LMFDB - Embedded newform 105.3.w.a.38.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,3,Mod(17,105)] 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("105.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			38.8
Character	$\chi$	$=$	105.38
Dual form			105.3.w.a.47.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.532431 + 1.98706i) q^{2} +(-2.87591 - 0.853896i) q^{3} +(-0.200820 - 0.115943i) q^{4} +(3.64989 + 3.41735i) q^{5} +(3.22797 - 5.25996i) q^{6} +(-6.58378 + 2.37777i) q^{7} +(-5.48120 + 5.48120i) q^{8} +(7.54172 + 4.91146i) q^{9} +(-8.73379 + 5.43305i) q^{10} +(-17.6674 - 10.2003i) q^{11} +(0.478537 + 0.504923i) q^{12} +(-3.04150 + 3.04150i) q^{13} +(-1.21935 - 14.3484i) q^{14} +(-7.57870 - 12.9446i) q^{15} +(-8.43689 - 14.6131i) q^{16} +(3.18014 + 11.8684i) q^{17} +(-13.7748 + 12.3708i) q^{18} +(11.1709 + 19.3486i) q^{19} +(-0.336752 - 1.10945i) q^{20} +(20.9647 - 1.21638i) q^{21} +(29.6753 - 29.6753i) q^{22} +(-5.69233 - 1.52525i) q^{23} +(20.4438 - 11.0831i) q^{24} +(1.64344 + 24.9459i) q^{25} +(-4.42425 - 7.66303i) q^{26} +(-17.4954 - 20.5648i) q^{27} +(1.59784 + 0.285844i) q^{28} +11.9728 q^{29} +(29.7569 - 8.16722i) q^{30} +(30.9809 + 17.8869i) q^{31} +(3.57934 - 0.959081i) q^{32} +(42.0999 + 44.4213i) q^{33} -25.2765 q^{34} +(-32.1558 - 13.8205i) q^{35} +(-0.945077 - 1.86073i) q^{36} +(17.5430 + 4.70065i) q^{37} +(-44.3945 + 11.8955i) q^{38} +(11.3442 - 6.14996i) q^{39} +(-38.7370 + 1.27462i) q^{40} +6.29801 q^{41} +(-8.74526 + 42.3058i) q^{42} +(8.41810 + 8.41810i) q^{43} +(2.36531 + 4.09685i) q^{44} +(10.7423 + 43.6990i) q^{45} +(6.06154 - 10.4989i) q^{46} +(57.8113 + 15.4905i) q^{47} +(11.7857 + 49.2302i) q^{48} +(37.6924 - 31.3094i) q^{49} +(-50.4440 - 10.0164i) q^{50} +(0.988619 - 36.8481i) q^{51} +(0.963437 - 0.258152i) q^{52} +(-14.3227 - 53.4531i) q^{53} +(50.1785 - 23.8152i) q^{54} +(-29.6262 - 97.6057i) q^{55} +(23.0540 - 49.1201i) q^{56} +(-15.6049 - 65.1836i) q^{57} +(-6.37467 + 23.7906i) q^{58} +(60.6100 + 34.9932i) q^{59} +(0.0211110 + 3.47824i) q^{60} +(-80.4746 + 46.4620i) q^{61} +(-52.0374 + 52.0374i) q^{62} +(-61.3314 - 14.4035i) q^{63} -59.8721i q^{64} +(-21.4950 + 0.707281i) q^{65} +(-110.683 + 60.0038i) q^{66} +(5.88684 + 21.9700i) q^{67} +(0.737433 - 2.75214i) q^{68} +(15.0682 + 9.24715i) q^{69} +(44.5829 - 56.5370i) q^{70} +27.7403i q^{71} +(-68.2584 + 14.4170i) q^{72} +(-7.78414 - 29.0508i) q^{73} +(-18.6809 + 32.3563i) q^{74} +(16.5748 - 73.1456i) q^{75} -5.18078i q^{76} +(140.572 + 25.1475i) q^{77} +(6.18033 + 25.8161i) q^{78} +(-110.523 + 63.8104i) q^{79} +(19.1444 - 82.1681i) q^{80} +(32.7552 + 74.0817i) q^{81} +(-3.35326 + 12.5145i) q^{82} +(16.3782 + 16.3782i) q^{83} +(-4.35117 - 2.18645i) q^{84} +(-28.9515 + 54.1862i) q^{85} +(-21.2093 + 12.2452i) q^{86} +(-34.4326 - 10.2235i) q^{87} +(152.749 - 40.9289i) q^{88} +(-74.4534 + 42.9857i) q^{89} +(-92.5520 - 1.92108i) q^{90} +(12.7926 - 27.2566i) q^{91} +(0.966290 + 0.966290i) q^{92} +(-73.8249 - 77.8955i) q^{93} +(-61.5611 + 106.627i) q^{94} +(-25.3483 + 108.795i) q^{95} +(-11.1128 - 0.298152i) q^{96} +(0.194287 + 0.194287i) q^{97} +(42.1450 + 91.5672i) q^{98} +(-83.1445 - 163.701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) $ 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.532431	+	1.98706i	−0.266215	+	0.993530i	0.695287	+	0.718732i	$0.255277\pi$
$2$	−0.532431	+	1.98706i	−0.266215	+	0.993530i	−0.961502	+	0.274797i	$0.911389\pi$
$3$	−2.87591	−	0.853896i	−0.958637	−	0.284632i
$3$	−2.87591	−	0.853896i	−0.958637	−	0.284632i
$4$	−0.200820	−	0.115943i	−0.0502050	−	0.0289859i
$5$	3.64989	+	3.41735i	0.729979	+	0.683470i
$5$	3.64989	+	3.41735i	0.729979	+	0.683470i
$6$	3.22797	−	5.25996i	0.537994	−	0.876661i
$7$	−6.58378	+	2.37777i	−0.940541	+	0.339681i
$7$	−6.58378	+	2.37777i	−0.940541	+	0.339681i
$8$	−5.48120	+	5.48120i	−0.685150	+	0.685150i
$9$	7.54172	+	4.91146i	0.837969	+	0.545717i
$10$	−8.73379	+	5.43305i	−0.873379	+	0.543305i
$11$	−17.6674	−	10.2003i	−1.60613	−	0.927299i	−0.990225	−	0.139478i	$-0.955458\pi$
$11$	−17.6674	−	10.2003i	−1.60613	−	0.927299i	−0.615904	−	0.787821i	$-0.711209\pi$
$12$	0.478537	+	0.504923i	0.0398781	+	0.0420769i
$13$	−3.04150	+	3.04150i	−0.233962	+	0.233962i	−0.814344	−	0.580382i	$-0.802903\pi$
$13$	−3.04150	+	3.04150i	−0.233962	+	0.233962i	0.580382	+	0.814344i	$0.302903\pi$
$14$	−1.21935	−	14.3484i	−0.0870967	−	1.02488i
$15$	−7.57870	−	12.9446i	−0.505247	−	0.862975i
$16$	−8.43689	−	14.6131i	−0.527306	−	0.913320i
$17$	3.18014	+	11.8684i	0.187067	+	0.698144i	0.994179	+	0.107745i	$0.0343630\pi$
$17$	3.18014	+	11.8684i	0.187067	+	0.698144i	−0.807111	+	0.590399i	$0.798970\pi$
$18$	−13.7748	+	12.3708i	−0.765267	+	0.687269i
$19$	11.1709	+	19.3486i	0.587943	+	1.01835i	0.994501	+	0.104722i	$0.0333954\pi$
$19$	11.1709	+	19.3486i	0.587943	+	1.01835i	−0.406559	+	0.913625i	$0.633271\pi$
$20$	−0.336752	−	1.10945i	−0.0168376	−	0.0554727i
$21$	20.9647	−	1.21638i	0.998321	−	0.0579228i
$22$	29.6753	−	29.6753i	1.34888	−	1.34888i
$23$	−5.69233	−	1.52525i	−0.247492	−	0.0663154i	0.132940	−	0.991124i	$-0.457558\pi$
$23$	−5.69233	−	1.52525i	−0.247492	−	0.0663154i	−0.380433	+	0.924809i	$0.624225\pi$
$24$	20.4438	−	11.0831i	0.851826	−	0.461795i
$25$	1.64344	+	24.9459i	0.0657376	+	0.997837i
$26$	−4.42425	−	7.66303i	−0.170164	−	0.294732i
$27$	−17.4954	−	20.5648i	−0.647980	−	0.761658i
$28$	1.59784	+	0.285844i	0.0570658	+	0.0102087i
$29$	11.9728			0.412854			0.206427	−	0.978462i	$-0.433816\pi$
$29$	11.9728			0.412854			0.206427	+	0.978462i	$0.433816\pi$
$30$	29.7569	−	8.16722i	0.991896	−	0.272241i
$31$	30.9809	+	17.8869i	0.999385	+	0.576995i	0.908066	−	0.418826i	$-0.137558\pi$
$31$	30.9809	+	17.8869i	0.999385	+	0.576995i	0.0913189	+	0.995822i	$0.470892\pi$
$32$	3.57934	−	0.959081i	0.111854	−	0.0299713i
$33$	42.0999	+	44.4213i	1.27576	+	1.34610i
$34$	−25.2765			−0.743427
$35$	−32.1558	−	13.8205i	−0.918736	−	0.394871i
$36$	−0.945077	−	1.86073i	−0.0262522	−	0.0516870i
$37$	17.5430	+	4.70065i	0.474136	+	0.127044i	0.487971	−	0.872860i	$-0.337737\pi$
$37$	17.5430	+	4.70065i	0.474136	+	0.127044i	−0.0138346	+	0.999904i	$0.504404\pi$
$38$	−44.3945	+	11.8955i	−1.16828	+	0.313039i
$39$	11.3442	−	6.14996i	0.290877	−	0.157691i
$40$	−38.7370	+	1.27462i	−0.968425	+	0.0318654i
$41$	6.29801			0.153610			0.0768050	−	0.997046i	$-0.475528\pi$
$41$	6.29801			0.153610			0.0768050	+	0.997046i	$0.475528\pi$
$42$	−8.74526	+	42.3058i	−0.208220	+	1.00728i
$43$	8.41810	+	8.41810i	0.195770	+	0.195770i	0.798184	−	0.602414i	$-0.205794\pi$
$43$	8.41810	+	8.41810i	0.195770	+	0.195770i	−0.602414	+	0.798184i	$0.705794\pi$
$44$	2.36531	+	4.09685i	0.0537571	+	0.0931101i
$45$	10.7423	+	43.6990i	0.238718	+	0.971089i
$46$	6.06154	−	10.4989i	0.131773	−	0.228237i
$47$	57.8113	+	15.4905i	1.23003	+	0.329585i	0.814591	−	0.580036i	$-0.196962\pi$
$47$	57.8113	+	15.4905i	1.23003	+	0.329585i	0.415438	+	0.909622i	$0.363628\pi$
$48$	11.7857	+	49.2302i	0.245534	+	1.02563i
$49$	37.6924	−	31.3094i	0.769234	−	0.638968i
$50$	−50.4440	−	10.0164i	−1.00888	−	0.200327i
$51$	0.988619	−	36.8481i	0.0193847	−	0.722512i
$52$	0.963437	−	0.258152i	0.0185276	−	0.00496446i
$53$	−14.3227	−	53.4531i	−0.270240	−	1.00855i	−0.958965	−	0.283526i	$-0.908496\pi$
$53$	−14.3227	−	53.4531i	−0.270240	−	1.00855i	0.688725	−	0.725023i	$-0.258171\pi$
$54$	50.1785	−	23.8152i	0.929232	−	0.441022i
$55$	−29.6262	−	97.6057i	−0.538659	−	1.77465i
$56$	23.0540	−	49.1201i	0.411679	−	0.877145i
$57$	−15.6049	−	65.1836i	−0.273770	−	1.14357i
$58$	−6.37467	+	23.7906i	−0.109908	+	0.410183i
$59$	60.6100	+	34.9932i	1.02729	+	0.593105i	0.916207	−	0.400706i	$-0.131235\pi$
$59$	60.6100	+	34.9932i	1.02729	+	0.593105i	0.111082	+	0.993811i	$0.464568\pi$
$60$	0.0211110	+	3.47824i	0.000351851	+	0.0579707i
$61$	−80.4746	+	46.4620i	−1.31926	+	0.761673i	−0.983609	−	0.180315i	$-0.942288\pi$
$61$	−80.4746	+	46.4620i	−1.31926	+	0.761673i	−0.335647	+	0.941988i	$0.608955\pi$
$62$	−52.0374	+	52.0374i	−0.839314	+	0.839314i
$63$	−61.3314	−	14.4035i	−0.973514	−	0.228627i
$64$		−	59.8721i		−	0.935502i
$65$	−21.4950	+	0.707281i	−0.330693	+	0.0108812i
$66$	−110.683	+	60.0038i	−1.67701	+	0.909149i
$67$	5.88684	+	21.9700i	0.0878633	+	0.327910i	0.995841	−	0.0911082i	$-0.0290409\pi$
$67$	5.88684	+	21.9700i	0.0878633	+	0.327910i	−0.907978	+	0.419018i	$0.862374\pi$
$68$	0.737433	−	2.75214i	0.0108446	−	0.0404726i
$69$	15.0682	+	9.24715i	0.218380	+	0.134017i
$70$	44.5829	−	56.5370i	0.636898	−	0.807671i
$71$			27.7403i			0.390708i	0.980733	+	0.195354i	$0.0625855\pi$
$71$			27.7403i			0.390708i	−0.980733	+	0.195354i	$0.937414\pi$
$72$	−68.2584	+	14.4170i	−0.948034	+	0.200236i
$73$	−7.78414	−	29.0508i	−0.106632	−	0.397956i	0.891893	−	0.452246i	$-0.149377\pi$
$73$	−7.78414	−	29.0508i	−0.106632	−	0.397956i	−0.998525	+	0.0542900i	$0.982710\pi$
$74$	−18.6809	+	32.3563i	−0.252445	+	0.437247i
$75$	16.5748	−	73.1456i	0.220998	−	0.975274i
$76$		−	5.18078i		−	0.0681682i
$77$	140.572	+	25.1475i	1.82562	+	0.326591i
$78$	6.18033	+	25.8161i	0.0792350	+	0.330975i
$79$	−110.523	+	63.8104i	−1.39902	+	0.807726i	−0.994290	−	0.106709i	$-0.965969\pi$
