LMFDB - Embedded newform 105.3.w.a.68.8

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			68.8
Character	$\chi$	$=$	105.68
Dual form			105.3.w.a.17.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.98706 + 0.532431i) q^{2} +(-0.853896 - 2.87591i) q^{3} +(0.200820 - 0.115943i) q^{4} +(1.13457 - 4.86958i) q^{5} +(3.22797 + 5.25996i) q^{6} +(-2.37777 + 6.58378i) q^{7} +(5.48120 - 5.48120i) q^{8} +(-7.54172 + 4.91146i) q^{9} +(0.338264 + 10.2802i) q^{10} +(-17.6674 + 10.2003i) q^{11} +(-0.504923 - 0.478537i) q^{12} +(3.04150 - 3.04150i) q^{13} +(1.21935 - 14.3484i) q^{14} +(-14.9733 + 0.895203i) q^{15} +(-8.43689 + 14.6131i) q^{16} +(-11.8684 - 3.18014i) q^{17} +(12.3708 - 13.7748i) 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} +(-1.52525 - 5.69233i) q^{23} +(-20.4438 - 11.0831i) q^{24} +(-22.4255 - 11.0497i) q^{25} +(-4.42425 + 7.66303i) q^{26} +(20.5648 + 17.4954i) q^{27} +(0.285844 + 1.59784i) q^{28} -11.9728 q^{29} +(29.2761 - 9.75105i) q^{30} +(30.9809 - 17.8869i) q^{31} +(0.959081 - 3.57934i) q^{32} +(44.4213 + 42.0999i) q^{33} +25.2765 q^{34} +(29.3625 + 19.0485i) q^{35} +(-0.945077 + 1.86073i) q^{36} +(-4.70065 - 17.5430i) q^{37} +(11.8955 - 44.3945i) q^{38} +(-11.3442 - 6.14996i) q^{39} +(-20.4724 - 32.9099i) q^{40} +6.29801 q^{41} +(-42.3058 + 8.74526i) q^{42} +(8.41810 + 8.41810i) q^{43} +(-2.36531 + 4.09685i) q^{44} +(15.3601 + 42.2974i) q^{45} +(6.06154 + 10.4989i) q^{46} +(-15.4905 - 57.8113i) q^{47} +(49.2302 + 11.7857i) q^{48} +(-37.6924 - 31.3094i) q^{49} +(50.4440 + 10.0164i) q^{50} +(0.988619 + 36.8481i) q^{51} +(0.258152 - 0.963437i) q^{52} +(-53.4531 - 14.3227i) q^{53} +(-50.1785 - 23.8152i) q^{54} +(29.6262 + 97.6057i) q^{55} +(23.0540 + 49.1201i) q^{56} +(65.1836 + 15.6049i) q^{57} +(23.7906 - 6.37467i) q^{58} +(-60.6100 + 34.9932i) q^{59} +(-2.90314 + 1.91583i) q^{60} +(-80.4746 - 46.4620i) q^{61} +(-52.0374 + 52.0374i) q^{62} +(-14.4035 - 61.3314i) q^{63} -59.8721i q^{64} +(-11.3600 - 18.2616i) q^{65} +(-110.683 - 60.0038i) q^{66} +(-21.9700 - 5.88684i) q^{67} +(-2.75214 + 0.737433i) q^{68} +(-15.0682 + 9.24715i) q^{69} +(-68.4870 - 22.2169i) q^{70} -27.7403i q^{71} +(-14.4170 + 68.2584i) q^{72} +(-29.0508 - 7.78414i) q^{73} +(18.6809 + 32.3563i) q^{74} +(-12.6289 + 73.9291i) q^{75} +5.18078i q^{76} +(-25.1475 - 140.572i) q^{77} +(25.8161 + 6.18033i) q^{78} +(110.523 + 63.8104i) q^{79} +(61.5875 + 57.6636i) q^{80} +(32.7552 - 74.0817i) q^{81} +(-12.5145 + 3.35326i) 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} +(10.2235 + 34.4326i) q^{87} +(-40.9289 + 152.749i) q^{88} +(74.4534 + 42.9857i) q^{89} +(-53.0419 - 75.8691i) q^{90} +(12.7926 + 27.2566i) q^{91} +(-0.966290 - 0.966290i) q^{92} +(-77.8955 - 73.8249i) q^{93} +(61.5611 + 106.627i) q^{94} +(81.5453 + 76.3499i) q^{95} +(-11.1128 + 0.298152i) q^{96} +(-0.194287 - 0.194287i) q^{97} +(91.5672 + 42.1450i) 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.98706	+	0.532431i	−0.993530	+	0.266215i	−0.718732	−	0.695287i	$-0.755277\pi$
$2$	−1.98706	+	0.532431i	−0.993530	+	0.266215i	−0.274797	+	0.961502i	$0.588611\pi$
$3$	−0.853896	−	2.87591i	−0.284632	−	0.958637i
$3$	−0.853896	−	2.87591i	−0.284632	−	0.958637i
$4$	0.200820	−	0.115943i	0.0502050	−	0.0289859i
$5$	1.13457	−	4.86958i	0.226913	−	0.973915i
$5$	1.13457	−	4.86958i	0.226913	−	0.973915i
$6$	3.22797	+	5.25996i	0.537994	+	0.876661i
$7$	−2.37777	+	6.58378i	−0.339681	+	0.940541i
$7$	−2.37777	+	6.58378i	−0.339681	+	0.940541i
$8$	5.48120	−	5.48120i	0.685150	−	0.685150i
$9$	−7.54172	+	4.91146i	−0.837969	+	0.545717i
$10$	0.338264	+	10.2802i	0.0338264	+	1.02802i
$11$	−17.6674	+	10.2003i	−1.60613	+	0.927299i	−0.615904	+	0.787821i	$0.711209\pi$
$11$	−17.6674	+	10.2003i	−1.60613	+	0.927299i	−0.990225	+	0.139478i	$0.955458\pi$
$12$	−0.504923	−	0.478537i	−0.0420769	−	0.0398781i
$13$	3.04150	−	3.04150i	0.233962	−	0.233962i	−0.580382	−	0.814344i	$-0.697097\pi$
$13$	3.04150	−	3.04150i	0.233962	−	0.233962i	0.814344	+	0.580382i	$0.197097\pi$
$14$	1.21935	−	14.3484i	0.0870967	−	1.02488i
$15$	−14.9733	+	0.895203i	−0.998218	+	0.0596802i
$16$	−8.43689	+	14.6131i	−0.527306	+	0.913320i
$17$	−11.8684	−	3.18014i	−0.698144	−	0.187067i	−0.107745	−	0.994179i	$-0.534363\pi$
$17$	−11.8684	−	3.18014i	−0.698144	−	0.187067i	−0.590399	+	0.807111i	$0.701030\pi$
$18$	12.3708	−	13.7748i	0.687269	−	0.765267i
$19$	−11.1709	+	19.3486i	−0.587943	+	1.01835i	0.406559	+	0.913625i	$0.366729\pi$
$19$	−11.1709	+	19.3486i	−0.587943	+	1.01835i	−0.994501	+	0.104722i	$0.966605\pi$
$20$	−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
$23$	−1.52525	−	5.69233i	−0.0663154	−	0.247492i	0.924809	−	0.380433i	$-0.124225\pi$
$23$	−1.52525	−	5.69233i	−0.0663154	−	0.247492i	−0.991124	+	0.132940i	$0.957558\pi$
$24$	−20.4438	−	11.0831i	−0.851826	−	0.461795i
$25$	−22.4255	−	11.0497i	−0.897021	−	0.441988i
$26$	−4.42425	+	7.66303i	−0.170164	+	0.294732i
$27$	20.5648	+	17.4954i	0.761658	+	0.647980i
$28$	0.285844	+	1.59784i	0.0102087	+	0.0570658i
$29$	−11.9728			−0.412854			−0.206427	−	0.978462i	$-0.566184\pi$
$29$	−11.9728			−0.412854			−0.206427	+	0.978462i	$0.566184\pi$
$30$	29.2761	−	9.75105i	0.975871	−	0.325035i
$31$	30.9809	−	17.8869i	0.999385	−	0.576995i	0.0913189	−	0.995822i	$-0.470892\pi$
$31$	30.9809	−	17.8869i	0.999385	−	0.576995i	0.908066	+	0.418826i	$0.137558\pi$
$32$	0.959081	−	3.57934i	0.0299713	−	0.111854i
$33$	44.4213	+	42.0999i	1.34610	+	1.27576i
$34$	25.2765			0.743427
$35$	29.3625	+	19.0485i	0.838929	+	0.544241i
$36$	−0.945077	+	1.86073i	−0.0262522	+	0.0516870i
$37$	−4.70065	−	17.5430i	−0.127044	−	0.474136i	0.872860	−	0.487971i	$-0.162263\pi$
$37$	−4.70065	−	17.5430i	−0.127044	−	0.474136i	−0.999904	+	0.0138346i	$0.995596\pi$
$38$	11.8955	−	44.3945i	0.313039	−	1.16828i
$39$	−11.3442	−	6.14996i	−0.290877	−	0.157691i
$40$	−20.4724	−	32.9099i	−0.511809	−	0.822748i
$41$	6.29801			0.153610			0.0768050	−	0.997046i	$-0.475528\pi$
$41$	6.29801			0.153610			0.0768050	+	0.997046i	$0.475528\pi$
$42$	−42.3058	+	8.74526i	−1.00728	+	0.208220i
$43$	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
$45$	15.3601	+	42.2974i	0.341336	+	0.939941i
$46$	6.06154	+	10.4989i	0.131773	+	0.228237i
$47$	−15.4905	−	57.8113i	−0.329585	−	1.23003i	−0.909622	−	0.415438i	$-0.863628\pi$
$47$	−15.4905	−	57.8113i	−0.329585	−	1.23003i	0.580036	−	0.814591i	$-0.303038\pi$
$48$	49.2302	+	11.7857i	1.02563	+	0.245534i
$49$	−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
$52$	0.258152	−	0.963437i	0.00496446	−	0.0185276i
$53$	−53.4531	−	14.3227i	−1.00855	−	0.270240i	−0.283526	−	0.958965i	$-0.591504\pi$
$53$	−53.4531	−	14.3227i	−1.00855	−	0.270240i	−0.725023	+	0.688725i	$0.758171\pi$
$54$	−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
$57$	65.1836	+	15.6049i	1.14357	+	0.273770i
$58$	23.7906	−	6.37467i	0.410183	−	0.109908i
$59$	−60.6100	+	34.9932i	−1.02729	+	0.593105i	−0.916207	−	0.400706i	$-0.868765\pi$
$59$	−60.6100	+	34.9932i	−1.02729	+	0.593105i	−0.111082	+	0.993811i	$0.535432\pi$
$60$	−2.90314	+	1.91583i	−0.0483856	+	0.0319305i
$61$	−80.4746	−	46.4620i	−1.31926	−	0.761673i	−0.335647	−	0.941988i	$-0.608955\pi$
$61$	−80.4746	−	46.4620i	−1.31926	−	0.761673i	−0.983609	+	0.180315i	$0.942288\pi$
$62$	−52.0374	+	52.0374i	−0.839314	+	0.839314i
$63$	−14.4035	−	61.3314i	−0.228627	−	0.973514i
$64$		−	59.8721i		−	0.935502i
$65$	−11.3600	−	18.2616i	−0.174770	−	0.280948i
$66$	−110.683	−	60.0038i	−1.67701	−	0.909149i
$67$	−21.9700	−	5.88684i	−0.327910	−	0.0878633i	0.0911082	−	0.995841i	$-0.470959\pi$
$67$	−21.9700	−	5.88684i	−0.327910	−	0.0878633i	−0.419018	+	0.907978i	$0.637626\pi$
$68$	−2.75214	+	0.737433i	−0.0404726	+	0.0108446i
$69$	−15.0682	+	9.24715i	−0.218380	+	0.134017i
$70$	−68.4870	−	22.2169i	−0.978386	−	0.317384i
$71$		−	27.7403i		−	0.390708i	−0.980733	−	0.195354i	$-0.937414\pi$
$71$		−	27.7403i		−	0.390708i	0.980733	−	0.195354i	$-0.0625855\pi$
$72$	−14.4170	+	68.2584i	−0.200236	+	0.948034i
$73$	−29.0508	−	7.78414i	−0.397956	−	0.106632i	0.0542900	−	0.998525i	$-0.482710\pi$
$73$	−29.0508	−	7.78414i	−0.397956	−	0.106632i	−0.452246	+	0.891893i	$0.649377\pi$
$74$	18.6809	+	32.3563i	0.252445	+	0.437247i
$75$	−12.6289	+	73.9291i	−0.168385	+	0.985721i
$76$			5.18078i			0.0681682i
$77$	−25.1475	−	140.572i	−0.326591	−	1.82562i
$78$	25.8161	+	6.18033i	0.330975	+	0.0792350i
