LMFDB - Embedded newform 160.4.o.a.47.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,4,Mod(47,160)] 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("160.47"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.o (of order $4$, degree $2$, not 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:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.9
Character	$\chi$	$=$	160.47
Dual form			160.4.o.a.143.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.56085 - 1.56085i) q^{3} +(-10.5634 - 3.66270i) q^{5} +(18.5221 - 18.5221i) q^{7} +22.1275i q^{9} -13.0709 q^{11} +(-51.6789 - 51.6789i) q^{13} +(-22.2047 + 10.7709i) q^{15} +(-57.6873 - 57.6873i) q^{17} -28.4226i q^{19} -57.8204i q^{21} +(-102.782 - 102.782i) q^{23} +(98.1693 + 77.3808i) q^{25} +(76.6805 + 76.6805i) q^{27} -9.08265 q^{29} -115.940i q^{31} +(-20.4017 + 20.4017i) q^{33} +(-263.497 + 127.815i) q^{35} +(-19.9147 + 19.9147i) q^{37} -161.325 q^{39} -96.6271 q^{41} +(285.182 - 285.182i) q^{43} +(81.0464 - 233.741i) q^{45} +(-5.83951 + 5.83951i) q^{47} -343.139i q^{49} -180.082 q^{51} +(291.191 + 291.191i) q^{53} +(138.073 + 47.8749i) q^{55} +(-44.3632 - 44.3632i) q^{57} +184.669i q^{59} +270.307i q^{61} +(409.849 + 409.849i) q^{63} +(356.619 + 735.187i) q^{65} +(151.797 + 151.797i) q^{67} -320.854 q^{69} +742.577i q^{71} +(40.1228 - 40.1228i) q^{73} +(274.007 - 32.4477i) q^{75} +(-242.102 + 242.102i) q^{77} +1106.08 q^{79} -358.070 q^{81} +(807.395 - 807.395i) q^{83} +(398.081 + 820.663i) q^{85} +(-14.1766 + 14.1766i) q^{87} -1122.56i q^{89} -1914.41 q^{91} +(-180.965 - 180.965i) q^{93} +(-104.103 + 300.238i) q^{95} +(424.428 + 424.428i) q^{97} -289.228i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 8 q^{11} + 48 q^{17} + 40 q^{25} - 104 q^{27} - 112 q^{33} + 460 q^{35} - 8 q^{41} + 868 q^{43} - 1480 q^{51} + 104 q^{57} + 520 q^{65} + 1852 q^{67} - 744 q^{73} - 3300 q^{75} - 1240 q^{81}+ \cdots - 584 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 8 * q^11 + 48 * q^17 + 40 * q^25 - 104 * q^27 - 112 * q^33 + 460 * q^35 - 8 * q^41 + 868 * q^43 - 1480 * q^51 + 104 * q^57 + 520 * q^65 + 1852 * q^67 - 744 * q^73 - 3300 * q^75 - 1240 * q^81 - 2676 * q^83 + 1704 * q^91 - 584 * q^97

Character values

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

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	1.56085	−	1.56085i	0.300385	−	0.300385i	−0.540779	−	0.841164i	$-0.681871\pi$
$3$	1.56085	−	1.56085i	0.300385	−	0.300385i	0.841164	+	0.540779i	$0.181871\pi$
$4$		0			0
$5$	−10.5634	−	3.66270i	−0.944816	−	0.327601i
$5$	−10.5634	−	3.66270i	−0.944816	−	0.327601i
$6$		0			0
$7$	18.5221	−	18.5221i	1.00010	−	1.00010i	0.000101443	−	1.00000i	$-0.499968\pi$
$7$	18.5221	−	18.5221i	1.00010	−	1.00010i	1.00000		0.000101443i	$-3.22903e-5\pi$
$8$		0			0
$9$			22.1275i			0.819538i
$10$		0			0
$11$	−13.0709			−0.358276			−0.179138	−	0.983824i	$-0.557331\pi$
$11$	−13.0709			−0.358276			−0.179138	+	0.983824i	$0.557331\pi$
$12$		0			0
$13$	−51.6789	−	51.6789i	−1.10255	−	1.10255i	−0.994102	−	0.108447i	$-0.965412\pi$
$13$	−51.6789	−	51.6789i	−1.10255	−	1.10255i	−0.108447	−	0.994102i	$-0.534588\pi$
$14$		0			0
$15$	−22.2047	+	10.7709i	−0.382215	+	0.185402i
$16$		0			0
$17$	−57.6873	−	57.6873i	−0.823013	−	0.823013i	0.163526	−	0.986539i	$-0.447713\pi$
$17$	−57.6873	−	57.6873i	−0.823013	−	0.823013i	−0.986539	+	0.163526i	$0.947713\pi$
$18$		0			0
$19$		−	28.4226i		−	0.343188i	−0.985168	−	0.171594i	$-0.945108\pi$
$19$		−	28.4226i		−	0.343188i	0.985168	−	0.171594i	$-0.0548918\pi$
$20$		0			0
$21$		−	57.8204i		−	0.600831i
$22$		0			0
$23$	−102.782	−	102.782i	−0.931806	−	0.931806i	0.0660125	−	0.997819i	$-0.478972\pi$
$23$	−102.782	−	102.782i	−0.931806	−	0.931806i	−0.997819	+	0.0660125i	$0.978972\pi$
$24$		0			0
$25$	98.1693	+	77.3808i	0.785355	+	0.619046i
$26$		0			0
$27$	76.6805	+	76.6805i	0.546562	+	0.546562i
$28$		0			0
$29$	−9.08265			−0.0581588			−0.0290794	−	0.999577i	$-0.509258\pi$
$29$	−9.08265			−0.0581588			−0.0290794	+	0.999577i	$0.509258\pi$
$30$		0			0
$31$		−	115.940i		−	0.671726i	−0.941911	−	0.335863i	$-0.890972\pi$
$31$		−	115.940i		−	0.671726i	0.941911	−	0.335863i	$-0.109028\pi$
$32$		0			0
$33$	−20.4017	+	20.4017i	−0.107621	+	0.107621i
$34$		0			0
$35$	−263.497	+	127.815i	−1.27255	+	0.617277i
$36$		0			0
$37$	−19.9147	+	19.9147i	−0.0884853	+	0.0884853i	−0.749964	−	0.661479i	$-0.769929\pi$
$37$	−19.9147	+	19.9147i	−0.0884853	+	0.0884853i	0.661479	+	0.749964i	$0.269929\pi$
$38$		0			0
$39$	−161.325			−0.662378
$40$		0			0
$41$	−96.6271			−0.368064			−0.184032	−	0.982920i	$-0.558915\pi$
$41$	−96.6271			−0.368064			−0.184032	+	0.982920i	$0.558915\pi$
$42$		0			0
$43$	285.182	−	285.182i	1.01139	−	1.01139i	0.0114565	−	0.999934i	$-0.496353\pi$
$43$	285.182	−	285.182i	1.01139	−	1.01139i	0.999934	−	0.0114565i	$-0.00364679\pi$
$44$		0			0
$45$	81.0464	−	233.741i	0.268482	−	0.774312i
$46$		0			0
$47$	−5.83951	+	5.83951i	−0.0181230	+	0.0181230i	−0.716110	−	0.697987i	$-0.754079\pi$
$47$	−5.83951	+	5.83951i	−0.0181230	+	0.0181230i	0.697987	+	0.716110i	$0.254079\pi$
$48$		0			0
$49$		−	343.139i		−	1.00041i
$50$		0			0
$51$	−180.082			−0.494442
$52$		0			0
$53$	291.191	+	291.191i	0.754683	+	0.754683i	0.975349	−	0.220666i	$-0.0708232\pi$
$53$	291.191	+	291.191i	0.754683	+	0.754683i	−0.220666	+	0.975349i	$0.570823\pi$
$54$		0			0
$55$	138.073	+	47.8749i	0.338505	+	0.117372i
$56$		0			0
$57$	−44.3632	−	44.3632i	−0.103089	−	0.103089i
$58$		0			0
$59$			184.669i			0.407489i	0.979024	+	0.203744i	$0.0653111\pi$
$59$			184.669i			0.407489i	−0.979024	+	0.203744i	$0.934689\pi$
$60$		0			0
$61$			270.307i			0.567365i	0.958918	+	0.283682i	$0.0915561\pi$
$61$			270.307i			0.567365i	−0.958918	+	0.283682i	$0.908444\pi$
$62$		0			0
$63$	409.849	+	409.849i	0.819621	+	0.819621i
$64$		0			0
$65$	356.619	+	735.187i	0.680509	+	1.40290i
$66$		0			0
$67$	151.797	+	151.797i	0.276790	+	0.276790i	0.831826	−	0.555036i	$-0.187296\pi$
$67$	151.797	+	151.797i	0.276790	+	0.276790i	−0.555036	+	0.831826i	$0.687296\pi$
$68$		0			0
$69$	−320.854			−0.559801
$70$		0			0
$71$			742.577i			1.24123i	0.784114	+	0.620617i	$0.213118\pi$
$71$			742.577i			1.24123i	−0.784114	+	0.620617i	$0.786882\pi$
$72$		0			0
$73$	40.1228	−	40.1228i	0.0643289	−	0.0643289i	−0.674210	−	0.738539i	$-0.735516\pi$
