	0.356862	+	0.517004i
$179$	−66.0971	+	268.167i	−0.369258	+	1.49814i	0.433128	+	0.901332i	$0.357410\pi$
$179$	−66.0971	+	268.167i	−0.369258	+	1.49814i	−0.802386	+	0.596805i	$0.796436\pi$
$180$	0.283124	−	0.0518844i	0.00157291	−	0.000288246i
$181$	184.717	+	208.502i	1.02053	+	1.15195i	0.988309	+	0.152465i	$0.0487212\pi$
$181$	184.717	+	208.502i	1.02053	+	1.15195i	0.0322261	+	0.999481i	$0.489740\pi$
$182$	51.1874	+	270.118i	0.281249	+	1.48416i
$183$	−139.877	−	123.921i	−0.764357	−	0.677161i
$184$	157.189	−	260.022i	0.854288	−	1.41317i
$185$	0.189241	+	0.167653i	0.00102292	+	0.000906231i
$186$	−29.9030	−	121.321i	−0.160769	−	0.652265i
$187$	−21.0627	−	46.7995i	−0.112635	−	0.250265i
$188$	53.0509	−	53.0509i	0.282186	−	0.282186i
$189$	−112.050	+	248.965i	−0.592858	+	1.31728i
$190$	1.15773	+	1.91512i	0.00609333	+	0.0100796i
$191$	18.9220			0.0990683			0.0495341	−	0.998772i	$-0.484226\pi$
$191$	18.9220			0.0990683			0.0495341	+	0.998772i	$0.484226\pi$
$192$		−	90.2277i		−	0.469936i
$193$	39.0891	+	64.6613i	0.202534	+	0.335033i	0.940493	−	0.339813i	$-0.110364\pi$
$193$	39.0891	+	64.6613i	0.202534	+	0.335033i	−0.737959	+	0.674846i	$0.764210\pi$
$194$	262.432	+	31.8650i	1.35274	+	0.164253i
$195$	−1.77929	+	0.687106i	−0.00912459	+	0.00352362i
$196$	4.79023	+	39.4511i	0.0244400	+	0.201281i
$197$	68.1769	+	87.0213i	0.346075	+	0.441733i	0.928601	−	0.371080i	$-0.121012\pi$
$197$	68.1769	+	87.0213i	0.346075	+	0.441733i	−0.582526	+	0.812812i	$0.697935\pi$
$198$	28.9721	+	41.9734i	0.146324	+	0.211987i
$199$	32.0571	−	36.1850i	0.161091	−	0.181834i	−0.662423	−	0.749130i	$-0.730472\pi$
$199$	32.0571	−	36.1850i	0.161091	−	0.181834i	0.823514	+	0.567296i	$0.192010\pi$
$200$	132.933	+	104.146i	0.664663	+	0.520730i
$201$	63.2219	+	80.6968i	0.314537	+	0.401477i
$202$	−72.0934	−	22.4652i	−0.356898	−	0.111214i
$203$	−23.0204	−	380.572i	−0.113401	−	1.87474i
$204$	−11.5993	+	16.8045i	−0.0568594	+	0.0823751i
$205$	0.625408	+	2.53738i	0.00305077	+	0.0123775i
$206$	−65.2718	+	83.3133i	−0.316853	+	0.404433i
$207$	−161.373	+	111.388i	−0.779578	+	0.538104i
$208$	45.8369	+	241.883i	0.220370	+	1.16290i
$209$	−43.9348	+	63.6505i	−0.210214	+	0.304548i
$210$	−2.96235	+	0.923104i	−0.0141064	+	0.00439573i
$211$	−60.8419	−	160.427i	−0.288350	−	0.760317i	−0.998420	−	0.0561858i	$-0.982106\pi$
$211$	−60.8419	−	160.427i	−0.288350	−	0.760317i	0.710070	−	0.704131i	$-0.248663\pi$
$212$	−89.4912	−	10.8662i	−0.422128	−	0.0512557i
$213$	109.789	+	20.1195i	0.515440	+	0.0944579i
$214$	30.0368	−	18.1579i	0.140359	−	0.0848498i
$215$	0.282720	−	1.54275i	0.00131498	−	0.00717560i
$216$	−79.7963	+	177.300i	−0.369427	+	0.820833i
$217$	−87.5408	−	230.826i	−0.403414	−	1.06372i
$218$	−225.568	−	429.785i	−1.03472	−	1.97149i
$219$	106.202	+	33.0940i	0.484942	+	0.151114i
$220$	−0.0829056	+	0.336361i	−0.000376844	+	0.00152892i
$221$	−51.4799	+	116.253i	−0.232941	+	0.526031i
$222$	17.3055	−	4.26543i	0.0779528	−	0.0192136i
$223$	10.6436	−	175.960i	0.0477291	−	0.789056i	−0.893033	−	0.449990i	$-0.851427\pi$
$223$	10.6436	−	175.960i	0.0477291	−	0.789056i	0.940763	−	0.339066i	$-0.110111\pi$
$224$	17.3710	+	143.063i	0.0775492	+	0.638675i
$225$	−50.6455	−	96.4969i	−0.225091	−	0.428875i
$226$	−225.412	+	70.2412i	−0.997397	+	0.310802i
$227$	155.915	+	346.429i	0.686851	+	1.52612i	0.842725	+	0.538344i	$0.180950\pi$
$227$	155.915	+	346.429i	0.686851	+	1.52612i	−0.155874	+	0.987777i	$0.549819\pi$
$228$	30.7155	+	1.85795i	0.134717	+	0.00814889i
$229$	−1.90041	+	1.48888i	−0.00829873	+	0.00650164i	−0.620860	−	0.783922i	$-0.713216\pi$
$229$	−1.90041	+	1.48888i	−0.00829873	+	0.00650164i	0.612561	+	0.790423i	$0.290139\pi$
$230$	−6.63009	−	1.63417i	−0.0288265	−	0.00710509i
$231$	−71.1098	−	80.2664i	−0.307835	−	0.347473i
$232$	−16.3939	−	271.024i	−0.0706634	−	1.16821i
$233$	−113.879	−	216.979i	−0.488752	−	0.931239i	−0.997523	−	0.0703372i	$-0.977592\pi$
$233$	−113.879	−	216.979i	−0.488752	−	0.931239i	0.508771	−	0.860902i	$-0.330100\pi$
$234$	29.4968	−	122.859i	0.126055	−	0.525037i
$235$	4.66844	+	2.45018i	0.0198657	+	0.0104263i
$236$	85.5690	+	38.5115i	0.362581	+	0.163184i
$237$	−16.4171	+	135.207i	−0.0692704	+	0.570493i
$238$	−96.1188	+	183.139i	−0.403861	+	0.769492i
$239$	−13.3483	+	13.3483i	−0.0558506	+	0.0558506i	−0.734480	−	0.678630i	$-0.762574\pi$
$239$	−13.3483	+	13.3483i	−0.0558506	+	0.0558506i	0.678630	+	0.734480i	$0.262574\pi$
$240$	−2.65270	+	0.826615i	−0.0110529	+	0.00344423i
$241$	−8.26987	−	136.717i	−0.0343148	−	0.567292i	−0.974184	−	0.225756i	$-0.927515\pi$
$241$	−8.26987	−	136.717i	−0.0343148	−	0.567292i	0.939869	−	0.341535i	$-0.110947\pi$
$242$	204.935	−	37.5558i	0.846840	−	0.155189i
$243$	157.187	−	139.255i	0.646859	−	0.573067i
$244$	69.2014	+	47.7663i	0.283612	+	0.195763i
$245$	−2.54672	+	1.14619i	−0.0103948	+	0.00467831i
$246$	172.261	+	65.3299i	0.700247	+	0.265569i
$247$	190.063	−	24.2425i	0.769488	−	0.0981476i
$248$	−62.3420	−	164.382i	−0.251379	−	0.662832i
$249$	−238.111	+	238.111i	−0.956270	+	0.956270i
$250$	2.69184	−	7.09779i	0.0107674	−	0.0283912i
$251$	−226.667	+	27.5224i	−0.903056	+	0.109651i	−0.558875	−	0.829252i	$-0.688767\pi$
$251$	−226.667	+	27.5224i	−0.903056	+	0.109651i	−0.344182	+	0.938903i	$0.611844\pi$
$252$	11.9272	−	38.2756i	0.0473300	−	0.151887i
$253$	−42.5393	−	232.129i	−0.168139	−	0.917507i
$254$	−430.667	+	78.9227i	−1.69554	+	0.310719i
$255$	−1.36996	−	0.426897i	−0.00537239	−	0.00167410i
$256$	21.2206	+	174.767i	0.0828929	+	0.682684i
$257$	61.3533	+	23.2682i	0.238729	+	0.0905378i	0.471068	−	0.882097i	$-0.343869\pi$
$257$	61.3533	+	23.2682i	0.238729	+	0.0905378i	−0.232339	+	0.972635i	$0.574638\pi$
$258$	−78.1859	−	78.1859i	−0.303046	−	0.303046i
$259$	32.9255	−	12.4870i	0.127126	−	0.0482124i
$260$	0.757508	−	0.403419i	0.00291349	−	0.00155161i
$261$	−62.1349	+	163.836i	−0.238065	+	0.627725i
$262$	−22.8099	−	50.6815i	−0.0870606	−	0.193441i
$263$	−84.4127	+	122.293i	−0.320961	+	0.464992i	−0.949941	−	0.312429i	$-0.898857\pi$
$263$	−84.4127	+	122.293i	−0.320961	+	0.464992i	0.628980	+	0.777421i	$0.283473\pi$
$264$	−50.6407	−	57.1615i	−0.191821	−	0.216521i
$265$	−1.14194	−	6.23135i	−0.00430920	−	0.0235145i
$266$	311.127	−	18.8197i	1.16965	−	0.0707508i
$267$	32.1460	+	103.160i	0.120397	+	0.386368i
$268$	−32.6167	−	32.6167i	−0.121704	−	0.121704i
$269$	−225.308	−	118.251i	−0.837577	−	0.439594i	−0.00932951	−	0.999956i	$-0.502970\pi$
$269$	−225.308	−	118.251i	−0.837577	−	0.439594i	−0.828248	+	0.560362i	$0.810662\pi$
$270$	4.33772	+	0.526695i	0.0160656	+	0.00195072i
$271$	125.335	−	278.483i	0.462491	−	1.02761i	−0.522123	−	0.852870i	$-0.674860\pi$
$271$	125.335	−	278.483i	0.462491	−	1.02761i	0.984614	−	0.174743i	$-0.0559094\pi$
$272$	−86.0718	+	163.996i	−0.316440	+	0.602927i
$273$	−30.4301	+	263.913i	−0.111465	+	0.966713i
$274$	252.790	−	132.674i	0.922590	−	0.484213i
$275$	130.923	−	7.91940i	0.476085	−	0.0287978i
$276$	−70.2816	+	62.2641i	−0.254643	+	0.225594i
$277$	89.0970	−	361.481i	0.321650	−	1.30498i	−0.558190	−	0.829713i	$-0.688504\pi$
$277$	89.0970	−	361.481i	0.321650	−	1.30498i	0.879839	−	0.475271i	$-0.157650\pi$
$278$	−114.329	−	145.930i	−0.411254	−	0.524927i
$279$	−6.85029	+	113.249i	−0.0245530	+	0.405910i
$280$	−3.98106	+	1.79173i	−0.0142181	+	0.00639903i
$281$	47.9876	+	153.998i	0.170774	+	0.548034i	0.999940	−	0.0109691i	$-0.00349166\pi$
$281$	47.9876	+	153.998i	0.170774	+	0.548034i	−0.829166	+	0.559003i	$0.811184\pi$
$282$	329.114	−	172.732i	1.16707	−	0.612526i
