LMFDB - Embedded newform 189.2.o.a.125.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(62,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("189.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.3
Root			$0.474636 + 0.274031i$ of defining polynomial
Character	$\chi$	$=$	189.125
Dual form			189.2.o.a.62.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.555632 - 0.320794i) q^{2} +(-0.794182 + 1.37556i) q^{4} +(-1.10552 + 1.91482i) q^{5} +(-0.906161 + 2.48573i) q^{7} +2.30225i q^{8} +O(q^{10})$	\(q+(0.555632 - 0.320794i) q^{2} +(-0.794182 + 1.37556i) q^{4} +(-1.10552 + 1.91482i) q^{5} +(-0.906161 + 2.48573i) q^{7} +2.30225i q^{8} +1.41858i q^{10} +(2.93818 - 1.69636i) q^{11} +(-1.56060 - 0.901012i) q^{13} +(0.293917 + 1.67184i) q^{14} +(-0.849814 - 1.47192i) q^{16} +5.96901 q^{17} -1.64419i q^{19} +(-1.75597 - 3.04144i) q^{20} +(1.08836 - 1.88510i) q^{22} +(-2.05563 - 1.18682i) q^{23} +(0.0556321 + 0.0963576i) q^{25} -1.15616 q^{26} +(-2.69963 - 3.22061i) q^{28} +(-2.44437 + 1.41126i) q^{29} +(9.28558 + 5.36103i) q^{31} +(-4.93199 - 2.84748i) q^{32} +(3.31657 - 1.91482i) q^{34} +(-3.75796 - 4.48318i) q^{35} +1.69963 q^{37} +(-0.527445 - 0.913562i) q^{38} +(-4.40841 - 2.54520i) q^{40} +(0.455074 - 0.788211i) q^{41} +(-1.96108 - 3.39669i) q^{43} +5.38887i q^{44} -1.52290 q^{46} +(-0.123005 - 0.213051i) q^{47} +(-5.35774 - 4.50495i) q^{49} +(0.0618219 + 0.0356929i) q^{50} +(2.47880 - 1.43113i) q^{52} +7.87589i q^{53} +7.50146i q^{55} +(-5.72279 - 2.08621i) q^{56} +(-0.905446 + 1.56828i) q^{58} +(5.39093 - 9.33736i) q^{59} +(1.22853 - 0.709292i) q^{61} +6.87916 q^{62} -0.254572 q^{64} +(3.45056 - 1.99218i) q^{65} +(3.99381 - 6.91748i) q^{67} +(-4.74048 + 8.21075i) q^{68} +(-3.52622 - 1.28547i) q^{70} -12.1743i q^{71} +0.426103i q^{73} +(0.944368 - 0.545231i) q^{74} +(2.26168 + 1.30578i) q^{76} +(1.55423 + 8.84070i) q^{77} +(2.49381 + 4.31941i) q^{79} +3.75796 q^{80} -0.583940i q^{82} +(4.28541 + 7.42254i) q^{83} +(-6.59888 + 11.4296i) q^{85} +(-2.17928 - 1.25821i) q^{86} +(3.90545 + 6.76443i) q^{88} -10.5358 q^{89} +(3.65383 - 3.06277i) q^{91} +(3.26509 - 1.88510i) q^{92} +(-0.136691 - 0.0789188i) q^{94} +(3.14833 + 1.81769i) q^{95} +(-6.30108 + 3.63793i) q^{97} +(-4.42210 - 0.784360i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7}+O(q^{10}) $ 12 * q + 6 * q^2 + 2 * q^4 - 2 * q^7	$ 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7} + 12 q^{14} + 2 q^{16} - 10 q^{22} - 24 q^{23} - 8 q^{28} - 30 q^{29} + 12 q^{32} - 4 q^{37} - 10 q^{43} - 40 q^{46} + 6 q^{49} + 36 q^{50} - 42 q^{56} + 2 q^{58} + 16 q^{64} + 78 q^{65} + 12 q^{67} + 18 q^{70} + 12 q^{74} + 24 q^{77} - 6 q^{79} - 6 q^{85} - 96 q^{86} + 34 q^{88} - 24 q^{91} - 30 q^{92} - 72 q^{95}+O(q^{100}) $ 12 * q + 6 * q^2 + 2 * q^4 - 2 * q^7 + 12 * q^14 + 2 * q^16 - 10 * q^22 - 24 * q^23 - 8 * q^28 - 30 * q^29 + 12 * q^32 - 4 * q^37 - 10 * q^43 - 40 * q^46 + 6 * q^49 + 36 * q^50 - 42 * q^56 + 2 * q^58 + 16 * q^64 + 78 * q^65 + 12 * q^67 + 18 * q^70 + 12 * q^74 + 24 * q^77 - 6 * q^79 - 6 * q^85 - 96 * q^86 + 34 * q^88 - 24 * q^91 - 30 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.555632	−	0.320794i	0.392891	−	0.226836i	−0.290521	−	0.956869i	$-0.593829\pi$
$2$	0.555632	−	0.320794i	0.392891	−	0.226836i	0.683412	+	0.730033i	$0.260495\pi$
$3$		0			0
$3$		0			0
$4$	−0.794182	+	1.37556i	−0.397091	+	0.687782i
$5$	−1.10552	+	1.91482i	−0.494405	+	0.856335i	−0.999979	−	0.00644798i	$-0.997948\pi$
$5$	−1.10552	+	1.91482i	−0.494405	+	0.856335i	0.505574	+	0.862783i	$0.331281\pi$
$6$		0			0
$7$	−0.906161	+	2.48573i	−0.342497	+	0.939519i
$7$	−0.906161	+	2.48573i	−0.342497	+	0.939519i
$8$			2.30225i			0.813970i
$9$		0			0
$10$			1.41858i			0.448596i
$11$	2.93818	−	1.69636i	0.885894	−	0.511471i	0.0132968	−	0.999912i	$-0.495767\pi$
$11$	2.93818	−	1.69636i	0.885894	−	0.511471i	0.872597	+	0.488440i	$0.162434\pi$
$12$		0			0
$13$	−1.56060	−	0.901012i	−0.432832	−	0.249896i	0.267720	−	0.963497i	$-0.413730\pi$
$13$	−1.56060	−	0.901012i	−0.432832	−	0.249896i	−0.700552	+	0.713601i	$0.747063\pi$
$14$	0.293917	+	1.67184i	0.0785527	+	0.446819i
$15$		0			0
$16$	−0.849814	−	1.47192i	−0.212454	−	0.367980i
$17$	5.96901			1.44770			0.723849	−	0.689959i	$-0.242371\pi$
$17$	5.96901			1.44770			0.723849	+	0.689959i	$0.242371\pi$
$18$		0			0
$19$		−	1.64419i		−	0.377202i	−0.982054	−	0.188601i	$-0.939605\pi$
$19$		−	1.64419i		−	0.377202i	0.982054	−	0.188601i	$-0.0603953\pi$
$20$	−1.75597	−	3.04144i	−0.392648	−	0.680086i
$21$		0			0
$22$	1.08836	−	1.88510i	0.232040	−	0.401905i
$23$	−2.05563	−	1.18682i	−0.428629	−	0.247469i	0.270133	−	0.962823i	$-0.412932\pi$
$23$	−2.05563	−	1.18682i	−0.428629	−	0.247469i	−0.698762	+	0.715354i	$0.746266\pi$
$24$		0			0
$25$	0.0556321	+	0.0963576i	0.0111264	+	0.0192715i
$26$	−1.15616			−0.226741
$27$		0			0
$28$	−2.69963	−	3.22061i	−0.510182	−	0.608638i
$29$	−2.44437	+	1.41126i	−0.453908	+	0.262064i	−0.709479	−	0.704726i	$-0.751070\pi$
$29$	−2.44437	+	1.41126i	−0.453908	+	0.262064i	0.255571	+	0.966790i	$0.417736\pi$
$30$		0			0
$31$	9.28558	+	5.36103i	1.66774	+	0.962870i	0.968853	+	0.247638i	$0.0796544\pi$
$31$	9.28558	+	5.36103i	1.66774	+	0.962870i	0.698887	+	0.715232i	$0.253679\pi$
$32$	−4.93199	−	2.84748i	−0.871861	−	0.503369i
$33$		0			0
$34$	3.31657	−	1.91482i	0.568788	−	0.328390i
$35$	−3.75796	−	4.48318i	−0.635211	−	0.757795i
$36$		0			0
$37$	1.69963			0.279417			0.139709	−	0.990193i	$-0.455383\pi$
$37$	1.69963			0.279417			0.139709	+	0.990193i	$0.455383\pi$
$38$	−0.527445	−	0.913562i	−0.0855630	−	0.148199i
$39$		0			0
$40$	−4.40841	−	2.54520i	−0.697031	−	0.402431i
$41$	0.455074	−	0.788211i	0.0710706	−	0.123098i	−0.828300	−	0.560285i	$-0.810692\pi$
$41$	0.455074	−	0.788211i	0.0710706	−	0.123098i	0.899371	+	0.437187i	$0.144025\pi$
$42$		0			0
$43$	−1.96108	−	3.39669i	−0.299062	−	0.517990i	0.676860	−	0.736112i	$-0.263340\pi$
$43$	−1.96108	−	3.39669i	−0.299062	−	0.517990i	−0.975922	+	0.218122i	$0.930007\pi$
$44$			5.38887i			0.812402i
$45$		0			0
$46$	−1.52290			−0.224539
$47$	−0.123005	−	0.213051i	−0.0179422	−	0.0310767i	0.856915	−	0.515458i	$-0.172378\pi$
$47$	−0.123005	−	0.213051i	−0.0179422	−	0.0310767i	−0.874857	+	0.484381i	$0.839045\pi$
$48$		0			0
$49$	−5.35774	−	4.50495i	−0.765392	−	0.643564i
$50$	0.0618219	+	0.0356929i	0.00874294	+	0.00504774i
$51$		0			0
$52$	2.47880	−	1.43113i	0.343747	−	0.198463i
$53$			7.87589i			1.08184i	0.841075	+	0.540919i	$0.181923\pi$
$53$			7.87589i			1.08184i	−0.841075	+	0.540919i	$0.818077\pi$
$54$		0			0
$55$			7.50146i			1.01150i
$56$	−5.72279	−	2.08621i	−0.764740	−	0.278782i
$57$		0			0
$58$	−0.905446	+	1.56828i	−0.118891	+	0.205925i
$59$	5.39093	−	9.33736i	0.701839	−	1.21562i	−0.265981	−	0.963978i	$-0.585696\pi$
$59$	5.39093	−	9.33736i	0.701839	−	1.21562i	0.967820	−	0.251643i	$-0.0809709\pi$
$60$		0			0
$61$	1.22853	−	0.709292i	0.157297	−	0.0908155i	−0.419285	−	0.907855i	$-0.637719\pi$
$61$	1.22853	−	0.709292i	0.157297	−	0.0908155i	0.576582	+	0.817039i	$0.304386\pi$
$62$	6.87916			0.873654
$63$		0			0
$64$	−0.254572			−0.0318214
$65$	3.45056	−	1.99218i	0.427989	−	0.247100i
$66$		0			0
$67$	3.99381	−	6.91748i	0.487922	−	0.845105i	−0.511982	−	0.858996i	$-0.671089\pi$
$67$	3.99381	−	6.91748i	0.487922	−	0.845105i	0.999904	+	0.0138913i	$0.00442187\pi$
$68$	−4.74048	+	8.21075i	−0.574868	+	0.995700i
$69$		0			0
$70$	−3.52622	−	1.28547i	−0.421464	−	0.153642i
$71$		−	12.1743i		−	1.44482i	−0.691463	−	0.722412i	$-0.743034\pi$
$71$		−	12.1743i		−	1.44482i	0.691463	−	0.722412i	$-0.256966\pi$
