LMFDB - Embedded newform 273.3.w.c.116.8

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			116.8
Root			$-1.95177 + 0.330355i$ of defining polynomial
Character	$\chi$	$=$	273.116
Dual form			273.3.w.c.233.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70956 + 2.96105i) q^{2} +(0.447581 + 2.96642i) q^{3} +(-3.84521 + 6.66010i) q^{4} +(-3.81256 - 6.60355i) q^{5} +(-8.01856 + 6.39660i) q^{6} +(-4.11804 + 5.66055i) q^{7} -12.6180 q^{8} +(-8.59934 + 2.65543i) q^{9} +O(q^{10})$	\(q+(1.70956 + 2.96105i) q^{2} +(0.447581 + 2.96642i) 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} +(-8.59934 + 2.65543i) q^{9} +(13.0356 - 22.5784i) q^{10} +(1.31613 - 2.27960i) q^{11} +(-21.4777 - 8.42558i) 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} +(-22.5640 - 20.9234i) q^{18} +(1.27488 - 0.736052i) q^{19} +58.6404 q^{20} +(-18.6347 - 9.68229i) q^{21} +9.00000 q^{22} +(-28.1602 + 16.2583i) q^{23} +(-5.64758 - 37.4303i) 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} +(72.8115 + 28.5635i) q^{30} +(13.6290 + 7.86870i) q^{31} +(-4.07018 + 7.04976i) q^{32} +(7.35133 + 2.88388i) 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} +(-5.81856 - 38.5635i) q^{39} +(48.1069 + 83.3235i) q^{40} +47.3245 q^{41} +(-3.18751 - 71.7308i) q^{42} -12.6904 q^{43} +(10.1216 + 17.5311i) q^{44} +(50.3208 + 46.6622i) 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} +(-30.1105 + 76.7549i) q^{51} +(49.9877 - 86.5812i) q^{52} +(78.1152 + 45.0998i) q^{53} +(51.9686 - 76.2993i) 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} +(26.2463 + 173.952i) q^{60} +(32.6069 + 56.4768i) q^{61} +53.8081i q^{62} +(20.3812 - 59.6121i) q^{63} -77.3562 q^{64} +(49.5633 + 85.8461i) q^{65} +(4.02823 + 26.6978i) 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} +(108.506 - 33.5062i) q^{72} +(-92.0638 - 53.1531i) q^{73} +(17.4359 + 10.0666i) q^{74} +(-92.5600 - 36.3108i) 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} +(66.8974 - 45.6699i) q^{81} +(80.9042 + 140.130i) q^{82} +11.2598 q^{83} +(136.139 - 86.8787i) q^{84} -209.563i q^{85} +(-21.6951 - 37.5769i) q^{86} +(-114.825 + 17.3251i) 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} +(-17.2418 + 43.9512i) q^{93} +(39.0589 - 67.6521i) q^{94} +(-9.72111 - 5.61249i) q^{95} +(-22.7343 - 8.91854i) 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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	0.876848	+	0.480768i	$0.159642\pi$
$2$	1.70956	+	2.96105i	0.854781	+	1.48052i	−0.0220666	+	0.999757i	$0.507025\pi$
$3$	0.447581	+	2.96642i	0.149194	+	0.988808i
$3$	0.447581	+	2.96642i	0.149194	+	0.988808i
$4$	−3.84521	+	6.66010i	−0.961302	+	1.66502i
$5$	−3.81256	−	6.60355i	−0.762512	−	1.32071i	−0.941552	−	0.336868i	$-0.890632\pi$
$5$	−3.81256	−	6.60355i	−0.762512	−	1.32071i	0.179040	−	0.983842i	$-0.442701\pi$
$6$	−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
$9$	−8.59934	+	2.65543i	−0.955482	+	0.295048i
$10$	13.0356	−	22.5784i	1.30356	−	2.25784i
$11$	1.31613	−	2.27960i	0.119648	−	0.207236i	−0.799980	−	0.600026i	$-0.795157\pi$
$11$	1.31613	−	2.27960i	0.119648	−	0.207236i	0.919628	+	0.392790i	$0.128490\pi$
$12$	−21.4777	−	8.42558i	−1.78981	−	0.702132i
$13$	−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	$-0.0337046\pi$
$17$	23.8012	+	13.7416i	1.40007	+	0.808331i	0.405671	+	0.914019i	$0.367038\pi$
$18$	−22.5640	−	20.9234i	−1.25355	−	1.16241i
$19$	1.27488	−	0.736052i	0.0670989	−	0.0387396i	−0.466075	−	0.884745i	$-0.654332\pi$
$19$	1.27488	−	0.736052i	0.0670989	−	0.0387396i	0.533174	+	0.846006i	$0.320999\pi$
$20$	58.6404			2.93202
$21$	−18.6347	−	9.68229i	−0.887368	−	0.461061i
$22$	9.00000			0.409091
$23$	−28.1602	+	16.2583i	−1.22436	+	0.706882i	−0.965843	−	0.259126i	$-0.916565\pi$
$23$	−28.1602	+	16.2583i	−1.22436	+	0.706882i	−0.258512	+	0.966008i	$0.583232\pi$
$24$	−5.64758	−	37.4303i	−0.235316	−	1.55960i
$25$	−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	$0.767414\pi$
$30$	72.8115	+	28.5635i	2.42705	+	0.952118i
$31$	13.6290	+	7.86870i	0.439645	+	0.253829i	0.703447	−	0.710748i	$-0.251643\pi$
$31$	13.6290	+	7.86870i	0.439645	+	0.253829i	−0.263802	+	0.964577i	$0.584977\pi$
$32$	−4.07018	+	7.04976i	−0.127193	+	0.220305i
$33$	7.35133	+	2.88388i	0.222767	+	0.0873904i
$34$			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	−0.429502	−	0.903066i	$-0.641311\pi$
$37$	5.09952	−	2.94421i	0.137825	−	0.0795732i	0.567327	+	0.823493i	$0.307978\pi$
$38$	4.35897	+	2.51665i	0.114710	+	0.0662277i
$39$	−5.81856	−	38.5635i	−0.149194	−	0.988808i
$40$	48.1069	+	83.3235i	1.20267	+	2.08309i
$41$	47.3245			1.15426			0.577128	−	0.816654i	$-0.304173\pi$
$41$	47.3245			1.15426			0.577128	+	0.816654i	$0.304173\pi$
$42$	−3.18751	−	71.7308i	−0.0758930	−	1.70788i
$43$	−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
$45$	50.3208	+	46.6622i	1.11824	+	1.03694i
$46$	−96.2831	−	55.5891i	−2.09311	−	1.20846i
$47$	−11.4237	−	19.7864i	−0.243057	−	0.420987i	0.718527	−	0.695499i	$-0.244817\pi$
$47$	−11.4237	−	19.7864i	−0.243057	−	0.420987i	−0.961583	+	0.274513i	$0.911483\pi$
$48$	29.0356	−	23.1624i	0.604909	−	0.482550i
$49$	−15.0835	−	46.6207i	−0.307827	−	0.951442i
$50$	−113.318			−2.26637
$51$	−30.1105	+	76.7549i	−0.590402	+	1.50500i
$52$	49.9877	−	86.5812i	0.961302	−	1.66502i
$53$	78.1152	+	45.0998i	1.47387	+	0.850940i	0.999567	−	0.0294208i	$-0.00936629\pi$
$53$	78.1152	+	45.0998i	1.47387	+	0.850940i	0.474304	+	0.880361i	$0.342700\pi$
$54$	51.9686	−	76.2993i	0.962382	−	1.41295i
$55$	−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	$-0.733854\pi$
$59$	18.1401	−	31.4196i	0.307460	−	0.532536i	0.977806	+	0.209513i	$0.0671878\pi$
$60$	26.2463	+	173.952i	0.437439	+	2.89920i
$61$	32.6069	+	56.4768i	0.534539	+	0.925848i	0.999186	+	0.0403523i	$0.0128480\pi$
$61$	32.6069	+	56.4768i	0.534539	+	0.925848i	−0.464647	+	0.885496i	$0.653819\pi$
$62$			53.8081i			0.867873i
$63$	20.3812	−	59.6121i	0.323511	−	0.946224i
$64$	−77.3562			−1.20869
$65$	49.5633	+	85.8461i	0.762512	+	1.32071i
$66$	4.02823	+	26.6978i	0.0610338	+	0.404512i
$67$	−8.13479	−	4.69662i	−0.121415	−	0.0700989i	0.438063	−	0.898944i	$-0.355665\pi$
$67$	−8.13479	−	4.69662i	−0.121415	−	0.0700989i	−0.559477	+	0.828846i	$0.688998\pi$
$68$	−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	$-0.732311\pi$
$71$	−94.6770			−1.33348			−0.666739	+	0.745291i	$0.732311\pi$
$72$	108.506	−	33.5062i	1.50703	−	0.465364i
$73$	−92.0638	−	53.1531i	−1.26115	−	0.728124i	−0.287851	−	0.957675i	$-0.592941\pi$
$73$	−92.0638	−	53.1531i	−1.26115	−	0.728124i	−0.973297	+	0.229551i	$0.926274\pi$
$74$	17.4359	+	10.0666i	0.235620	+	0.136035i
$75$	−92.5600	−	36.3108i	−1.23413	−	0.484143i
