LMFDB - Embedded newform 144.4.l.a.35.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,4,Mod(35,144)] 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("144.35"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.l (of order $4$, degree $2$, 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:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			35.11
Character	$\chi$	$=$	144.35
Dual form			144.4.l.a.107.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.272518 + 2.81527i) q^{2} +(-7.85147 - 1.53442i) q^{4} +(-6.30986 - 6.30986i) q^{5} +27.2034 q^{7} +(6.45947 - 21.6858i) q^{8} +(19.4835 - 16.0444i) q^{10} +(4.03980 - 4.03980i) q^{11} +(37.9212 + 37.9212i) q^{13} +(-7.41340 + 76.5848i) q^{14} +(59.2911 + 24.0949i) q^{16} +79.8655i q^{17} +(75.2269 - 75.2269i) q^{19} +(39.8597 + 59.2236i) q^{20} +(10.2722 + 12.4740i) q^{22} +25.2124i q^{23} -45.3714i q^{25} +(-117.093 + 96.4241i) q^{26} +(-213.586 - 41.7414i) q^{28} +(107.714 - 107.714i) q^{29} +237.126i q^{31} +(-83.9916 + 160.354i) q^{32} +(-224.843 - 21.7648i) q^{34} +(-171.649 - 171.649i) q^{35} +(210.098 - 210.098i) q^{37} +(191.283 + 232.285i) q^{38} +(-177.593 + 96.0761i) q^{40} +378.638 q^{41} +(191.327 + 191.327i) q^{43} +(-37.9171 + 25.5196i) q^{44} +(-70.9796 - 6.87083i) q^{46} -417.483 q^{47} +397.023 q^{49} +(127.733 + 12.3645i) q^{50} +(-239.550 - 355.924i) q^{52} +(-139.419 - 139.419i) q^{53} -50.9811 q^{55} +(175.719 - 589.928i) q^{56} +(273.891 + 332.599i) q^{58} +(282.641 - 282.641i) q^{59} +(-255.821 - 255.821i) q^{61} +(-667.574 - 64.6211i) q^{62} +(-428.550 - 280.158i) q^{64} -478.555i q^{65} +(-348.674 + 348.674i) q^{67} +(122.547 - 627.061i) q^{68} +(530.016 - 436.461i) q^{70} -321.318i q^{71} +135.177i q^{73} +(534.228 + 648.739i) q^{74} +(-706.072 + 475.212i) q^{76} +(109.896 - 109.896i) q^{77} -522.058i q^{79} +(-222.083 - 526.154i) q^{80} +(-103.186 + 1065.97i) q^{82} +(-444.221 - 444.221i) q^{83} +(503.940 - 503.940i) q^{85} +(-590.778 + 486.498i) q^{86} +(-61.5114 - 113.701i) q^{88} +1102.27 q^{89} +(1031.58 + 1031.58i) q^{91} +(38.6864 - 197.954i) q^{92} +(113.772 - 1175.33i) q^{94} -949.342 q^{95} -1069.15 q^{97} +(-108.196 + 1117.73i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 120 q^{10} - 144 q^{16} - 48 q^{19} + 72 q^{22} + 72 q^{28} - 984 q^{34} - 1272 q^{40} + 864 q^{43} - 1416 q^{46} + 2352 q^{49} - 648 q^{52} - 576 q^{55} + 1128 q^{58} + 1824 q^{61} + 3024 q^{64}+ \cdots - 11304 q^{94}+O(q^{100}) $ 48 * q - 120 * q^10 - 144 * q^16 - 48 * q^19 + 72 * q^22 + 72 * q^28 - 984 * q^34 - 1272 * q^40 + 864 * q^43 - 1416 * q^46 + 2352 * q^49 - 648 * q^52 - 576 * q^55 + 1128 * q^58 + 1824 * q^61 + 3024 * q^64 + 816 * q^67 + 2664 * q^70 + 1920 * q^76 + 1200 * q^82 - 480 * q^85 - 4560 * q^88 - 3600 * q^91 - 11304 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	−0.272518	+	2.81527i	−0.0963496	+	0.995348i
$2$	−0.272518	+	2.81527i	−0.0963496	+	0.995348i
$3$		0			0
$3$		0			0
$4$	−7.85147	−	1.53442i	−0.981433	−	0.191803i
$5$	−6.30986	−	6.30986i	−0.564371	−	0.564371i	0.366175	−	0.930546i	$-0.380667\pi$
$5$	−6.30986	−	6.30986i	−0.564371	−	0.564371i	−0.930546	+	0.366175i	$0.880667\pi$
$6$		0			0
$7$	27.2034			1.46884			0.734422	−	0.678693i	$-0.237453\pi$
$7$	27.2034			1.46884			0.734422	+	0.678693i	$0.237453\pi$
$8$	6.45947	−	21.6858i	0.285471	−	0.958387i
$9$		0			0
$10$	19.4835	−	16.0444i	0.616122	−	0.507368i
$11$	4.03980	−	4.03980i	0.110731	−	0.110731i	−0.649570	−	0.760302i	$-0.725051\pi$
$11$	4.03980	−	4.03980i	0.110731	−	0.110731i	0.760302	+	0.649570i	$0.225051\pi$
$12$		0			0
$13$	37.9212	+	37.9212i	0.809034	+	0.809034i	0.984488	−	0.175453i	$-0.0561391\pi$
$13$	37.9212	+	37.9212i	0.809034	+	0.809034i	−0.175453	+	0.984488i	$0.556139\pi$
$14$	−7.41340	+	76.5848i	−0.141523	+	1.46201i
$15$		0			0
$16$	59.2911	+	24.0949i	0.926423	+	0.376483i
$17$			79.8655i			1.13943i	0.821844	+	0.569713i	$0.192945\pi$
$17$			79.8655i			1.13943i	−0.821844	+	0.569713i	$0.807055\pi$
$18$		0			0
$19$	75.2269	−	75.2269i	0.908328	−	0.908328i	−0.0878089	−	0.996137i	$-0.527986\pi$
$19$	75.2269	−	75.2269i	0.908328	−	0.908328i	0.996137	+	0.0878089i	$0.0279865\pi$
$20$	39.8597	+	59.2236i	0.445645	+	0.662140i
$21$		0			0
$22$	10.2722	+	12.4740i	0.0995473	+	0.120885i
$23$			25.2124i			0.228572i	0.993448	+	0.114286i	$0.0364580\pi$
$23$			25.2124i			0.228572i	−0.993448	+	0.114286i	$0.963542\pi$
$24$		0			0
$25$		−	45.3714i		−	0.362971i
$26$	−117.093	+	96.4241i	−0.883221	+	0.727320i
$27$		0			0
$28$	−213.586	−	41.7414i	−1.44157	−	0.281728i
$29$	107.714	−	107.714i	0.689726	−	0.689726i	−0.272445	−	0.962171i	$-0.587832\pi$
$29$	107.714	−	107.714i	0.689726	−	0.689726i	0.962171	+	0.272445i	$0.0878324\pi$
$30$		0			0
$31$			237.126i			1.37384i	0.726732	+	0.686921i	$0.241038\pi$
$31$			237.126i			1.37384i	−0.726732	+	0.686921i	$0.758962\pi$
$32$	−83.9916	+	160.354i	−0.463992	+	0.885839i
$33$		0			0
$34$	−224.843	−	21.7648i	−1.13412	−	0.109783i
$35$	−171.649	−	171.649i	−0.828973	−	0.828973i
$36$		0			0
$37$	210.098	−	210.098i	0.933512	−	0.933512i	−0.0644112	−	0.997923i	$-0.520517\pi$
$37$	210.098	−	210.098i	0.933512	−	0.933512i	0.997923	+	0.0644112i	$0.0205169\pi$
$38$	191.283	+	232.285i	0.816585	+	0.991620i
$39$		0			0
$40$	−177.593	+	96.0761i	−0.701997	+	0.379774i
$41$	378.638			1.44228			0.721139	−	0.692790i	$-0.243619\pi$
$41$	378.638			1.44228			0.721139	+	0.692790i	$0.243619\pi$
$42$		0			0
$43$	191.327	+	191.327i	0.678538	+	0.678538i	0.959669	−	0.281131i	$-0.0907096\pi$
$43$	191.327	+	191.327i	0.678538	+	0.678538i	−0.281131	+	0.959669i	$0.590710\pi$
$44$	−37.9171	+	25.5196i	−0.129914	+	0.0874369i
$45$		0			0
$46$	−70.9796	−	6.87083i	−0.227508	−	0.0220228i
$47$	−417.483			−1.29566			−0.647831	−	0.761784i	$-0.724324\pi$
$47$	−417.483			−1.29566			−0.647831	+	0.761784i	$0.724324\pi$
$48$		0			0
$49$	397.023			1.15750
$50$	127.733	+	12.3645i	0.361283	+	0.0349721i
$51$		0			0
$52$	−239.550	−	355.924i	−0.638838	−	0.949188i
$53$	−139.419	−	139.419i	−0.361335	−	0.361335i	0.502970	−	0.864304i	$-0.332241\pi$
$53$	−139.419	−	139.419i	−0.361335	−	0.361335i	−0.864304	+	0.502970i	$0.832241\pi$
$54$		0			0
$55$	−50.9811			−0.124987
$56$	175.719	−	589.928i	0.419313	−	1.40772i
$57$		0			0
$58$	273.891	+	332.599i	0.620062	+	0.752972i
$59$	282.641	−	282.641i	0.623674	−	0.623674i	−0.322795	−	0.946469i	$-0.604623\pi$
$59$	282.641	−	282.641i	0.623674	−	0.623674i	0.946469	+	0.322795i	$0.104623\pi$
$60$		0			0
$61$	−255.821	−	255.821i	−0.536960	−	0.536960i	0.385675	−	0.922635i	$-0.373969\pi$
$61$	−255.821	−	255.821i	−0.536960	−	0.536960i	−0.922635	+	0.385675i	$0.873969\pi$
$62$	−667.574	−	64.6211i	−1.36745	−	0.132369i
$63$		0			0
$64$	−428.550	−	280.158i	−0.837012	−	0.547184i
$65$		−	478.555i		−	0.913191i
$66$		0			0
$67$	−348.674	+	348.674i	−0.635781	+	0.635781i	−0.949512	−	0.313731i	$-0.898421\pi$
$67$	−348.674	+	348.674i	−0.635781	+	0.635781i	0.313731	+	0.949512i	$0.398421\pi$
$68$	122.547	−	627.061i	0.218545	−	1.11827i
$69$		0			0
$70$	530.016	−	436.461i	0.904987	−	0.745245i
$71$		−	321.318i		−	0.537090i	−0.963267	−	0.268545i	$-0.913457\pi$
$71$		−	321.318i		−	0.537090i	0.963267	−	0.268545i	$-0.0865428\pi$
$72$		0			0
$73$			135.177i			0.216729i	0.994111	+	0.108365i	$0.0345614\pi$
