LMFDB - Embedded newform 151.3.i.a.23.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [151,3,Mod(23,151)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("151.23"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(151, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([23])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	151.i (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.11445199184$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$24$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	151.23
Dual form			151.3.i.a.46.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.52844 + 2.64734i) q^{2} +(-1.17971 - 0.383311i) q^{3} +(-2.67228 - 4.62852i) q^{4} +(-6.31759 + 2.81277i) q^{5} +(2.81787 - 2.53722i) q^{6} +(1.77668 + 3.99049i) q^{7} +4.11014 q^{8} +(-6.03637 - 4.38568i) q^{9} +(2.20971 - 21.0240i) q^{10} +(17.9605 + 3.81763i) q^{11} +(1.37835 + 6.48461i) q^{12} +(-4.17350 - 19.6348i) q^{13} +(-13.2797 - 1.39576i) q^{14} +(8.53108 - 0.896652i) q^{15} +(4.40699 - 7.63313i) q^{16} +(-0.548745 - 5.22096i) q^{17} +(20.8366 - 9.27706i) q^{18} -3.45053 q^{19} +(29.9013 + 21.7246i) q^{20} +(-0.566369 - 5.38864i) q^{21} +(-37.5582 + 41.7127i) q^{22} +(-13.1709 - 7.60424i) q^{23} +(-4.84877 - 1.57546i) q^{24} +(15.2720 - 16.9612i) q^{25} +(58.3589 + 18.9620i) q^{26} +(12.0020 + 16.5193i) q^{27} +(13.7223 - 18.8871i) q^{28} +(3.09043 + 9.51138i) q^{29} +(-10.6655 + 23.9552i) q^{30} +(-0.234369 - 2.22987i) q^{31} +(21.6919 + 37.5715i) q^{32} +(-19.7249 - 11.3882i) q^{33} +(14.6604 + 6.52723i) q^{34} +(-22.4487 - 20.2129i) q^{35} +(-4.16835 + 39.6592i) q^{36} +(-44.5983 - 49.5314i) q^{37} +(5.27393 - 9.13472i) q^{38} +(-2.60270 + 24.7631i) q^{39} +(-25.9662 + 11.5609i) q^{40} +(-56.0823 - 18.2223i) q^{41} +(15.1312 + 6.73685i) q^{42} +(-54.8026 - 24.3997i) q^{43} +(-30.3256 - 93.3324i) q^{44} +(50.4712 + 10.7280i) q^{45} +(40.2620 - 23.2453i) q^{46} +(35.4509 - 7.53533i) q^{47} +(-8.12482 + 7.31562i) q^{48} +(20.0200 - 22.2344i) q^{49} +(21.5599 + 66.3544i) q^{50} +(-1.35389 + 6.36955i) q^{51} +(-79.7272 + 71.7867i) q^{52} +(-86.1195 + 27.9819i) q^{53} +(-62.0766 + 6.52451i) q^{54} +(-124.205 + 26.4007i) q^{55} +(7.30241 + 16.4015i) q^{56} +(4.07061 + 1.32262i) q^{57} +(-29.9034 - 6.35617i) q^{58} +39.8486 q^{59} +(-26.9476 - 37.0901i) q^{60} +(59.4783 + 53.5545i) q^{61} +(6.26146 + 2.78778i) q^{62} +(6.77631 - 31.8800i) q^{63} -97.3637 q^{64} +(81.5946 + 112.305i) q^{65} +(60.2967 - 34.8123i) q^{66} +(-65.1045 - 89.6087i) q^{67} +(-22.6989 + 16.4917i) q^{68} +(12.6231 + 14.0193i) q^{69} +(87.8219 - 28.5351i) q^{70} +(-69.8565 - 7.34221i) q^{71} +(-24.8103 - 18.0257i) q^{72} +(26.9326 - 37.0696i) q^{73} +(199.292 - 42.3609i) q^{74} +(-24.5179 + 14.1554i) q^{75} +(9.22075 + 15.9708i) q^{76} +(16.6759 + 78.4541i) q^{77} +(-61.5782 - 44.7392i) q^{78} +(23.7053 - 32.6275i) q^{79} +(-6.37130 + 60.6188i) q^{80} +(12.9244 + 39.7771i) q^{81} +(133.959 - 120.617i) q^{82} +(45.1882 + 62.1962i) q^{83} +(-23.4279 + 17.0214i) q^{84} +(18.1521 + 31.4404i) q^{85} +(148.357 - 107.788i) q^{86} -12.4053i q^{87} +(73.8203 + 15.6910i) q^{88} +(26.9726 - 60.5815i) q^{89} +(-105.543 + 117.217i) q^{90} +(70.9375 - 51.5391i) q^{91} +81.2825i q^{92} +(-0.578247 + 2.72044i) q^{93} +(-34.2361 + 105.368i) q^{94} +(21.7990 - 9.70554i) q^{95} +(-11.1886 - 52.6382i) q^{96} +(9.48319 + 90.2265i) q^{97} +(28.2627 + 86.9838i) q^{98} +(-91.6736 - 101.814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 5 q^{2} - 10 q^{3} - 181 q^{4} - 9 q^{5} + 13 q^{6} - 31 q^{7} + 80 q^{8} + 124 q^{9} + 41 q^{10} + 25 q^{11} + 55 q^{12} - 28 q^{13} + 7 q^{14} - 34 q^{15} - 321 q^{16} - 82 q^{17} - 194 q^{18}+ \cdots - 1441 q^{99}+O(q^{100}) $ 192 * q - 5 * q^2 - 10 * q^3 - 181 * q^4 - 9 * q^5 + 13 * q^6 - 31 * q^7 + 80 * q^8 + 124 * q^9 + 41 * q^10 + 25 * q^11 + 55 * q^12 - 28 * q^13 + 7 * q^14 - 34 * q^15 - 321 * q^16 - 82 * q^17 - 194 * q^18 - 72 * q^19 + 127 * q^20 - 38 * q^21 - 114 * q^22 + 165 * q^23 - 55 * q^24 + 203 * q^25 - 125 * q^26 + 155 * q^27 + 50 * q^28 + 55 * q^29 + 253 * q^30 + 108 * q^31 - 40 * q^32 + 117 * q^33 - 123 * q^34 + 186 * q^35 - 503 * q^36 - 377 * q^37 - 128 * q^38 + 261 * q^39 - 650 * q^40 + 60 * q^41 + 1000 * q^42 + 150 * q^43 - 274 * q^44 - 41 * q^45 + 93 * q^46 - 135 * q^47 - 644 * q^48 - 293 * q^49 + 350 * q^50 - 166 * q^51 + 606 * q^52 + 225 * q^53 + 382 * q^54 + 458 * q^55 - 713 * q^56 + 20 * q^57 + 216 * q^58 + 368 * q^59 - 120 * q^60 - 128 * q^61 - 522 * q^62 - 717 * q^63 + 788 * q^64 + 445 * q^65 + 759 * q^66 + 130 * q^67 + 218 * q^68 - 127 * q^69 - 1025 * q^70 - 247 * q^71 + 396 * q^72 + 350 * q^73 + 86 * q^74 - 882 * q^75 + 145 * q^76 - 260 * q^77 + 564 * q^78 - 1030 * q^79 + 151 * q^80 - 506 * q^81 + 268 * q^82 + 250 * q^83 - 320 * q^84 - 466 * q^85 - 294 * q^86 - 253 * q^88 - 479 * q^89 + 1861 * q^90 + 1252 * q^91 - 863 * q^93 + 7 * q^94 - 583 * q^95 + 1067 * q^96 - 278 * q^97 + 554 * q^98 - 1441 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{23}{30}\right)$

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 $

$2$	−1.52844	+	2.64734i	−0.764221	+	1.32367i	0.176436	+	0.984312i	$0.443543\pi$
$2$	−1.52844	+	2.64734i	−0.764221	+	1.32367i	−0.940657	+	0.339358i	$0.889790\pi$
$3$	−1.17971	−	0.383311i	−0.393236	−	0.127770i	0.105723	−	0.994396i	$-0.466284\pi$
$3$	−1.17971	−	0.383311i	−0.393236	−	0.127770i	−0.498959	+	0.866625i	$0.666284\pi$
$4$	−2.67228	−	4.62852i	−0.668069	−	1.15713i
$5$	−6.31759	+	2.81277i	−1.26352	+	0.562554i	−0.925558	−	0.378606i	$-0.876403\pi$
$5$	−6.31759	+	2.81277i	−1.26352	+	0.562554i	−0.337960	+	0.941161i	$0.609737\pi$
$6$	2.81787	−	2.53722i	0.469645	−	0.422870i
$7$	1.77668	+	3.99049i	0.253812	+	0.570070i	0.994846	−	0.101397i	$-0.0323312\pi$
$7$	1.77668	+	3.99049i	0.253812	+	0.570070i	−0.741034	+	0.671467i	$0.765664\pi$
$8$	4.11014			0.513767
$9$	−6.03637	−	4.38568i	−0.670708	−	0.487298i
$10$	2.20971	−	21.0240i	0.220971	−	2.10240i
$11$	17.9605	+	3.81763i	1.63278	+	0.347057i	0.930909	−	0.365250i	$-0.119017\pi$
$11$	17.9605	+	3.81763i	1.63278	+	0.347057i	0.701867	+	0.712308i	$0.252350\pi$
$12$	1.37835	+	6.48461i	0.114862	+	0.540384i
$13$	−4.17350	−	19.6348i	−0.321039	−	1.51037i	−0.782186	−	0.623045i	$-0.785896\pi$
$13$	−4.17350	−	19.6348i	−0.321039	−	1.51037i	0.461148	−	0.887323i	$-0.347438\pi$
$14$	−13.2797	−	1.39576i	−0.948553	−	0.0996970i
$15$	8.53108	−	0.896652i	0.568739	−	0.0597768i
$16$	4.40699	−	7.63313i	0.275437	−	0.477071i
$17$	−0.548745	−	5.22096i	−0.0322791	−	0.307115i	−0.998735	−	0.0502828i	$-0.983988\pi$
$17$	−0.548745	−	5.22096i	−0.0322791	−	0.307115i	0.966456	−	0.256833i	$-0.0826789\pi$
$18$	20.8366	−	9.27706i	1.15759	−	0.515392i
$19$	−3.45053			−0.181607			−0.0908033	−	0.995869i	$-0.528943\pi$
$19$	−3.45053			−0.181607			−0.0908033	+	0.995869i	$0.528943\pi$
$20$	29.9013	+	21.7246i	1.49506	+	1.08623i
$21$	−0.566369	−	5.38864i	−0.0269699	−	0.256602i
$22$	−37.5582	+	41.7127i	−1.70719	+	1.89603i
$23$	−13.1709	−	7.60424i	−0.572649	−	0.330619i	0.185558	−	0.982633i	$-0.440591\pi$
$23$	−13.1709	−	7.60424i	−0.572649	−	0.330619i	−0.758207	+	0.652014i	$0.773924\pi$
$24$	−4.84877	−	1.57546i	−0.202032	−	0.0656441i
$25$	15.2720	−	16.9612i	0.610879	−	0.678450i
$26$	58.3589	+	18.9620i	2.24457	+	0.729306i
$27$	12.0020	+	16.5193i	0.444518	+	0.611826i
$28$	13.7223	−	18.8871i	0.490081	−	0.674539i
$29$	3.09043	+	9.51138i	0.106567	+	0.327979i	0.990095	−	0.140399i	$-0.0448386\pi$
$29$	3.09043	+	9.51138i	0.106567	+	0.327979i	−0.883528	+	0.468378i	$0.844839\pi$
$30$	−10.6655	+	23.9552i	−0.355517	+	0.798505i
$31$	−0.234369	−	2.22987i	−0.00756030	−	0.0719314i	0.990091	−	0.140426i	$-0.0448471\pi$
$31$	−0.234369	−	2.22987i	−0.00756030	−	0.0719314i	−0.997652	+	0.0684944i	$0.978180\pi$
$32$	21.6919	+	37.5715i	0.677873	+	1.17411i
$33$	−19.7249	−	11.3882i	−0.597723	−	0.345096i
$34$	14.6604	+	6.52723i	0.431188	+	0.191977i
$35$	−22.4487	−	20.2129i	−0.641391	−	0.577511i
$36$	−4.16835	+	39.6592i	−0.115787	+	1.10164i
$37$	−44.5983	−	49.5314i	−1.20536	−	1.33869i	−0.925548	−	0.378631i	$-0.876395\pi$
$37$	−44.5983	−	49.5314i	−1.20536	−	1.33869i	−0.279811	−	0.960055i	$-0.590272\pi$
$38$	5.27393	−	9.13472i	0.138788	−	0.240387i
$39$	−2.60270	+	24.7631i	−0.0667360	+	0.634950i
$40$	−25.9662	+	11.5609i	−0.649154	+	0.289022i
$41$	−56.0823	−	18.2223i	−1.36786	−	0.444445i	−0.469202	−	0.883091i	$-0.655458\pi$
$41$	−56.0823	−	18.2223i	−1.36786	−	0.444445i	−0.898660	+	0.438646i	$0.855458\pi$
$42$	15.1312	+	6.73685i	0.360267	+	0.160401i
$43$	−54.8026	−	24.3997i	−1.27448	−	0.567434i	−0.345796	−	0.938310i	$-0.612391\pi$
$43$	−54.8026	−	24.3997i	−1.27448	−	0.567434i	−0.928683	+	0.370876i	$0.879058\pi$
$44$	−30.3256	−	93.3324i	−0.689217	−	2.12119i
$45$	50.4712	+	10.7280i	1.12158	+	0.238400i
$46$	40.2620	−	23.2453i	0.875262	−	0.505333i
$47$	35.4509	−	7.53533i	0.754275	−	0.160326i	0.185301	−	0.982682i	$-0.440674\pi$
$47$	35.4509	−	7.53533i	0.754275	−	0.160326i	0.568974	+	0.822356i	$0.307341\pi$
$48$	−8.12482	+	7.31562i	−0.169267	+	0.152409i
$49$	20.0200	−	22.2344i	0.408571	−	0.453764i
$50$	21.5599	+	66.3544i	0.431197	+	1.32709i
$51$	−1.35389	+	6.36955i	−0.0265469	+	0.124893i
$52$	−79.7272	+	71.7867i	−1.53321	+	1.38051i
$53$	−86.1195	+	27.9819i	−1.62490	+	0.527961i	−0.973090	−	0.230424i	$-0.925989\pi$
$53$	−86.1195	+	27.9819i	−1.62490	+	0.527961i	−0.651807	+	0.758385i	$0.725989\pi$
$54$	−62.0766	+	6.52451i	−1.14957	+	0.120824i
$55$	−124.205	+	26.4007i	−2.25828	+	0.480012i
$56$	7.30241	+	16.4015i	0.130400	+	0.292883i