$79$	−110.523	+	63.8104i	−1.39902	+	0.807726i	−0.404732	+	0.914435i	$0.632635\pi$
$80$	19.1444	−	82.1681i	0.239305	−	1.02710i
$81$	32.7552	+	74.0817i	0.404385	+	0.914589i
$82$	−3.35326	+	12.5145i	−0.0408934	+	0.152616i
$83$	16.3782	+	16.3782i	0.197327	+	0.197327i	0.798853	−	0.601526i	$-0.205440\pi$
$83$	16.3782	+	16.3782i	0.197327	+	0.197327i	−0.601526	+	0.798853i	$0.705440\pi$
$84$	−4.35117	−	2.18645i	−0.0517997	−	0.0260292i
$85$	−28.9515	+	54.1862i	−0.340605	+	0.637485i
$86$	−21.2093	+	12.2452i	−0.246620	+	0.142386i
$87$	−34.4326	−	10.2235i	−0.395777	−	0.117512i
$88$	152.749	−	40.9289i	1.73578	−	0.465101i
$89$	−74.4534	+	42.9857i	−0.836555	+	0.482985i	−0.856092	−	0.516824i	$-0.827114\pi$
$89$	−74.4534	+	42.9857i	−0.836555	+	0.482985i	0.0195368	+	0.999809i	$0.493781\pi$
$90$	−92.5520	−	1.92108i	−1.02836	−	0.0213453i
$91$	12.7926	−	27.2566i	0.140578	−	0.299523i
$92$	0.966290	+	0.966290i	0.0105032	+	0.0105032i
$93$	−73.8249	−	77.8955i	−0.793816	−	0.837586i
$94$	−61.5611	+	106.627i	−0.654905	+	1.13433i
$95$	−25.3483	+	108.795i	−0.266824	+	1.14521i
$96$	−11.1128	−	0.298152i	−0.115758	−	0.00310575i
$97$	0.194287	+	0.194287i	0.00200296	+	0.00200296i	0.708108	−	0.706105i	$-0.249549\pi$
$97$	0.194287	+	0.194287i	0.00200296	+	0.00200296i	−0.706105	+	0.708108i	$0.749549\pi$
$98$	42.1450	+	91.5672i	0.430051	+	0.934359i
$99$	−83.1445	−	163.701i	−0.839844	−	1.65354i
$100$	2.56228	−	5.20019i	0.0256228	−	0.0520019i
$101$	55.3301	−	95.8346i	0.547823	−	0.948857i	−0.450600	−	0.892726i	$-0.648790\pi$
$101$	55.3301	−	95.8346i	0.547823	−	0.948857i	0.998423	−	0.0561315i	$-0.0178766\pi$
$102$	72.6930	+	21.5835i	0.712676	+	0.211603i
$103$	−13.1131	−	3.51364i	−0.127312	−	0.0341130i	0.194601	−	0.980883i	$-0.437659\pi$
$103$	−13.1131	−	3.51364i	−0.127312	−	0.0341130i	−0.321912	+	0.946770i	$0.604326\pi$
$104$		−	33.3422i		−	0.320598i
$105$	80.6759	+	67.2042i	0.768342	+	0.640040i
$106$	113.840			1.07397
$107$	−9.81236	+	36.6202i	−0.0917043	+	0.342245i	−0.996499	−	0.0836026i	$-0.973357\pi$
$107$	−9.81236	+	36.6202i	−0.0917043	+	0.342245i	0.904795	+	0.425848i	$0.140024\pi$
$108$	1.12909	+	6.15830i	0.0104545	+	0.0570213i
$109$	−61.2903	−	35.3860i	−0.562297	−	0.324642i	0.191770	−	0.981440i	$-0.438577\pi$
$109$	−61.2903	−	35.3860i	−0.562297	−	0.324642i	−0.754067	+	0.656798i	$0.771911\pi$
$110$	209.722	−	6.90079i	1.90657	−	0.0627344i
$111$	−46.4384	−	28.4986i	−0.418364	−	0.256744i
$112$	90.2933	+	76.1487i	0.806190	+	0.679899i
$113$	58.6040	−	58.6040i	0.518620	−	0.518620i	−0.398534	−	0.917154i	$-0.630481\pi$
$113$	58.6040	−	58.6040i	0.518620	−	0.518620i	0.917154	+	0.398534i	$0.130481\pi$
$114$	137.832	+	3.69798i	1.20905	+	0.0324384i
$115$	−15.5641	−	25.0197i	−0.135340	−	0.217563i
$116$	−2.40437	−	1.38816i	−0.0207273	−	0.0119669i
$117$	−37.8764	+	7.99996i	−0.323730	+	0.0683757i
$118$	−101.804	+	101.804i	−0.862748	+	0.862748i
$119$	−49.1578	−	70.5777i	−0.413091	−	0.593090i
$120$	112.493	+	29.4117i	0.937438	+	0.245097i
$121$	147.592	+	255.637i	1.21977	+	2.11270i
$122$	−49.4756	−	184.646i	−0.405538	−	1.51349i
$123$	−18.1125	−	5.37785i	−0.147256	−	0.0437223i
$124$	−4.14773	−	7.18408i	−0.0334494	−	0.0579361i
$125$	−79.2506	+	96.6662i	−0.634005	+	0.773329i
$126$	61.2754	−	114.200i	0.486312	−	0.906351i
$127$	39.9851	−	39.9851i	0.314843	−	0.314843i	−0.531939	−	0.846782i	$-0.678537\pi$
$127$	39.9851	−	39.9851i	0.314843	−	0.314843i	0.846782	+	0.531939i	$0.178537\pi$
$128$	133.287	+	35.7141i	1.04130	+	0.279016i
$129$	−17.0215	−	31.3979i	−0.131950	−	0.243394i
$130$	10.0392	−	43.0885i	0.0772247	−	0.331450i
$131$	−36.0576	−	62.4535i	−0.275248	−	0.476744i	0.694949	−	0.719059i	$-0.255427\pi$
$131$	−36.0576	−	62.4535i	−0.275248	−	0.476744i	−0.970198	+	0.242314i	$0.922093\pi$
$132$	−3.30415	−	13.8019i	−0.0250315	−	0.104560i
$133$	−119.553	−	100.825i	−0.898898	−	0.758084i
$134$	−46.7900			−0.349179
$135$	6.42046	−	134.847i	0.0475590	−	0.998868i
$136$	−82.4844	−	47.6224i	−0.606503	−	0.350165i
$137$	89.8290	−	24.0696i	0.655686	−	0.175691i	0.0843878	−	0.996433i	$-0.473107\pi$
$137$	89.8290	−	24.0696i	0.655686	−	0.175691i	0.571298	+	0.820742i	$0.306440\pi$
$138$	−26.3974	+	25.0180i	−0.191286	+	0.181290i
$139$	157.063			1.12995			0.564974	−	0.825109i	$-0.308886\pi$
$139$	157.063			1.12995			0.564974	+	0.825109i	$0.308886\pi$
$140$	4.85513	+	6.50369i	0.0346795	+	0.0464549i
$141$	−153.033	−	93.9142i	−1.08534	−	0.666058i
$142$	−55.1215	−	14.7698i	−0.388180	−	0.104012i
$143$	84.7597	−	22.7113i	0.592725	−	0.158820i
$144$	8.14303	−	151.646i	0.0565488	−	1.05309i
$145$	43.6993	+	40.9151i	0.301375	+	0.282173i
$146$	61.8702			0.423768
$147$	−135.135	+	57.8577i	−0.919286	+	0.393590i
$148$	−2.97799	−	2.97799i	−0.0201215	−	0.0201215i
$149$	13.4879	+	23.3617i	0.0905227	+	0.156790i	0.907731	−	0.419552i	$-0.137813\pi$
$149$	13.4879	+	23.3617i	0.0905227	+	0.156790i	−0.817209	+	0.576342i	$0.804480\pi$
$150$	136.520	+	71.8801i	0.910131	+	0.479201i
$151$	62.3433	−	107.982i	0.412870	−	0.715111i	−0.582333	−	0.812951i	$-0.697860\pi$
$151$	62.3433	−	107.982i	0.412870	−	0.715111i	0.995202	+	0.0978396i	$0.0311932\pi$
$152$	−167.284	−	44.8235i	−1.10055	−	0.294892i
$153$	−34.3076	+	105.128i	−0.224233	+	0.687109i
$154$	−124.815	+	265.936i	−0.810485	+	1.72686i
$155$	51.9515	+	171.158i	0.335171	+	1.10424i
$156$	−2.99119	−	0.0802525i	−0.0191743	−	0.000514439i
$157$	85.5363	−	22.9194i	0.544817	−	0.145983i	0.0240952	−	0.999710i	$-0.492330\pi$
$157$	85.5363	−	22.9194i	0.544817	−	0.145983i	0.520722	+	0.853726i	$0.325663\pi$
$158$	−67.9492	−	253.590i	−0.430058	−	1.60500i
$159$	−4.45254	+	165.956i	−0.0280034	+	1.04375i
$160$	16.3417	+	8.73131i	0.102136	+	0.0545707i
$161$	41.1038	−	3.49308i	0.255303	−	0.0216962i
$162$	−164.645	+	25.6431i	−1.01632	+	0.158291i
$163$	70.8881	−	264.558i	0.434896	−	1.62306i	−0.306418	−	0.951897i	$-0.599130\pi$
$163$	70.8881	−	264.558i	0.434896	−	1.62306i	0.741314	−	0.671158i	$-0.234203\pi$
$164$	−1.26477	−	0.730213i	−0.00771199	−	0.00445252i
$165$	1.85727	+	306.003i	0.0112562	+	1.85456i
$166$	−41.2647	+	23.8242i	−0.248582	+	0.143519i
$167$	−57.6592	+	57.6592i	−0.345265	+	0.345265i	−0.858342	−	0.513078i	$-0.828505\pi$
$167$	−57.6592	+	57.6592i	−0.345265	+	0.345265i	0.513078	+	0.858342i	$0.328505\pi$
$168$	−108.245	+	121.579i	−0.644314	+	0.723686i
$169$			150.499i			0.890524i
$170$	−92.2566	−	86.3787i	−0.542686	−	0.508110i
$171$	−10.7818	+	200.787i	−0.0630517	+	1.17419i
$172$	−0.714499	−	2.66655i	−0.00415406	−	0.0155032i
$173$	−30.8987	+	115.315i	−0.178605	+	0.666563i	0.817304	+	0.576206i	$0.195467\pi$
$173$	−30.8987	+	115.315i	−0.178605	+	0.666563i	−0.995909	+	0.0903569i	$0.971199\pi$
$174$	38.6477	−	62.9763i	0.222113	−	0.361933i
$175$	−70.1357	−	160.331i	−0.400775	−	0.916176i
$176$			344.235i			1.95588i
$177$	−144.428	−	152.392i	−0.815980	−	0.860972i
$178$	−45.7738	−	170.830i	−0.257156	−	0.959720i
$179$	−73.7339	+	127.711i	−0.411921	+	0.713469i	−0.995100	−	0.0988752i	$-0.968476\pi$
$179$	−73.7339	+	127.711i	−0.411921	+	0.713469i	0.583178	+	0.812344i	$0.301809\pi$
$180$	2.90934	−	10.0211i	0.0161630	−	0.0556730i
$181$		−	167.742i		−	0.926749i	−0.886162	−	0.463375i	$-0.846638\pi$
$181$		−	167.742i		−	0.926749i	0.886162	−	0.463375i	$-0.153362\pi$
$182$	47.3493	+	39.9319i	0.260161	+	0.219406i
$183$	271.111	−	64.9037i	1.48148	−	0.354665i
$184$	39.5610	−	22.8406i	0.215006	−	0.124134i
$185$	47.9665	+	77.1076i	0.259278	+	0.416798i
$186$	194.090	−	105.220i	1.04349	−	0.565702i
$187$	64.8767	−	242.123i	0.346934	−	1.29478i
$188$	−9.81365	−	9.81365i	−0.0522003	−	0.0522003i
$189$	164.084	+	93.7938i	0.868172	+	0.496264i
$190$	−202.686	−	108.294i	−1.06677	−	0.569971i
$191$	−281.218	+	162.362i	−1.47235	+	0.850061i	−0.999517	−	0.0310923i	$-0.990101\pi$
$191$	−281.218	+	162.362i	−1.47235	+	0.850061i	−0.472832	+	0.881153i	$0.656768\pi$
$192$	−51.1246	+	172.187i	−0.266274	+	0.896806i
$193$	−211.530	+	56.6792i	−1.09601	+	0.293675i	−0.761138	−	0.648589i	$-0.775359\pi$
$193$	−211.530	+	56.6792i	−1.09601	+	0.293675i	−0.334870	+	0.942264i	$0.608693\pi$
$194$	−0.489504	+	0.282615i	−0.00252321	+	0.00145678i
$195$	62.4217	+	16.3204i	0.320111	+	0.0836946i
$196$	−11.1995	+	1.91736i	−0.0571404	+	0.00978247i
$197$	−75.4491	−	75.4491i	−0.382990	−	0.382990i	0.489188	−	0.872178i	$-0.337293\pi$
$197$	−75.4491	−	75.4491i	−0.382990	−	0.382990i	−0.872178	+	0.489188i	$0.837293\pi$
$198$	369.551	−	78.0538i	1.86642	−	0.394211i
$199$	−25.0899	+	43.4570i	−0.126080	+	0.218377i	−0.922155	−	0.386822i	$-0.873573\pi$
$199$	−25.0899	+	43.4570i	−0.126080	+	0.218377i	0.796075	+	0.605198i	$0.206906\pi$
$200$	−145.742	−	127.726i	−0.728709	−	0.638628i
$201$	1.83006	−	68.2105i	0.00910477	−	0.339356i
$202$	160.970	+	160.970i	0.796879	+	0.796879i
$203$	−78.8261	+	28.4685i	−0.388306	+	0.140239i
$204$	−4.47083	+	7.28521i	−0.0219158	+	0.0357118i
$205$	22.9871	+	21.5225i	0.112132	+	0.104988i
$206$	13.9636	−	24.1857i	0.0677846	−	0.117406i
$207$	−35.4387	−	39.4607i	−0.171202	−	0.190631i
$208$	70.1066	+	18.7850i	0.337051	+	0.0903126i
$209$		−	455.786i		−	2.18080i
$210$	−176.493	+	124.526i	−0.840443	+	0.592982i
$211$	−133.700			−0.633647			−0.316824	−	0.948484i	$-0.602616\pi$
