LMFDB - Embedded newform 273.3.w.c.233.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,3,Mod(116,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("273.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	273.w (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.43871121704$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 16 x^{14} - 176 x^{13} + 344 x^{12} + 4576 x^{11} + 11040 x^{10} - 37664 x^{9} + \cdots + 97900608 $ x^16 - 16x^14 - 176x^13 + 344x^12 + 4576x^11 + 11040x^10 - 37664x^9 - 313120x^8 - 230912x^7 + 2040576x^6 + 9332224x^5 + 33838912x^4 + 73579264x^3 + 95390464x^2 + 117266688x + 97900608
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			233.1
Root			$-2.73864 + 0.330355i$ of defining polynomial
Character	$\chi$	$=$	273.233
Dual form			273.3.w.c.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70956 + 2.96105i) q^{2} +(-2.79279 - 1.09560i) q^{3} +(-3.84521 - 6.66010i) q^{4} +(3.81256 - 6.60355i) q^{5} +(8.01856 - 6.39660i) q^{6} +(-4.11804 - 5.66055i) q^{7} +12.6180 q^{8} +(6.59934 + 6.11953i) q^{9} +O(q^{10})$	\(q+(-1.70956 + 2.96105i) q^{2} +(-2.79279 - 1.09560i) q^{3} +(-3.84521 - 6.66010i) q^{4} +(3.81256 - 6.60355i) q^{5} +(8.01856 - 6.39660i) q^{6} +(-4.11804 - 5.66055i) q^{7} +12.6180 q^{8} +(6.59934 + 6.11953i) q^{9} +(13.0356 + 22.5784i) q^{10} +(-1.31613 - 2.27960i) q^{11} +(3.44209 + 22.8130i) q^{12} -13.0000 q^{13} +(23.8012 - 2.51665i) q^{14} +(-17.8825 + 14.2653i) q^{15} +(-6.19042 + 10.7221i) q^{16} +(-23.8012 + 13.7416i) q^{17} +(-29.4022 + 9.07925i) q^{18} +(1.27488 + 0.736052i) q^{19} -58.6404 q^{20} +(5.29914 + 20.3204i) q^{21} +9.00000 q^{22} +(28.1602 + 16.2583i) q^{23} +(-35.2394 - 13.8242i) q^{24} +(-16.5712 - 28.7022i) q^{25} +(22.2243 - 38.4936i) q^{26} +(-11.7260 - 24.3208i) q^{27} +(-21.8651 + 49.1925i) q^{28} +38.7082i q^{29} +(-11.6690 - 77.3384i) q^{30} +(13.6290 - 7.86870i) q^{31} +(4.07018 + 7.04976i) q^{32} +(1.17815 + 7.80838i) q^{33} -93.9687i q^{34} +(-53.0800 + 5.61249i) q^{35} +(15.3808 - 67.4831i) q^{36} +(5.09952 + 2.94421i) q^{37} +(-4.35897 + 2.51665i) q^{38} +(36.3063 + 14.2427i) q^{39} +(48.1069 - 83.3235i) q^{40} -47.3245 q^{41} +(-69.2289 - 19.0480i) q^{42} -12.6904 q^{43} +(-10.1216 + 17.5311i) q^{44} +(65.5710 - 20.2480i) q^{45} +(-96.2831 + 55.5891i) q^{46} +(11.4237 - 19.7864i) q^{47} +(29.0356 - 23.1624i) q^{48} +(-15.0835 + 46.6207i) q^{49} +113.318 q^{50} +(81.5270 - 12.3010i) q^{51} +(49.9877 + 86.5812i) q^{52} +(-78.1152 + 45.0998i) q^{53} +(92.0614 + 6.85650i) q^{54} -20.0712 q^{55} +(-51.9614 - 71.4247i) q^{56} +(-2.75405 - 3.45239i) q^{57} +(-114.617 - 66.1741i) q^{58} +(-18.1401 - 31.4196i) q^{59} +(163.770 + 64.2461i) q^{60} +(32.6069 - 56.4768i) q^{61} +53.8081i q^{62} +(7.46356 - 62.5563i) q^{63} -77.3562 q^{64} +(-49.5633 + 85.8461i) q^{65} +(-25.1351 - 9.86036i) q^{66} +(-8.13479 + 4.69662i) q^{67} +(183.041 + 105.679i) q^{68} +(-60.8329 - 76.2581i) q^{69} +(74.1247 - 166.767i) q^{70} +94.6770 q^{71} +(83.2705 + 77.2162i) q^{72} +(-92.0638 + 53.1531i) q^{73} +(-17.4359 + 10.0666i) q^{74} +(14.8340 + 98.3147i) q^{75} -11.3211i q^{76} +(-7.48391 + 16.8375i) q^{77} +(-104.241 + 83.1558i) q^{78} +(-18.4521 + 31.9599i) q^{79} +(47.2027 + 81.7574i) q^{80} +(6.10263 + 80.7698i) q^{81} +(80.9042 - 140.130i) q^{82} -11.2598 q^{83} +(114.960 - 113.429i) q^{84} +209.563i q^{85} +(21.6951 - 37.5769i) q^{86} +(42.4085 - 108.104i) q^{87} +(-16.6069 - 28.7639i) q^{88} +(-77.0661 + 133.482i) q^{89} +(-52.1425 + 228.774i) q^{90} +(53.5345 + 73.5871i) q^{91} -250.066i q^{92} +(-46.6838 + 7.04377i) q^{93} +(39.0589 + 67.6521i) q^{94} +(9.72111 - 5.61249i) q^{95} +(-3.64347 - 24.1478i) q^{96} -22.6422i q^{97} +(-112.260 - 124.364i) q^{98} +(5.26450 - 23.0979i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) $ 16 * q - 24 * q^4 - 16 * q^9	$ 16 q - 24 q^{4} - 16 q^{9} + 96 q^{10} - 88 q^{12} - 208 q^{13} - 24 q^{16} + 144 q^{22} - 40 q^{25} + 264 q^{30} + 96 q^{36} + 432 q^{40} - 448 q^{42} - 128 q^{43} + 352 q^{48} - 504 q^{49} + 280 q^{51} + 312 q^{52} - 96 q^{55} + 184 q^{61} - 112 q^{64} - 448 q^{69} - 528 q^{75} + 80 q^{79} + 584 q^{81} + 544 q^{82} - 448 q^{87} + 72 q^{88} - 384 q^{90} - 88 q^{94}+O(q^{100}) $ 16 * q - 24 * q^4 - 16 * q^9 + 96 * q^10 - 88 * q^12 - 208 * q^13 - 24 * q^16 + 144 * q^22 - 40 * q^25 + 264 * q^30 + 96 * q^36 + 432 * q^40 - 448 * q^42 - 128 * q^43 + 352 * q^48 - 504 * q^49 + 280 * q^51 + 312 * q^52 - 96 * q^55 + 184 * q^61 - 112 * q^64 - 448 * q^69 - 528 * q^75 + 80 * q^79 + 584 * q^81 + 544 * q^82 - 448 * q^87 + 72 * q^88 - 384 * q^90 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.70956	+	2.96105i	−0.854781	+	1.48052i	0.0220666	+	0.999757i	$0.492975\pi$
$2$	−1.70956	+	2.96105i	−0.854781	+	1.48052i	−0.876848	+	0.480768i	$0.840358\pi$
$3$	−2.79279	−	1.09560i	−0.930930	−	0.365198i
$3$	−2.79279	−	1.09560i	−0.930930	−	0.365198i
$4$	−3.84521	−	6.66010i	−0.961302	−	1.66502i
$5$	3.81256	−	6.60355i	0.762512	−	1.32071i	−0.179040	−	0.983842i	$-0.557299\pi$
$5$	3.81256	−	6.60355i	0.762512	−	1.32071i	0.941552	−	0.336868i	$-0.109368\pi$
$6$	8.01856	−	6.39660i	1.33643	−	1.06610i
$7$	−4.11804	−	5.66055i	−0.588291	−	0.808649i
$7$	−4.11804	−	5.66055i	−0.588291	−	0.808649i
$8$	12.6180			1.57725
$9$	6.59934	+	6.11953i	0.733260	+	0.679948i
$10$	13.0356	+	22.5784i	1.30356	+	2.25784i
$11$	−1.31613	−	2.27960i	−0.119648	−	0.207236i	0.799980	−	0.600026i	$-0.204843\pi$
$11$	−1.31613	−	2.27960i	−0.119648	−	0.207236i	−0.919628	+	0.392790i	$0.871510\pi$
$12$	3.44209	+	22.8130i	0.286840	+	1.90109i
$13$	−13.0000			−1.00000
$13$	−13.0000			−1.00000
$14$	23.8012	−	2.51665i	1.70009	−	0.179761i
$15$	−17.8825	+	14.2653i	−1.19217	+	0.951020i
$16$	−6.19042	+	10.7221i	−0.386901	+	0.670132i
$17$	−23.8012	+	13.7416i	−1.40007	+	0.808331i	−0.994399	−	0.105688i	$-0.966295\pi$
$17$	−23.8012	+	13.7416i	−1.40007	+	0.808331i	−0.405671	+	0.914019i	$0.632962\pi$
$18$	−29.4022	+	9.07925i	−1.63346	+	0.504403i
$19$	1.27488	+	0.736052i	0.0670989	+	0.0387396i	0.533174	−	0.846006i	$-0.320999\pi$
$19$	1.27488	+	0.736052i	0.0670989	+	0.0387396i	−0.466075	+	0.884745i	$0.654332\pi$
$20$	−58.6404			−2.93202
$21$	5.29914	+	20.3204i	0.252340	+	0.967639i
$22$	9.00000			0.409091
$23$	28.1602	+	16.2583i	1.22436	+	0.706882i	0.965843	−	0.259126i	$-0.0834346\pi$
$23$	28.1602	+	16.2583i	1.22436	+	0.706882i	0.258512	+	0.966008i	$0.416768\pi$
$24$	−35.2394	−	13.8242i	−1.46831	−	0.576009i
$25$	−16.5712	−	28.7022i	−0.662850	−	1.14809i
$26$	22.2243	−	38.4936i	0.854781	−	1.48052i
$27$	−11.7260	−	24.3208i	−0.434298	−	0.900769i
$28$	−21.8651	+	49.1925i	−0.780895	+	1.75687i
$29$			38.7082i			1.33477i	0.744715	+	0.667383i	$0.232586\pi$
$29$			38.7082i			1.33477i	−0.744715	+	0.667383i	$0.767414\pi$
$30$	−11.6690	−	77.3384i	−0.388967	−	2.57795i
$31$	13.6290	−	7.86870i	0.439645	−	0.253829i	−0.263802	−	0.964577i	$-0.584977\pi$
$31$	13.6290	−	7.86870i	0.439645	−	0.253829i	0.703447	+	0.710748i	$0.251643\pi$
$32$	4.07018	+	7.04976i	0.127193	+	0.220305i
$33$	1.17815	+	7.80838i	0.0357014	+	0.236617i
$34$		−	93.9687i		−	2.76378i
$35$	−53.0800	+	5.61249i	−1.51657	+	0.160357i
$36$	15.3808	−	67.4831i	0.427245	−	1.87453i
$37$	5.09952	+	2.94421i	0.137825	+	0.0795732i	0.567327	−	0.823493i	$-0.307978\pi$
$37$	5.09952	+	2.94421i	0.137825	+	0.0795732i	−0.429502	+	0.903066i	$0.641311\pi$
$38$	−4.35897	+	2.51665i	−0.114710	+	0.0662277i
$39$	36.3063	+	14.2427i	0.930930	+	0.365198i
$40$	48.1069	−	83.3235i	1.20267	−	2.08309i
$41$	−47.3245			−1.15426			−0.577128	−	0.816654i	$-0.695827\pi$
$41$	−47.3245			−1.15426			−0.577128	+	0.816654i	$0.695827\pi$
$42$	−69.2289	−	19.0480i	−1.64831	−	0.453524i
$43$	−12.6904			−0.295126			−0.147563	−	0.989053i	$-0.547143\pi$
$43$	−12.6904			−0.295126			−0.147563	+	0.989053i	$0.547143\pi$
$44$	−10.1216	+	17.5311i	−0.230035	+	0.398433i
$45$	65.5710	−	20.2480i	1.45713	−	0.449955i
$46$	−96.2831	+	55.5891i	−2.09311	+	1.20846i
$47$	11.4237	−	19.7864i	0.243057	−	0.420987i	−0.718527	−	0.695499i	$-0.755183\pi$
$47$	11.4237	−	19.7864i	0.243057	−	0.420987i	0.961583	+	0.274513i	$0.0885165\pi$
$48$	29.0356	−	23.1624i	0.604909	−	0.482550i
$49$	−15.0835	+	46.6207i	−0.307827	+	0.951442i
$50$	113.318			2.26637
$51$	81.5270	−	12.3010i	1.59857	−	0.241196i
$52$	49.9877	+	86.5812i	0.961302	+	1.66502i
$53$	−78.1152	+	45.0998i	−1.47387	+	0.850940i	−0.999567	−	0.0294208i	$-0.990634\pi$
$53$	−78.1152	+	45.0998i	−1.47387	+	0.850940i	−0.474304	+	0.880361i	$0.657300\pi$
$54$	92.0614	+	6.85650i	1.70484	+	0.126972i
$55$	−20.0712			−0.364932
$56$	−51.9614	−	71.4247i	−0.927881	−	1.27544i
$57$	−2.75405	−	3.45239i	−0.0483167	−	0.0605682i
$58$	−114.617	−	66.1741i	−1.97615	−	1.14093i
$59$	−18.1401	−	31.4196i	−0.307460	−	0.532536i	0.670346	−	0.742048i	$-0.266146\pi$
$59$	−18.1401	−	31.4196i	−0.307460	−	0.532536i	−0.977806	+	0.209513i	$0.932812\pi$
$60$	163.770	+	64.2461i	2.72950	+	1.07077i
$61$	32.6069	−	56.4768i	0.534539	−	0.925848i	−0.464647	−	0.885496i	$-0.653819\pi$