$76$			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	0.725286	−	0.688448i	$-0.241708\pi$
$79$	−18.4521	−	31.9599i	−0.233571	−	0.404556i	−0.958856	+	0.283892i	$0.908374\pi$
$80$	−47.2027	+	81.7574i	−0.590033	+	1.02197i
$81$	66.8974	−	45.6699i	0.825893	−	0.563826i
$82$	80.9042	+	140.130i	0.986636	+	1.70890i
$83$	11.2598			0.135660			0.0678302	−	0.997697i	$-0.478392\pi$
$83$	11.2598			0.135660			0.0678302	+	0.997697i	$0.478392\pi$
$84$	136.139	−	86.8787i	1.62071	−	1.03427i
$85$		−	209.563i		−	2.46545i
$86$	−21.6951	−	37.5769i	−0.252268	−	0.436941i
$87$	−114.825	+	17.3251i	−1.31983	+	0.199139i
$88$	−16.6069	+	28.7639i	−0.188714	+	0.326863i
$89$	77.0661	+	133.482i	0.865912	+	1.49980i	0.866139	+	0.499803i	$0.166594\pi$
$89$	77.0661	+	133.482i	0.865912	+	1.49980i	−0.000227621		1.00000i	$0.500072\pi$
$90$	−52.1425	+	228.774i	−0.579361	+	2.54194i
$91$	53.5345	−	73.5871i	0.588291	−	0.808649i
$92$		−	250.066i		−	2.71811i
$93$	−17.2418	+	43.9512i	−0.185396	+	0.472594i
$94$	39.0589	−	67.6521i	0.415521	−	0.719703i
$95$	−9.72111	−	5.61249i	−0.102327	−	0.0590788i
$96$	−22.7343	−	8.91854i	−0.236816	−	0.0929015i
$97$			22.6422i			0.233425i	0.993166	+	0.116712i	$0.0372355\pi$
$97$			22.6422i			0.233425i	−0.993166	+	0.116712i	$0.962764\pi$
$98$	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	$-0.290527\pi$
$101$	23.4549	+	13.5417i	0.232227	+	0.134076i	−0.379372	+	0.925244i	$0.623860\pi$
$102$	−278.751	+	42.0586i	−2.73285	+	0.412339i
$103$	−53.9644	−	93.4690i	−0.523926	−	0.907466i	−0.999612	−	0.0278513i	$-0.991134\pi$
$103$	−53.9644	−	93.4690i	−0.523926	−	0.907466i	0.475686	−	0.879615i	$-0.342200\pi$
$104$	164.034			1.57725
$105$	7.10858	+	159.970i	0.0677008	+	1.52352i
$106$			308.404i			2.90947i
$107$	12.7306	−	7.35002i	0.118978	−	0.0686918i	−0.439330	−	0.898326i	$-0.644784\pi$
$107$	12.7306	−	7.35002i	0.118978	−	0.0686918i	0.558308	+	0.829634i	$0.311451\pi$
$108$	207.068	+	15.4219i	1.91729	+	0.142795i
$109$	125.211	+	72.2904i	1.14872	+	0.663215i	0.948575	−	0.316551i	$-0.102525\pi$
$109$	125.211	+	72.2904i	1.14872	+	0.663215i	0.200146	+	0.979766i	$0.435858\pi$
$110$	−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	$-0.0420944\pi$
$114$	−5.51447	+	14.0570i	−0.0483725	+	0.123307i
$115$	214.725	+	123.971i	1.86717	+	1.07801i
$116$	−257.800	−	148.841i	−2.22242	−	1.28311i
$117$	111.791	−	34.5206i	0.955482	−	0.295048i
$118$	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
$123$	21.1815	+	140.384i	0.172208	+	1.14134i
$124$	−104.813	+	60.5136i	−0.845263	+	0.488013i
$125$	62.0875			0.496700
$126$	211.357	−	41.5609i	1.67744	−	0.329848i
$127$	−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
$129$	−5.67999	−	37.6452i	−0.0440309	−	0.291823i
$130$	−169.463	+	293.519i	−1.30356	+	2.25784i
$131$	127.067	−	73.3622i	0.969977	−	0.560017i	0.0707481	−	0.997494i	$-0.477461\pi$
$131$	127.067	−	73.3622i	0.969977	−	0.560017i	0.899229	+	0.437477i	$0.144128\pi$
$132$	−47.4743	+	37.8714i	−0.359654	+	0.286905i
$133$	−1.08354	+	10.2476i	−0.00814695	+	0.0770496i
$134$		−	32.1167i		−	0.239677i
$135$	−115.897	+	170.158i	−0.858498	+	1.26043i
$136$	−300.323	−	173.392i	−2.20826	−	1.27494i
$137$	46.2002	−	80.0212i	0.337228	−	0.584096i	−0.646682	−	0.762760i	$-0.723844\pi$
$137$	46.2002	−	80.0212i	0.337228	−	0.584096i	0.983910	+	0.178664i	$0.0571773\pi$
$138$	121.806	−	310.497i	0.882654	−	2.24998i
$139$	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
$144$	81.7053	+	75.7649i	0.567398	+	0.526145i
$145$	255.612	−	147.577i	1.76284	−	1.01778i
$146$		−	363.474i		−	2.48955i
$147$	131.546	−	65.6107i	0.894868	−	0.446331i
$148$			45.2844i			0.305975i
$149$	56.6732	+	98.1608i	0.380357	+	0.658798i	0.991113	−	0.133021i	$-0.0424678\pi$
$149$	56.6732	+	98.1608i	0.380357	+	0.658798i	−0.610756	+	0.791819i	$0.709134\pi$
$150$	−50.7192	−	336.150i	−0.338128	−	2.24100i
$151$	−108.637	−	62.7217i	−0.719452	−	0.415376i	0.0950990	−	0.995468i	$-0.469683\pi$
$151$	−108.637	−	62.7217i	−0.719452	−	0.415376i	−0.814551	+	0.580092i	$0.803017\pi$
$152$	−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
$156$	279.210	+	109.533i	1.78981	+	0.702132i
$157$	−72.7383	+	125.986i	−0.463302	+	0.802462i	−0.999123	−	0.0418695i	$-0.986669\pi$
$157$	−72.7383	+	125.986i	−0.463302	+	0.802462i	0.535822	+	0.844331i	$0.320002\pi$
$158$	63.0900	−	109.275i	0.399304	−	0.691614i
$159$	−98.8223	+	251.909i	−0.621524	+	1.58433i
$160$	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	−0.979337	−	0.202234i	$-0.935180\pi$
$163$	−210.900	+	121.763i	−1.29387	+	0.747014i	−0.314528	+	0.949248i	$0.601846\pi$
$164$	−181.972	+	315.186i	−1.10959	+	1.92186i
$165$	−8.98351	−	59.5398i	−0.0544455	−	0.360847i
$166$	19.2494	+	33.3409i	0.115960	+	0.200849i
$167$	67.4361			0.403809			0.201905	−	0.979405i	$-0.435287\pi$
$167$	67.4361			0.403809			0.201905	+	0.979405i	$0.435287\pi$
$168$	235.133	+	122.171i	1.39960	+	0.727209i
$169$	169.000			1.00000
$170$	620.527	−	358.261i	3.65016	−	2.10742i
$171$	−9.00859	+	9.71492i	−0.0526818	+	0.0568124i
$172$	48.7973	−	84.5194i	0.283705	−	0.491392i
$173$	39.2307	−	22.6499i	0.226767	−	0.130924i	−0.382313	−	0.924033i	$-0.624872\pi$
$173$	39.2307	−	22.6499i	0.226767	−	0.130924i	0.609080	+	0.793109i	$0.291539\pi$
$174$	−247.601	−	310.384i	−1.42299	−	1.78382i
$175$	−94.2293	−	211.999i	−0.538453	−	1.21142i
$176$	−32.5895			−0.185167
$177$	101.323	+	39.7485i	0.572447	+	0.224568i
$178$	−263.499	+	456.393i	−1.48033	+	2.56401i
$179$	98.2143	+	56.7040i	0.548683	+	0.316782i	0.748591	−	0.663032i	$-0.230731\pi$
$179$	98.2143	+	56.7040i	0.548683	+	0.316782i	−0.199908	+	0.979815i	$0.564064\pi$
$180$	−504.269	+	155.715i	−2.80149	+	0.865086i
$181$	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
$186$	−159.618	+	24.0835i	−0.858160	+	0.129481i
$187$	62.6507	−	36.1714i	0.335031	−	0.193430i
$188$	175.706			0.934604
$189$	185.957	+	33.7781i	0.983900	+	0.178720i
$190$		−	38.3796i		−	0.201998i
$191$	99.9100	−	57.6831i	0.523089	−	0.302006i	−0.215108	−	0.976590i	$-0.569010\pi$
$191$	99.9100	−	57.6831i	0.523089	−	0.302006i	0.738198	+	0.674584i	$0.235677\pi$
$192$	−34.6232	−	229.471i	−0.180329	−	1.19516i
$193$	−139.629	−	80.6149i	−0.723466	−	0.417694i	0.0925608	−	0.995707i	$-0.470495\pi$
$193$	−139.629	−	80.6149i	−0.723466	−	0.417694i	−0.816027	+	0.578013i	$0.803828\pi$
$194$	−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	$-0.504253\pi$
$197$	−5.26450			−0.0267234			−0.0133617	+	0.999911i	$0.504253\pi$
$198$	−77.3941	+	23.8989i	−0.390879	+	0.120701i
$199$	150.499	−	260.671i	0.756275	−	1.30991i	−0.188463	−	0.982080i	$-0.560351\pi$
$199$	150.499	−	260.671i	0.756275	−	1.30991i	0.944738	−	0.327826i	$-0.106316\pi$