$73$	40.1228	−	40.1228i	0.0643289	−	0.0643289i	0.738539	+	0.674210i	$0.235516\pi$
$74$		0			0
$75$	274.007	−	32.4477i	0.421861	−	0.0499565i
$76$		0			0
$77$	−242.102	+	242.102i	−0.358313	+	0.358313i
$78$		0			0
$79$	1106.08			1.57524			0.787618	−	0.616164i	$-0.211314\pi$
$79$	1106.08			1.57524			0.787618	+	0.616164i	$0.211314\pi$
$80$		0			0
$81$	−358.070			−0.491180
$82$		0			0
$83$	807.395	−	807.395i	1.06775	−	1.06775i	0.0702169	−	0.997532i	$-0.477631\pi$
$83$	807.395	−	807.395i	1.06775	−	1.06775i	0.997532	−	0.0702169i	$-0.0223691\pi$
$84$		0			0
$85$	398.081	+	820.663i	0.507976	+	1.04722i
$86$		0			0
$87$	−14.1766	+	14.1766i	−0.0174700	+	0.0174700i
$88$		0			0
$89$		−	1122.56i		−	1.33698i	−0.743722	−	0.668489i	$-0.766941\pi$
$89$		−	1122.56i		−	1.33698i	0.743722	−	0.668489i	$-0.233059\pi$
$90$		0			0
$91$	−1914.41			−2.20532
$92$		0			0
$93$	−180.965	−	180.965i	−0.201776	−	0.201776i
$94$		0			0
$95$	−104.103	+	300.238i	−0.112429	+	0.324250i
$96$		0			0
$97$	424.428	+	424.428i	0.444270	+	0.444270i	0.893444	−	0.449175i	$-0.148282\pi$
$97$	424.428	+	424.428i	0.444270	+	0.444270i	−0.449175	+	0.893444i	$0.648282\pi$
$98$		0			0
$99$		−	289.228i		−	0.293621i
$100$		0			0
$101$		−	51.8161i		−	0.0510485i	−0.999674	−	0.0255242i	$-0.991874\pi$
$101$		−	51.8161i		−	0.0510485i	0.999674	−	0.0255242i	$-0.00812550\pi$
$102$		0			0
$103$	−1192.28	−	1192.28i	−1.14057	−	1.14057i	−0.988345	−	0.152228i	$-0.951355\pi$
$103$	−1192.28	−	1192.28i	−1.14057	−	1.14057i	−0.152228	−	0.988345i	$-0.548645\pi$
$104$		0			0
$105$	−211.779	+	610.778i	−0.196833	+	0.567675i
$106$		0			0
$107$	744.659	+	744.659i	0.672793	+	0.672793i	0.958359	−	0.285566i	$-0.0921815\pi$
$107$	744.659	+	744.659i	0.672793	+	0.672793i	−0.285566	+	0.958359i	$0.592182\pi$
$108$		0			0
$109$	1019.02			0.895451			0.447726	−	0.894171i	$-0.352234\pi$
$109$	1019.02			0.895451			0.447726	+	0.894171i	$0.352234\pi$
$110$		0			0
$111$			62.1676i			0.0531593i
$112$		0			0
$113$	302.602	−	302.602i	0.251915	−	0.251915i	−0.569841	−	0.821755i	$-0.692995\pi$
$113$	302.602	−	302.602i	0.251915	−	0.251915i	0.821755	+	0.569841i	$0.192995\pi$
$114$		0			0
$115$	709.265	+	1462.18i	0.575124	+	1.18565i
$116$		0			0
$117$	1143.53	−	1143.53i	0.903581	−	0.903581i
$118$		0			0
$119$	−2136.98			−1.64619
$120$		0			0
$121$	−1160.15			−0.871638
$122$		0			0
$123$	−150.820	+	150.820i	−0.110561	+	0.110561i
$124$		0			0
$125$	−753.576	−	1176.97i	−0.539215	−	0.842168i
$126$		0			0
$127$	658.914	−	658.914i	0.460387	−	0.460387i	−0.438395	−	0.898782i	$-0.644453\pi$
$127$	658.914	−	658.914i	0.460387	−	0.460387i	0.898782	+	0.438395i	$0.144453\pi$
$128$		0			0
$129$		−	890.249i		−	0.607613i
$130$		0			0
$131$	−449.934			−0.300083			−0.150042	−	0.988680i	$-0.547941\pi$
$131$	−449.934			−0.300083			−0.150042	+	0.988680i	$0.547941\pi$
$132$		0			0
$133$	−526.446	−	526.446i	−0.343223	−	0.343223i
$134$		0			0
$135$	−529.147	−	1090.86i	−0.337346	−	0.695455i
$136$		0			0
$137$	1186.91	+	1186.91i	0.740182	+	0.740182i	0.972613	−	0.232431i	$-0.0746679\pi$
$137$	1186.91	+	1186.91i	0.740182	+	0.740182i	−0.232431	+	0.972613i	$0.574668\pi$
$138$		0			0
$139$		−	2289.25i		−	1.39692i	−0.715650	−	0.698459i	$-0.753869\pi$
$139$		−	2289.25i		−	1.39692i	0.715650	−	0.698459i	$-0.246131\pi$
$140$		0			0
$141$			18.2292i			0.0108877i
$142$		0			0
$143$	675.492	+	675.492i	0.395017	+	0.395017i
$144$		0			0
$145$	95.9434	+	33.2670i	0.0549494	+	0.0190529i
$146$		0			0
$147$	−535.587	−	535.587i	−0.300507	−	0.300507i
$148$		0			0
$149$	−3135.20			−1.72380			−0.861899	−	0.507080i	$-0.830725\pi$
$149$	−3135.20			−1.72380			−0.861899	+	0.507080i	$0.830725\pi$
$150$		0			0
$151$		−	2401.48i		−	1.29424i	−0.762389	−	0.647118i	$-0.775974\pi$
$151$		−	2401.48i		−	1.29424i	0.762389	−	0.647118i	$-0.224026\pi$
$152$		0			0
$153$	1276.48	−	1276.48i	0.674490	−	0.674490i
$154$		0			0
$155$	−424.654	+	1224.72i	−0.220058	+	0.634657i
$156$		0			0
$157$	−1154.01	+	1154.01i	−0.586623	+	0.586623i	−0.936715	−	0.350092i	$-0.886150\pi$
$157$	−1154.01	+	1154.01i	−0.586623	+	0.586623i	0.350092	+	0.936715i	$0.386150\pi$
$158$		0			0
$159$	909.009			0.453391
$160$		0			0
$161$	−3807.49			−1.86380
$162$		0			0
$163$	−554.582	+	554.582i	−0.266492	+	0.266492i	−0.827685	−	0.561193i	$-0.810343\pi$
$163$	−554.582	+	554.582i	−0.266492	+	0.266492i	0.561193	+	0.827685i	$0.310343\pi$
$164$		0			0
$165$	290.236	−	140.786i	0.136939	−	0.0664251i
$166$		0			0
$167$	−1710.74	+	1710.74i	−0.792700	+	0.792700i	−0.981932	−	0.189232i	$-0.939400\pi$
$167$	−1710.74	+	1710.74i	−0.792700	+	0.792700i	0.189232	+	0.981932i	$0.439400\pi$
$168$		0			0
$169$			3144.41i			1.43123i
$170$		0			0
$171$	628.921			0.281256
$172$		0			0
$173$	−865.781	−	865.781i	−0.380486	−	0.380486i	0.490791	−	0.871277i	$-0.336708\pi$
$173$	−865.781	−	865.781i	−0.380486	−	0.380486i	−0.871277	+	0.490791i	$0.836708\pi$
$174$		0			0
$175$	3251.56	−	385.048i	1.40454	−	0.166325i
$176$		0			0
$177$	288.239	+	288.239i	0.122403	+	0.122403i
$178$		0			0
$179$		−	1481.79i		−	0.618739i	−0.950942	−	0.309370i	$-0.899882\pi$
$179$		−	1481.79i		−	0.618739i	0.950942	−	0.309370i	$-0.100118\pi$
$180$		0			0
$181$		−	1632.92i		−	0.670573i	−0.942116	−	0.335286i	$-0.891167\pi$
$181$		−	1632.92i		−	0.670573i	0.942116	−	0.335286i	$-0.108833\pi$
$182$		0			0
$183$	421.907	+	421.907i	0.170428	+	0.170428i
$184$		0			0
$185$	283.308	−	137.425i	0.112590	−	0.0546144i
$186$		0			0
$187$	754.028	+	754.028i	0.294866	+	0.294866i
$188$		0			0
$189$	2840.57			1.09323
$190$		0			0
$191$			2140.07i			0.810732i	0.914154	+	0.405366i	$0.132856\pi$
$191$			2140.07i			0.810732i	−0.914154	+	0.405366i	$0.867144\pi$
$192$		0			0
$193$	2959.91	−	2959.91i	1.10393	−	1.10393i	0.110000	−	0.993932i	$-0.464915\pi$
$193$	2959.91	−	2959.91i	1.10393	−	1.10393i	0.993932	−	0.110000i	$-0.0350851\pi$
$194$		0			0
$195$	1704.14	+	590.886i	0.625826	+	0.216996i
$196$		0			0
$197$	−277.029	+	277.029i	−0.100190	+	0.100190i	−0.755425	−	0.655235i	$-0.772570\pi$
$197$	−277.029	+	277.029i	−0.100190	+	0.100190i	0.655235	+	0.755425i	$0.272570\pi$
$198$		0			0
$199$	−2049.30			−0.730005			−0.365003	−	0.931007i	$-0.618932\pi$
$199$	−2049.30			−0.730005			−0.365003	+	0.931007i	$0.618932\pi$
$200$		0			0
$201$	473.863			0.166287
$202$		0			0