$61$	32.6069	−	56.4768i	0.534539	−	0.925848i	0.999186	−	0.0403523i	$-0.0128480\pi$
$62$			53.8081i			0.867873i
$63$	7.46356	−	62.5563i	0.118469	−	0.992958i
$64$	−77.3562			−1.20869
$65$	−49.5633	+	85.8461i	−0.762512	+	1.32071i
$66$	−25.1351	−	9.86036i	−0.380835	−	0.149399i
$67$	−8.13479	+	4.69662i	−0.121415	+	0.0700989i	−0.559477	−	0.828846i	$-0.688998\pi$
$67$	−8.13479	+	4.69662i	−0.121415	+	0.0700989i	0.438063	+	0.898944i	$0.355665\pi$
$68$	183.041	+	105.679i	2.69178	+	1.55410i
$69$	−60.8329	−	76.2581i	−0.881636	−	1.10519i
$70$	74.1247	−	166.767i	1.05892	−	2.38239i
$71$	94.6770			1.33348			0.666739	−	0.745291i	$-0.267689\pi$
$71$	94.6770			1.33348			0.666739	+	0.745291i	$0.267689\pi$
$72$	83.2705	+	77.2162i	1.15653	+	1.07245i
$73$	−92.0638	+	53.1531i	−1.26115	+	0.728124i	−0.973297	−	0.229551i	$-0.926274\pi$
$73$	−92.0638	+	53.1531i	−1.26115	+	0.728124i	−0.287851	+	0.957675i	$0.592941\pi$
$74$	−17.4359	+	10.0666i	−0.235620	+	0.136035i
$75$	14.8340	+	98.3147i	0.197786	+	1.31086i
$76$		−	11.3211i		−	0.148962i
$77$	−7.48391	+	16.8375i	−0.0971936	+	0.218668i
$78$	−104.241	+	83.1558i	−1.33643	+	1.06610i
$79$	−18.4521	+	31.9599i	−0.233571	+	0.404556i	−0.958856	−	0.283892i	$-0.908374\pi$
$79$	−18.4521	+	31.9599i	−0.233571	+	0.404556i	0.725286	+	0.688448i	$0.241708\pi$
$80$	47.2027	+	81.7574i	0.590033	+	1.02197i
$81$	6.10263	+	80.7698i	0.0753411	+	0.997158i
$82$	80.9042	−	140.130i	0.986636	−	1.70890i
$83$	−11.2598			−0.135660			−0.0678302	−	0.997697i	$-0.521608\pi$
$83$	−11.2598			−0.135660			−0.0678302	+	0.997697i	$0.521608\pi$
$84$	114.960	−	113.429i	1.36857	−	1.35035i
$85$			209.563i			2.46545i
$86$	21.6951	−	37.5769i	0.252268	−	0.436941i
$87$	42.4085	−	108.104i	0.487455	−	1.24257i
$88$	−16.6069	−	28.7639i	−0.188714	−	0.326863i
$89$	−77.0661	+	133.482i	−0.865912	+	1.49980i	0.000227621		1.00000i	$0.499928\pi$
$89$	−77.0661	+	133.482i	−0.865912	+	1.49980i	−0.866139	+	0.499803i	$0.833406\pi$
$90$	−52.1425	+	228.774i	−0.579361	+	2.54194i
$91$	53.5345	+	73.5871i	0.588291	+	0.808649i
$92$		−	250.066i		−	2.71811i
$93$	−46.6838	+	7.04377i	−0.501976	+	0.0757394i
$94$	39.0589	+	67.6521i	0.415521	+	0.719703i
$95$	9.72111	−	5.61249i	0.102327	−	0.0590788i
$96$	−3.64347	−	24.1478i	−0.0379528	−	0.251539i
$97$		−	22.6422i		−	0.233425i	−0.993166	−	0.116712i	$-0.962764\pi$
$97$		−	22.6422i		−	0.233425i	0.993166	−	0.116712i	$-0.0372355\pi$
$98$	−112.260	−	124.364i	−1.14551	−	1.26902i
$99$	5.26450	−	23.0979i	0.0531768	−	0.233312i
$100$	−127.440	+	220.732i	−1.27440	+	2.20732i
$101$	−23.4549	+	13.5417i	−0.232227	+	0.134076i	−0.611599	−	0.791168i	$-0.709473\pi$
$101$	−23.4549	+	13.5417i	−0.232227	+	0.134076i	0.379372	+	0.925244i	$0.376140\pi$
$102$	−102.952	+	262.435i	−1.00933	+	2.57289i
$103$	−53.9644	+	93.4690i	−0.523926	+	0.907466i	0.475686	+	0.879615i	$0.342200\pi$
$103$	−53.9644	+	93.4690i	−0.523926	+	0.907466i	−0.999612	+	0.0278513i	$0.991134\pi$
$104$	−164.034			−1.57725
$105$	154.390	+	42.4797i	1.47038	+	0.404568i
$106$		−	308.404i		−	2.90947i
$107$	−12.7306	−	7.35002i	−0.118978	−	0.0686918i	0.439330	−	0.898326i	$-0.355216\pi$
$107$	−12.7306	−	7.35002i	−0.118978	−	0.0686918i	−0.558308	+	0.829634i	$0.688549\pi$
$108$	−116.890	+	171.615i	−1.08231	+	1.58903i
$109$	125.211	−	72.2904i	1.14872	−	0.663215i	0.200146	−	0.979766i	$-0.435858\pi$
$109$	125.211	−	72.2904i	1.14872	−	0.663215i	0.948575	+	0.316551i	$0.102525\pi$
$110$	34.3131	−	59.4319i	0.311937	−	0.540290i
$111$	−11.0162	−	13.8096i	−0.0992452	−	0.124410i
$112$	86.1854	−	9.11293i	0.769512	−	0.0813655i
$113$		−	29.8000i		−	0.263717i	−0.991269	−	0.131858i	$-0.957906\pi$
$113$		−	29.8000i		−	0.263717i	0.991269	−	0.131858i	$-0.0420944\pi$
$114$	14.9309	−	2.25281i	0.130973	−	0.0197615i
$115$	214.725	−	123.971i	1.86717	−	1.07801i
$116$	257.800	−	148.841i	2.22242	−	1.28311i
$117$	−85.7914	−	79.5539i	−0.733260	−	0.679948i
$118$	124.047			1.05124
$119$	175.799	+	78.1392i	1.47730	+	0.656632i
$120$	−225.641	+	179.999i	−1.88034	+	1.50000i
$121$	57.0356	−	98.7886i	0.471369	−	0.816435i
$122$	111.487	+	193.101i	0.913828	+	1.58280i
$123$	132.167	+	51.8485i	1.07453	+	0.421532i
$124$	−104.813	−	60.5136i	−0.845263	−	0.488013i
$125$	−62.0875			−0.496700
$126$	172.473	+	129.044i	1.36883	+	1.02416i
$127$	−35.1179			−0.276519			−0.138259	−	0.990396i	$-0.544151\pi$
$127$	−35.1179			−0.276519			−0.138259	+	0.990396i	$0.544151\pi$
$128$	115.965	−	200.857i	0.905973	−	1.56919i
$129$	35.4417	+	13.9036i	0.274742	+	0.107780i
$130$	−169.463	−	293.519i	−1.30356	−	2.25784i
$131$	−127.067	−	73.3622i	−0.969977	−	0.560017i	−0.0707481	−	0.997494i	$-0.522539\pi$
$131$	−127.067	−	73.3622i	−0.969977	−	0.560017i	−0.899229	+	0.437477i	$0.855872\pi$
$132$	47.4743	−	37.8714i	0.359654	−	0.286905i
$133$	−1.08354	−	10.2476i	−0.00814695	−	0.0770496i
$134$		−	32.1167i		−	0.239677i
$135$	−205.310	−	15.2910i	−1.52081	−	0.113266i
$136$	−300.323	+	173.392i	−2.20826	+	1.27494i
$137$	−46.2002	−	80.0212i	−0.337228	−	0.584096i	0.646682	−	0.762760i	$-0.276156\pi$
$137$	−46.2002	−	80.0212i	−0.337228	−	0.584096i	−0.983910	+	0.178664i	$0.942823\pi$
$138$	329.802	−	49.7613i	2.38987	−	0.360589i
$139$	203.118			1.46128			0.730640	−	0.682763i	$-0.239222\pi$
$139$	203.118			1.46128			0.730640	+	0.682763i	$0.239222\pi$
$140$	241.483	+	331.936i	1.72488	+	2.37097i
$141$	−53.5818	+	42.7435i	−0.380012	+	0.303145i
$142$	−161.856	+	280.343i	−1.13983	+	1.97425i
$143$	17.1096	+	29.6348i	0.119648	+	0.207236i
$144$	−106.467	+	32.8764i	−0.739354	+	0.228309i
$145$	255.612	+	147.577i	1.76284	+	1.01778i
$146$		−	363.474i		−	2.48955i
$147$	93.2025	−	113.676i	0.634031	−	0.773308i
$148$		−	45.2844i		−	0.305975i
$149$	−56.6732	+	98.1608i	−0.380357	+	0.658798i	−0.991113	−	0.133021i	$-0.957532\pi$
$149$	−56.6732	+	98.1608i	−0.380357	+	0.658798i	0.610756	+	0.791819i	$0.290866\pi$
$150$	−316.474	−	124.151i	−2.10983	−	0.827674i
$151$	−108.637	+	62.7217i	−0.719452	+	0.415376i	−0.814551	−	0.580092i	$-0.803017\pi$
$151$	−108.637	+	62.7217i	−0.719452	+	0.415376i	0.0950990	+	0.995468i	$0.469683\pi$
$152$	16.0864	+	9.28750i	0.105832	+	0.0611020i
$153$	−241.165	−	54.9665i	−1.57624	−	0.359258i
$154$	−37.0623	−	50.9449i	−0.240664	−	0.330811i
$155$		−	120.000i		−	0.774191i
$156$	−44.7471	−	296.569i	−0.286840	−	1.90109i
$157$	−72.7383	−	125.986i	−0.463302	−	0.802462i	0.535822	−	0.844331i	$-0.320002\pi$
$157$	−72.7383	−	125.986i	−0.463302	−	0.802462i	−0.999123	+	0.0418695i	$0.986669\pi$
$158$	−63.0900	−	109.275i	−0.399304	−	0.691614i
$159$	267.570	−	40.3717i	1.68283	−	0.253910i
$160$	62.0712			0.387945
$161$	−23.9339	−	226.354i	−0.148658	−	1.40593i
$162$	−249.596	−	120.011i	−1.54072	−	0.740807i
$163$	−210.900	−	121.763i	−1.29387	−	0.747014i	−0.314528	−	0.949248i	$-0.601846\pi$
$163$	−210.900	−	121.763i	−1.29387	−	0.747014i	−0.979337	+	0.202234i	$0.935180\pi$
$164$	181.972	+	315.186i	1.10959	+	1.92186i
$165$	56.0548	+	21.9900i	0.339726	+	0.133273i
$166$	19.2494	−	33.3409i	0.115960	−	0.200849i
$167$	−67.4361			−0.403809			−0.201905	−	0.979405i	$-0.564713\pi$
$167$	−67.4361			−0.403809			−0.201905	+	0.979405i	$0.564713\pi$
$168$	66.8645	+	256.403i	0.398003	+	1.52621i
$169$	169.000			1.00000
$170$	−620.527	−	358.261i	−3.65016	−	2.10742i
$171$	3.90907	+	12.6591i	0.0228601	+	0.0740300i
$172$	48.7973	+	84.5194i	0.283705	+	0.491392i
$173$	−39.2307	−	22.6499i	−0.226767	−	0.130924i	0.382313	−	0.924033i	$-0.375128\pi$
$173$	−39.2307	−	22.6499i	−0.226767	−	0.130924i	−0.609080	+	0.793109i	$0.708461\pi$
$174$	247.601	+	310.384i	1.42299	+	1.78382i
$175$	−94.2293	+	211.999i	−0.538453	+	1.21142i
$176$	32.5895			0.185167
$177$	16.2384	+	107.623i	0.0917421	+	0.608037i
$178$	−263.499	−	456.393i	−1.48033	−	2.56401i
$179$	−98.2143	+	56.7040i	−0.548683	+	0.316782i	−0.748591	−	0.663032i	$-0.769269\pi$
$179$	−98.2143	+	56.7040i	−0.548683	+	0.316782i	0.199908	+	0.979815i	$0.435936\pi$
$180$	−386.988	−	358.852i	−2.14993	−	1.99362i
$181$	108.047			0.596943			0.298471	−	0.954419i	$-0.403523\pi$
$181$	108.047			0.596943			0.298471	+	0.954419i	$0.403523\pi$
$182$	−309.416	+	32.7165i	−1.70009	+	0.179761i
$183$	−152.940	+	122.004i	−0.835737	+	0.666687i
$184$	355.325	+	205.147i	1.93111	+	1.11493i
$185$	38.8844	−	22.4499i	0.210186	−	0.121351i
$186$	58.9519	−	150.275i	0.316946	−	0.807929i
$187$	62.6507	+	36.1714i	0.335031	+	0.193430i
$188$	−175.706			−0.934604
$189$	−89.3806	+	166.530i	−0.472913	+	0.881109i
$190$			38.3796i			0.201998i
$191$	−99.9100	−	57.6831i	−0.523089	−	0.302006i	0.215108	−	0.976590i	$-0.430990\pi$
$191$	−99.9100	−	57.6831i	−0.523089	−	0.302006i	−0.738198	+	0.674584i	$0.764323\pi$
$192$	216.040	+	84.7511i	1.12521	+	0.441412i
$193$	−139.629	+	80.6149i	−0.723466	+	0.417694i	−0.816027	−	0.578013i	$-0.803828\pi$
$193$	−139.629	+	80.6149i	−0.723466	+	0.417694i	0.0925608	+	0.995707i	$0.470495\pi$
$194$	67.0446	+	38.7082i	0.345591	+	0.199527i
$195$	232.472	−	185.449i	1.19217	−	0.951020i
$196$	368.497	−	78.8083i	1.88009	−	0.402083i
$197$	5.26450			0.0267234			0.0133617	−	0.999911i	$-0.495747\pi$