$72$		0			0
$73$			0.426103i			0.0498715i	0.999689	+	0.0249358i	$0.00793812\pi$
$73$			0.426103i			0.0498715i	−0.999689	+	0.0249358i	$0.992062\pi$
$74$	0.944368	−	0.545231i	0.109781	−	0.0633818i
$75$		0			0
$76$	2.26168	+	1.30578i	0.259433	+	0.149784i
$77$	1.55423	+	8.84070i	0.177121	+	1.00749i
$78$		0			0
$79$	2.49381	+	4.31941i	0.280576	+	0.485971i	0.971527	−	0.236930i	$-0.0761413\pi$
$79$	2.49381	+	4.31941i	0.280576	+	0.485971i	−0.690951	+	0.722902i	$0.742808\pi$
$80$	3.75796			0.420153
$81$		0			0
$82$		−	0.583940i		−	0.0644854i
$83$	4.28541	+	7.42254i	0.470384	+	0.814730i	0.999426	−	0.0338660i	$-0.0107819\pi$
$83$	4.28541	+	7.42254i	0.470384	+	0.814730i	−0.529042	+	0.848596i	$0.677449\pi$
$84$		0			0
$85$	−6.59888	+	11.4296i	−0.715750	+	1.23971i
$86$	−2.17928	−	1.25821i	−0.234997	−	0.135676i
$87$		0			0
$88$	3.90545	+	6.76443i	0.416322	+	0.721091i
$89$	−10.5358			−1.11680			−0.558399	−	0.829573i	$-0.688584\pi$
$89$	−10.5358			−1.11680			−0.558399	+	0.829573i	$0.688584\pi$
$90$		0			0
$91$	3.65383	−	3.06277i	0.383025	−	0.321065i
$92$	3.26509	−	1.88510i	0.340409	−	0.196535i
$93$		0			0
$94$	−0.136691	−	0.0789188i	−0.0140986	−	0.00813985i
$95$	3.14833	+	1.81769i	0.323012	+	0.186491i
$96$		0			0
$97$	−6.30108	+	3.63793i	−0.639777	+	0.369376i	−0.784529	−	0.620092i	$-0.787095\pi$
$97$	−6.30108	+	3.63793i	−0.639777	+	0.369376i	0.144751	+	0.989468i	$0.453762\pi$
$98$	−4.42210	−	0.784360i	−0.446699	−	0.0792324i
$99$		0			0
$100$	−0.176728			−0.0176728
$101$	2.33405	+	4.04270i	0.232247	+	0.402264i	0.958469	−	0.285197i	$-0.0920589\pi$
$101$	2.33405	+	4.04270i	0.232247	+	0.402264i	−0.726222	+	0.687460i	$0.758726\pi$
$102$		0			0
$103$	−5.40462	−	3.12036i	−0.532533	−	0.307458i	0.209515	−	0.977806i	$-0.432812\pi$
$103$	−5.40462	−	3.12036i	−0.532533	−	0.307458i	−0.742047	+	0.670348i	$0.766145\pi$
$104$	2.07436	−	3.59289i	0.203407	−	0.352312i
$105$		0			0
$106$	2.52654	+	4.37610i	0.245399	+	0.425044i
$107$			1.48939i			0.143985i	0.997405	+	0.0719925i	$0.0229358\pi$
$107$			1.48939i			0.143985i	−0.997405	+	0.0719925i	$0.977064\pi$
$108$		0			0
$109$	−4.38688			−0.420187			−0.210093	−	0.977681i	$-0.567377\pi$
$109$	−4.38688			−0.420187			−0.210093	+	0.977681i	$0.567377\pi$
$110$	2.40643	+	4.16805i	0.229444	+	0.397408i
$111$		0			0
$112$	4.42887	−	0.778614i	0.418489	−	0.0735721i
$113$	14.8764	+	8.58887i	1.39945	+	0.807973i	0.994335	−	0.106293i	$-0.0338981\pi$
$113$	14.8764	+	8.58887i	1.39945	+	0.807973i	0.405115	+	0.914266i	$0.367231\pi$
$114$		0			0
$115$	4.54510	−	2.62412i	0.423833	−	0.244700i
$116$		−	4.48318i		−	0.416253i
$117$		0			0
$118$		−	6.91752i		−	0.636809i
$119$	−5.40888	+	14.8374i	−0.495831	+	1.36014i
$120$		0			0
$121$	0.255260	−	0.442124i	0.0232055	−	0.0401931i
$122$	0.455074	−	0.788211i	0.0412004	−	0.0713612i
$123$		0			0
$124$	−14.7489	+	8.51527i	−1.32449	+	0.764694i
$125$	−11.3013			−1.01081
$126$		0			0
$127$	6.32141			0.560935			0.280467	−	0.959864i	$-0.409511\pi$
$127$	6.32141			0.560935			0.280467	+	0.959864i	$0.409511\pi$
$128$	9.72253	−	5.61330i	0.859358	−	0.496151i
$129$		0			0
$130$	1.27816	−	2.21384i	0.112102	−	0.194167i
$131$	8.51213	−	14.7434i	0.743708	−	1.28814i	−0.207088	−	0.978322i	$-0.566399\pi$
$131$	8.51213	−	14.7434i	0.743708	−	1.28814i	0.950796	−	0.309818i	$-0.100268\pi$
$132$		0			0
$133$	4.08701	+	1.48990i	0.354389	+	0.129190i
$134$		−	5.12477i		−	0.442712i
$135$		0			0
$136$			13.7422i			1.17838i
$137$	−5.42580	+	3.13259i	−0.463557	+	0.267635i	−0.713539	−	0.700616i	$-0.752909\pi$
$137$	−5.42580	+	3.13259i	−0.463557	+	0.267635i	0.249982	+	0.968251i	$0.419575\pi$
$138$		0			0
$139$	6.65488	+	3.84220i	0.564460	+	0.325891i	0.754934	−	0.655801i	$-0.227669\pi$
$139$	6.65488	+	3.84220i	0.564460	+	0.325891i	−0.190474	+	0.981692i	$0.561002\pi$
$140$	9.15140	−	1.60885i	0.773435	−	0.135973i
$141$		0			0
$142$	−3.90545	−	6.76443i	−0.327738	−	0.567658i
$143$	−6.11375			−0.511258
$144$		0			0
$145$		−	6.24071i		−	0.518263i
$146$	0.136691	+	0.236756i	0.0113127	+	0.0195941i
$147$		0			0
$148$	−1.34981	+	2.33795i	−0.110954	+	0.192178i
$149$	−13.3695	−	7.71887i	−1.09527	−	0.632355i	−0.160296	−	0.987069i	$-0.551245\pi$
$149$	−13.3695	−	7.71887i	−1.09527	−	0.632355i	−0.934975	+	0.354714i	$0.884578\pi$
$150$		0			0
$151$	−5.84362	−	10.1215i	−0.475547	−	0.823672i	0.524060	−	0.851681i	$-0.324417\pi$
$151$	−5.84362	−	10.1215i	−0.475547	−	0.823672i	−0.999608	+	0.0280089i	$0.991083\pi$
$152$	3.78533			0.307031
$153$		0			0
$154$	3.69963	+	4.41359i	0.298125	+	0.355657i
$155$	−20.5309	+	11.8535i	−1.64908	+	0.952096i
$156$		0			0
$157$	−4.93586	−	2.84972i	−0.393924	−	0.227432i	0.289935	−	0.957046i	$-0.406366\pi$
$157$	−4.93586	−	2.84972i	−0.393924	−	0.227432i	−0.683859	+	0.729614i	$0.739700\pi$
$158$	2.77128	+	1.60000i	0.220471	+	0.127289i
$159$		0			0
$160$	10.9049	−	6.29593i	0.862105	−	0.497737i
$161$	4.81285	−	4.03430i	0.379306	−	0.317948i
$162$		0			0
$163$	−10.2101			−0.799721			−0.399860	−	0.916576i	$-0.630941\pi$
$163$	−10.2101			−0.799721			−0.399860	+	0.916576i	$0.630941\pi$
$164$	0.722823	+	1.25197i	0.0564430	+	0.0977621i
$165$		0			0
$166$	4.76222	+	2.74947i	0.369620	+	0.213400i
$167$	−1.80661	+	3.12914i	−0.139800	+	0.242140i	−0.927421	−	0.374020i	$-0.877979\pi$
$167$	−1.80661	+	3.12914i	−0.139800	+	0.242140i	0.787621	+	0.616160i	$0.211312\pi$
$168$		0			0
$169$	−4.87636	−	8.44610i	−0.375104	−	0.649700i
$170$			8.46754i			0.649431i
$171$		0			0
$172$	6.22981			0.475019
$173$	−9.03957	−	15.6570i	−0.687266	−	1.19038i	−0.972719	−	0.231987i	$-0.925477\pi$
$173$	−9.03957	−	15.6570i	−0.687266	−	1.19038i	0.285453	−	0.958393i	$-0.407856\pi$
$174$		0			0
$175$	−0.289931	+	0.0509711i	−0.0219167	+	0.00385305i
$176$	−4.99381	−	2.88318i	−0.376423	−	0.217328i
$177$		0			0
$178$	−5.85406	+	3.37984i	−0.438780	+	0.253330i
$179$		−	5.03194i		−	0.376105i	−0.982159	−	0.188052i	$-0.939783\pi$
$179$		−	5.03194i		−	0.376105i	0.982159	−	0.188052i	$-0.0602175\pi$
$180$		0			0
$181$		−	13.5592i		−	1.00785i	−0.863747	−	0.503925i	$-0.831889\pi$
$181$		−	13.5592i		−	1.00785i	0.863747	−	0.503925i	$-0.168111\pi$
$182$	1.04766	−	2.87390i	0.0776581	−	0.213028i
$183$		0			0
$184$	2.73236	−	4.73259i	0.201432	−	0.348891i
$185$	−1.87898	+	3.25449i	−0.138145	+	0.239275i
$186$		0			0
$187$	17.5380	−	10.1256i	1.28251	−	0.740455i
$188$	0.390754			0.0284987
$189$		0			0
$190$	2.33242			0.169211
$191$	8.86948	−	5.12080i	0.641773	−	0.370528i	−0.143524	−	0.989647i	$-0.545844\pi$
$191$	8.86948	−	5.12080i	0.641773	−	0.370528i	0.785297	+	0.619119i	$0.212510\pi$
$192$		0			0
$193$	−8.06615	+	13.9710i	−0.580614	+	1.00565i	0.414792	+	0.909916i	$0.363854\pi$
$193$	−8.06615	+	13.9710i	−0.580614	+	1.00565i	−0.995407	+	0.0957374i	$0.969479\pi$
$194$	−2.33405	+	4.04270i	−0.167575	+	0.290249i
$195$		0			0
$196$	10.4519	−	3.79217i	0.746562	−	0.270869i
$197$		−	3.86303i		−	0.275230i	−0.990486	−	0.137615i	$-0.956056\pi$
$197$		−	3.86303i		−	0.275230i	0.990486	−	0.137615i	$-0.0439436\pi$
$198$		0			0
$199$		−	15.2034i		−	1.07774i	−0.842388	−	0.538871i	$-0.818851\pi$
$199$		−	15.2034i		−	1.07774i	0.842388	−	0.538871i	$-0.181149\pi$
$200$	−0.221840	+	0.128079i	−0.0156864	+	0.00905656i
$201$		0			0
$202$	2.59375	+	1.49750i	0.182496	+	0.105364i
$203$	−1.29302	−	7.35487i	−0.0907520	−	0.516211i
$204$		0			0
$205$	1.00619	+	1.74277i	0.0702753	+	0.121720i
$206$	−4.00397			−0.278970
$207$		0			0
$208$			3.06277i			0.212365i
$209$	−2.78913	−	4.83091i	−0.192928	−	0.334161i
$210$		0			0
$211$	11.9523	−	20.7021i	0.822833	−	1.42519i	−0.0807311	−	0.996736i	$-0.525726\pi$