$203$	−168.230	+	168.230i	−0.0581647	+	0.0581647i
$204$		0			0
$205$	1020.71	+	353.916i	0.347753	+	0.120578i
$206$		0			0
$207$	2274.31	−	2274.31i	0.763651	−	0.763651i
$208$		0			0
$209$			371.510i			0.122956i
$210$		0			0
$211$	−369.963			−0.120708			−0.0603538	−	0.998177i	$-0.519223\pi$
$211$	−369.963			−0.120708			−0.0603538	+	0.998177i	$0.519223\pi$
$212$		0			0
$213$	1159.05	+	1159.05i	0.372848	+	0.372848i
$214$		0			0
$215$	−4057.01	+	1967.94i	−1.28691	+	0.624245i
$216$		0			0
$217$	−2147.46	−	2147.46i	−0.671794	−	0.671794i
$218$		0			0
$219$		−	125.251i		−	0.0386469i
$220$		0			0
$221$			5962.43i			1.81482i
$222$		0			0
$223$	1977.85	+	1977.85i	0.593933	+	0.593933i	0.938691	−	0.344759i	$-0.112039\pi$
$223$	1977.85	+	1977.85i	0.593933	+	0.593933i	−0.344759	+	0.938691i	$0.612039\pi$
$224$		0			0
$225$	−1712.24	+	2172.24i	−0.507332	+	0.643628i
$226$		0			0
$227$	−1647.44	−	1647.44i	−0.481693	−	0.481693i	0.423979	−	0.905672i	$-0.360633\pi$
$227$	−1647.44	−	1647.44i	−0.481693	−	0.481693i	−0.905672	+	0.423979i	$0.860633\pi$
$228$		0			0
$229$	4265.02			1.23074			0.615372	−	0.788237i	$-0.289006\pi$
$229$	4265.02			1.23074			0.615372	+	0.788237i	$0.289006\pi$
$230$		0			0
$231$			755.767i			0.215263i
$232$		0			0
$233$	−628.530	+	628.530i	−0.176723	+	0.176723i	−0.789925	−	0.613203i	$-0.789881\pi$
$233$	−628.530	+	628.530i	−0.176723	+	0.176723i	0.613203	+	0.789925i	$0.289881\pi$
$234$		0			0
$235$	83.0732	−	40.2965i	0.0230600	−	0.0111858i
$236$		0			0
$237$	1726.42	−	1726.42i	0.473177	−	0.473177i
$238$		0			0
$239$	2845.14			0.770028			0.385014	−	0.922911i	$-0.374197\pi$
$239$	2845.14			0.770028			0.385014	+	0.922911i	$0.374197\pi$
$240$		0			0
$241$	3330.81			0.890275			0.445138	−	0.895462i	$-0.353155\pi$
$241$	3330.81			0.890275			0.445138	+	0.895462i	$0.353155\pi$
$242$		0			0
$243$	−2629.27	+	2629.27i	−0.694105	+	0.694105i
$244$		0			0
$245$	−1256.81	+	3624.70i	−0.327734	+	0.945199i
$246$		0			0
$247$	−1468.85	+	1468.85i	−0.378382	+	0.378382i
$248$		0			0
$249$		−	2520.44i		−	0.641471i
$250$		0			0
$251$	3887.66			0.977638			0.488819	−	0.872385i	$-0.337428\pi$
$251$	3887.66			0.977638			0.488819	+	0.872385i	$0.337428\pi$
$252$		0			0
$253$	1343.46	+	1343.46i	0.333844	+	0.333844i
$254$		0			0
$255$	1902.27	+	659.585i	0.467156	+	0.161980i
$256$		0			0
$257$	2310.47	+	2310.47i	0.560790	+	0.560790i	0.929532	−	0.368742i	$-0.120211\pi$
$257$	2310.47	+	2310.47i	0.560790	+	0.560790i	−0.368742	+	0.929532i	$0.620211\pi$
$258$		0			0
$259$			737.726i			0.176989i
$260$		0			0
$261$		−	200.977i		−	0.0476634i
$262$		0			0
$263$	−2756.14	−	2756.14i	−0.646202	−	0.646202i	0.305871	−	0.952073i	$-0.401052\pi$
$263$	−2756.14	−	2756.14i	−0.646202	−	0.646202i	−0.952073	+	0.305871i	$0.901052\pi$
$264$		0			0
$265$	−2009.41	−	4142.50i	−0.465801	−	0.960272i
$266$		0			0
$267$	−1752.14	−	1752.14i	−0.401608	−	0.401608i
$268$		0			0
$269$	−4022.51			−0.911736			−0.455868	−	0.890047i	$-0.650671\pi$
$269$	−4022.51			−0.911736			−0.455868	+	0.890047i	$0.650671\pi$
$270$		0			0
$271$			3298.25i			0.739314i	0.929168	+	0.369657i	$0.120525\pi$
$271$			3298.25i			0.739314i	−0.929168	+	0.369657i	$0.879475\pi$
$272$		0			0
$273$	−2988.09	+	2988.09i	−0.662445	+	0.662445i
$274$		0			0
$275$	−1283.17	−	1011.44i	−0.281374	−	0.221790i
$276$		0			0
$277$	45.1601	−	45.1601i	0.00979569	−	0.00979569i	−0.702192	−	0.711988i	$-0.747795\pi$
$277$	45.1601	−	45.1601i	0.00979569	−	0.00979569i	0.711988	+	0.702192i	$0.247795\pi$
$278$		0			0
$279$	2565.47			0.550505
$280$		0			0
$281$	5107.58			1.08431			0.542157	−	0.840277i	$-0.317608\pi$
$281$	5107.58			1.08431			0.542157	+	0.840277i	$0.317608\pi$
$282$		0			0
$283$	4963.39	−	4963.39i	1.04255	−	1.04255i	0.0435010	−	0.999053i	$-0.486149\pi$
$283$	4963.39	−	4963.39i	1.04255	−	1.04255i	0.999053	−	0.0435010i	$-0.0138512\pi$
$284$		0			0
$285$	306.136	+	631.114i	0.0636278	+	0.131172i
$286$		0			0
$287$	−1789.74	+	1789.74i	−0.368101	+	0.368101i
$288$		0			0
$289$			1742.65i			0.354702i
$290$		0			0
$291$	1324.93			0.266904
$292$		0			0
$293$	−1209.67	−	1209.67i	−0.241192	−	0.241192i	0.576151	−	0.817343i	$-0.304554\pi$
$293$	−1209.67	−	1209.67i	−0.241192	−	0.241192i	−0.817343	+	0.576151i	$0.804554\pi$
$294$		0			0
$295$	676.386	−	1950.72i	0.133494	−	0.385002i
$296$		0			0
$297$	−1002.29	−	1002.29i	−0.195820	−	0.195820i
$298$		0			0
$299$			10623.3i			2.05472i
$300$		0			0
$301$		−	10564.4i		−	2.02299i
$302$		0			0
$303$	−80.8770	−	80.8770i	−0.0153342	−	0.0153342i
$304$		0			0
$305$	990.052	−	2855.35i	0.185870	−	0.536055i
$306$		0			0
$307$	913.033	+	913.033i	0.169738	+	0.169738i	0.786864	−	0.617126i	$-0.211703\pi$
$307$	913.033	+	913.033i	0.169738	+	0.169738i	−0.617126	+	0.786864i	$0.711703\pi$
$308$		0			0
$309$	−3721.94			−0.685222
$310$		0			0
$311$		−	6480.20i		−	1.18154i	−0.806841	−	0.590769i	$-0.798824\pi$
$311$		−	6480.20i		−	1.18154i	0.806841	−	0.590769i	$-0.201176\pi$
$312$		0			0
$313$	−7227.98	+	7227.98i	−1.30527	+	1.30527i	−0.380481	+	0.924789i	$0.624241\pi$
$313$	−7227.98	+	7227.98i	−1.30527	+	1.30527i	−0.924789	+	0.380481i	$0.875759\pi$
$314$		0			0
$315$	−2828.23	−	5830.54i	−0.505882	−	1.04290i
$316$		0			0
$317$	−2011.28	+	2011.28i	−0.356356	+	0.356356i	−0.862468	−	0.506112i	$-0.831082\pi$
$317$	−2011.28	+	2011.28i	−0.356356	+	0.356356i	0.506112	+	0.862468i	$0.331082\pi$
$318$		0			0
$319$	118.719			0.0208369
$320$		0			0
$321$	2324.60			0.404194
$322$		0			0
$323$	−1639.62	+	1639.62i	−0.282449	+	0.282449i
$324$		0			0
$325$	−1074.33	−	9072.23i	−0.183363	−	1.54842i
$326$		0			0
$327$	1590.53	−	1590.53i	0.268980	−	0.268980i
$328$		0			0
$329$			216.320i			0.0362496i
$330$		0			0
$331$	−5760.25			−0.956532			−0.478266	−	0.878215i	$-0.658735\pi$
$331$	−5760.25			−0.956532			−0.478266	+	0.878215i	$0.658735\pi$
$332$		0			0
$333$	−440.663	−	440.663i	−0.0725171	−	0.0725171i
$334$		0			0
$335$	−1047.50	−	2159.47i	−0.170839	−	0.352193i
$336$		0			0
$337$	−5516.83	−	5516.83i	−0.891753	−	0.891753i	0.102935	−	0.994688i	$-0.467177\pi$
$337$	−5516.83	−	5516.83i	−0.891753	−	0.891753i	−0.994688	+	0.102935i	$0.967177\pi$
$338$		0			0
$339$		−	944.629i		−	0.151343i
$340$		0			0
$341$			1515.45i			0.240663i
$342$		0			0
$343$	−2.57791	−	2.57791i	−0.000405814	−	0.000405814i
$344$		0			0