$197$	5.26450			0.0267234			0.0133617	+	0.999911i	$0.495747\pi$
$198$	59.3941	+	55.0758i	0.299970	+	0.278161i
$199$	150.499	+	260.671i	0.756275	+	1.30991i	0.944738	+	0.327826i	$0.106316\pi$
$199$	150.499	+	260.671i	0.756275	+	1.30991i	−0.188463	+	0.982080i	$0.560351\pi$
$200$	−209.096	−	362.165i	−1.04548	−	1.81082i
$201$	27.8644	−	4.20424i	0.138629	−	0.0209166i
$202$		−	92.6015i		−	0.458423i
$203$	219.110	−	159.402i	1.07936	−	0.785231i
$204$	−395.414	−	495.678i	−1.93830	−	2.42979i
$205$	−180.427	+	312.510i	−0.880134	+	1.52444i
$206$	−184.511	−	319.582i	−0.895684	−	1.55137i
$207$	86.3455	+	279.621i	0.417128	+	1.35083i
$208$	80.4754	−	139.387i	0.386901	−	0.670132i
$209$		−	3.87495i		−	0.0185404i
$210$	−389.724	+	384.535i	−1.85583	+	1.83112i
$211$	38.9533			0.184613			0.0923065	−	0.995731i	$-0.470576\pi$
$211$	38.9533			0.184613			0.0923065	+	0.995731i	$0.470576\pi$
$212$	600.738	+	346.836i	2.83367	+	1.63602i
$213$	−264.413	−	103.728i	−1.24137	−	0.486984i
$214$	43.5276	−	25.1306i	0.203400	−	0.117433i
$215$	−48.3830	+	83.8018i	−0.225037	+	0.389776i
$216$	−147.959	−	306.879i	−0.684996	−	1.42074i
$217$	−100.666	−	44.7439i	−0.463898	−	0.206193i
$218$			494.340i			2.26761i
$219$	315.349	−	47.5806i	1.43995	−	0.217263i
$220$	77.1781	+	133.676i	0.350810	+	0.607620i
$221$	309.416	−	178.641i	1.40007	−	0.808331i
$222$	59.7237	−	9.01126i	0.269026	−	0.0405912i
$223$		−	102.696i		−	0.460522i	−0.973129	−	0.230261i	$-0.926042\pi$
$223$		−	102.696i		−	0.460522i	0.973129	−	0.230261i	$-0.0739580\pi$
$224$	23.1443	−	52.0706i	0.103323	−	0.232458i
$225$	66.2850	−	290.824i	0.294600	−	1.29255i
$226$	88.2392	+	50.9449i	0.390439	+	0.225420i
$227$	−62.7246	−	108.642i	−0.276320	−	0.478600i	0.694148	−	0.719833i	$-0.255782\pi$
$227$	−62.7246	−	108.642i	−0.276320	−	0.478600i	−0.970467	+	0.241233i	$0.922448\pi$
$228$	−12.4033	+	31.6174i	−0.0544006	+	0.138673i
$229$	−374.053	−	215.960i	−1.63342	−	0.943056i	−0.983028	−	0.183458i	$-0.941271\pi$
$229$	−374.053	−	215.960i	−1.63342	−	0.943056i	−0.650393	−	0.759598i	$-0.725396\pi$
$230$			847.747i			3.68586i
$231$	39.3480	−	38.8241i	0.170338	−	0.168070i
$232$			488.420i			2.10526i
$233$	116.689	+	67.3705i	0.500811	+	0.289144i	0.729049	−	0.684462i	$-0.239963\pi$
$233$	116.689	+	67.3705i	0.500811	+	0.289144i	−0.228237	+	0.973606i	$0.573296\pi$
$234$	382.229	−	118.030i	1.63346	−	0.504403i
$235$	−87.1069	−	150.874i	−0.370668	−	0.642015i
$236$	−139.505	+	241.630i	−0.591123	+	1.02386i
$237$	86.5479	−	69.0414i	0.365181	−	0.291314i
$238$	−531.914	+	386.966i	−2.23493	+	1.62591i
$239$	−219.958			−0.920326			−0.460163	−	0.887834i	$-0.652209\pi$
$239$	−219.958			−0.920326			−0.460163	+	0.887834i	$0.652209\pi$
$240$	−42.2541	−	280.046i	−0.176059	−	1.16686i
$241$	112.644	−	65.0348i	0.467401	−	0.269854i	−0.247750	−	0.968824i	$-0.579691\pi$
$241$	112.644	−	65.0348i	0.467401	−	0.269854i	0.715151	+	0.698970i	$0.246358\pi$
$242$	195.012	+	337.771i	0.805834	+	1.39575i
$243$	71.4476	−	232.259i	0.294023	−	0.955798i
$244$	−501.521			−2.05541
$245$	250.355	+	277.349i	1.02186	+	1.13204i
$246$	−379.474	+	302.716i	−1.54258	+	1.23055i
$247$	−16.5734	−	9.56867i	−0.0670989	−	0.0387396i
$248$	171.970	−	99.2872i	0.693429	−	0.400352i
$249$	31.4463	+	12.3362i	0.126290	+	0.0495430i
$250$	106.142	−	183.844i	0.424570	−	0.735377i
$251$		−	217.191i		−	0.865302i	−0.901562	−	0.432651i	$-0.857578\pi$
$251$		−	217.191i		−	0.865302i	0.901562	−	0.432651i	$-0.142422\pi$
$252$	−445.330	+	190.834i	−1.76718	+	0.757278i
$253$		−	85.5918i		−	0.338307i
$254$	60.0362	−	103.986i	0.236363	−	0.409393i
$255$	229.596	−	585.266i	0.900378	−	2.29516i
$256$	241.785	+	418.784i	0.944473	+	1.63587i
$257$	363.383	+	209.799i	1.41394	+	0.816340i	0.995757	−	0.0920216i	$-0.0293329\pi$
$257$	363.383	+	209.799i	1.41394	+	0.816340i	0.418185	+	0.908362i	$0.362666\pi$
$258$	−101.759	+	81.1755i	−0.394414	+	0.314634i
$259$	−4.33418	−	40.9904i	−0.0167343	−	0.158264i
$260$	762.325			2.93202
$261$	−236.876	+	255.449i	−0.907572	+	0.978731i
$262$	434.458	−	250.835i	1.65824	−	0.957384i
$263$	−296.339	+	171.091i	−1.12676	+	0.650537i	−0.943119	−	0.332456i	$-0.892123\pi$
$263$	−296.339	+	171.091i	−1.12676	+	0.650537i	−0.183644	+	0.982993i	$0.558789\pi$
$264$	14.8658	+	98.5260i	0.0563100	+	0.373205i
$265$			687.783i			2.59541i
$266$	32.1960	+	14.3105i	0.121038	+	0.0537988i
$267$	361.472	−	288.355i	1.35383	−	1.07998i
$268$	62.5599	+	36.1190i	0.233433	+	0.134772i
$269$	−71.7141	+	41.4042i	−0.266595	+	0.153919i	−0.627339	−	0.778746i	$-0.715856\pi$
$269$	−71.7141	+	41.4042i	−0.266595	+	0.153919i	0.360744	+	0.932665i	$0.382523\pi$
$270$	396.267	−	581.791i	1.46766	−	2.15478i
$271$	−451.032	−	260.403i	−1.66432	−	0.960897i	−0.970614	−	0.240642i	$-0.922642\pi$
$271$	−451.032	−	260.403i	−1.66432	−	0.960897i	−0.693709	−	0.720255i	$-0.744025\pi$
$272$		−	340.266i		−	1.25098i
$273$	−68.8888	−	264.165i	−0.252340	−	0.967639i
$274$	315.929			1.15302
$275$	−43.6197	+	75.5515i	−0.158617	+	0.274733i
$276$	−273.971	+	698.381i	−0.992648	+	2.53037i
$277$	−76.3685	−	132.274i	−0.275699	−	0.477524i	0.694612	−	0.719384i	$-0.255576\pi$
$277$	−76.3685	−	132.274i	−0.275699	−	0.477524i	−0.970311	+	0.241860i	$0.922243\pi$
$278$	−347.243	+	601.442i	−1.24907	+	2.16346i
$279$	138.095	+	31.4748i	0.494965	+	0.112813i
$280$	−669.763	+	70.8183i	−2.39201	+	0.252923i
$281$	−321.417			−1.14383			−0.571917	−	0.820312i	$-0.693800\pi$
$281$	−321.417			−1.14383			−0.571917	+	0.820312i	$0.693800\pi$
$282$	−34.9641	−	231.731i	−0.123986	−	0.821740i
$283$	27.7973	+	48.1463i	0.0982236	+	0.170128i	0.910949	−	0.412518i	$-0.135351\pi$
$283$	27.7973	+	48.1463i	0.0982236	+	0.170128i	−0.812726	+	0.582646i	$0.802017\pi$
$284$	−364.053	−	630.558i	−1.28188	−	2.22027i
$285$	−33.2980	+	5.02409i	−0.116835	+	0.0176284i
$286$	−117.000			−0.409091
$287$	194.884	+	267.882i	0.679038	+	0.933388i
$288$	−16.2807	+	71.4314i	−0.0565303	+	0.248026i
$289$	233.165	−	403.853i	0.806798	−	1.39741i
$290$	−873.968	+	504.586i	−3.01368	+	1.73995i
$291$	−24.8067	+	63.2348i	−0.0852463	+	0.217302i
$292$	708.009	+	408.769i	2.42469	+	1.39989i
$293$	506.781			1.72963			0.864813	−	0.502093i	$-0.167437\pi$
$293$	506.781			1.72963			0.864813	+	0.502093i	$0.167437\pi$
$294$	177.265	+	470.314i	0.602943	+	1.59971i
$295$	−276.641			−0.937767
$296$	64.3457	+	37.1500i	0.217384	+	0.125507i
$297$	−40.0086	+	58.7399i	−0.134709	+	0.197777i
$298$	−193.773	−	335.624i	−0.650244	−	1.12626i
$299$	−366.082	−	211.358i	−1.22436	−	0.706882i
$300$	597.746	−	476.836i	1.99249	−	1.58945i
$301$	52.2596	+	71.8347i	0.173620	+	0.238653i
$302$		−	428.907i		−	1.42022i
$303$	80.3408	−	12.1220i	0.265151	−	0.0400066i
$304$	−15.7841	+	9.11293i	−0.0519213	+	0.0299768i
$305$	−248.631	−	430.642i	−0.815185	−	1.41194i
$306$	575.044	−	620.131i	1.87923	−	2.02657i
$307$			199.468i			0.649734i	0.945760	+	0.324867i	$0.105319\pi$
$307$			199.468i			0.649734i	−0.945760	+	0.324867i	$0.894681\pi$
$308$	140.916	−	14.9000i	0.457520	−	0.0483766i
$309$	253.115	−	201.916i	0.819144	−	0.653451i
$310$	355.325	+	205.147i	1.14621	+	0.661764i
$311$	140.108	−	80.8915i	0.450509	−	0.260101i	−0.257536	−	0.966269i	$-0.582911\pi$
$311$	140.108	−	80.8915i	0.450509	−	0.260101i	0.708045	+	0.706167i	$0.249577\pi$
$312$	458.112	+	179.715i	1.46831	+	0.576009i
$313$	−195.142	+	337.997i	−0.623458	+	1.07986i	0.365378	+	0.930859i	$0.380940\pi$
$313$	−195.142	+	337.997i	−0.623458	+	1.07986i	−0.988837	+	0.149003i	$0.952394\pi$
$314$	497.403			1.58409
$315$	−384.639	−	287.786i	−1.22107	−	0.913606i
$316$	283.808			0.898128
$317$	−22.9875	+	39.8155i	−0.0725158	+	0.125601i	−0.900003	−	0.435883i	$-0.856436\pi$
$317$	−22.9875	+	39.8155i	−0.0725158	+	0.125601i	0.827488	+	0.561484i	$0.189769\pi$
$318$	−337.886	+	861.307i	−1.06253	+	2.70851i
$319$	88.2392	−	50.9449i	0.276612	−	0.159702i
$320$	−294.925	+	510.826i	−0.921642	+	1.59633i
$321$	27.5013	+	34.4747i	0.0856737	+	0.107398i
$322$	711.162	+	316.097i	2.20858	+	0.981668i
$323$	−40.4582			−0.125258
$324$	514.469	−	351.221i	1.58787	−	1.08401i
$325$	215.426	+	373.129i	0.662850	+	1.14809i
$326$	721.094	−	416.324i	2.21194	−	1.27707i
$327$	−428.888	+	64.7117i	−1.31158	+	0.197895i
$328$	−597.140			−1.82055
$329$	−159.045	+	16.8168i	−0.483419	+	0.0511150i
$330$	−160.942	+	128.388i	−0.487704	+	0.389054i
$331$	42.8290	+	24.7274i	0.129393	+	0.0747050i	0.563299	−	0.826253i	$-0.309532\pi$
$331$	42.8290	+	24.7274i	0.129393	+	0.0747050i	−0.433906	+	0.900958i	$0.642865\pi$
$332$	43.2963	+	74.9915i	0.130411	+	0.225878i
$333$	15.6363	+	50.6365i	0.0469558	+	0.152062i
$334$	115.286	−	199.682i	0.345168	−	0.597849i
$335$			71.6247i			0.213805i
$336$	−250.682	−	68.9738i	−0.746076	−	0.205279i
$337$	111.882			0.331994			0.165997	−	0.986126i	$-0.446916\pi$
$337$	111.882			0.331994			0.165997	+	0.986126i	$0.446916\pi$
$338$	−288.916	+	500.417i	−0.854781	+	1.48052i
$339$	−32.6487	+	83.2250i	−0.0963089	+	0.245502i
$340$	1395.71	−	805.814i	4.10503	−	2.37004i
$341$	−35.8749	−	20.7124i	−0.105205	−	0.0607402i