$73$			135.177i			0.216729i	−0.994111	+	0.108365i	$0.965439\pi$
$74$	534.228	+	648.739i	0.839226	+	1.01911i
$75$		0			0
$76$	−706.072	+	475.212i	−1.06568	+	0.717244i
$77$	109.896	−	109.896i	0.162647	−	0.162647i
$78$		0			0
$79$		−	522.058i		−	0.743495i	−0.928334	−	0.371747i	$-0.878759\pi$
$79$		−	522.058i		−	0.743495i	0.928334	−	0.371747i	$-0.121241\pi$
$80$	−222.083	−	526.154i	−0.310370	−	0.735322i
$81$		0			0
$82$	−103.186	+	1065.97i	−0.138963	+	1.43557i
$83$	−444.221	−	444.221i	−0.587465	−	0.587465i	0.349479	−	0.936944i	$-0.386359\pi$
$83$	−444.221	−	444.221i	−0.587465	−	0.587465i	−0.936944	+	0.349479i	$0.886359\pi$
$84$		0			0
$85$	503.940	−	503.940i	0.643058	−	0.643058i
$86$	−590.778	+	486.498i	−0.740758	+	0.610004i
$87$		0			0
$88$	−61.5114	−	113.701i	−0.0745130	−	0.137734i
$89$	1102.27			1.31281			0.656405	−	0.754409i	$-0.272076\pi$
$89$	1102.27			1.31281			0.656405	+	0.754409i	$0.272076\pi$
$90$		0			0
$91$	1031.58	+	1031.58i	1.18835	+	1.18835i
$92$	38.6864	−	197.954i	0.0438407	−	0.224328i
$93$		0			0
$94$	113.772	−	1175.33i	0.124837	−	1.28963i
$95$	−949.342			−1.02527
$96$		0			0
$97$	−1069.15			−1.11913			−0.559565	−	0.828786i	$-0.689032\pi$
$97$	−1069.15			−1.11913			−0.559565	+	0.828786i	$0.689032\pi$
$98$	−108.196	+	1117.73i	−0.111525	+	1.15212i
$99$		0			0
$100$	−69.6189	+	356.232i	−0.0696189	+	0.356232i
$101$	1184.31	+	1184.31i	1.16677	+	1.16677i	0.982963	+	0.183805i	$0.0588415\pi$
$101$	1184.31	+	1184.31i	1.16677	+	1.16677i	0.183805	+	0.982963i	$0.441159\pi$
$102$		0			0
$103$	−1973.70			−1.88810			−0.944049	−	0.329806i	$-0.893017\pi$
$103$	−1973.70			−1.88810			−0.944049	+	0.329806i	$0.893017\pi$
$104$	1067.30	−	577.402i	1.00632	−	0.544412i
$105$		0			0
$106$	430.497	−	354.509i	0.394468	−	0.324839i
$107$	−1025.91	+	1025.91i	−0.926901	+	0.926901i	−0.997504	−	0.0706038i	$-0.977507\pi$
$107$	−1025.91	+	1025.91i	−0.926901	+	0.926901i	0.0706038	+	0.997504i	$0.477507\pi$
$108$		0			0
$109$	−1201.58	−	1201.58i	−1.05587	−	1.05587i	−0.998344	−	0.0575281i	$-0.981678\pi$
$109$	−1201.58	−	1201.58i	−1.05587	−	1.05587i	−0.0575281	−	0.998344i	$-0.518322\pi$
$110$	13.8933	−	143.526i	0.0120425	−	0.124406i
$111$		0			0
$112$	1612.92	+	655.463i	1.36077	+	0.552995i
$113$			1755.12i			1.46113i	0.682842	+	0.730566i	$0.260744\pi$
$113$			1755.12i			1.46113i	−0.682842	+	0.730566i	$0.739256\pi$
$114$		0			0
$115$	159.087	−	159.087i	0.128999	−	0.128999i
$116$	−1011.00	+	680.437i	−0.809212	+	0.544629i
$117$		0			0
$118$	718.686	+	872.735i	0.560681	+	0.680863i
$119$			2172.61i			1.67364i
$120$		0			0
$121$			1298.36i			0.975477i
$122$	789.922	−	650.490i	0.586198	−	0.482726i
$123$		0			0
$124$	363.851	−	1861.79i	0.263507	−	1.34833i
$125$	−1075.02	+	1075.02i	−0.769221	+	0.769221i
$126$		0			0
$127$			1185.87i			0.828575i	0.910146	+	0.414288i	$0.135969\pi$
$127$			1185.87i			0.828575i	−0.910146	+	0.414288i	$0.864031\pi$
$128$	905.508	−	1130.14i	0.625284	−	0.780397i
$129$		0			0
$130$	1347.26	+	130.415i	0.908942	+	0.0879856i
$131$	−1081.59	−	1081.59i	−0.721367	−	0.721367i	0.247516	−	0.968884i	$-0.420386\pi$
$131$	−1081.59	−	1081.59i	−0.721367	−	0.721367i	−0.968884	+	0.247516i	$0.920386\pi$
$132$		0			0
$133$	2046.43	−	2046.43i	1.33419	−	1.33419i
$134$	−886.591	−	1076.63i	−0.571566	−	0.694080i
$135$		0			0
$136$	1731.95	+	515.889i	1.09201	+	0.325273i
$137$	2165.11			1.35020			0.675101	−	0.737725i	$-0.264100\pi$
$137$	2165.11			1.35020			0.675101	+	0.737725i	$0.264100\pi$
$138$		0			0
$139$	342.051	+	342.051i	0.208722	+	0.208722i	0.803724	−	0.595002i	$-0.202849\pi$
$139$	342.051	+	342.051i	0.208722	+	0.208722i	−0.595002	+	0.803724i	$0.702849\pi$
$140$	1084.32	+	1611.08i	0.654582	+	0.972581i
$141$		0			0
$142$	904.596	+	87.5649i	0.534591	+	0.0517484i
$143$	306.388			0.179171
$144$		0			0
$145$	−1359.32			−0.778522
$146$	−380.559	−	36.8381i	−0.215721	−	0.0208818i
$147$		0			0
$148$	−1971.96	+	1327.20i	−1.09523	+	0.737130i
$149$	−1937.50	−	1937.50i	−1.06528	−	1.06528i	−0.997715	−	0.0675623i	$-0.978478\pi$
$149$	−1937.50	−	1937.50i	−1.06528	−	1.06528i	−0.0675623	−	0.997715i	$-0.521522\pi$
$150$		0			0
$151$	−2341.03			−1.26166			−0.630828	−	0.775923i	$-0.717285\pi$
$151$	−2341.03			−1.26166			−0.630828	+	0.775923i	$0.717285\pi$
$152$	−1145.43	−	2117.28i	−0.611229	−	1.12983i
$153$		0			0
$154$	279.439	+	339.336i	0.146219	+	0.177561i
$155$	1496.23	−	1496.23i	0.775356	−	0.775356i
$156$		0			0
$157$	856.893	+	856.893i	0.435589	+	0.435589i	0.890525	−	0.454935i	$-0.150338\pi$
$157$	856.893	+	856.893i	0.435589	+	0.435589i	−0.454935	+	0.890525i	$0.650338\pi$
$158$	1469.73	+	142.270i	0.740036	+	0.0716354i
$159$		0			0
$160$	1541.79	−	481.836i	0.761805	−	0.238078i
$161$			685.862i			0.335736i
$162$		0			0
$163$	1737.64	−	1737.64i	0.834982	−	0.834982i	−0.153211	−	0.988193i	$-0.548961\pi$
$163$	1737.64	−	1737.64i	0.834982	−	0.834982i	0.988193	+	0.153211i	$0.0489615\pi$
$164$	−2972.87	−	580.991i	−1.41550	−	0.276633i
$165$		0			0
$166$	1371.66	−	1129.54i	0.641334	−	0.528130i
$167$			2472.59i			1.14572i	0.819655	+	0.572858i	$0.194165\pi$
$167$			2472.59i			1.14572i	−0.819655	+	0.572858i	$0.805835\pi$
$168$		0			0
$169$			679.034i			0.309073i
$170$	1281.39	+	1556.06i	0.578108	+	0.702025i
$171$		0			0
$172$	−1208.62	−	1795.78i	−0.535795	−	0.796086i
$173$	1114.69	−	1114.69i	0.489875	−	0.489875i	−0.418392	−	0.908267i	$-0.637406\pi$
$173$	1114.69	−	1114.69i	0.489875	−	0.489875i	0.908267	+	0.418392i	$0.137406\pi$
$174$		0			0
$175$		−	1234.25i		−	0.533148i
$176$	336.863	−	142.186i	0.144273	−	0.0608957i
$177$		0			0
$178$	−300.388	+	3103.18i	−0.126489	+	1.30670i
$179$	1364.12	+	1364.12i	0.569602	+	0.569602i	0.932017	−	0.362415i	$-0.118048\pi$
$179$	1364.12	+	1364.12i	0.569602	+	0.569602i	−0.362415	+	0.932017i	$0.618048\pi$
$180$		0			0
$181$	−443.476	+	443.476i	−0.182118	+	0.182118i	−0.792278	−	0.610160i	$-0.791105\pi$
$181$	−443.476	+	443.476i	−0.182118	+	0.182118i	0.610160	+	0.792278i	$0.291105\pi$
$182$	−3185.31	+	2623.06i	−1.29731	+	1.06832i
$183$		0			0
$184$	546.752	+	162.859i	0.219060	+	0.0652506i
$185$	−2651.38			−1.05369
$186$		0			0
$187$	322.641	+	322.641i	0.126170	+	0.126170i
$188$	3277.85	+	640.595i	1.27161	+	0.248512i
$189$		0			0
$190$	258.713	−	2672.65i	0.0987842	−	1.02050i
$191$	642.969			0.243579			0.121790	−	0.992556i	$-0.461137\pi$
$191$	642.969			0.243579			0.121790	+	0.992556i	$0.461137\pi$
$192$		0			0
$193$	−1038.09			−0.387168			−0.193584	−	0.981084i	$-0.562011\pi$
$193$	−1038.09			−0.387168			−0.193584	+	0.981084i	$0.562011\pi$
$194$	291.362	−	3009.94i	0.107828	−	1.11392i
$195$		0			0
$196$	−3117.21	−	609.201i	−1.13601	−	0.222012i
$197$	−2641.47	−	2641.47i	−0.955315	−	0.955315i	0.0437288	−	0.999043i	$-0.486076\pi$
$197$	−2641.47	−	2641.47i	−0.955315	−	0.955315i	−0.999043	+	0.0437288i	$0.986076\pi$
$198$		0			0
$199$	−2547.50			−0.907476			−0.453738	−	0.891135i	$-0.649910\pi$
$199$	−2547.50			−0.907476			−0.453738	+	0.891135i	$0.649910\pi$
$200$	−983.916	−	293.075i	−0.347867	−	0.103618i
$201$		0			0
$202$	−3656.90	+	3011.41i	−1.27376	+	1.04892i
$203$	2930.19	−	2930.19i	1.01310	−	1.01310i
$204$		0			0
$205$	−2389.15	−	2389.15i	−0.813980	−	0.813980i
$206$	537.867	−	5556.48i	0.181917	−	1.87931i
$207$		0			0
