LMFDB - Embedded newform 160.4.z.a.29.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,4,Mod(29,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("160.29");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.z (of order $8$, degree $4$, 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:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.13
Character	$\chi$	$=$	160.29
Dual form			160.4.z.a.149.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.42251 - 1.45995i) q^{2} +(2.54494 - 6.14403i) q^{3} +(3.73710 + 7.07348i) q^{4} +(-0.364663 + 11.1744i) q^{5} +(-15.1351 + 11.1685i) q^{6} +(-1.31712 - 1.31712i) q^{7} +(1.27377 - 22.5915i) q^{8} +(-12.1805 - 12.1805i) q^{9} +(17.1974 - 26.5377i) q^{10} +(37.8288 - 15.6692i) q^{11} +(52.9703 - 4.95924i) q^{12} +(22.5926 + 9.35817i) q^{13} +(1.26781 + 5.11367i) q^{14} +(67.7277 + 30.6787i) q^{15} +(-36.0682 + 52.8685i) q^{16} +54.7975 q^{17} +(11.7244 + 47.2902i) q^{18} +(51.5106 - 124.358i) q^{19} +(-80.4046 + 39.1803i) q^{20} +(-11.4444 + 4.74043i) q^{21} +(-114.517 - 17.2693i) q^{22} +(-23.4950 + 23.4950i) q^{23} +(-135.561 - 65.3202i) q^{24} +(-124.734 - 8.14976i) q^{25} +(-41.0684 - 55.6543i) q^{26} +(60.0529 - 24.8747i) q^{27} +(4.39442 - 14.2388i) q^{28} +(-167.969 - 69.5749i) q^{29} +(-119.282 - 173.198i) q^{30} +259.197 q^{31} +(164.561 - 75.4167i) q^{32} -272.298i q^{33} +(-132.747 - 80.0016i) q^{34} +(15.1983 - 14.2377i) q^{35} +(40.6388 - 131.678i) q^{36} +(29.2490 - 12.1153i) q^{37} +(-306.341 + 226.055i) q^{38} +(114.994 - 114.994i) q^{39} +(251.982 + 22.4719i) q^{40} +(127.187 + 127.187i) q^{41} +(34.6450 + 5.22453i) q^{42} +(-118.949 - 287.169i) q^{43} +(252.205 + 209.024i) q^{44} +(140.551 - 131.668i) q^{45} +(91.2182 - 22.6153i) q^{46} -389.290 q^{47} +(233.034 + 356.151i) q^{48} -339.530i q^{49} +(290.271 + 201.848i) q^{50} +(139.456 - 336.677i) q^{51} +(18.2360 + 194.781i) q^{52} +(97.4325 + 235.223i) q^{53} +(-181.795 - 27.4150i) q^{54} +(161.299 + 428.427i) q^{55} +(-31.4335 + 28.0781i) q^{56} +(-632.966 - 632.966i) q^{57} +(305.330 + 413.772i) q^{58} +(147.801 + 356.822i) q^{59} +(36.1002 + 593.720i) q^{60} +(463.711 + 192.076i) q^{61} +(-627.906 - 378.414i) q^{62} +32.0863i q^{63} +(-508.755 - 57.5530i) q^{64} +(-112.811 + 249.046i) q^{65} +(-397.542 + 659.645i) q^{66} +(-187.045 + 451.568i) q^{67} +(204.783 + 387.609i) q^{68} +(84.5604 + 204.147i) q^{69} +(-57.6044 + 12.3022i) q^{70} +(-93.9317 + 93.9317i) q^{71} +(-290.691 + 259.661i) q^{72} +(500.811 - 500.811i) q^{73} +(-88.5436 - 13.3525i) q^{74} +(-367.513 + 745.629i) q^{75} +(1072.14 - 100.377i) q^{76} +(-70.4633 - 29.1868i) q^{77} +(-446.458 + 110.688i) q^{78} +19.2873i q^{79} +(-577.621 - 422.320i) q^{80} -897.368i q^{81} +(-122.425 - 493.797i) q^{82} +(704.447 + 291.791i) q^{83} +(-76.3003 - 63.2364i) q^{84} +(-19.9826 + 612.329i) q^{85} +(-131.097 + 869.330i) q^{86} +(-854.941 + 854.941i) q^{87} +(-305.806 - 874.569i) q^{88} +(-295.498 + 295.498i) q^{89} +(-532.715 + 113.768i) q^{90} +(-17.4314 - 42.0830i) q^{91} +(-253.994 - 78.3882i) q^{92} +(659.640 - 1592.51i) q^{93} +(943.058 + 568.344i) q^{94} +(1370.84 + 620.948i) q^{95} +(-44.5647 - 1203.00i) q^{96} -219.976i q^{97} +(-495.697 + 822.515i) q^{98} +(-651.631 - 269.914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} + 200 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 464 q^{24} - 4 q^{25} - 48 q^{26} - 8 q^{29} + 1124 q^{30} + 1472 q^{31} - 72 q^{34}+ \cdots + 5520 q^{99}+O(q^{100}) $ 280 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 + 200 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 464 * q^24 - 4 * q^25 - 48 * q^26 - 8 * q^29 + 1124 * q^30 + 1472 * q^31 - 72 * q^34 - 460 * q^35 - 888 * q^36 - 8 * q^39 - 1112 * q^40 - 8 * q^41 - 8 * q^44 - 112 * q^45 - 8 * q^46 + 3556 * q^50 - 1712 * q^51 + 856 * q^54 + 284 * q^55 + 328 * q^56 - 1384 * q^59 - 5248 * q^60 - 1832 * q^61 + 832 * q^64 - 8 * q^65 + 6088 * q^66 + 1048 * q^69 - 616 * q^70 + 216 * q^71 - 2064 * q^74 + 2204 * q^75 - 5128 * q^76 - 656 * q^80 - 6904 * q^84 - 504 * q^85 - 1192 * q^86 - 8 * q^89 + 2720 * q^90 - 8 * q^91 - 920 * q^94 - 8 * q^95 - 4152 * q^96 + 5520 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−2.42251	−	1.45995i	−0.856486	−	0.516170i
$2$	−2.42251	−	1.45995i	−0.856486	−	0.516170i
$3$	2.54494	−	6.14403i	0.489774	−	1.18242i	−0.465060	−	0.885279i	$-0.653967\pi$
$3$	2.54494	−	6.14403i	0.489774	−	1.18242i	0.954834	−	0.297140i	$-0.0960327\pi$
$4$	3.73710	+	7.07348i	0.467137	+	0.884185i
$5$	−0.364663	+	11.1744i	−0.0326164	+	0.999468i
$5$	−0.364663	+	11.1744i	−0.0326164	+	0.999468i
$6$	−15.1351	+	11.1685i	−1.02981	+	0.759919i
$7$	−1.31712	−	1.31712i	−0.0711178	−	0.0711178i	0.670653	−	0.741771i	$-0.266014\pi$
$7$	−1.31712	−	1.31712i	−0.0711178	−	0.0711178i	−0.741771	+	0.670653i	$0.766014\pi$
$8$	1.27377	−	22.5915i	0.0562934	−	0.998414i
$9$	−12.1805	−	12.1805i	−0.451129	−	0.451129i
$10$	17.1974	−	26.5377i	0.543831	−	0.839195i
$11$	37.8288	−	15.6692i	1.03689	−	0.429494i	0.201696	−	0.979448i	$-0.435355\pi$
$11$	37.8288	−	15.6692i	1.03689	−	0.429494i	0.835195	+	0.549954i	$0.185355\pi$
$12$	52.9703	−	4.95924i	1.27427	−	0.119301i
$13$	22.5926	+	9.35817i	0.482005	+	0.199653i	0.610436	−	0.792065i	$-0.290994\pi$
$13$	22.5926	+	9.35817i	0.482005	+	0.199653i	−0.128431	+	0.991718i	$0.540994\pi$
$14$	1.26781	+	5.11367i	0.0242025	+	0.0976203i
$15$	67.7277	+	30.6787i	1.16582	+	0.528080i
$16$	−36.0682	+	52.8685i	−0.563566	+	0.826071i
$17$	54.7975			0.781785			0.390892	−	0.920436i	$-0.372166\pi$
$17$	54.7975			0.781785			0.390892	+	0.920436i	$0.372166\pi$
$18$	11.7244	+	47.2902i	0.153526	+	0.619245i
$19$	51.5106	−	124.358i	0.621966	−	1.50156i	−0.227426	−	0.973795i	$-0.573031\pi$
$19$	51.5106	−	124.358i	0.621966	−	1.50156i	0.849392	−	0.527763i	$-0.176969\pi$
$20$	−80.4046	+	39.1803i	−0.898951	+	0.438050i
$21$	−11.4444	+	4.74043i	−0.118923	+	0.0492594i
$22$	−114.517	−	17.2693i	−1.10978	−	0.167356i
$23$	−23.4950	+	23.4950i	−0.213002	+	0.213002i	−0.805541	−	0.592540i	$-0.798125\pi$
$23$	−23.4950	+	23.4950i	−0.213002	+	0.213002i	0.592540	+	0.805541i	$0.298125\pi$
$24$	−135.561	−	65.3202i	−1.15297	−	0.555560i
$25$	−124.734	−	8.14976i	−0.997872	−	0.0651981i
$26$	−41.0684	−	55.6543i	−0.309776	−	0.419797i
$27$	60.0529	−	24.8747i	0.428044	−	0.177302i
$28$	4.39442	−	14.2388i	0.0296595	−	0.0961031i
$29$	−167.969	−	69.5749i	−1.07555	−	0.445508i	−0.226605	−	0.973987i	$-0.572763\pi$
$29$	−167.969	−	69.5749i	−1.07555	−	0.445508i	−0.848947	+	0.528478i	$0.822763\pi$
$30$	−119.282	−	173.198i	−0.725926	−	1.05405i
$31$	259.197			1.50171			0.750856	−	0.660466i	$-0.229641\pi$
$31$	259.197			1.50171			0.750856	+	0.660466i	$0.229641\pi$
$32$	164.561	−	75.4167i	0.909080	−	0.416622i
$33$		−	272.298i		−	1.43639i
$34$	−132.747	−	80.0016i	−0.669588	−	0.403534i
$35$	15.1983	−	14.2377i	0.0733996	−	0.0687604i
$36$	40.6388	−	131.678i	0.188142	−	0.609621i
$37$	29.2490	−	12.1153i	0.129959	−	0.0538310i	−0.316756	−	0.948507i	$-0.602594\pi$
$37$	29.2490	−	12.1153i	0.129959	−	0.0538310i	0.446715	+	0.894676i	$0.352594\pi$
$38$	−306.341	+	226.055i	−1.30776	+	0.965024i
$39$	114.994	−	114.994i	0.472147	−	0.472147i
$40$	251.982	+	22.4719i	0.996047	+	0.0888281i
$41$	127.187	+	127.187i	0.484468	+	0.484468i	0.906555	−	0.422087i	$-0.138702\pi$
$41$	127.187	+	127.187i	0.484468	+	0.484468i	−0.422087	+	0.906555i	$0.638702\pi$
$42$	34.6450	+	5.22453i	0.127282	+	0.0191943i
$43$	−118.949	−	287.169i	−0.421851	−	1.01844i	−0.981801	−	0.189912i	$-0.939180\pi$
$43$	−118.949	−	287.169i	−0.421851	−	1.01844i	0.559950	−	0.828527i	$-0.310820\pi$
$44$	252.205	+	209.024i	0.864123	+	0.716171i
$45$	140.551	−	131.668i	0.465603	−	0.436175i
$46$	91.2182	−	22.6153i	0.292378	−	0.0724879i
$47$	−389.290			−1.20817			−0.604083	−	0.796922i	$-0.706460\pi$
$47$	−389.290			−1.20817			−0.604083	+	0.796922i	$0.706460\pi$
$48$	233.034	+	356.151i	0.700742	+	1.07096i
$49$		−	339.530i		−	0.989885i
$50$	290.271	+	201.848i	0.821011	+	0.570913i
$51$	139.456	−	336.677i	0.382898	−	0.924397i
$52$	18.2360	+	194.781i	0.0486322	+	0.519447i
$53$	97.4325	+	235.223i	0.252517	+	0.609629i	0.998406	−	0.0564409i	$-0.0179753\pi$
$53$	97.4325	+	235.223i	0.252517	+	0.609629i	−0.745889	+	0.666070i	$0.767975\pi$
$54$	−181.795	−	27.4150i	−0.458132	−	0.0690871i
$55$	161.299	+	428.427i	0.395446	+	1.05035i
$56$	−31.4335	+	28.0781i	−0.0750085	+	0.0670016i
$57$	−632.966	−	632.966i	−1.47085	−	1.47085i
$58$	305.330	+	413.772i	0.691238	+	0.936740i
$59$	147.801	+	356.822i	0.326136	+	0.787362i	0.998872	+	0.0474793i	$0.0151188\pi$
$59$	147.801	+	356.822i	0.326136	+	0.787362i	−0.672736	+	0.739882i	$0.734881\pi$
$60$	36.1002	+	593.720i	0.0776753	+	1.27748i
$61$	463.711	+	192.076i	0.973314	+	0.403160i	0.811945	−	0.583734i	$-0.198409\pi$
$61$	463.711	+	192.076i	0.973314	+	0.403160i	0.161369	+	0.986894i	$0.448409\pi$
$62$	−627.906	−	378.414i	−1.28620	−	0.775139i
$63$			32.0863i			0.0641666i
$64$	−508.755	−	57.5530i	−0.993662	−	0.112408i
$65$	−112.811	+	249.046i	−0.215268	+	0.475237i
$66$	−397.542	+	659.645i	−0.741424	+	1.23025i
$67$	−187.045	+	451.568i	−0.341063	+	0.823400i	0.656546	+	0.754286i	$0.272017\pi$
