LMFDB - Embedded newform 1008.2.bf.g.31.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(31,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-3,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.11
Character	$\chi$	$=$	1008.31
Dual form			1008.2.bf.g.943.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.55599 + 0.760852i) q^{3} -1.99968i q^{5} +(2.18955 - 1.48522i) q^{7} +(1.84221 + 2.36776i) q^{9} -1.36249i q^{11} +(-1.71030 - 0.987444i) q^{13} +(1.52146 - 3.11148i) q^{15} +(0.868852 + 0.501632i) q^{17} +(0.774396 + 1.34129i) q^{19} +(4.53695 - 0.645056i) q^{21} -8.77155i q^{23} +1.00128 q^{25} +(1.06494 + 5.08585i) q^{27} +(0.854529 + 1.48009i) q^{29} +(-0.261122 - 0.452277i) q^{31} +(1.03665 - 2.12002i) q^{33} +(-2.96996 - 4.37840i) q^{35} +(1.53855 + 2.66485i) q^{37} +(-1.90992 - 2.83774i) q^{39} +(0.386794 + 0.223316i) q^{41} +(-5.49888 + 3.17478i) q^{43} +(4.73475 - 3.68383i) q^{45} +(-0.819743 + 1.41984i) q^{47} +(2.58827 - 6.50391i) q^{49} +(0.970257 + 1.44160i) q^{51} +(1.24313 - 2.15316i) q^{53} -2.72454 q^{55} +(0.184426 + 2.67624i) q^{57} +(-6.31421 - 10.9365i) q^{59} +(9.13080 + 5.27167i) q^{61} +(7.55024 + 2.44825i) q^{63} +(-1.97457 + 3.42006i) q^{65} +(-5.63337 + 3.25243i) q^{67} +(6.67385 - 13.6484i) q^{69} -1.57299i q^{71} +(13.6347 + 7.87199i) q^{73} +(1.55799 + 0.761828i) q^{75} +(-2.02359 - 2.98324i) q^{77} +(-5.16095 - 2.97967i) q^{79} +(-2.21254 + 8.72380i) q^{81} +(4.80565 + 8.32363i) q^{83} +(1.00310 - 1.73743i) q^{85} +(0.203511 + 2.95317i) q^{87} +(-1.10887 + 0.640207i) q^{89} +(-5.21136 + 0.378111i) q^{91} +(-0.0621876 - 0.902414i) q^{93} +(2.68215 - 1.54854i) q^{95} +(-8.31781 + 4.80229i) q^{97} +(3.22604 - 2.50999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 8 q^{7} - q^{9} + 3 q^{13} - 6 q^{15} - 3 q^{17} + 4 q^{19} - 20 q^{21} - 30 q^{25} - 9 q^{27} + 18 q^{29} + 17 q^{31} - 12 q^{33} + 42 q^{35} - 3 q^{37} - 42 q^{39} - 36 q^{41} + 24 q^{43}+ \cdots + 30 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 8 * q^7 - q^9 + 3 * q^13 - 6 * q^15 - 3 * q^17 + 4 * q^19 - 20 * q^21 - 30 * q^25 - 9 * q^27 + 18 * q^29 + 17 * q^31 - 12 * q^33 + 42 * q^35 - 3 * q^37 - 42 * q^39 - 36 * q^41 + 24 * q^43 + 12 * q^45 - 21 * q^47 - 24 * q^49 + 18 * q^51 - 12 * q^53 + 30 * q^55 - 13 * q^57 - 6 * q^59 - 48 * q^61 - 6 * q^63 + 42 * q^67 - 6 * q^69 + 48 * q^73 - 33 * q^75 + 36 * q^77 - 30 * q^79 + 23 * q^81 + 48 * q^83 - 21 * q^85 - 15 * q^87 + 39 * q^89 - 9 * q^91 - 8 * q^93 - 33 * q^95 - 3 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.55599	+	0.760852i	0.898351	+	0.439278i
$3$	1.55599	+	0.760852i	0.898351	+	0.439278i
$4$		0			0
$5$		−	1.99968i		−	0.894284i	−0.894463	−	0.447142i	$-0.852442\pi$
$5$		−	1.99968i		−	0.894284i	0.894463	−	0.447142i	$-0.147558\pi$
$6$		0			0
$7$	2.18955	−	1.48522i	0.827572	−	0.561359i
$7$	2.18955	−	1.48522i	0.827572	−	0.561359i
$8$		0			0
$9$	1.84221	+	2.36776i	0.614069	+	0.789252i
$10$		0			0
$11$		−	1.36249i		−	0.410805i	−0.978678	−	0.205403i	$-0.934150\pi$
$11$		−	1.36249i		−	0.410805i	0.978678	−	0.205403i	$-0.0658504\pi$
$12$		0			0
$13$	−1.71030	−	0.987444i	−0.474353	−	0.273868i	0.243707	−	0.969849i	$-0.421636\pi$
$13$	−1.71030	−	0.987444i	−0.474353	−	0.273868i	−0.718060	+	0.695981i	$0.754970\pi$
$14$		0			0
$15$	1.52146	−	3.11148i	0.392839	−	0.803381i
$16$		0			0
$17$	0.868852	+	0.501632i	0.210728	+	0.121664i	0.601649	−	0.798760i	$-0.294510\pi$
$17$	0.868852	+	0.501632i	0.210728	+	0.121664i	−0.390922	+	0.920424i	$0.627844\pi$
$18$		0			0
$19$	0.774396	+	1.34129i	0.177659	+	0.307714i	0.941078	−	0.338189i	$-0.109814\pi$
$19$	0.774396	+	1.34129i	0.177659	+	0.307714i	−0.763420	+	0.645903i	$0.776481\pi$
$20$		0			0
$21$	4.53695	−	0.645056i	0.990043	−	0.140763i
$22$		0			0
$23$		−	8.77155i		−	1.82900i	−0.404592	−	0.914498i	$-0.632586\pi$
$23$		−	8.77155i		−	1.82900i	0.404592	−	0.914498i	$-0.367414\pi$
$24$		0			0
$25$	1.00128			0.200257
$26$		0			0
$27$	1.06494	+	5.08585i	0.204949	+	0.978773i
$28$		0			0
$29$	0.854529	+	1.48009i	0.158682	+	0.274846i	0.934394	−	0.356242i	$-0.115942\pi$
$29$	0.854529	+	1.48009i	0.158682	+	0.274846i	−0.775712	+	0.631088i	$0.782609\pi$
$30$		0			0
$31$	−0.261122	−	0.452277i	−0.0468989	−	0.0812313i	0.841623	−	0.540065i	$-0.181601\pi$
$31$	−0.261122	−	0.452277i	−0.0468989	−	0.0812313i	−0.888522	+	0.458834i	$0.848267\pi$
$32$		0			0
$33$	1.03665	−	2.12002i	0.180458	−	0.369047i
$34$		0			0
$35$	−2.96996	−	4.37840i	−0.502014	−	0.740085i
$36$		0			0
$37$	1.53855	+	2.66485i	0.252936	+	0.438099i	0.964333	−	0.264692i	$-0.0852703\pi$
$37$	1.53855	+	2.66485i	0.252936	+	0.438099i	−0.711397	+	0.702791i	$0.751937\pi$
$38$		0			0
$39$	−1.90992	−	2.83774i	−0.305831	−	0.454402i
$40$		0			0
$41$	0.386794	+	0.223316i	0.0604071	+	0.0348761i	0.529899	−	0.848061i	$-0.322230\pi$
$41$	0.386794	+	0.223316i	0.0604071	+	0.0348761i	−0.469492	+	0.882937i	$0.655563\pi$
$42$		0			0
$43$	−5.49888	+	3.17478i	−0.838572	+	0.484150i	−0.856779	−	0.515685i	$-0.827538\pi$
$43$	−5.49888	+	3.17478i	−0.838572	+	0.484150i	0.0182067	+	0.999834i	$0.494204\pi$
$44$		0			0
$45$	4.73475	−	3.68383i	0.705815	−	0.549152i
$46$		0			0
$47$	−0.819743	+	1.41984i	−0.119572	+	0.207104i	−0.919598	−	0.392861i	$-0.871485\pi$
$47$	−0.819743	+	1.41984i	−0.119572	+	0.207104i	0.800026	+	0.599965i	$0.204819\pi$
$48$		0			0
$49$	2.58827	−	6.50391i	0.369752	−	0.929130i
$50$		0			0
$51$	0.970257	+	1.44160i	0.135863	+	0.201865i
$52$		0			0
$53$	1.24313	−	2.15316i	0.170757	−	0.295760i	−0.767928	−	0.640537i	$-0.778712\pi$
$53$	1.24313	−	2.15316i	0.170757	−	0.295760i	0.938685	+	0.344777i	$0.112045\pi$
$54$		0			0
$55$	−2.72454			−0.367377
$56$		0			0
$57$	0.184426	+	2.67624i	0.0244279	+	0.354476i
$58$		0			0
$59$	−6.31421	−	10.9365i	−0.822040	−	1.42381i	−0.904161	−	0.427193i	$-0.859503\pi$
$59$	−6.31421	−	10.9365i	−0.822040	−	1.42381i	0.0821208	−	0.996622i	$-0.473831\pi$
$60$		0			0
$61$	9.13080	+	5.27167i	1.16908	+	0.674968i	0.953463	−	0.301510i	$-0.0974907\pi$
$61$	9.13080	+	5.27167i	1.16908	+	0.674968i	0.215616	+	0.976478i	$0.430824\pi$
$62$		0			0
$63$	7.55024	+	2.44825i	0.951241	+	0.308450i
$64$		0			0
$65$	−1.97457	+	3.42006i	−0.244915	+	0.424206i
$66$		0			0
$67$	−5.63337	+	3.25243i	−0.688226	+	0.397347i	−0.802947	−	0.596050i	$-0.796736\pi$
$67$	−5.63337	+	3.25243i	−0.688226	+	0.397347i	0.114721	+	0.993398i	$0.463403\pi$
$68$		0			0
$69$	6.67385	−	13.6484i	0.803438	−	1.64308i
$70$		0			0
$71$		−	1.57299i		−	0.186679i	−0.995634	−	0.0933396i	$-0.970246\pi$
$71$		−	1.57299i		−	0.186679i	0.995634	−	0.0933396i	$-0.0297542\pi$
$72$		0			0
$73$	13.6347	+	7.87199i	1.59582	+	0.921346i	0.992281	+	0.124012i	$0.0395760\pi$
$73$	13.6347	+	7.87199i	1.59582	+	0.921346i	0.603538	+	0.797334i	$0.293757\pi$