$79$	110.523	+	63.8104i	1.39902	+	0.807726i	0.994290	−	0.106709i	$-0.0340314\pi$
$79$	110.523	+	63.8104i	1.39902	+	0.807726i	0.404732	+	0.914435i	$0.367365\pi$
$80$	61.5875	+	57.6636i	0.769844	+	0.720795i
$81$	32.7552	−	74.0817i	0.404385	−	0.914589i
$82$	−12.5145	+	3.35326i	−0.152616	+	0.0408934i
$83$	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
$87$	10.2235	+	34.4326i	0.117512	+	0.395777i
$88$	−40.9289	+	152.749i	−0.465101	+	1.73578i
$89$	74.4534	+	42.9857i	0.836555	+	0.482985i	0.856092	−	0.516824i	$-0.172886\pi$
$89$	74.4534	+	42.9857i	0.836555	+	0.482985i	−0.0195368	+	0.999809i	$0.506219\pi$
$90$	−53.0419	−	75.8691i	−0.589355	−	0.842990i
$91$	12.7926	+	27.2566i	0.140578	+	0.299523i
$92$	−0.966290	−	0.966290i	−0.0105032	−	0.0105032i
$93$	−77.8955	−	73.8249i	−0.837586	−	0.793816i
$94$	61.5611	+	106.627i	0.654905	+	1.13433i
$95$	81.5453	+	76.3499i	0.858372	+	0.803683i
$96$	−11.1128	+	0.298152i	−0.115758	+	0.00310575i
$97$	−0.194287	−	0.194287i	−0.00200296	−	0.00200296i	0.706105	−	0.708108i	$-0.250451\pi$
$97$	−0.194287	−	0.194287i	−0.00200296	−	0.00200296i	−0.708108	+	0.706105i	$0.750451\pi$
$98$	91.5672	+	42.1450i	0.934359	+	0.430051i
$99$	83.1445	−	163.701i	0.839844	−	1.65354i
$100$	−5.78463	+	0.381092i	−0.0578463	+	0.00381092i
$101$	55.3301	+	95.8346i	0.547823	+	0.948857i	0.998423	+	0.0561315i	$0.0178766\pi$
$101$	55.3301	+	95.8346i	0.547823	+	0.948857i	−0.450600	+	0.892726i	$0.648790\pi$
$102$	−21.5835	−	72.6930i	−0.211603	−	0.712676i
$103$	−3.51364	−	13.1131i	−0.0341130	−	0.127312i	0.946770	−	0.321912i	$-0.104326\pi$
$103$	−3.51364	−	13.1131i	−0.0341130	−	0.127312i	−0.980883	+	0.194601i	$0.937659\pi$
$104$		−	33.3422i		−	0.320598i
$105$	29.7091	−	100.709i	0.282944	−	0.959136i
$106$	113.840			1.07397
$107$	−36.6202	+	9.81236i	−0.342245	+	0.0917043i	−0.425848	−	0.904795i	$-0.640024\pi$
$107$	−36.6202	+	9.81236i	−0.342245	+	0.0917043i	0.0836026	+	0.996499i	$0.473357\pi$
$108$	6.15830	+	1.12909i	0.0570213	+	0.0104545i
$109$	61.2903	−	35.3860i	0.562297	−	0.324642i	−0.191770	−	0.981440i	$-0.561423\pi$
$109$	61.2903	−	35.3860i	0.562297	−	0.324642i	0.754067	+	0.656798i	$0.228089\pi$
$110$	−110.837	−	178.174i	−1.00761	−	1.61977i
$111$	−46.4384	+	28.4986i	−0.418364	+	0.256744i
$112$	−76.1487	−	90.2933i	−0.679899	−	0.806190i
$113$	−58.6040	+	58.6040i	−0.518620	+	0.518620i	−0.917154	−	0.398534i	$-0.869519\pi$
$113$	−58.6040	+	58.6040i	−0.518620	+	0.518620i	0.398534	+	0.917154i	$0.369519\pi$
$114$	−137.832	+	3.69798i	−1.20905	+	0.0324384i
$115$	−29.4497	+	0.969025i	−0.256084	+	0.00842631i
$116$	−2.40437	+	1.38816i	−0.0207273	+	0.0119669i
$117$	−7.99996	+	37.8764i	−0.0683757	+	0.323730i
$118$	101.804	−	101.804i	0.862748	−	0.862748i
$119$	49.1578	−	70.5777i	0.413091	−	0.593090i
$120$	−77.1647	+	86.9783i	−0.643039	+	0.724819i
$121$	147.592	−	255.637i	1.21977	−	2.11270i
$122$	184.646	+	49.4756i	1.51349	+	0.405538i
$123$	−5.37785	−	18.1125i	−0.0437223	−	0.147256i
$124$	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	$0.178537\pi$
$128$	35.7141	+	133.287i	0.279016	+	1.04130i
$129$	17.0215	−	31.3979i	0.131950	−	0.243394i
$130$	32.2961	+	30.2385i	0.248432	+	0.232603i
$131$	−36.0576	+	62.4535i	−0.275248	+	0.476744i	−0.970198	−	0.242314i	$-0.922093\pi$
$131$	−36.0576	+	62.4535i	−0.275248	+	0.476744i	0.694949	+	0.719059i	$0.255427\pi$
$132$	13.8019	+	3.30415i	0.104560	+	0.0250315i
$133$	−100.825	−	119.553i	−0.758084	−	0.898898i
$134$	46.7900			0.349179
$135$	108.527	−	80.2919i	0.803907	−	0.594755i
$136$	−82.4844	+	47.6224i	−0.606503	+	0.350165i
$137$	24.0696	−	89.8290i	0.175691	−	0.655686i	−0.820742	−	0.571298i	$-0.806440\pi$
$137$	24.0696	−	89.8290i	0.175691	−	0.655686i	0.996433	−	0.0843878i	$-0.0268935\pi$
$138$	25.0180	−	26.3974i	0.181290	−	0.191286i
$139$	−157.063			−1.12995			−0.564974	−	0.825109i	$-0.691114\pi$
$139$	−157.063			−1.12995			−0.564974	+	0.825109i	$0.691114\pi$
$140$	8.10512	+	0.420919i	0.0578937	+	0.00300656i
$141$	−153.033	+	93.9142i	−1.08534	+	0.666058i
$142$	14.7698	+	55.1215i	0.104012	+	0.388180i
$143$	−22.7113	+	84.7597i	−0.158820	+	0.592725i
$144$	−8.14303	−	151.646i	−0.0565488	−	1.05309i
$145$	−13.5839	+	58.3023i	−0.0936820	+	0.402085i
$146$	61.8702			0.423768
$147$	−57.8577	+	135.135i	−0.393590	+	0.919286i
$148$	−2.97799	−	2.97799i	−0.0201215	−	0.0201215i
$149$	−13.4879	+	23.3617i	−0.0905227	+	0.156790i	−0.907731	−	0.419552i	$-0.862187\pi$
$149$	−13.4879	+	23.3617i	−0.0905227	+	0.156790i	0.817209	+	0.576342i	$0.195520\pi$
$150$	−14.2678	−	153.626i	−0.0951186	−	1.02417i
$151$	62.3433	+	107.982i	0.412870	+	0.715111i	0.995202	−	0.0978396i	$-0.0311932\pi$
$151$	62.3433	+	107.982i	0.412870	+	0.715111i	−0.582333	+	0.812951i	$0.697860\pi$
$152$	44.8235	+	167.284i	0.294892	+	1.10055i
$153$	105.128	−	34.3076i	0.687109	−	0.224233i
$154$	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
$157$	22.9194	−	85.5363i	0.145983	−	0.544817i	−0.853726	−	0.520722i	$-0.825663\pi$
$157$	22.9194	−	85.5363i	0.145983	−	0.544817i	0.999710	−	0.0240952i	$-0.00767048\pi$
$158$	−253.590	−	67.9492i	−1.60500	−	0.430058i
$159$	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
$162$	−25.6431	+	164.645i	−0.158291	+	1.01632i
$163$	−264.558	+	70.8881i	−1.62306	+	0.434896i	−0.951897	−	0.306418i	$-0.900870\pi$
$163$	−264.558	+	70.8881i	−1.62306	+	0.434896i	−0.671158	+	0.741314i	$0.734203\pi$
$164$	1.26477	−	0.730213i	0.00771199	−	0.00445252i
$165$	255.408	−	168.548i	1.54792	−	1.02150i
$166$	−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	$0.328505\pi$
$168$	121.579	−	108.245i	0.723686	−	0.644314i
$169$			150.499i			0.890524i
$170$	28.6779	−	123.086i	0.168693	−	0.724035i
$171$	−10.7818	−	200.787i	−0.0630517	−	1.17419i
$172$	2.66655	+	0.714499i	0.0155032	+	0.00415406i
$173$	115.315	−	30.8987i	0.666563	−	0.178605i	0.0903569	−	0.995909i	$-0.471199\pi$
$173$	115.315	−	30.8987i	0.666563	−	0.178605i	0.576206	+	0.817304i	$0.304533\pi$
$174$	−38.6477	−	62.9763i	−0.222113	−	0.361933i
$175$	126.072	−	121.371i	0.720409	−	0.693550i
$176$		−	344.235i		−	1.95588i
$177$	152.392	+	144.428i	0.860972	+	0.815980i
$178$	−170.830	−	45.7738i	−0.959720	−	0.257156i
$179$	73.7339	+	127.711i	0.411921	+	0.713469i	0.995100	−	0.0988752i	$-0.0315245\pi$
$179$	73.7339	+	127.711i	0.411921	+	0.713469i	−0.583178	+	0.812344i	$0.698191\pi$
$180$	7.98873	+	6.71325i	0.0443818	+	0.0372958i
$181$			167.742i			0.926749i	0.886162	+	0.463375i	$0.153362\pi$
$181$			167.742i			0.926749i	−0.886162	+	0.463375i	$0.846638\pi$
$182$	−39.9319	−	47.3493i	−0.219406	−	0.260161i
$183$	−64.9037	+	271.111i	−0.354665	+	1.48148i
$184$	−39.5610	−	22.8406i	−0.215006	−	0.124134i
$185$	−90.7604	+	2.98642i	−0.490597	+	0.0161428i
$186$	194.090	+	105.220i	1.04349	+	0.565702i
$187$	242.123	−	64.8767i	1.29478	−	0.346934i
$188$	−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	−0.472832	−	0.881153i	$-0.656768\pi$
$191$	−281.218	−	162.362i	−1.47235	−	0.850061i	−0.999517	+	0.0310923i	$0.990101\pi$
$192$	−172.187	+	51.1246i	−0.896806	+	0.266274i
$193$	56.6792	−	211.530i	0.293675	−	1.09601i	−0.648589	−	0.761138i	$-0.724641\pi$
$193$	56.6792	−	211.530i	0.293675	−	1.09601i	0.942264	−	0.334870i	$-0.108693\pi$
$194$	0.489504	+	0.282615i	0.00252321	+	0.00145678i
$195$	−42.8184	+	48.2640i	−0.219582	+	0.247508i
$196$	−11.1995	−	1.91736i	−0.0571404	−	0.00978247i
$197$	75.4491	+	75.4491i	0.382990	+	0.382990i	0.872178	−	0.489188i	$-0.162707\pi$
$197$	75.4491	+	75.4491i	0.382990	+	0.382990i	−0.489188	+	0.872178i	$0.662707\pi$
$198$	−78.0538	+	369.551i	−0.394211	+	1.86642i
$199$	25.0899	+	43.4570i	0.126080	+	0.218377i	0.922155	−	0.386822i	$-0.126427\pi$
$199$	25.0899	+	43.4570i	0.126080	+	0.218377i	−0.796075	+	0.605198i	$0.793094\pi$
$200$	−183.485	+	62.3532i	−0.917423	+	0.311766i
$201$	1.83006	+	68.2105i	0.00910477	+	0.339356i
$202$	−160.970	−	160.970i	−0.796879	−	0.796879i
$203$	28.4685	−	78.8261i	0.140239	−	0.388306i
$204$	4.47083	+	7.28521i	0.0219158	+	0.0357118i
$205$	7.14550	−	30.6686i	0.0348561	−	0.149603i
$206$	13.9636	+	24.1857i	0.0677846	+	0.117406i
$207$	39.4607	+	35.4387i	0.190631	+	0.171202i
$208$	18.7850	+	70.1066i	0.0903126	+	0.337051i
$209$		−	455.786i		−	2.18080i
$210$	−5.41301	+	215.933i	−0.0257762	+	1.02825i
$211$	−133.700			−0.633647			−0.316824	−	0.948484i	$-0.602616\pi$
$211$	−133.700			−0.633647			−0.316824	+	0.948484i	$0.602616\pi$