$200$	209.096	−	362.165i	1.04548	−	1.81082i
$201$	10.2912	−	26.2334i	0.0512000	−	0.130514i
$202$			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
$207$	198.986	−	214.588i	0.961286	−	1.03666i
$208$	80.4754	+	139.387i	0.386901	+	0.670132i
$209$		−	3.87495i		−	0.0185404i
$210$	−461.526	+	294.527i	−2.19774	+	1.40251i
$211$	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
$213$	−42.3756	−	280.852i	−0.198947	−	1.31855i
$214$	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
$219$	116.468	−	296.891i	0.531820	−	1.35566i
$220$	77.1781	−	133.676i	0.350810	−	0.607620i
$221$	−309.416	−	178.641i	−1.40007	−	0.808331i
$222$	−22.0579	+	56.2279i	−0.0993598	+	0.253279i
$223$			102.696i			0.460522i	0.973129	+	0.230261i	$0.0739580\pi$
$223$			102.696i			0.460522i	−0.973129	+	0.230261i	$0.926042\pi$
$224$	−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	$-0.744218\pi$
$227$	62.7246	−	108.642i	0.276320	−	0.478600i	0.970467	+	0.241233i	$0.0775518\pi$
$228$	−33.5832	+	5.06711i	−0.147295	+	0.0222242i
$229$	−374.053	+	215.960i	−1.63342	+	0.943056i	−0.650393	+	0.759598i	$0.725396\pi$
$229$	−374.053	+	215.960i	−1.63342	+	0.943056i	−0.983028	+	0.183458i	$0.941271\pi$
$230$			847.747i			3.68586i
$231$	−46.5974	+	29.7366i	−0.201720	+	0.128730i
$232$		−	488.420i		−	2.10526i
$233$	−116.689	+	67.3705i	−0.500811	+	0.289144i	−0.729049	−	0.684462i	$-0.760037\pi$
$233$	−116.689	+	67.3705i	−0.500811	+	0.289144i	0.228237	+	0.973606i	$0.426704\pi$
$234$	293.332	+	272.005i	1.25355	+	1.16241i
$235$	−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	$-0.347791\pi$
$239$	219.958			0.920326			0.460163	+	0.887834i	$0.347791\pi$
$240$	−263.654	−	103.430i	−1.09856	−	0.430959i
$241$	112.644	+	65.0348i	0.467401	+	0.269854i	0.715151	−	0.698970i	$-0.246358\pi$
$241$	112.644	+	65.0348i	0.467401	+	0.269854i	−0.247750	+	0.968824i	$0.579691\pi$
$242$	−195.012	+	337.771i	−0.805834	+	1.39575i
$243$	165.418	+	178.005i	0.680734	+	0.732531i
$244$	−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
$249$	5.03968	+	33.4014i	0.0202397	+	0.134142i
$250$	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	$-0.142422\pi$
$252$	318.652	+	364.962i	1.26449	+	1.44826i
$253$			85.5918i			0.338307i
$254$	−60.0362	−	103.986i	−0.236363	−	0.409393i
$255$	621.653	−	93.7965i	2.43786	−	0.367830i
$256$	241.785	−	418.784i	0.944473	−	1.63587i
$257$	−363.383	+	209.799i	−1.41394	+	0.816340i	−0.995757	−	0.0920216i	$-0.970667\pi$
$257$	−363.383	+	209.799i	−1.41394	+	0.816340i	−0.418185	+	0.908362i	$0.637334\pi$
$258$	101.759	−	81.1755i	0.394414	−	0.314634i
$259$	−4.33418	+	40.9904i	−0.0167343	+	0.158264i
$260$	−762.325			−2.93202
$261$	−102.787	−	332.865i	−0.393820	−	1.27535i
$262$	434.458	+	250.835i	1.65824	+	0.957384i
$263$	296.339	+	171.091i	1.12676	+	0.650537i	0.943119	−	0.332456i	$-0.107877\pi$
$263$	296.339	+	171.091i	1.12676	+	0.650537i	0.183644	+	0.982993i	$0.441211\pi$
$264$	−92.7590	−	36.3888i	−0.351360	−	0.137836i
$265$		−	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	$-0.284144\pi$
$269$	71.7141	+	41.4042i	0.266595	+	0.153919i	−0.360744	+	0.932665i	$0.617477\pi$
$270$	−701.979	−	52.2817i	−2.59992	−	0.193636i
$271$	−451.032	+	260.403i	−1.66432	+	0.960897i	−0.693709	+	0.720255i	$0.744025\pi$
$271$	−451.032	+	260.403i	−1.66432	+	0.960897i	−0.970614	+	0.240642i	$0.922642\pi$
$272$		−	340.266i		−	1.25098i
$273$	242.252	+	125.870i	0.887368	+	0.461061i
$274$	315.929			1.15302
$275$	43.6197	+	75.5515i	0.158617	+	0.274733i
$276$	741.801	−	111.925i	2.68769	−	0.405525i
$277$	−76.3685	+	132.274i	−0.275699	+	0.477524i	−0.970311	−	0.241860i	$-0.922243\pi$
$277$	−76.3685	+	132.274i	−0.275699	+	0.477524i	0.694612	+	0.719384i	$0.255576\pi$
$278$	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	$-0.306200\pi$
$281$	321.417			1.14383			0.571917	+	0.820312i	$0.306200\pi$
$282$	218.167	+	85.5856i	0.773641	+	0.303495i
$283$	27.7973	−	48.1463i	0.0982236	−	0.170128i	−0.812726	−	0.582646i	$-0.802017\pi$
$283$	27.7973	−	48.1463i	0.0982236	−	0.170128i	0.910949	+	0.412518i	$0.135351\pi$
$284$	364.053	−	630.558i	1.28188	−	2.22027i
$285$	12.2980	−	31.3490i	0.0431510	−	0.109996i
$286$	−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
$291$	−67.1663	+	10.1342i	−0.230812	+	0.0348255i
$292$	708.009	−	408.769i	2.42469	−	1.39989i
$293$	−506.781			−1.72963			−0.864813	−	0.502093i	$-0.832563\pi$
$293$	−506.781			−1.72963			−0.864813	+	0.502093i	$0.832563\pi$
$294$	419.162	+	277.347i	1.42572	+	0.943358i
$295$	−276.641			−0.937767
$296$	−64.3457	+	37.1500i	−0.217384	+	0.125507i
$297$	−70.8745	−	5.27856i	−0.238635	−	0.0177729i
$298$	−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
$303$	−29.6724	+	75.6382i	−0.0979288	+	0.249631i
$304$	−15.7841	−	9.11293i	−0.0519213	−	0.0299768i
$305$	248.631	−	430.642i	0.815185	−	1.41194i
$306$	−249.527	−	808.069i	−0.815449	−	2.64075i
$307$		−	199.468i		−	0.649734i	−0.945760	−	0.324867i	$-0.894681\pi$
$307$		−	199.468i		−	0.649734i	0.945760	−	0.324867i	$-0.105319\pi$
$308$	−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	$-0.417089\pi$
$311$	−140.108	−	80.8915i	−0.450509	−	0.260101i	−0.708045	+	0.706167i	$0.750423\pi$
$312$	73.4185	+	486.594i	0.235316	+	1.55960i
$313$	−195.142	−	337.997i	−0.623458	−	1.07986i	−0.988837	−	0.149003i	$-0.952394\pi$
$313$	−195.142	−	337.997i	−0.623458	−	1.07986i	0.365378	−	0.930859i	$-0.380940\pi$
$314$	−497.403			−1.58409
$315$	−471.356	+	92.6865i	−1.49637	+	0.294243i
$316$	283.808			0.898128
$317$	22.9875	+	39.8155i	0.0725158	+	0.125601i	0.900003	−	0.435883i	$-0.143564\pi$
$317$	22.9875	+	39.8155i	0.0725158	+	0.125601i	−0.827488	+	0.561484i	$0.810231\pi$
$318$	−914.857	+	138.036i	−2.87691	+	0.434075i
$319$	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
$324$	46.9318	+	621.153i	0.144851	+	1.91714i
$325$	215.426	−	373.129i	0.662850	−	1.14809i
$326$	−721.094	−	416.324i	−2.21194	−	1.27707i
$327$	−158.402	+	403.784i	−0.484410	+	1.23481i
$328$	−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	−0.433906	−	0.900958i	$-0.642865\pi$
$331$	42.8290	−	24.7274i	0.129393	−	0.0747050i	0.563299	+	0.826253i	$0.309532\pi$
$332$	−43.2963	+	74.9915i	−0.130411	+	0.225878i
$333$	−36.0344	+	38.8597i	−0.108211	+	0.116696i
$334$	115.286	+	199.682i	0.345168	+	0.597849i
$335$			71.6247i			0.213805i
$336$	11.5421	+	259.741i	0.0343516	+	0.773039i
$337$	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
$339$	88.3993	−	13.3379i	0.260765	−	0.0393449i
$340$	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
$345$	−271.645	+	692.452i	−0.787377	+	2.00711i
$346$	134.135	+	77.4428i	0.387673	+	0.223823i
$347$	481.422	+	277.949i	1.38738	+	0.801006i	0.993020	−	0.117949i	$-0.0376320\pi$