$345$	3389.30	+	1175.19i	0.528909	+	0.183392i
$346$		0			0
$347$	−2447.45	−	2447.45i	−0.378634	−	0.378634i	0.491975	−	0.870609i	$-0.336275\pi$
$347$	−2447.45	−	2447.45i	−0.378634	−	0.378634i	−0.870609	+	0.491975i	$0.836275\pi$
$348$		0			0
$349$	−5458.15			−0.837158			−0.418579	−	0.908180i	$-0.637472\pi$
$349$	−5458.15			−0.837158			−0.418579	+	0.908180i	$0.637472\pi$
$350$		0			0
$351$		−	7925.52i		−	1.20522i
$352$		0			0
$353$	−1843.89	+	1843.89i	−0.278018	+	0.278018i	−0.832317	−	0.554299i	$-0.812986\pi$
$353$	−1843.89	+	1843.89i	−0.278018	+	0.278018i	0.554299	+	0.832317i	$0.312986\pi$
$354$		0			0
$355$	2719.83	−	7844.11i	0.406630	−	1.17274i
$356$		0			0
$357$	−3335.50	+	3335.50i	−0.494492	+	0.494492i
$358$		0			0
$359$	−7558.73			−1.11124			−0.555619	−	0.831437i	$-0.687519\pi$
$359$	−7558.73			−1.11124			−0.555619	+	0.831437i	$0.687519\pi$
$360$		0			0
$361$	6051.16			0.882222
$362$		0			0
$363$	−1810.82	+	1810.82i	−0.261827	+	0.261827i
$364$		0			0
$365$	−570.789	+	276.874i	−0.0818533	+	0.0397048i
$366$		0			0
$367$	2308.09	−	2308.09i	0.328287	−	0.328287i	−0.523648	−	0.851935i	$-0.675429\pi$
$367$	2308.09	−	2308.09i	0.328287	−	0.328287i	0.851935	+	0.523648i	$0.175429\pi$
$368$		0			0
$369$		−	2138.12i		−	0.301642i
$370$		0			0
$371$	10787.0			1.50952
$372$		0			0
$373$	985.468	+	985.468i	0.136798	+	0.136798i	0.772190	−	0.635392i	$-0.219161\pi$
$373$	985.468	+	985.468i	0.136798	+	0.136798i	−0.635392	+	0.772190i	$0.719161\pi$
$374$		0			0
$375$	−3013.28	−	660.846i	−0.414947	−	0.0910025i
$376$		0			0
$377$	469.381	+	469.381i	0.0641230	+	0.0641230i
$378$		0			0
$379$			9451.57i			1.28099i	0.767963	+	0.640494i	$0.221270\pi$
$379$			9451.57i			1.28099i	−0.767963	+	0.640494i	$0.778730\pi$
$380$		0			0
$381$		−	2056.93i		−	0.276587i
$382$		0			0
$383$	−1316.62	−	1316.62i	−0.175655	−	0.175655i	0.613804	−	0.789459i	$-0.289639\pi$
$383$	−1316.62	−	1316.62i	−0.175655	−	0.175655i	−0.789459	+	0.613804i	$0.789639\pi$
$384$		0			0
$385$	3444.16	−	1670.66i	0.455923	−	0.221156i
$386$		0			0
$387$	6310.36	+	6310.36i	0.828873	+	0.828873i
$388$		0			0
$389$	10651.3			1.38828			0.694140	−	0.719840i	$-0.255785\pi$
$389$	10651.3			1.38828			0.694140	+	0.719840i	$0.255785\pi$
$390$		0			0
$391$			11858.4i			1.53378i
$392$		0			0
$393$	−702.277	+	702.277i	−0.0901405	+	0.0901405i
$394$		0			0
$395$	−11683.9	−	4051.23i	−1.48831	−	0.516050i
$396$		0			0
$397$	7186.17	−	7186.17i	0.908473	−	0.908473i	−0.0876763	−	0.996149i	$-0.527944\pi$
$397$	7186.17	−	7186.17i	0.908473	−	0.908473i	0.996149	+	0.0876763i	$0.0279441\pi$
$398$		0			0
$399$	−1643.40			−0.206198
$400$		0			0
$401$	−2873.18			−0.357805			−0.178902	−	0.983867i	$-0.557255\pi$
$401$	−2873.18			−0.357805			−0.178902	+	0.983867i	$0.557255\pi$
$402$		0			0
$403$	−5991.66	+	5991.66i	−0.740611	+	0.740611i
$404$		0			0
$405$	3782.43	+	1311.50i	0.464075	+	0.160911i
$406$		0			0
$407$	260.304	−	260.304i	0.0317022	−	0.0317022i
$408$		0			0
$409$			10161.4i			1.22848i	0.789118	+	0.614242i	$0.210538\pi$
$409$			10161.4i			1.22848i	−0.789118	+	0.614242i	$0.789462\pi$
$410$		0			0
$411$	3705.18			0.444679
$412$		0			0
$413$	3420.46	+	3420.46i	0.407530	+	0.407530i
$414$		0			0
$415$	−11486.1	+	5571.57i	−1.35862	+	0.659030i
$416$		0			0
$417$	−3573.17	−	3573.17i	−0.419613	−	0.419613i
$418$		0			0
$419$		−	7118.17i		−	0.829941i	−0.909835	−	0.414970i	$-0.863792\pi$
$419$		−	7118.17i		−	0.829941i	0.909835	−	0.414970i	$-0.136208\pi$
$420$		0			0
$421$			10158.3i			1.17598i	0.808869	+	0.587989i	$0.200080\pi$
$421$			10158.3i			1.17598i	−0.808869	+	0.587989i	$0.799920\pi$
$422$		0			0
$423$	−129.214	−	129.214i	−0.0148525	−	0.0148525i
$424$		0			0
$425$	−1199.24	−	10127.0i	−0.136874	−	1.15584i
$426$		0			0
$427$	5006.66	+	5006.66i	0.567422	+	0.567422i
$428$		0			0
$429$	2108.68			0.237314
$430$		0			0
$431$		−	2673.44i		−	0.298782i	−0.988778	−	0.149391i	$-0.952269\pi$
$431$		−	2673.44i		−	0.298782i	0.988778	−	0.149391i	$-0.0477314\pi$
$432$		0			0
$433$	−1021.29	+	1021.29i	−0.113349	+	0.113349i	−0.761506	−	0.648158i	$-0.775540\pi$
$433$	−1021.29	+	1021.29i	−0.113349	+	0.113349i	0.648158	+	0.761506i	$0.275540\pi$
$434$		0			0
$435$	201.677	−	97.8282i	0.0222292	−	0.0107828i
$436$		0			0
$437$	−2921.33	+	2921.33i	−0.319785	+	0.319785i
$438$		0			0
$439$	12951.6			1.40807			0.704037	−	0.710163i	$-0.251379\pi$
$439$	12951.6			1.40807			0.704037	+	0.710163i	$0.251379\pi$
$440$		0			0
$441$	7592.82			0.819870
$442$		0			0
$443$	2459.86	−	2459.86i	0.263818	−	0.263818i	−0.562785	−	0.826603i	$-0.690270\pi$
$443$	2459.86	−	2459.86i	0.263818	−	0.263818i	0.826603	+	0.562785i	$0.190270\pi$
$444$		0			0
$445$	−4111.59	+	11858.0i	−0.437996	+	1.26320i
$446$		0			0
$447$	−4893.57	+	4893.57i	−0.517803	+	0.517803i
$448$		0			0
$449$		−	3444.14i		−	0.362002i	−0.983483	−	0.181001i	$-0.942066\pi$
$449$		−	3444.14i		−	0.362002i	0.983483	−	0.181001i	$-0.0579337\pi$
$450$		0			0
$451$	1263.01			0.131869
$452$		0			0
$453$	−3748.34	−	3748.34i	−0.388769	−	0.388769i
$454$		0			0
$455$	20222.6	+	7011.89i	2.08362	+	0.722467i
$456$		0			0
$457$	−4526.18	−	4526.18i	−0.463295	−	0.463295i	0.436439	−	0.899734i	$-0.356239\pi$
$457$	−4526.18	−	4526.18i	−0.463295	−	0.463295i	−0.899734	+	0.436439i	$0.856239\pi$
$458$		0			0
$459$		−	8846.98i		−	0.899655i
$460$		0			0
$461$		−	5004.01i		−	0.505553i	−0.967525	−	0.252776i	$-0.918656\pi$
$461$		−	5004.01i		−	0.505553i	0.967525	−	0.252776i	$-0.0813437\pi$
$462$		0			0
$463$	310.425	+	310.425i	0.0311591	+	0.0311591i	0.722515	−	0.691356i	$-0.242986\pi$
$463$	310.425	+	310.425i	0.0311591	+	0.0311591i	−0.691356	+	0.722515i	$0.742986\pi$
$464$		0			0
$465$	1248.78	+	2574.42i	0.124539	+	0.256744i
$466$		0			0
$467$	−12315.5	−	12315.5i	−1.22033	−	1.22033i	−0.967515	−	0.252814i	$-0.918644\pi$
$467$	−12315.5	−	12315.5i	−1.22033	−	1.22033i	−0.252814	−	0.967515i	$-0.581356\pi$
$468$		0			0
$469$	5623.21			0.553637
$470$		0			0
$471$			3602.45i			0.352425i
$472$		0			0
$473$	−3727.60	+	3727.60i	−0.362357	+	0.362357i
$474$		0			0
$475$	2199.36	−	2790.22i	0.212450	−	0.269525i
$476$		0			0
$477$	−6443.34	+	6443.34i	−0.618491	+	0.618491i
$478$		0			0
$479$	6285.14			0.599531			0.299766	−	0.954013i	$-0.403092\pi$
$479$	6285.14			0.599531			0.299766	+	0.954013i	$0.403092\pi$
$480$		0			0
$481$	2058.34			0.195119