$212$	−12.3951	+	3.32125i	−0.0584673	+	0.0156663i
$213$	−79.7785	+	23.6873i	−0.374547	+	0.111208i
$214$	67.5421	−	38.9955i	0.315617	−	0.182222i
$215$	50.5434	−	31.4417i	0.235086	−	0.146240i
$216$	208.616	−	16.8235i	0.965814	−	0.0778867i
$217$	44.0977	+	246.503i	0.203215	+	1.13596i
$218$	−102.947	+	102.947i	−0.472234	+	0.472234i
$219$	2.41988	+	90.1943i	0.0110497	+	0.411846i
$220$	17.2663	+	16.1662i	0.0784831	+	0.0734828i
$221$	−45.7703	+	26.4255i	−0.207105	+	0.119572i
$222$	77.1023	−	81.3536i	0.347308	−	0.366458i
$223$	63.9114	−	63.9114i	0.286598	−	0.286598i	−0.549135	−	0.835733i	$-0.685043\pi$
$223$	63.9114	−	63.9114i	0.286598	−	0.286598i	0.835733	+	0.549135i	$0.185043\pi$
$224$	21.2851	+	14.8252i	0.0950229	+	0.0661840i
$225$	223.397	−	26.8082i	0.992877	−	0.119148i
$226$	85.2471	−	147.652i	0.377199	−	0.653329i
$227$	223.353	+	59.8472i	0.983933	+	0.263644i	0.714700	−	0.699431i	$-0.246563\pi$
$227$	223.353	+	59.8472i	0.983933	+	0.263644i	0.269233	+	0.963075i	$0.413230\pi$
$228$	14.8995	−	4.42385i	0.0653485	−	0.0194028i
$229$	18.8007	−	32.5638i	0.0820992	−	0.142200i	−0.822052	−	0.569412i	$-0.807171\pi$
$229$	18.8007	−	32.5638i	0.0820992	−	0.142200i	0.904151	+	0.427212i	$0.140504\pi$
$230$	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
$233$	−8.81095	−	32.8829i	−0.0378152	−	0.141128i	0.944437	−	0.328692i	$-0.106608\pi$
$233$	−8.81095	−	32.8829i	−0.0378152	−	0.141128i	−0.982253	+	0.187563i	$0.939941\pi$
$234$	−4.27016	−	79.5220i	−0.0182485	−	0.339838i
$235$	−299.092	+	9.84143i	−1.27273	+	0.0418784i
$236$	−8.11447	+	14.0547i	−0.0343834	+	0.0595537i
$237$	89.1379	−	372.341i	0.376109	−	1.57106i
$238$	−60.1017	+	166.415i	−0.252528	+	0.699223i
$239$	−320.856			−1.34249			−0.671247	−	0.741233i	$-0.734241\pi$
$239$	−320.856			−1.34249			−0.671247	+	0.741233i	$0.734241\pi$
$240$	113.246	−	226.359i	0.471859	−	0.943162i
$241$	293.702	−	169.569i	1.21868	−	0.703605i	0.254044	−	0.967193i	$-0.418239\pi$
$241$	293.702	−	169.569i	1.21868	−	0.703605i	0.964635	+	0.263588i	$0.0849058\pi$
$242$	−157.165	+	586.547i	−0.649442	+	2.42375i
$243$	−241.022	−	30.9429i	−0.991860	−	0.127337i
$244$	−21.5479			−0.0883110
$245$	−195.228	+	148.024i	−0.796849	+	0.604178i
$246$	20.3298	+	33.1273i	0.0826413	+	0.134664i
$247$	24.8724	+	92.8251i	0.100698	+	0.375810i
$248$	71.7714	−	267.854i	0.289401	−	1.08006i
$249$	33.1169	−	61.0874i	0.133000	−	0.245331i
$250$	106.008	−	234.277i	0.424030	−	0.937107i
$251$	−70.5213			−0.280961			−0.140481	−	0.990083i	$-0.544865\pi$
$251$	−70.5213			−0.280961			−0.140481	+	0.990083i	$0.544865\pi$
$252$	−10.0035	−	10.6466i	−0.0396964	−	0.0422483i
$253$	85.0107	+	85.0107i	0.336011	+	0.336011i
$254$	−58.1634	+	100.742i	−0.228990	+	0.396622i
$255$	180.556	+	36.9924i	0.708064	+	0.145068i
$256$	−22.1878	−	38.4304i	−0.0866710	−	0.150119i
$257$	−44.4202	−	165.778i	−0.172841	−	0.645052i	−0.996909	−	0.0785611i	$-0.974967\pi$
$257$	−44.4202	−	165.778i	−0.172841	−	0.645052i	0.824068	−	0.566491i	$-0.191699\pi$
$258$	−17.1056	+	71.4522i	−0.0663006	+	0.276947i
$259$	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
$262$	38.3963	−	143.297i	0.146551	−	0.546935i
$263$	−105.154	−	28.1758i	−0.399823	−	0.107132i	0.0533036	−	0.998578i	$-0.483025\pi$
$263$	−105.154	−	28.1758i	−0.399823	−	0.107132i	−0.453127	+	0.891446i	$0.649692\pi$
$264$	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
$267$	60.0475	−	250.827i	0.224897	−	0.939425i
$268$	−5.09455	+	1.36508i	−0.0190095	+	0.00509359i
$269$	57.7621	−	33.3490i	0.214729	−	0.123974i	−0.388778	−	0.921331i	$-0.627103\pi$
$269$	57.7621	−	33.3490i	0.214729	−	0.123974i	0.603507	+	0.797357i	$0.293769\pi$
$270$	−172.901	+	217.328i	−0.640373	+	0.804919i
$271$	107.612	+	62.1301i	0.397094	+	0.229262i	0.685229	−	0.728327i	$-0.259702\pi$
$271$	107.612	+	62.1301i	0.397094	+	0.229262i	−0.288135	+	0.957590i	$0.593035\pi$
$272$	146.605	−	146.605i	0.538987	−	0.538987i
$273$	67.4639	−	60.0647i	0.247121	−	0.220017i
$274$			191.311i			0.698215i
$275$	508.911	−	33.5271i	1.85059	−	0.121917i
$276$	−1.95385	+	3.60407i	−0.00707918	+	0.0130582i
$277$	−109.556	−	29.3555i	−0.395509	−	0.105976i	0.0555822	−	0.998454i	$-0.482299\pi$
$277$	−109.556	−	29.3555i	−0.395509	−	0.105976i	−0.451091	+	0.892478i	$0.648965\pi$
$278$	312.093	−	83.6251i	1.12264	−	0.300810i
$279$	−145.799	+	287.059i	−0.522578	+	1.02889i
$280$	265.350	−	56.5334i	0.947680	−	0.201905i
$281$		−	292.683i		−	1.04158i	−0.853685	−	0.520789i	$-0.825638\pi$
$281$		−	292.683i		−	1.04158i	0.853685	−	0.520789i	$-0.174362\pi$
$282$	254.083	−	268.092i	0.901003	−	0.950683i
$283$	321.464	+	86.1361i	1.13592	+	0.304368i	0.777308	−	0.629120i	$-0.216585\pi$
$283$	321.464	+	86.1361i	1.13592	+	0.304368i	0.358608	+	0.933488i	$0.383251\pi$
$284$	−3.21630	−	5.57080i	−0.0113250	−	0.0196155i
$285$	149.944	−	299.712i	0.526120	−	1.05162i
$286$		−	180.515i		−	0.631170i
$287$	−14.9752	+	41.4648i	−0.0521784	+	0.144476i
$288$	10.3466	+	31.7049i	0.0359258	+	0.110086i
$289$	−119.535	−	69.0133i	−0.413615	−	0.238800i
$290$	−4.04996	−	123.083i	−0.0139654	−	0.424423i
$291$	−0.392851	+	0.724652i	−0.00135000	+	0.00249021i
$292$	−6.73650	+	1.80504i	−0.0230702	+	0.00618164i
$293$	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
$297$	−541.785	−	99.3329i	−1.82419	−	0.334454i
$298$	14.3627	−	53.6024i	0.0481971	−	0.179874i
$299$	−21.9523	−	12.6742i	−0.0734190	−	0.0423885i
$300$	6.03546	+	16.3107i	0.0201182	+	0.0543689i
$301$	−75.4392	+	35.4067i	−0.250629	+	0.117630i
$302$	−181.373	−	181.373i	−0.600572	−	0.600572i
$303$	228.366	−	240.957i	0.753682	−	0.795238i
$304$	−188.496	−	326.484i	−0.620051	−	1.07396i
$305$	−317.554	+	339.163i	−1.04116	+	1.11201i
$306$	−190.628	+	124.145i	−0.622969	+	0.405701i
$307$	−257.864	−	257.864i	−0.839949	−	0.839949i	0.148903	−	0.988852i	$-0.452426\pi$
$307$	−257.864	−	257.864i	−0.839949	−	0.839949i	−0.988852	+	0.148903i	$0.952426\pi$
$308$	−21.3486	−	25.3141i	−0.0693136	−	0.0821885i
$309$	−34.7118	+	21.3021i	−0.112336	+	0.0689389i
$310$	194.360	+	312.440i	0.626969	+	1.00787i
$311$	127.428	+	220.712i	0.409737	+	0.709686i	0.994860	−	0.101259i	$-0.0322870\pi$
$311$	127.428	+	220.712i	0.409737	+	0.709686i	−0.585123	+	0.810945i	$0.698954\pi$
$312$	−95.8891	+	28.4708i	−0.307337	+	0.0912524i
$313$	80.1686	+	299.193i	0.256130	+	0.955889i	0.967458	+	0.253030i	$0.0814271\pi$
$313$	80.1686	+	299.193i	0.256130	+	0.955889i	−0.711329	+	0.702859i	$0.751906\pi$
$314$			182.169i			0.580155i
$315$	−315.000	+	0.554536i	−0.999998	+	0.00176043i
$316$	29.5936			0.0936506
$317$	−14.0667	+	3.76915i	−0.0443743	+	0.0118901i	−0.280938	−	0.959726i	$-0.590646\pi$
$317$	−14.0667	+	3.76915i	−0.0443743	+	0.0118901i	0.236564	+	0.971616i	$0.423979\pi$
$318$	−97.2078	−	327.395i	−0.305685	−	1.02954i
$319$	211.528	−	122.126i	0.663097	−	0.382839i
$320$	−291.552	−	67.9288i	−0.911099	−	0.212278i
$321$	59.4893	+	96.9377i	0.185325	+	0.301987i
$322$	−83.5354	+	14.9439i	−0.259427	+	0.0464098i
$323$	194.113	−	194.113i	0.600968	−	0.600968i
$324$	−2.01140	−	18.6748i	−0.00620801	−	0.0576384i
$325$	−101.815	+	34.5996i	−0.313277	+	0.106460i
$326$	487.950	−	281.718i	1.49678	−	0.864165i
$327$	−154.103	−	146.050i	−0.471262	−	0.446635i
$328$	34.5207	−	34.5207i	0.105246	−	0.105246i
$329$	417.450	+	35.4758i	1.26885	+	0.107829i
$330$	−417.770	+	470.901i	−1.26597	+	1.42697i
$331$	−265.401	+	459.689i	−0.801817	+	1.38879i	0.116602	+	0.993179i	$0.462800\pi$
$331$	−265.401	+	459.689i	−0.801817	+	1.38879i	−0.918419	+	0.395609i	$0.870534\pi$
$332$	5.18801	+	1.39012i	0.0156265	+	0.00418712i
$333$	121.613	+	109.218i	0.365204	+	0.327981i
$334$	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	$0.396249\pi$
$338$	−80.1301	−	299.049i	−0.237071	−	0.884762i
$339$	218.582	+	118.498i	0.644784	+	0.349552i
$340$	0.468506	+	14.2384i	0.00137796	+	0.0418777i
$341$	−364.902	+	632.029i	−1.07009	+	1.85346i
$342$	128.329	+	393.236i	0.375232	+	1.14981i
$343$	295.758	−	173.712i	0.862269	−	0.506450i
$344$	92.2826			0.268263
$345$	27.9338	+	83.8673i	0.0809676	+	0.243094i
$346$	−212.687	+	122.795i	−0.614703	+	0.354899i
$347$	78.2365	−	291.982i	0.225465	−	0.841448i	−0.756752	−	0.653702i	$-0.773215\pi$
$347$	78.2365	−	291.982i	0.225465	−	0.841448i	0.982218	−	0.187746i	$-0.0601183\pi$
$348$	6.04532	+	5.72941i	0.0173716	+	0.0164638i
$349$	213.085			0.610558			0.305279	−	0.952263i	$-0.401250\pi$