$57$	4.07061	+	1.32262i	0.0714143	+	0.0232039i
$58$	−29.9034	−	6.35617i	−0.515576	−	0.109589i
$59$	39.8486			0.675400			0.337700	−	0.941254i	$-0.390351\pi$
$59$	39.8486			0.675400			0.337700	+	0.941254i	$0.390351\pi$
$60$	−26.9476	−	37.0901i	−0.449126	−	0.618169i
$61$	59.4783	+	53.5545i	0.975053	+	0.877942i	0.992542	−	0.121905i	$-0.0389004\pi$
$61$	59.4783	+	53.5545i	0.975053	+	0.877942i	−0.0174884	+	0.999847i	$0.505567\pi$
$62$	6.26146	+	2.78778i	0.100991	+	0.0449642i
$63$	6.77631	−	31.8800i	0.107560	−	0.506032i
$64$	−97.3637			−1.52131
$65$	81.5946	+	112.305i	1.25530	+	1.72777i
$66$	60.2967	−	34.8123i	0.913586	−	0.527459i
$67$	−65.1045	−	89.6087i	−0.971710	−	1.33744i	−0.941179	−	0.337910i	$-0.890280\pi$
$67$	−65.1045	−	89.6087i	−0.971710	−	1.33744i	−0.0305310	−	0.999534i	$-0.509720\pi$
$68$	−22.6989	+	16.4917i	−0.333808	+	0.242525i
$69$	12.6231	+	14.0193i	0.182943	+	0.203179i
$70$	87.8219	−	28.5351i	1.25460	−	0.407644i
$71$	−69.8565	−	7.34221i	−0.983894	−	0.103411i	−0.401102	−	0.916033i	$-0.631373\pi$
$71$	−69.8565	−	7.34221i	−0.983894	−	0.103411i	−0.582791	+	0.812622i	$0.698040\pi$
$72$	−24.8103	−	18.0257i	−0.344588	−	0.250358i
$73$	26.9326	−	37.0696i	0.368940	−	0.507803i	−0.583672	−	0.811989i	$-0.698385\pi$
$73$	26.9326	−	37.0696i	0.368940	−	0.507803i	0.952612	+	0.304187i	$0.0983847\pi$
$74$	199.292	−	42.3609i	2.69314	−	0.572445i
$75$	−24.5179	+	14.1554i	−0.326905	+	0.188739i
$76$	9.22075	+	15.9708i	0.121326	+	0.210142i
$77$	16.6759	+	78.4541i	0.216571	+	1.01888i
$78$	−61.5782	−	44.7392i	−0.789464	−	0.573579i
$79$	23.7053	−	32.6275i	0.300067	−	0.413007i	−0.632184	−	0.774818i	$-0.717841\pi$
$79$	23.7053	−	32.6275i	0.300067	−	0.413007i	0.932251	+	0.361811i	$0.117841\pi$
$80$	−6.37130	+	60.6188i	−0.0796412	+	0.757735i
$81$	12.9244	+	39.7771i	0.159560	+	0.491076i
$82$	133.959	−	120.617i	1.63365	−	1.47094i
$83$	45.1882	+	62.1962i	0.544436	+	0.749351i	0.989244	−	0.146274i	$-0.0467282\pi$
$83$	45.1882	+	62.1962i	0.544436	+	0.749351i	−0.444808	+	0.895626i	$0.646728\pi$
$84$	−23.4279	+	17.0214i	−0.278904	+	0.202635i
$85$	18.1521	+	31.4404i	0.213554	+	0.369887i
$86$	148.357	−	107.788i	1.72508	−	1.25334i
$87$		−	12.4053i		−	0.142589i
$88$	73.8203	+	15.6910i	0.838867	+	0.178307i
$89$	26.9726	−	60.5815i	0.303063	−	0.680691i	−0.696248	−	0.717801i	$-0.745149\pi$
$89$	26.9726	−	60.5815i	0.303063	−	0.680691i	0.999311	+	0.0371100i	$0.0118152\pi$
$90$	−105.543	+	117.217i	−1.17270	+	1.30241i
$91$	70.9375	−	51.5391i	0.779532	−	0.566363i
$92$			81.2825i			0.883506i
$93$	−0.578247	+	2.72044i	−0.00621771	+	0.0292520i
$94$	−34.2361	+	105.368i	−0.364214	+	1.12094i
$95$	21.7990	−	9.70554i	0.229463	−	0.102164i
$96$	−11.1886	−	52.6382i	−0.116548	−	0.548315i
$97$	9.48319	+	90.2265i	0.0977648	+	0.930170i	0.927956	+	0.372691i	$0.121565\pi$
$97$	9.48319	+	90.2265i	0.0977648	+	0.930170i	−0.830191	+	0.557479i	$0.811769\pi$
$98$	28.2627	+	86.9838i	0.288395	+	0.887589i
$99$	−91.6736	−	101.814i	−0.925995	−	1.02842i
$100$	−119.316	−	25.3615i	−1.19316	−	0.253615i
$101$	−11.7647	+	3.82259i	−0.116483	+	0.0378475i	−0.366678	−	0.930348i	$-0.619505\pi$
$101$	−11.7647	+	3.82259i	−0.116483	+	0.0378475i	0.250196	+	0.968195i	$0.419505\pi$
$102$	−14.7930	−	13.3197i	−0.145030	−	0.130585i
$103$	−13.5224	−	15.0182i	−0.131286	−	0.145808i	0.673917	−	0.738807i	$-0.264610\pi$
$103$	−13.5224	−	15.0182i	−0.131286	−	0.145808i	−0.805203	+	0.592999i	$0.797944\pi$
$104$	−17.1537	−	80.7017i	−0.164939	−	0.775978i
$105$	18.7351	+	32.4501i	0.178429	+	0.309049i
$106$	57.5511	−	270.757i	0.542935	−	2.55431i
$107$	−30.9572	+	10.0586i	−0.289319	+	0.0940056i	−0.450081	−	0.892988i	$-0.648605\pi$
$107$	−30.9572	+	10.0586i	−0.289319	+	0.0940056i	0.160762	+	0.986993i	$0.448605\pi$
$108$	44.3873	−	99.6955i	0.410993	−	0.923106i
$109$	−19.3830	+	43.5349i	−0.177825	+	0.399402i	−0.980364	−	0.197198i	$-0.936816\pi$
$109$	−19.3830	+	43.5349i	−0.177825	+	0.399402i	0.802538	+	0.596601i	$0.203482\pi$
$110$	119.949	−	369.166i	1.09045	−	3.35606i
$111$	33.6271	+	75.5276i	0.302946	+	0.680429i
$112$	38.2898	+	4.02442i	0.341873	+	0.0359323i
$113$	−119.849	−	69.1948i	−1.06061	−	0.612343i	−0.135009	−	0.990844i	$-0.543106\pi$
$113$	−119.849	−	69.1948i	−1.06061	−	0.612343i	−0.925601	+	0.378501i	$0.876440\pi$
$114$	−9.72314	+	8.75475i	−0.0852907	+	0.0767961i
$115$	104.598	+	10.9936i	0.909544	+	0.0955969i
$116$	35.7651	−	39.7212i	0.308320	−	0.342424i
$117$	−60.9190	+	136.826i	−0.520676	+	1.16946i
$118$	−60.9063	+	105.493i	−0.516155	+	0.894007i
$119$	19.8593	−	11.4657i	0.166885	−	0.0963508i
$120$	35.0639	−	3.68537i	0.292199	−	0.0307114i
$121$	197.468	+	87.9184i	1.63197	+	0.726598i
$122$	−232.686	+	75.6043i	−1.90726	+	0.619707i
$123$	59.1760	+	42.9939i	0.481106	+	0.349544i
$124$	−9.69471	+	7.04362i	−0.0781832	+	0.0568034i
$125$	4.65095	−	14.3141i	0.0372076	−	0.114513i
$126$	74.0401	+	66.6660i	0.587620	+	0.529095i
$127$	−52.0430	+	160.172i	−0.409787	+	1.26119i	0.507044	+	0.861920i	$0.330738\pi$
$127$	−52.0430	+	160.172i	−0.409787	+	1.26119i	−0.916831	+	0.399275i	$0.869262\pi$
$128$	62.0470	−	107.469i	0.484742	−	0.839598i
$129$	55.2984	+	49.7909i	0.428670	+	0.385976i
$130$	−422.023	+	44.3564i	−3.24633	+	0.341203i
$131$	25.8962	−	35.6430i	0.197681	−	0.272084i	−0.698656	−	0.715457i	$-0.746218\pi$
$131$	25.8962	−	35.6430i	0.197681	−	0.272084i	0.896337	+	0.443373i	$0.146218\pi$
$132$			121.729i			0.922191i
$133$	−6.13048	−	13.7693i	−0.0460939	−	0.103529i
$134$	336.733	−	35.3921i	2.51294	−	0.264120i
$135$	−122.289	−	70.6033i	−0.905841	−	0.522988i
$136$	−2.25542	−	21.4589i	−0.0165840	−	0.157786i
$137$	8.03503	−	76.4482i	0.0586498	−	0.558016i	−0.925258	−	0.379339i	$-0.876152\pi$
$137$	8.03503	−	76.4482i	0.0586498	−	0.558016i	0.983908	−	0.178677i	$-0.0571818\pi$
$138$	−56.4076	+	11.9898i	−0.408751	+	0.0868827i
$139$	26.5830	−	5.65040i	0.191245	−	0.0406504i	−0.111293	−	0.993788i	$-0.535499\pi$
$139$	26.5830	−	5.65040i	0.191245	−	0.0406504i	0.302538	+	0.953137i	$0.402166\pi$
$140$	−33.5666	+	157.918i	−0.239762	+	1.12799i
$141$	−44.7101	−	4.69923i	−0.317093	−	0.0333278i
$142$	126.209	−	173.712i	0.888795	−	1.22332i
$143$		−	368.584i		−	2.57751i
$144$	−60.0787	+	26.7487i	−0.417213	+	0.185755i
$145$	−46.2774	−	51.3963i	−0.319155	−	0.354457i
$146$	56.9709	+	127.959i	0.390211	+	0.876429i
$147$	−32.1404	+	18.5563i	−0.218642	+	0.126233i
$148$	−110.078	+	338.785i	−0.743771	+	2.28909i
$149$	−176.110	−	101.677i	−1.18195	−	0.682397i	−0.225483	−	0.974247i	$-0.572396\pi$
$149$	−176.110	−	101.677i	−1.18195	−	0.682397i	−0.956464	+	0.291850i	$0.905729\pi$
$150$		−	86.5430i		−	0.576953i
$151$	0.466764	−	150.999i	0.00309115	−	0.999995i
$151$	0.466764	−	150.999i	0.00309115	−	0.999995i
$152$	−14.1821			−0.0933035
$153$	−19.5850	+	33.9223i	−0.128007	+	0.221714i
$154$	−233.183	−	75.7657i	−1.51418	−	0.491985i
$155$	7.75278	+	13.4282i	0.0500179	+	0.0866336i
$156$	121.571	−	54.1271i	0.779304	−	0.346968i
$157$	−20.7266	+	18.6623i	−0.132017	+	0.118868i	−0.732494	−	0.680773i	$-0.761644\pi$
$157$	−20.7266	+	18.6623i	−0.132017	+	0.118868i	0.600477	+	0.799642i	$0.294977\pi$
$158$	50.1440	+	112.625i	0.317367	+	0.712819i
$159$	112.322			0.706426
$160$	−242.721	−	176.347i	−1.51701	−	1.10217i
$161$	6.94411	−	66.0688i	0.0431311	−	0.410365i
$162$	−125.058	−	26.5819i	−0.771962	−	0.164086i
$163$	42.2048	+	198.558i	0.258925	+	1.21815i	0.894839	+	0.446388i	$0.147290\pi$
$163$	42.2048	+	198.558i	0.258925	+	1.21815i	−0.635914	+	0.771760i	$0.719377\pi$
$164$	65.5254	+	308.273i	0.399545	+	1.87971i
$165$	156.646	+	16.4641i	0.949369	+	0.0997827i
$166$	−233.722	+	24.5652i	−1.40796	+	0.147983i
$167$	100.583	−	174.215i	0.602293	−	1.04320i	−0.390180	−	0.920739i	$-0.627587\pi$
$167$	100.583	−	174.215i	0.602293	−	1.04320i	0.992473	−	0.122463i	$-0.0390794\pi$
$168$	−2.32785	−	22.1480i	−0.0138563	−	0.131834i
$169$	−213.717	+	95.1531i	−1.26460	+	0.563036i
$170$	−110.978			−0.652811
$171$	20.8286	+	15.1329i	0.121805	+	0.0884965i
$172$	33.5132	+	318.857i	0.194844	+	1.85382i
$173$	−43.4274	+	48.2310i	−0.251025	+	0.278792i	−0.855467	−	0.517858i	$-0.826730\pi$
$173$	−43.4274	+	48.2310i	−0.251025	+	0.278792i	0.604441	+	0.796650i	$0.293396\pi$
$174$	32.8409	+	18.9607i	0.188741	+	0.108970i
$175$	94.8171	+	30.8080i	0.541812	+	0.176045i
$176$	108.292	−	120.271i	0.615298	−	0.683357i
$177$	−47.0097	−	15.2744i	−0.265592	−	0.0862960i
$178$	119.154	+	164.001i	0.669404	+	0.921355i
$179$	−29.3174	+	40.3519i	−0.163784	+	0.225430i	−0.883019	−	0.469338i	$-0.844493\pi$
$179$	−29.3174	+	40.3519i	−0.163784	+	0.225430i	0.719234	+	0.694767i	$0.244493\pi$
$180$	−85.2183	−	262.275i	−0.473435	−	1.45708i
$181$	−49.5578	+	111.309i	−0.273800	+	0.614964i	−0.997144	−	0.0755231i	$-0.975937\pi$
$181$	−49.5578	+	111.309i	−0.273800	+	0.614964i	0.723344	+	0.690488i	$0.242604\pi$
$182$	28.0177	+	266.570i	0.153943	+	1.46467i
$183$	−49.6390	−	85.9773i	−0.271251	−	0.469821i
$184$	−54.1344	−	31.2545i	−0.294208	−	0.169861i
$185$	421.074	+	187.474i	2.27608	+	1.01337i
$186$	−6.31811	−	5.68885i	−0.0339683	−	0.0305852i
$187$	10.0759	−	95.8662i	0.0538821	−	0.512654i
$188$	−129.612	−	143.949i	−0.689426	−	0.765685i
$189$	−44.5965	+	77.2433i	−0.235960	+	0.408695i
$190$	−7.62465	+	72.5437i	−0.0401298	+	0.381809i
$191$	−247.057	+	109.997i	−1.29349	+	0.575900i	−0.934008	−	0.357251i	$-0.883714\pi$
$191$	−247.057	+	109.997i	−1.29349	+	0.575900i	−0.359485	+	0.933151i	$0.617047\pi$
$192$	114.861	+	37.3205i	0.598233	+	0.194378i
$193$	271.359	+	120.817i	1.40601	+	0.625994i	0.962748	−	0.270399i	$-0.0871558\pi$
