LMFDB - Embedded newform 160.4.o.a.47.6

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			47.6
Character	$\chi$	$=$	160.47
Dual form			160.4.o.a.143.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.49003 + 3.49003i) q^{3} +(4.99441 - 10.0028i) q^{5} +(-4.97302 + 4.97302i) q^{7} +2.63942i q^{9} -29.8229 q^{11} +(-13.5734 - 13.5734i) q^{13} +(17.4794 + 52.3406i) q^{15} +(-61.7929 - 61.7929i) q^{17} -131.323i q^{19} -34.7119i q^{21} +(-1.13009 - 1.13009i) q^{23} +(-75.1118 - 99.9161i) q^{25} +(-103.442 - 103.442i) q^{27} +179.304 q^{29} -276.096i q^{31} +(104.083 - 104.083i) q^{33} +(24.9068 + 74.5813i) q^{35} +(-278.964 + 278.964i) q^{37} +94.7429 q^{39} -225.140 q^{41} +(-171.874 + 171.874i) q^{43} +(26.4016 + 13.1824i) q^{45} +(-86.1627 + 86.1627i) q^{47} +293.538i q^{49} +431.318 q^{51} +(108.361 + 108.361i) q^{53} +(-148.948 + 298.312i) q^{55} +(458.322 + 458.322i) q^{57} +157.272i q^{59} -791.867i q^{61} +(-13.1259 - 13.1259i) q^{63} +(-203.563 + 67.9807i) q^{65} +(3.80296 + 3.80296i) q^{67} +7.88811 q^{69} +58.6097i q^{71} +(452.731 - 452.731i) q^{73} +(610.852 + 86.5677i) q^{75} +(148.310 - 148.310i) q^{77} +821.590 q^{79} +650.769 q^{81} +(-512.512 + 512.512i) q^{83} +(-926.721 + 309.483i) q^{85} +(-625.775 + 625.775i) q^{87} +500.262i q^{89} +135.001 q^{91} +(963.581 + 963.581i) q^{93} +(-1313.60 - 655.882i) q^{95} +(-60.7068 - 60.7068i) q^{97} -78.7153i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.49003	+	3.49003i	−0.671656	+	0.671656i	−0.958098	−	0.286442i	$-0.907528\pi$
$3$	−3.49003	+	3.49003i	−0.671656	+	0.671656i	0.286442	+	0.958098i	$0.407528\pi$
$4$		0			0
$5$	4.99441	−	10.0028i	0.446713	−	0.894677i
$5$	4.99441	−	10.0028i	0.446713	−	0.894677i
$6$		0			0
$7$	−4.97302	+	4.97302i	−0.268518	+	0.268518i	−0.828503	−	0.559985i	$-0.810807\pi$
$7$	−4.97302	+	4.97302i	−0.268518	+	0.268518i	0.559985	+	0.828503i	$0.310807\pi$
$8$		0			0
$9$			2.63942i			0.0977564i
$10$		0			0
$11$	−29.8229			−0.817449			−0.408725	−	0.912658i	$-0.634026\pi$
$11$	−29.8229			−0.817449			−0.408725	+	0.912658i	$0.634026\pi$
$12$		0			0
$13$	−13.5734	−	13.5734i	−0.289583	−	0.289583i	0.547332	−	0.836915i	$-0.315643\pi$
$13$	−13.5734	−	13.5734i	−0.289583	−	0.289583i	−0.836915	+	0.547332i	$0.815643\pi$
$14$		0			0
$15$	17.4794	+	52.3406i	0.300877	+	0.900953i
$16$		0			0
$17$	−61.7929	−	61.7929i	−0.881588	−	0.881588i	0.112108	−	0.993696i	$-0.464240\pi$
$17$	−61.7929	−	61.7929i	−0.881588	−	0.881588i	−0.993696	+	0.112108i	$0.964240\pi$
$18$		0			0
$19$		−	131.323i		−	1.58566i	−0.609440	−	0.792832i	$-0.708606\pi$
$19$		−	131.323i		−	1.58566i	0.609440	−	0.792832i	$-0.291394\pi$
$20$		0			0
$21$		−	34.7119i		−	0.360703i
$22$		0			0
$23$	−1.13009	−	1.13009i	−0.0102452	−	0.0102452i	0.701966	−	0.712211i	$-0.252306\pi$
$23$	−1.13009	−	1.13009i	−0.0102452	−	0.0102452i	−0.712211	+	0.701966i	$0.752306\pi$
$24$		0			0
$25$	−75.1118	−	99.9161i	−0.600894	−	0.799329i
$26$		0			0
$27$	−103.442	−	103.442i	−0.737315	−	0.737315i
$28$		0			0
$29$	179.304			1.14813			0.574067	−	0.818809i	$-0.305365\pi$
$29$	179.304			1.14813			0.574067	+	0.818809i	$0.305365\pi$
$30$		0			0
$31$		−	276.096i		−	1.59962i	−0.600253	−	0.799810i	$-0.704933\pi$
$31$		−	276.096i		−	1.59962i	0.600253	−	0.799810i	$-0.295067\pi$
$32$		0			0
$33$	104.083	−	104.083i	0.549045	−	0.549045i
$34$		0			0
$35$	24.9068	+	74.5813i	0.120286	+	0.360187i
$36$		0			0
$37$	−278.964	+	278.964i	−1.23950	+	1.23950i	−0.279289	+	0.960207i	$0.590099\pi$
$37$	−278.964	+	278.964i	−1.23950	+	1.23950i	−0.960207	+	0.279289i	$0.909901\pi$
$38$		0			0
$39$	94.7429			0.389000
$40$		0			0
$41$	−225.140			−0.857585			−0.428793	−	0.903403i	$-0.641061\pi$
$41$	−225.140			−0.857585			−0.428793	+	0.903403i	$0.641061\pi$
$42$		0			0
$43$	−171.874	+	171.874i	−0.609546	+	0.609546i	−0.942827	−	0.333281i	$-0.891844\pi$
$43$	−171.874	+	171.874i	−0.609546	+	0.609546i	0.333281	+	0.942827i	$0.391844\pi$
$44$		0			0
$45$	26.4016	+	13.1824i	0.0874604	+	0.0436691i
$46$		0			0
$47$	−86.1627	+	86.1627i	−0.267407	+	0.267407i	−0.828055	−	0.560648i	$-0.810552\pi$
$47$	−86.1627	+	86.1627i	−0.267407	+	0.267407i	0.560648	+	0.828055i	$0.310552\pi$
$48$		0			0
$49$			293.538i			0.855797i
$50$		0			0
$51$	431.318			1.18425
$52$		0			0
$53$	108.361	+	108.361i	0.280841	+	0.280841i	0.833444	−	0.552603i	$-0.186366\pi$
$53$	108.361	+	108.361i	0.280841	+	0.280841i	−0.552603	+	0.833444i	$0.686366\pi$
$54$		0			0
$55$	−148.948	+	298.312i	−0.365166	+	0.731353i
$56$		0			0
$57$	458.322	+	458.322i	1.06502	+	1.06502i
$58$		0			0
$59$			157.272i			0.347034i	0.984831	+	0.173517i	$0.0555132\pi$
$59$			157.272i			0.347034i	−0.984831	+	0.173517i	$0.944487\pi$
$60$		0			0
$61$		−	791.867i		−	1.66210i	−0.556197	−	0.831051i	$-0.687740\pi$
$61$		−	791.867i		−	1.66210i	0.556197	−	0.831051i	$-0.312260\pi$
$62$		0			0
$63$	−13.1259	−	13.1259i	−0.0262493	−	0.0262493i
$64$		0			0
$65$	−203.563	+	67.9807i	−0.388444	+	0.129723i
$66$		0			0
$67$	3.80296	+	3.80296i	0.00693440	+	0.00693440i	0.710565	−	0.703631i	$-0.248439\pi$
$67$	3.80296	+	3.80296i	0.00693440	+	0.00693440i	−0.703631	+	0.710565i	$0.748439\pi$
$68$		0			0
$69$	7.88811			0.0137626
$70$		0			0
$71$			58.6097i			0.0979676i	0.998800	+	0.0489838i	$0.0155983\pi$
$71$			58.6097i			0.0979676i	−0.998800	+	0.0489838i	$0.984402\pi$
$72$		0			0
$73$	452.731	−	452.731i	0.725865	−	0.725865i	−0.243928	−	0.969793i	$-0.578436\pi$
$73$	452.731	−	452.731i	0.725865	−	0.725865i	0.969793	+	0.243928i	$0.0784361\pi$
$74$		0			0
$75$	610.852	+	86.5677i	0.940468	+	0.133280i
$76$		0			0
$77$	148.310	−	148.310i	0.219500	−	0.219500i
$78$		0			0
$79$	821.590			1.17008			0.585039	−	0.811005i	$-0.301079\pi$
$79$	821.590			1.17008			0.585039	+	0.811005i	$0.301079\pi$
$80$		0			0
$81$	650.769			0.892687
$82$		0			0
$83$	−512.512	+	512.512i	−0.677777	+	0.677777i	−0.959497	−	0.281720i	$-0.909095\pi$
$83$	−512.512	+	512.512i	−0.677777	+	0.677777i	0.281720	+	0.959497i	$0.409095\pi$
$84$		0			0
$85$	−926.721	+	309.483i	−1.18255	+	0.394919i
$86$		0			0
$87$	−625.775	+	625.775i	−0.771151	+	0.771151i
$88$		0			0
$89$			500.262i			0.595817i	0.954594	+	0.297908i	$0.0962890\pi$
