LMFDB - Embedded newform 968.2.q.b.89.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [968,2,Mod(89,968)] 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("968.89"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(968, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 12])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.q (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [170] 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$170$
Relative dimension:	$17$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			89.6
Character	$\chi$	$=$	968.89
Dual form			968.2.q.b.881.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.03194 q^{3} +(-0.0505481 - 0.110685i) q^{5} +(-3.31366 + 2.12956i) q^{7} -1.93511 q^{9} +(3.09778 - 1.18479i) q^{11} +(-3.90411 - 1.14635i) q^{13} +(0.0521624 + 0.114220i) q^{15} +(4.31900 - 4.98439i) q^{17} +(1.13169 + 1.30604i) q^{19} +(3.41949 - 2.19757i) q^{21} +(4.81785 + 3.09625i) q^{23} +(3.26461 - 3.76756i) q^{25} +5.09272 q^{27} +(2.91158 + 3.36015i) q^{29} +(3.13451 - 0.920376i) q^{31} +(-3.19672 + 1.22263i) q^{33} +(0.403210 + 0.259127i) q^{35} +(-6.01821 + 1.76711i) q^{37} +(4.02879 + 1.18296i) q^{39} +(1.16314 - 8.08979i) q^{41} +(0.333493 - 0.730249i) q^{43} +(0.0978160 + 0.214187i) q^{45} +(1.50265 + 10.4512i) q^{47} +(3.53743 - 7.74589i) q^{49} +(-4.45693 + 5.14357i) q^{51} +(10.2471 - 6.58539i) q^{53} +(-0.287726 - 0.282989i) q^{55} +(-1.16783 - 1.34775i) q^{57} +(-1.20250 - 8.36354i) q^{59} +(-0.693238 - 4.82158i) q^{61} +(6.41230 - 4.12093i) q^{63} +(0.0704616 + 0.490071i) q^{65} +(0.206455 - 1.43592i) q^{67} +(-4.97172 - 3.19513i) q^{69} +(3.09387 + 3.57051i) q^{71} +(7.52630 + 4.83686i) q^{73} +(-3.36887 + 3.88788i) q^{75} +(-7.74193 + 10.5229i) q^{77} +(-4.11585 - 9.01245i) q^{79} +0.549968 q^{81} +(4.47837 - 2.87807i) q^{83} +(-0.770014 - 0.226096i) q^{85} +(-3.00457 - 3.46746i) q^{87} +(-2.61871 + 3.02215i) q^{89} +(15.3781 - 4.51542i) q^{91} +(-3.23462 + 0.949769i) q^{93} +(0.0873538 - 0.191278i) q^{95} +(-6.85320 + 15.0064i) q^{97} +(-5.99455 + 2.29270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 170 q + 10 q^{3} - 3 q^{5} + 2 q^{7} + 180 q^{9} + 2 q^{11} + 3 q^{13} + 10 q^{15} - 6 q^{17} + 9 q^{19} + 16 q^{21} + 23 q^{23} - 18 q^{25} - 26 q^{27} + q^{29} - 38 q^{31} + q^{33} - 10 q^{35} - 24 q^{37}+ \cdots - 74 q^{99}+O(q^{100}) $ 170 * q + 10 * q^3 - 3 * q^5 + 2 * q^7 + 180 * q^9 + 2 * q^11 + 3 * q^13 + 10 * q^15 - 6 * q^17 + 9 * q^19 + 16 * q^21 + 23 * q^23 - 18 * q^25 - 26 * q^27 + q^29 - 38 * q^31 + q^33 - 10 * q^35 - 24 * q^37 + 79 * q^39 - 4 * q^41 + 3 * q^43 - 37 * q^45 - 25 * q^47 - 39 * q^49 + 9 * q^51 + 17 * q^53 + 69 * q^55 + 63 * q^57 - 28 * q^59 + 34 * q^61 + 22 * q^63 + 84 * q^65 - 19 * q^67 - 12 * q^69 + 15 * q^71 - 46 * q^73 + 23 * q^75 + 108 * q^77 + 47 * q^79 + 226 * q^81 - 9 * q^83 - 8 * q^85 - 91 * q^87 - 100 * q^89 - 16 * q^91 - 6 * q^93 + 45 * q^95 + 18 * q^97 - 74 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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
$3$	−1.03194			−0.595789			−0.297894	−	0.954599i	$-0.596284\pi$
$3$	−1.03194			−0.595789			−0.297894	+	0.954599i	$0.596284\pi$
$4$		0			0
$5$	−0.0505481	−	0.110685i	−0.0226058	−	0.0494998i	0.897992	−	0.440011i	$-0.145025\pi$
$5$	−0.0505481	−	0.110685i	−0.0226058	−	0.0494998i	−0.920598	+	0.390511i	$0.872298\pi$
$6$		0			0
$7$	−3.31366	+	2.12956i	−1.25245	+	0.804899i	−0.987232	−	0.159290i	$-0.949079\pi$
$7$	−3.31366	+	2.12956i	−1.25245	+	0.804899i	−0.265215	+	0.964189i	$0.585443\pi$
$8$		0			0
$9$	−1.93511			−0.645036
$10$		0			0
$11$	3.09778	−	1.18479i	0.934017	−	0.357228i
$11$	3.09778	−	1.18479i	0.934017	−	0.357228i
$12$		0			0
$13$	−3.90411	−	1.14635i	−1.08280	−	0.317940i	−0.308804	−	0.951126i	$-0.599929\pi$
$13$	−3.90411	−	1.14635i	−1.08280	−	0.317940i	−0.774000	+	0.633186i	$0.781747\pi$
$14$		0			0
$15$	0.0521624	+	0.114220i	0.0134683	+	0.0294914i
$16$		0			0
$17$	4.31900	−	4.98439i	1.04751	−	1.20889i	0.0701009	−	0.997540i	$-0.477668\pi$
$17$	4.31900	−	4.98439i	1.04751	−	1.20889i	0.977410	−	0.211352i	$-0.0677867\pi$
$18$		0			0
$19$	1.13169	+	1.30604i	0.259627	+	0.299625i	0.870565	−	0.492053i	$-0.163753\pi$
$19$	1.13169	+	1.30604i	0.259627	+	0.299625i	−0.610939	+	0.791678i	$0.709208\pi$
$20$		0			0
$21$	3.41949	−	2.19757i	0.746194	−	0.479550i
$22$		0			0
$23$	4.81785	+	3.09625i	1.00459	+	0.645612i	0.935988	−	0.352032i	$-0.114509\pi$
$23$	4.81785	+	3.09625i	1.00459	+	0.645612i	0.0686040	+	0.997644i	$0.478145\pi$
$24$		0			0
$25$	3.26461	−	3.76756i	0.652922	−	0.753512i
$26$		0			0
$27$	5.09272			0.980094
$28$		0			0
$29$	2.91158	+	3.36015i	0.540668	+	0.623964i	0.958683	−	0.284476i	$-0.0918197\pi$
$29$	2.91158	+	3.36015i	0.540668	+	0.623964i	−0.418015	+	0.908440i	$0.637274\pi$
$30$		0			0
$31$	3.13451	−	0.920376i	0.562975	−	0.165304i	0.0121517	−	0.999926i	$-0.496132\pi$
$31$	3.13451	−	0.920376i	0.562975	−	0.165304i	0.550824	+	0.834622i	$0.314314\pi$
$32$		0			0
$33$	−3.19672	+	1.22263i	−0.556477	+	0.212832i
$34$		0			0
$35$	0.403210	+	0.259127i	0.0681549	+	0.0438005i
$36$		0			0
$37$	−6.01821	+	1.76711i	−0.989387	+	0.290510i	−0.736094	−	0.676879i	$-0.763332\pi$
$37$	−6.01821	+	1.76711i	−0.989387	+	0.290510i	−0.253293	+	0.967390i	$0.581514\pi$
$38$		0			0
$39$	4.02879	+	1.18296i	0.645122	+	0.189425i
$40$		0			0
$41$	1.16314	−	8.08979i	0.181651	−	1.26341i	−0.671207	−	0.741270i	$-0.734224\pi$
$41$	1.16314	−	8.08979i	0.181651	−	1.26341i	0.852858	−	0.522143i	$-0.174867\pi$
$42$		0			0
$43$	0.333493	−	0.730249i	0.0508573	−	0.111362i	−0.882498	−	0.470317i	$-0.844140\pi$
$43$	0.333493	−	0.730249i	0.0508573	−	0.111362i	0.933355	+	0.358955i	$0.116867\pi$
$44$		0			0
$45$	0.0978160	+	0.214187i	0.0145816	+	0.0319291i
$46$		0			0
$47$	1.50265	+	10.4512i	0.219184	+	1.52446i	0.741060	+	0.671439i	$0.234323\pi$
$47$	1.50265	+	10.4512i	0.219184	+	1.52446i	−0.521876	+	0.853021i	$0.674768\pi$
$48$		0			0
$49$	3.53743	−	7.74589i	0.505347	−	1.10656i
$50$		0			0
$51$	−4.45693	+	5.14357i	−0.624095	+	0.720244i
$52$		0			0
$53$	10.2471	−	6.58539i	1.40754	−	0.904573i	0.407580	−	0.913169i	$-0.366373\pi$
$53$	10.2471	−	6.58539i	1.40754	−	0.904573i	0.999963	+	0.00859620i	$0.00273629\pi$
$54$		0			0
$55$	−0.287726	−	0.282989i	−0.0387969	−	0.0381582i
$56$		0			0
$57$	−1.16783	−	1.34775i	−0.154683	−	0.178513i
$58$		0			0
$59$	−1.20250	−	8.36354i	−0.156552	−	1.08884i	−0.904928	−	0.425565i	$-0.860075\pi$
$59$	−1.20250	−	8.36354i	−0.156552	−	1.08884i	0.748376	−	0.663275i	$-0.230834\pi$
$60$		0			0
$61$	−0.693238	−	4.82158i	−0.0887600	−	0.617340i	−0.984842	−	0.173452i	$-0.944508\pi$
$61$	−0.693238	−	4.82158i	−0.0887600	−	0.617340i	0.896082	−	0.443888i	$-0.146401\pi$
$62$		0			0
$63$	6.41230	−	4.12093i	0.807874	−	0.519189i
$64$		0			0
$65$	0.0704616	+	0.490071i	0.00873969	+	0.0607859i
$66$		0			0
$67$	0.206455	−	1.43592i	0.0252224	−	0.175426i	−0.973316	−	0.229468i	$-0.926301\pi$