$193$	271.359	+	120.817i	1.40601	+	0.625994i	0.443258	+	0.896394i	$0.353822\pi$
$194$	−253.355	−	112.801i	−1.30595	−	0.581447i
$195$	−53.2100	−	163.764i	−0.272872	−	0.839814i
$196$	−156.411	−	33.2463i	−0.798017	−	0.169624i
$197$	−196.992	+	113.733i	−0.999959	+	0.577327i	−0.908236	−	0.418458i	$-0.862571\pi$
$197$	−196.992	+	113.733i	−0.999959	+	0.577327i	−0.0917229	+	0.995785i	$0.529237\pi$
$198$	409.654	−	87.0746i	2.06896	−	0.439770i
$199$	202.531	−	182.360i	1.01774	−	0.916380i	0.0212262	−	0.999775i	$-0.493243\pi$
$199$	202.531	−	182.360i	1.01774	−	0.916380i	0.996517	+	0.0833950i	$0.0265763\pi$
$200$	62.7699	−	69.7131i	0.313850	−	0.348565i
$201$	42.4564	+	130.667i	0.211226	+	0.650087i
$202$	7.86202	−	36.9879i	0.0389209	−	0.183108i
$203$	−32.4644	+	29.2310i	−0.159923	+	0.143995i
$204$	33.0996	−	10.7547i	0.162253	−	0.0527191i
$205$	405.560	−	42.6261i	1.97834	−	0.207932i
$206$	60.4265	−	12.8441i	0.293333	−	0.0623498i
$207$	46.1548	+	103.665i	0.222970	+	0.500799i
$208$	−168.267	−	54.6734i	−0.808978	−	0.262853i
$209$	−61.9733	−	13.1728i	−0.296523	−	0.0630279i
$210$	−114.542			−0.545438
$211$	80.5637	+	110.886i	0.381819	+	0.525528i	0.956065	−	0.293154i	$-0.0947049\pi$
$211$	80.5637	+	110.886i	0.381819	+	0.525528i	−0.574247	+	0.818682i	$0.694705\pi$
$212$	359.650	+	323.830i	1.69646	+	1.52750i
$213$	79.5959	+	35.4384i	0.373690	+	0.166377i
$214$	20.6877	−	97.3282i	0.0966717	−	0.454805i
$215$	414.851			1.92954
$216$	49.3298	+	67.8966i	0.228379	+	0.314336i
$217$	8.48190	−	4.89702i	0.0390871	−	0.0225669i
$218$	−85.6259	−	117.854i	−0.392779	−	0.540614i
$219$	−45.9818	+	33.4078i	−0.209963	+	0.152547i
$220$	454.107	+	504.337i	2.06412	+	2.29244i
$221$	−100.222	+	32.5642i	−0.453494	+	0.147349i
$222$	−251.344	−	26.4174i	−1.13218	−	0.118997i
$223$	−186.430	−	135.449i	−0.836007	−	0.607395i	0.0852454	−	0.996360i	$-0.472833\pi$
$223$	−186.430	−	135.449i	−0.836007	−	0.607395i	−0.921252	+	0.388965i	$0.872833\pi$
$224$	−111.389	+	153.314i	−0.497273	+	0.684438i
$225$	−166.574	+	35.4064i	−0.740328	+	0.157362i
$226$	366.364	−	211.521i	1.62108	−	0.935932i
$227$	−96.5415	−	167.215i	−0.425293	−	0.736629i	0.571155	−	0.820842i	$-0.306496\pi$
$227$	−96.5415	−	167.215i	−0.425293	−	0.736629i	−0.996448	+	0.0842134i	$0.973162\pi$
$228$	−4.75602	−	22.3753i	−0.0208597	−	0.0981374i
$229$	−327.396	−	237.867i	−1.42968	−	1.03872i	−0.990077	−	0.140526i	$-0.955121\pi$
$229$	−327.396	−	237.867i	−1.42968	−	1.03872i	−0.439599	−	0.898194i	$-0.644879\pi$
$230$	−188.975	+	260.102i	−0.821632	+	1.13088i
$231$	10.3995	−	98.9451i	0.0450197	−	0.428334i
$232$	12.7021	+	39.0931i	0.0547505	+	0.168505i
$233$	178.859	−	161.045i	0.767633	−	0.691180i	−0.189161	−	0.981946i	$-0.560577\pi$
$233$	178.859	−	161.045i	0.767633	−	0.691180i	0.956794	+	0.290766i	$0.0939101\pi$
$234$	−269.115	−	370.405i	−1.15006	−	1.58293i
$235$	−202.769	+	147.320i	−0.862848	+	0.626896i
$236$	−106.486	−	184.440i	−0.451214	−	0.781525i
$237$	−40.4718	+	29.4045i	−0.170767	+	0.124070i
$238$			70.0990i			0.294534i
$239$	24.9324	+	5.29955i	0.104320	+	0.0221739i	0.259776	−	0.965669i	$-0.416351\pi$
$239$	24.9324	+	5.29955i	0.104320	+	0.0221739i	−0.155456	+	0.987843i	$0.549685\pi$
$240$	30.7521	−	69.0704i	0.128134	−	0.287793i
$241$	215.435	−	239.265i	0.893922	−	0.992801i	−0.106076	−	0.994358i	$-0.533829\pi$
$241$	215.435	−	239.265i	0.893922	−	0.992801i	0.999999	+	0.00155653i	$0.000495459\pi$
$242$	−534.568	+	388.387i	−2.20896	+	1.60490i
$243$		−	235.650i		−	0.969754i
$244$	88.9354	−	418.408i	0.364490	−	1.71479i
$245$	−63.9376	+	196.780i	−0.260970	+	0.803182i
$246$	−204.267	+	90.9454i	−0.830352	+	0.369697i
$247$	14.4008	+	67.7503i	0.0583027	+	0.274293i
$248$	−0.963290	−	9.16509i	−0.00388423	−	0.0369560i
$249$	−29.4684	−	90.6945i	−0.118347	−	0.364235i
$250$	30.7857	+	34.1910i	0.123143	+	0.136764i
$251$	−7.02663	−	1.49356i	−0.0279945	−	0.00595042i	0.193893	−	0.981023i	$-0.437888\pi$
$251$	−7.02663	−	1.49356i	−0.0279945	−	0.00595042i	−0.221888	+	0.975072i	$0.571222\pi$
$252$	−165.665	+	53.8280i	−0.657402	+	0.213603i
$253$	−207.527	−	186.858i	−0.820265	−	0.738570i
$254$	−344.485	−	382.589i	−1.35624	−	1.50626i
$255$	−9.36278	−	44.0484i	−0.0367168	−	0.172739i
$256$	−5.05664	−	8.75835i	−0.0197525	−	0.0342123i
$257$	−56.8411	+	267.417i	−0.221172	+	1.04053i	0.717723	+	0.696328i	$0.245184\pi$
$257$	−56.8411	+	267.417i	−0.221172	+	1.04053i	−0.938895	+	0.344203i	$0.888149\pi$
$258$	−216.334	+	70.2912i	−0.838504	+	0.272446i
$259$	118.418	−	265.971i	0.457211	−	1.02691i
$260$	301.764	−	677.773i	1.16063	−	2.60682i
$261$	23.0588	−	70.9678i	0.0883481	−	0.271907i
$262$	54.7784	+	123.034i	0.209078	+	0.469597i
$263$	97.4650	+	10.2440i	0.370589	+	0.0389505i	0.287993	−	0.957633i	$-0.407012\pi$
$263$	97.4650	+	10.2440i	0.370589	+	0.0389505i	0.0825965	+	0.996583i	$0.473679\pi$
$264$	−81.0720	−	46.8069i	−0.307091	−	0.177299i
$265$	465.361	−	419.013i	1.75608	−	1.58118i
$266$	45.8221	+	4.81610i	0.172264	+	0.0181056i
$267$	−55.0414	+	61.1297i	−0.206148	+	0.228950i
$268$	−240.778	+	540.797i	−0.898426	+	2.01790i
$269$	−149.360	+	258.699i	−0.555242	+	0.961708i	0.442643	+	0.896698i	$0.354041\pi$
$269$	−149.360	+	258.699i	−0.555242	+	0.961708i	−0.997885	+	0.0650094i	$0.979292\pi$
$270$	373.822	−	215.826i	1.38453	−	0.799357i
$271$	−431.097	+	45.3101i	−1.59076	+	0.167196i	−0.858132	−	0.513430i	$-0.828375\pi$
$271$	−431.097	+	45.3101i	−1.59076	+	0.167196i	−0.732631	+	0.680626i	$0.761708\pi$
$272$	−42.2706	−	18.8201i	−0.155407	−	0.0691915i
$273$	−103.441	+	33.6100i	−0.378905	+	0.123114i
$274$	190.103	+	138.118i	0.693808	+	0.504081i
$275$	339.045	−	246.330i	1.23289	−	0.895747i
$276$	31.1564	−	95.8897i	0.112886	−	0.347426i
$277$	145.806	+	131.284i	0.526375	+	0.473950i	0.888950	−	0.458005i	$-0.151436\pi$
$277$	145.806	+	131.284i	0.526375	+	0.473950i	−0.362575	+	0.931955i	$0.618102\pi$
$278$	−25.6721	+	79.0107i	−0.0923458	+	0.284211i
$279$	−8.36477	+	14.4882i	−0.0299813	+	0.0519291i
$280$	−92.2672	−	83.0778i	−0.329526	−	0.296706i
$281$	256.610	−	26.9707i	0.913201	−	0.0959813i	0.363740	−	0.931501i	$-0.381500\pi$
$281$	256.610	−	26.9707i	0.913201	−	0.0959813i	0.549461	+	0.835519i	$0.314833\pi$
$282$	80.7773	−	111.180i	0.286444	−	0.394257i
$283$			49.0543i			0.173337i	0.996237	+	0.0866683i	$0.0276220\pi$
$283$			49.0543i			0.173337i	−0.996237	+	0.0866683i	$0.972378\pi$
$284$	152.692	+	342.952i	0.537648	+	1.20758i
$285$	−29.4367	+	3.09392i	−0.103287	+	0.0108559i
$286$	975.768	+	563.360i	3.41178	+	1.96979i
$287$	−26.9247	−	256.171i	−0.0938142	−	0.892583i
$288$	33.8362	−	321.930i	0.117487	−	1.11781i
$289$	255.727	−	54.3565i	0.884870	−	0.188085i
$290$	206.796	−	43.9558i	0.713089	−	0.151572i
$291$	23.3974	−	110.076i	0.0804033	−	0.378268i
$292$	−243.549	−	25.5980i	−0.834071	−	0.0876644i
$293$	−302.108	+	415.816i	−1.03108	+	1.41917i	−0.126955	+	0.991908i	$0.540520\pi$
$293$	−302.108	+	415.816i	−1.03108	+	1.41917i	−0.904130	+	0.427258i	$0.859480\pi$
$294$		−	113.449i		−	0.385881i
$295$	−251.747	+	112.085i	−0.853380	+	0.379949i
$296$	−183.305	−	203.581i	−0.619274	−	0.687773i
$297$	152.497	+	342.515i	0.513459	+	1.15325i
$298$	538.348	−	310.816i	1.80654	−	1.04301i
$299$	−94.3387	+	290.345i	−0.315514	+	0.971053i
$300$	131.037	+	75.6543i	0.436791	+	0.252181i
$301$		−	262.040i		−	0.870563i
$302$	399.033	+	232.029i	1.32130	+	0.768309i
$303$	15.3442			0.0506409
$304$	−15.2064	+	26.3383i	−0.0500212	+	0.0866392i
$305$	−526.396	−	171.036i	−1.72589	−	0.560775i
$306$	−59.8692	−	103.697i	−0.195651	−	0.338877i
$307$	−440.968	+	196.332i	−1.43638	+	0.639516i	−0.969564	−	0.244839i	$-0.921265\pi$
$307$	−440.968	+	196.332i	−1.43638	+	0.639516i	−0.466814	+	0.884356i	$0.654598\pi$
$308$	318.564	−	286.836i	1.03430	−	0.931285i
$309$	10.1959	+	22.9004i	0.0329964	+	0.0741112i
$310$	−47.3987			−0.152899
$311$	−152.306	−	110.657i	−0.489731	−	0.355810i	0.315350	−	0.948975i	$-0.397878\pi$
$311$	−152.306	−	110.657i	−0.489731	−	0.355810i	−0.805081	+	0.593165i	$0.797878\pi$
$312$	−10.6975	+	101.780i	−0.0342868	+	0.326217i
$313$	170.548	+	36.2512i	0.544883	+	0.115818i	0.472126	−	0.881531i	$-0.343487\pi$
$313$	170.548	+	36.2512i	0.544883	+	0.115818i	0.0727572	+	0.997350i	$0.476820\pi$
$314$	−17.7261	−	83.3948i	−0.0564526	−	0.265588i
$315$	46.8613	+	220.465i	0.148766	+	0.699889i
$316$	−214.364	−	22.5306i	−0.678368	−	0.0712993i
$317$	−173.338	+	18.2185i	−0.546806	+	0.0574717i	−0.373904	−	0.927467i	$-0.621981\pi$
$317$	−173.338	+	18.2185i	−0.546806	+	0.0574717i	−0.172902	+	0.984939i	$0.555314\pi$
$318$	−171.677	+	297.354i	−0.539866	+	0.935075i
$319$	19.1949	+	182.628i	0.0601722	+	0.572501i
$320$	615.103	−	273.862i	1.92220	−	0.855818i
$321$	40.3760			0.125782
$322$	164.293	+	119.366i	0.510227	+	0.370701i
$323$	1.89346	+	18.0151i	0.00586210	+	0.0557742i
$324$	149.572	−	166.116i	0.461641	−	0.512704i
$325$	−396.768	−	229.074i	−1.22082	−	0.704843i
$326$	−590.159	−	191.754i	−1.81030	−	0.588203i
$327$	39.5536	−	43.9288i	0.120959	−	0.134339i
$328$	−230.506	−	74.8960i	−0.702763	−	0.228341i
$329$	93.0547	+	128.079i	0.282841	+	0.389297i
$330$	−283.011	+	389.531i	−0.857608	+	1.18040i
$331$	84.3967	+	259.746i	0.254975	+	0.784732i	0.993835	+	0.110873i	$0.0353646\pi$
$331$	84.3967	+	259.746i	0.254975	+	0.784732i	−0.738860	+	0.673859i	$0.764635\pi$
$332$	167.121	−	375.359i	0.503376	−	1.13060i
$333$	51.9828	+	494.583i	0.156105	+	1.48524i
$334$	307.470	+	532.554i	0.920570	+	1.59447i
$335$	663.352	+	382.987i	1.98016	+	1.14324i
$336$	−43.6282	−	19.4245i	−0.129846	−	0.0578110i
$337$	67.6252	+	60.8900i	0.200668	+	0.180683i	0.763338	−	0.645999i	$-0.223559\pi$