$89$			500.262i			0.595817i	−0.954594	+	0.297908i	$0.903711\pi$
$90$		0			0
$91$	135.001			0.155516
$92$		0			0
$93$	963.581	+	963.581i	1.07439	+	1.07439i
$94$		0			0
$95$	−1313.60	−	655.882i	−1.41866	−	0.708337i
$96$		0			0
$97$	−60.7068	−	60.7068i	−0.0635448	−	0.0635448i	0.674620	−	0.738165i	$-0.264307\pi$
$97$	−60.7068	−	60.7068i	−0.0635448	−	0.0635448i	−0.738165	+	0.674620i	$0.764307\pi$
$98$		0			0
$99$		−	78.7153i		−	0.0799109i
$100$		0			0
$101$		−	428.534i		−	0.422185i	−0.977466	−	0.211093i	$-0.932298\pi$
$101$		−	428.534i		−	0.422185i	0.977466	−	0.211093i	$-0.0677021\pi$
$102$		0			0
$103$	946.098	+	946.098i	0.905066	+	0.905066i	0.995869	−	0.0908027i	$-0.0289433\pi$
$103$	946.098	+	946.098i	0.905066	+	0.905066i	−0.0908027	+	0.995869i	$0.528943\pi$
$104$		0			0
$105$	−347.216	−	173.366i	−0.322713	−	0.161131i
$106$		0			0
$107$	85.2152	+	85.2152i	0.0769912	+	0.0769912i	0.744554	−	0.667563i	$-0.232662\pi$
$107$	85.2152	+	85.2152i	0.0769912	+	0.0769912i	−0.667563	+	0.744554i	$0.732662\pi$
$108$		0			0
$109$	−82.8322			−0.0727879			−0.0363940	−	0.999338i	$-0.511587\pi$
$109$	−82.8322			−0.0727879			−0.0363940	+	0.999338i	$0.511587\pi$
$110$		0			0
$111$		−	1947.18i		−	1.66503i
$112$		0			0
$113$	−1123.03	+	1123.03i	−0.934917	+	0.934917i	−0.998008	−	0.0630908i	$-0.979904\pi$
$113$	−1123.03	+	1123.03i	−0.934917	+	0.934917i	0.0630908	+	0.998008i	$0.479904\pi$
$114$		0			0
$115$	−16.9482	+	5.65994i	−0.0137429	+	0.00458950i
$116$		0			0
$117$	35.8259	−	35.8259i	0.0283086	−	0.0283086i
$118$		0			0
$119$	614.595			0.473444
$120$		0			0
$121$	−441.595			−0.331777
$122$		0			0
$123$	785.746	−	785.746i	0.576002	−	0.576002i
$124$		0			0
$125$	−1374.58	+	252.306i	−0.983568	+	0.180535i
$126$		0			0
$127$	1307.29	−	1307.29i	0.913412	−	0.913412i	−0.0831268	−	0.996539i	$-0.526491\pi$
$127$	1307.29	−	1307.29i	0.913412	−	0.913412i	0.996539	+	0.0831268i	$0.0264906\pi$
$128$		0			0
$129$		−	1199.69i		−	0.818810i
$130$		0			0
$131$	−1395.75			−0.930894			−0.465447	−	0.885076i	$-0.654106\pi$
$131$	−1395.75			−0.930894			−0.465447	+	0.885076i	$0.654106\pi$
$132$		0			0
$133$	653.073	+	653.073i	0.425779	+	0.425779i
$134$		0			0
$135$	−1551.35	+	518.079i	−0.989027	+	0.330290i
$136$		0			0
$137$	−1203.46	−	1203.46i	−0.750499	−	0.750499i	0.224073	−	0.974572i	$-0.428064\pi$
$137$	−1203.46	−	1203.46i	−0.750499	−	0.750499i	−0.974572	+	0.224073i	$0.928064\pi$
$138$		0			0
$139$		−	682.041i		−	0.416187i	−0.978109	−	0.208093i	$-0.933274\pi$
$139$		−	682.041i		−	0.416187i	0.978109	−	0.208093i	$-0.0667258\pi$
$140$		0			0
$141$		−	601.421i		−	0.359211i
$142$		0			0
$143$	404.798	+	404.798i	0.236719	+	0.236719i
$144$		0			0
$145$	895.516	−	1793.54i	0.512887	−	1.02721i
$146$		0			0
$147$	−1024.46	−	1024.46i	−0.574801	−	0.574801i
$148$		0			0
$149$	2193.85			1.20622			0.603111	−	0.797657i	$-0.293928\pi$
$149$	2193.85			1.20622			0.603111	+	0.797657i	$0.293928\pi$
$150$		0			0
$151$			1358.69i			0.732245i	0.930567	+	0.366122i	$0.119315\pi$
$151$			1358.69i			0.732245i	−0.930567	+	0.366122i	$0.880685\pi$
$152$		0			0
$153$	163.098	−	163.098i	0.0861809	−	0.0861809i
$154$		0			0
$155$	−2761.73	−	1378.93i	−1.43114	−	0.714572i
$156$		0			0
$157$	−315.821	+	315.821i	−0.160543	+	0.160543i	−0.782807	−	0.622264i	$-0.786213\pi$
$157$	−315.821	+	315.821i	−0.160543	+	0.160543i	0.622264	+	0.782807i	$0.286213\pi$
$158$		0			0
$159$	−756.368			−0.377257
$160$		0			0
$161$	11.2399			0.00550206
$162$		0			0
$163$	965.741	−	965.741i	0.464065	−	0.464065i	−0.435920	−	0.899985i	$-0.643577\pi$
$163$	965.741	−	965.741i	0.464065	−	0.464065i	0.899985	+	0.435920i	$0.143577\pi$
$164$		0			0
$165$	−521.286	−	1560.95i	−0.245952	−	0.736483i
$166$		0			0
$167$	−1617.68	+	1617.68i	−0.749578	+	0.749578i	−0.974400	−	0.224822i	$-0.927820\pi$
$167$	−1617.68	+	1617.68i	−0.749578	+	0.749578i	0.224822	+	0.974400i	$0.427820\pi$
$168$		0			0
$169$		−	1828.53i		−	0.832283i
$170$		0			0
$171$	346.618			0.155009
$172$		0			0
$173$	−906.331	−	906.331i	−0.398307	−	0.398307i	0.479329	−	0.877635i	$-0.340880\pi$
$173$	−906.331	−	906.331i	−0.398307	−	0.398307i	−0.877635	+	0.479329i	$0.840880\pi$
$174$		0			0
$175$	870.416	+	123.352i	0.375984	+	0.0532831i
$176$		0			0
$177$	−548.882	−	548.882i	−0.233088	−	0.233088i
$178$		0			0
$179$			1840.26i			0.768421i	0.923246	+	0.384211i	$0.125526\pi$
$179$			1840.26i			0.768421i	−0.923246	+	0.384211i	$0.874474\pi$
$180$		0			0
$181$		−	1686.59i		−	0.692613i	−0.938121	−	0.346307i	$-0.887436\pi$
$181$		−	1686.59i		−	0.692613i	0.938121	−	0.346307i	$-0.112564\pi$
$182$		0			0
$183$	2763.64	+	2763.64i	1.11636	+	1.11636i
$184$		0			0
$185$	1397.16	+	4183.68i	0.555249	+	1.66265i
$186$		0			0
$187$	1842.84	+	1842.84i	0.720653	+	0.720653i
$188$		0			0
$189$	1028.84			0.395964
$190$		0			0
$191$		−	5087.58i		−	1.92735i	−0.267069	−	0.963677i	$-0.586055\pi$
$191$		−	5087.58i		−	1.92735i	0.267069	−	0.963677i	$-0.413945\pi$
$192$		0			0
$193$	−780.214	+	780.214i	−0.290990	+	0.290990i	−0.837471	−	0.546482i	$-0.815967\pi$
$193$	−780.214	+	780.214i	−0.290990	+	0.290990i	0.546482	+	0.837471i	$0.315967\pi$
$194$		0			0
$195$	473.185	−	947.694i	0.173772	−	0.348030i
$196$		0			0
$197$	−438.351	+	438.351i	−0.158534	+	0.158534i	−0.781917	−	0.623383i	$-0.785758\pi$
$197$	−438.351	+	438.351i	−0.158534	+	0.158534i	0.623383	+	0.781917i	$0.285758\pi$
$198$		0			0
$199$	−1062.57			−0.378510			−0.189255	−	0.981928i	$-0.560607\pi$
$199$	−1062.57			−0.378510			−0.189255	+	0.981928i	$0.560607\pi$
$200$		0			0
$201$	−26.5448			−0.00931506
$202$		0			0
$203$	−891.680	+	891.680i	−0.308294	+	0.308294i
$204$		0			0
$205$	−1124.44	+	2252.03i	−0.383095	+	0.767262i
$206$		0			0
$207$	2.98279	−	2.98279i	0.00100154	−	0.00100154i
$208$		0			0
$209$			3916.44i			1.29620i
$210$		0			0
$211$	2549.46			0.831810			0.415905	−	0.909408i	$-0.363465\pi$
$211$	2549.46			0.831810			0.415905	+	0.909408i	$0.363465\pi$
$212$		0			0
$213$	−204.550	−	204.550i	−0.0658005	−	0.0658005i
$214$		0			0
$215$	860.809	+	2577.62i	0.273054	+	0.817639i
$216$		0			0
$217$	1373.03	+	1373.03i	0.429526	+	0.429526i
$218$		0			0
$219$			3160.09i			0.975063i
$220$		0			0
$221$			1677.48i			0.510585i