$67$	0.206455	−	1.43592i	0.0252224	−	0.175426i	0.998539	+	0.0540420i	$0.0172105\pi$
$68$		0			0
$69$	−4.97172	−	3.19513i	−0.598524	−	0.384648i
$70$		0			0
$71$	3.09387	+	3.57051i	0.367174	+	0.423742i	0.909031	−	0.416729i	$-0.136824\pi$
$71$	3.09387	+	3.57051i	0.367174	+	0.423742i	−0.541856	+	0.840471i	$0.682278\pi$
$72$		0			0
$73$	7.52630	+	4.83686i	0.880887	+	0.566111i	0.901065	−	0.433685i	$-0.142787\pi$
$73$	7.52630	+	4.83686i	0.880887	+	0.566111i	−0.0201780	+	0.999796i	$0.506423\pi$
$74$		0			0
$75$	−3.36887	+	3.88788i	−0.389003	+	0.448934i
$76$		0			0
$77$	−7.74193	+	10.5229i	−0.882275	+	1.19920i
$78$		0			0
$79$	−4.11585	−	9.01245i	−0.463069	−	1.01398i	−0.986777	−	0.162082i	$-0.948179\pi$
$79$	−4.11585	−	9.01245i	−0.463069	−	1.01398i	0.523708	−	0.851898i	$-0.324548\pi$
$80$		0			0
$81$	0.549968			0.0611076
$82$		0			0
$83$	4.47837	−	2.87807i	0.491565	−	0.315910i	−0.271270	−	0.962503i	$-0.587443\pi$
$83$	4.47837	−	2.87807i	0.491565	−	0.315910i	0.762834	+	0.646594i	$0.223807\pi$
$84$		0			0
$85$	−0.770014	−	0.226096i	−0.0835197	−	0.0245236i
$86$		0			0
$87$	−3.00457	−	3.46746i	−0.322124	−	0.371750i
$88$		0			0
$89$	−2.61871	+	3.02215i	−0.277582	+	0.320347i	−0.877372	−	0.479811i	$-0.840705\pi$
$89$	−2.61871	+	3.02215i	−0.277582	+	0.320347i	0.599790	+	0.800158i	$0.295251\pi$
$90$		0			0
$91$	15.3781	−	4.51542i	1.61206	−	0.473345i
$92$		0			0
$93$	−3.23462	+	0.949769i	−0.335414	+	0.0984865i
$94$		0			0
$95$	0.0873538	−	0.191278i	0.00896231	−	0.0196247i
$96$		0			0
$97$	−6.85320	+	15.0064i	−0.695837	+	1.52367i	0.149110	+	0.988821i	$0.452359\pi$
$97$	−6.85320	+	15.0064i	−0.695837	+	1.52367i	−0.844947	+	0.534850i	$0.820368\pi$
$98$		0			0
$99$	−5.99455	+	2.29270i	−0.602475	+	0.230425i
$100$		0			0
$101$	−2.22365	−	15.4658i	−0.221261	−	1.53890i	−0.733278	−	0.679929i	$-0.762011\pi$
$101$	−2.22365	−	15.4658i	−0.221261	−	1.53890i	0.512017	−	0.858975i	$-0.328899\pi$
$102$		0			0
$103$	0.655773	−	4.56100i	0.0646152	−	0.449409i	−0.931671	−	0.363304i	$-0.881649\pi$
$103$	0.655773	−	4.56100i	0.0646152	−	0.449409i	0.996286	−	0.0861053i	$-0.0274421\pi$
$104$		0			0
$105$	−0.416087	−	0.267403i	−0.0406059	−	0.0260958i
$106$		0			0
$107$	0.631521	+	1.38284i	0.0610514	+	0.133684i	0.937699	−	0.347450i	$-0.112952\pi$
$107$	0.631521	+	1.38284i	0.0610514	+	0.133684i	−0.876647	+	0.481134i	$0.840225\pi$
$108$		0			0
$109$	7.62515	+	2.23895i	0.730357	+	0.214452i	0.625708	−	0.780057i	$-0.284810\pi$
$109$	7.62515	+	2.23895i	0.730357	+	0.214452i	0.104649	+	0.994509i	$0.466628\pi$
$110$		0			0
$111$	6.21041	−	1.82354i	0.589466	−	0.173083i
$112$		0			0
$113$	2.61876	−	5.73429i	0.246353	−	0.539437i	−0.745548	−	0.666452i	$-0.767812\pi$
$113$	2.61876	−	5.73429i	0.246353	−	0.539437i	0.991901	+	0.127015i	$0.0405396\pi$
$114$		0			0
$115$	0.0991744	−	0.689773i	0.00924806	−	0.0643217i
$116$		0			0
$117$	7.55487	+	2.21831i	0.698448	+	0.205083i
$118$		0			0
$119$	−3.69714	+	25.7142i	−0.338916	+	2.35721i
$120$		0			0
$121$	8.19254	−	7.34046i	0.744776	−	0.667315i
$122$		0			0
$123$	−1.20028	+	8.34815i	−0.108226	+	0.752727i
$124$		0			0
$125$	−1.16579	−	0.342307i	−0.104272	−	0.0306169i
$126$		0			0
$127$	−1.07885	+	7.50353i	−0.0957320	+	0.665831i	0.884289	+	0.466939i	$0.154643\pi$
$127$	−1.07885	+	7.50353i	−0.0957320	+	0.665831i	−0.980021	+	0.198892i	$0.936266\pi$
$128$		0			0
$129$	−0.344144	+	0.753570i	−0.0303002	+	0.0663481i
$130$		0			0
$131$	−9.14270	+	2.68454i	−0.798801	+	0.234549i	−0.655564	−	0.755139i	$-0.727569\pi$
$131$	−9.14270	+	2.68454i	−0.798801	+	0.234549i	−0.143237	+	0.989688i	$0.545751\pi$
$132$		0			0
$133$	−6.53131	−	1.91777i	−0.566337	−	0.166291i
$134$		0			0
$135$	−0.257427	−	0.563687i	−0.0221558	−	0.0485144i
$136$		0			0
$137$	−3.84970	−	2.47405i	−0.328902	−	0.211372i	0.365759	−	0.930709i	$-0.380809\pi$
$137$	−3.84970	−	2.47405i	−0.328902	−	0.211372i	−0.694661	+	0.719337i	$0.744446\pi$
$138$		0			0
$139$	2.02183	−	14.0621i	0.171489	−	1.19274i	−0.704250	−	0.709952i	$-0.748717\pi$
$139$	2.02183	−	14.0621i	0.171489	−	1.19274i	0.875740	−	0.482784i	$-0.160374\pi$
$140$		0			0
$141$	−1.55064	−	10.7849i	−0.130587	−	0.908256i
$142$		0			0
$143$	−13.4523	+	1.07441i	−1.12493	+	0.0898468i
$144$		0			0
$145$	0.224742	−	0.492117i	0.0186638	−	0.0408681i
$146$		0			0
$147$	−3.65040	+	7.99326i	−0.301080	+	0.659273i
$148$		0			0
$149$	9.76329	−	2.86676i	0.799840	−	0.234854i	0.143826	−	0.989603i	$-0.454059\pi$
$149$	9.76329	−	2.86676i	0.799840	−	0.234854i	0.656014	+	0.754749i	$0.272241\pi$
$150$		0			0
$151$	15.4548	−	4.53793i	1.25769	−	0.369291i	0.416056	−	0.909339i	$-0.363412\pi$
$151$	15.4548	−	4.53793i	1.25769	−	0.369291i	0.841634	+	0.540048i	$0.181594\pi$
$152$		0			0
$153$	−8.35773	+	9.64533i	−0.675682	+	0.779779i
$154$		0			0
$155$	−0.260315	−	0.300420i	−0.0209090	−	0.0241303i
$156$		0			0
$157$	15.2695	+	4.48354i	1.21864	+	0.357825i	0.826952	−	0.562273i	$-0.190073\pi$
$157$	15.2695	+	4.48354i	1.21864	+	0.357825i	0.391689	+	0.920098i	$0.371891\pi$
$158$		0			0
$159$	−10.5743	+	6.79570i	−0.838598	+	0.538934i
$160$		0			0
$161$	−22.5584			−1.77785
$162$		0			0
$163$	5.18905	+	11.3624i	0.406438	+	0.889975i	0.996577	+	0.0826732i	$0.0263458\pi$
$163$	5.18905	+	11.3624i	0.406438	+	0.889975i	−0.590139	+	0.807302i	$0.700927\pi$
$164$		0			0
$165$	0.296914	+	0.292026i	0.0231148	+	0.0227342i
$166$		0			0
$167$	−1.10927	+	1.28017i	−0.0858378	+	0.0990622i	−0.797044	−	0.603922i	$-0.793604\pi$
$167$	−1.10927	+	1.28017i	−0.0858378	+	0.0990622i	0.711206	+	0.702984i	$0.248149\pi$
$168$		0			0
$169$	2.99163	+	1.92260i	0.230125	+	0.147893i
$170$		0			0
$171$	−2.18994	−	2.52732i	−0.167469	−	0.193269i
$172$		0			0
$173$	−16.1267	−	10.3640i	−1.22609	−	0.787959i	−0.242811	−	0.970074i	$-0.578069\pi$
$173$	−16.1267	−	10.3640i	−1.22609	−	0.787959i	−0.983277	+	0.182115i	$0.941706\pi$
$174$		0			0
$175$	−2.79456	+	19.4366i	−0.211249	+	1.46927i
$176$		0			0
$177$	1.24090	+	8.63064i	0.0932716	+	0.648718i
$178$		0			0
$179$	−9.46731	+	6.08427i	−0.707620	+	0.454760i	−0.844311	−	0.535854i	$-0.819990\pi$
$179$	−9.46731	+	6.08427i	−0.707620	+	0.454760i	0.136691	+	0.990614i	$0.456353\pi$
$180$		0			0
$181$	−3.62507	−	25.2129i	−0.269449	−	1.87406i	−0.453663	−	0.891174i	$-0.649883\pi$
$181$	−3.62507	−	25.2129i	−0.269449	−	1.87406i	0.184213	−	0.982886i	$-0.441026\pi$
$182$		0			0
$183$	0.715377	+	4.97556i	0.0528822	+	0.367804i
$184$		0			0
$185$	0.499801	+	0.576801i	0.0367461	+	0.0424072i
$186$		0			0
$187$	7.47386	−	20.5577i	0.546543	−	1.50333i
$188$		0			0
$189$	−16.8755	+	10.8453i	−1.22752	+	0.788876i
$190$		0			0
$191$	−10.6053	+	12.2392i	−0.767376	+	0.885599i	−0.996131	−	0.0878851i	$-0.971989\pi$
$191$	−10.6053	+	12.2392i	−0.767376	+	0.885599i	0.228755	+	0.973484i	$0.426535\pi$
$192$		0			0
$193$	−5.55238	+	12.1580i	−0.399669	+	0.875152i	0.597635	+	0.801768i	$0.296107\pi$
$193$	−5.55238	+	12.1580i	−0.399669	+	0.875152i	−0.997304	+	0.0733841i	$0.976620\pi$