$349$	213.085			0.610558			0.305279	+	0.952263i	$0.401250\pi$
$350$	−185.890	+	308.296i	−0.531114	+	0.880846i
$351$	115.760	−	9.33532i	0.329801	−	0.0265963i
$352$	19.5658	+	73.0206i	0.0555847	+	0.207445i
$353$	−175.400	+	654.603i	−0.496885	+	1.85440i	0.0223224	+	0.999751i	$0.492894\pi$
$353$	−175.400	+	654.603i	−0.496885	+	1.85440i	−0.519207	+	0.854648i	$0.673773\pi$
$354$	−379.710	−	205.850i	−1.07263	−	0.581496i
$355$	−135.083	−	31.4731i	−0.380516	−	0.0886567i
$356$	19.9356			0.0559990
$357$	−244.951	−	81.1074i	−0.686136	−	0.227191i
$358$	−214.511	−	214.511i	−0.599193	−	0.599193i
$359$	−297.612	+	515.479i	−0.829002	+	1.43587i	0.0698193	+	0.997560i	$0.477758\pi$
$359$	−297.612	+	515.479i	−0.829002	+	1.43587i	−0.898822	+	0.438315i	$0.855576\pi$
$360$	316.032	+	147.648i	0.877868	+	0.410134i
$361$	−69.0787	−	119.648i	−0.191354	−	0.331435i
$362$	−89.3108	−	333.313i	−0.246715	−	0.920753i
$363$	−861.216	−	206.174i	−2.37250	−	0.567972i
$364$	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
$367$	−45.9346	+	171.430i	−0.125162	+	0.467112i	−0.999845	−	0.0175830i	$-0.994403\pi$
$367$	−45.9346	+	171.430i	−0.125162	+	0.467112i	0.874683	+	0.484695i	$0.161070\pi$
$368$	96.0511	+	25.7368i	0.261008	+	0.0699370i
$369$	−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
$372$	−24.2025	−	5.79404i	−0.0650605	−	0.0155754i
$373$	−529.357	+	141.841i	−1.41919	+	0.380270i	−0.885195	−	0.465220i	$-0.845975\pi$
$373$	−529.357	+	141.841i	−1.41919	+	0.380270i	−0.533992	+	0.845490i	$0.679309\pi$
$374$	−446.571	+	257.828i	−1.19404	+	0.689379i
$375$	345.675	+	145.375i	0.921800	+	0.387666i
$376$	−401.782	−	231.969i	−1.06857	−	0.616939i
$377$	−36.4152	+	36.4152i	−0.0965921	+	0.0965921i
$378$	276.107	−	273.738i	0.730441	−	0.724173i
$379$		−	592.243i		−	1.56265i	−0.624127	−	0.781323i	$-0.714545\pi$
$379$		−	592.243i		−	1.56265i	0.624127	−	0.781323i	$-0.285455\pi$
$380$	25.2282	+	5.87793i	0.0663900	+	0.0154682i
$381$	−149.137	−	80.8504i	−0.391434	−	0.212206i
$382$	645.244	+	172.893i	1.68912	+	0.452599i
$383$	638.585	−	171.108i	1.66732	−	0.446758i	0.702936	−	0.711253i	$-0.251872\pi$
$383$	638.585	−	171.108i	1.66732	−	0.446758i	0.964387	+	0.264495i	$0.0852053\pi$
$384$	352.825	−	216.524i	0.918814	−	0.563863i
$385$	−713.059	−	37.0309i	−1.85210	−	0.0961843i
$386$			450.500i			1.16710i
$387$	−104.832	−	22.1418i	−0.270884	−	0.0572140i
$388$	−0.0615429	−	0.0164904i	−0.000158616	−	4.25010e-5i
$389$	−115.707	−	200.410i	−0.297446	−	0.515192i	0.678105	−	0.734965i	$-0.262802\pi$
$389$	−115.707	−	200.410i	−0.297446	−	0.515192i	−0.975551	+	0.219773i	$0.929468\pi$
$390$	59.3856	−	118.701i	0.152271	−	0.304362i
$391$			72.4096i			0.185191i
$392$	−378.213	+	34.9867i	−0.964830	+	0.0892517i
$393$	210.400	+	50.3695i	0.535369	+	0.128167i
$394$	−190.093	−	109.750i	−0.482470	−	0.278554i
$395$	436.125	−	465.802i	1.10411	−	1.17925i
$396$	−2.28293	−	42.5144i	−0.00576498	−	0.107360i
$397$	202.712	−	54.3165i	0.510609	−	0.136817i	0.00568968	−	0.999984i	$-0.498189\pi$
$397$	202.712	−	54.3165i	0.510609	−	0.136817i	0.504919	+	0.863167i	$0.331522\pi$
$398$	−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	0.377724	−	0.925918i	$-0.376707\pi$
$401$	−94.3487	−	54.4722i	−0.235284	−	0.135841i	−0.613007	+	0.790077i	$0.710040\pi$
$402$	−39.9538	−	134.564i	−0.0993875	−	0.334736i
$403$	39.8257	−	148.631i	0.0988230	−	0.368813i
$404$	22.2228	+	12.8303i	0.0550069	+	0.0317583i
$405$	−323.584	−	243.554i	−0.798972	−	0.601369i
$406$	−14.5990	+	171.790i	−0.0359582	+	0.423127i
$407$	261.992	+	261.992i	0.643716	+	0.643716i
$408$	207.391	+	196.553i	0.508311	+	0.481748i
$409$	−108.632	−	188.156i	−0.265604	−	0.460039i	0.702118	−	0.712061i	$-0.252238\pi$
$409$	−108.632	−	188.156i	−0.265604	−	0.460039i	−0.967722	+	0.252021i	$0.918905\pi$
$410$	2.13039	+	64.7449i	0.00519608	+	0.157914i
$411$	−278.893	+	7.48259i	−0.678572	+	0.0182058i
$412$	−2.22599	−	2.22599i	−0.00540288	−	0.00540288i
$413$	−86.2713	−	482.249i	−0.208889	−	1.16767i
$414$	−97.2794	−	49.4088i	−0.234974	−	0.119345i
$415$	98.3369	−	61.1727i	0.236956	−	0.147404i
$416$	−7.96952	−	13.8036i	−0.0191575	−	0.0331818i
$417$	134.115	+	451.699i	0.321619	+	1.08321i
$418$	242.675	+	905.674i	0.580562	+	2.16669i
$419$		−	11.8203i		−	0.0282107i	−0.999901	−	0.0141053i	$-0.995510\pi$
$419$		−	11.8203i		−	0.0282107i	0.999901	−	0.0141053i	$-0.00449002\pi$
$420$	−5.71041	−	23.6690i	−0.0135962	−	0.0563548i
$421$	178.317			0.423555			0.211778	−	0.977318i	$-0.432075\pi$
$421$	178.317			0.423555			0.211778	+	0.977318i	$0.432075\pi$
$422$	265.669	−	71.1858i	0.629547	−	0.168687i
$423$	400.763	+	359.916i	0.947430	+	0.850866i
$424$	−371.493	+	214.482i	−0.876163	+	0.505853i
$425$	231.017	+	202.459i	0.543568	+	0.476374i
$426$	145.913	−	89.5446i	0.342518	−	0.210199i
$427$	497.246	−	419.352i	1.16451	−	0.982088i
$428$	−6.21639	+	6.21639i	−0.0145243	+	0.0145243i
$429$	263.154	−	7.06032i	0.613413	−	0.0164576i
$430$	−83.6923	+	89.3874i	−0.194633	+	0.207878i
$431$	649.475	−	374.974i	1.50690	−	0.870010i	0.506934	−	0.861985i	$-0.330779\pi$
$431$	649.475	−	374.974i	1.50690	−	0.870010i	0.999968	−	0.00802521i	$-0.00255453\pi$
$432$	−429.166	+	152.908i	−0.993439	+	0.353954i
$433$	333.096	−	333.096i	0.769274	−	0.769274i	−0.208705	−	0.977979i	$-0.566925\pi$
$433$	333.096	−	333.096i	0.769274	−	0.769274i	0.977979	+	0.208705i	$0.0669248\pi$
$434$	−218.870	−	466.336i	−0.504310	−	1.07451i
$435$	179.271	−	10.7181i	0.412118	−	0.0246392i
$436$	8.20555	−	14.2124i	0.0188201	−	0.0325973i
$437$	127.177	+	34.0770i	0.291023	+	0.0779794i
$438$	−52.8307	−	177.933i	−0.120618	−	0.406240i
$439$	−368.605	+	638.442i	−0.839646	+	1.45431i	0.0505449	+	0.998722i	$0.483904\pi$
$439$	−368.605	+	638.442i	−0.839646	+	1.45431i	−0.890191	+	0.455588i	$0.849429\pi$
$440$	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
$443$	168.720	+	629.672i	0.380858	+	1.42138i	0.844594	+	0.535408i	$0.179842\pi$
$443$	168.720	+	629.672i	0.380858	+	1.42138i	−0.463735	+	0.885974i	$0.653491\pi$
$444$	−6.02153	+	11.1073i	−0.0135620	+	0.0250165i
$445$	293.794	−	313.786i	0.660212	−	0.705138i
$446$	−92.9673	+	161.024i	−0.208447	+	0.361040i
$447$	78.7034	+	18.8415i	0.176070	+	0.0421509i
$448$	394.185	+	142.362i	0.879877	+	0.317772i
$449$	−110.067			−0.245137			−0.122569	−	0.992460i	$-0.539113\pi$
$449$	−110.067			−0.245137			−0.122569	+	0.992460i	$0.539113\pi$
$450$	−429.630	+	172.213i	−0.954733	+	0.382696i
$451$	−111.270	+	64.2415i	−0.246718	+	0.142442i
$452$	−4.97411	+	18.5636i	−0.0110047	+	0.0410700i
$453$	257.311	−	271.499i	0.568016	−	0.599335i
$454$	−475.680			−1.04775
$455$	147.242	−	31.3702i	0.323609	−	0.0689455i
$456$	442.818	−	271.751i	0.971093	−	0.595946i
$457$	−120.933	−	451.330i	−0.264625	−	0.987593i	−0.962480	−	0.271354i	$-0.912529\pi$
$457$	−120.933	−	451.330i	−0.264625	−	0.987593i	0.697855	−	0.716239i	$-0.254138\pi$
$458$	−20.0202	+	74.7163i	−0.0437121	+	0.163136i
$459$	−188.434	−	273.043i	−0.410531	−	0.594864i
$460$	−5.80174	+	3.60910i	−0.0126125	+	0.00784588i
$461$	−640.069			−1.38844			−0.694218	−	0.719764i	$-0.744250\pi$
$461$	−640.069			−1.38844			−0.694218	+	0.719764i	$0.744250\pi$
$462$	658.231	−	586.038i	1.42474	−	1.26848i
$463$	−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
$465$	−447.873	+	295.559i	−0.963169	+	0.635610i
$466$	35.0157	+	60.6491i	0.0751411	+	0.130148i
$467$	−41.2821	−	154.067i	−0.0883985	−	0.329908i	0.907538	−	0.419971i	$-0.137960\pi$
$467$	−41.2821	−	154.067i	−0.0883985	−	0.329908i	−0.995936	+	0.0900632i	$0.971293\pi$
$468$	2.78497	+	8.53388i	0.00595078	+	0.0182348i
$469$	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
$472$	−140.411	+	524.021i	−0.297481	+	1.11021i
$473$	−234.593	−	62.8590i	−0.495968	−	0.132894i
$474$	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
$477$	473.474	−	154.515i	0.992608	−	0.323930i
$478$	637.560	−	170.834i	1.33381	−	0.357393i
$479$	17.2667	−	9.96894i	0.0360474	−	0.0208120i	−0.481868	−	0.876244i	$-0.660042\pi$
$479$	17.2667	−	9.96894i	0.0360474	−	0.0208120i	0.517915	+	0.855432i	$0.326708\pi$
$480$	−11.1563	+	54.4529i	−0.0232424	+	0.113444i
$481$	−67.6542	−	39.0602i	−0.140653	−	0.0812062i
$482$	−493.319	+	493.319i	−1.02348	+	1.02348i
$483$	−25.0525	−	121.193i	−0.0518686	−	0.250918i
$484$		−	68.4493i		−	0.141424i
$485$	−1.16652	+	0.725663i	−0.00240521	+	0.00149621i
$486$	495.400	−	66.8421i	1.01934	−	0.137535i