$283$	−205.942	+	25.0059i	−0.727709	+	0.0883599i	−0.476003	−	0.879444i	$-0.657915\pi$
$283$	−205.942	+	25.0059i	−0.727709	+	0.0883599i	−0.251707	+	0.967804i	$0.580992\pi$
$284$	−50.1316	−	3.03240i	−0.176520	−	0.0106775i
$285$	0.517510	+	2.09962i	0.00181583	+	0.00736709i
$286$	120.270	+	93.0595i	0.420523	+	0.325383i
$287$	353.413	+	87.1085i	1.23140	+	0.303514i
$288$	19.7042	−	63.2329i	0.0684173	−	0.219559i
$289$	171.203	−	89.8541i	0.592397	−	0.310914i
$290$	−5.70555	+	2.16383i	−0.0196743	+	0.00746149i
$291$	232.946	+	104.841i	0.800503	+	0.360277i
$292$	−49.2333	−	9.02233i	−0.168607	−	0.0308984i
$293$	−25.8940	−	42.8340i	−0.0883755	−	0.146191i	0.808466	−	0.588543i	$-0.200298\pi$
$293$	−25.8940	−	42.8340i	−0.0883755	−	0.146191i	−0.896842	+	0.442352i	$0.854144\pi$
$294$	−35.4892	+	193.658i	−0.120711	+	0.658701i
$295$	−0.794850	+	6.54618i	−0.00269441	+	0.0221904i
$296$	23.4478	−	8.89259i	0.0792157	−	0.0300425i
$297$	44.9270	+	144.176i	0.151269	+	0.485441i
$298$	−304.008	−	209.842i	−1.02016	−	0.704167i
$299$	−357.781	+	462.393i	−1.19659	+	1.54647i
$300$	−29.6448	−	42.9479i	−0.0988161	−	0.143160i
$301$	−171.966	−	134.726i	−0.571314	−	0.447596i
$302$	373.092	−	91.9590i	1.23541	−	0.304500i
$303$	−60.0515	−	41.4506i	−0.198190	−	0.136801i
$304$	278.606	−	16.8525i	0.916466	−	0.0554360i
$305$	−1.75797	+	5.64152i	−0.00576384	+	0.0184968i
$306$	74.8257	−	58.6222i	0.244529	−	0.191576i
$307$	141.404	−	180.488i	0.460598	−	0.587910i	−0.499940	−	0.866060i	$-0.666645\pi$
$307$	141.404	−	180.488i	0.460598	−	0.587910i	0.960537	+	0.278151i	$0.0897214\pi$
$308$	36.1167	+	31.9966i	0.117262	+	0.103885i
$309$	−84.1673	+	58.0965i	−0.272386	+	0.188014i
$310$	−3.11022	+	2.43670i	−0.0100330	+	0.00786032i
$311$	−28.7109	+	3.48614i	−0.0923181	+	0.0112094i	−0.166565	−	0.986030i	$-0.553268\pi$
$311$	−28.7109	+	3.48614i	−0.0923181	+	0.0112094i	0.0742473	+	0.997240i	$0.476345\pi$
$312$	−21.6707	+	187.945i	−0.0694574	+	0.602387i
$313$	31.5974	−	260.228i	0.100950	−	0.831398i	−0.851004	−	0.525159i	$-0.824006\pi$
$313$	31.5974	−	260.228i	0.100950	−	0.831398i	0.951954	−	0.306240i	$-0.0990709\pi$
$314$	73.3340	−	44.3320i	0.233548	−	0.141185i
$315$	2.81736			0.00894400
$316$		−	61.2845i		−	0.193938i
$317$	−358.223	+	216.553i	−1.13004	+	0.683133i	−0.953570	−	0.301173i	$-0.902622\pi$
$317$	−358.223	+	216.553i	−1.13004	+	0.683133i	−0.176471	+	0.984306i	$0.556468\pi$
$318$	−407.265	−	183.295i	−1.28071	−	0.576399i
$319$	−149.121	−	149.121i	−0.467465	−	0.467465i
$320$	−2.60170	+	1.17093i	−0.00813032	+	0.00365916i
$321$	32.9304	−	8.11662i	0.102587	−	0.0252854i
$322$	−630.691	+	711.903i	−1.95867	+	2.21088i
$323$	123.357	+	74.5722i	0.381912	+	0.230874i
$324$	14.6223	−	16.5051i	0.0451304	−	0.0509417i
$325$	−231.149	−	228.377i	−0.711228	−	0.702697i
$326$	67.4360	−	59.7431i	0.206859	−	0.183261i
$327$	−84.5445	−	461.344i	−0.258546	−	1.41084i
$328$	251.682	+	62.0341i	0.767324	+	0.189128i
$329$	604.355	−	417.156i	1.83695	−	1.26795i
$330$	−0.887888	+	1.46875i	−0.00269057	+	0.00445075i
$331$	188.296	−	311.480i	0.568870	−	0.941026i	−0.430393	−	0.902642i	$-0.641625\pi$
$331$	188.296	−	311.480i	0.568870	−	0.941026i	0.999263	−	0.0383847i	$-0.0122212\pi$
$332$	93.4450	−	119.274i	0.281461	−	0.359258i
$333$	−16.1540	−	0.977140i	−0.0485107	−	0.00293435i
$334$	17.9563	−	47.3469i	0.0537614	−	0.141757i
$335$	1.50642	−	2.87024i	0.00449677	−	0.00856788i
$336$	−69.7583	+	380.659i	−0.207614	+	1.13291i
$337$			561.794i			1.66705i	0.552485	+	0.833523i	$0.313680\pi$
$337$			561.794i			1.66705i	−0.552485	+	0.833523i	$0.686320\pi$
$338$	−27.2827	−	375.742i	−0.0807180	−	1.11166i
$339$	−228.147			−0.672999
$340$	0.635086	+	0.116384i	0.00186790	+	0.000342305i
$341$	−120.909	−	63.4578i	−0.354571	−	0.186093i
$342$	−133.940	−	50.7968i	−0.391638	−	0.148529i
$343$	4.58134	−	75.7385i	0.0133567	−	0.220812i
$344$	−122.465	−	95.9452i	−0.356003	−	0.278910i
$345$	−5.64681	−	3.41361i	−0.0163676	−	0.00989453i
$346$	33.3699	+	20.1728i	0.0964448	+	0.0583029i
$347$	85.7639	+	124.250i	0.247158	+	0.358070i	0.926853	−	0.375425i	$-0.122503\pi$
$347$	85.7639	+	124.250i	0.247158	+	0.358070i	−0.679695	+	0.733495i	$0.737888\pi$
$348$	−20.0801	+	81.4683i	−0.0577016	+	0.234104i
$349$	−46.9117	+	8.59689i	−0.134418	+	0.0246329i	−0.247043	−	0.969005i	$-0.579459\pi$
$349$	−46.9117	+	8.59689i	−0.134418	+	0.0246329i	0.112625	+	0.993638i	$0.464074\pi$
$350$	−350.529	−	395.666i	−1.00151	−	1.13047i
$351$	191.610	−	321.325i	0.545898	−	0.915457i
$352$	59.6663	+	52.8597i	0.169506	+	0.150170i
$353$	10.9412	−	18.0989i	0.0309949	−	0.0512718i	−0.839900	−	0.542742i	$-0.817386\pi$
$353$	10.9412	−	18.0989i	0.0309949	−	0.0512718i	0.870895	+	0.491470i	$0.163540\pi$
$354$	347.967	+	308.272i	0.982959	+	0.870826i
$355$	−0.844641	−	3.42684i	−0.00237927	−	0.00965308i
$356$	−19.9540	−	44.3361i	−0.0560507	−	0.124539i
$357$	−141.323	+	141.323i	−0.395863	+	0.395863i
$358$	252.684	−	561.441i	0.705821	−	1.56827i
$359$	86.8245	+	143.625i	0.241851	+	0.400070i	0.953000	−	0.302971i	$-0.0979786\pi$
$359$	86.8245	+	143.625i	0.241851	+	0.400070i	−0.711149	+	0.703042i	$0.751825\pi$
$360$	2.00638			0.00557327
$361$			143.770i			0.398256i
$362$	−321.242	−	531.399i	−0.887408	−	1.46795i
$363$	199.860	+	24.2673i	0.550577	+	0.0668522i
$364$	−0.721261	−	119.535i	−0.00198149	−	0.328392i
$365$	−0.423982	−	3.49180i	−0.00116159	−	0.00956659i
$366$	256.910	+	327.922i	0.701941	+	0.895962i
$367$	71.0555	+	102.942i	0.193612	+	0.280495i	0.907752	−	0.419508i	$-0.137797\pi$
$367$	71.0555	+	102.942i	0.193612	+	0.280495i	−0.714140	+	0.700003i	$0.753182\pi$
$368$	−564.767	+	637.490i	−1.53469	+	1.73231i
$369$	−131.682	−	103.166i	−0.356861	−	0.279583i
$370$	−0.347576	−	0.443647i	−0.000939394	−	0.00119905i
$371$	−842.419	−	262.508i	−2.27067	−	0.707570i
$372$	3.28030	+	54.2299i	0.00881802	+	0.145779i
$373$	144.543	−	209.407i	0.387515	−	0.561413i	−0.579874	−	0.814706i	$-0.696898\pi$
$373$	144.543	−	209.407i	0.387515	−	0.561413i	0.967390	+	0.253293i	$0.0815137\pi$
$374$	27.3785	+	111.079i	0.0732046	+	0.297003i
$375$	4.52382	−	5.77423i	0.0120635	−	0.0153979i
$376$	430.390	−	297.077i	1.14466	−	0.790099i
$377$	−28.3977	+	521.681i	−0.0753256	+	1.38377i
$378$	345.728	−	500.873i	0.914624	−	1.32506i
$379$	−410.137	+	127.804i	−1.08216	+	0.337213i	−0.786190	−	0.617985i	$-0.787949\pi$
$379$	−410.137	+	127.804i	−1.08216	+	0.337213i	−0.295966	+	0.955198i	$0.595642\pi$
$380$	−0.345038	−	0.909789i	−0.000907994	−	0.00239418i
$381$	−420.001	−	50.9973i	−1.10236	−	0.133851i
$382$	−41.4897	−	7.60327i	−0.108612	−	0.0199039i
$383$	478.382	−	289.192i	1.24904	−	0.755070i	0.270816	−	0.962631i	$-0.412707\pi$
$383$	478.382	−	289.192i	1.24904	−	0.755070i	0.978222	+	0.207561i	$0.0665527\pi$
$384$	−59.8486	+	326.583i	−0.155856	+	0.850477i
$385$	−1.39164	+	3.09210i	−0.00361465	+	0.00803142i
$386$	−59.7271	−	157.488i	−0.154734	−	0.407999i
$387$	46.6574	+	88.8983i	0.120562	+	0.229711i
$388$	−109.739	−	34.1959i	−0.282831	−	0.0881338i
$389$	34.5213	−	140.058i	0.0887436	−	0.360047i	−0.909735	−	0.415190i	$-0.863715\pi$
$389$	34.5213	−	140.058i	0.0887436	−	0.360047i	0.998478	+	0.0551426i	$0.0175613\pi$
$390$	4.17749	−	0.791636i	0.0107115	−	0.00202984i
$391$	−427.059	+	105.261i	−1.09222	+	0.269209i
$392$	−16.7257	+	276.508i	−0.0426675	+	0.705378i
$393$	−6.47344	−	53.3135i	−0.0164718	−	0.135658i
$394$	−114.522	−	218.204i	−0.290665	−	0.553816i
$395$	4.11172	−	1.28127i	0.0104094	−	0.00324371i
$396$	−9.10105	−	20.2217i	−0.0229824	−	0.0510649i
