LMFDB - Embedded newform 560.3.v.b.223.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,3,Mod(223,560)] 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("560.223"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	560.v (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$15.2588948042$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.23
Character	$\chi$	$=$	560.223
Dual form			560.3.v.b.447.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.33745 + 2.33745i) q^{3} +(-4.70145 - 1.70187i) q^{5} +(6.43840 - 2.74719i) q^{7} +1.92736i q^{9} -11.8428i q^{11} +(-0.694125 + 0.694125i) q^{13} +(-7.01136 - 14.9675i) q^{15} +(-16.8449 - 16.8449i) q^{17} -10.7208i q^{19} +(21.4709 + 8.62802i) q^{21} +(-6.37492 + 6.37492i) q^{23} +(19.2072 + 16.0026i) q^{25} +(16.5320 - 16.5320i) q^{27} -1.46982i q^{29} -32.9829 q^{31} +(27.6819 - 27.6819i) q^{33} +(-34.9452 + 1.95843i) q^{35} +(47.6627 - 47.6627i) q^{37} -3.24497 q^{39} -33.1632i q^{41} +(43.6176 - 43.6176i) q^{43} +(3.28012 - 9.06138i) q^{45} +(-34.1921 + 34.1921i) q^{47} +(33.9059 - 35.3750i) q^{49} -78.7484i q^{51} +(56.5110 + 56.5110i) q^{53} +(-20.1549 + 55.6782i) q^{55} +(25.0593 - 25.0593i) q^{57} +22.3963i q^{59} +68.2453i q^{61} +(5.29482 + 12.4091i) q^{63} +(4.44471 - 2.08208i) q^{65} +(67.8953 + 67.8953i) q^{67} -29.8021 q^{69} -71.4041i q^{71} +(10.2149 - 10.2149i) q^{73} +(7.49082 + 82.3012i) q^{75} +(-32.5343 - 76.2485i) q^{77} -61.2432 q^{79} +94.6315 q^{81} +(-80.3770 - 80.3770i) q^{83} +(50.5276 + 107.864i) q^{85} +(3.43563 - 3.43563i) q^{87} +27.7670 q^{89} +(-2.56216 + 6.37594i) q^{91} +(-77.0960 - 77.0960i) q^{93} +(-18.2455 + 50.4033i) q^{95} +(4.28781 + 4.28781i) q^{97} +22.8253 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 16 q^{21} - 72 q^{25} + 72 q^{37} + 272 q^{53} - 376 q^{57} - 88 q^{65} + 24 q^{77} - 432 q^{81} + 384 q^{85} + 840 q^{93}+O(q^{100}) $ 64 * q + 16 * q^21 - 72 * q^25 + 72 * q^37 + 272 * q^53 - 376 * q^57 - 88 * q^65 + 24 * q^77 - 432 * q^81 + 384 * q^85 + 840 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$	2.33745	+	2.33745i	0.779151	+	0.779151i	0.979686	−	0.200536i	$-0.0642683\pi$
$3$	2.33745	+	2.33745i	0.779151	+	0.779151i	−0.200536	+	0.979686i	$0.564268\pi$
$4$		0			0
$5$	−4.70145	−	1.70187i	−0.940290	−	0.340375i
$5$	−4.70145	−	1.70187i	−0.940290	−	0.340375i
$6$		0			0
$7$	6.43840	−	2.74719i	0.919771	−	0.392456i
$7$	6.43840	−	2.74719i	0.919771	−	0.392456i
$8$		0			0
$9$			1.92736i			0.214151i
$10$		0			0
$11$		−	11.8428i		−	1.07662i	−0.842748	−	0.538308i	$-0.819064\pi$
$11$		−	11.8428i		−	1.07662i	0.842748	−	0.538308i	$-0.180936\pi$
$12$		0			0
$13$	−0.694125	+	0.694125i	−0.0533942	+	0.0533942i	−0.733300	−	0.679906i	$-0.762021\pi$
$13$	−0.694125	+	0.694125i	−0.0533942	+	0.0533942i	0.679906	+	0.733300i	$0.262021\pi$
$14$		0			0
$15$	−7.01136	−	14.9675i	−0.467424	−	0.997831i
$16$		0			0
$17$	−16.8449	−	16.8449i	−0.990878	−	0.990878i	0.00908054	−	0.999959i	$-0.497110\pi$
$17$	−16.8449	−	16.8449i	−0.990878	−	0.990878i	−0.999959	+	0.00908054i	$0.997110\pi$
$18$		0			0
$19$		−	10.7208i		−	0.564253i	−0.959377	−	0.282126i	$-0.908960\pi$
$19$		−	10.7208i		−	0.564253i	0.959377	−	0.282126i	$-0.0910397\pi$
$20$		0			0
$21$	21.4709	+	8.62802i	1.02242	+	0.410858i
$22$		0			0
$23$	−6.37492	+	6.37492i	−0.277171	+	0.277171i	−0.831978	−	0.554808i	$-0.812792\pi$
$23$	−6.37492	+	6.37492i	−0.277171	+	0.277171i	0.554808	+	0.831978i	$0.312792\pi$
$24$		0			0
$25$	19.2072	+	16.0026i	0.768290	+	0.640102i
$26$		0			0
$27$	16.5320	−	16.5320i	0.612295	−	0.612295i
$28$		0			0
$29$		−	1.46982i		−	0.0506834i	−0.999679	−	0.0253417i	$-0.991933\pi$
$29$		−	1.46982i		−	0.0506834i	0.999679	−	0.0253417i	$-0.00806738\pi$
$30$		0			0
$31$	−32.9829			−1.06397			−0.531983	−	0.846755i	$-0.678553\pi$
$31$	−32.9829			−1.06397			−0.531983	+	0.846755i	$0.678553\pi$
$32$		0			0
$33$	27.6819	−	27.6819i	0.838846	−	0.838846i
$34$		0			0
$35$	−34.9452	+	1.95843i	−0.998433	+	0.0559550i
$36$		0			0
$37$	47.6627	−	47.6627i	1.28818	−	1.28818i	0.352290	−	0.935891i	$-0.385403\pi$
$37$	47.6627	−	47.6627i	1.28818	−	1.28818i	0.935891	−	0.352290i	$-0.114597\pi$
$38$		0			0
$39$	−3.24497			−0.0832043
$40$		0			0
$41$		−	33.1632i		−	0.808857i	−0.914570	−	0.404429i	$-0.867470\pi$
$41$		−	33.1632i		−	0.808857i	0.914570	−	0.404429i	$-0.132530\pi$
$42$		0			0
$43$	43.6176	−	43.6176i	1.01436	−	1.01436i	0.0144669	−	0.999895i	$-0.495395\pi$
$43$	43.6176	−	43.6176i	1.01436	−	1.01436i	0.999895	−	0.0144669i	$-0.00460511\pi$
$44$		0			0
$45$	3.28012	−	9.06138i	0.0728917	−	0.201364i
$46$		0			0
$47$	−34.1921	+	34.1921i	−0.727492	+	0.727492i	−0.970119	−	0.242628i	$-0.921991\pi$
$47$	−34.1921	+	34.1921i	−0.727492	+	0.727492i	0.242628	+	0.970119i	$0.421991\pi$
$48$		0			0
$49$	33.9059	−	35.3750i	0.691957	−	0.721938i
$50$		0			0
$51$		−	78.7484i		−	1.54409i
$52$		0			0
$53$	56.5110	+	56.5110i	1.06625	+	1.06625i	0.997644	+	0.0686018i	$0.0218538\pi$
$53$	56.5110	+	56.5110i	1.06625	+	1.06625i	0.0686018	+	0.997644i	$0.478146\pi$
$54$		0			0
$55$	−20.1549	+	55.6782i	−0.366453	+	1.01233i
$56$		0			0
$57$	25.0593	−	25.0593i	0.439638	−	0.439638i
$58$		0			0
$59$			22.3963i			0.379598i	0.981823	+	0.189799i	$0.0607836\pi$
$59$			22.3963i			0.379598i	−0.981823	+	0.189799i	$0.939216\pi$
$60$		0			0
$61$			68.2453i			1.11878i	0.828906	+	0.559388i	$0.188964\pi$
$61$			68.2453i			1.11878i	−0.828906	+	0.559388i	$0.811036\pi$
$62$		0			0
$63$	5.29482	+	12.4091i	0.0840448	+	0.196970i
$64$		0			0
$65$	4.44471	−	2.08208i	0.0683801	−	0.0320320i
$66$		0			0
$67$	67.8953	+	67.8953i	1.01336	+	1.01336i	0.999910	+	0.0134530i	$0.00428234\pi$
$67$	67.8953	+	67.8953i	1.01336	+	1.01336i	0.0134530	+	0.999910i	$0.495718\pi$
$68$		0			0
$69$	−29.8021			−0.431915
$70$		0			0
$71$		−	71.4041i		−	1.00569i	−0.864376	−	0.502846i	$-0.832286\pi$
$71$		−	71.4041i		−	1.00569i	0.864376	−	0.502846i	$-0.167714\pi$
$72$		0			0
$73$	10.2149	−	10.2149i	0.139930	−	0.139930i	−0.633672	−	0.773602i	$-0.718453\pi$
$73$	10.2149	−	10.2149i	0.139930	−	0.139930i	0.773602	+	0.633672i	$0.218453\pi$
$74$		0			0
$75$	7.49082	+	82.3012i	0.0998777	+	1.09735i
$76$		0			0
$77$	−32.5343	−	76.2485i	−0.422524	−	0.990240i
$78$		0			0
$79$	−61.2432			−0.775231			−0.387615	−	0.921821i	$-0.626701\pi$
