LMFDB - Embedded newform 288.4.p.b.239.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,4,Mod(47,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("288.47");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$288 = 2^{5} \cdot 3^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	288.p (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$16.9925500817$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			239.31
Character	$\chi$	$=$	288.239
Dual form			288.4.p.b.47.31

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.18814 - 0.288534i) q^{3} +(-5.34568 + 9.25900i) q^{5} +(15.5169 - 8.95867i) q^{7} +(26.8335 - 2.99391i) q^{9} +(19.0639 - 11.0065i) q^{11} +(-17.9061 - 10.3381i) q^{13} +(-25.0626 + 49.5793i) q^{15} -36.2107i q^{17} +125.564 q^{19} +(77.9188 - 50.9559i) q^{21} +(-88.1103 + 152.612i) q^{23} +(5.34734 + 9.26186i) q^{25} +(138.352 - 23.2752i) q^{27} +(77.3286 + 133.937i) q^{29} +(243.700 + 140.701i) q^{31} +(95.7301 - 62.6039i) q^{33} +191.561i q^{35} -223.656i q^{37} +(-95.8823 - 48.4690i) q^{39} +(47.3067 + 27.3125i) q^{41} +(-157.422 - 272.663i) q^{43} +(-115.723 + 264.456i) q^{45} +(-230.270 - 398.839i) q^{47} +(-10.9844 + 19.0256i) q^{49} +(-10.4480 - 187.866i) q^{51} +158.027 q^{53} +235.349i q^{55} +(651.443 - 36.2295i) q^{57} +(403.976 + 233.236i) q^{59} +(-382.288 + 220.714i) q^{61} +(389.550 - 286.849i) q^{63} +(191.441 - 110.529i) q^{65} +(193.518 - 335.182i) q^{67} +(-413.095 + 817.192i) q^{69} -20.3800 q^{71} -370.437 q^{73} +(30.4151 + 46.5089i) q^{75} +(197.208 - 341.574i) q^{77} +(562.808 - 324.937i) q^{79} +(711.073 - 160.674i) q^{81} +(-516.463 + 298.180i) q^{83} +(335.275 + 193.571i) q^{85} +(439.837 + 672.572i) q^{87} +1210.30i q^{89} -370.463 q^{91} +(1304.95 + 659.657i) q^{93} +(-671.225 + 1162.60i) q^{95} +(-794.702 - 1376.46i) q^{97} +(478.597 - 352.419i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$64 q - 6 q^{3} + 42 q^{9} - 48 q^{11} + 220 q^{19} - 902 q^{25} + 252 q^{27} - 660 q^{33} + 1620 q^{41} + 292 q^{43} + 1762 q^{49} + 1794 q^{51} - 294 q^{57} - 5592 q^{59} - 6 q^{65} - 68 q^{67} - 868 q^{73}+ \cdots + 2118 q^{99}+O(q^{100})$ 64 * q - 6 * q^3 + 42 * q^9 - 48 * q^11 + 220 * q^19 - 902 * q^25 + 252 * q^27 - 660 * q^33 + 1620 * q^41 + 292 * q^43 + 1762 * q^49 + 1794 * q^51 - 294 * q^57 - 5592 * q^59 - 6 * q^65 - 68 * q^67 - 868 * q^73 + 4254 * q^75 + 498 * q^81 - 3654 * q^83 + 1380 * q^91 - 1912 * q^97 + 2118 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$ .

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	5.18814	−	0.288534i	0.998457	−	0.0555285i
$3$	5.18814	−	0.288534i	0.998457	−	0.0555285i
$4$		0			0
$5$	−5.34568	+	9.25900i	−0.478132	+	0.828150i	−0.999686	−	0.0250690i	$-0.992019\pi$
$5$	−5.34568	+	9.25900i	−0.478132	+	0.828150i	0.521553	+	0.853219i	$0.325353\pi$
$6$		0			0
$7$	15.5169	−	8.95867i	0.837832	−	0.483723i	−0.0186945	−	0.999825i	$-0.505951\pi$
$7$	15.5169	−	8.95867i	0.837832	−	0.483723i	0.856527	+	0.516103i	$0.172618\pi$
$8$		0			0
$9$	26.8335	−	2.99391i	0.993833	−	0.110886i
$10$		0			0
$11$	19.0639	−	11.0065i	0.522543	−	0.301690i	−0.215432	−	0.976519i	$-0.569116\pi$
$11$	19.0639	−	11.0065i	0.522543	−	0.301690i	0.737974	+	0.674829i	$0.235783\pi$
$12$		0			0
$13$	−17.9061	−	10.3381i	−0.382021	−	0.220560i	0.296676	−	0.954978i	$-0.404122\pi$
$13$	−17.9061	−	10.3381i	−0.382021	−	0.220560i	−0.678697	+	0.734418i	$0.737455\pi$
$14$		0			0
$15$	−25.0626	+	49.5793i	−0.431409	+	0.853422i
$16$		0			0
$17$		−	36.2107i		−	0.516611i	−0.966063	−	0.258306i	$-0.916836\pi$
$17$		−	36.2107i		−	0.516611i	0.966063	−	0.258306i	$-0.0831642\pi$
$18$		0			0
$19$	125.564			1.51612			0.758062	−	0.652182i	$-0.226146\pi$
$19$	125.564			1.51612			0.758062	+	0.652182i	$0.226146\pi$
$20$		0			0
$21$	77.9188	−	50.9559i	0.809679	−	0.529500i
$22$		0			0
$23$	−88.1103	+	152.612i	−0.798794	+	1.38355i	0.121607	+	0.992578i	$0.461195\pi$
$23$	−88.1103	+	152.612i	−0.798794	+	1.38355i	−0.920402	+	0.390974i	$0.872138\pi$
$24$		0			0
$25$	5.34734	+	9.26186i	0.0427787	+	0.0740949i
$26$		0			0
$27$	138.352	−	23.2752i	0.986142	−	0.165900i
$28$		0			0
$29$	77.3286	+	133.937i	0.495157	+	0.857638i	0.999984	−	0.00558276i	$-0.00177706\pi$
$29$	77.3286	+	133.937i	0.495157	+	0.857638i	−0.504827	+	0.863221i	$0.668444\pi$
$30$		0			0
$31$	243.700	+	140.701i	1.41193	+	0.815179i	0.995570	−	0.0940195i	$-0.0299716\pi$
$31$	243.700	+	140.701i	1.41193	+	0.815179i	0.416362	+	0.909199i	$0.363305\pi$
$32$		0			0
$33$	95.7301	−	62.6039i	0.504984	−	0.330241i
$34$		0			0
$35$			191.561i			0.925134i
$36$		0			0
$37$		−	223.656i		−	0.993754i	−0.867821	−	0.496877i	$-0.834480\pi$
$37$		−	223.656i		−	0.993754i	0.867821	−	0.496877i	$-0.165520\pi$
$38$		0			0
$39$	−95.8823	−	48.4690i	−0.393678	−	0.199006i
$40$		0			0
$41$	47.3067	+	27.3125i	0.180197	+	0.104037i	0.587385	−	0.809308i	$-0.300157\pi$
$41$	47.3067	+	27.3125i	0.180197	+	0.104037i	−0.407188	+	0.913344i	$0.633491\pi$
$42$		0			0
$43$	−157.422	−	272.663i	−0.558294	−	0.966994i	−0.997639	−	0.0686756i	$-0.978123\pi$
$43$	−157.422	−	272.663i	−0.558294	−	0.966994i	0.439345	−	0.898319i	$-0.355211\pi$
$44$		0			0
$45$	−115.723	+	264.456i	−0.383354	+	0.876061i
$46$		0			0
$47$	−230.270	−	398.839i	−0.714644	−	1.23780i	−0.963097	−	0.269156i	$-0.913255\pi$
$47$	−230.270	−	398.839i	−0.714644	−	1.23780i	0.248453	−	0.968644i	$-0.420078\pi$
$48$		0			0
$49$	−10.9844	+	19.0256i	−0.0320246	+	0.0554683i
$50$		0			0
$51$	−10.4480	−	187.866i	−0.0286866	−	0.515814i
$52$		0			0
$53$	158.027			0.409560			0.204780	−	0.978808i	$-0.434352\pi$
$53$	158.027			0.409560			0.204780	+	0.978808i	$0.434352\pi$
$54$		0			0
$55$			235.349i			0.576991i
$56$		0			0
$57$	651.443	−	36.2295i	1.51379	−	0.0841880i
$58$		0			0
$59$	403.976	+	233.236i	0.891410	+	0.514656i	0.874403	−	0.485200i	$-0.161253\pi$
$59$	403.976	+	233.236i	0.891410	+	0.514656i	0.0170066	+	0.999855i	$0.494586\pi$
$60$		0			0
$61$	−382.288	+	220.714i	−0.802409	+	0.463271i	−0.844313	−	0.535851i	$-0.819991\pi$
$61$	−382.288	+	220.714i	−0.802409	+	0.463271i	0.0419039	+	0.999122i	$0.486658\pi$
$62$		0			0
$63$	389.550	−	286.849i	0.779028	−	0.573643i
$64$		0			0
$65$	191.441	−	110.529i	0.365313	−	0.210913i
$66$		0			0
$67$	193.518	−	335.182i	0.352865	−	0.611180i	−0.633885	−	0.773427i	$-0.718541\pi$
$67$	193.518	−	335.182i	0.352865	−	0.611180i	0.986750	+	0.162247i	$0.0518742\pi$
$68$		0			0
$69$	−413.095	+	817.192i	−0.720735	+	1.42577i
