LMFDB - Embedded newform 836.2.j.b.609.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [836,2,Mod(229,836)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(836, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("836.229"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 836 = 2^{2} \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	836.j (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [20] 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:	$6.67549360898$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 3 x^{18} - x^{17} + 54 x^{16} - 67 x^{15} + 423 x^{14} - 418 x^{13} + 1762 x^{12} - 726 x^{11} + \cdots + 81 $ x^20 + 3x^18 - x^17 + 54x^16 - 67x^15 + 423x^14 - 418x^13 + 1762x^12 - 726x^11 + 3458x^10 + 2637x^9 + 9293x^8 + 10286x^7 + 19508x^6 + 18758x^5 + 20611x^4 + 10338x^3 + 3429x^2 + 675*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			609.5
Root			$-0.627273 - 1.93055i$ of defining polynomial
Character	$\chi$	$=$	836.609
Dual form			836.2.j.b.685.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.627273 - 1.93055i) q^{3} +(-0.156441 + 0.113661i) q^{5} +(-0.823967 - 2.53591i) q^{7} +(-0.906495 - 0.658608i) q^{9} +(3.30064 - 0.325253i) q^{11} +(-4.86112 - 3.53181i) q^{13} +(0.121297 + 0.373314i) q^{15} +(0.847482 - 0.615731i) q^{17} +(0.309017 - 0.951057i) q^{19} -5.41255 q^{21} -3.40760 q^{23} +(-1.53353 + 4.71972i) q^{25} +(3.08657 - 2.24253i) q^{27} +(-0.874304 - 2.69083i) q^{29} +(0.424174 + 0.308181i) q^{31} +(1.44249 - 6.57606i) q^{33} +(0.417136 + 0.303067i) q^{35} +(-2.63392 - 8.10638i) q^{37} +(-9.86757 + 7.16921i) q^{39} +(0.664517 - 2.04517i) q^{41} -0.320274 q^{43} +0.216671 q^{45} +(-1.15667 + 3.55988i) q^{47} +(-0.0887904 + 0.0645100i) q^{49} +(-0.657097 - 2.02234i) q^{51} +(-2.57428 - 1.87032i) q^{53} +(-0.479387 + 0.426037i) q^{55} +(-1.64222 - 1.19314i) q^{57} +(3.98389 + 12.2612i) q^{59} +(-1.13014 + 0.821094i) q^{61} +(-0.923246 + 2.84146i) q^{63} +1.16191 q^{65} -9.38456 q^{67} +(-2.13749 + 6.57853i) q^{69} +(10.9966 - 7.98949i) q^{71} +(0.117946 + 0.363001i) q^{73} +(8.14971 + 5.92111i) q^{75} +(-3.54443 - 8.10212i) q^{77} +(-1.64017 - 1.19165i) q^{79} +(-3.43193 - 10.5624i) q^{81} +(4.81529 - 3.49851i) q^{83} +(-0.0625962 + 0.192651i) q^{85} -5.74321 q^{87} -8.50041 q^{89} +(-4.95094 + 15.2374i) q^{91} +(0.861031 - 0.625575i) q^{93} +(0.0597552 + 0.183907i) q^{95} +(9.66260 + 7.02029i) q^{97} +(-3.20623 - 1.87898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} + 15 q^{7} + 9 q^{9} + 2 q^{11} + 4 q^{13} + 15 q^{15} + 7 q^{17} - 5 q^{19} - 12 q^{21} - 16 q^{23} - 5 q^{25} - 3 q^{27} + 16 q^{29} + q^{31} - 27 q^{33} - 13 q^{35} + 14 q^{37} - 29 q^{39}+ \cdots - 35 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 15 * q^7 + 9 * q^9 + 2 * q^11 + 4 * q^13 + 15 * q^15 + 7 * q^17 - 5 * q^19 - 12 * q^21 - 16 * q^23 - 5 * q^25 - 3 * q^27 + 16 * q^29 + q^31 - 27 * q^33 - 13 * q^35 + 14 * q^37 - 29 * q^39 - 5 * q^41 + 28 * q^43 - 4 * q^47 - 4 * q^49 + 4 * q^51 - 17 * q^55 + 42 * q^59 + 27 * q^61 + 22 * q^63 - 14 * q^65 - 34 * q^67 - 11 * q^69 + 32 * q^71 - 7 * q^73 + 13 * q^75 - 60 * q^77 + 2 * q^79 - 9 * q^81 + 33 * q^83 + 27 * q^85 - 2 * q^87 - 70 * q^89 - 10 * q^91 + 7 * q^93 - 4 * q^95 - 6 * q^97 - 35 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/836\mathbb{Z}\right)^\times$.

$n$	$419$	$705$	$761$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	0.627273	−	1.93055i	0.362156	−	1.11460i	−0.589586	−	0.807705i	$-0.700709\pi$
$3$	0.627273	−	1.93055i	0.362156	−	1.11460i	0.951743	−	0.306897i	$-0.0992908\pi$
$4$		0			0
$5$	−0.156441	+	0.113661i	−0.0699625	+	0.0508308i	−0.622217	−	0.782845i	$-0.713768\pi$
$5$	−0.156441	+	0.113661i	−0.0699625	+	0.0508308i	0.552254	+	0.833676i	$0.313768\pi$
$6$		0			0
$7$	−0.823967	−	2.53591i	−0.311430	−	0.958483i	−0.977199	−	0.212325i	$-0.931896\pi$
$7$	−0.823967	−	2.53591i	−0.311430	−	0.958483i	0.665769	−	0.746158i	$-0.268104\pi$
$8$		0			0
$9$	−0.906495	−	0.658608i	−0.302165	−	0.219536i
$10$		0			0
$11$	3.30064	−	0.325253i	0.995180	−	0.0980673i
$11$	3.30064	−	0.325253i	0.995180	−	0.0980673i
$12$		0			0
$13$	−4.86112	−	3.53181i	−1.34823	−	0.979547i	−0.999098	−	0.0424741i	$-0.986476\pi$
$13$	−4.86112	−	3.53181i	−1.34823	−	0.979547i	−0.349133	−	0.937073i	$-0.613524\pi$
$14$		0			0
$15$	0.121297	+	0.373314i	0.0313187	+	0.0963891i
$16$		0			0
$17$	0.847482	−	0.615731i	0.205544	−	0.149337i	−0.480251	−	0.877131i	$-0.659454\pi$
$17$	0.847482	−	0.615731i	0.205544	−	0.149337i	0.685795	+	0.727794i	$0.259454\pi$
$18$		0			0
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$		0			0
$21$	−5.41255			−1.18111
$22$		0			0
$23$	−3.40760			−0.710533			−0.355267	−	0.934765i	$-0.615610\pi$
$23$	−3.40760			−0.710533			−0.355267	+	0.934765i	$0.615610\pi$
$24$		0			0
$25$	−1.53353	+	4.71972i	−0.306706	+	0.943944i
$26$		0			0
$27$	3.08657	−	2.24253i	0.594011	−	0.431575i
$28$		0			0
$29$	−0.874304	−	2.69083i	−0.162354	−	0.499675i	0.836477	−	0.548001i	$-0.184611\pi$
$29$	−0.874304	−	2.69083i	−0.162354	−	0.499675i	−0.998832	+	0.0483267i	$0.984611\pi$
$30$		0			0
$31$	0.424174	+	0.308181i	0.0761839	+	0.0553509i	0.625225	−	0.780444i	$-0.285007\pi$
$31$	0.424174	+	0.308181i	0.0761839	+	0.0553509i	−0.549041	+	0.835795i	$0.685007\pi$
$32$		0			0
$33$	1.44249	−	6.57606i	0.251105	−	1.14475i
$34$		0			0
$35$	0.417136	+	0.303067i	0.0705089	+	0.0512277i
$36$		0			0
$37$	−2.63392	−	8.10638i	−0.433014	−	1.33268i	−0.895108	−	0.445850i	$-0.852902\pi$
$37$	−2.63392	−	8.10638i	−0.433014	−	1.33268i	0.462094	−	0.886831i	$-0.347098\pi$
$38$		0			0
$39$	−9.86757	+	7.16921i	−1.58008	+	1.14799i
$40$		0			0
$41$	0.664517	−	2.04517i	0.103780	−	0.319402i	−0.885662	−	0.464330i	$-0.846295\pi$
$41$	0.664517	−	2.04517i	0.103780	−	0.319402i	0.989442	+	0.144928i	$0.0462951\pi$
$42$		0			0
$43$	−0.320274			−0.0488414			−0.0244207	−	0.999702i	$-0.507774\pi$
$43$	−0.320274			−0.0488414			−0.0244207	+	0.999702i	$0.507774\pi$
$44$		0			0
$45$	0.216671			0.0322994
$46$		0			0
$47$	−1.15667	+	3.55988i	−0.168718	+	0.519262i	−0.999291	−	0.0376486i	$-0.988013\pi$
$47$	−1.15667	+	3.55988i	−0.168718	+	0.519262i	0.830573	+	0.556910i	$0.188013\pi$
$48$		0			0
$49$	−0.0887904	+	0.0645100i	−0.0126843	+	0.00921571i
$50$		0			0
$51$	−0.657097	−	2.02234i	−0.0920120	−	0.283184i
$52$		0			0
$53$	−2.57428	−	1.87032i	−0.353604	−	0.256908i	0.396775	−	0.917916i	$-0.370129\pi$
$53$	−2.57428	−	1.87032i	−0.353604	−	0.256908i	−0.750379	+	0.661007i	$0.770129\pi$
$54$		0			0
$55$	−0.479387	+	0.426037i	−0.0646405	+	0.0574468i
$56$		0			0
$57$	−1.64222	−	1.19314i	−0.217518	−	0.158036i
$58$		0			0
$59$	3.98389	+	12.2612i	0.518659	+	1.59627i	0.776525	+	0.630087i	$0.216981\pi$
$59$	3.98389	+	12.2612i	0.518659	+	1.59627i	−0.257866	+	0.966181i	$0.583019\pi$
$60$		0			0