$67$	−187.045	+	451.568i	−0.341063	+	0.823400i	−0.997609	+	0.0691132i	$0.977983\pi$
$68$	204.783	+	387.609i	0.365201	+	0.691242i
$69$	84.5604	+	204.147i	0.147534	+	0.356180i
$70$	−57.6044	+	12.3022i	−0.0983578	+	0.0210056i
$71$	−93.9317	+	93.9317i	−0.157009	+	0.157009i	−0.781240	−	0.624231i	$-0.785412\pi$
$71$	−93.9317	+	93.9317i	−0.157009	+	0.157009i	0.624231	+	0.781240i	$0.285412\pi$
$72$	−290.691	+	259.661i	−0.475809	+	0.425018i
$73$	500.811	−	500.811i	0.802952	−	0.802952i	−0.180604	−	0.983556i	$-0.557805\pi$
$73$	500.811	−	500.811i	0.802952	−	0.802952i	0.983556	+	0.180604i	$0.0578052\pi$
$74$	−88.5436	−	13.3525i	−0.139094	−	0.0209757i
$75$	−367.513	+	745.629i	−0.565823	+	1.14797i
$76$	1072.14	−	100.377i	1.61820	−	0.151501i
$77$	−70.4633	−	29.1868i	−0.104286	−	0.0431967i
$78$	−446.458	+	110.688i	−0.648096	+	0.160679i
$79$			19.2873i			0.0274682i	0.999906	+	0.0137341i	$0.00437183\pi$
$79$			19.2873i			0.0274682i	−0.999906	+	0.0137341i	$0.995628\pi$
$80$	−577.621	−	422.320i	−0.807250	−	0.590210i
$81$		−	897.368i		−	1.23096i
$82$	−122.425	−	493.797i	−0.164872	−	0.665009i
$83$	704.447	+	291.791i	0.931604	+	0.385883i	0.796287	−	0.604919i	$-0.206795\pi$
$83$	704.447	+	291.791i	0.931604	+	0.385883i	0.135317	+	0.990802i	$0.456795\pi$
$84$	−76.3003	−	63.2364i	−0.0991076	−	0.0821388i
$85$	−19.9826	+	612.329i	−0.0254990	+	0.781369i
$86$	−131.097	+	869.330i	−0.164378	+	1.09003i
$87$	−854.941	+	854.941i	−1.05355	+	1.05355i
$88$	−305.806	−	874.569i	−0.370443	−	1.05942i
$89$	−295.498	+	295.498i	−0.351941	+	0.351941i	−0.860831	−	0.508890i	$-0.830056\pi$
$89$	−295.498	+	295.498i	−0.351941	+	0.351941i	0.508890	+	0.860831i	$0.330056\pi$
$90$	−532.715	+	113.768i	−0.623923	+	0.133247i
$91$	−17.4314	−	42.0830i	−0.0200803	−	0.0484780i
$92$	−253.994	−	78.3882i	−0.287834	−	0.0888319i
$93$	659.640	−	1592.51i	0.735500	−	1.77565i
$94$	943.058	+	568.344i	1.03478	+	0.623619i
$95$	1370.84	+	620.948i	1.48047	+	0.670610i
$96$	−44.5647	−	1203.00i	−0.0473788	−	1.27896i
$97$		−	219.976i		−	0.230260i	−0.993350	−	0.115130i	$-0.963272\pi$
$97$		−	219.976i		−	0.230260i	0.993350	−	0.115130i	$-0.0367284\pi$
$98$	−495.697	+	822.515i	−0.510949	+	0.847822i
$99$	−651.631	−	269.914i	−0.661529	−	0.274014i
$100$	−408.496	−	912.760i	−0.408496	−	0.912760i
$101$	627.514	+	1514.95i	0.618218	+	1.49251i	0.853771	+	0.520649i	$0.174310\pi$
$101$	627.514	+	1514.95i	0.618218	+	1.49251i	−0.235553	+	0.971862i	$0.575690\pi$
$102$	−829.366	+	612.005i	−0.805093	+	0.594093i
$103$	352.701	+	352.701i	0.337405	+	0.337405i	0.855390	−	0.517985i	$-0.173318\pi$
$103$	352.701	+	352.701i	0.337405	+	0.337405i	−0.517985	+	0.855390i	$0.673318\pi$
$104$	240.193	−	498.482i	0.226470	−	0.470002i
$105$	−48.7981	−	129.613i	−0.0453544	−	0.120466i
$106$	107.382	−	712.076i	0.0983952	−	0.652480i
$107$	734.477	+	1773.18i	0.663594	+	1.60206i	0.792130	+	0.610352i	$0.208972\pi$
$107$	734.477	+	1773.18i	0.663594	+	1.60206i	−0.128536	+	0.991705i	$0.541028\pi$
$108$	400.375	+	331.824i	0.356723	+	0.295646i
$109$	627.162	−	1514.10i	0.551112	−	1.33050i	−0.365532	−	0.930799i	$-0.619113\pi$
$109$	627.162	−	1514.10i	0.551112	−	1.33050i	0.916644	−	0.399704i	$-0.130887\pi$
$110$	234.734	−	1273.36i	0.203464	−	1.10373i
$111$		−	210.539i		−	0.180031i
$112$	117.140	−	22.1280i	0.0988280	−	0.0186688i
$113$	−1522.85			−1.26777			−0.633885	−	0.773427i	$-0.718541\pi$
$113$	−1522.85			−1.26777			−0.633885	+	0.773427i	$0.718541\pi$
$114$	609.267	+	2457.46i	0.500553	+	2.01897i
$115$	−253.974	−	271.110i	−0.205941	−	0.219836i
$116$	−135.578	−	1448.13i	−0.108519	−	1.15910i
$117$	−161.202	−	389.176i	−0.127377	−	0.307516i
$118$	162.894	−	1080.19i	0.127082	−	0.842706i
$119$	−72.1749	−	72.1749i	−0.0555988	−	0.0555988i
$120$	779.348	−	1491.00i	0.592870	−	1.13424i
$121$	244.333	−	244.333i	0.183571	−	0.183571i
$122$	−842.924	−	1142.30i	−0.625531	−	0.847696i
$123$	1105.12	−	457.756i	0.810125	−	0.335565i
$124$	968.643	+	1833.42i	0.701506	+	1.32779i
$125$	136.554	−	1390.86i	0.0977104	−	0.995215i
$126$	46.8444	−	77.7294i	0.0331209	−	0.0549578i
$127$		−	1362.37i		−	0.951893i	−0.879474	−	0.475947i	$-0.842106\pi$
$127$		−	1362.37i		−	0.951893i	0.879474	−	0.475947i	$-0.157894\pi$
$128$	1148.44	+	882.179i	0.793036	+	0.609175i
$129$	−2067.09			−1.41083
$130$	636.879	−	438.619i	0.429677	−	0.295919i
$131$	−1549.82	−	641.957i	−1.03365	−	0.428153i	−0.199623	−	0.979873i	$-0.563972\pi$
$131$	−1549.82	−	641.957i	−1.03365	−	0.428153i	−0.834029	+	0.551720i	$0.813972\pi$
$132$	1926.10	−	1017.60i	1.27004	−	0.670993i
$133$	−231.640	+	95.9483i	−0.151020	+	0.0625547i
$134$	1112.39	−	820.850i	0.717130	−	0.529184i
$135$	256.061	+	680.126i	0.163246	+	0.433599i
$136$	69.7996	−	1237.96i	0.0440093	−	0.780545i
$137$	−185.200	+	185.200i	−0.115494	+	0.115494i	−0.762492	−	0.646998i	$-0.776024\pi$
$137$	−185.200	+	185.200i	−0.115494	+	0.115494i	0.646998	+	0.762492i	$0.276024\pi$
$138$	93.1958	−	618.002i	0.0574881	−	0.381216i
$139$	−1270.27	+	526.164i	−0.775131	+	0.321070i	−0.734949	−	0.678123i	$-0.762794\pi$
$139$	−1270.27	+	526.164i	−0.775131	+	0.321070i	−0.0401820	+	0.999192i	$0.512794\pi$
$140$	157.508	+	54.2973i	0.0950846	+	0.0327783i
$141$	−990.720	+	2391.81i	−0.591728	+	1.42856i
$142$	364.686	−	90.4148i	0.215519	−	0.0534327i
$143$	1001.29			0.585537
$144$	1083.29	−	204.636i	0.626906	−	0.118424i
$145$	838.710	−	1851.58i	0.480352	−	1.06045i
$146$	−1944.38	+	482.060i	−1.10218	+	0.273258i
$147$	−2086.08	−	864.084i	−1.17046	−	0.484820i
$148$	195.004	+	161.616i	0.108305	+	0.0897617i
$149$	−2784.33	+	1153.31i	−1.53088	+	0.634111i	−0.979735	−	0.200300i	$-0.935808\pi$
$149$	−2784.33	+	1153.31i	−1.53088	+	0.634111i	−0.551144	+	0.834410i	$0.685808\pi$
$150$	1978.88	−	1269.74i	1.07717	−	0.691160i
$151$	−1244.78	−	1244.78i	−0.670854	−	0.670854i	0.287059	−	0.957913i	$-0.407322\pi$
$151$	−1244.78	−	1244.78i	−0.670854	−	0.670854i	−0.957913	+	0.287059i	$0.907322\pi$
$152$	−2743.82	−	1322.11i	−1.46416	−	0.705507i
$153$	−667.460	−	667.460i	−0.352686	−	0.352686i
$154$	128.087	+	173.578i	0.0670228	+	0.0908268i
$155$	−94.5193	+	2896.36i	−0.0489805	+	1.50091i
$156$	1243.15	+	383.663i	0.638023	+	0.196908i
$157$	−180.359	+	435.425i	−0.0916829	+	0.221342i	−0.963068	−	0.269257i	$-0.913222\pi$
$157$	−180.359	+	435.425i	−0.0916829	+	0.221342i	0.871386	+	0.490599i	$0.163222\pi$
$158$	28.1584	−	46.7235i	0.0141782	−	0.0235261i
$159$	1693.18			0.844513
$160$	782.727	+	1866.37i	0.386750	+	0.922185i
$161$	61.8914			0.0302964
$162$	−1310.11	+	2173.88i	−0.635384	+	1.05430i
$163$	−1225.78	+	2959.29i	−0.589021	+	1.42202i	0.295418	+	0.955368i	$0.404541\pi$
$163$	−1225.78	+	2959.29i	−0.589021	+	1.42202i	−0.884439	+	0.466655i	$0.845459\pi$
$164$	−424.343	+	1374.96i	−0.202047	+	0.654673i
$165$	3042.77	+	99.2969i	1.43563	+	0.0468500i
$166$	−1280.53	−	1735.32i	−0.598724	−	0.811369i
$167$	−2272.90	−	2272.90i	−1.05319	−	1.05319i	−0.998504	−	0.0546860i	$-0.982584\pi$
$167$	−2272.90	−	2272.90i	−1.05319	−	1.05319i	−0.0546860	−	0.998504i	$-0.517416\pi$
$168$	92.5161	+	264.585i	0.0424867	+	0.121507i
$169$	−1130.66	−	1130.66i	−0.514639	−	0.514639i
$170$	942.377	−	1454.20i	0.425159	−	0.656070i
$171$	−2142.16	+	887.312i	−0.957983	+	0.396810i
$172$	1586.76	−	1914.56i	0.703426	−	0.848745i
$173$	144.046	+	59.6657i	0.0633040	+	0.0262214i	0.414111	−	0.910226i	$-0.364093\pi$
$173$	144.046	+	59.6657i	0.0633040	+	0.0262214i	−0.350807	+	0.936448i	$0.614093\pi$
$174$	3319.27	−	822.931i	1.44617	−	0.358542i
$175$	153.556	+	175.024i	0.0663298	+	0.0756033i
$176$	−536.009	+	2565.11i	−0.229564	+	1.09859i
$177$	2568.47			1.09072
$178$	1147.26	−	284.434i	0.483094	−	0.119771i
$179$	−367.380	+	886.935i	−0.153404	+	0.370350i	−0.981834	−	0.189743i	$-0.939235\pi$
$179$	−367.380	+	886.935i	−0.153404	+	0.370350i	0.828430	+	0.560093i	$0.189235\pi$
$180$	1456.60	+	502.132i	0.603160	+	0.207926i
$181$	−1427.16	+	591.149i	−0.586077	+	0.242761i	−0.655962	−	0.754794i	$-0.727737\pi$
$181$	−1427.16	+	591.149i	−0.586077	+	0.242761i	0.0698848	+	0.997555i	$0.477737\pi$
$182$	−19.2115	+	127.395i	−0.00782445	+	0.0518856i
$183$	2360.24	−	2360.24i	0.953408	−	0.953408i
$184$	500.860	+	560.714i	0.200673	+	0.224654i
$185$	124.715	+	331.257i	0.0495635	+	0.131646i
$186$	−3922.97	+	2894.83i	−1.54648	+	1.14118i
$187$	2072.92	−	858.632i	0.810626	−	0.335772i
$188$	−1454.81	−	2753.64i	−0.564379	−	1.06824i
$189$	−111.860	−	46.3339i	−0.0430509	−	0.0178323i
$190$	−2414.31	−	3505.61i	−0.921856	−	1.33854i
$191$	4171.90			1.58046			0.790230	−	0.612810i	$-0.209961\pi$
$191$	4171.90			1.58046			0.790230	+	0.612810i	$0.209961\pi$
$192$	−1648.36	+	2979.34i	−0.619583	+	1.11987i
$193$			5076.57i			1.89337i	0.322167	+	0.946683i	$0.395589\pi$
$193$			5076.57i			1.89337i	−0.322167	+	0.946683i	$0.604411\pi$
$194$	−321.154	+	532.894i	−0.118853	+	0.197214i
$195$	1243.05	+	1326.92i	0.456496	+	0.487296i
$196$	2401.66	−	1268.86i	0.875241	−	0.462412i
$197$	−2603.19	+	1078.28i	−0.941471	+	0.389970i	−0.800019	−	0.599975i	$-0.795177\pi$
$197$	−2603.19	+	1078.28i	−0.941471	+	0.389970i	−0.141453	+	0.989945i	$0.545177\pi$
$198$	1184.52	+	1605.22i	0.425152	+	0.576151i
$199$	474.708	−	474.708i	0.169101	−	0.169101i	−0.617483	−	0.786584i	$-0.711848\pi$
$199$	474.708	−	474.708i	0.169101	−	0.169101i	0.786584	+	0.617483i	$0.211848\pi$