$342$	−44.1671	−	10.0666i	−0.129144	−	0.0294345i
$343$	326.013	−	106.605i	0.950475	−	0.310800i
$344$	−160.128			−0.465487
$345$	−735.503	+	110.975i	−2.13189	+	0.321665i
$346$	134.135	−	77.4428i	0.387673	−	0.223823i
$347$	−481.422	+	277.949i	−1.38738	+	0.801006i	−0.993020	−	0.117949i	$-0.962368\pi$
$347$	−481.422	+	277.949i	−1.38738	+	0.801006i	−0.394363	+	0.918955i	$0.629035\pi$
$348$	−883.052	+	133.237i	−2.53751	+	0.382865i
$349$			121.834i			0.349094i	0.984649	+	0.174547i	$0.0558461\pi$
$349$			121.834i			0.349094i	−0.984649	+	0.174547i	$0.944154\pi$
$350$	−466.649	−	641.444i	−1.33328	−	1.83270i
$351$	152.439	+	316.170i	0.434298	+	0.900769i
$352$	10.7137	−	18.5567i	0.0304368	−	0.0527180i
$353$	−177.017	−	306.603i	−0.501465	−	0.868564i	−0.999999	−	0.00169298i	$-0.999461\pi$
$353$	−177.017	−	306.603i	−0.501465	−	0.868564i	0.498533	−	0.866871i	$-0.333872\pi$
$354$	−346.436	−	135.905i	−0.978633	−	0.383912i
$355$	360.962	−	625.204i	1.01679	−	1.76114i
$356$	1185.34			3.32961
$357$	−405.361	−	410.831i	−1.13547	−	1.15079i
$358$		−	387.756i		−	1.08312i
$359$	230.318	−	398.922i	0.641554	−	1.11120i	−0.343532	−	0.939141i	$-0.611624\pi$
$359$	230.318	−	398.922i	0.641554	−	1.11120i	0.985086	−	0.172063i	$-0.0550431\pi$
$360$	827.375	−	255.489i	2.29826	−	0.709692i
$361$	−179.416	−	310.758i	−0.496998	−	0.860827i
$362$	−184.713	+	319.931i	−0.510256	+	0.883789i
$363$	−267.521	+	213.408i	−0.736972	+	0.587900i
$364$	284.246	−	639.502i	0.780895	−	1.75687i
$365$			810.597i			2.22081i
$366$	−99.7989	−	661.435i	−0.272675	−	1.80720i
$367$	−197.260	−	341.665i	−0.537494	−	0.930967i	−0.999038	−	0.0438500i	$-0.986038\pi$
$367$	−197.260	−	341.665i	−0.537494	−	0.930967i	0.461544	−	0.887117i	$-0.347296\pi$
$368$	−348.646	+	201.291i	−0.947408	+	0.546986i
$369$	−312.310	−	289.604i	−0.846370	−	0.784834i
$370$			153.518i			0.414914i
$371$	576.971	+	256.452i	1.55518	+	0.691245i
$372$	226.421	+	283.834i	0.608659	+	0.762994i
$373$	8.71374	−	15.0926i	0.0233612	−	0.0404629i	−0.854108	−	0.520095i	$-0.825897\pi$
$373$	8.71374	−	15.0926i	0.0233612	−	0.0404629i	0.877470	+	0.479632i	$0.159230\pi$
$374$	−214.211	+	123.675i	−0.572756	+	0.330681i
$375$	173.397	+	68.0228i	0.462393	+	0.181394i
$376$	144.144	−	249.664i	0.383361	−	0.664001i
$377$		−	503.207i		−	1.33477i
$378$	−340.301	−	549.353i	−0.900266	−	1.45331i
$379$		−	364.695i		−	0.962255i	−0.876651	−	0.481128i	$-0.840227\pi$
$379$		−	364.695i		−	0.962255i	0.876651	−	0.481128i	$-0.159773\pi$
$380$	−74.7594	−	43.1624i	−0.196735	−	0.113585i
$381$	98.0769	+	38.4750i	0.257420	+	0.100984i
$382$	341.605	−	197.226i	0.894254	−	0.516298i
$383$	189.775	−	328.701i	0.495497	−	0.858226i	−0.504489	−	0.863418i	$-0.668319\pi$
$383$	189.775	−	328.701i	0.495497	−	0.858226i	0.999987	+	0.00519153i	$0.00165252\pi$
$384$	−543.922	+	433.900i	−1.41646	+	1.12995i
$385$	82.6541	+	113.614i	0.214686	+	0.295102i
$386$		−	551.265i		−	1.42815i
$387$	−83.7484	−	77.6594i	−0.216404	−	0.200670i
$388$	−150.799	+	87.0639i	−0.388657	+	0.224391i
$389$	3.35580	−	1.93747i	0.00862675	−	0.00498065i	−0.495680	−	0.868505i	$-0.665081\pi$
$389$	3.35580	−	1.93747i	0.00862675	−	0.00498065i	0.504307	+	0.863524i	$0.331748\pi$
$390$	151.697	+	1005.40i	0.388967	+	2.57795i
$391$	−893.661			−2.28558
$392$	−190.324	+	588.259i	−0.485521	+	1.50066i
$393$	274.496	+	344.099i	0.698464	+	0.875570i
$394$	−9.00000	+	15.5885i	−0.0228426	+	0.0395646i
$395$	140.699	+	243.698i	0.356201	+	0.616958i
$396$	−174.077	+	53.7542i	−0.439590	+	0.135743i
$397$	566.438	+	327.033i	1.42680	+	0.823761i	0.996867	−	0.0791018i	$-0.0252052\pi$
$397$	566.438	+	327.033i	1.42680	+	0.823761i	0.429929	+	0.902863i	$0.358539\pi$
$398$	−1029.15			−2.58580
$399$	−8.20111	+	29.8065i	−0.0205542	+	0.0747030i
$400$	410.332			1.02583
$401$	−49.3294	+	85.4410i	−0.123016	+	0.213070i	−0.920956	−	0.389667i	$-0.872590\pi$
$401$	−49.3294	+	85.4410i	−0.123016	+	0.213070i	0.797940	+	0.602737i	$0.205923\pi$
$402$	−35.1869	+	89.6951i	−0.0875296	+	0.223122i
$403$	−177.177	+	102.293i	−0.439645	+	0.253829i
$404$	180.378	+	104.141i	0.446480	+	0.257775i
$405$	556.634	+	267.641i	1.37440	+	0.660841i
$406$	97.4152	+	921.302i	0.239939	+	2.26922i
$407$		−	15.4998i		−	0.0380830i
$408$	1028.71	−	155.214i	2.52134	−	0.380426i
$409$	−337.204	+	194.685i	−0.824460	+	0.476002i	−0.851952	−	0.523620i	$-0.824581\pi$
$409$	−337.204	+	194.685i	−0.824460	+	0.476002i	0.0274923	+	0.999622i	$0.491248\pi$
$410$	−616.904	−	1068.51i	−1.50464	−	2.60612i
$411$	41.3567	+	274.099i	0.100625	+	0.666907i
$412$	830.017			2.01460
$413$	−103.150	+	232.070i	−0.249759	+	0.561913i
$414$	−975.585	−	222.356i	−2.35648	−	0.537093i
$415$	−42.9288	+	74.3548i	−0.103443	+	0.179168i
$416$	−52.9123	−	91.6469i	−0.127193	−	0.220305i
$417$	−567.265	−	222.535i	−1.36035	−	0.533657i
$418$	11.4739	+	6.62447i	0.0274496	+	0.0158480i
$419$		−	101.383i		−	0.241965i	−0.992655	−	0.120983i	$-0.961395\pi$
$419$		−	101.383i		−	0.241965i	0.992655	−	0.120983i	$-0.0386045\pi$
$420$	−310.744	−	1191.60i	−0.739866	−	2.83713i
$421$		−	89.7621i		−	0.213212i	−0.994301	−	0.106606i	$-0.966002\pi$
$421$		−	89.7621i		−	0.213212i	0.994301	−	0.106606i	$-0.0339983\pi$
$422$	−66.5932	+	115.343i	−0.157804	+	0.273324i
$423$	196.472	−	60.6695i	0.464473	−	0.143427i
$424$	−985.657	+	569.069i	−2.32466	+	1.34214i
$425$	788.831	+	455.432i	1.85607	+	1.07160i
$426$	759.173	−	605.611i	1.78210	−	1.42162i
$427$	−453.966	+	48.0007i	−1.06315	+	0.112414i
$428$			113.049i			0.264134i
$429$	−15.3159	−	101.509i	−0.0357014	−	0.236617i
$430$	−165.427	−	286.529i	−0.384715	−	0.666346i
$431$	323.225	+	559.842i	0.749941	+	1.29894i	0.947850	+	0.318716i	$0.103252\pi$
$431$	323.225	+	559.842i	0.749941	+	1.29894i	−0.197909	+	0.980220i	$0.563415\pi$
$432$	333.359	+	24.8278i	0.771665	+	0.0574717i
$433$	−571.521			−1.31991			−0.659955	−	0.751305i	$-0.729425\pi$
$433$	−571.521			−1.31991			−0.659955	+	0.751305i	$0.729425\pi$
$434$	304.583	−	221.584i	0.701805	−	0.510562i
$435$	−552.184	−	692.200i	−1.26939	−	1.59126i
$436$	−962.922	−	555.943i	−2.20854	−	1.27510i
$437$	23.9339	+	41.4547i	0.0547686	+	0.0948620i
$438$	−398.220	+	1015.11i	−0.909179	+	2.31759i
$439$	−192.296	+	333.066i	−0.438032	+	0.758694i	−0.997538	−	0.0701329i	$-0.977658\pi$
$439$	−192.296	+	333.066i	−0.438032	+	0.758694i	0.559506	+	0.828826i	$0.310991\pi$
$440$	−253.259			−0.575588
$441$	−384.838	+	215.361i	−0.872649	+	0.488348i
$442$			1221.59i			2.76378i
$443$	429.496	+	247.970i	0.969517	+	0.559751i	0.899089	−	0.437766i	$-0.144230\pi$
$443$	429.496	+	247.970i	0.969517	+	0.559751i	0.0704282	+	0.997517i	$0.477563\pi$
$444$	−49.6133	+	126.470i	−0.111742	+	0.284842i
$445$	587.639	+	1017.82i	1.32054	+	2.28724i
$446$	304.089	+	175.566i	0.681814	+	0.393646i
$447$	265.821	−	212.052i	0.594677	−	0.474388i
$448$	318.556	+	437.878i	0.711062	+	0.977407i
$449$	−568.342			−1.26580			−0.632898	−	0.774235i	$-0.718135\pi$
$449$	−568.342			−1.26580			−0.632898	+	0.774235i	$0.718135\pi$
$450$	747.826	+	693.455i	1.66184	+	1.54101i
$451$	62.2850	+	107.881i	0.138104	+	0.239203i
$452$	−198.471	+	114.587i	−0.439094	+	0.253511i
$453$	372.119	−	56.1461i	0.821454	−	0.123943i
$454$	428.926			0.944771
$455$	690.039	−	72.9623i	1.51657	−	0.160357i
$456$	−34.7506	−	43.5622i	−0.0762075	−	0.0955312i
$457$	178.846	+	103.257i	0.391349	+	0.225945i	0.682744	−	0.730657i	$-0.260786\pi$
$457$	178.846	+	103.257i	0.391349	+	0.225945i	−0.291396	+	0.956603i	$0.594120\pi$
$458$	1278.93	−	738.393i	2.79243	−	1.61221i
$459$	613.301	+	417.729i	1.33617	+	0.910084i
$460$	−1651.32	−	953.391i	−3.58983	−	2.07259i
$461$	−223.957			−0.485807			−0.242903	−	0.970050i	$-0.578100\pi$
$461$	−223.957			−0.485807			−0.242903	+	0.970050i	$0.578100\pi$
$462$	47.6923	+	182.884i	0.103230	+	0.395852i
$463$		−	779.264i		−	1.68307i	−0.540199	−	0.841537i	$-0.681651\pi$
$463$		−	779.264i		−	1.68307i	0.540199	−	0.841537i	$-0.318349\pi$
$464$	−415.034	−	239.620i	−0.894470	−	0.516422i
$465$	−131.471	+	335.134i	−0.282733	+	0.720717i
$466$	−398.975	+	230.348i	−0.856168	+	0.494309i
$467$	−125.682	−	72.5624i	−0.269126	−	0.155380i	0.359364	−	0.933197i	$-0.382994\pi$
$467$	−125.682	−	72.5624i	−0.269126	−	0.155380i	−0.628490	+	0.777817i	$0.716327\pi$
$468$	−199.951	+	877.281i	−0.427245	+	1.87453i
$469$	60.0848	+	26.7065i	0.128113	+	0.0569435i
$470$	595.659			1.26736
$471$	65.1126	+	431.545i	0.138243	+	0.916232i
$472$	−228.892	−	396.452i	−0.484940	−	0.839941i
$473$	16.7022	+	28.9290i	0.0353112	+	0.0611608i
$474$	56.4758	+	374.303i	0.119147	+	0.789669i
$475$		−	48.7892i		−	0.102714i
$476$	−155.570	−	1471.30i	−0.326828	−	3.09097i
$477$	−791.499	−	180.399i	−1.65933	−	0.378196i
$478$	376.032	−	651.306i	0.786677	−	1.36257i
$479$	−315.482	−	546.431i	−0.658627	−	1.14077i	−0.980971	−	0.194153i	$-0.937804\pi$
$479$	−315.482	−	546.431i	−0.658627	−	1.14077i	0.322345	−	0.946622i	$-0.395529\pi$
$480$	−173.352	−	68.0050i	−0.361150	−	0.141677i
$481$	−66.2937	−	38.2747i	−0.137825	−	0.0795732i
$482$			444.724i			0.922664i
$483$	−181.150	+	658.381i	−0.375052	+	1.36311i