$397$	382.722	+	23.1504i	0.964035	+	0.0583134i	0.534890	−	0.844922i	$-0.320353\pi$
$397$	382.722	+	23.1504i	0.964035	+	0.0583134i	0.429146	+	0.903235i	$0.358815\pi$
$398$	−84.8304	+	66.4604i	−0.213142	+	0.166986i
$399$	292.441	+	72.0801i	0.732934	+	0.180652i
$400$	−313.890	−	354.308i	−0.784724	−	0.885770i
$401$	−0.516470	−	8.53827i	−0.00128796	−	0.0212925i	0.997475	−	0.0710213i	$-0.0226258\pi$
$401$	−0.516470	−	8.53827i	−0.00128796	−	0.0212925i	−0.998763	+	0.0497288i	$0.984164\pi$
$402$	−106.199	−	202.345i	−0.264176	−	0.503346i
$403$	82.9374	+	327.961i	0.205800	+	0.813799i
$404$	29.0719	+	15.2581i	0.0719602	+	0.0377676i
$405$	1.41307	+	0.635972i	0.00348907	+	0.00157030i
$406$	−102.446	+	843.718i	−0.252330	+	2.07812i
$407$	9.05175	−	17.2467i	0.0222402	−	0.0423751i
$408$	−100.643	+	100.643i	−0.246674	+	0.246674i
$409$	303.772	−	94.6590i	0.742718	−	0.231440i	0.0972842	−	0.995257i	$-0.468984\pi$
$409$	303.772	−	94.6590i	0.742718	−	0.231440i	0.645434	+	0.763816i	$0.276677\pi$
$410$	−0.351739	−	5.81493i	−0.000857899	−	0.0141828i
$411$	271.352	−	49.7271i	0.660224	−	0.120991i
$412$	34.4448	−	30.5154i	0.0836039	−	0.0740666i
$413$	755.882	+	521.748i	1.83022	+	1.26331i
$414$	398.594	−	179.393i	0.962788	−	0.433316i
$415$	9.95599	+	3.77581i	0.0239903	+	0.00909833i
$416$	−1.19155	−	197.477i	−0.00286431	−	0.474703i
$417$	−63.5223	−	167.495i	−0.152332	−	0.401666i
$418$	121.910	−	121.910i	0.291651	−	0.291651i
$419$	−117.504	+	309.832i	−0.280439	+	0.739457i	0.718591	+	0.695432i	$0.244787\pi$
$419$	−117.504	+	309.832i	−0.280439	+	0.739457i	−0.999030	+	0.0440243i	$0.985982\pi$
$420$	1.33927	−	0.162617i	0.00318874	−	0.000387184i
$421$	−228.603	+	733.612i	−0.543000	+	1.74255i	0.118851	+	0.992912i	$0.462079\pi$
$421$	−228.603	+	733.612i	−0.543000	+	1.74255i	−0.661851	+	0.749635i	$0.730229\pi$
$422$	68.9430	+	376.210i	0.163372	+	0.891493i
$423$	−331.963	+	60.8344i	−0.784782	+	0.143817i
$424$	−599.927	−	186.945i	−1.41492	−	0.440907i
$425$	−29.4660	−	242.675i	−0.0693318	−	0.570999i
$426$	−232.645	−	88.2308i	−0.546116	−	0.207115i
$427$	581.971	+	581.971i	1.36293	+	1.36293i
$428$	−14.2691	+	5.41157i	−0.0333391	+	0.0126438i
$429$	84.2021	+	120.427i	0.196275	+	0.280716i
$430$	−1.23982	+	3.26914i	−0.00288330	+	0.00760265i
$431$	−122.252	−	271.633i	−0.283647	−	0.630238i	0.713899	−	0.700249i	$-0.246927\pi$
$431$	−122.252	−	271.633i	−0.283647	−	0.630238i	−0.997546	+	0.0700105i	$0.977697\pi$
$432$	309.590	−	448.518i	0.716643	−	1.03824i
$433$	322.862	+	364.435i	0.745639	+	0.841652i	0.991830	−	0.127569i	$-0.0407175\pi$
$433$	322.862	+	364.435i	0.745639	+	0.841652i	−0.246191	+	0.969221i	$0.579179\pi$
$434$	99.1970	+	541.300i	0.228564	+	1.24724i
$435$	−5.88571	+	0.356020i	−0.0135304	+	0.000818437i
$436$	62.7860	+	201.487i	0.144005	+	0.462127i
$437$	468.702	+	468.702i	1.07254	+	1.07254i
$438$	−219.568	−	115.238i	−0.501297	−	0.263101i
$439$	215.268	+	26.1382i	0.490359	+	0.0595404i	0.361982	−	0.932185i	$-0.382100\pi$
$439$	215.268	+	26.1382i	0.490359	+	0.0595404i	0.128377	+	0.991725i	$0.459023\pi$
$440$	−0.991054	+	2.20203i	−0.00225240	+	0.00500462i
$441$	83.0779	−	158.292i	0.188385	−	0.358938i
$442$	159.591	−	234.218i	0.361066	−	0.529905i
$443$	−230.251	+	120.845i	−0.519753	+	0.272787i	−0.704134	−	0.710068i	$-0.748664\pi$
$443$	−230.251	+	120.845i	−0.519753	+	0.272787i	0.184381	+	0.982855i	$0.440972\pi$
$444$	−7.73546	+	0.467909i	−0.0174222	+	0.00105385i
$445$	2.55743	−	2.26569i	0.00574704	−	0.00509144i
$446$	−94.0421	+	381.544i	−0.210857	+	0.855479i
$447$	−220.138	−	280.985i	−0.492479	−	0.628603i
$448$	−23.9933	+	396.656i	−0.0535564	+	0.885393i
$449$	332.130	−	149.480i	0.739710	−	0.332917i	−0.00528514	−	0.999986i	$-0.501682\pi$
$449$	332.130	−	149.480i	0.739710	−	0.332917i	0.744996	+	0.667069i	$0.232452\pi$
$450$	72.2741	+	231.936i	0.160609	+	0.515413i
$451$	178.271	−	93.5639i	0.395280	−	0.207459i
$452$	101.908	−	12.3739i	0.225461	−	0.0273759i
$453$	370.633	+	22.4192i	0.818174	+	0.0494904i
$454$	−202.667	−	822.254i	−0.446404	−	1.81113i
$455$	8.00479	−	2.54748i	0.0175929	−	0.00559886i
$456$	208.261	+	51.3317i	0.456713	+	0.112570i
$457$	−60.0484	+	192.702i	−0.131397	+	0.421667i	−0.996849	−	0.0793245i	$-0.974724\pi$
$457$	−60.0484	+	192.702i	−0.131397	+	0.421667i	0.865452	+	0.500992i	$0.167031\pi$
$458$	4.76522	−	2.50098i	0.0104044	−	0.00546066i
$459$	263.165	−	99.8052i	0.573343	−	0.217440i
$460$	2.70745	+	1.21853i	0.00588577	+	0.00264897i
$461$	−301.789	−	55.3049i	−0.654641	−	0.119967i	−0.157338	−	0.987545i	$-0.550291\pi$
$461$	−301.789	−	55.3049i	−0.654641	−	0.119967i	−0.497302	+	0.867577i	$0.665676\pi$
$462$	123.667	+	204.571i	0.267678	+	0.442794i
$463$	4.58329	−	25.0102i	0.00989911	−	0.0540177i	−0.978299	−	0.207196i	$-0.933566\pi$
$463$	4.58329	−	25.0102i	0.00989911	−	0.0540177i	0.988199	+	0.153178i	$0.0489509\pi$
$464$	−91.7375	+	755.526i	−0.197710	+	1.62829i
$465$	−3.56983	+	1.35386i	−0.00767705	+	0.00291152i
$466$	162.512	+	521.521i	0.348739	+	1.11914i
$467$	−339.550	−	234.374i	−0.727087	−	0.501872i	0.146092	−	0.989271i	$-0.453330\pi$
$467$	−339.550	−	234.374i	−0.727087	−	0.501872i	−0.873179	+	0.487399i	$0.837946\pi$
$468$	−22.2441	+	50.2319i	−0.0475300	+	0.107333i
$469$	−256.475	−	371.569i	−0.546856	−	0.792257i
$470$	−9.25179	−	7.24831i	−0.0196847	−	0.0154219i
$471$	80.3988	−	19.8165i	0.170698	−	0.0420733i
$472$	538.300	+	371.562i	1.14047	+	0.787207i
$473$	−120.614	+	7.29580i	−0.254998	+	0.0154245i
$474$	90.3262	−	289.867i	0.190562	−	0.611533i
$475$	−289.998	+	227.199i	−0.610522	+	0.478313i
$476$	55.4612	−	70.7909i	0.116515	−	0.148720i
$477$	303.536	+	268.910i	0.636344	+	0.563752i
$478$	34.6319	−	23.9047i	0.0724518	−	0.0500098i
$479$	485.565	−	380.416i	1.01371	−	0.794188i	0.0349855	−	0.999388i	$-0.488862\pi$
$479$	485.565	−	380.416i	1.01371	−	0.794188i	0.978720	+	0.205200i	$0.0657846\pi$
$480$	2.21253	−	0.268650i	0.00460945	−	0.000559688i
$481$	−46.7810	+	11.8304i	−0.0972579	+	0.0245953i
$482$	−36.8028	+	303.098i	−0.0763544	+	0.628835i
$483$	−786.501	+	475.457i	−1.62837	+	0.984382i
$484$	−90.5893			−0.187168
$485$		−	8.07755i		−	0.0166547i
$486$	−400.613	+	242.179i	−0.824307	+	0.498311i
$487$	441.297	+	198.612i	0.906155	+	0.407827i	0.809249	−	0.587466i	$-0.199875\pi$
$487$	441.297	+	198.612i	0.906155	+	0.407827i	0.0969061	+	0.995294i	$0.469105\pi$
$488$	414.450	+	414.450i	0.849282	+	0.849282i
$489$	79.3880	−	35.7296i	0.162348	−	0.0730667i
$490$	6.04467	−	1.48988i	0.0123361	−	0.00304056i
$491$	385.867	−	435.554i	0.785880	−	0.887075i	−0.210005	−	0.977700i	$-0.567348\pi$
$491$	385.867	−	435.554i	0.785880	−	0.887075i	0.995885	+	0.0906251i	$0.0288865\pi$
$492$	−68.5516	−	41.4409i	−0.139333	−	0.0842294i
$493$	−260.640	+	294.202i	−0.528681	+	0.596758i
$494$	−426.487	−	23.2158i	−0.863334	−	0.0469956i
$495$	1.16645	−	1.03338i	0.00235646	−	0.00208764i
$496$	88.8282	+	484.720i	0.179089	+	0.977258i
$497$	−477.299	−	117.644i	−0.960360	−	0.236708i
$498$	617.776	−	426.420i	1.24051	−	0.856265i
$499$	323.346	−	534.879i	0.647988	−	1.07190i	−0.343178	−	0.939271i	$-0.611503\pi$
$499$	323.346	−	534.879i	0.647988	−	1.07190i	0.991165	−	0.132632i	$-0.0423429\pi$
$500$	−1.70752	+	2.82459i	−0.00341504	+	0.00564917i
$501$	30.1768	−	38.5179i	0.0602332	−	0.0768820i
$502$	508.064	+	30.7322i	1.01208	+	0.0612196i
$503$	77.1064	−	203.313i	0.153293	−	0.404201i	−0.836267	−	0.548323i	$-0.815267\pi$
$503$	77.1064	−	203.313i	0.153293	−	0.404201i	0.989560	+	0.144122i	$0.0460358\pi$