$222$		0			0
$223$	−4159.52	−	4159.52i	−1.24907	−	1.24907i	−0.956132	−	0.292937i	$-0.905367\pi$
$223$	−4159.52	−	4159.52i	−1.24907	−	1.24907i	−0.292937	−	0.956132i	$-0.594633\pi$
$224$		0			0
$225$	263.721	−	198.252i	0.0781395	−	0.0587413i
$226$		0			0
$227$	2668.93	+	2668.93i	0.780367	+	0.780367i	0.979893	−	0.199526i	$-0.0639401\pi$
$227$	2668.93	+	2668.93i	0.780367	+	0.780367i	−0.199526	+	0.979893i	$0.563940\pi$
$228$		0			0
$229$	1174.62			0.338956			0.169478	−	0.985534i	$-0.445792\pi$
$229$	1174.62			0.338956			0.169478	+	0.985534i	$0.445792\pi$
$230$		0			0
$231$			1035.21i			0.294856i
$232$		0			0
$233$	−626.021	+	626.021i	−0.176017	+	0.176017i	−0.789617	−	0.613600i	$-0.789721\pi$
$233$	−626.021	+	626.021i	−0.176017	+	0.176017i	0.613600	+	0.789617i	$0.289721\pi$
$234$		0			0
$235$	431.536	+	1292.20i	0.119789	+	0.358697i
$236$		0			0
$237$	−2867.37	+	2867.37i	−0.785890	+	0.785890i
$238$		0			0
$239$	2756.36			0.746000			0.373000	−	0.927831i	$-0.378329\pi$
$239$	2756.36			0.746000			0.373000	+	0.927831i	$0.378329\pi$
$240$		0			0
$241$	5484.17			1.46584			0.732918	−	0.680317i	$-0.238158\pi$
$241$	5484.17			1.46584			0.732918	+	0.680317i	$0.238158\pi$
$242$		0			0
$243$	521.743	−	521.743i	0.137736	−	0.137736i
$244$		0			0
$245$	2936.20	+	1466.05i	0.765662	+	0.382296i
$246$		0			0
$247$	−1782.50	+	1782.50i	−0.459181	+	0.459181i
$248$		0			0
$249$		−	3577.36i		−	0.910466i
$250$		0			0
$251$	−2541.79			−0.639190			−0.319595	−	0.947554i	$-0.603547\pi$
$251$	−2541.79			−0.639190			−0.319595	+	0.947554i	$0.603547\pi$
$252$		0			0
$253$	33.7026	+	33.7026i	0.00837497	+	0.00837497i
$254$		0			0
$255$	2154.18	−	4314.39i	0.529019	−	1.05952i
$256$		0			0
$257$	−985.343	−	985.343i	−0.239160	−	0.239160i	0.577342	−	0.816502i	$-0.304090\pi$
$257$	−985.343	−	985.343i	−0.239160	−	0.239160i	−0.816502	+	0.577342i	$0.804090\pi$
$258$		0			0
$259$		−	2774.58i		−	0.665653i
$260$		0			0
$261$			473.258i			0.112237i
$262$		0			0
$263$	−1805.99	−	1805.99i	−0.423431	−	0.423431i	0.462952	−	0.886383i	$-0.346790\pi$
$263$	−1805.99	−	1805.99i	−0.423431	−	0.423431i	−0.886383	+	0.462952i	$0.846790\pi$
$264$		0			0
$265$	1625.12	−	542.715i	0.376718	−	0.125807i
$266$		0			0
$267$	−1745.93	−	1745.93i	−0.400184	−	0.400184i
$268$		0			0
$269$	−5145.02			−1.16616			−0.583080	−	0.812414i	$-0.698153\pi$
$269$	−5145.02			−1.16616			−0.583080	+	0.812414i	$0.698153\pi$
$270$		0			0
$271$			3799.86i			0.851754i	0.904781	+	0.425877i	$0.140034\pi$
$271$			3799.86i			0.851754i	−0.904781	+	0.425877i	$0.859966\pi$
$272$		0			0
$273$	−471.158	+	471.158i	−0.104453	+	0.104453i
$274$		0			0
$275$	2240.05	+	2979.79i	0.491201	+	0.653411i
$276$		0			0
$277$	2570.79	−	2570.79i	0.557631	−	0.557631i	−0.371002	−	0.928632i	$-0.620986\pi$
$277$	2570.79	−	2570.79i	0.557631	−	0.557631i	0.928632	+	0.371002i	$0.120986\pi$
$278$		0			0
$279$	728.733			0.156373
$280$		0			0
$281$	−4622.48			−0.981330			−0.490665	−	0.871348i	$-0.663246\pi$
$281$	−4622.48			−0.981330			−0.490665	+	0.871348i	$0.663246\pi$
$282$		0			0
$283$	3903.74	−	3903.74i	0.819977	−	0.819977i	−0.166127	−	0.986104i	$-0.553126\pi$
$283$	3903.74	−	3903.74i	0.819977	−	0.819977i	0.986104	+	0.166127i	$0.0531263\pi$
$284$		0			0
$285$	6873.54	−	2295.45i	1.42861	−	0.477091i
$286$		0			0
$287$	1119.63	−	1119.63i	0.230277	−	0.230277i
$288$		0			0
$289$			2723.73i			0.554393i
$290$		0			0
$291$	423.737			0.0853604
$292$		0			0
$293$	−3519.01	−	3519.01i	−0.701647	−	0.701647i	0.263117	−	0.964764i	$-0.415249\pi$
$293$	−3519.01	−	3519.01i	−0.701647	−	0.701647i	−0.964764	+	0.263117i	$0.915249\pi$
$294$		0			0
$295$	1573.16	+	785.479i	0.310484	+	0.155025i
$296$		0			0
$297$	3084.95	+	3084.95i	0.602717	+	0.602717i
$298$		0			0
$299$			30.6783i			0.00593369i
$300$		0			0
$301$		−	1709.46i		−	0.327348i
$302$		0			0
$303$	1495.59	+	1495.59i	0.283563	+	0.283563i
$304$		0			0
$305$	−7920.88	−	3954.91i	−1.48704	−	0.742483i
$306$		0			0
$307$	−5492.90	−	5492.90i	−1.02116	−	1.02116i	−0.999771	−	0.0213898i	$-0.993191\pi$
$307$	−5492.90	−	5492.90i	−1.02116	−	1.02116i	−0.0213898	−	0.999771i	$-0.506809\pi$
$308$		0			0
$309$	−6603.82			−1.21579
$310$		0			0
$311$			8143.33i			1.48478i	0.669969	+	0.742389i	$0.266307\pi$
$311$			8143.33i			1.48478i	−0.669969	+	0.742389i	$0.733693\pi$
$312$		0			0
$313$	2547.32	−	2547.32i	0.460009	−	0.460009i	−0.438649	−	0.898658i	$-0.644543\pi$
$313$	2547.32	−	2547.32i	0.460009	−	0.460009i	0.898658	+	0.438649i	$0.144543\pi$
$314$		0			0
$315$	−196.852	+	65.7395i	−0.0352106	+	0.0117587i
$316$		0			0
$317$	6080.74	−	6080.74i	1.07738	−	1.07738i	0.0806321	−	0.996744i	$-0.474306\pi$
$317$	6080.74	−	6080.74i	1.07738	−	1.07738i	0.996744	−	0.0806321i	$-0.0256939\pi$
$318$		0			0
$319$	−5347.36			−0.938541
$320$		0			0
$321$	−594.806			−0.103423
$322$		0			0
$323$	−8114.85	+	8114.85i	−1.39790	+	1.39790i
$324$		0			0
$325$	−336.678	+	2375.72i	−0.0574632	+	0.405481i
$326$		0			0
$327$	289.086	−	289.086i	0.0488884	−	0.0488884i
$328$		0			0
$329$		−	856.977i		−	0.143607i
$330$		0			0
$331$	−3018.02			−0.501164			−0.250582	−	0.968095i	$-0.580622\pi$
$331$	−3018.02			−0.501164			−0.250582	+	0.968095i	$0.580622\pi$
$332$		0			0
$333$	−736.303	−	736.303i	−0.121169	−	0.121169i
$334$		0			0
$335$	57.0337	−	19.0467i	0.00930174	−	0.00310636i
$336$		0			0
$337$	−1097.58	−	1097.58i	−0.177415	−	0.177415i	0.612813	−	0.790228i	$-0.290038\pi$
$337$	−1097.58	−	1097.58i	−0.177415	−	0.177415i	−0.790228	+	0.612813i	$0.790038\pi$
$338$		0			0
$339$		−	7838.80i		−	1.25589i
$340$		0			0
$341$			8233.97i			1.30761i
$342$		0			0
$343$	−3165.51	−	3165.51i	−0.498314	−	0.498314i
$344$		0			0
$345$	39.3964	−	78.9031i	0.00614792	−	0.0123130i
$346$		0			0
$347$	−56.2142	−	56.2142i	−0.00869665	−	0.00869665i	0.702745	−	0.711442i	$-0.251957\pi$
$347$	−56.2142	−	56.2142i	−0.00869665	−	0.00869665i	−0.711442	+	0.702745i	$0.751957\pi$
$348$		0			0
$349$	4674.06			0.716897			0.358448	−	0.933550i	$-0.383306\pi$
$349$	4674.06			0.716897			0.358448	+	0.933550i	$0.383306\pi$
$350$		0			0
$351$			2808.13i			0.427028i
$352$		0			0
$353$	4857.43	−	4857.43i	0.732393	−	0.732393i	−0.238700	−	0.971093i	$-0.576721\pi$