$484$	−877.255			−1.81251
$485$	−149.519	−	86.3247i	−0.308286	−	0.177989i
$486$	565.586	+	608.621i	1.16376	+	1.25231i
$487$	−398.367	+	229.997i	−0.818002	+	0.472273i	−0.849727	−	0.527223i	$-0.823233\pi$
$487$	−398.367	+	229.997i	−0.818002	+	0.472273i	0.0317252	+	0.999497i	$0.489900\pi$
$488$	411.433	−	712.623i	0.843101	−	1.46029i
$489$	455.596	+	571.120i	0.931690	+	1.16793i
$490$	−1249.24	+	267.168i	−2.54947	+	0.545240i
$491$		−	589.214i		−	1.20003i	−0.799989	−	0.600015i	$-0.795161\pi$
$491$		−	589.214i		−	1.20003i	0.799989	−	0.600015i	$-0.204839\pi$
$492$	−162.895	−	1079.61i	−0.331087	−	2.19434i
$493$	−531.914	−	921.302i	−1.07893	−	1.86877i
$494$	56.6666	−	32.7165i	0.114710	−	0.0662277i
$495$	−132.457	−	122.827i	−0.267590	−	0.248135i
$496$			194.842i			0.392827i
$497$	−389.883	−	535.923i	−0.784474	−	1.07832i
$498$	−90.2875	+	72.0245i	−0.181300	+	0.144628i
$499$	217.184	+	125.391i	0.435238	+	0.251285i	0.701575	−	0.712595i	$-0.252480\pi$
$499$	217.184	+	125.391i	0.435238	+	0.251285i	−0.266338	+	0.963880i	$0.585814\pi$
$500$	238.739	+	413.509i	0.477479	+	0.827018i
$501$	188.335	+	73.8827i	0.375918	+	0.147470i
$502$	643.112	+	371.301i	1.28110	+	0.739644i
$503$			312.424i			0.621121i	0.950554	+	0.310560i	$0.100517\pi$
$503$			312.424i			0.621121i	−0.950554	+	0.310560i	$0.899483\pi$
$504$	94.1751	−	789.335i	0.186855	−	1.56614i
$505$			206.514i			0.408939i
$506$	253.441	+	146.325i	0.500873	+	0.289179i
$507$	−471.981	−	185.156i	−0.930930	−	0.365198i
$508$	135.036	+	233.889i	0.265818	+	0.460411i
$509$	20.4403	−	35.4037i	0.0401578	−	0.0695554i	−0.845248	−	0.534374i	$-0.820547\pi$
$509$	20.4403	−	35.4037i	0.0401578	−	0.0695554i	0.885406	+	0.464819i	$0.153881\pi$
$510$	1340.49	+	1680.39i	2.62841	+	3.29489i
$511$	679.997	+	302.245i	1.33072	+	0.591478i
$512$	−725.669			−1.41732
$513$	2.95207	−	39.6370i	0.00575452	−	0.0772652i
$514$	−1242.45	+	717.330i	−2.41722	+	1.39558i
$515$	411.485	+	712.713i	0.799000	+	1.38391i
$516$	−43.6815	−	289.507i	−0.0846541	−	0.561060i
$517$	−60.1400			−0.116325
$518$	128.784	+	57.2419i	0.248618	+	0.110506i
$519$	84.7481	+	106.237i	0.163291	+	0.204696i
$520$	−625.389	+	1083.21i	−1.20267	+	2.08309i
$521$	−356.672	+	205.924i	−0.684590	+	0.395248i	−0.801582	−	0.597884i	$-0.796008\pi$
$521$	−356.672	+	205.924i	−0.684590	+	0.395248i	0.116992	+	0.993133i	$0.462675\pi$
$522$	−351.442	−	1138.11i	−0.673260	−	2.18028i
$523$	−22.1289	+	38.3284i	−0.0423115	+	0.0732857i	−0.886406	−	0.462909i	$-0.846806\pi$
$523$	−22.1289	+	38.3284i	−0.0423115	+	0.0732857i	0.844094	+	0.536195i	$0.180139\pi$
$524$			1128.37i			2.15338i
$525$	495.428	−	488.832i	0.943672	−	0.931108i
$526$		−	1169.96i		−	2.22427i
$527$	−216.257	+	374.569i	−0.410356	+	0.710757i
$528$	−91.0155	−	35.7049i	−0.172378	−	0.0676229i
$529$	264.163	+	457.544i	0.499363	+	0.864923i
$530$	−2036.56	−	1175.81i	−3.84257	−	2.21851i
$531$	72.5605	−	318.358i	0.136649	−	0.599544i
$532$	−64.0835	+	46.6207i	−0.120458	+	0.0876328i
$533$	615.218			1.15426
$534$	235.874	+	1563.30i	0.441712	+	2.92752i
$535$	−97.0725	+	56.0448i	−0.181444	+	0.104757i
$536$	−102.645	+	59.2620i	−0.191501	+	0.110563i
$537$	336.416	−	50.7593i	0.626474	−	0.0945239i
$538$		−	283.132i		−	0.526268i
$539$	126.128	−	26.9743i	0.234004	−	0.0500450i
$540$	687.619	+	1426.18i	1.27337	+	2.64107i
$541$	−570.140	−	329.171i	−1.05386	−	0.608449i	−0.130135	−	0.991496i	$-0.541541\pi$
$541$	−570.140	−	329.171i	−1.05386	−	0.608449i	−0.923729	+	0.383048i	$0.874874\pi$
$542$	1542.13	−	890.351i	2.84526	−	1.64271i
$543$	−301.752	−	118.375i	−0.555712	−	0.218003i
$544$	−193.750	−	111.862i	−0.356159	−	0.205628i
$545$		−	1102.45i		−	2.02284i
$546$	899.976	+	247.624i	1.64831	+	0.453524i
$547$	188.044			0.343774			0.171887	−	0.985117i	$-0.445014\pi$
$547$	188.044			0.343774			0.171887	+	0.985117i	$0.445014\pi$
$548$	−355.299	+	615.396i	−0.648356	+	1.12299i
$549$	560.795	−	173.171i	1.02149	−	0.315429i
$550$	−149.141	−	258.320i	−0.271166	−	0.469673i
$551$	−28.4913	+	49.3483i	−0.0517083	+	0.0895614i
$552$	−767.589	−	962.224i	−1.39056	−	1.74316i
$553$	256.897	−	27.1634i	0.464552	−	0.0491200i
$554$	522.227			0.942648
$555$	−133.192	+	20.0963i	−0.239986	+	0.0362096i
$556$	−781.031	−	1352.78i	−1.40473	−	2.43307i
$557$	−89.8156	−	155.565i	−0.161249	−	0.279291i	0.774068	−	0.633102i	$-0.218219\pi$
$557$	−89.8156	−	155.565i	−0.161249	−	0.279291i	−0.935317	+	0.353811i	$0.884886\pi$
$558$	−329.281	+	355.098i	−0.590109	+	0.636377i
$559$	164.975			0.295126
$560$	268.409	−	603.873i	0.479302	−	1.07834i
$561$	−135.341	−	169.659i	−0.241250	−	0.302423i
$562$	549.483	−	951.732i	0.977727	−	1.69347i
$563$	559.119	−	322.808i	0.993107	−	0.573371i	0.0869053	−	0.996217i	$-0.472302\pi$
$563$	559.119	−	322.808i	0.993107	−	0.573371i	0.906202	+	0.422846i	$0.138969\pi$
$564$	490.708	+	192.502i	0.870050	+	0.341316i
$565$	−196.786	−	113.614i	−0.348293	−	0.201087i
$566$	−190.085			−0.335839
$567$	432.070	−	367.157i	0.762028	−	0.647544i
$568$	1194.63			2.10323
$569$	−293.747	−	169.595i	−0.516251	−	0.298058i	0.219148	−	0.975692i	$-0.429672\pi$
$569$	−293.747	−	169.595i	−0.516251	−	0.298058i	−0.735399	+	0.677634i	$0.763005\pi$
$570$	42.0485	−	107.186i	0.0737693	−	0.188046i
$571$	236.817	+	410.179i	0.414740	+	0.718352i	0.995401	−	0.0957941i	$-0.0305390\pi$
$571$	236.817	+	410.179i	0.414740	+	0.718352i	−0.580661	+	0.814146i	$0.697206\pi$
$572$	131.580	−	227.904i	0.230035	−	0.398433i
$573$	215.830	+	270.558i	0.376667	+	0.472177i
$574$	−1126.38	+	119.099i	−1.96233	+	0.207490i
$575$		−	1077.68i		−	1.87423i
$576$	−510.500	−	473.384i	−0.886285	−	0.821847i
$577$	428.206	−	247.225i	0.742125	−	0.428466i	−0.0807167	−	0.996737i	$-0.525721\pi$
$577$	428.206	−	247.225i	0.742125	−	0.428466i	0.822841	+	0.568271i	$0.192388\pi$
$578$	797.219	+	1380.82i	1.37927	+	2.38897i
$579$	478.276	−	72.1634i	0.826037	−	0.124635i
$580$		−	2269.86i		−	3.91356i
$581$	46.3684	+	63.7367i	0.0798078	+	0.109702i
$582$	−144.833	−	181.558i	−0.248854	−	0.311955i
$583$	205.619	+	118.714i	0.352691	+	0.203626i
$584$	−1161.66	+	670.685i	−1.98914	+	1.14843i
$585$	−852.423	+	263.224i	−1.45713	+	0.449955i
$586$	−866.373	+	1500.60i	−1.47845	+	2.56076i
$587$	−805.107			−1.37156			−0.685781	−	0.727808i	$-0.740539\pi$
$587$	−805.107			−1.37156			−0.685781	+	0.727808i	$0.740539\pi$
$588$	−1115.48	−	183.629i	−1.89707	−	0.312294i
$589$	23.1671			0.0393329
$590$	472.935	−	819.148i	0.801586	−	1.38839i
$591$	−14.7027	−	5.76777i	−0.0248776	−	0.00975933i
$592$	−63.1363	+	36.4517i	−0.106649	+	0.0615739i
$593$	234.927	−	406.905i	0.396167	−	0.686181i	−0.597083	−	0.802180i	$-0.703674\pi$
$593$	234.927	−	406.905i	0.396167	−	0.686181i	0.993249	+	0.115999i	$0.0370069\pi$
$594$	−105.534	−	218.887i	−0.177667	−	0.368497i
$595$	1186.24	−	862.989i	1.99368	−	1.45040i
$596$	871.681			1.46255
$597$	−134.721	−	892.886i	−0.225663	−	1.49562i
$598$	1251.68	−	722.658i	2.09311	−	1.20846i
$599$	331.592	−	191.445i	0.553577	−	0.319608i	−0.196987	−	0.980406i	$-0.563116\pi$
$599$	331.592	−	191.445i	0.553577	−	0.319608i	0.750563	+	0.660799i	$0.229782\pi$
$600$	187.175	+	1240.53i	0.311958	+	2.06756i
$601$	−136.830			−0.227671			−0.113836	−	0.993500i	$-0.536314\pi$
$601$	−136.830			−0.227671			−0.113836	+	0.993500i	$0.536314\pi$
$602$	−302.047	+	31.9374i	−0.501739	+	0.0530521i
$603$	−82.4254	−	18.7865i	−0.136692	−	0.0311550i
$604$	835.466	+	482.356i	1.38322	+	0.798603i
$605$	−434.904	−	753.275i	−0.718849	−	1.24508i
$606$	−101.454	+	258.616i	−0.167415	+	0.426760i
$607$	163.797	−	283.705i	0.269847	−	0.467389i	−0.698975	−	0.715146i	$-0.746360\pi$
$607$	163.797	−	283.705i	0.269847	−	0.467389i	0.968822	+	0.247757i	$0.0796935\pi$
$608$			11.9835i			0.0197096i
$609$	−786.567	+	205.120i	−1.29157	+	0.336815i
$610$	1700.20			2.78722
$611$	−148.508	+	257.223i	−0.243057	+	0.420987i
$612$	561.246	+	1817.54i	0.917068	+	2.96983i
$613$	−606.899	+	350.393i	−0.990047	+	0.571604i	−0.905288	−	0.424798i	$-0.860345\pi$
$613$	−606.899	+	350.393i	−0.990047	+	0.571604i	−0.0847586	+	0.996402i	$0.527012\pi$
$614$	−590.635	−	341.003i	−0.961946	−	0.555380i
$615$	846.280	−	675.098i	1.37606	−	1.09772i
$616$	−94.4319	+	212.455i	−0.153299	+	0.344894i
$617$	−197.729			−0.320469			−0.160234	−	0.987079i	$-0.551225\pi$
$617$	−197.729			−0.320469			−0.160234	+	0.987079i	$0.551225\pi$
$618$	165.167	+	1094.68i	0.267261	+	1.77132i
$619$	−353.048	+	203.832i	−0.570351	+	0.329293i	−0.757290	−	0.653079i	$-0.773477\pi$
$619$	−353.048	+	203.832i	−0.570351	+	0.329293i	0.186938	+	0.982372i	$0.440144\pi$
$620$	−799.209	+	461.423i	−1.28905	+	0.744231i
$621$	65.2067	−	875.522i	0.105003	−	1.40986i
$622$			553.156i			0.889319i
$623$	1072.94	−	113.449i	1.72222	−	0.182102i
$624$	−377.463	+	301.111i	−0.604909	+	0.482550i
$625$	177.569	−	307.558i	0.284110	−	0.492093i
$626$	−667.217	−	1155.65i	−1.06584	−	1.84609i
$627$	−4.24538	+	10.8219i	−0.00677093	+	0.0172598i
$628$	−559.388	+	968.889i	−0.890745	+	1.54282i
$629$	−161.833			−0.257286
$630$	1509.71	−	646.946i	2.39637	−	1.02690i