$347$	481.422	+	277.949i	1.38738	+	0.801006i	0.394363	+	0.918955i	$0.370965\pi$
$348$	326.139	−	831.364i	0.937182	−	2.38898i
$349$		−	121.834i		−	0.349094i	−0.984649	−	0.174547i	$-0.944154\pi$
$349$		−	121.834i		−	0.349094i	0.984649	−	0.174547i	$-0.0558461\pi$
$350$	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	−0.498533	−	0.866871i	$-0.666128\pi$
$353$	177.017	−	306.603i	0.501465	−	0.868564i	0.999999	−	0.00169298i	$-0.000538894\pi$
$354$	55.5210	+	367.975i	0.156839	+	1.03948i
$355$	360.962	+	625.204i	1.01679	+	1.76114i
$356$	−1185.34			−3.32961
$357$	−310.478	−	486.522i	−0.869688	−	1.36281i
$358$			387.756i			1.08312i
$359$	−230.318	−	398.922i	−0.641554	−	1.11120i	−0.985086	−	0.172063i	$-0.944957\pi$
$359$	−230.318	−	398.922i	−0.641554	−	1.11120i	0.343532	−	0.939141i	$-0.388376\pi$
$360$	−634.947	−	588.783i	−1.76374	−	1.63551i
$361$	−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
$366$	−622.719	−	244.289i	−1.70142	−	0.667457i
$367$	−197.260	+	341.665i	−0.537494	+	0.930967i	0.461544	+	0.887117i	$0.347296\pi$
$367$	−197.260	+	341.665i	−0.537494	+	0.930967i	−0.999038	+	0.0438500i	$0.986038\pi$
$368$	348.646	+	201.291i	0.947408	+	0.546986i
$369$	−406.959	+	125.667i	−1.10287	+	0.340561i
$370$		−	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	0.877470	−	0.479632i	$-0.159230\pi$
$373$	8.71374	+	15.0926i	0.0233612	+	0.0404629i	−0.854108	+	0.520095i	$0.825897\pi$
$374$	214.211	+	123.675i	0.572756	+	0.330681i
$375$	27.7892	+	184.178i	0.0741046	+	0.491141i
$376$	144.144	+	249.664i	0.383361	+	0.664001i
$377$		−	503.207i		−	1.33477i
$378$	217.887	+	608.374i	0.576420	+	1.60945i
$379$			364.695i			0.962255i	0.876651	+	0.481128i	$0.159773\pi$
$379$			364.695i			0.962255i	−0.876651	+	0.481128i	$0.840227\pi$
$380$	74.7594	−	43.1624i	0.196735	−	0.113585i
$381$	−15.7181	−	104.175i	−0.0412549	−	0.273424i
$382$	341.605	+	197.226i	0.894254	+	0.516298i
$383$	−189.775	−	328.701i	−0.495497	−	0.858226i	0.504489	−	0.863418i	$-0.331681\pi$
$383$	−189.775	−	328.701i	−0.495497	−	0.858226i	−0.999987	+	0.00519153i	$0.998347\pi$
$384$	543.922	−	433.900i	1.41646	−	1.12995i
$385$	82.6541	−	113.614i	0.214686	−	0.295102i
$386$		−	551.265i		−	1.42815i
$387$	109.129	−	33.6985i	0.281988	−	0.0870763i
$388$	−150.799	−	87.0639i	−0.388657	−	0.224391i
$389$	−3.35580	−	1.93747i	−0.00862675	−	0.00498065i	0.495680	−	0.868505i	$-0.334919\pi$
$389$	−3.35580	−	1.93747i	−0.00862675	−	0.00498065i	−0.504307	+	0.863524i	$0.668252\pi$
$390$	−946.549	−	371.326i	−2.42705	−	0.952118i
$391$	−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
$396$	−133.591	−	123.878i	−0.337352	−	0.312824i
$397$	566.438	−	327.033i	1.42680	−	0.823761i	0.429929	−	0.902863i	$-0.358539\pi$
$397$	566.438	−	327.033i	1.42680	−	0.823761i	0.996867	+	0.0791018i	$0.0252052\pi$
$398$	1029.15			2.58580
$399$	−30.8837	+	1.37238i	−0.0774028	+	0.00343955i
$400$	410.332			1.02583
$401$	49.3294	+	85.4410i	0.123016	+	0.213070i	0.920956	−	0.389667i	$-0.127410\pi$
$401$	49.3294	+	85.4410i	0.123016	+	0.213070i	−0.797940	+	0.602737i	$0.794077\pi$
$402$	95.2717	−	14.3748i	0.236994	−	0.0357583i
$403$	−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
$408$	379.934	−	968.493i	0.931212	−	2.37376i
$409$	−337.204	−	194.685i	−0.824460	−	0.476002i	0.0274923	−	0.999622i	$-0.491248\pi$
$409$	−337.204	−	194.685i	−0.824460	−	0.476002i	−0.851952	+	0.523620i	$0.824581\pi$
$410$	616.904	−	1068.51i	1.50464	−	2.60612i
$411$	258.055	+	101.234i	0.627871	+	0.246310i
$412$	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
$417$	90.9118	+	602.534i	0.218014	+	1.44493i
$418$	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	$-0.0386045\pi$
$420$	−1092.75	−	567.773i	−2.60178	−	1.35184i
$421$			89.7621i			0.213212i	0.994301	+	0.106606i	$0.0339983\pi$
$421$			89.7621i			0.213212i	−0.994301	+	0.106606i	$0.966002\pi$
$422$	66.5932	+	115.343i	0.157804	+	0.273324i
$423$	150.777	+	139.815i	0.356448	+	0.330532i
$424$	−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
$429$	−95.5672	−	37.4905i	−0.222767	−	0.0873904i
$430$	−165.427	+	286.529i	−0.384715	+	0.666346i
$431$	−323.225	+	559.842i	−0.749941	+	1.29894i	0.197909	+	0.980220i	$0.436585\pi$
$431$	−323.225	+	559.842i	−0.749941	+	1.29894i	−0.947850	+	0.318716i	$0.896748\pi$
$432$	−188.181	+	276.284i	−0.435604	+	0.639545i
$433$	−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
$438$	1078.22	−	162.684i	2.46168	−	0.371425i
$439$	−192.296	−	333.066i	−0.438032	−	0.758694i	0.559506	−	0.828826i	$-0.310991\pi$
$439$	−192.296	−	333.066i	−0.438032	−	0.758694i	−0.997538	+	0.0701329i	$0.977658\pi$
$440$	253.259			0.575588
$441$	253.507	+	360.854i	0.574845	+	0.818262i
$442$		−	1221.59i		−	2.76378i
$443$	−429.496	+	247.970i	−0.969517	+	0.559751i	−0.899089	−	0.437766i	$-0.855770\pi$
$443$	−429.496	+	247.970i	−0.969517	+	0.559751i	−0.0704282	+	0.997517i	$0.522437\pi$
$444$	−134.333	+	20.2684i	−0.302551	+	0.0456496i
$445$	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	$-0.281865\pi$
$449$	568.342			1.26580			0.632898	+	0.774235i	$0.281865\pi$
$450$	974.463	−	300.909i	2.16547	−	0.668687i
$451$	62.2850	−	107.881i	0.138104	−	0.239203i
$452$	198.471	+	114.587i	0.439094	+	0.253511i
$453$	137.435	−	350.337i	0.303389	−	0.773371i
$454$	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	−0.291396	−	0.956603i	$-0.594120\pi$
$457$	178.846	−	103.257i	0.391349	−	0.225945i	0.682744	+	0.730657i	$0.260786\pi$
$458$	−1278.93	−	738.393i	−2.79243	−	1.61221i
$459$	55.1132	−	739.998i	0.120072	−	1.61220i
$460$	−1651.32	+	953.391i	−3.58983	+	2.07259i
$461$	223.957			0.485807			0.242903	−	0.970050i	$-0.421900\pi$
$461$	223.957			0.485807			0.242903	+	0.970050i	$0.421900\pi$
$462$	−167.713	−	87.1406i	−0.363014	−	0.188616i
$463$			779.264i			1.68307i	0.540199	+	0.841537i	$0.318349\pi$
$463$			779.264i			1.68307i	−0.540199	+	0.841537i	$0.681651\pi$
$464$	415.034	−	239.620i	0.894470	−	0.516422i
$465$	355.970	−	53.7096i	0.765526	−	0.115504i
$466$	−398.975	−	230.348i	−0.856168	−	0.494309i
$467$	125.682	−	72.5624i	0.269126	−	0.155380i	−0.359364	−	0.933197i	$-0.617006\pi$
$467$	125.682	−	72.5624i	0.269126	−	0.155380i	0.628490	+	0.777817i	$0.283673\pi$
$468$	−199.951	+	877.281i	−0.427245	+	1.87453i
$469$	60.0848	−	26.7065i	0.128113	−	0.0569435i
$470$	−595.659			−1.26736
$471$	−406.286	−	159.384i	−0.862602	−	0.338394i
$472$	−228.892	+	396.452i	−0.484940	+	0.839941i
$473$	−16.7022	+	28.9290i	−0.0353112	+	0.0611608i
$474$	352.394	+	138.242i	0.743447	+	0.291650i
$475$			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	−0.322345	−	0.946622i	$-0.604471\pi$
$479$	315.482	−	546.431i	0.658627	−	1.14077i	0.980971	−	0.194153i	$-0.0621957\pi$