$79$	−61.2432			−0.775231			−0.387615	+	0.921821i	$0.626701\pi$
$80$		0			0
$81$	94.6315			1.16829
$82$		0			0
$83$	−80.3770	−	80.3770i	−0.968397	−	0.968397i	0.0311186	−	0.999516i	$-0.490093\pi$
$83$	−80.3770	−	80.3770i	−0.968397	−	0.968397i	−0.999516	+	0.0311186i	$0.990093\pi$
$84$		0			0
$85$	50.5276	+	107.864i	0.594443	+	1.26898i
$86$		0			0
$87$	3.43563	−	3.43563i	0.0394900	−	0.0394900i
$88$		0			0
$89$	27.7670			0.311989			0.155995	−	0.987758i	$-0.450142\pi$
$89$	27.7670			0.311989			0.155995	+	0.987758i	$0.450142\pi$
$90$		0			0
$91$	−2.56216	+	6.37594i	−0.0281556	+	0.0700653i
$92$		0			0
$93$	−77.0960	−	77.0960i	−0.828989	−	0.828989i
$94$		0			0
$95$	−18.2455	+	50.4033i	−0.192057	+	0.530561i
$96$		0			0
$97$	4.28781	+	4.28781i	0.0442042	+	0.0442042i	0.728863	−	0.684659i	$-0.240049\pi$
$97$	4.28781	+	4.28781i	0.0442042	+	0.0442042i	−0.684659	+	0.728863i	$0.740049\pi$
$98$		0			0
$99$	22.8253			0.230559
$100$		0			0
$101$			98.9763i			0.979963i	0.871733	+	0.489981i	$0.162996\pi$
$101$			98.9763i			0.979963i	−0.871733	+	0.489981i	$0.837004\pi$
$102$		0			0
$103$	−65.9655	−	65.9655i	−0.640442	−	0.640442i	0.310222	−	0.950664i	$-0.399596\pi$
$103$	−65.9655	−	65.9655i	−0.640442	−	0.640442i	−0.950664	+	0.310222i	$0.899596\pi$
$104$		0			0
$105$	−86.2604	−	77.1049i	−0.821527	−	0.734332i
$106$		0			0
$107$	25.3142	+	25.3142i	0.236581	+	0.236581i	0.815433	−	0.578852i	$-0.196499\pi$
$107$	25.3142	+	25.3142i	0.236581	+	0.236581i	−0.578852	+	0.815433i	$0.696499\pi$
$108$		0			0
$109$			151.648i			1.39127i	0.718397	+	0.695633i	$0.244876\pi$
$109$			151.648i			1.39127i	−0.718397	+	0.695633i	$0.755124\pi$
$110$		0			0
$111$	222.818			2.00737
$112$		0			0
$113$	−98.2840	−	98.2840i	−0.869769	−	0.869769i	0.122677	−	0.992447i	$-0.460852\pi$
$113$	−98.2840	−	98.2840i	−0.869769	−	0.869769i	−0.992447	+	0.122677i	$0.960852\pi$
$114$		0			0
$115$	40.8207	−	19.1221i	0.354963	−	0.166279i
$116$		0			0
$117$	−1.33783	−	1.33783i	−0.0114344	−	0.0114344i
$118$		0			0
$119$	−154.731	−	62.1781i	−1.30026	−	0.522505i
$120$		0			0
$121$	−19.2513			−0.159102
$122$		0			0
$123$	77.5173	−	77.5173i	0.630222	−	0.630222i
$124$		0			0
$125$	−63.0676	−	107.923i	−0.504541	−	0.863388i
$126$		0			0
$127$	−32.6662	−	32.6662i	−0.257214	−	0.257214i	0.566706	−	0.823920i	$-0.308218\pi$
$127$	−32.6662	−	32.6662i	−0.257214	−	0.257214i	−0.823920	+	0.566706i	$0.808218\pi$
$128$		0			0
$129$	203.908			1.58068
$130$		0			0
$131$	−26.8150			−0.204695			−0.102347	−	0.994749i	$-0.532635\pi$
$131$	−26.8150			−0.204695			−0.102347	+	0.994749i	$0.532635\pi$
$132$		0			0
$133$	−29.4521	−	69.0248i	−0.221444	−	0.518983i
$134$		0			0
$135$	−105.859	+	49.5888i	−0.784144	+	0.367325i
$136$		0			0
$137$	−152.219	+	152.219i	−1.11109	+	1.11109i	−0.118083	+	0.993004i	$0.537675\pi$
$137$	−152.219	+	152.219i	−1.11109	+	1.11109i	−0.993004	+	0.118083i	$0.962325\pi$
$138$		0			0
$139$		−	198.862i		−	1.43066i	−0.698787	−	0.715330i	$-0.746276\pi$
$139$		−	198.862i		−	1.43066i	0.698787	−	0.715330i	$-0.253724\pi$
$140$		0			0
$141$	−159.845			−1.13365
$142$		0			0
$143$	8.22037	+	8.22037i	0.0574851	+	0.0574851i
$144$		0			0
$145$	−2.50145	+	6.91028i	−0.0172514	+	0.0476571i
$146$		0			0
$147$	161.941	−	3.43389i	1.10164	−	0.0233598i
$148$		0			0
$149$		−	215.157i		−	1.44400i	−0.691891	−	0.722002i	$-0.743222\pi$
$149$		−	215.157i		−	1.44400i	0.691891	−	0.722002i	$-0.256778\pi$
$150$		0			0
$151$		−	43.1892i		−	0.286021i	−0.989721	−	0.143011i	$-0.954322\pi$
$151$		−	43.1892i		−	0.286021i	0.989721	−	0.143011i	$-0.0456783\pi$
$152$		0			0
$153$	32.4662	−	32.4662i	0.212198	−	0.212198i
$154$		0			0
$155$	155.068	+	56.1328i	1.00044	+	0.362147i
$156$		0			0
$157$	−31.6517	−	31.6517i	−0.201603	−	0.201603i	0.599084	−	0.800687i	$-0.295532\pi$
$157$	−31.6517	−	31.6517i	−0.201603	−	0.201603i	−0.800687	+	0.599084i	$0.795532\pi$
$158$		0			0
$159$			264.184i			1.66153i
$160$		0			0
$161$	−23.5312	+	58.5574i	−0.146156	+	0.363711i
$162$		0			0
$163$	−11.5565	+	11.5565i	−0.0708990	+	0.0708990i	−0.741667	−	0.670768i	$-0.765965\pi$
$163$	−11.5565	+	11.5565i	−0.0708990	+	0.0708990i	0.670768	+	0.741667i	$0.265965\pi$
$164$		0			0
$165$	−177.256	+	83.0340i	−1.07428	+	0.503236i
$166$		0			0
$167$	68.8404	−	68.8404i	0.412218	−	0.412218i	−0.470292	−	0.882511i	$-0.655852\pi$
$167$	68.8404	−	68.8404i	0.412218	−	0.412218i	0.882511	+	0.470292i	$0.155852\pi$
$168$		0			0
$169$			168.036i			0.994298i
$170$		0			0
$171$	20.6628			0.120835
$172$		0			0
$173$	46.3017	−	46.3017i	0.267640	−	0.267640i	−0.560509	−	0.828149i	$-0.689394\pi$
$173$	46.3017	−	46.3017i	0.267640	−	0.267640i	0.828149	+	0.560509i	$0.189394\pi$
$174$		0			0
$175$	167.626	+	50.2648i	0.957862	+	0.287228i
$176$		0			0
$177$	−52.3502	+	52.3502i	−0.295764	+	0.295764i
$178$		0			0
$179$	118.638			0.662780			0.331390	−	0.943494i	$-0.392482\pi$
$179$	118.638			0.662780			0.331390	+	0.943494i	$0.392482\pi$
$180$		0			0
$181$			350.006i			1.93374i	0.255277	+	0.966868i	$0.417833\pi$
$181$			350.006i			1.93374i	−0.255277	+	0.966868i	$0.582167\pi$
$182$		0			0
$183$	−159.520	+	159.520i	−0.871695	+	0.871695i
$184$		0			0
$185$	−305.200	+	142.968i	−1.64973	+	0.772799i
$186$		0			0
$187$	−199.491	+	199.491i	−1.06680	+	1.06680i
$188$		0			0
$189$	61.0229	−	151.856i	0.322872	−	0.803469i
$190$		0			0
$191$			236.909i			1.24036i	0.784460	+	0.620180i	$0.212940\pi$
$191$			236.909i			1.24036i	−0.784460	+	0.620180i	$0.787060\pi$
$192$		0			0
$193$	−24.3886	−	24.3886i	−0.126366	−	0.126366i	0.641096	−	0.767461i	$-0.278480\pi$
$193$	−24.3886	−	24.3886i	−0.126366	−	0.126366i	−0.767461	+	0.641096i	$0.778480\pi$
$194$		0			0
$195$	15.2560	+	5.52253i	0.0782361	+	0.0283206i
$196$		0			0
$197$	29.2737	−	29.2737i	0.148597	−	0.148597i	−0.628894	−	0.777491i	$-0.716492\pi$
$197$	29.2737	−	29.2737i	0.148597	−	0.148597i	0.777491	+	0.628894i	$0.216492\pi$
$198$		0			0
$199$		−	38.3169i		−	0.192547i	−0.995355	−	0.0962736i	$-0.969308\pi$
$199$		−	38.3169i		−	0.192547i	0.995355	−	0.0962736i	$-0.0306924\pi$
$200$		0			0
$201$			317.404i			1.57912i
$202$		0			0
$203$	−4.03787	−	9.46328i	−0.0198910	−	0.0466171i
$204$		0			0
$205$	−56.4395	+	155.915i	−0.275315	+	0.760560i
$206$		0			0
$207$	−12.2868	−	12.2868i	−0.0593564	−	0.0593564i