$482$		0			0
$483$	−5942.90	+	5942.90i	−0.559858	+	0.559858i
$484$		0			0
$485$	−2928.84	−	6037.94i	−0.274210	−	0.565296i
$486$		0			0
$487$	8725.74	−	8725.74i	0.811911	−	0.811911i	−0.173009	−	0.984920i	$-0.555349\pi$
$487$	8725.74	−	8725.74i	0.811911	−	0.811911i	0.984920	+	0.173009i	$0.0553489\pi$
$488$		0			0
$489$			1731.23i			0.160100i
$490$		0			0
$491$	8937.16			0.821443			0.410721	−	0.911761i	$-0.365277\pi$
$491$	8937.16			0.821443			0.410721	+	0.911761i	$0.365277\pi$
$492$		0			0
$493$	523.954	+	523.954i	0.0478655	+	0.0478655i
$494$		0			0
$495$	−1059.35	+	3055.22i	−0.0961906	+	0.277418i
$496$		0			0
$497$	13754.1	+	13754.1i	1.24136	+	1.24136i
$498$		0			0
$499$			6370.54i			0.571512i	0.958302	+	0.285756i	$0.0922447\pi$
$499$			6370.54i			0.571512i	−0.958302	+	0.285756i	$0.907755\pi$
$500$		0			0
$501$			5340.40i			0.476230i
$502$		0			0
$503$	13190.6	+	13190.6i	1.16926	+	1.16926i	0.982383	+	0.186880i	$0.0598376\pi$
$503$	13190.6	+	13190.6i	1.16926	+	1.16926i	0.186880	+	0.982383i	$0.440162\pi$
$504$		0			0
$505$	−189.787	+	547.353i	−0.0167236	+	0.0482314i
$506$		0			0
$507$	4907.94	+	4907.94i	0.429919	+	0.429919i
$508$		0			0
$509$	−5948.50			−0.518001			−0.259001	−	0.965877i	$-0.583393\pi$
$509$	−5948.50			−0.518001			−0.259001	+	0.965877i	$0.583393\pi$
$510$		0			0
$511$		−	1486.32i		−	0.128671i
$512$		0			0
$513$	2179.46	−	2179.46i	0.187574	−	0.187574i
$514$		0			0
$515$	8227.54	+	16961.5i	0.703978	+	1.45129i
$516$		0			0
$517$	76.3279	−	76.3279i	0.00649304	−	0.00649304i
$518$		0			0
$519$	−2702.70			−0.228585
$520$		0			0
$521$	−12777.4			−1.07445			−0.537226	−	0.843438i	$-0.680528\pi$
$521$	−12777.4			−1.07445			−0.537226	+	0.843438i	$0.680528\pi$
$522$		0			0
$523$	9802.60	−	9802.60i	0.819575	−	0.819575i	−0.166471	−	0.986046i	$-0.553237\pi$
$523$	9802.60	−	9802.60i	0.819575	−	0.819575i	0.986046	+	0.166471i	$0.0532374\pi$
$524$		0			0
$525$	4474.19	−	5676.19i	0.371942	−	0.471865i
$526$		0			0
$527$	−6688.29	+	6688.29i	−0.552839	+	0.552839i
$528$		0			0
$529$			8961.31i			0.736526i
$530$		0			0
$531$	−4086.26			−0.333952
$532$		0			0
$533$	4993.58	+	4993.58i	0.405808	+	0.405808i
$534$		0			0
$535$	−5138.64	−	10593.6i	−0.415258	−	0.856074i
$536$		0			0
$537$	−2312.85	−	2312.85i	−0.185860	−	0.185860i
$538$		0			0
$539$			4485.15i			0.358422i
$540$		0			0
$541$			15215.3i			1.20917i	0.796543	+	0.604583i	$0.206660\pi$
$541$			15215.3i			1.20917i	−0.796543	+	0.604583i	$0.793340\pi$
$542$		0			0
$543$	−2548.73	−	2548.73i	−0.201430	−	0.201430i
$544$		0			0
$545$	−10764.3	−	3732.35i	−0.846037	−	0.293351i
$546$		0			0
$547$	−17454.7	−	17454.7i	−1.36437	−	1.36437i	−0.868263	−	0.496104i	$-0.834763\pi$
$547$	−17454.7	−	17454.7i	−1.36437	−	1.36437i	−0.496104	−	0.868263i	$-0.665237\pi$
$548$		0			0
$549$	−5981.22			−0.464977
$550$		0			0
$551$			258.152i			0.0199594i
$552$		0			0
$553$	20487.0	−	20487.0i	1.57540	−	1.57540i
$554$		0			0
$555$	227.701	−	656.699i	0.0174151	−	0.0502258i
$556$		0			0
$557$	15166.0	−	15166.0i	1.15369	−	1.15369i	0.167881	−	0.985807i	$-0.446308\pi$
$557$	15166.0	−	15166.0i	1.15369	−	1.15369i	0.985807	−	0.167881i	$-0.0536924\pi$
$558$		0			0
$559$	−29475.7			−2.23022
$560$		0			0
$561$	2353.84			0.177147
$562$		0			0
$563$	−2073.66	+	2073.66i	−0.155230	+	0.155230i	−0.780449	−	0.625219i	$-0.785010\pi$
$563$	−2073.66	+	2073.66i	−0.155230	+	0.155230i	0.625219	+	0.780449i	$0.285010\pi$
$564$		0			0
$565$	−4304.83	+	2088.15i	−0.320541	+	0.155485i
$566$		0			0
$567$	−6632.23	+	6632.23i	−0.491230	+	0.491230i
$568$		0			0
$569$		−	8026.07i		−	0.591336i	−0.955291	−	0.295668i	$-0.904458\pi$
$569$		−	8026.07i		−	0.591336i	0.955291	−	0.295668i	$-0.0955423\pi$
$570$		0			0
$571$	−19770.1			−1.44896			−0.724478	−	0.689297i	$-0.757919\pi$
$571$	−19770.1			−1.44896			−0.724478	+	0.689297i	$0.757919\pi$
$572$		0			0
$573$	3340.32	+	3340.32i	0.243532	+	0.243532i
$574$		0			0
$575$	−2136.69	−	18043.4i	−0.154967	−	1.30863i
$576$		0			0
$577$	−4806.16	−	4806.16i	−0.346764	−	0.346764i	0.512139	−	0.858903i	$-0.328853\pi$
$577$	−4806.16	−	4806.16i	−0.346764	−	0.346764i	−0.858903	+	0.512139i	$0.828853\pi$
$578$		0			0
$579$		−	9239.92i		−	0.663209i
$580$		0			0
$581$		−	29909.4i		−	2.13571i
$582$		0			0
$583$	−3806.15	−	3806.15i	−0.270385	−	0.270385i
$584$		0			0
$585$	−16267.9	+	7891.09i	−1.14973	+	0.557703i
$586$		0			0
$587$	10220.3	+	10220.3i	0.718633	+	0.718633i	0.968325	−	0.249693i	$-0.0803296\pi$
$587$	10220.3	+	10220.3i	0.718633	+	0.718633i	−0.249693	+	0.968325i	$0.580330\pi$
$588$		0			0
$589$	−3295.32			−0.230529
$590$		0			0
$591$			864.798i			0.0601912i
$592$		0			0
$593$	2295.45	−	2295.45i	0.158959	−	0.158959i	−0.623146	−	0.782105i	$-0.714146\pi$
$593$	2295.45	−	2295.45i	0.158959	−	0.158959i	0.782105	+	0.623146i	$0.214146\pi$
$594$		0			0
$595$	22573.7	+	7827.12i	1.55535	+	0.539295i
$596$		0			0
$597$	−3198.64	+	3198.64i	−0.219283	+	0.219283i
$598$		0			0
$599$	18976.1			1.29440			0.647199	−	0.762321i	$-0.275940\pi$
$599$	18976.1			1.29440			0.647199	+	0.762321i	$0.275940\pi$
$600$		0			0
$601$	−7743.31			−0.525551			−0.262776	−	0.964857i	$-0.584638\pi$
$601$	−7743.31			−0.525551			−0.262776	+	0.964857i	$0.584638\pi$
$602$		0			0
$603$	−3358.89	+	3358.89i	−0.226840	+	0.226840i
$604$		0			0
$605$	12255.1	+	4249.28i	0.823538	+	0.285550i
$606$		0			0
$607$	−4831.26	+	4831.26i	−0.323055	+	0.323055i	−0.849938	−	0.526883i	$-0.823361\pi$
$607$	−4831.26	+	4831.26i	−0.323055	+	0.323055i	0.526883	+	0.849938i	$0.323361\pi$
$608$		0			0
$609$			525.163i			0.0349436i
$610$		0			0
$611$	603.559			0.0399630
$612$		0			0
$613$	−10161.3	−	10161.3i	−0.669509	−	0.669509i	0.288093	−	0.957602i	$-0.406979\pi$
$613$	−10161.3	−	10161.3i	−0.669509	−	0.669509i	−0.957602	+	0.288093i	$0.906979\pi$
$614$		0			0
$615$	2145.57	−	1040.76i	0.140680	−	0.0682397i
$616$		0			0
$617$	15287.4	+	15287.4i	0.997482	+	0.997482i	0.999997	−	0.00251480i	$-0.000800485\pi$
$617$	15287.4	+	15287.4i	0.997482	+	0.997482i	−0.00251480	+	0.999997i	$0.500800\pi$
$618$		0			0
$619$			1347.25i			0.0874808i	0.999043	+	0.0437404i	$0.0139274\pi$
$619$			1347.25i			0.0874808i	−0.999043	+	0.0437404i	$0.986073\pi$
$620$		0			0
$621$		−	15762.8i		−	1.01858i
$622$		0			0
$623$	−20792.2	−	20792.2i	−1.33711	−	1.33711i
$624$		0			0