$480$	27.7819	+	184.130i	0.0578790	+	0.383603i
$481$	−66.2937	+	38.2747i	−0.137825	+	0.0795732i
$482$			444.724i			0.922664i
$483$	682.175	−	30.3138i	1.41237	−	0.0627615i
$484$	−877.255			−1.81251
$485$	149.519	−	86.3247i	0.308286	−	0.177989i
$486$	−244.288	+	794.123i	−0.502651	+	1.63400i
$487$	−398.367	−	229.997i	−0.818002	−	0.472273i	0.0317252	−	0.999497i	$-0.489900\pi$
$487$	−398.367	−	229.997i	−0.818002	−	0.472273i	−0.849727	+	0.527223i	$0.823233\pi$
$488$	−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	$-0.204839\pi$
$492$	−1016.42	−	398.736i	−2.06590	−	0.810440i
$493$	−531.914	+	921.302i	−1.07893	+	1.86877i
$494$	−56.6666	−	32.7165i	−0.114710	−	0.0662277i
$495$	172.600	−	53.2978i	0.348686	−	0.107672i
$496$		−	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	−0.266338	−	0.963880i	$-0.585814\pi$
$499$	217.184	−	125.391i	0.435238	−	0.251285i	0.701575	+	0.712595i	$0.252480\pi$
$500$	−238.739	+	413.509i	−0.477479	+	0.827018i
$501$	30.1831	+	200.044i	0.0602458	+	0.399290i
$502$	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	$0.899483\pi$
$504$	−257.170	+	752.185i	−0.510258	+	1.49243i
$505$		−	206.514i		−	0.408939i
$506$	−253.441	+	146.325i	−0.500873	+	0.289179i
$507$	75.6412	+	501.326i	0.149194	+	0.988808i
$508$	135.036	−	233.889i	0.265818	−	0.460411i
$509$	−20.4403	−	35.4037i	−0.0401578	−	0.0695554i	0.845248	−	0.534374i	$-0.179453\pi$
$509$	−20.4403	−	35.4037i	−0.0401578	−	0.0695554i	−0.885406	+	0.464819i	$0.846119\pi$
$510$	1340.49	+	1680.39i	2.62841	+	3.29489i
$511$	679.997	−	302.245i	1.33072	−	0.591478i
$512$	725.669			1.41732
$513$	−32.8506	−	22.3751i	−0.0640363	−	0.0436161i
$514$	−1242.45	−	717.330i	−2.41722	−	1.39558i
$515$	−411.485	+	712.713i	−0.799000	+	1.38391i
$516$	272.561	+	106.924i	0.528219	+	0.207217i
$517$	−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	$-0.203992\pi$
$521$	356.672	+	205.924i	0.684590	+	0.395248i	−0.116992	+	0.993133i	$0.537325\pi$
$522$	809.910	−	873.411i	1.55155	−	1.67320i
$523$	−22.1289	−	38.3284i	−0.0423115	−	0.0732857i	0.844094	−	0.536195i	$-0.180139\pi$
$523$	−22.1289	−	38.3284i	−0.0423115	−	0.0732857i	−0.886406	+	0.462909i	$0.846806\pi$
$524$			1128.37i			2.15338i
$525$	586.704	−	374.411i	1.11753	−	0.713164i
$526$			1169.96i			2.22427i
$527$	216.257	+	374.569i	0.410356	+	0.710757i
$528$	−14.5864	−	96.6742i	−0.0276258	−	0.183095i
$529$	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
$534$	−1471.79	−	577.376i	−2.75617	−	1.08123i
$535$	−97.0725	−	56.0448i	−0.181444	−	0.104757i
$536$	102.645	+	59.2620i	0.191501	+	0.110563i
$537$	−124.249	+	316.725i	−0.231377	+	0.589804i
$538$			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	−0.923729	−	0.383048i	$-0.874874\pi$
$541$	−570.140	+	329.171i	−1.05386	+	0.608449i	−0.130135	+	0.991496i	$0.541541\pi$
$542$	−1542.13	−	890.351i	−2.84526	−	1.64271i
$543$	48.3597	+	320.512i	0.0890601	+	0.590262i
$544$	−193.750	+	111.862i	−0.356159	+	0.205628i
$545$		−	1102.45i		−	2.02284i
$546$	41.4376	+	932.501i	0.0758930	+	1.70788i
$547$	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
$549$	−430.368	−	399.078i	−0.783912	−	0.726917i
$550$	−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
$555$	49.1921	−	125.396i	0.0886344	−	0.225939i
$556$	−781.031	+	1352.78i	−1.40473	+	2.43307i
$557$	89.8156	−	155.565i	0.161249	−	0.279291i	−0.774068	−	0.633102i	$-0.781781\pi$
$557$	89.8156	−	155.565i	0.161249	−	0.279291i	0.935317	+	0.353811i	$0.115114\pi$
$558$	−142.884	−	462.715i	−0.256064	−	0.829238i
$559$	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	$-0.527698\pi$
$563$	−559.119	−	322.808i	−0.993107	−	0.573371i	−0.906202	+	0.422846i	$0.861031\pi$
$564$	78.6425	+	521.217i	0.139437	+	0.924144i
$565$	−196.786	+	113.614i	−0.348293	+	0.201087i
$566$	190.085			0.335839
$567$	−16.9691	+	566.746i	−0.0299280	+	0.999552i
$568$	1194.63			2.10323
$569$	293.747	−	169.595i	0.516251	−	0.298058i	−0.219148	−	0.975692i	$-0.570328\pi$
$569$	293.747	−	169.595i	0.516251	−	0.298058i	0.735399	+	0.677634i	$0.236995\pi$
$570$	113.850	−	17.1780i	0.199737	−	0.0301368i
$571$	236.817	−	410.179i	0.414740	−	0.718352i	−0.580661	−	0.814146i	$-0.697206\pi$
$571$	236.817	−	410.179i	0.414740	−	0.718352i	0.995401	+	0.0957941i	$0.0305390\pi$
$572$	−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
$576$	665.213	−	205.414i	1.15488	−	0.356622i
$577$	428.206	+	247.225i	0.742125	+	0.428466i	0.822841	−	0.568271i	$-0.192388\pi$
$577$	428.206	+	247.225i	0.742125	+	0.428466i	−0.0807167	+	0.996737i	$0.525721\pi$
$578$	−797.219	+	1380.82i	−1.37927	+	2.38897i
$579$	176.643	−	450.281i	0.305082	−	0.777687i
$580$			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
$585$	−654.170	−	606.608i	−1.11824	−	1.03694i
$586$	−866.373	−	1500.60i	−1.47845	−	2.56076i
$587$	805.107			1.37156			0.685781	−	0.727808i	$-0.259461\pi$
$587$	805.107			1.37156			0.685781	+	0.727808i	$0.259461\pi$
$588$	−68.8463	+	1128.39i	−0.117086	+	1.91904i
$589$	23.1671			0.0393329
$590$	−472.935	−	819.148i	−0.801586	−	1.38839i
$591$	−2.35629	−	15.6168i	−0.00398696	−	0.0264243i
$592$	−63.1363	−	36.4517i	−0.106649	−	0.0615739i
$593$	−234.927	−	406.905i	−0.396167	−	0.686181i	0.597083	−	0.802180i	$-0.296326\pi$
$593$	−234.927	−	406.905i	−0.396167	−	0.686181i	−0.993249	+	0.115999i	$0.962993\pi$
$594$	−105.534	−	218.887i	−0.177667	−	0.368497i
$595$	1186.24	+	862.989i	1.99368	+	1.45040i
$596$	−871.681			−1.46255
$597$	840.622	+	329.771i	1.40808	+	0.552381i
$598$	1251.68	+	722.658i	2.09311	+	1.20846i
$599$	−331.592	−	191.445i	−0.553577	−	0.319608i	0.196987	−	0.980406i	$-0.436884\pi$
$599$	−331.592	−	191.445i	−0.553577	−	0.319608i	−0.750563	+	0.660799i	$0.770218\pi$
$600$	1167.92	+	458.169i	1.94654	+	0.763615i
$601$	−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
$606$	−274.695	+	41.4467i	−0.453292	+	0.0683938i
$607$	163.797	+	283.705i	0.269847	+	0.467389i	0.968822	−	0.247757i	$-0.0796935\pi$
$607$	163.797	+	283.705i	0.269847	+	0.467389i	−0.698975	+	0.715146i	$0.746360\pi$
$608$			11.9835i			0.0197096i
$609$	374.784	−	721.317i	0.615409	−	1.18443i
$610$	1700.20			2.78722
$611$	148.508	+	257.223i	0.243057	+	0.420987i
$612$	1293.41	−	1394.82i	2.11342	−	2.27912i
$613$	−606.899	−	350.393i	−0.990047	−	0.571604i	−0.0847586	−	0.996402i	$-0.527012\pi$
$613$	−606.899	−	350.393i	−0.990047	−	0.571604i	−0.905288	+	0.424798i	$0.860345\pi$
$614$	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	$-0.448775\pi$
$617$	197.729			0.320469			0.160234	+	0.987079i	$0.448775\pi$
$618$	1030.60	+	404.299i	1.66764	+	0.654205i
$619$	−353.048	−	203.832i	−0.570351	−	0.329293i	0.186938	−	0.982372i	$-0.440144\pi$