$70$		0			0
$71$	−20.3800			−0.0340657			−0.0170328	−	0.999855i	$-0.505422\pi$
$71$	−20.3800			−0.0340657			−0.0170328	+	0.999855i	$0.505422\pi$
$72$		0			0
$73$	−370.437			−0.593922			−0.296961	−	0.954890i	$-0.595973\pi$
$73$	−370.437			−0.593922			−0.296961	+	0.954890i	$0.595973\pi$
$74$		0			0
$75$	30.4151	+	46.5089i	0.0468271	+	0.0716051i
$76$		0			0
$77$	197.208	−	341.574i	0.291869	−	0.505531i
$78$		0			0
$79$	562.808	−	324.937i	0.801530	−	0.462763i	−0.0424761	−	0.999097i	$-0.513525\pi$
$79$	562.808	−	324.937i	0.801530	−	0.462763i	0.844006	+	0.536334i	$0.180191\pi$
$80$		0			0
$81$	711.073	−	160.674i	0.975409	−	0.220403i
$82$		0			0
$83$	−516.463	+	298.180i	−0.683002	+	0.394331i	−0.800985	−	0.598684i	$-0.795690\pi$
$83$	−516.463	+	298.180i	−0.683002	+	0.394331i	0.117983	+	0.993016i	$0.462357\pi$
$84$		0			0
$85$	335.275	+	193.571i	0.427832	+	0.247009i
$86$		0			0
$87$	439.837	+	672.572i	0.542017	+	0.828819i
$88$		0			0
$89$			1210.30i			1.44148i	0.693206	+	0.720739i	$0.256197\pi$
$89$			1210.30i			1.44148i	−0.693206	+	0.720739i	$0.743803\pi$
$90$		0			0
$91$	−370.463			−0.426759
$92$		0			0
$93$	1304.95	+	659.657i	1.45502	+	0.735519i
$94$		0			0
$95$	−671.225	+	1162.60i	−0.724908	+	1.25558i
$96$		0			0
$97$	−794.702	−	1376.46i	−0.831853	−	1.44081i	−0.896567	−	0.442908i	$-0.853947\pi$
$97$	−794.702	−	1376.46i	−0.831853	−	1.44081i	0.0647144	−	0.997904i	$-0.479386\pi$
$98$		0			0
$99$	478.597	−	352.419i	0.485867	−	0.357772i
$100$		0			0
$101$	−636.447	−	1102.36i	−0.627018	−	1.08603i	−0.988147	−	0.153511i	$-0.950942\pi$
$101$	−636.447	−	1102.36i	−0.627018	−	1.08603i	0.361129	−	0.932516i	$-0.382391\pi$
$102$		0			0
$103$	−1190.34	−	687.241i	−1.13871	−	0.657436i	−0.192601	−	0.981277i	$-0.561692\pi$
$103$	−1190.34	−	687.241i	−1.13871	−	0.657436i	−0.946111	+	0.323841i	$0.895026\pi$
$104$		0			0
$105$	55.2719	+	993.844i	0.0513713	+	0.923707i
$106$		0			0
$107$			1612.72i			1.45708i	0.685004	+	0.728540i	$0.259801\pi$
$107$			1612.72i			1.45708i	−0.685004	+	0.728540i	$0.740199\pi$
$108$		0			0
$109$		−	1546.65i		−	1.35911i	−0.733626	−	0.679554i	$-0.762174\pi$
$109$		−	1546.65i		−	1.35911i	0.733626	−	0.679554i	$-0.237826\pi$
$110$		0			0
$111$	−64.5326	−	1160.36i	−0.0551816	−	0.992221i
$112$		0			0
$113$	−1193.12	−	688.848i	−0.993267	−	0.573463i	−0.0870178	−	0.996207i	$-0.527734\pi$
$113$	−1193.12	−	688.848i	−0.993267	−	0.573463i	−0.906249	+	0.422744i	$0.861067\pi$
$114$		0			0
$115$	−942.020	−	1631.63i	−0.763859	−	1.32304i
$116$		0			0
$117$	−511.435	−	223.798i	−0.404122	−	0.176839i
$118$		0			0
$119$	−324.400	−	561.877i	−0.249897	−	0.432834i
$120$		0			0
$121$	−423.213	+	733.026i	−0.317966	+	0.550734i
$122$		0			0
$123$	253.314	+	128.051i	0.185696	+	0.0938700i
$124$		0			0
$125$	−1450.76			−1.03808
$126$		0			0
$127$			266.075i			0.185908i	0.995670	+	0.0929539i	$0.0296309\pi$
$127$			266.075i			0.185908i	−0.995670	+	0.0929539i	$0.970369\pi$
$128$		0			0
$129$	−895.400	−	1369.19i	−0.611129	−	0.934501i
$130$		0			0
$131$	−284.037	−	163.989i	−0.189438	−	0.109372i	0.402281	−	0.915516i	$-0.368217\pi$
$131$	−284.037	−	163.989i	−0.189438	−	0.109372i	−0.591720	+	0.806144i	$0.701551\pi$
$132$		0			0
$133$	1948.36	−	1124.89i	1.27026	−	0.733384i
$134$		0			0
$135$	−524.081	+	1405.42i	−0.334116	+	0.895996i
$136$		0			0
$137$	−1793.30	+	1035.36i	−1.11833	+	0.645671i	−0.940975	−	0.338476i	$-0.890089\pi$
$137$	−1793.30	+	1035.36i	−1.11833	+	0.645671i	−0.177359	+	0.984146i	$0.556755\pi$
$138$		0			0
$139$	−874.266	+	1514.27i	−0.533484	+	0.924022i	0.465751	+	0.884916i	$0.345784\pi$
$139$	−874.266	+	1514.27i	−0.533484	+	0.924022i	−0.999235	+	0.0391059i	$0.987549\pi$
$140$		0			0
$141$	−1309.75	−	2002.79i	−0.782274	−	1.19621i
$142$		0			0
$143$	−455.146			−0.266163
$144$		0			0
$145$	−1653.50			−0.947003
$146$		0			0
$147$	−51.4992	+	101.877i	−0.0288951	+	0.0571610i
$148$		0			0
$149$	−51.5884	+	89.3538i	−0.0283644	+	0.0491285i	−0.879859	−	0.475235i	$-0.842363\pi$
$149$	−51.5884	+	89.3538i	−0.0283644	+	0.0491285i	0.851495	+	0.524363i	$0.175697\pi$
$150$		0			0
$151$	2205.07	−	1273.10i	1.18838	−	0.686114i	0.230446	−	0.973085i	$-0.425982\pi$
$151$	2205.07	−	1273.10i	1.18838	−	0.686114i	0.957939	+	0.286971i	$0.0926483\pi$
$152$		0			0
$153$	−108.412	−	971.661i	−0.0572847	−	0.513426i
$154$		0			0
$155$	−2605.49	+	1504.28i	−1.35018	+	0.779528i
$156$		0			0
$157$	−154.698	−	89.3150i	−0.0786386	−	0.0454020i	0.460165	−	0.887833i	$-0.347790\pi$
$157$	−154.698	−	89.3150i	−0.0786386	−	0.0454020i	−0.538804	+	0.842431i	$0.681124\pi$
$158$		0			0
$159$	819.865	−	45.5962i	0.408928	−	0.0227422i
$160$		0			0
$161$			3157.41i			1.54558i
$162$		0			0
$163$	−2230.94			−1.07203			−0.536014	−	0.844209i	$-0.680071\pi$
$163$	−2230.94			−1.07203			−0.536014	+	0.844209i	$0.680071\pi$
$164$		0			0
$165$	67.9064	+	1221.03i	0.0320394	+	0.576101i
$166$		0			0
$167$	922.538	−	1597.88i	0.427474	−	0.740406i	−0.569174	−	0.822217i	$-0.692737\pi$
$167$	922.538	−	1597.88i	0.427474	−	0.740406i	0.996648	+	0.0818106i	$0.0260703\pi$
$168$		0			0
$169$	−884.747	−	1532.43i	−0.402707	−	0.697509i
$170$		0			0
$171$	3369.32	−	375.927i	1.50677	−	0.168116i
$172$		0			0
$173$	1557.87	+	2698.32i	0.684642	+	1.18583i	0.973549	+	0.228477i	$0.0733746\pi$
$173$	1557.87	+	2698.32i	0.684642	+	1.18583i	−0.288908	+	0.957357i	$0.593292\pi$
$174$		0			0
$175$	165.948	+	95.8100i	0.0716827	+	0.0413860i
$176$		0			0
$177$	2163.18	+	1093.50i	0.918613	+	0.464363i
$178$		0			0
$179$		−	2456.16i		−	1.02560i	−0.858509	−	0.512799i	$-0.828609\pi$
$179$		−	2456.16i		−	1.02560i	0.858509	−	0.512799i	$-0.171391\pi$
$180$		0			0
$181$			3026.42i			1.24283i	0.783482	+	0.621415i	$0.213442\pi$
$181$			3026.42i			1.24283i	−0.783482	+	0.621415i	$0.786558\pi$
$182$		0			0
$183$	−1919.68	+	1255.40i	−0.775446	+	0.507113i
$184$		0			0
$185$	2070.83	+	1195.60i	0.822977	+	0.475146i
$186$		0			0
$187$	−398.554	−	690.316i	−0.155857	−	0.269951i
$188$		0			0
$189$	1938.27	−	1600.61i	0.745972	−	0.616016i
$190$		0			0
$191$	−976.763	−	1691.80i	−0.370032	−	0.640914i	0.619538	−	0.784967i	$-0.287320\pi$
$191$	−976.763	−	1691.80i	−0.370032	−	0.640914i	−0.989570	+	0.144052i	$0.953987\pi$
$192$		0			0
$193$	807.292	−	1398.27i	0.301089	−	0.521501i	−0.675294	−	0.737549i	$-0.735983\pi$
$193$	807.292	−	1398.27i	0.301089	−	0.521501i	0.976383	+	0.216047i	$0.0693165\pi$
$194$		0			0
$195$	961.331	−	628.674i	0.353037	−	0.230873i