$487$	−913.243	−	244.703i	−1.87524	−	0.502470i	−0.999817	−	0.0191167i	$-0.993915\pi$
$487$	−913.243	−	244.703i	−1.87524	−	0.502470i	−0.875426	−	0.483353i	$-0.839419\pi$
$488$	−695.766	+	186.430i	−1.42575	+	0.382028i
$489$	429.773	+	700.314i	0.878881	+	1.43214i
$490$	309.117	−	398.077i	0.630852	−	0.812402i
$491$			600.751i			1.22353i	0.791041	+	0.611763i	$0.209539\pi$
$491$			600.751i			1.22353i	−0.791041	+	0.611763i	$0.790461\pi$
$492$	−3.18001	−	3.01383i	−0.00646343	−	0.00612567i
$493$	142.098	+	38.0751i	0.288232	+	0.0772314i
$494$	−98.8460	−	171.206i	−0.200093	−	0.346571i
$495$	−702.819	−	590.607i	−1.41984	−	1.19315i
$496$			603.638i			1.21701i
$497$	182.636	+	65.9599i	0.367477	+	0.132716i
$498$	−33.2804	+	139.017i	−0.0668282	+	0.279150i
$499$	−504.601	−	291.332i	−1.01123	−	0.583831i	−0.0996751	−	0.995020i	$-0.531780\pi$
$499$	−504.601	−	291.332i	−1.01123	−	0.583831i	−0.911550	+	0.411189i	$0.865114\pi$
$500$	−4.70729	+	28.6011i	−0.00941457	+	0.0572022i
$501$	215.058	+	116.588i	0.429257	+	0.232710i
$502$	140.130	−	37.5477i	0.279143	−	0.0747963i
$503$	−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
$507$	432.820	−	128.510i	0.853689	−	0.253472i
$508$	3.39379	−	12.6658i	0.00668070	−	0.0249327i
$509$	−207.603	−	119.860i	−0.407865	−	0.235481i	0.282007	−	0.959412i	$-0.409000\pi$
$509$	−207.603	−	119.860i	−0.407865	−	0.235481i	−0.689872	+	0.723931i	$0.742333\pi$
$510$	−378.472	+	22.6276i	−0.742102	+	0.0443679i
$511$	120.325	−	172.755i	0.235470	−	0.338073i
$512$	−325.741	−	325.741i	−0.636212	−	0.636212i
$513$	−568.240	+	202.459i	−1.10768	+	0.394657i
$514$	176.531	+	305.761i	0.343445	+	0.594865i
$515$	−67.8416	+	2.23229i	−0.131731	+	0.00433454i
$516$	−0.222118	−	8.27886i	−0.000430462	−	0.0160443i
$517$	863.370	+	863.370i	1.66996	+	1.66996i
$518$	−257.446	+	46.0554i	−0.497000	+	0.0889100i
$519$	−187.329	−	305.253i	−0.360943	−	0.588155i
$520$	−162.362	−	37.8289i	−0.312235	−	0.0727478i
$521$	67.6776	+	117.221i	0.129899	+	0.224992i	0.923637	−	0.383267i	$-0.125201\pi$
$521$	67.6776	+	117.221i	0.129899	+	0.224992i	−0.793738	+	0.608260i	$0.791868\pi$
$522$	−148.113	+	164.923i	−0.283742	+	0.315944i
$523$	−99.6034	−	371.725i	−0.190446	−	0.710755i	−0.993399	−	0.114712i	$-0.963405\pi$
$523$	−99.6034	−	371.725i	−0.190446	−	0.710755i	0.802953	−	0.596043i	$-0.203261\pi$
$524$			16.7226i			0.0319133i
$525$	−456.705	−	258.932i	−0.869914	−	0.493204i
$526$	223.948			0.425756
$527$	−424.578	+	113.765i	−0.805652	+	0.215874i
$528$	−989.989	+	293.941i	−1.87498	+	0.556706i
$529$	428.051	−	247.136i	0.809171	−	0.467175i
$530$	129.159	−	554.354i	0.243697	−	1.04595i
$531$	285.236	−	561.593i	0.537168	−	1.05761i
$532$	−34.1091	−	12.3187i	−0.0641149	−	0.0231554i
$533$	19.1554	−	19.1554i	0.0359389	−	0.0359389i
$534$	14.2298	+	530.378i	0.0266476	+	0.993218i
$535$	6.23399	+	189.458i	0.0116523	+	0.354126i
$536$	−152.689	+	88.1550i	−0.284867	+	0.164468i
$537$	304.324	−	321.104i	0.566712	−	0.597959i
$538$	−97.0207	+	97.0207i	−0.180336	+	0.180336i
$539$	985.293	+	168.683i	1.82800	+	0.312955i
$540$	12.4852	−	28.7073i	0.0231207	−	0.0531616i
$541$	138.386	−	239.692i	0.255798	−	0.443054i	−0.709314	−	0.704892i	$-0.750995\pi$
$541$	138.386	−	239.692i	0.255798	−	0.443054i	0.965112	+	0.261838i	$0.0843286\pi$
$542$	−246.912	−	66.1599i	−0.455558	−	0.122066i
$543$	482.410	−	143.234i	0.888416	−	0.263783i
$544$	−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	$0.490826\pi$
$548$	−5.58143	−	20.8302i	−0.0101851	−	0.0380113i
$549$	835.113	−	44.8438i	1.52115	−	0.0816826i
$550$	−993.386	+	337.581i	−1.80616	+	0.613783i
$551$	133.747	−	231.656i	0.242735	−	0.420429i
$552$	−31.9064	+	133.277i	−0.0578015	+	0.241445i
$553$	−682.911	+	575.932i	−1.23492	+	1.04147i
$554$	233.324			0.421163
$555$	86.0886	+	258.469i	0.155115	+	0.465709i
$556$	−31.5414	+	18.2104i	−0.0567291	+	0.0327525i
$557$	111.301	−	415.380i	0.199822	−	0.745745i	−0.791144	−	0.611630i	$-0.790514\pi$
$557$	111.301	−	415.380i	0.199822	−	0.745745i	0.990966	−	0.134115i	$-0.0428193\pi$
$558$	136.872	−	648.032i	0.245291	−	1.16135i
$559$	51.2073			0.0916052
$560$	−526.085	+	268.368i	−0.939438	+	0.479229i
$561$	−393.328	−	640.927i	−0.701119	−	1.14247i
$562$	155.834	+	581.579i	0.277284	+	1.03484i
$563$	210.089	−	784.064i	0.373161	−	1.39265i	−0.482853	−	0.875701i	$-0.660399\pi$
$563$	210.089	−	784.064i	0.373161	−	1.39265i	0.856014	−	0.516953i	$-0.172934\pi$
$564$	−19.8433	+	36.6030i	−0.0351832	+	0.0648990i
$565$	218.887	+	351.867i	0.387410	+	0.622773i
$566$	−684.630			−1.20959
$567$	409.854	+	391.802i	0.722846	+	0.691009i
$568$	−152.050	−	152.050i	−0.267694	−	0.267694i
$569$	323.444	−	560.222i	0.568443	−	0.984572i	−0.428277	−	0.903647i	$-0.640879\pi$
$569$	323.444	−	560.222i	0.568443	−	0.984572i	0.996720	−	0.0809249i	$-0.0257874\pi$
$570$	−138.372	+	675.380i	−0.242758	+	1.18488i
$571$	138.940	+	240.651i	0.243328	+	0.421456i	0.961660	−	0.274244i	$-0.0884277\pi$
$571$	138.940	+	240.651i	0.243328	+	0.421456i	−0.718333	+	0.695700i	$0.755094\pi$
$572$	5.26645	+	19.6547i	0.00920709	+	0.0343613i
$573$	−226.806	+	947.399i	−0.395822	+	1.65340i
$574$	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
$577$	−188.143	+	702.159i	−0.326071	+	1.21691i	0.587160	+	0.809471i	$0.300246\pi$
$577$	−188.143	+	702.159i	−0.326071	+	1.21691i	−0.913231	+	0.407443i	$0.866421\pi$
$578$	274.267	+	73.4897i	0.474511	+	0.127145i
$579$	−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
$582$	0.394790	−	1.64909i	0.000678334	−	0.00283349i
$583$	1090.47	−	292.192i	1.87045	−	0.501186i
$584$	−201.900	+	116.567i	−0.345719	+	0.199601i
$585$	175.365	+	81.9296i	0.299770	+	0.140051i
$586$	−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	$0.129354\pi$
$588$	4.04906	+	33.8460i	0.00688615	+	0.0575613i
$589$			799.250i			1.35696i
$590$	−380.240	−	611.247i	−0.644474	−	1.03601i
$591$	152.559	−	281.410i	0.258137	−	0.476160i
$592$	296.017	+	79.3176i	0.500029	+	0.133983i
$593$	−263.863	+	70.7019i	−0.444963	+	0.119228i	−0.474342	−	0.880341i	$-0.657314\pi$
$593$	−263.863	+	70.7019i	−0.444963	+	0.119228i	0.0293785	+	0.999568i	$0.490647\pi$
$594$	1129.45	−	91.0826i	1.90143	−	0.153338i
$595$	−287.911	−	319.452i	−0.483883	−	0.536895i
$596$			6.25533i			0.0104955i
$597$	103.554	−	109.264i	0.173458	−	0.183022i
$598$	50.3686	+	13.4962i	0.0842284	+	0.0225689i
$599$	234.625	+	406.382i	0.391694	+	0.678433i	0.992673	−	0.120831i	$-0.0385560\pi$
$599$	234.625	+	406.382i	0.391694	+	0.678433i	−0.600979	+	0.799265i	$0.705223\pi$
$600$	335.999	+	474.442i	0.559998	+	0.790737i
$601$			761.886i			1.26770i	0.773457	+	0.633848i	$0.218526\pi$
$601$			761.886i			1.26770i	−0.773457	+	0.633848i	$0.781474\pi$
$602$	131.051	−	110.521i	0.217692	−	0.183590i
$603$	194.605	−	63.5077i	0.322727	−	0.105320i
$604$	25.0396	+	14.4566i	0.0414562	+	0.0239348i
$605$	−1077.39	−	1008.75i	−1.78081	−	1.66735i
$606$	−325.483	+	600.385i	−0.537100	+	0.990735i
$607$	−811.631	+	217.476i	−1.33712	+	0.358280i	−0.855364	−	0.518027i	$-0.826667\pi$
$607$	−811.631	+	217.476i	−1.33712	+	0.358280i	−0.481754	+	0.876307i	$0.660000\pi$
$608$	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
$612$	17.1340	−	19.0785i	0.0279967	−	0.0311741i
$613$	−149.534	+	558.069i	−0.243938	+	0.910390i	0.729976	+	0.683473i	$0.239531\pi$
$613$	−149.534	+	558.069i	−0.243938	+	0.910390i	−0.973914	+	0.226917i	$0.927135\pi$
$614$	649.686	+	375.097i	1.05812	+	0.610907i
$615$	−94.3018	+	5.63800i	−0.153336	+	0.00916748i
$616$	−908.345	−	632.668i	−1.47459	−	1.02706i
$617$	408.277	+	408.277i	0.661714	+	0.661714i	0.955784	−	0.294070i	$-0.0950100\pi$
$617$	408.277	+	408.277i	0.661714	+	0.661714i	−0.294070	+	0.955784i	$0.595010\pi$
$618$	57.6325	−	60.8102i	0.0932564	−	0.0983984i
$619$	−566.755	−	981.649i	−0.915598	−	1.58586i	−0.806023	−	0.591884i	$-0.798384\pi$
$619$	−566.755	−	981.649i	−0.915598	−	1.58586i	−0.109575	−	0.993979i	$-0.534949\pi$
$620$	−30.2775	−	28.3485i	−0.0488347	−	0.0457234i
$621$	68.2233	−	143.746i	0.109860	−	0.231476i
$622$	−370.722	−	370.722i	−0.596016	−	0.596016i
$623$	−460.041	+	387.975i	−0.738429	+	0.622753i
$624$	185.580	−	113.888i	0.297404	−	0.182513i
$625$	380.808	+	495.591i	0.609293	+	0.792945i
$626$	−318.600	−	551.831i	−0.508945	−	0.881519i
$627$	−1310.80	+	389.194i	−2.09059	+	0.620724i
$628$	−5.31471	−	19.8347i	−0.00846291	−	0.0315840i
$629$			223.157i			0.354781i