$211$	11.9523	−	20.7021i	0.822833	−	1.42519i	0.903564	−	0.428453i	$-0.140941\pi$
$212$	−10.8338	−	6.25489i	−0.744068	−	0.429588i
$213$		0			0
$214$	0.477789	+	0.827554i	0.0326610	+	0.0565704i
$215$	8.67208			0.591431
$216$		0			0
$217$	−21.7403	+	18.2235i	−1.47583	+	1.23709i
$218$	−2.43749	+	1.40729i	−0.165088	+	0.0953134i
$219$		0			0
$220$	−10.3187	−	5.95752i	−0.695689	−	0.401656i
$221$	−9.31522	−	5.37815i	−0.626610	−	0.361773i
$222$		0			0
$223$	−16.6198	+	9.59545i	−1.11294	+	0.642559i	−0.939591	−	0.342300i	$-0.888794\pi$
$223$	−16.6198	+	9.59545i	−1.11294	+	0.642559i	−0.173354	+	0.984860i	$0.555461\pi$
$224$	11.5473	−	9.67933i	0.771534	−	0.646727i
$225$		0			0
$226$	11.0210			0.733109
$227$	−4.33604	−	7.51024i	−0.287793	−	0.498472i	0.685490	−	0.728082i	$-0.259588\pi$
$227$	−4.33604	−	7.51024i	−0.287793	−	0.498472i	−0.973283	+	0.229610i	$0.926255\pi$
$228$		0			0
$229$	12.4437	+	7.18439i	0.822304	+	0.474758i	0.851211	−	0.524824i	$-0.175869\pi$
$229$	12.4437	+	7.18439i	0.822304	+	0.474758i	−0.0289060	+	0.999582i	$0.509202\pi$
$230$	1.68360	−	2.91609i	0.111014	−	0.192281i
$231$		0			0
$232$	−3.24907	−	5.62755i	−0.213312	−	0.369467i
$233$			29.7160i			1.94676i	0.229194	+	0.973381i	$0.426391\pi$
$233$			29.7160i			1.94676i	−0.229194	+	0.973381i	$0.573609\pi$
$234$		0			0
$235$	0.543941			0.0354828
$236$	8.56276	+	14.8311i	0.557388	+	0.965425i
$237$		0			0
$238$	1.75439	+	9.97926i	0.113721	+	0.646859i
$239$	13.7101	+	7.91556i	0.886836	+	0.512015i	0.872906	−	0.487888i	$-0.162233\pi$
$239$	13.7101	+	7.91556i	0.886836	+	0.512015i	0.0139296	+	0.999903i	$0.495566\pi$
$240$		0			0
$241$	−4.34973	+	2.51132i	−0.280190	+	0.161768i	−0.633510	−	0.773735i	$-0.718386\pi$
$241$	−4.34973	+	2.51132i	−0.280190	+	0.161768i	0.353319	+	0.935503i	$0.385053\pi$
$242$		−	0.327544i		−	0.0210553i
$243$		0			0
$244$			2.25323i			0.144248i
$245$	14.5493	−	5.27881i	0.929521	−	0.337251i
$246$		0			0
$247$	−1.48143	+	2.56591i	−0.0942612	+	0.163265i
$248$	−12.3425	+	21.3778i	−0.783747	+	1.35749i
$249$		0			0
$250$	−6.27934	+	3.62538i	−0.397140	+	0.229289i
$251$	7.29728			0.460600			0.230300	−	0.973120i	$-0.426029\pi$
$251$	7.29728			0.460600			0.230300	+	0.973120i	$0.426029\pi$
$252$		0			0
$253$	−8.05308			−0.506293
$254$	3.51238	−	2.02787i	0.220386	−	0.127240i
$255$		0			0
$256$	3.85600	−	6.67879i	0.241000	−	0.417425i
$257$	4.00397	−	6.93508i	0.249761	−	0.432598i	−0.713699	−	0.700453i	$-0.752981\pi$
$257$	4.00397	−	6.93508i	0.249761	−	0.432598i	0.963459	+	0.267855i	$0.0863147\pi$
$258$		0			0
$259$	−1.54014	+	4.22482i	−0.0956994	+	0.262518i
$260$			6.32862i			0.392484i
$261$		0			0
$262$		−	10.9226i		−	0.674798i
$263$	13.6051	−	7.85489i	0.838925	−	0.484353i	−0.0179738	−	0.999838i	$-0.505722\pi$
$263$	13.6051	−	7.85489i	0.838925	−	0.484353i	0.856899	+	0.515485i	$0.172388\pi$
$264$		0			0
$265$	−15.0810	−	8.70699i	−0.926416	−	0.534866i
$266$	2.74882	−	0.483255i	0.168541	−	0.0296302i
$267$		0			0
$268$	6.34362	+	10.9875i	0.387499	+	0.671167i
$269$	−10.4924			−0.639731			−0.319866	−	0.947463i	$-0.603638\pi$
$269$	−10.4924			−0.639731			−0.319866	+	0.947463i	$0.603638\pi$
$270$		0			0
$271$			22.2537i			1.35181i	0.736987	+	0.675907i	$0.236248\pi$
$271$			22.2537i			1.35181i	−0.736987	+	0.675907i	$0.763752\pi$
$272$	−5.07255	−	8.78591i	−0.307568	−	0.532724i
$273$		0			0
$274$	−2.00983	+	3.48113i	−0.121418	+	0.210303i
$275$	0.326914	+	0.188744i	0.0197137	+	0.0113817i
$276$		0			0
$277$	11.4251	+	19.7889i	0.686468	+	1.18900i	0.972973	+	0.230919i	$0.0741733\pi$
$277$	11.4251	+	19.7889i	0.686468	+	1.18900i	−0.286505	+	0.958079i	$0.592493\pi$
$278$	4.93022			0.295695
$279$		0			0
$280$	10.3214	−	8.65178i	0.616822	−	0.517043i
$281$	−0.796041	+	0.459595i	−0.0474878	+	0.0274171i	−0.523556	−	0.851991i	$-0.675395\pi$
$281$	−0.796041	+	0.459595i	−0.0474878	+	0.0274171i	0.476068	+	0.879408i	$0.342062\pi$
$282$		0			0
$283$	−19.1573	−	11.0605i	−1.13878	−	0.657477i	−0.192654	−	0.981267i	$-0.561710\pi$
$283$	−19.1573	−	11.0605i	−1.13878	−	0.657477i	−0.946129	+	0.323790i	$0.895043\pi$
$284$	16.7465	+	9.66861i	0.993723	+	0.573726i
$285$		0			0
$286$	−3.39700	+	1.96126i	−0.200869	+	0.115972i
$287$	1.54691	+	1.84544i	0.0913113	+	0.108933i
$288$		0			0
$289$	18.6291			1.09583
$290$	−2.00199	−	3.46754i	−0.117561	−	0.203621i
$291$		0			0
$292$	−0.586131	−	0.338403i	−0.0343007	−	0.0198035i
$293$	−14.6259	+	25.3328i	−0.854453	+	1.47996i	0.0226986	+	0.999742i	$0.492774\pi$
$293$	−14.6259	+	25.3328i	−0.854453	+	1.47996i	−0.877152	+	0.480214i	$0.840559\pi$
$294$		0			0
$295$	11.9196	+	20.6454i	0.693986	+	1.20202i
$296$			3.91298i			0.227437i
$297$		0			0
$298$	−9.90468			−0.573763
$299$	2.13868	+	3.70430i	0.123683	+	0.214225i
$300$		0			0
$301$	10.2203	−	1.79677i	0.589089	−	0.103564i
$302$	−6.49381	−	3.74920i	−0.373677	−	0.215742i
$303$		0			0
$304$	−2.42011	+	1.39725i	−0.138803	+	0.0801379i
$305$			3.13656i			0.179599i
$306$		0			0
$307$			14.8451i			0.847254i	0.905837	+	0.423627i	$0.139243\pi$
$307$			14.8451i			0.847254i	−0.905837	+	0.423627i	$0.860757\pi$
$308$	−13.3953	−	4.88318i	−0.763267	−	0.278245i
$309$		0			0
$310$	−7.60507	+	13.1724i	−0.431939	+	0.748141i
$311$	−9.69002	+	16.7836i	−0.549471	+	0.951711i	0.448840	+	0.893612i	$0.351837\pi$
$311$	−9.69002	+	16.7836i	−0.549471	+	0.951711i	−0.998311	+	0.0580991i	$0.981496\pi$
$312$		0			0
$313$	12.6608	−	7.30974i	0.715633	−	0.413171i	−0.0975102	−	0.995235i	$-0.531088\pi$
$313$	12.6608	−	7.30974i	0.715633	−	0.413171i	0.813143	+	0.582064i	$0.197755\pi$
$314$	−3.65669			−0.206359
$315$		0			0
$316$	−7.92216			−0.445656
$317$	14.7046	−	8.48973i	0.825895	−	0.476831i	−0.0265499	−	0.999647i	$-0.508452\pi$
$317$	14.7046	−	8.48973i	0.825895	−	0.476831i	0.852445	+	0.522817i	$0.175119\pi$
$318$		0			0
$319$	−4.78799	+	8.29305i	−0.268076	+	0.464321i
$320$	0.281435	−	0.487460i	0.0157327	−	0.0272498i
$321$		0			0
$322$	1.37999	−	3.78552i	0.0769040	−	0.210959i
$323$		−	9.81416i		−	0.546074i
$324$		0			0
$325$		−	0.200501i		−	0.0111218i
$326$	−5.67309	+	3.27536i	−0.314203	+	0.181405i
$327$		0			0
$328$	1.81466	+	1.04769i	0.100198	+	0.0578493i
$329$	0.641051	−	0.112699i	0.0353423	−	0.00621332i
$330$		0			0
$331$	−9.94801	−	17.2305i	−0.546792	−	0.947072i	−0.998492	−	0.0549016i	$-0.982515\pi$
$331$	−9.94801	−	17.2305i	−0.546792	−	0.947072i	0.451700	−	0.892170i	$-0.350818\pi$
$332$	−13.6136			−0.747142
$333$		0			0
$334$			2.31820i			0.126846i
$335$	8.83051	+	15.2949i	0.482462	+	0.835649i
$336$		0			0
$337$	0.490168	−	0.848996i	0.0267012	−	0.0462478i	−0.852366	−	0.522946i	$-0.824833\pi$
$337$	0.490168	−	0.848996i	0.0267012	−	0.0462478i	0.879067	+	0.476698i	$0.158166\pi$
$338$	−5.41892	−	3.12861i	−0.294750	−	0.170174i
$339$		0			0
$340$	−10.4814	−	18.1544i	−0.568435	−	0.984559i
$341$	36.3769			1.96992
$342$		0			0
$343$	16.0531	−	9.23572i	0.866785	−	0.498682i
$344$	7.82004	−	4.51490i	0.421628	−	0.243427i
$345$		0			0
$346$	−10.0454	−	5.79969i	−0.540041	−	0.311793i
$347$	−18.3702	−	10.6060i	−0.986162	−	0.569361i	−0.0820373	−	0.996629i	$-0.526143\pi$
$347$	−18.3702	−	10.6060i	−0.986162	−	0.569361i	−0.904125	+	0.427268i	$0.859476\pi$
$348$		0			0
$349$	8.69945	−	5.02263i	0.465671	−	0.268855i	−0.248755	−	0.968566i	$-0.580021\pi$
$349$	8.69945	−	5.02263i	0.465671	−	0.268855i	0.714426	+	0.699711i	$0.246688\pi$
$350$	−0.144744	+	0.121329i	−0.00773688	+	0.00648533i
$351$		0			0
$352$	−19.3214			−1.02983
$353$	−1.37327	−	2.37858i	−0.0730920	−	0.126599i	0.827163	−	0.561962i	$-0.189953\pi$