$200$	−342.999	+	2807.55i	−0.121268	+	0.992620i
$201$	2298.43	+	2298.43i	0.806559	+	0.806559i
$202$	691.597	−	4586.13i	0.240894	−	1.59742i
$203$	129.597	+	312.874i	0.0448074	+	0.108175i
$204$	2902.64	−	271.754i	0.996204	−	0.0932676i
$205$	−1467.61	+	1374.85i	−0.500012	+	0.468409i
$206$	−339.496	−	1369.35i	−0.114824	−	0.463141i
$207$	572.360			0.192182
$208$	−1309.63	+	856.906i	−0.436569	+	0.285653i
$209$		−	5511.43i		−	1.82408i
$210$	−71.0147	+	385.232i	−0.0233356	+	0.126588i
$211$	−385.864	+	931.558i	−0.125896	+	0.303939i	−0.974243	−	0.225501i	$-0.927598\pi$
$211$	−385.864	+	931.558i	−0.125896	+	0.303939i	0.848347	+	0.529440i	$0.177598\pi$
$212$	−1299.73	+	1568.24i	−0.421065	+	0.508052i
$213$	338.068	+	816.169i	0.108751	+	0.262549i
$214$	809.482	−	5367.85i	0.258575	−	1.71467i
$215$	3252.32	−	1224.47i	1.03166	−	0.388409i
$216$	−485.465	−	1388.37i	−0.152924	−	0.437346i
$217$	−341.393	−	341.393i	−0.106799	−	0.106799i
$218$	−3729.82	+	2752.30i	−1.15879	+	0.855089i
$219$	−1802.46	−	4351.53i	−0.556161	−	1.34269i
$220$	−2427.68	+	2742.02i	−0.743974	+	0.840304i
$221$	1238.02	+	512.804i	0.376824	+	0.156086i
$222$	−307.377	+	510.033i	−0.0929268	+	0.154194i
$223$			3237.42i			0.972169i	0.873912	+	0.486085i	$0.161575\pi$
$223$			3237.42i			0.972169i	−0.873912	+	0.486085i	$0.838425\pi$
$224$	−316.080	−	117.414i	−0.0942810	−	0.0350225i
$225$	1420.05	+	1618.59i	0.420756	+	0.479582i
$226$	3689.13	+	2223.29i	1.08583	+	0.654385i
$227$	−1236.57	+	2985.34i	−0.361560	+	0.872882i	0.633513	+	0.773732i	$0.281612\pi$
$227$	−1236.57	+	2985.34i	−0.361560	+	0.872882i	−0.995073	+	0.0991500i	$0.968388\pi$
$228$	2111.82	−	6842.72i	0.613414	−	1.98759i
$229$	223.005	+	538.381i	0.0643519	+	0.155359i	0.952784	−	0.303649i	$-0.0982049\pi$
$229$	223.005	+	538.381i	0.0643519	+	0.155359i	−0.888432	+	0.459008i	$0.848205\pi$
$230$	219.448	+	1027.55i	0.0629130	+	0.294587i
$231$	−358.650	+	358.650i	−0.102153	+	0.102153i
$232$	−1785.76	+	3706.05i	−0.505348	+	1.04877i
$233$	−3895.82	+	3895.82i	−1.09538	+	1.09538i	−0.100439	+	0.994943i	$0.532025\pi$
$233$	−3895.82	+	3895.82i	−1.09538	+	1.09538i	−0.994943	+	0.100439i	$0.967975\pi$
$234$	−177.664	+	1178.13i	−0.0496336	+	0.329131i
$235$	141.959	−	4350.08i	0.0394060	−	1.20752i
$236$	−1971.63	+	2378.95i	−0.543823	+	0.656170i
$237$	118.501	+	49.0849i	0.0324789	+	0.0134532i
$238$	69.4726	+	280.216i	0.0189212	+	0.0763181i
$239$		−	1932.13i		−	0.522924i	−0.965214	−	0.261462i	$-0.915795\pi$
$239$		−	1932.13i		−	0.522924i	0.965214	−	0.261462i	$-0.0842046\pi$
$240$	−4064.75	+	2474.14i	−1.09325	+	0.665438i
$241$			223.475i			0.0597315i	0.999554	+	0.0298657i	$0.00950798\pi$
$241$			223.475i			0.0597315i	−0.999554	+	0.0298657i	$0.990492\pi$
$242$	−948.613	+	235.185i	−0.251980	+	0.0624722i
$243$	−3892.03	−	1612.13i	−1.02746	−	0.425589i
$244$	374.292	+	3997.86i	0.0982031	+	1.04892i
$245$	3794.05	+	123.814i	0.989358	+	0.0322865i
$246$	−3345.46	−	504.502i	−0.867069	−	0.130756i
$247$	2327.52	−	2327.52i	0.599581	−	0.599581i
$248$	330.158	−	5855.65i	0.0845365	−	1.49933i
$249$	3585.55	−	3585.55i	0.912550	−	0.912550i
$250$	−2361.38	+	3170.00i	−0.597388	+	0.801953i
$251$	−1966.48	−	4747.51i	−0.494515	−	1.19386i	−0.952400	−	0.304853i	$-0.901393\pi$
$251$	−1966.48	−	4747.51i	−0.494515	−	1.19386i	0.457885	−	0.889011i	$-0.348607\pi$
$252$	−226.962	+	119.910i	−0.0567352	+	0.0299746i
$253$	−520.638	+	1256.93i	−0.129376	+	0.312342i
$254$	−1988.99	+	3300.34i	−0.491339	+	0.815283i
$255$	3711.31	+	1681.11i	0.911417	+	0.412845i
$256$	−1494.17	−	3813.75i	−0.364787	−	0.931091i
$257$		−	4725.28i		−	1.14691i	−0.819238	−	0.573453i	$-0.805604\pi$
$257$		−	4725.28i		−	1.14691i	0.819238	−	0.573453i	$-0.194396\pi$
$258$	5007.55	+	3017.85i	1.20836	+	0.728230i
$259$	−54.4817	−	22.5671i	−0.0130708	−	0.00541409i
$260$	−2183.21	+	132.747i	−0.520757	+	0.0316638i
$261$	1198.48	+	2893.40i	0.284231	+	0.686195i
$262$	2817.23	+	3817.80i	0.664309	+	0.900247i
$263$	−4207.50	−	4207.50i	−0.986484	−	0.986484i	0.0134258	−	0.999910i	$-0.495726\pi$
$263$	−4207.50	−	4207.50i	−0.986484	−	0.986484i	−0.999910	+	0.0134258i	$0.995726\pi$
$264$	−6151.63	−	346.846i	−1.43412	−	0.0808595i
$265$	−2664.00	+	1002.97i	−0.617541	+	0.232498i
$266$	701.229	+	105.747i	0.161636	+	0.0243750i
$267$	1063.52	+	2567.57i	0.243770	+	0.588513i
$268$	−3893.16	+	364.490i	−0.887361	+	0.0830774i
$269$	−189.686	+	457.942i	−0.0429939	+	0.103796i	−0.943918	−	0.330181i	$-0.892890\pi$
$269$	−189.686	+	457.942i	−0.0429939	+	0.103796i	0.900924	+	0.433977i	$0.142890\pi$
$270$	372.639	−	2021.45i	0.0839930	−	0.455635i
$271$		−	440.058i		−	0.0986406i	−0.998783	−	0.0493203i	$-0.984294\pi$
$271$		−	440.058i		−	0.0986406i	0.998783	−	0.0493203i	$-0.0157055\pi$
$272$	−1976.45	+	2897.06i	−0.440587	+	0.645810i
$273$	−302.921			−0.0671561
$274$	719.029	−	178.266i	0.158533	−	0.0393044i
$275$	−4846.24	+	1646.19i	−1.06269	+	0.360977i
$276$	−1128.02	+	1361.05i	−0.246010	+	0.296833i
$277$	2447.40	+	5908.55i	0.530867	+	1.28163i	0.930950	+	0.365147i	$0.118981\pi$
$277$	2447.40	+	5908.55i	0.530867	+	1.28163i	−0.400083	+	0.916479i	$0.631019\pi$
$278$	3845.42	+	579.897i	0.829615	+	0.125108i
$279$	−3157.14	−	3157.14i	−0.677466	−	0.677466i
$280$	−302.293	−	361.489i	−0.0645194	−	0.0771540i
$281$	660.691	−	660.691i	0.140262	−	0.140262i	−0.633490	−	0.773751i	$-0.718378\pi$
$281$	660.691	−	660.691i	0.140262	−	0.140262i	0.773751	+	0.633490i	$0.218378\pi$
$282$	5891.95	−	4347.78i	1.24419	−	0.918108i
$283$	4915.19	−	2035.94i	1.03243	−	0.427646i	0.198841	−	0.980032i	$-0.436282\pi$
$283$	4915.19	−	2035.94i	1.03243	−	0.427646i	0.833589	+	0.552385i	$0.186282\pi$
$284$	−1015.46	−	313.392i	−0.212170	−	0.0654803i
$285$	7303.82	−	6842.19i	1.51804	−	1.42209i
$286$	−2425.62	−	1461.83i	−0.501504	−	0.302236i
$287$		−	335.040i		−	0.0689087i
$288$	−2923.04	−	1085.82i	−0.598063	−	0.222162i
$289$	−1910.24			−0.388812
$290$	−4734.99	+	3260.99i	−0.958787	+	0.660317i
$291$	−1351.54	−	559.826i	−0.272263	−	0.112775i
$292$	5414.06	+	1670.90i	1.08505	+	0.334870i
$293$	−5137.24	+	2127.92i	−1.02430	+	0.424281i	−0.830653	−	0.556790i	$-0.812033\pi$
$293$	−5137.24	+	2127.92i	−1.02430	+	0.424281i	−0.193651	+	0.981071i	$0.562033\pi$
$294$	3792.04	+	5138.83i	0.752232	+	1.01940i
$295$	−4041.17	+	1521.46i	−0.797580	+	0.300281i
$296$	−236.447	−	676.211i	−0.0464297	−	0.132784i
$297$	1881.96	−	1881.96i	0.367685	−	0.367685i
$298$	8428.82	+	1271.08i	1.63849	+	0.247087i
$299$	−750.682	+	310.943i	−0.145194	+	0.0601414i
$300$	−6647.62	+	186.891i	−1.27934	+	0.0359671i
$301$	−221.566	+	534.907i	−0.0424280	+	0.102430i
$302$	1198.18	+	4832.82i	0.228302	+	0.920852i
$303$	10904.9			2.06756
$304$	4716.71	+	7208.65i	0.889875	+	1.36001i
$305$	−2315.43	+	5111.65i	−0.434691	+	0.959647i
$306$	642.470	+	2591.39i	0.120025	+	0.484116i
$307$	2491.35	+	1031.95i	0.463157	+	0.191846i	0.602045	−	0.798462i	$-0.294353\pi$
$307$	2491.35	+	1031.95i	0.463157	+	0.191846i	−0.138888	+	0.990308i	$0.544353\pi$
$308$	−56.8755	−	607.494i	−0.0105220	−	0.112387i
$309$	3064.61	−	1269.40i	0.564206	−	0.233702i
$310$	4457.52	−	6878.48i	0.816678	−	1.26023i
$311$	6572.10	+	6572.10i	1.19830	+	1.19830i	0.974677	+	0.223618i	$0.0717869\pi$
$311$	6572.10	+	6572.10i	1.19830	+	1.19830i	0.223618	+	0.974677i	$0.428213\pi$
$312$	−2451.41	−	2744.36i	−0.444820	−	0.497977i
$313$	−5505.83	−	5505.83i	−0.994275	−	0.994275i	0.00570834	−	0.999984i	$-0.498183\pi$
$313$	−5505.83	−	5505.83i	−0.994275	−	0.994275i	−0.999984	+	0.00570834i	$0.998183\pi$
$314$	1072.62	−	791.506i	0.192775	−	0.142253i
$315$	−358.545	−	11.7007i	−0.0641325	−	0.00209288i
$316$	−136.428	+	72.0783i	−0.0242869	+	0.0128314i
$317$	−492.055	+	1187.93i	−0.0871816	+	0.210475i	−0.961457	−	0.274955i	$-0.911337\pi$
$317$	−492.055	+	1187.93i	−0.0871816	+	0.210475i	0.874275	+	0.485430i	$0.161337\pi$
$318$	−4101.73	−	2471.95i	−0.723313	−	0.435912i
$319$	−7444.23			−1.30657
$320$	828.644	−	5664.04i	0.144758	−	0.989467i
$321$	12763.7			2.21931
$322$	−149.932	−	90.3583i	−0.0259485	−	0.0156381i
$323$	2822.65	−	6814.49i	0.486243	−	1.17390i
$324$	6347.52	−	3353.55i	1.08839	−	0.575026i
$325$	−2741.80	−	1351.41i	−0.467963	−	0.230654i
$326$	7289.88	−	5379.34i	1.23849	−	0.913908i
$327$	−7706.60	−	7706.60i	−1.30329	−	1.30329i
$328$	3035.35	−	2711.33i	0.510973	−	0.456428i
$329$	512.742	+	512.742i	0.0859221	+	0.0859221i
$330$	−7226.16	−	4682.83i	−1.20542	−	0.781156i
$331$	−791.540	+	327.867i	−0.131441	+	0.0544446i	−0.447434	−	0.894317i	$-0.647662\pi$
$331$	−791.540	+	327.867i	−0.131441	+	0.0544446i	0.315993	+	0.948761i	$0.397662\pi$
$332$	568.605	+	6073.34i	0.0939947	+	1.00397i
$333$	−503.837	−	208.696i	−0.0829132	−	0.0343438i
$334$	2187.81	+	8824.46i	0.358417	+	1.44567i
$335$	−4977.79	−	2254.79i	−0.811837	−	0.367738i
$336$	162.160	−	776.029i	0.0263290	−	0.126000i
$337$	10579.8			1.71014			0.855071	−	0.518511i	$-0.173513\pi$
$337$	10579.8			1.71014			0.855071	+	0.518511i	$0.173513\pi$
$338$	1088.33	+	4389.75i	0.175140	+	0.706423i
$339$	−3875.57	+	9356.45i	−0.620921	+	1.49903i
$340$	−4405.97	+	2146.98i	−0.702786	+	0.342460i
$341$	9805.09	−	4061.40i	1.55711	−	0.644977i
$342$	6484.83	+	977.925i	1.02532	+	0.154620i
$343$	−898.975	+	898.975i	−0.141516	+	0.141516i