$208$		0			0
$209$	−126.964			−0.607483
$210$		0			0
$211$			280.171i			1.32783i	0.747810	+	0.663913i	$0.231106\pi$
$211$			280.171i			1.32783i	−0.747810	+	0.663913i	$0.768894\pi$
$212$		0			0
$213$	166.904	−	166.904i	0.783586	−	0.783586i
$214$		0			0
$215$	−279.297	+	130.834i	−1.29906	+	0.608531i
$216$		0			0
$217$	−212.357	+	90.6103i	−0.978605	+	0.417559i
$218$		0			0
$219$	47.7538			0.218054
$220$		0			0
$221$	23.3850			0.105814
$222$		0			0
$223$	−23.0014	−	23.0014i	−0.103145	−	0.103145i	0.653651	−	0.756796i	$-0.273236\pi$
$223$	−23.0014	−	23.0014i	−0.103145	−	0.103145i	−0.756796	+	0.653651i	$0.773236\pi$
$224$		0			0
$225$	−30.8427	+	37.0193i	−0.137079	+	0.164530i
$226$		0			0
$227$	−203.741	+	203.741i	−0.897539	+	0.897539i	−0.995218	−	0.0976791i	$-0.968858\pi$
$227$	−203.741	+	203.741i	−0.897539	+	0.897539i	0.0976791	+	0.995218i	$0.468858\pi$
$228$		0			0
$229$	385.293			1.68250			0.841252	−	0.540643i	$-0.181819\pi$
$229$	385.293			1.68250			0.841252	+	0.540643i	$0.181819\pi$
$230$		0			0
$231$	102.180	−	254.275i	0.442336	−	1.10076i
$232$		0			0
$233$	−117.149	−	117.149i	−0.502784	−	0.502784i	0.409518	−	0.912302i	$-0.365697\pi$
$233$	−117.149	−	117.149i	−0.502784	−	0.502784i	−0.912302	+	0.409518i	$0.865697\pi$
$234$		0			0
$235$	218.943	−	102.562i	0.931673	−	0.436433i
$236$		0			0
$237$	−143.153	−	143.153i	−0.604022	−	0.604022i
$238$		0			0
$239$	−88.5591			−0.370540			−0.185270	−	0.982688i	$-0.559316\pi$
$239$	−88.5591			−0.370540			−0.185270	+	0.982688i	$0.559316\pi$
$240$		0			0
$241$			163.954i			0.680306i	0.940370	+	0.340153i	$0.110479\pi$
$241$			163.954i			0.680306i	−0.940370	+	0.340153i	$0.889521\pi$
$242$		0			0
$243$	72.4090	+	72.4090i	0.297980	+	0.297980i
$244$		0			0
$245$	−219.611	+	108.610i	−0.896370	+	0.443306i
$246$		0			0
$247$	7.44157	+	7.44157i	0.0301278	+	0.0301278i
$248$		0			0
$249$		−	375.755i		−	1.50905i
$250$		0			0
$251$	299.670			1.19390			0.596952	−	0.802277i	$-0.296378\pi$
$251$	299.670			1.19390			0.596952	+	0.802277i	$0.296378\pi$
$252$		0			0
$253$	75.4968	+	75.4968i	0.298406	+	0.298406i
$254$		0			0
$255$	−134.020	+	370.232i	−0.525568	+	1.45189i
$256$		0			0
$257$	264.763	+	264.763i	1.03021	+	1.03021i	0.999529	+	0.0306786i	$0.00976682\pi$
$257$	264.763	+	264.763i	1.03021	+	1.03021i	0.0306786	+	0.999529i	$0.490233\pi$
$258$		0			0
$259$	175.933	−	437.810i	0.679278	−	1.69039i
$260$		0			0
$261$	2.83287			0.0108539
$262$		0			0
$263$	−242.402	+	242.402i	−0.921680	+	0.921680i	−0.997148	−	0.0754684i	$-0.975955\pi$
$263$	−242.402	+	242.402i	−0.921680	+	0.921680i	0.0754684	+	0.997148i	$0.475955\pi$
$264$		0			0
$265$	−169.509	−	361.858i	−0.639657	−	1.36550i
$266$		0			0
$267$	64.9041	+	64.9041i	0.243087	+	0.243087i
$268$		0			0
$269$	219.938			0.817614			0.408807	−	0.912621i	$-0.365945\pi$
$269$	219.938			0.817614			0.408807	+	0.912621i	$0.365945\pi$
$270$		0			0
$271$	19.9310			0.0735460			0.0367730	−	0.999324i	$-0.488292\pi$
$271$	19.9310			0.0735460			0.0367730	+	0.999324i	$0.488292\pi$
$272$		0			0
$273$	−20.8924	+	8.91454i	−0.0765289	+	0.0326540i
$274$		0			0
$275$	189.515	−	227.467i	0.689144	−	0.827153i
$276$		0			0
$277$	−200.462	+	200.462i	−0.723688	+	0.723688i	−0.969355	−	0.245666i	$-0.920993\pi$
$277$	−200.462	+	200.462i	−0.723688	+	0.723688i	0.245666	+	0.969355i	$0.420993\pi$
$278$		0			0
$279$		−	63.5700i		−	0.227849i
$280$		0			0
$281$	456.950			1.62616			0.813078	−	0.582154i	$-0.197790\pi$
$281$	456.950			1.62616			0.813078	+	0.582154i	$0.197790\pi$
$282$		0			0
$283$	−99.2594	−	99.2594i	−0.350740	−	0.350740i	0.509645	−	0.860385i	$-0.329777\pi$
$283$	−99.2594	−	99.2594i	−0.350740	−	0.350740i	−0.860385	+	0.509645i	$0.829777\pi$
$284$		0			0
$285$	−160.463	+	75.1674i	−0.563028	+	0.263745i
$286$		0			0
$287$	−91.1054	−	213.518i	−0.317441	−	0.743964i
$288$		0			0
$289$			278.503i			0.963679i
$290$		0			0
$291$			20.0451i			0.0688835i
$292$		0			0
$293$	329.073	−	329.073i	1.12312	−	1.12312i	0.131847	−	0.991270i	$-0.457909\pi$
$293$	329.073	−	329.073i	1.12312	−	1.12312i	0.991270	−	0.131847i	$-0.0420908\pi$
$294$		0			0
$295$	38.1156	−	105.295i	0.129206	−	0.356932i
$296$		0			0
$297$	−195.784	−	195.784i	−0.659206	−	0.659206i
$298$		0			0
$299$		−	8.84998i		−	0.0295986i
$300$		0			0
$301$	161.002	−	400.653i	0.534889	−	1.33107i
$302$		0			0
$303$	−231.352	+	231.352i	−0.763539	+	0.763539i
$304$		0			0
$305$	116.145	−	320.852i	0.380803	−	1.05197i
$306$		0			0
$307$	322.086	−	322.086i	1.04914	−	1.04914i	0.0504101	−	0.998729i	$-0.483947\pi$
$307$	322.086	−	322.086i	1.04914	−	1.04914i	0.998729	−	0.0504101i	$-0.0160528\pi$
$308$		0			0
$309$		−	308.382i		−	0.998001i
$310$		0			0
$311$	221.719			0.712924			0.356462	−	0.934310i	$-0.383983\pi$
$311$	221.719			0.712924			0.356462	+	0.934310i	$0.383983\pi$
$312$		0			0
$313$	204.070	−	204.070i	0.651980	−	0.651980i	−0.301489	−	0.953470i	$-0.597484\pi$
$313$	204.070	−	204.070i	0.651980	−	0.651980i	0.953470	+	0.301489i	$0.0974838\pi$
$314$		0			0
$315$	−3.77459	−	67.3519i	−0.0119828	−	0.213816i
$316$		0			0
$317$	131.794	−	131.794i	0.415753	−	0.415753i	−0.467984	−	0.883737i	$-0.655019\pi$
$317$	131.794	−	131.794i	0.415753	−	0.415753i	0.883737	+	0.467984i	$0.155019\pi$
$318$		0			0
$319$	−17.4067			−0.0545666
$320$		0			0
$321$			118.341i			0.368665i
$322$		0			0
$323$	−180.591	+	180.591i	−0.559106	+	0.559106i
$324$		0			0
$325$	−24.4400	+	2.22446i	−0.0752000	+	0.00684449i
$326$		0			0
$327$	−354.470	+	354.470i	−1.08401	+	1.08401i
$328$		0			0
$329$	−126.210	+	314.075i	−0.383618	+	0.954634i
$330$		0			0
$331$		−	541.530i		−	1.63604i	−0.575187	−	0.818022i	$-0.695071\pi$
$331$		−	541.530i		−	1.63604i	0.575187	−	0.818022i	$-0.304929\pi$
$332$		0			0
$333$	91.8632	+	91.8632i	0.275865	+	0.275865i
$334$		0			0
$335$	−203.657	−	434.755i	−0.607931	−	1.29778i
$336$		0			0
$337$	−63.8693	+	63.8693i	−0.189523	+	0.189523i	−0.795490	−	0.605967i	$-0.792786\pi$
$337$	−63.8693	+	63.8693i	−0.189523	+	0.189523i	0.605967	+	0.795490i	$0.292786\pi$
$338$		0			0
$339$		−	459.468i		−	1.35536i
$340$		0			0
$341$			390.609i			1.14548i
$342$		0			0
$343$	121.118	−	320.904i	0.353114	−	0.935580i
$344$		0			0
$345$	140.113	+	50.7195i	0.406125	+	0.147013i
$346$		0			0