$194$		0			0
$195$	−0.0727119	−	0.505722i	−0.00520700	−	0.0362155i
$196$		0			0
$197$	−3.72933	−	8.16609i	−0.265704	−	0.581810i	0.729009	−	0.684504i	$-0.239981\pi$
$197$	−3.72933	−	8.16609i	−0.265704	−	0.581810i	−0.994713	+	0.102694i	$0.967254\pi$
$198$		0			0
$199$	−4.98167	+	10.9083i	−0.353141	+	0.773272i	0.646802	+	0.762658i	$0.276106\pi$
$199$	−4.98167	+	10.9083i	−0.353141	+	0.773272i	−0.999944	+	0.0106141i	$0.996621\pi$
$200$		0			0
$201$	−0.213048	+	1.48178i	−0.0150272	+	0.104517i
$202$		0			0
$203$	−16.8037	−	4.93400i	−1.17939	−	0.346299i
$204$		0			0
$205$	−0.954212	+	0.280182i	−0.0666450	+	0.0195687i
$206$		0			0
$207$	−9.32307	−	5.99157i	−0.647998	−	0.416443i
$208$		0			0
$209$	5.05310	+	2.70500i	0.349530	+	0.187109i
$210$		0			0
$211$	−11.0362	+	3.24052i	−0.759762	+	0.223086i	−0.638592	−	0.769545i	$-0.720483\pi$
$211$	−11.0362	+	3.24052i	−0.759762	+	0.223086i	−0.121170	+	0.992632i	$0.538665\pi$
$212$		0			0
$213$	−3.19267	−	3.68454i	−0.218758	−	0.252461i
$214$		0			0
$215$	−0.0976849			−0.00666206
$216$		0			0
$217$	−8.42673	+	9.72496i	−0.572043	+	0.660173i
$218$		0			0
$219$	−7.76666	−	4.99133i	−0.524822	−	0.337283i
$220$		0			0
$221$	−22.5757	+	14.5085i	−1.51860	+	0.975948i
$222$		0			0
$223$	−10.5566	−	12.1829i	−0.706919	−	0.815828i	0.282751	−	0.959193i	$-0.408753\pi$
$223$	−10.5566	−	12.1829i	−0.706919	−	0.815828i	−0.989670	+	0.143365i	$0.954208\pi$
$224$		0			0
$225$	−6.31737	+	7.29063i	−0.421158	+	0.486042i
$226$		0			0
$227$	−6.26164	−	13.7111i	−0.415599	−	0.910036i	−0.995448	−	0.0953113i	$-0.969615\pi$
$227$	−6.26164	−	13.7111i	−0.415599	−	0.910036i	0.579848	−	0.814725i	$-0.303112\pi$
$228$		0			0
$229$	22.3191	+	6.55349i	1.47489	+	0.433067i	0.917685	−	0.397308i	$-0.130056\pi$
$229$	22.3191	+	6.55349i	1.47489	+	0.433067i	0.557205	+	0.830375i	$0.311874\pi$
$230$		0			0
$231$	7.98917	−	10.8590i	0.525649	−	0.714469i
$232$		0			0
$233$	−12.7601			−0.835944			−0.417972	−	0.908460i	$-0.637259\pi$
$233$	−12.7601			−0.835944			−0.417972	+	0.908460i	$0.637259\pi$
$234$		0			0
$235$	1.08083	−	0.694608i	0.0705056	−	0.0453112i
$236$		0			0
$237$	4.24729	+	9.30027i	0.275891	+	0.604117i
$238$		0			0
$239$	21.4311			1.38627			0.693133	−	0.720810i	$-0.256230\pi$
$239$	21.4311			1.38627			0.693133	+	0.720810i	$0.256230\pi$
$240$		0			0
$241$	3.20411			0.206395			0.103197	−	0.994661i	$-0.467093\pi$
$241$	3.20411			0.206395			0.103197	+	0.994661i	$0.467093\pi$
$242$		0			0
$243$	−15.8457			−1.01650
$244$		0			0
$245$	−1.03616			−0.0661980
$246$		0			0
$247$	−2.92105	−	6.39621i	−0.185862	−	0.406981i
$248$		0			0
$249$	−4.62139	+	2.96999i	−0.292869	+	0.188215i
$250$		0			0
$251$	30.8243			1.94561			0.972807	−	0.231619i	$-0.0744022\pi$
$251$	30.8243			1.94561			0.972807	+	0.231619i	$0.0744022\pi$
$252$		0			0
$253$	18.5931	+	3.88335i	1.16894	+	0.244144i
$254$		0			0
$255$	0.794605	+	0.233317i	0.0497601	+	0.0146109i
$256$		0			0
$257$	8.53104	+	18.6804i	0.532152	+	1.16525i	0.964631	+	0.263605i	$0.0849117\pi$
$257$	8.53104	+	18.6804i	0.532152	+	1.16525i	−0.432479	+	0.901644i	$0.642361\pi$
$258$		0			0
$259$	16.1792	−	18.6717i	1.00532	−	1.16021i
$260$		0			0
$261$	−5.63423	−	6.50225i	−0.348750	−	0.402479i
$262$		0			0
$263$	−22.7670	+	14.6315i	−1.40388	+	0.902216i	−0.999921	−	0.0125633i	$-0.996001\pi$
$263$	−22.7670	+	14.6315i	−1.40388	+	0.902216i	−0.403954	+	0.914779i	$0.632364\pi$
$264$		0			0
$265$	−1.24687	−	0.801317i	−0.0765948	−	0.0492245i
$266$		0			0
$267$	2.70234	−	3.11866i	0.165380	−	0.190859i
$268$		0			0
$269$	8.02078			0.489035			0.244518	−	0.969645i	$-0.421370\pi$
$269$	8.02078			0.489035			0.244518	+	0.969645i	$0.421370\pi$
$270$		0			0
$271$	6.06597	+	7.00050i	0.368481	+	0.425250i	0.909463	−	0.415784i	$-0.136493\pi$
$271$	6.06597	+	7.00050i	0.368481	+	0.425250i	−0.540982	+	0.841034i	$0.681947\pi$
$272$		0			0
$273$	−15.8692	+	4.65963i	−0.960450	+	0.282013i
$274$		0			0
$275$	5.64928	−	15.5390i	0.340664	−	0.937035i
$276$		0			0
$277$	9.49211	+	6.10021i	0.570326	+	0.366526i	0.793795	−	0.608185i	$-0.208102\pi$
$277$	9.49211	+	6.10021i	0.570326	+	0.366526i	−0.223470	+	0.974711i	$0.571738\pi$
$278$		0			0
$279$	−6.06562	+	1.78103i	−0.363139	+	0.106627i
$280$		0			0
$281$	25.4206	+	7.46417i	1.51647	+	0.445275i	0.930877	−	0.365332i	$-0.119045\pi$
$281$	25.4206	+	7.46417i	1.51647	+	0.445275i	0.585590	+	0.810607i	$0.300863\pi$
$282$		0			0
$283$	2.35740	−	16.3960i	0.140133	−	0.974644i	−0.791481	−	0.611194i	$-0.790690\pi$
$283$	2.35740	−	16.3960i	0.140133	−	0.974644i	0.931614	−	0.363450i	$-0.118401\pi$
$284$		0			0
$285$	−0.0901435	+	0.197387i	−0.00533964	+	0.0116922i
$286$		0			0
$287$	13.3735	+	29.2838i	0.789411	+	1.72857i
$288$		0			0
$289$	−3.77104	−	26.2282i	−0.221826	−	1.54283i
$290$		0			0
$291$	7.07206	−	15.4857i	0.414572	−	0.907785i
$292$		0			0
$293$	−6.49272	+	7.49300i	−0.379309	+	0.437746i	−0.913016	−	0.407923i	$-0.866253\pi$
$293$	−6.49272	+	7.49300i	−0.379309	+	0.437746i	0.533707	+	0.845669i	$0.320798\pi$
$294$		0			0
$295$	−0.864933	+	0.555859i	−0.0503584	+	0.0323634i
$296$		0			0
$297$	15.7761	−	6.03381i	0.915424	−	0.350117i
$298$		0			0
$299$	−15.2600	−	17.6110i	−0.882511	−	1.01847i
$300$		0			0
$301$	0.450025	+	3.12999i	0.0259390	+	0.180410i
$302$		0			0
$303$	2.29466	+	15.9597i	0.131825	+	0.916862i
$304$		0			0
$305$	−0.498634	+	0.320452i	−0.0285517	+	0.0183490i
$306$		0			0
$307$	0.523305	+	3.63967i	0.0298666	+	0.207727i	0.999290	−	0.0376658i	$-0.0119922\pi$
$307$	0.523305	+	3.63967i	0.0298666	+	0.207727i	−0.969424	+	0.245393i	$0.921083\pi$
$308$		0			0
$309$	−0.676716	+	4.70666i	−0.0384970	+	0.267753i
$310$		0			0
$311$	1.43453	+	0.921914i	0.0813445	+	0.0522769i	0.580681	−	0.814131i	$-0.302786\pi$
$311$	1.43453	+	0.921914i	0.0813445	+	0.0522769i	−0.499336	+	0.866408i	$0.666423\pi$
$312$		0			0
$313$	17.5925	+	20.3028i	0.994385	+	1.14758i	0.989048	+	0.147595i	$0.0471533\pi$
$313$	17.5925	+	20.3028i	0.994385	+	1.14758i	0.00533692	+	0.999986i	$0.498301\pi$
$314$		0			0
$315$	−0.780254	−	0.501439i	−0.0439624	−	0.0282529i
$316$		0			0
$317$	1.60775	−	1.85545i	0.0903004	−	0.104212i	−0.708801	−	0.705409i	$-0.750764\pi$
$317$	1.60775	−	1.85545i	0.0903004	−	0.104212i	0.799101	+	0.601196i	$0.205309\pi$
$318$		0			0
$319$	13.0005	+	6.95939i	0.727890	+	0.389651i
$320$		0			0
$321$	−0.651689	−	1.42700i	−0.0363737	−	0.0796474i
$322$		0			0
$323$	11.3975			0.634176
$324$		0			0
$325$	−17.0643	+	10.9666i	−0.946558	+	0.608316i
$326$		0			0
$327$	−7.86867	−	2.31045i	−0.435138	−	0.127768i
$328$		0			0
$329$	−27.2357	−	31.4317i	−1.50155	−	1.73288i
$330$		0			0
$331$	15.6924	−	18.1100i	0.862531	−	0.995414i	−0.137457	−	0.990508i	$-0.543893\pi$
$331$	15.6924	−	18.1100i	0.862531	−	0.995414i	0.999988	−	0.00490642i	$-0.00156177\pi$
$332$		0			0
$333$	11.6459	−	3.41954i	0.638191	−	0.187390i
$334$		0			0
$335$	−0.169371	+	0.0497318i	−0.00925372	+	0.00271714i
$336$		0			0