$353$	−1.37327	−	2.37858i	−0.0730920	−	0.126599i	−0.900255	+	0.435363i	$0.856620\pi$
$354$		0			0
$355$	23.3116	+	13.4590i	1.23725	+	0.714329i
$356$	8.36738	−	14.4927i	0.443470	−	0.768113i
$357$		0			0
$358$	−1.61422	−	2.79591i	−0.0853140	−	0.147768i
$359$		−	10.0013i		−	0.527849i	−0.964543	−	0.263925i	$-0.914983\pi$
$359$		−	10.0013i		−	0.527849i	0.964543	−	0.263925i	$-0.0850170\pi$
$360$		0			0
$361$	16.2967			0.857719
$362$	−4.34973	−	7.53395i	−0.228616	−	0.395975i
$363$		0			0
$364$	1.31123	+	7.45847i	0.0687271	+	0.390930i
$365$	−0.815912	−	0.471067i	−0.0427068	−	0.0246568i
$366$		0			0
$367$	−5.03560	+	2.90731i	−0.262856	+	0.151760i	−0.625637	−	0.780114i	$-0.715161\pi$
$367$	−5.03560	+	2.90731i	−0.262856	+	0.151760i	0.362781	+	0.931875i	$0.381827\pi$
$368$			4.03430i			0.210303i
$369$		0			0
$370$			2.41106i			0.125345i
$371$	−19.5774	−	7.13683i	−1.01641	−	0.370526i
$372$		0			0
$373$	7.75959	−	13.4400i	0.401776	−	0.695897i	−0.592164	−	0.805817i	$-0.701726\pi$
$373$	7.75959	−	13.4400i	0.401776	−	0.695897i	0.993940	+	0.109920i	$0.0350596\pi$
$374$	6.49645	−	11.2522i	0.335924	−	0.581837i
$375$		0			0
$376$	0.490498	−	0.283189i	0.0252955	−	0.0146044i
$377$	5.08623			0.261954
$378$		0			0
$379$	2.79714			0.143679			0.0718396	−	0.997416i	$-0.477113\pi$
$379$	2.79714			0.143679			0.0718396	+	0.997416i	$0.477113\pi$
$380$	−5.00069	+	2.88715i	−0.256530	+	0.148108i
$381$		0			0
$382$	3.28544	−	5.69056i	0.168098	−	0.291154i
$383$	1.74229	−	3.01773i	0.0890268	−	0.154199i	−0.818073	−	0.575114i	$-0.804958\pi$
$383$	1.74229	−	3.01773i	0.0890268	−	0.154199i	0.907100	+	0.420915i	$0.138291\pi$
$384$		0			0
$385$	−18.6466	−	6.79753i	−0.950320	−	0.346434i
$386$			10.3503i			0.526817i
$387$		0			0
$388$		−	11.5567i		−	0.586703i
$389$	6.37017	−	3.67782i	0.322980	−	0.186473i	−0.329740	−	0.944072i	$-0.606961\pi$
$389$	6.37017	−	3.67782i	0.322980	−	0.186473i	0.652720	+	0.757599i	$0.273628\pi$
$390$		0			0
$391$	−12.2701	−	7.08414i	−0.620525	−	0.358260i
$392$	10.3715	−	12.3349i	0.523842	−	0.623006i
$393$		0			0
$394$	−1.23924	−	2.14642i	−0.0624319	−	0.108135i
$395$	−11.0279			−0.554872
$396$		0			0
$397$		−	19.2838i		−	0.967825i	−0.875116	−	0.483912i	$-0.839215\pi$
$397$		−	19.2838i		−	0.967825i	0.875116	−	0.483912i	$-0.160785\pi$
$398$	−4.87717	−	8.44751i	−0.244470	−	0.423435i
$399$		0			0
$400$	0.0945538	−	0.163772i	0.00472769	−	0.00818860i
$401$	−9.60576	−	5.54589i	−0.479689	−	0.276949i	0.240598	−	0.970625i	$-0.422656\pi$
$401$	−9.60576	−	5.54589i	−0.479689	−	0.276949i	−0.720287	+	0.693676i	$0.755990\pi$
$402$		0			0
$403$	−9.66071	−	16.7328i	−0.481234	−	0.833522i
$404$	−7.41465			−0.368893
$405$		0			0
$406$	−3.07784	−	3.67181i	−0.152751	−	0.182229i
$407$	4.99381	−	2.88318i	0.247534	−	0.142914i
$408$		0			0
$409$	17.5597	+	10.1381i	0.868274	+	0.501298i	0.866774	−	0.498701i	$-0.166189\pi$
$409$	17.5597	+	10.1381i	0.868274	+	0.501298i	0.00149954	+	0.999999i	$0.499523\pi$
$410$	1.11814	+	0.645560i	0.0552211	+	0.0318819i
$411$		0			0
$412$	8.58450	−	4.95626i	0.422928	−	0.244178i
$413$	18.3252	+	21.8616i	0.901722	+	1.07574i
$414$		0			0
$415$	−18.9505			−0.930243
$416$	5.13123	+	8.88756i	0.251579	+	0.435748i
$417$		0			0
$418$	−3.09946	−	1.78947i	−0.151599	−	0.0875260i
$419$	5.54936	−	9.61177i	0.271104	−	0.469566i	−0.698041	−	0.716058i	$-0.745945\pi$
$419$	5.54936	−	9.61177i	0.271104	−	0.469566i	0.969145	+	0.246492i	$0.0792779\pi$
$420$		0			0
$421$	4.59269	+	7.95478i	0.223834	+	0.387692i	0.955969	−	0.293467i	$-0.0948092\pi$
$421$	4.59269	+	7.95478i	0.223834	+	0.387692i	−0.732135	+	0.681160i	$0.761476\pi$
$422$		−	15.3370i		−	0.746592i
$423$		0			0
$424$	−18.1323			−0.880583
$425$	0.332068	+	0.575159i	0.0161077	+	0.0278993i
$426$		0			0
$427$	0.649865	+	3.69653i	0.0314492	+	0.178888i
$428$	−2.04875	−	1.18285i	−0.0990302	−	0.0571751i
$429$		0			0
$430$	4.81849	−	2.78195i	0.232368	−	0.134158i
$431$			15.1102i			0.727833i	0.931432	+	0.363916i	$0.118561\pi$
$431$			15.1102i			0.727833i	−0.931432	+	0.363916i	$0.881439\pi$
$432$		0			0
$433$			3.33578i			0.160307i	0.996783	+	0.0801537i	$0.0255411\pi$
$433$			3.33578i			0.160307i	−0.996783	+	0.0801537i	$0.974459\pi$
$434$	−6.23362	+	17.0998i	−0.299223	+	0.820814i
$435$		0			0
$436$	3.48398	−	6.03443i	0.166852	−	0.288997i
$437$	−1.95135	+	3.37984i	−0.0933458	+	0.161680i
$438$		0			0
$439$	5.91032	−	3.41233i	0.282084	−	0.162861i	−0.352282	−	0.935894i	$-0.614594\pi$
$439$	5.91032	−	3.41233i	0.282084	−	0.162861i	0.634367	+	0.773032i	$0.281261\pi$
$440$	−17.2703			−0.823327
$441$		0			0
$442$	−6.90112			−0.328253
$443$	−9.77747	+	5.64503i	−0.464542	+	0.268203i	−0.713952	−	0.700195i	$-0.753097\pi$
$443$	−9.77747	+	5.64503i	−0.464542	+	0.268203i	0.249410	+	0.968398i	$0.419763\pi$
$444$		0			0
$445$	11.6476	−	20.1743i	0.552151	−	0.956354i
$446$	−6.15633	+	10.6631i	−0.291511	+	0.504912i
$447$		0			0
$448$	0.230683	−	0.632797i	0.0108987	−	0.0298968i
$449$		−	24.8554i		−	1.17300i	−0.809950	−	0.586498i	$-0.800506\pi$
$449$		−	24.8554i		−	1.17300i	0.809950	−	0.586498i	$-0.199494\pi$
$450$		0			0
$451$		−	3.08787i		−	0.145402i
$452$	−23.6291	+	13.6422i	−1.11142	+	0.641677i
$453$		0			0
$454$	−4.81849	−	2.78195i	−0.226143	−	0.130564i
$455$	1.82527	+	10.3824i	0.0855700	+	0.486735i
$456$		0			0
$457$	6.30470	+	10.9201i	0.294922	+	0.510819i	0.974967	−	0.222351i	$-0.0713732\pi$
$457$	6.30470	+	10.9201i	0.294922	+	0.510819i	−0.680045	+	0.733170i	$0.738040\pi$
$458$	9.21884			0.430768
$459$		0			0
$460$			8.33610i			0.388673i
$461$	−14.4031	−	24.9470i	−0.670821	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$461$	−14.4031	−	24.9470i	−0.670821	−	1.16190i	0.306851	−	0.951758i	$-0.400725\pi$
$462$		0			0
$463$	−12.5858	+	21.7993i	−0.584912	+	1.01310i	0.409974	+	0.912097i	$0.365538\pi$
$463$	−12.5858	+	21.7993i	−0.584912	+	1.01310i	−0.994886	+	0.101001i	$0.967796\pi$
$464$	4.15452	+	2.39861i	0.192869	+	0.111353i
$465$		0			0
$466$	9.53273	+	16.5112i	0.441595	+	0.764865i
$467$	−25.5951			−1.18440			−0.592199	−	0.805792i	$-0.701740\pi$
$467$	−25.5951			−1.18440			−0.592199	+	0.805792i	$0.701740\pi$
$468$		0			0
$469$	13.5760	+	16.1959i	0.626881	+	0.747857i
$470$	0.302231	−	0.174493i	0.0139409	−	0.00804877i
$471$		0			0
$472$	21.4970	+	12.4113i	0.989479	+	0.571276i
$473$	−11.5240	−	6.65338i	−0.529874	−	0.305923i
$474$		0			0
$475$	0.158430	−	0.0914695i	0.00726926	−	0.00419691i
$476$	−16.1141	−	19.2238i	−0.738589	−	0.881123i
$477$		0			0
$478$	10.1571			0.464573
$479$	0.267749	+	0.463755i	0.0122338	+	0.0211895i	0.872077	−	0.489368i	$-0.162772\pi$
$479$	0.267749	+	0.463755i	0.0122338	+	0.0211895i	−0.859844	+	0.510557i	$0.829439\pi$
$480$		0			0
$481$	−2.65244	−	1.53138i	−0.120941	−	0.0698251i
$482$	−1.61123	+	2.79073i	−0.0733896	+	0.127114i
$483$		0			0
$484$	0.405446	+	0.702253i	0.0184294	+	0.0319206i
$485$		−	16.0873i		−	0.730485i
$486$		0			0
$487$	34.1323			1.54668			0.773341	−	0.633990i	$-0.218584\pi$
$487$	34.1323			1.54668			0.773341	+	0.633990i	$0.218584\pi$
$488$	1.63297	+	2.82839i	0.0739211	+	0.128035i
$489$		0			0
$490$	6.39065	−	7.60041i	0.288700	−	0.343352i
$491$	−5.86948	−	3.38874i	−0.264886	−	0.152932i	0.361675	−	0.932304i	$-0.382205\pi$
$491$	−5.86948	−	3.38874i	−0.264886	−	0.152932i	−0.626561	+	0.779372i	$0.715538\pi$
$492$		0			0
$493$	−14.5905	+	8.42380i	−0.657121	+	0.379389i
$494$			1.90094i			0.0855272i
$495$		0			0
$496$		−	18.2235i		−	0.818260i
$497$	30.2621	+	11.0319i	1.35744	+	0.494847i
$498$		0			0
$499$	−4.30037	+	7.44846i	−0.192511	+	0.333439i	−0.946082	−	0.323928i	$-0.894996\pi$