$74$		0			0
$75$	1.55799	+	0.761828i	0.179901	+	0.0879684i
$76$		0			0
$77$	−2.02359	−	2.98324i	−0.230609	−	0.339971i
$78$		0			0
$79$	−5.16095	−	2.97967i	−0.580652	−	0.335240i	0.180740	−	0.983531i	$-0.442151\pi$
$79$	−5.16095	−	2.97967i	−0.580652	−	0.335240i	−0.761392	+	0.648291i	$0.775484\pi$
$80$		0			0
$81$	−2.21254	+	8.72380i	−0.245838	+	0.969311i
$82$		0			0
$83$	4.80565	+	8.32363i	0.527489	+	0.913637i	0.999487	+	0.0320377i	$0.0101997\pi$
$83$	4.80565	+	8.32363i	0.527489	+	0.913637i	−0.471998	+	0.881600i	$0.656467\pi$
$84$		0			0
$85$	1.00310	−	1.73743i	0.108802	−	0.188450i
$86$		0			0
$87$	0.203511	+	2.95317i	0.0218186	+	0.316613i
$88$		0			0
$89$	−1.10887	+	0.640207i	−0.117540	+	0.0678618i	−0.557617	−	0.830098i	$-0.688284\pi$
$89$	−1.10887	+	0.640207i	−0.117540	+	0.0678618i	0.440077	+	0.897960i	$0.354951\pi$
$90$		0			0
$91$	−5.21136	+	0.378111i	−0.546299	+	0.0396368i
$92$		0			0
$93$	−0.0621876	−	0.902414i	−0.00644856	−	0.0935759i
$94$		0			0
$95$	2.68215	−	1.54854i	0.275183	−	0.158877i
$96$		0			0
$97$	−8.31781	+	4.80229i	−0.844546	+	0.487599i	−0.858807	−	0.512299i	$-0.828794\pi$
$97$	−8.31781	+	4.80229i	−0.844546	+	0.487599i	0.0142608	+	0.999898i	$0.495460\pi$
$98$		0			0
$99$	3.22604	−	2.50999i	0.324229	−	0.252263i
$100$		0			0
$101$			11.2707i			1.12147i	0.827994	+	0.560737i	$0.189482\pi$
$101$			11.2707i			1.12147i	−0.827994	+	0.560737i	$0.810518\pi$
$102$		0			0
$103$	9.61201			0.947099			0.473550	−	0.880767i	$-0.342972\pi$
$103$	9.61201			0.947099			0.473550	+	0.880767i	$0.342972\pi$
$104$		0			0
$105$	−1.28991	−	9.07244i	−0.125882	−	0.885380i
$106$		0			0
$107$	11.0876	−	6.40144i	1.07188	−	0.618850i	0.143186	−	0.989696i	$-0.454265\pi$
$107$	11.0876	−	6.40144i	1.07188	−	0.618850i	0.928695	+	0.370845i	$0.120932\pi$
$108$		0			0
$109$	−7.28182	+	12.6125i	−0.697472	+	1.20806i	0.271869	+	0.962334i	$0.412358\pi$
$109$	−7.28182	+	12.6125i	−0.697472	+	1.20806i	−0.969340	+	0.245722i	$0.920975\pi$
$110$		0			0
$111$	0.366414	+	5.31709i	0.0347785	+	0.504676i
$112$		0			0
$113$	−9.07922	+	15.7257i	−0.854101	+	1.47935i	0.0233754	+	0.999727i	$0.492559\pi$
$113$	−9.07922	+	15.7257i	−0.854101	+	1.47935i	−0.877476	+	0.479620i	$0.840775\pi$
$114$		0			0
$115$	−17.5403			−1.63564
$116$		0			0
$117$	−0.812708	−	5.86866i	−0.0751349	−	0.542558i
$118$		0			0
$119$	2.64743	−	0.192084i	0.242689	−	0.0176083i
$120$		0			0
$121$	9.14363			0.831239
$122$		0			0
$123$	0.431938	+	0.641771i	0.0389465	+	0.0578665i
$124$		0			0
$125$		−	12.0006i		−	1.07337i
$126$		0			0
$127$			13.2304i			1.17401i	0.809585	+	0.587003i	$0.199692\pi$
$127$			13.2304i			1.17401i	−0.809585	+	0.587003i	$0.800308\pi$
$128$		0			0
$129$	−10.9717	+	0.756091i	−0.966008	+	0.0665701i
$130$		0			0
$131$	−8.54252			−0.746364			−0.373182	−	0.927758i	$-0.621733\pi$
$131$	−8.54252			−0.746364			−0.373182	+	0.927758i	$0.621733\pi$
$132$		0			0
$133$	3.68769	+	1.78668i	0.319763	+	0.154925i
$134$		0			0
$135$	10.1701	−	2.12955i	0.875300	−	0.183282i
$136$		0			0
$137$	−3.85512			−0.329365			−0.164683	−	0.986347i	$-0.552660\pi$
$137$	−3.85512			−0.329365			−0.164683	+	0.986347i	$0.552660\pi$
$138$		0			0
$139$	−7.59749	+	13.1592i	−0.644410	+	1.11615i	0.340027	+	0.940416i	$0.389564\pi$
$139$	−7.59749	+	13.1592i	−0.644410	+	1.11615i	−0.984437	+	0.175736i	$0.943770\pi$
$140$		0			0
$141$	−2.35580	+	1.58555i	−0.198394	+	0.133527i
$142$		0			0
$143$	−1.34538	+	2.33027i	−0.112506	+	0.194867i
$144$		0			0
$145$	2.95970	−	1.70878i	0.245790	−	0.141907i
$146$		0			0
$147$	8.97583	−	8.15073i	0.740314	−	0.672261i
$148$		0			0
$149$	11.5550			0.946626			0.473313	−	0.880894i	$-0.343058\pi$
$149$	11.5550			0.946626			0.473313	+	0.880894i	$0.343058\pi$
$150$		0			0
$151$		−	22.6580i		−	1.84388i	−0.387330	−	0.921941i	$-0.626603\pi$
$151$		−	22.6580i		−	1.84388i	0.387330	−	0.921941i	$-0.373397\pi$
$152$		0			0
$153$	0.412864	+	2.98134i	0.0333781	+	0.241027i
$154$		0			0
$155$	−0.904409	+	0.522161i	−0.0726439	+	0.0419409i
$156$		0			0
$157$	−12.6679	+	7.31381i	−1.01101	+	0.583706i	−0.911487	−	0.411330i	$-0.865064\pi$
$157$	−12.6679	+	7.31381i	−1.01101	+	0.583706i	−0.0995213	+	0.995035i	$0.531731\pi$
$158$		0			0
$159$	3.57254	−	2.40446i	0.283321	−	0.190686i
$160$		0			0
$161$	−13.0276	−	19.2058i	−1.02672	−	1.51363i
$162$		0			0
$163$	−10.4437	+	6.02970i	−0.818017	+	0.472282i	−0.849732	−	0.527215i	$-0.823236\pi$
$163$	−10.4437	+	6.02970i	−0.818017	+	0.472282i	0.0317152	+	0.999497i	$0.489903\pi$
$164$		0			0
$165$	−4.23935	−	2.07297i	−0.330033	−	0.161380i
$166$		0			0
$167$	11.0887	−	19.2062i	0.858069	−	1.48622i	−0.0156998	−	0.999877i	$-0.504998\pi$
$167$	11.0887	−	19.2062i	0.858069	−	1.48622i	0.873769	−	0.486342i	$-0.161669\pi$
$168$		0			0
$169$	−4.54991	−	7.88067i	−0.349993	−	0.606206i
$170$		0			0
$171$	−1.74926	+	4.30452i	−0.133769	+	0.329175i
$172$		0			0
$173$	−12.9649	−	7.48531i	−0.985706	−	0.569097i	−0.0817177	−	0.996656i	$-0.526041\pi$
$173$	−12.9649	−	7.48531i	−0.985706	−	0.569097i	−0.903988	+	0.427558i	$0.859374\pi$
$174$		0			0
$175$	2.19236	−	1.48712i	0.165727	−	0.112416i
$176$		0			0
$177$	−1.50376	−	21.8213i	−0.113030	−	1.64019i
$178$		0			0
$179$	−12.1951	−	7.04084i	−0.911505	−	0.526257i	−0.0305897	−	0.999532i	$-0.509739\pi$
$179$	−12.1951	−	7.04084i	−0.911505	−	0.526257i	−0.880915	+	0.473275i	$0.843072\pi$
$180$		0			0
$181$		−	4.70875i		−	0.349999i	−0.984569	−	0.174999i	$-0.944008\pi$
$181$		−	4.70875i		−	0.349999i	0.984569	−	0.174999i	$-0.0559924\pi$
$182$		0			0
$183$	10.1965	+	15.1499i	0.753745	+	1.11991i
$184$		0			0
$185$	5.32885	−	3.07661i	0.391785	−	0.226197i
$186$		0			0
$187$	0.683467	−	1.18380i	0.0499801	−	0.0865680i
$188$		0			0
$189$	9.88534	+	9.55406i	0.719053	+	0.694956i
$190$		0			0
$191$	7.47754	+	4.31716i	0.541056	+	0.312379i	0.745507	−	0.666498i	$-0.232207\pi$
$191$	7.47754	+	4.31716i	0.541056	+	0.312379i	−0.204451	+	0.978877i	$0.565541\pi$
$192$		0			0
$193$	−5.46399	−	9.46391i	−0.393307	−	0.681227i	0.599577	−	0.800317i	$-0.295336\pi$
$193$	−5.46399	−	9.46391i	−0.393307	−	0.681227i	−0.992883	+	0.119090i	$0.962002\pi$
$194$		0			0
$195$	−5.67457	+	3.81922i	−0.406364	+	0.273500i
$196$		0			0
$197$	−19.7147			−1.40461			−0.702305	−	0.711876i	$-0.747846\pi$
$197$	−19.7147			−1.40461			−0.702305	+	0.711876i	$0.747846\pi$
$198$		0			0
$199$	−13.3575	+	23.1359i	−0.946889	+	1.64006i	−0.194965	+	0.980810i	$0.562459\pi$
$199$	−13.3575	+	23.1359i	−0.946889	+	1.64006i	−0.751924	+	0.659249i	$0.770874\pi$
$200$		0			0
$201$	−11.2401	+	0.774583i	−0.792814	+	0.0546349i
$202$		0			0
$203$	4.06929	+	1.97157i	0.285608	+	0.138377i
$204$		0			0
$205$	0.446560	−	0.773465i	0.0311891	−	0.0540211i
$206$		0			0
$207$	20.7689	−	16.1590i	1.44354	−	1.12313i
$208$		0			0