$61$	−1.13014	+	0.821094i	−0.144699	+	0.105130i	−0.657780	−	0.753210i	$-0.728504\pi$
$61$	−1.13014	+	0.821094i	−0.144699	+	0.105130i	0.513080	+	0.858341i	$0.328504\pi$
$62$		0			0
$63$	−0.923246	+	2.84146i	−0.116318	+	0.357990i
$64$		0			0
$65$	1.16191			0.144117
$66$		0			0
$67$	−9.38456			−1.14651			−0.573253	−	0.819378i	$-0.694319\pi$
$67$	−9.38456			−1.14651			−0.573253	+	0.819378i	$0.694319\pi$
$68$		0			0
$69$	−2.13749	+	6.57853i	−0.257324	+	0.791962i
$70$		0			0
$71$	10.9966	−	7.98949i	1.30505	−	0.948178i	0.305064	−	0.952332i	$-0.401322\pi$
$71$	10.9966	−	7.98949i	1.30505	−	0.948178i	0.999991	+	0.00415409i	$0.00132229\pi$
$72$		0			0
$73$	0.117946	+	0.363001i	0.0138045	+	0.0424860i	0.957722	−	0.287697i	$-0.0928896\pi$
$73$	0.117946	+	0.363001i	0.0138045	+	0.0424860i	−0.943917	+	0.330183i	$0.892890\pi$
$74$		0			0
$75$	8.14971	+	5.92111i	0.941047	+	0.683711i
$76$		0			0
$77$	−3.54443	−	8.10212i	−0.403925	−	0.923322i
$78$		0			0
$79$	−1.64017	−	1.19165i	−0.184533	−	0.134071i	0.491683	−	0.870774i	$-0.336382\pi$
$79$	−1.64017	−	1.19165i	−0.184533	−	0.134071i	−0.676217	+	0.736703i	$0.736382\pi$
$80$		0			0
$81$	−3.43193	−	10.5624i	−0.381326	−	1.17360i
$82$		0			0
$83$	4.81529	−	3.49851i	0.528547	−	0.384012i	−0.291267	−	0.956642i	$-0.594077\pi$
$83$	4.81529	−	3.49851i	0.528547	−	0.384012i	0.819814	+	0.572630i	$0.194077\pi$
$84$		0			0
$85$	−0.0625962	+	0.192651i	−0.00678951	+	0.0208960i
$86$		0			0
$87$	−5.74321			−0.615736
$88$		0			0
$89$	−8.50041			−0.901042			−0.450521	−	0.892766i	$-0.648762\pi$
$89$	−8.50041			−0.901042			−0.450521	+	0.892766i	$0.648762\pi$
$90$		0			0
$91$	−4.95094	+	15.2374i	−0.519000	+	1.59732i
$92$		0			0
$93$	0.861031	−	0.625575i	0.0892847	−	0.0648691i
$94$		0			0
$95$	0.0597552	+	0.183907i	0.00613075	+	0.0188685i
$96$		0			0
$97$	9.66260	+	7.02029i	0.981089	+	0.712803i	0.957952	−	0.286930i	$-0.0926346\pi$
$97$	9.66260	+	7.02029i	0.981089	+	0.712803i	0.0231371	+	0.999732i	$0.492635\pi$
$98$		0			0
$99$	−3.20623	−	1.87898i	−0.322238	−	0.188845i
$100$		0			0
$101$	4.94315	+	3.59141i	0.491862	+	0.357359i	0.805900	−	0.592052i	$-0.201682\pi$
$101$	4.94315	+	3.59141i	0.491862	+	0.357359i	−0.314038	+	0.949410i	$0.601682\pi$
$102$		0			0
$103$	5.31315	+	16.3522i	0.523521	+	1.61123i	0.767223	+	0.641381i	$0.221638\pi$
$103$	5.31315	+	16.3522i	0.523521	+	1.61123i	−0.243702	+	0.969850i	$0.578362\pi$
$104$		0			0
$105$	0.846744	−	0.615196i	0.0826338	−	0.0600370i
$106$		0			0
$107$	4.07855	−	12.5525i	0.394288	−	1.21349i	−0.535226	−	0.844709i	$-0.679774\pi$
$107$	4.07855	−	12.5525i	0.394288	−	1.21349i	0.929514	−	0.368786i	$-0.120226\pi$
$108$		0			0
$109$	10.2794			0.984584			0.492292	−	0.870430i	$-0.336159\pi$
$109$	10.2794			0.984584			0.492292	+	0.870430i	$0.336159\pi$
$110$		0			0
$111$	−17.3020			−1.64223
$112$		0			0
$113$	1.17643	−	3.62067i	0.110669	−	0.340604i	−0.880350	−	0.474324i	$-0.842692\pi$
$113$	1.17643	−	3.62067i	0.110669	−	0.340604i	0.991019	+	0.133721i	$0.0426925\pi$
$114$		0			0
$115$	0.533088	−	0.387311i	0.0497107	−	0.0361169i
$116$		0			0
$117$	2.08050	+	6.40314i	0.192343	+	0.591970i
$118$		0			0
$119$	−2.25973	−	1.64179i	−0.207150	−	0.150503i
$120$		0			0
$121$	10.7884	−	2.14708i	0.980766	−	0.195189i
$122$		0			0
$123$	−3.53147	−	2.56576i	−0.318422	−	0.231347i
$124$		0			0
$125$	−0.595317	−	1.83220i	−0.0532468	−	0.163877i
$126$		0			0
$127$	16.1924	−	11.7645i	1.43685	−	1.04393i	0.448157	−	0.893955i	$-0.352080\pi$
$127$	16.1924	−	11.7645i	1.43685	−	1.04393i	0.988690	−	0.149976i	$-0.0479195\pi$
$128$		0			0
$129$	−0.200900	+	0.618305i	−0.0176882	+	0.0544387i
$130$		0			0
$131$	−11.9783			−1.04655			−0.523275	−	0.852164i	$-0.675290\pi$
$131$	−11.9783			−1.04655			−0.523275	+	0.852164i	$0.675290\pi$
$132$		0			0
$133$	−2.66641			−0.231207
$134$		0			0
$135$	−0.227979	+	0.701647i	−0.0196213	+	0.0603881i
$136$		0			0
$137$	6.10728	−	4.43720i	0.521780	−	0.379095i	−0.295494	−	0.955345i	$-0.595484\pi$
$137$	6.10728	−	4.43720i	0.521780	−	0.379095i	0.817274	+	0.576249i	$0.195484\pi$
$138$		0			0
$139$	2.78669	+	8.57656i	0.236364	+	0.727454i	0.996938	+	0.0782022i	$0.0249180\pi$
$139$	2.78669	+	8.57656i	0.236364	+	0.727454i	−0.760573	+	0.649252i	$0.775082\pi$
$140$		0			0
$141$	6.14697	+	4.46603i	0.517668	+	0.376108i
$142$		0			0
$143$	−17.1935	−	10.0761i	−1.43779	−	0.842608i
$144$		0			0
$145$	0.442620	+	0.321582i	0.0367576	+	0.0267059i
$146$		0			0
$147$	0.0688438	+	0.211880i	0.00567814	+	0.0174755i
$148$		0			0
$149$	11.2253	−	8.15565i	0.919611	−	0.668137i	−0.0238160	−	0.999716i	$-0.507582\pi$
$149$	11.2253	−	8.15565i	0.919611	−	0.668137i	0.943427	+	0.331580i	$0.107582\pi$
$150$		0			0
$151$	2.46458	−	7.58520i	0.200565	−	0.617275i	−0.799302	−	0.600930i	$-0.794797\pi$
$151$	2.46458	−	7.58520i	0.200565	−	0.617275i	0.999866	−	0.0163449i	$-0.00520298\pi$
$152$		0			0
$153$	−1.17376			−0.0948932
$154$		0			0
$155$	−0.101386			−0.00814355
$156$		0			0
$157$	0.670387	−	2.06324i	0.0535027	−	0.164664i	−0.920735	−	0.390189i	$-0.872410\pi$
$157$	0.670387	−	2.06324i	0.0535027	−	0.164664i	0.974237	+	0.225525i	$0.0724096\pi$
$158$		0			0
$159$	−5.22552	+	3.79656i	−0.414411	+	0.301087i
$160$		0			0
$161$	2.80775	+	8.64135i	0.221281	+	0.681034i
$162$		0			0
$163$	15.2410	+	11.0732i	1.19377	+	0.867323i	0.993657	−	0.112451i	$-0.0358700\pi$
$163$	15.2410	+	11.0732i	1.19377	+	0.867323i	0.200110	+	0.979773i	$0.435870\pi$
$164$		0			0
$165$	0.521778	+	1.19272i	0.0406204	+	0.0928532i
$166$		0			0
$167$	8.68212	+	6.30793i	0.671843	+	0.488122i	0.870641	−	0.491918i	$-0.163704\pi$
$167$	8.68212	+	6.30793i	0.671843	+	0.488122i	−0.198799	+	0.980040i	$0.563704\pi$
$168$		0			0
$169$	7.13956	+	21.9733i	0.549197	+	1.69026i
$170$		0			0
$171$	−0.906495	+	0.658608i	−0.0693214	+	0.0503650i
$172$		0			0
$173$	7.02364	−	21.6165i	0.533997	−	1.64348i	−0.211808	−	0.977311i	$-0.567935\pi$
$173$	7.02364	−	21.6165i	0.533997	−	1.64348i	0.745805	−	0.666164i	$-0.232065\pi$
$174$		0			0
$175$	13.2324			1.00027
$176$		0			0
$177$	26.1698			1.96704
$178$		0			0
$179$	0.101234	−	0.311567i	0.00756661	−	0.0232876i	−0.947202	−	0.320638i	$-0.896103\pi$
$179$	0.101234	−	0.311567i	0.00756661	−	0.0232876i	0.954769	+	0.297350i	$0.0961028\pi$
$180$		0			0
$181$	−2.72770	+	1.98179i	−0.202748	+	0.147305i	−0.684527	−	0.728988i	$-0.739991\pi$
$181$	−2.72770	+	1.98179i	−0.202748	+	0.147305i	0.481778	+	0.876293i	$0.339991\pi$
$182$		0			0
$183$	0.876255	+	2.69684i	0.0647747	+	0.199356i
$184$		0			0
$185$	1.33343	+	0.968796i	0.0980360	+	0.0712273i
$186$		0			0
$187$	2.59696	−	2.30795i	0.189909	−	0.168774i
$188$		0			0
$189$	−8.23008	−	5.97950i	−0.598650	−	0.434945i
$190$		0			0
$191$	1.22340	+	3.76523i	0.0885219	+	0.272442i	0.985511	−	0.169610i	$-0.0542507\pi$
$191$	1.22340	+	3.76523i	0.0885219	+	0.272442i	−0.896989	+	0.442052i	$0.854251\pi$