$353$	4857.43	−	4857.43i	0.732393	−	0.732393i	0.971093	+	0.238700i	$0.0767214\pi$
$354$		0			0
$355$	586.261	+	292.721i	0.0876493	+	0.0437634i
$356$		0			0
$357$	−2144.95	+	2144.95i	−0.317991	+	0.317991i
$358$		0			0
$359$	−132.300			−0.0194500			−0.00972499	−	0.999953i	$-0.503096\pi$
$359$	−132.300			−0.0194500			−0.00972499	+	0.999953i	$0.503096\pi$
$360$		0			0
$361$	−10386.8			−1.51433
$362$		0			0
$363$	1541.18	−	1541.18i	0.222840	−	0.222840i
$364$		0			0
$365$	−2267.45	−	6789.70i	−0.325161	−	0.973669i
$366$		0			0
$367$	7636.05	−	7636.05i	1.08610	−	1.08610i	0.0901736	−	0.995926i	$-0.471258\pi$
$367$	7636.05	−	7636.05i	1.08610	−	1.08610i	0.995926	−	0.0901736i	$-0.0287422\pi$
$368$		0			0
$369$		−	594.240i		−	0.0838345i
$370$		0			0
$371$	−1077.77			−0.150822
$372$		0			0
$373$	3945.34	+	3945.34i	0.547673	+	0.547673i	0.925767	−	0.378094i	$-0.123420\pi$
$373$	3945.34	+	3945.34i	0.547673	+	0.547673i	−0.378094	+	0.925767i	$0.623420\pi$
$374$		0			0
$375$	3916.76	−	5677.87i	0.539362	−	0.781877i
$376$		0			0
$377$	−2433.76	−	2433.76i	−0.332480	−	0.332480i
$378$		0			0
$379$		−	996.022i		−	0.134993i	−0.997720	−	0.0674963i	$-0.978499\pi$
$379$		−	996.022i		−	0.134993i	0.997720	−	0.0674963i	$-0.0215011\pi$
$380$		0			0
$381$			9124.96i			1.22700i
$382$		0			0
$383$	−4031.81	−	4031.81i	−0.537901	−	0.537901i	0.385011	−	0.922912i	$-0.374198\pi$
$383$	−4031.81	−	4031.81i	−0.537901	−	0.537901i	−0.922912	+	0.385011i	$0.874198\pi$
$384$		0			0
$385$	−742.792	−	2224.23i	−0.0983278	−	0.294435i
$386$		0			0
$387$	−453.647	−	453.647i	−0.0595870	−	0.0595870i
$388$		0			0
$389$	−7014.26			−0.914234			−0.457117	−	0.889407i	$-0.651118\pi$
$389$	−7014.26			−0.914234			−0.457117	+	0.889407i	$0.651118\pi$
$390$		0			0
$391$			139.663i			0.0180642i
$392$		0			0
$393$	4871.20	−	4871.20i	0.625240	−	0.625240i
$394$		0			0
$395$	4103.36	−	8218.20i	0.522689	−	1.04684i
$396$		0			0
$397$	2159.35	−	2159.35i	0.272984	−	0.272984i	−0.557316	−	0.830300i	$-0.688169\pi$
$397$	2159.35	−	2159.35i	0.272984	−	0.272984i	0.830300	+	0.557316i	$0.188169\pi$
$398$		0			0
$399$	−4558.48			−0.571954
$400$		0			0
$401$	2696.76			0.335835			0.167917	−	0.985801i	$-0.446296\pi$
$401$	2696.76			0.335835			0.167917	+	0.985801i	$0.446296\pi$
$402$		0			0
$403$	−3747.55	+	3747.55i	−0.463223	+	0.463223i
$404$		0			0
$405$	3250.21	−	6509.51i	0.398775	−	0.798667i
$406$		0			0
$407$	8319.51	−	8319.51i	1.01323	−	1.01323i
$408$		0			0
$409$		−	307.849i		−	0.0372180i	−0.999827	−	0.0186090i	$-0.994076\pi$
$409$		−	307.849i		−	0.0372180i	0.999827	−	0.0186090i	$-0.00592377\pi$
$410$		0			0
$411$	8400.20			1.00815
$412$		0			0
$413$	−782.115	−	782.115i	−0.0931848	−	0.0931848i
$414$		0			0
$415$	2566.86	+	7686.25i	0.303620	+	0.909164i
$416$		0			0
$417$	2380.34	+	2380.34i	0.279534	+	0.279534i
$418$		0			0
$419$		−	5297.21i		−	0.617627i	−0.951123	−	0.308813i	$-0.900068\pi$
$419$		−	5297.21i		−	0.617627i	0.951123	−	0.308813i	$-0.0999318\pi$
$420$		0			0
$421$			6230.79i			0.721307i	0.932700	+	0.360654i	$0.117446\pi$
$421$			6230.79i			0.721307i	−0.932700	+	0.360654i	$0.882554\pi$
$422$		0			0
$423$	−227.420	−	227.420i	−0.0261407	−	0.0261407i
$424$		0			0
$425$	−1532.73	+	10815.5i	−0.174937	+	1.23442i
$426$		0			0
$427$	3937.97	+	3937.97i	0.446304	+	0.446304i
$428$		0			0
$429$	−2825.51			−0.317988
$430$		0			0
$431$			9290.49i			1.03830i	0.854683	+	0.519150i	$0.173751\pi$
$431$			9290.49i			1.03830i	−0.854683	+	0.519150i	$0.826249\pi$
$432$		0			0
$433$	−7427.65	+	7427.65i	−0.824365	+	0.824365i	−0.986731	−	0.162365i	$-0.948088\pi$
$433$	−7427.65	+	7427.65i	−0.824365	+	0.824365i	0.162365	+	0.986731i	$0.448088\pi$
$434$		0			0
$435$	3134.12	+	9384.87i	0.345447	+	1.03441i
$436$		0			0
$437$	−148.407	+	148.407i	−0.0162455	+	0.0162455i
$438$		0			0
$439$	−13789.5			−1.49917			−0.749587	−	0.661906i	$-0.769748\pi$
$439$	−13789.5			−1.49917			−0.749587	+	0.661906i	$0.769748\pi$
$440$		0			0
$441$	−774.772			−0.0836596
$442$		0			0
$443$	−532.124	+	532.124i	−0.0570699	+	0.0570699i	−0.735066	−	0.677996i	$-0.762849\pi$
$443$	−532.124	+	532.124i	−0.0570699	+	0.0570699i	0.677996	+	0.735066i	$0.262849\pi$
$444$		0			0
$445$	5004.02	+	2498.51i	0.533064	+	0.266159i
$446$		0			0
$447$	−7656.59	+	7656.59i	−0.810166	+	0.810166i
$448$		0			0
$449$			8042.60i			0.845331i	0.906286	+	0.422666i	$0.138905\pi$
$449$			8042.60i			0.845331i	−0.906286	+	0.422666i	$0.861095\pi$
$450$		0			0
$451$	6714.33			0.701033
$452$		0			0
$453$	−4741.88	−	4741.88i	−0.491817	−	0.491817i
$454$		0			0
$455$	674.251	−	1350.39i	0.0694712	−	0.139137i
$456$		0			0
$457$	7997.03	+	7997.03i	0.818567	+	0.818567i	0.985900	−	0.167333i	$-0.0535155\pi$
$457$	7997.03	+	7997.03i	0.818567	+	0.818567i	−0.167333	+	0.985900i	$0.553516\pi$
$458$		0			0
$459$			12784.0i			1.30001i
$460$		0			0
$461$			4431.07i			0.447669i	0.974627	+	0.223835i	$0.0718576\pi$
$461$			4431.07i			0.447669i	−0.974627	+	0.223835i	$0.928142\pi$
$462$		0			0
$463$	5675.69	+	5675.69i	0.569701	+	0.569701i	0.932045	−	0.362343i	$-0.118023\pi$
$463$	5675.69	+	5675.69i	0.569701	+	0.569701i	−0.362343	+	0.932045i	$0.618023\pi$
$464$		0			0
$465$	14451.0	−	4825.99i	1.44118	−	0.481290i
$466$		0			0
$467$	2816.21	+	2816.21i	0.279055	+	0.279055i	0.832732	−	0.553677i	$-0.186776\pi$
$467$	2816.21	+	2816.21i	0.279055	+	0.279055i	−0.553677	+	0.832732i	$0.686776\pi$
$468$		0			0
$469$	−37.8243			−0.00372402
$470$		0			0
$471$		−	2204.45i		−	0.215659i
$472$		0			0
$473$	5125.77	−	5125.77i	0.498273	−	0.498273i
$474$		0			0
$475$	−13121.3	+	9863.92i	−1.26747	+	0.952816i
$476$		0			0
$477$	−286.012	+	286.012i	−0.0274540	+	0.0274540i
$478$		0			0
$479$	5793.27			0.552612			0.276306	−	0.961070i	$-0.410890\pi$
$479$	5793.27			0.552612			0.276306	+	0.961070i	$0.410890\pi$
$480$		0			0
$481$	7572.96			0.717874
$482$		0			0
$483$	−39.2277	+	39.2277i	−0.00369549	+	0.00369549i
$484$		0			0
$485$	−910.432	+	304.043i	−0.0852383	+	0.0284657i
$486$		0			0
$487$	5340.84	−	5340.84i	0.496954	−	0.496954i	−0.413535	−	0.910488i	$-0.635706\pi$
$487$	5340.84	−	5340.84i	0.496954	−	0.496954i	0.910488	+	0.413535i	$0.135706\pi$
$488$		0			0
$489$			6740.92i			0.623385i