$344$	−6639.11	+	2321.46i	−1.04057	+	0.363851i
$345$	−2312.05	+	870.467i	−0.360802	+	0.135839i
$346$	−261.843	−	354.840i	−0.0406843	−	0.0551339i
$347$	11633.4	−	4818.71i	1.79975	−	0.745480i	0.813206	−	0.581975i	$-0.197720\pi$
$347$	11633.4	−	4818.71i	1.79975	−	0.745480i	0.986543	−	0.163505i	$-0.0522800\pi$
$348$	−9242.40	−	2852.41i	−1.42369	−	0.439383i
$349$	−4592.83	−	1902.41i	−0.704437	−	0.291787i	0.00156340	−	0.999999i	$-0.499502\pi$
$349$	−4592.83	−	1902.41i	−0.704437	−	0.291787i	−0.706000	+	0.708211i	$0.749502\pi$
$350$	−116.463	−	648.180i	−0.0177864	−	0.0989906i
$351$	1589.54			0.241718
$352$	5043.42	−	5431.46i	0.763680	−	0.822437i
$353$			2625.08i			0.395805i	0.980222	+	0.197902i	$0.0634129\pi$
$353$			2625.08i			0.395805i	−0.980222	+	0.197902i	$0.936587\pi$
$354$	−6222.14	−	3749.84i	−0.934190	−	0.562999i
$355$	−1015.38	−	1083.88i	−0.151804	−	0.162047i
$356$	−3194.50	−	985.895i	−0.475585	−	0.146776i
$357$	−627.125	+	259.764i	−0.0929720	+	0.0385103i
$358$	2184.86	−	1612.25i	0.322552	−	0.238017i
$359$	5305.41	−	5305.41i	0.779969	−	0.779969i	−0.199856	−	0.979825i	$-0.564048\pi$
$359$	5305.41	−	5305.41i	0.779969	−	0.779969i	0.979825	+	0.199856i	$0.0640475\pi$
$360$	−2795.55	−	3342.98i	−0.409273	−	0.489419i
$361$	−7961.44	−	7961.44i	−1.16073	−	1.16073i
$362$	4320.35	+	651.518i	0.627273	+	0.0945939i
$363$	−879.376	−	2123.00i	−0.127150	−	0.306966i
$364$	232.531	−	280.569i	0.0334833	−	0.0404006i
$365$	5413.63	+	5778.89i	0.776336	+	0.828714i
$366$	−9163.51	+	2271.87i	−1.30870	+	0.324460i
$367$	−10253.3			−1.45836			−0.729180	−	0.684322i	$-0.760098\pi$
$367$	−10253.3			−1.45836			−0.729180	+	0.684322i	$0.760098\pi$
$368$	−394.723	−	2089.57i	−0.0559140	−	0.295995i
$369$		−	3098.39i		−	0.437116i
$370$	181.495	−	984.552i	0.0255013	−	0.138336i
$371$	181.486	−	438.147i	0.0253971	−	0.0613139i
$372$	13729.7	−	1285.42i	1.91359	−	0.179156i
$373$	−448.361	−	1082.44i	−0.0622393	−	0.150259i	0.889700	−	0.456546i	$-0.150913\pi$
$373$	−448.361	−	1082.44i	−0.0622393	−	0.150259i	−0.951939	+	0.306287i	$0.900913\pi$
$374$	−6275.23	−	946.316i	−0.867605	−	0.130837i
$375$	−8197.93	−	4378.64i	−1.12890	−	0.602965i
$376$	−495.868	+	8794.66i	−0.0680118	+	1.20625i
$377$	−3143.76	−	3143.76i	−0.429475	−	0.429475i
$378$	203.337	+	275.554i	0.0276680	+	0.0374947i
$379$	−4804.97	−	11600.2i	−0.651226	−	1.57220i	−0.811001	−	0.585045i	$-0.801077\pi$
$379$	−4804.97	−	11600.2i	−0.651226	−	1.57220i	0.159775	−	0.987153i	$-0.448923\pi$
$380$	730.684	+	12017.1i	0.0986402	+	1.62228i
$381$	−8370.42	−	3467.14i	−1.12554	−	0.466212i
$382$	−10106.5	−	6090.76i	−1.35364	−	0.815786i
$383$		−	1129.41i		−	0.150679i	−0.997158	−	0.0753396i	$-0.975996\pi$
$383$		−	1129.41i		−	0.150679i	0.997158	−	0.0753396i	$-0.0240041\pi$
$384$	8342.84	−	4810.95i	1.10871	−	0.639343i
$385$	351.840	−	776.741i	0.0465752	−	0.102822i
$386$	7411.54	−	12298.0i	0.977299	−	1.62164i
$387$	−2049.00	+	4946.72i	−0.269138	+	0.649757i
$388$	1556.00	−	822.072i	0.203592	−	0.107563i
$389$	4022.27	+	9710.61i	0.524260	+	1.26567i	0.935235	+	0.354028i	$0.115188\pi$
$389$	4022.27	+	9710.61i	0.524260	+	1.26567i	−0.410975	+	0.911647i	$0.634812\pi$
$390$	−1074.07	−	5029.26i	−0.139455	−	0.652991i
$391$	−1287.46	+	1287.46i	−0.166521	+	0.166521i
$392$	−7670.51	−	432.485i	−0.988315	−	0.0557240i
$393$	−7888.40	+	7888.40i	−1.01251	+	1.01251i
$394$	7880.49	+	1188.39i	1.00765	+	0.151955i
$395$	−215.523	−	7.03334i	−0.0274536	−	0.000895913i
$396$	−525.974	−	5617.99i	−0.0667454	−	0.712916i
$397$	9051.24	+	3749.15i	1.14425	+	0.473965i	0.872603	−	0.488430i	$-0.162430\pi$
$397$	9051.24	+	3749.15i	1.14425	+	0.473965i	0.271651	+	0.962396i	$0.412430\pi$
$398$	−1843.03	+	456.934i	−0.232118	+	0.0575479i
$399$			1667.38i			0.209207i
$400$	4929.80	−	6300.56i	0.616225	−	0.787570i
$401$			136.721i			0.0170263i	0.999964	+	0.00851314i	$0.00270985\pi$
$401$			136.721i			0.0170263i	−0.999964	+	0.00851314i	$0.997290\pi$
$402$	−2212.37	−	8923.54i	−0.274485	−	1.10713i
$403$	5855.93	+	2425.61i	0.723833	+	0.299822i
$404$	−8370.91	+	10100.2i	−1.03086	+	1.24383i
$405$	10027.5	+	327.237i	1.23030	+	0.0401494i
$406$	142.831	−	947.144i	0.0174596	−	0.115778i
$407$	916.615	−	916.615i	0.111634	−	0.111634i
$408$	−7428.42	−	3579.38i	−0.901377	−	0.434328i
$409$	−10630.3	+	10630.3i	−1.28517	+	1.28517i	−0.347488	+	0.937684i	$0.612965\pi$
$409$	−10630.3	+	10630.3i	−1.28517	+	1.28517i	−0.937684	+	0.347488i	$0.887035\pi$
$410$	5562.52	−	1187.95i	0.670032	−	0.143094i
$411$	666.549	+	1609.19i	0.0799963	+	0.193128i
$412$	−1176.75	+	3812.91i	−0.140714	+	0.455943i
$413$	275.307	−	664.650i	0.0328014	−	0.0791895i
$414$	−1386.55	−	835.616i	−0.164602	−	0.0991988i
$415$	−3517.48	+	7765.36i	−0.416063	+	0.918522i
$416$	4423.63	−	163.872i	0.521361	−	0.0193136i
$417$			9143.65i			1.07378i
$418$	−8046.40	+	13351.5i	−0.941537	+	1.56230i
$419$	6222.86	+	2577.60i	0.725553	+	0.300534i	0.714723	−	0.699407i	$-0.246553\pi$
$419$	6222.86	+	2577.60i	0.725553	+	0.300534i	0.0108300	+	0.999941i	$0.496553\pi$
$420$	734.452	−	829.549i	0.0853276	−	0.0963758i
$421$	−3764.27	−	9087.75i	−0.435770	−	1.05204i	−0.977395	−	0.211422i	$-0.932191\pi$
$421$	−3764.27	−	9087.75i	−0.435770	−	1.05204i	0.541625	−	0.840620i	$-0.317809\pi$
$422$	2294.79	−	1693.37i	0.264712	−	0.195336i
$423$	4741.74	+	4741.74i	0.545039	+	0.545039i
$424$	5438.15	−	1901.53i	0.622877	−	0.217798i
$425$	−6835.11	−	446.587i	−0.780122	−	0.0509709i
$426$	372.592	−	2470.74i	0.0423759	−	0.281004i
$427$	−357.777	−	863.750i	−0.0405481	−	0.0978918i
$428$	−9797.77	+	11821.9i	−1.10653	+	1.33512i
$429$	2548.21	−	6151.93i	0.286781	−	0.692350i
$430$	−9666.42	−	1781.94i	−1.08408	−	0.199843i
$431$			6087.19i			0.680301i	0.940371	+	0.340151i	$0.110478\pi$
$431$			6087.19i			0.680301i	−0.940371	+	0.340151i	$0.889522\pi$
$432$	−850.911	+	4072.10i	−0.0947674	+	0.453516i
$433$	1333.40			0.147988			0.0739942	−	0.997259i	$-0.476425\pi$
$433$	1333.40			0.147988			0.0739942	+	0.997259i	$0.476425\pi$
$434$	328.611	+	1325.44i	0.0363453	+	0.146598i
$435$	−9241.68	−	9865.21i	−1.01863	−	1.08736i
$436$	13053.7	−	1222.13i	1.43385	−	0.134242i
$437$	1711.54	+	4132.02i	0.187355	+	0.452314i
$438$	−1986.53	+	13173.1i	−0.216713	+	1.43707i
$439$	10307.7	+	10307.7i	1.12063	+	1.12063i	0.991646	+	0.128987i	$0.0411725\pi$
$439$	10307.7	+	10307.7i	1.12063	+	1.12063i	0.128987	+	0.991646i	$0.458827\pi$
$440$	9884.29	−	3098.27i	1.07094	−	0.335691i
$441$	−4135.64	+	4135.64i	−0.446566	+	0.446566i
$442$	−2250.44	−	3049.72i	−0.242178	−	0.328191i
$443$	7872.22	−	3260.78i	0.844290	−	0.349716i	0.0817462	−	0.996653i	$-0.473950\pi$
$443$	7872.22	−	3260.78i	0.844290	−	0.349716i	0.762544	+	0.646937i	$0.223950\pi$
$444$	1489.24	−	786.805i	0.159181	−	0.0840994i
$445$	−3194.25	−	3409.77i	−0.340275	−	0.363233i
$446$	4726.47	−	7842.68i	0.501805	−	0.832650i
$447$			20042.1i			2.12071i
$448$	594.287	+	745.896i	0.0626729	+	0.0786613i
$449$	−11033.1			−1.15965			−0.579827	−	0.814739i	$-0.696880\pi$
$449$	−11033.1			−1.15965			−0.579827	+	0.814739i	$0.696880\pi$
$450$	−1077.03	−	5994.25i	−0.112826	−	0.627937i
$451$	6804.22	+	2818.40i	0.710417	+	0.294265i
$452$	−5691.05	−	10771.9i	−0.592222	−	1.12094i
$453$	−10815.9	+	4480.08i	−1.12180	+	0.464664i
$454$	7354.05	−	5426.69i	0.760226	−	0.560985i
$455$	476.609	−	179.439i	0.0491072	−	0.0184884i
$456$	−15105.9	+	13493.4i	−1.55131	+	1.38572i
$457$	9092.83	−	9092.83i	0.930732	−	0.930732i	−0.0670196	−	0.997752i	$-0.521349\pi$
$457$	9092.83	−	9092.83i	0.930732	−	0.930732i	0.997752	+	0.0670196i	$0.0213490\pi$
$458$	245.778	−	1629.81i	0.0250753	−	0.166279i
$459$	3290.75	−	1363.07i	0.334638	−	0.138612i
$460$	968.562	−	2809.64i	0.0981727	−	0.284783i
$461$	−4238.00	+	10231.4i	−0.428163	+	1.03368i	0.551707	+	0.834038i	$0.313977\pi$
$461$	−4238.00	+	10231.4i	−0.428163	+	1.03368i	−0.979870	+	0.199639i	$0.936023\pi$
$462$	1392.44	−	345.221i	0.140221	−	0.0347644i
$463$	452.209			0.0453908			0.0226954	−	0.999742i	$-0.492775\pi$
$463$	452.209			0.0453908			0.0226954	+	0.999742i	$0.492775\pi$
$464$	9736.66	−	6370.82i	0.974166	−	0.637409i
$465$	17554.8	+	7951.80i	1.75072	+	0.793024i
$466$	15125.4	−	3749.96i	1.50358	−	0.372776i
$467$	10052.1	+	4163.72i	0.996053	+	0.412579i	0.820348	−	0.571864i	$-0.193780\pi$
$467$	10052.1	+	4163.72i	0.996053	+	0.412579i	0.175705	+	0.984443i	$0.443780\pi$
$468$	2150.40	−	2594.65i	0.212398	−	0.256277i
$469$	841.130	−	348.408i	0.0828141	−	0.0343027i
$470$	−6694.79	+	10330.9i	−0.657038	+	1.01389i
$471$	2216.26	+	2216.26i	0.216815	+	0.216815i
$472$	8249.43	−	2884.53i	0.804472	−	0.281295i
$473$	−8999.41	−	8999.41i	−0.874828	−	0.874828i
$474$	−215.409	−	291.915i	−0.0208736	−	0.0282871i
$475$	−7438.61	+	15091.8i	−0.718541	+	1.45781i
$476$	240.803	−	780.252i	0.0231874	−	0.0751319i
$477$	1678.35	−	4051.90i	0.161104	−	0.388939i
$478$	−2820.81	+	4680.59i	−0.269918	+	0.447877i
$479$	−15760.5			−1.50337			−0.751687	−	0.659519i	$-0.770760\pi$
$479$	−15760.5			−1.50337			−0.751687	+	0.659519i	$0.770760\pi$
$480$	13459.0	−	59.2947i	1.27983	−	0.00563837i
$481$	774.188			0.0733886
$482$	326.262	−	541.370i	0.0308316	−	0.0511592i
$483$	157.510	−	380.262i	0.0148384	−	0.0358231i
$484$	2641.38	+	815.189i	0.248064	+	0.0765579i
$485$	2458.10	+	80.2170i	0.230137	+	0.00751024i