$192$		0			0
$193$	−9.75462	+	7.08714i	−0.702153	+	0.510144i	−0.880633	−	0.473800i	$-0.842882\pi$
$193$	−9.75462	+	7.08714i	−0.702153	+	0.510144i	0.178480	+	0.983944i	$0.442882\pi$
$194$		0			0
$195$	0.728833	−	2.24312i	0.0521928	−	0.160633i
$196$		0			0
$197$	14.7630			1.05182			0.525911	−	0.850539i	$-0.323724\pi$
$197$	14.7630			1.05182			0.525911	+	0.850539i	$0.323724\pi$
$198$		0			0
$199$	11.1440			0.789976			0.394988	−	0.918686i	$-0.370749\pi$
$199$	11.1440			0.789976			0.394988	+	0.918686i	$0.370749\pi$
$200$		0			0
$201$	−5.88668	+	18.1174i	−0.415215	+	1.27790i
$202$		0			0
$203$	−6.10330	+	4.43431i	−0.428368	+	0.311227i
$204$		0			0
$205$	0.128499	+	0.395479i	0.00897474	+	0.0276214i
$206$		0			0
$207$	3.08897	+	2.24427i	0.214698	+	0.155988i
$208$		0			0
$209$	0.710620	−	3.23960i	0.0491546	−	0.224088i
$210$		0			0
$211$	15.3563	+	11.1570i	1.05717	+	0.768080i	0.973563	−	0.228418i	$-0.0733554\pi$
$211$	15.3563	+	11.1570i	1.05717	+	0.768080i	0.0836088	+	0.996499i	$0.473355\pi$
$212$		0			0
$213$	−8.52623	−	26.2410i	−0.584208	−	1.79801i
$214$		0			0
$215$	0.0501040	−	0.0364027i	0.00341707	−	0.00248264i
$216$		0			0
$217$	0.432012	−	1.32960i	0.0293269	−	0.0902589i
$218$		0			0
$219$	0.774775			0.0523544
$220$		0			0
$221$	−6.29435			−0.423404
$222$		0			0
$223$	−5.78776	+	17.8129i	−0.387577	+	1.19284i	0.547017	+	0.837122i	$0.315763\pi$
$223$	−5.78776	+	17.8129i	−0.387577	+	1.19284i	−0.934594	+	0.355717i	$0.884237\pi$
$224$		0			0
$225$	4.49858	−	3.26841i	0.299905	−	0.217894i
$226$		0			0
$227$	−0.475488	−	1.46340i	−0.0315592	−	0.0971293i	0.934036	−	0.357179i	$-0.116261\pi$
$227$	−0.475488	−	1.46340i	−0.0315592	−	0.0971293i	−0.965595	+	0.260049i	$0.916261\pi$
$228$		0			0
$229$	9.75599	+	7.08814i	0.644694	+	0.468397i	0.861460	−	0.507826i	$-0.169551\pi$
$229$	9.75599	+	7.08814i	0.644694	+	0.468397i	−0.216766	+	0.976224i	$0.569551\pi$
$230$		0			0
$231$	−17.8649	+	1.76044i	−1.17542	+	0.115829i
$232$		0			0
$233$	−9.67570	−	7.02981i	−0.633876	−	0.460538i	0.223865	−	0.974620i	$-0.428133\pi$
$233$	−9.67570	−	7.02981i	−0.633876	−	0.460538i	−0.857741	+	0.514082i	$0.828133\pi$
$234$		0			0
$235$	−0.223668	−	0.688380i	−0.0145905	−	0.0449049i
$236$		0			0
$237$	−3.32938	+	2.41893i	−0.216266	+	0.157127i
$238$		0			0
$239$	−7.56735	+	23.2899i	−0.489491	+	1.50650i	0.335878	+	0.941906i	$0.390967\pi$
$239$	−7.56735	+	23.2899i	−0.489491	+	1.50650i	−0.825369	+	0.564594i	$0.809033\pi$
$240$		0			0
$241$	−7.10535			−0.457696			−0.228848	−	0.973462i	$-0.573496\pi$
$241$	−7.10535			−0.457696			−0.228848	+	0.973462i	$0.573496\pi$
$242$		0			0
$243$	−11.0984			−0.711960
$244$		0			0
$245$	0.00655818	−	0.0201840i	0.000418987	−	0.00128951i
$246$		0			0
$247$	−4.86112	+	3.53181i	−0.309305	+	0.224724i
$248$		0			0
$249$	−3.73355	−	11.4907i	−0.236604	−	0.728192i
$250$		0			0
$251$	9.20667	+	6.68904i	0.581120	+	0.422208i	0.839128	−	0.543934i	$-0.183066\pi$
$251$	9.20667	+	6.68904i	0.581120	+	0.422208i	−0.258008	+	0.966143i	$0.583066\pi$
$252$		0			0
$253$	−11.2472	+	1.10833i	−0.707108	+	0.0696801i
$254$		0			0
$255$	0.332658	+	0.241690i	0.0208318	+	0.0151352i
$256$		0			0
$257$	−2.96122	−	9.11371i	−0.184716	−	0.568498i	0.815227	−	0.579141i	$-0.196612\pi$
$257$	−2.96122	−	9.11371i	−0.184716	−	0.568498i	−0.999943	+	0.0106435i	$0.996612\pi$
$258$		0			0
$259$	−18.3868	+	13.3588i	−1.14250	+	0.830074i
$260$		0			0
$261$	−0.979649	+	3.01505i	−0.0606387	+	0.186627i
$262$		0			0
$263$	−25.7833			−1.58987			−0.794933	−	0.606697i	$-0.792494\pi$
$263$	−25.7833			−1.58987			−0.794933	+	0.606697i	$0.792494\pi$
$264$		0			0
$265$	0.615305			0.0377979
$266$		0			0
$267$	−5.33208	+	16.4105i	−0.326318	+	1.00430i
$268$		0			0
$269$	9.06680	−	6.58741i	0.552812	−	0.401642i	−0.276009	−	0.961155i	$-0.589012\pi$
$269$	9.06680	−	6.58741i	0.552812	−	0.401642i	0.828821	+	0.559513i	$0.189012\pi$
$270$		0			0
$271$	−1.67938	−	5.16860i	−0.102015	−	0.313970i	0.887003	−	0.461763i	$-0.152783\pi$
$271$	−1.67938	−	5.16860i	−0.102015	−	0.313970i	−0.989018	+	0.147793i	$0.952783\pi$
$272$		0			0
$273$	26.3110	+	19.1161i	1.59242	+	1.15696i
$274$		0			0
$275$	−3.52653	+	16.0769i	−0.212658	+	0.969472i
$276$		0			0
$277$	6.95680	+	5.05441i	0.417993	+	0.303690i	0.776830	−	0.629710i	$-0.216826\pi$
$277$	6.95680	+	5.05441i	0.417993	+	0.303690i	−0.358836	+	0.933400i	$0.616826\pi$
$278$		0			0
$279$	−0.181542	−	0.558729i	−0.0108686	−	0.0334502i
$280$		0			0
$281$	10.1858	−	7.40040i	0.607632	−	0.441471i	−0.240947	−	0.970538i	$-0.577458\pi$
$281$	10.1858	−	7.40040i	0.607632	−	0.441471i	0.848580	+	0.529067i	$0.177458\pi$
$282$		0			0
$283$	1.56784	−	4.82531i	0.0931984	−	0.286835i	−0.893582	−	0.448901i	$-0.851816\pi$
$283$	1.56784	−	4.82531i	0.0931984	−	0.286835i	0.986780	+	0.162066i	$0.0518157\pi$
$284$		0			0
$285$	0.392525			0.0232512
$286$		0			0
$287$	−5.73391			−0.338462
$288$		0			0
$289$	−4.91419	+	15.1243i	−0.289070	+	0.889666i
$290$		0			0
$291$	19.6141	−	14.2505i	1.14980	−	0.835378i
$292$		0			0
$293$	8.02183	+	24.6887i	0.468640	+	1.44233i	0.854346	+	0.519705i	$0.173958\pi$
$293$	8.02183	+	24.6887i	0.468640	+	1.44233i	−0.385706	+	0.922622i	$0.626042\pi$
$294$		0			0
$295$	−2.01686	−	1.46534i	−0.117426	−	0.0853151i
$296$		0			0
$297$	9.45828	−	8.40569i	0.548825	−	0.487747i
$298$		0			0
$299$	16.5647	+	12.0350i	0.957963	+	0.696001i
$300$		0			0
$301$	0.263895	+	0.812186i	0.0152107	+	0.0468136i
$302$		0			0
$303$	10.0341	−	7.29020i	0.576444	−	0.418811i
$304$		0			0
$305$	0.0834736	−	0.256905i	0.00477969	−	0.0147104i
$306$		0			0
$307$	−28.4105			−1.62147			−0.810735	−	0.585413i	$-0.800932\pi$
$307$	−28.4105			−1.62147			−0.810735	+	0.585413i	$0.800932\pi$
$308$		0			0
$309$	34.9015			1.98548
$310$		0			0
$311$	−6.84317	+	21.0611i	−0.388040	+	1.19427i	0.546210	+	0.837648i	$0.316070\pi$
$311$	−6.84317	+	21.0611i	−0.388040	+	1.19427i	−0.934251	+	0.356617i	$0.883930\pi$
$312$		0			0
$313$	−20.8756	+	15.1670i	−1.17996	+	0.857289i	−0.992167	−	0.124920i	$-0.960133\pi$
$313$	−20.8756	+	15.1670i	−1.17996	+	0.857289i	−0.187791	+	0.982209i	$0.560133\pi$
$314$		0			0
$315$	−0.178530	−	0.549458i	−0.0100590	−	0.0309585i
$316$		0			0
$317$	−24.9102	−	18.0983i	−1.39909	−	1.01650i	−0.994797	−	0.101873i	$-0.967516\pi$
$317$	−24.9102	−	18.0983i	−1.39909	−	1.01650i	−0.404296	−	0.914628i	$-0.632484\pi$
$318$		0			0
$319$	−3.76096	−	8.59709i	−0.210573	−	0.481344i
$320$		0			0
$321$	−21.6748	−	15.7477i	−1.20977	−	0.878950i
$322$		0			0
$323$	−0.323709	−	0.996274i	−0.0180117	−	0.0554342i
$324$		0			0
$325$	24.1238	−	17.5270i	1.33815	−	0.972222i
$326$		0			0
$327$	6.44797	−	19.8448i	0.356573	−	1.09742i
$328$		0			0
$329$	9.98059			0.550247
$330$		0			0
$331$	21.5948			1.18696			0.593479	−	0.804849i	$-0.297754\pi$
$331$	21.5948			1.18696			0.593479	+	0.804849i	$0.297754\pi$