$631$			974.420i			1.54425i	0.635472	+	0.772124i	$0.280806\pi$
$631$			974.420i			1.54425i	−0.635472	+	0.772124i	$0.719194\pi$
$632$	−232.828	+	403.270i	−0.368399	+	0.638086i
$633$	−108.788	−	42.6771i	−0.171862	−	0.0674204i
$634$	−78.5971	−	136.134i	−0.123970	−	0.214723i
$635$	−133.889	+	231.903i	−0.210849	+	0.365201i
$636$	−1297.74	−	1626.81i	−2.04048	−	2.55787i
$637$	196.086	−	606.069i	0.307827	−	0.951442i
$638$			348.374i			0.546041i
$639$	624.806	+	579.379i	0.977787	+	0.906696i
$640$	−884.244	−	1531.56i	−1.38163	−	2.39306i
$641$	−436.447	+	251.983i	−0.680884	+	0.393109i	−0.800188	−	0.599749i	$-0.795267\pi$
$641$	−436.447	+	251.983i	−0.680884	+	0.393109i	0.119304	+	0.992858i	$0.461934\pi$
$642$	−149.096	+	22.4960i	−0.232237	+	0.0350405i
$643$		−	806.217i		−	1.25384i	−0.779085	−	0.626919i	$-0.784316\pi$
$643$		−	806.217i		−	1.25384i	0.779085	−	0.626919i	$-0.215684\pi$
$644$	−1415.51	+	1029.78i	−2.19800	+	1.59904i
$645$	226.936	−	181.033i	0.351839	−	0.280671i
$646$	69.1658	−	119.799i	0.107068	−	0.185447i
$647$	−415.070	+	239.641i	−0.641530	+	0.370387i	−0.785204	−	0.619238i	$-0.787442\pi$
$647$	−415.070	+	239.641i	−0.641530	+	0.370387i	0.143674	+	0.989625i	$0.454108\pi$
$648$	77.0030	+	1019.15i	0.118832	+	1.57277i
$649$	−47.7494	+	82.7043i	−0.0735738	+	0.127433i
$650$	−1473.14			−2.26637
$651$	232.117	+	235.249i	0.356555	+	0.361366i
$652$			1872.82i			2.87242i
$653$	−440.531	−	254.341i	−0.674626	−	0.389496i	0.123201	−	0.992382i	$-0.460684\pi$
$653$	−440.531	−	254.341i	−0.674626	−	0.389496i	−0.797827	+	0.602886i	$0.794017\pi$
$654$	541.596	−	1380.59i	0.828129	−	2.11099i
$655$	−968.902	+	559.396i	−1.47924	+	0.854039i
$656$	292.958	−	507.419i	0.446583	−	0.773504i
$657$	−932.832	−	212.612i	−1.41984	−	0.323611i
$658$	222.101	−	499.689i	0.337540	−	0.759405i
$659$			443.924i			0.673633i	0.941570	+	0.336817i	$0.109350\pi$
$659$			443.924i			0.673633i	−0.941570	+	0.336817i	$0.890650\pi$
$660$	−69.0870	−	457.886i	−0.104677	−	0.693767i
$661$	508.855	−	293.788i	0.769826	−	0.444459i	−0.0629863	−	0.998014i	$-0.520062\pi$
$661$	508.855	−	293.788i	0.769826	−	0.444459i	0.832813	+	0.553555i	$0.186729\pi$
$662$	−146.438	+	84.5459i	−0.221205	+	0.127713i
$663$	−1059.85	+	159.913i	−1.59857	+	0.241196i
$664$	−142.076			−0.213970
$665$	−71.8016	−	31.9144i	−0.107972	−	0.0479915i
$666$	−176.668	−	40.2665i	−0.265268	−	0.0604601i
$667$	−629.329	+	1090.03i	−0.943522	+	1.63423i
$668$	259.306	+	449.131i	0.388182	+	0.672352i
$669$	−112.514	+	286.809i	−0.168182	+	0.428714i
$670$	−212.084	−	122.447i	−0.316543	−	0.182756i
$671$	−171.659			−0.255826
$672$	−121.686	+	120.065i	−0.181080	+	0.178669i
$673$	986.044			1.46515			0.732574	−	0.680688i	$-0.238319\pi$
$673$	986.044			1.46515			0.732574	+	0.680688i	$0.238319\pi$
$674$	−191.269	+	331.288i	−0.283783	+	0.491526i
$675$	−503.746	+	739.589i	−0.746290	+	1.09569i
$676$	−649.840	−	1125.56i	−0.961302	−	1.66502i
$677$	−129.730	−	74.8998i	−0.191625	−	0.110635i	0.401118	−	0.916026i	$-0.368622\pi$
$677$	−129.730	−	74.8998i	−0.191625	−	0.110635i	−0.592743	+	0.805392i	$0.701955\pi$
$678$	−190.618	−	238.953i	−0.281148	−	0.352438i
$679$	−128.167	+	93.2413i	−0.188759	+	0.137322i
$680$			2644.27i			3.88863i
$681$	56.1487	+	372.135i	0.0824503	+	0.546454i
$682$	122.661	−	70.8183i	0.179855	−	0.103839i
$683$	320.414	+	554.973i	0.469127	+	0.812552i	0.999377	−	0.0352896i	$-0.0112354\pi$
$683$	320.414	+	554.973i	0.469127	+	0.812552i	−0.530250	+	0.847841i	$0.677902\pi$
$684$	69.2798	−	74.7117i	0.101286	−	0.109228i
$685$	−704.565			−1.02856
$686$	−241.678	+	1147.59i	−0.352301	+	1.67287i
$687$	808.047	+	1012.94i	1.17620	+	1.47444i
$688$	78.5589	−	136.068i	0.114185	−	0.197773i
$689$	1015.50	−	586.298i	1.47387	−	0.850940i
$690$	928.788	−	2367.58i	1.34607	−	3.43127i
$691$	666.727	+	384.935i	0.964873	+	0.557070i	0.897669	−	0.440670i	$-0.145259\pi$
$691$	666.727	+	384.935i	0.964873	+	0.557070i	0.0672037	+	0.997739i	$0.478592\pi$
$692$			348.374i			0.503431i
$693$	−152.426	+	65.3181i	−0.219951	+	0.0942541i
$694$		−	1900.68i		−	2.73874i
$695$	774.399	−	1341.30i	1.11424	−	1.92993i
$696$	535.111	−	1364.05i	0.768837	−	1.95985i
$697$	1126.38	−	650.315i	1.61604	−	0.933021i
$698$	−360.756	−	208.282i	−0.516842	−	0.298399i
$699$	−252.077	−	315.995i	−0.360625	−	0.452068i
$700$	1774.27	−	187.605i	2.53467	−	0.268007i
$701$			1220.21i			1.74067i	0.492457	+	0.870337i	$0.336099\pi$
$701$			1220.21i			1.74067i	−0.492457	+	0.870337i	$0.663901\pi$
$702$	−1196.80	−	89.1345i	−1.70484	−	0.126972i
$703$	4.33418	+	7.50702i	0.00616526	+	0.0106785i
$704$	101.811	+	176.341i	0.144617	+	0.250484i
$705$	77.9748	+	516.792i	0.110603	+	0.733038i
$706$	1210.49			1.71457
$707$	173.241	+	77.0023i	0.245037	+	0.108914i
$708$	654.337	−	521.980i	0.924204	−	0.737260i
$709$	−612.879	−	353.846i	−0.864427	−	0.499077i	0.00106550	−	0.999999i	$-0.499661\pi$
$709$	−612.879	−	353.846i	−0.864427	−	0.499077i	−0.865492	+	0.500922i	$0.832994\pi$
$710$	1234.17	+	2137.65i	1.73827	+	3.01078i
$711$	−317.351	+	97.9965i	−0.446345	+	0.137829i
$712$	−972.420	+	1684.28i	−1.36576	+	2.36556i
$713$	511.726			0.717708
$714$	1909.48	−	497.953i	2.67434	−	0.697414i
$715$	260.926			0.364932
$716$	755.309	+	436.078i	1.05490	+	0.609047i
$717$	614.296	+	240.985i	0.856759	+	0.336102i
$718$	787.485	+	1363.96i	1.09678	+	1.89967i
$719$	1030.82	+	595.144i	1.43369	+	0.827739i	0.997400	−	0.0720695i	$-0.0229603\pi$
$719$	1030.82	+	595.144i	1.43369	+	0.827739i	0.436286	+	0.899808i	$0.356294\pi$
$720$	−188.811	+	828.404i	−0.262237	+	1.15056i
$721$	751.313	−	79.4412i	1.04204	−	0.110182i
$722$	1226.89			1.69930
$723$	−385.841	+	58.2167i	−0.533667	+	0.0805210i
$724$	−415.462	−	719.601i	−0.573842	−	0.993924i
$725$	1111.01	−	641.444i	1.53243	−	0.884750i
$726$	−174.567	−	1156.98i	−0.240451	−	1.59363i
$727$	−301.359			−0.414524			−0.207262	−	0.978285i	$-0.566455\pi$
$727$	−301.359			−0.414524			−0.207262	+	0.978285i	$0.566455\pi$
$728$	675.498	+	928.521i	0.927881	+	1.27544i
$729$	−454.000	+	570.373i	−0.622771	+	0.782404i
$730$	−2400.22	−	1385.77i	−3.28797	−	1.89831i
$731$	302.047	−	174.387i	0.413197	−	0.238559i
$732$	1400.64	+	549.464i	1.91345	+	0.750634i
$733$	879.905	+	508.013i	1.20042	+	0.693060i	0.960648	−	0.277770i	$-0.0895953\pi$
$733$	879.905	+	508.013i	1.20042	+	0.693060i	0.239768	+	0.970830i	$0.422929\pi$
$734$	1348.92			1.83776
$735$	−395.326	−	1048.87i	−0.537859	−	1.42703i
$736$			264.697i			0.359642i
$737$	21.4128	+	12.3627i	0.0290540	+	0.0167744i
$738$	1391.45	−	429.671i	1.88543	−	0.582210i
$739$	930.201	−	537.052i	1.25873	−	0.726728i	0.285902	−	0.958259i	$-0.407707\pi$
$739$	930.201	−	537.052i	1.25873	−	0.726728i	0.972828	+	0.231531i	$0.0743734\pi$
$740$	−299.038	−	172.649i	−0.404105	−	0.233310i
$741$	35.8027	+	44.8811i	0.0483167	+	0.0605682i
$742$	−1745.73	+	1270.02i	−2.35274	+	1.71162i
$743$	−530.788			−0.714385			−0.357192	−	0.934031i	$-0.616266\pi$
$743$	−530.788			−0.714385			−0.357192	+	0.934031i	$0.616266\pi$
$744$	−589.056	+	88.8782i	−0.791742	+	0.119460i
$745$	432.140	+	748.488i	0.580054	+	1.00468i
$746$	29.7934	+	51.6036i	0.0399375	+	0.0691738i
$747$	−74.3074	−	68.9048i	−0.0994744	−	0.0922421i
$748$		−	556.347i		−	0.743779i
$749$	10.8200	+	102.330i	0.0144459	+	0.136622i
$750$	−497.852	+	397.149i	−0.663803	+	0.529532i
$751$	259.436	−	449.356i	0.345454	−	0.598344i	−0.639982	−	0.768390i	$-0.721058\pi$
$751$	259.436	−	449.356i	0.345454	−	0.598344i	0.985436	+	0.170046i	$0.0543916\pi$
$752$	141.435	+	244.972i	0.188078	+	0.325760i
$753$	−237.953	+	606.568i	−0.316007	+	0.805535i
$754$	1490.02	+	860.264i	1.97615	+	1.14093i
$755$			956.522i			1.26692i
$756$	1452.79	−	45.0578i	1.92168	−	0.0596003i
$757$	216.211			0.285616			0.142808	−	0.989750i	$-0.454387\pi$
$757$	216.211			0.285616			0.142808	+	0.989750i	$0.454387\pi$
$758$	1079.88	+	623.468i	1.42464	+	0.822518i
$759$	−93.7740	+	239.040i	−0.123549	+	0.314940i
$760$	122.661	−	70.8183i	0.161396	−	0.0931820i
$761$	−316.996	+	549.052i	−0.416551	+	0.721488i	−0.995590	−	0.0938121i	$-0.970095\pi$
$761$	−316.996	+	549.052i	−0.416551	+	0.721488i	0.579039	+	0.815300i	$0.303428\pi$
$762$	−281.595	+	224.635i	−0.369547	+	0.294797i
$763$	−924.825	−	411.066i	−1.21209	−	0.538750i
$764$			887.214i			1.16127i
$765$	−1282.43	+	1382.98i	−1.67638	+	1.80782i
$766$	648.866	+	1123.87i	0.847084	+	1.46719i
$767$	235.822	+	408.455i	0.307460	+	0.532536i
$768$	−216.437	−	1434.47i	−0.281819	−	1.86780i
$769$			819.151i			1.06522i	0.846362	+	0.532608i	$0.178788\pi$
$769$			819.151i			1.06522i	−0.846362	+	0.532608i	$0.821212\pi$
$770$	−477.720	+	50.5124i	−0.620415	+	0.0656005i
$771$	−784.997	−	984.046i	−1.01815	−	1.27632i
$772$	1073.81	+	619.962i	1.39094	+	0.803059i
$773$	568.343	+	984.399i	0.735244	+	1.27348i	0.954616	+	0.297838i	$0.0962656\pi$
$773$	568.343	+	984.399i	0.735244	+	1.27348i	−0.219373	+	0.975641i	$0.570401\pi$
$774$	373.126	−	115.219i	0.482076	−	0.148862i
$775$	−451.699	−	260.788i	−0.582837	−	0.336501i
$776$		−	285.699i		−	0.368169i
$777$	−32.8044	+	119.226i	−0.0422194	+	0.153444i