$208$	1334.68	+	3162.10i	0.444920	+	1.05410i
$209$		−	607.804i		−	0.201161i
$210$		0			0
$211$	−1159.93	+	1159.93i	−0.378448	+	0.378448i	−0.870542	−	0.492094i	$-0.836232\pi$
$211$	−1159.93	+	1159.93i	−0.378448	+	0.378448i	0.492094	+	0.870542i	$0.336232\pi$
$212$	880.719	+	1308.58i	0.285321	+	0.423931i
$213$		0			0
$214$	−2608.63	−	3167.79i	−0.833282	−	1.01189i
$215$		−	2414.50i		−	0.765894i
$216$		0			0
$217$			6450.63i			2.01796i
$218$	3710.21	−	3055.31i	1.15269	−	0.949227i
$219$		0			0
$220$	400.277	+	78.2266i	0.122667	+	0.0239729i
$221$	−3028.59	+	3028.59i	−0.921834	+	0.921834i
$222$		0			0
$223$		−	3613.80i		−	1.08519i	−0.839994	−	0.542596i	$-0.817441\pi$
$223$		−	3613.80i		−	1.08519i	0.839994	−	0.542596i	$-0.182559\pi$
$224$	−2284.85	+	4362.17i	−0.681532	+	1.30116i
$225$		0			0
$226$	−4941.14	−	478.302i	−1.45433	−	0.140780i
$227$	−444.232	−	444.232i	−0.129889	−	0.129889i	0.639174	−	0.769062i	$-0.279276\pi$
$227$	−444.232	−	444.232i	−0.129889	−	0.129889i	−0.769062	+	0.639174i	$0.779276\pi$
$228$		0			0
$229$	−188.918	+	188.918i	−0.0545154	+	0.0545154i	−0.733839	−	0.679324i	$-0.762273\pi$
$229$	−188.918	+	188.918i	−0.0545154	+	0.0545154i	0.679324	+	0.733839i	$0.262273\pi$
$230$	404.517	+	491.225i	0.115970	+	0.140828i
$231$		0			0
$232$	−1640.10	−	3031.65i	−0.464128	−	0.857922i
$233$	6015.55			1.69138			0.845691	−	0.533673i	$-0.179189\pi$
$233$	6015.55			1.69138			0.845691	+	0.533673i	$0.179189\pi$
$234$		0			0
$235$	2634.26	+	2634.26i	0.731234	+	0.731234i
$236$	−2652.84	+	1785.46i	−0.731716	+	0.492472i
$237$		0			0
$238$	−6116.48	−	592.075i	−1.66585	−	0.161254i
$239$	−3866.73			−1.04652			−0.523260	−	0.852173i	$-0.675284\pi$
$239$	−3866.73			−1.04652			−0.523260	+	0.852173i	$0.675284\pi$
$240$		0			0
$241$	6049.74			1.61700			0.808501	−	0.588494i	$-0.200279\pi$
$241$	6049.74			1.61700			0.808501	+	0.588494i	$0.200279\pi$
$242$	−3655.23	−	353.826i	−0.970939	−	0.0939869i
$243$		0			0
$244$	1616.04	+	2401.11i	0.424000	+	0.629981i
$245$	−2505.16	−	2505.16i	−0.653260	−	0.653260i
$246$		0			0
$247$	5705.39			1.46974
$248$	5142.28	+	1531.71i	1.31667	+	0.392192i
$249$		0			0
$250$	−2733.51	−	3319.43i	−0.691528	−	0.839757i
$251$	3748.61	−	3748.61i	0.942670	−	0.942670i	−0.0557730	−	0.998443i	$-0.517762\pi$
$251$	3748.61	−	3748.61i	0.942670	−	0.942670i	0.998443	+	0.0557730i	$0.0177623\pi$
$252$		0			0
$253$	101.853	+	101.853i	0.0253101	+	0.0253101i
$254$	−3338.55	−	323.171i	−0.824721	−	0.0798329i
$255$		0			0
$256$	2934.87	+	2857.23i	0.716521	+	0.697566i
$257$		−	4593.31i		−	1.11488i	−0.830219	−	0.557438i	$-0.811785\pi$
$257$		−	4593.31i		−	1.11488i	0.830219	−	0.557438i	$-0.188215\pi$
$258$		0			0
$259$	5715.38	−	5715.38i	1.37118	−	1.37118i
$260$	−734.305	+	3757.36i	−0.175152	+	0.896236i
$261$		0			0
$262$	3339.72	−	2750.22i	0.787515	−	0.648508i
$263$			3477.14i			0.815246i	0.913150	+	0.407623i	$0.133642\pi$
$263$			3477.14i			0.815246i	−0.913150	+	0.407623i	$0.866358\pi$
$264$		0			0
$265$			1759.43i			0.407853i
$266$	5203.55	+	6318.92i	1.19944	+	1.45653i
$267$		0			0
$268$	3272.62	−	2202.59i	0.745921	−	0.502032i
$269$	115.440	−	115.440i	0.0261654	−	0.0261654i	−0.693903	−	0.720068i	$-0.744110\pi$
$269$	115.440	−	115.440i	0.0261654	−	0.0261654i	0.720068	+	0.693903i	$0.244110\pi$
$270$		0			0
$271$		−	2252.96i		−	0.505009i	−0.967596	−	0.252504i	$-0.918746\pi$
$271$		−	2252.96i		−	0.505009i	0.967596	−	0.252504i	$-0.0812542\pi$
$272$	−1924.35	+	4735.31i	−0.428974	+	1.05559i
$273$		0			0
$274$	−590.031	+	6095.36i	−0.130091	+	1.34392i
$275$	−183.291	−	183.291i	−0.0401923	−	0.0401923i
$276$		0			0
$277$	1423.92	−	1423.92i	0.308864	−	0.308864i	−0.535605	−	0.844469i	$-0.679916\pi$
$277$	1423.92	−	1423.92i	0.308864	−	0.308864i	0.844469	+	0.535605i	$0.179916\pi$
$278$	−1056.18	+	869.749i	−0.227861	+	0.187641i
$279$		0			0
$280$	−4831.12	+	2613.59i	−1.03112	+	0.557829i
$281$	−5780.83			−1.22724			−0.613621	−	0.789600i	$-0.710288\pi$
$281$	−5780.83			−1.22724			−0.613621	+	0.789600i	$0.710288\pi$
$282$		0			0
$283$	2544.53	+	2544.53i	0.534476	+	0.534476i	0.921901	−	0.387425i	$-0.126635\pi$
$283$	2544.53	+	2544.53i	0.534476	+	0.534476i	−0.387425	+	0.921901i	$0.626635\pi$
$284$	−493.037	+	2522.82i	−0.103015	+	0.527118i
$285$		0			0
$286$	−83.4963	+	862.565i	−0.0172631	+	0.178337i
$287$	10300.2			2.11848
$288$		0			0
$289$	−1465.50			−0.298289
$290$	370.440	−	3826.86i	0.0750104	−	0.774900i
$291$		0			0
$292$	207.418	−	1061.34i	0.0415693	−	0.212705i
$293$	−423.704	−	423.704i	−0.0844815	−	0.0844815i	0.663603	−	0.748085i	$-0.269026\pi$
$293$	−423.704	−	423.704i	−0.0844815	−	0.0844815i	−0.748085	+	0.663603i	$0.769026\pi$
$294$		0			0
$295$	−3566.85			−0.703966
$296$	−3199.03	−	5913.28i	−0.628175	−	1.16116i
$297$		0			0
$298$	5982.59	−	4926.58i	1.16296	−	0.957682i
$299$	−956.084	+	956.084i	−0.184922	+	0.184922i
$300$		0			0
$301$	5204.75	+	5204.75i	0.996667	+	0.996667i
$302$	637.971	−	6590.62i	0.121560	−	1.25579i
$303$		0			0
$304$	6272.87	−	2647.70i	1.18347	−	0.499526i
$305$			3228.39i			0.606089i
$306$		0			0
$307$	687.135	−	687.135i	0.127742	−	0.127742i	−0.640345	−	0.768087i	$-0.721209\pi$
$307$	687.135	−	687.135i	0.127742	−	0.127742i	0.768087	+	0.640345i	$0.221209\pi$
$308$	−1031.47	+	694.219i	−0.190824	+	0.128431i
$309$		0			0
$310$	3804.54	+	4620.04i	0.697044	+	0.846454i
$311$		−	441.970i		−	0.0805846i	−0.999188	−	0.0402923i	$-0.987171\pi$
$311$		−	441.970i		−	0.0805846i	0.999188	−	0.0402923i	$-0.0128289\pi$
$312$		0			0
$313$			1949.31i			0.352018i	0.984389	+	0.176009i	$0.0563188\pi$
$313$			1949.31i			0.352018i	−0.984389	+	0.176009i	$0.943681\pi$
$314$	−2645.90	+	2178.87i	−0.475532	+	0.391594i
$315$		0			0
$316$	−801.057	+	4098.92i	−0.142604	+	0.729691i
$317$	−1627.66	+	1627.66i	−0.288386	+	0.288386i	−0.836442	−	0.548056i	$-0.815368\pi$
$317$	−1627.66	+	1627.66i	−0.288386	+	0.288386i	0.548056	+	0.836442i	$0.315368\pi$
$318$		0			0
$319$		−	870.289i		−	0.152749i
$320$	936.334	+	4471.85i	0.163571	+	0.781200i
$321$		0			0
$322$	−1930.89	−	186.910i	−0.334174	−	0.0323480i
$323$	6008.03	+	6008.03i	1.03497	+	1.03497i
$324$		0			0
$325$	1720.54	−	1720.54i	0.293656	−	0.293656i
$326$	4418.37	+	5365.45i	0.750647	+	0.911548i
$327$		0			0
$328$	2445.81	−	8211.09i	0.411729	−	1.38226i
$329$	−11356.9			−1.90313
$330$		0			0
$331$	−5461.11	−	5461.11i	−0.906857	−	0.906857i	0.0891603	−	0.996017i	$-0.471582\pi$
$331$	−5461.11	−	5461.11i	−0.906857	−	0.906857i	−0.996017	+	0.0891603i	$0.971582\pi$
$332$	2806.17	+	4169.41i	0.463881	+	0.689236i
$333$		0			0
$334$	−6960.99	−	673.824i	−1.14038	−	0.110389i
$335$	4400.17			0.717632
$336$		0			0
$337$	−7450.74			−1.20436			−0.602178	−	0.798362i	$-0.705700\pi$
$337$	−7450.74			−1.20436			−0.602178	+	0.798362i	$0.705700\pi$
$338$	−1911.66	−	185.049i	−0.307635	−	0.0297791i
$339$		0			0
$340$	−4729.92	+	3183.41i	−0.754459	+	0.507779i
$341$	957.942	+	957.942i	0.152128	+	0.152128i
$342$		0			0
$343$	1469.61			0.231346
$344$	5384.97	−	2913.22i	0.844006	−	0.456599i
$345$		0			0
$346$	2834.38	+	3441.92i	0.440396	+	0.534795i
$347$	−7071.55	+	7071.55i	−1.09401	+	1.09401i	−0.0989122	+	0.995096i	$0.531536\pi$
$347$	−7071.55	+	7071.55i	−1.09401	+	1.09401i	−0.995096	+	0.0989122i	$0.968464\pi$
$348$		0			0