$490$		0			0
$491$	−11910.1			−1.09470			−0.547348	−	0.836905i	$-0.684363\pi$
$491$	−11910.1			−1.09470			−0.547348	+	0.836905i	$0.684363\pi$
$492$		0			0
$493$	−11079.7	−	11079.7i	−1.01218	−	1.01218i
$494$		0			0
$495$	−787.373	−	393.136i	−0.0714945	−	0.0356973i
$496$		0			0
$497$	−291.467	−	291.467i	−0.0263060	−	0.0263060i
$498$		0			0
$499$			9075.03i			0.814137i	0.913398	+	0.407068i	$0.133449\pi$
$499$			9075.03i			0.814137i	−0.913398	+	0.407068i	$0.866551\pi$
$500$		0			0
$501$		−	11291.5i		−	1.00692i
$502$		0			0
$503$	−4875.24	−	4875.24i	−0.432160	−	0.432160i	0.457203	−	0.889362i	$-0.348851\pi$
$503$	−4875.24	−	4875.24i	−0.432160	−	0.432160i	−0.889362	+	0.457203i	$0.848851\pi$
$504$		0			0
$505$	−4286.53	−	2140.27i	−0.377719	−	0.188596i
$506$		0			0
$507$	6381.61	+	6381.61i	0.559008	+	0.559008i
$508$		0			0
$509$	16594.1			1.44503			0.722517	−	0.691353i	$-0.242985\pi$
$509$	16594.1			1.44503			0.722517	+	0.691353i	$0.242985\pi$
$510$		0			0
$511$			4502.88i			0.389815i
$512$		0			0
$513$	−13584.4	+	13584.4i	−1.16913	+	1.16913i
$514$		0			0
$515$	14188.8	−	4738.42i	1.21405	−	0.405437i
$516$		0			0
$517$	2569.62	−	2569.62i	0.218592	−	0.218592i
$518$		0			0
$519$	6326.24			0.535050
$520$		0			0
$521$	16453.8			1.38360			0.691800	−	0.722089i	$-0.256818\pi$
$521$	16453.8			1.38360			0.691800	+	0.722089i	$0.256818\pi$
$522$		0			0
$523$	14010.1	−	14010.1i	1.17136	−	1.17136i	0.189472	−	0.981886i	$-0.439322\pi$
$523$	14010.1	−	14010.1i	1.17136	−	1.17136i	0.981886	−	0.189472i	$-0.0606778\pi$
$524$		0			0
$525$	−3468.28	+	2607.27i	−0.288320	+	0.216744i
$526$		0			0
$527$	−17060.8	+	17060.8i	−1.41021	+	1.41021i
$528$		0			0
$529$		−	12164.4i		−	0.999790i
$530$		0			0
$531$	−415.107			−0.0339248
$532$		0			0
$533$	3055.91	+	3055.91i	0.248342	+	0.248342i
$534$		0			0
$535$	1277.99	−	426.790i	0.103275	−	0.0344893i
$536$		0			0
$537$	−6422.55	−	6422.55i	−0.516115	−	0.516115i
$538$		0			0
$539$		−	8754.16i		−	0.699570i
$540$		0			0
$541$		−	12838.9i		−	1.02031i	−0.860082	−	0.510156i	$-0.829588\pi$
$541$		−	12838.9i		−	1.02031i	0.860082	−	0.510156i	$-0.170412\pi$
$542$		0			0
$543$	5886.23	+	5886.23i	0.465198	+	0.465198i
$544$		0			0
$545$	−413.698	+	828.553i	−0.0325153	+	0.0651217i
$546$		0			0
$547$	−8650.51	−	8650.51i	−0.676178	−	0.676178i	0.282956	−	0.959133i	$-0.408685\pi$
$547$	−8650.51	−	8650.51i	−0.676178	−	0.676178i	−0.959133	+	0.282956i	$0.908685\pi$
$548$		0			0
$549$	2090.07			0.162481
$550$		0			0
$551$		−	23546.7i		−	1.82055i
$552$		0			0
$553$	−4085.78	+	4085.78i	−0.314186	+	0.314186i
$554$		0			0
$555$	−19477.3	−	9725.02i	−1.48966	−	0.743791i
$556$		0			0
$557$	−13918.5	+	13918.5i	−1.05879	+	1.05879i	−0.0606281	+	0.998160i	$0.519310\pi$
$557$	−13918.5	+	13918.5i	−1.05879	+	1.05879i	−0.998160	+	0.0606281i	$0.980690\pi$
$558$		0			0
$559$	4665.81			0.353028
$560$		0			0
$561$	−12863.2			−0.968062
$562$		0			0
$563$	7416.37	−	7416.37i	0.555173	−	0.555173i	−0.372756	−	0.927929i	$-0.621587\pi$
$563$	7416.37	−	7416.37i	0.555173	−	0.555173i	0.927929	+	0.372756i	$0.121587\pi$
$564$		0			0
$565$	5624.56	+	16842.3i	0.418809	+	1.25409i
$566$		0			0
$567$	−3236.28	+	3236.28i	−0.239702	+	0.239702i
$568$		0			0
$569$		−	12648.3i		−	0.931892i	−0.884813	−	0.465946i	$-0.845714\pi$
$569$		−	12648.3i		−	0.931892i	0.884813	−	0.465946i	$-0.154286\pi$
$570$		0			0
$571$	−10159.1			−0.744561			−0.372281	−	0.928120i	$-0.621424\pi$
$571$	−10159.1			−0.744561			−0.372281	+	0.928120i	$0.621424\pi$
$572$		0			0
$573$	17755.8	+	17755.8i	1.29452	+	1.29452i
$574$		0			0
$575$	−28.0312	+	197.798i	−0.00203301	+	0.0143456i
$576$		0			0
$577$	−9741.36	−	9741.36i	−0.702839	−	0.702839i	0.262180	−	0.965019i	$-0.415559\pi$
$577$	−9741.36	−	9741.36i	−0.702839	−	0.702839i	−0.965019	+	0.262180i	$0.915559\pi$
$578$		0			0
$579$		−	5445.93i		−	0.390890i
$580$		0			0
$581$		−	5097.46i		−	0.363990i
$582$		0			0
$583$	−3231.65	−	3231.65i	−0.229573	−	0.229573i
$584$		0			0
$585$	−179.430	−	537.288i	−0.0126812	−	0.0379729i
$586$		0			0
$587$	8598.06	+	8598.06i	0.604566	+	0.604566i	0.941521	−	0.336955i	$-0.109397\pi$
$587$	8598.06	+	8598.06i	0.604566	+	0.604566i	−0.336955	+	0.941521i	$0.609397\pi$
$588$		0			0
$589$	−36257.8			−2.53646
$590$		0			0
$591$		−	3059.71i		−	0.212961i
$592$		0			0
$593$	8087.66	−	8087.66i	0.560068	−	0.560068i	−0.369259	−	0.929327i	$-0.620388\pi$
$593$	8087.66	−	8087.66i	0.560068	−	0.560068i	0.929327	+	0.369259i	$0.120388\pi$
$594$		0			0
$595$	3069.54	−	6147.66i	0.211494	−	0.423579i
$596$		0			0
$597$	3708.39	−	3708.39i	0.254229	−	0.254229i
$598$		0			0
$599$	21309.5			1.45356			0.726779	−	0.686872i	$-0.241017\pi$
$599$	21309.5			1.45356			0.726779	+	0.686872i	$0.241017\pi$
$600$		0			0
$601$	−6521.01			−0.442592			−0.221296	−	0.975207i	$-0.571029\pi$
$601$	−6521.01			−0.442592			−0.221296	+	0.975207i	$0.571029\pi$
$602$		0			0
$603$	−10.0376	+	10.0376i	−0.000677882	+	0.000677882i
$604$		0			0
$605$	−2205.50	+	4417.18i	−0.148209	+	0.296833i
$606$		0			0
$607$	2019.89	−	2019.89i	0.135066	−	0.135066i	−0.636342	−	0.771407i	$-0.719553\pi$
$607$	2019.89	−	2019.89i	0.135066	−	0.135066i	0.771407	+	0.636342i	$0.219553\pi$
$608$		0			0
$609$		−	6223.98i		−	0.414135i
$610$		0			0
$611$	2339.04			0.154873
$612$		0			0
$613$	−1205.07	−	1205.07i	−0.0794004	−	0.0794004i	0.666291	−	0.745692i	$-0.267881\pi$
$613$	−1205.07	−	1205.07i	−0.0794004	−	0.0794004i	−0.745692	+	0.666291i	$0.767881\pi$
$614$		0			0
$615$	−3935.32	−	11784.0i	−0.258028	−	0.772644i
$616$		0			0
$617$	−11429.9	−	11429.9i	−0.745789	−	0.745789i	0.227897	−	0.973685i	$-0.426815\pi$
$617$	−11429.9	−	11429.9i	−0.745789	−	0.745789i	−0.973685	+	0.227897i	$0.926815\pi$
$618$		0			0
$619$			27070.5i			1.75777i	0.477037	+	0.878883i	$0.341711\pi$
$619$			27070.5i			1.75777i	−0.477037	+	0.878883i	$0.658289\pi$
$620$		0			0
$621$			233.799i			0.0151079i
$622$		0			0
$623$	−2487.81	−	2487.81i	−0.159987	−	0.159987i
$624$		0			0
$625$	−4341.44	+	15009.7i	−0.277852	+	0.960624i
$626$		0			0
$627$	−13668.5	−	13668.5i	−0.870600	−	0.870600i
$628$		0			0
$629$	34476.0			2.18545
$630$		0			0
$631$		−	24755.1i		−	1.56178i	−0.624668	−	0.780891i	$-0.714766\pi$