$504$	129.868	−	247.443i	0.257675	−	0.490959i
$505$	−0.415902	+	2.26950i	−0.000823568	+	0.00449406i
$506$			526.075i			1.03967i
$507$	82.8481	−	354.484i	0.163408	−	0.699180i
$508$	190.372			0.374747
$509$	−450.312	−	82.5227i	−0.884699	−	0.162127i	−0.281351	−	0.959605i	$-0.590782\pi$
$509$	−450.312	−	82.5227i	−0.884699	−	0.162127i	−0.603348	+	0.797478i	$0.706167\pi$
$510$	2.83233	+	1.48652i	0.00555358	+	0.00291474i
$511$	−458.083	−	173.728i	−0.896443	−	0.339976i
$512$	−13.5308	+	223.691i	−0.0264274	+	0.436897i
$513$	−333.888	−	261.585i	−0.650854	−	0.509912i
$514$	−125.178	−	75.6725i	−0.243536	−	0.147223i
$515$	2.76749	+	1.67300i	0.00537376	+	0.00324855i
$516$	27.3105	+	39.5660i	0.0529273	+	0.0766784i
$517$	97.2069	−	394.384i	0.188021	−	0.762831i
$518$	−77.2122	+	14.1497i	−0.149058	+	0.0273159i
$519$	24.9862	+	28.2035i	0.0481429	+	0.0543421i
$520$	5.70059	−	1.81418i	0.0109627	−	0.00348882i
$521$	274.001	+	242.744i	0.525914	+	0.465919i	0.883813	−	0.467841i	$-0.154968\pi$
$521$	274.001	+	242.744i	0.525914	+	0.465919i	−0.357898	+	0.933761i	$0.616507\pi$
$522$	202.074	−	334.271i	0.387115	−	0.640366i
$523$	−616.281	−	545.977i	−1.17836	−	1.04393i	−0.998180	−	0.0602995i	$-0.980794\pi$
$523$	−616.281	−	545.977i	−1.17836	−	1.04393i	−0.180177	−	0.983634i	$-0.557667\pi$
$524$	5.78310	+	23.4630i	0.0110365	+	0.0447766i
$525$	−209.636	−	465.791i	−0.399306	−	0.887221i
$526$	234.229	−	234.229i	0.445302	−	0.445302i
$527$	−104.449	+	232.076i	−0.198195	+	0.440372i
$528$	110.741	+	183.188i	0.209736	+	0.346946i
$529$	−1493.57			−2.82339
$530$			14.1221i			0.0266455i
$531$	−218.372	−	361.232i	−0.411247	−	0.680286i
$532$	−134.537	−	16.3357i	−0.252888	−	0.0307062i
$533$	−467.423	−	174.052i	−0.876967	−	0.326551i
$534$	−29.0336	−	239.113i	−0.0543700	−	0.447777i
$535$	−0.661397	−	0.844211i	−0.00123626	−	0.00157796i
$536$	−182.648	−	264.612i	−0.340762	−	0.493679i
$537$	394.516	−	445.316i	0.734666	−	0.829267i
$538$	446.510	+	349.818i	0.829944	+	0.650220i
$539$	132.691	+	169.368i	0.246181	+	0.314226i
$540$	−1.81386	−	0.565222i	−0.00335900	−	0.00104671i
$541$	10.4726	+	173.132i	0.0193578	+	0.320022i	0.994946	+	0.100414i	$0.0320166\pi$
$541$	10.4726	+	173.132i	0.0193578	+	0.320022i	−0.975588	+	0.219609i	$0.929522\pi$
$542$	−386.718	+	560.258i	−0.713502	+	1.03369i
$543$	−143.596	−	582.592i	−0.264449	−	1.07291i
$544$	91.6242	−	116.950i	0.168427	−	0.214981i
$545$	−12.2056	+	8.42493i	−0.0223956	+	0.0154586i
$546$	172.769	−	566.445i	0.316426	−	1.03744i
$547$	71.9254	−	104.202i	0.131491	−	0.190497i	−0.751708	−	0.659496i	$-0.770770\pi$
$547$	71.9254	−	104.202i	0.131491	−	0.190497i	0.883199	+	0.468999i	$0.155385\pi$
$548$	−118.510	+	36.9293i	−0.216260	+	0.0673893i
$549$	−134.129	−	353.669i	−0.244315	−	0.644205i
$550$	−290.253	−	35.2431i	−0.527733	−	0.0640784i
$551$	582.627	+	106.770i	1.05740	+	0.193776i
$552$	−560.105	+	338.595i	−1.01468	+	0.613398i
$553$	108.126	−	590.026i	0.195527	−	1.06696i
$554$	−340.610	+	756.805i	−0.614820	+	1.36607i
$555$	−0.193117	−	0.509208i	−0.000347959	−	0.000917491i
$556$	37.4585	+	71.3711i	0.0673713	+	0.128365i
$557$	49.0300	+	15.2784i	0.0880251	+	0.0274297i	0.341199	−	0.939991i	$-0.389167\pi$
$557$	49.0300	+	15.2784i	0.0880251	+	0.0274297i	−0.253174	+	0.967421i	$0.581475\pi$
$558$	60.5261	−	245.564i	0.108470	−	0.440079i
$559$	212.948	+	210.393i	0.380944	+	0.376374i
$560$	11.8815	−	2.92853i	0.0212170	−	0.00522952i
$561$	−6.67475	+	110.347i	−0.0118979	+	0.196697i
$562$	−43.3413	−	356.948i	−0.0771197	−	0.635138i
$563$	−400.440	−	762.976i	−0.711262	−	1.35520i	−0.925625	−	0.378442i	$-0.876460\pi$
$563$	−400.440	−	762.976i	−0.711262	−	1.35520i	0.214363	−	0.976754i	$-0.431232\pi$
$564$	−154.292	+	48.0793i	−0.273567	+	0.0852470i
$565$	2.96078	+	6.57857i	0.00524031	+	0.0116435i
$566$	461.609	+	27.9222i	0.815564	+	0.0493326i
$567$	169.899	−	133.107i	0.299645	−	0.234757i
$568$	−339.908	−	83.7797i	−0.598429	−	0.147499i
$569$	−324.207	−	365.954i	−0.569784	−	0.643153i	0.391020	−	0.920382i	$-0.372122\pi$
$569$	−324.207	−	365.954i	−0.569784	−	0.643153i	−0.960804	+	0.277229i	$0.910584\pi$
$570$	−0.291055	−	4.81171i	−0.000510623	−	0.00844160i
$571$	464.831	+	885.662i	0.814065	+	1.55107i	0.834322	+	0.551277i	$0.185859\pi$
$571$	464.831	+	885.662i	0.814065	+	1.55107i	−0.0202572	+	0.999795i	$0.506449\pi$
$572$	−44.1429	−	49.2254i	−0.0771729	−	0.0860584i
$573$	−36.0906	−	18.9418i	−0.0629853	−	0.0330572i
$574$	−739.914	−	333.008i	−1.28905	−	0.580154i
$575$	135.497	−	1115.92i	0.235647	−	1.94073i
$576$	84.8716	−	161.709i	0.147347	−	0.280745i
$577$	−350.032	+	350.032i	−0.606641	+	0.606641i	−0.942067	−	0.335425i	$-0.891120\pi$
$577$	−350.032	+	350.032i	−0.606641	+	0.606641i	0.335425	+	0.942067i	$0.391120\pi$
$578$	−411.496	+	128.227i	−0.711930	+	0.221846i
$579$	−9.82705	−	162.460i	−0.0169724	−	0.280588i
$580$	2.60972	−	0.478249i	0.00449951	−	0.000824566i
$581$	1110.09	−	983.458i	1.91066	−	1.69270i
$582$	−468.646	−	323.483i	−0.805234	−	0.555813i
$583$	−445.065	+	200.308i	−0.763405	+	0.343581i
$584$	−326.223	−	123.720i	−0.558600	−	0.211849i
$585$	−3.83523	−	0.442216i	−0.00655595	−	0.000755925i
$586$	39.5654	+	104.325i	0.0675177	+	0.178030i
$587$	124.443	−	124.443i	0.211999	−	0.211999i	−0.593117	−	0.805116i	$-0.702103\pi$
$587$	124.443	−	124.443i	0.211999	−	0.211999i	0.805116	+	0.593117i	$0.202103\pi$
$588$	30.3557	−	80.0415i	0.0516254	−	0.136125i
$589$	380.734	−	46.2295i	0.646407	−	0.0784880i
$590$	4.37323	−	14.0342i	0.00741226	−	0.0237868i
$591$	−42.9236	−	234.226i	−0.0726287	−	0.396322i
$592$	−69.1414	+	12.6706i	−0.116793	+	0.0214031i
$593$	−612.423	−	190.839i	−1.03275	−	0.321819i	−0.266145	−	0.963933i	$-0.585750\pi$
$593$	−612.423	−	190.839i	−1.03275	−	0.321819i	−0.766609	+	0.642114i	$0.778058\pi$
$594$	−40.5771	−	334.182i	−0.0683115	−	0.562596i
$595$	5.90905	+	2.24101i	0.00993117	+	0.00376640i
$596$	113.571	+	113.571i	0.190555	+	0.190555i
$597$	−97.3663	+	36.9262i	−0.163093	+	0.0618528i
$598$	970.293	−	870.110i	1.62256	−	1.45503i
$599$	−308.276	+	812.856i	−0.514650	+	1.35702i	0.386009	+	0.922495i	$0.373853\pi$
$599$	−308.276	+	812.856i	−0.514650	+	1.35702i	−0.900659	+	0.434526i	$0.856916\pi$
$600$	−149.292	−	331.712i	−0.248819	−	0.552854i
$601$	−363.566	+	526.717i	−0.604935	+	0.876400i	−0.999090	−	0.0426437i	$-0.986422\pi$
$601$	−363.566	+	526.717i	−0.604935	+	0.876400i	0.394155	+	0.919044i	$0.371037\pi$
$602$	322.927	+	364.509i	0.536424	+	0.605497i
$603$	37.4021	+	204.097i	0.0620267	+	0.338469i
$604$	−166.770	+	10.0877i	−0.276109	+	0.0167015i
$605$	−1.89393	−	6.07785i	−0.00313047	−	0.0100460i
$606$	115.017	+	115.017i	0.189797	+	0.189797i
$607$	−620.037	−	325.421i	−1.02148	−	0.536113i	−0.131116	−	0.991367i	$-0.541856\pi$
$607$	−620.037	−	325.421i	−1.02148	−	0.536113i	−0.890362	+	0.455254i	$0.849548\pi$
$608$	−222.260	−	26.9873i	−0.365559	−	0.0443869i
$609$	−337.062	+	748.921i	−0.553468	+	1.22976i
$610$	6.12152	−	11.6636i	0.0100353	−	0.0191206i
$611$	−888.178	+	473.009i	−1.45365	+	0.774155i
$612$	−36.5957	+	19.2069i	−0.0597968	+	0.0313838i
$613$	373.766	−	22.6087i	0.609733	−	0.0368820i	0.247373	−	0.968920i	$-0.420433\pi$
$613$	373.766	−	22.6087i	0.609733	−	0.0368820i	0.362360	+	0.932038i	$0.381971\pi$
$614$	−382.575	+	338.931i	−0.623086	+	0.552006i
$615$	1.34717	−	5.46569i	0.00219052	−	0.00888729i
$616$	207.425	+	264.758i	0.336728	+	0.429802i
$617$	23.6676	−	391.271i	0.0383591	−	0.634152i	−0.927297	−	0.374327i	$-0.877874\pi$