$630$	625.627	−	168.817i	0.993059	−	0.267964i
$631$	869.095			1.37733			0.688665	−	0.725080i	$-0.258197\pi$
$631$	869.095			1.37733			0.688665	+	0.725080i	$0.258197\pi$
$632$	955.555	−	256.040i	1.51195	−	0.405127i
$633$	114.166	+	384.508i	0.180356	+	0.607438i
$634$	25.9445	−	14.9791i	0.0409219	−	0.0236263i
$635$	−149.345	−	240.076i	−0.235188	−	0.378072i
$636$	20.1357	+	32.8111i	0.0316599	+	0.0515898i
$637$	−209.869	+	19.4140i	−0.329465	+	0.0304772i
$638$	−355.295	+	355.295i	−0.556889	+	0.556889i
$639$	136.245	+	209.209i	0.213216	+	0.327401i
$640$	689.570	−	22.6899i	1.07745	−	0.0354529i
$641$	−289.798	+	167.315i	−0.452103	+	0.261022i	−0.708718	−	0.705492i	$-0.750726\pi$
$641$	−289.798	+	167.315i	−0.452103	+	0.261022i	0.256615	+	0.966514i	$0.417393\pi$
$642$	−169.821	−	160.947i	−0.264519	−	0.250696i
$643$	−93.9647	+	93.9647i	−0.146135	+	0.146135i	−0.776389	−	0.630254i	$-0.782951\pi$
$643$	−93.9647	+	93.9647i	−0.146135	+	0.146135i	0.630254	+	0.776389i	$0.282951\pi$
$644$	8.65946	−	4.06423i	0.0134464	−	0.00631092i
$645$	−133.582	−	118.510i	−0.207104	−	0.183737i
$646$	−282.362	+	489.065i	−0.437093	+	0.757067i
$647$	−864.836	−	231.732i	−1.33669	−	0.358164i	−0.481482	−	0.876456i	$-0.659901\pi$
$647$	−864.836	−	231.732i	−1.33669	−	0.358164i	−0.855204	+	0.518292i	$0.826568\pi$
$648$	−226.519	−	585.595i	−0.349567	−	0.903696i
$649$	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
$653$	262.227	+	978.645i	0.401573	+	1.49869i	0.810290	+	0.586029i	$0.199310\pi$
$653$	262.227	+	978.645i	0.401573	+	1.49869i	−0.408717	+	0.912661i	$0.634024\pi$
$654$	383.972	+	208.160i	0.587113	+	0.318288i
$655$	263.212	+	246.443i	0.401851	+	0.376248i
$656$	−53.1356	+	92.0336i	−0.0809994	+	0.140295i
$657$	257.324	−	83.9759i	0.391666	−	0.127817i
$658$	−848.387	+	151.771i	−1.28934	+	0.230655i
$659$	295.701			0.448711			0.224356	−	0.974507i	$-0.427972\pi$
$659$	295.701			0.448711			0.224356	+	0.974507i	$0.427972\pi$
$660$	31.7490	−	63.4606i	0.0481045	−	0.0961524i
$661$	154.880	−	89.4201i	0.234312	−	0.135280i	−0.378248	−	0.925704i	$-0.623473\pi$
$661$	154.880	−	89.4201i	0.234312	−	0.135280i	0.612560	+	0.790424i	$0.290140\pi$
$662$	282.616	−	1054.74i	0.426912	−	1.59326i
$663$	115.080	+	109.067i	0.173575	+	0.164505i
$664$	179.544			0.270398
$665$	−696.567	+	355.335i	−1.04747	+	0.534338i
$666$	−299.803	−	152.272i	−0.450155	−	0.228636i
$667$	18.2615	+	68.1529i	0.0273786	+	0.102178i
$668$	−4.89391	+	18.2643i	−0.00732621	+	0.0273418i
$669$	−238.377	−	129.230i	−0.356318	−	0.193168i
$670$	53.0863	−	227.847i	0.0792333	−	0.340071i
$671$	1895.70			2.82519
$672$	24.4607	−	73.8733i	0.0363999	−	0.109930i
$673$	−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
$675$	−267.856	−	619.579i	−0.396824	−	0.917895i
$676$	17.4493	+	30.2231i	0.0258126	+	0.0447088i
$677$	251.720	+	939.430i	0.371816	+	1.38764i	0.857941	+	0.513748i	$0.171743\pi$
$677$	251.720	+	939.430i	0.371816	+	1.38764i	−0.486125	+	0.873889i	$0.661590\pi$
$678$	−497.427	−	119.083i	−0.733668	−	0.175639i
$679$	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
$682$	388.570	−	1450.16i	0.569751	−	2.12634i
$683$	−723.377	−	193.828i	−1.05912	−	0.283789i	−0.313102	−	0.949719i	$-0.601368\pi$
$683$	−723.377	−	193.828i	−1.05912	−	0.283789i	−0.746014	+	0.665930i	$0.768035\pi$
$684$	−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
$687$	−109.704	−	26.2631i	−0.159686	−	0.0382286i
$688$	−194.037	+	51.9921i	−0.282031	+	0.0755699i
$689$	−206.140	+	119.015i	−0.299188	+	0.172736i
$690$	−100.160	−	151.776i	−0.145159	−	0.219966i
$691$	−40.1591	−	23.1858i	−0.0581173	−	0.0335540i	0.470660	−	0.882315i	$-0.344016\pi$
$691$	−40.1591	−	23.1858i	−0.0581173	−	0.0335540i	−0.528777	+	0.848761i	$0.677349\pi$
$692$	19.5751	−	19.5751i	0.0282878	−	0.0282878i
$693$	880.071	+	936.647i	1.26994	+	1.35158i
$694$			621.842i			0.896026i
$695$	−178.198	+	764.829i	−0.256400	+	1.10047i
$696$	244.769	+	132.695i	0.351680	+	0.190654i
$697$	−74.7476	−	20.0286i	−0.107242	−	0.0287354i
$698$	−423.412	+	113.453i	−0.606607	+	0.162540i
$699$	−87.0447	+	53.4181i	−0.124527	+	0.0764207i
$700$	11.2455	−	38.9909i	0.0160650	−	0.0557013i
$701$		−	167.792i		−	0.239361i	−0.992812	−	0.119681i	$-0.961813\pi$
$701$		−	167.792i		−	0.239361i	0.992812	−	0.119681i	$-0.0381870\pi$
$702$	−225.052	+	80.1841i	−0.320587	+	0.114222i
$703$	391.944	+	105.021i	0.557530	+	0.149390i
$704$	610.713	+	1057.79i	0.867490	+	1.50254i
$705$	283.696	+	851.757i	0.402406	+	1.20817i
$706$		−	1394.12i		−	1.97468i
$707$	−762.516	+	136.409i	−1.07852	+	0.192941i
$708$	47.3489	+	11.3353i	0.0668770	+	0.0160103i
$709$	−4.74846	−	2.74153i	−0.00669741	−	0.00386675i	0.496648	−	0.867952i	$-0.334564\pi$
$709$	−4.74846	−	2.74153i	−0.00669741	−	0.00386675i	−0.503345	+	0.864086i	$0.667897\pi$
$710$	285.176	−	9.38353i	0.401656	−	0.0132162i
$711$	−1146.93	+	61.5879i	−1.61313	+	0.0866215i
$712$	643.708	−	172.481i	0.904084	−	0.242248i
$713$	−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
$717$	273.978	+	922.754i	0.382117	+	1.28696i
$718$	316.915	−	1182.74i	0.441386	−	1.64728i
$719$	−607.419	−	350.694i	−0.844811	−	0.487752i	0.0140854	−	0.999901i	$-0.495516\pi$
$719$	−607.419	−	350.694i	−0.844811	−	0.487752i	−0.858897	+	0.512149i	$0.828850\pi$
$720$	−747.688	−	132.399i	−1.03846	−	0.183887i
$721$	94.6884	+	8.04681i	0.131329	+	0.0111606i
$722$	200.968	+	200.968i	0.278349	+	0.278349i
$723$	−738.455	−	699.866i	−1.02138	−	0.968003i
$724$	19.4486	+	33.6859i	0.0268626	+	0.0465275i
$725$	268.496	+	132.296i	0.370339	+	0.182477i
$726$	1821.06	−	48.8583i	2.50835	−	0.0672979i
$727$	−179.080	−	179.080i	−0.246328	−	0.246328i	0.573134	−	0.819462i	$-0.305727\pi$
$727$	−179.080	−	179.080i	−0.246328	−	0.246328i	−0.819462	+	0.573134i	$0.805727\pi$
$728$	219.518	+	79.2800i	0.301535	+	0.108901i
$729$	116.819	+	719.579i	0.160245	+	0.987077i
$730$	70.1957	−	301.281i	0.0961585	−	0.412714i
$731$	−73.1390	−	126.680i	−0.100053	−	0.173298i
$732$	18.3996	+	61.9698i	0.0251361	+	0.0846582i
$733$	−83.5574	−	311.841i	−0.113994	−	0.425431i	0.885216	−	0.465180i	$-0.154011\pi$
$733$	−83.5574	−	311.841i	−0.113994	−	0.425431i	−0.999210	+	0.0397499i	$0.987344\pi$
$734$		−	365.099i		−	0.497410i
$735$	592.407	+	435.062i	0.805996	+	0.591921i
$736$	−21.8376			−0.0296707
$737$	448.200	−	120.095i	0.608142	−	0.162951i
$738$	77.9117	−	86.7539i	0.105571	−	0.117553i
$739$	−613.293	+	354.085i	−0.829896	+	0.479141i	−0.853817	−	0.520573i	$-0.825718\pi$
$739$	−613.293	+	354.085i	−0.829896	+	0.479141i	0.0239209	+	0.999714i	$0.492385\pi$
$740$	−17.8802	+	11.1228i	−0.0241625	+	0.0150308i
$741$	245.718	−	150.794i	0.331604	−	0.203501i
$742$	−270.686	+	749.500i	−0.364806	+	1.01011i
$743$	214.444	−	214.444i	0.288619	−	0.288619i	−0.547915	−	0.836534i	$-0.684578\pi$
$743$	214.444	−	214.444i	0.288619	−	0.288619i	0.836534	+	0.547915i	$0.184578\pi$
$744$	−831.610	+	22.3118i	−1.11776	+	0.0299889i
$745$	98.4586	+	92.1856i	0.132159	+	0.123739i
$746$	976.343	−	563.692i	1.30877	−	0.755619i
$747$	−203.960	−	43.0790i	−0.273039	−	0.0576693i
$748$	41.1012	−	41.1012i	0.0549481	−	0.0549481i
$749$	22.4719	−	264.431i	0.0300025	−	0.353046i
$750$	−764.279	−	104.820i	−1.01904	−	0.139760i
$751$	365.338	−	632.784i	0.486468	−	0.842588i	−0.513411	−	0.858143i	$-0.671618\pi$
$751$	365.338	−	632.784i	0.486468	−	0.842588i	0.999879	+	0.0155551i	$0.00495153\pi$
$752$	975.496	+	261.383i	1.29720	+	0.347584i
$753$	60.2179	+	202.813i	0.0799706	+	0.269340i
$754$	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	$0.241632\pi$
$758$	315.328	+	1176.82i	0.416000	+	1.55253i
$759$	171.893	−	317.073i	0.226473	−	0.417752i
$760$	865.456	−	28.4773i	1.13876	−	0.0374701i
$761$	275.544	−	477.255i	0.362081	−	0.627143i	−0.626222	−	0.779645i	$-0.715400\pi$
$761$	275.544	−	477.255i	0.362081	−	0.627143i	0.988303	+	0.152502i	$0.0487331\pi$
$762$	339.390	+	81.2496i	0.445394	+	0.106627i
$763$	87.2396	+	487.662i	0.114338	+	0.639138i
$764$	−75.2991			−0.0985590
$765$	−47.7894	−	550.851i	−0.0624698	−	0.720067i
$766$	−1177.80	+	680.005i	−1.53760	+	0.887734i
$767$	−77.9136	+	290.777i	−0.101582	+	0.379110i
$768$	−91.5762	+	96.6256i	−0.119240	+	0.125815i
$769$	−242.237			−0.315002			−0.157501	−	0.987519i	$-0.550344\pi$
$769$	−242.237			−0.315002			−0.157501	+	0.987519i	$0.550344\pi$
$770$	1436.61	−	306.072i	1.86572	−	0.397496i
$771$	−438.833	+	269.306i	−0.569174	+	0.349294i