$211$	−133.700			−0.633647			−0.316824	+	0.948484i	$0.602616\pi$
$212$	−3.32125	+	12.3951i	−0.0156663	+	0.0584673i
$213$	23.6873	−	79.7785i	0.111208	−	0.374547i
$214$	−67.5421	−	38.9955i	−0.315617	−	0.182222i
$215$	1.95757	+	59.4927i	0.00910499	+	0.276710i
$216$	208.616	+	16.8235i	0.965814	+	0.0778867i
$217$	−246.503	−	44.0977i	−1.13596	−	0.203215i
$218$	102.947	−	102.947i	0.472234	−	0.472234i
$219$	−2.41988	+	90.1943i	−0.0110497	+	0.411846i
$220$	−5.36721	+	23.0362i	−0.0243964	+	0.104710i
$221$	−45.7703	−	26.4255i	−0.207105	−	0.119572i
$222$	81.3536	−	77.1023i	0.366458	−	0.347308i
$223$	−63.9114	+	63.9114i	−0.286598	+	0.286598i	−0.835733	−	0.549135i	$-0.814957\pi$
$223$	−63.9114	+	63.9114i	−0.286598	+	0.286598i	0.549135	+	0.835733i	$0.314957\pi$
$224$	−21.2851	+	14.8252i	−0.0950229	+	0.0661840i
$225$	−110.126	+	196.207i	−0.489451	+	0.872031i
$226$	85.2471	+	147.652i	0.377199	+	0.653329i
$227$	−59.8472	−	223.353i	−0.263644	−	0.983933i	−0.963075	−	0.269233i	$-0.913230\pi$
$227$	−59.8472	−	223.353i	−0.263644	−	0.983933i	0.699431	−	0.714700i	$-0.253437\pi$
$228$	−4.42385	+	14.8995i	−0.0194028	+	0.0653485i
$229$	−18.8007	−	32.5638i	−0.0820992	−	0.142200i	0.822052	−	0.569412i	$-0.192829\pi$
$229$	−18.8007	−	32.5638i	−0.0820992	−	0.142200i	−0.904151	+	0.427212i	$0.859496\pi$
$230$	58.0024	−	17.6055i	0.252184	−	0.0765454i
$231$	−382.800	−	192.356i	−1.65714	−	0.832711i
$232$	−65.6252	+	65.6252i	−0.282867	+	0.282867i
$233$	−32.8829	−	8.81095i	−0.141128	−	0.0378152i	0.187563	−	0.982253i	$-0.439941\pi$
$233$	−32.8829	−	8.81095i	−0.141128	−	0.0378152i	−0.328692	+	0.944437i	$0.606608\pi$
$234$	4.27016	−	79.5220i	0.0182485	−	0.339838i
$235$	158.069	+	254.100i	0.672633	+	1.08128i
$236$	−8.11447	−	14.0547i	−0.0343834	−	0.0595537i
$237$	372.341	−	89.1379i	1.57106	−	0.376109i
$238$	166.415	−	60.1017i	0.699223	−	0.252528i
$239$	320.856			1.34249			0.671247	−	0.741233i	$-0.265759\pi$
$239$	320.856			1.34249			0.671247	+	0.741233i	$0.265759\pi$
$240$	−125.221	+	219.961i	−0.521753	+	0.916504i
$241$	293.702	+	169.569i	1.21868	+	0.703605i	0.964635	−	0.263588i	$-0.0849058\pi$
$241$	293.702	+	169.569i	1.21868	+	0.703605i	0.254044	+	0.967193i	$0.418239\pi$
$242$	−586.547	+	157.165i	−2.42375	+	0.649442i
$243$	−30.9429	−	241.022i	−0.127337	−	0.991860i
$244$	21.5479			0.0883110
$245$	244.569	+	14.5322i	0.998239	+	0.0593152i
$246$	20.3298	−	33.1273i	0.0826413	−	0.134664i
$247$	−92.8251	−	24.8724i	−0.375810	−	0.100698i
$248$	−267.854	+	71.7714i	−1.08006	+	0.289401i
$249$	−33.1169	−	61.0874i	−0.133000	−	0.245331i
$250$	−149.886	−	208.944i	−0.599544	−	0.835774i
$251$	−70.5213			−0.280961			−0.140481	−	0.990083i	$-0.544865\pi$
$251$	−70.5213			−0.280961			−0.140481	+	0.990083i	$0.544865\pi$
$252$	10.6466	+	10.0035i	0.0422483	+	0.0396964i
$253$	85.0107	+	85.0107i	0.336011	+	0.336011i
$254$	58.1634	+	100.742i	0.228990	+	0.396622i
$255$	129.531	−	131.113i	0.507966	−	0.514169i
$256$	−22.1878	+	38.4304i	−0.0866710	+	0.150119i
$257$	165.778	+	44.4202i	0.645052	+	0.172841i	0.566491	−	0.824068i	$-0.308301\pi$
$257$	165.778	+	44.4202i	0.645052	+	0.172841i	0.0785611	+	0.996909i	$0.474967\pi$
$258$	71.4522	−	17.1056i	0.276947	−	0.0663006i
$259$	−126.677	+	10.7653i	−0.489099	+	0.0415647i
$260$	4.39864	+	2.35017i	0.0169178	+	0.00903913i
$261$	90.2953	+	58.8038i	0.345959	+	0.225302i
$262$	143.297	−	38.3963i	0.546935	−	0.146551i
$263$	−28.1758	−	105.154i	−0.107132	−	0.399823i	0.891446	−	0.453127i	$-0.149692\pi$
$263$	−28.1758	−	105.154i	−0.107132	−	0.399823i	−0.998578	+	0.0533036i	$0.983025\pi$
$264$	−474.240	−	12.7237i	−1.79636	−	0.0481957i
$265$	130.392	−	244.044i	0.492044	−	0.920920i
$266$	263.999	−	183.877i	0.992479	−	0.691268i
$267$	250.827	−	60.0475i	0.939425	−	0.224897i
$268$	1.36508	−	5.09455i	0.00509359	−	0.0190095i
$269$	−57.7621	−	33.3490i	−0.214729	−	0.123974i	0.388778	−	0.921331i	$-0.372897\pi$
$269$	−57.7621	−	33.3490i	−0.214729	−	0.123974i	−0.603507	+	0.797357i	$0.706231\pi$
$270$	264.531	+	84.5547i	0.979744	+	0.313165i
$271$	107.612	−	62.1301i	0.397094	−	0.229262i	−0.288135	−	0.957590i	$-0.593035\pi$
$271$	107.612	−	62.1301i	0.397094	−	0.229262i	0.685229	+	0.728327i	$0.259702\pi$
$272$	146.605	−	146.605i	0.538987	−	0.538987i
$273$	−60.0647	+	67.4639i	−0.220017	+	0.247121i
$274$			191.311i			0.698215i
$275$	225.420	−	457.494i	0.819710	−	1.66361i
$276$	−1.95385	−	3.60407i	−0.00707918	−	0.0130582i
$277$	29.3555	+	109.556i	0.105976	+	0.395509i	0.998454	−	0.0555822i	$-0.0177015\pi$
$277$	29.3555	+	109.556i	0.105976	+	0.395509i	−0.892478	+	0.451091i	$0.851035\pi$
$278$	−83.6251	+	312.093i	−0.300810	+	1.12264i
$279$	145.799	+	287.059i	0.522578	+	1.02889i
$280$	252.005	−	100.499i	0.900019	−	0.358926i
$281$			292.683i			1.04158i	0.853685	+	0.520789i	$0.174362\pi$
$281$			292.683i			1.04158i	−0.853685	+	0.520789i	$0.825638\pi$
$282$	268.092	−	254.083i	0.950683	−	0.901003i
$283$	86.1361	+	321.464i	0.304368	+	1.13592i	0.933488	+	0.358608i	$0.116749\pi$
$283$	86.1361	+	321.464i	0.304368	+	1.13592i	−0.629120	+	0.777308i	$0.716585\pi$
$284$	3.21630	−	5.57080i	0.0113250	−	0.0196155i
$285$	165.799	−	291.241i	0.581751	−	1.02190i
$286$			180.515i			0.631170i
$287$	−41.4648	+	14.9752i	−0.144476	+	0.0521784i
$288$	31.7049	+	10.3466i	0.110086	+	0.0359258i
$289$	119.535	−	69.0133i	0.413615	−	0.238800i
$290$	−104.568	+	65.0487i	−0.360578	+	0.224306i
$291$	−0.392851	−	0.724652i	−0.00135000	−	0.00249021i
$292$	−1.80504	+	6.73650i	−0.00618164	+	0.0230702i
$293$	125.441	+	125.441i	0.428126	+	0.428126i	0.887989	−	0.459864i	$-0.152102\pi$
$293$	125.441	+	125.441i	0.428126	+	0.428126i	−0.459864	+	0.887989i	$0.652102\pi$
$294$	−43.0165	−	299.327i	−0.146315	−	1.01812i
$295$	101.636	+	334.847i	0.344529	+	1.13508i
$296$	−121.922	+	70.3918i	−0.411899	+	0.237810i
$297$	99.3329	+	541.785i	0.334454	+	1.82419i
$298$	−53.6024	+	14.3627i	−0.179874	+	0.0481971i
$299$	21.9523	−	12.6742i	0.0734190	−	0.0423885i
$300$	−11.8093	+	12.7674i	−0.0393644	+	0.0425578i
$301$	−75.4392	−	35.4067i	−0.250629	−	0.117630i
$302$	181.373	+	181.373i	0.600572	+	0.600572i
$303$	−240.957	+	228.366i	−0.795238	+	0.753682i
$304$	188.496	−	326.484i	0.620051	−	1.07396i
$305$	−452.501	−	105.428i	−1.48361	−	0.345667i
$306$	−190.628	−	124.145i	−0.622969	−	0.405701i
$307$	257.864	+	257.864i	0.839949	+	0.839949i	0.988852	−	0.148903i	$-0.0475742\pi$
$307$	257.864	+	257.864i	0.839949	+	0.839949i	−0.148903	+	0.988852i	$0.547574\pi$
$308$	−25.3141	−	21.3486i	−0.0821885	−	0.0693136i
$309$	34.7118	+	21.3021i	0.112336	+	0.0689389i
$310$	−367.761	+	12.1010i	−1.18633	+	0.0390354i
$311$	127.428	−	220.712i	0.409737	−	0.709686i	−0.585123	−	0.810945i	$-0.698954\pi$
$311$	127.428	−	220.712i	0.409737	−	0.709686i	0.994860	+	0.101259i	$0.0322870\pi$
$312$	−28.4708	+	95.8891i	−0.0912524	+	0.307337i
$313$	299.193	+	80.1686i	0.955889	+	0.256130i	0.702859	−	0.711329i	$-0.251906\pi$
$313$	299.193	+	80.1686i	0.955889	+	0.256130i	0.253030	+	0.967458i	$0.418573\pi$
$314$			182.169i			0.580155i
$315$	−174.631	−	262.162i	−0.554385	−	0.832261i
$316$	29.5936			0.0936506
$317$	−3.76915	+	14.0667i	−0.0118901	+	0.0443743i	−0.971616	−	0.236564i	$-0.923979\pi$
$317$	−3.76915	+	14.0667i	−0.0118901	+	0.0443743i	0.959726	+	0.280938i	$0.0906455\pi$
$318$	−327.395	−	97.2078i	−1.02954	−	0.305685i
$319$	−211.528	−	122.126i	−0.663097	−	0.382839i
$320$	204.604	−	218.527i	0.639387	−	0.682896i
$321$	59.4893	−	96.9377i	0.185325	−	0.301987i
$322$	−14.9439	+	83.5354i	−0.0464098	+	0.259427i
$323$	−194.113	+	194.113i	−0.600968	+	0.600968i
$324$	2.01140	−	18.6748i	0.00620801	−	0.0576384i
$325$	−80.8716	−	70.8745i	−0.248836	−	0.218076i
$326$	487.950	+	281.718i	1.49678	+	0.864165i
$327$	146.050	+	154.103i	0.446635	+	0.471262i
$328$	−34.5207	+	34.5207i	−0.105246	+	0.105246i
$329$	−417.450	+	35.4758i	−1.26885	+	0.107829i
$330$	−609.035	−	159.235i	−1.84556	−	0.482530i
$331$	−265.401	−	459.689i	−0.801817	−	1.38879i	−0.918419	−	0.395609i	$-0.870534\pi$
$331$	−265.401	−	459.689i	−0.801817	−	1.38879i	0.116602	−	0.993179i	$-0.462800\pi$
$332$	−1.39012	−	5.18801i	−0.00418712	−	0.0156265i
$333$	109.218	+	121.613i	0.327981	+	0.365204i
$334$	−83.8727	−	145.272i	−0.251116	−	0.434945i
$335$	−53.5928	+	100.305i	−0.159978	+	0.299419i
$336$	−194.652	−	296.098i	−0.579322	−	0.881244i
$337$	−211.349	+	211.349i	−0.627148	+	0.627148i	−0.947349	−	0.320202i	$-0.896249\pi$
$337$	−211.349	+	211.349i	−0.627148	+	0.627148i	0.320202	+	0.947349i	$0.396249\pi$
$338$	−299.049	−	80.1301i	−0.884762	−	0.237071i
$339$	−218.582	+	118.498i	−0.644784	+	0.349552i
$340$	12.0966	−	7.52494i	0.0355782	−	0.0221322i
$341$	−364.902	−	632.029i	−1.07009	−	1.85346i
$342$	−393.236	−	128.329i	−1.14981	−	0.375232i
$343$	−173.712	+	295.758i	−0.506450	+	0.862269i
$344$	−92.2826			−0.268263
$345$	23.3966	+	85.2445i	0.0678163	+	0.247085i
$346$	−212.687	−	122.795i	−0.614703	−	0.354899i
$347$	291.982	−	78.2365i	0.841448	−	0.225465i	0.187746	−	0.982218i	$-0.439882\pi$
$347$	291.982	−	78.2365i	0.841448	−	0.225465i	0.653702	+	0.756752i	$0.273215\pi$
$348$	5.72941	+	6.04532i	0.0164638	+	0.0173716i
$349$	−213.085			−0.610558			−0.305279	−	0.952263i	$-0.598750\pi$
