LMFDB - Embedded newform 273.3.w.c.233.8

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			233.8
Root			$-1.95177 - 0.330355i$ of defining polynomial
Character	$\chi$	$=$	273.233
Dual form			273.3.w.c.116.8

$q$-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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

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

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	$-0.507025\pi$
$2$	1.70956	−	2.96105i	0.854781	−	1.48052i	0.876848	−	0.480768i	$-0.159642\pi$
$3$	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	0.179040	+	0.983842i	$0.442701\pi$
$5$	−3.81256	+	6.60355i	−0.762512	+	1.32071i	−0.941552	+	0.336868i	$0.890632\pi$
$6$	−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	0.919628	−	0.392790i	$-0.128490\pi$
$11$	1.31613	+	2.27960i	0.119648	+	0.207236i	−0.799980	+	0.600026i	$0.795157\pi$
$12$	−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	0.405671	−	0.914019i	$-0.367038\pi$
$17$	23.8012	−	13.7416i	1.40007	−	0.808331i	0.994399	+	0.105688i	$0.0337046\pi$
$18$	−22.5640	+	20.9234i	−1.25355	+	1.16241i
$19$	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
$21$	−18.6347	+	9.68229i	−0.887368	+	0.461061i
$22$	9.00000			0.409091
$23$	−28.1602	−	16.2583i	−1.22436	−	0.706882i	−0.258512	−	0.966008i	$-0.583232\pi$
$23$	−28.1602	−	16.2583i	−1.22436	−	0.706882i	−0.965843	+	0.259126i	$0.916565\pi$
$24$	−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	$-0.767414\pi$
$29$		−	38.7082i		−	1.33477i	0.744715	−	0.667383i	$-0.232586\pi$
$30$	72.8115	−	28.5635i	2.42705	−	0.952118i
$31$	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
$33$	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	0.567327	−	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
$39$	−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	−0.961583	−	0.274513i	$-0.911483\pi$
$47$	−11.4237	+	19.7864i	−0.243057	+	0.420987i	0.718527	+	0.695499i	$0.244817\pi$
$48$	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	0.474304	−	0.880361i	$-0.342700\pi$
$53$	78.1152	−	45.0998i	1.47387	−	0.850940i	0.999567	+	0.0294208i	$0.00936629\pi$
$54$	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	0.977806	−	0.209513i	$-0.0671878\pi$
$59$	18.1401	+	31.4196i	0.307460	+	0.532536i	−0.670346	+	0.742048i	$0.733854\pi$
$60$	26.2463	−	173.952i	0.437439	−	2.89920i
$61$	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
$63$	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	−0.559477	−	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	$-0.732311\pi$
$71$	−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	−0.973297	−	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
$75$	−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	−0.958856	−	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
$81$	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	−0.000227621	−	1.00000i	$-0.500072\pi$
$89$	77.0661	−	133.482i	0.865912	−	1.49980i	0.866139	−	0.499803i	$-0.166594\pi$
$90$	−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	$-0.962764\pi$
$97$		−	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	−0.379372	−	0.925244i	$-0.623860\pi$
$101$	23.4549	−	13.5417i	0.232227	−	0.134076i	0.611599	+	0.791168i	$0.290527\pi$
$102$	−278.751	−	42.0586i	−2.73285	−	0.412339i
$103$	−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
$105$	7.10858	−	159.970i	0.0677008	−	1.52352i
$106$		−	308.404i		−	2.90947i
$107$	12.7306	+	7.35002i	0.118978	+	0.0686918i	0.558308	−	0.829634i	$-0.311451\pi$
$107$	12.7306	+	7.35002i	0.118978	+	0.0686918i	−0.439330	+	0.898326i	$0.644784\pi$
$108$	207.068	−	15.4219i	1.91729	−	0.142795i
$109$	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	$0.0420944\pi$
$113$			29.8000i			0.263717i	−0.991269	+	0.131858i	$0.957906\pi$
$114$	−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	0.899229	−	0.437477i	$-0.144128\pi$
$131$	127.067	+	73.3622i	0.969977	+	0.560017i	0.0707481	+	0.997494i	$0.477461\pi$
$132$	−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	0.983910	−	0.178664i	$-0.0571773\pi$
$137$	46.2002	+	80.0212i	0.337228	+	0.584096i	−0.646682	+	0.762760i	$0.723844\pi$
$138$	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	−0.610756	−	0.791819i	$-0.709134\pi$