$625$	3649.43	+	15192.8i	0.233564	+	0.972342i
$626$		0			0
$627$	579.869	+	579.869i	0.0369342	+	0.0369342i
$628$		0			0
$629$	2297.65			0.145649
$630$		0			0
$631$		−	19990.0i		−	1.26116i	−0.776125	−	0.630579i	$-0.782817\pi$
$631$		−	19990.0i		−	1.26116i	0.776125	−	0.630579i	$-0.217183\pi$
$632$		0			0
$633$	−577.455	+	577.455i	−0.0362587	+	0.0362587i
$634$		0			0
$635$	−9373.75	+	4546.95i	−0.585805	+	0.284158i
$636$		0			0
$637$	−17733.0	+	17733.0i	−1.10300	+	1.10300i
$638$		0			0
$639$	−16431.4			−1.01724
$640$		0			0
$641$	−4738.38			−0.291973			−0.145986	−	0.989287i	$-0.546636\pi$
$641$	−4738.38			−0.291973			−0.145986	+	0.989287i	$0.546636\pi$
$642$		0			0
$643$	−11003.8	+	11003.8i	−0.674878	+	0.674878i	−0.958837	−	0.283958i	$-0.908352\pi$
$643$	−11003.8	+	11003.8i	−0.674878	+	0.674878i	0.283958	+	0.958837i	$0.408352\pi$
$644$		0			0
$645$	−3260.71	+	9404.03i	−0.199055	+	0.574083i
$646$		0			0
$647$	13557.6	−	13557.6i	0.823811	−	0.823811i	−0.162841	−	0.986652i	$-0.552066\pi$
$647$	13557.6	−	13557.6i	0.823811	−	0.823811i	0.986652	+	0.162841i	$0.0520659\pi$
$648$		0			0
$649$		−	2413.80i		−	0.145993i
$650$		0			0
$651$	−6703.72			−0.403594
$652$		0			0
$653$	−18540.2	−	18540.2i	−1.11108	−	1.11108i	−0.993005	−	0.118071i	$-0.962329\pi$
$653$	−18540.2	−	18540.2i	−1.11108	−	1.11108i	−0.118071	−	0.993005i	$-0.537671\pi$
$654$		0			0
$655$	4752.82	+	1647.97i	0.283523	+	0.0983077i
$656$		0			0
$657$	887.817	+	887.817i	0.0527200	+	0.0527200i
$658$		0			0
$659$		−	25451.6i		−	1.50448i	−0.658887	−	0.752242i	$-0.728973\pi$
$659$		−	25451.6i		−	1.50448i	0.658887	−	0.752242i	$-0.271027\pi$
$660$		0			0
$661$			11710.3i			0.689077i	0.938772	+	0.344538i	$0.111965\pi$
$661$			11710.3i			0.689077i	−0.938772	+	0.344538i	$0.888035\pi$
$662$		0			0
$663$	9306.43	+	9306.43i	0.545146	+	0.545146i
$664$		0			0
$665$	3632.83	+	7489.26i	0.211842	+	0.436723i
$666$		0			0
$667$	933.534	+	933.534i	0.0541928	+	0.0541928i
$668$		0			0
$669$	6174.25			0.356817
$670$		0			0
$671$		−	3533.17i		−	0.203273i
$672$		0			0
$673$	11598.3	−	11598.3i	0.664313	−	0.664313i	−0.292080	−	0.956394i	$-0.594347\pi$
$673$	11598.3	−	11598.3i	0.664313	−	0.664313i	0.956394	+	0.292080i	$0.0943475\pi$
$674$		0			0
$675$	1594.08	+	13461.3i	0.0908978	+	0.767592i
$676$		0			0
$677$	22840.8	−	22840.8i	1.29667	−	1.29667i	0.366085	−	0.930582i	$-0.380698\pi$
$677$	22840.8	−	22840.8i	1.29667	−	1.29667i	0.930582	−	0.366085i	$-0.119302\pi$
$678$		0			0
$679$	15722.6			0.888629
$680$		0			0
$681$	−5142.79			−0.289386
$682$		0			0
$683$	18296.4	−	18296.4i	1.02503	−	1.02503i	0.0253478	−	0.999679i	$-0.491931\pi$
$683$	18296.4	−	18296.4i	1.02503	−	1.02503i	0.999679	−	0.0253478i	$-0.00806932\pi$
$684$		0			0
$685$	−8190.51	−	16885.1i	−0.456851	−	0.941821i
$686$		0			0
$687$	6657.03	−	6657.03i	0.369697	−	0.369697i
$688$		0			0
$689$		−	30096.9i		−	1.66415i
$690$		0			0
$691$	9143.59			0.503384			0.251692	−	0.967807i	$-0.419013\pi$
$691$	9143.59			0.503384			0.251692	+	0.967807i	$0.419013\pi$
$692$		0			0
$693$	−5357.11	−	5357.11i	−0.293651	−	0.293651i
$694$		0			0
$695$	−8384.82	+	24182.2i	−0.457632	+	1.31983i
$696$		0			0
$697$	5574.16	+	5574.16i	0.302921	+	0.302921i
$698$		0			0
$699$			1962.08i			0.106170i
$700$		0			0
$701$			33525.6i			1.80634i	0.429283	+	0.903170i	$0.358766\pi$
$701$			33525.6i			1.80634i	−0.429283	+	0.903170i	$0.641234\pi$
$702$		0			0
$703$	566.027	+	566.027i	0.0303671	+	0.0303671i
$704$		0			0
$705$	66.7678	−	192.561i	0.00356684	−	0.0102869i
$706$		0			0
$707$	−959.745	−	959.745i	−0.0510537	−	0.0510537i
$708$		0			0
$709$	−19771.1			−1.04728			−0.523638	−	0.851941i	$-0.675426\pi$
$709$	−19771.1			−1.04728			−0.523638	+	0.851941i	$0.675426\pi$
$710$		0			0
$711$			24474.8i			1.29097i
$712$		0			0
$713$	−11916.6	+	11916.6i	−0.625918	+	0.625918i
$714$		0			0
$715$	−4661.34	−	9609.58i	−0.243810	−	0.502627i
$716$		0			0
$717$	4440.82	−	4440.82i	0.231305	−	0.231305i
$718$		0			0
$719$	4021.45			0.208588			0.104294	−	0.994547i	$-0.466742\pi$
$719$	4021.45			0.208588			0.104294	+	0.994547i	$0.466742\pi$
$720$		0			0
$721$	−44167.2			−2.28138
$722$		0			0
$723$	5198.88	−	5198.88i	0.267425	−	0.267425i
$724$		0			0
$725$	−891.638	−	702.823i	−0.0456753	−	0.0360030i
$726$		0			0
$727$	−6313.44	+	6313.44i	−0.322080	+	0.322080i	−0.849565	−	0.527484i	$-0.823135\pi$
$727$	−6313.44	+	6313.44i	−0.322080	+	0.322080i	0.527484	+	0.849565i	$0.323135\pi$
$728$		0			0
$729$		−	1460.14i		−	0.0741828i
$730$		0			0
$731$	−32902.7			−1.66478
$732$		0			0
$733$	10732.6	+	10732.6i	0.540816	+	0.540816i	0.923768	−	0.382952i	$-0.125093\pi$
$733$	10732.6	+	10732.6i	0.540816	+	0.540816i	−0.382952	+	0.923768i	$0.625093\pi$
$734$		0			0
$735$	3695.91	+	7619.30i	0.185477	+	0.382370i
$736$		0			0
$737$	−1984.13	−	1984.13i	−0.0991674	−	0.0991674i
$738$		0			0
$739$		−	2500.37i		−	0.124462i	−0.998062	−	0.0622312i	$-0.980178\pi$
$739$		−	2500.37i		−	0.124462i	0.998062	−	0.0622312i	$-0.0198216\pi$
$740$		0			0
$741$			4585.28i			0.227321i
$742$		0			0
$743$	9766.31	+	9766.31i	0.482222	+	0.482222i	0.905841	−	0.423619i	$-0.139240\pi$
$743$	9766.31	+	9766.31i	0.482222	+	0.482222i	−0.423619	+	0.905841i	$0.639240\pi$
$744$		0			0
$745$	33118.3	+	11483.3i	1.62867	+	0.564719i
$746$		0			0
$747$	17865.7	+	17865.7i	0.875060	+	0.875060i
$748$		0			0
$749$	27585.3			1.34572
$750$		0			0
$751$			25285.0i			1.22858i	0.789081	+	0.614289i	$0.210557\pi$
$751$			25285.0i			1.22858i	−0.789081	+	0.614289i	$0.789443\pi$
$752$		0			0
$753$	6068.04	−	6068.04i	0.293668	−	0.293668i
$754$		0			0
$755$	−8795.90	+	25367.7i	−0.423994	+	1.22282i
$756$		0			0
$757$	−13444.0	+	13444.0i	−0.645483	+	0.645483i	−0.951898	−	0.306415i	$-0.900870\pi$
$757$	−13444.0	+	13444.0i	−0.645483	+	0.645483i	0.306415	+	0.951898i	$0.400870\pi$
$758$		0			0
$759$	4193.87			0.200563
$760$		0			0
$761$	−2862.64			−0.136361			−0.0681805	−	0.997673i	$-0.521719\pi$
$761$	−2862.64			−0.136361			−0.0681805	+	0.997673i	$0.521719\pi$
$762$		0			0
$763$	18874.4	−	18874.4i	0.895542	−	0.895542i
$764$		0			0
$765$	−18159.2	+	8808.54i	−0.858233	+	0.416305i
$766$		0			0
$767$	9543.47	−	9543.47i	0.449276	−	0.449276i
$768$		0			0
$769$			29021.2i			1.36090i	0.732796	+	0.680448i	$0.238215\pi$
$769$			29021.2i			1.36090i	−0.732796	+	0.680448i	$0.761785\pi$