$778$			13.2489i			0.0170295i
$779$	−60.3330	−	34.8333i	−0.0774493	−	0.0447154i
$780$	−2129.01	−	835.199i	−2.72950	−	1.07077i
$781$	−124.607	−	215.825i	−0.159548	−	0.276345i
$782$	1527.77	−	2646.17i	1.95367	−	3.38385i
$783$	941.414	−	453.894i	1.20232	−	0.579686i
$784$	−406.499	−	450.329i	−0.518493	−	0.574399i
$785$	−1109.28			−1.41309
$786$	−1488.16	+	224.538i	−1.89334	+	0.285671i
$787$	930.596	−	537.280i	1.18246	−	0.682694i	0.225878	−	0.974156i	$-0.427475\pi$
$787$	930.596	−	537.280i	1.18246	−	0.682694i	0.956582	+	0.291462i	$0.0941417\pi$
$788$	−20.2431	−	35.0621i	−0.0256892	−	0.0444951i
$789$	1015.06	−	153.154i	1.28651	−	0.194112i
$790$	−962.137			−1.21790
$791$	−168.684	+	122.717i	−0.213254	+	0.155142i
$792$	66.4275	−	291.449i	0.0838731	−	0.367992i
$793$	−423.889	+	734.198i	−0.534539	+	0.925848i
$794$	−1936.72	+	1118.17i	−2.43920	+	1.40827i
$795$	753.532	−	1920.83i	0.947839	−	2.41614i
$796$	1157.40	−	2004.67i	1.45402	−	2.51843i
$797$			119.200i			0.149561i	0.997200	+	0.0747803i	$0.0238256\pi$
$797$			119.200i			0.149561i	−0.997200	+	0.0747803i	$0.976174\pi$
$798$	−74.2382	−	75.2400i	−0.0930304	−	0.0942857i
$799$			627.919i			0.785881i
$800$	134.896	−	233.647i	0.168620	−	0.292058i
$801$	−1325.44	+	409.288i	−1.65473	+	0.510971i
$802$	−168.663	−	292.133i	−0.210303	−	0.364256i
$803$	242.335	+	139.912i	0.301787	+	0.174237i
$804$	−135.145	−	169.413i	−0.168091	−	0.210713i
$805$	−1585.99	−	704.940i	−1.97017	−	0.875702i
$806$		−	699.506i		−	0.867873i
$807$	245.645	−	37.0635i	0.304392	−	0.0459275i
$808$	−295.954	+	170.869i	−0.366279	+	0.211471i
$809$	−348.228	+	201.050i	−0.430443	+	0.248516i	−0.699535	−	0.714598i	$-0.746610\pi$
$809$	−348.228	+	201.050i	−0.430443	+	0.248516i	0.269092	+	0.963114i	$0.413276\pi$
$810$	−1744.10	+	1190.67i	−2.15321	+	1.46997i
$811$		−	1280.62i		−	1.57906i	−0.613712	−	0.789530i	$-0.710324\pi$
$811$		−	1280.62i		−	1.57906i	0.613712	−	0.789530i	$-0.289676\pi$
$812$	−1904.15	−	846.358i	−2.34502	−	1.04231i
$813$	974.339	+	1221.40i	1.19845	+	1.50234i
$814$	45.8957	+	26.4979i	0.0563829	+	0.0325527i
$815$	−1608.14	+	928.459i	−1.97318	+	1.13921i
$816$	−372.793	+	950.290i	−0.456854	+	1.16457i
$817$	−16.1787	−	9.34080i	−0.0198026	−	0.0114331i
$818$		−	1331.30i		−	1.62751i
$819$	−97.0263	+	813.232i	−0.118469	+	0.992958i
$820$	2775.12			3.38430
$821$	−404.665	+	700.900i	−0.492893	+	0.853716i	−0.999966	−	0.00818719i	$-0.997394\pi$
$821$	−404.665	+	700.900i	−0.492893	+	0.853716i	0.507074	+	0.861903i	$0.330727\pi$
$822$	−882.322	−	346.130i	−1.07338	−	0.421083i
$823$	36.0687	+	62.4728i	0.0438259	+	0.0759087i	0.887106	−	0.461565i	$-0.152712\pi$
$823$	36.0687	+	62.4728i	0.0438259	+	0.0759087i	−0.843280	+	0.537474i	$0.819379\pi$
$824$	−680.922	+	1179.39i	−0.826362	+	1.43130i
$825$	204.595	−	163.210i	0.247993	−	0.197830i
$826$	−510.829	−	702.172i	−0.618437	−	0.850087i
$827$	−645.671			−0.780739			−0.390370	−	0.920658i	$-0.627653\pi$
$827$	−645.671			−0.780739			−0.390370	+	0.920658i	$0.627653\pi$
$828$	1530.29	−	1650.27i	1.84817	−	1.99308i
$829$	468.985	+	812.306i	0.565724	+	0.979863i	0.996982	+	0.0776340i	$0.0247366\pi$
$829$	468.985	+	812.306i	0.565724	+	0.979863i	−0.431258	+	0.902229i	$0.641930\pi$
$830$	−146.779	−	254.228i	−0.176842	−	0.306299i
$831$	68.3622	+	453.083i	0.0822650	+	0.545226i
$832$	1005.63			1.20869
$833$	−281.637	−	1316.90i	−0.338100	−	1.58091i
$834$	1628.71	−	1299.26i	1.95289	−	1.55787i
$835$	−257.104	+	445.318i	−0.307909	+	0.533315i
$836$	−25.8075	+	14.9000i	−0.0308703	+	0.0178229i
$837$	−351.187	−	239.199i	−0.419578	−	0.285781i
$838$	300.201	+	173.321i	0.358235	+	0.206827i
$839$	−743.899			−0.886650			−0.443325	−	0.896361i	$-0.646201\pi$
$839$	−743.899			−0.886650			−0.443325	+	0.896361i	$0.646201\pi$
$840$	1948.09	+	536.008i	2.31916	+	0.638105i
$841$	−657.327			−0.781601
$842$	265.790	+	153.454i	0.315665	+	0.182249i
$843$	897.650	+	352.143i	1.06483	+	0.417726i
$844$	−149.784	−	259.433i	−0.177469	−	0.307385i
$845$	644.323	−	1116.00i	0.762512	−	1.32071i
$846$	−156.236	+	685.482i	−0.184676	+	0.810262i
$847$	−794.072	+	83.9624i	−0.937511	+	0.0991291i
$848$		−	1116.75i		−	1.31692i
$849$	−24.8831	−	164.917i	−0.0293087	−	0.194249i
$850$	−2697.11	+	1557.18i	−3.17307	+	1.83197i
$851$	95.7355	+	165.819i	0.112498	+	0.194852i
$852$	325.886	+	2159.87i	0.382496	+	2.53506i
$853$			857.426i			1.00519i	0.864522	+	0.502594i	$0.167621\pi$
$853$			857.426i			1.00519i	−0.864522	+	0.502594i	$0.832379\pi$
$854$	633.950	−	1426.27i	0.742330	−	1.67011i
$855$	98.4987	+	22.4499i	0.115203	+	0.0262572i
$856$	−160.635	−	92.7425i	−0.187657	−	0.108344i
$857$	−604.822	+	349.194i	−0.705744	+	0.407461i	−0.809483	−	0.587143i	$-0.800253\pi$
$857$	−604.822	+	349.194i	−0.705744	+	0.407461i	0.103739	+	0.994605i	$0.466919\pi$
$858$	326.756	+	128.185i	0.380835	+	0.149399i
$859$	−50.3096	+	87.1388i	−0.0585676	+	0.101442i	−0.893823	−	0.448421i	$-0.851987\pi$
$859$	−50.3096	+	87.1388i	−0.0585676	+	0.101442i	0.835255	+	0.549863i	$0.185320\pi$
$860$	744.171			0.865315
$861$	−250.779	−	961.653i	−0.291265	−	1.11690i
$862$	−2210.29			−2.56414
$863$	426.398	−	738.543i	0.494088	−	0.855785i	−0.505889	−	0.862599i	$-0.668835\pi$
$863$	426.398	−	738.543i	0.494088	−	0.855785i	0.999977	+	0.00681331i	$0.00216876\pi$
$864$	123.728	−	181.656i	0.143204	−	0.210250i
$865$	−299.139	+	172.708i	−0.345826	+	0.199663i
$866$	977.051	−	1692.30i	1.12823	−	1.95416i
$867$	−1093.64	+	872.422i	−1.26141	+	1.00625i
$868$	89.0823	+	842.494i	0.102629	+	0.970615i
$869$	97.1411			0.111785
$870$	2993.63	−	451.686i	3.44096	−	0.519180i
$871$	105.752	−	61.0561i	0.121415	−	0.0700989i
$872$	1579.91	−	912.160i	1.81182	−	1.04605i
$873$	138.560	−	149.423i	0.158717	−	0.171161i
$874$	−163.666			−0.187261
$875$	255.679	+	351.449i	0.292204	+	0.401656i
$876$	−1529.47	−	1917.30i	−1.74598	−	2.18870i
$877$	408.625	+	235.920i	0.465935	+	0.269008i	0.714537	−	0.699598i	$-0.246638\pi$
$877$	408.625	+	235.920i	0.465935	+	0.269008i	−0.248601	+	0.968606i	$0.579971\pi$
$878$	−657.484	−	1138.80i	−0.748843	−	1.29703i
$879$	−1415.33	−	555.226i	−1.61016	−	0.631657i
$880$	124.249	−	215.206i	0.141192	−	0.244553i
$881$		−	702.898i		−	0.797842i	−0.916985	−	0.398921i	$-0.869385\pi$
$881$		−	702.898i		−	0.797842i	0.916985	−	0.398921i	$-0.130615\pi$
$882$	20.2090	−	1507.70i	0.0229127	−	1.70941i
$883$	936.948			1.06110			0.530548	−	0.847655i	$-0.321986\pi$
$883$	936.948			1.06110			0.530548	+	0.847655i	$0.321986\pi$
$884$	−2379.53	−	1373.82i	−2.69178	−	1.55410i
$885$	772.601	+	303.087i	0.872995	+	0.342471i
$886$	−1468.50	+	847.839i	−1.65745	+	0.956929i
$887$	−892.025	−	515.011i	−1.00567	−	0.580621i	−0.0957459	−	0.995406i	$-0.530524\pi$
$887$	−892.025	−	515.011i	−1.00567	−	0.580621i	−0.909920	+	0.414785i	$0.863857\pi$
$888$	−139.003	−	174.249i	−0.156534	−	0.196226i
$889$	144.617	+	198.786i	0.162674	+	0.223607i
$890$	−4018.42			−4.51508
$891$	176.091	−	120.215i	0.197633	−	0.134921i
$892$	−683.968	+	394.889i	−0.766780	+	0.442701i
$893$	29.1276	−	16.8168i	0.0326177	−	0.0188318i
$894$	173.458	+	1149.62i	0.194025	+	1.28593i
$895$			864.751i			0.966202i
$896$	−1614.50	+	170.712i	−1.80190	+	0.190527i
$897$	790.828	+	991.355i	0.881636	+	1.10519i
$898$	971.617	−	1682.89i	1.08198	−	1.87404i
$899$	304.583	+	527.554i	0.338802	+	0.586823i
$900$	−2191.80	+	676.815i	−2.43533	+	0.752017i
$901$	1239.49	−	2146.86i	1.37568	−	2.38275i
$902$	−425.920			−0.472195
$903$	−67.2483	−	257.874i	−0.0744721	−	0.285575i
$904$		−	376.016i		−	0.415947i
$905$	411.934	−	713.491i	0.455176	−	0.788388i
$906$	−469.908	+	1197.85i	−0.518663	+	1.32213i
$907$	−454.488	−	787.196i	−0.501089	−	0.867912i	−0.999999	−	0.00125790i	$-0.999600\pi$
$907$	−454.488	−	787.196i	−0.501089	−	0.867912i	0.498910	−	0.866654i	$-0.333734\pi$
$908$	−482.378	+	835.503i	−0.531253	+	0.920158i
$909$	−237.656	−	54.1668i	−0.261447	−	0.0595894i
$910$	−963.621	+	2167.97i	−1.05892	+	2.38239i
$911$			80.1743i			0.0880069i	0.999031	+	0.0440035i	$0.0140113\pi$
$911$			80.1743i			0.0880069i	−0.999031	+	0.0440035i	$0.985989\pi$
$912$	54.0657	−	8.15756i	0.0592825	−	0.00894469i
$913$	14.8193	+	25.6679i	0.0162315	+	0.0281138i
$914$	−611.498	+	353.049i	−0.669035	+	0.386268i
$915$	222.565	+	1475.09i	0.243241	+	1.61212i
$916$			3321.64i			3.62625i
$917$	107.997	+	1021.38i	0.117772	+	1.11382i
$918$	−2285.39	+	1101.88i	−2.48953	+	1.20031i
$919$	−395.033	+	684.217i	−0.429851	+	0.744524i	−0.996860	−	0.0791880i	$-0.974767\pi$
$919$	−395.033	+	684.217i	−0.429851	+	0.744524i	0.567009	+	0.823712i	$0.308101\pi$
$920$	2709.39	−	1564.27i	2.94499	−	1.70029i
$921$	218.536	−	557.073i	0.237282	−	0.604856i
$922$	382.869	−	663.148i	0.415259	−	0.719249i
$923$	−1230.80			−1.33348
$924$	−409.874	−	112.775i	−0.443586	−	0.122051i
$925$		−	195.157i		−	0.210980i
$926$	2307.44	+	1332.20i	2.49183	+	1.43866i
$927$	−928.116	+	286.597i	−1.00120	+	0.309167i
$928$	−272.884	+	157.549i	−0.294056	+	0.169773i
$929$	−623.696	+	1080.27i	−0.671363	+	1.16283i	0.306155	+	0.951982i	$0.400957\pi$