$772$	−13.1432	−	49.0510i	−0.0170248	−	0.0635375i
$773$	26.8366	−	100.156i	0.0347175	−	0.129567i	−0.946392	−	0.323020i	$-0.895302\pi$
$773$	26.8366	−	100.156i	0.0347175	−	0.129567i	0.981110	+	0.193453i	$0.0619686\pi$
$774$	220.097	−	11.8187i	0.284362	−	0.0152696i
$775$	−892.408	+	58.7920i	−1.15149	+	0.0758606i
$776$	−2.12985			−0.00274465
$777$	−77.2088	−	373.503i	−0.0993679	−	0.480699i
$778$	336.620	+	336.620i	0.432674	+	0.432674i
$779$	−70.3546	+	121.858i	−0.0903139	+	0.156428i
$780$	−3.00291	+	14.6569i	−0.00384988	+	0.0187909i
$781$	282.959	+	490.099i	0.362303	+	0.627527i
$782$	−38.5531	−	143.882i	−0.0493007	−	0.183993i
$783$	−246.217	−	209.469i	−0.314454	−	0.267521i
$784$	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
$787$	328.007	−	1224.14i	0.416781	−	1.55545i	−0.364461	−	0.931219i	$-0.618747\pi$
$787$	328.007	−	1224.14i	0.416781	−	1.55545i	0.781242	−	0.624229i	$-0.214587\pi$
$788$	23.8995	+	6.40385i	0.0303293	+	0.00812672i
$789$	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
$792$	−441.544	−	1353.01i	−0.557505	−	1.70834i
$793$	−386.078	+	103.449i	−0.486857	+	0.130453i
$794$	−373.881	+	215.860i	−0.470882	+	0.271864i
$795$	813.189	+	166.606i	1.02288	+	0.209568i
$796$	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	$0.889999\pi$
$798$	303.386	−	916.251i	0.380183	−	1.14818i
$799$			735.393i			0.920392i
$800$	−61.0585	+	69.6710i	−0.0763231	+	0.0870887i
$801$	−772.629	+	41.4885i	−0.964581	+	0.0517959i
$802$	216.479	+	58.0054i	0.269924	+	0.0723259i
$803$	592.653	−	158.801i	0.738049	−	0.197760i
$804$	8.27607	+	13.4858i	0.0102936	+	0.0167734i
$805$	63.6447	−	196.195i	0.0790618	−	0.243720i
$806$			316.544i			0.392734i
$807$	−145.232	−	137.642i	−0.179965	−	0.170560i
$808$	828.565	+	222.013i	1.02545	+	0.274769i
$809$	−655.920	−	1136.09i	−0.810779	−	1.40431i	−0.912320	−	0.409479i	$-0.865710\pi$
$809$	−655.920	−	1136.09i	−0.810779	−	1.40431i	0.101541	−	0.994831i	$-0.467623\pi$
$810$	772.655	+	311.671i	0.953896	+	0.384779i
$811$			257.476i			0.317480i	0.987320	+	0.158740i	$0.0507431\pi$
$811$			257.476i			0.317480i	−0.987320	+	0.158740i	$0.949257\pi$
$812$	−3.42234	−	19.1306i	−0.00421471	−	0.0235599i
$813$	86.7907	−	362.536i	0.106754	−	0.445924i
$814$	−660.087	−	381.102i	−0.810918	−	0.468184i
$815$	45.0367	+	1368.71i	0.0552597	+	1.67940i
$816$	−546.807	−	296.437i	−0.670106	−	0.363280i
$817$	−256.916	+	68.8405i	−0.314463	+	0.0842601i
$818$	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	0.565028	−	0.825072i	$-0.308866\pi$
$821$	109.200	+	63.0464i	0.133008	+	0.0767922i	−0.432020	+	0.901864i	$0.642199\pi$
$822$	550.193	−	163.360i	0.669335	−	0.198734i
$823$	−358.458	+	1337.78i	−0.435551	+	1.62550i	0.304194	+	0.952610i	$0.401613\pi$
$823$	−358.458	+	1337.78i	−0.435551	+	1.62550i	−0.739745	+	0.672887i	$0.765054\pi$
$824$	−91.1345	−	52.6165i	−0.110600	−	0.0638550i
$825$	−530.978	−	1434.95i	−0.643610	−	1.73934i
$826$	428.190	+	912.324i	0.518390	+	1.10451i
$827$	−342.391	−	342.391i	−0.414015	−	0.414015i	0.469120	−	0.883135i	$-0.344571\pi$
$827$	−342.391	−	342.391i	−0.414015	−	0.414015i	−0.883135	+	0.469120i	$0.844571\pi$
$828$	12.0334	+	2.54160i	0.0145331	+	0.00306956i
$829$	467.316	+	809.415i	0.563711	+	0.976375i	0.997168	+	0.0752016i	$0.0239600\pi$
$829$	467.316	+	809.415i	0.563711	+	0.976375i	−0.433458	+	0.901174i	$0.642707\pi$
$830$	−162.831	+	173.911i	−0.196182	+	0.209532i
$831$	9.12581	+	340.140i	0.0109817	+	0.409314i
$832$	−182.101	−	182.101i	−0.218872	−	0.218872i
$833$	347.782	+	491.461i	0.417506	+	0.589990i
$834$	−506.993	−	826.145i	−0.607906	−	0.990581i
$835$	215.358	+	346.194i	0.257913	+	0.414603i
$836$	−52.8455	−	91.5310i	−0.0632123	−	0.109487i
$837$	950.054	+	174.187i	1.13507	+	0.208108i
$838$	6.29348	+	23.4876i	0.00751012	+	0.0280281i
$839$		−	428.103i		−	0.510254i	−0.966907	−	0.255127i	$-0.917883\pi$
$839$		−	428.103i		−	0.510254i	0.966907	−	0.255127i	$-0.0821173\pi$
$840$	−389.167	−	714.850i	−0.463294	−	0.851012i
$841$	−697.653			−0.829551
$842$	−354.326	+	94.9414i	−0.420815	+	0.112757i
$843$	−841.731	+	249.921i	−0.998495	+	0.296466i
$844$	−26.8496	+	15.5016i	−0.0318123	+	0.0183668i
$845$	732.864	+	170.750i	0.867295	+	0.202071i
$846$	−987.970	−	501.796i	−1.16781	−	0.593140i
$847$	1332.12	+	1579.56i	1.57275	+	1.86488i
$848$	660.277	−	660.277i	0.778629	−	0.778629i
$849$	−26.7774	−	998.054i	−0.0315399	−	1.17556i
$850$	−566.839	−	279.298i	−0.666869	−	0.328586i
$851$	−92.6911	+	53.5152i	−0.108920	+	0.0628851i
$852$	−13.2747	+	14.0067i	−0.0155807	+	0.0164398i
$853$	336.763	−	336.763i	0.394799	−	0.394799i	−0.481595	−	0.876394i	$-0.659942\pi$
$853$	336.763	−	336.763i	0.394799	−	0.394799i	0.876394	+	0.481595i	$0.159942\pi$
$854$	−764.781	+	1098.03i	−0.895528	+	1.28574i
$855$	−989.981	−	175.303i	−1.15787	−	0.205033i
$856$	−146.939	+	254.506i	−0.171658	+	0.297321i
$857$	247.109	+	66.2128i	0.288342	+	0.0772611i	0.400091	−	0.916475i	$-0.368979\pi$
$857$	247.109	+	66.2128i	0.288342	+	0.0772611i	−0.111749	+	0.993736i	$0.535645\pi$
$858$	−519.144	+	154.141i	−0.605063	+	0.179651i
$859$	166.820	−	288.942i	0.194203	−	0.336370i	−0.752436	−	0.658665i	$-0.771121\pi$
$859$	166.820	−	288.942i	0.194203	−	0.336370i	0.946639	+	0.322296i	$0.104455\pi$
$860$	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
$863$	−324.469	−	1210.94i	−0.375978	−	1.40317i	−0.851910	−	0.523688i	$-0.824556\pi$
$863$	−324.469	−	1210.94i	−0.375978	−	1.40317i	0.475932	−	0.879482i	$-0.342111\pi$
$864$	82.3454	−	56.8287i	0.0953072	−	0.0657739i
$865$	−19.6306	−	596.594i	−0.0226943	−	0.689704i
$866$	−484.530	+	839.231i	−0.559504	+	0.969089i
$867$	−96.4060	+	402.701i	−0.111195	+	0.464476i
$868$	37.4361	+	44.3898i	0.0431291	+	0.0511403i
$869$	−2603.54			−2.99601
$870$	−350.516	+	116.747i	−0.402892	+	0.134192i
$871$	−84.7266	+	48.9169i	−0.0972751	+	0.0561618i
$872$	141.987	−	529.903i	0.162829	−	0.607687i
$873$	2.41949	+	0.511026i	0.00277146	+	0.000585367i
$874$	−270.852			−0.309899
$875$	−447.990	−	751.618i	−0.511988	−	0.858992i
$876$	10.9434	+	17.8323i	0.0124925	+	0.0203565i
$877$	−255.818	−	954.726i	−0.291697	−	1.08863i	−0.943805	−	0.330502i	$-0.892782\pi$
$877$	−255.818	−	954.726i	−0.291697	−	1.08863i	0.652109	−	0.758126i	$-0.273885\pi$
$878$	392.513	−	1464.88i	0.447053	−	1.66843i
$879$	253.643	−	467.870i	0.288559	−	0.532275i
$880$	−1676.28	−	390.557i	−1.90486	−	0.443815i
$881$	253.105			0.287292			0.143646	−	0.989629i	$-0.454117\pi$
$881$	253.105			0.287292			0.143646	+	0.989629i	$0.454117\pi$
$882$	−897.568	+	131.882i	−1.01765	+	0.149526i
$883$	−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
$885$	876.204	−	578.221i	0.990061	−	0.653357i
$886$	−670.514	−	1161.36i	−0.756788	−	1.31079i
$887$	397.109	+	1482.03i	0.447699	+	1.67084i	0.708709	+	0.705501i	$0.249278\pi$
$887$	397.109	+	1482.03i	0.447699	+	1.67084i	−0.261010	+	0.965336i	$0.584055\pi$
$888$	−98.3317	+	410.745i	−0.110734	+	0.462550i
$889$	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
$892$	5.42458	−	20.2448i	0.00608136	−	0.0226960i
$893$	1291.61	+	346.086i	1.44637	+	0.387555i
$894$	−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
$897$	−17.7048	+	73.9552i	−0.0197378	+	0.0824473i
$898$	218.709	−	58.6029i	0.243551	−	0.0652594i
$899$	−370.928	+	214.155i	−0.412600	+	0.238215i
$900$	41.7544	−	31.2851i	0.0463938	−	0.0347612i
$901$	588.857	+	339.977i	0.653559	+	0.377333i
$902$	186.895	−	186.895i	0.207201	−	0.207201i
$903$	166.244	+	186.723i	0.184101	+	0.206781i
$904$			642.441i			0.710665i
$905$	816.830	+	190.314i	0.902575	+	0.210291i
$906$	−366.738	+	676.485i	−0.404788	+	0.746672i
$907$	842.257	+	225.682i	0.928618	+	0.248822i	0.691265	−	0.722601i	$-0.257054\pi$
$907$	842.257	+	225.682i	0.928618	+	0.248822i	0.237353	+	0.971424i	$0.423720\pi$
$908$	51.7926	−	13.8778i	0.0570403	−	0.0152839i
$909$	−887.972	−	451.006i	−0.976867	−	0.496157i
$910$	−275.876	+	140.731i	−0.303161	+	0.154649i
$911$			751.515i			0.824935i	0.910972	+	0.412467i	$0.135333\pi$
$911$			751.515i			0.824935i	−0.910972	+	0.412467i	$0.864667\pi$
$912$	−777.983	+	820.880i	−0.853051	+	0.900087i
$913$	−456.422	−	122.298i	−0.499915	−	0.133952i
$914$	480.604	+	832.430i	0.525825	+	0.910755i
$915$	1246.56	+	623.647i	1.36236	+	0.681582i
$916$		−	8.71928i		−	0.00951887i
$917$	−325.444	−	385.895i	−0.354901	−	0.420823i
$918$	519.805	+	442.224i	0.566237	+	0.481725i