$149$	56.6732	−	98.1608i	0.380357	−	0.658798i	0.991113	+	0.133021i	$0.0424678\pi$
$150$	−50.7192	+	336.150i	−0.338128	+	2.24100i
$151$	−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
$156$	279.210	−	109.533i	1.78981	−	0.702132i
$157$	−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
$159$	−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	−0.314528	−	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
$165$	−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	0.609080	−	0.793109i	$-0.291539\pi$
$173$	39.2307	+	22.6499i	0.226767	+	0.130924i	−0.382313	+	0.924033i	$0.624872\pi$
$174$	−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	−0.199908	−	0.979815i	$-0.564064\pi$
$179$	98.2143	−	56.7040i	0.548683	−	0.316782i	0.748591	+	0.663032i	$0.230731\pi$
$180$	−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	0.738198	−	0.674584i	$-0.235677\pi$
$191$	99.9100	+	57.6831i	0.523089	+	0.302006i	−0.215108	+	0.976590i	$0.569010\pi$
$192$	−34.6232	+	229.471i	−0.180329	+	1.19516i
$193$	−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	$-0.504253\pi$
$197$	−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	0.944738	+	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
$201$	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	$-0.926042\pi$
$223$		−	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	0.970467	−	0.241233i	$-0.0775518\pi$
$227$	62.7246	+	108.642i	0.276320	+	0.478600i	−0.694148	+	0.719833i	$0.744218\pi$
$228$	−33.5832	−	5.06711i	−0.147295	−	0.0222242i
$229$	−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
$231$	−46.5974	−	29.7366i	−0.201720	−	0.128730i
$232$			488.420i			2.10526i
$233$	−116.689	−	67.3705i	−0.500811	−	0.289144i	0.228237	−	0.973606i	$-0.426704\pi$
$233$	−116.689	−	67.3705i	−0.500811	−	0.289144i	−0.729049	+	0.684462i	$0.760037\pi$
$234$	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	−0.247750	−	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
$243$	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	$0.142422\pi$
$251$			217.191i			0.865302i	−0.901562	+	0.432651i	$0.857578\pi$
$252$	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	−0.418185	−	0.908362i	$-0.637334\pi$
$257$	−363.383	−	209.799i	−1.41394	−	0.816340i	−0.995757	+	0.0920216i	$0.970667\pi$
$258$	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	0.183644	−	0.982993i	$-0.441211\pi$
$263$	296.339	−	171.091i	1.12676	−	0.650537i	0.943119	+	0.332456i	$0.107877\pi$
$264$	−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	−0.360744	−	0.932665i	$-0.617477\pi$
$269$	71.7141	−	41.4042i	0.266595	−	0.153919i	0.627339	+	0.778746i	$0.284144\pi$
$270$	−701.979	+	52.2817i	−2.59992	+	0.193636i
$271$	−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
$273$	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	0.694612	−	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	$-0.306200\pi$
$281$	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	0.910949	−	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
$285$	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	$0.105319\pi$
$307$			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	−0.708045	−	0.706167i	$-0.750423\pi$
$311$	−140.108	+	80.8915i	−0.450509	+	0.260101i	0.257536	+	0.966269i	$0.417089\pi$
$312$	73.4185	−	486.594i	0.235316	−	1.55960i
$313$	−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
$315$	−471.356	−	92.6865i	−1.49637	−	0.294243i
$316$	283.808			0.898128
$317$	22.9875	−	39.8155i	0.0725158	−	0.125601i	−0.827488	−	0.561484i	$-0.810231\pi$
$317$	22.9875	−	39.8155i	0.0725158	−	0.125601i	0.900003	+	0.435883i	$0.143564\pi$
$318$	−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	0.563299	−	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
$333$	−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	0.394363	−	0.918955i	$-0.370965\pi$
$347$	481.422	−	277.949i	1.38738	−	0.801006i	0.993020	+	0.117949i	$0.0376320\pi$
$348$	326.139	+	831.364i	0.937182	+	2.38898i
$349$			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	$0.000538894\pi$
$353$	177.017	+	306.603i	0.501465	+	0.868564i	−0.498533	+	0.866871i	$0.666128\pi$
$354$	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	0.343532	+	0.939141i	$0.388376\pi$