$209$	1.82749	−	1.05510i	0.126410	−	0.0729831i
$210$		0			0
$211$	6.27293	+	3.62168i	0.431846	+	0.249327i	0.700133	−	0.714012i	$-0.253124\pi$
$211$	6.27293	+	3.62168i	0.431846	+	0.249327i	−0.268286	+	0.963339i	$0.586457\pi$
$212$		0			0
$213$	1.19681	−	2.44755i	0.0820041	−	0.167704i
$214$		0			0
$215$	6.34854	+	10.9960i	0.432967	+	0.749921i
$216$		0			0
$217$	−1.24347	−	0.602460i	−0.0844122	−	0.0408977i
$218$		0			0
$219$	15.2260	+	22.6227i	1.02888	+	1.52870i
$220$		0			0
$221$	−0.990667	−	1.71589i	−0.0666395	−	0.115423i
$222$		0			0
$223$	9.80779	+	16.9876i	0.656778	+	1.13757i	0.981445	+	0.191744i	$0.0614145\pi$
$223$	9.80779	+	16.9876i	0.656778	+	1.13757i	−0.324667	+	0.945828i	$0.605252\pi$
$224$		0			0
$225$	1.84457	+	2.37079i	0.122971	+	0.158053i
$226$		0			0
$227$	−20.7784			−1.37911			−0.689557	−	0.724231i	$-0.742195\pi$
$227$	−20.7784			−1.37911			−0.689557	+	0.724231i	$0.742195\pi$
$228$		0			0
$229$			22.1275i			1.46223i	0.682256	+	0.731113i	$0.260999\pi$
$229$			22.1275i			1.46223i	−0.682256	+	0.731113i	$0.739001\pi$
$230$		0			0
$231$	−0.878881	−	6.18153i	−0.0578261	−	0.406715i
$232$		0			0
$233$	−1.95965	−	3.39421i	−0.128381	−	0.222362i	0.794669	−	0.607043i	$-0.207645\pi$
$233$	−1.95965	−	3.39421i	−0.128381	−	0.222362i	−0.923049	+	0.384681i	$0.874311\pi$
$234$		0			0
$235$	2.83922	+	1.63922i	0.185210	+	0.106931i
$236$		0			0
$237$	−5.76329	−	8.56306i	−0.374366	−	0.556231i
$238$		0			0
$239$	−7.38657	−	4.26464i	−0.477798	−	0.275857i	0.241701	−	0.970351i	$-0.422295\pi$
$239$	−7.38657	−	4.26464i	−0.477798	−	0.275857i	−0.719498	+	0.694494i	$0.755628\pi$
$240$		0			0
$241$			2.42227i			0.156032i	0.996952	+	0.0780161i	$0.0248586\pi$
$241$			2.42227i			0.156032i	−0.996952	+	0.0780161i	$0.975141\pi$
$242$		0			0
$243$	−10.0802	+	11.8907i	−0.646646	+	0.762791i
$244$		0			0
$245$	−13.0057	−	5.17570i	−0.830906	−	0.330664i
$246$		0			0
$247$		−	3.05869i		−	0.194620i
$248$		0			0
$249$	1.14449	+	16.6079i	0.0725292	+	1.05248i
$250$		0			0
$251$	1.09792			0.0693002			0.0346501	−	0.999400i	$-0.488968\pi$
$251$	1.09792			0.0693002			0.0346501	+	0.999400i	$0.488968\pi$
$252$		0			0
$253$	−11.9511			−0.751361
$254$		0			0
$255$	2.88274	−	1.94020i	0.180524	−	0.121500i
$256$		0			0
$257$			21.0489i			1.31300i	0.754328	+	0.656498i	$0.227963\pi$
$257$			21.0489i			1.31300i	−0.754328	+	0.656498i	$0.772037\pi$
$258$		0			0
$259$	7.32662	+	3.54974i	0.455254	+	0.220570i
$260$		0			0
$261$	−1.93027	+	4.74995i	−0.119481	+	0.294014i
$262$		0			0
$263$		−	24.4623i		−	1.50841i	−0.656638	−	0.754206i	$-0.728022\pi$
$263$		−	24.4623i		−	1.50841i	0.656638	−	0.754206i	$-0.271978\pi$
$264$		0			0
$265$	−4.30564	−	2.48586i	−0.264493	−	0.152705i
$266$		0			0
$267$	−2.21249	+	0.152469i	−0.135402	+	0.00933093i
$268$		0			0
$269$	−9.79690	−	5.65624i	−0.597327	−	0.344867i	0.170662	−	0.985330i	$-0.445409\pi$
$269$	−9.79690	−	5.65624i	−0.597327	−	0.344867i	−0.767989	+	0.640462i	$0.778743\pi$
$270$		0			0
$271$	−0.480849	−	0.832856i	−0.0292095	−	0.0505924i	0.851051	−	0.525083i	$-0.175966\pi$
$271$	−0.480849	−	0.832856i	−0.0292095	−	0.0505924i	−0.880261	+	0.474490i	$0.842632\pi$
$272$		0			0
$273$	−8.39651	−	3.37674i	−0.508180	−	0.204370i
$274$		0			0
$275$		−	1.36424i		−	0.0822665i
$276$		0			0
$277$	−25.0498			−1.50510			−0.752549	−	0.658536i	$-0.771176\pi$
$277$	−25.0498			−1.50510			−0.752549	+	0.658536i	$0.771176\pi$
$278$		0			0
$279$	0.589840	−	1.45146i	0.0353128	−	0.0868967i
$280$		0			0
$281$	11.0324	+	19.1087i	0.658139	+	1.13993i	0.981097	+	0.193517i	$0.0619896\pi$
$281$	11.0324	+	19.1087i	0.658139	+	1.13993i	−0.322958	+	0.946413i	$0.604677\pi$
$282$		0			0
$283$	−2.63432	−	4.56278i	−0.156594	−	0.271229i	0.777044	−	0.629446i	$-0.216718\pi$
$283$	−2.63432	−	4.56278i	−0.156594	−	0.271229i	−0.933638	+	0.358217i	$0.883385\pi$
$284$		0			0
$285$	5.35162	−	0.368794i	0.317002	−	0.0218455i
$286$		0			0
$287$	1.17858	−	0.0855118i	0.0695693	−	0.00504760i
$288$		0			0
$289$	−7.99673	−	13.8507i	−0.470396	−	0.814750i
$290$		0			0
$291$	−16.5963	+	1.14369i	−0.972890	+	0.0670444i
$292$		0			0
$293$	12.1084	+	6.99080i	0.707381	+	0.408407i	0.810091	−	0.586305i	$-0.199418\pi$
$293$	12.1084	+	6.99080i	0.707381	+	0.408407i	−0.102709	+	0.994711i	$0.532751\pi$
$294$		0			0
$295$	−21.8696	+	12.6264i	−1.27329	+	0.735137i
$296$		0			0
$297$	6.92941	−	1.45097i	0.402085	−	0.0841941i
$298$		0			0
$299$	−8.66142	+	15.0020i	−0.500903	+	0.867589i
$300$		0			0
$301$	−7.32485	+	15.1184i	−0.422197	+	0.871409i
$302$		0			0
$303$	−8.57532	+	17.5371i	−0.492639	+	1.00748i
$304$		0			0
$305$	10.5416	−	18.2587i	0.603613	−	1.04549i
$306$		0			0
$307$	16.2755			0.928893			0.464446	−	0.885601i	$-0.346253\pi$
$307$	16.2755			0.928893			0.464446	+	0.885601i	$0.346253\pi$
$308$		0			0
$309$	14.9562	+	7.31332i	0.850828	+	0.416040i
$310$		0			0
$311$	−3.19487	−	5.53367i	−0.181164	−	0.313786i	0.761113	−	0.648619i	$-0.224653\pi$
$311$	−3.19487	−	5.53367i	−0.181164	−	0.313786i	−0.942277	+	0.334834i	$0.891320\pi$
$312$		0			0
$313$	22.2074	+	12.8215i	1.25524	+	0.724711i	0.972145	−	0.234382i	$-0.0753065\pi$
$313$	22.2074	+	12.8215i	1.25524	+	0.724711i	0.283092	+	0.959093i	$0.408640\pi$
$314$		0			0
$315$	4.89571	−	15.0981i	0.275842	−	0.850679i
$316$		0			0
$317$	−14.6521	+	25.3782i	−0.822945	+	1.42538i	0.0805354	+	0.996752i	$0.474337\pi$
$317$	−14.6521	+	25.3782i	−0.822945	+	1.42538i	−0.903480	+	0.428630i	$0.858996\pi$
$318$		0			0
$319$	2.01660	−	1.16429i	0.112908	−	0.0651875i
$320$		0			0
$321$	22.1228	−	1.52454i	1.23477	−	0.0850913i
$322$		0			0
$323$			1.55385i			0.0864583i
$324$		0			0
$325$	−1.71250	−	0.988711i	−0.0949923	−	0.0548438i
$326$		0			0
$327$	−20.9267	+	14.0845i	−1.15725	+	0.778875i
$328$		0			0
$329$	0.313895	+	4.32630i	0.0173056	+	0.238517i
$330$		0			0
$331$	−0.115780	−	0.0668456i	−0.00636384	−	0.00367417i	0.496815	−	0.867857i	$-0.334503\pi$
$331$	−0.115780	−	0.0668456i	−0.00636384	−	0.00367417i	−0.503179	+	0.864182i	$0.667836\pi$
$332$		0			0
$333$	−3.47538	+	8.55213i	−0.190450	+	0.468654i
$334$		0			0
$335$	6.50381	+	11.2649i	0.355341	+	0.615469i
$336$		0			0
$337$	9.96606	−	17.2617i	0.542886	−	0.940306i	−0.455851	−	0.890056i	$-0.650665\pi$
$337$	9.96606	−	17.2617i	0.542886	−	0.940306i	0.998737	−	0.0502498i	$-0.0160017\pi$
$338$		0			0
$339$	−26.0921	+	17.5610i	−1.41713	+	0.953785i
$340$		0			0
$341$	−0.616222	+	0.355776i	−0.0333703	+	0.0192663i
$342$		0			0
$343$	−3.99257	−	18.0848i	−0.215579	−	0.976486i
$344$		0			0
$345$	−27.2925	−	13.3456i	−1.46938	−	0.718501i
$346$		0			0
$347$	4.81148	−	2.77791i	0.258294	−	0.149126i	−0.365262	−	0.930905i	$-0.619021\pi$
$347$	4.81148	−	2.77791i	0.258294	−	0.149126i	0.623556	+	0.781779i	$0.285687\pi$
$348$		0			0