$619$	−353.048	−	203.832i	−0.570351	−	0.329293i	−0.757290	+	0.653079i	$0.773477\pi$
$620$	799.209	+	461.423i	1.28905	+	0.744231i
$621$	725.621	+	494.232i	1.16847	+	0.795864i
$622$		−	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
$627$	11.4947	−	1.73435i	0.0183329	−	0.00276612i
$628$	−559.388	−	968.889i	−0.890745	−	1.54282i
$629$	161.833			0.257286
$630$	−1080.26	−	1237.26i	−1.71470	−	1.96390i
$631$		−	974.420i		−	1.54425i	−0.635472	−	0.772124i	$-0.719194\pi$
$631$		−	974.420i		−	1.54425i	0.635472	−	0.772124i	$-0.280806\pi$
$632$	232.828	+	403.270i	0.368399	+	0.638086i
$633$	17.4348	+	115.552i	0.0275431	+	0.182547i
$634$	−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
$639$	814.160	−	251.408i	1.27412	−	0.393440i
$640$	−884.244	+	1531.56i	−1.38163	+	2.39306i
$641$	436.447	+	251.983i	0.680884	+	0.393109i	0.800188	−	0.599749i	$-0.204733\pi$
$641$	436.447	+	251.983i	0.680884	+	0.393109i	−0.119304	+	0.992858i	$0.538066\pi$
$642$	−55.0660	+	140.369i	−0.0857726	+	0.218644i
$643$			806.217i			1.25384i	0.779085	+	0.626919i	$0.215684\pi$
$643$			806.217i			1.25384i	−0.779085	+	0.626919i	$0.784316\pi$
$644$	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	$-0.212558\pi$
$647$	415.070	+	239.641i	0.641530	+	0.370387i	−0.143674	+	0.989625i	$0.545892\pi$
$648$	−844.111	+	576.263i	−1.30264	+	0.889294i
$649$	−47.7494	−	82.7043i	−0.0735738	−	0.127433i
$650$	1473.14			2.26637
$651$	−177.786	−	278.591i	−0.273096	−	0.427943i
$652$		−	1872.82i		−	2.87242i
$653$	440.531	−	254.341i	0.674626	−	0.389496i	−0.123201	−	0.992382i	$-0.539316\pi$
$653$	440.531	−	254.341i	0.674626	−	0.389496i	0.797827	+	0.602886i	$0.205983\pi$
$654$	−1466.42	+	221.257i	−2.24224	+	0.338314i
$655$	−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	$0.890650\pi$
$660$	431.084	+	169.112i	0.653158	+	0.256230i
$661$	508.855	+	293.788i	0.769826	+	0.444459i	0.832813	−	0.553555i	$-0.186729\pi$
$661$	508.855	+	293.788i	0.769826	+	0.444459i	−0.0629863	+	0.998014i	$0.520062\pi$
$662$	146.438	+	84.5459i	0.221205	+	0.127713i
$663$	391.437	−	997.814i	0.590402	−	1.50500i
$664$	−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
$669$	−304.641	+	45.9650i	−0.455368	+	0.0687070i
$670$	−212.084	+	122.447i	−0.316543	+	0.182756i
$671$	171.659			0.255826
$672$	144.105	−	91.9617i	0.214441	−	0.136848i
$673$	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
$675$	892.376	+	66.4619i	1.32204	+	0.0984621i
$676$	−649.840	+	1125.56i	−0.961302	+	1.66502i
$677$	129.730	−	74.8998i	0.191625	−	0.110635i	−0.401118	−	0.916026i	$-0.631378\pi$
$677$	129.730	−	74.8998i	0.191625	−	0.110635i	0.592743	+	0.805392i	$0.298045\pi$
$678$	190.618	+	238.953i	0.281148	+	0.352438i
$679$	−128.167	−	93.2413i	−0.188759	−	0.137322i
$680$			2644.27i			3.88863i
$681$	350.353	+	137.441i	0.514468	+	0.201823i
$682$	122.661	+	70.8183i	0.179855	+	0.103839i
$683$	−320.414	+	554.973i	−0.469127	+	0.812552i	−0.999377	−	0.0352896i	$-0.988765\pi$
$683$	−320.414	+	554.973i	−0.469127	+	0.812552i	0.530250	+	0.847841i	$0.322098\pi$
$684$	−30.0624	−	97.3539i	−0.0439508	−	0.142330i
$685$	−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
$690$	−2514.78	+	379.436i	−3.64461	+	0.549907i
$691$	666.727	−	384.935i	0.964873	−	0.557070i	0.0672037	−	0.997739i	$-0.478592\pi$
$691$	666.727	−	384.935i	0.964873	−	0.557070i	0.897669	+	0.440670i	$0.145259\pi$
$692$			348.374i			0.503431i
$693$	−109.067	−	124.918i	−0.157384	−	0.180257i
$694$			1900.68i			2.73874i
$695$	−774.399	−	1341.30i	−1.11424	−	1.92993i
$696$	1448.86	−	218.608i	2.08170	−	0.314091i
$697$	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	$0.663901\pi$
$702$	−675.592	+	991.890i	−0.962382	+	1.41295i
$703$	4.33418	−	7.50702i	0.00616526	−	0.0106785i
$704$	−101.811	+	176.341i	−0.144617	+	0.250484i
$705$	−486.542	−	190.868i	−0.690131	−	0.270734i
$706$	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	−0.865492	−	0.500922i	$-0.832994\pi$
$709$	−612.879	+	353.846i	−0.864427	+	0.499077i	0.00106550	+	0.999999i	$0.499661\pi$
$710$	−1234.17	+	2137.65i	−1.73827	+	3.01078i
$711$	243.543	+	225.836i	0.342536	+	0.317632i
$712$	−972.420	−	1684.28i	−1.36576	−	2.36556i
$713$	−511.726			−0.717708
$714$	909.832	−	1751.08i	1.27427	−	2.45249i
$715$	260.926			0.364932
$716$	−755.309	+	436.078i	−1.05490	+	0.609047i
$717$	98.4490	+	652.488i	0.137307	+	0.910026i
$718$	787.485	−	1363.96i	1.09678	−	1.89967i
$719$	−1030.82	+	595.144i	−1.43369	+	0.827739i	−0.997400	−	0.0720695i	$-0.977040\pi$
$719$	−1030.82	+	595.144i	−1.43369	+	0.827739i	−0.436286	+	0.899808i	$0.643706\pi$
$720$	188.811	−	828.404i	0.262237	−	1.15056i
$721$	751.313	+	79.4412i	1.04204	+	0.110182i
$722$	−1226.89			−1.69930
$723$	−142.504	+	363.257i	−0.197100	+	0.502430i
$724$	−415.462	+	719.601i	−0.573842	+	0.993924i
$725$	−1111.01	−	641.444i	−1.53243	−	0.884750i
$726$	−1089.25	−	427.308i	−1.50035	−	0.588579i
$727$	−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
$732$	−224.471	−	1487.72i	−0.306655	−	2.03241i
$733$	879.905	−	508.013i	1.20042	−	0.693060i	0.239768	−	0.970830i	$-0.422929\pi$
$733$	879.905	−	508.013i	1.20042	−	0.693060i	0.960648	+	0.277770i	$0.0895953\pi$
$734$	−1348.92			−1.83776
$735$	−934.789	−	618.523i	−1.27182	−	0.841528i
$736$		−	264.697i		−	0.359642i
$737$	−21.4128	+	12.3627i	−0.0290540	+	0.0167744i
$738$	−1067.83	−	990.191i	−1.44692	−	1.34172i
$739$	930.201	+	537.052i	1.25873	+	0.726728i	0.972828	−	0.231531i	$-0.0743734\pi$
$739$	930.201	+	537.052i	1.25873	+	0.726728i	0.285902	+	0.958259i	$0.407707\pi$
$740$	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	$-0.383734\pi$
$743$	530.788			0.714385			0.357192	+	0.934031i	$0.383734\pi$
$744$	217.557	−	554.576i	0.292416	−	0.745399i
$745$	432.140	−	748.488i	0.580054	−	1.00468i
$746$	−29.7934	+	51.6036i	−0.0399375	+	0.0691738i
$747$	−96.8270	+	29.8997i	−0.129621	+	0.0400263i
$748$			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	0.985436	−	0.170046i	$-0.0543916\pi$
$751$	259.436	+	449.356i	0.345454	+	0.598344i	−0.639982	+	0.768390i	$0.721058\pi$
$752$	−141.435	+	244.972i	−0.188078	+	0.325760i
$753$	644.280	−	97.2105i	0.855617	−	0.129098i
$754$	1490.02	−	860.264i	1.97615	−	1.14093i
$755$			956.522i			1.26692i
$756$	−940.009	+	1108.61i	−1.24340	+	1.46641i
$757$	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
$759$	−253.902	+	38.3093i	−0.334521	+	0.0504734i
$760$	122.661	+	70.8183i	0.161396	+	0.0931820i
$761$	316.996	+	549.052i	0.416551	+	0.721488i	0.995590	−	0.0938121i	$-0.0299053\pi$
$761$	316.996	+	549.052i	0.416551	+	0.721488i	−0.579039	+	0.815300i	$0.696572\pi$
$762$	281.595	−	224.635i	0.369547	−	0.294797i
$763$	−924.825	+	411.066i	−1.21209	+	0.538750i
$764$			887.214i			1.16127i