$499$	−4.30037	+	7.44846i	−0.192511	+	0.333439i	0.753571	+	0.657367i	$0.228330\pi$
$500$	8.97525	−	15.5456i	0.401385	−	0.695220i
$501$		0			0
$502$	4.05460	−	2.34093i	0.180966	−	0.104481i
$503$	2.96518			0.132211			0.0661055	−	0.997813i	$-0.478943\pi$
$503$	2.96518			0.132211			0.0661055	+	0.997813i	$0.478943\pi$
$504$		0			0
$505$	−10.3214			−0.459297
$506$	−4.47455	+	2.58338i	−0.198918	+	0.114845i
$507$		0			0
$508$	−5.02035	+	8.69551i	−0.222742	+	0.385801i
$509$	3.04882	−	5.28072i	0.135137	−	0.234064i	−0.790513	−	0.612445i	$-0.790186\pi$
$509$	3.04882	−	5.28072i	0.135137	−	0.234064i	0.925650	+	0.378382i	$0.123519\pi$
$510$		0			0
$511$	−1.05918	−	0.386118i	−0.0468553	−	0.0170808i
$512$			17.5053i			0.773631i
$513$		0			0
$514$		−	5.13780i		−	0.226619i
$515$	11.9499	−	6.89926i	0.526574	−	0.304018i
$516$		0			0
$517$	−0.722823	−	0.417322i	−0.0317897	−	0.0183538i
$518$	0.499550	+	2.84151i	0.0219490	+	0.124849i
$519$		0			0
$520$	4.58650	+	7.94406i	0.201132	+	0.348370i
$521$	32.6929			1.43230			0.716150	−	0.697946i	$-0.245903\pi$
$521$	32.6929			1.43230			0.716150	+	0.697946i	$0.245903\pi$
$522$		0			0
$523$		−	2.00252i		−	0.0875643i	−0.999041	−	0.0437821i	$-0.986059\pi$
$523$		−	2.00252i		−	0.0875643i	0.999041	−	0.0437821i	$-0.0139407\pi$
$524$	13.5204	+	23.4179i	0.590639	+	1.02302i
$525$		0			0
$526$	5.03961	−	8.72886i	0.219737	−	0.380596i
$527$	55.4257	+	32.0001i	2.41438	+	1.39394i
$528$		0			0
$529$	−8.68292	−	15.0393i	−0.377518	−	0.653881i
$530$	−11.1726			−0.485307
$531$		0			0
$532$	−5.29528	+	4.43869i	−0.229579	+	0.192442i
$533$	−1.42037	+	0.820053i	−0.0615232	+	0.0355204i
$534$		0			0
$535$	−2.85192	−	1.64656i	−0.123299	−	0.0711870i
$536$	15.9258	+	9.19476i	0.687890	+	0.397153i
$537$		0			0
$538$	−5.82990	+	3.36589i	−0.251345	+	0.145114i
$539$	−23.3840	−	4.14769i	−1.00722	−	0.178654i
$540$		0			0
$541$	−11.4451			−0.492061			−0.246031	−	0.969262i	$-0.579126\pi$
$541$	−11.4451			−0.492061			−0.246031	+	0.969262i	$0.579126\pi$
$542$	7.13885	+	12.3649i	0.306640	+	0.531116i
$543$		0			0
$544$	−29.4391	−	16.9967i	−1.26219	−	0.728726i
$545$	4.84980	−	8.40010i	0.207743	−	0.359821i
$546$		0			0
$547$	−3.91961	−	6.78896i	−0.167590	−	0.290275i	0.769982	−	0.638066i	$-0.220265\pi$
$547$	−3.91961	−	6.78896i	−0.167590	−	0.290275i	−0.937572	+	0.347791i	$0.886932\pi$
$548$		−	9.95137i		−	0.425102i
$549$		0			0
$550$	0.242192			0.0103271
$551$	2.32037	+	4.01899i	0.0988510	+	0.171215i
$552$		0			0
$553$	−12.9967	+	2.28487i	−0.552675	+	0.0971626i
$554$	12.6963	+	7.33022i	0.539415	+	0.311431i
$555$		0			0
$556$	−10.5704	+	6.10281i	−0.448284	+	0.258817i
$557$		−	0.0134996i		−	0.000571997i	−1.00000		0.000285998i	$-0.999909\pi$
$557$		−	0.0134996i		−	0.000571997i	1.00000		0.000285998i	$-9.10361e-5\pi$
$558$		0			0
$559$			7.06782i			0.298937i
$560$	−3.40532	+	9.34129i	−0.143901	+	0.394742i
$561$		0			0
$562$	−0.294871	+	0.510731i	−0.0124384	+	0.0215439i
$563$	9.54528	−	16.5329i	0.402286	−	0.696779i	−0.591716	−	0.806147i	$-0.701549\pi$
$563$	9.54528	−	16.5329i	0.402286	−	0.696779i	0.994001	+	0.109368i	$0.0348826\pi$
$564$		0			0
$565$	−32.8923	+	18.9904i	−1.38379	+	0.798932i
$566$	−14.1925			−0.596557
$567$		0			0
$568$	28.0283			1.17604
$569$	−32.3406	+	18.6719i	−1.35579	+	0.782765i	−0.989053	−	0.147561i	$-0.952858\pi$
$569$	−32.3406	+	18.6719i	−1.35579	+	0.782765i	−0.366735	+	0.930325i	$0.619525\pi$
$570$		0			0
$571$	−22.6421	+	39.2173i	−0.947544	+	1.64119i	−0.196968	+	0.980410i	$0.563110\pi$
$571$	−22.6421	+	39.2173i	−0.947544	+	1.64119i	−0.750576	+	0.660784i	$0.770224\pi$
$572$	4.85543	−	8.40986i	0.203016	−	0.351634i
$573$		0			0
$574$	1.45152	+	0.529144i	0.0605853	+	0.0220860i
$575$		−	0.264101i		−	0.0110138i
$576$		0			0
$577$			37.0988i			1.54444i	0.635354	+	0.772221i	$0.280854\pi$
$577$			37.0988i			1.54444i	−0.635354	+	0.772221i	$0.719146\pi$
$578$	10.3509	−	5.97610i	0.430541	−	0.248573i
$579$		0			0
$580$	8.58450	+	4.95626i	0.356452	+	0.205798i
$581$	−22.3337	+	3.92636i	−0.926559	+	0.162893i
$582$		0			0
$583$	13.3603	+	23.1408i	0.553329	+	0.958393i
$584$	−0.980996			−0.0405939
$585$		0			0
$586$			18.7676i			0.775282i
$587$	17.0612	+	29.5509i	0.704191	+	1.21969i	0.966983	+	0.254842i	$0.0820235\pi$
$587$	17.0612	+	29.5509i	0.704191	+	1.21969i	−0.262792	+	0.964853i	$0.584643\pi$
$588$		0			0
$589$	8.81453	−	15.2672i	0.363197	−	0.629075i
$590$	13.2458	+	7.64749i	0.545322	+	0.314842i
$591$		0			0
$592$	−1.44437	−	2.50172i	−0.0593632	−	0.102820i
$593$	−19.6999			−0.808980			−0.404490	−	0.914542i	$-0.632551\pi$
$593$	−19.6999			−0.808980			−0.404490	+	0.914542i	$0.632551\pi$
$594$		0			0
$595$	−22.4313	−	26.7601i	−0.919594	−	1.09706i
$596$	21.2356	−	12.2604i	0.869844	−	0.502205i
$597$		0			0
$598$	2.37663	+	1.37215i	0.0971878	+	0.0561114i
$599$	9.74033	+	5.62358i	0.397979	+	0.229773i	0.685612	−	0.727967i	$-0.259535\pi$
$599$	9.74033	+	5.62358i	0.397979	+	0.229773i	−0.287632	+	0.957741i	$0.592868\pi$
$600$		0			0
$601$	29.7646	−	17.1846i	1.21412	−	0.700975i	0.250469	−	0.968125i	$-0.419415\pi$
$601$	29.7646	−	17.1846i	1.21412	−	0.700975i	0.963655	+	0.267150i	$0.0860818\pi$
$602$	5.10234	−	4.27696i	0.207956	−	0.174316i
$603$		0			0
$604$	18.5636			0.755342
$605$	0.564393	+	0.977557i	0.0229458	+	0.0397433i
$606$		0			0
$607$	−33.7888	−	19.5080i	−1.37145	−	0.791804i	−0.380335	−	0.924849i	$-0.624191\pi$
$607$	−33.7888	−	19.5080i	−1.37145	−	0.791804i	−0.991110	+	0.133044i	$0.957525\pi$
$608$	−4.68179	+	8.10910i	−0.189872	+	0.328868i
$609$		0			0
$610$	1.00619	+	1.74277i	0.0407394	+	0.0705628i
$611$			0.443317i			0.0179347i
$612$		0			0
$613$	−16.1099			−0.650672			−0.325336	−	0.945598i	$-0.605477\pi$
$613$	−16.1099			−0.650672			−0.325336	+	0.945598i	$0.605477\pi$
$614$	4.76222	+	8.24840i	0.192187	+	0.332878i
$615$		0			0
$616$	−20.3535	+	3.57824i	−0.820067	+	0.144171i
$617$	−7.03569	−	4.06205i	−0.283246	−	0.163532i	0.351646	−	0.936133i	$-0.385622\pi$
$617$	−7.03569	−	4.06205i	−0.283246	−	0.163532i	−0.634892	+	0.772601i	$0.718955\pi$
$618$		0			0
$619$	32.4018	−	18.7072i	1.30234	−	0.751906i	0.321535	−	0.946898i	$-0.395801\pi$
$619$	32.4018	−	18.7072i	1.30234	−	0.751906i	0.980805	+	0.194991i	$0.0624678\pi$
$620$		−	37.6554i		−	1.51228i
$621$		0			0
$622$			12.4340i			0.498559i
$623$	9.54718	−	26.1893i	0.382499	−	1.04925i
$624$		0			0
$625$	12.2156	−	21.1581i	0.488626	−	0.846325i
$626$	4.68985	−	8.12305i	0.187444	−	0.324662i
$627$		0			0
$628$	7.83994	−	4.52639i	0.312848	−	0.180623i
$629$	10.1451			0.404511
$630$		0			0
$631$	−19.8268			−0.789294			−0.394647	−	0.918833i	$-0.629133\pi$
$631$	−19.8268			−0.789294			−0.394647	+	0.918833i	$0.629133\pi$
$632$	−9.94437	+	5.74138i	−0.395566	+	0.228380i
$633$		0			0
$634$	5.44692	−	9.43434i	0.216325	−	0.374685i
$635$	−6.98848	+	12.1044i	−0.277329	+	0.480348i
$636$		0			0
$637$	4.30227	+	11.8578i	0.170462	+	0.469823i
$638$			6.14384i			0.243237i
$639$		0			0
$640$			24.8226i			0.981199i
$641$	8.01849	−	4.62948i	0.316711	−	0.182853i	−0.333214	−	0.942851i	$-0.608133\pi$
$641$	8.01849	−	4.62948i	0.316711	−	0.182853i	0.649926	+	0.759998i	$0.274800\pi$
$642$		0			0
$643$	36.3456	+	20.9841i	1.43333	+	0.827534i	0.997373	−	0.0724332i	$-0.0230764\pi$
$643$	36.3456	+	20.9841i	1.43333	+	0.827534i	0.435958	+	0.899967i	$0.356410\pi$
$644$	1.72716	+	9.82435i	0.0680597	+	0.387134i
$645$		0			0
$646$	−3.14833	−	5.45306i	−0.123869	−	0.214548i
$647$	−6.28587			−0.247123			−0.123561	−	0.992337i	$-0.539432\pi$
$647$	−6.28587			−0.247123			−0.123561	+	0.992337i	$0.539432\pi$
$648$		0			0