$337$	67.6252	+	60.8900i	0.200668	+	0.180683i	−0.562670	+	0.826682i	$0.690226\pi$
$338$	74.7521	−	711.219i	0.221160	−	2.10420i
$339$	114.864	+	127.569i	0.338831	+	0.376310i
$340$	97.0149	−	168.035i	0.285338	−	0.494220i
$341$	4.30344	−	40.9445i	0.0126201	−	0.120072i
$342$	−71.8973	+	32.0107i	−0.210226	+	0.0935987i
$343$	327.858	+	106.528i	0.955855	+	0.310576i
$344$	−225.246	−	100.286i	−0.654785	−	0.291529i
$345$	−119.181	−	53.0626i	−0.345451	−	0.153805i
$346$	−61.3076	−	188.685i	−0.177190	−	0.545333i
$347$	−567.066	−	120.534i	−1.63420	−	0.347359i	−0.702806	−	0.711382i	$-0.748070\pi$
$347$	−567.066	−	120.534i	−1.63420	−	0.347359i	−0.931390	+	0.364023i	$0.881403\pi$
$348$	−57.4179	+	33.1503i	−0.164994	+	0.0952593i
$349$	331.522	−	70.4671i	0.949919	−	0.201911i	0.293203	−	0.956050i	$-0.405279\pi$
$349$	331.522	−	70.4671i	0.949919	−	0.201911i	0.656715	+	0.754139i	$0.271945\pi$
$350$	−226.482	+	203.925i	−0.647091	+	0.582643i
$351$	274.263	−	304.600i	0.781375	−	0.867805i
$352$	246.165	+	757.617i	0.699332	+	2.15232i
$353$	76.8861	−	361.721i	0.217808	−	1.02470i	−0.724324	−	0.689460i	$-0.757848\pi$
$353$	76.8861	−	361.721i	0.217808	−	1.02470i	0.942131	−	0.335244i	$-0.108819\pi$
$354$	112.288	−	101.105i	0.317198	−	0.285607i
$355$	461.976	−	150.105i	1.30134	−	0.422832i
$356$	−352.481	+	37.0472i	−0.990115	+	0.104065i
$357$	−27.8231	+	5.91398i	−0.0779358	+	0.0165658i
$358$	−62.0153	−	139.289i	−0.173227	−	0.389075i
$359$	−98.0731	−	31.8659i	−0.273184	−	0.0887629i	0.169221	−	0.985578i	$-0.445875\pi$
$359$	−98.0731	−	31.8659i	−0.273184	−	0.0887629i	−0.442405	+	0.896815i	$0.645875\pi$
$360$	207.444	+	44.0935i	0.576232	+	0.122482i
$361$	−349.094			−0.967019
$362$	−218.925	−	301.325i	−0.604767	−	0.832390i
$363$	−199.254	−	179.410i	−0.548910	−	0.494241i
$364$	−428.114	−	190.609i	−1.17614	−	0.523650i
$365$	−65.8810	+	309.946i	−0.180496	+	0.849167i
$366$	303.482			0.829185
$367$	141.526	+	194.794i	0.385630	+	0.530774i	0.957065	−	0.289873i	$-0.0936132\pi$
$367$	141.526	+	194.794i	0.385630	+	0.530774i	−0.571435	+	0.820647i	$0.693613\pi$
$368$	−116.088	+	67.0236i	−0.315457	+	0.182129i
$369$	258.617	+	355.955i	0.700858	+	0.964648i
$370$	−1139.90	+	828.183i	−3.08080	+	2.23833i
$371$	−264.669	−	293.944i	−0.713393	−	0.792303i
$372$	14.1368	−	4.59333i	0.0380022	−	0.0123477i
$373$	66.7833	+	7.01921i	0.179044	+	0.0188182i	0.193626	−	0.981075i	$-0.437975\pi$
$373$	66.7833	+	7.01921i	0.179044	+	0.0188182i	−0.0145823	+	0.999894i	$0.504642\pi$
$374$	238.390	+	173.201i	0.637407	+	0.463103i
$375$	−10.9735	+	15.1038i	−0.0292627	+	0.0402767i
$376$	145.708	−	30.9712i	0.387522	−	0.0823703i
$377$	173.856	−	100.376i	0.461156	−	0.266249i
$378$	−136.326	−	236.124i	−0.360652	−	0.624667i
$379$	27.1756	+	127.851i	0.0717035	+	0.337338i	0.999347	−	0.0361281i	$-0.0115024\pi$
$379$	27.1756	+	127.851i	0.0717035	+	0.337338i	−0.927644	+	0.373466i	$0.878169\pi$
$380$	−103.175	−	74.9612i	−0.271514	−	0.197266i
$381$	122.791	−	169.007i	0.322286	−	0.443589i
$382$	86.4134	−	822.169i	0.226213	−	2.15227i
$383$	136.394	+	419.779i	0.356121	+	1.09603i	0.955356	+	0.295456i	$0.0954715\pi$
$383$	136.394	+	419.779i	0.356121	+	1.09603i	−0.599235	+	0.800573i	$0.704529\pi$
$384$	−114.391	+	102.998i	−0.297894	+	0.268225i
$385$	−326.025	−	448.735i	−0.846819	−	1.16555i
$386$	−734.601	+	533.719i	−1.90311	+	1.38269i
$387$	223.799	+	387.632i	0.578293	+	1.00163i
$388$	392.273	−	285.003i	1.01101	−	0.734544i
$389$		−	118.677i		−	0.305082i	−0.988297	−	0.152541i	$-0.951254\pi$
$389$		−	118.677i		−	0.305082i	0.988297	−	0.152541i	$-0.0487456\pi$
$390$	514.867	+	109.438i	1.32017	+	0.280611i
$391$	−32.4740	+	72.9377i	−0.0830536	+	0.186542i
$392$	82.2849	−	91.3866i	0.209910	−	0.233129i
$393$	−44.2123	+	32.1221i	−0.112499	+	0.0817357i
$394$		−	695.340i		−	1.76482i
$395$	−57.9865	+	272.805i	−0.146801	+	0.690646i
$396$	−226.270	+	696.387i	−0.571389	+	1.75855i
$397$	218.675	−	97.3604i	0.550819	−	0.245240i	−0.112404	−	0.993663i	$-0.535855\pi$
$397$	218.675	−	97.3604i	0.550819	−	0.245240i	0.663223	+	0.748422i	$0.269188\pi$
$398$	173.211	+	814.894i	0.435204	+	2.04747i
$399$	1.95427	+	18.5936i	0.00489792	+	0.0466006i
$400$	−62.1640	−	191.321i	−0.155410	−	0.478302i
$401$	−127.487	−	141.589i	−0.317923	−	0.353089i	0.562909	−	0.826519i	$-0.309682\pi$
$401$	−127.487	−	141.589i	−0.317923	−	0.353089i	−0.880831	+	0.473430i	$0.843016\pi$
$402$	−410.813	−	87.3211i	−1.02192	−	0.217217i
$403$	−42.8050	+	13.9082i	−0.106216	+	0.0345116i
$404$	49.1316	+	44.2382i	0.121613	+	0.109501i
$405$	−193.535	−	214.942i	−0.477864	−	0.530722i
$406$	−27.7646	−	130.622i	−0.0683857	−	0.321730i
$407$	−611.917	−	1059.87i	−1.50348	−	2.60410i
$408$	−5.56468	+	26.1797i	−0.0136389	+	0.0641661i
$409$	591.520	−	192.197i	1.44626	−	0.469918i	0.522417	−	0.852690i	$-0.325030\pi$
$409$	591.520	−	192.197i	1.44626	−	0.469918i	0.923843	+	0.382772i	$0.125030\pi$
$410$	−507.030	+	1138.81i	−1.23666	+	2.77758i
$411$	−38.7824	+	87.1067i	−0.0943611	+	0.211938i
$412$	−33.3763	+	102.722i	−0.0810103	+	0.249324i
$413$	70.7983	+	159.016i	0.171424	+	0.385026i
$414$	−344.983	−	36.2592i	−0.833292	−	0.0875825i
$415$	−460.424	−	265.826i	−1.10945	−	0.640544i
$416$	647.178	−	582.721i	1.55572	−	1.40077i
$417$	−33.5261	−	3.52373i	−0.0803983	−	0.00845020i
$418$	129.596	−	143.931i	0.310037	−	0.344332i
$419$	−146.743	+	329.590i	−0.350222	+	0.786610i	0.649435	+	0.760417i	$0.275005\pi$
$419$	−146.743	+	329.590i	−0.350222	+	0.786610i	−0.999657	+	0.0261936i	$0.991661\pi$
$420$	100.131	−	173.431i	0.238406	−	0.412932i
$421$	−226.051	+	130.510i	−0.536937	+	0.310001i	−0.743837	−	0.668361i	$-0.766996\pi$
$421$	−226.051	+	130.510i	−0.536937	+	0.310001i	0.206899	+	0.978362i	$0.433663\pi$
$422$	−416.691	+	43.7960i	−0.987420	+	0.103782i
$423$	−247.042	−	109.990i	−0.584025	−	0.260024i
$424$	−353.963	+	115.010i	−0.834819	+	0.271249i
$425$	−96.9344	−	70.4270i	−0.228081	−	0.165711i
$426$	−215.475	+	156.552i	−0.505811	+	0.367493i
$427$	−108.035	+	332.497i	−0.253009	+	0.778681i
$428$	129.282	+	116.406i	0.302062	+	0.271978i
$429$	−141.282	+	434.822i	−0.329329	+	1.01357i
$430$	−634.076	+	1098.25i	−1.47459	+	2.55407i
$431$	373.233	+	336.061i	0.865970	+	0.779723i	0.976808	−	0.214115i	$-0.0686869\pi$
$431$	373.233	+	336.061i	0.865970	+	0.779723i	−0.110838	+	0.993838i	$0.535354\pi$
$432$	178.987	−	18.8122i	0.414321	−	0.0435469i
$433$	−133.805	+	184.167i	−0.309019	+	0.425328i	−0.935075	−	0.354450i	$-0.884668\pi$
$433$	−133.805	+	184.167i	−0.309019	+	0.425328i	0.626056	+	0.779778i	$0.284668\pi$
$434$			29.9393i			0.0689845i
$435$	34.8931	+	78.3713i	0.0802141	+	0.180164i
$436$	253.299	−	26.6227i	0.580960	−	0.0610613i
$437$	45.4466	+	26.2386i	0.103997	+	0.0600426i
$438$	−18.1611	−	172.791i	−0.0414637	−	0.394501i
$439$	−5.07072	+	48.2447i	−0.0115506	+	0.109897i	−0.998778	−	0.0494204i	$-0.984263\pi$
$439$	−5.07072	+	48.2447i	−0.0115506	+	0.109897i	0.987227	+	0.159317i	$0.0509292\pi$
$440$	−510.502	+	108.510i	−1.16023	+	0.246615i
$441$	−218.361	+	46.4141i	−0.495150	+	0.105247i
$442$	66.9755	−	315.095i	0.151528	−	0.712885i
$443$	−531.999	−	55.9153i	−1.20090	−	0.126220i	−0.517123	−	0.855911i	$-0.672997\pi$
$443$	−531.999	−	55.9153i	−1.20090	−	0.126220i	−0.683777	+	0.729691i	$0.739664\pi$
$444$	259.720	−	357.474i	0.584955	−	0.805122i
$445$			458.597i			1.03056i
$446$	643.527	−	286.517i	1.44288	−	0.642414i
$447$	168.785	+	187.454i	0.377594	+	0.419361i
$448$	−172.984	−	388.529i	−0.386125	−	0.867252i
$449$	498.080	−	287.567i	1.10931	−	0.640460i	0.170659	−	0.985330i	$-0.445410\pi$
$449$	498.080	−	287.567i	1.10931	−	0.640460i	0.938651	+	0.344870i	$0.112077\pi$
$450$	160.866	−	495.094i	0.357480	−	1.10021i
$451$	−937.703	−	541.383i	−2.07916	−	1.20041i
$452$			739.630i			1.63635i
$453$	−58.4303	+	177.956i	−0.128985	+	0.392839i
$454$	590.233			1.30007
$455$	−303.186	+	525.133i	−0.666343	+	1.15414i
$456$	16.7308	+	5.43616i	0.0366903	+	0.0119214i
$457$	−171.338	−	296.767i	−0.374920	−	0.649380i	0.615395	−	0.788219i	$-0.288996\pi$
$457$	−171.338	−	296.767i	−0.374920	−	0.649380i	−0.990315	+	0.138839i	$0.955663\pi$
$458$	1130.12	−	503.162i	2.46751	−	1.09861i
$459$	79.6606	−	71.7268i	0.173553	−	0.156267i
$460$	−228.629	−	513.509i	−0.497020	−	1.11632i
$461$	241.408			0.523661			0.261831	−	0.965114i	$-0.415674\pi$
$461$	241.408			0.523661			0.261831	+	0.965114i	$0.415674\pi$
$462$	246.046	+	178.763i	0.532567	+	0.386933i
$463$	95.5863	−	909.443i	0.206450	−	1.96424i	−0.0533440	−	0.998576i	$-0.516988\pi$
$463$	95.5863	−	909.443i	0.206450	−	1.96424i	0.259794	−	0.965664i	$-0.416345\pi$
$464$	86.2211	+	18.3269i	0.185821	+	0.0394976i
$465$	−3.99884	−	18.8131i	−0.00859967	−	0.0404582i
$466$	152.966	+	719.648i	0.328253	+	1.54431i
$467$	414.487	+	43.5643i	0.887552	+	0.0932855i	0.537321	−	0.843378i	$-0.319436\pi$
$467$	414.487	+	43.5643i	0.887552	+	0.0932855i	0.350231	+	0.936663i	$0.386103\pi$
$468$	796.096	−	83.6730i	1.70106	−	0.178789i
$469$	241.913	−	419.005i	0.515805	−	0.893401i
$470$	−80.0863	−	761.970i	−0.170396	−	1.62121i
$471$	31.6049	−	14.0714i	0.0671016	−	0.0298756i
$472$	163.783			0.346999
$473$	−891.135	−	647.447i	−1.88401	−	1.36881i
$474$	−15.9849	−	152.086i	−0.0337233	−	0.320856i
$475$	−52.6963	+	58.5252i	−0.110940	+	0.123211i
$476$	−106.139	−	61.2793i	−0.222981	−	0.128738i
$477$	642.569	+	208.783i	1.34710	+	0.437701i
$478$	−52.1375	+	57.9046i	−0.109074	+	0.121139i
$479$	−36.1019	−	11.7302i	−0.0753693	−	0.0244890i	0.271090	−	0.962554i	$-0.412616\pi$