$332$		0			0
$333$	−2.95128	+	9.08312i	−0.161729	+	0.497752i
$334$		0			0
$335$	1.46813	−	1.06666i	0.0802125	−	0.0582778i
$336$		0			0
$337$	−2.61045	−	8.03413i	−0.142200	−	0.437647i	0.854440	−	0.519550i	$-0.173900\pi$
$337$	−2.61045	−	8.03413i	−0.142200	−	0.437647i	−0.996640	+	0.0819028i	$0.973900\pi$
$338$		0			0
$339$	−6.25193	−	4.54229i	−0.339558	−	0.246704i
$340$		0			0
$341$	1.50028	+	0.879229i	0.0812448	+	0.0476129i
$342$		0			0
$343$	−14.8635	−	10.7989i	−0.802551	−	0.583088i
$344$		0			0
$345$	−0.413331	−	1.27210i	−0.0222530	−	0.0684877i
$346$		0			0
$347$	28.7993	−	20.9239i	1.54603	−	1.12325i	0.599617	−	0.800287i	$-0.295319\pi$
$347$	28.7993	−	20.9239i	1.54603	−	1.12325i	0.946410	−	0.322968i	$-0.104681\pi$
$348$		0			0
$349$	5.97764	−	18.3973i	0.319976	−	0.984784i	−0.653682	−	0.756769i	$-0.726777\pi$
$349$	5.97764	−	18.3973i	0.319976	−	0.984784i	0.973658	−	0.228014i	$-0.0732234\pi$
$350$		0			0
$351$	−22.9244			−1.22361
$352$		0			0
$353$	−21.9354			−1.16750			−0.583752	−	0.811932i	$-0.698416\pi$
$353$	−21.9354			−1.16750			−0.583752	+	0.811932i	$0.698416\pi$
$354$		0			0
$355$	−0.812224	+	2.49977i	−0.0431084	+	0.132674i
$356$		0			0
$357$	−4.58703	+	3.33267i	−0.242772	+	0.176384i
$358$		0			0
$359$	−3.73528	−	11.4960i	−0.197140	−	0.606736i	−0.999945	−	0.0104936i	$-0.996660\pi$
$359$	−3.73528	−	11.4960i	−0.197140	−	0.606736i	0.802804	−	0.596242i	$-0.203340\pi$
$360$		0			0
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$		0			0
$363$	2.62224	−	22.1744i	0.137632	−	1.16385i
$364$		0			0
$365$	−0.0597106	−	0.0433823i	−0.00312540	−	0.00227073i
$366$		0			0
$367$	4.53801	+	13.9666i	0.236882	+	0.729049i	0.996866	+	0.0791070i	$0.0252069\pi$
$367$	4.53801	+	13.9666i	0.236882	+	0.729049i	−0.759984	+	0.649942i	$0.774793\pi$
$368$		0			0
$369$	−1.94935	+	1.41628i	−0.101479	+	0.0737288i
$370$		0			0
$371$	−2.62184	+	8.06921i	−0.136119	+	0.418932i
$372$		0			0
$373$	−34.5323			−1.78802			−0.894008	−	0.448051i	$-0.852118\pi$
$373$	−34.5323			−1.78802			−0.894008	+	0.448051i	$0.852118\pi$
$374$		0			0
$375$	−3.91057			−0.201941
$376$		0			0
$377$	−5.25340	+	16.1683i	−0.270564	+	0.832710i
$378$		0			0
$379$	23.3608	−	16.9726i	1.19996	−	0.871825i	0.205683	−	0.978619i	$-0.434058\pi$
$379$	23.3608	−	16.9726i	1.19996	−	0.871825i	0.994281	+	0.106794i	$0.0340585\pi$
$380$		0			0
$381$	−12.5548	−	38.6399i	−0.643204	−	1.97958i
$382$		0			0
$383$	−14.7066	−	10.6849i	−0.751471	−	0.545975i	0.144812	−	0.989459i	$-0.453742\pi$
$383$	−14.7066	−	10.6849i	−0.751471	−	0.545975i	−0.896282	+	0.443484i	$0.853742\pi$
$384$		0			0
$385$	1.47539	+	0.864640i	0.0751928	+	0.0440662i
$386$		0			0
$387$	0.290327	+	0.210935i	0.0147582	+	0.0107224i
$388$		0			0
$389$	−4.64677	−	14.3013i	−0.235601	−	0.725105i	−0.997041	−	0.0768697i	$-0.975507\pi$
$389$	−4.64677	−	14.3013i	−0.235601	−	0.725105i	0.761440	−	0.648235i	$-0.224493\pi$
$390$		0			0
$391$	−2.88788	+	2.09816i	−0.146046	+	0.106109i
$392$		0			0
$393$	−7.51368	+	23.1247i	−0.379015	+	1.16649i
$394$		0			0
$395$	0.392034			0.0197254
$396$		0			0
$397$	11.4739			0.575858			0.287929	−	0.957652i	$-0.407033\pi$
$397$	11.4739			0.575858			0.287929	+	0.957652i	$0.407033\pi$
$398$		0			0
$399$	−1.67257	+	5.14764i	−0.0837332	+	0.257704i
$400$		0			0
$401$	11.9701	−	8.69681i	0.597760	−	0.434298i	−0.247323	−	0.968933i	$-0.579551\pi$
$401$	11.9701	−	8.69681i	0.597760	−	0.434298i	0.845083	+	0.534635i	$0.179551\pi$
$402$		0			0
$403$	−0.973525	−	2.99620i	−0.0484947	−	0.149251i
$404$		0			0
$405$	1.73743	+	1.26232i	0.0863336	+	0.0627250i
$406$		0			0
$407$	−11.3302	−	25.8995i	−0.561619	−	1.28379i
$408$		0			0
$409$	−8.09094	−	5.87841i	−0.400071	−	0.290669i	0.369499	−	0.929231i	$-0.379529\pi$
$409$	−8.09094	−	5.87841i	−0.400071	−	0.290669i	−0.769570	+	0.638562i	$0.779529\pi$
$410$		0			0
$411$	−4.73529	−	14.5737i	−0.233575	−	0.718869i
$412$		0			0
$413$	27.8106	−	20.2056i	1.36847	−	0.994251i
$414$		0			0
$415$	−0.355664	+	1.09462i	−0.0174589	+	0.0537329i
$416$		0			0
$417$	18.3055			0.896423
$418$		0			0
$419$	−20.1247			−0.983155			−0.491578	−	0.870834i	$-0.663580\pi$
$419$	−20.1247			−0.983155			−0.491578	+	0.870834i	$0.663580\pi$
$420$		0			0
$421$	0.117423	−	0.361390i	0.00572284	−	0.0176131i	−0.948154	−	0.317810i	$-0.897052\pi$
$421$	0.117423	−	0.361390i	0.00572284	−	0.0176131i	0.953877	+	0.300197i	$0.0970525\pi$
$422$		0			0
$423$	3.39308	−	2.46522i	0.164977	−	0.119863i
$424$		0			0
$425$	1.60644	+	4.94412i	0.0779238	+	0.239825i
$426$		0			0
$427$	3.01341	+	2.18937i	0.145829	+	0.105951i
$428$		0			0
$429$	−30.2375	+	26.8724i	−1.45988	+	1.29741i
$430$		0			0
$431$	−16.4025	−	11.9171i	−0.790079	−	0.574026i	0.117908	−	0.993025i	$-0.462381\pi$
$431$	−16.4025	−	11.9171i	−0.790079	−	0.574026i	−0.907987	+	0.418999i	$0.862381\pi$
$432$		0			0
$433$	0.285724	+	0.879367i	0.0137310	+	0.0422597i	0.957687	−	0.287811i	$-0.0929275\pi$
$433$	0.285724	+	0.879367i	0.0137310	+	0.0422597i	−0.943956	+	0.330071i	$0.892927\pi$
$434$		0			0
$435$	0.898473	−	0.652779i	0.0430785	−	0.0312984i
$436$		0			0
$437$	−1.05301	+	3.24082i	−0.0503721	+	0.155029i
$438$		0			0
$439$	7.21669			0.344434			0.172217	−	0.985059i	$-0.444907\pi$
$439$	7.21669			0.344434			0.172217	+	0.985059i	$0.444907\pi$
$440$		0			0
$441$	0.122975			0.00585594
$442$		0			0
$443$	12.5024	−	38.4784i	0.594007	−	1.82817i	0.0344001	−	0.999408i	$-0.489048\pi$
$443$	12.5024	−	38.4784i	0.594007	−	1.82817i	0.559607	−	0.828758i	$-0.310952\pi$
$444$		0			0
$445$	1.32981	−	0.966166i	0.0630392	−	0.0458006i
$446$		0			0
$447$	−8.70355	−	26.7868i	−0.411664	−	1.26697i
$448$		0			0
$449$	6.60878	+	4.80156i	0.311888	+	0.226600i	0.732706	−	0.680545i	$-0.238257\pi$
$449$	6.60878	+	4.80156i	0.311888	+	0.226600i	−0.420818	+	0.907145i	$0.638257\pi$
$450$		0			0
$451$	1.52813	−	6.96651i	0.0719569	−	0.328040i
$452$		0			0
$453$	−13.0976	−	9.51599i	−0.615381	−	0.447100i
$454$		0			0
$455$	−0.957372	−	2.94649i	−0.0448823	−	0.138134i
$456$		0			0
$457$	−16.9312	+	12.3013i	−0.792009	+	0.575428i	−0.908559	−	0.417757i	$-0.862816\pi$
$457$	−16.9312	+	12.3013i	−0.792009	+	0.575428i	0.116550	+	0.993185i	$0.462816\pi$
$458$		0			0
$459$	1.23502	−	3.80100i	0.0576458	−	0.177416i
$460$		0			0
$461$	−18.6651			−0.869321			−0.434660	−	0.900594i	$-0.643132\pi$
$461$	−18.6651			−0.869321			−0.434660	+	0.900594i	$0.643132\pi$
$462$		0			0
$463$	25.1689			1.16970			0.584849	−	0.811142i	$-0.301154\pi$
$463$	25.1689			1.16970			0.584849	+	0.811142i	$0.301154\pi$
$464$		0			0
$465$	−0.0635970	+	0.195731i	−0.00294924	+	0.00907682i
$466$		0			0
$467$	−1.62156	+	1.17813i	−0.0750369	+	0.0545175i	−0.624671	−	0.780888i	$-0.714767\pi$
$467$	−1.62156	+	1.17813i	−0.0750369	+	0.0545175i	0.549634	+	0.835405i	$0.314767\pi$
$468$		0			0
$469$	7.73256	+	23.7984i	0.357057	+	1.09891i