$347$	−481.326	−	481.326i	−1.38711	−	1.38711i	−0.831333	−	0.555774i	$-0.812422\pi$
$347$	−481.326	−	481.326i	−1.38711	−	1.38711i	−0.555774	−	0.831333i	$-0.687578\pi$
$348$		0			0
$349$	−585.475			−1.67758			−0.838790	−	0.544456i	$-0.816736\pi$
$349$	−585.475			−1.67758			−0.838790	+	0.544456i	$0.816736\pi$
$350$		0			0
$351$			22.9505i			0.0653860i
$352$		0			0
$353$	−202.309	+	202.309i	−0.573114	+	0.573114i	−0.932997	−	0.359883i	$-0.882816\pi$
$353$	−202.309	+	202.309i	−0.573114	+	0.573114i	0.359883	+	0.932997i	$0.382816\pi$
$354$		0			0
$355$	−121.521	+	335.703i	−0.342312	+	0.945642i
$356$		0			0
$357$	−216.337	−	507.014i	−0.605985	−	1.42021i
$358$		0			0
$359$	6.77828			0.0188810			0.00944051	−	0.999955i	$-0.496995\pi$
$359$	6.77828			0.0188810			0.00944051	+	0.999955i	$0.496995\pi$
$360$		0			0
$361$	246.064			0.681619
$362$		0			0
$363$	−44.9991	−	44.9991i	−0.123964	−	0.123964i
$364$		0			0
$365$	−65.4095	+	30.6404i	−0.179204	+	0.0839464i
$366$		0			0
$367$	−200.068	+	200.068i	−0.545145	+	0.545145i	−0.925033	−	0.379887i	$-0.875963\pi$
$367$	−200.068	+	200.068i	−0.545145	+	0.545145i	0.379887	+	0.925033i	$0.375963\pi$
$368$		0			0
$369$	63.9173			0.173218
$370$		0			0
$371$	519.087	+	208.594i	1.39916	+	0.562248i
$372$		0			0
$373$	485.180	+	485.180i	1.30075	+	1.30075i	0.927886	+	0.372864i	$0.121624\pi$
$373$	485.180	+	485.180i	1.30075	+	1.30075i	0.372864	+	0.927886i	$0.378376\pi$
$374$		0			0
$375$	104.849	−	399.683i	0.279596	−	1.06582i
$376$		0			0
$377$	1.02024	+	1.02024i	0.00270620	+	0.00270620i
$378$		0			0
$379$	115.940			0.305909			0.152955	−	0.988233i	$-0.451121\pi$
$379$	115.940			0.305909			0.152955	+	0.988233i	$0.451121\pi$
$380$		0			0
$381$		−	152.711i		−	0.400817i
$382$		0			0
$383$	51.3188	+	51.3188i	0.133992	+	0.133992i	0.770922	−	0.636930i	$-0.219796\pi$
$383$	51.3188	+	51.3188i	0.133992	+	0.133992i	−0.636930	+	0.770922i	$0.719796\pi$
$384$		0			0
$385$	23.1932	+	413.848i	0.0602421	+	1.07493i
$386$		0			0
$387$	84.0668	+	84.0668i	0.217227	+	0.217227i
$388$		0			0
$389$		−	529.574i		−	1.36137i	−0.732575	−	0.680686i	$-0.761682\pi$
$389$		−	529.574i		−	1.36137i	0.732575	−	0.680686i	$-0.238318\pi$
$390$		0			0
$391$	214.770			0.549284
$392$		0			0
$393$	−62.6788	−	62.6788i	−0.159488	−	0.159488i
$394$		0			0
$395$	287.932	+	104.228i	0.728942	+	0.263869i
$396$		0			0
$397$	82.3039	+	82.3039i	0.207314	+	0.207314i	0.803125	−	0.595811i	$-0.203169\pi$
$397$	82.3039	+	82.3039i	0.207314	+	0.207314i	−0.595811	+	0.803125i	$0.703169\pi$
$398$		0			0
$399$	92.4993	−	230.185i	0.231828	−	0.576904i
$400$		0			0
$401$	407.733			1.01679			0.508396	−	0.861124i	$-0.330239\pi$
$401$	407.733			1.01679			0.508396	+	0.861124i	$0.330239\pi$
$402$		0			0
$403$	22.8943	−	22.8943i	0.0568096	−	0.0568096i
$404$		0			0
$405$	−444.905	−	161.051i	−1.09853	−	0.397657i
$406$		0			0
$407$	−564.459	−	564.459i	−1.38688	−	1.38688i
$408$		0			0
$409$	663.869			1.62315			0.811576	−	0.584246i	$-0.198610\pi$
$409$	663.869			1.62315			0.811576	+	0.584246i	$0.198610\pi$
$410$		0			0
$411$	−711.608			−1.73141
$412$		0			0
$413$	61.5268	+	144.196i	0.148975	+	0.349143i
$414$		0			0
$415$	241.097	+	514.680i	0.580956	+	1.24019i
$416$		0			0
$417$	464.830	−	464.830i	1.11470	−	1.11470i
$418$		0			0
$419$			424.414i			1.01292i	0.862263	+	0.506460i	$0.169046\pi$
$419$			424.414i			1.01292i	−0.862263	+	0.506460i	$0.830954\pi$
$420$		0			0
$421$	358.075			0.850534			0.425267	−	0.905068i	$-0.360180\pi$
$421$	358.075			0.850534			0.425267	+	0.905068i	$0.360180\pi$
$422$		0			0
$423$	−65.9005	−	65.9005i	−0.155793	−	0.155793i
$424$		0			0
$425$	−53.9829	−	593.107i	−0.127019	−	1.39554i
$426$		0			0
$427$	187.483	+	439.390i	0.439070	+	1.02902i
$428$		0			0
$429$			38.4294i			0.0895790i
$430$		0			0
$431$			265.535i			0.616091i	0.951372	+	0.308046i	$0.0996749\pi$
$431$			265.535i			0.616091i	−0.951372	+	0.308046i	$0.900325\pi$
$432$		0			0
$433$	450.253	−	450.253i	1.03984	−	1.03984i	0.0406719	−	0.999173i	$-0.487050\pi$
$433$	450.253	−	450.253i	1.03984	−	1.03984i	0.999173	−	0.0406719i	$-0.0129498\pi$
$434$		0			0
$435$	−21.9994	+	10.3054i	−0.0505734	+	0.0236906i
$436$		0			0
$437$	68.3443	+	68.3443i	0.156394	+	0.156394i
$438$		0			0
$439$			856.030i			1.94995i	0.222307	+	0.974977i	$0.428641\pi$
$439$			856.030i			1.94995i	−0.222307	+	0.974977i	$0.571359\pi$
$440$		0			0
$441$	68.1803	+	65.3489i	0.154604	+	0.148183i
$442$		0			0
$443$	469.402	−	469.402i	1.05960	−	1.05960i	0.0614901	−	0.998108i	$-0.480415\pi$
$443$	469.402	−	469.402i	1.05960	−	1.05960i	0.998108	−	0.0614901i	$-0.0195853\pi$
$444$		0			0
$445$	−130.545	−	47.2560i	−0.293360	−	0.106193i
$446$		0			0
$447$	502.918	−	502.918i	1.12510	−	1.12510i
$448$		0			0
$449$		−	327.406i		−	0.729190i	−0.931166	−	0.364595i	$-0.881207\pi$
$449$		−	327.406i		−	0.729190i	0.931166	−	0.364595i	$-0.118793\pi$
$450$		0			0
$451$	−392.744			−0.870829
$452$		0			0
$453$	100.953	−	100.953i	0.222854	−	0.222854i
$454$		0			0
$455$	22.8969	−	25.6157i	0.0503229	−	0.0562982i
$456$		0			0
$457$	−326.389	+	326.389i	−0.714200	+	0.714200i	−0.967411	−	0.253211i	$-0.918513\pi$
$457$	−326.389	+	326.389i	−0.714200	+	0.714200i	0.253211	+	0.967411i	$0.418513\pi$
$458$		0			0
$459$	−556.959			−1.21342
$460$		0			0
$461$			509.128i			1.10440i	0.833712	+	0.552200i	$0.186211\pi$
$461$			509.128i			1.10440i	−0.833712	+	0.552200i	$0.813789\pi$
$462$		0			0
$463$	491.163	−	491.163i	1.06083	−	1.06083i	0.0628005	−	0.998026i	$-0.479997\pi$
$463$	491.163	−	491.163i	1.06083	−	1.06083i	0.998026	−	0.0628005i	$-0.0200032\pi$
$464$		0			0
$465$	231.255	+	493.671i	0.497323	+	1.06166i
$466$		0			0
$467$	−531.454	+	531.454i	−1.13802	+	1.13802i	−0.149212	+	0.988805i	$0.547674\pi$
$467$	−531.454	+	531.454i	−1.13802	+	1.13802i	−0.988805	+	0.149212i	$0.952326\pi$
$468$		0			0
$469$	623.658	+	250.616i	1.32976	+	0.534362i
$470$		0			0
$471$		−	147.969i		−	0.314158i
$472$		0			0
$473$	−516.553	−	516.553i	−1.09208	−	1.09208i
$474$		0			0
$475$	171.560	−	205.917i	0.361179	−	0.433510i
$476$		0			0
$477$	−108.917	+	108.917i	−0.228338	+	0.228338i
$478$		0			0
$479$			116.226i			0.242643i	0.992613	+	0.121321i	$0.0387132\pi$
$479$			116.226i			0.242643i	−0.992613	+	0.121321i	$0.961287\pi$
$480$		0			0
$481$			66.1677i			0.137563i