$196$		0			0
$197$	−3469.85			−1.25491			−0.627453	−	0.778654i	$-0.715903\pi$
$197$	−3469.85			−1.25491			−0.627453	+	0.778654i	$0.715903\pi$
$198$		0			0
$199$		−	1323.61i		−	0.471500i	−0.971814	−	0.235750i	$-0.924245\pi$
$199$		−	1323.61i		−	0.471500i	0.971814	−	0.235750i	$-0.0757546\pi$
$200$		0			0
$201$	907.284	−	1794.81i	0.318383	−	0.629831i
$202$		0			0
$203$	2399.80	+	1385.52i	0.829718	+	0.479038i
$204$		0			0
$205$	−505.773	+	292.008i	−0.172316	+	0.0994865i
$206$		0			0
$207$	−1907.40	+	4358.90i	−0.640452	+	1.46360i
$208$		0			0
$209$	2393.73	−	1382.02i	0.792239	−	0.457400i
$210$		0			0
$211$	73.6849	−	127.626i	0.0240411	−	0.0416405i	−0.853755	−	0.520676i	$-0.825680\pi$
$211$	73.6849	−	127.626i	0.0240411	−	0.0416405i	0.877796	+	0.479035i	$0.159013\pi$
$212$		0			0
$213$	−105.734	+	5.88033i	−0.0340131	+	0.00189161i
$214$		0			0
$215$	3366.12			1.06775
$216$		0			0
$217$	5041.96			1.57728
$218$		0			0
$219$	−1921.88	+	106.884i	−0.593006	+	0.0329796i
$220$		0			0
$221$	−374.351	+	648.394i	−0.113944	+	0.197356i
$222$		0			0
$223$	−1045.36	+	603.537i	−0.313911	+	0.181237i	−0.648675	−	0.761065i	$-0.724677\pi$
$223$	−1045.36	+	603.537i	−0.313911	+	0.181237i	0.334764	+	0.942302i	$0.391343\pi$
$224$		0			0
$225$	171.217	+	232.519i	0.0507309	+	0.0688944i
$226$		0			0
$227$	461.434	−	266.409i	0.134918	−	0.0778951i	−0.431022	−	0.902342i	$-0.641847\pi$
$227$	461.434	−	266.409i	0.134918	−	0.0778951i	0.565940	+	0.824447i	$0.308513\pi$
$228$		0			0
$229$	−438.805	−	253.344i	−0.126625	−	0.0731069i	0.435350	−	0.900261i	$-0.356625\pi$
$229$	−438.805	−	253.344i	−0.126625	−	0.0731069i	−0.561974	+	0.827155i	$0.689958\pi$
$230$		0			0
$231$	924.584	−	1829.03i	0.263347	−	0.520958i
$232$		0			0
$233$		−	401.945i		−	0.113014i	−0.998402	−	0.0565070i	$-0.982004\pi$
$233$		−	401.945i		−	0.113014i	0.998402	−	0.0565070i	$-0.0179963\pi$
$234$		0			0
$235$	4923.79			1.36678
$236$		0			0
$237$	2826.17	−	1848.21i	0.774596	−	0.506557i
$238$		0			0
$239$	−437.215	+	757.279i	−0.118331	+	0.204955i	−0.919106	−	0.394010i	$-0.871088\pi$
$239$	−437.215	+	757.279i	−0.118331	+	0.204955i	0.800775	+	0.598965i	$0.204421\pi$
$240$		0			0
$241$	−479.685	−	830.839i	−0.128213	−	0.222071i	0.794772	−	0.606909i	$-0.207591\pi$
$241$	−479.685	−	830.839i	−0.128213	−	0.222071i	−0.922984	+	0.384838i	$0.874257\pi$
$242$		0			0
$243$	3642.78	−	1038.77i	0.961665	−	0.274226i
$244$		0			0
$245$	−117.439	−	203.410i	−0.0306240	−	0.0530424i
$246$		0			0
$247$	−2248.37	−	1298.09i	−0.579191	−	0.334396i
$248$		0			0
$249$	−2593.44	+	1696.01i	−0.660051	+	0.431649i
$250$		0			0
$251$		−	1486.12i		−	0.373719i	−0.982387	−	0.186859i	$-0.940169\pi$
$251$		−	1486.12i		−	0.373719i	0.982387	−	0.186859i	$-0.0598308\pi$
$252$		0			0
$253$			3879.15i			0.963953i
$254$		0			0
$255$	1795.30	+	907.535i	0.440888	+	0.222871i
$256$		0			0
$257$	810.352	+	467.857i	0.196686	+	0.113557i	0.595109	−	0.803645i	$-0.297109\pi$
$257$	810.352	+	467.857i	0.196686	+	0.113557i	−0.398423	+	0.917202i	$0.630442\pi$
$258$		0			0
$259$	−2003.66	−	3470.45i	−0.480701	−	0.832599i
$260$		0			0
$261$	2475.99	+	3362.49i	0.587203	+	0.797443i
$262$		0			0
$263$	723.768	+	1253.60i	0.169694	+	0.293918i	0.938312	−	0.345789i	$-0.112389\pi$
$263$	723.768	+	1253.60i	0.169694	+	0.293918i	−0.768619	+	0.639707i	$0.779056\pi$
$264$		0			0
$265$	−844.762	+	1463.17i	−0.195824	+	0.339177i
$266$		0			0
$267$	349.213	+	6279.20i	0.0800431	+	1.43925i
$268$		0			0
$269$	−2458.16			−0.557161			−0.278581	−	0.960413i	$-0.589864\pi$
$269$	−2458.16			−0.557161			−0.278581	+	0.960413i	$0.589864\pi$
$270$		0			0
$271$			484.315i			0.108561i	0.998526	+	0.0542806i	$0.0172865\pi$
$271$			484.315i			0.108561i	−0.998526	+	0.0542806i	$0.982713\pi$
$272$		0			0
$273$	−1922.01	+	106.891i	−0.426100	+	0.0236973i
$274$		0			0
$275$	203.882	+	117.711i	0.0447074	+	0.0258118i
$276$		0			0
$277$	3576.88	−	2065.11i	0.775862	−	0.447944i	−0.0590999	−	0.998252i	$-0.518823\pi$
$277$	3576.88	−	2065.11i	0.775862	−	0.447944i	0.834962	+	0.550308i	$0.185490\pi$
$278$		0			0
$279$	6960.58	+	3045.87i	1.49362	+	0.653589i
$280$		0			0
$281$	734.232	−	423.909i	0.155874	−	0.0899939i	−0.420034	−	0.907508i	$-0.637982\pi$
$281$	734.232	−	423.909i	0.155874	−	0.0899939i	0.575908	+	0.817514i	$0.304649\pi$
$282$		0			0
$283$	−2706.55	+	4687.88i	−0.568507	+	0.984683i	0.428207	+	0.903681i	$0.359146\pi$
$283$	−2706.55	+	4687.88i	−0.568507	+	0.984683i	−0.996714	+	0.0810026i	$0.974188\pi$
$284$		0			0
$285$	−3146.96	+	6225.38i	−0.654069	+	1.29389i
$286$		0			0
$287$	978.735			0.201299
$288$		0			0
$289$	3601.78			0.733113
$290$		0			0
$291$	−4520.18	−	6911.98i	−0.910575	−	1.39240i
$292$		0			0
$293$	4158.79	−	7203.24i	0.829213	−	1.43624i	−0.0694441	−	0.997586i	$-0.522123\pi$
$293$	4158.79	−	7203.24i	0.829213	−	1.43624i	0.898657	−	0.438653i	$-0.144544\pi$
$294$		0			0
$295$	−4319.06	+	2493.61i	−0.852424	+	0.492147i
$296$		0			0
$297$	2381.34	−	1966.49i	0.465251	−	0.384199i
$298$		0			0
$299$	3155.43	−	1821.79i	0.610312	−	0.352364i
$300$		0			0
$301$	−4885.40	−	2820.59i	−0.935514	−	0.540119i
$302$		0			0
$303$	−3620.04	−	5535.54i	−0.686356	−	1.04953i
$304$		0			0
$305$		−	4719.47i		−	0.886020i
$306$		0			0
$307$	7799.02			1.44988			0.724940	−	0.688812i	$-0.241867\pi$
$307$	7799.02			1.44988			0.724940	+	0.688812i	$0.241867\pi$
$308$		0			0
$309$	−6373.92	−	3222.05i	−1.17346	−	0.593191i
$310$		0			0
$311$	−2762.34	+	4784.52i	−0.503660	+	0.872364i	0.496331	+	0.868133i	$0.334680\pi$
$311$	−2762.34	+	4784.52i	−0.503660	+	0.872364i	−0.999991	+	0.00423108i	$0.998653\pi$
$312$		0			0
$313$	−1521.85	−	2635.91i	−0.274824	−	0.476008i	0.695267	−	0.718752i	$-0.255286\pi$
$313$	−1521.85	−	2635.91i	−0.274824	−	0.476008i	−0.970091	+	0.242743i	$0.921953\pi$
$314$		0			0
$315$	573.516	+	5140.25i	0.102584	+	0.919429i
$316$		0			0
$317$	3235.14	+	5603.42i	0.573197	+	0.992806i	0.996235	+	0.0866940i	$0.0276302\pi$
$317$	3235.14	+	5603.42i	0.573197	+	0.992806i	−0.423038	+	0.906112i	$0.639036\pi$
$318$		0			0
$319$	2948.36	+	1702.24i	0.517482	+	0.298768i
$320$		0			0
$321$	465.325	+	8367.01i	0.0809094	+	1.45483i
$322$		0			0
$323$		−	4546.77i		−	0.783247i
$324$		0			0
$325$		−	221.125i		−	0.0377410i
$326$		0			0
$327$	−446.263	−	8024.26i	−0.0754691	−	1.35701i
$328$		0			0
$329$	−7146.13	−	4125.82i	−1.19750	−	0.691379i
$330$		0			0
$331$	3283.78	+	5687.67i	0.545295	+	0.944479i	0.998588	+	0.0531172i	$0.0169157\pi$