$337$	−10.3467	+	22.6561i	−0.563621	+	1.23416i	0.386504	+	0.922288i	$0.373683\pi$
$337$	−10.3467	+	22.6561i	−0.563621	+	1.23416i	−0.950125	+	0.311870i	$0.899045\pi$
$338$		0			0
$339$	−2.70240	+	5.91742i	−0.146774	+	0.321390i
$340$		0			0
$341$	8.61959	−	6.56487i	0.466777	−	0.355508i
$342$		0			0
$343$	0.849495	+	5.90837i	0.0458684	+	0.319022i
$344$		0			0
$345$	−0.102342	+	0.711801i	−0.00550989	+	0.0383221i
$346$		0			0
$347$	−7.44452	−	4.78430i	−0.399643	−	0.256835i	0.325347	−	0.945595i	$-0.394519\pi$
$347$	−7.44452	−	4.78430i	−0.399643	−	0.256835i	−0.724989	+	0.688760i	$0.758155\pi$
$348$		0			0
$349$	−1.79773	−	3.93649i	−0.0962305	−	0.210715i	0.855395	−	0.517977i	$-0.173315\pi$
$349$	−1.79773	−	3.93649i	−0.0962305	−	0.210715i	−0.951625	+	0.307261i	$0.900587\pi$
$350$		0			0
$351$	−19.8825	−	5.83803i	−1.06125	−	0.311611i
$352$		0			0
$353$	−3.12118	+	0.916460i	−0.166123	+	0.0487782i	−0.363737	−	0.931502i	$-0.618499\pi$
$353$	−3.12118	+	0.916460i	−0.166123	+	0.0487782i	0.197613	+	0.980280i	$0.436681\pi$
$354$		0			0
$355$	0.238813	−	0.522927i	0.0126749	−	0.0277541i
$356$		0			0
$357$	3.81521	−	26.5354i	0.201922	−	1.40440i
$358$		0			0
$359$	16.1188	+	4.73292i	0.850720	+	0.249794i	0.677895	−	0.735159i	$-0.262892\pi$
$359$	16.1188	+	4.73292i	0.850720	+	0.249794i	0.172825	+	0.984953i	$0.444711\pi$
$360$		0			0
$361$	2.27897	−	15.8506i	0.119946	−	0.834240i
$362$		0			0
$363$	−8.45417	+	7.57488i	−0.443729	+	0.397578i
$364$		0			0
$365$	0.154927	−	1.07754i	0.00810925	−	0.0564011i
$366$		0			0
$367$	−10.7345	−	3.15193i	−0.560336	−	0.164529i	−0.0107133	−	0.999943i	$-0.503410\pi$
$367$	−10.7345	−	3.15193i	−0.560336	−	0.164529i	−0.549622	+	0.835413i	$0.685228\pi$
$368$		0			0
$369$	−2.25079	+	15.6546i	−0.117172	+	0.814947i
$370$		0			0
$371$	−19.9313	+	43.6436i	−1.03478	+	2.26586i
$372$		0			0
$373$	1.40990	−	0.413984i	0.0730018	−	0.0214353i	−0.245028	−	0.969516i	$-0.578797\pi$
$373$	1.40990	−	0.413984i	0.0730018	−	0.0214353i	0.318030	+	0.948081i	$0.396979\pi$
$374$		0			0
$375$	1.20302	+	0.353239i	0.0621238	+	0.0182412i
$376$		0			0
$377$	−7.51523	−	16.4561i	−0.387054	−	0.847530i
$378$		0			0
$379$	−27.5070	−	17.6777i	−1.41294	−	0.908042i	−0.412945	−	0.910756i	$-0.635500\pi$
$379$	−27.5070	−	17.6777i	−1.41294	−	0.908042i	−0.999996	+	0.00271392i	$0.999136\pi$
$380$		0			0
$381$	1.11330	−	7.74317i	0.0570360	−	0.396694i
$382$		0			0
$383$	−2.71603	−	18.8904i	−0.138783	−	0.965255i	−0.933577	−	0.358376i	$-0.883330\pi$
$383$	−2.71603	−	18.8904i	−0.138783	−	0.965255i	0.794794	−	0.606879i	$-0.207579\pi$
$384$		0			0
$385$	1.55607	+	0.325000i	0.0793046	+	0.0165636i
$386$		0			0
$387$	−0.645346	+	1.41311i	−0.0328048	+	0.0718324i
$388$		0			0
$389$	−14.9879	+	32.8188i	−0.759914	+	1.66398i	−0.0122304	+	0.999925i	$0.503893\pi$
$389$	−14.9879	+	32.8188i	−0.759914	+	1.66398i	−0.747684	+	0.664055i	$0.768834\pi$
$390$		0			0
$391$	36.2412	−	10.6414i	1.83280	−	0.538158i
$392$		0			0
$393$	9.43468	−	2.77027i	0.475917	−	0.139742i
$394$		0			0
$395$	−0.789493	+	0.911124i	−0.0397237	+	0.0458436i
$396$		0			0
$397$	8.82670	+	10.1866i	0.442999	+	0.511248i	0.932705	−	0.360639i	$-0.117441\pi$
$397$	8.82670	+	10.1866i	0.442999	+	0.511248i	−0.489706	+	0.871888i	$0.662896\pi$
$398$		0			0
$399$	6.73990	+	1.97901i	0.337417	+	0.0990745i
$400$		0			0
$401$	22.1208	−	14.2161i	1.10466	−	0.709920i	0.144535	−	0.989500i	$-0.453831\pi$
$401$	22.1208	−	14.2161i	1.10466	−	0.709920i	0.960123	+	0.279579i	$0.0901950\pi$
$402$		0			0
$403$	−13.2925			−0.662149
$404$		0			0
$405$	−0.0277998	−	0.0608732i	−0.00138139	−	0.00302481i
$406$		0			0
$407$	−16.5495	+	12.6044i	−0.820326	+	0.624779i
$408$		0			0
$409$	11.3524	−	13.1014i	0.561341	−	0.647822i	−0.402146	−	0.915575i	$-0.631736\pi$
$409$	11.3524	−	13.1014i	0.561341	−	0.647822i	0.963488	+	0.267753i	$0.0862812\pi$
$410$		0			0
$411$	3.97264	+	2.55306i	0.195956	+	0.125933i
$412$		0			0
$413$	21.7953	+	25.1532i	1.07248	+	1.23771i
$414$		0			0
$415$	−0.544932	−	0.350207i	−0.0267497	−	0.0171910i
$416$		0			0
$417$	−2.08640	+	14.5112i	−0.102171	+	0.710618i
$418$		0			0
$419$	−0.0339283	−	0.235976i	−0.00165750	−	0.0115282i	0.988976	−	0.148077i	$-0.0473082\pi$
$419$	−0.0339283	−	0.235976i	−0.00165750	−	0.0115282i	−0.990633	+	0.136548i	$0.956399\pi$
$420$		0			0
$421$	−4.49417	+	2.88823i	−0.219033	+	0.140764i	−0.645556	−	0.763713i	$-0.723374\pi$
$421$	−4.49417	+	2.88823i	−0.219033	+	0.140764i	0.426524	+	0.904476i	$0.359738\pi$
$422$		0			0
$423$	−2.90779	−	20.2241i	−0.141382	−	0.983332i
$424$		0			0
$425$	−4.67914	−	32.5442i	−0.226972	−	1.57862i
$426$		0			0
$427$	12.5650	+	14.5008i	0.608063	+	0.701742i
$428$		0			0
$429$	13.8819	−	1.10872i	0.670223	−	0.0535297i
$430$		0			0
$431$	32.3397	−	20.7835i	1.55775	−	1.00111i	0.574573	−	0.818454i	$-0.305168\pi$
$431$	32.3397	−	20.7835i	1.55775	−	1.00111i	0.983178	−	0.182652i	$-0.0584681\pi$
$432$		0			0
$433$	25.4857	−	29.4121i	1.22477	−	1.41346i	0.344628	−	0.938739i	$-0.388005\pi$
$433$	25.4857	−	29.4121i	1.22477	−	1.41346i	0.880139	−	0.474716i	$-0.157449\pi$
$434$		0			0
$435$	−0.231920	+	0.507834i	−0.0111197	+	0.0243488i
$436$		0			0
$437$	1.40849	+	9.79627i	0.0673773	+	0.468619i
$438$		0			0
$439$	4.75257	+	10.4067i	0.226828	+	0.496684i	0.988489	−	0.151292i	$-0.0483433\pi$
$439$	4.75257	+	10.4067i	0.226828	+	0.496684i	−0.761661	+	0.647975i	$0.775616\pi$
$440$		0			0
$441$	−6.84530	+	14.9891i	−0.325967	+	0.713768i
$442$		0			0
$443$	0.130523	−	0.907807i	0.00620133	−	0.0431312i	−0.986486	−	0.163847i	$-0.947610\pi$
$443$	0.130523	−	0.907807i	0.00620133	−	0.0431312i	0.992687	+	0.120715i	$0.0385189\pi$
$444$		0			0
$445$	0.466877	+	0.137087i	0.0221321	+	0.00649856i
$446$		0			0
$447$	−10.0751	+	2.95831i	−0.476536	+	0.139923i
$448$		0			0
$449$	29.5673	+	19.0017i	1.39537	+	0.896747i	0.999765	−	0.0216753i	$-0.00690000\pi$
$449$	29.5673	+	19.0017i	1.39537	+	0.896747i	0.395601	+	0.918423i	$0.370536\pi$
$450$		0			0
$451$	−5.98157	−	26.4385i	−0.281661	−	1.24494i
$452$		0			0
$453$	−15.9483	+	4.68285i	−0.749318	+	0.220019i
$454$		0			0
$455$	−1.27712	−	1.47388i	−0.0598725	−	0.0690965i
$456$		0			0
$457$	−18.2712			−0.854689			−0.427345	−	0.904089i	$-0.640551\pi$
$457$	−18.2712			−0.854689			−0.427345	+	0.904089i	$0.640551\pi$
$458$		0			0
$459$	21.9954	−	25.3841i	1.02666	−	1.18483i
$460$		0			0
$461$	−21.5447	−	13.8459i	−1.00344	−	0.644869i	−0.0677499	−	0.997702i	$-0.521582\pi$
$461$	−21.5447	−	13.8459i	−1.00344	−	0.644869i	−0.935686	+	0.352833i	$0.885218\pi$
$462$		0			0
$463$	−0.899424	+	0.578025i	−0.0417998	+	0.0268631i	−0.561374	−	0.827562i	$-0.689727\pi$
$463$	−0.899424	+	0.578025i	−0.0417998	+	0.0268631i	0.519574	+	0.854425i	$0.326091\pi$
$464$		0			0
$465$	0.268629	+	0.310014i	0.0124574	+	0.0143766i
$466$		0			0
$467$	21.2492	−	24.5229i	0.983296	−	1.13478i	−0.00757489	−	0.999971i	$-0.502411\pi$
$467$	21.2492	−	24.5229i	0.983296	−	1.13478i	0.990871	−	0.134813i	$-0.0430434\pi$
$468$		0			0