$770$		0			0
$771$	7212.56			0.336906
$772$		0			0
$773$	27828.4	+	27828.4i	1.29485	+	1.29485i	0.931751	+	0.363098i	$0.118281\pi$
$773$	27828.4	+	27828.4i	1.29485	+	1.29485i	0.363098	+	0.931751i	$0.381719\pi$
$774$		0			0
$775$	8971.55	−	11381.8i	0.415829	−	0.527543i
$776$		0			0
$777$	1151.48	+	1151.48i	0.0531647	+	0.0531647i
$778$		0			0
$779$			2746.39i			0.126315i
$780$		0			0
$781$		−	9706.18i		−	0.444705i
$782$		0			0
$783$	−696.462	−	696.462i	−0.0317874	−	0.0317874i
$784$		0			0
$785$	16417.0	−	7963.42i	0.746429	−	0.362072i
$786$		0			0
$787$	10873.6	+	10873.6i	0.492506	+	0.492506i	0.909095	−	0.416589i	$-0.136775\pi$
$787$	10873.6	+	10873.6i	0.492506	+	0.492506i	−0.416589	+	0.909095i	$0.636775\pi$
$788$		0			0
$789$	−8603.83			−0.388218
$790$		0			0
$791$		−	11209.7i		−	0.503881i
$792$		0			0
$793$	13969.2	−	13969.2i	0.625548	−	0.625548i
$794$		0			0
$795$	−9602.20	−	3329.43i	−0.428371	−	0.148531i
$796$		0			0
$797$	−10826.0	+	10826.0i	−0.481150	+	0.481150i	−0.905499	−	0.424349i	$-0.860503\pi$
$797$	−10826.0	+	10826.0i	−0.481150	+	0.481150i	0.424349	+	0.905499i	$0.360503\pi$
$798$		0			0
$799$	673.731			0.0298309
$800$		0			0
$801$	24839.5			1.09570
$802$		0			0
$803$	−524.442	+	524.442i	−0.0230475	+	0.0230475i
$804$		0			0
$805$	40219.9	+	13945.7i	1.76095	+	0.610584i
$806$		0			0
$807$	−6278.52	+	6278.52i	−0.273872	+	0.273872i
$808$		0			0
$809$		−	17041.0i		−	0.740579i	−0.928916	−	0.370290i	$-0.879258\pi$
$809$		−	17041.0i		−	0.740579i	0.928916	−	0.370290i	$-0.120742\pi$
$810$		0			0
$811$	−33520.8			−1.45139			−0.725693	−	0.688018i	$-0.758481\pi$
$811$	−33520.8			−1.45139			−0.725693	+	0.688018i	$0.758481\pi$
$812$		0			0
$813$	5148.05	+	5148.05i	0.222079	+	0.222079i
$814$		0			0
$815$	7889.52	−	3826.99i	0.339089	−	0.164483i
$816$		0			0
$817$	−8105.59	−	8105.59i	−0.347098	−	0.347098i
$818$		0			0
$819$		−	42361.1i		−	1.80734i
$820$		0			0
$821$			7107.57i			0.302139i	0.988523	+	0.151069i	$0.0482717\pi$
$821$			7107.57i			0.302139i	−0.988523	+	0.151069i	$0.951728\pi$
$822$		0			0
$823$	3119.89	+	3119.89i	0.132142	+	0.132142i	0.770084	−	0.637942i	$-0.220214\pi$
$823$	3119.89	+	3119.89i	0.132142	+	0.132142i	−0.637942	+	0.770084i	$0.720214\pi$
$824$		0			0
$825$	−3581.53	+	424.122i	−0.151143	+	0.0178982i
$826$		0			0
$827$	11667.6	+	11667.6i	0.490596	+	0.490596i	0.908494	−	0.417898i	$-0.137233\pi$
$827$	11667.6	+	11667.6i	0.490596	+	0.490596i	−0.417898	+	0.908494i	$0.637233\pi$
$828$		0			0
$829$	12145.3			0.508833			0.254416	−	0.967095i	$-0.418117\pi$
$829$	12145.3			0.508833			0.254416	+	0.967095i	$0.418117\pi$
$830$		0			0
$831$		−	140.976i		−	0.00588496i
$832$		0			0
$833$	−19794.8	+	19794.8i	−0.823347	+	0.823347i
$834$		0			0
$835$	24337.1	−	11805.2i	1.00865	−	0.489266i
$836$		0			0
$837$	8890.36	−	8890.36i	0.367140	−	0.367140i
$838$		0			0
$839$	−19564.3			−0.805048			−0.402524	−	0.915409i	$-0.631867\pi$
$839$	−19564.3			−0.805048			−0.402524	+	0.915409i	$0.631867\pi$
$840$		0			0
$841$	−24306.5			−0.996618
$842$		0			0
$843$	7972.14	−	7972.14i	0.325712	−	0.325712i
$844$		0			0
$845$	11517.0	−	33215.5i	0.468873	−	1.35225i
$846$		0			0
$847$	−21488.5	+	21488.5i	−0.871727	+	0.871727i
$848$		0			0
$849$		−	15494.2i		−	0.626335i
$850$		0			0
$851$	4093.75			0.164902
$852$		0			0
$853$	1090.28	+	1090.28i	0.0437636	+	0.0437636i	0.728650	−	0.684886i	$-0.240148\pi$
$853$	1090.28	+	1090.28i	0.0437636	+	0.0437636i	−0.684886	+	0.728650i	$0.740148\pi$
$854$		0			0
$855$	−6643.52	−	2303.54i	−0.265735	−	0.0921398i
$856$		0			0
$857$	−20982.1	−	20982.1i	−0.836330	−	0.836330i	0.152044	−	0.988374i	$-0.451414\pi$
$857$	−20982.1	−	20982.1i	−0.836330	−	0.836330i	−0.988374	+	0.152044i	$0.951414\pi$
$858$		0			0
$859$			49480.2i			1.96536i	0.185312	+	0.982680i	$0.440670\pi$
$859$			49480.2i			1.96536i	−0.185312	+	0.982680i	$0.559330\pi$
$860$		0			0
$861$			5587.02i			0.221144i
$862$		0			0
$863$	5022.50	+	5022.50i	0.198109	+	0.198109i	0.799189	−	0.601080i	$-0.205263\pi$
$863$	5022.50	+	5022.50i	0.198109	+	0.198109i	−0.601080	+	0.799189i	$0.705263\pi$
$864$		0			0
$865$	5974.47	+	12316.7i	0.234842	+	0.484137i
$866$		0			0
$867$	2720.01	+	2720.01i	0.106547	+	0.106547i
$868$		0			0
$869$	−14457.5			−0.564370
$870$		0			0
$871$		−	15689.4i		−	0.610350i
$872$		0			0
$873$	−9391.54	+	9391.54i	−0.364096	+	0.364096i
$874$		0			0
$875$	−35757.8	−	7842.08i	−1.38152	−	0.302984i
$876$		0			0
$877$	−8642.81	+	8642.81i	−0.332779	+	0.332779i	−0.853641	−	0.520862i	$-0.825611\pi$
$877$	−8642.81	+	8642.81i	−0.332779	+	0.332779i	0.520862	+	0.853641i	$0.325611\pi$
$878$		0			0
$879$	−3776.20			−0.144901
$880$		0			0
$881$	32939.2			1.25965			0.629823	−	0.776739i	$-0.283127\pi$
$881$	32939.2			1.25965			0.629823	+	0.776739i	$0.283127\pi$
$882$		0			0
$883$	−22022.6	+	22022.6i	−0.839321	+	0.839321i	−0.988770	−	0.149448i	$-0.952250\pi$
$883$	−22022.6	+	22022.6i	−0.839321	+	0.839321i	0.149448	+	0.988770i	$0.452250\pi$
$884$		0			0
$885$	−1989.05	−	4100.51i	−0.0755492	−	0.155748i
$886$		0			0
$887$	8853.58	−	8853.58i	0.335146	−	0.335146i	−0.519391	−	0.854537i	$-0.673841\pi$
$887$	8853.58	−	8853.58i	0.335146	−	0.335146i	0.854537	+	0.519391i	$0.173841\pi$
$888$		0			0
$889$		−	24409.0i		−	0.920868i
$890$		0			0
$891$	4680.32			0.175978
$892$		0			0
$893$	165.974	+	165.974i	0.00621960	+	0.00621960i
$894$		0			0
$895$	−5427.35	+	15652.7i	−0.202700	+	0.584595i
$896$		0			0
$897$	16581.4	+	16581.4i	0.617208	+	0.617208i
$898$		0			0
$899$			1053.05i			0.0390668i
$900$		0			0
$901$		−	33596.1i		−	1.24223i
$902$		0			0
$903$	−16489.3	−	16489.3i	−0.607675	−	0.607675i
$904$		0			0
$905$	−5980.87	+	17249.1i	−0.219681	+	0.633568i
$906$		0			0
$907$	−2952.76	−	2952.76i	−0.108098	−	0.108098i	0.650989	−	0.759087i	$-0.274354\pi$
$907$	−2952.76	−	2952.76i	−0.108098	−	0.108098i	−0.759087	+	0.650989i	$0.774354\pi$
$908$		0			0
$909$	1146.56			0.0418362
$910$		0			0
$911$			1300.26i			0.0472880i	0.999720	+	0.0236440i	$0.00752682\pi$
$911$			1300.26i			0.0472880i	−0.999720	+	0.0236440i	$0.992473\pi$
$912$		0			0
$913$	−10553.4	+	10553.4i	−0.382549	+	0.382549i
$914$		0			0
$915$	−2911.44	−	6002.08i	−0.105191	−	0.216855i
$916$		0			0
$917$	−8333.74	+	8333.74i	−0.300114	+	0.300114i
$918$		0			0
$919$	−13474.9			−0.483674			−0.241837	−	0.970317i	$-0.577750\pi$