$331$	3283.78	+	5687.67i	0.545295	+	0.944479i	−0.453293	+	0.891361i	$0.649751\pi$
$332$		0			0
$333$	−669.607	−	6001.48i	−0.110193	−	0.987625i
$334$		0			0
$335$	2068.97	+	3583.56i	0.337432	+	0.584450i
$336$		0			0
$337$	−5965.59	+	10332.7i	−0.964292	+	1.67020i	−0.252786	+	0.967522i	$0.581347\pi$
$337$	−5965.59	+	10332.7i	−0.964292	+	1.67020i	−0.711506	+	0.702680i	$0.751986\pi$
$338$		0			0
$339$	−6388.82	−	3229.58i	−1.02358	−	0.517424i
$340$		0			0
$341$	6194.49			0.983726
$342$		0			0
$343$			6539.27i			1.02941i
$344$		0			0
$345$	−5358.11	−	8193.29i	−0.836147	−	1.27859i
$346$		0			0
$347$	1257.88	+	726.237i	0.194601	+	0.112353i	0.594135	−	0.804366i	$-0.297495\pi$
$347$	1257.88	+	726.237i	0.194601	+	0.112353i	−0.399534	+	0.916718i	$0.630828\pi$
$348$		0			0
$349$	2775.33	−	1602.34i	0.425673	−	0.245763i	−0.271828	−	0.962346i	$-0.587628\pi$
$349$	2775.33	−	1602.34i	0.425673	−	0.245763i	0.697502	+	0.716583i	$0.254295\pi$
$350$		0			0
$351$	−2717.97	−	1013.53i	−0.413318	−	0.154126i
$352$		0			0
$353$	3481.39	−	2009.98i	0.524917	−	0.303061i	−0.214027	−	0.976828i	$-0.568658\pi$
$353$	3481.39	−	2009.98i	0.524917	−	0.303061i	0.738944	+	0.673767i	$0.235325\pi$
$354$		0			0
$355$	108.945	−	188.698i	0.0162879	−	0.0282115i
$356$		0			0
$357$	−1845.15	−	2821.50i	−0.273546	−	0.418290i
$358$		0			0
$359$	−4423.07			−0.650253			−0.325126	−	0.945671i	$-0.605407\pi$
$359$	−4423.07			−0.650253			−0.325126	+	0.945671i	$0.605407\pi$
$360$		0			0
$361$	8907.32			1.29863
$362$		0			0
$363$	−1984.18	+	3925.15i	−0.286894	+	0.567540i
$364$		0			0
$365$	1980.24	−	3429.87i	0.283974	−	0.491857i
$366$		0			0
$367$	−1037.58	+	599.048i	−0.147579	+	0.0852045i	−0.571971	−	0.820274i	$-0.693821\pi$
$367$	−1037.58	+	599.048i	−0.147579	+	0.0852045i	0.424392	+	0.905478i	$0.360488\pi$
$368$		0			0
$369$	1351.17	+	591.258i	0.190622	+	0.0834138i
$370$		0			0
$371$	2452.08	−	1415.71i	0.343142	−	0.198113i
$372$		0			0
$373$	1831.97	+	1057.69i	0.254305	+	0.146823i	0.621734	−	0.783229i	$-0.286429\pi$
$373$	1831.97	+	1057.69i	0.254305	+	0.146823i	−0.367429	+	0.930052i	$0.619762\pi$
$374$		0			0
$375$	−7526.75	+	418.594i	−1.03648	+	0.0576430i
$376$		0			0
$377$		−	3197.73i		−	0.436847i
$378$		0			0
$379$	4201.28			0.569406			0.284703	−	0.958616i	$-0.408105\pi$
$379$	4201.28			0.569406			0.284703	+	0.958616i	$0.408105\pi$
$380$		0			0
$381$	76.7716	+	1380.43i	0.0103232	+	0.185621i
$382$		0			0
$383$	1040.16	−	1801.61i	0.138772	−	0.240360i	−0.788260	−	0.615342i	$-0.789018\pi$
$383$	1040.16	−	1801.61i	0.138772	−	0.240360i	0.927032	+	0.374982i	$0.122351\pi$
$384$		0			0
$385$	2108.42	+	3651.89i	0.279104	+	0.483422i
$386$		0			0
$387$	−5040.52	−	6845.20i	−0.662077	−	0.899124i
$388$		0			0
$389$	−1695.86	−	2937.32i	−0.221038	−	0.382848i	0.734086	−	0.679057i	$-0.237611\pi$
$389$	−1695.86	−	2937.32i	−0.221038	−	0.382848i	−0.955123	+	0.296208i	$0.904278\pi$
$390$		0			0
$391$	5526.18	+	3190.54i	0.714759	+	0.412666i
$392$		0			0
$393$	−1520.94	−	768.841i	−0.195219	−	0.0986842i
$394$		0			0
$395$			6948.05i			0.885049i
$396$		0			0
$397$			2852.23i			0.360577i	0.983614	+	0.180289i	$0.0577031\pi$
$397$			2852.23i			0.360577i	−0.983614	+	0.180289i	$0.942297\pi$
$398$		0			0
$399$	9783.79	−	6398.23i	1.22757	−	0.802788i
$400$		0			0
$401$	784.032	+	452.661i	0.0976376	+	0.0563711i	0.548024	−	0.836463i	$-0.315380\pi$
$401$	784.032	+	452.661i	0.0976376	+	0.0563711i	−0.450386	+	0.892834i	$0.648714\pi$
$402$		0			0
$403$	−2909.15	−	5038.80i	−0.359591	−	0.622831i
$404$		0			0
$405$	−2313.49	+	7442.73i	−0.283848	+	0.913167i
$406$		0			0
$407$	−2461.68	−	4263.75i	−0.299806	−	0.519279i
$408$		0			0
$409$	−3943.23	+	6829.88i	−0.476724	+	0.825711i	−0.999644	−	0.0266709i	$-0.991509\pi$
$409$	−3943.23	+	6829.88i	−0.476724	+	0.825711i	0.522920	+	0.852382i	$0.324843\pi$
$410$		0			0
$411$	−9005.14	+	5889.02i	−1.08076	+	0.706774i
$412$		0			0
$413$	8357.93			0.995803
$414$		0			0
$415$		−	6375.90i		−	0.754170i
$416$		0			0
$417$	−4098.89	+	8108.51i	−0.481352	+	0.952220i
$418$		0			0
$419$	−12290.9	−	7096.16i	−1.43306	−	0.827375i	−0.435703	−	0.900091i	$-0.643500\pi$
$419$	−12290.9	−	7096.16i	−1.43306	−	0.827375i	−0.997353	+	0.0727158i	$0.976833\pi$
$420$		0			0
$421$	−13997.7	+	8081.57i	−1.62044	+	0.935562i	−0.633640	+	0.773628i	$0.718440\pi$
$421$	−13997.7	+	8081.57i	−1.62044	+	0.935562i	−0.986802	+	0.161935i	$0.948227\pi$
$422$		0			0
$423$	−7373.02	−	10012.8i	−0.847491	−	1.15092i
$424$		0			0
$425$	335.379	−	193.631i	0.0382782	−	0.0221000i
$426$		0			0
$427$	−3954.61	+	6849.58i	−0.448189	+	0.776287i
$428$		0			0
$429$	−2361.36	+	131.325i	−0.265752	+	0.0147796i
$430$		0			0
$431$	9955.69			1.11264			0.556321	−	0.830968i	$-0.312213\pi$
$431$	9955.69			1.11264			0.556321	+	0.830968i	$0.312213\pi$
$432$		0			0
$433$	−3785.69			−0.420158			−0.210079	−	0.977684i	$-0.567372\pi$
$433$	−3785.69			−0.420158			−0.210079	+	0.977684i	$0.567372\pi$
$434$		0			0
$435$	−8578.57	+	477.091i	−0.945542	+	0.0525856i
$436$		0			0
$437$	−11063.5	+	19162.5i	−1.21107	+	2.09764i
$438$		0			0
$439$	13629.0	−	7868.72i	1.48173	−	0.855475i	0.481941	−	0.876204i	$-0.339932\pi$
$439$	13629.0	−	7868.72i	1.48173	−	0.855475i	0.999785	+	0.0207289i	$0.00659870\pi$
$440$		0			0
$441$	−237.790	+	543.410i	−0.0256765	+	0.0586773i
$442$		0			0
$443$	−5151.93	+	2974.47i	−0.552541	+	0.319010i	−0.750146	−	0.661272i	$-0.770017\pi$
$443$	−5151.93	+	2974.47i	−0.552541	+	0.319010i	0.197605	+	0.980282i	$0.436684\pi$
$444$		0			0
$445$	−11206.2	−	6469.88i	−1.19376	−	0.689218i
$446$		0			0
$447$	−241.866	+	478.465i	−0.0255926	+	0.0506277i
$448$		0			0
$449$		−	15116.6i		−	1.58886i	−0.607356	−	0.794430i	$-0.707770\pi$
$449$		−	15116.6i		−	1.58886i	0.607356	−	0.794430i	$-0.292230\pi$
$450$		0			0
$451$	1202.46			0.125547
$452$		0			0
$453$	11072.9	−	7241.24i	1.14845	−	0.751045i
$454$		0			0
$455$	1980.38	−	3430.11i	0.204047	−	0.353420i
$456$		0			0
$457$	1777.87	+	3079.37i	0.181981	+	0.315201i	0.942555	−	0.334051i	$-0.108416\pi$
$457$	1777.87	+	3079.37i	0.181981	+	0.315201i	−0.760574	+	0.649251i	$0.775082\pi$
$458$		0			0
$459$	−842.812	−	5009.83i	−0.0857061	−	0.509452i
$460$		0			0
$461$	−4424.78	−	7663.95i	−0.447034	−	0.774286i	0.551157	−	0.834401i	$-0.314186\pi$
$461$	−4424.78	−	7663.95i	−0.447034	−	0.774286i	−0.998191	+	0.0601155i	$0.980853\pi$
$462$		0			0
$463$	−11428.3	−	6598.13i	−1.14712	−	0.662292i	−0.198939	−	0.980012i	$-0.563750\pi$