$617$	23.6676	−	391.271i	0.0383591	−	0.634152i	0.965656	−	0.259824i	$-0.0836647\pi$
$618$	207.895	−	93.5660i	0.336400	−	0.151401i
$619$	−56.1246	−	180.110i	−0.0906698	−	0.290970i	0.898236	−	0.439513i	$-0.144849\pi$
$619$	−56.1246	−	180.110i	−0.0906698	−	0.290970i	−0.988906	+	0.148544i	$0.952541\pi$
$620$	1.52114	−	0.798356i	0.00245345	−	0.00128767i
$621$	1284.81	−	156.004i	2.06894	−	0.251215i
$622$	64.3543	+	3.89272i	0.103463	+	0.00625839i
$623$	−113.887	−	462.058i	−0.182804	−	0.741666i
$624$	154.710	−	507.236i	0.247932	−	0.812878i
$625$	606.501	+	149.489i	0.970401	+	0.239182i
$626$	−173.847	+	557.896i	−0.277711	+	0.891207i
$627$	147.515	−	77.4218i	0.235271	−	0.123480i
$628$	−34.8377	+	13.2122i	−0.0554741	+	0.0210385i
$629$	−33.1038	−	14.8988i	−0.0526292	−	0.0236865i
$630$	−6.17753	−	1.13207i	−0.00980560	−	0.00179694i
$631$	111.896	+	185.099i	0.177332	+	0.293343i	0.931785	−	0.363012i	$-0.118252\pi$
$631$	111.896	+	185.099i	0.177332	+	0.293343i	−0.754453	+	0.656354i	$0.772098\pi$
$632$	77.0020	−	420.186i	0.121839	−	0.664851i
$633$	−44.5488	+	366.892i	−0.0703772	+	0.579609i
$634$	872.478	−	330.887i	1.37615	−	0.521904i
$635$	3.98006	+	12.7725i	0.00626782	+	0.0201141i
$636$	159.812	+	110.310i	0.251276	+	0.173443i
$637$	92.9153	−	524.865i	0.145864	−	0.823963i
$638$	267.053	+	386.893i	0.418579	+	0.606416i
$639$	177.842	+	139.330i	0.278313	+	0.218044i
$640$	10.1937	−	2.51251i	0.0159276	−	0.00392580i
$641$	582.198	+	401.862i	0.908265	+	0.626930i	0.927881	−	0.372877i	$-0.121629\pi$
$641$	582.198	+	401.862i	0.908265	+	0.626930i	−0.0196152	+	0.999808i	$0.506244\pi$
$642$	−75.4669	+	4.56490i	−0.117550	+	0.00711044i
$643$	−67.0945	+	215.314i	−0.104346	+	0.334858i	−0.992098	−	0.125463i	$-0.959958\pi$
$643$	−67.0945	+	215.314i	−0.104346	+	0.334858i	0.887752	+	0.460322i	$0.152266\pi$
$644$	325.527	−	255.034i	0.505476	−	0.396015i
$645$	−2.08360	+	2.65952i	−0.00323039	+	0.00412329i
$646$	−240.517	−	213.079i	−0.372317	−	0.329844i
$647$	179.183	−	123.681i	0.276945	−	0.191161i	−0.421494	−	0.906831i	$-0.638494\pi$
$647$	179.183	−	123.681i	0.276945	−	0.191161i	0.698438	+	0.715670i	$0.253879\pi$
$648$	120.993	−	94.7919i	0.186717	−	0.146284i
$649$	504.324	−	61.2360i	0.777078	−	0.0943544i
$650$	415.067	+	593.634i	0.638564	+	0.913283i
$651$	−64.0979	+	527.894i	−0.0984607	+	0.810897i
$652$	−33.5231	+	20.2654i	−0.0514158	+	0.0310819i
$653$	549.651			0.841732			0.420866	−	0.907123i	$-0.361726\pi$
$653$	549.651			0.841732			0.420866	+	0.907123i	$0.361726\pi$
$654$			1045.55i			1.59869i
$655$	−1.45328	+	0.878538i	−0.00221875	+	0.00134128i
$656$	−662.573	−	298.200i	−1.01002	−	0.454573i
$657$	159.210	+	159.210i	0.242329	+	0.242329i
$658$	−1492.77	+	671.842i	−2.26865	+	1.02104i
$659$	243.131	−	59.9265i	0.368940	−	0.0909355i	−0.0504867	−	0.998725i	$-0.516077\pi$
$659$	243.131	−	59.9265i	0.368940	−	0.0909355i	0.419427	+	0.907789i	$0.362231\pi$
$660$	0.494841	−	0.558560i	0.000749759	−	0.000846303i
$661$	−26.5191	−	16.0314i	−0.0401197	−	0.0242532i	0.497136	−	0.867673i	$-0.334385\pi$
$661$	−26.5191	−	16.0314i	−0.0401197	−	0.0242532i	−0.537256	+	0.843420i	$0.680539\pi$
$662$	−538.029	+	607.310i	−0.812733	+	0.917386i
$663$	214.563	−	170.199i	0.323625	−	0.256710i
$664$	790.551	−	700.367i	1.19059	−	1.05477i
$665$	−1.71673	−	9.36790i	−0.00258155	−	0.0140871i
$666$	35.0278	+	8.63357i	0.0525943	+	0.0129633i
$667$	−1487.47	+	1026.72i	−2.23009	+	1.53932i
$668$	−11.3903	+	18.8418i	−0.0170513	+	0.0282063i
$669$	−196.444	+	324.958i	−0.293638	+	0.485737i
$670$	−4.45639	+	5.68817i	−0.00665133	+	0.00848980i
$671$	454.411	+	27.4868i	0.677214	+	0.0409639i
$672$	110.080	−	290.258i	0.163810	−	0.431931i
$673$	−151.047	+	287.797i	−0.224439	+	0.427632i	−0.971472	−	0.237154i	$-0.923785\pi$
$673$	−151.047	+	287.797i	−0.224439	+	0.427632i	0.747033	+	0.664787i	$0.231478\pi$
$674$	225.741	−	1231.83i	0.334927	−	1.82764i
$675$			719.324i			1.06567i
$676$	−17.7805	+	162.834i	−0.0263025	+	0.240879i
$677$	−594.281			−0.877815			−0.438908	−	0.898532i	$-0.644634\pi$
$677$	−594.281			−0.877815			−0.438908	+	0.898532i	$0.644634\pi$
$678$	500.249	+	91.6741i	0.737831	+	0.135212i
$679$	−996.192	−	522.842i	−1.46715	−	0.770017i
$680$	4.20812	+	1.59593i	0.00618841	+	0.00234695i
$681$	49.4093	−	816.833i	0.0725540	−	1.19946i
$682$	239.614	+	187.725i	0.351340	+	0.275257i
$683$	873.499	+	528.049i	1.27892	+	0.773132i	0.983268	−	0.182165i	$-0.0583107\pi$
$683$	873.499	+	528.049i	1.27892	+	0.773132i	0.295648	+	0.955297i	$0.404465\pi$
$684$	53.3018	+	32.2221i	0.0779266	+	0.0471083i
$685$	−4.95535	−	7.17907i	−0.00723409	−	0.0104804i
$686$	−40.4787	+	164.228i	−0.0590068	+	0.239400i
$687$	5.11514	−	0.937384i	0.00744562	−	0.00136446i
$688$	289.173	+	326.408i	0.420309	+	0.474431i
$689$	1105.57	+	489.576i	1.60460	+	0.710560i
$690$	11.0099	+	9.75392i	0.0159564	+	0.0141361i
$691$	213.812	−	353.688i	0.309424	−	0.511849i	−0.661906	−	0.749587i	$-0.730252\pi$
$691$	213.812	−	353.688i	0.309424	−	0.511849i	0.971329	+	0.237738i	$0.0764060\pi$
$692$	−12.6905	−	11.2428i	−0.0183388	−	0.0162468i
$693$	−51.9439	−	210.745i	−0.0749552	−	0.304105i
$694$	−138.125	−	306.901i	−0.199028	−	0.442221i
$695$	−4.00532	+	4.00532i	−0.00576305	+	0.00576305i
$696$	−240.038	+	533.343i	−0.344882	+	0.766297i
$697$	−194.125	−	321.121i	−0.278514	−	0.460719i
$698$	106.316			0.152315
$699$			527.848i			0.755147i
$700$	118.903	+	196.689i	0.169861	+	0.280985i
$701$	−1153.00	−	140.000i	−1.64479	−	0.199714i	−0.754886	−	0.655856i	$-0.772308\pi$
$701$	−1153.00	−	140.000i	−1.64479	−	0.199714i	−0.889907	+	0.456141i	$0.849231\pi$
$702$	−549.252	+	627.566i	−0.782411	+	0.893969i
$703$	6.59426	+	54.3087i	0.00938018	+	0.0772527i
$704$	135.556	+	173.025i	0.192551	+	0.245774i
$705$	−6.45151	−	9.34662i	−0.00915107	−	0.0132576i
$706$	−31.2629	+	35.2885i	−0.0442818	+	0.0499838i
$707$	252.974	+	198.192i	0.357813	+	0.280329i
$708$	−124.657	−	159.112i	−0.176069	−	0.224735i
$709$	889.003	+	277.025i	1.25388	+	0.390726i	0.851311	−	0.524662i	$-0.175808\pi$
$709$	889.003	+	277.025i	1.25388	+	0.390726i	0.402573	+	0.915388i	$0.368116\pi$
$710$	0.475038	+	7.85331i	0.000669068	+	0.0110610i
$711$	−156.604	+	226.880i	−0.220259	+	0.319100i
$712$	−81.1044	−	329.054i	−0.113911	−	0.462154i
$713$	−721.737	+	921.229i	−1.01225	+	1.29205i
$714$	366.661	−	253.088i	0.513530	−	0.354464i
$715$	2.37976	−	3.99080i	0.00332834	−	0.00558153i
$716$	−152.070	+	220.311i	−0.212388	+	0.307697i
$717$	38.8218	−	12.0974i	0.0541448	−	0.0168722i
$718$	−132.665	−	349.810i	−0.184771	−	0.487201i
$719$	1157.84	+	140.587i	1.61034	+	0.195531i	0.875678	−	0.482896i	$-0.160415\pi$
$719$	1157.84	+	140.587i	1.61034	+	0.195531i	0.734667	+	0.678428i	$0.237338\pi$
$720$	−5.53181	−	1.01374i	−0.00768307	−	0.00140797i
$721$	385.462	−	233.020i	0.534622	−	0.323190i
$722$	57.7699	−	315.240i	0.0800137	−	0.436621i
$723$	−121.087	+	269.043i	−0.167478	+	0.372121i
$724$	95.7393	+	252.444i	0.132237	+	0.348679i
$725$	−466.829	−	889.468i	−0.643902	−	1.22685i
$726$	−428.474	−	133.518i	−0.590185	−	0.183909i
$727$	14.3354	−	58.1610i	0.0197186	−	0.0800014i	−0.960258	−	0.279113i	$-0.909960\pi$
$727$	14.3354	−	58.1610i	0.0197186	−	0.0800014i	0.979977	+	0.199112i	$0.0638057\pi$
$728$	145.246	−	820.474i	0.199514	−	1.12702i
$729$	−638.011	+	157.255i	−0.875186	+	0.215714i
$730$	−0.473430	+	7.82673i	−0.000648534	+	0.0107215i
$731$	27.1458	+	223.565i	0.0371351	+	0.305835i
$732$	−84.1737	−	160.380i	−0.114991	−	0.219098i
$733$	353.236	−	110.073i	0.481905	−	0.150168i	−0.0469201	−	0.998899i	$-0.514941\pi$