$765$	556.481	+	1802.11i	0.727426	+	2.35569i
$766$	648.866	−	1123.87i	0.847084	−	1.46719i
$767$	−235.822	+	408.455i	−0.307460	+	0.532536i
$768$	1350.51	+	529.797i	1.75848	+	0.689840i
$769$		−	819.151i		−	1.06522i	−0.846362	−	0.532608i	$-0.821212\pi$
$769$		−	819.151i		−	1.06522i	0.846362	−	0.532608i	$-0.178788\pi$
$770$	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	0.219373	+	0.975641i	$0.429599\pi$
$773$	−568.343	+	984.399i	−0.735244	+	1.27348i	−0.954616	+	0.297838i	$0.903734\pi$
$774$	286.346	+	265.527i	0.369956	+	0.343058i
$775$	−451.699	+	260.788i	−0.582837	+	0.336501i
$776$		−	285.699i		−	0.368169i
$777$	−123.535	+	5.48952i	−0.158989	+	0.00706502i
$778$		−	13.2489i		−	0.0170295i
$779$	60.3330	−	34.8333i	0.0774493	−	0.0447154i
$780$	−341.202	−	2261.38i	−0.437439	−	2.89920i
$781$	−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
$786$	−549.626	+	1401.06i	−0.699270	+	1.78251i
$787$	930.596	+	537.280i	1.18246	+	0.682694i	0.956582	−	0.291462i	$-0.0941417\pi$
$787$	930.596	+	537.280i	1.18246	+	0.682694i	0.225878	+	0.974156i	$0.427475\pi$
$788$	20.2431	−	35.0621i	0.0256892	−	0.0444951i
$789$	−374.893	+	955.643i	−0.475150	+	1.21121i
$790$	−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
$795$	2040.26	−	307.839i	2.56636	−	0.387219i
$796$	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	$0.976174\pi$
$798$	−56.8613	−	89.1020i	−0.0712548	−	0.111657i
$799$		−	627.919i		−	0.785881i
$800$	−134.896	−	233.647i	−0.168620	−	0.292058i
$801$	−1017.17	−	943.217i	−1.26988	−	1.17755i
$802$	−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
$807$	−90.7244	+	231.266i	−0.112422	+	0.286575i
$808$	−295.954	−	170.869i	−0.366279	−	0.211471i
$809$	348.228	+	201.050i	0.430443	+	0.248516i	0.699535	−	0.714598i	$-0.253390\pi$
$809$	348.228	+	201.050i	0.430443	+	0.248516i	−0.269092	+	0.963114i	$0.586724\pi$
$810$	−159.103	−	2105.77i	−0.196424	−	2.59971i
$811$			1280.62i			1.57906i	0.613712	+	0.789530i	$0.289676\pi$
$811$			1280.62i			1.57906i	−0.613712	+	0.789530i	$0.710324\pi$
$812$	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
$816$	1009.37	−	152.296i	1.23698	−	0.186638i
$817$	−16.1787	+	9.34080i	−0.0198026	+	0.0114331i
$818$		−	1331.30i		−	1.62751i
$819$	−264.956	+	774.958i	−0.323511	+	0.946224i
$820$	2775.12			3.38430
$821$	404.665	+	700.900i	0.492893	+	0.853716i	0.999966	−	0.00818719i	$-0.00260609\pi$
$821$	404.665	+	700.900i	0.492893	+	0.853716i	−0.507074	+	0.861903i	$0.669273\pi$
$822$	141.404	+	937.179i	0.172024	+	1.14012i
$823$	36.0687	−	62.4728i	0.0438259	−	0.0759087i	−0.843280	−	0.537474i	$-0.819379\pi$
$823$	36.0687	−	62.4728i	0.0438259	−	0.0759087i	0.887106	+	0.461565i	$0.152712\pi$
$824$	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	$-0.372347\pi$
$827$	645.671			0.780739			0.390370	+	0.920658i	$0.372347\pi$
$828$	664.033	+	2150.40i	0.801972	+	2.59710i
$829$	468.985	−	812.306i	0.565724	−	0.979863i	−0.431258	−	0.902229i	$-0.641930\pi$
$829$	468.985	−	812.306i	0.565724	−	0.979863i	0.996982	−	0.0776340i	$-0.0247366\pi$
$830$	146.779	−	254.228i	0.176842	−	0.306299i
$831$	−426.562	−	167.338i	−0.513312	−	0.201369i
$832$	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
$837$	31.5588	−	423.736i	0.0377047	−	0.506256i
$838$	300.201	−	173.321i	0.358235	−	0.206827i
$839$	743.899			0.886650			0.443325	−	0.896361i	$-0.353799\pi$
$839$	743.899			0.886650			0.443325	+	0.896361i	$0.353799\pi$
$840$	−89.6960	−	2018.50i	−0.106781	−	2.40297i
$841$	−657.327			−0.781601
$842$	−265.790	+	153.454i	−0.315665	+	0.182249i
$843$	143.860	+	953.459i	0.170653	+	1.13103i
$844$	−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
$849$	155.264	+	60.9092i	0.182879	+	0.0717422i
$850$	−2697.11	−	1557.18i	−3.17307	−	1.83197i
$851$	−95.7355	+	165.819i	−0.112498	+	0.194852i
$852$	2033.44	+	797.709i	2.38667	+	0.936278i
$853$		−	857.426i		−	1.00519i	−0.864522	−	0.502594i	$-0.832379\pi$
$853$		−	857.426i		−	1.00519i	0.864522	−	0.502594i	$-0.167621\pi$
$854$	−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	$-0.199747\pi$
$857$	604.822	+	349.194i	0.705744	+	0.407461i	−0.103739	+	0.994605i	$0.533081\pi$
$858$	−52.3670	−	347.072i	−0.0610338	−	0.404512i
$859$	−50.3096	−	87.1388i	−0.0585676	−	0.101442i	0.835255	−	0.549863i	$-0.185320\pi$
$859$	−50.3096	−	87.1388i	−0.0585676	−	0.101442i	−0.893823	+	0.448421i	$0.851987\pi$
$860$	−744.171			−0.865315
$861$	−881.879	−	458.209i	−1.02425	−	0.532183i
$862$	−2210.29			−2.56414
$863$	−426.398	−	738.543i	−0.494088	−	0.855785i	0.505889	−	0.862599i	$-0.331165\pi$
$863$	−426.398	−	738.543i	−0.494088	−	0.855785i	−0.999977	+	0.00681331i	$0.997831\pi$
$864$	219.183	+	16.3242i	0.253684	+	0.0188937i
$865$	−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
$870$	−1105.64	+	2818.40i	−1.27085	+	3.23954i
$871$	105.752	+	61.0561i	0.121415	+	0.0700989i
$872$	−1579.91	−	912.160i	−1.81182	−	1.04605i
$873$	−60.1248	−	194.708i	−0.0688714	−	0.223033i
$874$	−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	−0.248601	−	0.968606i	$-0.579971\pi$
$877$	408.625	−	235.920i	0.465935	−	0.269008i	0.714537	+	0.699598i	$0.246638\pi$
$878$	657.484	−	1138.80i	0.748843	−	1.29703i
$879$	−226.826	−	1503.33i	−0.258050	−	1.71027i
$880$	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	$-0.130615\pi$
$882$	−635.120	+	1367.55i	−0.720091	+	1.55051i
$883$	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
$885$	−123.819	−	820.635i	−0.139909	−	0.927271i
$886$	−1468.50	−	847.839i	−1.65745	−	0.956929i
$887$	892.025	−	515.011i	1.00567	−	0.580621i	0.0957459	−	0.995406i	$-0.469476\pi$
$887$	892.025	−	515.011i	1.00567	−	0.580621i	0.909920	+	0.414785i	$0.136143\pi$
$888$	−139.003	−	174.249i	−0.156534	−	0.196226i
$889$	144.617	−	198.786i	0.162674	−	0.223607i
$890$	4018.42			4.51508
$891$	−16.0637	−	212.606i	−0.0180288	−	0.238616i
$892$	−683.968	−	394.889i	−0.766780	−	0.442701i
$893$	−29.1276	−	16.8168i	−0.0326177	−	0.0188318i
$894$	−1082.33	−	424.593i	−1.21066	−	0.474936i
$895$		−	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
$900$	1682.04	+	1559.74i	1.86893	+	1.73305i
$901$	1239.49	+	2146.86i	1.37568	+	2.38275i
$902$	425.920			0.472195
$903$	236.483	+	122.872i	0.261885	+	0.136071i
$904$			376.016i			0.415947i
$905$	−411.934	−	713.491i	−0.455176	−	0.788388i
$906$	1272.32	−	191.971i	1.40433	−	0.211888i
$907$	−454.488	+	787.196i	−0.501089	+	0.867912i	0.498910	+	0.866654i	$0.333734\pi$
$907$	−454.488	+	787.196i	−0.501089	+	0.867912i	−0.999999	+	0.00125790i	$0.999600\pi$
$908$	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	$0.985989\pi$
$912$	19.9682	−	50.9010i	0.0218949	−	0.0558125i
$913$	14.8193	−	25.6679i	0.0162315	−	0.0281138i