$919$	819.856	+	473.344i	0.892118	+	0.515064i	0.874635	−	0.484783i	$-0.161101\pi$
$919$	819.856	+	473.344i	0.892118	+	0.515064i	0.0174832	+	0.999847i	$0.494435\pi$
$920$	−156.108	+	166.731i	−0.169683	+	0.181230i
$921$	−521.405	+	961.784i	−0.566130	+	1.04428i
$922$	1271.86	−	340.793i	1.37945	−	0.369623i
$923$	−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
$927$	90.9033	+	81.6382i	0.0980618	+	0.0880671i
$928$	−11.4829	+	42.8546i	−0.0123738	+	0.0461795i
$929$	790.789	+	456.562i	0.851226	+	0.491456i	0.861064	−	0.508496i	$-0.169798\pi$
$929$	790.789	+	456.562i	0.851226	+	0.491456i	−0.00983804	+	0.999952i	$0.503132\pi$
$930$	732.586	−	825.755i	0.787727	−	0.887908i
$931$	1026.85	−	379.541i	1.10296	−	0.407670i
$932$	−5.58197	−	5.58197i	−0.00598924	−	0.00598924i
$933$	525.938	−	554.938i	0.563707	−	0.594789i
$934$	164.060	+	284.160i	0.175653	+	0.304240i
$935$	−41.2175	−	1252.64i	−0.0440829	−	1.33973i
$936$	163.759	+	251.458i	0.174956	+	0.268651i
$937$	−849.169	−	849.169i	−0.906264	−	0.906264i	0.0897045	−	0.995968i	$-0.471408\pi$
$937$	−849.169	−	849.169i	−0.906264	−	0.906264i	−0.995968	+	0.0897045i	$0.971408\pi$
$938$	−111.256	+	308.055i	−0.118610	+	0.328417i
$939$	791.998	−	486.038i	0.843448	−	0.517612i
$940$	−58.9225	+	36.6541i	−0.0626836	+	0.0389937i
$941$	−35.6310	−	61.7148i	−0.0378651	−	0.0655842i	0.846472	−	0.532434i	$-0.178722\pi$
$941$	−35.6310	−	61.7148i	−0.0378651	−	0.0655842i	−0.884337	+	0.466849i	$0.845389\pi$
$942$	523.901	−	155.553i	0.556158	−	0.165131i
$943$	−9.60607	−	35.8503i	−0.0101867	−	0.0380173i
$944$		−	1180.94i		−	1.25099i
$945$	270.572	+	905.437i	0.286319	+	0.958134i
$946$	499.618			0.528138
$947$	−1538.66	+	412.282i	−1.62477	+	0.435356i	−0.952398	−	0.304856i	$-0.901392\pi$
$947$	−1538.66	+	412.282i	−1.62477	+	0.435356i	−0.672373	+	0.740213i	$0.734725\pi$
$948$	−25.2698	−	85.1085i	−0.0266560	−	0.0897769i
$949$	−112.034	+	64.6826i	−0.118054	+	0.0681587i
$950$	−757.309	+	864.129i	−0.797167	+	0.909610i
$951$	22.8512	+	37.2360i	0.0240286	+	0.0391546i
$952$	−117.407	−	656.294i	−0.123326	−	0.689385i
$953$	−30.0619	+	30.0619i	−0.0315445	+	0.0315445i	−0.722703	−	0.691159i	$-0.757101\pi$
$953$	−30.0619	+	30.0619i	−0.0315445	+	0.0315445i	0.691159	+	0.722703i	$0.257101\pi$
$954$	−858.552	+	559.122i	−0.899950	+	0.586082i
$955$	−1109.69	+	1185.20i	−1.16198	+	1.24105i
$956$	−64.4344	+	37.2012i	−0.0674000	+	0.0389134i
$957$	−531.846	−	504.053i	−0.555743	−	0.526701i
$958$	−29.0022	+	29.0022i	−0.0302737	+	0.0302737i
$959$	534.183	+	372.062i	0.557021	+	0.387968i
$960$	53.5977	+	896.481i	0.0558309	+	0.933834i
$961$	159.379	−	276.053i	0.165847	−	0.287256i
$962$	155.230	+	41.5937i	0.161362	+	0.0432367i
$963$	227.987	−	253.861i	0.236746	−	0.263614i
$964$	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	$0.140277\pi$
$968$	−592.215	−	2210.18i	−0.611793	−	2.28324i
$969$	−724.003	−	392.499i	−0.747165	−	0.405055i
$970$	1.93159	−	2.06303i	0.00199133	−	0.00212683i
$971$	522.569	−	905.116i	0.538176	−	0.932148i	−0.460826	−	0.887490i	$-0.652447\pi$
$971$	522.569	−	905.116i	0.538176	−	0.932148i	0.999002	−	0.0446579i	$-0.0142198\pi$
$972$	−51.9896	+	21.7310i	−0.0534873	+	0.0223570i
$973$	373.459	−	1034.07i	0.383822	−	1.06276i
$974$	1944.96			1.99687
$975$	186.445	+	263.266i	0.191225	+	0.270017i
$976$	1357.91	−	783.990i	1.39130	−	0.803268i
$977$	356.821	−	1331.68i	0.365221	−	1.36302i	−0.501899	−	0.864926i	$-0.667365\pi$
$977$	356.821	−	1331.68i	0.365221	−	1.36302i	0.867120	−	0.498099i	$-0.165968\pi$
$978$	−1226.85	−	1162.74i	−1.25445	−	1.18890i
$979$	−1753.87			−1.79149
$980$	−22.0433	+	52.3615i	−0.0224932	+	0.0534301i
$981$	−288.438	+	567.896i	−0.294024	+	0.578895i
$982$	−319.859	−	1193.73i	−0.325722	−	1.21561i
$983$	189.410	−	706.887i	0.192685	−	0.719112i	−0.800169	−	0.599775i	$-0.795257\pi$
$983$	189.410	−	706.887i	0.192685	−	0.719112i	0.992854	−	0.119336i	$-0.0380767\pi$
$984$	−128.755	−	69.8013i	−0.130849	−	0.0709363i
$985$	453.007	−	281.803i	0.459905	−	0.286094i
$986$	−302.630			−0.306927
$987$	−254.434	−	1230.84i	−0.257785	−	1.24705i
$988$	15.7574	+	15.7574i	0.0159487	+	0.0159487i
$989$	35.0788	−	60.7583i	0.0354690	−	0.0614341i
$990$	1711.00	+	799.369i	1.72828	+	0.807444i
$991$	651.871	+	1129.07i	0.657791	+	1.13933i	0.981186	+	0.193063i	$0.0618423\pi$
$991$	651.871	+	1129.07i	0.657791	+	1.13933i	−0.323395	+	0.946264i	$0.604824\pi$
$992$	−34.3099	−	128.046i	−0.0345866	−	0.129079i
$993$	1548.65	+	370.744i	1.55957	+	0.373358i
$994$	−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
$997$	−11.0607	+	41.2790i	−0.0110940	+	0.0414032i	−0.971251	−	0.238058i	$-0.923489\pi$
$997$	−11.0607	+	41.2790i	−0.0110940	+	0.0414032i	0.960157	+	0.279461i	$0.0901558\pi$
$998$	1157.79	+	310.228i	1.16011	+	0.310850i
$999$	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.68.8	yes	112
3.2	odd	2	inner	105.3.w.a.68.21	yes	112
5.2	odd	4	inner	105.3.w.a.47.8	yes	112
7.3	odd	6	inner	105.3.w.a.38.21	yes	112
15.2	even	4	inner	105.3.w.a.47.21	yes	112
21.17	even	6	inner	105.3.w.a.38.8	yes	112
35.17	even	12	inner	105.3.w.a.17.21	yes	112
105.17	odd	12	inner	105.3.w.a.17.8	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.8	✓	112	105.17	odd	12	inner
105.3.w.a.17.21	yes	112	35.17	even	12	inner
105.3.w.a.38.8	yes	112	21.17	even	6	inner
105.3.w.a.38.21	yes	112	7.3	odd	6	inner
105.3.w.a.47.8	yes	112	5.2	odd	4	inner
105.3.w.a.47.21	yes	112	15.2	even	4	inner
105.3.w.a.68.8	yes	112	1.1	even	1	trivial
105.3.w.a.68.21	yes	112	3.2	odd	2	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+(-1.98706 + 0.532431i) q^{2} +(-0.853896 - 2.87591i) q^{3} +(0.200820 - 0.115943i) q^{4} +(1.13457 - 4.86958i) q^{5} +(3.22797 + 5.25996i) q^{6} +(-2.37777 + 6.58378i) q^{7} +(5.48120 - 5.48120i) q^{8} +(-7.54172 + 4.91146i) q^{9} +(0.338264 + 10.2802i) q^{10} +(-17.6674 + 10.2003i) q^{11} +(-0.504923 - 0.478537i) q^{12} +(3.04150 - 3.04150i) q^{13} +(1.21935 - 14.3484i) q^{14} +(-14.9733 + 0.895203i) q^{15} +(-8.43689 + 14.6131i) q^{16} +(-11.8684 - 3.18014i) q^{17} +(12.3708 - 13.7748i) 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} +(-1.52525 - 5.69233i) q^{23} +(-20.4438 - 11.0831i) q^{24} +(-22.4255 - 11.0497i) q^{25} +(-4.42425 + 7.66303i) q^{26} +(20.5648 + 17.4954i) q^{27} +(0.285844 + 1.59784i) q^{28} -11.9728 q^{29} +(29.2761 - 9.75105i) q^{30} +(30.9809 - 17.8869i) q^{31} +(0.959081 - 3.57934i) q^{32} +(44.4213 + 42.0999i) q^{33} +25.2765 q^{34} +(29.3625 + 19.0485i) q^{35} +(-0.945077 + 1.86073i) q^{36} +(-4.70065 - 17.5430i) q^{37} +(11.8955 - 44.3945i) q^{38} +(-11.3442 - 6.14996i) q^{39} +(-20.4724 - 32.9099i) q^{40} +6.29801 q^{41} +(-42.3058 + 8.74526i) q^{42} +(8.41810 + 8.41810i) q^{43} +(-2.36531 + 4.09685i) q^{44} +(15.3601 + 42.2974i) q^{45} +(6.06154 + 10.4989i) q^{46} +(-15.4905 - 57.8113i) q^{47} +(49.2302 + 11.7857i) q^{48} +(-37.6924 - 31.3094i) q^{49} +(50.4440 + 10.0164i) q^{50} +(0.988619 + 36.8481i) q^{51} +(0.258152 - 0.963437i) q^{52} +(-53.4531 - 14.3227i) q^{53} +(-50.1785 - 23.8152i) q^{54} +(29.6262 + 97.6057i) q^{55} +(23.0540 + 49.1201i) q^{56} +(65.1836 + 15.6049i) q^{57} +(23.7906 - 6.37467i) q^{58} +(-60.6100 + 34.9932i) q^{59} +(-2.90314 + 1.91583i) q^{60} +(-80.4746 - 46.4620i) q^{61} +(-52.0374 + 52.0374i) q^{62} +(-14.4035 - 61.3314i) q^{63} -59.8721i q^{64} +(-11.3600 - 18.2616i) q^{65} +(-110.683 - 60.0038i) q^{66} +(-21.9700 - 5.88684i) q^{67} +(-2.75214 + 0.737433i) q^{68} +(-15.0682 + 9.24715i) q^{69} +(-68.4870 - 22.2169i) q^{70} -27.7403i q^{71} +(-14.4170 + 68.2584i) q^{72} +(-29.0508 - 7.78414i) q^{73} +(18.6809 + 32.3563i) q^{74} +(-12.6289 + 73.9291i) q^{75} +5.18078i q^{76} +(-25.1475 - 140.572i) q^{77} +(25.8161 + 6.18033i) q^{78} +(110.523 + 63.8104i) q^{79} +(61.5875 + 57.6636i) q^{80} +(32.7552 - 74.0817i) q^{81} +(-12.5145 + 3.35326i) 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} +(10.2235 + 34.4326i) q^{87} +(-40.9289 + 152.749i) q^{88} +(74.4534 + 42.9857i) q^{89} +(-53.0419 - 75.8691i) q^{90} +(12.7926 + 27.2566i) q^{91} +(-0.966290 - 0.966290i) q^{92} +(-77.8955 - 73.8249i) q^{93} +(61.5611 + 106.627i) q^{94} +(81.5453 + 76.3499i) q^{95} +(-11.1128 + 0.298152i) q^{96} +(-0.194287 - 0.194287i) q^{97} +(91.5672 + 42.1450i) 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

L-functions

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