$349$	−213.085			−0.610558			−0.305279	+	0.952263i	$0.598750\pi$
$350$	355.929	−	53.9986i	1.01694	−	0.154282i
$351$	115.760	+	9.33532i	0.329801	+	0.0265963i
$352$	−73.0206	−	19.5658i	−0.207445	−	0.0555847i
$353$	654.603	−	175.400i	1.85440	−	0.496885i	0.854648	−	0.519207i	$-0.173773\pi$
$353$	654.603	−	175.400i	1.85440	−	0.496885i	0.999751	+	0.0223224i	$0.00710604\pi$
$354$	379.710	−	205.850i	1.07263	−	0.581496i
$355$	−94.7981	+	101.249i	−0.267037	+	0.285208i
$356$	19.9356			0.0559990
$357$	81.1074	+	244.951i	0.227191	+	0.686136i
$358$	−214.511	−	214.511i	−0.599193	−	0.599193i
$359$	297.612	+	515.479i	0.829002	+	1.43587i	0.898822	+	0.438315i	$0.144424\pi$
$359$	297.612	+	515.479i	0.829002	+	1.43587i	−0.0698193	+	0.997560i	$0.522242\pi$
$360$	−298.404	−	180.642i	−0.828900	−	0.501784i
$361$	−69.0787	+	119.648i	−0.191354	+	0.331435i
$362$	333.313	+	89.3108i	0.920753	+	0.246715i
$363$	−206.174	−	861.216i	−0.567972	−	2.37250i
$364$	−5.72923	+	3.99045i	−0.0157397	+	0.0109628i
$365$	70.8655	−	132.633i	0.194152	−	0.363379i
$366$	−15.3806	+	573.271i	−0.0420236	+	1.56632i
$367$	−171.430	+	45.9346i	−0.467112	+	0.125162i	−0.484695	−	0.874683i	$-0.661070\pi$
$367$	−171.430	+	45.9346i	−0.467112	+	0.125162i	0.0175830	+	0.999845i	$0.494403\pi$
$368$	25.7368	+	96.0511i	0.0699370	+	0.261008i
$369$	47.4979	+	30.9324i	0.128720	+	0.0838277i
$370$	−178.756	+	54.2578i	−0.483125	+	0.146643i
$371$	221.397	+	317.868i	0.596757	+	0.856786i
$372$	5.79404	+	24.2025i	0.0155754	+	0.0650605i
$373$	141.841	−	529.357i	0.380270	−	1.41919i	−0.465220	−	0.885195i	$-0.654025\pi$
$373$	141.841	−	529.357i	0.380270	−	1.41919i	0.845490	−	0.533992i	$-0.179309\pi$
$374$	446.571	+	257.828i	1.19404	+	0.689379i
$375$	310.460	−	210.332i	0.827894	−	0.560884i
$376$	−401.782	+	231.969i	−1.06857	+	0.616939i
$377$	−36.4152	+	36.4152i	−0.0965921	+	0.0965921i
$378$	−273.738	+	276.107i	−0.724173	+	0.730441i
$379$		−	592.243i		−	1.56265i	−0.624127	−	0.781323i	$-0.714545\pi$
$379$		−	592.243i		−	1.56265i	0.624127	−	0.781323i	$-0.285455\pi$
$380$	17.7045	−	18.9093i	0.0465909	−	0.0497613i
$381$	−149.137	+	80.8504i	−0.391434	+	0.212206i
$382$	−172.893	−	645.244i	−0.452599	−	1.68912i
$383$	−171.108	+	638.585i	−0.446758	+	1.66732i	0.264495	+	0.964387i	$0.414795\pi$
$383$	−171.108	+	638.585i	−0.446758	+	1.66732i	−0.711253	+	0.702936i	$0.751872\pi$
$384$	−352.825	−	216.524i	−0.918814	−	0.563863i
$385$	427.137	+	572.171i	1.10945	+	1.48616i
$386$		−	450.500i		−	1.16710i
$387$	22.1418	+	104.832i	0.0572140	+	0.270884i
$388$	−0.0164904	−	0.0615429i	−4.25010e−5	−	0.000158616i
$389$	115.707	−	200.410i	0.297446	−	0.515192i	−0.678105	−	0.734965i	$-0.737198\pi$
$389$	115.707	−	200.410i	0.297446	−	0.515192i	0.975551	+	0.219773i	$0.0705318\pi$
$390$	−65.6650	+	115.346i	−0.168372	+	0.295759i
$391$		−	72.4096i		−	0.185191i
$392$	−34.9867	+	378.213i	−0.0892517	+	0.964830i
$393$	50.3695	+	210.400i	0.128167	+	0.535369i
$394$	190.093	−	109.750i	0.482470	−	0.278554i
$395$	−621.459	−	144.794i	−1.57331	−	0.366567i
$396$	−2.28293	+	42.5144i	−0.00576498	+	0.107360i
$397$	54.3165	−	202.712i	0.136817	−	0.510609i	−0.863167	−	0.504919i	$-0.831522\pi$
$397$	54.3165	−	202.712i	0.136817	−	0.510609i	0.999984	−	0.00568968i	$-0.00181109\pi$
$398$	−72.9929	−	72.9929i	−0.183399	−	0.183399i
$399$	257.731	+	392.050i	0.645941	+	0.982582i
$400$	350.672	−	234.482i	0.876681	−	0.586204i
$401$	−94.3487	+	54.4722i	−0.235284	+	0.135841i	−0.613007	−	0.790077i	$-0.710040\pi$
$401$	−94.3487	+	54.4722i	−0.235284	+	0.135841i	0.377724	+	0.925918i	$0.376707\pi$
$402$	134.564	+	39.9538i	0.334736	+	0.0993875i
$403$	−148.631	+	39.8257i	−0.368813	+	0.0988230i
$404$	−22.2228	+	12.8303i	−0.0550069	+	0.0317583i
$405$	−133.610	+	382.326i	−0.329902	+	0.944015i
$406$	−14.5990	−	171.790i	−0.0359582	−	0.423127i
$407$	−261.992	−	261.992i	−0.643716	−	0.643716i
$408$	196.553	+	207.391i	0.481748	+	0.508311i
$409$	108.632	−	188.156i	0.265604	−	0.460039i	−0.702118	−	0.712061i	$-0.747762\pi$
$409$	108.632	−	188.156i	0.265604	−	0.460039i	0.967722	+	0.252021i	$0.0810954\pi$
$410$	−55.0055	+	34.2174i	−0.134160	+	0.0834571i
$411$	−278.893	−	7.48259i	−0.678572	−	0.0182058i
$412$	2.22599	+	2.22599i	0.00540288	+	0.00540288i
$413$	−482.249	−	86.2713i	−1.16767	−	0.208889i
$414$	97.2794	−	49.4088i	0.234974	−	0.119345i
$415$	3.80864	+	115.749i	0.00917744	+	0.278912i
$416$	−7.96952	+	13.8036i	−0.0191575	+	0.0331818i
$417$	−451.699	−	134.115i	−1.08321	−	0.321619i
$418$	905.674	+	242.675i	2.16669	+	0.580562i
$419$		−	11.8203i		−	0.0282107i	−0.999901	−	0.0141053i	$-0.995510\pi$
$419$		−	11.8203i		−	0.0282107i	0.999901	−	0.0141053i	$-0.00449002\pi$
$420$	−8.40944	−	22.8498i	−0.0200225	−	0.0544043i
$421$	178.317			0.423555			0.211778	−	0.977318i	$-0.432075\pi$
$421$	178.317			0.423555			0.211778	+	0.977318i	$0.432075\pi$
$422$	71.1858	−	265.669i	0.168687	−	0.629547i
$423$	359.916	+	400.763i	0.850866	+	0.947430i
$424$	371.493	+	214.482i	0.876163	+	0.505853i
$425$	−290.843	+	98.8366i	−0.684336	+	0.232557i
$426$	145.913	+	89.5446i	0.342518	+	0.210199i
$427$	419.352	−	497.246i	0.982088	−	1.16451i
$428$	6.21639	−	6.21639i	0.0145243	−	0.0145243i
$429$	−263.154	−	7.06032i	−0.613413	−	0.0164576i
$430$	−119.258	−	27.7860i	−0.277344	−	0.0646185i
$431$	649.475	+	374.974i	1.50690	+	0.870010i	0.999968	+	0.00802521i	$0.00255453\pi$
$431$	649.475	+	374.974i	1.50690	+	0.870010i	0.506934	+	0.861985i	$0.330779\pi$
$432$	−152.908	+	429.166i	−0.353954	+	0.993439i
$433$	−333.096	+	333.096i	−0.769274	+	0.769274i	−0.977979	−	0.208705i	$-0.933075\pi$
$433$	−333.096	+	333.096i	−0.769274	+	0.769274i	0.208705	+	0.977979i	$0.433075\pi$
$434$	218.870	−	466.336i	0.504310	−	1.07451i
$435$	−90.7381	−	154.983i	−0.208593	−	0.356283i
$436$	8.20555	+	14.2124i	0.0188201	+	0.0325973i
$437$	−34.0770	−	127.177i	−0.0779794	−	0.291023i
$438$	−177.933	−	52.8307i	−0.406240	−	0.120618i
$439$	368.605	+	638.442i	0.839646	+	1.45431i	0.890191	+	0.455588i	$0.150571\pi$
$439$	368.605	+	638.442i	0.839646	+	1.45431i	−0.0505449	+	0.998722i	$0.516096\pi$
$440$	697.384	+	372.609i	1.58496	+	0.846840i
$441$	438.041	−	51.0021i	0.993290	−	0.115651i
$442$	76.8786	−	76.8786i	0.173933	−	0.173933i
$443$	629.672	+	168.720i	1.42138	+	0.380858i	0.885974	−	0.463735i	$-0.153491\pi$
$443$	629.672	+	168.720i	1.42138	+	0.380858i	0.535408	+	0.844594i	$0.320158\pi$
$444$	6.02153	+	11.1073i	0.0135620	+	0.0250165i
$445$	−418.644	−	97.5401i	−0.940773	−	0.219191i
$446$	−92.9673	−	161.024i	−0.208447	−	0.361040i
$447$	−18.8415	−	78.7034i	−0.0421509	−	0.176070i
$448$	142.362	+	394.185i	0.317772	+	0.879877i
$449$	110.067			0.245137			0.122569	−	0.992460i	$-0.460887\pi$
$449$	110.067			0.245137			0.122569	+	0.992460i	$0.460887\pi$
$450$	−331.240	−	323.294i	−0.736089	−	0.718432i
$451$	−111.270	−	64.2415i	−0.246718	−	0.142442i
$452$	−18.5636	+	4.97411i	−0.0410700	+	0.0110047i
$453$	−271.499	+	257.311i	−0.599335	+	0.568016i
$454$	475.680			1.04775
$455$	139.837	−	55.7668i	0.307334	−	0.122564i
$456$	442.818	+	271.751i	0.971093	+	0.595946i
$457$	451.330	+	120.933i	0.987593	+	0.264625i	0.716239	−	0.697855i	$-0.245862\pi$
$457$	451.330	+	120.933i	0.987593	+	0.264625i	0.271354	+	0.962480i	$0.412529\pi$
$458$	74.7163	−	20.0202i	0.163136	−	0.0437121i
$459$	188.434	−	273.043i	0.410531	−	0.594864i
$460$	0.224704	+	6.82901i	0.000488488	+	0.0148457i
$461$	−640.069			−1.38844			−0.694218	−	0.719764i	$-0.744250\pi$
$461$	−640.069			−1.38844			−0.694218	+	0.719764i	$0.744250\pi$
$462$	586.038	−	658.231i	1.26848	−	1.42474i
$463$	−573.273	−	573.273i	−1.23817	−	1.23817i	−0.960748	−	0.277423i	$-0.910520\pi$
$463$	−573.273	−	573.273i	−1.23817	−	1.23817i	−0.277423	−	0.960748i	$-0.589480\pi$
$464$	−101.013	−	174.960i	−0.217700	−	0.377068i
$465$	−3.25685	−	536.596i	−0.00700397	−	1.15397i
$466$	35.0157	−	60.6491i	0.0751411	−	0.130148i
$467$	154.067	+	41.2821i	0.329908	+	0.0883985i	0.419971	−	0.907538i	$-0.362040\pi$
$467$	154.067	+	41.2821i	0.329908	+	0.0883985i	−0.0900632	+	0.995936i	$0.528707\pi$
$468$	8.53388	+	2.78497i	0.0182348	+	0.00595078i
$469$	−90.9972	−	130.648i	−0.194024	−	0.278567i
$470$	−589.073	+	178.801i	−1.25335	+	0.380428i
$471$	−265.565	−	7.12501i	−0.563833	−	0.0151274i
$472$	−524.021	+	140.411i	−1.11021	+	0.297481i
$473$	−62.8590	−	234.593i	−0.132894	−	0.495968i
$474$	−21.1236	+	787.323i	−0.0445645	+	1.66102i
$475$	−464.310	+	310.467i	−0.977494	+	0.653615i
$476$	1.68884	+	19.8729i	0.00354799	+	0.0417499i
$477$	154.515	−	473.474i	0.323930	−	0.992608i
$478$	−170.834	+	637.560i	−0.357393	+	1.33381i
$479$	−17.2667	−	9.96894i	−0.0360474	−	0.0208120i	0.481868	−	0.876244i	$-0.339958\pi$
$479$	−17.2667	−	9.96894i	−0.0360474	−	0.0208120i	−0.517915	+	0.855432i	$0.673292\pi$
$480$	−39.5417	−	39.0646i	−0.0823785	−	0.0813846i
$481$	−67.6542	+	39.0602i	−0.140653	+	0.0812062i
$482$	−493.319	+	493.319i	−1.02348	+	1.02348i
$483$	−121.193	−	25.0525i	−0.250918	−	0.0518686i
$484$		−	68.4493i		−	0.141424i
$485$	0.0451801	+	1.37307i	9.31548e−5	+	0.00283108i
$486$	495.400	+	66.8421i	1.01934	+	0.137535i
$487$	244.703	+	913.243i	0.502470	+	1.87524i	0.483353	+	0.875426i	$0.339419\pi$
$487$	244.703	+	913.243i	0.502470	+	1.87524i	0.0191167	+	0.999817i	$0.493915\pi$