$479$	−36.1019	−	11.7302i	−0.0753693	−	0.0244890i	−0.346459	+	0.938065i	$0.612616\pi$
$480$	218.744	+	301.076i	0.455717	+	0.627241i
$481$	−786.407	+	1082.40i	−1.63494	+	2.25031i
$482$	304.136	+	936.034i	0.630987	+	1.94198i
$483$	−33.5169	+	75.2802i	−0.0693932	+	0.155860i
$484$	−120.757	−	1148.93i	−0.249498	−	2.37381i
$485$	−313.697	−	543.340i	−0.646799	−	1.12029i
$486$	623.847	+	360.178i	1.28364	+	0.741107i
$487$	−243.298	−	108.323i	−0.499586	−	0.222430i	0.141443	−	0.989946i	$-0.454826\pi$
$487$	−243.298	−	108.323i	−0.499586	−	0.222430i	−0.641029	+	0.767516i	$0.721492\pi$
$488$	244.464	+	220.116i	0.500951	+	0.451058i
$489$	26.3200	−	250.418i	0.0538242	−	0.512103i
$490$	−423.218	−	470.031i	−0.863710	−	0.959247i
$491$	−263.844	+	456.991i	−0.537360	+	0.930736i	0.461685	+	0.887044i	$0.347245\pi$
$491$	−263.844	+	456.991i	−0.537360	+	0.930736i	−0.999045	+	0.0436914i	$0.986088\pi$
$492$	40.8633	−	388.789i	0.0830556	−	0.790221i
$493$	47.9627	−	21.3544i	0.0972874	−	0.0433152i
$494$	−201.369	−	65.4287i	−0.407629	−	0.132447i
$495$	865.535	+	385.361i	1.74855	+	0.778507i
$496$	−18.0538	−	8.03806i	−0.0363988	−	0.0162058i
$497$	−94.8136	−	291.806i	−0.190772	−	0.587136i
$498$	285.140	+	60.6084i	0.572570	+	0.121704i
$499$	471.767	−	272.375i	0.945425	−	0.545841i	0.0537682	−	0.998553i	$-0.482877\pi$
$499$	471.767	−	272.375i	0.945425	−	0.545841i	0.891657	+	0.452712i	$0.149543\pi$
$500$	−78.6819	+	16.7243i	−0.157364	+	0.0334487i
$501$	−185.437	+	166.968i	−0.370133	+	0.333270i
$502$	14.6938	−	16.3191i	0.0292704	−	0.0325081i
$503$	−304.152	−	936.084i	−0.604676	−	1.86100i	−0.499001	−	0.866601i	$-0.666300\pi$
$503$	−304.152	−	936.084i	−0.604676	−	1.86100i	−0.105675	−	0.994401i	$-0.533700\pi$
$504$	27.8516	−	131.031i	0.0552610	−	0.259983i
$505$	63.5727	−	57.2411i	0.125886	−	0.113349i
$506$	811.870	−	263.793i	1.60449	−	0.521329i
$507$	288.597	−	30.3328i	0.569226	−	0.0598280i
$508$	880.431	−	187.141i	1.73313	−	0.368388i
$509$	40.5773	+	91.1380i	0.0797196	+	0.179053i	0.949008	−	0.315252i	$-0.102089\pi$
$509$	40.5773	+	91.1380i	0.0797196	+	0.179053i	−0.869288	+	0.494305i	$0.835422\pi$
$510$	130.922	+	42.5390i	0.256709	+	0.0834098i
$511$	195.777	+	41.6136i	0.383125	+	0.0814356i
$512$	527.291			1.02987
$513$	−41.4131	−	57.0003i	−0.0807274	−	0.111112i
$514$	−621.064	−	559.209i	−1.20830	−	1.08796i
$515$	127.672	+	56.8432i	0.247907	+	0.110375i
$516$	82.6855	−	389.005i	0.160243	−	0.753885i
$517$	665.485			1.28721
$518$	523.120	+	720.013i	1.00988	+	1.38999i
$519$	69.7191	−	40.2523i	0.134333	−	0.0775575i
$520$	335.365	+	461.591i	0.644933	+	0.887674i
$521$	320.215	−	232.650i	0.614617	−	0.446545i	−0.236420	−	0.971651i	$-0.575974\pi$
$521$	320.215	−	232.650i	0.614617	−	0.446545i	0.851037	+	0.525106i	$0.175974\pi$
$522$	152.632	+	169.515i	0.292398	+	0.324741i
$523$	378.008	−	122.822i	0.722769	−	0.234842i	0.0755458	−	0.997142i	$-0.475930\pi$
$523$	378.008	−	122.822i	0.722769	−	0.234842i	0.647223	+	0.762300i	$0.275930\pi$
$524$	−234.176	−	24.6129i	−0.446901	−	0.0469712i
$525$	−100.048	−	72.6888i	−0.190567	−	0.138455i
$526$	−176.089	+	242.366i	−0.334770	+	0.460771i
$527$	−11.5135	+	2.44727i	−0.0218472	+	0.00464377i
$528$	−173.855	+	100.375i	−0.329270	+	0.190104i
$529$	−148.851	−	257.818i	−0.281382	−	0.487368i
$530$	397.992	+	1872.41i	0.750929	+	3.53284i
$531$	−240.541	−	174.763i	−0.452996	−	0.329121i
$532$	−47.3491	+	65.1704i	−0.0890020	+	0.122501i
$533$	−123.730	+	1177.22i	−0.232139	+	2.20866i
$534$	−77.7034	−	239.147i	−0.145512	−	0.447840i
$535$	167.282	−	150.622i	0.312677	−	0.281536i
$536$	−267.589	−	368.304i	−0.499233	−	0.687135i
$537$	50.0533	−	36.3658i	0.0932091	−	0.0677204i
$538$	−456.577	−	790.814i	−0.848656	−	1.46992i
$539$	444.453	−	322.914i	0.824587	−	0.599098i
$540$			754.686i			1.39757i
$541$	−791.474	−	168.233i	−1.46298	−	0.310967i	−0.593462	−	0.804862i	$-0.702239\pi$
$541$	−791.474	−	168.233i	−1.46298	−	0.310967i	−0.869521	+	0.493896i	$0.835573\pi$
$542$	538.955	−	1210.51i	0.994383	−	2.23342i
$543$	101.129	−	112.316i	0.186242	−	0.206843i
$544$	184.256	−	133.870i	0.338706	−	0.246085i
$545$		−	329.555i		−	0.604689i
$546$	69.1265	−	325.215i	0.126605	−	0.595631i
$547$	243.829	−	750.428i	0.445757	−	1.37190i	−0.435895	−	0.899998i	$-0.643568\pi$
$547$	243.829	−	750.428i	0.445757	−	1.37190i	0.881652	−	0.471901i	$-0.156432\pi$
$548$	−375.314	+	167.100i	−0.684879	+	0.304928i
$549$	−124.160	−	584.127i	−0.226157	−	1.06398i
$550$	133.910	+	1274.07i	0.243473	+	2.31649i
$551$	−10.6636	−	32.8193i	−0.0193532	−	0.0595631i
$552$	51.8826	+	57.6215i	0.0939902	+	0.104387i
$553$	172.317	+	36.6270i	0.311603	+	0.0662334i
$554$	−570.410	+	185.337i	−1.02962	+	0.334544i
$555$	−424.884	−	382.567i	−0.765556	−	0.689310i
$556$	−97.1902	−	107.941i	−0.174802	−	0.194138i
$557$	160.371	+	754.487i	0.287919	+	1.35455i	0.849699	+	0.527268i	$0.176784\pi$
$557$	160.371	+	754.487i	0.287919	+	1.35455i	−0.561780	+	0.827287i	$0.689883\pi$
$558$	−25.5702	−	44.2888i	−0.0458246	−	0.0793706i
$559$	−250.364	+	1177.87i	−0.447878	+	2.10710i
$560$	−253.219	+	82.2757i	−0.452176	+	0.146921i
$561$	−48.6332	+	109.232i	−0.0866902	+	0.194709i
$562$	−320.812	+	720.556i	−0.570840	+	1.28213i
$563$	12.8337	−	39.4979i	0.0227951	−	0.0701562i	−0.939012	−	0.343885i	$-0.888257\pi$
$563$	12.8337	−	39.4979i	0.0227951	−	0.0701562i	0.961807	+	0.273729i	$0.0882570\pi$
$564$	97.7274	+	219.499i	0.173275	+	0.389183i
$565$	951.785	+	100.037i	1.68458	+	0.177056i
$566$	−129.863	−	74.9766i	−0.229441	−	0.132468i
$567$	−135.768	+	122.246i	−0.239449	+	0.215601i
$568$	−287.120	−	30.1775i	−0.505493	−	0.0531294i
$569$	1.70687	−	1.89567i	0.00299977	−	0.00333158i	−0.741643	−	0.670795i	$-0.765953\pi$
$569$	1.70687	−	1.89567i	0.00299977	−	0.00333158i	0.744643	+	0.667463i	$0.232620\pi$
$570$	36.8017	−	82.6579i	0.0645643	−	0.145014i
$571$	549.505	−	951.771i	0.962356	−	1.66685i	0.245800	−	0.969321i	$-0.420950\pi$
$571$	549.505	−	951.771i	0.962356	−	1.66685i	0.716557	−	0.697529i	$-0.245717\pi$
$572$	−1706.00	+	984.959i	−2.98252	+	1.72196i
$573$	333.618	−	35.0647i	0.582231	−	0.0611950i
$574$	719.325	+	320.264i	1.25318	+	0.557952i
$575$	−330.123	+	107.264i	−0.574128	+	0.186545i
$576$	587.723	+	427.006i	1.02035	+	0.741329i
$577$	532.315	−	386.749i	0.922556	−	0.670276i	−0.0216029	−	0.999767i	$-0.506877\pi$
$577$	532.315	−	386.749i	0.922556	−	0.670276i	0.944159	+	0.329490i	$0.106877\pi$
$578$	−246.964	+	760.078i	−0.427274	+	1.31501i
$579$	−273.814	−	246.544i	−0.472909	−	0.425809i
$580$	−114.223	+	351.541i	−0.196935	+	0.606105i
$581$	−167.908	+	290.826i	−0.288999	+	0.500561i
$582$	255.647	+	230.186i	0.439256	+	0.395508i
$583$	−1653.58	+	173.798i	−2.83633	+	0.298110i
$584$	110.697	−	152.361i	0.189549	−	0.260892i
$585$		−	1035.76i		−	1.77054i
$586$	−639.051	−	1435.33i	−1.09053	−	2.44937i
$587$	363.458	−	38.2009i	0.619178	−	0.0650782i	0.210254	−	0.977647i	$-0.432571\pi$
$587$	363.458	−	38.2009i	0.619178	−	0.0650782i	0.408924	+	0.912569i	$0.365904\pi$
$588$	171.776	+	99.1750i	0.292136	+	0.168665i
$589$	0.808697	+	7.69424i	0.00137300	+	0.0130632i
$590$	88.0538	−	837.776i	0.149244	−	1.41996i
$591$	275.988	−	58.6631i	0.466985	−	0.0992608i
$592$	−574.624	+	122.140i	−0.970648	+	0.206318i
$593$	24.0341	−	113.071i	0.0405296	−	0.190677i	−0.953225	−	0.302260i	$-0.902259\pi$
$593$	24.0341	−	113.071i	0.0405296	−	0.190677i	0.993755	+	0.111583i	$0.0355922\pi$
$594$	−1139.84	−	119.802i	−1.91892	−	0.201686i
$595$	−93.2121	+	128.295i	−0.156659	+	0.215623i
$596$			1086.84i			1.82355i
$597$	−308.828	+	137.499i	−0.517299	+	0.230316i
$598$	−624.450	−	693.522i	−1.04423	−	1.15974i
$599$	−76.6880	−	172.244i	−0.128027	−	0.287553i	0.838147	−	0.545444i	$-0.183639\pi$
$599$	−76.6880	−	172.244i	−0.128027	−	0.287553i	−0.966174	+	0.257891i	$0.916972\pi$
$600$	−100.772	+	58.1807i	−0.167953	+	0.0969679i
$601$	−291.787	+	898.027i	−0.485502	+	1.49422i	0.345751	+	0.938326i	$0.387624\pi$
$601$	−291.787	+	898.027i	−0.485502	+	1.49422i	−0.831253	+	0.555895i	$0.812376\pi$
$602$	693.708	+	400.513i	1.15234	+	0.665303i
$603$			826.439i			1.37055i
$604$	−700.150	+	401.351i	−1.15919	+	0.664489i
$605$	−1494.81			−2.47077
$606$	−23.4527	+	40.6213i	−0.0387009	+	0.0670319i
$607$	117.983	+	38.3350i	0.194371	+	0.0631548i	0.404585	−	0.914501i	$-0.367416\pi$
$607$	117.983	+	38.3350i	0.194371	+	0.0631548i	−0.210214	+	0.977655i	$0.567416\pi$
$608$	−74.8486	−	129.642i	−0.123106	−	0.213226i
$609$	49.5031	−	22.0402i	0.0812858	−	0.0361908i
$610$	1257.36	−	1132.13i	2.06124	−	1.85595i
$611$	−295.909	−	664.623i	−0.484303	−	1.08776i
$612$	209.346			0.342069
$613$	361.449	+	262.608i	0.589640	+	0.428399i	0.842187	−	0.539186i	$-0.181268\pi$
$613$	361.449	+	262.608i	0.589640	+	0.428399i	−0.252547	+	0.967585i	$0.581268\pi$
$614$	154.238	−	1467.47i	0.251201	−	2.39002i
$615$	−494.782	−	105.169i	−0.804523	−	0.171007i
$616$	68.5404	+	322.457i	0.111267	+	0.523470i
$617$	105.792	+	497.712i	0.171462	+	0.806664i	0.976852	+	0.213919i	$0.0686227\pi$
$617$	105.792	+	497.712i	0.171462	+	0.806664i	−0.805390	+	0.592746i	$0.798044\pi$
$618$	−76.2089	−	8.00988i	−0.123315	−	0.0129610i
$619$	990.575	−	104.114i	1.60028	−	0.168197i	0.738064	−	0.674731i	$-0.235740\pi$
$619$	990.575	−	104.114i	1.60028	−	0.168197i	0.862220	+	0.506535i	$0.169074\pi$
$620$	41.4351	−	71.7677i	0.0668308	−	0.115754i
$621$	−32.4605	−	308.841i	−0.0522713	−	0.497328i
$622$	525.738	−	234.074i	0.845238	−	0.376324i
$623$	289.672			0.464963
$624$	177.550	+	128.997i	0.284535	+	0.206727i
$625$	70.5226	+	670.977i	0.112836	+	1.07356i
$626$	−356.643	+	396.092i	−0.569717	+	0.632734i