$359$	−230.318	+	398.922i	−0.641554	+	1.11120i	−0.985086	+	0.172063i	$0.944957\pi$
$360$	−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	−0.999038	−	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
$369$	−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	−0.854108	−	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
$375$	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	$-0.840227\pi$
$379$		−	364.695i		−	0.962255i	0.876651	−	0.481128i	$-0.159773\pi$
$380$	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	−0.999987	−	0.00519153i	$-0.998347\pi$
$383$	−189.775	+	328.701i	−0.495497	+	0.858226i	0.504489	+	0.863418i	$0.331681\pi$
$384$	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	−0.504307	−	0.863524i	$-0.668252\pi$
$389$	−3.35580	+	1.93747i	−0.00862675	+	0.00498065i	0.495680	+	0.868505i	$0.334919\pi$
$390$	−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	0.996867	−	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
$399$	−30.8837	−	1.37238i	−0.0774028	−	0.00343955i
$400$	410.332			1.02583
$401$	49.3294	−	85.4410i	0.123016	−	0.213070i	−0.797940	−	0.602737i	$-0.794077\pi$
$401$	49.3294	−	85.4410i	0.123016	−	0.213070i	0.920956	+	0.389667i	$0.127410\pi$
$402$	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	−0.851952	−	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
$411$	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	$0.0386045\pi$
$419$			101.383i			0.241965i	−0.992655	+	0.120983i	$0.961395\pi$
$420$	−1092.75	+	567.773i	−2.60178	+	1.35184i
$421$		−	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
$423$	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	−0.947850	−	0.318716i	$-0.896748\pi$
$431$	−323.225	−	559.842i	−0.749941	−	1.29894i	0.197909	−	0.980220i	$-0.436585\pi$
$432$	−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	−0.997538	−	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
$441$	253.507	−	360.854i	0.574845	−	0.818262i
$442$			1221.59i			2.76378i
$443$	−429.496	−	247.970i	−0.969517	−	0.559751i	−0.0704282	−	0.997517i	$-0.522437\pi$
$443$	−429.496	−	247.970i	−0.969517	−	0.559751i	−0.899089	+	0.437766i	$0.855770\pi$
$444$	−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	0.682744	−	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
$459$	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	$-0.681651\pi$
$463$		−	779.264i		−	1.68307i	0.540199	−	0.841537i	$-0.318349\pi$
$464$	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	0.628490	−	0.777817i	$-0.283673\pi$
$467$	125.682	+	72.5624i	0.269126	+	0.155380i	−0.359364	+	0.933197i	$0.617006\pi$
$468$	−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	0.980971	+	0.194153i	$0.0621957\pi$
$479$	315.482	+	546.431i	0.658627	+	1.14077i	−0.322345	+	0.946622i	$0.604471\pi$
$480$	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	−0.849727	−	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	$0.204839\pi$
$491$			589.214i			1.20003i	−0.799989	+	0.600015i	$0.795161\pi$
$492$	−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	0.701575	−	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
$501$	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	$-0.899483\pi$
$503$		−	312.424i		−	0.621121i	0.950554	−	0.310560i	$-0.100517\pi$
$504$	−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	−0.885406	−	0.464819i	$-0.846119\pi$
$509$	−20.4403	+	35.4037i	−0.0401578	+	0.0695554i	0.845248	+	0.534374i	$0.179453\pi$
$510$	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	−0.116992	−	0.993133i	$-0.537325\pi$
$521$	356.672	−	205.924i	0.684590	−	0.395248i	0.801582	+	0.597884i	$0.203992\pi$
$522$	809.910	+	873.411i	1.55155	+	1.67320i
$523$	−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
$525$	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	−0.130135	−	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
$543$	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	0.935317	−	0.353811i	$-0.115114\pi$
$557$	89.8156	+	155.565i	0.161249	+	0.279291i	−0.774068	+	0.633102i	$0.781781\pi$
$558$	−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	−0.906202	−	0.422846i	$-0.861031\pi$
$563$	−559.119	+	322.808i	−0.993107	+	0.573371i	−0.0869053	+	0.996217i	$0.527698\pi$