$488$	186.430	−	695.766i	0.382028	−	1.42575i
$489$	−429.773	+	700.314i	−0.878881	+	1.43214i
$490$	−159.092	+	478.235i	−0.324678	+	0.975990i
$491$		−	600.751i		−	1.22353i	−0.791041	−	0.611763i	$-0.790461\pi$
$491$		−	600.751i		−	1.22353i	0.791041	−	0.611763i	$-0.209539\pi$
$492$	3.01383	+	3.18001i	0.00612567	+	0.00646343i
$493$	38.0751	+	142.098i	0.0772314	+	0.288232i
$494$	98.8460	−	171.206i	0.200093	−	0.346571i
$495$	255.953	−	881.623i	0.517078	−	1.78106i
$496$		−	603.638i		−	1.21701i
$497$	−65.9599	−	182.636i	−0.132716	−	0.367477i
$498$	139.017	−	33.2804i	0.279150	−	0.0668282i
$499$	504.601	−	291.332i	1.01123	−	0.583831i	0.0996751	−	0.995020i	$-0.468220\pi$
$499$	504.601	−	291.332i	1.01123	−	0.583831i	0.911550	+	0.411189i	$0.134886\pi$
$500$	27.1229	−	10.2239i	0.0542458	−	0.0204478i
$501$	215.058	−	116.588i	0.429257	−	0.232710i
$502$	37.5477	−	140.130i	0.0747963	−	0.279143i
$503$	−174.648	−	174.648i	−0.347212	−	0.347212i	0.511858	−	0.859070i	$-0.328957\pi$
$503$	−174.648	−	174.648i	−0.347212	−	0.347212i	−0.859070	+	0.511858i	$0.828957\pi$
$504$	415.118	−	257.221i	0.823648	−	0.510360i
$505$	529.449	−	160.704i	1.04841	−	0.318225i
$506$	−214.184	+	123.659i	−0.423288	+	0.244385i
$507$	128.510	−	432.820i	0.253472	−	0.853689i
$508$	−12.6658	+	3.39379i	−0.0249327	+	0.00668070i
$509$	207.603	−	119.860i	0.407865	−	0.235481i	−0.282007	−	0.959412i	$-0.591000\pi$
$509$	207.603	−	119.860i	0.407865	−	0.235481i	0.689872	+	0.723931i	$0.257667\pi$
$510$	191.563	+	327.195i	0.375614	+	0.641559i
$511$	120.325	+	172.755i	0.235470	+	0.338073i
$512$	325.741	+	325.741i	0.636212	+	0.636212i
$513$	202.459	−	568.240i	0.394657	−	1.10768i
$514$	−176.531	+	305.761i	−0.343445	+	0.594865i
$515$	−35.8540	−	57.6364i	−0.0696195	−	0.111915i
$516$	−0.222118	+	8.27886i	−0.000430462	+	0.0160443i
$517$	−863.370	−	863.370i	−1.66996	−	1.66996i
$518$	46.0554	−	257.446i	0.0889100	−	0.497000i
$519$	187.329	−	305.253i	0.360943	−	0.588155i
$520$	113.942	−	121.695i	0.219119	−	0.234030i
$521$	67.6776	−	117.221i	0.129899	−	0.224992i	−0.793738	−	0.608260i	$-0.791868\pi$
$521$	67.6776	−	117.221i	0.129899	−	0.224992i	0.923637	+	0.383267i	$0.125201\pi$
$522$	−164.923	+	148.113i	−0.315944	+	0.283742i
$523$	−371.725	−	99.6034i	−0.710755	−	0.190446i	−0.114712	−	0.993399i	$-0.536595\pi$
$523$	−371.725	−	99.6034i	−0.710755	−	0.190446i	−0.596043	+	0.802953i	$0.703261\pi$
$524$			16.7226i			0.0319133i
$525$	64.7980	+	520.986i	0.123425	+	0.992354i
$526$	223.948			0.425756
$527$	−113.765	+	424.578i	−0.215874	+	0.805652i
$528$	293.941	−	989.989i	0.556706	−	1.87498i
$529$	−428.051	−	247.136i	−0.809171	−	0.467175i
$530$	415.505	+	389.032i	0.783972	+	0.734023i
$531$	285.236	+	561.593i	0.537168	+	1.05761i
$532$	12.3187	+	34.1091i	0.0231554	+	0.0641149i
$533$	−19.1554	+	19.1554i	−0.0359389	+	0.0359389i
$534$	−14.2298	+	530.378i	−0.0266476	+	0.993218i
$535$	−160.958	+	100.128i	−0.300856	+	0.187154i
$536$	−152.689	−	88.1550i	−0.284867	−	0.164468i
$537$	321.104	−	304.324i	0.597959	−	0.566712i
$538$	97.0207	−	97.0207i	0.180336	−	0.180336i
$539$	−985.293	+	168.683i	−1.82800	+	0.312955i
$540$	−16.9240	+	26.3356i	−0.0313408	+	0.0487697i
$541$	138.386	+	239.692i	0.255798	+	0.443054i	0.965112	−	0.261838i	$-0.0843286\pi$
$541$	138.386	+	239.692i	0.255798	+	0.443054i	−0.709314	+	0.704892i	$0.750995\pi$
$542$	66.1599	+	246.912i	0.122066	+	0.455558i
$543$	−143.234	+	482.410i	−0.263783	+	0.888416i
$544$	22.7656	+	39.4312i	0.0418485	+	0.0724838i
$545$	−102.777	−	338.606i	−0.188581	−	0.621295i
$546$	−102.075	−	155.272i	−0.186950	−	0.284381i
$547$	−531.010	+	531.010i	−0.970768	+	0.970768i	−0.999585	−	0.0288163i	$-0.990826\pi$
$547$	−531.010	+	531.010i	−0.970768	+	0.970768i	0.0288163	+	0.999585i	$0.490826\pi$
$548$	−20.8302	−	5.58143i	−0.0380113	−	0.0101851i
$549$	−835.113	−	44.8438i	−1.52115	−	0.0816826i
$550$	789.046	+	691.507i	1.43463	+	1.25729i
$551$	133.747	+	231.656i	0.242735	+	0.420429i
$552$	−133.277	+	31.9064i	−0.241445	+	0.0578015i
$553$	575.932	−	682.911i	1.04147	−	1.23492i
$554$	−233.324			−0.421163
$555$	−72.1055	−	262.713i	−0.129920	−	0.473357i
$556$	−31.5414	−	18.2104i	−0.0567291	−	0.0327525i
$557$	415.380	−	111.301i	0.745745	−	0.199822i	0.134115	−	0.990966i	$-0.457181\pi$
$557$	415.380	−	111.301i	0.745745	−	0.199822i	0.611630	+	0.791144i	$0.290514\pi$
$558$	−648.032	+	136.872i	−1.16135	+	0.245291i
$559$	−51.2073			−0.0916052
$560$	69.3341	+	586.498i	0.123811	+	1.04732i
$561$	−393.328	+	640.927i	−0.701119	+	1.14247i
$562$	−581.579	−	155.834i	−1.03484	−	0.277284i
$563$	−784.064	+	210.089i	−1.39265	+	0.373161i	−0.875701	−	0.482853i	$-0.839601\pi$
$563$	−784.064	+	210.089i	−1.39265	+	0.373161i	−0.516953	+	0.856014i	$0.672934\pi$
$564$	19.8433	+	36.6030i	0.0351832	+	0.0648990i
$565$	414.169	−	13.6280i	0.733042	−	0.0241203i
$566$	−684.630			−1.20959
$567$	−391.802	−	409.854i	−0.691009	−	0.722846i
$568$	−152.050	−	152.050i	−0.267694	−	0.267694i
$569$	−323.444	−	560.222i	−0.568443	−	0.984572i	−0.996720	−	0.0809249i	$-0.974213\pi$
$569$	−323.444	−	560.222i	−0.568443	−	0.984572i	0.428277	−	0.903647i	$-0.359121\pi$
$570$	490.436	+	484.518i	0.860413	+	0.850032i
$571$	138.940	−	240.651i	0.243328	−	0.421456i	−0.718333	−	0.695700i	$-0.755094\pi$
$571$	138.940	−	240.651i	0.243328	−	0.421456i	0.961660	+	0.274244i	$0.0884277\pi$
$572$	−19.6547	−	5.26645i	−0.0343613	−	0.00920709i
$573$	947.399	−	226.806i	1.65340	−	0.395822i
$574$	−7.67951	−	90.3662i	−0.0133789	−	0.157432i
$575$	28.6939	−	144.507i	0.0499024	−	0.251317i
$576$	294.059	−	451.539i	0.510520	−	0.783922i
$577$	−702.159	+	188.143i	−1.21691	+	0.326071i	−0.809471	−	0.587160i	$-0.800246\pi$
$577$	−702.159	+	188.143i	−1.21691	+	0.326071i	−0.407443	+	0.913231i	$0.633579\pi$
$578$	73.4897	+	274.267i	0.127145	+	0.474511i
$579$	656.739	+	17.6200i	1.13426	+	0.0304318i
$580$	−4.03186	−	13.2832i	−0.00695148	−	0.0229021i
$581$	−146.774	−	68.8869i	−0.252623	−	0.118566i
$582$	1.64909	−	0.394790i	0.00283349	−	0.000678334i
$583$	−292.192	+	1090.47i	−0.501186	+	1.87045i
$584$	201.900	+	116.567i	0.345719	+	0.199601i
$585$	−165.583	−	100.238i	−0.283048	−	0.171347i
$586$	−316.047	+	182.470i	−0.539329	+	0.311382i
$587$	307.161	−	307.161i	0.523272	−	0.523272i	−0.395286	−	0.918558i	$-0.629354\pi$
$587$	307.161	−	307.161i	0.523272	−	0.523272i	0.918558	+	0.395286i	$0.129354\pi$
$588$	33.8460	+	4.04906i	0.0575613	+	0.00688615i
$589$			799.250i			1.35696i
$590$	−719.475	+	23.6739i	−1.21945	+	0.0401253i
$591$	152.559	+	281.410i	0.258137	+	0.476160i
$592$	−79.3176	−	296.017i	−0.133983	−	0.500029i
$593$	70.7019	−	263.863i	0.119228	−	0.444963i	−0.880341	−	0.474342i	$-0.842686\pi$
$593$	70.7019	−	263.863i	0.119228	−	0.444963i	0.999568	+	0.0293785i	$0.00935280\pi$
$594$	−1129.45	−	91.0826i	−1.90143	−	0.153338i
$595$	61.7680	−	425.590i	0.103812	−	0.715278i
$596$		−	6.25533i		−	0.0104955i
$597$	109.264	−	103.554i	0.183022	−	0.173458i
$598$	13.4962	+	50.3686i	0.0225689	+	0.0842284i
$599$	−234.625	+	406.382i	−0.391694	+	0.678433i	−0.992673	−	0.120831i	$-0.961444\pi$
$599$	−234.625	+	406.382i	−0.391694	+	0.678433i	0.600979	+	0.799265i	$0.294777\pi$
$600$	310.076	+	491.776i	0.516793	+	0.819626i
$601$		−	761.886i		−	1.26770i	−0.773457	−	0.633848i	$-0.781474\pi$
$601$		−	761.886i		−	1.26770i	0.773457	−	0.633848i	$-0.218526\pi$
$602$	110.521	−	131.051i	0.183590	−	0.217692i
$603$	−63.5077	+	194.605i	−0.105320	+	0.322727i
$604$	−25.0396	+	14.4566i	−0.0414562	+	0.0239348i
$605$	−334.905	+	1437.42i	−0.553562	+	2.37590i
$606$	−325.483	−	600.385i	−0.537100	−	0.990735i
$607$	−217.476	+	811.631i	−0.358280	+	1.33712i	0.518027	+	0.855364i	$0.326667\pi$
$607$	−217.476	+	811.631i	−0.358280	+	1.33712i	−0.876307	+	0.481754i	$0.840000\pi$
$608$	58.5414	+	58.5414i	0.0962851	+	0.0962851i
$609$	251.006	−	14.5634i	0.412161	−	0.0239137i
$610$	450.418	−	843.012i	0.738390	−	1.38199i
$611$	−222.948	+	128.719i	−0.364890	+	0.210669i
$612$	19.0785	−	17.1340i	0.0311741	−	0.0279967i
$613$	558.069	−	149.534i	0.910390	−	0.243938i	0.226917	−	0.973914i	$-0.427135\pi$
$613$	558.069	−	149.534i	0.910390	−	0.243938i	0.683473	+	0.729976i	$0.260469\pi$
$614$	−649.686	+	375.097i	−1.05812	+	0.610907i
$615$	−47.7308	−	81.5254i	−0.0776110	−	0.132562i
$616$	−908.345	+	632.668i	−1.47459	+	1.02706i
$617$	−408.277	−	408.277i	−0.661714	−	0.661714i	0.294070	−	0.955784i	$-0.404990\pi$
$617$	−408.277	−	408.277i	−0.661714	−	0.661714i	−0.955784	+	0.294070i	$0.904990\pi$
$618$	−60.8102	+	57.6325i	−0.0983984	+	0.0932564i
$619$	566.755	−	981.649i	0.915598	−	1.58586i	0.109575	−	0.993979i	$-0.465051\pi$
$619$	566.755	−	981.649i	0.915598	−	1.58586i	0.806023	−	0.591884i	$-0.201616\pi$
$620$	9.41174	−	40.3954i	0.0151802	−	0.0651538i
$621$	68.2233	+	143.746i	0.109860	+	0.231476i
$622$	370.722	+	370.722i	0.596016	+	0.596016i
$623$	387.975	−	460.041i	0.622753	−	0.738429i
$624$	−185.580	−	113.888i	−0.297404	−	0.182513i
$625$	−619.598	+	81.9943i	−0.991357	+	0.131191i
$626$	−318.600	+	551.831i	−0.508945	+	0.881519i
$627$	−389.194	+	1310.80i	−0.620724	+	2.09059i
$628$	−19.8347	−	5.31471i	−0.0315840	−	0.00846291i
$629$			223.157i			0.354781i