$349$	−0.710293	+	0.410088i	−0.0380211	+	0.0219515i	−0.518890	−	0.854841i	$-0.673655\pi$
$349$	−0.710293	+	0.410088i	−0.0380211	+	0.0219515i	0.480869	+	0.876792i	$0.340321\pi$
$350$		0			0
$351$	3.20062	−	9.74992i	0.170836	−	0.520412i
$352$		0			0
$353$			21.4172i			1.13992i	0.821671	+	0.569962i	$0.193042\pi$
$353$			21.4172i			1.13992i	−0.821671	+	0.569962i	$0.806958\pi$
$354$		0			0
$355$	−3.14547			−0.166944
$356$		0			0
$357$	4.26552	+	1.71542i	0.225755	+	0.0907896i
$358$		0			0
$359$	−5.64573	+	3.25956i	−0.297970	+	0.172033i	−0.641531	−	0.767097i	$-0.721700\pi$
$359$	−5.64573	+	3.25956i	−0.297970	+	0.172033i	0.343560	+	0.939131i	$0.388367\pi$
$360$		0			0
$361$	8.30062	−	14.3771i	0.436875	−	0.756689i
$362$		0			0
$363$	14.2274	+	6.95695i	0.746744	+	0.365145i
$364$		0			0
$365$	15.7414	−	27.2650i	0.823945	−	1.42711i
$366$		0			0
$367$	13.1692			0.687426			0.343713	−	0.939075i	$-0.388315\pi$
$367$	13.1692			0.687426			0.343713	+	0.939075i	$0.388315\pi$
$368$		0			0
$369$	0.183798	+	1.32723i	0.00956816	+	0.0690928i
$370$		0			0
$371$	−0.476018	−	6.56078i	−0.0247136	−	0.340619i
$372$		0			0
$373$	29.4869			1.52678			0.763388	−	0.645941i	$-0.223535\pi$
$373$	29.4869			1.52678			0.763388	+	0.645941i	$0.223535\pi$
$374$		0			0
$375$	9.13071	−	18.6729i	0.471508	−	0.964263i
$376$		0			0
$377$		−	3.37520i		−	0.173832i
$378$		0			0
$379$		−	25.2566i		−	1.29735i	−0.761067	−	0.648673i	$-0.775324\pi$
$379$		−	25.2566i		−	1.29735i	0.761067	−	0.648673i	$-0.224676\pi$
$380$		0			0
$381$	−10.0664	+	20.5863i	−0.515715	+	1.05467i
$382$		0			0
$383$	−5.22545			−0.267008			−0.133504	−	0.991048i	$-0.542623\pi$
$383$	−5.22545			−0.267008			−0.133504	+	0.991048i	$0.542623\pi$
$384$		0			0
$385$	−5.96551	+	4.04653i	−0.304031	+	0.206230i
$386$		0			0
$387$	−17.6472	−	7.17141i	−0.897057	−	0.364543i
$388$		0			0
$389$	−25.9660			−1.31653			−0.658264	−	0.752787i	$-0.728709\pi$
$389$	−25.9660			−1.31653			−0.658264	+	0.752787i	$0.728709\pi$
$390$		0			0
$391$	4.40009	−	7.62118i	0.222522	−	0.385420i
$392$		0			0
$393$	−13.2921	−	6.49960i	−0.670497	−	0.327861i
$394$		0			0
$395$	−5.95839	+	10.3202i	−0.299799	+	0.519268i
$396$		0			0
$397$	12.5913	−	7.26961i	0.631941	−	0.364851i	−0.149562	−	0.988752i	$-0.547786\pi$
$397$	12.5913	−	7.26961i	0.631941	−	0.364851i	0.781503	+	0.623901i	$0.214453\pi$
$398$		0			0
$399$	4.37860	+	5.58585i	0.219204	+	0.279642i
$400$		0			0
$401$	13.7228			0.685282			0.342641	−	0.939466i	$-0.388679\pi$
$401$	13.7228			0.685282			0.342641	+	0.939466i	$0.388679\pi$
$402$		0			0
$403$			1.03137i			0.0513764i
$404$		0			0
$405$	17.4448	+	4.42437i	0.866839	+	0.219848i
$406$		0			0
$407$	3.63082	−	2.09626i	0.179973	−	0.103908i
$408$		0			0
$409$	8.66188	−	5.00094i	0.428303	−	0.247281i	−0.270321	−	0.962770i	$-0.587130\pi$
$409$	8.66188	−	5.00094i	0.428303	−	0.247281i	0.698623	+	0.715490i	$0.253796\pi$
$410$		0			0
$411$	−5.99853	−	2.93318i	−0.295886	−	0.144683i
$412$		0			0
$413$	−30.0684	−	14.5681i	−1.47957	−	0.716851i
$414$		0			0
$415$	16.6446	−	9.60976i	0.817051	−	0.471725i
$416$		0			0
$417$	−21.8338	+	14.6951i	−1.06921	+	0.719621i
$418$		0			0
$419$	−3.51452	+	6.08732i	−0.171695	+	0.297385i	−0.939013	−	0.343882i	$-0.888258\pi$
$419$	−3.51452	+	6.08732i	−0.171695	+	0.297385i	0.767317	+	0.641268i	$0.221591\pi$
$420$		0			0
$421$	−3.01107	−	5.21533i	−0.146751	−	0.254179i	0.783274	−	0.621676i	$-0.213548\pi$
$421$	−3.01107	−	5.21533i	−0.146751	−	0.254179i	−0.930025	+	0.367497i	$0.880215\pi$
$422$		0			0
$423$	−4.87196	+	0.674683i	−0.236883	+	0.0328042i
$424$		0			0
$425$	0.869967	+	0.502276i	0.0421996	+	0.0243639i
$426$		0			0
$427$	27.8219	−	2.01862i	1.34640	−	0.0976879i
$428$		0			0
$429$	−3.86639	+	2.60224i	−0.186671	+	0.125637i
$430$		0			0
$431$	−14.3683	−	8.29555i	−0.692097	−	0.399582i	0.112300	−	0.993674i	$-0.464178\pi$
$431$	−14.3683	−	8.29555i	−0.692097	−	0.399582i	−0.804397	+	0.594092i	$0.797512\pi$
$432$		0			0
$433$			6.42380i			0.308708i	0.988016	+	0.154354i	$0.0493297\pi$
$433$			6.42380i			0.308708i	−0.988016	+	0.154354i	$0.950670\pi$
$434$		0			0
$435$	5.90540	−	0.406956i	0.283142	−	0.0195121i
$436$		0			0
$437$	11.7652	−	6.79265i	0.562807	−	0.324937i
$438$		0			0
$439$	−2.23155	+	3.86517i	−0.106506	+	0.184474i	−0.914353	−	0.404919i	$-0.867300\pi$
$439$	−2.23155	+	3.86517i	−0.106506	+	0.184474i	0.807846	+	0.589393i	$0.200633\pi$
$440$		0			0
$441$	20.1678	−	5.85318i	0.960372	−	0.278723i
$442$		0			0
$443$	23.8533	+	13.7717i	1.13331	+	0.654315i	0.944764	−	0.327751i	$-0.106291\pi$
$443$	23.8533	+	13.7717i	1.13331	+	0.654315i	0.188542	+	0.982065i	$0.439624\pi$
$444$		0			0
$445$	1.28021	+	2.21739i	0.0606877	+	0.105114i
$446$		0			0
$447$	17.9795	+	8.79167i	0.850402	+	0.415832i
$448$		0			0
$449$	38.3329			1.80904			0.904520	−	0.426432i	$-0.140229\pi$
$449$	38.3329			1.80904			0.904520	+	0.426432i	$0.140229\pi$
$450$		0			0
$451$	0.304265	−	0.527003i	0.0143273	−	0.0248156i
$452$		0			0
$453$	17.2394	−	35.2556i	0.809977	−	1.65645i
$454$		0			0
$455$	0.756100	+	10.4211i	0.0354465	+	0.488547i
$456$		0			0
$457$	17.1583	−	29.7190i	0.802629	−	1.39019i	−0.115250	−	0.993336i	$-0.536767\pi$
$457$	17.1583	−	29.7190i	0.802629	−	1.39019i	0.917880	−	0.396858i	$-0.129900\pi$
$458$		0			0
$459$	−1.62595	+	4.95306i	−0.0758927	+	0.231189i
$460$		0			0
$461$	13.9331	−	8.04429i	0.648930	−	0.374660i	−0.139116	−	0.990276i	$-0.544426\pi$
$461$	13.9331	−	8.04429i	0.648930	−	0.374660i	0.788046	+	0.615616i	$0.211093\pi$
$462$		0			0
$463$	−15.7583	−	9.09805i	−0.732349	−	0.422822i	0.0869318	−	0.996214i	$-0.472294\pi$
$463$	−15.7583	−	9.09805i	−0.732349	−	0.422822i	−0.819281	+	0.573392i	$0.805627\pi$
$464$		0			0
$465$	−1.80454	+	0.124355i	−0.0836834	+	0.00576684i
$466$		0			0
$467$	7.08122	+	12.2650i	0.327680	+	0.567558i	0.982051	−	0.188615i	$-0.0603999\pi$
$467$	7.08122	+	12.2650i	0.327680	+	0.567558i	−0.654371	+	0.756173i	$0.727067\pi$
$468$		0			0
$469$	−7.50399	+	15.4881i	−0.346502	+	0.715175i
$470$		0			0
$471$	−25.2758	+	1.74182i	−1.16465	+	0.0802590i
$472$		0			0
$473$	4.32560	+	7.49216i	0.198891	+	0.344490i
$474$		0			0
$475$	0.775389	+	1.34301i	0.0355773	+	0.0616217i
$476$		0			0
$477$	7.38827	−	1.02315i	0.338286	−	0.0468467i
$478$		0			0
$479$	33.7963			1.54419			0.772096	−	0.635506i	$-0.219208\pi$
$479$	33.7963			1.54419			0.772096	+	0.635506i	$0.219208\pi$
$480$		0			0
$481$		−	6.07694i		−	0.277084i
$482$		0			0
$483$	−5.65815	−	39.7961i	−0.257455	−	1.81078i
$484$		0			0
$485$	9.60304	+	16.6330i	0.436052	+	0.755264i
$486$		0			0
$487$	−9.41218	−	5.43412i	−0.426506	−	0.246244i	0.271351	−	0.962481i	$-0.412530\pi$
$487$	−9.41218	−	5.43412i	−0.426506	−	0.246244i	−0.697857	+	0.716237i	$0.745863\pi$
$488$		0			0
$489$	−20.8381	+	1.43600i	−0.942330	+	0.0649384i
$490$		0			0