$463$	−11428.3	−	6598.13i	−1.14712	−	0.662292i	−0.948185	+	0.317720i	$0.897083\pi$
$464$		0			0
$465$	−13083.6	+	8556.19i	−1.30481	+	0.853298i
$466$		0			0
$467$		−	8917.23i		−	0.883598i	−0.897114	−	0.441799i	$-0.854340\pi$
$467$		−	8917.23i		−	0.883598i	0.897114	−	0.441799i	$-0.145660\pi$
$468$		0			0
$469$		−	6934.64i		−	0.682755i
$470$		0			0
$471$	−828.365	−	418.743i	−0.0810383	−	0.0409653i
$472$		0			0
$473$	−6002.15	−	3465.34i	−0.583465	−	0.336864i
$474$		0			0
$475$	671.433	+	1162.96i	0.0648578	+	0.112337i
$476$		0			0
$477$	4240.41	−	473.118i	0.407034	−	0.0454142i
$478$		0			0
$479$	−3252.43	−	5633.38i	−0.310245	−	0.537360i	0.668170	−	0.744009i	$-0.267078\pi$
$479$	−3252.43	−	5633.38i	−0.310245	−	0.537360i	−0.978415	+	0.206648i	$0.933744\pi$
$480$		0			0
$481$	−2312.18	+	4004.82i	−0.219182	+	0.379634i
$482$		0			0
$483$	911.020	+	16381.0i	0.0858237	+	1.54320i
$484$		0			0
$485$	16992.9			1.59094
$486$		0			0
$487$			20850.6i			1.94010i	0.242898	+	0.970052i	$0.421902\pi$
$487$			20850.6i			1.94010i	−0.242898	+	0.970052i	$0.578098\pi$
$488$		0			0
$489$	−11574.4	+	643.703i	−1.07037	+	0.0595281i
$490$		0			0
$491$	3316.39	+	1914.72i	0.304820	+	0.175988i	0.644606	−	0.764515i	$-0.277021\pi$
$491$	3316.39	+	1914.72i	0.304820	+	0.175988i	−0.339786	+	0.940503i	$0.610355\pi$
$492$		0			0
$493$	4849.96	−	2800.13i	0.443065	−	0.255804i
$494$		0			0
$495$	704.615	+	6315.25i	0.0639800	+	0.573433i
$496$		0			0
$497$	−316.234	+	182.578i	−0.0285413	+	0.0164783i
$498$		0			0
$499$	−1634.90	+	2831.73i	−0.146670	+	0.254040i	−0.929995	−	0.367573i	$-0.880189\pi$
$499$	−1634.90	+	2831.73i	−0.146670	+	0.254040i	0.783325	+	0.621613i	$0.213522\pi$
$500$		0			0
$501$	4325.21	−	8556.22i	0.385701	−	0.763001i
$502$		0			0
$503$	−15404.4			−1.36550			−0.682750	−	0.730652i	$-0.739216\pi$
$503$	−15404.4			−1.36550			−0.682750	+	0.730652i	$0.739216\pi$
$504$		0			0
$505$	13609.0			1.19919
$506$		0			0
$507$	−5032.34	−	7695.16i	−0.440817	−	0.674071i
$508$		0			0
$509$	4493.67	−	7783.27i	0.391314	−	0.677775i	−0.601309	−	0.799016i	$-0.705354\pi$
$509$	4493.67	−	7783.27i	0.391314	−	0.677775i	0.992623	+	0.121241i	$0.0386874\pi$
$510$		0			0
$511$	−5748.02	+	3318.62i	−0.497607	+	0.287294i
$512$		0			0
$513$	17372.0	−	2922.53i	1.49511	−	0.251526i
$514$		0			0
$515$	12726.3	−	7347.55i	1.08891	−	0.628683i
$516$		0			0
$517$	−8779.65	−	5068.93i	−0.746864	−	0.431202i
$518$		0			0
$519$	8861.02	+	13549.7i	0.749433	+	1.14599i
$520$		0			0
$521$			14007.5i			1.17789i	0.808175	+	0.588943i	$0.200456\pi$
$521$			14007.5i			1.17789i	−0.808175	+	0.588943i	$0.799544\pi$
$522$		0			0
$523$	12759.6			1.06681			0.533403	−	0.845862i	$-0.320913\pi$
$523$	12759.6			1.06681			0.533403	+	0.845862i	$0.320913\pi$
$524$		0			0
$525$	888.604	+	449.194i	0.0738702	+	0.0373418i
$526$		0			0
$527$	5094.87	−	8824.57i	0.421131	−	0.729420i
$528$		0			0
$529$	−9443.36	−	16356.4i	−0.776145	−	1.34432i
$530$		0			0
$531$	11538.4	+	5049.06i	0.942981	+	0.412638i
$532$		0			0
$533$	−564.720	−	978.123i	−0.0458925	−	0.0794882i
$534$		0			0
$535$	−14932.2	−	8621.09i	−1.20668	−	0.696677i
$536$		0			0
$537$	−708.686	−	12742.9i	−0.0569499	−	1.02402i
$538$		0			0
$539$			483.602i			0.0386460i
$540$		0			0
$541$			11304.7i			0.898389i	0.893434	+	0.449194i	$0.148289\pi$
$541$			11304.7i			0.898389i	−0.893434	+	0.449194i	$0.851711\pi$
$542$		0			0
$543$	873.227	+	15701.5i	0.0690124	+	1.24091i
$544$		0			0
$545$	14320.5	+	8267.93i	1.12554	+	0.649833i
$546$		0			0
$547$	−4074.44	−	7057.14i	−0.318484	−	0.551630i	0.661688	−	0.749779i	$-0.269840\pi$
$547$	−4074.44	−	7057.14i	−0.318484	−	0.551630i	−0.980172	+	0.198149i	$0.936507\pi$
$548$		0			0
$549$	−9597.32	+	7067.06i	−0.746091	+	0.549390i
$550$		0			0
$551$	9709.69	+	16817.7i	0.750720	+	1.30029i
$552$		0			0
$553$	5822.01	−	10084.0i	0.447698	−	0.775436i
$554$		0			0
$555$	11088.7	+	5605.41i	0.848091	+	0.428714i
$556$		0			0
$557$	−9696.33			−0.737607			−0.368803	−	0.929507i	$-0.620232\pi$
$557$	−9696.33			−0.737607			−0.368803	+	0.929507i	$0.620232\pi$
$558$		0			0
$559$			6509.79i			0.492549i
$560$		0			0
$561$	−2266.93	−	3466.46i	−0.170606	−	0.260880i
$562$		0			0
$563$	4632.29	+	2674.46i	0.346763	+	0.200204i	0.663259	−	0.748390i	$-0.269173\pi$
$563$	4632.29	+	2674.46i	0.346763	+	0.200204i	−0.316495	+	0.948594i	$0.602506\pi$
$564$		0			0
$565$	12756.1	−	7364.72i	0.949827	−	0.548383i
$566$		0			0
$567$	9594.20	−	8863.43i	0.710615	−	0.656489i
$568$		0			0
$569$	−6251.55	+	3609.33i	−0.460595	+	0.265924i	−0.712294	−	0.701881i	$-0.752344\pi$
$569$	−6251.55	+	3609.33i	−0.460595	+	0.265924i	0.251700	+	0.967805i	$0.419011\pi$
$570$		0			0
$571$	−1605.63	+	2781.03i	−0.117677	+	0.203822i	−0.918847	−	0.394615i	$-0.870878\pi$
$571$	−1605.63	+	2781.03i	−0.117677	+	0.203822i	0.801170	+	0.598437i	$0.204211\pi$
$572$		0			0
$573$	−5555.72	−	8495.48i	−0.405050	−	0.619378i
$574$		0			0
$575$	−1884.62			−0.136685
$576$		0			0
$577$	−4892.69			−0.353008			−0.176504	−	0.984300i	$-0.556479\pi$
$577$	−4892.69			−0.353008			−0.176504	+	0.984300i	$0.556479\pi$
$578$		0			0
$579$	3784.89	−	7487.35i	0.271666	−	0.537416i
$580$		0			0
$581$	−5342.59	+	9253.64i	−0.381494	+	0.660767i
$582$		0			0
$583$	3012.60	−	1739.33i	0.214012	−	0.123560i
$584$		0			0
$585$	4806.12	−	3539.02i	0.339673	−	0.250121i
$586$		0			0
$587$	8416.04	−	4859.01i	0.591767	−	0.341657i	−0.174029	−	0.984741i	$-0.555679\pi$
$587$	8416.04	−	4859.01i	0.591767	−	0.341657i	0.765796	+	0.643084i	$0.222345\pi$
$588$		0			0
$589$	30600.0	+	17666.9i	2.14066	+	1.23591i
$590$		0			0
$591$	−18002.0	+	1001.17i	−1.25297	+	0.0696830i
$592$		0			0
$593$		−	8952.48i		−	0.619957i	−0.950744	−	0.309978i	$-0.899678\pi$
$593$		−	8952.48i		−	0.619957i	0.950744	−	0.309978i	$-0.100322\pi$
$594$		0			0
$595$	6936.56			0.477935
$596$		0			0
$597$	−381.908	−	6867.08i	−0.0261816	−	0.470772i
$598$		0			0
$599$	1335.01	−	2312.30i	0.0910634	−	0.157726i	−0.816895	−	0.576786i	$-0.804307\pi$
$599$	1335.01	−	2312.30i	0.0910634	−	0.157726i	0.907959	+	0.419059i	$0.137640\pi$
$600$		0			0
$601$	10279.6	+	17804.8i	0.697692	+	1.20844i	0.969265	+	0.246021i	$0.0791231\pi$
$601$	10279.6	+	17804.8i	0.697692	+	1.20844i	−0.271572	+	0.962418i	$0.587544\pi$
$602$		0			0
$603$	4189.25	−	9573.49i	0.282918	−	0.646539i
$604$		0			0
$605$	−4524.73	−	7837.06i	−0.304060	−	0.526647i
$606$		0			0
$607$	10811.7	+	6242.12i	0.722952	+	0.417396i	0.815838	−	0.578280i	$-0.196276\pi$