$482$		0			0
$483$	−191.878	+	81.8721i	−0.397263	+	0.169507i
$484$		0			0
$485$	−12.8616	−	27.4562i	−0.0265188	−	0.0566108i
$486$		0			0
$487$	−140.913	−	140.913i	−0.289349	−	0.289349i	0.547474	−	0.836823i	$-0.315590\pi$
$487$	−140.913	−	140.913i	−0.289349	−	0.289349i	−0.836823	+	0.547474i	$0.815590\pi$
$488$		0			0
$489$	−54.0257			−0.110482
$490$		0			0
$491$		−	365.973i		−	0.745363i	−0.927959	−	0.372682i	$-0.878438\pi$
$491$		−	365.973i		−	0.745363i	0.927959	−	0.372682i	$-0.121562\pi$
$492$		0			0
$493$	−24.7590	+	24.7590i	−0.0502211	+	0.0502211i
$494$		0			0
$495$	−107.312	−	38.8458i	−0.216792	−	0.0784763i
$496$		0			0
$497$	−196.161	−	459.728i	−0.394689	−	0.925006i
$498$		0			0
$499$	−208.048			−0.416930			−0.208465	−	0.978030i	$-0.566847\pi$
$499$	−208.048			−0.416930			−0.208465	+	0.978030i	$0.566847\pi$
$500$		0			0
$501$	321.822			0.642360
$502$		0			0
$503$	−325.306	−	325.306i	−0.646732	−	0.646732i	0.305470	−	0.952202i	$-0.401186\pi$
$503$	−325.306	−	325.306i	−0.646732	−	0.646732i	−0.952202	+	0.305470i	$0.901186\pi$
$504$		0			0
$505$	168.445	−	465.332i	0.333555	−	0.921449i
$506$		0			0
$507$	−392.777	+	392.777i	−0.774708	+	0.774708i
$508$		0			0
$509$	−58.0745			−0.114095			−0.0570476	−	0.998371i	$-0.518169\pi$
$509$	−58.0745			−0.114095			−0.0570476	+	0.998371i	$0.518169\pi$
$510$		0			0
$511$	37.7054	−	93.8300i	0.0737875	−	0.183620i
$512$		0			0
$513$	−177.236	−	177.236i	−0.345489	−	0.345489i
$514$		0			0
$515$	197.868	+	422.398i	0.384211	+	0.820191i
$516$		0			0
$517$	404.930	+	404.930i	0.783229	+	0.783229i
$518$		0			0
$519$	216.456			0.417064
$520$		0			0
$521$		−	479.844i		−	0.921006i	−0.887658	−	0.460503i	$-0.847669\pi$
$521$		−	479.844i		−	0.921006i	0.887658	−	0.460503i	$-0.152331\pi$
$522$		0			0
$523$	−159.477	−	159.477i	−0.304927	−	0.304927i	0.538011	−	0.842938i	$-0.319176\pi$
$523$	−159.477	−	159.477i	−0.304927	−	0.304927i	−0.842938	+	0.538011i	$0.819176\pi$
$524$		0			0
$525$	274.326	+	509.309i	0.522525	+	0.970113i
$526$		0			0
$527$	555.595	+	555.595i	1.05426	+	1.05426i
$528$		0			0
$529$			447.721i			0.846353i
$530$		0			0
$531$	−43.1657			−0.0812913
$532$		0			0
$533$	23.0194	+	23.0194i	0.0431883	+	0.0431883i
$534$		0			0
$535$	−75.9318	−	162.095i	−0.141929	−	0.302981i
$536$		0			0
$537$	277.310	+	277.310i	0.516406	+	0.516406i
$538$		0			0
$539$	−418.938	−	401.540i	−0.777250	−	0.744972i
$540$		0			0
$541$	−370.078			−0.684063			−0.342032	−	0.939688i	$-0.611115\pi$
$541$	−370.078			−0.684063			−0.342032	+	0.939688i	$0.611115\pi$
$542$		0			0
$543$	−818.123	+	818.123i	−1.50667	+	1.50667i
$544$		0			0
$545$	258.086	−	712.965i	0.473552	−	1.30819i
$546$		0			0
$547$	514.878	+	514.878i	0.941276	+	0.941276i	0.998369	−	0.0570931i	$-0.0181832\pi$
$547$	514.878	+	514.878i	0.941276	+	0.941276i	−0.0570931	+	0.998369i	$0.518183\pi$
$548$		0			0
$549$	−131.533			−0.239587
$550$		0			0
$551$	−15.7576			−0.0285982
$552$		0			0
$553$	−394.308	+	168.247i	−0.713035	+	0.304244i
$554$		0			0
$555$	−1047.57	−	379.209i	−1.88751	−	0.683260i
$556$		0			0
$557$	141.065	−	141.065i	0.253259	−	0.253259i	−0.569047	−	0.822305i	$-0.692688\pi$
$557$	141.065	−	141.065i	0.253259	−	0.253259i	0.822305	+	0.569047i	$0.192688\pi$
$558$		0			0
$559$			60.5521i			0.108322i
$560$		0			0
$561$	−932.600			−1.66239
$562$		0			0
$563$	576.803	+	576.803i	1.02452	+	1.02452i	0.999692	+	0.0248245i	$0.00790271\pi$
$563$	576.803	+	576.803i	1.02452	+	1.02452i	0.0248245	+	0.999692i	$0.492097\pi$
$564$		0			0
$565$	294.810	+	629.344i	0.521788	+	1.11388i
$566$		0			0
$567$	609.275	−	259.971i	1.07456	−	0.458502i
$568$		0			0
$569$			371.899i			0.653601i	0.945093	+	0.326801i	$0.105971\pi$
$569$			371.899i			0.653601i	−0.945093	+	0.326801i	$0.894029\pi$
$570$		0			0
$571$			933.276i			1.63446i	0.576313	+	0.817229i	$0.304491\pi$
$571$			933.276i			1.63446i	−0.576313	+	0.817229i	$0.695509\pi$
$572$		0			0
$573$	−553.763	+	553.763i	−0.966427	+	0.966427i
$574$		0			0
$575$	−224.460	+	20.4297i	−0.390365	+	0.0355299i
$576$		0			0
$577$	−249.709	−	249.709i	−0.432772	−	0.432772i	0.456798	−	0.889570i	$-0.348996\pi$
$577$	−249.709	−	249.709i	−0.432772	−	0.432772i	−0.889570	+	0.456798i	$0.848996\pi$
$578$		0			0
$579$		−	114.014i		−	0.196916i
$580$		0			0
$581$	−738.309	−	296.688i	−1.27076	−	0.510651i
$582$		0			0
$583$	669.248	−	669.248i	1.14794	−	1.14794i
$584$		0			0
$585$	4.01292	+	8.56655i	0.00685969	+	0.0146437i
$586$		0			0
$587$	281.508	−	281.508i	0.479571	−	0.479571i	−0.425423	−	0.904994i	$-0.639875\pi$
$587$	281.508	−	281.508i	0.479571	−	0.479571i	0.904994	+	0.425423i	$0.139875\pi$
$588$		0			0
$589$			353.603i			0.600345i
$590$		0			0
$591$	136.852			0.231559
$592$		0			0
$593$	−164.513	+	164.513i	−0.277425	+	0.277425i	−0.832080	−	0.554655i	$-0.812850\pi$
$593$	−164.513	+	164.513i	−0.277425	+	0.277425i	0.554655	+	0.832080i	$0.312850\pi$
$594$		0			0
$595$	621.638	+	555.659i	1.04477	+	0.933881i
$596$		0			0
$597$	89.5639	−	89.5639i	0.150023	−	0.150023i
$598$		0			0
$599$	1036.54			1.73045			0.865225	−	0.501384i	$-0.167176\pi$
$599$	1036.54			1.73045			0.865225	+	0.501384i	$0.167176\pi$
$600$		0			0
$601$		−	255.180i		−	0.424593i	−0.977205	−	0.212296i	$-0.931906\pi$
$601$		−	255.180i		−	0.424593i	0.977205	−	0.212296i	$-0.0680942\pi$
$602$		0			0
$603$	−130.859	+	130.859i	−0.217013	+	0.217013i
$604$		0			0
$605$	90.5092	+	32.7634i	0.149602	+	0.0541543i
$606$		0			0
$607$	624.120	−	624.120i	1.02820	−	1.02820i	0.0286133	−	0.999591i	$-0.490891\pi$
$607$	624.120	−	624.120i	1.02820	−	1.02820i	0.999591	−	0.0286133i	$-0.00910915\pi$
$608$		0			0
$609$	12.6816	−	31.5583i	0.0208237	−	0.0518198i
$610$		0			0
$611$		−	47.4672i		−	0.0776877i
$612$		0			0
$613$	139.250	+	139.250i	0.227161	+	0.227161i	0.811506	−	0.584345i	$-0.198648\pi$
$613$	139.250	+	139.250i	0.227161	+	0.227161i	−0.584345	+	0.811506i	$0.698648\pi$
$614$		0			0
$615$	−496.368	+	232.519i	−0.807103	+	0.378079i
$616$		0			0
$617$	−404.370	+	404.370i	−0.655381	+	0.655381i	−0.954284	−	0.298903i	$-0.903379\pi$
$617$	−404.370	+	404.370i	−0.655381	+	0.655381i	0.298903	+	0.954284i	$0.403379\pi$
$618$		0			0
$619$		−	107.575i		−	0.173789i	−0.996218	−	0.0868943i	$-0.972306\pi$
$619$		−	107.575i		−	0.173789i	0.996218	−	0.0868943i	$-0.0276942\pi$