$649$		−	36.5798i		−	1.43588i
$650$	−0.0643195	−	0.111405i	−0.00252282	−	0.00436965i
$651$		0			0
$652$	8.10872	−	14.0447i	0.317562	−	0.550033i
$653$	−20.1668	−	11.6433i	−0.789189	−	0.455638i	0.0504882	−	0.998725i	$-0.483922\pi$
$653$	−20.1668	−	11.6433i	−0.789189	−	0.455638i	−0.839677	+	0.543086i	$0.817256\pi$
$654$		0			0
$655$	18.8207	+	32.5985i	0.735387	+	1.27373i
$656$	−1.54691			−0.0603968
$657$		0			0
$658$	0.320035	−	0.268265i	0.0124763	−	0.0104581i
$659$	−25.8880	+	14.9464i	−1.00845	+	0.582230i	−0.910738	−	0.412984i	$-0.864486\pi$
$659$	−25.8880	+	14.9464i	−1.00845	+	0.582230i	−0.0977141	+	0.995215i	$0.531153\pi$
$660$		0			0
$661$	17.6184	+	10.1720i	0.685278	+	0.395645i	0.801841	−	0.597538i	$-0.203854\pi$
$661$	17.6184	+	10.1720i	0.685278	+	0.395645i	−0.116563	+	0.993183i	$0.537188\pi$
$662$	−11.0549	−	6.38253i	−0.429660	−	0.248064i
$663$		0			0
$664$	−17.0886	+	9.86609i	−0.663165	+	0.382879i
$665$	−7.37118	+	6.17878i	−0.285842	+	0.239603i
$666$		0			0
$667$	6.69963			0.259411
$668$	−2.86955	−	4.97021i	−0.111026	−	0.192303i
$669$		0			0
$670$	9.81303	+	5.66555i	0.379110	+	0.218879i
$671$	2.40643	−	4.16805i	0.0928990	−	0.160906i
$672$		0			0
$673$	−8.55996	−	14.8263i	−0.329962	−	0.571511i	0.652542	−	0.757753i	$-0.273703\pi$
$673$	−8.55996	−	14.8263i	−0.329962	−	0.571511i	−0.982504	+	0.186241i	$0.940369\pi$
$674$		−	0.628973i		−	0.0242271i
$675$		0			0
$676$	15.4909			0.595802
$677$	−14.2078	−	24.6085i	−0.546048	−	0.945783i	−0.998540	−	0.0540148i	$-0.982798\pi$
$677$	−14.2078	−	24.6085i	−0.546048	−	0.945783i	0.452492	−	0.891769i	$-0.350535\pi$
$678$		0			0
$679$	−3.33313	−	18.9593i	−0.127914	−	0.727593i
$680$	−26.3138	−	15.1923i	−1.00909	−	0.582598i
$681$		0			0
$682$	20.2122	−	11.6695i	0.773965	−	0.446849i
$683$			20.9274i			0.800764i	0.916348	+	0.400382i	$0.131123\pi$
$683$			20.9274i			0.800764i	−0.916348	+	0.400382i	$0.868877\pi$
$684$		0			0
$685$		−	13.8526i		−	0.529281i
$686$	5.95684	−	10.2814i	0.227433	−	0.392546i
$687$		0			0
$688$	−3.33310	+	5.77311i	−0.127073	+	0.220098i
$689$	7.09627	−	12.2911i	0.270346	−	0.468254i
$690$		0			0
$691$	−20.7918	+	12.0041i	−0.790957	+	0.456659i	−0.840299	−	0.542123i	$-0.817621\pi$
$691$	−20.7918	+	12.0041i	−0.790957	+	0.456659i	0.0493424	+	0.998782i	$0.484287\pi$
$692$	28.7163			1.09163
$693$		0			0
$694$	−13.6094			−0.516606
$695$	−14.7143	+	8.49529i	−0.558144	+	0.322245i
$696$		0			0
$697$	2.71634	−	4.70484i	0.102889	−	0.178208i
$698$	3.22246	−	5.58147i	0.121972	−	0.211262i
$699$		0			0
$700$	0.160144	−	0.439299i	0.00605287	−	0.0166039i
$701$			42.0117i			1.58676i	0.608728	+	0.793379i	$0.291680\pi$
$701$			42.0117i			1.58676i	−0.608728	+	0.793379i	$0.708320\pi$
$702$		0			0
$703$		−	2.79450i		−	0.105397i
$704$	−0.747976	+	0.431844i	−0.0281904	+	0.0162757i
$705$		0			0
$706$	−1.52607	−	0.881077i	−0.0574344	−	0.0331598i
$707$	−12.1641	+	2.13850i	−0.457478	+	0.0804266i
$708$		0			0
$709$	−18.6094	−	32.2324i	−0.698891	−	1.21051i	−0.968851	−	0.247643i	$-0.920344\pi$
$709$	−18.6094	−	32.2324i	−0.698891	−	1.21051i	0.269960	−	0.962871i	$-0.412989\pi$
$710$	17.2703			0.648141
$711$		0			0
$712$		−	24.2562i		−	0.909039i
$713$	−12.7252	−	22.0406i	−0.476561	−	0.825428i
$714$		0			0
$715$	6.75890	−	11.7068i	0.252769	−	0.437808i
$716$	6.92175	+	3.99627i	0.258678	+	0.149348i
$717$		0			0
$718$	−3.20837	−	5.55705i	−0.119735	−	0.207387i
$719$	−18.2978			−0.682392			−0.341196	−	0.939992i	$-0.610832\pi$
$719$	−18.2978			−0.682392			−0.341196	+	0.939992i	$0.610832\pi$
$720$		0			0
$721$	12.6538	−	10.6069i	0.471253	−	0.395021i
$722$	9.05494	−	5.22787i	0.336990	−	0.194561i
$723$		0			0
$724$	18.6516	+	10.7685i	0.693181	+	0.400208i
$725$	−0.271971	−	0.157022i	−0.0101007	−	0.00583166i
$726$		0			0
$727$	−28.3214	+	16.3514i	−1.05038	+	0.606439i	−0.922756	−	0.385384i	$-0.874069\pi$
$727$	−28.3214	+	16.3514i	−1.05038	+	0.606439i	−0.127626	+	0.991822i	$0.540736\pi$
$728$	7.05127	+	8.41204i	0.261338	+	0.311771i
$729$		0			0
$730$	−0.604462			−0.0223722
$731$	−11.7057	−	20.2749i	−0.432951	−	0.749893i
$732$		0			0
$733$	0.431812	+	0.249307i	0.0159494	+	0.00920836i	0.507953	−	0.861385i	$-0.330402\pi$
$733$	0.431812	+	0.249307i	0.0159494	+	0.00920836i	−0.492004	+	0.870593i	$0.663736\pi$
$734$	−1.86529	+	3.23078i	−0.0688493	+	0.119250i
$735$		0			0
$736$	6.75890	+	11.7068i	0.249136	+	0.431517i
$737$		−	27.0997i		−	0.998231i
$738$		0			0
$739$	−47.7046			−1.75484			−0.877421	−	0.479722i	$-0.840737\pi$
$739$	−47.7046			−1.75484			−0.877421	+	0.479722i	$0.840737\pi$
$740$	−2.98450	−	5.16931i	−0.109713	−	0.190028i
$741$		0			0
$742$	−13.1673	+	2.31486i	−0.483386	+	0.0849812i
$743$	−9.20534	−	5.31470i	−0.337711	−	0.194978i	0.321548	−	0.946893i	$-0.395797\pi$
$743$	−9.20534	−	5.31470i	−0.337711	−	0.194978i	−0.659259	+	0.751916i	$0.729130\pi$
$744$		0			0
$745$	29.5606	−	17.0668i	1.08302	−	0.625279i
$746$		−	9.95693i		−	0.364549i
$747$		0			0
$748$			32.1662i			1.17611i
$749$	−3.70223	−	1.34963i	−0.135277	−	0.0493144i
$750$		0			0
$751$	−9.55927	+	16.5571i	−0.348823	+	0.604179i	−0.986041	−	0.166505i	$-0.946752\pi$
$751$	−9.55927	+	16.5571i	−0.348823	+	0.604179i	0.637218	+	0.770684i	$0.280085\pi$
$752$	−0.209063	+	0.362108i	−0.00762375	+	0.0132047i
$753$		0			0
$754$	2.82607	−	1.63164i	0.102920	−	0.0594206i
$755$	25.8411			0.940453
$756$		0			0
$757$	28.5388			1.03726			0.518631	−	0.854998i	$-0.326442\pi$
$757$	28.5388			1.03726			0.518631	+	0.854998i	$0.326442\pi$
$758$	1.55418	−	0.897305i	0.0564503	−	0.0325916i
$759$		0			0
$760$	−4.18478	+	7.24825i	−0.151798	+	0.262922i
$761$	−21.6650	+	37.5249i	−0.785355	+	1.36028i	0.143431	+	0.989660i	$0.454186\pi$
$761$	−21.6650	+	37.5249i	−0.785355	+	1.36028i	−0.928787	+	0.370615i	$0.879147\pi$
$762$		0			0
$763$	3.97522	−	10.9046i	0.143912	−	0.394773i
$764$			16.2674i			0.588533i
$765$		0			0
$766$		−	2.23567i		−	0.0807779i
$767$	−16.8261	+	9.71458i	−0.607557	+	0.350773i
$768$		0			0
$769$	5.75189	+	3.32086i	0.207419	+	0.119753i	0.600111	−	0.799917i	$-0.295123\pi$
$769$	5.75189	+	3.32086i	0.207419	+	0.119753i	−0.392693	+	0.919670i	$0.628456\pi$
$770$	−12.5413	+	2.20481i	−0.451956	+	0.0794558i
$771$		0			0
$772$	−12.8120	−	22.1910i	−0.461113	−	0.798672i
$773$	44.4831			1.59995			0.799973	−	0.600036i	$-0.204847\pi$
$773$	44.4831			1.59995			0.799973	+	0.600036i	$0.204847\pi$
$774$		0			0
$775$			1.19298i			0.0428532i
$776$	−8.37543	−	14.5067i	−0.300661	−	0.520759i
$777$		0			0
$778$	2.35965	−	4.08703i	0.0845974	−	0.146527i
$779$	−1.29596	−	0.748226i	−0.0464328	−	0.0268080i
$780$		0			0
$781$	−20.6520	−	35.7703i	−0.738986	−	1.27996i
$782$	−9.09020			−0.325065
$783$		0			0
$784$	−2.07784	+	11.7145i	−0.0742087	+	0.418377i
$785$	10.9134	−	6.30087i	0.389517	−	0.224888i
$786$		0			0
$787$	−19.0399	−	10.9927i	−0.678700	−	0.391848i	0.120665	−	0.992693i	$-0.461497\pi$
$787$	−19.0399	−	10.9927i	−0.678700	−	0.391848i	−0.799365	+	0.600846i	$0.794831\pi$
$788$	5.31385	+	3.06795i	0.189298	+	0.109291i
$789$		0			0
$790$	−6.12744	+	3.53768i	−0.218004	+	0.125865i
$791$	−34.8300	+	29.1958i	−1.23841	+	1.03808i
$792$		0			0
$793$	−2.55632			−0.0907776
$794$	−6.18612	−	10.7147i	−0.219537	−	0.380250i
$795$		0			0
$796$	20.9133	+	12.0743i	0.741251	+	0.427962i
$797$	9.71892	−	16.8337i	0.344262	−	0.596279i	−0.640958	−	0.767576i	$-0.721463\pi$
$797$	9.71892	−	16.8337i	0.344262	−	0.596279i	0.985219	+	0.171297i	$0.0547959\pi$
$798$		0			0
$799$	−0.734219	−	1.27171i	−0.0259748	−	0.0449897i
$800$		−	0.633646i		−	0.0224028i
$801$		0			0
$802$	−7.11636			−0.251287