$349$	3300.15	+	3300.15i	0.506170	+	0.506170i	0.913348	−	0.407179i	$-0.133487\pi$
$349$	3300.15	+	3300.15i	0.506170	+	0.506170i	−0.407179	+	0.913348i	$0.633487\pi$
$350$	3474.76	+	336.357i	0.530668	+	0.0513686i
$351$		0			0
$352$	308.489	+	987.108i	0.0467117	+	0.149469i
$353$			18.3891i			0.00277268i	0.999999	+	0.00138634i	$0.000441285\pi$
$353$			18.3891i			0.00277268i	−0.999999	+	0.00138634i	$0.999559\pi$
$354$		0			0
$355$	−2027.47	+	2027.47i	−0.303118	+	0.303118i
$356$	−8654.42	−	1691.34i	−1.28844	−	0.251801i
$357$		0			0
$358$	−4212.10	+	3468.61i	−0.621833	+	0.512071i
$359$		−	670.681i		−	0.0985995i	−0.998784	−	0.0492997i	$-0.984301\pi$
$359$		−	670.681i		−	0.0985995i	0.998784	−	0.0492997i	$-0.0156990\pi$
$360$		0			0
$361$		−	4459.18i		−	0.650121i
$362$	−1127.65	−	1369.36i	−0.163723	−	0.198817i
$363$		0			0
$364$	−6516.56	−	9682.34i	−0.938354	−	1.39421i
$365$	852.946	−	852.946i	0.122316	−	0.122316i
$366$		0			0
$367$			5038.40i			0.716627i	0.933601	+	0.358314i	$0.116648\pi$
$367$			5038.40i			0.716627i	−0.933601	+	0.358314i	$0.883352\pi$
$368$	−607.491	+	1494.87i	−0.0860534	+	0.211754i
$369$		0			0
$370$	722.549	−	7464.35i	0.101523	−	1.04879i
$371$	−3792.68	−	3792.68i	−0.530744	−	0.530744i
$372$		0			0
$373$	−3151.66	+	3151.66i	−0.437498	+	0.437498i	−0.891169	−	0.453671i	$-0.850114\pi$
$373$	−3151.66	+	3151.66i	−0.437498	+	0.437498i	0.453671	+	0.891169i	$0.350114\pi$
$374$	−996.245	+	820.395i	−0.137740	+	0.113427i
$375$		0			0
$376$	−2696.72	+	9053.47i	−0.369874	+	1.24175i
$377$	8169.31			1.11602
$378$		0			0
$379$	−1494.63	−	1494.63i	−0.202570	−	0.202570i	0.598530	−	0.801100i	$-0.295752\pi$
$379$	−1494.63	−	1494.63i	−0.202570	−	0.202570i	−0.801100	+	0.598530i	$0.795752\pi$
$380$	7453.73	+	1456.69i	1.00623	+	0.196649i
$381$		0			0
$382$	−175.221	+	1810.13i	−0.0234688	+	0.242446i
$383$	−2530.45			−0.337598			−0.168799	−	0.985650i	$-0.553989\pi$
$383$	−2530.45			−0.337598			−0.168799	+	0.985650i	$0.553989\pi$
$384$		0			0
$385$	−1386.86			−0.183587
$386$	282.899	−	2922.51i	0.0373035	−	0.385367i
$387$		0			0
$388$	8394.39	+	1640.53i	1.09835	+	0.214652i
$389$	6128.44	+	6128.44i	0.798776	+	0.798776i	0.982903	−	0.184126i	$-0.0589455\pi$
$389$	6128.44	+	6128.44i	0.798776	+	0.798776i	−0.184126	+	0.982903i	$0.558945\pi$
$390$		0			0
$391$	−2013.60			−0.260440
$392$	2564.56	−	8609.78i	0.330433	−	1.10934i
$393$		0			0
$394$	8156.30	−	6716.60i	1.04291	−	0.858826i
$395$	−3294.11	+	3294.11i	−0.419607	+	0.419607i
$396$		0			0
$397$	−6952.91	−	6952.91i	−0.878983	−	0.878983i	0.114446	−	0.993429i	$-0.463491\pi$
$397$	−6952.91	−	6952.91i	−0.878983	−	0.878983i	−0.993429	+	0.114446i	$0.963491\pi$
$398$	694.240	−	7171.90i	0.0874350	−	0.903254i
$399$		0			0
$400$	1093.22	−	2690.12i	0.136653	−	0.336265i
$401$			845.400i			0.105280i	0.998614	+	0.0526399i	$0.0167636\pi$
$401$			845.400i			0.105280i	−0.998614	+	0.0526399i	$0.983236\pi$
$402$		0			0
$403$	−8992.10	+	8992.10i	−1.11149	+	1.11149i
$404$	−7481.36	−	11115.8i	−0.921316	−	1.36889i
$405$		0			0
$406$	7450.75	+	9047.81i	0.910775	+	1.10600i
$407$		−	1697.51i		−	0.206738i
$408$		0			0
$409$		−	14578.4i		−	1.76249i	−0.472662	−	0.881244i	$-0.656707\pi$
$409$		−	14578.4i		−	1.76249i	0.472662	−	0.881244i	$-0.343293\pi$
$410$	7377.20	−	6075.02i	0.888619	−	0.731766i
$411$		0			0
$412$	15496.4	+	3028.48i	1.85304	+	0.362142i
$413$	7688.79	−	7688.79i	0.916079	−	0.916079i
$414$		0			0
$415$			5605.95i			0.663097i
$416$	−9265.88	+	2895.76i	−1.09206	+	0.341289i
$417$		0			0
$418$	1711.13	+	165.637i	0.200225	+	0.0193818i
$419$	−4924.02	−	4924.02i	−0.574115	−	0.574115i	0.359161	−	0.933276i	$-0.383063\pi$
$419$	−4924.02	−	4924.02i	−0.574115	−	0.574115i	−0.933276	+	0.359161i	$0.883063\pi$
$420$		0			0
$421$	−6264.27	+	6264.27i	−0.725182	+	0.725182i	−0.969656	−	0.244474i	$-0.921385\pi$
$421$	−6264.27	+	6264.27i	−0.725182	+	0.725182i	0.244474	+	0.969656i	$0.421385\pi$
$422$	−2949.40	−	3581.60i	−0.340224	−	0.413151i
$423$		0			0
$424$	−3924.00	+	2122.85i	−0.449449	+	0.243148i
$425$	3623.61			0.413578
$426$		0			0
$427$	−6959.20	−	6959.20i	−0.788711	−	0.788711i
$428$	9629.07	−	6480.71i	1.08747	−	0.731909i
$429$		0			0
$430$	6797.45	+	657.994i	0.762331	+	0.0737936i
$431$	−14200.7			−1.58707			−0.793533	−	0.608527i	$-0.791761\pi$
$431$	−14200.7			−1.58707			−0.793533	+	0.608527i	$0.791761\pi$
$432$		0			0
$433$	−1574.27			−0.174722			−0.0873611	−	0.996177i	$-0.527843\pi$
$433$	−1574.27			−0.174722			−0.0873611	+	0.996177i	$0.527843\pi$
$434$	−18160.2	−	1757.91i	−2.00857	−	0.194430i
$435$		0			0
$436$	7590.41	+	11277.9i	0.833749	+	1.23879i
$437$	1896.65	+	1896.65i	0.207618	+	0.207618i
$438$		0			0
$439$	−1716.76			−0.186644			−0.0933220	−	0.995636i	$-0.529749\pi$
$439$	−1716.76			−0.186644			−0.0933220	+	0.995636i	$0.529749\pi$
$440$	−329.311	+	1105.57i	−0.0356802	+	0.119786i
$441$		0			0
$442$	−7700.96	−	9351.65i	−0.828727	−	1.00636i
$443$	6531.76	−	6531.76i	0.700527	−	0.700527i	−0.263997	−	0.964524i	$-0.585041\pi$
$443$	6531.76	−	6531.76i	0.700527	−	0.700527i	0.964524	+	0.263997i	$0.0850408\pi$
$444$		0			0
$445$	−6955.15	−	6955.15i	−0.740912	−	0.740912i
$446$	10173.8	+	984.825i	1.08014	+	0.104558i
$447$		0			0
$448$	−11658.0	−	7621.24i	−1.22944	−	0.803728i
$449$			2179.52i			0.229082i	0.993419	+	0.114541i	$0.0365397\pi$
$449$			2179.52i			0.229082i	−0.993419	+	0.114541i	$0.963460\pi$
$450$		0			0
$451$	1529.62	−	1529.62i	0.159706	−	0.159706i
$452$	2693.10	−	13780.3i	0.280249	−	1.43400i
$453$		0			0
$454$	1371.69	−	1129.57i	0.141799	−	0.116770i
$455$		−	13018.3i		−	1.34133i
$456$		0			0
$457$			833.132i			0.0852785i	0.999091	+	0.0426392i	$0.0135766\pi$
$457$			833.132i			0.0852785i	−0.999091	+	0.0426392i	$0.986423\pi$
$458$	−480.370	−	583.337i	−0.0490092	−	0.0595143i
$459$		0			0
$460$	−1493.17	+	1004.96i	−0.151346	+	0.101862i
$461$	−6435.20	+	6435.20i	−0.650146	+	0.650146i	−0.953028	−	0.302882i	$-0.902051\pi$
$461$	−6435.20	+	6435.20i	−0.650146	+	0.650146i	0.302882	+	0.953028i	$0.402051\pi$
$462$		0			0
$463$		−	2144.06i		−	0.215211i	−0.994194	−	0.107606i	$-0.965682\pi$
$463$		−	2144.06i		−	0.215211i	0.994194	−	0.107606i	$-0.0343184\pi$
$464$	8981.87	−	3791.13i	0.898649	−	0.379308i
$465$		0			0
$466$	−1639.35	+	16935.4i	−0.162964	+	1.68351i
$467$	1590.87	+	1590.87i	0.157638	+	0.157638i	0.781519	−	0.623881i	$-0.214445\pi$
$467$	1590.87	+	1590.87i	0.157638	+	0.157638i	−0.623881	+	0.781519i	$0.714445\pi$
$468$		0			0
$469$	−9485.11	+	9485.11i	−0.933863	+	0.933863i
$470$	−8134.03	+	6698.26i	−0.798286	+	0.657378i
$471$		0			0
$472$	−4303.59	−	7955.02i	−0.419680	−	0.775762i
$473$	1545.85			0.150271
$474$		0			0
$475$	−3413.15	−	3413.15i	−0.329697	−	0.329697i
$476$	3333.70	−	17058.2i	0.321008	−	1.64256i
$477$		0			0
$478$	1053.75	−	10885.9i	0.100832	−	1.04165i
$479$	3087.11			0.294475			0.147238	−	0.989101i	$-0.452962\pi$
$479$	3087.11			0.294475			0.147238	+	0.989101i	$0.452962\pi$
$480$		0			0
$481$	15934.4			1.51049
$482$	−1648.66	+	17031.6i	−0.155798	+	1.60948i
$483$		0			0
$484$	1992.23	−	10194.0i	0.187099	−	0.957366i
$485$	6746.18	+	6746.18i	0.631604	+	0.631604i
$486$		0			0
$487$	20640.5			1.92055			0.960276	−	0.279051i	$-0.0900198\pi$
$487$	20640.5			1.92055			0.960276	+	0.279051i	$0.0900198\pi$