$733$	353.236	−	110.073i	0.481905	−	0.150168i	0.528825	+	0.848731i	$0.322633\pi$
$734$	−114.437	−	254.268i	−0.155908	−	0.346414i
$735$	6.00482	+	0.363224i	0.00816982	+	0.000494183i
$736$	537.784	−	421.327i	0.730685	−	0.572455i
$737$	−242.474	−	59.7646i	−0.329002	−	0.0810917i
$738$	247.280	+	279.121i	0.335068	+	0.378213i
$739$	63.0850	+	1042.92i	0.0853653	+	1.41126i	0.748687	+	0.662923i	$0.230684\pi$
$739$	63.0850	+	1042.92i	0.0853653	+	1.41126i	−0.663322	+	0.748334i	$0.730854\pi$
$740$	0.113879	+	0.216979i	0.000153891	+	0.000293214i
$741$	−386.781	−	144.023i	−0.521972	−	0.194364i
$742$	1741.66	+	914.094i	2.34725	+	1.23193i
$743$	655.805	+	295.154i	0.882645	+	0.397246i	0.800471	−	0.599372i	$-0.204583\pi$
$743$	655.805	+	295.154i	0.882645	+	0.397246i	0.0821742	+	0.996618i	$0.473814\pi$
$744$	−45.6472	+	375.939i	−0.0613538	+	0.505294i
$745$	−5.24533	+	9.99414i	−0.00704071	+	0.0134150i
$746$	−401.079	+	401.079i	−0.537640	+	0.537640i
$747$	−650.727	+	202.775i	−0.871121	+	0.271452i
$748$	−3.00337	−	49.6516i	−0.00401520	−	0.0663792i
$749$	−146.926	+	26.9252i	−0.196163	+	0.0359482i
$750$	−12.2394	+	10.8432i	−0.0163192	+	0.0144576i
$751$	1137.34	+	785.052i	1.51444	+	1.04534i	0.979734	+	0.200303i	$0.0641925\pi$
$751$	1137.34	+	785.052i	1.51444	+	1.04534i	0.534705	+	0.845039i	$0.320423\pi$
$752$	−1336.74	+	601.616i	−1.77758	+	0.800022i
$753$	459.880	+	174.409i	0.610730	+	0.231620i
$754$	271.889	−	1132.46i	0.360596	−	1.50194i
$755$	−4.16344	−	10.9781i	−0.00551449	−	0.0145405i
$756$	−187.115	+	187.115i	−0.247507	+	0.247507i
$757$	162.451	−	428.348i	0.214598	−	0.565849i	−0.783885	−	0.620906i	$-0.786765\pi$
$757$	162.451	−	428.348i	0.214598	−	0.565849i	0.998483	+	0.0550569i	$0.0175340\pi$
$758$	950.648	−	115.430i	1.25415	−	0.152282i
$759$	−151.235	+	485.331i	−0.199256	+	0.639435i
$760$	−1.22257	−	6.67133i	−0.00160864	−	0.00877807i
$761$	1175.87	−	215.486i	1.54517	−	0.283162i	0.661018	−	0.750370i	$-0.270125\pi$
$761$	1175.87	−	215.486i	1.54517	−	0.283162i	0.884148	+	0.467208i	$0.154740\pi$
$762$	900.429	+	280.585i	1.18167	+	0.368222i
$763$	248.991	+	2050.63i	0.326332	+	2.68759i
$764$	17.1483	+	6.50348i	0.0224454	+	0.00851240i
$765$	−2.05373	−	2.05373i	−0.00268462	−	0.00268462i
$766$	−1165.13	+	441.877i	−1.52106	+	0.576863i
$767$	−947.078	−	828.892i	−1.23478	−	1.08069i
$768$	134.475	−	354.581i	0.175098	−	0.461694i
$769$	−127.868	−	284.112i	−0.166279	−	0.369456i	0.809854	−	0.586632i	$-0.199546\pi$
$769$	−127.868	−	284.112i	−0.166279	−	0.369456i	−0.976133	+	0.217175i	$0.930316\pi$
$770$	4.29387	−	6.22075i	0.00557646	−	0.00807889i
$771$	−93.7284	−	105.797i	−0.121567	−	0.137221i
$772$	13.2009	+	72.0347i	0.0170996	+	0.0933092i
$773$	−966.638	+	58.4708i	−1.25050	+	0.0756414i	−0.672316	−	0.740264i	$-0.734700\pi$
$773$	−966.638	+	58.4708i	−1.25050	+	0.0756414i	−0.578185	+	0.815905i	$0.696239\pi$
$774$	−66.5830	−	213.672i	−0.0860245	−	0.276062i
$775$	−459.922	−	459.922i	−0.593448	−	0.593448i
$776$	−709.436	−	372.341i	−0.914222	−	0.479821i
$777$	−75.2999	−	9.14306i	−0.0969110	−	0.0117671i
$778$	−131.972	+	293.230i	−0.169630	+	0.376902i
$779$	−262.795	+	500.714i	−0.337349	+	0.642765i
$780$	−1.84866	+	0.0111546i	−0.00237007	+	1.43008e-5i
$781$	−240.763	+	126.362i	−0.308275	+	0.161795i
$782$	978.694	−	59.2001i	1.25153	−	0.0757034i
$783$	865.700	−	766.943i	1.10562	−	0.979494i
$784$	185.823	−	753.913i	0.237019	−	0.961624i
$785$	−1.61478	−	2.06112i	−0.00205705	−	0.00262563i
$786$	−7.22841	+	119.500i	−0.00919646	+	0.152036i
$787$	939.717	−	422.932i	1.19405	−	0.537398i	0.286800	−	0.957990i	$-0.407408\pi$
$787$	939.717	−	422.932i	1.19405	−	0.537398i	0.907250	+	0.420592i	$0.138178\pi$
$788$	31.8767	+	102.296i	0.0404527	+	0.129817i
$789$	283.423	−	148.752i	0.359219	−	0.188532i
$790$	−9.53048	+	1.15721i	−0.0120639	+	0.00146482i
$791$	1002.97	+	60.6685i	1.26798	+	0.0766985i
$792$	−36.9918	−	150.081i	−0.0467068	−	0.189497i
$793$	−700.883	−	883.577i	−0.883837	−	1.11422i
$794$	−829.879	−	204.547i	−1.04519	−	0.257616i
$795$	−4.05981	+	13.0284i	−0.00510667	+	0.0163879i
$796$	41.4887	−	21.7750i	0.0521215	−	0.0273555i
$797$	326.199	−	123.711i	0.409284	−	0.155221i	−0.141366	−	0.989957i	$-0.545149\pi$
$797$	326.199	−	123.711i	0.409284	−	0.155221i	0.550649	+	0.834737i	$0.314380\pi$
$798$	−612.261	−	275.556i	−0.767244	−	0.345309i
$799$	−744.638	−	136.460i	−0.931963	−	0.170789i
$800$	196.433	+	324.939i	0.245541	+	0.406174i
$801$	−39.4232	+	215.125i	−0.0492174	+	0.268571i
$802$	−2.29841	+	18.9291i	−0.00286585	+	0.0236024i
$803$	−253.378	+	96.0935i	−0.315539	+	0.119668i
$804$	29.5600	+	94.8615i	0.0367662	+	0.117987i
$805$	23.9166	+	16.5084i	0.0297100	+	0.0205073i
$806$	−50.0723	−	752.435i	−0.0621245	−	0.933542i
$807$	311.363	+	451.087i	0.385828	+	0.558968i
$808$	180.155	+	141.142i	0.222964	+	0.174681i
$809$	−331.984	+	81.8268i	−0.410364	+	0.101146i	−0.439093	−	0.898442i	$-0.644700\pi$
$809$	−331.984	+	81.8268i	−0.410364	+	0.101146i	0.0287292	+	0.999587i	$0.490854\pi$
$810$	−2.84285	−	1.96228i	−0.00350969	−	0.00242256i
$811$	−954.782	+	57.7537i	−1.17729	+	0.0712129i	−0.637407	−	0.770527i	$-0.719993\pi$
$811$	−954.782	+	57.7537i	−1.17729	+	0.0712129i	−0.539883	+	0.841740i	$0.681531\pi$
$812$	109.940	−	352.809i	0.135394	−	0.434493i
$813$	−517.829	+	405.693i	−0.636936	+	0.499008i
$814$	−26.7775	+	34.1790i	−0.0328962	+	0.0419890i
$815$	−2.06052	−	1.82546i	−0.00252824	−	0.00223983i
$816$	328.335	−	226.633i	0.402371	−	0.277737i
$817$	267.162	−	209.308i	0.327004	−	0.256191i
$818$	−704.105	+	85.4939i	−0.860765	+	0.104516i
$819$	−302.784	+	444.370i	−0.369700	+	0.542576i
$820$	−0.305313	+	2.51447i	−0.000372332	+	0.00306643i
$821$	−756.389	+	457.253i	−0.921302	+	0.556947i	−0.896645	−	0.442749i	$-0.854003\pi$
$821$	−756.389	+	457.253i	−0.921302	+	0.556947i	−0.0246570	+	0.999696i	$0.507849\pi$
$822$	−614.966			−0.748134
$823$			853.146i			1.03663i	0.855190	+	0.518315i	$0.173440\pi$
$823$			853.146i			1.03663i	−0.855190	+	0.518315i	$0.826560\pi$
$824$	274.506	−	165.945i	0.333139	−	0.201389i
$825$	−257.642	−	115.955i	−0.312293	−	0.140552i
$826$	−1447.75	−	1447.75i	−1.75272	−	1.75272i
$827$	199.187	−	89.6468i	0.240855	−	0.108400i	−0.286391	−	0.958113i	$-0.592456\pi$
$827$	199.187	−	89.6468i	0.240855	−	0.108400i	0.527246	+	0.849713i	$0.323225\pi$
$828$	−184.529	+	45.4823i	−0.222861	+	0.0549303i
$829$	−328.474	+	370.770i	−0.396229	+	0.447250i	−0.912439	−	0.409212i	$-0.865804\pi$
$829$	−328.474	+	370.770i	−0.396229	+	0.447250i	0.516211	+	0.856462i	$0.327342\pi$
$830$	−20.3130	−	12.2796i	−0.0244734	−	0.0147947i
$831$	−531.795	+	600.273i	−0.639946	+	0.722350i
$832$	94.9213	−	536.196i	0.114088	−	0.644467i
$833$	300.155	−	265.914i	0.360330	−	0.319225i
$834$	71.9804	+	392.784i	0.0863074	+	0.470964i
$835$	−1.50228	−	0.370278i	−0.00179913	−	0.000443447i
$836$	−61.6928	+	42.5835i	−0.0737952	+	0.0509372i
$837$	387.418	−	640.867i	0.462865	−	0.765672i
$838$	382.144	−	632.143i	0.456019	−	0.754348i
$839$	710.719	−	907.165i	0.847102	−	1.08125i	−0.148624	−	0.988894i	$-0.547484\pi$
$839$	710.719	−	907.165i	0.847102	−	1.08125i	0.995726	−	0.0923523i	$-0.0294386\pi$
$840$	9.38679	+	0.567796i	0.0111748	+	0.000675948i
$841$	−274.511	+	723.826i	−0.326410	+	0.860674i
$842$	796.031	−	1516.71i	0.945405	−	1.80132i
$843$	62.6302	−	341.762i	0.0742944	−	0.405411i
$844$		−	166.299i		−	0.197037i
$845$	−11.2967	+	2.21141i	−0.0133688	+	0.00261706i
$846$	752.328			0.889276