$627$	68.0612	+	39.2951i	0.108551	+	0.0626717i
$628$	141.766	+	46.0626i	0.225742	+	0.0733482i
$629$	−234.128	+	260.026i	−0.372223	+	0.413396i
$630$	−655.271	−	212.910i	−1.04011	−	0.337953i
$631$	494.123	+	680.102i	0.783079	+	1.07782i	0.994936	+	0.100515i	$0.0320490\pi$
$631$	494.123	+	680.102i	0.783079	+	1.07782i	−0.211857	+	0.977301i	$0.567951\pi$
$632$	97.4321	−	134.104i	0.154165	−	0.212189i
$633$	−52.5378	−	161.695i	−0.0829981	−	0.255442i
$634$	216.706	−	486.730i	0.341808	−	0.767713i
$635$	−121.741	−	1158.28i	−0.191717	−	1.82407i
$636$	−300.155	−	519.883i	−0.471941	−	0.817426i
$637$	−520.122	−	300.292i	−0.816518	−	0.471417i
$638$	−512.816	−	228.320i	−0.803787	−	0.357869i
$639$	389.479	+	350.688i	0.609513	+	0.548808i
$640$	−89.7029	+	853.467i	−0.140161	+	1.33354i
$641$	−238.637	−	265.033i	−0.372288	−	0.413468i	0.527666	−	0.849452i	$-0.323067\pi$
$641$	−238.637	−	265.033i	−0.372288	−	0.413468i	−0.899954	+	0.435984i	$0.856400\pi$
$642$	−61.7124	+	106.889i	−0.0961253	+	0.166494i
$643$	38.7310	−	368.501i	0.0602348	−	0.573096i	−0.922229	−	0.386644i	$-0.873634\pi$
$643$	38.7310	−	368.501i	0.0602348	−	0.573096i	0.982464	−	0.186452i	$-0.0596990\pi$
$644$	−324.357	+	144.413i	−0.503660	+	0.224244i
$645$	−489.403	−	159.017i	−0.758764	−	0.246537i
$646$	−50.5861	−	22.5224i	−0.0783066	−	0.0348643i
$647$	−167.499	−	74.5752i	−0.258885	−	0.115263i	0.273190	−	0.961960i	$-0.411921\pi$
$647$	−167.499	−	74.5752i	−0.258885	−	0.115263i	−0.532075	+	0.846697i	$0.678588\pi$
$648$	53.1210	+	163.490i	0.0819768	+	0.252299i
$649$	715.703	+	152.127i	1.10278	+	0.234403i
$650$	1212.87	−	700.253i	1.86596	−	1.07731i
$651$	−11.8832	+	2.52586i	−0.0182538	+	0.00387997i
$652$	806.247	−	725.948i	1.23658	−	1.11342i
$653$	666.789	−	740.544i	1.02112	−	1.13406i	0.0302055	−	0.999544i	$-0.490384\pi$
$653$	666.789	−	740.544i	1.02112	−	1.13406i	0.990911	−	0.134521i	$-0.0429495\pi$
$654$	55.8389	+	171.855i	0.0853806	+	0.262775i
$655$	−63.3457	+	298.018i	−0.0967110	+	0.454989i
$656$	−386.247	+	347.778i	−0.588791	+	0.530150i
$657$	−325.151	+	105.648i	−0.494902	+	0.160803i
$658$	−481.297	+	50.5863i	−0.731454	+	0.0768789i
$659$	−428.885	+	91.1624i	−0.650813	+	0.138334i	−0.521476	−	0.853266i	$-0.674618\pi$
$659$	−428.885	+	91.1624i	−0.650813	+	0.138334i	−0.129337	+	0.991601i	$0.541285\pi$
$660$	−342.396	−	769.035i	−0.518782	−	1.16520i
$661$	−462.817	−	150.378i	−0.700177	−	0.227501i	−0.0627693	−	0.998028i	$-0.519993\pi$
$661$	−462.817	−	150.378i	−0.700177	−	0.227501i	−0.637408	+	0.770527i	$0.719993\pi$
$662$	−816.632	−	173.581i	−1.23358	−	0.262206i
$663$	130.715			0.197157
$664$	185.730	+	255.635i	0.279713	+	0.384992i
$665$	77.4597	+	69.7451i	0.116481	+	0.104880i
$666$	−1388.78	−	618.326i	−2.08526	−	0.928418i
$667$	31.6229	−	148.774i	0.0474107	−	0.223050i
$668$	−1075.14			−1.60949
$669$	168.014	+	231.251i	0.251141	+	0.345666i
$670$	−2027.79	+	1170.75i	−3.02656	+	1.74738i
$671$	863.811	+	1188.93i	1.28735	+	1.77188i
$672$	190.174	−	138.169i	0.282997	−	0.205609i
$673$	−448.651	−	498.277i	−0.666643	−	0.740382i	0.311057	−	0.950391i	$-0.399317\pi$
$673$	−448.651	−	498.277i	−0.666643	−	0.740382i	−0.977699	+	0.210010i	$0.932650\pi$
$674$	−264.558	+	85.9601i	−0.392519	+	0.127537i
$675$	463.482	+	48.7139i	0.686640	+	0.0721687i
$676$	1011.53	+	734.919i	1.49635	+	1.08716i
$677$	752.527	−	1035.76i	1.11156	−	1.52993i	0.292466	−	0.956276i	$-0.405524\pi$
$677$	752.527	−	1035.76i	1.11156	−	1.52993i	0.819096	−	0.573657i	$-0.194476\pi$
$678$	−513.281	+	109.101i	−0.757052	+	0.160916i
$679$	−343.199	+	198.146i	−0.505448	+	0.291821i
$680$	74.6077	+	129.224i	0.109717	+	0.190036i
$681$	49.7956	+	234.270i	0.0731214	+	0.344009i
$682$	101.816	+	73.9740i	0.149291	+	0.108466i
$683$	432.671	−	595.521i	0.633487	−	0.871919i	−0.364761	−	0.931101i	$-0.618849\pi$
$683$	432.671	−	595.521i	0.633487	−	0.871919i	0.998247	+	0.0591819i	$0.0188492\pi$
$684$	14.3830	−	136.845i	0.0210278	−	0.200066i
$685$	164.269	+	505.569i	0.239809	+	0.738057i
$686$	−783.128	+	705.131i	−1.14159	+	1.02789i
$687$	295.055	+	406.108i	0.429483	+	0.591132i
$688$	−427.760	+	310.786i	−0.621744	+	0.451724i
$689$	908.839	+	1574.16i	1.31907	+	2.28470i
$690$	322.636	−	234.408i	0.467588	−	0.339722i
$691$			1113.14i			1.61091i	0.592659	+	0.805454i	$0.298078\pi$
$691$			1113.14i			1.61091i	−0.592659	+	0.805454i	$0.701922\pi$
$692$	339.288	+	72.1178i	0.490300	+	0.104217i
$693$	243.412	−	546.713i	0.351244	−	0.788908i
$694$	1185.82	−	1316.99i	1.70868	−	1.89768i
$695$	−152.047	+	110.469i	−0.218773	+	0.158948i
$696$		−	50.9873i		−	0.0732576i
$697$	−64.3628	+	302.803i	−0.0923426	+	0.434438i
$698$	−320.161	+	985.355i	−0.458684	+	1.41168i
$699$	−272.731	+	121.428i	−0.390173	+	0.173716i
$700$	−110.782	−	521.190i	−0.158261	−	0.744557i
$701$	34.1576	+	324.988i	0.0487269	+	0.463606i	0.991494	+	0.130153i	$0.0415470\pi$
$701$	34.1576	+	324.988i	0.0487269	+	0.463606i	−0.942767	+	0.333452i	$0.891786\pi$
$702$	387.184	+	1191.63i	0.551544	+	1.69748i
$703$	153.887	+	170.909i	0.218901	+	0.243114i
$704$	−1748.70	−	371.699i	−2.48396	−	0.527981i
$705$	295.678	−	96.0716i	0.419402	−	0.136272i
$706$	840.082	+	756.413i	1.18992	+	1.07141i
$707$	−36.1562	−	40.1555i	−0.0511403	−	0.0567971i
$708$	54.9252	+	258.403i	0.0775780	+	0.364976i
$709$	236.424	+	409.499i	0.333462	+	0.577573i	0.983188	−	0.182595i	$-0.0584498\pi$
$709$	236.424	+	409.499i	0.333462	+	0.577573i	−0.649726	+	0.760168i	$0.725116\pi$
$710$	−308.725	+	1452.44i	−0.434824	+	2.04568i
$711$	−286.188	+	92.9881i	−0.402515	+	0.130785i
$712$	110.861	−	248.999i	0.155704	−	0.349717i
$713$	−13.8696	+	31.1517i	−0.0194525	+	0.0436911i
$714$	26.8697	−	82.6964i	0.0376326	−	0.115821i
$715$	1036.74	+	2328.56i	1.44999	+	3.25673i
$716$	265.114	+	27.8646i	0.370271	+	0.0389170i
$717$	−27.3816	−	15.8088i	−0.0381892	−	0.0220485i
$718$	234.259	−	210.928i	0.326266	−	0.293771i
$719$	672.735	+	70.7073i	0.935654	+	0.0983412i	0.560068	−	0.828446i	$-0.310775\pi$
$719$	672.735	+	70.7073i	0.935654	+	0.0983412i	0.375586	+	0.926788i	$0.377442\pi$
$720$	304.314	−	337.975i	0.422659	−	0.469410i
$721$	35.9049	−	80.6437i	0.0497987	−	0.111850i
$722$	533.570	−	924.170i	0.739017	−	1.28001i
$723$	−345.864	+	199.685i	−0.478373	+	0.276189i
$724$	647.626	−	68.0682i	0.894510	−	0.0940168i
$725$	208.522	+	92.8399i	0.287616	+	0.128055i
$726$	779.507	−	253.277i	1.07370	−	0.348867i
$727$	1012.40	+	735.555i	1.39258	+	1.01177i	0.995577	+	0.0939488i	$0.0299490\pi$
$727$	1012.40	+	735.555i	1.39258	+	1.01177i	0.397001	+	0.917818i	$0.370051\pi$
$728$	291.563	−	211.833i	0.400498	−	0.290979i
$729$	25.9921	−	79.9955i	0.0356545	−	0.109733i
$730$	−719.837	−	648.144i	−0.986078	−	0.887869i
$731$	−97.3171	+	299.511i	−0.133129	+	0.409728i
$732$	−265.298	+	459.510i	−0.362429	+	0.627746i
$733$	−609.485	−	548.783i	−0.831494	−	0.748681i	0.138874	−	0.990310i	$-0.455652\pi$
$733$	−609.485	−	548.783i	−0.831494	−	0.748681i	−0.970369	+	0.241629i	$0.922318\pi$
$734$	−732.000	+	76.9363i	−0.997276	+	0.104818i
$735$	150.855	−	207.635i	0.205245	−	0.282496i
$736$		−	659.803i		−	0.896471i
$737$	−827.220	−	1857.97i	−1.12242	−	2.52099i
$738$	−1337.62	+	140.589i	−1.81249	+	0.190500i
$739$	66.3809	+	38.3250i	0.0898253	+	0.0518607i	0.544240	−	0.838930i	$-0.316818\pi$
$739$	66.3809	+	38.3250i	0.0898253	+	0.0518607i	−0.454415	+	0.890790i	$0.650151\pi$
$740$	−257.498	−	2449.93i	−0.347970	−	3.31072i
$741$	8.98069	−	85.4456i	0.0121197	−	0.115311i
$742$	1182.70	−	251.391i	1.59394	−	0.338802i
$743$	741.767	−	157.667i	0.998340	−	0.212204i	0.320369	−	0.947293i	$-0.396193\pi$
$743$	741.767	−	157.667i	0.998340	−	0.212204i	0.677971	+	0.735089i	$0.262860\pi$
$744$	−2.37668	+	11.1814i	−0.00319446	+	0.0150287i
$745$	1398.59	+	146.997i	1.87730	+	0.197312i
$746$	−120.657	+	166.070i	−0.161738	+	0.222613i
$747$		−	573.620i		−	0.767898i
$748$	−470.644	+	209.544i	−0.629203	+	0.280139i
$749$	−95.1398	−	105.663i	−0.127022	−	0.141073i
$750$	−23.2124	−	52.1359i	−0.0309499	−	0.0695145i
$751$	−759.256	+	438.356i	−1.01099	+	0.583697i	−0.911482	−	0.411340i	$-0.865061\pi$
$751$	−759.256	+	438.356i	−1.01099	+	0.583697i	−0.0995106	+	0.995037i	$0.531728\pi$
$752$	98.7138	−	303.810i	0.131268	−	0.404002i
$753$	7.71688	+	4.45534i	0.0102482	+	0.00591679i
$754$			613.675i			0.813892i
$755$	421.778	+	955.264i	0.558646	+	1.26525i
$756$	476.696			0.630550
$757$	−143.068	+	247.801i	−0.188993	+	0.327346i	−0.944915	−	0.327316i	$-0.893856\pi$
$757$	−143.068	+	247.801i	−0.188993	+	0.327346i	0.755921	+	0.654662i	$0.227189\pi$
$758$	−380.002	−	123.470i	−0.501322	−	0.162889i
$759$	173.197	+	299.985i	0.228191	+	0.395238i
$760$	89.5969	−	39.8911i	0.117891	−	0.0524883i
$761$	−72.1833	+	64.9942i	−0.0948533	+	0.0854063i	−0.715193	−	0.698927i	$-0.753661\pi$
$761$	−72.1833	+	64.9942i	−0.0948533	+	0.0854063i	0.620340	+	0.784333i	$0.286995\pi$
$762$	259.741	+	583.388i	0.340867	+	0.765601i
$763$	−208.163			−0.272822
$764$	1169.33	+	849.566i	1.53053	+	1.11200i
$765$	28.3146	−	269.395i	0.0370125	−	0.352151i
$766$	−1319.77	−	280.526i	−1.72294	−	0.366221i
$767$	−166.308	−	782.419i	−0.216830	−	1.02010i
$768$	2.60819	+	12.2706i	0.00339608	+	0.0159773i
$769$	27.4180	+	2.88175i	0.0356541	+	0.00374740i	0.122339	−	0.992488i	$-0.460961\pi$
$769$	27.4180	+	2.88175i	0.0356541	+	0.00374740i	−0.0866846	+	0.996236i	$0.527627\pi$
$770$	1686.27	−	177.234i	2.18996	−	0.230174i
$771$	169.560	−	293.686i	0.219922	−	0.380915i
$772$	−165.944	−	1578.85i	−0.214953	−	2.04514i
$773$	677.348	−	301.575i	0.876259	−	0.390136i	0.0812217	−	0.996696i	$-0.474118\pi$