$470$		0			0
$471$	−3.56267	−	2.58843i	−0.164159	−	0.119268i
$472$		0			0
$473$	−1.05711	+	0.104170i	−0.0486059	+	0.00478974i
$474$		0			0
$475$	4.01483	+	2.91695i	0.184213	+	0.133839i
$476$		0			0
$477$	1.10176	+	3.39087i	0.0504462	+	0.155257i
$478$		0			0
$479$	−12.4528	+	9.04745i	−0.568981	+	0.413389i	−0.834735	−	0.550652i	$-0.814379\pi$
$479$	−12.4528	+	9.04745i	−0.568981	+	0.413389i	0.265754	+	0.964041i	$0.414379\pi$
$480$		0			0
$481$	−15.8264	+	48.7086i	−0.721620	+	2.22092i
$482$		0			0
$483$	18.4438			0.839221
$484$		0			0
$485$	−2.30956			−0.104872
$486$		0			0
$487$	−5.87316	+	18.0757i	−0.266138	+	0.819089i	0.725291	+	0.688442i	$0.241705\pi$
$487$	−5.87316	+	18.0757i	−0.266138	+	0.819089i	−0.991429	+	0.130646i	$0.958295\pi$
$488$		0			0
$489$	30.9377	−	22.4776i	1.39905	−	1.01647i
$490$		0			0
$491$	10.6810	+	32.8727i	0.482026	+	1.48352i	0.836243	+	0.548360i	$0.184747\pi$
$491$	10.6810	+	32.8727i	0.482026	+	1.48352i	−0.354217	+	0.935163i	$0.615253\pi$
$492$		0			0
$493$	−2.39779	−	1.74209i	−0.107991	−	0.0784599i
$494$		0			0
$495$	0.715153	−	0.0704728i	0.0321437	−	0.00316752i
$496$		0			0
$497$	−29.3214	−	21.3033i	−1.31525	−	0.955582i
$498$		0			0
$499$	−5.65798	−	17.4135i	−0.253286	−	0.779534i	−0.994163	−	0.107893i	$-0.965590\pi$
$499$	−5.65798	−	17.4135i	−0.253286	−	0.779534i	0.740876	−	0.671641i	$-0.234410\pi$
$500$		0			0
$501$	17.6238	−	12.8045i	0.787374	−	0.572061i
$502$		0			0
$503$	1.11408	−	3.42879i	0.0496744	−	0.152882i	−0.923142	−	0.384458i	$-0.874388\pi$
$503$	1.11408	−	3.42879i	0.0496744	−	0.152882i	0.972817	+	0.231576i	$0.0743883\pi$
$504$		0			0
$505$	−1.18152			−0.0525767
$506$		0			0
$507$	46.8990			2.08286
$508$		0			0
$509$	−10.6577	+	32.8011i	−0.472396	+	1.45388i	0.377043	+	0.926196i	$0.376941\pi$
$509$	−10.6577	+	32.8011i	−0.472396	+	1.45388i	−0.849438	+	0.527688i	$0.823059\pi$
$510$		0			0
$511$	0.823353	−	0.598201i	0.0364230	−	0.0264628i
$512$		0			0
$513$	−1.17897	−	3.62849i	−0.0520526	−	0.160202i
$514$		0			0
$515$	−2.68980	−	1.95426i	−0.118527	−	0.0861148i
$516$		0			0
$517$	−2.65990	+	12.1261i	−0.116982	+	0.533304i
$518$		0			0
$519$	−37.3260	−	27.1190i	−1.63843	−	1.19039i
$520$		0			0
$521$	−9.19452	−	28.2978i	−0.402819	−	1.23975i	−0.922703	−	0.385513i	$-0.874025\pi$
$521$	−9.19452	−	28.2978i	−0.402819	−	1.23975i	0.519884	−	0.854237i	$-0.325975\pi$
$522$		0			0
$523$	5.38812	−	3.91470i	0.235606	−	0.171178i	−0.463717	−	0.885983i	$-0.653485\pi$
$523$	5.38812	−	3.91470i	0.235606	−	0.171178i	0.699323	+	0.714805i	$0.253485\pi$
$524$		0			0
$525$	8.30030	−	25.5457i	0.362255	−	1.11491i
$526$		0			0
$527$	0.549236			0.0239251
$528$		0			0
$529$	−11.3883			−0.495143
$530$		0			0
$531$	4.46391	−	13.7385i	0.193717	−	0.596201i
$532$		0			0
$533$	−10.4534	+	7.59487i	−0.452789	+	0.328971i
$534$		0			0
$535$	0.788676	+	2.42730i	0.0340974	+	0.104941i
$536$		0			0
$537$	−0.537994	−	0.390875i	−0.0232161	−	0.0168675i
$538$		0			0
$539$	−0.272083	+	0.241803i	−0.0117194	+	0.0104152i
$540$		0			0
$541$	−30.8249	−	22.3956i	−1.32527	−	0.962863i	−0.999850	−	0.0172920i	$-0.994496\pi$
$541$	−30.8249	−	22.3956i	−1.32527	−	0.962863i	−0.325416	−	0.945571i	$-0.605504\pi$
$542$		0			0
$543$	2.11493	+	6.50908i	0.0907602	+	0.279331i
$544$		0			0
$545$	−1.60811	+	1.16836i	−0.0688840	+	0.0500472i
$546$		0			0
$547$	−7.08243	+	21.7975i	−0.302823	+	0.931993i	0.677658	+	0.735377i	$0.262995\pi$
$547$	−7.08243	+	21.7975i	−0.302823	+	0.931993i	−0.980481	+	0.196615i	$0.937005\pi$
$548$		0			0
$549$	1.56524			0.0668030
$550$		0			0
$551$	−2.82931			−0.120533
$552$		0			0
$553$	−1.67048	+	5.14120i	−0.0710359	+	0.218626i
$554$		0			0
$555$	2.70673	−	1.96656i	0.114895	−	0.0834757i
$556$		0			0
$557$	7.64413	+	23.5262i	0.323892	+	0.996838i	0.971938	+	0.235237i	$0.0755865\pi$
$557$	7.64413	+	23.5262i	0.323892	+	0.996838i	−0.648046	+	0.761601i	$0.724413\pi$
$558$		0			0
$559$	1.55689	+	1.13115i	0.0658494	+	0.0478424i
$560$		0			0
$561$	−2.82661	−	6.46128i	−0.119340	−	0.272795i
$562$		0			0
$563$	8.11393	+	5.89511i	0.341961	+	0.248449i	0.745489	−	0.666518i	$-0.232216\pi$
$563$	8.11393	+	5.89511i	0.341961	+	0.248449i	−0.403528	+	0.914967i	$0.632216\pi$
$564$		0			0
$565$	0.227487	+	0.700134i	0.00957047	+	0.0294549i
$566$		0			0
$567$	−23.9575	+	17.4061i	−1.00612	+	0.730989i
$568$		0			0
$569$	−4.95808	+	15.2594i	−0.207854	+	0.639707i	0.791731	+	0.610870i	$0.209180\pi$
$569$	−4.95808	+	15.2594i	−0.207854	+	0.639707i	−0.999584	+	0.0288370i	$0.990820\pi$
$570$		0			0
$571$	−2.07588			−0.0868730			−0.0434365	−	0.999056i	$-0.513831\pi$
$571$	−2.07588			−0.0868730			−0.0434365	+	0.999056i	$0.513831\pi$
$572$		0			0
$573$	8.03636			0.335724
$574$		0			0
$575$	5.22565	−	16.0829i	0.217925	−	0.670704i
$576$		0			0
$577$	−30.6945	+	22.3008i	−1.27783	+	0.928396i	−0.999485	−	0.0320860i	$-0.989785\pi$
$577$	−30.6945	+	22.3008i	−1.27783	+	0.928396i	−0.278342	+	0.960482i	$0.589785\pi$
$578$		0			0
$579$	7.56327	+	23.2773i	0.314319	+	0.967373i
$580$		0			0
$581$	−12.8395	−	9.32847i	−0.532674	−	0.387010i
$582$		0			0
$583$	−9.10508	−	5.33596i	−0.377094	−	0.220993i
$584$		0			0
$585$	−1.05326	−	0.765241i	−0.0435471	−	0.0316388i
$586$		0			0
$587$	−3.30866	−	10.1830i	−0.136563	−	0.420298i	0.859267	−	0.511528i	$-0.170920\pi$
$587$	−3.30866	−	10.1830i	−0.136563	−	0.420298i	−0.995830	+	0.0912297i	$0.970920\pi$
$588$		0			0
$589$	0.424174	−	0.308181i	0.0174778	−	0.0126984i
$590$		0			0
$591$	9.26046	−	28.5008i	0.380924	−	1.17236i
$592$		0			0
$593$	−15.9385			−0.654515			−0.327257	−	0.944935i	$-0.606124\pi$
$593$	−15.9385			−0.654515			−0.327257	+	0.944935i	$0.606124\pi$
$594$		0			0
$595$	0.540123			0.0221429
$596$		0			0
$597$	6.99032	−	21.5140i	0.286095	−	0.880509i
$598$		0			0
$599$	−8.21285	+	5.96698i	−0.335568	+	0.243804i	−0.742789	−	0.669525i	$-0.766498\pi$
$599$	−8.21285	+	5.96698i	−0.335568	+	0.243804i	0.407222	+	0.913329i	$0.366498\pi$
$600$		0			0
$601$	8.55184	+	26.3199i	0.348837	+	1.07361i	0.959498	+	0.281717i	$0.0909040\pi$
$601$	8.55184	+	26.3199i	0.348837	+	1.07361i	−0.610661	+	0.791892i	$0.709096\pi$
$602$		0			0
$603$	8.50706	+	6.18074i	0.346434	+	0.251699i
$604$		0			0
$605$	−1.44371	+	1.56212i	−0.0586952	+	0.0635090i
$606$		0			0
$607$	5.00247	+	3.63451i	0.203044	+	0.147520i	0.684661	−	0.728862i	$-0.259950\pi$
$607$	5.00247	+	3.63451i	0.203044	+	0.147520i	−0.481617	+	0.876382i	$0.659950\pi$
$608$		0			0
$609$	4.73221	+	14.5642i	0.191759	+	0.590173i
$610$		0			0
$611$	18.1955	−	13.2198i	0.736113	−	0.534817i
$612$		0			0
$613$	−12.3395	+	37.9771i	−0.498389	+	1.53388i	0.313220	+	0.949681i	$0.398592\pi$
$613$	−12.3395	+	37.9771i	−0.498389	+	1.53388i	−0.811608	+	0.584202i	$0.801408\pi$
$614$		0			0
$615$	0.844094			0.0340372
$616$		0			0
$617$	22.0143			0.886263			0.443131	−	0.896457i	$-0.353868\pi$