$620$		0			0
$621$			210.780i			0.339420i
$622$		0			0
$623$	178.775	−	76.2813i	0.286959	−	0.122442i
$624$		0			0
$625$	112.837	+	614.730i	0.180539	+	0.983568i
$626$		0			0
$627$	−296.772	−	296.772i	−0.473321	−	0.473321i
$628$		0			0
$629$	−1605.75			−2.55286
$630$		0			0
$631$		−	952.010i		−	1.50873i	−0.656454	−	0.754366i	$-0.727944\pi$
$631$		−	952.010i		−	1.50873i	0.656454	−	0.754366i	$-0.272056\pi$
$632$		0			0
$633$	−654.887	+	654.887i	−1.03458	+	1.03458i
$634$		0			0
$635$	97.9847	+	209.172i	0.154307	+	0.329405i
$636$		0			0
$637$	1.01972	+	48.0896i	0.00160082	+	0.0754939i
$638$		0			0
$639$	137.621			0.215370
$640$		0			0
$641$	−650.367			−1.01461			−0.507307	−	0.861766i	$-0.669359\pi$
$641$	−650.367			−1.01461			−0.507307	+	0.861766i	$0.669359\pi$
$642$		0			0
$643$	208.966	+	208.966i	0.324986	+	0.324986i	0.850676	−	0.525690i	$-0.176193\pi$
$643$	208.966	+	208.966i	0.324986	+	0.324986i	−0.525690	+	0.850676i	$0.676193\pi$
$644$		0			0
$645$	−958.663	−	347.026i	−1.48630	−	0.538024i
$646$		0			0
$647$	367.425	−	367.425i	0.567891	−	0.567891i	−0.363646	−	0.931537i	$-0.618468\pi$
$647$	367.425	−	367.425i	0.567891	−	0.567891i	0.931537	+	0.363646i	$0.118468\pi$
$648$		0			0
$649$	265.234			0.408681
$650$		0			0
$651$	−708.172	−	284.577i	−1.08782	−	0.437139i
$652$		0			0
$653$	−780.417	−	780.417i	−1.19513	−	1.19513i	−0.975609	−	0.219517i	$-0.929552\pi$
$653$	−780.417	−	780.417i	−1.19513	−	1.19513i	−0.219517	−	0.975609i	$-0.570448\pi$
$654$		0			0
$655$	126.069	+	45.6358i	0.192472	+	0.0696729i
$656$		0			0
$657$	19.6878	+	19.6878i	0.0299663	+	0.0299663i
$658$		0			0
$659$	−1175.20			−1.78331			−0.891657	−	0.452711i	$-0.850457\pi$
$659$	−1175.20			−1.78331			−0.891657	+	0.452711i	$0.850457\pi$
$660$		0			0
$661$		−	371.534i		−	0.562079i	−0.959696	−	0.281039i	$-0.909321\pi$
$661$		−	371.534i		−	0.562079i	0.959696	−	0.281039i	$-0.0906791\pi$
$662$		0			0
$663$	54.6612	+	54.6612i	0.0824453	+	0.0824453i
$664$		0			0
$665$	20.9959	+	374.640i	0.0315728	+	0.563369i
$666$		0			0
$667$	9.36998	+	9.36998i	0.0140479	+	0.0140479i
$668$		0			0
$669$		−	107.529i		−	0.160731i
$670$		0			0
$671$	808.214			1.20449
$672$		0			0
$673$	250.852	+	250.852i	0.372737	+	0.372737i	0.868473	−	0.495736i	$-0.165102\pi$
$673$	250.852	+	250.852i	0.372737	+	0.372737i	−0.495736	+	0.868473i	$0.665102\pi$
$674$		0			0
$675$	582.087	−	52.9799i	0.862351	−	0.0784887i
$676$		0			0
$677$	190.191	+	190.191i	0.280931	+	0.280931i	0.833480	−	0.552549i	$-0.186345\pi$
$677$	190.191	+	190.191i	0.280931	+	0.280931i	−0.552549	+	0.833480i	$0.686345\pi$
$678$		0			0
$679$	39.3861	+	15.8272i	0.0580060	+	0.0233096i
$680$		0			0
$681$	−952.471			−1.39864
$682$		0			0
$683$	104.495	−	104.495i	0.152994	−	0.152994i	−0.626460	−	0.779454i	$-0.715497\pi$
$683$	104.495	−	104.495i	0.152994	−	0.152994i	0.779454	+	0.626460i	$0.215497\pi$
$684$		0			0
$685$	974.706	−	456.592i	1.42293	−	0.666557i
$686$		0			0
$687$	900.605	+	900.605i	1.31092	+	1.31092i
$688$		0			0
$689$	−78.4514			−0.113863
$690$		0			0
$691$	892.593			1.29174			0.645871	−	0.763447i	$-0.276495\pi$
$691$	892.593			1.29174			0.645871	+	0.763447i	$0.276495\pi$
$692$		0			0
$693$	146.958	−	62.7054i	0.212061	−	0.0904840i
$694$		0			0
$695$	−338.438	+	934.938i	−0.486961	+	1.34523i
$696$		0			0
$697$	−558.631	+	558.631i	−0.801479	+	0.801479i
$698$		0			0
$699$		−	547.659i		−	0.783489i
$700$		0			0
$701$	108.789			0.155191			0.0775954	−	0.996985i	$-0.475276\pi$
$701$	108.789			0.155191			0.0775954	+	0.996985i	$0.475276\pi$
$702$		0			0
$703$	−510.982	−	510.982i	−0.726859	−	0.726859i
$704$		0			0
$705$	751.502	+	272.036i	1.06596	+	0.385866i
$706$		0			0
$707$	271.906	+	637.248i	0.384592	+	0.901341i
$708$		0			0
$709$			122.262i			0.172443i	0.996276	+	0.0862215i	$0.0274793\pi$
$709$			122.262i			0.172443i	−0.996276	+	0.0862215i	$0.972521\pi$
$710$		0			0
$711$		−	118.038i		−	0.166017i
$712$		0			0
$713$	210.264	−	210.264i	0.294900	−	0.294900i
$714$		0			0
$715$	−24.6576	−	52.6377i	−0.0344862	−	0.0736191i
$716$		0			0
$717$	−207.003	−	207.003i	−0.288707	−	0.288707i
$718$		0			0
$719$			416.163i			0.578808i	0.957207	+	0.289404i	$0.0934570\pi$
$719$			416.163i			0.578808i	−0.957207	+	0.289404i	$0.906543\pi$
$720$		0			0
$721$	−605.932	−	243.492i	−0.840404	−	0.337715i
$722$		0			0
$723$	−383.234	+	383.234i	−0.530060	+	0.530060i
$724$		0			0
$725$	23.5208	−	28.2312i	0.0324425	−	0.0389395i
$726$		0			0
$727$	−63.6571	+	63.6571i	−0.0875614	+	0.0875614i	−0.749531	−	0.661969i	$-0.769721\pi$
$727$	−63.6571	+	63.6571i	−0.0875614	+	0.0875614i	0.661969	+	0.749531i	$0.269721\pi$
$728$		0			0
$729$		−	513.179i		−	0.703949i
$730$		0			0
$731$	−1469.47			−2.01022
$732$		0			0
$733$	−152.595	+	152.595i	−0.208179	+	0.208179i	−0.803493	−	0.595314i	$-0.797028\pi$
$733$	−152.595	+	152.595i	−0.208179	+	0.208179i	0.595314	+	0.803493i	$0.297028\pi$
$734$		0			0
$735$	−767.200	−	259.459i	−1.04381	−	0.353005i
$736$		0			0
$737$	804.069	−	804.069i	1.09100	−	1.09100i
$738$		0			0
$739$	−109.841			−0.148634			−0.0743171	−	0.997235i	$-0.523678\pi$
$739$	−109.841			−0.148634			−0.0743171	+	0.997235i	$0.523678\pi$
$740$		0			0
$741$			34.7886i			0.0469482i
$742$		0			0
$743$	46.8932	−	46.8932i	0.0631133	−	0.0631133i	−0.674846	−	0.737959i	$-0.735790\pi$
$743$	46.8932	−	46.8932i	0.0631133	−	0.0631133i	0.737959	+	0.674846i	$0.235790\pi$
$744$		0			0
$745$	−366.170	+	1011.55i	−0.491503	+	1.35778i
$746$		0			0
$747$	154.915	−	154.915i	0.207383	−	0.207383i
$748$		0			0
$749$	232.526	+	93.4400i	0.310448	+	0.124753i
$750$		0			0
$751$			280.895i			0.374028i	0.982357	+	0.187014i	$0.0598810\pi$
$751$			280.895i			0.374028i	−0.982357	+	0.187014i	$0.940119\pi$
$752$		0			0
$753$	700.464	+	700.464i	0.930232	+	0.930232i
$754$		0			0
$755$	−73.5026	+	203.052i	−0.0973545	+	0.268943i
$756$		0			0
$757$	−131.961	+	131.961i	−0.174321	+	0.174321i	−0.788875	−	0.614554i	$-0.789336\pi$
$757$	−131.961	+	131.961i	−0.174321	+	0.174321i	0.614554	+	0.788875i	$0.289336\pi$
$758$		0			0
$759$			352.940i			0.465007i
$760$		0			0
$761$			7.26565i			0.00954750i	0.999989	+	0.00477375i	$0.00151954\pi$
$761$			7.26565i			0.00954750i	−0.999989	+	0.00477375i	$0.998480\pi$
$762$		0			0
$763$	416.606	+	976.370i	0.546010	+	1.27965i