$631$		−	24755.1i		−	1.56178i	0.624668	−	0.780891i	$-0.285234\pi$
$632$		0			0
$633$	−8897.67	+	8897.67i	−0.558690	+	0.558690i
$634$		0			0
$635$	−6547.42	−	19605.7i	−0.409175	−	1.22524i
$636$		0			0
$637$	3984.31	−	3984.31i	0.247824	−	0.247824i
$638$		0			0
$639$	−154.696			−0.00957696
$640$		0			0
$641$	18471.2			1.13817			0.569087	−	0.822277i	$-0.307297\pi$
$641$	18471.2			1.13817			0.569087	+	0.822277i	$0.307297\pi$
$642$		0			0
$643$	−18811.1	+	18811.1i	−1.15372	+	1.15372i	−0.167914	+	0.985802i	$0.553703\pi$
$643$	−18811.1	+	18811.1i	−1.15372	+	1.15372i	−0.985802	+	0.167914i	$0.946297\pi$
$644$		0			0
$645$	−12000.2	−	5991.73i	−0.732571	−	0.365774i
$646$		0			0
$647$	−7872.94	+	7872.94i	−0.478388	+	0.478388i	−0.904616	−	0.426228i	$-0.859842\pi$
$647$	−7872.94	+	7872.94i	−0.478388	+	0.478388i	0.426228	+	0.904616i	$0.359842\pi$
$648$		0			0
$649$		−	4690.30i		−	0.283683i
$650$		0			0
$651$	−9583.81			−0.576988
$652$		0			0
$653$	−6473.08	−	6473.08i	−0.387919	−	0.387919i	0.486026	−	0.873945i	$-0.338446\pi$
$653$	−6473.08	−	6473.08i	−0.387919	−	0.387919i	−0.873945	+	0.486026i	$0.838446\pi$
$654$		0			0
$655$	−6970.94	+	13961.4i	−0.415843	+	0.832849i
$656$		0			0
$657$	1194.95	+	1194.95i	0.0709580	+	0.0709580i
$658$		0			0
$659$		−	9716.99i		−	0.574386i	−0.957873	−	0.287193i	$-0.907278\pi$
$659$		−	9716.99i		−	0.574386i	0.957873	−	0.287193i	$-0.0927221\pi$
$660$		0			0
$661$		−	14769.4i		−	0.869080i	−0.900653	−	0.434540i	$-0.856911\pi$
$661$		−	14769.4i		−	0.869080i	0.900653	−	0.434540i	$-0.143089\pi$
$662$		0			0
$663$	−5854.44	−	5854.44i	−0.342938	−	0.342938i
$664$		0			0
$665$	9794.26	−	3270.84i	0.571136	−	0.190733i
$666$		0			0
$667$	−202.630	−	202.630i	−0.0117629	−	0.0117629i
$668$		0			0
$669$	29033.7			1.67789
$670$		0			0
$671$			23615.8i			1.35868i
$672$		0			0
$673$	2123.24	−	2123.24i	0.121612	−	0.121612i	−0.643681	−	0.765294i	$-0.722594\pi$
$673$	2123.24	−	2123.24i	0.121612	−	0.121612i	0.765294	+	0.643681i	$0.222594\pi$
$674$		0			0
$675$	−2565.82	+	18105.3i	−0.146309	+	1.03240i
$676$		0			0
$677$	−859.467	+	859.467i	−0.0487918	+	0.0487918i	−0.731082	−	0.682290i	$-0.760984\pi$
$677$	−859.467	+	859.467i	−0.0487918	+	0.0487918i	0.682290	+	0.731082i	$0.260984\pi$
$678$		0			0
$679$	603.792			0.0341258
$680$		0			0
$681$	−18629.3			−1.04828
$682$		0			0
$683$	20317.2	−	20317.2i	1.13824	−	1.13824i	0.149470	−	0.988766i	$-0.452243\pi$
$683$	20317.2	−	20317.2i	1.13824	−	1.13824i	0.988766	−	0.149470i	$-0.0477568\pi$
$684$		0			0
$685$	−18048.5	+	6027.38i	−1.00671	+	0.336196i
$686$		0			0
$687$	−4099.45	+	4099.45i	−0.227662	+	0.227662i
$688$		0			0
$689$		−	2941.66i		−	0.162654i
$690$		0			0
$691$	12106.1			0.666481			0.333240	−	0.942842i	$-0.391858\pi$
$691$	12106.1			0.666481			0.333240	+	0.942842i	$0.391858\pi$
$692$		0			0
$693$	391.452	+	391.452i	0.0214575	+	0.0214575i
$694$		0			0
$695$	−6822.31	−	3406.39i	−0.372353	−	0.185916i
$696$		0			0
$697$	13912.1	+	13912.1i	0.756037	+	0.756037i
$698$		0			0
$699$		−	4369.66i		−	0.236446i
$700$		0			0
$701$		−	10561.1i		−	0.569028i	−0.958672	−	0.284514i	$-0.908168\pi$
$701$		−	10561.1i		−	0.569028i	0.958672	−	0.284514i	$-0.0918322\pi$
$702$		0			0
$703$	36634.4	+	36634.4i	1.96542	+	1.96542i
$704$		0			0
$705$	−6015.89	−	3003.74i	−0.321378	−	0.160464i
$706$		0			0
$707$	2131.10	+	2131.10i	0.113364	+	0.113364i
$708$		0			0
$709$	−16116.9			−0.853715			−0.426857	−	0.904319i	$-0.640379\pi$
$709$	−16116.9			−0.853715			−0.426857	+	0.904319i	$0.640379\pi$
$710$		0			0
$711$			2168.52i			0.114383i
$712$		0			0
$713$	−312.014	+	312.014i	−0.0163885	+	0.0163885i
$714$		0			0
$715$	6070.83	−	2027.38i	0.317533	−	0.106042i
$716$		0			0
$717$	−9619.77	+	9619.77i	−0.501055	+	0.501055i
$718$		0			0
$719$	−14382.8			−0.746018			−0.373009	−	0.927828i	$-0.621674\pi$
$719$	−14382.8			−0.746018			−0.373009	+	0.927828i	$0.621674\pi$
$720$		0			0
$721$	−9409.92			−0.486052
$722$		0			0
$723$	−19139.9	+	19139.9i	−0.984538	+	0.984538i
$724$		0			0
$725$	−13467.8	−	17915.3i	−0.689907	−	0.917736i
$726$		0			0
$727$	10573.2	−	10573.2i	0.539391	−	0.539391i	−0.383959	−	0.923350i	$-0.625440\pi$
$727$	10573.2	−	10573.2i	0.539391	−	0.539391i	0.923350	+	0.383959i	$0.125440\pi$
$728$		0			0
$729$			21212.6i			1.07771i
$730$		0			0
$731$	21241.1			1.07474
$732$		0			0
$733$	17085.0	+	17085.0i	0.860911	+	0.860911i	0.991444	−	0.130533i	$-0.0416690\pi$
$733$	17085.0	+	17085.0i	0.860911	+	0.860911i	−0.130533	+	0.991444i	$0.541669\pi$
$734$		0			0
$735$	−15364.0	+	5130.87i	−0.771032	+	0.257490i
$736$		0			0
$737$	−113.415	−	113.415i	−0.00566852	−	0.00566852i
$738$		0			0
$739$		−	23749.0i		−	1.18217i	−0.806611	−	0.591083i	$-0.798700\pi$
$739$		−	23749.0i		−	1.18217i	0.806611	−	0.591083i	$-0.201300\pi$
$740$		0			0
$741$		−	12441.9i		−	0.616824i
$742$		0			0
$743$	18377.5	+	18377.5i	0.907407	+	0.907407i	0.996062	−	0.0886553i	$-0.0282569\pi$
$743$	18377.5	+	18377.5i	0.907407	+	0.907407i	−0.0886553	+	0.996062i	$0.528257\pi$
$744$		0			0
$745$	10957.0	−	21944.6i	0.538836	−	1.07918i
$746$		0			0
$747$	−1352.74	−	1352.74i	−0.0662571	−	0.0662571i
$748$		0			0
$749$	−847.553			−0.0413470
$750$		0			0
$751$		−	37016.3i		−	1.79859i	−0.437338	−	0.899297i	$-0.644079\pi$
$751$		−	37016.3i		−	1.79859i	0.437338	−	0.899297i	$-0.355921\pi$
$752$		0			0
$753$	8870.93	−	8870.93i	0.429316	−	0.429316i
$754$		0			0
$755$	13590.7	+	6785.87i	0.655123	+	0.327104i
$756$		0			0
$757$	−2000.79	+	2000.79i	−0.0960633	+	0.0960633i	−0.753505	−	0.657442i	$-0.771639\pi$
$757$	−2000.79	+	2000.79i	−0.0960633	+	0.0960633i	0.657442	+	0.753505i	$0.271639\pi$
$758$		0			0
$759$	−235.246			−0.0112502
$760$		0			0
$761$	28665.3			1.36546			0.682730	−	0.730671i	$-0.260792\pi$
$761$	28665.3			1.36546			0.682730	+	0.730671i	$0.260792\pi$
$762$		0			0
$763$	411.926	−	411.926i	0.0195448	−	0.0195448i
$764$		0			0
$765$	−816.856	−	2446.01i	−0.0386059	−	0.115602i
$766$		0			0
$767$	2134.71	−	2134.71i	0.100495	−	0.100495i
$768$		0			0
$769$			13291.2i			0.623268i	0.950202	+	0.311634i	$0.100876\pi$
$769$			13291.2i			0.623268i	−0.950202	+	0.311634i	$0.899124\pi$
$770$		0			0
$771$	6877.75			0.321266