$773$	677.348	−	301.575i	0.876259	−	0.390136i	0.795037	+	0.606560i	$0.207451\pi$
$774$	−1368.26			−1.76778
$775$	−41.4007	−	30.0794i	−0.0534203	−	0.0388121i
$776$	38.9772	+	370.843i	0.0502284	+	0.477891i
$777$	−241.648	+	268.377i	−0.311001	+	0.345401i
$778$	314.178	+	181.391i	0.403828	+	0.233150i
$779$	193.514	+	62.8764i	0.248413	+	0.0807142i
$780$	−615.791	+	683.905i	−0.789476	+	0.876802i
$781$	−1226.63	−	398.556i	−1.57059	−	0.510315i
$782$	−143.456	−	197.451i	−0.183448	−	0.252495i
$783$	−120.030	+	165.207i	−0.153295	+	0.210993i
$784$	−81.4905	−	250.802i	−0.103942	−	0.319900i
$785$	78.4494	−	176.200i	0.0999356	−	0.224459i
$786$	−17.4622	−	166.142i	−0.0222166	−	0.211376i
$787$	290.000	+	502.294i	0.368488	+	0.638239i	0.989329	−	0.145697i	$-0.0465424\pi$
$787$	290.000	+	502.294i	0.368488	+	0.638239i	−0.620842	+	0.783936i	$0.713209\pi$
$788$	1052.83	+	607.854i	1.33608	+	0.771388i
$789$	−111.054	−	49.4443i	−0.140752	−	0.0626670i
$790$	−633.579	−	570.477i	−0.801998	−	0.722123i
$791$	63.1879	−	601.193i	0.0798836	−	0.760042i
$792$	−376.791	−	418.469i	−0.475746	−	0.528370i
$793$	803.298	−	1391.35i	1.01299	−	1.75454i
$794$	−76.4862	+	727.717i	−0.0963302	+	0.916521i
$795$	−709.602	+	315.935i	−0.892582	+	0.397403i
$796$	−1385.27	−	450.102i	−1.74029	−	0.565455i
$797$	853.504	+	380.005i	1.07090	+	0.476794i	0.864996	−	0.501779i	$-0.167321\pi$
$797$	853.504	+	380.005i	1.07090	+	0.476794i	0.205901	+	0.978573i	$0.433988\pi$
$798$	−52.2107	−	23.2457i	−0.0654269	−	0.0291299i
$799$	−58.7952	−	180.953i	−0.0735860	−	0.226474i
$800$	968.539	+	205.869i	1.21067	+	0.257337i
$801$	−428.508	+	247.399i	−0.534966	+	0.308863i
$802$	569.690	−	121.091i	0.710337	−	0.150987i
$803$	625.243	−	562.971i	0.778634	−	0.701085i
$804$	491.341	−	545.690i	0.611121	−	0.678718i
$805$	141.966	+	436.928i	0.176356	+	0.542767i
$806$	28.6053	−	134.577i	0.0354904	−	0.166969i
$807$	275.364	−	247.939i	0.341219	−	0.307235i
$808$	−48.3547	+	15.7114i	−0.0598449	+	0.0194448i
$809$	−1123.43	+	118.077i	−1.38867	+	0.145955i	−0.769170	−	0.639044i	$-0.779330\pi$
$809$	−1123.43	+	118.077i	−1.38867	+	0.145955i	−0.619497	+	0.784999i	$0.712663\pi$
$810$	864.832	−	183.826i	1.06769	−	0.226945i
$811$	−132.441	−	297.468i	−0.163306	−	0.366791i	0.813295	−	0.581852i	$-0.197672\pi$
$811$	−132.441	−	297.468i	−0.163306	−	0.366791i	−0.976601	+	0.215061i	$0.931005\pi$
$812$	222.050	+	72.1485i	0.273461	+	0.0888528i
$813$	525.936	+	111.791i	0.646908	+	0.137505i
$814$	3741.12			4.59597
$815$	−825.132	−	1135.70i	−1.01243	−	1.39349i
$816$	42.6531	+	38.4050i	0.0522709	+	0.0470649i
$817$	189.098	+	84.1917i	0.231454	+	0.103050i
$818$	−395.295	+	1859.72i	−0.483246	+	2.27349i
$819$	−654.238			−0.798826
$820$	−1281.06	−	1763.23i	−1.56227	−	2.15028i
$821$	98.0017	−	56.5813i	0.119369	−	0.0689175i	−0.439127	−	0.898425i	$-0.644712\pi$
$821$	98.0017	−	56.5813i	0.119369	−	0.0689175i	0.558496	+	0.829508i	$0.311379\pi$
$822$	−171.324	−	235.808i	−0.208424	−	0.286871i
$823$	−1151.70	+	836.760i	−1.39939	+	1.01672i	−0.404634	+	0.914479i	$0.632601\pi$
$823$	−1151.70	+	836.760i	−1.39939	+	1.01672i	−0.994760	+	0.102241i	$0.967399\pi$
$824$	−55.5791	−	61.7268i	−0.0674503	−	0.0749112i
$825$	−494.395	+	160.639i	−0.599267	+	0.194714i
$826$	−529.179	−	55.6190i	−0.640653	−	0.0673354i
$827$	−551.033	−	400.349i	−0.666303	−	0.484097i	0.202483	−	0.979286i	$-0.435099\pi$
$827$	−551.033	−	400.349i	−0.666303	−	0.484097i	−0.868786	+	0.495188i	$0.835099\pi$
$828$	356.479	−	490.651i	0.430530	−	0.592574i
$829$	−450.132	+	95.6785i	−0.542982	+	0.115414i	−0.471234	−	0.882008i	$-0.656191\pi$
$829$	−450.132	+	95.6785i	−0.542982	+	0.115414i	−0.0717482	+	0.997423i	$0.522858\pi$
$830$	1407.46	−	812.599i	1.69574	−	0.979035i
$831$	−121.686	−	210.766i	−0.146433	−	0.253629i
$832$	406.347	+	1911.71i	0.488398	+	2.29773i
$833$	−127.071	−	92.3225i	−0.152546	−	0.110831i
$834$	60.5713	−	83.3692i	0.0726274	−	0.0999630i
$835$	−145.415	+	1383.53i	−0.174150	+	1.65693i
$836$	104.639	+	322.046i	0.125166	+	0.385222i
$837$	34.0231	−	30.6345i	0.0406488	−	0.0366004i
$838$	−648.248	−	892.237i	−0.773566	−	1.06472i
$839$	−683.099	+	496.300i	−0.814182	+	0.591538i	−0.915040	−	0.403363i	$-0.867841\pi$
$839$	−683.099	+	496.300i	−0.814182	+	0.591538i	0.100858	+	0.994901i	$0.467841\pi$
$840$	77.0038	+	133.375i	0.0916712	+	0.158779i
$841$	599.468	−	435.539i	0.712803	−	0.517882i
$842$		−	797.911i		−	0.947637i
$843$	−313.063	−	66.5435i	−0.371367	−	0.0789366i
$844$	297.951	−	669.210i	0.353023	−	0.792903i
$845$	1082.53	−	1202.28i	1.28111	−	1.42281i
$846$	668.772	−	485.891i	0.790511	−	0.574340i
$847$			944.197i			1.11475i
$848$	−165.938	+	780.678i	−0.195682	+	0.920610i
$849$	18.8030	−	57.8697i	0.0221473	−	0.0681622i
$850$	334.603	−	148.975i	0.393651	−	0.175265i
$851$	210.752	+	991.511i	0.247652	+	1.16511i
$852$	−48.6751	−	463.112i	−0.0571303	−	0.543559i
$853$	−328.316	−	1010.45i	−0.384895	−	1.18459i	−0.936556	−	0.350518i	$-0.886006\pi$
$853$	−328.316	−	1010.45i	−0.384895	−	1.18459i	0.551661	−	0.834069i	$-0.313994\pi$
$854$	−715.107	−	794.207i	−0.837362	−	0.929985i
$855$	−174.152	−	37.0172i	−0.203687	−	0.0432950i
$856$	−127.238	+	41.3422i	−0.148643	+	0.0482970i
$857$	−125.108	−	112.648i	−0.145984	−	0.131444i	0.592903	−	0.805274i	$-0.297982\pi$
$857$	−125.108	−	112.648i	−0.145984	−	0.131444i	−0.738887	+	0.673829i	$0.764648\pi$
$858$	−935.180	−	1038.62i	−1.08995	−	1.21052i
$859$	248.248	+	1167.92i	0.288997	+	1.35962i	0.847797	+	0.530321i	$0.177929\pi$
$859$	248.248	+	1167.92i	0.288997	+	1.35962i	−0.558800	+	0.829303i	$0.688738\pi$
$860$	−1108.60	−	1920.14i	−1.28906	−	2.23273i
$861$	−66.4299	+	312.528i	−0.0771543	+	0.362982i
$862$	−1460.13	+	474.426i	−1.69389	+	0.550378i
$863$	561.455	−	1261.05i	0.650585	−	1.46124i	−0.223125	−	0.974790i	$-0.571626\pi$
$863$	561.455	−	1261.05i	0.650585	−	1.46124i	0.873710	−	0.486448i	$-0.161708\pi$
$864$	−360.310	+	809.269i	−0.417025	+	0.936654i
$865$	138.694	−	426.855i	0.160339	−	0.493474i
$866$	−283.040	−	635.717i	−0.326836	−	0.734085i
$867$	−322.519	−	33.8981i	−0.371994	−	0.0390982i
$868$	−45.3319	−	26.1724i	−0.0522257	−	0.0301525i
$869$	550.320	−	495.510i	0.633280	−	0.570208i
$870$	−260.808	−	27.4120i	−0.299779	−	0.0315080i
$871$	−1487.73	+	1652.30i	−1.70808	+	1.89701i
$872$	−79.6667	+	178.934i	−0.0913609	+	0.205200i
$873$	338.460	−	586.230i	0.387698	−	0.671512i
$874$	−138.925	+	80.2085i	−0.158953	+	0.0917717i
$875$	65.3837	−	6.87211i	0.0747243	−	0.00785384i
$876$	277.505	+	123.553i	0.316786	+	0.141042i
$877$	−828.726	+	269.270i	−0.944956	+	0.307035i	−0.740664	−	0.671875i	$-0.765489\pi$
$877$	−828.726	+	269.270i	−0.944956	+	0.307035i	−0.204292	+	0.978910i	$0.565489\pi$
$878$	−119.970	−	87.1631i	−0.136640	−	0.0992746i
$879$	515.786	−	374.740i	0.586787	−	0.426326i
$880$	−345.852	+	1064.42i	−0.393014	+	1.20957i
$881$	−140.493	−	126.500i	−0.159470	−	0.143587i	0.585533	−	0.810648i	$-0.300885\pi$
$881$	−140.493	−	126.500i	−0.159470	−	0.143587i	−0.745003	+	0.667061i	$0.767552\pi$
$882$	210.878	−	649.017i	0.239091	−	0.735847i
$883$	255.664	−	442.822i	0.289540	−	0.501498i	−0.684160	−	0.729332i	$-0.739831\pi$
$883$	255.664	−	442.822i	0.289540	−	0.501498i	0.973700	+	0.227834i	$0.0731644\pi$
$884$	418.545	+	376.860i	0.473468	+	0.426312i
$885$	339.952	−	35.7304i	0.384126	−	0.0403733i
$886$	961.156	−	1322.92i	1.08483	−	1.49314i
$887$			136.580i			0.153980i	0.997032	+	0.0769901i	$0.0245310\pi$
$887$			136.580i			0.153980i	−0.997032	+	0.0769901i	$0.975469\pi$
$888$	138.212	+	310.429i	0.155644	+	0.349582i
$889$	−731.628	+	76.8972i	−0.822978	+	0.0864985i
$890$	−1214.06	−	700.939i	−1.36412	−	0.787572i
$891$	80.2744	+	763.759i	0.0900947	+	0.857194i
$892$	−128.737	+	1224.85i	−0.144324	+	1.37315i
$893$	−122.324	+	26.0008i	−0.136981	+	0.0291163i
$894$	−754.233	+	160.317i	−0.843661	+	0.179326i
$895$	71.7144	−	337.390i	0.0801279	−	0.376972i
$896$	539.090	+	56.6607i	0.601663	+	0.0632374i
$897$	222.584	−	306.361i	0.248143	−	0.341540i
$898$			1758.12i			1.95781i
$899$	20.4849	−	9.12046i	0.0227863	−	0.0101451i
$900$	609.010	+	676.374i	0.676678	+	0.751527i
$901$	193.350	+	434.272i	0.214595	+	0.481989i
$902$	2866.45	−	1654.95i	3.17788	−	1.83475i
$903$	−100.443	+	309.130i	−0.111232	+	0.342337i
$904$	−492.596	−	284.400i	−0.544907	−	0.314602i
$905$		−	842.596i		−	0.931046i
$906$	−381.803	−	426.681i	−0.421417	−	0.470950i
$907$	531.375			0.585860			0.292930	−	0.956134i	$-0.405370\pi$
$907$	531.375			0.585860			0.292930	+	0.956134i	$0.405370\pi$
$908$	−515.971	+	893.688i	−0.568250	+	0.984238i
$909$	87.7809	+	28.5218i	0.0965687	+	0.0313771i
$910$	−926.805	−	1605.27i	−1.01847	−	1.76404i
$911$	293.395	−	130.628i	0.322058	−	0.143390i	−0.239339	−	0.970936i	$-0.576931\pi$
$911$	293.395	−	130.628i	0.322058	−	0.143390i	0.561397	+	0.827546i	$0.310264\pi$
$912$	28.0349	−	25.2427i	0.0307400	−	0.0276784i
$913$	574.162	+	1289.59i	0.628874	+	1.41247i
$914$	1047.52			1.14609
$915$	555.433	+	403.546i	0.607031	+	0.441034i
$916$	−226.079	+	2151.00i	−0.246812	+	2.34826i
$917$	188.243	+	40.0122i	0.205281	+	0.0436338i
$918$	68.1284	+	320.519i	0.0742140	+	0.349149i
$919$	36.2646	+	170.612i	0.0394609	+	0.185649i	0.993464	−	0.114149i	$-0.0364141\pi$
$919$	36.2646	+	170.612i	0.0394609	+	0.185649i	−0.954003	+	0.299798i	$0.903081\pi$
$920$	429.910	+	45.1854i	0.467294	+	0.0491146i
$921$	595.469	−	62.5864i	0.646547	−	0.0679548i
$922$	−368.978	+	639.089i	−0.400193	+	0.693155i
$923$	147.383	+	1402.26i	0.159679	+	1.51924i
$924$	−485.759	+	216.274i	−0.525714	+	0.234063i
$925$	−1521.22			−1.64456
$926$	2261.51	+	1643.08i	2.44223	+	1.77439i