$469$	2.37377	+	5.19782i	0.109610	+	0.240013i
$470$		0			0
$471$	−15.7572	−	4.62672i	−0.726052	−	0.213188i
$472$		0			0
$473$	0.167898	−	2.65727i	0.00771995	−	0.122182i
$474$		0			0
$475$	8.61508			0.395287
$476$		0			0
$477$	−19.8292	+	12.7434i	−0.907916	+	0.583482i
$478$		0			0
$479$	−6.97244	−	15.2675i	−0.318579	−	0.697591i	0.680813	−	0.732457i	$-0.261627\pi$
$479$	−6.97244	−	15.2675i	−0.318579	−	0.697591i	−0.999392	+	0.0348667i	$0.988899\pi$
$480$		0			0
$481$	25.5214			1.16368
$482$		0			0
$483$	23.2788			1.05922
$484$		0			0
$485$	2.00740			0.0911513
$486$		0			0
$487$	4.42400			0.200471			0.100235	−	0.994964i	$-0.468040\pi$
$487$	4.42400			0.200471			0.100235	+	0.994964i	$0.468040\pi$
$488$		0			0
$489$	−5.35477	−	11.7253i	−0.242151	−	0.530237i
$490$		0			0
$491$	−22.9912	+	14.7755i	−1.03758	+	0.666811i	−0.944387	−	0.328837i	$-0.893343\pi$
$491$	−22.9912	+	14.7755i	−1.03758	+	0.666811i	−0.0931918	+	0.995648i	$0.529707\pi$
$492$		0			0
$493$	29.3234			1.32066
$494$		0			0
$495$	0.556780	+	0.547614i	0.0250254	+	0.0246134i
$496$		0			0
$497$	−17.8557	−	5.24290i	−0.800936	−	0.235176i
$498$		0			0
$499$	10.7131	+	23.4584i	0.479584	+	1.05014i	0.982578	+	0.185853i	$0.0595048\pi$
$499$	10.7131	+	23.4584i	0.479584	+	1.05014i	−0.502993	+	0.864290i	$0.667768\pi$
$500$		0			0
$501$	1.14469	−	1.32105i	0.0511412	−	0.0590201i
$502$		0			0
$503$	−10.0134	−	11.5561i	−0.446476	−	0.515260i	0.487244	−	0.873266i	$-0.338002\pi$
$503$	−10.0134	−	11.5561i	−0.446476	−	0.515260i	−0.933719	+	0.358006i	$0.883457\pi$
$504$		0			0
$505$	−1.59943	+	1.02789i	−0.0711736	+	0.0457405i
$506$		0			0
$507$	−3.08717	−	1.98400i	−0.137106	−	0.0881127i
$508$		0			0
$509$	−4.61884	+	5.33043i	−0.204727	+	0.236267i	−0.848823	−	0.528677i	$-0.822688\pi$
$509$	−4.61884	+	5.33043i	−0.204727	+	0.236267i	0.644096	+	0.764944i	$0.277234\pi$
$510$		0			0
$511$	−35.2400			−1.55893
$512$		0			0
$513$	5.76336	+	6.65127i	0.254458	+	0.293661i
$514$		0			0
$515$	−0.537982	+	0.157966i	−0.0237063	+	0.00696080i
$516$		0			0
$517$	17.0374	+	30.5951i	0.749302	+	1.34557i
$518$		0			0
$519$	16.6417	+	10.6950i	0.730489	+	0.469457i
$520$		0			0
$521$	7.01912	−	2.06100i	0.307513	−	0.0902940i	−0.124335	−	0.992240i	$-0.539680\pi$
$521$	7.01912	−	2.06100i	0.307513	−	0.0902940i	0.431848	+	0.901946i	$0.357862\pi$
$522$		0			0
$523$	3.77899	+	1.10961i	0.165244	+	0.0485199i	0.363308	−	0.931669i	$-0.381647\pi$
$523$	3.77899	+	1.10961i	0.165244	+	0.0485199i	−0.198064	+	0.980189i	$0.563465\pi$
$524$		0			0
$525$	2.88381	−	20.0573i	0.125860	−	0.875374i
$526$		0			0
$527$	8.95044	−	19.5987i	0.389887	−	0.853734i
$528$		0			0
$529$	4.07043	+	8.91300i	0.176975	+	0.387522i
$530$		0			0
$531$	2.32696	+	16.1844i	0.100981	+	0.702341i
$532$		0			0
$533$	−13.8147	+	30.2500i	−0.598382	+	1.31027i
$534$		0			0
$535$	0.121137	−	0.139800i	0.00523721	−	0.00604407i
$536$		0			0
$537$	9.76966	−	6.27858i	0.421592	−	0.270941i
$538$		0			0
$539$	1.78092	−	28.1862i	0.0767099	−	1.21407i
$540$		0			0
$541$	−6.68278	−	7.71234i	−0.287315	−	0.331579i	0.593683	−	0.804699i	$-0.297673\pi$
$541$	−6.68278	−	7.71234i	−0.287315	−	0.331579i	−0.880998	+	0.473120i	$0.843128\pi$
$542$		0			0
$543$	3.74084	+	26.0181i	0.160535	+	1.11654i
$544$		0			0
$545$	−0.137619	−	0.957163i	−0.00589496	−	0.0410004i
$546$		0			0
$547$	2.90510	−	1.86699i	0.124213	−	0.0798269i	−0.477059	−	0.878871i	$-0.658297\pi$
$547$	2.90510	−	1.86699i	0.124213	−	0.0798269i	0.601272	+	0.799044i	$0.294661\pi$
$548$		0			0
$549$	1.34149	+	9.33027i	0.0572534	+	0.398206i
$550$		0			0
$551$	−1.09347	+	7.60527i	−0.0465835	+	0.323995i
$552$		0			0
$553$	32.8311	+	21.0993i	1.39612	+	0.897232i
$554$		0			0
$555$	−0.515762	−	0.595222i	−0.0218929	−	0.0252657i
$556$		0			0
$557$	−5.61180	−	3.60648i	−0.237780	−	0.152812i	0.416325	−	0.909216i	$-0.363318\pi$
$557$	−5.61180	−	3.60648i	−0.237780	−	0.152812i	−0.654104	+	0.756404i	$0.726954\pi$
$558$		0			0
$559$	−2.13911	+	2.46867i	−0.0904748	+	0.104414i
$560$		0			0
$561$	−7.71255	+	21.2142i	−0.325624	+	0.895664i
$562$		0			0
$563$	−13.1766	−	28.8527i	−0.555327	−	1.21600i	−0.954249	−	0.299012i	$-0.903343\pi$
$563$	−13.1766	−	28.8527i	−0.555327	−	1.21600i	0.398922	−	0.916985i	$-0.369384\pi$
$564$		0			0
$565$	−0.767073			−0.0322710
$566$		0			0
$567$	−1.82241	+	1.17119i	−0.0765340	+	0.0491854i
$568$		0			0
$569$	−29.5899	−	8.68838i	−1.24047	−	0.364236i	−0.405280	−	0.914192i	$-0.632826\pi$
$569$	−29.5899	−	8.68838i	−1.24047	−	0.364236i	−0.835193	+	0.549956i	$0.814644\pi$
$570$		0			0
$571$	−22.4871	−	25.9515i	−0.941056	−	1.08604i	−0.996160	−	0.0875559i	$-0.972094\pi$
$571$	−22.4871	−	25.9515i	−0.941056	−	1.08604i	0.0551036	−	0.998481i	$-0.482451\pi$
$572$		0			0
$573$	10.9440	−	12.6301i	0.457194	−	0.527630i
$574$		0			0
$575$	27.3937	−	8.04351i	1.14240	−	0.335438i
$576$		0			0
$577$	−2.16447	+	0.635545i	−0.0901080	+	0.0264581i	−0.326476	−	0.945206i	$-0.605861\pi$
$577$	−2.16447	+	0.635545i	−0.0901080	+	0.0264581i	0.236368	+	0.971664i	$0.424043\pi$
$578$		0			0
$579$	5.72970	−	12.5463i	0.238118	−	0.521406i
$580$		0			0
$581$	−8.71077	+	19.0739i	−0.361384	+	0.791320i
$582$		0			0
$583$	23.9409	−	32.5408i	0.991531	−	1.34770i
$584$		0			0
$585$	−0.136351	−	0.948341i	−0.00563741	−	0.0392091i
$586$		0			0
$587$	−2.14565	+	14.9233i	−0.0885606	+	0.615952i	0.896409	+	0.443227i	$0.146166\pi$
$587$	−2.14565	+	14.9233i	−0.0885606	+	0.615952i	−0.984970	+	0.172725i	$0.944743\pi$
$588$		0			0
$589$	4.74933	+	3.05221i	0.195693	+	0.125764i
$590$		0			0
$591$	3.84843	+	8.42688i	0.158303	+	0.346635i
$592$		0			0
$593$	23.6267	+	6.93741i	0.970231	+	0.284885i	0.728186	−	0.685380i	$-0.240364\pi$
$593$	23.6267	+	6.93741i	0.970231	+	0.284885i	0.242045	+	0.970265i	$0.422182\pi$
$594$		0			0
$595$	3.03305	−	0.890585i	0.124343	−	0.0365104i
$596$		0			0
$597$	5.14077	−	11.2567i	0.210398	−	0.460707i
$598$		0			0
$599$	−4.43281	+	30.8309i	−0.181120	+	1.25972i	0.673001	+	0.739642i	$0.265005\pi$
$599$	−4.43281	+	30.8309i	−0.181120	+	1.25972i	−0.854121	+	0.520075i	$0.825904\pi$
$600$		0			0
$601$	−12.9727	−	3.80914i	−0.529169	−	0.155378i	0.00622460	−	0.999981i	$-0.498019\pi$
$601$	−12.9727	−	3.80914i	−0.529169	−	0.155378i	−0.535394	+	0.844603i	$0.679837\pi$
$602$		0			0
$603$	−0.399512	+	2.77867i	−0.0162694	+	0.113156i
$604$		0			0
$605$	−1.22659	−	0.535744i	−0.0498682	−	0.0217811i
$606$		0			0
$607$	5.55768	−	38.6545i	0.225579	−	1.56894i	−0.490828	−	0.871257i	$-0.663306\pi$
$607$	5.55768	−	38.6545i	0.225579	−	1.56894i	0.716407	−	0.697683i	$-0.245785\pi$
$608$		0			0
$609$	17.3403	+	5.09157i	0.702664	+	0.206321i
$610$		0			0
$611$	6.11418	−	42.5250i	0.247353	−	1.72038i
$612$		0			0
$613$	19.6697	−	43.0706i	0.794452	−	1.73961i	0.131006	−	0.991382i	$-0.458179\pi$
$613$	19.6697	−	43.0706i	0.794452	−	1.73961i	0.663446	−	0.748225i	$-0.269093\pi$
$614$		0			0
$615$	0.984685	−	0.289130i	0.0397063	−	0.0116588i
$616$		0			0
$617$	33.4517	+	9.82231i	1.34672	+	0.395431i	0.874061	−	0.485817i	$-0.161478\pi$