$491$	29.3930	+	16.9701i	1.32649	+	0.765848i	0.984755	−	0.173949i	$-0.0556529\pi$
$491$	29.3930	+	16.9701i	1.32649	+	0.765848i	0.341733	+	0.939797i	$0.388986\pi$
$492$		0			0
$493$			1.71464i			0.0772234i
$494$		0			0
$495$	−5.01917	−	6.45104i	−0.225595	−	0.289953i
$496$		0			0
$497$	−2.33623	−	3.44414i	−0.104794	−	0.154491i
$498$		0			0
$499$		−	2.97182i		−	0.133037i	−0.997785	−	0.0665185i	$-0.978811\pi$
$499$		−	2.97182i		−	0.133037i	0.997785	−	0.0665185i	$-0.0211891\pi$
$500$		0			0
$501$	31.8670	−	21.4478i	1.42371	−	0.958215i
$502$		0			0
$503$	−26.0651			−1.16219			−0.581093	−	0.813837i	$-0.697375\pi$
$503$	−26.0651			−1.16219			−0.581093	+	0.813837i	$0.697375\pi$
$504$		0			0
$505$	22.5377			1.00292
$506$		0			0
$507$	−1.08358	−	15.7241i	−0.0481237	−	0.698330i
$508$		0			0
$509$		−	17.7599i		−	0.787195i	−0.919283	−	0.393598i	$-0.871230\pi$
$509$		−	17.7599i		−	0.787195i	0.919283	−	0.393598i	$-0.128770\pi$
$510$		0			0
$511$	41.5454	−	3.01433i	1.83786	−	0.133346i
$512$		0			0
$513$	−5.99693	+	5.36686i	−0.264771	+	0.236953i
$514$		0			0
$515$		−	19.2209i		−	0.846976i
$516$		0			0
$517$	1.93451	+	1.11689i	0.0850796	+	0.0491207i
$518$		0			0
$519$	−14.4781	−	21.5115i	−0.635518	−	0.944248i
$520$		0			0
$521$	24.9679	+	14.4152i	1.09387	+	0.631543i	0.934603	−	0.355693i	$-0.115755\pi$
$521$	24.9679	+	14.4152i	1.09387	+	0.631543i	0.159262	+	0.987236i	$0.449088\pi$
$522$		0			0
$523$	−6.32766	−	10.9598i	−0.276689	−	0.479240i	0.693871	−	0.720100i	$-0.255904\pi$
$523$	−6.32766	−	10.9598i	−0.276689	−	0.479240i	−0.970560	+	0.240860i	$0.922571\pi$
$524$		0			0
$525$	4.54277	−	0.645884i	0.198263	−	0.0281887i
$526$		0			0
$527$		−	0.523949i		−	0.0228236i
$528$		0			0
$529$	−53.9401			−2.34522
$530$		0			0
$531$	14.2629	−	35.0979i	0.618959	−	1.52312i
$532$		0			0
$533$	−0.441024	−	0.763876i	−0.0191029	−	0.0330871i
$534$		0			0
$535$	−12.8008	−	22.1717i	−0.553428	−	0.958565i
$536$		0			0
$537$	−13.6184	−	20.2341i	−0.587678	−	0.873168i
$538$		0			0
$539$	−8.86150	−	3.52648i	−0.381692	−	0.151896i
$540$		0			0
$541$	−7.29665	−	12.6382i	−0.313708	−	0.543358i	0.665454	−	0.746439i	$-0.268238\pi$
$541$	−7.29665	−	12.6382i	−0.313708	−	0.543358i	−0.979162	+	0.203081i	$0.934905\pi$
$542$		0			0
$543$	3.58266	−	7.32677i	0.153747	−	0.314422i
$544$		0			0
$545$	25.2209	+	14.5613i	1.08035	+	0.623738i
$546$		0			0
$547$	5.61933	−	3.24432i	0.240265	−	0.138717i	−0.375033	−	0.927011i	$-0.622369\pi$
$547$	5.61933	−	3.24432i	0.240265	−	0.138717i	0.615299	+	0.788294i	$0.289035\pi$
$548$		0			0
$549$	4.33881	+	31.3310i	0.185176	+	1.33718i
$550$		0			0
$551$	−1.32349	+	2.29235i	−0.0563825	+	0.0976573i
$552$		0			0
$553$	−15.7256	+	1.14097i	−0.668721	+	0.0485191i
$554$		0			0
$555$	10.6325	−	0.732711i	0.451323	−	0.0311019i
$556$		0			0
$557$	18.2102	−	31.5410i	0.771590	−	1.33643i	−0.165101	−	0.986277i	$-0.552795\pi$
$557$	18.2102	−	31.5410i	0.771590	−	1.33643i	0.936691	−	0.350157i	$-0.113872\pi$
$558$		0			0
$559$	12.5397			0.530372
$560$		0			0
$561$	1.96416	−	1.32196i	0.0829271	−	0.0558133i
$562$		0			0
$563$	−3.77699	−	6.54194i	−0.159181	−	0.275710i	0.775392	−	0.631480i	$-0.217552\pi$
$563$	−3.77699	−	6.54194i	−0.159181	−	0.275710i	−0.934574	+	0.355770i	$0.884219\pi$
$564$		0			0
$565$	31.4463	+	18.1555i	1.32296	+	0.763809i
$566$		0			0
$567$	8.11226	+	22.3873i	0.340683	+	0.940178i
$568$		0			0
$569$	−11.9165	+	20.6399i	−0.499564	+	0.865270i	−1.00000		0.000503808i	$-0.999840\pi$
$569$	−11.9165	+	20.6399i	−0.499564	+	0.865270i	0.500436	+	0.865773i	$0.333173\pi$
$570$		0			0
$571$	−16.5695	+	9.56639i	−0.693411	+	0.400341i	−0.804889	−	0.593426i	$-0.797775\pi$
$571$	−16.5695	+	9.56639i	−0.693411	+	0.400341i	0.111478	+	0.993767i	$0.464442\pi$
$572$		0			0
$573$	8.35026	+	12.4068i	0.348837	+	0.518300i
$574$		0			0
$575$		−	8.78281i		−	0.366268i
$576$		0			0
$577$	0.278675	+	0.160893i	0.0116014	+	0.00669808i	0.505789	−	0.862657i	$-0.331201\pi$
$577$	0.278675	+	0.160893i	0.0116014	+	0.00669808i	−0.494188	+	0.869355i	$0.664535\pi$
$578$		0			0
$579$	−1.30128	−	18.8830i	−0.0540793	−	0.784752i
$580$		0			0
$581$	22.8846	+	11.0876i	0.949414	+	0.459991i
$582$		0			0
$583$	−2.93366	−	1.69375i	−0.121500	−	0.0701479i
$584$		0			0
$585$	−11.7354	+	1.62516i	−0.485200	+	0.0671919i
$586$		0			0
$587$	22.9285	+	39.7134i	0.946362	+	1.63915i	0.753001	+	0.658019i	$0.228605\pi$
$587$	22.9285	+	39.7134i	0.946362	+	1.63915i	0.193360	+	0.981128i	$0.438061\pi$
$588$		0			0
$589$	0.404424	−	0.700483i	0.0166640	−	0.0288629i
$590$		0			0
$591$	−30.6758	−	14.9999i	−1.26183	−	0.617015i
$592$		0			0
$593$	−24.8195	+	14.3295i	−1.01921	+	0.588443i	−0.913876	−	0.405993i	$-0.866926\pi$
$593$	−24.8195	+	14.3295i	−1.01921	+	0.588443i	−0.105338	+	0.994437i	$0.533592\pi$
$594$		0			0
$595$	−0.384107	−	5.29401i	−0.0157468	−	0.217033i
$596$		0			0
$597$	−38.3871	+	25.8361i	−1.57108	+	1.05740i
$598$		0			0
$599$	−21.1787	+	12.2275i	−0.865339	+	0.499604i	−0.865797	−	0.500396i	$-0.833188\pi$
$599$	−21.1787	+	12.2275i	−0.865339	+	0.499604i	0.000457342		1.00000i	$0.499854\pi$
$600$		0			0
$601$	6.86788	−	3.96517i	0.280147	−	0.161743i	−0.353343	−	0.935494i	$-0.614955\pi$
$601$	6.86788	−	3.96517i	0.280147	−	0.161743i	0.633490	+	0.773751i	$0.281622\pi$
$602$		0			0
$603$	−18.0788	−	7.34680i	−0.736226	−	0.299185i
$604$		0			0
$605$		−	18.2843i		−	0.743363i
$606$		0			0
$607$	4.90473			0.199077			0.0995384	−	0.995034i	$-0.468263\pi$
$607$	4.90473			0.199077			0.0995384	+	0.995034i	$0.468263\pi$
$608$		0			0
$609$	4.83170	+	6.16387i	0.195790	+	0.249772i
$610$		0			0
$611$	2.80402	−	1.61890i	0.113438	−	0.0654937i
$612$		0			0
$613$	9.53276	−	16.5112i	0.385025	−	0.666882i	−0.606748	−	0.794894i	$-0.707526\pi$
$613$	9.53276	−	16.5112i	0.385025	−	0.666882i	0.991773	+	0.128012i	$0.0408596\pi$
$614$		0			0
$615$	1.28334	−	0.863737i	0.0517491	−	0.0348292i
$616$		0			0
$617$	21.2636	−	36.8296i	0.856040	−	1.48270i	−0.0196377	−	0.999807i	$-0.506251\pi$
$617$	21.2636	−	36.8296i	0.856040	−	1.48270i	0.875677	−	0.482897i	$-0.160415\pi$
$618$		0			0
$619$	12.5249			0.503416			0.251708	−	0.967803i	$-0.419008\pi$
$619$	12.5249			0.503416			0.251708	+	0.967803i	$0.419008\pi$
$620$		0			0
$621$	44.6108	−	9.34122i	1.79017	−	0.374850i
$622$		0			0
$623$	−1.47708	+	3.04868i	−0.0591781	+	0.122143i
$624$		0			0
$625$	−18.9910			−0.759641
$626$		0			0
$627$	3.64634	−	0.251279i	0.145621	−	0.0100351i
$628$		0			0
$629$			3.08715i			0.123093i
$630$		0			0
$631$		−	17.8526i		−	0.710700i	−0.934733	−	0.355350i	$-0.884362\pi$
$631$		−	17.8526i		−	0.710700i	0.934733	−	0.355350i	$-0.115638\pi$
$632$		0			0
$633$	7.00506	+	10.4081i	0.278426	+	0.413684i
$634$		0			0
$635$	26.4565			1.04989
$636$		0			0
$637$	−10.8490	+	8.56789i	−0.429852	+	0.339472i