$927$	15.7615	+	149.960i	0.0170027	+	0.161769i
$928$	−290.320	+	322.433i	−0.312845	+	0.347449i
$929$	−141.299	−	81.5787i	−0.152097	−	0.0878135i	0.422020	−	0.906587i	$-0.361321\pi$
$929$	−141.299	−	81.5787i	−0.152097	−	0.0878135i	−0.574117	+	0.818773i	$0.694655\pi$
$930$	55.9167	+	18.1684i	0.0601254	+	0.0195359i
$931$	−69.0794	+	76.7205i	−0.0741992	+	0.0824065i
$932$	−1223.36	−	397.493i	−1.31262	−	0.426495i
$933$	137.261	+	188.924i	0.147118	+	0.202490i
$934$	−748.849	+	1030.70i	−0.801766	+	1.10354i
$935$	205.994	+	633.985i	0.220315	+	0.678059i
$936$	−250.386	+	562.375i	−0.267506	+	0.600829i
$937$	−50.7827	−	483.166i	−0.0541972	−	0.515652i	−0.987619	−	0.156871i	$-0.949859\pi$
$937$	−50.7827	−	483.166i	−0.0541972	−	0.515652i	0.933422	−	0.358781i	$-0.116807\pi$
$938$	739.500	+	1280.85i	0.788379	+	1.36551i
$939$	−187.302	−	108.139i	−0.199469	−	0.115164i
$940$	1223.73	+	544.840i	1.30184	+	0.579617i
$941$	−490.393	−	441.552i	−0.521140	−	0.469236i	0.366080	−	0.930583i	$-0.380700\pi$
$941$	−490.393	−	441.552i	−0.521140	−	0.469236i	−0.887220	+	0.461347i	$0.847366\pi$
$942$	−11.0545	+	105.176i	−0.0117351	+	0.111652i
$943$	600.090	+	666.468i	0.636363	+	0.706753i
$944$	175.612	−	304.170i	0.186030	−	0.322214i
$945$	64.4742	−	613.431i	0.0682267	−	0.649134i
$946$	3076.06	−	1369.55i	3.25165	−	1.44773i
$947$	−717.760	−	233.214i	−0.757931	−	0.246267i	−0.0955403	−	0.995426i	$-0.530458\pi$
$947$	−717.760	−	233.214i	−0.757931	−	0.246267i	−0.662390	+	0.749159i	$0.730458\pi$
$948$	244.251	+	108.748i	0.257649	+	0.114713i
$949$	−840.257	−	374.107i	−0.885413	−	0.394211i
$950$	−74.3928	−	228.958i	−0.0783082	−	0.241008i
$951$	211.471	+	44.9496i	0.222367	+	0.0472656i
$952$	81.6243	−	47.1258i	0.0857398	−	0.0495019i
$953$	596.686	−	126.830i	0.626113	−	0.133085i	0.116081	−	0.993240i	$-0.462967\pi$
$953$	596.686	−	126.830i	0.626113	−	0.133085i	0.510032	+	0.860155i	$0.329633\pi$
$954$	−1534.85	+	1381.99i	−1.60886	+	1.44862i
$955$	1251.41	−	1389.83i	1.31038	−	1.45532i
$956$	−42.0973	−	129.562i	−0.0440348	−	0.135525i
$957$	47.3587	−	222.805i	0.0494866	−	0.232816i
$958$	86.2336	−	77.6451i	0.0900142	−	0.0810491i
$959$	319.342	−	103.760i	0.332994	−	0.108196i
$960$	−830.617	+	87.3014i	−0.865226	+	0.0909389i
$961$	935.082	−	198.758i	0.973031	−	0.206824i
$962$	−1663.49	−	3736.27i	−1.72920	−	3.88386i
$963$	230.983	+	75.0508i	0.239857	+	0.0779344i
$964$	−1683.15	−	357.764i	−1.74600	−	0.371124i
$965$	−2054.17			−2.12867
$966$	−148.064	−	203.792i	−0.153275	−	0.210965i
$967$	−535.291	−	481.979i	−0.553559	−	0.498427i	0.344210	−	0.938893i	$-0.388147\pi$
$967$	−535.291	−	481.979i	−0.553559	−	0.498427i	−0.897769	+	0.440466i	$0.854813\pi$
$968$	811.620	+	361.357i	0.838451	+	0.373302i
$969$	4.67163	−	21.9783i	0.00482109	−	0.0226814i
$970$	1917.87			1.97719
$971$	−844.740	−	1162.68i	−0.869969	−	1.19741i	−0.979099	−	0.203382i	$-0.934807\pi$
$971$	−844.740	−	1162.68i	−0.869969	−	1.19741i	0.109130	−	0.994027i	$-0.465193\pi$
$972$	−1090.71	+	629.723i	−1.12213	+	0.647863i
$973$	69.7775	+	96.0404i	0.0717137	+	0.0987055i
$974$	658.637	−	478.528i	0.676218	−	0.491301i
$975$	380.264	+	422.326i	0.390014	+	0.433155i
$976$	670.908	−	217.991i	0.687406	−	0.223352i
$977$	−1037.36	−	109.031i	−1.06178	−	0.111598i	−0.442503	−	0.896767i	$-0.645909\pi$
$977$	−1037.36	−	109.031i	−1.06178	−	0.111598i	−0.619281	+	0.785169i	$0.712576\pi$
$978$	622.714	+	452.428i	0.636722	+	0.462606i
$979$	715.721	−	985.106i	0.731074	−	1.00624i
$980$	1081.66	−	229.913i	1.10373	−	0.234605i
$981$	307.933	−	177.785i	0.313897	−	0.181228i
$982$	−806.541	−	1396.97i	−0.821325	−	1.42258i
$983$	153.276	+	721.108i	0.155927	+	0.733579i	0.984737	+	0.174049i	$0.0556850\pi$
$983$	153.276	+	721.108i	0.155927	+	0.733579i	−0.828810	+	0.559530i	$0.810982\pi$
$984$	243.222	+	176.711i	0.247176	+	0.179584i
$985$	924.608	−	1272.61i	0.938688	−	1.29199i
$986$	−16.7760	+	159.613i	−0.0170142	+	0.161879i
$987$	−60.6835	−	186.764i	−0.0614827	−	0.189224i
$988$	275.101	−	247.702i	0.278442	−	0.250710i
$989$	536.260	+	738.098i	0.542224	+	0.746308i
$990$	−2343.10	+	1702.36i	−2.36677	+	1.71956i
$991$	−504.810	−	874.357i	−0.509395	−	0.882298i	−0.999941	−	0.0108827i	$-0.996536\pi$
$991$	−504.810	−	874.357i	−0.509395	−	0.882298i	0.490546	−	0.871415i	$-0.336797\pi$
$992$	78.6959	−	57.1759i	0.0793306	−	0.0576370i
$993$		−	338.775i		−	0.341163i
$994$	917.428	+	195.005i	0.922966	+	0.196182i
$995$	−766.571	+	1721.75i	−0.770423	+	1.73040i
$996$	−341.033	+	378.756i	−0.342403	+	0.380277i
$997$	−1370.37	+	995.635i	−1.37450	+	0.998631i	−0.377126	+	0.926162i	$0.623088\pi$
$997$	−1370.37	+	995.635i	−1.37450	+	0.998631i	−0.997371	+	0.0724688i	$0.976912\pi$
$998$			1665.24i			1.66857i
$999$	282.957	−	1331.21i	0.283240	−	1.33254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.3.i.a.23.4	✓	192
151.46	odd	30	inner	151.3.i.a.46.4	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.3.i.a.23.4	✓	192	1.1	even	1	trivial
151.3.i.a.46.4	yes	192	151.46	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	151.i (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52844 + 2.64734i) q^{2} +(-1.17971 - 0.383311i) q^{3} +(-2.67228 - 4.62852i) q^{4} +(-6.31759 + 2.81277i) q^{5} +(2.81787 - 2.53722i) q^{6} +(1.77668 + 3.99049i) q^{7} +4.11014 q^{8} +(-6.03637 - 4.38568i) q^{9} +(2.20971 - 21.0240i) q^{10} +(17.9605 + 3.81763i) q^{11} +(1.37835 + 6.48461i) q^{12} +(-4.17350 - 19.6348i) q^{13} +(-13.2797 - 1.39576i) q^{14} +(8.53108 - 0.896652i) q^{15} +(4.40699 - 7.63313i) q^{16} +(-0.548745 - 5.22096i) q^{17} +(20.8366 - 9.27706i) q^{18} -3.45053 q^{19} +(29.9013 + 21.7246i) q^{20} +(-0.566369 - 5.38864i) q^{21} +(-37.5582 + 41.7127i) q^{22} +(-13.1709 - 7.60424i) q^{23} +(-4.84877 - 1.57546i) q^{24} +(15.2720 - 16.9612i) q^{25} +(58.3589 + 18.9620i) q^{26} +(12.0020 + 16.5193i) q^{27} +(13.7223 - 18.8871i) q^{28} +(3.09043 + 9.51138i) q^{29} +(-10.6655 + 23.9552i) q^{30} +(-0.234369 - 2.22987i) q^{31} +(21.6919 + 37.5715i) q^{32} +(-19.7249 - 11.3882i) q^{33} +(14.6604 + 6.52723i) q^{34} +(-22.4487 - 20.2129i) q^{35} +(-4.16835 + 39.6592i) q^{36} +(-44.5983 - 49.5314i) q^{37} +(5.27393 - 9.13472i) q^{38} +(-2.60270 + 24.7631i) q^{39} +(-25.9662 + 11.5609i) q^{40} +(-56.0823 - 18.2223i) q^{41} +(15.1312 + 6.73685i) q^{42} +(-54.8026 - 24.3997i) q^{43} +(-30.3256 - 93.3324i) q^{44} +(50.4712 + 10.7280i) q^{45} +(40.2620 - 23.2453i) q^{46} +(35.4509 - 7.53533i) q^{47} +(-8.12482 + 7.31562i) q^{48} +(20.0200 - 22.2344i) q^{49} +(21.5599 + 66.3544i) q^{50} +(-1.35389 + 6.36955i) q^{51} +(-79.7272 + 71.7867i) q^{52} +(-86.1195 + 27.9819i) q^{53} +(-62.0766 + 6.52451i) q^{54} +(-124.205 + 26.4007i) q^{55} +(7.30241 + 16.4015i) q^{56} +(4.07061 + 1.32262i) q^{57} +(-29.9034 - 6.35617i) q^{58} +39.8486 q^{59} +(-26.9476 - 37.0901i) q^{60} +(59.4783 + 53.5545i) q^{61} +(6.26146 + 2.78778i) q^{62} +(6.77631 - 31.8800i) q^{63} -97.3637 q^{64} +(81.5946 + 112.305i) q^{65} +(60.2967 - 34.8123i) q^{66} +(-65.1045 - 89.6087i) q^{67} +(-22.6989 + 16.4917i) q^{68} +(12.6231 + 14.0193i) q^{69} +(87.8219 - 28.5351i) q^{70} +(-69.8565 - 7.34221i) q^{71} +(-24.8103 - 18.0257i) q^{72} +(26.9326 - 37.0696i) q^{73} +(199.292 - 42.3609i) q^{74} +(-24.5179 + 14.1554i) q^{75} +(9.22075 + 15.9708i) q^{76} +(16.6759 + 78.4541i) q^{77} +(-61.5782 - 44.7392i) q^{78} +(23.7053 - 32.6275i) q^{79} +(-6.37130 + 60.6188i) q^{80} +(12.9244 + 39.7771i) q^{81} +(133.959 - 120.617i) q^{82} +(45.1882 + 62.1962i) q^{83} +(-23.4279 + 17.0214i) q^{84} +(18.1521 + 31.4404i) q^{85} +(148.357 - 107.788i) q^{86} -12.4053i q^{87} +(73.8203 + 15.6910i) q^{88} +(26.9726 - 60.5815i) q^{89} +(-105.543 + 117.217i) q^{90} +(70.9375 - 51.5391i) q^{91} +81.2825i q^{92} +(-0.578247 + 2.72044i) q^{93} +(-34.2361 + 105.368i) q^{94} +(21.7990 - 9.70554i) q^{95} +(-11.1886 - 52.6382i) q^{96} +(9.48319 + 90.2265i) q^{97} +(28.2627 + 86.9838i) q^{98} +(-91.6736 - 101.814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 5 q^{2} - 10 q^{3} - 181 q^{4} - 9 q^{5} + 13 q^{6} - 31 q^{7} + 80 q^{8} + 124 q^{9} + 41 q^{10} + 25 q^{11} + 55 q^{12} - 28 q^{13} + 7 q^{14} - 34 q^{15} - 321 q^{16} - 82 q^{17} - 194 q^{18}+ \cdots - 1441 q^{99}+O(q^{100}) \) 192 * q - 5 * q^2 - 10 * q^3 - 181 * q^4 - 9 * q^5 + 13 * q^6 - 31 * q^7 + 80 * q^8 + 124 * q^9 + 41 * q^10 + 25 * q^11 + 55 * q^12 - 28 * q^13 + 7 * q^14 - 34 * q^15 - 321 * q^16 - 82 * q^17 - 194 * q^18 - 72 * q^19 + 127 * q^20 - 38 * q^21 - 114 * q^22 + 165 * q^23 - 55 * q^24 + 203 * q^25 - 125 * q^26 + 155 * q^27 + 50 * q^28 + 55 * q^29 + 253 * q^30 + 108 * q^31 - 40 * q^32 + 117 * q^33 - 123 * q^34 + 186 * q^35 - 503 * q^36 - 377 * q^37 - 128 * q^38 + 261 * q^39 - 650 * q^40 + 60 * q^41 + 1000 * q^42 + 150 * q^43 - 274 * q^44 - 41 * q^45 + 93 * q^46 - 135 * q^47 - 644 * q^48 - 293 * q^49 + 350 * q^50 - 166 * q^51 + 606 * q^52 + 225 * q^53 + 382 * q^54 + 458 * q^55 - 713 * q^56 + 20 * q^57 + 216 * q^58 + 368 * q^59 - 120 * q^60 - 128 * q^61 - 522 * q^62 - 717 * q^63 + 788 * q^64 + 445 * q^65 + 759 * q^66 + 130 * q^67 + 218 * q^68 - 127 * q^69 - 1025 * q^70 - 247 * q^71 + 396 * q^72 + 350 * q^73 + 86 * q^74 - 882 * q^75 + 145 * q^76 - 260 * q^77 + 564 * q^78 - 1030 * q^79 + 151 * q^80 - 506 * q^81 + 268 * q^82 + 250 * q^83 - 320 * q^84 - 466 * q^85 - 294 * q^86 - 253 * q^88 - 479 * q^89 + 1861 * q^90 + 1252 * q^91 - 863 * q^93 + 7 * q^94 - 583 * q^95 + 1067 * q^96 - 278 * q^97 + 554 * q^98 - 1441 * q^99

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