$772$		0			0
$773$	18096.1	+	18096.1i	0.842006	+	0.842006i	0.989120	−	0.147114i	$-0.0469984\pi$
$773$	18096.1	+	18096.1i	0.842006	+	0.842006i	−0.147114	+	0.989120i	$0.546998\pi$
$774$		0			0
$775$	−27586.4	+	20738.0i	−1.27862	+	0.961203i
$776$		0			0
$777$	9683.37	+	9683.37i	0.447090	+	0.447090i
$778$		0			0
$779$			29566.1i			1.35984i
$780$		0			0
$781$		−	1747.91i		−	0.0800835i
$782$		0			0
$783$	−18547.6	−	18547.6i	−0.846536	−	0.846536i
$784$		0			0
$785$	1581.75	+	4736.43i	0.0719175	+	0.215351i
$786$		0			0
$787$	4284.05	+	4284.05i	0.194041	+	0.194041i	0.797440	−	0.603399i	$-0.206187\pi$
$787$	4284.05	+	4284.05i	0.194041	+	0.194041i	−0.603399	+	0.797440i	$0.706187\pi$
$788$		0			0
$789$	12605.9			0.568800
$790$		0			0
$791$		−	11169.7i		−	0.502083i
$792$		0			0
$793$	−10748.3	+	10748.3i	−0.481316	+	0.481316i
$794$		0			0
$795$	−3777.61	+	7565.79i	−0.168526	+	0.337523i
$796$		0			0
$797$	11856.4	−	11856.4i	0.526946	−	0.526946i	−0.392714	−	0.919661i	$-0.628464\pi$
$797$	11856.4	−	11856.4i	0.526946	−	0.526946i	0.919661	+	0.392714i	$0.128464\pi$
$798$		0			0
$799$	10648.5			0.471485
$800$		0			0
$801$	−1320.40			−0.0582449
$802$		0			0
$803$	−13501.8	+	13501.8i	−0.593358	+	0.593358i
$804$		0			0
$805$	56.1368	−	112.431i	0.00245784	−	0.00492256i
$806$		0			0
$807$	17956.2	−	17956.2i	0.783259	−	0.783259i
$808$		0			0
$809$			12222.3i			0.531165i	0.964088	+	0.265583i	$0.0855643\pi$
$809$			12222.3i			0.531165i	−0.964088	+	0.265583i	$0.914436\pi$
$810$		0			0
$811$	−5458.95			−0.236362			−0.118181	−	0.992992i	$-0.537706\pi$
$811$	−5458.95			−0.236362			−0.118181	+	0.992992i	$0.537706\pi$
$812$		0			0
$813$	−13261.6	−	13261.6i	−0.572086	−	0.572086i
$814$		0			0
$815$	−4836.80	−	14483.4i	−0.207884	−	0.622493i
$816$		0			0
$817$	22571.0	+	22571.0i	0.966535	+	0.966535i
$818$		0			0
$819$			356.326i			0.0152027i
$820$		0			0
$821$			40454.9i			1.71972i	0.510533	+	0.859858i	$0.329448\pi$
$821$			40454.9i			1.71972i	−0.510533	+	0.859858i	$0.670552\pi$
$822$		0			0
$823$	2089.79	+	2089.79i	0.0885120	+	0.0885120i	0.749976	−	0.661464i	$-0.230065\pi$
$823$	2089.79	+	2089.79i	0.0885120	+	0.0885120i	−0.661464	+	0.749976i	$0.730065\pi$
$824$		0			0
$825$	−18217.4	−	2581.70i	−0.768785	−	0.108949i
$826$		0			0
$827$	26933.3	+	26933.3i	1.13248	+	1.13248i	0.989763	+	0.142720i	$0.0455848\pi$
$827$	26933.3	+	26933.3i	1.13248	+	1.13248i	0.142720	+	0.989763i	$0.454415\pi$
$828$		0			0
$829$	5301.98			0.222130			0.111065	−	0.993813i	$-0.464574\pi$
$829$	5301.98			0.222130			0.111065	+	0.993813i	$0.464574\pi$
$830$		0			0
$831$			17944.2i			0.749072i
$832$		0			0
$833$	18138.6	−	18138.6i	0.754460	−	0.754460i
$834$		0			0
$835$	8101.95	+	24260.6i	0.335784	+	1.00548i
$836$		0			0
$837$	−28560.0	+	28560.0i	−1.17942	+	1.17942i
$838$		0			0
$839$	−1557.99			−0.0641095			−0.0320548	−	0.999486i	$-0.510205\pi$
$839$	−1557.99			−0.0641095			−0.0320548	+	0.999486i	$0.510205\pi$
$840$		0			0
$841$	7760.83			0.318210
$842$		0			0
$843$	16132.6	−	16132.6i	0.659116	−	0.659116i
$844$		0			0
$845$	−18290.4	−	9132.41i	−0.744625	−	0.371792i
$846$		0			0
$847$	2196.06	−	2196.06i	0.0890879	−	0.0890879i
$848$		0			0
$849$			27248.3i			1.10148i
$850$		0			0
$851$	630.510			0.0253979
$852$		0			0
$853$	11289.6	+	11289.6i	0.453165	+	0.453165i	0.896404	−	0.443239i	$-0.146171\pi$
$853$	11289.6	+	11289.6i	0.453165	+	0.453165i	−0.443239	+	0.896404i	$0.646171\pi$
$854$		0			0
$855$	1731.15	−	3467.14i	0.0692445	−	0.138683i
$856$		0			0
$857$	−18130.4	−	18130.4i	−0.722662	−	0.722662i	0.246485	−	0.969147i	$-0.420724\pi$
$857$	−18130.4	−	18130.4i	−0.722662	−	0.722662i	−0.969147	+	0.246485i	$0.920724\pi$
$858$		0			0
$859$		−	7587.14i		−	0.301362i	−0.988582	−	0.150681i	$-0.951853\pi$
$859$		−	7587.14i		−	0.301362i	0.988582	−	0.150681i	$-0.0481466\pi$
$860$		0			0
$861$			7815.05i			0.309334i
$862$		0			0
$863$	−14875.7	−	14875.7i	−0.586763	−	0.586763i	0.349991	−	0.936753i	$-0.386185\pi$
$863$	−14875.7	−	14875.7i	−0.586763	−	0.586763i	−0.936753	+	0.349991i	$0.886185\pi$
$864$		0			0
$865$	−13592.4	+	4539.26i	−0.534285	+	0.178427i
$866$		0			0
$867$	−9505.91	−	9505.91i	−0.372362	−	0.372362i
$868$		0			0
$869$	−24502.2			−0.956479
$870$		0			0
$871$		−	103.238i		−	0.00401617i
$872$		0			0
$873$	160.231	−	160.231i	0.00621191	−	0.00621191i
$874$		0			0
$875$	5581.08	−	8090.52i	0.215629	−	0.312582i
$876$		0			0
$877$	14885.0	−	14885.0i	0.573125	−	0.573125i	−0.359875	−	0.933000i	$-0.617181\pi$
$877$	14885.0	−	14885.0i	0.573125	−	0.573125i	0.933000	+	0.359875i	$0.117181\pi$
$878$		0			0
$879$	24562.9			0.942531
$880$		0			0
$881$	−40612.6			−1.55309			−0.776546	−	0.630061i	$-0.783030\pi$
$881$	−40612.6			−1.55309			−0.776546	+	0.630061i	$0.783030\pi$
$882$		0			0
$883$	−26208.6	+	26208.6i	−0.998855	+	0.998855i	−0.999999	−	0.00114467i	$-0.999636\pi$
$883$	−26208.6	+	26208.6i	−0.998855	+	0.998855i	0.00114467	+	0.999999i	$0.499636\pi$
$884$		0			0
$885$	−8231.70	+	2749.01i	−0.312662	+	0.104415i
$886$		0			0
$887$	−13728.3	+	13728.3i	−0.519673	+	0.519673i	−0.917472	−	0.397800i	$-0.869774\pi$
$887$	−13728.3	+	13728.3i	−0.519673	+	0.519673i	0.397800	+	0.917472i	$0.369774\pi$
$888$		0			0
$889$			13002.4i			0.490535i
$890$		0			0
$891$	−19407.8			−0.729727
$892$		0			0
$893$	11315.2	+	11315.2i	0.424018	+	0.424018i
$894$		0			0
$895$	18407.7	+	9191.00i	0.687489	+	0.343264i
$896$		0			0
$897$	−107.068	−	107.068i	−0.00398540	−	0.00398540i
$898$		0			0
$899$		−	49505.0i		−	1.83658i
$900$		0			0
$901$		−	13391.9i		−	0.495172i
$902$		0			0
$903$	5966.06	+	5966.06i	0.219865	+	0.219865i
$904$		0			0
$905$	−16870.6	−	8423.50i	−0.619665	−	0.309400i
$906$		0			0
$907$	−18256.9	−	18256.9i	−0.668367	−	0.668367i	0.288971	−	0.957338i	$-0.406687\pi$
$907$	−18256.9	−	18256.9i	−0.668367	−	0.668367i	−0.957338	+	0.288971i	$0.906687\pi$
$908$		0			0
$909$	1131.08			0.0412713
$910$		0			0
$911$		−	2804.74i		−	0.102003i	−0.998699	−	0.0510017i	$-0.983759\pi$
$911$		−	2804.74i		−	0.102003i	0.998699	−	0.0510017i	$-0.0162414\pi$
$912$		0			0
$913$	15284.6	−	15284.6i	0.554049	−	0.554049i
$914$		0			0
$915$	41446.8	−	13841.4i	1.49748	−	0.500089i
$916$		0			0