$638$		0			0
$639$	3.72445	−	2.89777i	0.147337	−	0.114634i
$640$		0			0
$641$	39.1443			1.54611			0.773054	−	0.634340i	$-0.218728\pi$
$641$	39.1443			1.54611			0.773054	+	0.634340i	$0.218728\pi$
$642$		0			0
$643$	2.93372	−	5.08136i	0.115695	−	0.200389i	−0.802363	−	0.596837i	$-0.796424\pi$
$643$	2.93372	−	5.08136i	0.115695	−	0.200389i	0.918057	+	0.396448i	$0.129757\pi$
$644$		0			0
$645$	1.51194	+	21.9400i	0.0595326	+	0.863886i
$646$		0			0
$647$	−19.5795	+	33.9127i	−0.769750	+	1.33325i	0.167949	+	0.985796i	$0.446286\pi$
$647$	−19.5795	+	33.9127i	−0.769750	+	1.33325i	−0.937699	+	0.347450i	$0.887048\pi$
$648$		0			0
$649$	−14.9009	+	8.60303i	−0.584911	+	0.337698i
$650$		0			0
$651$	−1.47644	−	1.88352i	−0.0578663	−	0.0738209i
$652$		0			0
$653$	27.2522			1.06646			0.533231	−	0.845969i	$-0.320978\pi$
$653$	27.2522			1.06646			0.533231	+	0.845969i	$0.320978\pi$
$654$		0			0
$655$			17.0823i			0.667461i
$656$		0			0
$657$	6.47898	+	46.7854i	0.252769	+	1.82527i
$658$		0			0
$659$	−18.1766	+	10.4943i	−0.708061	+	0.408799i	−0.810343	−	0.585956i	$-0.800719\pi$
$659$	−18.1766	+	10.4943i	−0.708061	+	0.408799i	0.102282	+	0.994755i	$0.467386\pi$
$660$		0			0
$661$	−1.82514	+	1.05375i	−0.0709899	+	0.0409860i	−0.535075	−	0.844805i	$-0.679717\pi$
$661$	−1.82514	+	1.05375i	−0.0709899	+	0.0409860i	0.464085	+	0.885791i	$0.346383\pi$
$662$		0			0
$663$	−0.235933	−	3.42365i	−0.00916286	−	0.132964i
$664$		0			0
$665$	3.57279	−	7.37419i	0.138547	−	0.285959i
$666$		0			0
$667$	12.9827	−	7.49555i	0.502691	−	0.290229i
$668$		0			0
$669$	2.33578	+	33.8948i	0.0903063	+	1.31045i
$670$		0			0
$671$	7.18258	−	12.4406i	0.277281	−	0.480264i
$672$		0			0
$673$	3.40292	+	5.89403i	0.131173	+	0.227198i	0.924129	−	0.382081i	$-0.124792\pi$
$673$	3.40292	+	5.89403i	0.131173	+	0.227198i	−0.792956	+	0.609279i	$0.791459\pi$
$674$		0			0
$675$	1.06631	+	5.09238i	0.0410424	+	0.196006i
$676$		0			0
$677$	−37.5390	−	21.6732i	−1.44274	−	0.832967i	−0.444709	−	0.895675i	$-0.646693\pi$
$677$	−37.5390	−	21.6732i	−1.44274	−	0.832967i	−0.998032	+	0.0627082i	$0.980026\pi$
$678$		0			0
$679$	−11.0798	+	22.8686i	−0.425205	+	0.877617i
$680$		0			0
$681$	−32.3311	−	15.8093i	−1.23893	−	0.605815i
$682$		0			0
$683$	−25.2674	−	14.5882i	−0.966832	−	0.558201i	−0.0685629	−	0.997647i	$-0.521841\pi$
$683$	−25.2674	−	14.5882i	−0.966832	−	0.558201i	−0.898269	+	0.439446i	$0.855175\pi$
$684$		0			0
$685$			7.70901i			0.294546i
$686$		0			0
$687$	−16.8358	+	34.4302i	−0.642324	+	1.31359i
$688$		0			0
$689$	−4.25226	+	2.45504i	−0.161998	+	0.0935297i
$690$		0			0
$691$	23.5987	−	40.8741i	0.897736	−	1.55493i	0.0673555	−	0.997729i	$-0.478544\pi$
$691$	23.5987	−	40.8741i	0.897736	−	1.55493i	0.830381	−	0.557196i	$-0.188123\pi$
$692$		0			0
$693$	3.33570	−	10.2871i	0.126713	−	0.390775i
$694$		0			0
$695$	26.3142	+	15.1925i	0.998156	+	0.576286i
$696$		0			0
$697$	0.224045	+	0.388057i	0.00848630	+	0.0146987i
$698$		0			0
$699$	−0.466700	−	6.77236i	−0.0176522	−	0.256154i
$700$		0			0
$701$	14.7459			0.556946			0.278473	−	0.960444i	$-0.410172\pi$
$701$	14.7459			0.556946			0.278473	+	0.960444i	$0.410172\pi$
$702$		0			0
$703$	−2.38290	+	4.12730i	−0.0898726	+	0.155664i
$704$		0			0
$705$	3.17059	+	4.71084i	0.119411	+	0.177420i
$706$		0			0
$707$	16.7394	+	24.6777i	0.629549	+	0.928101i
$708$		0			0
$709$	14.6710	−	25.4109i	0.550981	−	0.954327i	−0.447223	−	0.894422i	$-0.647587\pi$
$709$	14.6710	−	25.4109i	0.550981	−	0.954327i	0.998204	−	0.0599043i	$-0.0190796\pi$
$710$		0			0
$711$	−2.45240	−	17.7090i	−0.0919721	−	0.664141i
$712$		0			0
$713$	−3.96717	+	2.29045i	−0.148572	+	0.0857779i
$714$		0			0
$715$	4.65978	+	2.69033i	0.174266	+	0.100613i
$716$		0			0
$717$	−8.24867	−	12.2558i	−0.308052	−	0.457702i
$718$		0			0
$719$	19.0100	+	32.9262i	0.708952	+	1.22794i	0.965246	+	0.261342i	$0.0841651\pi$
$719$	19.0100	+	32.9262i	0.708952	+	1.22794i	−0.256294	+	0.966599i	$0.582502\pi$
$720$		0			0
$721$	21.0460	−	14.2759i	0.783793	−	0.531663i
$722$		0			0
$723$	−1.84299	+	3.76903i	−0.0685416	+	0.140172i
$724$		0			0
$725$	0.855626	+	1.48199i	0.0317772	+	0.0550396i
$726$		0			0
$727$	1.33619	+	2.31435i	0.0495565	+	0.0858343i	0.889740	−	0.456469i	$-0.150886\pi$
$727$	1.33619	+	2.31435i	0.0495565	+	0.0858343i	−0.840183	+	0.542303i	$0.817553\pi$
$728$		0			0
$729$	−24.7318	+	10.8323i	−0.915992	+	0.401197i
$730$		0			0
$731$	−6.37029			−0.235614
$732$		0			0
$733$			3.28387i			0.121293i	0.998159	+	0.0606463i	$0.0193162\pi$
$733$			3.28387i			0.121293i	−0.998159	+	0.0606463i	$0.980684\pi$
$734$		0			0
$735$	−16.2988	−	17.9488i	−0.601192	−	0.662051i
$736$		0			0
$737$	4.43139	+	7.67540i	0.163232	+	0.282727i
$738$		0			0
$739$	22.7991	+	13.1631i	0.838680	+	0.484212i	0.856815	−	0.515624i	$-0.172440\pi$
$739$	22.7991	+	13.1631i	0.838680	+	0.484212i	−0.0181356	+	0.999836i	$0.505773\pi$
$740$		0			0
$741$	2.32721	−	4.75929i	0.0854922	−	0.174837i
$742$		0			0
$743$	−21.0356	−	12.1449i	−0.771720	−	0.445553i	0.0617681	−	0.998091i	$-0.480326\pi$
$743$	−21.0356	−	12.1449i	−0.771720	−	0.445553i	−0.833488	+	0.552538i	$0.813659\pi$
$744$		0			0
$745$		−	23.1064i		−	0.846552i
$746$		0			0
$747$	−10.8553	+	26.7125i	−0.397175	+	0.977358i
$748$		0			0
$749$	14.7694	−	30.4838i	0.539662	−	1.11385i
$750$		0			0
$751$		−	9.37486i		−	0.342094i	−0.985263	−	0.171047i	$-0.945285\pi$
$751$		−	9.37486i		−	0.342094i	0.985263	−	0.171047i	$-0.0547149\pi$
$752$		0			0
$753$	1.70835	+	0.835355i	0.0622559	+	0.0304420i
$754$		0			0
$755$	−45.3087			−1.64895
$756$		0			0
$757$	−50.8723			−1.84899			−0.924493	−	0.381200i	$-0.875511\pi$
$757$	−50.8723			−1.84899			−0.924493	+	0.381200i	$0.875511\pi$
$758$		0			0
$759$	−18.5958	−	9.09304i	−0.674986	−	0.330056i
$760$		0			0
$761$			42.3508i			1.53522i	0.640920	+	0.767608i	$0.278553\pi$
$761$			42.3508i			1.53522i	−0.640920	+	0.767608i	$0.721447\pi$
$762$		0			0
$763$	2.78834	+	38.4307i	0.100945	+	1.39129i
$764$		0			0
$765$	5.96172	−	0.825596i	0.215547	−	0.0298495i
$766$		0			0
$767$			24.9397i			0.900521i
$768$		0			0
$769$	3.61419	+	2.08665i	0.130331	+	0.0752467i	0.563748	−	0.825947i	$-0.309359\pi$
$769$	3.61419	+	2.08665i	0.130331	+	0.0752467i	−0.433417	+	0.901194i	$0.642692\pi$
$770$		0			0
$771$	−16.0151	+	32.7519i	−0.576770	+	1.17953i
$772$		0			0
$773$	−4.51890	−	2.60899i	−0.162534	−	0.0938389i	0.416527	−	0.909123i	$-0.363247\pi$
$773$	−4.51890	−	2.60899i	−0.162534	−	0.0938389i	−0.579061	+	0.815285i	$0.696581\pi$
$774$		0			0
$775$	−0.261457	−	0.452857i	−0.00939182	−	0.0162671i
$776$		0			0
$777$	8.69931	+	11.0978i	0.312086	+	0.398133i
$778$		0			0
$779$			0.691739i			0.0247841i
$780$		0			0
$781$	−2.14318			−0.0766888
$782$		0			0
$783$	−6.61748	+	5.92222i	−0.236490	+	0.211643i
$784$		0			0