$847$	−872.163	−	159.830i	−1.02971	−	0.188701i
$848$	1559.61	+	818.547i	1.83916	+	0.965268i
$849$	417.831	+	158.462i	0.492145	+	0.186646i
$850$	−32.9026	+	543.944i	−0.0387089	+	0.639935i
$851$	−131.406	−	102.950i	−0.154414	−	0.120975i
$852$	92.5819	+	55.9677i	0.108664	+	0.0656898i
$853$	1148.13	+	694.067i	1.34599	+	0.813677i	0.992557	−	0.121784i	$-0.0388615\pi$
$853$	1148.13	+	694.067i	1.34599	+	0.813677i	0.353430	+	0.935461i	$0.385015\pi$
$854$	−1042.22	−	1509.92i	−1.22040	−	1.76805i
$855$	−1.04748	+	4.24981i	−0.00122513	+	0.00497053i
$856$	−104.633	+	19.1747i	−0.122235	+	0.0224004i
$857$	770.714	+	869.956i	0.899316	+	1.01512i	0.999796	+	0.0201788i	$0.00642355\pi$
$857$	770.714	+	869.956i	0.899316	+	1.01512i	−0.100480	+	0.994939i	$0.532038\pi$
$858$	−136.237	−	297.890i	−0.158784	−	0.347191i
$859$	−462.484	−	409.725i	−0.538398	−	0.476979i	0.349553	−	0.936916i	$-0.386333\pi$
$859$	−462.484	−	409.725i	−0.538398	−	0.476979i	−0.887951	+	0.459937i	$0.847872\pi$
$860$	0.786459	−	1.30096i	0.000914487	−	0.00151275i
$861$	−586.876	−	519.926i	−0.681621	−	0.603863i
$862$	158.910	+	644.723i	0.184350	+	0.747938i
$863$	20.5917	+	45.7529i	0.0238606	+	0.0530161i	0.923445	−	0.383731i	$-0.125361\pi$
$863$	20.5917	+	45.7529i	0.0238606	+	0.0530161i	−0.899584	+	0.436747i	$0.856130\pi$
$864$	−309.122	+	309.122i	−0.357780	+	0.357780i
$865$	0.488987	−	1.08648i	0.000565303	−	0.00125605i
$866$	−561.490	−	928.817i	−0.648372	−	1.07254i
$867$	−416.488			−0.480378
$868$		−	239.276i		−	0.275663i
$869$	−171.650	−	283.943i	−0.197526	−	0.326747i
$870$	13.0485	+	1.58437i	0.0149982	+	0.00182112i
$871$	290.814	+	546.068i	0.333886	+	0.626944i
$872$	177.319	+	1460.35i	0.203347	+	1.67471i
$873$	318.878	+	407.017i	0.365267	+	0.466228i
$874$	−839.372	−	1216.04i	−0.960380	−	1.39135i
$875$	−21.4229	+	24.1815i	−0.0244834	+	0.0276360i
$876$	84.8724	+	66.4932i	0.0968862	+	0.0759055i
$877$	−696.778	−	889.372i	−0.794502	−	1.01411i	−0.999376	−	0.0353186i	$-0.988755\pi$
$877$	−696.778	−	889.372i	−0.794502	−	1.01411i	0.204874	−	0.978788i	$-0.434322\pi$
$878$	−461.507	−	143.811i	−0.525634	−	0.163794i
$879$	6.50978	+	107.620i	0.00740590	+	0.122434i
$880$	3.84505	−	5.57051i	0.00436937	−	0.00633013i
$881$	6.63796	+	26.9313i	0.00753458	+	0.0305690i	0.974589	−	0.224002i	$-0.0719121\pi$
$881$	6.63796	+	26.9313i	0.00753458	+	0.0305690i	−0.967054	+	0.254570i	$0.918066\pi$
$882$	−245.767	+	313.699i	−0.278648	+	0.355667i
$883$	701.375	−	484.124i	0.794309	−	0.548272i	−0.100387	−	0.994948i	$-0.532008\pi$
$883$	701.375	−	484.124i	0.794309	−	0.548272i	0.894695	+	0.446677i	$0.147393\pi$
$884$	−86.6100	+	87.6615i	−0.0979751	+	0.0991646i
$885$	8.06906	−	11.6900i	0.00911758	−	0.0132091i
$886$	553.420	−	172.453i	0.624628	−	0.194642i
$887$	236.132	+	622.628i	0.266214	+	0.701948i	0.999751	+	0.0222992i	$0.00709864\pi$
$887$	236.132	+	622.628i	0.266214	+	0.701948i	−0.733538	+	0.679649i	$0.762132\pi$
$888$	−53.6247	−	6.51121i	−0.0603881	−	0.00733245i
$889$	1832.83	+	335.879i	2.06168	+	0.377816i
$890$	−6.51800	+	3.94027i	−0.00732360	+	0.00442727i
$891$	21.5192	−	117.426i	0.0241517	−	0.131792i
$892$	70.1229	−	155.807i	0.0786131	−	0.174671i
$893$	404.557	+	1066.73i	0.453031	+	1.19454i
$894$	369.783	+	704.563i	0.413628	+	0.788102i
$895$	−17.9605	−	5.59670i	−0.0200676	−	0.00625330i
$896$	349.949	−	1419.80i	0.390568	−	1.58460i
$897$	1145.28	−	523.782i	1.27679	−	0.583927i
$898$	−788.314	+	194.302i	−0.877855	+	0.216372i
$899$	−63.1432	+	1043.88i	−0.0702371	+	1.16116i
$900$	−12.7320	−	104.858i	−0.0141467	−	0.116509i
$901$	422.730	+	805.445i	0.469179	+	0.893945i
$902$	−428.485	+	133.521i	−0.475039	+	0.148028i
$903$	193.128	+	429.113i	0.213874	+	0.475208i
$904$	714.263	+	43.2050i	0.790114	+	0.0477931i
$905$	−14.9354	+	11.7012i	−0.0165032	+	0.0129295i
$906$	−803.665	−	198.086i	−0.887048	−	0.218638i
$907$	−658.237	−	742.996i	−0.725730	−	0.819180i	0.263637	−	0.964622i	$-0.415078\pi$
$907$	−658.237	−	742.996i	−0.725730	−	0.819180i	−0.989367	+	0.145442i	$0.953540\pi$
$908$	22.2322	+	367.542i	0.0244848	+	0.404782i
$909$	−68.6365	−	130.776i	−0.0755077	−	0.143868i
$910$	−18.5755	+	2.36929i	−0.0204126	+	0.00260361i
$911$	497.365	+	261.037i	0.545955	+	0.286539i	0.715065	−	0.699058i	$-0.246397\pi$
$911$	497.365	+	261.037i	0.545955	+	0.286539i	−0.169110	+	0.985597i	$0.554089\pi$
$912$	−548.263	−	246.753i	−0.601166	−	0.270563i
$913$	98.8794	−	814.345i	0.108302	−	0.891944i
$914$	209.098	−	398.402i	0.228772	−	0.435889i
$915$	9.00044	−	9.00044i	0.00983655	−	0.00983655i
$916$	−2.23399	+	0.696138i	−0.00243885	+	0.000759976i
$917$	14.2812	+	236.097i	0.0155738	+	0.257466i
$918$	−617.136	+	113.094i	−0.672261	+	0.123196i
$919$	−475.987	+	421.688i	−0.517940	+	0.458855i	−0.881139	−	0.472857i	$-0.843223\pi$
$919$	−475.987	+	421.688i	−0.517940	+	0.458855i	0.363199	+	0.931711i	$0.381684\pi$
$920$	17.0321	+	11.7564i	0.0185132	+	0.0127787i
$921$	−450.380	+	202.699i	−0.489012	+	0.220086i
$922$	639.500	+	242.530i	0.693601	+	0.263048i
$923$	631.275	+	235.064i	0.683939	+	0.254674i
$924$	−36.8564	−	97.1824i	−0.0398879	−	0.105176i
$925$	65.6042	−	65.6042i	0.0709235	−	0.0709235i
$926$	−20.0992	+	52.9974i	−0.0217054	+	0.0572326i
$927$	−205.495	+	24.9516i	−0.221678	+	0.0269166i
$928$	181.625	−	582.855i	0.195717	−	0.628076i
$929$	−168.699	−	920.558i	−0.181592	−	0.990913i	−0.940520	−	0.339739i	$-0.889661\pi$
$929$	−168.699	−	920.558i	−0.181592	−	0.990913i	0.758928	−	0.651174i	$-0.225723\pi$
$930$	8.37145	−	1.53412i	0.00900156	−	0.00164960i
$931$	−576.953	−	179.786i	−0.619713	−	0.193110i
$932$	−28.6287	−	235.779i	−0.0307175	−	0.252982i
$933$	58.2510	+	22.0917i	0.0624341	+	0.0236781i
$934$	650.342	+	650.342i	0.696298	+	0.696298i
$935$	3.26845	−	1.23956i	0.00349567	−	0.00132573i
$936$	−215.627	+	316.457i	−0.230371	+	0.338095i
$937$	−82.7353	+	218.155i	−0.0882980	+	0.232823i	−0.971890	−	0.235434i	$-0.924349\pi$
$937$	−82.7353	+	218.155i	−0.0882980	+	0.232823i	0.883592	+	0.468257i	$0.155118\pi$
$938$	413.061	+	917.783i	0.440363	+	0.978447i
$939$	−320.766	+	464.710i	−0.341604	+	0.494899i
$940$	3.38868	+	3.82503i	0.00360498	+	0.00406918i
$941$	−69.2864	−	378.083i	−0.0736306	−	0.401789i	−0.999701	−	0.0244391i	$-0.992220\pi$
$941$	−69.2864	−	378.083i	−0.0736306	−	0.401789i	0.926071	−	0.377350i	$-0.123165\pi$
$942$	−184.250	+	11.1451i	−0.195595	+	0.0118313i
$943$	−513.342	−	1647.37i	−0.544371	−	1.74695i
$944$	−1296.42	−	1296.42i	−1.37332	−	1.37332i
$945$	−16.4660	−	8.64202i	−0.0174243	−	0.00914499i
$946$	267.398	+	32.4679i	0.282661	+	0.0343213i
$947$	−116.396	+	258.621i	−0.122910	+	0.273095i	−0.963074	−	0.269238i	$-0.913228\pi$
$947$	−116.396	+	258.621i	−0.122910	+	0.273095i	0.840164	+	0.542333i	$0.182459\pi$
$948$	−61.3485	+	116.890i	−0.0647136	+	0.123302i
$949$	596.313	+	308.394i	0.628359	+	0.324968i
$950$	727.162	−	381.644i	0.765434	−	0.401731i
$951$	900.028	−	54.4417i	0.946402	−	0.0572468i
$952$	469.206	−	415.680i	0.492863	−	0.436639i
$953$	85.1154	−	345.327i	0.0893132	−	0.362358i	−0.909231	−	0.416291i	$-0.863330\pi$
$953$	85.1154	−	345.327i	0.0893132	−	0.362358i	0.998545	+	0.0539334i	$0.0171759\pi$
$954$	−557.500	−	711.596i	−0.584382	−	0.745908i
$955$	−0.0778179	+	1.28648i	−8.14848e−5	+	0.00134710i
$956$	−16.6848	+	7.50921i	−0.0174527	+	0.00785482i
$957$	135.147	+	433.701i	0.141219	+	0.453188i
$958$	−1217.54	+	639.015i	−1.27092	+	0.667030i
$959$	−1206.13	+	146.451i	−1.25770	+	0.152712i
$960$	6.13446	+	0.371066i	0.00639006	+	0.000386528i