$564$	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	0.735399	−	0.677634i	$-0.236995\pi$
$569$	293.747	+	169.595i	0.516251	+	0.298058i	−0.219148	+	0.975692i	$0.570328\pi$
$570$	113.850	+	17.1780i	0.199737	+	0.0301368i
$571$	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
$576$	665.213	+	205.414i	1.15488	+	0.356622i
$577$	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
$579$	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	−0.993249	−	0.115999i	$-0.962993\pi$
$593$	−234.927	+	406.905i	−0.396167	+	0.686181i	0.597083	+	0.802180i	$0.296326\pi$
$594$	−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	−0.750563	−	0.660799i	$-0.770218\pi$
$599$	−331.592	+	191.445i	−0.553577	+	0.319608i	0.196987	+	0.980406i	$0.436884\pi$
$600$	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	−0.698975	−	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
$609$	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	−0.905288	−	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	$-0.448775\pi$
$617$	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	−0.757290	−	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
$621$	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	$0.280806\pi$
$631$			974.420i			1.54425i	−0.635472	+	0.772124i	$0.719194\pi$
$632$	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	−0.119304	−	0.992858i	$-0.538066\pi$
$641$	436.447	−	251.983i	0.680884	−	0.393109i	0.800188	+	0.599749i	$0.204733\pi$
$642$	−55.0660	−	140.369i	−0.0857726	−	0.218644i
$643$		−	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	−0.143674	−	0.989625i	$-0.545892\pi$
$647$	415.070	−	239.641i	0.641530	−	0.370387i	0.785204	+	0.619238i	$0.212558\pi$
$648$	−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	0.797827	−	0.602886i	$-0.205983\pi$
$653$	440.531	+	254.341i	0.674626	+	0.389496i	−0.123201	+	0.992382i	$0.539316\pi$
$654$	−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	$-0.890650\pi$
$659$		−	443.924i		−	0.673633i	0.941570	−	0.336817i	$-0.109350\pi$
$660$	431.084	−	169.112i	0.653158	−	0.256230i
$661$	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
$663$	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	0.592743	−	0.805392i	$-0.298045\pi$
$677$	129.730	+	74.8998i	0.191625	+	0.110635i	−0.401118	+	0.916026i	$0.631378\pi$
$678$	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	0.530250	−	0.847841i	$-0.322098\pi$
$683$	−320.414	−	554.973i	−0.469127	−	0.812552i	−0.999377	+	0.0352896i	$0.988765\pi$
$684$	−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	0.897669	−	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
$693$	−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	$-0.663901\pi$
$701$		−	1220.21i		−	1.74067i	0.492457	−	0.870337i	$-0.336099\pi$
$702$	−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	0.00106550	−	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
$711$	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	−0.436286	−	0.899808i	$-0.643706\pi$
$719$	−1030.82	−	595.144i	−1.43369	−	0.827739i	−0.997400	+	0.0720695i	$0.977040\pi$
$720$	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	0.960648	−	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
$735$	−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	0.285902	−	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	$-0.383734\pi$
$743$	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	−0.639982	−	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
$753$	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	−0.579039	−	0.815300i	$-0.696572\pi$
$761$	316.996	−	549.052i	0.416551	−	0.721488i	0.995590	+	0.0938121i	$0.0299053\pi$
$762$	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	$0.178788\pi$
$769$			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	$-0.903734\pi$
$773$	−568.343	−	984.399i	−0.735244	−	1.27348i	0.219373	−	0.975641i	$-0.429599\pi$
$774$	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	0.225878	−	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
$789$	−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	$-0.976174\pi$
$797$		−	119.200i		−	0.149561i	0.997200	−	0.0747803i	$-0.0238256\pi$