$486$	7074.84	+	9587.56i	0.660332	+	0.894857i
$487$	−6701.77	−	6701.77i	−0.623585	−	0.623585i	0.322861	−	0.946446i	$-0.395355\pi$
$487$	−6701.77	−	6701.77i	−0.623585	−	0.623585i	−0.946446	+	0.322861i	$0.895355\pi$
$488$	4929.95	−	10231.3i	0.457312	−	0.949075i
$489$	15062.5	+	15062.5i	1.39294	+	1.39294i
$490$	−9010.35	−	5839.05i	−0.830706	−	0.538330i
$491$	12599.2	−	5218.76i	1.15803	−	0.479673i	0.280813	−	0.959763i	$-0.409396\pi$
$491$	12599.2	−	5218.76i	1.15803	−	0.479673i	0.877219	+	0.480090i	$0.159396\pi$
$492$	7367.87	+	6106.37i	0.675140	+	0.559545i
$493$	−9204.27	−	3812.53i	−0.840851	−	0.348292i
$494$	−9036.50	+	2240.38i	−0.823019	+	0.204047i
$495$	3253.75	−	7183.15i	0.295445	−	0.652240i
$496$	−9348.76	+	13703.4i	−0.846314	+	1.24052i
$497$	247.439			0.0223323
$498$	−13920.7	+	3451.31i	−1.25262	+	0.310556i
$499$	−1651.48	+	3987.02i	−0.148157	+	0.357682i	−0.980483	−	0.196604i	$-0.937009\pi$
$499$	−1651.48	+	3987.02i	−0.148157	+	0.357682i	0.832326	+	0.554286i	$0.187009\pi$
$500$	10348.5	−	4231.84i	0.925598	−	0.378508i
$501$	−19749.2	+	8180.39i	−1.76114	+	0.729486i
$502$	−2167.30	+	14371.8i	−0.192692	+	1.27778i
$503$	12672.1	−	12672.1i	1.12331	−	1.12331i	0.132065	−	0.991241i	$-0.457839\pi$
$503$	12672.1	−	12672.1i	1.12331	−	1.12331i	0.991241	−	0.132065i	$-0.0421607\pi$
$504$	724.879	+	40.8707i	0.0640649	+	0.00361216i
$505$	−17157.5	+	6459.64i	−1.51188	+	0.569209i
$506$	3096.31	−	2284.82i	0.272031	−	0.200737i
$507$	−9824.29	+	4069.35i	−0.860576	+	0.356462i
$508$	9636.67	−	5091.29i	0.841650	−	0.444665i
$509$	−4721.28	−	1955.62i	−0.411134	−	0.170297i	0.167523	−	0.985868i	$-0.446423\pi$
$509$	−4721.28	−	1955.62i	−0.411134	−	0.170297i	−0.578657	+	0.815571i	$0.696423\pi$
$510$	−6536.34	−	9490.83i	−0.567518	−	0.824042i
$511$	−1319.26			−0.114208
$512$	−1948.25	+	11420.2i	−0.168167	+	0.985759i
$513$		−	8749.36i		−	0.753009i
$514$	−6898.67	+	11447.0i	−0.591999	+	0.982309i
$515$	−4069.84	+	3812.61i	−0.348230	+	0.326220i
$516$	−7724.93	−	14621.5i	−0.659052	−	1.24744i
$517$	−14726.4	+	6099.86i	−1.25274	+	0.518900i
$518$	99.0357	+	134.209i	0.00840034	+	0.0113838i
$519$	733.175	−	733.175i	0.0620093	−	0.0620093i
$520$	5482.64	+	2865.79i	0.462365	+	0.241679i
$521$	−2612.75	−	2612.75i	−0.219706	−	0.219706i	0.588669	−	0.808374i	$-0.299652\pi$
$521$	−2612.75	−	2612.75i	−0.219706	−	0.219706i	−0.808374	+	0.588669i	$0.799652\pi$
$522$	1320.87	−	8759.01i	0.110753	−	0.734428i
$523$	−891.386	−	2152.00i	−0.0745269	−	0.179924i	0.882226	−	0.470827i	$-0.156044\pi$
$523$	−891.386	−	2152.00i	−0.0745269	−	0.179924i	−0.956753	+	0.290903i	$0.906044\pi$
$524$	−1250.96	−	13361.7i	−0.104291	−	1.11395i
$525$	1466.14	−	498.024i	0.121881	−	0.0414011i
$526$	4049.96	+	16335.4i	0.335716	+	1.35410i
$527$	14203.3			1.17402
$528$	14396.0	+	9821.31i	1.18656	+	0.809503i
$529$			11063.0i			0.909261i
$530$	7917.85	+	1459.60i	0.648924	+	0.119624i
$531$	2545.99	−	6146.55i	0.208072	−	0.502331i
$532$	−1544.35	−	1279.93i	−0.125857	−	0.104308i
$533$	1683.24	+	4063.71i	0.136791	+	0.330242i
$534$	1172.13	−	7772.66i	0.0949871	−	0.629880i
$535$	−20082.1	+	7560.72i	−1.62285	+	0.610987i
$536$	9963.35	+	4800.84i	0.802894	+	0.386874i
$537$	4514.39	+	4514.39i	0.362775	+	0.362775i
$538$	1128.09	−	832.437i	0.0904002	−	0.0667080i
$539$	−5320.17	−	12844.0i	−0.425150	−	1.02640i
$540$	−3853.93	+	4352.94i	−0.307124	+	0.346890i
$541$	−20918.6	−	8664.78i	−1.66241	−	0.688592i	−0.664150	−	0.747600i	$-0.731206\pi$
$541$	−20918.6	−	8664.78i	−1.66241	−	0.688592i	−0.998257	+	0.0590083i	$0.981206\pi$
$542$	−642.462	+	1066.04i	−0.0509153	+	0.0844843i
$543$			10272.9i			0.811887i
$544$	9017.53	−	4132.65i	0.710705	−	0.325709i
$545$	16690.5	+	7560.29i	1.31182	+	0.594215i
$546$	733.829	+	442.250i	0.0575183	+	0.0346640i
$547$	−5522.31	+	13332.0i	−0.431658	+	1.04211i	0.547095	+	0.837070i	$0.315734\pi$
$547$	−5522.31	+	13332.0i	−0.431658	+	1.04211i	−0.978753	+	0.205043i	$0.934266\pi$
$548$	−2002.11	−	617.897i	−0.156069	−	0.0481665i
$549$	−3308.66	−	7987.80i	−0.257213	−	0.620967i
$550$	14143.4	+	3087.36i	1.09650	+	0.239355i
$551$	−17304.4	+	17304.4i	−1.33791	+	1.33791i
$552$	4719.70	−	1650.31i	0.363920	−	0.127250i
$553$	25.4036	−	25.4036i	0.00195348	−	0.00195348i
$554$	2697.33	−	17886.6i	0.206857	−	1.37171i
$555$	2352.65	+	76.7757i	0.179936	+	0.00587198i
$556$	−8468.95	−	7018.92i	−0.645977	−	0.535375i
$557$	−12390.1	−	5132.13i	−0.942519	−	0.390404i	−0.142105	−	0.989852i	$-0.545387\pi$
$557$	−12390.1	−	5132.13i	−0.942519	−	0.390404i	−0.800414	+	0.599447i	$0.795387\pi$
$558$	3038.94	+	12257.5i	0.230553	+	0.929928i
$559$		−	7601.05i		−	0.575117i
$560$	204.551	+	1317.04i	0.0154354	+	0.0993843i
$561$		−	14921.3i		−	1.12295i
$562$	−2565.10	+	635.954i	−0.192531	+	0.0477333i
$563$	−5361.14	−	2220.66i	−0.401323	−	0.166234i	0.172887	−	0.984942i	$-0.444691\pi$
$563$	−5361.14	−	2220.66i	−0.401323	−	0.166234i	−0.574210	+	0.818708i	$0.694691\pi$
$564$	−20620.8	+	1930.58i	−1.53953	+	0.144135i
$565$	555.328	−	17017.0i	0.0413501	−	1.26710i
$566$	−14879.4	−	2243.85i	−1.10500	−	0.166636i
$567$	−1181.94	+	1181.94i	−0.0875431	+	0.0875431i
$568$	2002.41	+	2241.71i	0.147921	+	0.165599i
$569$	4580.90	−	4580.90i	0.337507	−	0.337507i	−0.517922	−	0.855428i	$-0.673294\pi$
$569$	4580.90	−	4580.90i	0.337507	−	0.337507i	0.855428	+	0.517922i	$0.173294\pi$
$570$	−27682.8	+	5912.04i	−2.03422	+	0.434435i
$571$	1426.07	+	3442.84i	0.104517	+	0.252326i	0.967483	−	0.252935i	$-0.0813960\pi$
$571$	1426.07	+	3442.84i	0.104517	+	0.252326i	−0.862966	+	0.505262i	$0.831396\pi$
$572$	3741.90	+	7082.58i	0.273526	+	0.517723i
$573$	10617.2	−	25632.3i	0.774068	−	1.86877i
$574$	−489.142	+	811.638i	−0.0355686	+	0.0590193i
$575$	3122.10	−	2739.14i	0.226436	−	0.198661i
$576$	5495.86	+	6897.91i	0.397559	+	0.498980i
$577$		−	15359.8i		−	1.10821i	−0.832448	−	0.554104i	$-0.813061\pi$
$577$		−	15359.8i		−	1.10821i	0.832448	−	0.554104i	$-0.186939\pi$
$578$	4627.56	+	2788.85i	0.333012	+	0.200693i
$579$	31190.6	+	12919.6i	2.23875	+	0.927321i
$580$	16231.4	−	986.928i	1.16202	−	0.0706551i
$581$	−543.517	−	1312.17i	−0.0388105	−	0.0936968i
$582$	2456.80	+	3329.36i	0.174979	+	0.237124i
$583$	7371.50	+	7371.50i	0.523664	+	0.523664i
$584$	−10676.2	−	11952.0i	−0.756478	−	0.846880i
$585$	4407.59	−	1659.42i	0.311507	−	0.117279i
$586$	15551.7	+	2345.22i	1.09630	+	0.165325i
$587$	−1864.95	−	4502.39i	−0.131132	−	0.316582i	0.844652	−	0.535316i	$-0.179807\pi$
$587$	−1864.95	−	4502.39i	−0.131132	−	0.316582i	−0.975785	+	0.218734i	$0.929807\pi$
$588$	−1683.81	−	17985.0i	−0.118094	−	1.26138i
$589$	13351.4	−	32233.1i	0.934014	−	2.25491i
$590$	12011.0	+	2214.15i	0.838112	+	0.154500i
$591$			18738.2i			1.30421i
$592$	−414.439	+	1983.33i	−0.0287725	+	0.137693i
$593$	16295.4			1.12845			0.564224	−	0.825621i	$-0.309175\pi$
$593$	16295.4			1.12845			0.564224	+	0.825621i	$0.309175\pi$
$594$	−7306.64	+	1811.50i	−0.504705	+	0.125129i
$595$	832.830	−	780.191i	0.0573827	−	0.0537558i
$596$	−18563.2	−	15384.9i	−1.27580	−	1.05736i
$597$	−1708.51	−	4124.72i	−0.117127	−	0.282770i
$598$	2272.50	+	342.697i	0.155400	+	0.0234346i
$599$	−14811.4	−	14811.4i	−1.01031	−	1.01031i	−0.999946	−	0.0103660i	$-0.996700\pi$
$599$	−14811.4	−	14811.4i	−1.01031	−	1.01031i	−0.0103660	−	0.999946i	$-0.503300\pi$
$600$	16376.8	+	9252.45i	1.11430	+	0.629549i
$601$	10656.0	−	10656.0i	0.723238	−	0.723238i	−0.246026	−	0.969263i	$-0.579125\pi$
$601$	10656.0	−	10656.0i	0.723238	−	0.723238i	0.969263	+	0.246026i	$0.0791248\pi$
$602$	1317.68	−	972.342i	0.0892105	−	0.0658301i
$603$	7778.62	−	3222.01i	0.525323	−	0.217596i
$604$	4153.07	−	13456.8i	0.279778	−	0.906540i
$605$	2641.17	+	2819.37i	0.177486	+	0.189461i
$606$	−26417.2	−	15920.6i	−1.77084	−	1.06721i
$607$			5181.99i			0.346508i	0.984877	+	0.173254i	$0.0554282\pi$
$607$			5181.99i			0.346508i	−0.984877	+	0.173254i	$0.944572\pi$
$608$	−902.007	−	24349.2i	−0.0601665	−	1.62416i
$609$	2252.12			0.149853
$610$	13071.9	−	9002.61i	0.867648	−	0.597549i
$611$	−8795.08	−	3643.04i	−0.582342	−	0.241214i
$612$	2226.90	−	7215.63i	0.147087	−	0.476592i
$613$	−2245.01	+	929.914i	−0.147920	+	0.0612706i	−0.455415	−	0.890279i	$-0.650509\pi$
$613$	−2245.01	+	929.914i	−0.147920	+	0.0612706i	0.307495	+	0.951550i	$0.400509\pi$
$614$	−4528.73	−	6137.17i	−0.297662	−	0.403381i
$615$	4712.15	+	12516.0i	0.308963	+	0.820638i
$616$	−749.130	+	1554.70i	−0.0489989	+	0.101689i
$617$	7448.92	−	7448.92i	0.486033	−	0.486033i	−0.421019	−	0.907052i	$-0.638327\pi$
$617$	7448.92	−	7448.92i	0.486033	−	0.486033i	0.907052	+	0.421019i	$0.138327\pi$
$618$	−9277.31	−	1399.04i	−0.603865	−	0.0910639i
$619$	7294.65	−	3021.54i	0.473662	−	0.196197i	−0.133065	−	0.991107i	$-0.542482\pi$
$619$	7294.65	−	3021.54i	0.473662	−	0.196197i	0.606727	+	0.794910i	$0.292482\pi$
$620$	−20840.6	+	10155.4i	−1.34997	+	0.657825i
$621$	−826.510	+	1995.37i	−0.0534085	+	0.128940i
$622$	−6326.04	−	25515.9i	−0.407799	−	1.64485i
$623$	778.413			0.0500585
$624$	1931.93	+	10227.2i	0.123941	+	0.656113i
$625$	15492.2	+	2033.11i	0.991498	+	0.130119i
$626$	5299.69	+	21376.2i	0.338368	+	1.36480i
$627$	−33862.4	−	14026.2i	−2.15683	−	0.893388i
$628$	−3753.99	+	351.460i	−0.238536	+	0.0223325i
$629$	1602.77	−	663.889i	0.101600	−	0.0420842i