$764$		0			0
$765$	−207.892	+	97.3849i	−0.271754	+	0.127301i
$766$		0			0
$767$	−15.5458	−	15.5458i	−0.0202683	−	0.0202683i
$768$		0			0
$769$	−234.551			−0.305008			−0.152504	−	0.988303i	$-0.548734\pi$
$769$	−234.551			−0.305008			−0.152504	+	0.988303i	$0.548734\pi$
$770$		0			0
$771$			1237.74i			1.60537i
$772$		0			0
$773$	712.003	−	712.003i	0.921090	−	0.921090i	−0.0760161	−	0.997107i	$-0.524220\pi$
$773$	712.003	−	712.003i	0.921090	−	0.921090i	0.997107	+	0.0760161i	$0.0242201\pi$
$774$		0			0
$775$	−633.511	−	527.811i	−0.817434	−	0.681046i
$776$		0			0
$777$	1434.59	−	612.124i	1.84632	−	0.787805i
$778$		0			0
$779$	−355.535			−0.456400
$780$		0			0
$781$	−845.623			−1.08274
$782$		0			0
$783$	−24.2990	−	24.2990i	−0.0310332	−	0.0310332i
$784$		0			0
$785$	94.9416	+	202.676i	0.120945	+	0.258186i
$786$		0			0
$787$	325.898	−	325.898i	0.414101	−	0.414101i	−0.469063	−	0.883164i	$-0.655408\pi$
$787$	325.898	−	325.898i	0.414101	−	0.414101i	0.883164	+	0.469063i	$0.155408\pi$
$788$		0			0
$789$	−1133.20			−1.43625
$790$		0			0
$791$	−902.796	−	362.787i	−1.14133	−	0.458643i
$792$		0			0
$793$	−47.3708	−	47.3708i	−0.0597362	−	0.0597362i
$794$		0			0
$795$	449.607	−	1242.05i	0.565544	−	1.56232i
$796$		0			0
$797$	892.503	+	892.503i	1.11983	+	1.11983i	0.991766	+	0.128062i	$0.0408756\pi$
$797$	892.503	+	892.503i	1.11983	+	1.11983i	0.128062	+	0.991766i	$0.459124\pi$
$798$		0			0
$799$	1151.93			1.44171
$800$		0			0
$801$			53.5171i			0.0668128i
$802$		0			0
$803$	−120.973	−	120.973i	−0.150651	−	0.150651i
$804$		0			0
$805$	210.288	−	235.258i	0.261227	−	0.292245i
$806$		0			0
$807$	514.095	+	514.095i	0.637045	+	0.637045i
$808$		0			0
$809$			742.458i			0.917747i	0.888502	+	0.458874i	$0.151747\pi$
$809$			742.458i			0.917747i	−0.888502	+	0.458874i	$0.848253\pi$
$810$		0			0
$811$	−650.381			−0.801949			−0.400975	−	0.916089i	$-0.631328\pi$
$811$	−650.381			−0.801949			−0.400975	+	0.916089i	$0.631328\pi$
$812$		0			0
$813$	46.5876	+	46.5876i	0.0573034	+	0.0573034i
$814$		0			0
$815$	74.0002	−	34.6647i	0.0907978	−	0.0425334i
$816$		0			0
$817$	−467.615	−	467.615i	−0.572356	−	0.572356i
$818$		0			0
$819$	−12.2887	−	4.93820i	−0.0150046	−	0.00602955i
$820$		0			0
$821$	103.472			0.126031			0.0630156	−	0.998013i	$-0.479928\pi$
$821$	103.472			0.126031			0.0630156	+	0.998013i	$0.479928\pi$
$822$		0			0
$823$	493.880	−	493.880i	0.600097	−	0.600097i	−0.340241	−	0.940338i	$-0.610509\pi$
$823$	493.880	−	493.880i	0.600097	−	0.600097i	0.940338	+	0.340241i	$0.110509\pi$
$824$		0			0
$825$	974.675	−	88.7122i	1.18142	−	0.107530i
$826$		0			0
$827$	−718.843	−	718.843i	−0.869218	−	0.869218i	0.123168	−	0.992386i	$-0.460695\pi$
$827$	−718.843	−	718.843i	−0.869218	−	0.869218i	−0.992386	+	0.123168i	$0.960695\pi$
$828$		0			0
$829$	1281.53			1.54588			0.772940	−	0.634479i	$-0.218785\pi$
$829$	1281.53			1.54588			0.772940	+	0.634479i	$0.218785\pi$
$830$		0			0
$831$	−937.139			−1.12772
$832$		0			0
$833$	−1167.03	+	24.7464i	−1.40100	+	0.0297076i
$834$		0			0
$835$	−440.808	+	206.492i	−0.527913	+	0.247296i
$836$		0			0
$837$	−545.272	+	545.272i	−0.651460	+	0.651460i
$838$		0			0
$839$			1534.32i			1.82875i	0.404869	+	0.914375i	$0.367317\pi$
$839$			1534.32i			1.82875i	−0.404869	+	0.914375i	$0.632683\pi$
$840$		0			0
$841$	838.840			0.997431
$842$		0			0
$843$	1068.10	+	1068.10i	1.26702	+	1.26702i
$844$		0			0
$845$	285.977	−	790.014i	0.338434	−	0.934928i
$846$		0			0
$847$	−123.948	+	52.8871i	−0.146337	+	0.0624405i
$848$		0			0
$849$		−	464.028i		−	0.546558i
$850$		0			0
$851$			607.692i			0.714092i
$852$		0			0
$853$	−1079.81	+	1079.81i	−1.26590	+	1.26590i	−0.317711	+	0.948188i	$0.602914\pi$
$853$	−1079.81	+	1079.81i	−1.26590	+	1.26590i	−0.948188	+	0.317711i	$0.897086\pi$
$854$		0			0
$855$	−97.1453	−	35.1656i	−0.113620	−	0.0411293i
$856$		0			0
$857$	270.781	+	270.781i	0.315964	+	0.315964i	0.847215	−	0.531251i	$-0.178278\pi$
$857$	270.781	+	270.781i	0.315964	+	0.315964i	−0.531251	+	0.847215i	$0.678278\pi$
$858$		0			0
$859$			419.003i			0.487781i	0.969803	+	0.243890i	$0.0784237\pi$
$859$			419.003i			0.487781i	−0.969803	+	0.243890i	$0.921576\pi$
$860$		0			0
$861$	286.132	−	712.041i	0.332326	−	0.826994i
$862$		0			0
$863$	155.617	−	155.617i	0.180321	−	0.180321i	−0.611175	−	0.791496i	$-0.709303\pi$
$863$	155.617	−	155.617i	0.180321	−	0.180321i	0.791496	+	0.611175i	$0.209303\pi$
$864$		0			0
$865$	−296.485	+	138.885i	−0.342757	+	0.160561i
$866$		0			0
$867$	−650.988	+	650.988i	−0.750851	+	0.750851i
$868$		0			0
$869$			725.290i			0.834626i
$870$		0			0
$871$	−94.2556			−0.108215
$872$		0			0
$873$	−8.26416	+	8.26416i	−0.00946639	+	0.00946639i
$874$		0			0
$875$	−702.540	−	521.596i	−0.802903	−	0.596109i
$876$		0			0
$877$	466.187	−	466.187i	0.531570	−	0.531570i	−0.389470	−	0.921039i	$-0.627342\pi$
$877$	466.187	−	466.187i	0.531570	−	0.531570i	0.921039	+	0.389470i	$0.127342\pi$
$878$		0			0
$879$	1538.39			1.75015
$880$		0			0
$881$		−	351.663i		−	0.399163i	−0.979881	−	0.199582i	$-0.936042\pi$
$881$		−	351.663i		−	0.399163i	0.979881	−	0.199582i	$-0.0639583\pi$
$882$		0			0
$883$	−260.868	+	260.868i	−0.295434	+	0.295434i	−0.839222	−	0.543788i	$-0.816989\pi$
$883$	−260.868	+	260.868i	−0.295434	+	0.295434i	0.543788	+	0.839222i	$0.316989\pi$
$884$		0			0
$885$	335.215	−	157.028i	0.378774	−	0.177433i
$886$		0			0
$887$	393.767	−	393.767i	0.443931	−	0.443931i	−0.449400	−	0.893331i	$-0.648362\pi$
$887$	393.767	−	393.767i	0.443931	−	0.443931i	0.893331	+	0.449400i	$0.148362\pi$
$888$		0			0
$889$	−300.058	−	120.578i	−0.337523	−	0.135633i
$890$		0			0
$891$		−	1120.70i		−	1.25780i
$892$		0			0
$893$	366.567	+	366.567i	0.410489	+	0.410489i
$894$		0			0
$895$	−557.769	−	201.906i	−0.623206	−	0.225594i
$896$		0			0
$897$	20.6864	−	20.6864i	0.0230618	−	0.0230618i
$898$		0			0
$899$			48.4789i			0.0539254i
$900$		0			0
$901$		−	1903.85i		−	2.11304i
$902$		0			0
$903$	1312.84	−	560.174i	1.45387	−	0.620347i
$904$		0			0
$905$	595.667	−	1645.54i	0.658195	−	1.81827i
$906$		0			0
$907$	−877.122	−	877.122i	−0.967059	−	0.967059i	0.0324157	−	0.999474i	$-0.489680\pi$
$907$	−877.122	−	877.122i	−0.967059	−	0.967059i	−0.999474	+	0.0324157i	$0.989680\pi$
$908$		0			0
$909$	−190.763			−0.209860
$910$		0			0