$919$	−13474.9			−0.483674			−0.241837	+	0.970317i	$0.577750\pi$
$920$		0			0
$921$	2850.21			0.101973
$922$		0			0
$923$	38375.5	−	38375.5i	1.36852	−	1.36852i
$924$		0			0
$925$	−3496.03	+	413.998i	−0.124269	+	0.0147158i
$926$		0			0
$927$	26382.2	−	26382.2i	0.934743	−	0.934743i
$928$		0			0
$929$			3824.84i			0.135079i	0.997717	+	0.0675397i	$0.0215149\pi$
$929$			3824.84i			0.135079i	−0.997717	+	0.0675397i	$0.978485\pi$
$930$		0			0
$931$	−9752.89			−0.343328
$932$		0			0
$933$	−10114.6	−	10114.6i	−0.354916	−	0.354916i
$934$		0			0
$935$	−5203.29	−	10726.8i	−0.181996	−	0.375193i
$936$		0			0
$937$	−3488.68	−	3488.68i	−0.121633	−	0.121633i	0.643670	−	0.765303i	$-0.277411\pi$
$937$	−3488.68	−	3488.68i	−0.121633	−	0.121633i	−0.765303	+	0.643670i	$0.777411\pi$
$938$		0			0
$939$			22563.5i			0.784167i
$940$		0			0
$941$		−	23456.8i		−	0.812615i	−0.913736	−	0.406307i	$-0.866816\pi$
$941$		−	23456.8i		−	0.812615i	0.913736	−	0.406307i	$-0.133184\pi$
$942$		0			0
$943$	9931.53	+	9931.53i	0.342964	+	0.342964i
$944$		0			0
$945$	−30006.0	−	10404.2i	−1.03291	−	0.358145i
$946$		0			0
$947$	−9266.56	−	9266.56i	−0.317975	−	0.317975i	0.530014	−	0.847989i	$-0.322187\pi$
$947$	−9266.56	−	9266.56i	−0.317975	−	0.317975i	−0.847989	+	0.530014i	$0.822187\pi$
$948$		0			0
$949$	−4147.00			−0.141852
$950$		0			0
$951$			6278.60i			0.214088i
$952$		0			0
$953$	6489.55	−	6489.55i	0.220584	−	0.220584i	−0.588160	−	0.808745i	$-0.700147\pi$
$953$	6489.55	−	6489.55i	0.220584	−	0.220584i	0.808745	+	0.588160i	$0.200147\pi$
$954$		0			0
$955$	7838.42	−	22606.3i	0.265597	−	0.765993i
$956$		0			0
$957$	185.302	−	185.302i	0.00625910	−	0.00625910i
$958$		0			0
$959$	43968.4			1.48051
$960$		0			0
$961$	16348.8			0.548784
$962$		0			0
$963$	−16477.5	+	16477.5i	−0.551380	+	0.551380i
$964$		0			0
$965$	−42107.8	+	20425.3i	−1.40466	+	0.681363i
$966$		0			0
$967$	−6169.49	+	6169.49i	−0.205168	+	0.205168i	−0.802210	−	0.597042i	$-0.796343\pi$
$967$	−6169.49	+	6169.49i	−0.205168	+	0.205168i	0.597042	+	0.802210i	$0.296343\pi$
$968$		0			0
$969$			5118.39i			0.169687i
$970$		0			0
$971$	39459.3			1.30413			0.652065	−	0.758163i	$-0.273903\pi$
$971$	39459.3			1.30413			0.652065	+	0.758163i	$0.273903\pi$
$972$		0			0
$973$	−42401.8	−	42401.8i	−1.39706	−	1.39706i
$974$		0			0
$975$	−15837.2	−	12483.5i	−0.520202	−	0.410043i
$976$		0			0
$977$	7977.15	+	7977.15i	0.261220	+	0.261220i	0.825549	−	0.564330i	$-0.190865\pi$
$977$	7977.15	+	7977.15i	0.261220	+	0.261220i	−0.564330	+	0.825549i	$0.690865\pi$
$978$		0			0
$979$			14672.9i			0.479008i
$980$		0			0
$981$			22548.3i			0.733856i
$982$		0			0
$983$	−29760.7	−	29760.7i	−0.965634	−	0.965634i	0.0337946	−	0.999429i	$-0.489241\pi$
$983$	−29760.7	−	29760.7i	−0.965634	−	0.965634i	−0.999429	+	0.0337946i	$0.989241\pi$
$984$		0			0
$985$	3941.02	−	1911.68i	0.127484	−	0.0618388i
$986$		0			0
$987$	337.643	+	337.643i	0.0108888	+	0.0108888i
$988$		0			0
$989$	−58623.1			−1.88484
$990$		0			0
$991$		−	20841.8i		−	0.668074i	−0.942560	−	0.334037i	$-0.891589\pi$
$991$		−	20841.8i		−	0.668074i	0.942560	−	0.334037i	$-0.108411\pi$
$992$		0			0
$993$	−8990.87	+	8990.87i	−0.287328	+	0.287328i
$994$		0			0
$995$	21647.5	+	7505.96i	0.689721	+	0.239151i
$996$		0			0
$997$	33740.8	−	33740.8i	1.07180	−	1.07180i	0.0745821	−	0.997215i	$-0.476238\pi$
$997$	33740.8	−	33740.8i	1.07180	−	1.07180i	0.997215	−	0.0745821i	$-0.0237623\pi$
$998$		0			0
$999$	−3054.14			−0.0967254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.o.a.47.9		32
4.3	odd	2		40.4.k.a.27.6	yes	32
5.3	odd	4	inner	160.4.o.a.143.10		32
8.3	odd	2	inner	160.4.o.a.47.10		32
8.5	even	2		40.4.k.a.27.4	yes	32
20.3	even	4		40.4.k.a.3.4	✓	32
20.7	even	4		200.4.k.j.43.13		32
20.19	odd	2		200.4.k.j.107.11		32
40.3	even	4	inner	160.4.o.a.143.9		32
40.13	odd	4		40.4.k.a.3.6	yes	32
40.29	even	2		200.4.k.j.107.13		32
40.37	odd	4		200.4.k.j.43.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.k.a.3.4	✓	32	20.3	even	4
40.4.k.a.3.6	yes	32	40.13	odd	4
40.4.k.a.27.4	yes	32	8.5	even	2
40.4.k.a.27.6	yes	32	4.3	odd	2
160.4.o.a.47.9		32	1.1	even	1	trivial
160.4.o.a.47.10		32	8.3	odd	2	inner
160.4.o.a.143.9		32	40.3	even	4	inner
160.4.o.a.143.10		32	5.3	odd	4	inner
200.4.k.j.43.11		32	40.37	odd	4
200.4.k.j.43.13		32	20.7	even	4
200.4.k.j.107.11		32	20.19	odd	2
200.4.k.j.107.13		32	40.29	even	2

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.56085 - 1.56085i) q^{3} +(-10.5634 - 3.66270i) q^{5} +(18.5221 - 18.5221i) q^{7} +22.1275i q^{9} -13.0709 q^{11} +(-51.6789 - 51.6789i) q^{13} +(-22.2047 + 10.7709i) q^{15} +(-57.6873 - 57.6873i) q^{17} -28.4226i q^{19} -57.8204i q^{21} +(-102.782 - 102.782i) q^{23} +(98.1693 + 77.3808i) q^{25} +(76.6805 + 76.6805i) q^{27} -9.08265 q^{29} -115.940i q^{31} +(-20.4017 + 20.4017i) q^{33} +(-263.497 + 127.815i) q^{35} +(-19.9147 + 19.9147i) q^{37} -161.325 q^{39} -96.6271 q^{41} +(285.182 - 285.182i) q^{43} +(81.0464 - 233.741i) q^{45} +(-5.83951 + 5.83951i) q^{47} -343.139i q^{49} -180.082 q^{51} +(291.191 + 291.191i) q^{53} +(138.073 + 47.8749i) q^{55} +(-44.3632 - 44.3632i) q^{57} +184.669i q^{59} +270.307i q^{61} +(409.849 + 409.849i) q^{63} +(356.619 + 735.187i) q^{65} +(151.797 + 151.797i) q^{67} -320.854 q^{69} +742.577i q^{71} +(40.1228 - 40.1228i) q^{73} +(274.007 - 32.4477i) q^{75} +(-242.102 + 242.102i) q^{77} +1106.08 q^{79} -358.070 q^{81} +(807.395 - 807.395i) q^{83} +(398.081 + 820.663i) q^{85} +(-14.1766 + 14.1766i) q^{87} -1122.56i q^{89} -1914.41 q^{91} +(-180.965 - 180.965i) q^{93} +(-104.103 + 300.238i) q^{95} +(424.428 + 424.428i) q^{97} -289.228i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 8 q^{11} + 48 q^{17} + 40 q^{25} - 104 q^{27} - 112 q^{33} + 460 q^{35} - 8 q^{41} + 868 q^{43} - 1480 q^{51} + 104 q^{57} + 520 q^{65} + 1852 q^{67} - 744 q^{73} - 3300 q^{75} - 1240 q^{81}+ \cdots - 584 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 8 * q^11 + 48 * q^17 + 40 * q^25 - 104 * q^27 - 112 * q^33 + 460 * q^35 - 8 * q^41 + 868 * q^43 - 1480 * q^51 + 104 * q^57 + 520 * q^65 + 1852 * q^67 - 744 * q^73 - 3300 * q^75 - 1240 * q^81 - 2676 * q^83 + 1704 * q^91 - 584 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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