$803$	0.722823	+	1.25197i	0.0255079	+	0.0441809i
$804$		0			0
$805$	2.40426	+	13.6758i	0.0847390	+	0.482008i
$806$	−10.7356	−	6.19820i	−0.378145	−	0.218322i
$807$		0			0
$808$	−9.30732	+	5.37358i	−0.327430	+	0.189042i
$809$		−	21.0058i		−	0.738526i	−0.929325	−	0.369263i	$-0.879610\pi$
$809$		−	21.0058i		−	0.738526i	0.929325	−	0.369263i	$-0.120390\pi$
$810$		0			0
$811$		−	37.3291i		−	1.31080i	−0.755281	−	0.655401i	$-0.772500\pi$
$811$		−	37.3291i		−	1.31080i	0.755281	−	0.655401i	$-0.227500\pi$
$812$	11.1440	+	4.06248i	0.391077	+	0.142565i
$813$		0			0
$814$	1.84981	−	3.20397i	0.0648359	−	0.112299i
$815$	11.2876	−	19.5506i	0.395386	−	0.684829i
$816$		0			0
$817$	−5.58478	+	3.22438i	−0.195387	+	0.112807i
$818$	13.0090			0.454849
$819$		0			0
$820$	−3.19639			−0.111623
$821$	10.9017	−	6.29412i	0.380473	−	0.219666i	−0.297551	−	0.954706i	$-0.596170\pi$
$821$	10.9017	−	6.29412i	0.380473	−	0.219666i	0.678024	+	0.735040i	$0.262837\pi$
$822$		0			0
$823$	22.4189	−	38.8307i	0.781474	−	1.35355i	−0.149608	−	0.988745i	$-0.547801\pi$
$823$	22.4189	−	38.8307i	0.781474	−	1.35355i	0.931083	−	0.364808i	$-0.118865\pi$
$824$	7.18385	−	12.4428i	0.250261	−	0.433465i
$825$		0			0
$826$	17.1951	+	6.26839i	0.598294	+	0.218105i
$827$			25.7293i			0.894695i	0.894360	+	0.447347i	$0.147631\pi$
$827$			25.7293i			0.894695i	−0.894360	+	0.447347i	$0.852369\pi$
$828$		0			0
$829$			16.9628i			0.589142i	0.955630	+	0.294571i	$0.0951767\pi$
$829$			16.9628i			0.589142i	−0.955630	+	0.294571i	$0.904823\pi$
$830$	−10.5295	+	6.07921i	−0.365484	+	0.211012i
$831$		0			0
$832$	0.397284	+	0.229372i	0.0137733	+	0.00795204i
$833$	−31.9804	−	26.8901i	−1.10806	−	0.931686i
$834$		0			0
$835$	−3.99450	−	6.91867i	−0.138235	−	0.239431i
$836$	8.86030			0.306440
$837$		0			0
$838$		−	7.12081i		−	0.245984i
$839$	13.3539	+	23.1296i	0.461027	+	0.798522i	0.999012	−	0.0444321i	$-0.0141478\pi$
$839$	13.3539	+	23.1296i	0.461027	+	0.798522i	−0.537986	+	0.842954i	$0.680815\pi$
$840$		0			0
$841$	−10.5167	+	18.2155i	−0.362645	+	0.628120i
$842$	5.10370	+	2.94662i	0.175885	+	0.101547i
$843$		0			0
$844$	18.9847	+	32.8824i	0.653479	+	1.13186i
$845$	21.5637			0.741815
$846$		0			0
$847$	0.867695	+	1.03514i	0.0298144	+	0.0355680i
$848$	11.5927	−	6.69305i	0.398095	−	0.229840i
$849$		0			0
$850$	0.369016	+	0.213051i	0.0126571	+	0.00730760i
$851$	−3.49381	−	2.01715i	−0.119766	−	0.0691471i
$852$		0			0
$853$	37.6287	−	21.7249i	1.28838	−	0.743848i	0.310017	−	0.950731i	$-0.399665\pi$
$853$	37.6287	−	21.7249i	1.28838	−	0.743848i	0.978366	+	0.206883i	$0.0663319\pi$
$854$	1.54691	+	1.84544i	0.0529342	+	0.0631496i
$855$		0			0
$856$	−3.42896			−0.117199
$857$	7.83430	+	13.5694i	0.267615	+	0.463522i	0.968245	−	0.250002i	$-0.0804312\pi$
$857$	7.83430	+	13.5694i	0.267615	+	0.463522i	−0.700631	+	0.713524i	$0.747098\pi$
$858$		0			0
$859$	−17.3578	−	10.0216i	−0.592242	−	0.341931i	0.173742	−	0.984791i	$-0.444414\pi$
$859$	−17.3578	−	10.0216i	−0.592242	−	0.341931i	−0.765984	+	0.642860i	$0.777748\pi$
$860$	−6.88721	+	11.9290i	−0.234852	+	0.406775i
$861$		0			0
$862$	4.84727	+	8.39571i	0.165099	+	0.285959i
$863$		−	40.0219i		−	1.36236i	−0.732115	−	0.681181i	$-0.761467\pi$
$863$		−	40.0219i		−	1.36236i	0.732115	−	0.681181i	$-0.238533\pi$
$864$		0			0
$865$	39.9739			1.35915
$866$	1.07010	+	1.85347i	0.0363635	+	0.0629834i
$867$		0			0
$868$	−7.80184	−	44.3780i	−0.264812	−	1.50629i
$869$	14.6545	+	8.46079i	0.497120	+	0.287013i
$870$		0			0
$871$	−12.4655	+	7.19694i	−0.422376	+	0.243859i
$872$		−	10.0997i		−	0.342019i
$873$		0			0
$874$			2.50393i			0.0846967i
$875$	10.2408	−	28.0919i	0.346201	−	0.949680i
$876$		0			0
$877$	−22.6353	+	39.2054i	−0.764338	+	1.32387i	0.176257	+	0.984344i	$0.443601\pi$
$877$	−22.6353	+	39.2054i	−0.764338	+	1.32387i	−0.940596	+	0.339529i	$0.889732\pi$
$878$	2.18931	−	3.79200i	0.0738856	−	0.127974i
$879$		0			0
$880$	11.0416	−	6.37485i	0.372211	−	0.214896i
$881$	−45.3385			−1.52749			−0.763746	−	0.645517i	$-0.776642\pi$
$881$	−45.3385			−1.52749			−0.763746	+	0.645517i	$0.776642\pi$
$882$		0			0
$883$	12.5650			0.422845			0.211423	−	0.977395i	$-0.432190\pi$
$883$	12.5650			0.422845			0.211423	+	0.977395i	$0.432190\pi$
$884$	14.7960	−	8.54245i	0.497642	−	0.287314i
$885$		0			0
$886$	−3.62178	+	6.27311i	−0.121676	+	0.210749i
$887$	−17.8620	+	30.9379i	−0.599748	+	1.03879i	0.393110	+	0.919492i	$0.371399\pi$
$887$	−17.8620	+	30.9379i	−0.599748	+	1.03879i	−0.992858	+	0.119303i	$0.961934\pi$
$888$		0			0
$889$	−5.72822	+	15.7133i	−0.192118	+	0.527009i
$890$		−	14.9460i		−	0.500991i
$891$		0			0
$892$		−	30.4821i		−	1.02062i
$893$	−0.350296	+	0.202243i	−0.0117222	+	0.00676782i
$894$		0			0
$895$	9.63528	+	5.56293i	0.322072	+	0.185948i
$896$	5.14301	+	29.2542i	0.171816	+	0.977313i
$897$		0			0
$898$	−7.97346	−	13.8104i	−0.266078	−	0.460860i
$899$	−30.2632			−1.00933
$900$		0			0
$901$			47.0113i			1.56617i
$902$	−0.990571	−	1.71572i	−0.0329824	−	0.0571272i
$903$		0			0
$904$	−19.7738	+	34.2491i	−0.657665	+	1.13911i
$905$	25.9635	+	14.9901i	0.863058	+	0.498287i
$906$		0			0
$907$	4.52104	+	7.83067i	0.150119	+	0.260013i	0.931271	−	0.364327i	$-0.118701\pi$
$907$	4.52104	+	7.83067i	0.150119	+	0.260013i	−0.781152	+	0.624341i	$0.785368\pi$
$908$	13.7744			0.457120
$909$		0			0
$910$	4.34479	+	5.18326i	0.144029	+	0.171823i
$911$	35.5171	−	20.5058i	1.17673	−	0.679388i	0.221478	−	0.975165i	$-0.428912\pi$
$911$	35.5171	−	20.5058i	1.17673	−	0.679388i	0.955257	+	0.295777i	$0.0955787\pi$
$912$		0			0
$913$	25.1826	+	14.5392i	0.833421	+	0.481176i
$914$	7.00619	+	4.04503i	0.231744	+	0.133798i
$915$		0			0
$916$	−19.7652	+	11.4114i	−0.653059	+	0.377044i
$917$	28.9349	+	34.5188i	0.955515	+	1.13991i
$918$		0			0
$919$	10.2326			0.337541			0.168771	−	0.985655i	$-0.446020\pi$
$919$	10.2326			0.337541			0.168771	+	0.985655i	$0.446020\pi$
$920$	6.04138	+	10.4640i	0.199178	+	0.344987i
$921$		0			0
$922$	−16.0057	−	9.24088i	−0.527119	−	0.304332i
$923$	−10.9692	+	18.9992i	−0.361055	+	0.625366i
$924$		0			0
$925$	0.0945538	+	0.163772i	0.00310891	+	0.00538479i
$926$			16.1498i			0.530716i
$927$		0			0
$928$	16.0741			0.527659
$929$	12.8330	+	22.2273i	0.421036	+	0.729255i	0.996041	−	0.0888945i	$-0.0283334\pi$
$929$	12.8330	+	22.2273i	0.421036	+	0.729255i	−0.575005	+	0.818150i	$0.695000\pi$
$930$		0			0
$931$	−7.40697	+	8.80913i	−0.242754	+	0.288707i
$932$	−40.8763	−	23.5999i	−1.33895	−	0.773041i
$933$		0			0
$934$	−14.2214	+	8.21075i	−0.465340	+	0.268664i
$935$			44.7763i			1.46434i
$936$		0			0
$937$		−	15.9276i		−	0.520333i	−0.965564	−	0.260167i	$-0.916223\pi$
$937$		−	15.9276i		−	0.520333i	0.965564	−	0.260167i	$-0.0837775\pi$
$938$	12.7388	+	4.64386i	0.415937	+	0.151628i
$939$		0			0
$940$	−0.431988	+	0.748226i	−0.0140899	+	0.0244044i
$941$	−19.6767	+	34.0810i	−0.641442	+	1.11101i	0.343669	+	0.939091i	$0.388330\pi$
$941$	−19.6767	+	34.0810i	−0.641442	+	1.11101i	−0.985111	+	0.171919i	$0.945003\pi$
$942$		0			0
$943$	−1.87093	+	1.08018i	−0.0609258	+	0.0351755i
$944$	−18.3252			−0.596433
$945$		0			0
$946$	−8.53747			−0.277577
$947$	−28.9086	+	16.6904i	−0.939403	+	0.542365i	−0.889773	−	0.456403i	$-0.849138\pi$
$947$	−28.9086	+	16.6904i	−0.939403	+	0.542365i	−0.0496302	+	0.998768i	$0.515804\pi$
$948$		0			0
$949$	0.383923	−	0.664975i	0.0124627	−	0.0215860i
$950$	0.0586858	−	0.101647i	0.00190402	−	0.00329786i
$951$		0			0
$952$	−34.1594	−	12.4526i	−1.10711	−	0.403592i
$953$		−	44.4622i		−	1.44027i	−0.693832	−	0.720137i	$-0.744079\pi$
$953$		−	44.4622i		−	1.44027i	0.693832	−	0.720137i	$-0.255921\pi$
$954$		0			0