$607$	10811.7	+	6242.12i	0.722952	+	0.417396i	−0.0928863	+	0.995677i	$0.529609\pi$
$608$		0			0
$609$	12850.2	+	6495.86i	0.855038	+	0.432226i
$610$		0			0
$611$			9522.21i			0.630487i
$612$		0			0
$613$			18300.4i			1.20579i	0.797822	+	0.602893i	$0.205985\pi$
$613$			18300.4i			1.20579i	−0.797822	+	0.602893i	$0.794015\pi$
$614$		0			0
$615$	−2539.76	+	1660.91i	−0.166526	+	0.108901i
$616$		0			0
$617$	10889.8	+	6287.22i	0.710545	+	0.410233i	0.811263	−	0.584682i	$-0.198781\pi$
$617$	10889.8	+	6287.22i	0.710545	+	0.410233i	−0.100718	+	0.994915i	$0.532114\pi$
$618$		0			0
$619$	604.640	+	1047.27i	0.0392610	+	0.0680020i	0.884988	−	0.465613i	$-0.154166\pi$
$619$	604.640	+	1047.27i	0.0392610	+	0.0680020i	−0.845727	+	0.533616i	$0.820833\pi$
$620$		0			0
$621$	−8638.17	+	23164.9i	−0.558193	+	1.49690i
$622$		0			0
$623$	10842.7	+	18780.1i	0.697276	+	1.20772i
$624$		0			0
$625$	7086.90	−	12274.9i	0.453561	−	0.785591i
$626$		0			0
$627$	12020.3	−	7860.80i	0.765618	−	0.500686i
$628$		0			0
$629$	−8098.76			−0.513385
$630$		0			0
$631$		−	9244.14i		−	0.583207i	−0.956539	−	0.291603i	$-0.905811\pi$
$631$		−	9244.14i		−	0.583207i	0.956539	−	0.291603i	$-0.0941888\pi$
$632$		0			0
$633$	345.463	−	683.402i	0.0216918	−	0.0429112i
$634$		0			0
$635$	−2463.58	−	1422.35i	−0.153960	−	0.0888886i
$636$		0			0
$637$	393.378	−	227.117i	0.0244681	−	0.0141267i
$638$		0			0
$639$	−546.867	+	61.0159i	−0.0338556	+	0.00377739i
$640$		0			0
$641$	13346.5	−	7705.58i	0.822392	−	0.474808i	−0.0288488	−	0.999584i	$-0.509184\pi$
$641$	13346.5	−	7705.58i	0.822392	−	0.474808i	0.851241	+	0.524776i	$0.175851\pi$
$642$		0			0
$643$	−2947.93	+	5105.96i	−0.180801	+	0.313156i	−0.942154	−	0.335182i	$-0.891202\pi$
$643$	−2947.93	+	5105.96i	−0.180801	+	0.313156i	0.761353	+	0.648338i	$0.224536\pi$
$644$		0			0
$645$	17463.9	−	971.240i	1.06611	−	0.0592908i
$646$		0			0
$647$	30355.3			1.84450			0.922249	−	0.386596i	$-0.126349\pi$
$647$	30355.3			1.84450			0.922249	+	0.386596i	$0.126349\pi$
$648$		0			0
$649$	10268.5			0.621066
$650$		0			0
$651$	26158.4	−	1454.78i	1.57485	−	0.0875841i
$652$		0			0
$653$	−3997.18	+	6923.31i	−0.239543	+	0.414901i	−0.960583	−	0.277993i	$-0.910331\pi$
$653$	−3997.18	+	6923.31i	−0.239543	+	0.414901i	0.721040	+	0.692893i	$0.243664\pi$
$654$		0			0
$655$	3036.74	−	1753.26i	0.181153	−	0.104589i
$656$		0			0
$657$	−9940.11	+	1109.05i	−0.590260	+	0.0658574i
$658$		0			0
$659$	−7708.70	+	4450.62i	−0.455673	+	0.263083i	−0.710223	−	0.703977i	$-0.751406\pi$
$659$	−7708.70	+	4450.62i	−0.455673	+	0.263083i	0.254550	+	0.967060i	$0.418073\pi$
$660$		0			0
$661$	5648.33	+	3261.07i	0.332367	+	0.191892i	0.656892	−	0.753985i	$-0.271871\pi$
$661$	5648.33	+	3261.07i	0.332367	+	0.191892i	−0.324524	+	0.945877i	$0.605204\pi$
$662$		0			0
$663$	−1755.10	+	3471.97i	−0.102809	+	0.203379i
$664$		0			0
$665$			24053.2i			1.40262i
$666$		0			0
$667$	−27253.8			−1.58212
$668$		0			0
$669$	−5249.31	+	3432.85i	−0.303363	+	0.198388i
$670$		0			0
$671$	−4858.59	+	8415.32i	−0.279529	+	0.484158i
$672$		0			0
$673$	−13331.6	−	23091.1i	−0.763591	−	1.32258i	−0.940988	−	0.338440i	$-0.890101\pi$
$673$	−13331.6	−	23091.1i	−0.763591	−	1.32258i	0.177397	−	0.984139i	$-0.443232\pi$
$674$		0			0
$675$	955.386	+	1156.94i	0.0544783	+	0.0659711i
$676$		0			0
$677$	−4565.23	−	7907.21i	−0.259167	−	0.448890i	0.706852	−	0.707361i	$-0.250115\pi$
$677$	−4565.23	−	7907.21i	−0.259167	−	0.448890i	−0.966019	+	0.258471i	$0.916781\pi$
$678$		0			0
$679$	−24662.6	−	14238.9i	−1.39391	−	0.804772i
$680$		0			0
$681$	2317.11	−	1515.31i	0.130385	−	0.0852667i
$682$		0			0
$683$			4081.15i			0.228640i	0.993444	+	0.114320i	$0.0364689\pi$
$683$			4081.15i			0.228640i	−0.993444	+	0.114320i	$0.963531\pi$
$684$		0			0
$685$		−	22138.9i		−	1.23486i
$686$		0			0
$687$	−2349.68	−	1187.77i	−0.130489	−	0.0659628i
$688$		0			0
$689$	−2829.65	−	1633.70i	−0.156460	−	0.0903323i
$690$		0			0
$691$	−3245.02	−	5620.54i	−0.178649	−	0.309429i	0.762769	−	0.646671i	$-0.223839\pi$
$691$	−3245.02	−	5620.54i	−0.178649	−	0.309429i	−0.941418	+	0.337242i	$0.890506\pi$
$692$		0			0
$693$	4269.13	−	9756.03i	0.234013	−	0.534778i
$694$		0			0
$695$	−9347.10	−	16189.7i	−0.510152	−	0.883610i
$696$		0			0
$697$	989.007	−	1713.01i	0.0537465	−	0.0930916i
$698$		0			0
$699$	−115.975	−	2085.34i	−0.00627550	−	0.112840i
$700$		0			0
$701$	−29971.5			−1.61485			−0.807424	−	0.589971i	$-0.799139\pi$
$701$	−29971.5			−1.61485			−0.807424	+	0.589971i	$0.799139\pi$
$702$		0			0
$703$		−	28083.2i		−	1.50665i
$704$		0			0
$705$	25545.3	−	1420.68i	1.36467	−	0.0758951i
$706$		0			0
$707$	−19751.3	−	11403.4i	−1.05067	−	0.606606i
$708$		0			0
$709$	−2923.29	+	1687.77i	−0.154847	+	0.0894011i	−0.575421	−	0.817857i	$-0.695162\pi$
$709$	−2923.29	+	1687.77i	−0.154847	+	0.0894011i	0.420574	+	0.907258i	$0.361829\pi$
$710$		0			0
$711$	14129.3	−	10404.2i	0.745273	−	0.548788i
$712$		0			0
$713$	−42945.1	+	24794.3i	−2.25569	+	1.30232i
$714$		0			0
$715$	2433.07	−	4214.20i	0.127261	−	0.220422i
$716$		0			0
$717$	−2049.83	+	4055.02i	−0.106768	+	0.211210i
$718$		0			0
$719$	−36696.4			−1.90340			−0.951701	−	0.307025i	$-0.900666\pi$
$719$	−36696.4			−1.90340			−0.951701	+	0.307025i	$0.900666\pi$
$720$		0			0
$721$	−24627.1			−1.27207
$722$		0			0
$723$	−2728.40	−	4172.10i	−0.140346	−	0.214609i
$724$		0			0
$725$	−827.004	+	1432.41i	−0.0423644	+	0.0733772i
$726$		0			0
$727$	18148.3	−	10477.9i	0.925834	−	0.534531i	0.0403426	−	0.999186i	$-0.487155\pi$
$727$	18148.3	−	10477.9i	0.925834	−	0.534531i	0.885492	+	0.464655i	$0.153822\pi$
$728$		0			0
$729$	18599.5	−	6440.34i	0.944954	−	0.327203i
$730$		0			0
$731$	−9873.34	+	5700.37i	−0.499560	+	0.288421i
$732$		0			0
$733$	11601.1	+	6697.91i	0.584580	+	0.337508i	0.762952	−	0.646456i	$-0.223749\pi$
$733$	11601.1	+	6697.91i	0.584580	+	0.337508i	−0.178371	+	0.983963i	$0.557083\pi$
$734$		0			0
$735$	−667.979	−	1021.43i	−0.0335221	−	0.0512600i
$736$		0			0
$737$		−	8519.83i		−	0.425823i
$738$		0			0
$739$	−5570.50			−0.277286			−0.138643	−	0.990342i	$-0.544274\pi$
$739$	−5570.50			−0.277286			−0.138643	+	0.990342i	$0.544274\pi$
$740$		0			0
$741$	−12039.4	−	6085.96i	−0.596865	−	0.301718i
$742$		0			0
$743$	2503.74	−	4336.60i	0.123625	−	0.214124i	−0.797570	−	0.603227i	$-0.793881\pi$
$743$	2503.74	−	4336.60i	0.123625	−	0.214124i	0.921195	+	0.389102i	$0.127215\pi$
$744$		0			0
$745$	−551.551	−	955.314i	−0.0271238	−	0.0469799i