$961$	−67.9316	−	275.609i	−0.0706885	−	0.286794i
$962$	107.329	−	7.14242i	0.111568	−	0.00742455i
$963$	66.6539	+	16.4287i	0.0692148	+	0.0170599i
$964$	39.4949	−	126.743i	0.0409698	−	0.131477i
$965$	−4.55699	+	2.39169i	−0.00472227	+	0.00247844i
$966$	1915.58	−	726.485i	1.98301	−	0.752055i
$967$	−1005.73	−	452.641i	−1.04005	−	0.468088i	−0.182886	−	0.983134i	$-0.558544\pi$
$967$	−1005.73	−	452.641i	−1.04005	−	0.468088i	−0.857162	+	0.515047i	$0.827775\pi$
$968$	−621.109	−	113.822i	−0.641641	−	0.117585i
$969$	−160.633	−	265.720i	−0.165772	−	0.274221i
$970$	−3.24573	+	17.7114i	−0.00334611	+	0.0182591i
$971$	−71.5794	+	589.509i	−0.0737172	+	0.607115i	0.908299	+	0.418321i	$0.137381\pi$
$971$	−71.5794	+	589.509i	−0.0737172	+	0.607115i	−0.982017	+	0.188795i	$0.939542\pi$
$972$	190.313	−	72.1764i	0.195796	−	0.0742555i
$973$	234.715	+	753.226i	0.241228	+	0.774127i
$974$	−887.811	−	612.812i	−0.911510	−	0.629170i
$975$	212.263	+	666.980i	0.217706	+	0.684082i
$976$	−933.280	−	1352.09i	−0.956230	−	1.38534i
$977$	−763.676	−	598.302i	−0.781654	−	0.612387i	0.144512	−	0.989503i	$-0.453839\pi$
$977$	−763.676	−	598.302i	−0.781654	−	0.612387i	−0.926166	+	0.377116i	$0.876916\pi$
$978$	−188.428	+	46.4434i	−0.192667	+	0.0474881i
$979$	−216.630	−	149.529i	−0.221277	−	0.152737i
$980$	−2.70193	+	0.163436i	−0.00275707	+	0.000166772i
$981$	282.434	−	906.363i	0.287904	−	0.923917i
$982$	−1021.09	+	799.975i	−1.03981	+	0.814638i
$983$	−147.611	+	188.411i	−0.150163	+	0.191669i	−0.856410	−	0.516297i	$-0.827310\pi$
$983$	−147.611	+	188.411i	−0.150163	+	0.191669i	0.706246	+	0.707966i	$0.250387\pi$
$984$	−417.942	−	370.265i	−0.424738	−	0.376285i
$985$	−6.19684	+	4.27737i	−0.00629121	+	0.00434251i
$986$	689.713	−	540.355i	0.699506	−	0.548028i
$987$	−1570.30	+	190.669i	−1.59098	+	0.193180i
$988$	180.579	+	43.3546i	0.182772	+	0.0438811i
$989$	−124.828	+	1028.05i	−0.126216	+	1.03948i
$990$	−2.97286	+	1.79716i	−0.00300289	+	0.00181531i
$991$	−32.7191			−0.0330162			−0.0165081	−	0.999864i	$-0.505255\pi$
$991$	−32.7191			−0.0330162			−0.0165081	+	0.999864i	$0.505255\pi$
$992$		−	395.294i		−	0.398482i
$993$	−670.948	+	405.602i	−0.675677	+	0.408461i
$994$	999.286	+	449.742i	1.00532	+	0.452457i
$995$	2.32833	+	2.32833i	0.00234003	+	0.00234003i
$996$	−297.629	+	133.952i	−0.298824	+	0.134490i
$997$	1068.49	−	263.358i	1.07170	−	0.264151i	0.336281	−	0.941762i	$-0.390831\pi$
$997$	1068.49	−	263.358i	1.07170	−	0.264151i	0.735421	+	0.677611i	$0.236985\pi$
$998$	−923.915	+	1042.88i	−0.925767	+	1.04497i
$999$	91.4146	+	55.2621i	0.0915061	+	0.0553174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.j.a.5.10	✓	720
169.34	odd	52	inner	169.3.j.a.34.10	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.3.j.a.5.10	✓	720	1.1	even	1	trivial
169.3.j.a.34.10	yes	720	169.34	odd	52	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	169.j (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19267 - 0.401821i) q^{2} +(-1.90733 - 1.00104i) q^{3} +(0.906258 + 0.343698i) q^{4} +(-0.00411255 + 0.0679886i) q^{5} +(3.77990 + 2.96136i) q^{6} +(8.11874 + 4.90795i) q^{7} +(5.78175 + 3.49519i) q^{8} +(-2.47676 - 3.58821i) q^{9} +(0.0363367 - 0.147424i) q^{10} +(5.16153 - 0.945885i) q^{11} +(-1.38448 - 1.56275i) q^{12} +(-10.2816 - 7.95545i) q^{13} +(-15.8296 - 14.0238i) q^{14} +(0.0759036 - 0.125560i) q^{15} +(-14.1750 - 12.5579i) q^{16} +(-2.34053 - 9.49590i) q^{17} +(3.98890 + 8.86297i) q^{18} +(-10.4218 + 10.4218i) q^{19} +(-0.0270946 + 0.0602018i) q^{20} +(-10.5720 - 17.4883i) q^{21} -11.6976 q^{22} -44.9730i q^{23} +(-7.52886 - 12.4543i) q^{24} +(24.8131 + 3.01286i) q^{25} +(19.3474 + 21.5750i) q^{26} +(3.46884 + 28.5685i) q^{27} +(5.67082 + 7.23827i) q^{28} +(-22.8298 - 33.0747i) q^{29} +(-0.216884 + 0.244811i) q^{30} +(-20.4841 - 16.0482i) q^{31} +(9.36844 + 11.9579i) q^{32} +(-10.7916 - 3.36280i) q^{33} +(1.31635 + 21.7618i) q^{34} +(-0.367074 + 0.531798i) q^{35} +(-1.01133 - 4.10311i) q^{36} +(2.28915 - 2.92189i) q^{37} +(27.0393 - 18.6639i) q^{38} +(11.6466 + 25.4660i) q^{39} +(-0.261411 + 0.378719i) q^{40} +(36.6302 - 11.4144i) q^{41} +(16.1538 + 42.5941i) q^{42} +(-22.8592 - 2.77561i) q^{43} +(5.00277 + 0.916792i) q^{44} +(0.254144 - 0.153635i) q^{45} +(-18.0711 + 98.6108i) q^{46} +(31.7684 - 70.5866i) q^{47} +(14.4653 + 38.1418i) q^{48} +(19.0546 + 36.3054i) q^{49} +(-53.1962 - 16.5766i) q^{50} +(-5.04165 + 20.4548i) q^{51} +(-6.58348 - 10.7435i) q^{52} +(-90.3065 + 22.2585i) q^{53} +(3.87340 - 64.0350i) q^{54} +(0.0430824 + 0.354815i) q^{55} +(29.7863 + 56.7530i) q^{56} +(30.3106 - 9.44517i) q^{57} +(36.7680 + 81.6952i) q^{58} +(96.6370 + 5.84546i) q^{59} +(0.111943 - 0.0877017i) q^{60} +(84.2333 + 20.7616i) q^{61} +(38.4662 + 43.4193i) q^{62} +(-2.49744 - 41.2876i) q^{63} +(19.4659 + 37.0893i) q^{64} +(0.583164 - 0.666313i) q^{65} +(22.3111 + 11.7098i) q^{66} +(-43.3979 - 19.5318i) q^{67} +(1.14260 - 9.41017i) q^{68} +(-45.0200 + 85.7784i) q^{69} +(1.01856 - 1.01856i) q^{70} +(-49.4707 + 15.4157i) q^{71} +(-1.77855 - 29.4029i) q^{72} +(-50.7956 + 9.30864i) q^{73} +(-6.19342 + 5.48689i) q^{74} +(-44.3108 - 30.5855i) q^{75} +(-13.0269 + 5.86291i) q^{76} +(46.5475 + 17.6531i) q^{77} +(-15.3043 - 60.5182i) q^{78} +(-22.4214 - 59.1204i) q^{79} +(0.912091 - 0.912091i) q^{80} +(8.06738 - 21.2719i) q^{81} +(-84.9044 + 10.3093i) q^{82} +(46.5080 - 149.249i) q^{83} +(-3.57030 - 19.4825i) q^{84} +(0.655239 - 0.120077i) q^{85} +(49.0074 + 15.2713i) q^{86} +(10.4348 + 85.9379i) q^{87} +(33.1487 + 12.5716i) q^{88} +(-35.4701 - 35.4701i) q^{89} +(-0.618986 + 0.234750i) q^{90} +(-44.4285 - 115.050i) q^{91} +(15.4571 - 40.7572i) q^{92} +(23.0049 + 51.1147i) q^{93} +(-98.0208 + 142.008i) q^{94} +(-0.665707 - 0.751427i) q^{95} +(-5.89829 - 32.1859i) q^{96} +(-118.374 + 7.16032i) q^{97} +(-27.1920 - 87.2622i) q^{98} +(-16.1779 - 16.1779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 22 q^{2} - 22 q^{3} - 26 q^{4} - 34 q^{5} - 10 q^{6} - 14 q^{7} - 62 q^{8} - 202 q^{9} - 26 q^{10} - 22 q^{11} - 26 q^{12} - 34 q^{13} - 38 q^{14} + 2 q^{15} + 242 q^{16} - 26 q^{17} - 58 q^{18}+ \cdots - 178 q^{99}+O(q^{100}) \) 720 * q - 22 * q^2 - 22 * q^3 - 26 * q^4 - 34 * q^5 - 10 * q^6 - 14 * q^7 - 62 * q^8 - 202 * q^9 - 26 * q^10 - 22 * q^11 - 26 * q^12 - 34 * q^13 - 38 * q^14 + 2 * q^15 + 242 * q^16 - 26 * q^17 - 58 * q^18 - 26 * q^19 - 42 * q^20 - 58 * q^21 - 108 * q^22 + 262 * q^24 - 26 * q^25 + 62 * q^26 + 2 * q^27 - 30 * q^28 - 54 * q^29 - 858 * q^30 - 66 * q^31 - 696 * q^32 + 50 * q^33 + 82 * q^34 - 2 * q^35 - 26 * q^36 - 66 * q^37 + 884 * q^38 + 922 * q^39 - 522 * q^40 - 58 * q^41 - 106 * q^42 - 26 * q^43 + 42 * q^44 - 212 * q^45 - 54 * q^46 + 368 * q^47 + 94 * q^48 - 26 * q^49 + 102 * q^50 - 26 * q^51 - 1276 * q^52 + 620 * q^53 - 178 * q^54 - 834 * q^55 - 26 * q^56 + 14 * q^57 + 114 * q^58 - 82 * q^59 + 1338 * q^60 + 254 * q^61 + 1404 * q^62 - 1392 * q^63 - 26 * q^64 - 82 * q^65 - 304 * q^66 - 358 * q^67 - 434 * q^68 + 208 * q^69 + 838 * q^70 - 310 * q^71 + 22 * q^72 - 26 * q^73 - 1308 * q^74 + 1664 * q^75 - 106 * q^76 - 26 * q^77 - 574 * q^78 - 78 * q^79 + 62 * q^80 - 262 * q^81 + 1274 * q^82 + 26 * q^83 + 158 * q^84 + 1522 * q^85 - 1562 * q^86 - 122 * q^87 - 442 * q^88 - 616 * q^89 - 26 * q^90 - 182 * q^91 + 646 * q^92 + 544 * q^93 - 2394 * q^94 - 26 * q^95 - 4064 * q^96 + 1914 * q^97 - 250 * q^98 - 178 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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