$929$	−623.696	+	1080.27i	−0.671363	+	1.16283i	−0.977518	+	0.210853i	$0.932376\pi$
$930$	−767.589	−	962.224i	−0.825365	−	1.03465i
$931$	−53.5449	+	48.3335i	−0.0575134	+	0.0519156i
$932$		−	1036.21i		−	1.11182i
$933$	−479.917	+	72.4111i	−0.514381	+	0.0776110i
$934$	429.722	−	248.100i	0.460088	−	0.265632i
$935$	477.720	−	275.812i	0.510930	−	0.294986i
$936$	−1082.52	−	1003.81i	−1.15653	−	1.07245i
$937$	−1128.28			−1.20414			−0.602072	−	0.798442i	$-0.705658\pi$
$937$	−1128.28			−1.20414			−0.602072	+	0.798442i	$0.705658\pi$
$938$	−181.798	+	132.258i	−0.193814	+	0.141000i
$939$	915.299	−	730.156i	0.974760	−	0.777589i
$940$	−669.888	+	1160.28i	−0.712647	+	1.23434i
$941$	−190.627	−	330.176i	−0.202579	−	0.350878i	0.746780	−	0.665072i	$-0.231599\pi$
$941$	−190.627	−	330.176i	−0.202579	−	0.350878i	−0.949359	+	0.314194i	$0.898266\pi$
$942$	−1389.14	−	544.952i	−1.47467	−	0.578506i
$943$	−1332.67	−	769.415i	−1.41322	−	0.815922i
$944$	449.179			0.475826
$945$	758.918	+	1225.13i	0.803088	+	1.29644i
$946$	−114.214			−0.120733
$947$	521.905	−	903.966i	0.551114	−	0.954557i	−0.447081	−	0.894494i	$-0.647536\pi$
$947$	521.905	−	903.966i	0.551114	−	0.954557i	0.998195	−	0.0600635i	$-0.0191303\pi$
$948$	−792.617	−	310.939i	−0.836094	−	0.327995i
$949$	1196.83	−	690.990i	1.26115	−	0.728124i
$950$	144.467	+	83.4082i	0.152071	+	0.0877981i
$951$	107.821	−	86.0113i	0.113376	−	0.0904430i
$952$	2218.23	+	985.960i	2.33008	+	1.03567i
$953$		−	645.739i		−	0.677586i	−0.940861	−	0.338793i	$-0.889981\pi$
$953$		−	645.739i		−	0.677586i	0.940861	−	0.338793i	$-0.110019\pi$
$954$	1887.29	−	2035.26i	1.97829	−	2.13340i
$955$	−761.826	+	439.841i	−0.797724	+	0.460566i
$956$	845.784	+	1464.94i	0.884711	+	1.53236i
$957$	−302.248	+	45.6040i	−0.315829	+	0.0476531i
$958$	2157.35			2.25193
$959$	−262.709	+	591.049i	−0.273941	+	0.616318i
$960$	1383.32	−	1103.51i	1.44096	−	1.14949i
$961$	−356.667	+	617.766i	−0.371142	+	0.642836i
$962$	226.667	−	130.866i	0.235620	−	0.136035i
$963$	−39.0350	−	126.411i	−0.0405348	−	0.131268i
$964$	−866.276	−	500.144i	−0.898626	−	0.518822i
$965$			1229.40i			1.27399i
$966$	−1639.81	−	1661.94i	−1.69753	−	1.72043i
$967$			354.180i			0.366267i	0.983088	+	0.183134i	$0.0586241\pi$
$967$			354.180i			0.366267i	−0.983088	+	0.183134i	$0.941376\pi$
$968$	719.675	−	1246.51i	0.743466	−	1.28772i
$969$	112.991	+	44.3258i	0.116606	+	0.0457439i
$970$	511.223	−	295.155i	0.527034	−	0.304283i
$971$	804.917	+	464.719i	0.828957	+	0.478599i	0.853495	−	0.521100i	$-0.174478\pi$
$971$	804.917	+	464.719i	0.828957	+	0.478599i	−0.0245383	+	0.999699i	$0.507812\pi$
$972$	−1821.60	+	417.236i	−1.87407	+	0.429255i
$973$	−836.447	−	1149.76i	−0.859658	−	1.18166i
$974$		−	1572.78i		−	1.61476i
$975$	−192.841	−	1278.09i	−0.197786	−	1.31086i
$976$	403.700	+	699.229i	0.413627	+	0.716423i
$977$	523.426	+	906.600i	0.535748	+	0.927943i	0.999127	+	0.0417824i	$0.0133036\pi$
$977$	523.426	+	906.600i	0.535748	+	0.927943i	−0.463379	+	0.886160i	$0.653363\pi$
$978$	−2469.98	+	372.677i	−2.52555	+	0.381061i
$979$	405.715			0.414418
$980$	884.505	−	2733.85i	0.902556	−	2.78965i
$981$	1268.69	+	289.162i	1.29326	+	0.294762i
$982$	1744.69	+	1007.30i	1.77667	+	1.02576i
$983$	−439.404	−	761.070i	−0.447003	−	0.774232i	0.551186	−	0.834382i	$-0.314175\pi$
$983$	−439.404	−	761.070i	−0.447003	−	0.774232i	−0.998189	+	0.0601503i	$0.980842\pi$
$984$	1667.69	+	654.224i	1.69480	+	0.664861i
$985$	20.0712	−	34.7644i	0.0203769	−	0.0352938i
$986$	3637.36			3.68901
$987$	462.603	+	127.283i	0.468696	+	0.128959i
$988$			147.174i			0.148962i
$989$	−357.364	−	206.324i	−0.361339	−	0.208619i
$990$	590.139	−	182.232i	0.596100	−	0.184073i
$991$	−257.036	−	445.199i	−0.259370	−	0.449242i	0.706703	−	0.707510i	$-0.250182\pi$
$991$	−257.036	−	445.199i	−0.259370	−	0.449242i	−0.966073	+	0.258268i	$0.916848\pi$
$992$	110.945	+	64.0541i	0.111840	+	0.0645706i
$993$	−92.5213	−	115.982i	−0.0931735	−	0.116799i
$994$	2253.43	−	238.269i	2.26703	−	0.239707i
$995$	2295.14			2.30668
$996$	−38.7573	−	256.871i	−0.0389129	−	0.257902i
$997$	553.005	+	957.832i	0.554669	+	0.960714i	0.997929	+	0.0643215i	$0.0204883\pi$
$997$	553.005	+	957.832i	0.554669	+	0.960714i	−0.443261	+	0.896393i	$0.646178\pi$
$998$	−742.578	+	428.728i	−0.744066	+	0.429587i
$999$	11.8083	−	158.548i	0.0118201	−	0.158707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.3.w.c.233.1	yes	16
3.2	odd	2	inner	273.3.w.c.233.8	yes	16
7.4	even	3	inner	273.3.w.c.116.2	yes	16
13.12	even	2	inner	273.3.w.c.233.7	yes	16
21.11	odd	6	inner	273.3.w.c.116.7	yes	16
39.38	odd	2	inner	273.3.w.c.233.2	yes	16
91.25	even	6	inner	273.3.w.c.116.8	yes	16
273.116	odd	6	inner	273.3.w.c.116.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.3.w.c.116.1	✓	16	273.116	odd	6	inner
273.3.w.c.116.2	yes	16	7.4	even	3	inner
273.3.w.c.116.7	yes	16	21.11	odd	6	inner
273.3.w.c.116.8	yes	16	91.25	even	6	inner
273.3.w.c.233.1	yes	16	1.1	even	1	trivial
273.3.w.c.233.2	yes	16	39.38	odd	2	inner
273.3.w.c.233.7	yes	16	13.12	even	2	inner
273.3.w.c.233.8	yes	16	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	273.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70956 + 2.96105i) q^{2} +(-2.79279 - 1.09560i) q^{3} +(-3.84521 - 6.66010i) q^{4} +(3.81256 - 6.60355i) q^{5} +(8.01856 - 6.39660i) q^{6} +(-4.11804 - 5.66055i) q^{7} +12.6180 q^{8} +(6.59934 + 6.11953i) q^{9} +O(q^{10})\)	\(q+(-1.70956 + 2.96105i) q^{2} +(-2.79279 - 1.09560i) q^{3} +(-3.84521 - 6.66010i) q^{4} +(3.81256 - 6.60355i) q^{5} +(8.01856 - 6.39660i) q^{6} +(-4.11804 - 5.66055i) q^{7} +12.6180 q^{8} +(6.59934 + 6.11953i) q^{9} +(13.0356 + 22.5784i) q^{10} +(-1.31613 - 2.27960i) q^{11} +(3.44209 + 22.8130i) q^{12} -13.0000 q^{13} +(23.8012 - 2.51665i) q^{14} +(-17.8825 + 14.2653i) q^{15} +(-6.19042 + 10.7221i) q^{16} +(-23.8012 + 13.7416i) q^{17} +(-29.4022 + 9.07925i) q^{18} +(1.27488 + 0.736052i) q^{19} -58.6404 q^{20} +(5.29914 + 20.3204i) q^{21} +9.00000 q^{22} +(28.1602 + 16.2583i) q^{23} +(-35.2394 - 13.8242i) q^{24} +(-16.5712 - 28.7022i) q^{25} +(22.2243 - 38.4936i) q^{26} +(-11.7260 - 24.3208i) q^{27} +(-21.8651 + 49.1925i) q^{28} +38.7082i q^{29} +(-11.6690 - 77.3384i) q^{30} +(13.6290 - 7.86870i) q^{31} +(4.07018 + 7.04976i) q^{32} +(1.17815 + 7.80838i) q^{33} -93.9687i q^{34} +(-53.0800 + 5.61249i) q^{35} +(15.3808 - 67.4831i) q^{36} +(5.09952 + 2.94421i) q^{37} +(-4.35897 + 2.51665i) q^{38} +(36.3063 + 14.2427i) q^{39} +(48.1069 - 83.3235i) q^{40} -47.3245 q^{41} +(-69.2289 - 19.0480i) q^{42} -12.6904 q^{43} +(-10.1216 + 17.5311i) q^{44} +(65.5710 - 20.2480i) q^{45} +(-96.2831 + 55.5891i) q^{46} +(11.4237 - 19.7864i) q^{47} +(29.0356 - 23.1624i) q^{48} +(-15.0835 + 46.6207i) q^{49} +113.318 q^{50} +(81.5270 - 12.3010i) q^{51} +(49.9877 + 86.5812i) q^{52} +(-78.1152 + 45.0998i) q^{53} +(92.0614 + 6.85650i) q^{54} -20.0712 q^{55} +(-51.9614 - 71.4247i) q^{56} +(-2.75405 - 3.45239i) q^{57} +(-114.617 - 66.1741i) q^{58} +(-18.1401 - 31.4196i) q^{59} +(163.770 + 64.2461i) q^{60} +(32.6069 - 56.4768i) q^{61} +53.8081i q^{62} +(7.46356 - 62.5563i) q^{63} -77.3562 q^{64} +(-49.5633 + 85.8461i) q^{65} +(-25.1351 - 9.86036i) q^{66} +(-8.13479 + 4.69662i) q^{67} +(183.041 + 105.679i) q^{68} +(-60.8329 - 76.2581i) q^{69} +(74.1247 - 166.767i) q^{70} +94.6770 q^{71} +(83.2705 + 77.2162i) q^{72} +(-92.0638 + 53.1531i) q^{73} +(-17.4359 + 10.0666i) q^{74} +(14.8340 + 98.3147i) q^{75} -11.3211i q^{76} +(-7.48391 + 16.8375i) q^{77} +(-104.241 + 83.1558i) q^{78} +(-18.4521 + 31.9599i) q^{79} +(47.2027 + 81.7574i) q^{80} +(6.10263 + 80.7698i) q^{81} +(80.9042 - 140.130i) q^{82} -11.2598 q^{83} +(114.960 - 113.429i) q^{84} +209.563i q^{85} +(21.6951 - 37.5769i) q^{86} +(42.4085 - 108.104i) q^{87} +(-16.6069 - 28.7639i) q^{88} +(-77.0661 + 133.482i) q^{89} +(-52.1425 + 228.774i) q^{90} +(53.5345 + 73.5871i) q^{91} -250.066i q^{92} +(-46.6838 + 7.04377i) q^{93} +(39.0589 + 67.6521i) q^{94} +(9.72111 - 5.61249i) q^{95} +(-3.64347 - 24.1478i) q^{96} -22.6422i q^{97} +(-112.260 - 124.364i) q^{98} +(5.26450 - 23.0979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) \) 16 * q - 24 * q^4 - 16 * q^9	\( 16 q - 24 q^{4} - 16 q^{9} + 96 q^{10} - 88 q^{12} - 208 q^{13} - 24 q^{16} + 144 q^{22} - 40 q^{25} + 264 q^{30} + 96 q^{36} + 432 q^{40} - 448 q^{42} - 128 q^{43} + 352 q^{48} - 504 q^{49} + 280 q^{51} + 312 q^{52} - 96 q^{55} + 184 q^{61} - 112 q^{64} - 448 q^{69} - 528 q^{75} + 80 q^{79} + 584 q^{81} + 544 q^{82} - 448 q^{87} + 72 q^{88} - 384 q^{90} - 88 q^{94}+O(q^{100}) \) 16 * q - 24 * q^4 - 16 * q^9 + 96 * q^10 - 88 * q^12 - 208 * q^13 - 24 * q^16 + 144 * q^22 - 40 * q^25 + 264 * q^30 + 96 * q^36 + 432 * q^40 - 448 * q^42 - 128 * q^43 + 352 * q^48 - 504 * q^49 + 280 * q^51 + 312 * q^52 - 96 * q^55 + 184 * q^61 - 112 * q^64 - 448 * q^69 - 528 * q^75 + 80 * q^79 + 584 * q^81 + 544 * q^82 - 448 * q^87 + 72 * q^88 - 384 * q^90 - 88 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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