$617$	33.4517	+	9.82231i	1.34672	+	0.395431i	0.472654	+	0.881248i	$0.343296\pi$
$618$		0			0
$619$	15.5856	+	34.1276i	0.626437	+	1.37170i	0.910744	+	0.412972i	$0.135509\pi$
$619$	15.5856	+	34.1276i	0.626437	+	1.37170i	−0.284307	+	0.958733i	$0.591764\pi$
$620$		0			0
$621$	24.5360	+	15.7683i	0.984594	+	0.632760i
$622$		0			0
$623$	2.24166	−	15.5911i	0.0898102	−	0.624644i
$624$		0			0
$625$	−3.52629	−	24.5259i	−0.141052	−	0.981037i
$626$		0			0
$627$	−5.21448	−	2.79139i	−0.208246	−	0.111477i
$628$		0			0
$629$	−17.1847	+	37.6292i	−0.685198	+	1.50038i
$630$		0			0
$631$	−15.6107	+	34.1827i	−0.621452	+	1.36079i	0.293006	+	0.956111i	$0.405344\pi$
$631$	−15.6107	+	34.1827i	−0.621452	+	1.36079i	−0.914458	+	0.404680i	$0.867383\pi$
$632$		0			0
$633$	11.3886	−	3.34401i	0.452658	−	0.132912i
$634$		0			0
$635$	0.885061	−	0.259877i	0.0351226	−	0.0103129i
$636$		0			0
$637$	−22.6900	+	26.1856i	−0.899010	+	1.03751i
$638$		0			0
$639$	−5.98697	−	6.90933i	−0.236841	−	0.273329i
$640$		0			0
$641$	2.43497	+	0.714972i	0.0961755	+	0.0282397i	0.329466	−	0.944167i	$-0.393131\pi$
$641$	2.43497	+	0.714972i	0.0961755	+	0.0282397i	−0.233291	+	0.972407i	$0.574949\pi$
$642$		0			0
$643$	−5.29418	+	3.40236i	−0.208782	+	0.134176i	−0.640853	−	0.767663i	$-0.721419\pi$
$643$	−5.29418	+	3.40236i	−0.208782	+	0.134176i	0.432071	+	0.901840i	$0.357783\pi$
$644$		0			0
$645$	0.100805			0.00396918
$646$		0			0
$647$	19.9493	+	43.6830i	0.784290	+	1.71736i	0.692317	+	0.721594i	$0.256590\pi$
$647$	19.9493	+	43.6830i	0.784290	+	1.71736i	0.0919730	+	0.995761i	$0.470683\pi$
$648$		0			0
$649$	−13.6341	−	24.4837i	−0.535186	−	0.961071i
$650$		0			0
$651$	8.69584	−	10.0355i	0.340817	−	0.393324i
$652$		0			0
$653$	−0.297132	−	0.190955i	−0.0116277	−	0.00747264i	0.534814	−	0.844970i	$-0.320382\pi$
$653$	−0.297132	−	0.190955i	−0.0116277	−	0.00747264i	−0.546442	+	0.837497i	$0.684018\pi$
$654$		0			0
$655$	0.759284	+	0.876260i	0.0296677	+	0.0342383i
$656$		0			0
$657$	−14.5642	−	9.35984i	−0.568204	−	0.365162i
$658$		0			0
$659$	0.973449	−	6.77049i	0.0379202	−	0.263741i	−0.962038	−	0.272917i	$-0.912012\pi$
$659$	0.973449	−	6.77049i	0.0379202	−	0.263741i	0.999958	+	0.00917581i	$0.00292079\pi$
$660$		0			0
$661$	0.667806	+	4.64469i	0.0259746	+	0.180658i	0.998679	−	0.0513922i	$-0.0163658\pi$
$661$	0.667806	+	4.64469i	0.0259746	+	0.180658i	−0.972704	+	0.232050i	$0.925457\pi$
$662$		0			0
$663$	23.2967	−	14.9718i	0.904767	−	0.581458i
$664$		0			0
$665$	0.117878	+	0.819857i	0.00457110	+	0.0317927i
$666$		0			0
$667$	3.62374	+	25.2037i	0.140312	+	0.975891i
$668$		0			0
$669$	10.8937	+	12.5720i	0.421174	+	0.486061i
$670$		0			0
$671$	−7.86007	−	14.1149i	−0.303434	−	0.544898i
$672$		0			0
$673$	3.81420	−	2.45123i	0.147026	−	0.0944882i	−0.465059	−	0.885279i	$-0.653967\pi$
$673$	3.81420	−	2.45123i	0.147026	−	0.0944882i	0.612086	+	0.790791i	$0.290331\pi$
$674$		0			0
$675$	16.6257	−	19.1871i	0.639924	−	0.738512i
$676$		0			0
$677$	6.86046	−	15.0223i	0.263669	−	0.577354i	−0.730776	−	0.682618i	$-0.760841\pi$
$677$	6.86046	−	15.0223i	0.263669	−	0.577354i	0.994444	+	0.105264i	$0.0335687\pi$
$678$		0			0
$679$	−9.24790	−	64.3205i	−0.354902	−	2.46840i
$680$		0			0
$681$	6.46161	+	14.1490i	0.247609	+	0.542189i
$682$		0			0
$683$	3.02878	−	6.63211i	0.115893	−	0.253771i	−0.842792	−	0.538239i	$-0.819090\pi$
$683$	3.02878	−	6.63211i	0.115893	−	0.253771i	0.958685	+	0.284468i	$0.0918170\pi$
$684$		0			0
$685$	−0.0792451	+	0.551162i	−0.00302780	+	0.0210588i
$686$		0			0
$687$	−23.0319	−	6.76278i	−0.878723	−	0.258016i
$688$		0			0
$689$	−47.5548	+	13.9634i	−1.81169	+	0.531961i
$690$		0			0
$691$	−41.4524	−	26.6399i	−1.57693	−	1.01343i	−0.976965	−	0.213398i	$-0.931547\pi$
$691$	−41.4524	−	26.6399i	−1.57693	−	1.01343i	−0.599960	−	0.800030i	$-0.704817\pi$
$692$		0			0
$693$	14.9815	−	20.3630i	0.569099	−	0.773527i
$694$		0			0
$695$	−1.65867	+	0.487028i	−0.0629168	+	0.0184740i
$696$		0			0
$697$	−35.2991	−	40.7373i	−1.33705	−	1.54304i
$698$		0			0
$699$	13.1676			0.498046
$700$		0			0
$701$	−6.89547	+	7.95779i	−0.260438	+	0.300562i	−0.870876	−	0.491502i	$-0.836448\pi$
$701$	−6.89547	+	7.95779i	−0.260438	+	0.300562i	0.610438	+	0.792064i	$0.290993\pi$
$702$		0			0
$703$	−9.11863	−	5.86019i	−0.343916	−	0.221021i
$704$		0			0
$705$	−1.11535	+	0.716791i	−0.0420064	+	0.0269959i
$706$		0			0
$707$	40.3038	+	46.5131i	1.51578	+	1.74930i
$708$		0			0
$709$	16.9640	−	19.5776i	0.637098	−	0.735251i	−0.341761	−	0.939787i	$-0.611023\pi$
$709$	16.9640	−	19.5776i	0.637098	−	0.735251i	0.978859	+	0.204536i	$0.0655687\pi$
$710$		0			0
$711$	7.96461	+	17.4401i	0.298696	+	0.654053i
$712$		0			0
$713$	17.9513	+	5.27099i	0.672283	+	0.197400i
$714$		0			0
$715$	0.798907	+	1.43465i	0.0298774	+	0.0536530i
$716$		0			0
$717$	−22.1156			−0.825921
$718$		0			0
$719$	−43.3515	+	27.8603i	−1.61674	+	1.03901i	−0.658687	+	0.752417i	$0.728888\pi$
$719$	−43.3515	+	27.8603i	−1.61674	+	1.03901i	−0.958051	+	0.286598i	$0.907476\pi$
$720$		0			0
$721$	7.53993	+	16.5101i	0.280802	+	0.614870i
$722$		0			0
$723$	−3.30643			−0.122968
$724$		0			0
$725$	22.1647			0.823177
$726$		0			0
$727$	6.82310			0.253055			0.126527	−	0.991963i	$-0.459617\pi$
$727$	6.82310			0.253055			0.126527	+	0.991963i	$0.459617\pi$
$728$		0			0
$729$	14.7018			0.544512
$730$		0			0
$731$	−2.19949	−	4.81620i	−0.0813509	−	0.178134i
$732$		0			0
$733$	−32.2630	+	20.7342i	−1.19166	+	0.765834i	−0.977494	−	0.210963i	$-0.932340\pi$
$733$	−32.2630	+	20.7342i	−1.19166	+	0.765834i	−0.214167	+	0.976797i	$0.568704\pi$
$734$		0			0
$735$	1.06925			0.0394400
$736$		0			0
$737$	−1.06172	−	4.69279i	−0.0391089	−	0.172861i
$738$		0			0
$739$	−15.4582	−	4.53893i	−0.568638	−	0.166967i	−0.0152395	−	0.999884i	$-0.504851\pi$
$739$	−15.4582	−	4.53893i	−0.568638	−	0.166967i	−0.553398	+	0.832917i	$0.686669\pi$
$740$		0			0
$741$	3.01434	+	6.60048i	0.110734	+	0.242475i
$742$		0			0
$743$	−22.0109	+	25.4019i	−0.807502	+	0.931907i	−0.998768	−	0.0496314i	$-0.984195\pi$
$743$	−22.0109	+	25.4019i	−0.807502	+	0.931907i	0.191266	+	0.981538i	$0.438741\pi$
$744$		0			0
$745$	−0.810823	−	0.935740i	−0.0297063	−	0.0342828i
$746$		0			0
$747$	−8.66613	+	5.56938i	−0.317077	+	0.203773i
$748$		0			0
$749$	−5.03749	−	3.23740i	−0.184066	−	0.118292i
$750$		0			0
$751$	9.11326	−	10.5173i	0.332548	−	0.383780i	−0.564709	−	0.825290i	$-0.691012\pi$
$751$	9.11326	−	10.5173i	0.332548	−	0.383780i	0.897256	+	0.441510i	$0.145557\pi$
$752$		0			0
$753$	−31.8087			−1.15917
$754$		0			0
$755$	−1.28349	−	1.48122i	−0.0467109	−	0.0539073i
$756$		0			0
$757$	−28.2662	+	8.29971i	−1.02735	+	0.301658i	−0.751634	−	0.659580i	$-0.770734\pi$
$757$	−28.2662	+	8.29971i	−1.02735	+	0.301658i	−0.275719	+	0.961238i	$0.588916\pi$
$758$		0			0
$759$	−19.1869	−	4.00737i	−0.696439	−	0.145458i
$760$		0			0
$761$	−12.8873	−	8.28218i	−0.467165	−	0.300229i	0.285800	−	0.958289i	$-0.407741\pi$