$746$		0			0
$747$	−12965.8	+	9547.45i	−0.635064	+	0.467634i
$748$		0			0
$749$	14447.8	+	25024.4i	0.704822	+	1.22079i
$750$		0			0
$751$	14755.0	+	8518.83i	0.716936	+	0.413923i	0.813624	−	0.581391i	$-0.197491\pi$
$751$	14755.0	+	8518.83i	0.716936	+	0.413923i	−0.0966876	+	0.995315i	$0.530825\pi$
$752$		0			0
$753$	−428.798	−	7710.22i	−0.0207520	−	0.373142i
$754$		0			0
$755$			27222.3i			1.31221i
$756$		0			0
$757$		−	19829.1i		−	0.952049i	−0.879432	−	0.476024i	$-0.842077\pi$
$757$		−	19829.1i		−	0.952049i	0.879432	−	0.476024i	$-0.157923\pi$
$758$		0			0
$759$	1119.27	+	20125.6i	0.0535268	+	0.962466i
$760$		0			0
$761$	14809.3	+	8550.18i	0.705438	+	0.407285i	0.809370	−	0.587300i	$-0.199809\pi$
$761$	14809.3	+	8550.18i	0.705438	+	0.407285i	−0.103932	+	0.994584i	$0.533142\pi$
$762$		0			0
$763$	−13856.0	−	23999.2i	−0.657431	−	1.13870i
$764$		0			0
$765$	9576.14	+	4190.41i	0.452583	+	0.198045i
$766$		0			0
$767$	−4822.43	−	8352.70i	−0.227025	−	0.393218i
$768$		0			0
$769$	−11253.2	+	19491.1i	−0.527699	+	0.914002i	0.471779	+	0.881717i	$0.343612\pi$
$769$	−11253.2	+	19491.1i	−0.527699	+	0.914002i	−0.999479	+	0.0322854i	$0.989721\pi$
$770$		0			0
$771$	4339.21	+	2193.49i	0.202688	+	0.102460i
$772$		0			0
$773$	5523.17			0.256992			0.128496	−	0.991710i	$-0.458985\pi$
$773$	5523.17			0.256992			0.128496	+	0.991710i	$0.458985\pi$
$774$		0			0
$775$			3009.49i			0.139489i
$776$		0			0
$777$	−11396.6	−	17427.0i	−0.526193	−	0.804622i
$778$		0			0
$779$	5940.02	+	3429.47i	0.273200	+	0.157732i
$780$		0			0
$781$	−388.522	+	224.313i	−0.0178008	+	0.0102773i
$782$		0			0
$783$	13816.0	+	16730.6i	0.630578	+	0.763606i
$784$		0			0
$785$	1653.93	−	954.899i	0.0751993	−	0.0434163i
$786$		0			0
$787$	3299.97	−	5715.72i	0.149468	−	0.258886i	−0.781563	−	0.623826i	$-0.785577\pi$
$787$	3299.97	−	5715.72i	0.149468	−	0.258886i	0.931031	+	0.364940i	$0.118911\pi$
$788$		0			0
$789$	4116.71	+	6295.03i	0.185753	+	0.284042i
$790$		0			0
$791$	−24684.6			−1.10959
$792$		0			0
$793$	9127.06			0.408716
$794$		0			0
$795$	−3960.56	+	7834.87i	−0.176688	+	0.349527i
$796$		0			0
$797$	9315.82	−	16135.5i	0.414032	−	0.717124i	−0.581294	−	0.813693i	$-0.697454\pi$
$797$	9315.82	−	16135.5i	0.414032	−	0.717124i	0.995326	+	0.0965692i	$0.0307869\pi$
$798$		0			0
$799$	−14442.2	+	8338.23i	−0.639461	+	0.369193i
$800$		0			0
$801$	3623.53	+	32476.6i	0.159839	+	1.43259i
$802$		0			0
$803$	−7061.95	+	4077.22i	−0.310350	+	0.179180i
$804$		0			0
$805$	−29234.4	−	16878.5i	−1.27997	−	0.738992i
$806$		0			0
$807$	−12753.2	+	709.262i	−0.556302	+	0.0309383i
$808$		0			0
$809$			9731.56i			0.422921i	0.977387	+	0.211461i	$0.0678220\pi$
$809$			9731.56i			0.422921i	−0.977387	+	0.211461i	$0.932178\pi$
$810$		0			0
$811$	−12468.7			−0.539872			−0.269936	−	0.962878i	$-0.587003\pi$
$811$	−12468.7			−0.539872			−0.269936	+	0.962878i	$0.587003\pi$
$812$		0			0
$813$	139.742	+	2512.69i	0.00602823	+	0.108394i
$814$		0			0
$815$	11925.9	−	20656.3i	0.512572	−	0.887800i
$816$		0			0
$817$	−19766.6	−	34236.7i	−0.846444	−	1.46608i
$818$		0			0
$819$	−9940.81	+	1109.13i	−0.424127	+	0.0473214i
$820$		0			0
$821$	3801.24	+	6583.94i	0.161589	+	0.279880i	0.935439	−	0.353489i	$-0.115005\pi$
$821$	3801.24	+	6583.94i	0.161589	+	0.279880i	−0.773850	+	0.633369i	$0.781672\pi$
$822$		0			0
$823$	30246.1	+	17462.6i	1.28106	+	0.739622i	0.977043	−	0.213044i	$-0.0683377\pi$
$823$	30246.1	+	17462.6i	1.28106	+	0.739622i	0.304020	+	0.952666i	$0.401671\pi$
$824$		0			0
$825$	1091.73	+	551.874i	0.0460717	+	0.0232895i
$826$		0			0
$827$		−	8660.10i		−	0.364137i	−0.983286	−	0.182068i	$-0.941721\pi$
$827$		−	8660.10i		−	0.364137i	0.983286	−	0.182068i	$-0.0582792\pi$
$828$		0			0
$829$		−	15475.5i		−	0.648353i	−0.945997	−	0.324177i	$-0.894913\pi$
$829$		−	15475.5i		−	0.648353i	0.945997	−	0.324177i	$-0.105087\pi$
$830$		0			0
$831$	17961.5	−	11746.1i	0.749791	−	0.490335i
$832$		0			0
$833$	688.932	+	397.755i	0.0286555	+	0.0165443i
$834$		0			0
$835$	9863.19	+	17083.6i	0.408778	+	0.708025i
$836$		0			0
$837$	36991.3	+	13794.0i	1.52761	+	0.569643i
$838$		0			0
$839$	−4487.20	−	7772.06i	−0.184643	−	0.319811i	0.758813	−	0.651308i	$-0.225780\pi$
$839$	−4487.20	−	7772.06i	−0.184643	−	0.319811i	−0.943456	+	0.331497i	$0.892446\pi$
$840$		0			0
$841$	235.069	−	407.151i	0.00963831	−	0.0166940i
$842$		0			0
$843$	3686.98	−	2411.15i	0.150636	−	0.0985105i
$844$		0			0
$845$	18918.3			0.770189
$846$		0			0
$847$			15165.7i			0.615230i
$848$		0			0
$849$	−12689.3	+	25102.3i	−0.512952	+	1.01473i
$850$		0			0
$851$	34132.6	+	19706.4i	1.37491	+	0.793805i
$852$		0			0
$853$	−11129.3	+	6425.49i	−0.446728	+	0.257919i	−0.706447	−	0.707766i	$-0.749703\pi$
$853$	−11129.3	+	6425.49i	−0.446728	+	0.257919i	0.259719	+	0.965684i	$0.416370\pi$
$854$		0			0
$855$	−14530.6	+	33206.1i	−0.581212	+	1.32822i
$856$		0			0
$857$	−23236.8	+	13415.7i	−0.926199	+	0.534741i	−0.885607	−	0.464435i	$-0.846258\pi$
$857$	−23236.8	+	13415.7i	−0.926199	+	0.534741i	−0.0405914	+	0.999176i	$0.512924\pi$
$858$		0			0
$859$	13594.8	−	23546.9i	0.539987	−	0.935284i	−0.458918	−	0.888479i	$-0.651763\pi$
$859$	13594.8	−	23546.9i	0.539987	−	0.935284i	0.998904	−	0.0468052i	$-0.0149040\pi$
$860$		0			0
$861$	5077.81	−	282.399i	0.200989	−	0.0111778i
$862$		0			0
$863$	−10963.4			−0.432441			−0.216221	−	0.976345i	$-0.569373\pi$
$863$	−10963.4			−0.432441			−0.216221	+	0.976345i	$0.569373\pi$
$864$		0			0
$865$	−33311.6			−1.30940
$866$		0			0
$867$	18686.5	−	1039.24i	0.731982	−	0.0407086i
$868$		0			0
$869$	7152.86	−	12389.1i	0.279222	−	0.483627i
$870$		0			0
$871$	−6930.31	+	4001.21i	−0.269603	+	0.155656i
$872$		0			0
$873$	−25445.6	−	34556.1i	−0.986488	−	1.33969i
$874$		0			0
$875$	−22511.3	+	12996.9i	−0.869737	+	0.502143i
$876$		0			0
$877$	−23926.8	−	13814.2i	−0.921268	−	0.531894i	−0.0372287	−	0.999307i	$-0.511853\pi$
$877$	−23926.8	−	13814.2i	−0.921268	−	0.531894i	−0.884039	+	0.467412i	$0.845186\pi$
$878$		0			0
$879$	19498.0	−	38571.3i	0.748181	−	1.48007i
$880$		0			0
$881$		−	3160.30i		−	0.120855i	−0.998173	−	0.0604275i	$-0.980754\pi$
$881$		−	3160.30i		−	0.120855i	0.998173	−	0.0604275i	$-0.0192464\pi$
$882$		0			0
$883$	−25009.6			−0.953161			−0.476581	−	0.879131i	$-0.658124\pi$
$883$	−25009.6			−0.953161			−0.476581	+	0.879131i	$0.658124\pi$
$884$		0			0
$885$	−21688.4	+	14183.4i	−0.823781	+	0.538722i
$886$		0			0
$887$	482.657	−	835.987i	0.0182706	−	0.0316457i	−0.856746	−	0.515739i	$-0.827517\pi$