$488$	−7200.17	+	3895.23i	−0.667903	+	0.361329i
$489$		0			0
$490$	7735.40	−	6369.99i	0.713162	−	0.587280i
$491$	−13880.9	+	13880.9i	−1.27584	+	1.27584i	−0.332861	+	0.942976i	$0.608014\pi$
$491$	−13880.9	+	13880.9i	−1.27584	+	1.27584i	−0.942976	+	0.332861i	$0.891986\pi$
$492$		0			0
$493$	8602.66	+	8602.66i	0.785891	+	0.785891i
$494$	−1554.82	+	16062.2i	−0.141609	+	1.46290i
$495$		0			0
$496$	−5713.54	+	14059.5i	−0.517229	+	1.27276i
$497$		−	8740.93i		−	0.788902i
$498$		0			0
$499$	−8527.15	+	8527.15i	−0.764985	+	0.764985i	−0.977219	−	0.212234i	$-0.931926\pi$
$499$	−8527.15	+	8527.15i	−0.764985	+	0.764985i	0.212234	+	0.977219i	$0.431926\pi$
$500$	10090.0	−	6790.95i	0.902478	−	0.607401i
$501$		0			0
$502$	9531.78	+	11574.9i	0.847459	+	1.02911i
$503$			6352.16i			0.563079i	0.959550	+	0.281540i	$0.0908451\pi$
$503$			6352.16i			0.563079i	−0.959550	+	0.281540i	$0.909155\pi$
$504$		0			0
$505$		−	14945.7i		−	1.31698i
$506$	−314.500	+	258.987i	−0.0276309	+	0.0227537i
$507$		0			0
$508$	1819.63	−	9310.83i	0.158923	−	0.813192i
$509$	6383.68	−	6383.68i	0.555897	−	0.555897i	−0.372239	−	0.928137i	$-0.621410\pi$
$509$	6383.68	−	6383.68i	0.555897	−	0.555897i	0.928137	+	0.372239i	$0.121410\pi$
$510$		0			0
$511$			3677.26i			0.318342i
$512$	−8843.67	+	7483.80i	−0.763357	+	0.645977i
$513$		0			0
$514$	12931.4	+	1251.76i	1.10969	+	0.107418i
$515$	12453.7	+	12453.7i	1.06559	+	1.06559i
$516$		0			0
$517$	−1686.55	+	1686.55i	−0.143471	+	0.143471i
$518$	14532.8	+	17647.9i	1.23269	+	1.49692i
$519$		0			0
$520$	−10377.9	−	3091.21i	−0.875190	−	0.260690i
$521$	−14655.6			−1.23238			−0.616192	−	0.787596i	$-0.711326\pi$
$521$	−14655.6			−1.23238			−0.616192	+	0.787596i	$0.711326\pi$
$522$		0			0
$523$	5288.73	+	5288.73i	0.442180	+	0.442180i	0.892744	−	0.450564i	$-0.148777\pi$
$523$	5288.73	+	5288.73i	0.442180	+	0.442180i	−0.450564	+	0.892744i	$0.648777\pi$
$524$	6832.47	+	10151.7i	0.569614	+	0.846334i
$525$		0			0
$526$	−9789.08	−	947.583i	−0.811453	−	0.0785486i
$527$	−18938.2			−1.56539
$528$		0			0
$529$	11531.3			0.947755
$530$	−4953.28	−	479.477i	−0.405956	−	0.0392965i
$531$		0			0
$532$	−19207.5	+	12927.4i	−1.56532	+	1.05352i
$533$	14358.4	+	14358.4i	1.16685	+	1.16685i
$534$		0			0
$535$	12946.7			1.04623
$536$	5309.03	+	9813.54i	0.427827	+	0.790821i
$537$		0			0
$538$	293.535	+	356.454i	0.0235226	+	0.0285647i
$539$	1603.89	−	1603.89i	0.128172	−	0.128172i
$540$		0			0
$541$	−5155.04	−	5155.04i	−0.409672	−	0.409672i	0.471952	−	0.881624i	$-0.343550\pi$
$541$	−5155.04	−	5155.04i	−0.409672	−	0.409672i	−0.881624	+	0.471952i	$0.843550\pi$
$542$	6342.68	+	613.971i	0.502659	+	0.0486574i
$543$		0			0
$544$	−12806.8	−	6708.03i	−1.00935	−	0.528684i
$545$			15163.5i			1.19181i
$546$		0			0
$547$	−15716.4	+	15716.4i	−1.22849	+	1.22849i	−0.263956	+	0.964535i	$0.585027\pi$
$547$	−15716.4	+	15716.4i	−1.22849	+	1.22849i	−0.964535	+	0.263956i	$0.914973\pi$
$548$	−16999.3	−	3322.19i	−1.32513	−	0.258972i
$549$		0			0
$550$	565.965	−	466.064i	0.0438778	−	0.0361328i
$551$		−	16206.0i		−	1.25300i
$552$		0			0
$553$		−	14201.7i		−	1.09208i
$554$	3620.68	+	4396.77i	0.277668	+	0.337186i
$555$		0			0
$556$	−2160.75	−	3210.45i	−0.164813	−	0.244880i
$557$	6521.03	−	6521.03i	0.496059	−	0.496059i	−0.414150	−	0.910209i	$-0.635921\pi$
$557$	6521.03	−	6521.03i	0.496059	−	0.496059i	0.910209	+	0.414150i	$0.135921\pi$
$558$		0			0
$559$			14510.7i			1.09792i
$560$	−6041.40	−	14313.2i	−0.455885	−	1.08007i
$561$		0			0
$562$	1575.38	−	16274.6i	0.118244	−	1.22153i
$563$	−3081.99	−	3081.99i	−0.230711	−	0.230711i	0.582278	−	0.812989i	$-0.302161\pi$
$563$	−3081.99	−	3081.99i	−0.230711	−	0.230711i	−0.812989	+	0.582278i	$0.802161\pi$
$564$		0			0
$565$	11074.6	−	11074.6i	0.824620	−	0.824620i
$566$	−7856.97	+	6470.11i	−0.583486	+	0.480493i
$567$		0			0
$568$	−6968.04	−	2075.54i	−0.514740	−	0.153324i
$569$	15731.8			1.15907			0.579535	−	0.814948i	$-0.303234\pi$
$569$	15731.8			1.15907			0.579535	+	0.814948i	$0.303234\pi$
$570$		0			0
$571$	−15369.5	−	15369.5i	−1.12643	−	1.12643i	−0.990753	−	0.135680i	$-0.956678\pi$
$571$	−15369.5	−	15369.5i	−1.12643	−	1.12643i	−0.135680	−	0.990753i	$-0.543322\pi$
$572$	−2405.60	−	470.129i	−0.175844	−	0.0343655i
$573$		0			0
$574$	−2807.00	+	28997.9i	−0.204115	+	2.10862i
$575$	1143.92			0.0829649
$576$		0			0
$577$	−3414.08			−0.246326			−0.123163	−	0.992386i	$-0.539304\pi$
$577$	−3414.08			−0.246326			−0.123163	+	0.992386i	$0.539304\pi$
$578$	399.374	−	4125.76i	0.0287401	−	0.296902i
$579$		0			0
$580$	10672.7	+	2085.78i	0.764068	+	0.149323i
$581$	−12084.3	−	12084.3i	−0.862895	−	0.862895i
$582$		0			0
$583$	−1126.45			−0.0800222
$584$	2931.42	+	873.171i	0.207711	+	0.0618700i
$585$		0			0
$586$	1308.31	−	1077.37i	0.0922282	−	0.0759487i
$587$	−14858.9	+	14858.9i	−1.04479	+	1.04479i	−0.0458432	+	0.998949i	$0.514597\pi$
$587$	−14858.9	+	14858.9i	−1.04479	+	1.04479i	−0.998949	+	0.0458432i	$0.985403\pi$
$588$		0			0
$589$	17838.3	+	17838.3i	1.24790	+	1.24790i
$590$	972.031	−	10041.6i	0.0678269	−	0.700691i
$591$		0			0
$592$	17519.3	−	7394.66i	1.21628	−	0.513376i
$593$		−	10177.1i		−	0.704765i	−0.935856	−	0.352382i	$-0.885372\pi$
$593$		−	10177.1i		−	0.704765i	0.935856	−	0.352382i	$-0.114628\pi$
$594$		0			0
$595$	13708.9	−	13708.9i	0.944552	−	0.944552i
$596$	12239.3	+	18185.2i	0.841176	+	1.24982i
$597$		0			0
$598$	−2431.08	−	2952.18i	−0.166245	−	0.201879i
$599$			3301.30i			0.225188i	0.993641	+	0.112594i	$0.0359159\pi$
$599$			3301.30i			0.225188i	−0.993641	+	0.112594i	$0.964084\pi$
$600$		0			0
$601$		−	15622.6i		−	1.06033i	−0.847894	−	0.530166i	$-0.822130\pi$
$601$		−	15622.6i		−	1.06033i	0.847894	−	0.530166i	$-0.177870\pi$
$602$	−16071.1	+	13234.4i	−1.08806	+	0.896001i
$603$		0			0
$604$	18380.5	+	3592.12i	1.23823	+	0.241989i
$605$	8192.47	−	8192.47i	0.550531	−	0.550531i
$606$		0			0
$607$			8352.28i			0.558499i	0.960219	+	0.279249i	$0.0900856\pi$
$607$			8352.28i			0.558499i	−0.960219	+	0.279249i	$0.909914\pi$
$608$	5744.51	+	18381.4i	0.383176	+	1.22609i
$609$		0			0
$610$	−9088.79	−	879.795i	−0.603270	−	0.0583965i
$611$	−15831.5	−	15831.5i	−1.04824	−	1.04824i
$612$		0			0
$613$	−4415.12	+	4415.12i	−0.290906	+	0.290906i	−0.837438	−	0.546532i	$-0.815948\pi$
$613$	−4415.12	+	4415.12i	−0.290906	+	0.290906i	0.546532	+	0.837438i	$0.315948\pi$
$614$	1747.21	+	2121.72i	0.114840	+	0.139456i
$615$		0			0
$616$	−1673.32	−	3093.06i	−0.109448	−	0.202310i
$617$	908.905			0.0593049			0.0296525	−	0.999560i	$-0.490560\pi$
$617$	908.905			0.0593049			0.0296525	+	0.999560i	$0.490560\pi$
$618$		0			0
$619$	12163.4	+	12163.4i	0.789804	+	0.789804i	0.981462	−	0.191658i	$-0.0613863\pi$
$619$	12163.4	+	12163.4i	0.789804	+	0.789804i	−0.191658	+	0.981462i	$0.561386\pi$
$620$	−14043.5	+	9451.77i	−0.909676	+	0.612245i
$621$		0			0
$622$	1244.26	+	120.445i	0.0802097	+	0.00776430i
$623$	29985.4			1.92831
$624$		0			0
$625$	7895.01			0.505281
$626$	−5487.84	−	531.223i	−0.350380	−	0.0339168i
$627$		0			0
$628$	−5413.03	−	8042.71i	−0.343955	−	0.511049i
$629$	16779.6	+	16779.6i	1.06367	+	1.06367i
$630$		0			0
$631$	26228.8			1.65476			0.827380	−	0.561643i	$-0.189830\pi$
$631$	26228.8			1.65476			0.827380	+	0.561643i	$0.189830\pi$
$632$	−11321.3	−	3372.22i	−0.712556	−	0.212246i
$633$		0			0