$914$	611.498	+	353.049i	0.669035	+	0.386268i
$915$	1388.75	+	544.799i	1.51776	+	0.595408i
$916$		−	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	0.567009	−	0.823712i	$-0.308101\pi$
$919$	−395.033	−	684.217i	−0.429851	−	0.744524i	−0.996860	+	0.0791880i	$0.974767\pi$
$920$	−2709.39	−	1564.27i	−2.94499	−	1.70029i
$921$	591.707	−	89.2782i	0.642462	−	0.0969362i
$922$	382.869	+	663.148i	0.415259	+	0.719249i
$923$	1230.80			1.33348
$924$	−18.8718	−	424.686i	−0.0204240	−	0.459617i
$925$			195.157i			0.210980i
$926$	−2307.44	+	1332.20i	−2.49183	+	1.43866i
$927$	712.259	+	660.474i	0.768348	+	0.712485i
$928$	−272.884	−	157.549i	−0.294056	−	0.169773i
$929$	623.696	+	1080.27i	0.671363	+	1.16283i	0.977518	+	0.210853i	$0.0676240\pi$
$929$	623.696	+	1080.27i	0.671363	+	1.16283i	−0.306155	+	0.951982i	$0.599043\pi$
$930$	767.589	+	962.224i	0.825365	+	1.03465i
$931$	−53.5449	−	48.3335i	−0.0575134	−	0.0519156i
$932$		−	1036.21i		−	1.11182i
$933$	177.249	−	451.826i	0.189977	−	0.484272i
$934$	429.722	+	248.100i	0.460088	+	0.265632i
$935$	−477.720	−	275.812i	−0.510930	−	0.294986i
$936$	−1410.58	+	435.581i	−1.50703	+	0.465364i
$937$	−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	$-0.768401\pi$
$941$	190.627	−	330.176i	0.202579	−	0.350878i	0.949359	+	0.314194i	$0.101734\pi$
$942$	−222.628	−	1475.51i	−0.236336	−	1.56636i
$943$	−1332.67	+	769.415i	−1.41322	+	0.815922i
$944$	−449.179			−0.475826
$945$	−485.918	−	1356.76i	−0.514199	−	1.43572i
$946$	−114.214			−0.120733
$947$	−521.905	−	903.966i	−0.551114	−	0.954557i	−0.998195	−	0.0600635i	$-0.980870\pi$
$947$	−521.905	−	903.966i	−0.551114	−	0.954557i	0.447081	−	0.894494i	$-0.352464\pi$
$948$	127.027	+	841.896i	0.133995	+	0.888076i
$949$	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	$-0.110019\pi$
$954$	−818.945	−	2652.07i	−0.858433	−	2.77995i
$955$	−761.826	−	439.841i	−0.797724	−	0.460566i
$956$	−845.784	+	1464.94i	−0.884711	+	1.53236i
$957$	−111.630	+	284.557i	−0.116646	+	0.297342i
$958$	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
$963$	−89.9574	+	97.0106i	−0.0934137	+	0.100738i
$964$	−866.276	+	500.144i	−0.898626	+	0.518822i
$965$			1229.40i			1.27399i
$966$	1255.98	+	1968.13i	1.30019	+	2.03740i
$967$		−	354.180i		−	0.366267i	−0.983088	−	0.183134i	$-0.941376\pi$
$967$		−	354.180i		−	0.366267i	0.983088	−	0.183134i	$-0.0586241\pi$
$968$	−719.675	−	1246.51i	−0.743466	−	1.28772i
$969$	18.1083	+	120.016i	0.0186876	+	0.123856i
$970$	511.223	+	295.155i	0.527034	+	0.304283i
$971$	−804.917	+	464.719i	−0.828957	+	0.478599i	−0.853495	−	0.521100i	$-0.825522\pi$
$971$	−804.917	+	464.719i	−0.828957	+	0.478599i	0.0245383	+	0.999699i	$0.492188\pi$
$972$	−1821.60	+	417.236i	−1.87407	+	0.429255i
$973$	−836.447	+	1149.76i	−0.859658	+	1.18166i
$974$		−	1572.78i		−	1.61476i
$975$	1203.28	+	472.040i	1.23413	+	0.484143i
$976$	403.700	−	699.229i	0.413627	−	0.716423i
$977$	−523.426	+	906.600i	−0.535748	+	0.927943i	0.463379	+	0.886160i	$0.346637\pi$
$977$	−523.426	+	906.600i	−0.535748	+	0.927943i	−0.999127	+	0.0417824i	$0.986696\pi$
$978$	912.244	−	2325.41i	0.932765	−	2.37772i
$979$	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	$-0.685825\pi$
$983$	439.404	−	761.070i	0.447003	−	0.774232i	0.998189	+	0.0601503i	$0.0191580\pi$
$984$	−267.269	−	1771.37i	−0.271614	−	1.80017i
$985$	20.0712	+	34.7644i	0.0203769	+	0.0352938i
$986$	−3637.36			−3.68901
$987$	21.2996	+	479.321i	0.0215802	+	0.485634i
$988$		−	147.174i		−	0.148962i
$989$	357.364	−	206.324i	0.361339	−	0.208619i
$990$	452.887	+	419.960i	0.457462	+	0.424202i
$991$	−257.036	+	445.199i	−0.259370	+	0.449242i	−0.966073	−	0.258268i	$-0.916848\pi$
$991$	−257.036	+	445.199i	−0.259370	+	0.449242i	0.706703	+	0.707510i	$0.250182\pi$
$992$	−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
$996$	−241.835	−	94.8705i	−0.242806	−	0.0952516i
$997$	553.005	−	957.832i	0.554669	−	0.960714i	−0.443261	−	0.896393i	$-0.646178\pi$
$997$	553.005	−	957.832i	0.554669	−	0.960714i	0.997929	−	0.0643215i	$-0.0204883\pi$
$998$	742.578	+	428.728i	0.744066	+	0.429587i
$999$	−131.403	−	89.5003i	−0.131534	−	0.0895899i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.3.w.c.116.1	✓	16	3.2	odd	2	inner
273.3.w.c.116.2	yes	16	13.12	even	2	inner
273.3.w.c.116.7	yes	16	39.38	odd	2	inner
273.3.w.c.116.8	yes	16	1.1	even	1	trivial
273.3.w.c.233.1	yes	16	91.51	even	6	inner
273.3.w.c.233.2	yes	16	21.2	odd	6	inner
273.3.w.c.233.7	yes	16	7.2	even	3	inner
273.3.w.c.233.8	yes	16	273.233	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.70956 + 2.96105i) q^{2} +(0.447581 + 2.96642i) q^{3} +(-3.84521 + 6.66010i) q^{4} +(-3.81256 - 6.60355i) q^{5} +(-8.01856 + 6.39660i) q^{6} +(-4.11804 + 5.66055i) q^{7} -12.6180 q^{8} +(-8.59934 + 2.65543i) q^{9} +O(q^{10})\)	\(q+(1.70956 + 2.96105i) q^{2} +(0.447581 + 2.96642i) 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} +(-8.59934 + 2.65543i) q^{9} +(13.0356 - 22.5784i) q^{10} +(1.31613 - 2.27960i) q^{11} +(-21.4777 - 8.42558i) 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} +(-22.5640 - 20.9234i) q^{18} +(1.27488 - 0.736052i) q^{19} +58.6404 q^{20} +(-18.6347 - 9.68229i) q^{21} +9.00000 q^{22} +(-28.1602 + 16.2583i) q^{23} +(-5.64758 - 37.4303i) 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} +(72.8115 + 28.5635i) q^{30} +(13.6290 + 7.86870i) q^{31} +(-4.07018 + 7.04976i) q^{32} +(7.35133 + 2.88388i) 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} +(-5.81856 - 38.5635i) q^{39} +(48.1069 + 83.3235i) q^{40} +47.3245 q^{41} +(-3.18751 - 71.7308i) q^{42} -12.6904 q^{43} +(10.1216 + 17.5311i) q^{44} +(50.3208 + 46.6622i) 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} +(-30.1105 + 76.7549i) q^{51} +(49.9877 - 86.5812i) q^{52} +(78.1152 + 45.0998i) q^{53} +(51.9686 - 76.2993i) 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} +(26.2463 + 173.952i) q^{60} +(32.6069 + 56.4768i) q^{61} +53.8081i q^{62} +(20.3812 - 59.6121i) q^{63} -77.3562 q^{64} +(49.5633 + 85.8461i) q^{65} +(4.02823 + 26.6978i) 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} +(108.506 - 33.5062i) q^{72} +(-92.0638 - 53.1531i) q^{73} +(17.4359 + 10.0666i) q^{74} +(-92.5600 - 36.3108i) 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} +(66.8974 - 45.6699i) q^{81} +(80.9042 + 140.130i) q^{82} +11.2598 q^{83} +(136.139 - 86.8787i) q^{84} -209.563i q^{85} +(-21.6951 - 37.5769i) q^{86} +(-114.825 + 17.3251i) 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} +(-17.2418 + 43.9512i) q^{93} +(39.0589 - 67.6521i) q^{94} +(-9.72111 - 5.61249i) q^{95} +(-22.7343 - 8.91854i) 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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