$617$	22.0143			0.886263			0.443131	+	0.896457i	$0.353868\pi$
$618$		0			0
$619$	−1.33240	+	4.10072i	−0.0535539	+	0.164822i	−0.974256	−	0.225444i	$-0.927617\pi$
$619$	−1.33240	+	4.10072i	−0.0535539	+	0.164822i	0.920702	+	0.390266i	$0.127617\pi$
$620$		0			0
$621$	−10.5178	+	7.64163i	−0.422065	+	0.306648i
$622$		0			0
$623$	7.00405	+	21.5563i	0.280611	+	0.863633i
$624$		0			0
$625$	−19.7728	−	14.3658i	−0.790911	−	0.574631i
$626$		0			0
$627$	−5.80846	−	3.40400i	−0.231967	−	0.135943i
$628$		0			0
$629$	−7.22355	−	5.24822i	−0.288022	−	0.209260i
$630$		0			0
$631$	13.0523	+	40.1709i	0.519604	+	1.59918i	0.774745	+	0.632273i	$0.217878\pi$
$631$	13.0523	+	40.1709i	0.519604	+	1.59918i	−0.255141	+	0.966904i	$0.582122\pi$
$632$		0			0
$633$	31.1718	−	22.6476i	1.23897	−	0.900161i
$634$		0			0
$635$	−1.19600	+	3.68090i	−0.0474617	+	0.146072i
$636$		0			0
$637$	0.659457			0.0261286
$638$		0			0
$639$	−15.2303			−0.602501
$640$		0			0
$641$	12.5753	−	38.7027i	0.496694	−	1.52867i	−0.317607	−	0.948223i	$-0.602879\pi$
$641$	12.5753	−	38.7027i	0.496694	−	1.52867i	0.814300	−	0.580444i	$-0.197121\pi$
$642$		0			0
$643$	14.2166	−	10.3289i	0.560647	−	0.407334i	−0.271049	−	0.962566i	$-0.587370\pi$
$643$	14.2166	−	10.3289i	0.560647	−	0.407334i	0.831696	+	0.555232i	$0.187370\pi$
$644$		0			0
$645$	−0.0388483	−	0.119563i	−0.00152965	−	0.00470778i
$646$		0			0
$647$	38.5358	+	27.9979i	1.51500	+	1.10071i	0.963898	+	0.266270i	$0.0857914\pi$
$647$	38.5358	+	27.9979i	1.51500	+	1.10071i	0.551099	+	0.834440i	$0.314209\pi$
$648$		0			0
$649$	17.1374	+	39.1739i	0.672700	+	1.53771i
$650$		0			0
$651$	−2.29586	−	1.66804i	−0.0899819	−	0.0653757i
$652$		0			0
$653$	−2.77305	−	8.53458i	−0.108518	−	0.333984i	0.882022	−	0.471208i	$-0.156182\pi$
$653$	−2.77305	−	8.53458i	−0.108518	−	0.333984i	−0.990540	+	0.137224i	$0.956182\pi$
$654$		0			0
$655$	1.87390	−	1.36147i	0.0732193	−	0.0531970i
$656$		0			0
$657$	0.132157	−	0.406739i	0.00515595	−	0.0158684i
$658$		0			0
$659$	22.8623			0.890589			0.445294	−	0.895384i	$-0.353099\pi$
$659$	22.8623			0.890589			0.445294	+	0.895384i	$0.353099\pi$
$660$		0			0
$661$	−19.7189			−0.766977			−0.383489	−	0.923546i	$-0.625277\pi$
$661$	−19.7189			−0.766977			−0.383489	+	0.923546i	$0.625277\pi$
$662$		0			0
$663$	−3.94828	+	12.1516i	−0.153338	+	0.471927i
$664$		0			0
$665$	0.417136	−	0.303067i	0.0161758	−	0.0117524i
$666$		0			0
$667$	2.97928	+	9.16927i	0.115358	+	0.355035i
$668$		0			0
$669$	30.7581	+	22.3471i	1.18918	+	0.863989i
$670$		0			0
$671$	−3.46311	+	3.07771i	−0.133692	+	0.118814i
$672$		0			0
$673$	−28.3357	−	20.5871i	−1.09226	−	0.793574i	−0.112481	−	0.993654i	$-0.535880\pi$
$673$	−28.3357	−	20.5871i	−1.09226	−	0.793574i	−0.979779	+	0.200080i	$0.935880\pi$
$674$		0			0
$675$	5.85075	+	18.0067i	0.225195	+	0.693080i
$676$		0			0
$677$	5.12336	−	3.72234i	0.196907	−	0.143061i	−0.484963	−	0.874535i	$-0.661167\pi$
$677$	5.12336	−	3.72234i	0.196907	−	0.143061i	0.681870	+	0.731473i	$0.261167\pi$
$678$		0			0
$679$	9.84116	−	30.2880i	0.377669	−	1.16235i
$680$		0			0
$681$	−3.12343			−0.119690
$682$		0			0
$683$	28.9755			1.10872			0.554359	−	0.832278i	$-0.312963\pi$
$683$	28.9755			1.10872			0.554359	+	0.832278i	$0.312963\pi$
$684$		0			0
$685$	−0.451092	+	1.38832i	−0.0172354	+	0.0530450i
$686$		0			0
$687$	19.8037	−	14.3882i	0.755557	−	0.548944i
$688$		0			0
$689$	5.90824	+	18.1837i	0.225086	+	0.692743i
$690$		0			0
$691$	13.1761	+	9.57298i	0.501242	+	0.364173i	0.809491	−	0.587132i	$-0.199743\pi$
$691$	13.1761	+	9.57298i	0.501242	+	0.364173i	−0.308249	+	0.951306i	$0.599743\pi$
$692$		0			0
$693$	−2.12311	+	9.67892i	−0.0806503	+	0.367672i
$694$		0			0
$695$	−1.41077	−	1.02499i	−0.0535137	−	0.0388800i
$696$		0			0
$697$	−0.696111	−	2.14241i	−0.0263671	−	0.0811495i
$698$		0			0
$699$	−19.6407	+	14.2698i	−0.742880	+	0.539734i
$700$		0			0
$701$	−9.97055	+	30.6862i	−0.376583	+	1.15900i	0.565822	+	0.824527i	$0.308559\pi$
$701$	−9.97055	+	30.6862i	−0.376583	+	1.15900i	−0.942405	+	0.334475i	$0.891441\pi$
$702$		0			0
$703$	−8.52355			−0.321472
$704$		0			0
$705$	−1.46925			−0.0553352
$706$		0			0
$707$	5.03450	−	15.4946i	0.189342	−	0.582734i
$708$		0			0
$709$	−33.5000	+	24.3391i	−1.25812	+	0.914076i	−0.998664	−	0.0516799i	$-0.983542\pi$
$709$	−33.5000	+	24.3391i	−1.25812	+	0.914076i	−0.259454	+	0.965756i	$0.583542\pi$
$710$		0			0
$711$	0.701974	+	2.16045i	0.0263261	+	0.0810234i
$712$		0			0
$713$	−1.44541	−	1.05016i	−0.0541312	−	0.0393286i
$714$		0			0
$715$	3.83503	−	0.377913i	0.143422	−	0.0141332i
$716$		0			0
$717$	40.2155	+	29.2183i	1.50188	+	1.09118i
$718$		0			0
$719$	1.80346	+	5.55048i	0.0672577	+	0.206998i	0.979037	−	0.203683i	$-0.0652911\pi$
$719$	1.80346	+	5.55048i	0.0672577	+	0.206998i	−0.911779	+	0.410681i	$0.865291\pi$
$720$		0			0
$721$	37.0898	−	26.9473i	1.38130	−	1.00357i
$722$		0			0
$723$	−4.45700	+	13.7172i	−0.165758	+	0.510149i
$724$		0			0
$725$	14.0407			0.521460
$726$		0			0
$727$	45.2851			1.67953			0.839766	−	0.542948i	$-0.182692\pi$
$727$	45.2851			1.67953			0.839766	+	0.542948i	$0.182692\pi$
$728$		0			0
$729$	3.33410	−	10.2613i	0.123485	−	0.380048i
$730$		0			0
$731$	−0.271427	+	0.197203i	−0.0100391	+	0.00729381i
$732$		0			0
$733$	6.61365	+	20.3547i	0.244281	+	0.751818i	0.995754	+	0.0920549i	$0.0293435\pi$
$733$	6.61365	+	20.3547i	0.244281	+	0.751818i	−0.751473	+	0.659763i	$0.770656\pi$
$734$		0			0
$735$	−0.0348524	−	0.0253218i	−0.00128555	−	0.000934008i
$736$		0			0
$737$	−30.9750	+	3.05235i	−1.14098	+	0.112435i
$738$		0			0
$739$	−17.1932	−	12.4916i	−0.632462	−	0.459510i	0.224790	−	0.974407i	$-0.427830\pi$
$739$	−17.1932	−	12.4916i	−0.632462	−	0.459510i	−0.857252	+	0.514897i	$0.827830\pi$
$740$		0			0
$741$	3.76908	+	11.6000i	0.138461	+	0.426138i
$742$		0			0
$743$	−31.2172	+	22.6806i	−1.14525	+	0.832072i	−0.987842	−	0.155462i	$-0.950313\pi$
$743$	−31.2172	+	22.6806i	−1.14525	+	0.832072i	−0.157407	+	0.987534i	$0.550313\pi$
$744$		0			0
$745$	−0.829116	+	2.55176i	−0.0303764	+	0.0934891i
$746$		0			0
$747$	−6.66918			−0.244013
$748$		0			0
$749$	−35.1925			−1.28591
$750$		0			0
$751$	−3.98126	+	12.2530i	−0.145278	+	0.447120i	−0.997047	−	0.0767982i	$-0.975530\pi$
$751$	−3.98126	+	12.2530i	−0.145278	+	0.447120i	0.851769	+	0.523918i	$0.175530\pi$
$752$		0			0
$753$	18.6886	−	13.5781i	0.681051	−	0.494812i
$754$		0			0
$755$	0.476580	+	1.46676i	0.0173445	+	0.0533810i
$756$		0			0
$757$	−5.88578	−	4.27627i	−0.213922	−	0.155424i	0.475664	−	0.879627i	$-0.342208\pi$
$757$	−5.88578	−	4.27627i	−0.213922	−	0.155424i	−0.689587	+	0.724203i	$0.742208\pi$
$758$		0			0
$759$	−4.91541	+	22.4086i	−0.178418	+	0.813380i
$760$		0			0
$761$	−39.3375	−	28.5804i	−1.42598	−	1.03604i	−0.990747	−	0.135723i	$-0.956664\pi$
$761$	−39.3375	−	28.5804i	−1.42598	−	1.03604i	−0.435238	−	0.900316i	$-0.643336\pi$