$630$	851.496	+	551.803i	0.0538483	+	0.0348958i
$631$	−5075.38	−	5075.38i	−0.320202	−	0.320202i	0.528642	−	0.848845i	$-0.322701\pi$
$631$	−5075.38	−	5075.38i	−0.320202	−	0.320202i	−0.848845	+	0.528642i	$0.822701\pi$
$632$	435.729	+	24.5676i	0.0274246	+	0.00154628i
$633$	4741.52	+	4741.52i	0.297723	+	0.297723i
$634$	2926.32	−	2159.38i	0.183311	−	0.135268i
$635$	15223.6	+	496.804i	0.951387	+	0.0310473i
$636$	6327.56	+	11976.6i	0.394503	+	0.746705i
$637$	3177.38	−	7670.88i	0.197633	−	0.477129i
$638$	18033.7	+	10868.2i	1.11906	+	0.674414i
$639$	2288.27			0.141663
$640$	−10276.6	+	12511.4i	−0.634717	+	0.772745i
$641$	6558.87			0.404149			0.202075	−	0.979370i	$-0.435232\pi$
$641$	6558.87			0.404149			0.202075	+	0.979370i	$0.435232\pi$
$642$	−30920.1	−	18634.3i	−1.90081	−	1.14554i
$643$	−3025.23	+	7303.54i	−0.185542	+	0.447937i	−0.989092	−	0.147300i	$-0.952942\pi$
$643$	−3025.23	+	7303.54i	−0.185542	+	0.447937i	0.803550	+	0.595237i	$0.202942\pi$
$644$	231.294	+	437.787i	0.0141526	+	0.0267876i
$645$	753.792	−	23098.5i	0.0460163	−	1.41008i
$646$	−16786.7	+	12387.2i	−1.02239	+	0.754441i
$647$	−6460.77	−	6460.77i	−0.392580	−	0.392580i	0.483026	−	0.875606i	$-0.339538\pi$
$647$	−6460.77	−	6460.77i	−0.392580	−	0.392580i	−0.875606	+	0.483026i	$0.839538\pi$
$648$	−20272.9	−	1143.04i	−1.22901	−	0.0692948i
$649$	11182.2	+	11182.2i	0.676335	+	0.676335i
$650$	4669.05	+	7276.69i	0.281747	+	0.439100i
$651$	−2966.36	+	1228.70i	−0.178588	+	0.0739735i
$652$	−25513.4	+	2388.64i	−1.53249	+	0.143476i
$653$	−12035.6	−	4985.30i	−0.721269	−	0.298759i	−0.00831022	−	0.999965i	$-0.502645\pi$
$653$	−12035.6	−	4985.30i	−0.721269	−	0.298759i	−0.712959	+	0.701206i	$0.752645\pi$
$654$	7418.06	+	29920.6i	0.443531	+	1.78897i
$655$	7738.64	−	17084.2i	0.461639	−	1.01914i
$656$	−11311.6	+	2136.77i	−0.673235	+	0.127175i
$657$	−12200.2			−0.724470
$658$	−493.544	−	1990.70i	−0.0292407	−	0.117942i
$659$	−4873.42	+	11765.5i	−0.288075	+	0.695475i	−0.999977	−	0.00680399i	$-0.997834\pi$
$659$	−4873.42	+	11765.5i	−0.288075	+	0.695475i	0.711902	+	0.702279i	$0.247834\pi$
$660$	10668.7	+	21894.0i	0.629212	+	1.29125i
$661$	4021.07	−	1665.58i	0.236613	−	0.0980084i	−0.261226	−	0.965278i	$-0.584127\pi$
$661$	4021.07	−	1665.58i	0.236613	−	0.0980084i	0.497840	+	0.867269i	$0.334127\pi$
$662$	2396.18	+	361.349i	0.140680	+	0.0212148i
$663$	6301.37	−	6301.37i	0.369117	−	0.369117i
$664$	7489.32	−	15542.9i	0.437714	−	0.908404i
$665$	−987.694	−	2623.42i	−0.0575957	−	0.152980i
$666$	915.863	+	1241.14i	0.0532868	+	0.0722123i
$667$	5581.08	−	2311.76i	0.323988	−	0.134200i
$668$	7583.28	−	24571.4i	0.439231	−	1.42320i
$669$	19890.8	+	8239.04i	1.14951	+	0.476143i
$670$	8766.85	+	12729.6i	0.505512	+	0.734009i
$671$	20551.3			1.18238
$672$	−1525.80	+	1643.19i	−0.0875876	+	0.0943266i
$673$			16268.2i			0.931790i	0.884840	+	0.465895i	$0.154268\pi$
$673$			16268.2i			0.931790i	−0.884840	+	0.465895i	$0.845732\pi$
$674$	−25629.6	−	15446.0i	−1.46471	−	0.882724i
$675$	−7693.37	+	2613.31i	−0.438693	+	0.149017i
$676$	3772.32	−	12223.1i	0.214629	−	0.695443i
$677$	24021.6	−	9950.08i	1.36370	−	0.564864i	0.423628	−	0.905836i	$-0.360756\pi$
$677$	24021.6	−	9950.08i	1.36370	−	0.564864i	0.940073	+	0.340973i	$0.110756\pi$
$678$	23048.5	−	17008.0i	1.30557	−	0.963402i
$679$	−289.735	+	289.735i	−0.0163756	+	0.0163756i
$680$	13808.0	+	1231.41i	0.778694	+	0.0694445i
$681$	15195.0	+	15195.0i	0.855030	+	0.855030i
$682$	−29682.4	−	4476.15i	−1.66656	−	0.251321i
$683$	8106.50	+	19570.8i	0.454153	+	1.09642i	0.970728	+	0.240181i	$0.0772068\pi$
$683$	8106.50	+	19570.8i	0.454153	+	1.09642i	−0.516575	+	0.856242i	$0.672793\pi$
$684$	−14281.8	−	11836.6i	−0.798363	−	0.661670i
$685$	−2001.96	−	2137.03i	−0.111665	−	0.119199i
$686$	3490.23	−	865.317i	0.194253	−	0.0481603i
$687$	3875.36			0.215217
$688$	19472.5	+	4069.00i	1.07904	+	0.225479i
$689$			6226.09i			0.344260i
$690$	6871.81	+	1266.77i	0.379138	+	0.0698914i
$691$	9832.75	−	23738.4i	0.541325	−	1.30687i	−0.382463	−	0.923971i	$-0.624924\pi$
$691$	9832.75	−	23738.4i	0.541325	−	1.30687i	0.923788	−	0.382903i	$-0.125076\pi$
$692$	116.269	+	1241.88i	0.00638710	+	0.0682214i
$693$	502.767	+	1213.79i	0.0275592	+	0.0665338i
$694$	−35217.0	−	5310.80i	−1.92625	−	0.290483i
$695$	−5416.35	−	14386.4i	−0.295617	−	0.785190i
$696$	18225.4	+	20403.4i	0.992576	+	1.11119i
$697$	6969.50	+	6969.50i	0.378750	+	0.378750i
$698$	8348.74	+	11313.9i	0.452729	+	0.613521i
$699$	14021.4	+	33850.7i	0.758711	+	1.83169i
$700$	−664.177	+	1740.25i	−0.0358622	+	0.0939649i
$701$	6412.18	+	2656.01i	0.345484	+	0.143104i	0.548677	−	0.836034i	$-0.315132\pi$
$701$	6412.18	+	2656.01i	0.345484	+	0.143104i	−0.203192	+	0.979139i	$0.565132\pi$
$702$	−3850.66	−	2320.64i	−0.207028	−	0.124768i
$703$		−	4261.40i		−	0.228623i
$704$	−20147.4	+	5794.62i	−1.07860	+	0.310217i
$705$	−26365.7	−	11942.9i	−1.40850	−	0.638008i
$706$	3832.49	−	6359.28i	0.204302	−	0.339001i
$707$	1168.86	−	2821.89i	0.0621778	−	0.150110i
$708$	9598.62	+	18168.0i	0.509518	+	0.964402i
$709$	12505.0	+	30189.7i	0.662389	+	1.59915i	0.794049	+	0.607854i	$0.207969\pi$
$709$	12505.0	+	30189.7i	0.662389	+	1.59915i	−0.131659	+	0.991295i	$0.542031\pi$
$710$	877.343	+	4108.11i	0.0463748	+	0.217147i
$711$	234.928	−	234.928i	0.0123917	−	0.0123917i
$712$	6299.36	+	7052.15i	0.331571	+	0.371195i
$713$	−6089.81	+	6089.81i	−0.319867	+	0.319867i
$714$	1898.46	+	286.291i	0.0995070	+	0.0150058i
$715$	−365.131	+	11188.8i	−0.0190981	+	0.585225i
$716$	−7646.65	+	715.902i	−0.399118	+	0.0373667i
$717$	−11871.0	−	4917.15i	−0.618315	−	0.256115i
$718$	−20598.0	+	5106.77i	−1.07063	+	0.265436i
$719$			10345.2i			0.536595i	0.963336	+	0.268297i	$0.0864610\pi$
$719$			10345.2i			0.536595i	−0.963336	+	0.268297i	$0.913539\pi$
$720$	1891.65	+	12179.8i	0.0979132	+	0.630435i
$721$		−	929.101i		−	0.0479910i
$722$	7663.35	+	30909.9i	0.395015	+	1.59328i
$723$	1373.04	+	568.730i	0.0706276	+	0.0292549i
$724$	−9514.91	−	7885.81i	−0.488424	−	0.404798i
$725$	20384.4	+	10047.3i	1.04422	+	0.514684i
$726$	−969.179	+	6426.84i	−0.0495449	+	0.328543i
$727$	−14334.8	+	14334.8i	−0.731292	+	0.731292i	−0.970876	−	0.239584i	$-0.922989\pi$
$727$	−14334.8	+	14334.8i	−0.731292	+	0.731292i	0.239584	+	0.970876i	$0.422989\pi$
$728$	−972.924	+	340.197i	−0.0495316	+	0.0173194i
$729$	−2677.50	+	2677.50i	−0.136031	+	0.136031i
$730$	−4677.69	−	21903.0i	−0.237163	−	1.11050i
$731$	−6518.12	−	15736.1i	−0.329797	−	0.796200i
$732$	25515.5	+	7874.65i	1.28836	+	0.397617i
$733$	−8187.30	+	19765.9i	−0.412558	+	0.996003i	0.571891	+	0.820330i	$0.306210\pi$
$733$	−8187.30	+	19765.9i	−0.412558	+	0.996003i	−0.984449	+	0.175673i	$0.943790\pi$
$734$	24838.7	+	14969.3i	1.24906	+	0.752761i
$735$	10416.3	−	22995.6i	0.522738	−	1.15402i
$736$	−2094.44	+	5638.27i	−0.104894	+	0.282377i
$737$			20013.1i			1.00026i
$738$	−4523.49	+	7505.87i	−0.225626	+	0.374383i
$739$	26921.2	+	11151.1i	1.34007	+	0.555076i	0.933511	−	0.358548i	$-0.116728\pi$
$739$	26921.2	+	11151.1i	1.34007	+	0.555076i	0.406561	+	0.913624i	$0.366728\pi$
$740$	−1877.07	+	2120.11i	−0.0932465	+	0.105320i
$741$	−8376.95	−	20223.7i	−0.415297	−	1.00262i
$742$	−1079.32	+	796.454i	−0.0534006	+	0.0394053i
$743$	7975.66	+	7975.66i	0.393807	+	0.393807i	0.876042	−	0.482235i	$-0.160175\pi$
$743$	7975.66	+	7975.66i	0.393807	+	0.393807i	−0.482235	+	0.876042i	$0.660175\pi$
$744$	−35137.1	−	16930.8i	−1.73143	−	0.834291i
$745$	−11872.1	−	31533.7i	−0.583841	−	1.55075i
$746$	−494.148	+	3276.80i	−0.0242521	+	0.160821i
$747$	−5026.34	−	12134.7i	−0.246190	−	0.594356i
$748$	13820.2	+	11454.0i	0.675558	+	0.559892i
$749$	1368.10	−	3302.89i	0.0667415	−	0.161128i
$750$	13467.0	+	22575.8i	0.655659	+	1.09914i
$751$		−	11708.2i		−	0.568895i	−0.958692	−	0.284447i	$-0.908190\pi$
$751$		−	11708.2i		−	0.568895i	0.958692	−	0.284447i	$-0.0918101\pi$
$752$	14041.0	−	20581.2i	0.680881	−	0.998031i
$753$	−34173.4			−1.65385
$754$	3026.06	+	12205.5i	0.146157	+	0.589521i
$755$	14363.6	−	13455.8i	0.692378	−	0.648616i
$756$	−90.2894	−	964.394i	−0.00434364	−	0.0463950i
$757$	−14381.3	−	34719.5i	−0.690485	−	1.66698i	−0.743802	−	0.668400i	$-0.766979\pi$
$757$	−14381.3	−	34719.5i	−0.690485	−	1.66698i	0.0533168	−	0.998578i	$-0.483021\pi$
$758$	−5295.65	+	35116.6i	−0.253756	+	1.68271i
$759$	6397.63	+	6397.63i	0.305954	+	0.305954i
$760$	15774.3	−	30178.4i	0.752888	−	1.44037i
$761$	9955.61	−	9955.61i	0.474232	−	0.474232i	−0.429049	−	0.903281i	$-0.641151\pi$
$761$	9955.61	−	9955.61i	0.474232	−	0.474232i	0.903281	+	0.429049i	$0.141151\pi$
$762$	15215.6	+	20619.6i	0.723361	+	0.980273i
$763$	−2820.30	+	1168.21i	−0.133816	+	0.0554285i
$764$	15590.8	+	29509.8i	0.738291	+	1.39742i
$765$	7701.86	−	7215.06i	0.364002	−	0.340995i
$766$	−1648.88	+	2736.00i	−0.0777761	+	0.129055i
$767$			9444.70i			0.444626i
$768$	−27234.3	−	525.564i	−1.27960	−	0.0246936i
$769$	−35407.7			−1.66038			−0.830192	−	0.557477i	$-0.811769\pi$
$769$	−35407.7			−1.66038			−0.830192	+	0.557477i	$0.811769\pi$
$770$	−1986.34	+	1367.99i	−0.0929645	+	0.0640247i
$771$	−29032.3	−	12025.6i	−1.35612	−	0.561725i
$772$	−35909.0	+	18971.6i	−1.67409	+	0.884461i
$773$	−30492.8	+	12630.5i	−1.41882	+	0.587695i	−0.954564	−	0.298005i	$-0.903679\pi$