$887$	482.657	−	835.987i	0.0182706	−	0.0316457i	0.875016	+	0.484094i	$0.160851\pi$
$888$		0			0
$889$	2383.67	+	4128.64i	0.0899279	+	0.155760i
$890$		0			0
$891$	11787.3	−	10889.5i	0.443199	−	0.409441i
$892$		0			0
$893$	−28913.6	−	50079.8i	−1.08349	−	1.87666i
$894$		0			0
$895$	22741.6	+	13129.9i	0.849348	+	0.490372i
$896$		0			0
$897$	15845.1	−	10362.1i	0.589804	−	0.385710i
$898$		0			0
$899$			43520.7i			1.61457i
$900$		0			0
$901$		−	5722.27i		−	0.211583i
$902$		0			0
$903$	−26160.0	−	13224.0i	−0.964063	−	0.487338i
$904$		0			0
$905$	−28021.6	−	16178.3i	−1.02925	−	0.594237i
$906$		0			0
$907$	−14900.6	−	25808.6i	−0.545498	−	0.944830i	−0.998575	−	0.0533589i	$-0.983007\pi$
$907$	−14900.6	−	25808.6i	−0.545498	−	0.944830i	0.453078	−	0.891471i	$-0.350326\pi$
$908$		0			0
$909$	−20378.4	−	27674.6i	−0.743576	−	1.00980i
$910$		0			0
$911$	−4525.83	−	7838.97i	−0.164597	−	0.285090i	0.771915	−	0.635725i	$-0.219299\pi$
$911$	−4525.83	−	7838.97i	−0.164597	−	0.285090i	−0.936512	+	0.350636i	$0.885966\pi$
$912$		0			0
$913$	−6563.84	+	11368.9i	−0.237932	+	0.412110i
$914$		0			0
$915$	−1361.73	−	24485.2i	−0.0491993	−	0.884653i
$916$		0			0
$917$	−5876.48			−0.211623
$918$		0			0
$919$		−	25649.5i		−	0.920674i	−0.887744	−	0.460337i	$-0.847729\pi$
$919$		−	25649.5i		−	0.920674i	0.887744	−	0.460337i	$-0.152271\pi$
$920$		0			0
$921$	40462.3	−	2250.28i	1.44764	−	0.0805096i
$922$		0			0
$923$	364.927	+	210.691i	0.0130138	+	0.00751351i
$924$		0			0
$925$	2071.47	−	1195.97i	0.0736320	−	0.0425115i
$926$		0			0
$927$	−33998.4	−	14877.3i	−1.20459	−	0.527115i
$928$		0			0
$929$	48149.3	−	27799.0i	1.70046	−	0.981762i	0.755174	−	0.655525i	$-0.227553\pi$
$929$	48149.3	−	27799.0i	1.70046	−	0.981762i	0.945288	−	0.326237i	$-0.105781\pi$
$930$		0			0
$931$	−1379.25	+	2388.93i	−0.0485533	+	0.0840968i
$932$		0			0
$933$	−12950.9	+	25619.8i	−0.454442	+	0.898986i
$934$		0			0
$935$	8522.18			0.298080
$936$		0			0
$937$	−24617.9			−0.858304			−0.429152	−	0.903232i	$-0.641187\pi$
$937$	−24617.9			−0.858304			−0.429152	+	0.903232i	$0.641187\pi$
$938$		0			0
$939$	−8656.09	−	13236.4i	−0.300832	−	0.460014i
$940$		0			0
$941$	−5553.99	+	9619.80i	−0.192407	+	0.333259i	−0.946047	−	0.324028i	$-0.894963\pi$
$941$	−5553.99	+	9619.80i	−0.192407	+	0.333259i	0.753640	+	0.657287i	$0.228296\pi$
$942$		0			0
$943$	−8336.41	+	4813.03i	−0.287880	+	0.166208i
$944$		0			0
$945$	4458.62	+	26502.8i	0.153480	+	0.912314i
$946$		0			0
$947$	−17487.0	+	10096.1i	−0.600055	+	0.346442i	−0.769063	−	0.639173i	$-0.779277\pi$
$947$	−17487.0	+	10096.1i	−0.600055	+	0.346442i	0.169008	+	0.985615i	$0.445943\pi$
$948$		0			0
$949$	6633.09	+	3829.61i	0.226891	+	0.130995i
$950$		0			0
$951$	18401.1	+	28137.9i	0.627441	+	0.959445i
$952$		0			0
$953$			18808.4i			0.639310i	0.947534	+	0.319655i	$0.103567\pi$
$953$			18808.4i			0.639310i	−0.947534	+	0.319655i	$0.896433\pi$
$954$		0			0
$955$	20885.9			0.707697
$956$		0			0
$957$	15787.7	+	7980.74i	0.533273	+	0.269572i
$958$		0			0
$959$	−18550.9	+	32131.1i	−0.624651	+	1.08193i
$960$		0			0
$961$	24697.8	+	42777.8i	0.829035	+	1.43593i
$962$		0			0
$963$	4828.34	+	43274.9i	0.161569	+	1.44809i
$964$		0			0
$965$	8631.06	+	14949.4i	0.287921	+	0.498694i
$966$		0			0
$967$	−590.535	−	340.946i	−0.0196384	−	0.0113382i	0.490149	−	0.871639i	$-0.336942\pi$
$967$	−590.535	−	340.946i	−0.0196384	−	0.0113382i	−0.509787	+	0.860301i	$0.670276\pi$
$968$		0			0
$969$	−1311.90	−	23589.2i	−0.0434925	−	0.782039i
$970$		0			0
$971$		−	54483.2i		−	1.80067i	−0.435197	−	0.900335i	$-0.643321\pi$
$971$		−	54483.2i		−	1.80067i	0.435197	−	0.900335i	$-0.356679\pi$
$972$		0			0
$973$			31329.1i			1.03223i
$974$		0			0
$975$	−63.8022	−	1147.23i	−0.00209570	−	0.0376828i
$976$		0			0
$977$	−26948.6	−	15558.8i	−0.882458	−	0.509487i	−0.0109896	−	0.999940i	$-0.503498\pi$
$977$	−26948.6	−	15558.8i	−0.882458	−	0.509487i	−0.871468	+	0.490452i	$0.836832\pi$
$978$		0			0
$979$	13321.2	+	23073.0i	0.434880	+	0.753234i
$980$		0			0
$981$	−4630.55	−	41502.2i	−0.150705	−	1.35073i
$982$		0			0
$983$	5791.66	+	10031.4i	0.187920	+	0.325487i	0.944557	−	0.328349i	$-0.106492\pi$
$983$	5791.66	+	10031.4i	0.187920	+	0.325487i	−0.756637	+	0.653836i	$0.773159\pi$
$984$		0			0
$985$	18548.7	−	32127.3i	0.600011	−	1.03925i
$986$		0			0
$987$	−38265.5	−	19343.4i	−1.23405	−	0.623817i
$988$		0			0
$989$	55482.1			1.78385
$990$		0			0
$991$		−	23086.5i		−	0.740028i	−0.929026	−	0.370014i	$-0.879353\pi$
$991$		−	23086.5i		−	0.740028i	0.929026	−	0.370014i	$-0.120647\pi$
$992$		0			0
$993$	18677.8	+	28560.9i	0.596899	+	0.912742i
$994$		0			0
$995$	12255.3	+	7075.61i	0.390472	+	0.225439i
$996$		0			0
$997$	39030.9	−	22534.5i	1.23984	−	0.715822i	0.270779	−	0.962642i	$-0.412719\pi$
$997$	39030.9	−	22534.5i	1.23984	−	0.715822i	0.969062	+	0.246819i	$0.0793854\pi$
$998$		0			0
$999$	−5205.65	−	30943.3i	−0.164864	−	0.979983i

Display

a_p

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p

up to: 50 250 1000 (See

a_n

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a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.4.p.b.239.31		64
3.2	odd	2		864.4.p.b.719.25		64
4.3	odd	2		72.4.l.b.59.23	yes	64
8.3	odd	2	inner	288.4.p.b.239.32		64
8.5	even	2		72.4.l.b.59.31	yes	64
9.2	odd	6	inner	288.4.p.b.47.32		64
9.7	even	3		864.4.p.b.143.8		64
12.11	even	2		216.4.l.b.179.10		64
24.5	odd	2		216.4.l.b.179.2		64
24.11	even	2		864.4.p.b.719.8		64
36.7	odd	6		216.4.l.b.35.2		64
36.11	even	6		72.4.l.b.11.31	yes	64
72.11	even	6	inner	288.4.p.b.47.31		64
72.29	odd	6		72.4.l.b.11.23	✓	64
72.43	odd	6		864.4.p.b.143.25		64
72.61	even	6		216.4.l.b.35.10		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.23	✓	64	72.29	odd	6
72.4.l.b.11.31	yes	64	36.11	even	6
72.4.l.b.59.23	yes	64	4.3	odd	2
72.4.l.b.59.31	yes	64	8.5	even	2
216.4.l.b.35.2		64	36.7	odd	6
216.4.l.b.35.10		64	72.61	even	6
216.4.l.b.179.2		64	24.5	odd	2
216.4.l.b.179.10		64	12.11	even	2
288.4.p.b.47.31		64	72.11	even	6	inner
288.4.p.b.47.32		64	9.2	odd	6	inner
288.4.p.b.239.31		64	1.1	even	1	trivial
288.4.p.b.239.32		64	8.3	odd	2	inner
864.4.p.b.143.8		64	9.7	even	3
864.4.p.b.143.25		64	72.43	odd	6
864.4.p.b.719.8		64	24.11	even	2
864.4.p.b.719.25		64	3.2	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	288.4.p.b.239.31

Level	$288$
Weight	$4$
Character	288.239
Analytic conductor	$16.993$
Analytic rank	$0$
Dimension	$64$
Inner twists	$4$