$762$		0			0
$763$	−8.46985	−	26.0675i	−0.306629	−	0.943707i
$764$		0			0
$765$	0.183625	−	0.133411i	0.00663897	−	0.00482349i
$766$		0			0
$767$	23.9379	−	73.6733i	0.864347	−	2.66019i
$768$		0			0
$769$	−13.3111			−0.480011			−0.240005	−	0.970772i	$-0.577149\pi$
$769$	−13.3111			−0.480011			−0.240005	+	0.970772i	$0.577149\pi$
$770$		0			0
$771$	−19.4520			−0.700545
$772$		0			0
$773$	−5.88813	+	18.1218i	−0.211781	+	0.651796i	0.787585	+	0.616206i	$0.211331\pi$
$773$	−5.88813	+	18.1218i	−0.211781	+	0.651796i	−0.999366	+	0.0355901i	$0.988669\pi$
$774$		0			0
$775$	−2.10501	+	1.52938i	−0.0756142	+	0.0549369i
$776$		0			0
$777$	14.2562	+	43.8762i	0.511439	+	1.57405i
$778$		0			0
$779$	−1.73973	−	1.26399i	−0.0623322	−	0.0452870i
$780$		0			0
$781$	33.6972	−	29.9471i	1.20578	−	1.07159i
$782$		0			0
$783$	−8.73286	−	6.34480i	−0.312087	−	0.226745i
$784$		0			0
$785$	0.129634	+	0.398972i	0.00462683	+	0.0142399i
$786$		0			0
$787$	34.0606	−	24.7465i	1.21413	−	0.882117i	0.218531	−	0.975830i	$-0.429874\pi$
$787$	34.0606	−	24.7465i	1.21413	−	0.882117i	0.995599	+	0.0937130i	$0.0298736\pi$
$788$		0			0
$789$	−16.1732	+	49.7759i	−0.575780	+	1.77207i
$790$		0			0
$791$	−10.1510			−0.360928
$792$		0			0
$793$	8.39368			0.298068
$794$		0			0
$795$	0.385964	−	1.18788i	0.0136887	−	0.0421296i
$796$		0			0
$797$	22.6671	−	16.4686i	0.802909	−	0.583347i	−0.108857	−	0.994057i	$-0.534719\pi$
$797$	22.6671	−	16.4686i	0.802909	−	0.583347i	0.911766	+	0.410710i	$0.134719\pi$
$798$		0			0
$799$	1.21167	+	3.72913i	0.0428657	+	0.131927i
$800$		0			0
$801$	7.70558	+	5.59843i	0.272263	+	0.197811i
$802$		0			0
$803$	0.507364	+	1.15977i	0.0179045	+	0.0409274i
$804$		0			0
$805$	−1.42143	−	1.03273i	−0.0500989	−	0.0363990i
$806$		0			0
$807$	−7.02996	−	21.6360i	−0.247466	−	0.761623i
$808$		0			0
$809$	−15.4284	+	11.2094i	−0.542433	+	0.394101i	−0.824988	−	0.565151i	$-0.808818\pi$
$809$	−15.4284	+	11.2094i	−0.542433	+	0.394101i	0.282555	+	0.959251i	$0.408818\pi$
$810$		0			0
$811$	10.3439	−	31.8353i	0.363224	−	1.11789i	−0.587862	−	0.808961i	$-0.700030\pi$
$811$	10.3439	−	31.8353i	0.363224	−	1.11789i	0.951086	−	0.308926i	$-0.0999696\pi$
$812$		0			0
$813$	−11.0317			−0.386897
$814$		0			0
$815$	−3.64291			−0.127606
$816$		0			0
$817$	−0.0989702	+	0.304599i	−0.00346253	+	0.0106566i
$818$		0			0
$819$	14.5235	−	10.5519i	0.507492	−	0.368715i
$820$		0			0
$821$	1.22370	+	3.76615i	0.0427073	+	0.131440i	0.970137	−	0.242558i	$-0.0779866\pi$
$821$	1.22370	+	3.76615i	0.0427073	+	0.131440i	−0.927429	+	0.373998i	$0.877987\pi$
$822$		0			0
$823$	−23.0882	−	16.7745i	−0.804803	−	0.584724i	0.107516	−	0.994203i	$-0.465710\pi$
$823$	−23.0882	−	16.7745i	−0.804803	−	0.584724i	−0.912319	+	0.409479i	$0.865710\pi$
$824$		0			0
$825$	28.8251	+	16.8927i	1.00356	+	0.588129i
$826$		0			0
$827$	35.6548	+	25.9047i	1.23984	+	0.900795i	0.997588	−	0.0694188i	$-0.0221145\pi$
$827$	35.6548	+	25.9047i	1.23984	+	0.900795i	0.242250	+	0.970214i	$0.422114\pi$
$828$		0			0
$829$	−0.999027	−	3.07469i	−0.0346976	−	0.106788i	0.932208	−	0.361924i	$-0.117880\pi$
$829$	−0.999027	−	3.07469i	−0.0346976	−	0.106788i	−0.966905	+	0.255135i	$0.917880\pi$
$830$		0			0
$831$	14.1216	−	10.2599i	0.489873	−	0.355913i
$832$		0			0
$833$	−0.0355274	+	0.109342i	−0.00123095	+	0.00378848i
$834$		0			0
$835$	−2.07521			−0.0718154
$836$		0			0
$837$	2.00035			0.0691421
$838$		0			0
$839$	−1.05035	+	3.23264i	−0.0362621	+	0.111603i	−0.967549	−	0.252683i	$-0.918687\pi$
$839$	−1.05035	+	3.23264i	−0.0362621	+	0.111603i	0.931287	+	0.364286i	$0.118687\pi$
$840$		0			0
$841$	16.9853	−	12.3406i	0.585701	−	0.425537i
$842$		0			0
$843$	−7.89756	−	24.3062i	−0.272007	−	0.837150i
$844$		0			0
$845$	−3.61443	−	2.62604i	−0.124340	−	0.0903384i
$846$		0			0
$847$	−14.3341	−	25.5893i	−0.492526	−	0.879260i
$848$		0			0
$849$	−8.33204	−	6.05358i	−0.285955	−	0.207758i
$850$		0			0
$851$	8.97535	+	27.6233i	0.307671	+	0.946914i
$852$		0			0
$853$	−10.2308	+	7.43311i	−0.350296	+	0.254505i	−0.748993	−	0.662578i	$-0.769462\pi$
$853$	−10.2308	+	7.43311i	−0.350296	+	0.254505i	0.398697	+	0.917083i	$0.369462\pi$
$854$		0			0
$855$	0.0669551	−	0.206066i	0.00228981	−	0.00704732i
$856$		0			0
$857$	49.2552			1.68252			0.841262	−	0.540628i	$-0.181813\pi$
$857$	49.2552			1.68252			0.841262	+	0.540628i	$0.181813\pi$
$858$		0			0
$859$	8.70687			0.297075			0.148537	−	0.988907i	$-0.452543\pi$
$859$	8.70687			0.297075			0.148537	+	0.988907i	$0.452543\pi$
$860$		0			0
$861$	−3.59673	+	11.0696i	−0.122576	+	0.377251i
$862$		0			0
$863$	16.0602	−	11.6684i	0.546694	−	0.397197i	−0.279871	−	0.960038i	$-0.590292\pi$
$863$	16.0602	−	11.6684i	0.546694	−	0.397197i	0.826565	+	0.562841i	$0.190292\pi$
$864$		0			0
$865$	1.35817	+	4.18003i	0.0461793	+	0.142125i
$866$		0			0
$867$	26.1157	+	18.9742i	0.886935	+	0.644396i
$868$		0			0
$869$	−5.80119	−	3.39974i	−0.196792	−	0.115328i
$870$		0			0
$871$	45.6194	+	33.1445i	1.54576	+	1.12306i
$872$		0			0
$873$	−4.13549	−	12.7277i	−0.139965	−	0.430768i
$874$		0			0
$875$	−4.15576	+	3.01934i	−0.140490	+	0.102072i
$876$		0			0
$877$	−6.91405	+	21.2793i	−0.233471	+	0.718549i	0.763850	+	0.645394i	$0.223307\pi$
$877$	−6.91405	+	21.2793i	−0.233471	+	0.718549i	−0.997321	+	0.0731552i	$0.976693\pi$
$878$		0			0
$879$	52.6945			1.77734
$880$		0			0
$881$	48.1713			1.62293			0.811466	−	0.584400i	$-0.198670\pi$
$881$	48.1713			1.62293			0.811466	+	0.584400i	$0.198670\pi$
$882$		0			0
$883$	−2.77127	+	8.52909i	−0.0932606	+	0.287027i	−0.986796	−	0.161965i	$-0.948217\pi$
$883$	−2.77127	+	8.52909i	−0.0932606	+	0.287027i	0.893536	+	0.448992i	$0.148217\pi$
$884$		0			0
$885$	−4.09402	+	2.97448i	−0.137619	+	0.0999861i
$886$		0			0
$887$	−3.84797	−	11.8428i	−0.129202	−	0.397643i	0.865441	−	0.501011i	$-0.167038\pi$
$887$	−3.84797	−	11.8428i	−0.129202	−	0.397643i	−0.994643	+	0.103367i	$0.967038\pi$
$888$		0			0
$889$	−43.1757	−	31.3690i	−1.44807	−	1.05208i
$890$		0			0
$891$	−14.7630	−	33.7464i	−0.494580	−	1.13055i
$892$		0			0
$893$	3.02821	+	2.20013i	0.101335	+	0.0736244i
$894$		0			0
$895$	0.0195758	+	0.0602483i	0.000654348	+	0.00201388i
$896$		0			0
$897$	33.6247	−	24.4298i	1.12270	−	0.815687i
$898$		0			0
$899$	0.458405	−	1.41082i	0.0152886	−	0.0470536i
$900$		0			0
$901$	−3.33327			−0.111047
$902$		0			0
$903$	1.73350			0.0576872
$904$		0			0
$905$	0.201472	−	0.620066i	0.00669715	−	0.0206117i
$906$		0			0
$907$	44.5329	−	32.3550i	1.47869	−	1.07433i	0.500714	−	0.865613i	$-0.333071\pi$
$907$	44.5329	−	32.3550i	1.47869	−	1.07433i	0.977976	−	0.208718i	$-0.0669290\pi$
$908$		0			0
$909$	−2.11562	−	6.51120i	−0.0701705	−	0.215963i
$910$		0			0
$911$	32.4999	+	23.6126i	1.07677	+	0.782319i	0.977117	−	0.212703i	$-0.0682267\pi$
$911$	32.4999	+	23.6126i	1.07677	+	0.782319i	0.0996530	+	0.995022i	$0.468227\pi$