$630$	613.911	−	207.419i	0.974461	−	0.329237i
$631$	869.095			1.37733			0.688665	−	0.725080i	$-0.258197\pi$
$631$	869.095			1.37733			0.688665	+	0.725080i	$0.258197\pi$
$632$	256.040	−	955.555i	0.405127	−	1.51195i
$633$	384.508	+	114.166i	0.607438	+	0.180356i
$634$	−25.9445	−	14.9791i	−0.0409219	−	0.0236263i
$635$	282.584	−	9.29826i	0.445014	−	0.0146429i
$636$	20.1357	−	32.8111i	0.0316599	−	0.0515898i
$637$	−19.4140	+	209.869i	−0.0304772	+	0.329465i
$638$	355.295	−	355.295i	0.556889	−	0.556889i
$639$	−136.245	+	209.209i	−0.213216	+	0.327401i
$640$	364.435	+	585.840i	0.569430	+	0.915375i
$641$	−289.798	−	167.315i	−0.452103	−	0.261022i	0.256615	−	0.966514i	$-0.417393\pi$
$641$	−289.798	−	167.315i	−0.452103	−	0.261022i	−0.708718	+	0.705492i	$0.750726\pi$
$642$	160.947	+	169.821i	0.250696	+	0.264519i
$643$	93.9647	−	93.9647i	0.146135	−	0.146135i	−0.630254	−	0.776389i	$-0.717049\pi$
$643$	93.9647	−	93.9647i	0.146135	−	0.146135i	0.776389	+	0.630254i	$0.217049\pi$
$644$	−8.65946	−	4.06423i	−0.0134464	−	0.00631092i
$645$	45.1708	−	172.767i	0.0700323	−	0.267856i
$646$	−282.362	−	489.065i	−0.437093	−	0.757067i
$647$	231.732	+	864.836i	0.358164	+	1.33669i	0.876456	+	0.481482i	$0.159901\pi$
$647$	231.732	+	864.836i	0.358164	+	1.33669i	−0.518292	+	0.855204i	$0.673432\pi$
$648$	−585.595	−	226.519i	−0.903696	−	0.349567i
$649$	−713.882	−	1236.48i	−1.09997	−	1.90521i
$650$	183.890	−	122.961i	0.282908	−	0.189171i
$651$	671.265	+	337.309i	1.03113	+	0.518139i
$652$	−44.9095	+	44.9095i	−0.0688797	+	0.0688797i
$653$	978.645	+	262.227i	1.49869	+	0.401573i	0.912661	−	0.408717i	$-0.134024\pi$
$653$	978.645	+	262.227i	1.49869	+	0.401573i	0.586029	+	0.810290i	$0.300690\pi$
$654$	−383.972	+	208.160i	−0.587113	+	0.318288i
$655$	81.8193	−	351.170i	0.124915	−	0.536137i
$656$	−53.1356	−	92.0336i	−0.0809994	−	0.140295i
$657$	83.9759	−	257.324i	0.127817	−	0.391666i
$658$	151.771	−	848.387i	0.230655	−	1.28934i
$659$	−295.701			−0.448711			−0.224356	−	0.974507i	$-0.572028\pi$
$659$	−295.701			−0.448711			−0.224356	+	0.974507i	$0.572028\pi$
$660$	35.1061	−	61.6669i	0.0531910	−	0.0934347i
$661$	154.880	+	89.4201i	0.234312	+	0.135280i	0.612560	−	0.790424i	$-0.290140\pi$
$661$	154.880	+	89.4201i	0.234312	+	0.135280i	−0.378248	+	0.925704i	$0.623473\pi$
$662$	1054.74	−	282.616i	1.59326	−	0.426912i
$663$	109.067	+	115.080i	0.164505	+	0.173575i
$664$	−179.544			−0.270398
$665$	−91.8022	−	776.557i	−0.138048	−	1.16775i
$666$	−299.803	+	152.272i	−0.450155	+	0.228636i
$667$	−68.1529	−	18.2615i	−0.102178	−	0.0273786i
$668$	18.2643	−	4.89391i	0.0273418	−	0.00732621i
$669$	238.377	−	129.230i	0.356318	−	0.193168i
$670$	−170.778	−	159.898i	−0.254893	−	0.238653i
$671$	1895.70			2.82519
$672$	73.8733	−	24.4607i	0.109930	−	0.0363999i
$673$	−565.708	−	565.708i	−0.840577	−	0.840577i	0.148357	−	0.988934i	$-0.452601\pi$
$673$	−565.708	−	565.708i	−0.840577	−	0.840577i	−0.988934	+	0.148357i	$0.952601\pi$
$674$	−307.434	−	532.491i	−0.456133	−	0.790046i
$675$	484.254	−	470.237i	0.717414	−	0.696647i
$676$	17.4493	−	30.2231i	0.0258126	−	0.0447088i
$677$	−939.430	−	251.720i	−1.38764	−	0.371816i	−0.513748	−	0.857941i	$-0.671743\pi$
$677$	−939.430	−	251.720i	−1.38764	−	0.371816i	−0.873889	+	0.486125i	$0.838410\pi$
$678$	−119.083	−	497.427i	−0.175639	−	0.733668i
$679$	−1.74111	−	0.817173i	−0.00256423	−	0.00120350i
$680$	−138.317	−	455.695i	−0.203407	−	0.670139i
$681$	−18.6049	+	693.446i	−0.0273199	+	1.01828i
$682$	1450.16	−	388.570i	2.12634	−	0.569751i
$683$	−193.828	−	723.377i	−0.283789	−	1.05912i	−0.949719	−	0.313102i	$-0.898632\pi$
$683$	−193.828	−	723.377i	−0.283789	−	1.05912i	0.665930	−	0.746014i	$-0.268035\pi$
$684$	25.4452	−	39.0720i	0.0372006	−	0.0571228i
$685$	410.121	+	219.126i	0.598716	+	0.319891i
$686$	−495.199	−	502.648i	−0.721865	−	0.732723i
$687$	26.2631	+	109.704i	0.0382286	+	0.159686i
$688$	51.9921	−	194.037i	0.0755699	−	0.282031i
$689$	206.140	+	119.015i	0.299188	+	0.172736i
$690$	−181.843	+	1.10369i	−0.263540	+	0.00159955i
$691$	−40.1591	+	23.1858i	−0.0581173	+	0.0335540i	−0.528777	−	0.848761i	$-0.677349\pi$
$691$	−40.1591	+	23.1858i	−0.0581173	+	0.0335540i	0.470660	+	0.882315i	$0.344016\pi$
$692$	19.5751	−	19.5751i	0.0282878	−	0.0282878i
$693$	936.647	+	880.071i	1.35158	+	1.26994i
$694$			621.842i			0.896026i
$695$	573.262	+	536.738i	0.824838	+	0.772286i
$696$	244.769	−	132.695i	0.351680	−	0.190654i
$697$	20.0286	+	74.7476i	0.0287354	+	0.107242i
$698$	113.453	−	423.412i	0.162540	−	0.606607i
$699$	87.0447	+	53.4181i	0.124527	+	0.0764207i
$700$	−4.50468	+	40.3294i	−0.00643525	+	0.0576135i
$701$			167.792i			0.239361i	0.992812	+	0.119681i	$0.0381870\pi$
$701$			167.792i			0.239361i	−0.992812	+	0.119681i	$0.961813\pi$
$702$	−80.1841	+	225.052i	−0.114222	+	0.320587i
$703$	105.021	+	391.944i	0.149390	+	0.557530i
$704$	−610.713	+	1057.79i	−0.867490	+	1.50254i
$705$	−237.616	−	865.744i	−0.337045	−	1.22801i
$706$			1394.12i			1.97468i
$707$	−136.409	+	762.516i	−0.192941	+	1.07852i
$708$	11.3353	+	47.3489i	0.0160103	+	0.0668770i
$709$	4.74846	−	2.74153i	0.00669741	−	0.00386675i	−0.496648	−	0.867952i	$-0.665436\pi$
$709$	4.74846	−	2.74153i	0.00669741	−	0.00386675i	0.503345	+	0.864086i	$0.332103\pi$
$710$	−150.714	−	242.278i	−0.212274	−	0.341236i
$711$	−1146.93	−	61.5879i	−1.61313	−	0.0866215i
$712$	172.481	−	643.708i	0.242248	−	0.904084i
$713$	−149.072	−	149.072i	−0.209077	−	0.209077i
$714$	−529.916	+	30.7458i	−0.742179	+	0.0430614i
$715$	386.976	+	206.760i	0.541226	+	0.289174i
$716$	29.6145	−	17.0979i	0.0413610	−	0.0238798i
$717$	−922.754	−	273.978i	−1.28696	−	0.382117i
$718$	−1182.74	+	316.915i	−1.64728	+	0.441386i
$719$	607.419	−	350.694i	0.844811	−	0.487752i	−0.0140854	−	0.999901i	$-0.504484\pi$
$719$	607.419	−	350.694i	0.844811	−	0.487752i	0.858897	+	0.512149i	$0.171150\pi$
$720$	547.947	−	525.662i	0.761037	−	0.730087i
$721$	94.6884	−	8.04681i	0.131329	−	0.0111606i
$722$	−200.968	−	200.968i	−0.278349	−	0.278349i
$723$	−699.866	−	738.455i	−0.968003	−	1.02138i
$724$	−19.4486	+	33.6859i	−0.0268626	+	0.0465275i
$725$	19.6765	+	298.672i	0.0271401	+	0.411961i
$726$	1821.06	+	48.8583i	2.50835	+	0.0672979i
$727$	179.080	+	179.080i	0.246328	+	0.246328i	0.819462	−	0.573134i	$-0.194273\pi$
$727$	179.080	+	179.080i	0.246328	+	0.246328i	−0.573134	+	0.819462i	$0.694273\pi$
$728$	79.2800	+	219.518i	0.108901	+	0.301535i
$729$	−116.819	+	719.579i	−0.160245	+	0.987077i
$730$	225.819	+	211.432i	0.309342	+	0.289633i
$731$	−73.1390	+	126.680i	−0.100053	+	0.173298i
$732$	−61.9698	−	18.3996i	−0.0846582	−	0.0251361i
$733$	−311.841	−	83.5574i	−0.425431	−	0.113994i	0.0397499	−	0.999210i	$-0.487344\pi$
$733$	−311.841	−	83.5574i	−0.425431	−	0.113994i	−0.465180	+	0.885216i	$0.654011\pi$
$734$		−	365.099i		−	0.497410i
$735$	−690.948	−	250.630i	−0.940066	−	0.340993i
$736$	−21.8376			−0.0296707
$737$	120.095	−	448.200i	0.162951	−	0.608142i
$738$	−86.7539	+	77.9117i	−0.117553	+	0.105571i
$739$	613.293	+	354.085i	0.829896	+	0.479141i	0.853817	−	0.520573i	$-0.174282\pi$
$739$	613.293	+	354.085i	0.829896	+	0.479141i	−0.0239209	+	0.999714i	$0.507615\pi$
$740$	−0.692511	−	21.0462i	−0.000935826	−	0.0284407i
$741$	245.718	+	150.794i	0.331604	+	0.203501i
$742$	−749.500	+	270.686i	−1.01011	+	0.364806i
$743$	−214.444	+	214.444i	−0.288619	+	0.288619i	−0.836534	−	0.547915i	$-0.815422\pi$
$743$	−214.444	+	214.444i	−0.288619	+	0.288619i	0.547915	+	0.836534i	$0.315422\pi$
$744$	831.610	+	22.3118i	1.11776	+	0.0299889i
$745$	−30.6057	+	131.360i	−0.0410815	+	0.176323i
$746$	976.343	+	563.692i	1.30877	+	0.755619i
$747$	43.0790	+	203.960i	0.0576693	+	0.273039i
$748$	−41.1012	+	41.1012i	−0.0549481	+	0.0549481i
$749$	−22.4719	−	264.431i	−0.0300025	−	0.353046i
$750$	252.642	+	728.890i	0.336857	+	0.971854i
$751$	365.338	+	632.784i	0.486468	+	0.842588i	0.999879	−	0.0155551i	$-0.00495153\pi$
$751$	365.338	+	632.784i	0.486468	+	0.842588i	−0.513411	+	0.858143i	$0.671618\pi$
$752$	−261.383	−	975.496i	−0.347584	−	1.29720i
$753$	202.813	+	60.2179i	0.269340	+	0.0799706i
$754$	−52.9706	−	91.7477i	−0.0702528	−	0.121681i
$755$	596.558	−	181.073i	0.790143	−	0.239832i
$756$	−22.0767	−	37.8602i	−0.0292019	−	0.0500796i
$757$	28.1389	−	28.1389i	0.0371716	−	0.0371716i	−0.688277	−	0.725448i	$-0.741632\pi$
$757$	28.1389	−	28.1389i	0.0371716	−	0.0371716i	0.725448	+	0.688277i	$0.241632\pi$
$758$	1176.82	+	315.328i	1.55253	+	0.416000i
$759$	−171.893	−	317.073i	−0.226473	−	0.417752i
$760$	−457.390	−	735.268i	−0.601829	−	0.967458i
$761$	275.544	+	477.255i	0.362081	+	0.627143i	0.988303	−	0.152502i	$-0.0487331\pi$
$761$	275.544	+	477.255i	0.362081	+	0.627143i	−0.626222	+	0.779645i	$0.715400\pi$
$762$	−81.2496	−	339.390i	−0.106627	−	0.445394i
$763$	487.662	+	87.2396i	0.639138	+	0.114338i
$764$	75.2991			0.0985590
$765$	−484.477	+	266.464i	−0.633304	+	0.348318i
$766$	−1177.80	−	680.005i	−1.53760	−	0.887734i
$767$	−290.777	+	77.9136i	−0.379110	+	0.101582i
$768$	96.6256	−	91.5762i	0.125815	−	0.119240i
$769$	242.237			0.315002			0.157501	−	0.987519i	$-0.449656\pi$
$769$	242.237			0.315002			0.157501	+	0.987519i	$0.449656\pi$
$770$	−1364.36	+	544.104i	−1.77189	+	0.706629i