$785$	14.6253	+	25.3317i	0.521998	+	0.904128i
$786$		0			0
$787$	−14.7930	−	25.6223i	−0.527314	−	0.913335i	−0.999493	−	0.0318321i	$-0.989866\pi$
$787$	−14.7930	−	25.6223i	−0.527314	−	0.913335i	0.472179	−	0.881503i	$-0.343468\pi$
$788$		0			0
$789$	18.6122	−	38.0632i	0.662613	−	1.35508i
$790$		0			0
$791$	3.47660	+	47.9168i	0.123614	+	1.70372i
$792$		0			0
$793$	−10.4110	−	18.0323i	−0.369704	−	0.640346i
$794$		0			0
$795$	−4.80816	−	7.14393i	−0.170528	−	0.253369i
$796$		0			0
$797$	−41.7053	−	24.0785i	−1.47728	−	0.852906i	−0.477606	−	0.878574i	$-0.658495\pi$
$797$	−41.7053	−	24.0785i	−1.47728	−	0.852906i	−0.999671	+	0.0256682i	$0.991829\pi$
$798$		0			0
$799$	−1.42447	+	0.822418i	−0.0503941	+	0.0290951i
$800$		0			0
$801$	−3.55862	−	1.44614i	−0.125738	−	0.0510969i
$802$		0			0
$803$	10.7255	−	18.5771i	0.378494	−	0.655571i
$804$		0			0
$805$	−38.4054	+	26.0511i	−1.35361	+	0.918181i
$806$		0			0
$807$	−10.9403	−	16.2550i	−0.385117	−	0.572205i
$808$		0			0
$809$	−2.61482	+	4.52900i	−0.0919321	+	0.159231i	−0.908324	−	0.418267i	$-0.862638\pi$
$809$	−2.61482	+	4.52900i	−0.0919321	+	0.159231i	0.816392	+	0.577498i	$0.195971\pi$
$810$		0			0
$811$	28.4364			0.998538			0.499269	−	0.866447i	$-0.333602\pi$
$811$	28.4364			0.998538			0.499269	+	0.866447i	$0.333602\pi$
$812$		0			0
$813$	−0.114517	−	1.66177i	−0.00401628	−	0.0582808i
$814$		0			0
$815$	12.0575	+	20.8841i	0.422354	+	0.731539i
$816$		0			0
$817$	−8.51662	−	4.91707i	−0.297959	−	0.172027i
$818$		0			0
$819$	−10.4957	−	11.6427i	−0.366749	−	0.406828i
$820$		0			0
$821$	−2.58408	+	4.47576i	−0.0901851	+	0.156205i	−0.907589	−	0.419860i	$-0.862079\pi$
$821$	−2.58408	+	4.47576i	−0.0901851	+	0.156205i	0.817404	+	0.576065i	$0.195413\pi$
$822$		0			0
$823$	−14.8527	+	8.57519i	−0.517731	+	0.298912i	−0.736006	−	0.676975i	$-0.763290\pi$
$823$	−14.8527	+	8.57519i	−0.517731	+	0.298912i	0.218275	+	0.975887i	$0.429957\pi$
$824$		0			0
$825$	1.03798	−	2.12274i	0.0361379	−	0.0739042i
$826$		0			0
$827$		−	46.7499i		−	1.62565i	−0.582505	−	0.812827i	$-0.697927\pi$
$827$		−	46.7499i		−	1.62565i	0.582505	−	0.812827i	$-0.302073\pi$
$828$		0			0
$829$	−31.5449	−	18.2124i	−1.09560	−	0.632544i	−0.160538	−	0.987030i	$-0.551323\pi$
$829$	−31.5449	−	18.2124i	−1.09560	−	0.632544i	−0.935062	+	0.354485i	$0.884656\pi$
$830$		0			0
$831$	−38.9773	−	19.0592i	−1.35211	−	0.661157i
$832$		0			0
$833$	5.51139	−	4.35258i	0.190958	−	0.150808i
$834$		0			0
$835$	−38.4062	−	22.1738i	−1.32910	−	0.767357i
$836$		0			0
$837$	2.02213	−	1.80968i	0.0698951	−	0.0625517i
$838$		0			0
$839$	−5.36691	−	9.29577i	−0.185286	−	0.320925i	0.758387	−	0.651805i	$-0.225988\pi$
$839$	−5.36691	−	9.29577i	−0.185286	−	0.320925i	−0.943673	+	0.330880i	$0.892655\pi$
$840$		0			0
$841$	13.0396	−	22.5852i	0.449640	−	0.778799i
$842$		0			0
$843$	2.62743	+	38.1270i	0.0904935	+	1.31316i
$844$		0			0
$845$	−15.7588	+	9.09836i	−0.542120	+	0.312993i
$846$		0			0
$847$	20.0204	−	13.5803i	0.687910	−	0.466623i
$848$		0			0
$849$	−0.627378	−	9.10397i	−0.0215316	−	0.312448i
$850$		0			0
$851$	23.3749	−	13.4955i	0.801280	−	0.462619i
$852$		0			0
$853$	29.2849	−	16.9076i	1.00269	−	0.578906i	0.0936502	−	0.995605i	$-0.470146\pi$
$853$	29.2849	−	16.9076i	1.00269	−	0.578906i	0.909044	+	0.416699i	$0.136813\pi$
$854$		0			0
$855$	8.60766	+	3.49795i	0.294376	+	0.119627i
$856$		0			0
$857$			30.7052i			1.04887i	0.851451	+	0.524434i	$0.175723\pi$
$857$			30.7052i			1.04887i	−0.851451	+	0.524434i	$0.824277\pi$
$858$		0			0
$859$	25.8788			0.882975			0.441487	−	0.897267i	$-0.354451\pi$
$859$	25.8788			0.882975			0.441487	+	0.897267i	$0.354451\pi$
$860$		0			0
$861$	1.89892	+	0.763668i	0.0647149	+	0.0260258i
$862$		0			0
$863$	−24.1208	+	13.9262i	−0.821083	+	0.474052i	−0.850790	−	0.525506i	$-0.823876\pi$
$863$	−24.1208	+	13.9262i	−0.821083	+	0.474052i	0.0297071	+	0.999559i	$0.490543\pi$
$864$		0			0
$865$	−14.9682	+	25.9257i	−0.508935	+	0.881500i
$866$		0			0
$867$	−1.90446	−	27.6359i	−0.0646790	−	0.938566i
$868$		0			0
$869$	−4.05977	+	7.03173i	−0.137718	+	0.238535i
$870$		0			0
$871$	12.8464			0.435282
$872$		0			0
$873$	−26.6938	−	10.8477i	−0.903448	−	0.367140i
$874$		0			0
$875$	−17.8235	−	26.2760i	−0.602546	−	0.888291i
$876$		0			0
$877$	18.5099			0.625036			0.312518	−	0.949912i	$-0.398828\pi$
$877$	18.5099			0.625036			0.312518	+	0.949912i	$0.398828\pi$
$878$		0			0
$879$	13.5216	+	20.0903i	0.456073	+	0.677630i
$880$		0			0
$881$		−	37.6194i		−	1.26743i	−0.773567	−	0.633714i	$-0.781530\pi$
$881$		−	37.6194i		−	1.26743i	0.773567	−	0.633714i	$-0.218470\pi$
$882$		0			0
$883$		−	15.2541i		−	0.513340i	−0.966499	−	0.256670i	$-0.917375\pi$
$883$		−	15.2541i		−	0.513340i	0.966499	−	0.256670i	$-0.0826254\pi$
$884$		0			0
$885$	−43.6356	+	3.00704i	−1.46680	+	0.101081i
$886$		0			0
$887$	−17.9668			−0.603266			−0.301633	−	0.953424i	$-0.597532\pi$
$887$	−17.9668			−0.603266			−0.301633	+	0.953424i	$0.597532\pi$
$888$		0			0
$889$	19.6500	+	28.9686i	0.659039	+	0.971575i
$890$		0			0
$891$	11.8861	+	3.01455i	0.398198	+	0.100991i
$892$		0			0
$893$	−2.53922			−0.0849718
$894$		0			0
$895$	−14.0794	+	24.3863i	−0.470623	+	0.815144i
$896$		0			0
$897$	−24.8914	+	16.7529i	−0.831099	+	0.559364i
$898$		0			0
$899$	0.446273	−	0.772968i	0.0148840	−	0.0257799i
$900$		0			0
$901$	2.16019	−	1.24719i	0.0719664	−	0.0415498i
$902$		0			0
$903$	−22.9002	+	17.9509i	−0.762072	+	0.597369i
$904$		0			0
$905$	−9.41600			−0.312998
$906$		0			0
$907$			18.0310i			0.598710i	0.954142	+	0.299355i	$0.0967715\pi$
$907$			18.0310i			0.598710i	−0.954142	+	0.299355i	$0.903228\pi$
$908$		0			0
$909$	−26.6862	+	20.7629i	−0.885126	+	0.688663i
$910$		0			0
$911$	−7.79715	+	4.50169i	−0.258331	+	0.149148i	−0.623573	−	0.781765i	$-0.714320\pi$
$911$	−7.79715	+	4.50169i	−0.258331	+	0.149148i	0.365242	+	0.930913i	$0.380986\pi$
$912$		0			0
$913$	11.3408	−	6.54764i	0.375327	−	0.216695i
$914$		0			0
$915$	30.2948	−	20.3897i	1.00152	−	0.674062i
$916$		0			0
$917$	−18.7043	+	12.6875i	−0.617670	+	0.418978i
$918$		0			0
$919$	20.9938	−	12.1208i	0.692522	−	0.399828i	−0.112034	−	0.993704i	$-0.535737\pi$
$919$	20.9938	−	12.1208i	0.692522	−	0.399828i	0.804556	+	0.593876i	$0.202403\pi$
$920$		0			0
$921$	25.3245	+	12.3833i	0.834472	+	0.408042i
$922$		0			0
$923$	−1.55324	+	2.69028i	−0.0511254	+	0.0885518i
$924$		0			0
$925$	1.54053	+	2.66827i	0.0506522	+	0.0877322i
$926$		0			0
$927$	17.7073	+	22.7589i	0.581585	+	0.747500i
$928$		0			0
$929$	−39.6778	−	22.9080i	−1.30179	−	0.751586i	−0.321076	−	0.947054i	$-0.604044\pi$
$929$	−39.6778	−	22.9080i	−1.30179	−	0.751586i	−0.980710	+	0.195467i	$0.937378\pi$
$930$		0			0
$931$	10.7280	−	1.56498i	0.351596	−	0.0512901i
$932$		0			0
$933$	−0.760875	−	11.0412i	−0.0249099	−	0.361471i
$934$		0			0