$911$			843.406i			0.925802i	0.886410	+	0.462901i	$0.153191\pi$
$911$			843.406i			0.925802i	−0.886410	+	0.462901i	$0.846809\pi$
$912$		0			0
$913$	−951.886	+	951.886i	−1.04259	+	1.04259i
$914$		0			0
$915$	1021.46	−	478.493i	1.11635	−	0.522943i
$916$		0			0
$917$	−172.646	+	73.6659i	−0.188272	+	0.0803336i
$918$		0			0
$919$	−1279.77			−1.39257			−0.696285	−	0.717765i	$-0.745165\pi$
$919$	−1279.77			−1.39257			−0.696285	+	0.717765i	$0.745165\pi$
$920$		0			0
$921$	1505.72			1.63487
$922$		0			0
$923$	49.5634	+	49.5634i	0.0536981	+	0.0536981i
$924$		0			0
$925$	1678.19	−	152.744i	1.81426	−	0.165129i
$926$		0			0
$927$	127.139	−	127.139i	0.137151	−	0.137151i
$928$		0			0
$929$	−1646.37			−1.77220			−0.886098	−	0.463498i	$-0.846594\pi$
$929$	−1646.37			−1.77220			−0.886098	+	0.463498i	$0.846594\pi$
$930$		0			0
$931$	−379.248	−	363.498i	−0.407356	−	0.390439i
$932$		0			0
$933$	518.258	+	518.258i	0.555475	+	0.555475i
$934$		0			0
$935$	1277.40	−	598.387i	1.36621	−	0.639986i
$936$		0			0
$937$	530.267	+	530.267i	0.565920	+	0.565920i	0.930983	−	0.365063i	$-0.118952\pi$
$937$	530.267	+	530.267i	0.565920	+	0.565920i	−0.365063	+	0.930983i	$0.618952\pi$
$938$		0			0
$939$	954.007			1.01598
$940$		0			0
$941$		−	804.879i		−	0.855345i	−0.903934	−	0.427672i	$-0.859334\pi$
$941$		−	804.879i		−	0.855345i	0.903934	−	0.427672i	$-0.140666\pi$
$942$		0			0
$943$	211.413	+	211.413i	0.224191	+	0.224191i
$944$		0			0
$945$	−545.335	+	610.088i	−0.577074	+	0.645596i
$946$		0			0
$947$	270.028	+	270.028i	0.285140	+	0.285140i	0.835155	−	0.550015i	$-0.185378\pi$
$947$	270.028	+	270.028i	0.285140	+	0.285140i	−0.550015	+	0.835155i	$0.685378\pi$
$948$		0			0
$949$			14.1809i			0.0149430i
$950$		0			0
$951$	616.123			0.647869
$952$		0			0
$953$	1260.17	+	1260.17i	1.32232	+	1.32232i	0.911891	+	0.410432i	$0.134622\pi$
$953$	1260.17	+	1260.17i	1.32232	+	1.32232i	0.410432	+	0.911891i	$0.365378\pi$
$954$		0			0
$955$	403.189	−	1113.81i	0.422187	−	1.16630i
$956$		0			0
$957$	−40.6874	−	40.6874i	−0.0425156	−	0.0425156i
$958$		0			0
$959$	−561.871	+	1398.22i	−0.585893	+	1.45800i
$960$		0			0
$961$	126.874			0.132023
$962$		0			0
$963$	−48.7896	+	48.7896i	−0.0506641	+	0.0506641i
$964$		0			0
$965$	73.1553	+	156.168i	0.0758086	+	0.161832i
$966$		0			0
$967$	−1164.77	−	1164.77i	−1.20452	−	1.20452i	−0.972778	−	0.231739i	$-0.925559\pi$
$967$	−1164.77	−	1164.77i	−1.20452	−	1.20452i	−0.231739	−	0.972778i	$-0.574441\pi$
$968$		0			0
$969$	−844.246			−0.871255
$970$		0			0
$971$	120.566			0.124166			0.0620832	−	0.998071i	$-0.480226\pi$
$971$	120.566			0.124166			0.0620832	+	0.998071i	$0.480226\pi$
$972$		0			0
$973$	−546.311	−	1280.35i	−0.561470	−	1.31588i
$974$		0			0
$975$	−62.3269	−	51.9277i	−0.0639250	−	0.0532592i
$976$		0			0
$977$	−877.804	+	877.804i	−0.898468	+	0.898468i	−0.995301	−	0.0968323i	$-0.969129\pi$
$977$	−877.804	+	877.804i	−0.898468	+	0.898468i	0.0968323	+	0.995301i	$0.469129\pi$
$978$		0			0
$979$		−	328.839i		−	0.335893i
$980$		0			0
$981$	−292.280			−0.297941
$982$		0			0
$983$	−551.042	−	551.042i	−0.560572	−	0.560572i	0.368898	−	0.929470i	$-0.379735\pi$
$983$	−551.042	−	551.042i	−0.560572	−	0.560572i	−0.929470	+	0.368898i	$0.879735\pi$
$984$		0			0
$985$	−187.449	+	87.8086i	−0.190303	+	0.0891457i
$986$		0			0
$987$	−1029.14	+	439.124i	−1.04270	+	0.444908i
$988$		0			0
$989$			556.117i			0.562303i
$990$		0			0
$991$			834.871i			0.842453i	0.906955	+	0.421227i	$0.138400\pi$
$991$			834.871i			0.842453i	−0.906955	+	0.421227i	$0.861600\pi$
$992$		0			0
$993$	1265.80	−	1265.80i	1.27472	−	1.27472i
$994$		0			0
$995$	−65.2105	+	180.145i	−0.0655382	+	0.181050i
$996$		0			0
$997$	−554.709	−	554.709i	−0.556378	−	0.556378i	0.371896	−	0.928274i	$-0.378708\pi$
$997$	−554.709	−	554.709i	−0.556378	−	0.556378i	−0.928274	+	0.371896i	$0.878708\pi$
$998$		0			0
$999$		−	1575.91i		−	1.57749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.3.v.b.223.23	yes	64
4.3	odd	2	inner	560.3.v.b.223.10	yes	64
5.2	odd	4	inner	560.3.v.b.447.24	yes	64
7.6	odd	2	inner	560.3.v.b.223.9	✓	64
20.7	even	4	inner	560.3.v.b.447.9	yes	64
28.27	even	2	inner	560.3.v.b.223.24	yes	64
35.27	even	4	inner	560.3.v.b.447.10	yes	64
140.27	odd	4	inner	560.3.v.b.447.23	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.3.v.b.223.9	✓	64	7.6	odd	2	inner
560.3.v.b.223.10	yes	64	4.3	odd	2	inner
560.3.v.b.223.23	yes	64	1.1	even	1	trivial
560.3.v.b.223.24	yes	64	28.27	even	2	inner
560.3.v.b.447.9	yes	64	20.7	even	4	inner
560.3.v.b.447.10	yes	64	35.27	even	4	inner
560.3.v.b.447.23	yes	64	140.27	odd	4	inner
560.3.v.b.447.24	yes	64	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.33745 + 2.33745i) q^{3} +(-4.70145 - 1.70187i) q^{5} +(6.43840 - 2.74719i) q^{7} +1.92736i q^{9} -11.8428i q^{11} +(-0.694125 + 0.694125i) q^{13} +(-7.01136 - 14.9675i) q^{15} +(-16.8449 - 16.8449i) q^{17} -10.7208i q^{19} +(21.4709 + 8.62802i) q^{21} +(-6.37492 + 6.37492i) q^{23} +(19.2072 + 16.0026i) q^{25} +(16.5320 - 16.5320i) q^{27} -1.46982i q^{29} -32.9829 q^{31} +(27.6819 - 27.6819i) q^{33} +(-34.9452 + 1.95843i) q^{35} +(47.6627 - 47.6627i) q^{37} -3.24497 q^{39} -33.1632i q^{41} +(43.6176 - 43.6176i) q^{43} +(3.28012 - 9.06138i) q^{45} +(-34.1921 + 34.1921i) q^{47} +(33.9059 - 35.3750i) q^{49} -78.7484i q^{51} +(56.5110 + 56.5110i) q^{53} +(-20.1549 + 55.6782i) q^{55} +(25.0593 - 25.0593i) q^{57} +22.3963i q^{59} +68.2453i q^{61} +(5.29482 + 12.4091i) q^{63} +(4.44471 - 2.08208i) q^{65} +(67.8953 + 67.8953i) q^{67} -29.8021 q^{69} -71.4041i q^{71} +(10.2149 - 10.2149i) q^{73} +(7.49082 + 82.3012i) q^{75} +(-32.5343 - 76.2485i) q^{77} -61.2432 q^{79} +94.6315 q^{81} +(-80.3770 - 80.3770i) q^{83} +(50.5276 + 107.864i) q^{85} +(3.43563 - 3.43563i) q^{87} +27.7670 q^{89} +(-2.56216 + 6.37594i) q^{91} +(-77.0960 - 77.0960i) q^{93} +(-18.2455 + 50.4033i) q^{95} +(4.28781 + 4.28781i) q^{97} +22.8253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 16 q^{21} - 72 q^{25} + 72 q^{37} + 272 q^{53} - 376 q^{57} - 88 q^{65} + 24 q^{77} - 432 q^{81} + 384 q^{85} + 840 q^{93}+O(q^{100}) \) 64 * q + 16 * q^21 - 72 * q^25 + 72 * q^37 + 272 * q^53 - 376 * q^57 - 88 * q^65 + 24 * q^77 - 432 * q^81 + 384 * q^85 + 840 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more