$761$	−12.8873	−	8.28218i	−0.467165	−	0.300229i	−0.752965	+	0.658060i	$0.771377\pi$
$762$		0			0
$763$	−30.0352	+	8.81912i	−1.08735	+	0.319274i
$764$		0			0
$765$	1.49006	+	0.437521i	0.0538732	+	0.0158186i
$766$		0			0
$767$	−4.89286	+	34.0306i	−0.176671	+	1.22877i
$768$		0			0
$769$	5.69228	−	12.4643i	0.205269	−	0.449476i	−0.778798	−	0.627275i	$-0.784170\pi$
$769$	5.69228	−	12.4643i	0.205269	−	0.449476i	0.984067	+	0.177799i	$0.0568976\pi$
$770$		0			0
$771$	−8.80349	−	19.2769i	−0.317050	−	0.694242i
$772$		0			0
$773$	−6.09628	−	42.4006i	−0.219268	−	1.52504i	−0.740750	−	0.671780i	$-0.765530\pi$
$773$	−6.09628	−	42.4006i	−0.219268	−	1.52504i	0.521482	−	0.853262i	$-0.325379\pi$
$774$		0			0
$775$	6.76539	−	14.8141i	0.243020	−	0.532139i
$776$		0			0
$777$	−16.6959	+	19.2680i	−0.598961	+	0.691237i
$778$		0			0
$779$	11.8819	−	7.63601i	0.425712	−	0.273588i
$780$		0			0
$781$	13.8144	+	7.39509i	0.494320	+	0.264617i
$782$		0			0
$783$	14.8279	+	17.1123i	0.529905	+	0.611543i
$784$		0			0
$785$	−0.275586	−	1.91674i	−0.00983607	−	0.0684114i
$786$		0			0
$787$	−0.0476059	−	0.331106i	−0.00169697	−	0.0118027i	0.988955	−	0.148214i	$-0.0473523\pi$
$787$	−0.0476059	−	0.331106i	−0.00169697	−	0.0118027i	−0.990652	+	0.136411i	$0.956443\pi$
$788$		0			0
$789$	23.4941	−	15.0988i	0.836413	−	0.537530i
$790$		0			0
$791$	3.53383	+	24.5783i	0.125649	+	0.873905i
$792$		0			0
$793$	−2.82073	+	19.6186i	−0.100167	+	0.696678i
$794$		0			0
$795$	1.28669	+	0.826907i	0.0456343	+	0.0293274i
$796$		0			0
$797$	7.03783	+	8.12209i	0.249293	+	0.287699i	0.866579	−	0.499039i	$-0.166314\pi$
$797$	7.03783	+	8.12209i	0.249293	+	0.287699i	−0.617287	+	0.786738i	$0.711768\pi$
$798$		0			0
$799$	58.5827	+	37.6488i	2.07251	+	1.33192i
$800$		0			0
$801$	5.06748	−	5.84818i	0.179051	−	0.206635i
$802$		0			0
$803$	29.0455	+	6.06645i	1.02499	+	0.214080i
$804$		0			0
$805$	1.14028	+	2.49687i	0.0401897	+	0.0880032i
$806$		0			0
$807$	−8.27693			−0.291362
$808$		0			0
$809$	15.5471	−	9.99149i	0.546606	−	0.351282i	−0.238012	−	0.971262i	$-0.576496\pi$
$809$	15.5471	−	9.99149i	0.546606	−	0.351282i	0.784618	+	0.619980i	$0.212859\pi$
$810$		0			0
$811$	3.55355	+	1.04342i	0.124782	+	0.0366393i	0.343527	−	0.939143i	$-0.388378\pi$
$811$	3.55355	+	1.04342i	0.124782	+	0.0366393i	−0.218745	+	0.975782i	$0.570196\pi$
$812$		0			0
$813$	−6.25969	−	7.22407i	−0.219537	−	0.253359i
$814$		0			0
$815$	0.995354	−	1.14870i	0.0348657	−	0.0402372i
$816$		0			0
$817$	1.33114	−	0.390858i	0.0465707	−	0.0136744i
$818$		0			0
$819$	−29.7583	+	8.73783i	−1.03984	+	0.305325i
$820$		0			0
$821$	2.03258	−	4.45072i	0.0709374	−	0.155331i	−0.870842	−	0.491564i	$-0.836426\pi$
$821$	2.03258	−	4.45072i	0.0709374	−	0.155331i	0.941779	+	0.336232i	$0.109153\pi$
$822$		0			0
$823$	−14.1429	+	30.9686i	−0.492990	+	1.07950i	0.485695	+	0.874128i	$0.338567\pi$
$823$	−14.1429	+	30.9686i	−0.492990	+	1.07950i	−0.978685	+	0.205368i	$0.934161\pi$
$824$		0			0
$825$	−5.82969	+	16.0352i	−0.202964	+	0.558275i
$826$		0			0
$827$	5.76158	+	40.0727i	0.200350	+	1.39346i	0.803248	+	0.595645i	$0.203104\pi$
$827$	5.76158	+	40.0727i	0.200350	+	1.39346i	−0.602898	+	0.797818i	$0.705987\pi$
$828$		0			0
$829$	1.61926	−	11.2622i	0.0562391	−	0.391152i	−0.942188	−	0.335085i	$-0.891235\pi$
$829$	1.61926	−	11.2622i	0.0562391	−	0.391152i	0.998427	−	0.0560668i	$-0.0178560\pi$
$830$		0			0
$831$	−9.79525	−	6.29503i	−0.339793	−	0.218372i
$832$		0			0
$833$	−23.3304	−	51.0864i	−0.808349	−	1.77004i
$834$		0			0
$835$	0.197766	+	0.0580694i	0.00684399	+	0.00200958i
$836$		0			0
$837$	15.9632	−	4.68721i	0.551768	−	0.162014i
$838$		0			0
$839$	−13.9044	+	30.4464i	−0.480033	+	1.05113i	0.502422	+	0.864623i	$0.332443\pi$
$839$	−13.9044	+	30.4464i	−0.480033	+	1.05113i	−0.982454	+	0.186503i	$0.940285\pi$
$840$		0			0
$841$	1.31386	−	9.13812i	0.0453056	−	0.315107i
$842$		0			0
$843$	−26.2325	−	7.70255i	−0.903494	−	0.265290i
$844$		0			0
$845$	0.0615820	−	0.428312i	0.00211849	−	0.0147344i
$846$		0			0
$847$	−11.5153	+	41.7703i	−0.395672	+	1.43525i
$848$		0			0
$849$	−2.43268	+	16.9197i	−0.0834894	+	0.580682i
$850$		0			0
$851$	−34.4662	−	10.1202i	−1.18149	−	0.346916i
$852$		0			0
$853$	−5.34683	+	37.1880i	−0.183072	+	1.27329i	0.666374	+	0.745618i	$0.267845\pi$
$853$	−5.34683	+	37.1880i	−0.183072	+	1.27329i	−0.849446	+	0.527676i	$0.823064\pi$
$854$		0			0
$855$	−0.169039	+	0.370144i	−0.00578101	+	0.0126587i
$856$		0			0
$857$	17.5441	−	5.15142i	0.599295	−	0.175969i	0.0320063	−	0.999488i	$-0.489810\pi$
$857$	17.5441	−	5.15142i	0.599295	−	0.175969i	0.567289	+	0.823519i	$0.307992\pi$
$858$		0			0
$859$	6.46404	+	1.89801i	0.220550	+	0.0647593i	0.390141	−	0.920755i	$-0.372426\pi$
$859$	6.46404	+	1.89801i	0.220550	+	0.0647593i	−0.169591	+	0.985515i	$0.554245\pi$
$860$		0			0
$861$	−13.8006	−	30.2190i	−0.470322	−	1.02986i
$862$		0			0
$863$	8.16192	+	5.24535i	0.277835	+	0.178554i	0.672136	−	0.740428i	$-0.265377\pi$
$863$	8.16192	+	5.24535i	0.277835	+	0.178554i	−0.394301	+	0.918981i	$0.629013\pi$
$864$		0			0
$865$	−0.331964	+	2.30886i	−0.0112871	+	0.0785035i
$866$		0			0
$867$	3.89147	+	27.0658i	0.132161	+	0.919202i
$868$		0			0
$869$	−23.4279	−	23.0422i	−0.794736	−	0.781653i
$870$		0			0
$871$	−2.45209	+	5.36933i	−0.0830859	+	0.181933i
$872$		0			0
$873$	13.2617	−	29.0390i	0.448840	−	0.982822i
$874$		0			0
$875$	4.59201	−	1.34833i	0.155238	−	0.0455820i
$876$		0			0
$877$	−42.9081	+	12.5990i	−1.44890	+	0.425437i	−0.909179	−	0.416405i	$-0.863290\pi$
$877$	−42.9081	+	12.5990i	−1.44890	+	0.425437i	−0.539725	+	0.841841i	$0.681472\pi$
$878$		0			0
$879$	6.70008	−	7.73230i	0.225988	−	0.260804i
$880$		0			0
$881$	20.3285	+	23.4603i	0.684883	+	0.790397i	0.986627	−	0.162991i	$-0.0521143\pi$
$881$	20.3285	+	23.4603i	0.684883	+	0.790397i	−0.301744	+	0.953389i	$0.597569\pi$
$882$		0			0
$883$	48.0479	+	14.1081i	1.61694	+	0.474776i	0.960193	−	0.279336i	$-0.0901144\pi$
$883$	48.0479	+	14.1081i	1.61694	+	0.474776i	0.656746	+	0.754112i	$0.271933\pi$
$884$		0			0
$885$	0.892556	−	0.573611i	0.0300029	−	0.0192817i
$886$		0			0
$887$	−28.1877			−0.946451			−0.473226	−	0.880941i	$-0.656910\pi$
$887$	−28.1877			−0.946451			−0.473226	+	0.880941i	$0.656910\pi$
$888$		0			0
$889$	−12.4043	−	27.1617i	−0.416027	−	0.910973i
$890$		0			0
$891$	1.70368	−	0.651598i	0.0570755	−	0.0218294i
$892$		0			0
$893$	−11.9491	+	13.7900i	−0.399860	+	0.461464i
$894$		0			0
$895$	1.15199	+	0.740340i	0.0385068	+	0.0247468i
$896$		0			0
$897$	15.7474	+	18.1734i	0.525790	+	0.606794i
$898$		0			0
$899$	12.2190	+	7.85267i	0.407526	+	0.261901i
$900$		0			0
$901$	11.4329	−	79.5177i	0.380886	−	2.64912i
$902$		0			0
$903$	−0.464397	−	3.22995i	−0.0154542	−	0.107486i
$904$		0			0
$905$	−2.60745	+	1.67570i	−0.0866744	+	0.0557023i
$906$		0			0
$907$	5.20363	+	36.1921i	0.172784	+	1.20174i	0.872969	+	0.487776i	$0.162192\pi$
$907$	5.20363	+	36.1921i	0.172784	+	1.20174i	−0.700185	+	0.713962i	$0.746899\pi$
$908$		0			0