$771$	−438.833	−	269.306i	−0.569174	−	0.349294i
$772$	49.0510	+	13.1432i	0.0635375	+	0.0170248i
$773$	−100.156	+	26.8366i	−0.129567	+	0.0347175i	−0.323020	−	0.946392i	$-0.604698\pi$
$773$	−100.156	+	26.8366i	−0.129567	+	0.0347175i	0.193453	+	0.981110i	$0.438031\pi$
$774$	−220.097	−	11.8187i	−0.284362	−	0.0152696i
$775$	−395.289	+	802.244i	−0.510050	+	1.03515i
$776$	−2.12985			−0.00274465
$777$	373.503	+	77.2088i	0.480699	+	0.0993679i
$778$	336.620	+	336.620i	0.432674	+	0.432674i
$779$	70.3546	+	121.858i	0.0903139	+	0.156428i
$780$	−10.6433	−	10.5149i	−0.0136452	−	0.0134806i
$781$	282.959	−	490.099i	0.362303	−	0.627527i
$782$	143.882	+	38.5531i	0.183993	+	0.0493007i
$783$	−209.469	−	246.217i	−0.267521	−	0.314454i
$784$	−775.535	−	286.650i	−0.989203	−	0.365625i
$785$	390.522	+	208.654i	0.497480	+	0.265801i
$786$	−444.896	−	11.9364i	−0.566025	−	0.0151862i
$787$	1224.14	−	328.007i	1.55545	−	0.416781i	0.624229	−	0.781242i	$-0.285413\pi$
$787$	1224.14	−	328.007i	1.55545	−	0.416781i	0.931219	+	0.364461i	$0.118747\pi$
$788$	6.40385	+	23.8995i	0.00812672	+	0.0303293i
$789$	−8.75909	+	326.471i	−0.0111015	+	0.413779i
$790$	618.598	−	1157.78i	0.783036	−	1.46555i
$791$	−246.490	+	525.183i	−0.311618	+	0.663948i
$792$	1353.01	+	441.544i	1.70834	+	0.557505i
$793$	103.449	−	386.078i	0.130453	−	0.486857i
$794$	373.881	+	215.860i	0.470882	+	0.271864i
$795$	−583.382	+	590.507i	−0.733814	+	0.742776i
$796$	10.0771	−	5.81802i	0.0126597	−	0.00730907i
$797$	−1019.86	+	1019.86i	−1.27962	+	1.27962i	−0.338741	+	0.940880i	$0.610001\pi$
$797$	−1019.86	+	1019.86i	−1.27962	+	1.27962i	−0.940880	+	0.338741i	$0.889999\pi$
$798$	−916.251	+	303.386i	−1.14818	+	0.380183i
$799$			735.393i			0.920392i
$800$	29.8076	+	87.7137i	0.0372595	+	0.109642i
$801$	−772.629	−	41.4885i	−0.964581	−	0.0517959i
$802$	−58.0054	−	216.479i	−0.0723259	−	0.269924i
$803$	−158.801	+	592.653i	−0.197760	+	0.738049i
$804$	−8.27607	+	13.4858i	−0.0102936	+	0.0167734i
$805$	161.961	+	127.717i	0.201194	+	0.158654i
$806$		−	316.544i		−	0.392734i
$807$	137.642	+	145.232i	0.170560	+	0.179965i
$808$	222.013	+	828.565i	0.274769	+	1.02545i
$809$	655.920	−	1136.09i	0.810779	−	1.40431i	−0.101541	−	0.994831i	$-0.532377\pi$
$809$	655.920	−	1136.09i	0.810779	−	1.40431i	0.912320	−	0.409479i	$-0.134290\pi$
$810$	−688.567	−	469.054i	−0.850082	−	0.579079i
$811$		−	257.476i		−	0.317480i	−0.987320	−	0.158740i	$-0.949257\pi$
$811$		−	257.476i		−	0.317480i	0.987320	−	0.158740i	$-0.0507431\pi$
$812$	19.1306	+	3.42234i	0.0235599	+	0.00421471i
$813$	−362.536	+	86.7907i	−0.445924	+	0.106754i
$814$	660.087	−	381.102i	0.810918	−	0.468184i
$815$	1162.82	−	723.359i	1.42677	−	0.887557i
$816$	−546.807	+	296.437i	−0.670106	+	0.363280i
$817$	−68.8405	+	256.916i	−0.0842601	+	0.314463i
$818$	316.038	+	316.038i	0.386355	+	0.386355i
$819$	230.348	−	142.731i	0.281255	−	0.174275i
$820$	−2.12087	−	6.98735i	−0.00258643	−	0.00852116i
$821$	109.200	−	63.0464i	0.133008	−	0.0767922i	−0.432020	−	0.901864i	$-0.642199\pi$
$821$	109.200	−	63.0464i	0.133008	−	0.0767922i	0.565028	+	0.825072i	$0.308866\pi$
$822$	163.360	−	550.193i	0.198734	−	0.669335i
$823$	1337.78	−	358.458i	1.62550	−	0.435551i	0.672887	−	0.739745i	$-0.265054\pi$
$823$	1337.78	−	358.458i	1.62550	−	0.435551i	0.952610	+	0.304194i	$0.0983873\pi$
$824$	91.1345	−	52.6165i	0.110600	−	0.0638550i
$825$	−1038.94	+	1123.23i	−1.25932	+	1.36149i
$826$	428.190	−	912.324i	0.518390	−	1.10451i
$827$	342.391	+	342.391i	0.414015	+	0.414015i	0.883135	−	0.469120i	$-0.155429\pi$
$827$	342.391	+	342.391i	0.414015	+	0.414015i	−0.469120	+	0.883135i	$0.655429\pi$
$828$	2.54160	+	12.0334i	0.00306956	+	0.0145331i
$829$	−467.316	+	809.415i	−0.563711	+	0.976375i	0.433458	+	0.901174i	$0.357293\pi$
$829$	−467.316	+	809.415i	−0.563711	+	0.976375i	−0.997168	+	0.0752016i	$0.976040\pi$
$830$	−232.027	−	54.0601i	−0.279551	−	0.0651327i
$831$	9.12581	−	340.140i	0.0109817	−	0.409314i
$832$	182.101	+	182.101i	0.218872	+	0.218872i
$833$	491.461	+	347.782i	0.589990	+	0.417506i
$834$	506.993	−	826.145i	0.607906	−	0.990581i
$835$	−407.491	+	13.4083i	−0.488014	+	0.0160578i
$836$	−52.8455	+	91.5310i	−0.0632123	+	0.109487i
$837$	−174.187	−	950.054i	−0.208108	−	1.13507i
$838$	23.4876	+	6.29348i	0.0280281	+	0.00751012i
$839$		−	428.103i		−	0.510254i	−0.966907	−	0.255127i	$-0.917883\pi$
$839$		−	428.103i		−	0.510254i	0.966907	−	0.255127i	$-0.0821173\pi$
$840$	−810.561	+	73.8409i	−0.964953	+	0.0879058i
$841$	−697.653			−0.829551
$842$	−94.9414	+	354.326i	−0.112757	+	0.420815i
$843$	249.921	−	841.731i	0.296466	−	0.998495i
$844$	26.8496	+	15.5016i	0.0318123	+	0.0183668i
$845$	−514.306	+	549.304i	−0.608646	+	0.650063i
$846$	−987.970	+	501.796i	−1.16781	+	0.593140i
$847$	−1579.56	−	1332.12i	−1.86488	−	1.57275i
$848$	−660.277	+	660.277i	−0.778629	+	0.778629i
$849$	26.7774	−	998.054i	0.0315399	−	1.17556i
$850$	−41.5404	−	630.546i	−0.0488711	−	0.741819i
$851$	−92.6911	−	53.5152i	−0.108920	−	0.0628851i
$852$	−14.0067	+	13.2747i	−0.0164398	+	0.0155807i
$853$	−336.763	+	336.763i	−0.394799	+	0.394799i	−0.876394	−	0.481595i	$-0.840058\pi$
$853$	−336.763	+	336.763i	−0.394799	+	0.394799i	0.481595	+	0.876394i	$0.340058\pi$
$854$	764.781	+	1098.03i	0.895528	+	1.28574i
$855$	−725.513	+	696.007i	−0.848553	+	0.814043i
$856$	−146.939	−	254.506i	−0.171658	−	0.297321i
$857$	−66.2128	−	247.109i	−0.0772611	−	0.288342i	0.916475	−	0.400091i	$-0.131021\pi$
$857$	−66.2128	−	247.109i	−0.0772611	−	0.288342i	−0.993736	+	0.111749i	$0.964355\pi$
$858$	154.141	−	519.144i	0.179651	−	0.605063i
$859$	−166.820	−	288.942i	−0.194203	−	0.336370i	0.752436	−	0.658665i	$-0.228879\pi$
$859$	−166.820	−	288.942i	−0.194203	−	0.336370i	−0.946639	+	0.322296i	$0.895545\pi$
$860$	6.50468	−	12.1743i	0.00756358	−	0.0141562i
$861$	132.036	−	7.66077i	0.153352	−	0.00889752i
$862$	−1090.90	+	1090.90i	−1.26554	+	1.26554i
$863$	−1210.94	−	324.469i	−1.40317	−	0.375978i	−0.523688	−	0.851910i	$-0.675444\pi$
$863$	−1210.94	−	324.469i	−1.40317	−	0.375978i	−0.879482	+	0.475932i	$0.842111\pi$
$864$	−82.3454	−	56.8287i	−0.0953072	−	0.0657739i
$865$	−506.850	+	315.297i	−0.585954	+	0.364506i
$866$	−484.530	−	839.231i	−0.559504	−	0.969089i
$867$	−402.701	+	96.4060i	−0.464476	+	0.111195i
$868$	44.3898	+	37.4361i	0.0511403	+	0.0431291i
$869$	2603.54			2.99601
$870$	356.272	−	97.7842i	0.409508	−	0.112396i
$871$	−84.7266	−	48.9169i	−0.0972751	−	0.0561618i
$872$	529.903	−	141.987i	0.607687	−	0.162829i
$873$	0.511026	+	2.41949i	0.000585367	+	0.00277146i
$874$	270.852			0.309899
$875$	291.919	−	824.869i	0.333622	−	0.942707i
$876$	10.9434	−	17.8323i	0.0124925	−	0.0203565i
$877$	954.726	+	255.818i	1.08863	+	0.291697i	0.758126	−	0.652109i	$-0.226115\pi$
$877$	954.726	+	255.818i	1.08863	+	0.291697i	0.330502	+	0.943805i	$0.392782\pi$
$878$	−1464.88	+	392.513i	−1.66843	+	0.447053i
$879$	−253.643	−	467.870i	−0.288559	−	0.532275i
$880$	−1176.37	+	1256.42i	−1.33679	+	1.42775i
$881$	253.105			0.287292			0.143646	−	0.989629i	$-0.454117\pi$
$881$	253.105			0.287292			0.143646	+	0.989629i	$0.454117\pi$
$882$	−131.882	+	897.568i	−0.149526	+	1.01765i
$883$	−451.177	−	451.177i	−0.510960	−	0.510960i	0.403861	−	0.914820i	$-0.367668\pi$
$883$	−451.177	−	451.177i	−0.510960	−	0.510960i	−0.914820	+	0.403861i	$0.867668\pi$
$884$	6.12773	+	10.6135i	0.00693182	+	0.0120063i
$885$	−6.37158	−	1049.78i	−0.00719952	−	1.18619i
$886$	−670.514	+	1161.36i	−0.756788	+	1.31079i
$887$	−1482.03	−	397.109i	−1.67084	−	0.447699i	−0.705501	−	0.708709i	$-0.749278\pi$
$887$	−1482.03	−	397.109i	−1.67084	−	0.447699i	−0.965336	+	0.261010i	$0.915945\pi$
$888$	410.745	−	98.3317i	0.462550	−	0.110734i
$889$	−168.178	+	358.328i	−0.189176	+	0.403069i
$890$	416.717	−	779.937i	0.468221	−	0.876334i
$891$	176.955	−	1642.94i	0.198603	−	1.84393i
$892$	20.2448	−	5.42458i	0.0226960	−	0.00608136i
$893$	346.086	+	1291.61i	0.387555	+	1.44637i
$894$	166.420	+	4.46498i	0.186152	+	0.00499438i
$895$	−705.554	+	214.157i	−0.788328	+	0.239281i
$896$	−962.451	+	81.7911i	−1.07416	+	0.0912847i
$897$	−73.9552	+	17.7048i	−0.0824473	+	0.0197378i
$898$	−58.6029	+	218.709i	−0.0652594	+	0.243551i
$899$	370.928	+	214.155i	0.412600	+	0.238215i
$900$	44.8645	−	26.6338i	0.0498495	−	0.0295931i
$901$	588.857	−	339.977i	0.653559	−	0.377333i
$902$	186.895	−	186.895i	0.207201	−	0.207201i
$903$	186.723	+	166.244i	0.206781	+	0.184101i
$904$			642.441i			0.710665i
$905$	573.232	−	612.239i	0.633405	−	0.676507i
$906$	−366.738	−	676.485i	−0.404788	−	0.746672i
$907$	−225.682	−	842.257i	−0.248822	−	0.928618i	−0.971424	−	0.237353i	$-0.923720\pi$
$907$	−225.682	−	842.257i	−0.248822	−	0.928618i	0.722601	−	0.691265i	$-0.242946\pi$
$908$	−13.8778	+	51.7926i	−0.0152839	+	0.0570403i
$909$	887.972	−	451.006i	0.976867	−	0.496157i
$910$	36.3584	+	307.556i	0.0399543	+	0.337974i
$911$		−	751.515i		−	0.824935i	−0.910972	−	0.412467i	$-0.864667\pi$
$911$		−	751.515i		−	0.824935i	0.910972	−	0.412467i	$-0.135333\pi$
$912$	−820.880	+	777.983i	−0.900087	+	0.853051i
$913$	−122.298	−	456.422i	−0.133952	−	0.499915i
$914$	−480.604	+	832.430i	−0.525825	+	0.910755i
$915$	1211.33	+	689.591i	1.32385	+	0.753652i
$916$			8.71928i			0.00951887i