$634$	−4138.72	−	5025.85i	−0.259258	−	0.314830i
$635$	7482.68	−	7482.68i	0.467624	−	0.467624i
$636$		0			0
$637$	15055.6	+	15055.6i	0.936459	+	0.936459i
$638$	2450.10	+	237.169i	0.152038	+	0.0147173i
$639$		0			0
$640$	−12844.6	+	1417.37i	−0.793325	+	0.0875415i
$641$		−	9142.35i		−	0.563340i	−0.959511	−	0.281670i	$-0.909112\pi$
$641$		−	9142.35i		−	0.563340i	0.959511	−	0.281670i	$-0.0908883\pi$
$642$		0			0
$643$	14128.8	−	14128.8i	0.866541	−	0.866541i	−0.125547	−	0.992088i	$-0.540069\pi$
$643$	14128.8	−	14128.8i	0.866541	−	0.866541i	0.992088	+	0.125547i	$0.0400686\pi$
$644$	1052.40	−	5385.02i	0.0643951	−	0.329503i
$645$		0			0
$646$	−18551.5	+	15276.9i	−1.12988	+	0.930438i
$647$		−	16153.8i		−	0.981566i	−0.871282	−	0.490783i	$-0.836711\pi$
$647$		−	16153.8i		−	0.981566i	0.871282	−	0.490783i	$-0.163289\pi$
$648$		0			0
$649$		−	2283.63i		−	0.138121i
$650$	4374.90	+	5312.65i	0.263996	+	0.320584i
$651$		0			0
$652$	−16309.3	+	10976.7i	−0.979632	+	0.659328i
$653$	4351.77	−	4351.77i	0.260793	−	0.260793i	−0.564583	−	0.825376i	$-0.690963\pi$
$653$	4351.77	−	4351.77i	0.260793	−	0.260793i	0.825376	+	0.564583i	$0.190963\pi$
$654$		0			0
$655$			13649.4i			0.814237i
$656$	22449.9	+	9123.27i	1.33616	+	0.542994i
$657$		0			0
$658$	3094.97	−	31972.8i	0.183366	−	1.89427i
$659$	−21049.5	−	21049.5i	−1.24427	−	1.24427i	−0.958213	−	0.286056i	$-0.907656\pi$
$659$	−21049.5	−	21049.5i	−1.24427	−	1.24427i	−0.286056	−	0.958213i	$-0.592344\pi$
$660$		0			0
$661$	14180.5	−	14180.5i	0.834428	−	0.834428i	−0.153691	−	0.988119i	$-0.549116\pi$
$661$	14180.5	−	14180.5i	0.834428	−	0.834428i	0.988119	+	0.153691i	$0.0491159\pi$
$662$	16862.7	−	13886.2i	0.990013	−	0.815263i
$663$		0			0
$664$	−12502.7	+	6763.87i	−0.730724	+	0.395315i
$665$	−25825.3			−1.50596
$666$		0			0
$667$	2715.74	+	2715.74i	0.157652	+	0.157652i
$668$	3793.99	−	19413.4i	0.219751	−	1.12444i
$669$		0			0
$670$	−1199.12	+	12387.6i	−0.0691436	+	0.714293i
$671$	−2066.94			−0.118917
$672$		0			0
$673$	2224.60			0.127418			0.0637089	−	0.997969i	$-0.479707\pi$
$673$	2224.60			0.127418			0.0637089	+	0.997969i	$0.479707\pi$
$674$	2030.46	−	20975.8i	0.116039	−	1.19875i
$675$		0			0
$676$	1041.92	−	5331.41i	0.0592811	−	0.303335i
$677$	−11483.6	−	11483.6i	−0.651919	−	0.651919i	0.301536	−	0.953455i	$-0.402501\pi$
$677$	−11483.6	−	11483.6i	−0.651919	−	0.651919i	−0.953455	+	0.301536i	$0.902501\pi$
$678$		0			0
$679$	−29084.5			−1.64383
$680$	−7673.17	−	14183.5i	−0.432724	−	0.799873i
$681$		0			0
$682$	−2957.92	+	2435.81i	−0.166077	+	0.136762i
$683$	1941.72	−	1941.72i	0.108781	−	0.108781i	−0.650621	−	0.759403i	$-0.725491\pi$
$683$	1941.72	−	1941.72i	0.108781	−	0.108781i	0.759403	+	0.650621i	$0.225491\pi$
$684$		0			0
$685$	−13661.5	−	13661.5i	−0.762014	−	0.762014i
$686$	−400.496	+	4137.35i	−0.0222901	+	0.230269i
$687$		0			0
$688$	6733.99	+	15954.0i	0.373155	+	0.884072i
$689$		−	10573.9i		−	0.584664i
$690$		0			0
$691$	−203.904	+	203.904i	−0.0112256	+	0.0112256i	−0.712697	−	0.701472i	$-0.752527\pi$
$691$	−203.904	+	203.904i	−0.0112256	+	0.0112256i	0.701472	+	0.712697i	$0.252527\pi$
$692$	−10462.4	+	7041.55i	−0.574739	+	0.386820i
$693$		0			0
$694$	−17981.2	−	21835.4i	−0.983511	−	1.19433i
$695$		−	4316.58i		−	0.235593i
$696$		0			0
$697$			30240.1i			1.64337i
$698$	−10190.2	+	8391.47i	−0.552584	+	0.455045i
$699$		0			0
$700$	−1893.87	+	9690.71i	−0.102259	+	0.523249i
$701$	62.5193	−	62.5193i	0.00336850	−	0.00336850i	−0.705421	−	0.708789i	$-0.749242\pi$
$701$	62.5193	−	62.5193i	0.00336850	−	0.00336850i	0.708789	+	0.705421i	$0.249242\pi$
$702$		0			0
$703$		−	31610.1i		−	1.69587i
$704$	−2863.04	+	599.475i	−0.153274	+	0.0320931i
$705$		0			0
$706$	−51.7703	−	5.01137i	−0.00275978	−	0.000267146i
$707$	32217.3	+	32217.3i	1.71380	+	1.71380i
$708$		0			0
$709$	−19068.4	+	19068.4i	−1.01005	+	1.01005i	−0.0101050	+	0.999949i	$0.503217\pi$
$709$	−19068.4	+	19068.4i	−1.01005	+	1.01005i	−0.999949	+	0.0101050i	$0.996783\pi$
$710$	−5155.35	−	6260.39i	−0.272502	−	0.330913i
$711$		0			0
$712$	7120.07	−	23903.6i	0.374769	−	1.25818i
$713$	−5978.52			−0.314021
$714$		0			0
$715$	−1933.27	−	1933.27i	−0.101119	−	0.101119i
$716$	−8617.18	−	12803.4i	−0.449776	−	0.668278i
$717$		0			0
$718$	1888.15	+	182.773i	0.0981407	+	0.00950002i
$719$	4219.83			0.218878			0.109439	−	0.993994i	$-0.465095\pi$
$719$	4219.83			0.218878			0.109439	+	0.993994i	$0.465095\pi$
$720$		0			0
$721$	−53691.2			−2.77332
$722$	12553.8	+	1215.21i	0.647096	+	0.0626389i
$723$		0			0
$724$	4162.42	−	2801.46i	0.213667	−	0.143806i
$725$	−4887.15	−	4887.15i	−0.250351	−	0.250351i
$726$		0			0
$727$	3771.74			0.192415			0.0962077	−	0.995361i	$-0.469329\pi$
$727$	3771.74			0.192415			0.0962077	+	0.995361i	$0.469329\pi$
$728$	29034.2	−	15707.3i	1.47813	−	0.799657i
$729$		0			0
$730$	2168.83	+	2633.72i	0.109962	+	0.133532i
$731$	−15280.5	+	15280.5i	−0.773143	+	0.773143i
$732$		0			0
$733$	−5607.56	−	5607.56i	−0.282565	−	0.282565i	0.551566	−	0.834131i	$-0.314030\pi$
$733$	−5607.56	−	5607.56i	−0.282565	−	0.282565i	−0.834131	+	0.551566i	$0.814030\pi$
$734$	−14184.4	−	1373.05i	−0.713293	−	0.0690468i
$735$		0			0
$736$	−4042.91	−	2117.63i	−0.202478	−	0.106055i
$737$			2817.15i			0.140802i
$738$		0			0
$739$	−7137.31	+	7137.31i	−0.355277	+	0.355277i	−0.862069	−	0.506791i	$-0.830831\pi$
$739$	−7137.31	+	7137.31i	−0.355277	+	0.355277i	0.506791	+	0.862069i	$0.330831\pi$
$740$	20817.2	+	4068.34i	1.03413	+	0.202101i
$741$		0			0
$742$	11711.0	−	9643.83i	0.579412	−	0.477138i
$743$		−	17134.1i		−	0.846016i	−0.906126	−	0.423008i	$-0.860974\pi$
$743$		−	17134.1i		−	0.846016i	0.906126	−	0.423008i	$-0.139026\pi$
$744$		0			0
$745$			24450.7i			1.20242i
$746$	−8013.88	−	9731.65i	−0.393310	−	0.477615i
$747$		0			0
$748$	−2038.14	−	3028.27i	−0.0996278	−	0.148027i
$749$	−27908.2	+	27908.2i	−1.36147	+	1.36147i
$750$		0			0
$751$		−	17533.1i		−	0.851922i	−0.904742	−	0.425961i	$-0.859936\pi$
$751$		−	17533.1i		−	0.851922i	0.904742	−	0.425961i	$-0.140064\pi$
$752$	−24753.0	−	10059.2i	−1.20033	−	0.487795i
$753$		0			0
$754$	−2226.28	+	22998.8i	−0.107529	+	1.11083i
$755$	14771.5	+	14771.5i	0.712042	+	0.712042i
$756$		0			0
$757$	−19568.4	+	19568.4i	−0.939532	+	0.939532i	−0.998273	−	0.0587408i	$-0.981291\pi$
$757$	−19568.4	+	19568.4i	−0.939532	+	0.939532i	0.0587408	+	0.998273i	$0.481291\pi$
$758$	4615.09	−	3800.47i	0.221145	−	0.182110i
$759$		0			0
$760$	−6132.25	+	20587.3i	−0.292684	+	0.982604i
$761$	−4059.70			−0.193383			−0.0966913	−	0.995314i	$-0.530826\pi$
$761$	−4059.70			−0.193383			−0.0966913	+	0.995314i	$0.530826\pi$
$762$		0			0
$763$	−32686.9	−	32686.9i	−1.55091	−	1.55091i
$764$	−5048.25	−	986.586i	−0.239057	−	0.0467192i
$765$		0			0
$766$	689.593	−	7123.90i	0.0325274	−	0.336027i
$767$	21436.2			1.00915
$768$		0			0
$769$	21167.3			0.992602			0.496301	−	0.868150i	$-0.334691\pi$
$769$	21167.3			0.992602			0.496301	+	0.868150i	$0.334691\pi$
$770$	377.944	−	3904.38i	0.0176885	−	0.182733i
$771$		0			0
$772$	8150.54	+	1592.87i	0.379980	+	0.0742599i
$773$	1992.49	+	1992.49i	0.0927102	+	0.0927102i	0.751941	−	0.659231i	$-0.229118\pi$
$773$	1992.49	+	1992.49i	0.0927102	+	0.0927102i	−0.659231	+	0.751941i	$0.729118\pi$
$774$		0			0
$775$	10758.7			0.498665
$776$	−6906.14	+	23185.4i	−0.319479	+	1.07256i