$773$	−30492.8	+	12630.5i	−1.41882	+	0.587695i	−0.464258	+	0.885700i	$0.653679\pi$
$774$	12185.7	−	8992.04i	0.565898	−	0.417587i
$775$	−32330.6	−	2112.39i	−1.49852	−	0.0979088i
$776$	−4969.60	−	280.200i	−0.229894	−	0.0129621i
$777$	−277.305	+	277.305i	−0.0128034	+	0.0128034i
$778$	4433.02	−	29396.3i	0.204282	−	1.35464i
$779$	22368.1	−	9265.16i	1.02878	−	0.426135i
$780$	−4740.53	+	13751.5i	−0.217613	+	0.631261i
$781$	−2081.49	+	5025.15i	−0.0953667	+	0.230236i
$782$	4998.53	−	1239.26i	0.228577	−	0.0566699i
$783$	−11817.7			−0.539373
$784$	17950.5	+	12246.3i	0.817715	+	0.557865i
$785$	−4799.84	−	2174.19i	−0.218234	−	0.0988535i
$786$	30626.4	−	7593.05i	1.38983	−	0.344574i
$787$	−10788.1	−	4468.59i	−0.488634	−	0.202399i	0.124743	−	0.992189i	$-0.460189\pi$
$787$	−10788.1	−	4468.59i	−0.488634	−	0.202399i	−0.613377	+	0.789790i	$0.710189\pi$
$788$	−17355.6	−	14384.0i	−0.784602	−	0.650265i
$789$	−36558.8	+	15143.2i	−1.64959	+	0.683283i
$790$	511.839	+	331.691i	0.0230511	+	0.0149380i
$791$	2005.78	+	2005.78i	0.0901610	+	0.0901610i
$792$	−6927.81	+	14377.5i	−0.310820	+	0.645055i
$793$	8678.98	+	8678.98i	0.388650	+	0.388650i
$794$	−16453.1	−	22296.7i	−0.735391	−	0.996574i
$795$	−617.438	+	18920.2i	−0.0275450	+	0.844063i
$796$	5131.86	+	1583.81i	0.228510	+	0.0705233i
$797$	−7595.53	+	18337.2i	−0.337575	+	0.814979i	0.660372	+	0.750939i	$0.270399\pi$
$797$	−7595.53	+	18337.2i	−0.337575	+	0.814979i	−0.997947	+	0.0640404i	$0.979601\pi$
$798$	2434.30	−	4039.25i	0.107986	−	0.179183i
$799$	−21332.1			−0.944526
$800$	−21141.0	+	8065.90i	−0.934308	+	0.356466i
$801$	7198.62			0.317541
$802$	199.606	−	331.209i	0.00878845	−	0.0145828i
$803$	11097.8	−	26792.4i	0.487711	−	1.17744i
$804$	−7668.43	+	24847.3i	−0.336374	+	1.08992i
$805$	−22.5695	+	691.598i	−0.000988160	+	0.0302803i
$806$	−10644.8	−	14425.4i	−0.465194	−	0.630414i
$807$	2330.87	+	2330.87i	0.101674	+	0.101674i
$808$	35024.4	−	12246.8i	1.52495	−	0.533219i
$809$	31166.1	+	31166.1i	1.35444	+	1.35444i	0.880625	+	0.473815i	$0.157123\pi$
$809$	31166.1	+	31166.1i	1.35444	+	1.35444i	0.473815	+	0.880625i	$0.342877\pi$
$810$	−23814.1	−	15432.4i	−1.03301	−	0.669433i
$811$	−8476.91	+	3511.25i	−0.367034	+	0.152030i	−0.558575	−	0.829454i	$-0.688652\pi$
$811$	−8476.91	+	3511.25i	−0.367034	+	0.152030i	0.191541	+	0.981485i	$0.438652\pi$
$812$	−1728.79	+	2085.94i	−0.0747151	+	0.0901503i
$813$	−2703.73	−	1119.92i	−0.116635	−	0.0483116i
$814$	−3558.72	+	882.296i	−0.153235	+	0.0379907i
$815$	−32621.3	−	14776.5i	−1.40206	−	0.635089i
$816$	12769.7	+	19516.2i	0.547829	+	0.837260i
$817$	−41838.8			−1.79162
$818$	41271.8	−	10232.3i	1.76410	−	0.437365i
$819$	−300.269	+	724.914i	−0.0128111	+	0.0309286i
$820$	−15209.6	−	5243.17i	−0.647734	−	0.223292i
$821$	−19427.2	+	8047.02i	−0.825840	+	0.342074i	−0.755255	−	0.655432i	$-0.772487\pi$
$821$	−19427.2	+	8047.02i	−0.825840	+	0.342074i	−0.0705854	+	0.997506i	$0.522487\pi$
$822$	734.618	−	4871.41i	0.0311712	−	0.206703i
$823$	−19113.2	+	19113.2i	−0.809533	+	0.809533i	−0.984563	−	0.175030i	$-0.943998\pi$
$823$	−19113.2	+	19113.2i	−0.809533	+	0.809533i	0.175030	+	0.984563i	$0.443998\pi$
$824$	8417.33	−	7518.81i	0.355864	−	0.317876i
$825$	−2219.17	+	33964.9i	−0.0936502	+	1.43334i
$826$	−1637.29	+	1208.19i	−0.0689692	+	0.0508936i
$827$	16499.7	−	6834.41i	0.693774	−	0.287371i	−0.00779746	−	0.999970i	$-0.502482\pi$
$827$	16499.7	−	6834.41i	0.693774	−	0.287371i	0.701572	+	0.712599i	$0.252482\pi$
$828$	2138.96	+	4048.58i	0.0897755	+	0.169925i
$829$	18652.0	+	7725.91i	0.781436	+	0.323681i	0.737495	−	0.675353i	$-0.236009\pi$
$829$	18652.0	+	7725.91i	0.781436	+	0.323681i	0.0439411	+	0.999034i	$0.486009\pi$
$830$	19858.2	−	13676.3i	0.830466	−	0.571942i
$831$	42530.8			1.77542
$832$	−10955.5	−	6061.29i	−0.456508	−	0.252569i
$833$		−	18605.4i		−	0.773877i
$834$	13349.3	−	22150.6i	0.554253	−	0.919678i
$835$	26227.2	−	24569.5i	1.08698	−	1.01828i
$836$	38985.0	−	20596.7i	1.61283	−	0.852097i
$837$	15565.5	−	6447.45i	0.642799	−	0.266256i
$838$	−11311.8	−	15329.3i	−0.466300	−	0.631912i
$839$	23768.8	−	23768.8i	0.978058	−	0.978058i	−0.0217064	−	0.999764i	$-0.506910\pi$
$839$	23768.8	−	23768.8i	0.978058	−	0.978058i	0.999764	+	0.0217064i	$0.00690989\pi$
$840$	−2990.32	+	937.326i	−0.122828	+	0.0385010i
$841$	6127.21	+	6127.21i	0.251228	+	0.251228i
$842$	−4148.68	+	27510.8i	−0.169802	+	1.12599i
$843$	−2377.89	−	5740.72i	−0.0971515	−	0.234544i
$844$	−8031.37	+	751.921i	−0.327549	+	0.0306661i
$845$	13046.8	−	12222.2i	0.531151	−	0.497580i
$846$	−4564.21	−	18409.6i	−0.185485	−	0.748151i
$847$	−643.632			−0.0261103
$848$	−15950.1	−	3332.96i	−0.645907	−	0.134970i
$849$		−	35380.4i		−	1.43021i
$850$	15906.1	+	11060.8i	0.641854	+	0.446331i
$851$	−402.554	+	971.852i	−0.0162155	+	0.0391476i
$852$	−4509.76	+	5441.42i	−0.181340	+	0.218803i
$853$	17609.5	+	42513.0i	0.706843	+	1.70647i	0.707743	+	0.706470i	$0.249713\pi$
$853$	17609.5	+	42513.0i	0.706843	+	1.70647i	−0.000900358		1.00000i	$0.500287\pi$
$854$	−394.314	+	2614.78i	−0.0157999	+	0.104773i
$855$	−9134.01	−	24260.9i	−0.365353	−	0.970416i
$856$	40994.5	−	14334.3i	1.63687	−	0.572356i
$857$	4815.01	+	4815.01i	0.191922	+	0.191922i	0.796526	−	0.604604i	$-0.206669\pi$
$857$	4815.01	+	4815.01i	0.191922	+	0.191922i	−0.604604	+	0.796526i	$0.706669\pi$
$858$	−15154.6	+	11182.8i	−0.602994	+	0.444960i
$859$	1051.43	+	2538.37i	0.0417628	+	0.100824i	0.943385	−	0.331701i	$-0.107623\pi$
$859$	1051.43	+	2538.37i	0.0417628	+	0.100824i	−0.901622	+	0.432525i	$0.857623\pi$
$860$	20815.5	+	18429.2i	0.825350	+	0.730735i
$861$	−2058.50	−	852.657i	−0.0814789	−	0.0337497i
$862$	8886.99	−	14746.3i	0.351151	−	0.582669i
$863$		−	15729.2i		−	0.620425i	−0.950667	−	0.310213i	$-0.899600\pi$
$863$		−	15729.2i		−	0.620425i	0.950667	−	0.310213i	$-0.100400\pi$
$864$	8006.40	−	8622.41i	0.315258	−	0.339514i
$865$	−719.256	+	1587.87i	−0.0282722	+	0.0624151i
$866$	−3230.17	−	1946.69i	−0.126750	−	0.0763872i
$867$	−4861.43	+	11736.5i	−0.190430	+	0.459739i
$868$	1139.02	−	3690.66i	0.0445401	−	0.144319i
$869$	302.216	+	729.613i	0.0117974	+	0.0284815i
$870$	7985.34	+	37390.9i	0.311182	+	1.45709i
$871$	−8451.69	+	8451.69i	−0.328788	+	0.328788i
$872$	−33407.0	−	16097.2i	−1.29737	−	0.625137i
$873$	−2679.41	+	2679.41i	−0.103877	+	0.103877i
$874$	1886.32	−	12508.6i	0.0730043	−	0.484107i
$875$	−2011.78	+	1652.07i	−0.0777265	+	0.0638286i
$876$	24044.5	−	29011.8i	0.927384	−	1.11897i
$877$	43021.3	+	17820.0i	1.65647	+	0.686134i	0.997800	−	0.0662956i	$-0.0211180\pi$
$877$	43021.3	+	17820.0i	1.65647	+	0.686134i	0.658673	+	0.752429i	$0.271118\pi$
$878$	−9921.74	−	40019.1i	−0.381370	−	1.53824i
$879$			36978.8i			1.41896i
$880$	−28468.1	−	6924.98i	−1.09052	−	0.265274i
$881$			41962.3i			1.60471i	0.596850	+	0.802353i	$0.296419\pi$
$881$			41962.3i			1.60471i	−0.596850	+	0.802353i	$0.703581\pi$
$882$	16056.5	−	3980.80i	0.612981	−	0.151973i
$883$	30597.6	+	12673.9i	1.16613	+	0.483026i	0.879911	−	0.475139i	$-0.157602\pi$
$883$	30597.6	+	12673.9i	1.16613	+	0.483026i	0.286217	+	0.958165i	$0.407602\pi$
$884$	999.285	+	10673.5i	0.0380199	+	0.406096i
$885$	−936.625	+	28701.1i	−0.0355755	+	1.09014i
$886$	−23831.1	−	3593.77i	−0.903635	−	0.136270i
$887$	23573.1	−	23573.1i	0.892343	−	0.892343i	−0.102400	−	0.994743i	$-0.532652\pi$
$887$	23573.1	−	23573.1i	0.892343	−	0.892343i	0.994743	+	0.102400i	$0.0326523\pi$
$888$	−4756.40	−	268.179i	−0.179746	−	0.0101346i
$889$	−1794.40	+	1794.40i	−0.0676966	+	0.0676966i
$890$	2760.02	+	12923.6i	0.103951	+	0.486743i
$891$	−14061.0	−	33946.3i	−0.528690	−	1.27637i
$892$	−22899.8	+	12098.6i	−0.859578	+	0.454136i
$893$	−20052.6	+	48411.2i	−0.751438	+	1.81413i
$894$	29260.4	−	48552.1i	1.09465	−	1.81636i
$895$	−9776.98	−	4428.68i	−0.365149	−	0.165402i
$896$	−350.696	−	2674.57i	−0.0130758	−	0.0997222i
$897$			5403.55i			0.201136i
$898$	26727.8	+	16107.8i	0.993228	+	0.598579i
$899$	−43536.9	−	18033.6i	−1.61517	−	0.669026i
$900$	−6142.18	+	16093.5i	−0.227488	+	0.596057i
$901$	5339.05	+	12889.6i	0.197414	+	0.476599i
$902$	−12368.6	−	16761.4i	−0.456572	−	0.618730i
$903$	2722.61	+	2722.61i	0.100335	+	0.100335i
$904$	−1939.77	+	34403.6i	−0.0713671	+	1.26576i
$905$	−6085.30	−	16163.2i	−0.223516	−	0.593683i
$906$	32742.2	+	4937.59i	1.20065	+	0.181060i
$907$	−14231.1	−	34357.0i	−0.520989	−	1.25778i	−0.937290	−	0.348551i	$-0.886674\pi$
$907$	−14231.1	−	34357.0i	−0.520989	−	1.25778i	0.416301	−	0.909227i	$-0.363326\pi$
$908$	−25737.9	+	2409.66i	−0.940687	+	0.0880700i
$909$	10809.4	−	26096.3i	0.394419	−	0.952211i
$910$	−1416.56	−	261.133i	−0.0516028	−	0.00951260i
$911$			14141.4i			0.514297i	0.966372	+	0.257149i	$0.0827830\pi$
$911$			14141.4i			0.514297i	−0.966372	+	0.257149i	$0.917217\pi$
$912$	56293.9	−	10634.0i	2.04394	−	0.386105i
$913$	31220.5			1.13171
$914$	−35302.5	+	8752.39i	−1.27758	+	0.316743i
$915$	25513.5	+	27234.9i	0.921804	+	0.983997i
$916$	−2974.84	+	3589.40i	−0.107305	+	0.129473i
$917$	1195.77	+	2886.83i	0.0430618	+	0.103960i
$918$	−9961.89	−	1502.27i	−0.358160	−	0.0540113i
$919$	11961.3	+	11961.3i	0.429343	+	0.429343i	0.888405	−	0.459061i	$-0.151814\pi$
$919$	11961.3	+	11961.3i	0.429343	+	0.429343i	−0.459061	+	0.888405i	$0.651814\pi$
$920$	−6448.29	+	5392.33i	−0.231080	+	0.193239i