$917$	385.895	+	325.444i	0.420823	+	0.354901i
$918$	442.224	+	519.805i	0.481725	+	0.566237i
$919$	−819.856	+	473.344i	−0.892118	+	0.515064i	−0.874635	−	0.484783i	$-0.838899\pi$
$919$	−819.856	+	473.344i	−0.892118	+	0.515064i	−0.0174832	+	0.999847i	$0.505565\pi$
$920$	222.448	+	51.8282i	0.241791	+	0.0563350i
$921$	−521.405	−	961.784i	−0.566130	−	1.04428i
$922$	340.793	−	1271.86i	0.369623	−	1.37945i
$923$	−84.3720	−	84.3720i	−0.0914106	−	0.0914106i
$924$	54.5715	+	83.0122i	0.0590601	+	0.0898400i
$925$	−88.4310	+	445.353i	−0.0956011	+	0.481462i
$926$	1444.36	−	833.899i	1.55978	−	0.900539i
$927$	−81.6382	−	90.9033i	−0.0880671	−	0.0980618i
$928$	42.8546	−	11.4829i	0.0461795	−	0.0123738i
$929$	−790.789	+	456.562i	−0.851226	+	0.491456i	−0.861064	−	0.508496i	$-0.830202\pi$
$929$	−790.789	+	456.562i	−0.851226	+	0.491456i	0.00983804	+	0.999952i	$0.496868\pi$
$930$	1067.98	+	279.229i	1.14837	+	0.300246i
$931$	1026.85	+	379.541i	1.10296	+	0.407670i
$932$	5.58197	+	5.58197i	0.00598924	+	0.00598924i
$933$	−554.938	+	525.938i	−0.594789	+	0.563707i
$934$	−164.060	+	284.160i	−0.175653	+	0.304240i
$935$	1064.21	−	662.017i	1.13820	−	0.708040i
$936$	163.759	−	251.458i	0.174956	−	0.268651i
$937$	849.169	+	849.169i	0.906264	+	0.906264i	0.995968	−	0.0897045i	$-0.0285922\pi$
$937$	849.169	+	849.169i	0.906264	+	0.906264i	−0.0897045	+	0.995968i	$0.528592\pi$
$938$	308.055	−	111.256i	0.328417	−	0.118610i
$939$	−791.998	−	486.038i	−0.843448	−	0.517612i
$940$	−2.28210	−	69.3555i	−0.00242777	−	0.0737824i
$941$	−35.6310	+	61.7148i	−0.0378651	+	0.0655842i	−0.884337	−	0.466849i	$-0.845389\pi$
$941$	−35.6310	+	61.7148i	−0.0378651	+	0.0655842i	0.846472	+	0.532434i	$0.178722\pi$
$942$	155.553	−	523.901i	0.165131	−	0.556158i
$943$	−35.8503	−	9.60607i	−0.0380173	−	0.0101867i
$944$		−	1180.94i		−	1.25099i
$945$	278.364	+	903.072i	0.294566	+	0.955631i
$946$	499.618			0.528138
$947$	−412.282	+	1538.66i	−0.435356	+	1.62477i	0.304856	+	0.952398i	$0.401392\pi$
$947$	−412.282	+	1538.66i	−0.435356	+	1.62477i	−0.740213	+	0.672373i	$0.765275\pi$
$948$	−85.1085	−	25.2698i	−0.0897769	−	0.0266560i
$949$	112.034	+	64.6826i	0.118054	+	0.0681587i
$950$	−369.704	−	1087.91i	−0.389162	−	1.14517i
$951$	22.8512	−	37.2360i	0.0240286	−	0.0391546i
$952$	656.294	+	117.407i	0.689385	+	0.123326i
$953$	30.0619	−	30.0619i	0.0315445	−	0.0315445i	−0.691159	−	0.722703i	$-0.742899\pi$
$953$	30.0619	−	30.0619i	0.0315445	−	0.0315445i	0.722703	+	0.691159i	$0.242899\pi$
$954$	858.552	+	559.122i	0.899950	+	0.586082i
$955$	−1581.26	−	368.420i	−1.65577	−	0.385780i
$956$	−64.4344	−	37.2012i	−0.0674000	−	0.0389134i
$957$	504.053	+	531.846i	0.526701	+	0.555743i
$958$	29.0022	−	29.0022i	0.0302737	−	0.0302737i
$959$	−534.183	+	372.062i	−0.557021	+	0.387968i
$960$	−775.022	+	453.753i	−0.807314	+	0.472659i
$961$	159.379	+	276.053i	0.165847	+	0.287256i
$962$	−41.5937	−	155.230i	−0.0432367	−	0.161362i
$963$	−253.861	+	227.987i	−0.263614	+	0.236746i
$964$	−39.3208	−	68.1056i	−0.0407892	−	0.0706490i
$965$	−965.754	−	515.998i	−1.00078	−	0.534713i
$966$	114.308	−	227.480i	0.118331	−	0.235486i
$967$	462.121	−	462.121i	0.477892	−	0.477892i	−0.426565	−	0.904457i	$-0.640277\pi$
$967$	462.121	−	462.121i	0.477892	−	0.477892i	0.904457	+	0.426565i	$0.140277\pi$
$968$	−2210.18	−	592.215i	−2.28324	−	0.611793i
$969$	724.003	−	392.499i	0.747165	−	0.405055i
$970$	−2.75243	−	0.641290i	−0.00283756	−	0.000661124i
$971$	522.569	+	905.116i	0.538176	+	0.932148i	0.999002	+	0.0446579i	$0.0142198\pi$
$971$	522.569	+	905.116i	0.538176	+	0.932148i	−0.460826	+	0.887490i	$0.652447\pi$
$972$	−21.7310	+	51.9896i	−0.0223570	+	0.0534873i
$973$	−1034.07	+	373.459i	−1.06276	+	0.383822i
$974$	−1944.96			−1.99687
$975$	172.060	+	272.885i	0.176472	+	0.279882i
$976$	1357.91	+	783.990i	1.39130	+	0.803268i
$977$	1331.68	−	356.821i	1.36302	−	0.365221i	0.498099	−	0.867120i	$-0.334032\pi$
$977$	1331.68	−	356.821i	1.36302	−	0.365221i	0.864926	+	0.501899i	$0.167365\pi$
$978$	−1162.74	−	1226.85i	−1.18890	−	1.25445i
$979$	1753.87			1.79149
$980$	−47.4294	−	31.2745i	−0.0483973	−	0.0319128i
$981$	−288.438	−	567.896i	−0.294024	−	0.578895i
$982$	1193.73	+	319.859i	1.21561	+	0.325722i
$983$	−706.887	+	189.410i	−0.719112	+	0.192685i	−0.599775	−	0.800169i	$-0.704743\pi$
$983$	−706.887	+	189.410i	−0.719112	+	0.192685i	−0.119336	+	0.992854i	$0.538077\pi$
$984$	128.755	−	69.8013i	0.130849	−	0.0709363i
$985$	−17.5452	−	533.217i	−0.0178124	−	0.541337i
$986$	−302.630			−0.306927
$987$	1230.84	+	254.434i	1.24705	+	0.257785i
$988$	15.7574	+	15.7574i	0.0159487	+	0.0159487i
$989$	−35.0788	−	60.7583i	−0.0354690	−	0.0614341i
$990$	1615.56	+	977.998i	1.63188	+	0.987877i
$991$	651.871	−	1129.07i	0.657791	−	1.13933i	−0.323395	−	0.946264i	$-0.604824\pi$
$991$	651.871	−	1129.07i	0.657791	−	1.13933i	0.981186	−	0.193063i	$-0.0618423\pi$
$992$	128.046	+	34.3099i	0.129079	+	0.0345866i
$993$	370.744	+	1548.65i	0.373358	+	1.55957i
$994$	398.027	−	33.8252i	0.400430	−	0.0340294i
$995$	−240.083	+	72.8723i	−0.241289	+	0.0732385i
$996$	−0.432151	+	16.1073i	−0.000433887	+	0.0161720i
$997$	−41.2790	+	11.0607i	−0.0414032	+	0.0110940i	−0.279461	−	0.960157i	$-0.590156\pi$
$997$	−41.2790	+	11.0607i	−0.0414032	+	0.0110940i	0.238058	+	0.971251i	$0.423489\pi$
$998$	310.228	+	1157.79i	0.310850	+	1.16011i
$999$	−210.256	−	443.008i	−0.210466	−	0.443452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.38.8	yes	112
3.2	odd	2	inner	105.3.w.a.38.21	yes	112
5.2	odd	4	inner	105.3.w.a.17.8	✓	112
7.5	odd	6	inner	105.3.w.a.68.21	yes	112
15.2	even	4	inner	105.3.w.a.17.21	yes	112
21.5	even	6	inner	105.3.w.a.68.8	yes	112
35.12	even	12	inner	105.3.w.a.47.21	yes	112
105.47	odd	12	inner	105.3.w.a.47.8	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.8	✓	112	5.2	odd	4	inner
105.3.w.a.17.21	yes	112	15.2	even	4	inner
105.3.w.a.38.8	yes	112	1.1	even	1	trivial
105.3.w.a.38.21	yes	112	3.2	odd	2	inner
105.3.w.a.47.8	yes	112	105.47	odd	12	inner
105.3.w.a.47.21	yes	112	35.12	even	12	inner
105.3.w.a.68.8	yes	112	21.5	even	6	inner
105.3.w.a.68.21	yes	112	7.5	odd	6	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.532431 + 1.98706i) q^{2} +(-2.87591 - 0.853896i) q^{3} +(-0.200820 - 0.115943i) q^{4} +(3.64989 + 3.41735i) q^{5} +(3.22797 - 5.25996i) q^{6} +(-6.58378 + 2.37777i) q^{7} +(-5.48120 + 5.48120i) q^{8} +(7.54172 + 4.91146i) q^{9} +(-8.73379 + 5.43305i) q^{10} +(-17.6674 - 10.2003i) q^{11} +(0.478537 + 0.504923i) q^{12} +(-3.04150 + 3.04150i) q^{13} +(-1.21935 - 14.3484i) q^{14} +(-7.57870 - 12.9446i) q^{15} +(-8.43689 - 14.6131i) q^{16} +(3.18014 + 11.8684i) q^{17} +(-13.7748 + 12.3708i) q^{18} +(11.1709 + 19.3486i) q^{19} +(-0.336752 - 1.10945i) q^{20} +(20.9647 - 1.21638i) q^{21} +(29.6753 - 29.6753i) q^{22} +(-5.69233 - 1.52525i) q^{23} +(20.4438 - 11.0831i) q^{24} +(1.64344 + 24.9459i) q^{25} +(-4.42425 - 7.66303i) q^{26} +(-17.4954 - 20.5648i) q^{27} +(1.59784 + 0.285844i) q^{28} +11.9728 q^{29} +(29.7569 - 8.16722i) q^{30} +(30.9809 + 17.8869i) q^{31} +(3.57934 - 0.959081i) q^{32} +(42.0999 + 44.4213i) q^{33} -25.2765 q^{34} +(-32.1558 - 13.8205i) q^{35} +(-0.945077 - 1.86073i) q^{36} +(17.5430 + 4.70065i) q^{37} +(-44.3945 + 11.8955i) q^{38} +(11.3442 - 6.14996i) q^{39} +(-38.7370 + 1.27462i) q^{40} +6.29801 q^{41} +(-8.74526 + 42.3058i) q^{42} +(8.41810 + 8.41810i) q^{43} +(2.36531 + 4.09685i) q^{44} +(10.7423 + 43.6990i) q^{45} +(6.06154 - 10.4989i) q^{46} +(57.8113 + 15.4905i) q^{47} +(11.7857 + 49.2302i) q^{48} +(37.6924 - 31.3094i) q^{49} +(-50.4440 - 10.0164i) q^{50} +(0.988619 - 36.8481i) q^{51} +(0.963437 - 0.258152i) q^{52} +(-14.3227 - 53.4531i) q^{53} +(50.1785 - 23.8152i) q^{54} +(-29.6262 - 97.6057i) q^{55} +(23.0540 - 49.1201i) q^{56} +(-15.6049 - 65.1836i) q^{57} +(-6.37467 + 23.7906i) q^{58} +(60.6100 + 34.9932i) q^{59} +(0.0211110 + 3.47824i) q^{60} +(-80.4746 + 46.4620i) q^{61} +(-52.0374 + 52.0374i) q^{62} +(-61.3314 - 14.4035i) q^{63} -59.8721i q^{64} +(-21.4950 + 0.707281i) q^{65} +(-110.683 + 60.0038i) q^{66} +(5.88684 + 21.9700i) q^{67} +(0.737433 - 2.75214i) q^{68} +(15.0682 + 9.24715i) q^{69} +(44.5829 - 56.5370i) q^{70} +27.7403i q^{71} +(-68.2584 + 14.4170i) q^{72} +(-7.78414 - 29.0508i) q^{73} +(-18.6809 + 32.3563i) q^{74} +(16.5748 - 73.1456i) q^{75} -5.18078i q^{76} +(140.572 + 25.1475i) q^{77} +(6.18033 + 25.8161i) q^{78} +(-110.523 + 63.8104i) q^{79} +(19.1444 - 82.1681i) q^{80} +(32.7552 + 74.0817i) q^{81} +(-3.35326 + 12.5145i) q^{82} +(16.3782 + 16.3782i) q^{83} +(-4.35117 - 2.18645i) q^{84} +(-28.9515 + 54.1862i) q^{85} +(-21.2093 + 12.2452i) q^{86} +(-34.4326 - 10.2235i) q^{87} +(152.749 - 40.9289i) q^{88} +(-74.4534 + 42.9857i) q^{89} +(-92.5520 - 1.92108i) q^{90} +(12.7926 - 27.2566i) q^{91} +(0.966290 + 0.966290i) q^{92} +(-73.8249 - 77.8955i) q^{93} +(-61.5611 + 106.627i) q^{94} +(-25.3483 + 108.795i) q^{95} +(-11.1128 - 0.298152i) q^{96} +(0.194287 + 0.194287i) q^{97} +(42.1450 + 91.5672i) q^{98} +(-83.1445 - 163.701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) \) 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Introduction

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