$917$	6941.08	−	6941.08i	0.249961	−	0.249961i
$918$		0			0
$919$	−41252.0			−1.48072			−0.740358	−	0.672213i	$-0.765344\pi$
$919$	−41252.0			−1.48072			−0.740358	+	0.672213i	$0.765344\pi$
$920$		0			0
$921$	38340.7			1.37174
$922$		0			0
$923$	795.532	−	795.532i	0.0283697	−	0.0283697i
$924$		0			0
$925$	48826.4	+	6919.50i	1.73557	+	0.245959i
$926$		0			0
$927$	−2497.15	+	2497.15i	−0.0884760	+	0.0884760i
$928$		0			0
$929$		−	24888.6i		−	0.878974i	−0.898249	−	0.439487i	$-0.855160\pi$
$929$		−	24888.6i		−	0.878974i	0.898249	−	0.439487i	$-0.144840\pi$
$930$		0			0
$931$	38548.4			1.35701
$932$		0			0
$933$	−28420.5	−	28420.5i	−0.997260	−	0.997260i
$934$		0			0
$935$	27637.5	−	9229.68i	0.966677	−	0.322826i
$936$		0			0
$937$	−17583.8	−	17583.8i	−0.613061	−	0.613061i	0.330681	−	0.943742i	$-0.392721\pi$
$937$	−17583.8	−	17583.8i	−0.613061	−	0.613061i	−0.943742	+	0.330681i	$0.892721\pi$
$938$		0			0
$939$			17780.4i			0.617936i
$940$		0			0
$941$		−	48601.1i		−	1.68369i	−0.539720	−	0.841845i	$-0.681470\pi$
$941$		−	48601.1i		−	1.68369i	0.539720	−	0.841845i	$-0.318530\pi$
$942$		0			0
$943$	254.429	+	254.429i	0.00878617	+	0.00878617i
$944$		0			0
$945$	5138.45	−	10291.3i	0.176882	−	0.354260i
$946$		0			0
$947$	−36098.0	−	36098.0i	−1.23868	−	1.23868i	−0.960542	−	0.278135i	$-0.910284\pi$
$947$	−36098.0	−	36098.0i	−1.23868	−	1.23868i	−0.278135	−	0.960542i	$-0.589716\pi$
$948$		0			0
$949$	−12290.2			−0.420396
$950$		0			0
$951$			42443.9i			1.44725i
$952$		0			0
$953$	1709.99	−	1709.99i	0.0581240	−	0.0581240i	−0.677447	−	0.735571i	$-0.736914\pi$
$953$	1709.99	−	1709.99i	0.0581240	−	0.0581240i	0.735571	+	0.677447i	$0.236914\pi$
$954$		0			0
$955$	−50890.1	−	25409.5i	−1.72436	−	0.860975i
$956$		0			0
$957$	18662.4	−	18662.4i	0.630377	−	0.630377i
$958$		0			0
$959$	11969.6			0.403044
$960$		0			0
$961$	−46437.8			−1.55879
$962$		0			0
$963$	−224.919	+	224.919i	−0.00752639	+	0.00752639i
$964$		0			0
$965$	3907.61	+	11701.0i	0.130353	+	0.390331i
$966$		0			0
$967$	−27123.8	+	27123.8i	−0.902009	+	0.902009i	−0.995610	−	0.0936008i	$-0.970162\pi$
$967$	−27123.8	+	27123.8i	−0.902009	+	0.902009i	0.0936008	+	0.995610i	$0.470162\pi$
$968$		0			0
$969$		−	56642.1i		−	1.87782i
$970$		0			0
$971$	−49747.9			−1.64417			−0.822083	−	0.569368i	$-0.807188\pi$
$971$	−49747.9			−1.64417			−0.822083	+	0.569368i	$0.807188\pi$
$972$		0			0
$973$	3391.80	+	3391.80i	0.111753	+	0.111753i
$974$		0			0
$975$	−7116.31	−	9466.34i	−0.233748	−	0.310939i
$976$		0			0
$977$	13958.5	+	13958.5i	0.457085	+	0.457085i	0.897697	−	0.440613i	$-0.145239\pi$
$977$	13958.5	+	13958.5i	0.457085	+	0.457085i	−0.440613	+	0.897697i	$0.645239\pi$
$978$		0			0
$979$		−	14919.3i		−	0.487050i
$980$		0			0
$981$		−	218.629i		−	0.00711549i
$982$		0			0
$983$	−2694.11	−	2694.11i	−0.0874149	−	0.0874149i	0.662047	−	0.749462i	$-0.269688\pi$
$983$	−2694.11	−	2694.11i	−0.0874149	−	0.0874149i	−0.749462	+	0.662047i	$0.769688\pi$
$984$		0			0
$985$	2195.43	+	6574.04i	0.0710175	+	0.212656i
$986$		0			0
$987$	2990.87	+	2990.87i	0.0964545	+	0.0964545i
$988$		0			0
$989$	388.466			0.0124899
$990$		0			0
$991$		−	38020.4i		−	1.21873i	−0.792891	−	0.609363i	$-0.791425\pi$
$991$		−	38020.4i		−	1.21873i	0.792891	−	0.609363i	$-0.208575\pi$
$992$		0			0
$993$	10533.0	−	10533.0i	0.336610	−	0.336610i
$994$		0			0
$995$	−5306.90	+	10628.7i	−0.169086	+	0.338644i
$996$		0			0
$997$	9100.55	−	9100.55i	0.289085	−	0.289085i	−0.547634	−	0.836718i	$-0.684471\pi$
$997$	9100.55	−	9100.55i	0.289085	−	0.289085i	0.836718	+	0.547634i	$0.184471\pi$
$998$		0			0
$999$	57713.4			1.82780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.o.a.47.6		32
4.3	odd	2		40.4.k.a.27.5	yes	32
5.3	odd	4	inner	160.4.o.a.143.5		32
8.3	odd	2	inner	160.4.o.a.47.5		32
8.5	even	2		40.4.k.a.27.13	yes	32
20.3	even	4		40.4.k.a.3.13	yes	32
20.7	even	4		200.4.k.j.43.4		32
20.19	odd	2		200.4.k.j.107.12		32
40.3	even	4	inner	160.4.o.a.143.6		32
40.13	odd	4		40.4.k.a.3.5	✓	32
40.29	even	2		200.4.k.j.107.4		32
40.37	odd	4		200.4.k.j.43.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.k.a.3.5	✓	32	40.13	odd	4
40.4.k.a.3.13	yes	32	20.3	even	4
40.4.k.a.27.5	yes	32	4.3	odd	2
40.4.k.a.27.13	yes	32	8.5	even	2
160.4.o.a.47.5		32	8.3	odd	2	inner
160.4.o.a.47.6		32	1.1	even	1	trivial
160.4.o.a.143.5		32	5.3	odd	4	inner
160.4.o.a.143.6		32	40.3	even	4	inner
200.4.k.j.43.4		32	20.7	even	4
200.4.k.j.43.12		32	40.37	odd	4
200.4.k.j.107.4		32	40.29	even	2
200.4.k.j.107.12		32	20.19	odd	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)

\(f(q)\)	\(=\)	\(q+(-3.49003 + 3.49003i) q^{3} +(4.99441 - 10.0028i) q^{5} +(-4.97302 + 4.97302i) q^{7} +2.63942i q^{9} -29.8229 q^{11} +(-13.5734 - 13.5734i) q^{13} +(17.4794 + 52.3406i) q^{15} +(-61.7929 - 61.7929i) q^{17} -131.323i q^{19} -34.7119i q^{21} +(-1.13009 - 1.13009i) q^{23} +(-75.1118 - 99.9161i) q^{25} +(-103.442 - 103.442i) q^{27} +179.304 q^{29} -276.096i q^{31} +(104.083 - 104.083i) q^{33} +(24.9068 + 74.5813i) q^{35} +(-278.964 + 278.964i) q^{37} +94.7429 q^{39} -225.140 q^{41} +(-171.874 + 171.874i) q^{43} +(26.4016 + 13.1824i) q^{45} +(-86.1627 + 86.1627i) q^{47} +293.538i q^{49} +431.318 q^{51} +(108.361 + 108.361i) q^{53} +(-148.948 + 298.312i) q^{55} +(458.322 + 458.322i) q^{57} +157.272i q^{59} -791.867i q^{61} +(-13.1259 - 13.1259i) q^{63} +(-203.563 + 67.9807i) q^{65} +(3.80296 + 3.80296i) q^{67} +7.88811 q^{69} +58.6097i q^{71} +(452.731 - 452.731i) q^{73} +(610.852 + 86.5677i) q^{75} +(148.310 - 148.310i) q^{77} +821.590 q^{79} +650.769 q^{81} +(-512.512 + 512.512i) q^{83} +(-926.721 + 309.483i) q^{85} +(-625.775 + 625.775i) q^{87} +500.262i q^{89} +135.001 q^{91} +(963.581 + 963.581i) q^{93} +(-1313.60 - 655.882i) q^{95} +(-60.7068 - 60.7068i) q^{97} -78.7153i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 8 q^{11} + 48 q^{17} + 40 q^{25} - 104 q^{27} - 112 q^{33} + 460 q^{35} - 8 q^{41} + 868 q^{43} - 1480 q^{51} + 104 q^{57} + 520 q^{65} + 1852 q^{67} - 744 q^{73} - 3300 q^{75} - 1240 q^{81}+ \cdots - 584 q^{97}+O(q^{100}) \) 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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