$955$			22.6447i			0.732764i
$956$	−21.7767	+	12.5728i	−0.704309	+	0.406633i
$957$		0			0
$958$	0.297540	+	0.171785i	0.00961307	+	0.00555011i
$959$	−2.87013	−	16.3257i	−0.0926813	−	0.527185i
$960$		0			0
$961$	41.9814	+	72.7138i	1.35424	+	2.34561i
$962$	−1.96504			−0.0633554
$963$		0			0
$964$		−	7.97776i		−	0.256947i
$965$	−17.8347	−	30.8905i	−0.574118	−	0.994401i
$966$		0			0
$967$	−20.0556	+	34.7372i	−0.644943	+	1.11707i	0.339371	+	0.940652i	$0.389786\pi$
$967$	−20.0556	+	34.7372i	−0.644943	+	1.11707i	−0.984315	+	0.176422i	$0.943548\pi$
$968$	1.01788	+	0.587674i	0.0327159	+	0.0188886i
$969$		0			0
$970$	−5.16071	−	8.93861i	−0.165700	−	0.287001i
$971$	46.0026			1.47629			0.738147	−	0.674640i	$-0.235701\pi$
$971$	46.0026			1.47629			0.738147	+	0.674640i	$0.235701\pi$
$972$		0			0
$973$	−15.5811	+	13.0606i	−0.499506	+	0.418704i
$974$	18.9650	−	10.9494i	0.607678	−	0.350843i
$975$		0			0
$976$	−2.08804	−	1.20553i	−0.0668366	−	0.0385882i
$977$	46.8323	+	27.0386i	1.49830	+	0.865042i	0.999998	−	0.00196335i	$-0.000624955\pi$
$977$	46.8323	+	27.0386i	1.49830	+	0.865042i	0.498299	+	0.867005i	$0.333958\pi$
$978$		0			0
$979$	−30.9562	+	17.8726i	−0.989365	+	0.571210i
$980$	−4.29346	+	24.2058i	−0.137149	+	0.773227i
$981$		0			0
$982$	−4.34836			−0.138762
$983$	6.97890	+	12.0878i	0.222592	+	0.385541i	0.955594	−	0.294685i	$-0.0952148\pi$
$983$	6.97890	+	12.0878i	0.222592	+	0.385541i	−0.733002	+	0.680226i	$0.761881\pi$
$984$		0			0
$985$	7.39703	+	4.27068i	0.235689	+	0.136075i
$986$	−5.40462	+	9.36107i	−0.172118	+	0.298117i
$987$		0			0
$988$	−2.35305	−	4.07560i	−0.0748605	−	0.129662i
$989$			9.30979i			0.296034i
$990$		0			0
$991$	−37.0297			−1.17629			−0.588144	−	0.808756i	$-0.700141\pi$
$991$	−37.0297			−1.17629			−0.588144	+	0.808756i	$0.700141\pi$
$992$	−30.5309	−	52.8811i	−0.969358	−	1.67898i
$993$		0			0
$994$	20.3535	−	3.57824i	0.645575	−	0.113495i
$995$	29.1119	+	16.8077i	0.922909	+	0.532841i
$996$		0			0
$997$	−43.4282	+	25.0733i	−1.37538	+	0.794079i	−0.991600	−	0.129344i	$-0.958713\pi$
$997$	−43.4282	+	25.0733i	−1.37538	+	0.794079i	−0.383785	+	0.923422i	$0.625380\pi$
$998$			5.51814i			0.174674i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.o.a.125.3		12
3.2	odd	2		63.2.o.a.41.4	yes	12
4.3	odd	2		3024.2.cc.a.881.2		12
7.2	even	3		1323.2.s.c.962.4		12
7.3	odd	6		1323.2.i.c.1097.4		12
7.4	even	3		1323.2.i.c.1097.3		12
7.5	odd	6		1323.2.s.c.962.3		12
7.6	odd	2	inner	189.2.o.a.125.4		12
9.2	odd	6	inner	189.2.o.a.62.4		12
9.4	even	3		567.2.c.c.566.8		12
9.5	odd	6		567.2.c.c.566.5		12
9.7	even	3		63.2.o.a.20.3	✓	12
12.11	even	2		1008.2.cc.a.545.1		12
21.2	odd	6		441.2.s.c.374.3		12
21.5	even	6		441.2.s.c.374.4		12
21.11	odd	6		441.2.i.c.68.3		12
21.17	even	6		441.2.i.c.68.4		12
21.20	even	2		63.2.o.a.41.3	yes	12
28.27	even	2		3024.2.cc.a.881.5		12
36.7	odd	6		1008.2.cc.a.209.6		12
36.11	even	6		3024.2.cc.a.2897.5		12
63.2	odd	6		1323.2.i.c.521.4		12
63.11	odd	6		1323.2.s.c.656.3		12
63.13	odd	6		567.2.c.c.566.7		12
63.16	even	3		441.2.i.c.227.4		12
63.20	even	6	inner	189.2.o.a.62.3		12
63.25	even	3		441.2.s.c.362.4		12
63.34	odd	6		63.2.o.a.20.4	yes	12
63.38	even	6		1323.2.s.c.656.4		12
63.41	even	6		567.2.c.c.566.6		12
63.47	even	6		1323.2.i.c.521.3		12
63.52	odd	6		441.2.s.c.362.3		12
63.61	odd	6		441.2.i.c.227.3		12
84.83	odd	2		1008.2.cc.a.545.6		12
252.83	odd	6		3024.2.cc.a.2897.2		12
252.223	even	6		1008.2.cc.a.209.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.3	✓	12	9.7	even	3
63.2.o.a.20.4	yes	12	63.34	odd	6
63.2.o.a.41.3	yes	12	21.20	even	2
63.2.o.a.41.4	yes	12	3.2	odd	2
189.2.o.a.62.3		12	63.20	even	6	inner
189.2.o.a.62.4		12	9.2	odd	6	inner
189.2.o.a.125.3		12	1.1	even	1	trivial
189.2.o.a.125.4		12	7.6	odd	2	inner
441.2.i.c.68.3		12	21.11	odd	6
441.2.i.c.68.4		12	21.17	even	6
441.2.i.c.227.3		12	63.61	odd	6
441.2.i.c.227.4		12	63.16	even	3
441.2.s.c.362.3		12	63.52	odd	6
441.2.s.c.362.4		12	63.25	even	3
441.2.s.c.374.3		12	21.2	odd	6
441.2.s.c.374.4		12	21.5	even	6
567.2.c.c.566.5		12	9.5	odd	6
567.2.c.c.566.6		12	63.41	even	6
567.2.c.c.566.7		12	63.13	odd	6
567.2.c.c.566.8		12	9.4	even	3
1008.2.cc.a.209.1		12	252.223	even	6
1008.2.cc.a.209.6		12	36.7	odd	6
1008.2.cc.a.545.1		12	12.11	even	2
1008.2.cc.a.545.6		12	84.83	odd	2
1323.2.i.c.521.3		12	63.47	even	6
1323.2.i.c.521.4		12	63.2	odd	6
1323.2.i.c.1097.3		12	7.4	even	3
1323.2.i.c.1097.4		12	7.3	odd	6
1323.2.s.c.656.3		12	63.11	odd	6
1323.2.s.c.656.4		12	63.38	even	6
1323.2.s.c.962.3		12	7.5	odd	6
1323.2.s.c.962.4		12	7.2	even	3
3024.2.cc.a.881.2		12	4.3	odd	2
3024.2.cc.a.881.5		12	28.27	even	2
3024.2.cc.a.2897.2		12	252.83	odd	6
3024.2.cc.a.2897.5		12	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.555632 - 0.320794i) q^{2} +(-0.794182 + 1.37556i) q^{4} +(-1.10552 + 1.91482i) q^{5} +(-0.906161 + 2.48573i) q^{7} +2.30225i q^{8} +O(q^{10})\)	\(q+(0.555632 - 0.320794i) q^{2} +(-0.794182 + 1.37556i) q^{4} +(-1.10552 + 1.91482i) q^{5} +(-0.906161 + 2.48573i) q^{7} +2.30225i q^{8} +1.41858i q^{10} +(2.93818 - 1.69636i) q^{11} +(-1.56060 - 0.901012i) q^{13} +(0.293917 + 1.67184i) q^{14} +(-0.849814 - 1.47192i) q^{16} +5.96901 q^{17} -1.64419i q^{19} +(-1.75597 - 3.04144i) q^{20} +(1.08836 - 1.88510i) q^{22} +(-2.05563 - 1.18682i) q^{23} +(0.0556321 + 0.0963576i) q^{25} -1.15616 q^{26} +(-2.69963 - 3.22061i) q^{28} +(-2.44437 + 1.41126i) q^{29} +(9.28558 + 5.36103i) q^{31} +(-4.93199 - 2.84748i) q^{32} +(3.31657 - 1.91482i) q^{34} +(-3.75796 - 4.48318i) q^{35} +1.69963 q^{37} +(-0.527445 - 0.913562i) q^{38} +(-4.40841 - 2.54520i) q^{40} +(0.455074 - 0.788211i) q^{41} +(-1.96108 - 3.39669i) q^{43} +5.38887i q^{44} -1.52290 q^{46} +(-0.123005 - 0.213051i) q^{47} +(-5.35774 - 4.50495i) q^{49} +(0.0618219 + 0.0356929i) q^{50} +(2.47880 - 1.43113i) q^{52} +7.87589i q^{53} +7.50146i q^{55} +(-5.72279 - 2.08621i) q^{56} +(-0.905446 + 1.56828i) q^{58} +(5.39093 - 9.33736i) q^{59} +(1.22853 - 0.709292i) q^{61} +6.87916 q^{62} -0.254572 q^{64} +(3.45056 - 1.99218i) q^{65} +(3.99381 - 6.91748i) q^{67} +(-4.74048 + 8.21075i) q^{68} +(-3.52622 - 1.28547i) q^{70} -12.1743i q^{71} +0.426103i q^{73} +(0.944368 - 0.545231i) q^{74} +(2.26168 + 1.30578i) q^{76} +(1.55423 + 8.84070i) q^{77} +(2.49381 + 4.31941i) q^{79} +3.75796 q^{80} -0.583940i q^{82} +(4.28541 + 7.42254i) q^{83} +(-6.59888 + 11.4296i) q^{85} +(-2.17928 - 1.25821i) q^{86} +(3.90545 + 6.76443i) q^{88} -10.5358 q^{89} +(3.65383 - 3.06277i) q^{91} +(3.26509 - 1.88510i) q^{92} +(-0.136691 - 0.0789188i) q^{94} +(3.14833 + 1.81769i) q^{95} +(-6.30108 + 3.63793i) q^{97} +(-4.42210 - 0.784360i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7}+O(q^{10}) \) 12 * q + 6 * q^2 + 2 * q^4 - 2 * q^7	\( 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7} + 12 q^{14} + 2 q^{16} - 10 q^{22} - 24 q^{23} - 8 q^{28} - 30 q^{29} + 12 q^{32} - 4 q^{37} - 10 q^{43} - 40 q^{46} + 6 q^{49} + 36 q^{50} - 42 q^{56} + 2 q^{58} + 16 q^{64} + 78 q^{65} + 12 q^{67} + 18 q^{70} + 12 q^{74} + 24 q^{77} - 6 q^{79} - 6 q^{85} - 96 q^{86} + 34 q^{88} - 24 q^{91} - 30 q^{92} - 72 q^{95}+O(q^{100}) \) 12 * q + 6 * q^2 + 2 * q^4 - 2 * q^7 + 12 * q^14 + 2 * q^16 - 10 * q^22 - 24 * q^23 - 8 * q^28 - 30 * q^29 + 12 * q^32 - 4 * q^37 - 10 * q^43 - 40 * q^46 + 6 * q^49 + 36 * q^50 - 42 * q^56 + 2 * q^58 + 16 * q^64 + 78 * q^65 + 12 * q^67 + 18 * q^70 + 12 * q^74 + 24 * q^77 - 6 * q^79 - 6 * q^85 - 96 * q^86 + 34 * q^88 - 24 * q^91 - 30 * q^92 - 72 * q^95

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