$912$		0			0
$913$	14.7556	−	13.1135i	0.488340	−	0.433994i
$914$		0			0
$915$	−0.443608	−	0.322300i	−0.0146652	−	0.0106549i
$916$		0			0
$917$	9.86973	+	30.3759i	0.325927	+	1.00310i
$918$		0			0
$919$	−33.9805	+	24.6883i	−1.12091	+	0.814392i	−0.984347	−	0.176239i	$-0.943607\pi$
$919$	−33.9805	+	24.6883i	−1.12091	+	0.814392i	−0.136567	+	0.990631i	$0.543607\pi$
$920$		0			0
$921$	−17.8211	+	54.8478i	−0.587226	+	1.80730i
$922$		0			0
$923$	−81.6730			−2.68830
$924$		0			0
$925$	42.2990			1.39078
$926$		0			0
$927$	5.95334	−	18.3225i	0.195533	−	0.601789i
$928$		0			0
$929$	8.03420	−	5.83719i	0.263594	−	0.191512i	−0.448136	−	0.893965i	$-0.647912\pi$
$929$	8.03420	−	5.83719i	0.263594	−	0.191512i	0.711730	+	0.702453i	$0.247912\pi$
$930$		0			0
$931$	0.0339149	+	0.104379i	0.00111152	+	0.00342089i
$932$		0			0
$933$	36.3669	+	26.4221i	1.19060	+	0.865022i
$934$		0			0
$935$	−0.143947	+	0.656232i	−0.00470757	+	0.0214611i
$936$		0			0
$937$	−14.6402	−	10.6367i	−0.478273	−	0.347486i	0.322384	−	0.946609i	$-0.395516\pi$
$937$	−14.6402	−	10.6367i	−0.478273	−	0.347486i	−0.800657	+	0.599123i	$0.795516\pi$
$938$		0			0
$939$	16.1859	+	49.8152i	0.528208	+	1.62566i
$940$		0			0
$941$	3.08831	−	2.24379i	0.100676	−	0.0731455i	−0.536308	−	0.844022i	$-0.680182\pi$
$941$	3.08831	−	2.24379i	0.100676	−	0.0731455i	0.636984	+	0.770877i	$0.280182\pi$
$942$		0			0
$943$	−2.26441	+	6.96912i	−0.0737392	+	0.226946i
$944$		0			0
$945$	1.96716			0.0639917
$946$		0			0
$947$	17.5947			0.571752			0.285876	−	0.958267i	$-0.407715\pi$
$947$	17.5947			0.571752			0.285876	+	0.958267i	$0.407715\pi$
$948$		0			0
$949$	0.708699	−	2.18115i	0.0230053	−	0.0708032i
$950$		0			0
$951$	−50.5651	+	36.7377i	−1.63969	+	1.19130i
$952$		0			0
$953$	17.0578	+	52.4986i	0.552557	+	1.70060i	0.702309	+	0.711873i	$0.252153\pi$
$953$	17.0578	+	52.4986i	0.552557	+	1.70060i	−0.149752	+	0.988724i	$0.547847\pi$
$954$		0			0
$955$	−0.619350	−	0.449984i	−0.0200417	−	0.0145611i
$956$		0			0
$957$	−18.9562	+	1.86799i	−0.612768	+	0.0603836i
$958$		0			0
$959$	−16.2845	−	11.8314i	−0.525855	−	0.382056i
$960$		0			0
$961$	−9.49458	−	29.2213i	−0.306277	−	0.942623i
$962$		0			0
$963$	−11.9643	+	8.69261i	−0.385546	+	0.280115i
$964$		0			0
$965$	0.720490	−	2.21744i	0.0231934	−	0.0713819i
$966$		0			0
$967$	57.3979			1.84579			0.922897	−	0.385048i	$-0.125815\pi$
$967$	57.3979			1.84579			0.922897	+	0.385048i	$0.125815\pi$
$968$		0			0
$969$	−2.12641			−0.0683101
$970$		0			0
$971$	−7.53038	+	23.1761i	−0.241662	+	0.743758i	0.754506	+	0.656293i	$0.227876\pi$
$971$	−7.53038	+	23.1761i	−0.241662	+	0.743758i	−0.996168	+	0.0874647i	$0.972124\pi$
$972$		0			0
$973$	19.4532	−	14.1336i	0.623642	−	0.453102i
$974$		0			0
$975$	−18.7045	−	57.5664i	−0.599022	−	1.84360i
$976$		0			0
$977$	−22.1209	−	16.0718i	−0.707712	−	0.514183i	0.174723	−	0.984618i	$-0.444097\pi$
$977$	−22.1209	−	16.0718i	−0.707712	−	0.514183i	−0.882435	+	0.470435i	$0.844097\pi$
$978$		0			0
$979$	−28.0568	+	2.76478i	−0.896699	+	0.0883628i
$980$		0			0
$981$	−9.31819	−	6.77006i	−0.297507	−	0.216151i
$982$		0			0
$983$	−7.78741	−	23.9672i	−0.248380	−	0.764435i	−0.995062	−	0.0992538i	$-0.968354\pi$
$983$	−7.78741	−	23.9672i	−0.248380	−	0.764435i	0.746682	−	0.665181i	$-0.231646\pi$
$984$		0			0
$985$	−2.30954	+	1.67798i	−0.0735882	+	0.0534650i
$986$		0			0
$987$	6.26055	−	19.2680i	0.199276	−	0.613307i
$988$		0			0
$989$	1.09137			0.0347034
$990$		0			0
$991$	−17.2779			−0.548851			−0.274425	−	0.961608i	$-0.588488\pi$
$991$	−17.2779			−0.548851			−0.274425	+	0.961608i	$0.588488\pi$
$992$		0			0
$993$	13.5459	−	41.6899i	0.429865	−	1.32299i
$994$		0			0
$995$	−1.74338	+	1.26664i	−0.0552687	+	0.0401551i
$996$		0			0
$997$	1.98784	+	6.11795i	0.0629556	+	0.193757i	0.977587	−	0.210531i	$-0.0675193\pi$
$997$	1.98784	+	6.11795i	0.0629556	+	0.193757i	−0.914632	+	0.404288i	$0.867519\pi$
$998$		0			0
$999$	−26.3086	−	19.1143i	−0.832367	−	0.604750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	836.2.j.b.609.5	✓	20
11.3	even	5	inner	836.2.j.b.685.5	yes	20
11.5	even	5		9196.2.a.s.1.8		10
11.6	odd	10		9196.2.a.t.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
836.2.j.b.609.5	✓	20	1.1	even	1	trivial
836.2.j.b.685.5	yes	20	11.3	even	5	inner
9196.2.a.s.1.8		10	11.5	even	5
9196.2.a.t.1.8		10	11.6	odd	10

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:	\( N \)	\(=\)	\( 836 = 2^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	836.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.627273 - 1.93055i) q^{3} +(-0.156441 + 0.113661i) q^{5} +(-0.823967 - 2.53591i) q^{7} +(-0.906495 - 0.658608i) q^{9} +(3.30064 - 0.325253i) q^{11} +(-4.86112 - 3.53181i) q^{13} +(0.121297 + 0.373314i) q^{15} +(0.847482 - 0.615731i) q^{17} +(0.309017 - 0.951057i) q^{19} -5.41255 q^{21} -3.40760 q^{23} +(-1.53353 + 4.71972i) q^{25} +(3.08657 - 2.24253i) q^{27} +(-0.874304 - 2.69083i) q^{29} +(0.424174 + 0.308181i) q^{31} +(1.44249 - 6.57606i) q^{33} +(0.417136 + 0.303067i) q^{35} +(-2.63392 - 8.10638i) q^{37} +(-9.86757 + 7.16921i) q^{39} +(0.664517 - 2.04517i) q^{41} -0.320274 q^{43} +0.216671 q^{45} +(-1.15667 + 3.55988i) q^{47} +(-0.0887904 + 0.0645100i) q^{49} +(-0.657097 - 2.02234i) q^{51} +(-2.57428 - 1.87032i) q^{53} +(-0.479387 + 0.426037i) q^{55} +(-1.64222 - 1.19314i) q^{57} +(3.98389 + 12.2612i) q^{59} +(-1.13014 + 0.821094i) q^{61} +(-0.923246 + 2.84146i) q^{63} +1.16191 q^{65} -9.38456 q^{67} +(-2.13749 + 6.57853i) q^{69} +(10.9966 - 7.98949i) q^{71} +(0.117946 + 0.363001i) q^{73} +(8.14971 + 5.92111i) q^{75} +(-3.54443 - 8.10212i) q^{77} +(-1.64017 - 1.19165i) q^{79} +(-3.43193 - 10.5624i) q^{81} +(4.81529 - 3.49851i) q^{83} +(-0.0625962 + 0.192651i) q^{85} -5.74321 q^{87} -8.50041 q^{89} +(-4.95094 + 15.2374i) q^{91} +(0.861031 - 0.625575i) q^{93} +(0.0597552 + 0.183907i) q^{95} +(9.66260 + 7.02029i) q^{97} +(-3.20623 - 1.87898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} + 15 q^{7} + 9 q^{9} + 2 q^{11} + 4 q^{13} + 15 q^{15} + 7 q^{17} - 5 q^{19} - 12 q^{21} - 16 q^{23} - 5 q^{25} - 3 q^{27} + 16 q^{29} + q^{31} - 27 q^{33} - 13 q^{35} + 14 q^{37} - 29 q^{39}+ \cdots - 35 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 15 * q^7 + 9 * q^9 + 2 * q^11 + 4 * q^13 + 15 * q^15 + 7 * q^17 - 5 * q^19 - 12 * q^21 - 16 * q^23 - 5 * q^25 - 3 * q^27 + 16 * q^29 + q^31 - 27 * q^33 - 13 * q^35 + 14 * q^37 - 29 * q^39 - 5 * q^41 + 28 * q^43 - 4 * q^47 - 4 * q^49 + 4 * q^51 - 17 * q^55 + 42 * q^59 + 27 * q^61 + 22 * q^63 - 14 * q^65 - 34 * q^67 - 11 * q^69 + 32 * q^71 - 7 * q^73 + 13 * q^75 - 60 * q^77 + 2 * q^79 - 9 * q^81 + 33 * q^83 + 27 * q^85 - 2 * q^87 - 70 * q^89 - 10 * q^91 + 7 * q^93 - 4 * q^95 - 6 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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