$777$		0			0
$778$	−18923.3	+	15583.1i	−0.872022	+	0.718098i
$779$	28483.8	−	28483.8i	1.31006	−	1.31006i
$780$		0			0
$781$	−1298.06	−	1298.06i	−0.0594728	−	0.0594728i
$782$	548.742	−	5668.82i	0.0250933	−	0.259229i
$783$		0			0
$784$	23539.9	+	9566.25i	1.07234	+	0.435780i
$785$		−	10813.7i		−	0.491668i
$786$		0			0
$787$	−17873.4	+	17873.4i	−0.809551	+	0.809551i	−0.984566	−	0.175015i	$-0.944003\pi$
$787$	−17873.4	+	17873.4i	−0.809551	+	0.809551i	0.175015	+	0.984566i	$0.444003\pi$
$788$	16686.3	+	24792.6i	0.754346	+	1.12081i
$789$		0			0
$790$	−8376.10	−	10171.5i	−0.377226	−	0.458083i
$791$			47745.2i			2.14617i
$792$		0			0
$793$		−	19402.1i		−	0.868839i
$794$	21469.1	−	17679.5i	0.959584	−	0.790204i
$795$		0			0
$796$	20001.6	+	3908.95i	0.890627	+	0.174056i
$797$	−4327.93	+	4327.93i	−0.192350	+	0.192350i	−0.796711	−	0.604361i	$-0.793429\pi$
$797$	−4327.93	+	4327.93i	−0.192350	+	0.192350i	0.604361	+	0.796711i	$0.293429\pi$
$798$		0			0
$799$		−	33342.5i		−	1.47631i
$800$	7275.49	+	3810.82i	0.321534	+	0.168416i
$801$		0			0
$802$	−2380.03	−	230.387i	−0.104790	−	0.0101437i
$803$	546.087	+	546.087i	0.0239988	+	0.0239988i
$804$		0			0
$805$	4327.69	−	4327.69i	0.189480	−	0.189480i
$806$	−22864.7	−	27765.7i	−0.999223	−	1.21341i
$807$		0			0
$808$	33332.8	−	18032.8i	1.45129	−	0.785137i
$809$	−7284.89			−0.316592			−0.158296	−	0.987392i	$-0.550600\pi$
$809$	−7284.89			−0.316592			−0.158296	+	0.987392i	$0.550600\pi$
$810$		0			0
$811$	28534.9	+	28534.9i	1.23551	+	1.23551i	0.961819	+	0.273688i	$0.0882435\pi$
$811$	28534.9	+	28534.9i	1.23551	+	1.23551i	0.273688	+	0.961819i	$0.411756\pi$
$812$	−27502.5	+	18510.2i	−1.18861	+	0.799975i
$813$		0			0
$814$	4778.95	+	462.602i	0.205776	+	0.0199192i
$815$	−21928.5			−0.942479
$816$		0			0
$817$	28785.9			1.23267
$818$	41042.2	+	3972.89i	1.75429	+	0.169815i
$819$		0			0
$820$	15092.4	+	22424.3i	0.642743	+	0.954990i
$821$	−17928.4	−	17928.4i	−0.762128	−	0.762128i	0.214579	−	0.976707i	$-0.431162\pi$
$821$	−17928.4	−	17928.4i	−0.762128	−	0.762128i	−0.976707	+	0.214579i	$0.931162\pi$
$822$		0			0
$823$	−25241.2			−1.06908			−0.534540	−	0.845143i	$-0.679515\pi$
$823$	−25241.2			−1.06908			−0.534540	+	0.845143i	$0.679515\pi$
$824$	−12749.0	+	42801.2i	−0.538997	+	1.80953i
$825$		0			0
$826$	19550.7	+	23741.3i	0.823553	+	1.00008i
$827$	27181.2	−	27181.2i	1.14291	−	1.14291i	0.154990	−	0.987916i	$-0.450466\pi$
$827$	27181.2	−	27181.2i	1.14291	−	1.14291i	0.987916	−	0.154990i	$-0.0495344\pi$
$828$		0			0
$829$	−2755.03	−	2755.03i	−0.115424	−	0.115424i	0.647036	−	0.762460i	$-0.276008\pi$
$829$	−2755.03	−	2755.03i	−0.115424	−	0.115424i	−0.762460	+	0.647036i	$0.776008\pi$
$830$	−15782.2	−	1527.72i	−0.660012	−	0.0638891i
$831$		0			0
$832$	−5627.21	−	26875.1i	−0.234481	−	1.11986i
$833$			31708.4i			1.31889i
$834$		0			0
$835$	15601.7	−	15601.7i	0.646608	−	0.646608i
$836$	−932.627	+	4772.15i	−0.0385832	+	0.197426i
$837$		0			0
$838$	15204.3	−	12520.6i	0.626760	−	0.516128i
$839$			20544.0i			0.845361i	0.906279	+	0.422681i	$0.138911\pi$
$839$			20544.0i			0.845361i	−0.906279	+	0.422681i	$0.861089\pi$
$840$		0			0
$841$			1184.24i			0.0485561i
$842$	−15928.5	−	19342.7i	−0.651937	−	0.791679i
$843$		0			0
$844$	10886.9	−	7327.31i	0.444009	−	0.298835i
$845$	4284.61	−	4284.61i	0.174432	−	0.174432i
$846$		0			0
$847$			35319.8i			1.43282i
$848$	−4907.03	−	11625.6i	−0.198712	−	0.470785i
$849$		0			0
$850$	−987.498	+	10201.4i	−0.0398481	+	0.411654i
$851$	5297.08	+	5297.08i	0.213374	+	0.213374i
$852$		0			0
$853$	9553.45	−	9553.45i	0.383475	−	0.383475i	−0.488878	−	0.872352i	$-0.662594\pi$
$853$	9553.45	−	9553.45i	0.383475	−	0.383475i	0.872352	+	0.488878i	$0.162594\pi$
$854$	21488.5	−	17695.5i	0.861033	−	0.709049i
$855$		0			0
$856$	15620.9	+	28874.5i	0.623726	+	1.15293i
$857$	21465.0			0.855578			0.427789	−	0.903879i	$-0.359293\pi$
$857$	21465.0			0.855578			0.427789	+	0.903879i	$0.359293\pi$
$858$		0			0
$859$	4252.94	+	4252.94i	0.168927	+	0.168927i	0.786508	−	0.617580i	$-0.211887\pi$
$859$	4252.94	+	4252.94i	0.168927	+	0.168927i	−0.617580	+	0.786508i	$0.711887\pi$
$860$	−3704.86	+	18957.3i	−0.146901	+	0.751674i
$861$		0			0
$862$	3869.96	−	39978.9i	0.152913	−	1.57968i
$863$	−7487.36			−0.295333			−0.147667	−	0.989037i	$-0.547176\pi$
$863$	−7487.36			−0.295333			−0.147667	+	0.989037i	$0.547176\pi$
$864$		0			0
$865$	−14067.1			−0.552942
$866$	429.018	−	4432.00i	0.0168344	−	0.173909i
$867$		0			0
$868$	9897.99	−	50646.9i	0.387050	−	1.98049i
$869$	−2109.01	−	2109.01i	−0.0823282	−	0.0823282i
$870$		0			0
$871$	−26444.3			−1.02874
$872$	−33818.7	+	18295.6i	−1.31336	+	0.710513i
$873$		0			0
$874$	−5856.45	+	4822.71i	−0.226656	+	0.186648i
$875$	−29244.1	+	29244.1i	−1.12987	+	1.12987i
$876$		0			0
$877$	−14348.4	−	14348.4i	−0.552465	−	0.552465i	0.374686	−	0.927152i	$-0.377750\pi$
$877$	−14348.4	−	14348.4i	−0.552465	−	0.552465i	−0.927152	+	0.374686i	$0.877750\pi$
$878$	467.849	−	4833.15i	0.0179831	−	0.185776i
$879$		0			0
$880$	−3022.73	−	1228.39i	−0.115791	−	0.0470556i
$881$			17497.5i			0.669131i	0.942372	+	0.334566i	$0.108590\pi$
$881$			17497.5i			0.669131i	−0.942372	+	0.334566i	$0.891410\pi$
$882$		0			0
$883$	5399.20	−	5399.20i	0.205773	−	0.205773i	−0.596695	−	0.802468i	$-0.703520\pi$
$883$	5399.20	−	5399.20i	0.205773	−	0.205773i	0.802468	+	0.596695i	$0.203520\pi$
$884$	28426.1	−	19131.8i	1.08153	−	0.727908i
$885$		0			0
$886$	16608.6	+	20168.7i	0.629772	+	0.764763i
$887$			32588.2i			1.23360i	0.787119	+	0.616801i	$0.211572\pi$
$887$			32588.2i			1.23360i	−0.787119	+	0.616801i	$0.788428\pi$
$888$		0			0
$889$			32259.7i			1.21705i
$890$	21476.0	−	17685.2i	0.808851	−	0.666078i
$891$		0			0
$892$	−5545.10	+	28373.6i	−0.208143	+	1.06504i
$893$	−31406.0	+	31406.0i	−1.17689	+	1.17689i
$894$		0			0
$895$		−	17214.8i		−	0.642934i
$896$	24632.9	−	30743.5i	0.918444	−	1.14628i
$897$		0			0
$898$	−6135.92	−	593.957i	−0.228016	−	0.0220720i
$899$	25541.9	+	25541.9i	0.947575	+	0.947575i
$900$		0			0
$901$	11134.8	−	11134.8i	0.411714	−	0.411714i
$902$	3889.45	+	4723.15i	0.143575	+	0.174350i
$903$		0			0
$904$	38061.3	+	11337.2i	1.40033	+	0.417111i
$905$	5596.54			0.205564
$906$		0			0
$907$	175.952	+	175.952i	0.00644145	+	0.00644145i	0.710320	−	0.703879i	$-0.248550\pi$
$907$	175.952	+	175.952i	0.00644145	+	0.00644145i	−0.703879	+	0.710320i	$0.748550\pi$
$908$	2806.23	+	4169.51i	0.102564	+	0.152390i
$909$		0			0
$910$	36650.0	+	3547.72i	1.33509	+	0.129237i
$911$	−13051.9			−0.474676			−0.237338	−	0.971427i	$-0.576275\pi$
$911$	−13051.9			−0.474676			−0.237338	+	0.971427i	$0.576275\pi$
$912$		0			0
$913$	−3589.13			−0.130102
$914$	−2345.49	−	227.043i	−0.0848817	−	0.00821655i
$915$		0			0
$916$	1773.16	−	1193.40i	0.0639595	−	0.0430470i
$917$	−29422.9	−	29422.9i	−1.05958	−	1.05958i
$918$		0			0
$919$	−8004.68			−0.287323			−0.143662	−	0.989627i	$-0.545888\pi$
$919$	−8004.68			−0.287323			−0.143662	+	0.989627i	$0.545888\pi$
$920$	−2422.31	−	4477.54i	−0.0868056	−	0.160457i
$921$		0			0
$922$	−16363.1	−	19870.5i	−0.584480	−	0.709763i
$923$	12184.8	−	12184.8i	0.434524	−	0.434524i
$924$		0			0
$925$	−9532.46	−	9532.46i	−0.338838	−	0.338838i
$926$	6036.09	+	584.294i	0.214210	+	0.0207355i
$927$		0			0