$921$	12680.7	−	12680.7i	0.453684	−	0.453684i
$922$	25203.9	−	18598.5i	0.900269	−	0.664325i
$923$	−3001.19	+	1243.13i	−0.107026	+	0.0443318i
$924$	−3877.21	−	1196.59i	−0.138042	−	0.0426028i
$925$	−3747.08	+	1272.82i	−0.133193	+	0.0452433i
$926$	−1095.48	−	660.202i	−0.0388766	−	0.0234294i
$927$		−	8592.15i		−	0.304426i
$928$	−32888.2	+	1218.33i	−1.16337	+	0.0430967i
$929$	−11184.1			−0.394984			−0.197492	−	0.980305i	$-0.563280\pi$
$929$	−11184.1			−0.394984			−0.197492	+	0.980305i	$0.563280\pi$
$930$	−30917.4	−	44892.4i	−1.09013	−	1.58288i
$931$	−42223.2	−	17489.4i	−1.48637	−	0.615674i
$932$	−42116.1	−	12998.0i	−1.48021	−	0.456827i
$933$	57104.8	−	23653.6i	2.00378	−	0.829993i
$934$	−18272.5	−	24762.2i	−0.640145	−	0.867500i
$935$	8838.78	+	23476.7i	0.309154	+	0.821146i
$936$	−8997.42	+	3146.08i	−0.314199	+	0.109864i
$937$	−9304.51	+	9304.51i	−0.324402	+	0.324402i	−0.850453	−	0.526051i	$-0.823672\pi$
$937$	−9304.51	+	9304.51i	−0.324402	+	0.324402i	0.526051	+	0.850453i	$0.323672\pi$
$938$	−2546.30	−	383.987i	−0.0886351	−	0.0133663i
$939$	−47840.0	+	19816.0i	−1.66262	+	0.688680i
$940$	31300.7	−	15252.5i	1.08608	−	0.529236i
$941$	−7972.09	+	19246.3i	−0.276177	+	0.666750i	−0.999723	−	0.0235256i	$-0.992511\pi$
$941$	−7972.09	+	19246.3i	−0.276177	+	0.666750i	0.723546	+	0.690276i	$0.242511\pi$
$942$	−2133.28	−	8604.55i	−0.0737857	−	0.297613i
$943$	−5976.49			−0.206385
$944$	−24195.6	−	5055.95i	−0.834216	−	0.174319i
$945$	558.544	−	1233.07i	0.0192269	−	0.0424463i
$946$	8662.47	+	34939.8i	0.297718	+	1.20084i
$947$	−5552.76	−	2300.03i	−0.190539	−	0.0789238i	0.285374	−	0.958416i	$-0.407882\pi$
$947$	−5552.76	−	2300.03i	−0.190539	−	0.0789238i	−0.475913	+	0.879492i	$0.657882\pi$
$948$	95.6502	+	1021.65i	0.00327698	+	0.0350018i
$949$	16001.3	−	6627.96i	0.547339	−	0.226715i
$950$	40053.4	−	25700.1i	1.36790	−	0.877707i
$951$	6046.40	+	6046.40i	0.206170	+	0.206170i
$952$	−1722.48	+	1538.61i	−0.0586405	+	0.0523808i
$953$	−14990.2	−	14990.2i	−0.509528	−	0.509528i	0.404854	−	0.914381i	$-0.367322\pi$
$953$	−14990.2	−	14990.2i	−0.509528	−	0.509528i	−0.914381	+	0.404854i	$0.867322\pi$
$954$	−9981.39	+	7365.46i	−0.338742	+	0.249964i
$955$	−1521.33	+	46618.4i	−0.0515489	+	1.57962i
$956$	13666.9	−	7220.54i	0.462362	−	0.244277i
$957$	−18945.1	+	45737.6i	−0.639926	+	1.54492i
$958$	38180.0	+	23009.6i	1.28762	+	0.775997i
$959$	487.860			0.0164273
$960$	−32691.2	−	19505.9i	−1.09907	−	0.655780i
$961$	37391.9			1.25514
$962$	−1875.48	−	1130.27i	−0.0628563	−	0.0378810i
$963$	12652.0	−	30544.5i	0.423368	−	1.02210i
$964$	−1580.75	+	835.147i	−0.0528137	+	0.0279028i
$965$	−56727.6	−	1851.24i	−1.89236	−	0.0617548i
$966$	−936.733	+	691.233i	−0.0311997	+	0.0230228i
$967$	17067.8	+	17067.8i	0.567593	+	0.567593i	0.931453	−	0.363860i	$-0.118541\pi$
$967$	17067.8	+	17067.8i	0.567593	+	0.567593i	−0.363860	+	0.931453i	$0.618541\pi$
$968$	−5208.63	−	5831.08i	−0.172946	−	0.193614i
$969$	−34684.9	−	34684.9i	−1.14989	−	1.14989i
$970$	−5837.65	−	3783.03i	−0.193233	−	0.125222i
$971$	−26103.7	+	10812.5i	−0.862726	+	0.357353i	−0.769773	−	0.638318i	$-0.779631\pi$
$971$	−26103.7	+	10812.5i	−0.862726	+	0.357353i	−0.0929528	+	0.995671i	$0.529631\pi$
$972$	−3141.51	−	33554.9i	−0.103667	−	1.10728i
$973$	2366.12	+	980.081i	0.0779594	+	0.0322918i
$974$	6450.85	+	26019.3i	0.212216	+	0.855968i
$975$	−15280.8	+	13406.5i	−0.501926	+	0.440359i
$976$	−26880.0	+	17587.9i	−0.881565	+	0.576819i
$977$	−9744.99			−0.319109			−0.159555	−	0.987189i	$-0.551006\pi$
$977$	−9744.99			−0.319109			−0.159555	+	0.987189i	$0.551006\pi$
$978$	−14498.5	−	58479.3i	−0.474040	−	1.91203i
$979$	−6548.11	+	15808.5i	−0.213768	+	0.516081i
$980$	13302.9	+	27299.8i	0.433618	+	0.889858i
$981$	−26081.6	+	10803.4i	−0.848851	+	0.351606i
$982$	−38140.8	−	5751.70i	−1.23943	−	0.186909i
$983$	−3841.66	+	3841.66i	−0.124649	+	0.124649i	−0.766679	−	0.642030i	$-0.778092\pi$
$983$	−3841.66	+	3841.66i	−0.124649	+	0.124649i	0.642030	+	0.766679i	$0.278092\pi$
$984$	−8933.73	−	25549.4i	−0.289428	−	0.827730i
$985$	−11099.8	−	29482.3i	−0.359055	−	0.953690i
$986$	16731.3	+	22673.7i	0.540399	+	0.732329i
$987$	4455.20	−	1845.40i	0.143678	−	0.0595135i
$988$	25161.8	+	7765.50i	0.810227	+	0.250054i
$989$	9541.73	+	3952.32i	0.306784	+	0.127074i
$990$	−18369.3	+	12650.9i	−0.589711	+	0.406134i
$991$	−49661.6			−1.59188			−0.795940	−	0.605376i	$-0.793023\pi$
$991$	−49661.6			−1.59188			−0.795940	+	0.605376i	$0.793023\pi$
$992$	42653.7	−	19547.8i	1.36518	−	0.625647i
$993$			5697.65i			0.182084i
$994$	−599.422	−	361.248i	−0.0191273	−	0.0115273i
$995$	5131.46	+	5477.68i	0.163496	+	0.174527i
$996$	38761.9	+	11962.8i	1.23315	+	0.380577i
$997$	39411.9	−	16324.9i	1.25194	−	0.518571i	0.344515	−	0.938781i	$-0.388043\pi$
$997$	39411.9	−	16324.9i	1.25194	−	0.518571i	0.907427	+	0.420209i	$0.138043\pi$
$998$	9821.56	−	7247.52i	0.311519	−	0.229876i
$999$	1455.12	−	1455.12i	0.0460841	−	0.0460841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.z.a.29.13	✓	280
5.4	even	2	inner	160.4.z.a.29.58	yes	280
32.21	even	8	inner	160.4.z.a.149.58	yes	280
160.149	even	8	inner	160.4.z.a.149.13	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.z.a.29.13	✓	280	1.1	even	1	trivial
160.4.z.a.29.58	yes	280	5.4	even	2	inner
160.4.z.a.149.13	yes	280	160.149	even	8	inner
160.4.z.a.149.58	yes	280	32.21	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.z (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.42251 - 1.45995i) q^{2} +(2.54494 - 6.14403i) q^{3} +(3.73710 + 7.07348i) q^{4} +(-0.364663 + 11.1744i) q^{5} +(-15.1351 + 11.1685i) q^{6} +(-1.31712 - 1.31712i) q^{7} +(1.27377 - 22.5915i) q^{8} +(-12.1805 - 12.1805i) q^{9} +(17.1974 - 26.5377i) q^{10} +(37.8288 - 15.6692i) q^{11} +(52.9703 - 4.95924i) q^{12} +(22.5926 + 9.35817i) q^{13} +(1.26781 + 5.11367i) q^{14} +(67.7277 + 30.6787i) q^{15} +(-36.0682 + 52.8685i) q^{16} +54.7975 q^{17} +(11.7244 + 47.2902i) q^{18} +(51.5106 - 124.358i) q^{19} +(-80.4046 + 39.1803i) q^{20} +(-11.4444 + 4.74043i) q^{21} +(-114.517 - 17.2693i) q^{22} +(-23.4950 + 23.4950i) q^{23} +(-135.561 - 65.3202i) q^{24} +(-124.734 - 8.14976i) q^{25} +(-41.0684 - 55.6543i) q^{26} +(60.0529 - 24.8747i) q^{27} +(4.39442 - 14.2388i) q^{28} +(-167.969 - 69.5749i) q^{29} +(-119.282 - 173.198i) q^{30} +259.197 q^{31} +(164.561 - 75.4167i) q^{32} -272.298i q^{33} +(-132.747 - 80.0016i) q^{34} +(15.1983 - 14.2377i) q^{35} +(40.6388 - 131.678i) q^{36} +(29.2490 - 12.1153i) q^{37} +(-306.341 + 226.055i) q^{38} +(114.994 - 114.994i) q^{39} +(251.982 + 22.4719i) q^{40} +(127.187 + 127.187i) q^{41} +(34.6450 + 5.22453i) q^{42} +(-118.949 - 287.169i) q^{43} +(252.205 + 209.024i) q^{44} +(140.551 - 131.668i) q^{45} +(91.2182 - 22.6153i) q^{46} -389.290 q^{47} +(233.034 + 356.151i) q^{48} -339.530i q^{49} +(290.271 + 201.848i) q^{50} +(139.456 - 336.677i) q^{51} +(18.2360 + 194.781i) q^{52} +(97.4325 + 235.223i) q^{53} +(-181.795 - 27.4150i) q^{54} +(161.299 + 428.427i) q^{55} +(-31.4335 + 28.0781i) q^{56} +(-632.966 - 632.966i) q^{57} +(305.330 + 413.772i) q^{58} +(147.801 + 356.822i) q^{59} +(36.1002 + 593.720i) q^{60} +(463.711 + 192.076i) q^{61} +(-627.906 - 378.414i) q^{62} +32.0863i q^{63} +(-508.755 - 57.5530i) q^{64} +(-112.811 + 249.046i) q^{65} +(-397.542 + 659.645i) q^{66} +(-187.045 + 451.568i) q^{67} +(204.783 + 387.609i) q^{68} +(84.5604 + 204.147i) q^{69} +(-57.6044 + 12.3022i) q^{70} +(-93.9317 + 93.9317i) q^{71} +(-290.691 + 259.661i) q^{72} +(500.811 - 500.811i) q^{73} +(-88.5436 - 13.3525i) q^{74} +(-367.513 + 745.629i) q^{75} +(1072.14 - 100.377i) q^{76} +(-70.4633 - 29.1868i) q^{77} +(-446.458 + 110.688i) q^{78} +19.2873i q^{79} +(-577.621 - 422.320i) q^{80} -897.368i q^{81} +(-122.425 - 493.797i) q^{82} +(704.447 + 291.791i) q^{83} +(-76.3003 - 63.2364i) q^{84} +(-19.9826 + 612.329i) q^{85} +(-131.097 + 869.330i) q^{86} +(-854.941 + 854.941i) q^{87} +(-305.806 - 874.569i) q^{88} +(-295.498 + 295.498i) q^{89} +(-532.715 + 113.768i) q^{90} +(-17.4314 - 42.0830i) q^{91} +(-253.994 - 78.3882i) q^{92} +(659.640 - 1592.51i) q^{93} +(943.058 + 568.344i) q^{94} +(1370.84 + 620.948i) q^{95} +(-44.5647 - 1203.00i) q^{96} -219.976i q^{97} +(-495.697 + 822.515i) q^{98} +(-651.631 - 269.914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} + 200 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 464 q^{24} - 4 q^{25} - 48 q^{26} - 8 q^{29} + 1124 q^{30} + 1472 q^{31} - 72 q^{34}+ \cdots + 5520 q^{99}+O(q^{100}) \) 280 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 + 200 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 464 * q^24 - 4 * q^25 - 48 * q^26 - 8 * q^29 + 1124 * q^30 + 1472 * q^31 - 72 * q^34 - 460 * q^35 - 888 * q^36 - 8 * q^39 - 1112 * q^40 - 8 * q^41 - 8 * q^44 - 112 * q^45 - 8 * q^46 + 3556 * q^50 - 1712 * q^51 + 856 * q^54 + 284 * q^55 + 328 * q^56 - 1384 * q^59 - 5248 * q^60 - 1832 * q^61 + 832 * q^64 - 8 * q^65 + 6088 * q^66 + 1048 * q^69 - 616 * q^70 + 216 * q^71 - 2064 * q^74 + 2204 * q^75 - 5128 * q^76 - 656 * q^80 - 6904 * q^84 - 504 * q^85 - 1192 * q^86 - 8 * q^89 + 2720 * q^90 - 8 * q^91 - 920 * q^94 - 8 * q^95 - 4152 * q^96 + 5520 * q^99

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