$798$	−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	−0.269092	−	0.963114i	$-0.586724\pi$
$809$	348.228	−	201.050i	0.430443	−	0.248516i	0.699535	+	0.714598i	$0.253390\pi$
$810$	−159.103	+	2105.77i	−0.196424	+	2.59971i
$811$		−	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
$816$	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	−0.507074	−	0.861903i	$-0.669273\pi$
$821$	404.665	−	700.900i	0.492893	−	0.853716i	0.999966	+	0.00818719i	$0.00260609\pi$
$822$	141.404	−	937.179i	0.172024	−	1.14012i
$823$	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	$-0.372347\pi$
$827$	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	0.996982	+	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
$831$	−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	$0.167621\pi$
$853$			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	−0.103739	−	0.994605i	$-0.533081\pi$
$857$	604.822	−	349.194i	0.705744	−	0.407461i	0.809483	+	0.587143i	$0.199747\pi$
$858$	−52.3670	+	347.072i	−0.0610338	+	0.404512i
$859$	−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
$861$	−881.879	+	458.209i	−1.02425	+	0.532183i
$862$	−2210.29			−2.56414
$863$	−426.398	+	738.543i	−0.494088	+	0.855785i	−0.999977	−	0.00681331i	$-0.997831\pi$
$863$	−426.398	+	738.543i	−0.494088	+	0.855785i	0.505889	+	0.862599i	$0.331165\pi$
$864$	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	0.714537	−	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
$879$	−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	$0.130615\pi$
$881$			702.898i			0.797842i	−0.916985	+	0.398921i	$0.869385\pi$
$882$	−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	0.909920	−	0.414785i	$-0.136143\pi$
$887$	892.025	+	515.011i	1.00567	+	0.580621i	0.0957459	+	0.995406i	$0.469476\pi$
$888$	−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	−0.999999	−	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	$-0.985989\pi$
$911$		−	80.1743i		−	0.0880069i	0.999031	−	0.0440035i	$-0.0140113\pi$
$912$	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	−0.996860	−	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
$921$	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	−0.306155	−	0.951982i	$-0.599043\pi$
$929$	623.696	−	1080.27i	0.671363	−	1.16283i	0.977518	−	0.210853i	$-0.0676240\pi$
$930$	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	0.949359	−	0.314194i	$-0.101734\pi$
$941$	190.627	+	330.176i	0.202579	+	0.350878i	−0.746780	+	0.665072i	$0.768401\pi$
$942$	−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	0.447081	+	0.894494i	$0.352464\pi$
$947$	−521.905	+	903.966i	−0.551114	+	0.954557i	−0.998195	+	0.0600635i	$0.980870\pi$
$948$	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	$0.110019\pi$
$953$			645.739i			0.677586i	−0.940861	+	0.338793i	$0.889981\pi$
$954$	−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	$0.0586241\pi$
$967$			354.180i			0.366267i	−0.983088	+	0.183134i	$0.941376\pi$
$968$	−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	0.0245383	−	0.999699i	$-0.492188\pi$
$971$	−804.917	−	464.719i	−0.828957	−	0.478599i	−0.853495	+	0.521100i	$0.825522\pi$
$972$	−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	−0.999127	−	0.0417824i	$-0.986696\pi$
$977$	−523.426	−	906.600i	−0.535748	−	0.927943i	0.463379	−	0.886160i	$-0.346637\pi$
$978$	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	0.998189	−	0.0601503i	$-0.0191580\pi$
$983$	439.404	+	761.070i	0.447003	+	0.774232i	−0.551186	+	0.834382i	$0.685825\pi$
$984$	−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	0.706703	−	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
$996$	−241.835	+	94.8705i	−0.242806	+	0.0952516i
$997$	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
$999$	−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.233.8	yes	16
3.2	odd	2	inner	273.3.w.c.233.1	yes	16
7.4	even	3	inner	273.3.w.c.116.7	yes	16
13.12	even	2	inner	273.3.w.c.233.2	yes	16
21.11	odd	6	inner	273.3.w.c.116.2	yes	16
39.38	odd	2	inner	273.3.w.c.233.7	yes	16
91.25	even	6	inner	273.3.w.c.116.1	✓	16
273.116	odd	6	inner	273.3.w.c.116.8	yes	16

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

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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