$909$	4.30300	+	29.9280i	0.142721	+	0.992649i
$910$		0			0
$911$	−11.8188	−	13.6396i	−0.391575	−	0.451901i	0.525395	−	0.850858i	$-0.323918\pi$
$911$	−11.8188	−	13.6396i	−0.391575	−	0.451901i	−0.916969	+	0.398957i	$0.869372\pi$
$912$		0			0
$913$	10.4631	−	14.2216i	0.346278	−	0.470666i
$914$		0			0
$915$	0.514558	−	0.330686i	0.0170108	−	0.0109322i
$916$		0			0
$917$	24.5789	−	28.3656i	0.811668	−	0.936715i
$918$		0			0
$919$	−0.213374	+	0.467223i	−0.00703855	+	0.0154123i	−0.913119	−	0.407694i	$-0.866333\pi$
$919$	−0.213374	+	0.467223i	−0.00703855	+	0.0154123i	0.906080	+	0.423106i	$0.139060\pi$
$920$		0			0
$921$	−0.540017	−	3.75590i	−0.0177942	−	0.123761i
$922$		0			0
$923$	−7.98573	−	17.4863i	−0.262854	−	0.575569i
$924$		0			0
$925$	−12.9894	+	28.4429i	−0.427089	+	0.935195i
$926$		0			0
$927$	−1.26899	+	8.82603i	−0.0416792	+	0.289885i
$928$		0			0
$929$	−9.79741	−	2.87678i	−0.321443	−	0.0943841i	0.117031	−	0.993128i	$-0.462662\pi$
$929$	−9.79741	−	2.87678i	−0.321443	−	0.0943841i	−0.438473	+	0.898744i	$0.644481\pi$
$930$		0			0
$931$	14.1197	−	4.14591i	0.462753	−	0.135877i
$932$		0			0
$933$	−1.48034	−	0.951356i	−0.0484641	−	0.0311460i
$934$		0			0
$935$	−2.65321	+	0.211908i	−0.0867693	+	0.00693013i
$936$		0			0
$937$	−32.1642	+	9.44425i	−1.05076	+	0.308530i	−0.761123	−	0.648607i	$-0.775352\pi$
$937$	−32.1642	+	9.44425i	−1.05076	+	0.308530i	−0.289634	+	0.957138i	$0.593534\pi$
$938$		0			0
$939$	−18.1543	−	20.9512i	−0.592443	−	0.683716i
$940$		0			0
$941$	−48.0344			−1.56588			−0.782938	−	0.622100i	$-0.786280\pi$
$941$	−48.0344			−1.56588			−0.782938	+	0.622100i	$0.786280\pi$
$942$		0			0
$943$	30.6518	−	35.3741i	0.998160	−	1.15194i
$944$		0			0
$945$	2.05343	+	1.31966i	0.0667982	+	0.0429286i
$946$		0			0
$947$	1.72441	−	1.10821i	0.0560358	−	0.0360120i	−0.512323	−	0.858793i	$-0.671215\pi$
$947$	1.72441	−	1.10821i	0.0560358	−	0.0360120i	0.568359	+	0.822781i	$0.307579\pi$
$948$		0			0
$949$	−23.8387	−	27.5114i	−0.773838	−	0.893057i
$950$		0			0
$951$	−1.65910	+	1.91470i	−0.0538000	+	0.0620885i
$952$		0			0
$953$	−6.00969	−	13.1594i	−0.194673	−	0.426274i	0.786973	−	0.616988i	$-0.211647\pi$
$953$	−6.00969	−	13.1594i	−0.194673	−	0.426274i	−0.981646	+	0.190713i	$0.938920\pi$
$954$		0			0
$955$	1.89078	+	0.555182i	0.0611841	+	0.0179653i
$956$		0			0
$957$	−13.4157	−	7.18165i	−0.433669	−	0.232150i
$958$		0			0
$959$	18.0253			0.582066
$960$		0			0
$961$	−17.1008	+	10.9900i	−0.551638	+	0.354516i
$962$		0			0
$963$	−1.22206	−	2.67594i	−0.0393804	−	0.0862310i
$964$		0			0
$965$	1.62637			0.0523547
$966$		0			0
$967$	−46.1909			−1.48540			−0.742700	−	0.669625i	$-0.766455\pi$
$967$	−46.1909			−1.48540			−0.742700	+	0.669625i	$0.766455\pi$
$968$		0			0
$969$	−11.7615			−0.377835
$970$		0			0
$971$	−32.1071			−1.03037			−0.515183	−	0.857080i	$-0.672276\pi$
$971$	−32.1071			−1.03037			−0.515183	+	0.857080i	$0.672276\pi$
$972$		0			0
$973$	23.2465	+	50.9028i	0.745250	+	1.63187i
$974$		0			0
$975$	17.6093	−	11.3168i	0.563948	−	0.362427i
$976$		0			0
$977$	−56.6524			−1.81247			−0.906236	−	0.422772i	$-0.861057\pi$
$977$	−56.6524			−1.81247			−0.906236	+	0.422772i	$0.861057\pi$
$978$		0			0
$979$	−4.53157	+	12.4646i	−0.144830	+	0.398370i
$980$		0			0
$981$	−14.7555	−	4.33260i	−0.471107	−	0.138329i
$982$		0			0
$983$	19.1158	+	41.8577i	0.609698	+	1.33505i	0.922780	+	0.385327i	$0.125911\pi$
$983$	19.1158	+	41.8577i	0.609698	+	1.33505i	−0.313082	+	0.949726i	$0.601361\pi$
$984$		0			0
$985$	−0.715352	+	0.825560i	−0.0227930	+	0.0263045i
$986$		0			0
$987$	28.1055	+	32.4355i	0.894608	+	1.03243i
$988$		0			0
$989$	3.86775	−	2.48565i	0.122987	−	0.0790392i
$990$		0			0
$991$	44.4608	+	28.5732i	1.41235	+	0.907659i	0.999994	−	0.00336609i	$-0.00107146\pi$
$991$	44.4608	+	28.5732i	1.41235	+	0.907659i	0.412351	+	0.911025i	$0.364708\pi$
$992$		0			0
$993$	−16.1935	+	18.6883i	−0.513886	+	0.593056i
$994$		0			0
$995$	1.45920			0.0462598
$996$		0			0
$997$	−3.61845	−	4.17592i	−0.114598	−	0.132253i	0.695552	−	0.718476i	$-0.255160\pi$
$997$	−3.61845	−	4.17592i	−0.114598	−	0.132253i	−0.810150	+	0.586223i	$0.800614\pi$
$998$		0			0
$999$	−30.6490	+	8.99937i	−0.969692	+	0.284727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.q.b.89.6	✓	170
121.34	even	11	inner	968.2.q.b.881.6	yes	170

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.q.b.89.6	✓	170	1.1	even	1	trivial
968.2.q.b.881.6	yes	170	121.34	even	11	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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q-1.03194 q^{3} +(-0.0505481 - 0.110685i) q^{5} +(-3.31366 + 2.12956i) q^{7} -1.93511 q^{9} +(3.09778 - 1.18479i) q^{11} +(-3.90411 - 1.14635i) q^{13} +(0.0521624 + 0.114220i) q^{15} +(4.31900 - 4.98439i) q^{17} +(1.13169 + 1.30604i) q^{19} +(3.41949 - 2.19757i) q^{21} +(4.81785 + 3.09625i) q^{23} +(3.26461 - 3.76756i) q^{25} +5.09272 q^{27} +(2.91158 + 3.36015i) q^{29} +(3.13451 - 0.920376i) q^{31} +(-3.19672 + 1.22263i) q^{33} +(0.403210 + 0.259127i) q^{35} +(-6.01821 + 1.76711i) q^{37} +(4.02879 + 1.18296i) q^{39} +(1.16314 - 8.08979i) q^{41} +(0.333493 - 0.730249i) q^{43} +(0.0978160 + 0.214187i) q^{45} +(1.50265 + 10.4512i) q^{47} +(3.53743 - 7.74589i) q^{49} +(-4.45693 + 5.14357i) q^{51} +(10.2471 - 6.58539i) q^{53} +(-0.287726 - 0.282989i) q^{55} +(-1.16783 - 1.34775i) q^{57} +(-1.20250 - 8.36354i) q^{59} +(-0.693238 - 4.82158i) q^{61} +(6.41230 - 4.12093i) q^{63} +(0.0704616 + 0.490071i) q^{65} +(0.206455 - 1.43592i) q^{67} +(-4.97172 - 3.19513i) q^{69} +(3.09387 + 3.57051i) q^{71} +(7.52630 + 4.83686i) q^{73} +(-3.36887 + 3.88788i) q^{75} +(-7.74193 + 10.5229i) q^{77} +(-4.11585 - 9.01245i) q^{79} +0.549968 q^{81} +(4.47837 - 2.87807i) q^{83} +(-0.770014 - 0.226096i) q^{85} +(-3.00457 - 3.46746i) q^{87} +(-2.61871 + 3.02215i) q^{89} +(15.3781 - 4.51542i) q^{91} +(-3.23462 + 0.949769i) q^{93} +(0.0873538 - 0.191278i) q^{95} +(-6.85320 + 15.0064i) q^{97} +(-5.99455 + 2.29270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 170 q + 10 q^{3} - 3 q^{5} + 2 q^{7} + 180 q^{9} + 2 q^{11} + 3 q^{13} + 10 q^{15} - 6 q^{17} + 9 q^{19} + 16 q^{21} + 23 q^{23} - 18 q^{25} - 26 q^{27} + q^{29} - 38 q^{31} + q^{33} - 10 q^{35} - 24 q^{37}+ \cdots - 74 q^{99}+O(q^{100}) \) 170 * q + 10 * q^3 - 3 * q^5 + 2 * q^7 + 180 * q^9 + 2 * q^11 + 3 * q^13 + 10 * q^15 - 6 * q^17 + 9 * q^19 + 16 * q^21 + 23 * q^23 - 18 * q^25 - 26 * q^27 + q^29 - 38 * q^31 + q^33 - 10 * q^35 - 24 * q^37 + 79 * q^39 - 4 * q^41 + 3 * q^43 - 37 * q^45 - 25 * q^47 - 39 * q^49 + 9 * q^51 + 17 * q^53 + 69 * q^55 + 63 * q^57 - 28 * q^59 + 34 * q^61 + 22 * q^63 + 84 * q^65 - 19 * q^67 - 12 * q^69 + 15 * q^71 - 46 * q^73 + 23 * q^75 + 108 * q^77 + 47 * q^79 + 226 * q^81 - 9 * q^83 - 8 * q^85 - 91 * q^87 - 100 * q^89 - 16 * q^91 - 6 * q^93 + 45 * q^95 + 18 * q^97 - 74 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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