$928$	8225.33	+	26319.5i	0.290959	+	0.931014i
$929$		−	19953.1i		−	0.704672i	−0.935874	−	0.352336i	$-0.885387\pi$
$929$		−	19953.1i		−	0.704672i	0.935874	−	0.352336i	$-0.114613\pi$
$930$		0			0
$931$	29866.8	−	29866.8i	1.05139	−	1.05139i
$932$	−47230.9	−	9230.40i	−1.65998	−	0.324412i
$933$		0			0
$934$	−4912.27	+	4045.19i	−0.172093	+	0.141716i
$935$		−	4071.63i		−	0.142414i
$936$		0			0
$937$			47079.0i			1.64141i	0.571351	+	0.820706i	$0.306420\pi$
$937$			47079.0i			1.64141i	−0.571351	+	0.820706i	$0.693580\pi$
$938$	−24118.3	−	29288.0i	−0.839540	−	1.01950i
$939$		0			0
$940$	−16640.7	−	24724.9i	−0.577405	−	0.857911i
$941$	4612.54	−	4612.54i	0.159792	−	0.159792i	−0.622682	−	0.782475i	$-0.713957\pi$
$941$	4612.54	−	4612.54i	0.159792	−	0.159792i	0.782475	+	0.622682i	$0.213957\pi$
$942$		0			0
$943$			9546.38i			0.329664i
$944$	23568.3	−	9947.88i	0.812588	−	0.342983i
$945$		0			0
$946$	−421.271	+	4351.98i	−0.0144786	+	0.149572i
$947$	−35884.4	−	35884.4i	−1.23135	−	1.23135i	−0.963447	−	0.267899i	$-0.913671\pi$
$947$	−35884.4	−	35884.4i	−1.23135	−	1.23135i	−0.267899	−	0.963447i	$-0.586329\pi$
$948$		0			0
$949$	−5126.07	+	5126.07i	−0.175342	+	0.175342i
$950$	10539.1	−	8678.79i	0.359929	−	0.296397i
$951$		0			0
$952$	47114.9	+	14033.9i	1.60399	+	0.477775i
$953$	−2274.82			−0.0773228			−0.0386614	−	0.999252i	$-0.512309\pi$
$953$	−2274.82			−0.0773228			−0.0386614	+	0.999252i	$0.512309\pi$
$954$		0			0
$955$	−4057.04	−	4057.04i	−0.137469	−	0.137469i
$956$	30359.5	+	5933.20i	1.02709	+	0.200725i
$957$		0			0
$958$	−841.293	+	8691.04i	−0.0283726	+	0.293105i
$959$	58898.2			1.98324
$960$		0			0
$961$	−26437.8			−0.887442
$962$	−4342.40	+	44859.5i	−0.145535	+	1.50346i
$963$		0			0
$964$	−47499.3	−	9282.85i	−1.58698	−	0.310146i
$965$	6550.21	+	6550.21i	0.218506	+	0.218506i
$966$		0			0
$967$	−11693.6			−0.388874			−0.194437	−	0.980915i	$-0.562288\pi$
$967$	−11693.6			−0.388874			−0.194437	+	0.980915i	$0.562288\pi$
$968$	28156.0	+	8386.72i	0.934885	+	0.278471i
$969$		0			0
$970$	−20830.8	+	17153.8i	−0.689521	+	0.567811i
$971$	13147.9	−	13147.9i	0.434537	−	0.434537i	−0.455632	−	0.890168i	$-0.650587\pi$
$971$	13147.9	−	13147.9i	0.434537	−	0.434537i	0.890168	+	0.455632i	$0.150587\pi$
$972$		0			0
$973$	9304.93	+	9304.93i	0.306580	+	0.306580i
$974$	−5624.90	+	58108.5i	−0.185045	+	1.91162i
$975$		0			0
$976$	−9003.93	−	21331.9i	−0.295296	−	0.699609i
$977$			57554.9i			1.88469i	0.334642	+	0.942345i	$0.391385\pi$
$977$			57554.9i			1.88469i	−0.334642	+	0.942345i	$0.608615\pi$
$978$		0			0
$979$	4452.94	−	4452.94i	0.145369	−	0.145369i
$980$	15825.2	+	23513.2i	0.515834	+	0.766429i
$981$		0			0
$982$	−35295.6	−	42861.2i	−1.14697	−	1.39283i
$983$			29857.4i			0.968773i	0.874854	+	0.484386i	$0.160957\pi$
$983$			29857.4i			0.968773i	−0.874854	+	0.484386i	$0.839043\pi$
$984$		0			0
$985$			33334.6i			1.07830i
$986$	−26563.2	+	21874.4i	−0.857955	+	0.706514i
$987$		0			0
$988$	−44795.7	−	8754.48i	−1.44245	−	0.281900i
$989$	−4823.82	+	4823.82i	−0.155095	+	0.155095i
$990$		0			0
$991$		−	37310.0i		−	1.19596i	−0.801513	−	0.597978i	$-0.795971\pi$
$991$		−	37310.0i		−	1.19596i	0.801513	−	0.597978i	$-0.204029\pi$
$992$	−38024.1	−	19916.6i	−1.21700	−	0.637452i
$993$		0			0
$994$	24608.0	+	2382.06i	0.785231	+	0.0760104i
$995$	16074.4	+	16074.4i	0.512153	+	0.512153i
$996$		0			0
$997$	31495.0	−	31495.0i	1.00046	−	1.00046i	0.000458156	−	1.00000i	$-0.499854\pi$
$997$	31495.0	−	31495.0i	1.00046	−	1.00046i	1.00000		0.000458156i	$-0.000145836\pi$
$998$	−21682.4	−	26330.0i	−0.687720	−	0.835132i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.l.a.35.11	✓	48
3.2	odd	2	inner	144.4.l.a.35.14	yes	48
4.3	odd	2		576.4.l.a.431.8		48
8.3	odd	2		1152.4.l.a.863.17		48
8.5	even	2		1152.4.l.b.863.17		48
12.11	even	2		576.4.l.a.431.17		48
16.3	odd	4		1152.4.l.b.287.8		48
16.5	even	4		576.4.l.a.143.17		48
16.11	odd	4	inner	144.4.l.a.107.14	yes	48
16.13	even	4		1152.4.l.a.287.8		48
24.5	odd	2		1152.4.l.b.863.8		48
24.11	even	2		1152.4.l.a.863.8		48
48.5	odd	4		576.4.l.a.143.8		48
48.11	even	4	inner	144.4.l.a.107.11	yes	48
48.29	odd	4		1152.4.l.a.287.17		48
48.35	even	4		1152.4.l.b.287.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.4.l.a.35.11	✓	48	1.1	even	1	trivial
144.4.l.a.35.14	yes	48	3.2	odd	2	inner
144.4.l.a.107.11	yes	48	48.11	even	4	inner
144.4.l.a.107.14	yes	48	16.11	odd	4	inner
576.4.l.a.143.8		48	48.5	odd	4
576.4.l.a.143.17		48	16.5	even	4
576.4.l.a.431.8		48	4.3	odd	2
576.4.l.a.431.17		48	12.11	even	2
1152.4.l.a.287.8		48	16.13	even	4
1152.4.l.a.287.17		48	48.29	odd	4
1152.4.l.a.863.8		48	24.11	even	2
1152.4.l.a.863.17		48	8.3	odd	2
1152.4.l.b.287.8		48	16.3	odd	4
1152.4.l.b.287.17		48	48.35	even	4
1152.4.l.b.863.8		48	24.5	odd	2
1152.4.l.b.863.17		48	8.5	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.272518 + 2.81527i) q^{2} +(-7.85147 - 1.53442i) q^{4} +(-6.30986 - 6.30986i) q^{5} +27.2034 q^{7} +(6.45947 - 21.6858i) q^{8} +(19.4835 - 16.0444i) q^{10} +(4.03980 - 4.03980i) q^{11} +(37.9212 + 37.9212i) q^{13} +(-7.41340 + 76.5848i) q^{14} +(59.2911 + 24.0949i) q^{16} +79.8655i q^{17} +(75.2269 - 75.2269i) q^{19} +(39.8597 + 59.2236i) q^{20} +(10.2722 + 12.4740i) q^{22} +25.2124i q^{23} -45.3714i q^{25} +(-117.093 + 96.4241i) q^{26} +(-213.586 - 41.7414i) q^{28} +(107.714 - 107.714i) q^{29} +237.126i q^{31} +(-83.9916 + 160.354i) q^{32} +(-224.843 - 21.7648i) q^{34} +(-171.649 - 171.649i) q^{35} +(210.098 - 210.098i) q^{37} +(191.283 + 232.285i) q^{38} +(-177.593 + 96.0761i) q^{40} +378.638 q^{41} +(191.327 + 191.327i) q^{43} +(-37.9171 + 25.5196i) q^{44} +(-70.9796 - 6.87083i) q^{46} -417.483 q^{47} +397.023 q^{49} +(127.733 + 12.3645i) q^{50} +(-239.550 - 355.924i) q^{52} +(-139.419 - 139.419i) q^{53} -50.9811 q^{55} +(175.719 - 589.928i) q^{56} +(273.891 + 332.599i) q^{58} +(282.641 - 282.641i) q^{59} +(-255.821 - 255.821i) q^{61} +(-667.574 - 64.6211i) q^{62} +(-428.550 - 280.158i) q^{64} -478.555i q^{65} +(-348.674 + 348.674i) q^{67} +(122.547 - 627.061i) q^{68} +(530.016 - 436.461i) q^{70} -321.318i q^{71} +135.177i q^{73} +(534.228 + 648.739i) q^{74} +(-706.072 + 475.212i) q^{76} +(109.896 - 109.896i) q^{77} -522.058i q^{79} +(-222.083 - 526.154i) q^{80} +(-103.186 + 1065.97i) q^{82} +(-444.221 - 444.221i) q^{83} +(503.940 - 503.940i) q^{85} +(-590.778 + 486.498i) q^{86} +(-61.5114 - 113.701i) q^{88} +1102.27 q^{89} +(1031.58 + 1031.58i) q^{91} +(38.6864 - 197.954i) q^{92} +(113.772 - 1175.33i) q^{94} -949.342 q^{95} -1069.15 q^{97} +(-108.196 + 1117.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 120 q^{10} - 144 q^{16} - 48 q^{19} + 72 q^{22} + 72 q^{28} - 984 q^{34} - 1272 q^{40} + 864 q^{43} - 1416 q^{46} + 2352 q^{49} - 648 q^{52} - 576 q^{55} + 1128 q^{58} + 1824 q^{61} + 3024 q^{64}+ \cdots - 11304 q^{94}+O(q^{100}) \) 48 * q - 120 * q^10 - 144 * q^16 - 48 * q^19 + 72 * q^22 + 72 * q^28 - 984 * q^34 - 1272 * q^40 + 864 * q^43 - 1416 * q^46 + 2352 * q^49 - 648 * q^52 - 576 * q^55 + 1128 * q^58 + 1824 * q^61 + 3024 * q^64 + 816 * q^67 + 2664 * q^70 + 1920 * q^76 + 1200 * q^82 - 480 * q^85 - 4560 * q^88 - 3600 * q^91 - 11304 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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