$935$	−2.36722	−	1.36671i	−0.0774164	−	0.0446964i
$936$		0			0
$937$		−	16.0236i		−	0.523467i	−0.965140	−	0.261733i	$-0.915706\pi$
$937$		−	16.0236i		−	0.523467i	0.965140	−	0.261733i	$-0.0842941\pi$
$938$		0			0
$939$	24.7993	+	36.8466i	0.809293	+	1.20244i
$940$		0			0
$941$	−6.86496	+	3.96349i	−0.223791	+	0.129206i	−0.607705	−	0.794163i	$-0.707910\pi$
$941$	−6.86496	+	3.96349i	−0.223791	+	0.129206i	0.383913	+	0.923369i	$0.374576\pi$
$942$		0			0
$943$	1.95883	−	3.39279i	0.0637882	−	0.110484i
$944$		0			0
$945$	19.1051	−	19.7675i	0.621487	−	0.643037i
$946$		0			0
$947$	−13.2565	−	7.65366i	−0.430780	−	0.248711i	0.268899	−	0.963168i	$-0.413340\pi$
$947$	−13.2565	−	7.65366i	−0.430780	−	0.248711i	−0.699679	+	0.714458i	$0.746673\pi$
$948$		0			0
$949$	−15.5463	−	26.9270i	−0.504654	−	0.874086i
$950$		0			0
$951$	−42.1076	+	28.3401i	−1.36543	+	0.918992i
$952$		0			0
$953$	−36.5759			−1.18481			−0.592405	−	0.805640i	$-0.701821\pi$
$953$	−36.5759			−1.18481			−0.592405	+	0.805640i	$0.701821\pi$
$954$		0			0
$955$	8.63294	−	14.9527i	0.279355	−	0.483858i
$956$		0			0
$957$	4.02366	−	0.277281i	0.130066	−	0.00896321i
$958$		0			0
$959$	−8.44099	+	5.72569i	−0.272574	+	0.184892i
$960$		0			0
$961$	15.3636	−	26.6106i	0.495601	−	0.858406i
$962$		0			0
$963$	35.5827	+	14.4600i	1.14664	+	0.465967i
$964$		0			0
$965$	−18.9248	+	10.9262i	−0.609210	+	0.351728i
$966$		0			0
$967$	27.8653	+	16.0880i	0.896088	+	0.517357i	0.875929	−	0.482440i	$-0.160249\pi$
$967$	27.8653	+	16.0880i	0.896088	+	0.517357i	0.0201591	+	0.999797i	$0.493583\pi$
$968$		0			0
$969$	−1.18225	+	2.41777i	−0.0379792	+	0.0776699i
$970$		0			0
$971$	24.1287	+	41.7921i	0.774326	+	1.34117i	0.935172	+	0.354193i	$0.115244\pi$
$971$	24.1287	+	41.7921i	0.774326	+	1.34117i	−0.160846	+	0.986979i	$0.551422\pi$
$972$		0			0
$973$	2.90922	+	40.0967i	0.0932653	+	1.28544i
$974$		0			0
$975$	−1.91237	−	2.84138i	−0.0612447	−	0.0909970i
$976$		0			0
$977$	−1.30247	−	2.25594i	−0.0416697	−	0.0721740i	0.844438	−	0.535653i	$-0.179934\pi$
$977$	−1.30247	−	2.25594i	−0.0416697	−	0.0721740i	−0.886108	+	0.463479i	$0.846601\pi$
$978$		0			0
$979$	0.872274	+	1.51082i	0.0278780	+	0.0482861i
$980$		0			0
$981$	−43.2779	+	5.99324i	−1.38176	+	0.191350i
$982$		0			0
$983$	39.8000			1.26942			0.634711	−	0.772750i	$-0.281119\pi$
$983$	39.8000			1.26942			0.634711	+	0.772750i	$0.281119\pi$
$984$		0			0
$985$			39.4230i			1.25612i
$986$		0			0
$987$	−2.80326	+	6.97050i	−0.0892286	+	0.221874i
$988$		0			0
$989$	27.8478	+	48.2337i	0.885507	+	1.53374i
$990$		0			0
$991$	9.30303	+	5.37111i	0.295521	+	0.170619i	0.640429	−	0.768018i	$-0.278757\pi$
$991$	9.30303	+	5.37111i	0.295521	+	0.170619i	−0.344908	+	0.938636i	$0.612090\pi$
$992$		0			0
$993$	−0.129293	−	0.192103i	−0.00410298	−	0.00609619i
$994$		0			0
$995$	46.2644	+	26.7107i	1.46668	+	0.846787i
$996$		0			0
$997$		−	23.8585i		−	0.755605i	−0.925886	−	0.377803i	$-0.876680\pi$
$997$		−	23.8585i		−	0.755605i	0.925886	−	0.377803i	$-0.123320\pi$
$998$		0			0
$999$	−11.9146	+	10.6628i	−0.376960	+	0.337355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bf.g.31.11	✓	24
3.2	odd	2		3024.2.bf.h.1711.9		24
4.3	odd	2		1008.2.bf.h.31.2	yes	24
7.5	odd	6		1008.2.cz.g.607.10	yes	24
9.2	odd	6		3024.2.cz.g.2719.4		24
9.7	even	3		1008.2.cz.h.367.3	yes	24
12.11	even	2		3024.2.bf.g.1711.9		24
21.5	even	6		3024.2.cz.h.1279.4		24
28.19	even	6		1008.2.cz.h.607.3	yes	24
36.7	odd	6		1008.2.cz.g.367.10	yes	24
36.11	even	6		3024.2.cz.h.2719.4		24
63.47	even	6		3024.2.bf.g.2287.4		24
63.61	odd	6		1008.2.bf.h.943.2	yes	24
84.47	odd	6		3024.2.cz.g.1279.4		24
252.47	odd	6		3024.2.bf.h.2287.4		24
252.187	even	6	inner	1008.2.bf.g.943.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.11	✓	24	1.1	even	1	trivial
1008.2.bf.g.943.11	yes	24	252.187	even	6	inner
1008.2.bf.h.31.2	yes	24	4.3	odd	2
1008.2.bf.h.943.2	yes	24	63.61	odd	6
1008.2.cz.g.367.10	yes	24	36.7	odd	6
1008.2.cz.g.607.10	yes	24	7.5	odd	6
1008.2.cz.h.367.3	yes	24	9.7	even	3
1008.2.cz.h.607.3	yes	24	28.19	even	6
3024.2.bf.g.1711.9		24	12.11	even	2
3024.2.bf.g.2287.4		24	63.47	even	6
3024.2.bf.h.1711.9		24	3.2	odd	2
3024.2.bf.h.2287.4		24	252.47	odd	6
3024.2.cz.g.1279.4		24	84.47	odd	6
3024.2.cz.g.2719.4		24	9.2	odd	6
3024.2.cz.h.1279.4		24	21.5	even	6
3024.2.cz.h.2719.4		24	36.11	even	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.55599 + 0.760852i) q^{3} -1.99968i q^{5} +(2.18955 - 1.48522i) q^{7} +(1.84221 + 2.36776i) q^{9} -1.36249i q^{11} +(-1.71030 - 0.987444i) q^{13} +(1.52146 - 3.11148i) q^{15} +(0.868852 + 0.501632i) q^{17} +(0.774396 + 1.34129i) q^{19} +(4.53695 - 0.645056i) q^{21} -8.77155i q^{23} +1.00128 q^{25} +(1.06494 + 5.08585i) q^{27} +(0.854529 + 1.48009i) q^{29} +(-0.261122 - 0.452277i) q^{31} +(1.03665 - 2.12002i) q^{33} +(-2.96996 - 4.37840i) q^{35} +(1.53855 + 2.66485i) q^{37} +(-1.90992 - 2.83774i) q^{39} +(0.386794 + 0.223316i) q^{41} +(-5.49888 + 3.17478i) q^{43} +(4.73475 - 3.68383i) q^{45} +(-0.819743 + 1.41984i) q^{47} +(2.58827 - 6.50391i) q^{49} +(0.970257 + 1.44160i) q^{51} +(1.24313 - 2.15316i) q^{53} -2.72454 q^{55} +(0.184426 + 2.67624i) q^{57} +(-6.31421 - 10.9365i) q^{59} +(9.13080 + 5.27167i) q^{61} +(7.55024 + 2.44825i) q^{63} +(-1.97457 + 3.42006i) q^{65} +(-5.63337 + 3.25243i) q^{67} +(6.67385 - 13.6484i) q^{69} -1.57299i q^{71} +(13.6347 + 7.87199i) q^{73} +(1.55799 + 0.761828i) q^{75} +(-2.02359 - 2.98324i) q^{77} +(-5.16095 - 2.97967i) q^{79} +(-2.21254 + 8.72380i) q^{81} +(4.80565 + 8.32363i) q^{83} +(1.00310 - 1.73743i) q^{85} +(0.203511 + 2.95317i) q^{87} +(-1.10887 + 0.640207i) q^{89} +(-5.21136 + 0.378111i) q^{91} +(-0.0621876 - 0.902414i) q^{93} +(2.68215 - 1.54854i) q^{95} +(-8.31781 + 4.80229i) q^{97} +(3.22604 - 2.50999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 8 q^{7} - q^{9} + 3 q^{13} - 6 q^{15} - 3 q^{17} + 4 q^{19} - 20 q^{21} - 30 q^{25} - 9 q^{27} + 18 q^{29} + 17 q^{31} - 12 q^{33} + 42 q^{35} - 3 q^{37} - 42 q^{39} - 36 q^{41} + 24 q^{43}+ \cdots + 30 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 8 * q^7 - q^9 + 3 * q^13 - 6 * q^15 - 3 * q^17 + 4 * q^19 - 20 * q^21 - 30 * q^25 - 9 * q^27 + 18 * q^29 + 17 * q^31 - 12 * q^33 + 42 * q^35 - 3 * q^37 - 42 * q^39 - 36 * q^41 + 24 * q^43 + 12 * q^45 - 21 * q^47 - 24 * q^49 + 18 * q^51 - 12 * q^53 + 30 * q^55 - 13 * q^57 - 6 * q^59 - 48 * q^61 - 6 * q^63 + 42 * q^67 - 6 * q^69 + 48 * q^73 - 33 * q^75 + 36 * q^77 - 30 * q^79 + 23 * q^81 + 48 * q^83 - 21 * q^85 - 15 * q^87 + 39 * q^89 - 9 * q^91 - 8 * q^93 - 33 * q^95 - 3 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

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Representations

Groups

Database

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