LMFDB - Embedded newform 920.2.bv.a.17.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.18
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0410298 + 0.0224040i) q^{3} +(-0.288669 + 2.21736i) q^{5} +(1.73059 + 2.31180i) q^{7} +(-1.62074 + 2.52192i) q^{9} +(0.565611 - 0.258306i) q^{11} +(-0.890094 - 0.666316i) q^{13} +(-0.0378336 - 0.0974451i) q^{15} +(-0.149145 - 2.08532i) q^{17} +(1.43969 + 1.66149i) q^{19} +(-0.122799 - 0.0560805i) q^{21} +(-4.23404 + 2.25231i) q^{23} +(-4.83334 - 1.28017i) q^{25} +(0.0200025 - 0.279672i) q^{27} +(-1.86944 - 1.61988i) q^{29} +(-8.11526 + 2.38286i) q^{31} +(-0.0174198 + 0.0232702i) q^{33} +(-5.62564 + 3.16999i) q^{35} +(-0.876858 + 0.190749i) q^{37} +(0.0514485 + 0.00739718i) q^{39} +(6.19326 - 3.98017i) q^{41} +(2.73894 + 5.01600i) q^{43} +(-5.12414 - 4.32176i) q^{45} +(1.83333 + 1.83333i) q^{47} +(-0.377336 + 1.28509i) q^{49} +(0.0528390 + 0.0822190i) q^{51} +(2.56327 - 1.91884i) q^{53} +(0.409482 + 1.32873i) q^{55} +(-0.0962940 - 0.0359158i) q^{57} +(-6.13247 + 0.881716i) q^{59} +(3.88373 + 13.2268i) q^{61} +(-8.63501 + 0.617588i) q^{63} +(1.73440 - 1.78131i) q^{65} +(4.76778 + 12.7829i) q^{67} +(0.123261 - 0.187271i) q^{69} +(-0.404054 + 0.884756i) q^{71} +(3.80740 + 0.272310i) q^{73} +(0.226992 - 0.0557611i) q^{75} +(1.57599 + 0.860556i) q^{77} +(0.310067 + 2.15657i) q^{79} +(-3.73057 - 8.16880i) q^{81} +(2.23428 + 10.2708i) q^{83} +(4.66696 + 0.271261i) q^{85} +(0.112994 + 0.0245804i) q^{87} +(-9.66802 - 2.83879i) q^{89} -3.21083i q^{91} +(0.279582 - 0.279582i) q^{93} +(-4.09970 + 2.71268i) q^{95} +(2.33842 - 10.7495i) q^{97} +(-0.265282 + 1.84507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.0410298	+	0.0224040i	−0.0236886	+	0.0129349i	−0.491050	−	0.871132i	$-0.663387\pi$
$3$	−0.0410298	+	0.0224040i	−0.0236886	+	0.0129349i	0.467361	+	0.884067i	$0.345205\pi$
$4$		0			0
$5$	−0.288669	+	2.21736i	−0.129097	+	0.991632i
$5$	−0.288669	+	2.21736i	−0.129097	+	0.991632i
$6$		0			0
$7$	1.73059	+	2.31180i	0.654101	+	0.873777i	0.997867	−	0.0652785i	$-0.0207936\pi$
$7$	1.73059	+	2.31180i	0.654101	+	0.873777i	−0.343766	+	0.939055i	$0.611703\pi$
$8$		0			0
$9$	−1.62074	+	2.52192i	−0.540247	+	0.840641i
$10$		0			0
$11$	0.565611	−	0.258306i	0.170538	−	0.0778822i	−0.328317	−	0.944568i	$-0.606481\pi$
$11$	0.565611	−	0.258306i	0.170538	−	0.0778822i	0.498855	+	0.866686i	$0.333754\pi$
$12$		0			0
$13$	−0.890094	−	0.666316i	−0.246868	−	0.184803i	0.468677	−	0.883369i	$-0.344731\pi$
$13$	−0.890094	−	0.666316i	−0.246868	−	0.184803i	−0.715545	+	0.698567i	$0.753822\pi$
$14$		0			0
$15$	−0.0378336	−	0.0974451i	−0.00976858	−	0.0251602i
$16$		0			0
$17$	−0.149145	−	2.08532i	−0.0361730	−	0.505765i	−0.982950	−	0.183874i	$-0.941136\pi$
$17$	−0.149145	−	2.08532i	−0.0361730	−	0.505765i	0.946777	−	0.321891i	$-0.104318\pi$
$18$		0			0
$19$	1.43969	+	1.66149i	0.330287	+	0.381171i	0.896467	−	0.443110i	$-0.146125\pi$
$19$	1.43969	+	1.66149i	0.330287	+	0.381171i	−0.566180	+	0.824281i	$0.691579\pi$
$20$		0			0
$21$	−0.122799	−	0.0560805i	−0.0267970	−	0.0122378i
$22$		0			0
$23$	−4.23404	+	2.25231i	−0.882859	+	0.469639i
$23$	−4.23404	+	2.25231i	−0.882859	+	0.469639i
$24$		0			0
$25$	−4.83334	−	1.28017i	−0.966668	−	0.256033i
$26$		0			0
$27$	0.0200025	−	0.279672i	0.00384949	−	0.0538229i
$28$		0			0
$29$	−1.86944	−	1.61988i	−0.347145	−	0.300803i	0.463783	−	0.885949i	$-0.346492\pi$
$29$	−1.86944	−	1.61988i	−0.347145	−	0.300803i	−0.810928	+	0.585146i	$0.801037\pi$
$30$		0			0
$31$	−8.11526	+	2.38286i	−1.45754	+	0.427974i	−0.912028	−	0.410127i	$-0.865484\pi$
$31$	−8.11526	+	2.38286i	−1.45754	+	0.427974i	−0.545516	+	0.838101i	$0.683666\pi$
$32$		0			0
$33$	−0.0174198	+	0.0232702i	−0.00303241	+	0.00405082i
$34$		0			0
$35$	−5.62564	+	3.16999i	−0.950907	+	0.535826i
$36$		0			0
$37$	−0.876858	+	0.190749i	−0.144155	+	0.0313589i	−0.284064	−	0.958805i	$-0.591683\pi$
$37$	−0.876858	+	0.190749i	−0.144155	+	0.0313589i	0.139909	+	0.990164i	$0.455319\pi$
$38$		0			0
$39$	0.0514485	+	0.00739718i	0.00823836	+	0.00118450i
$40$		0			0
$41$	6.19326	−	3.98017i	0.967225	−	0.621597i	0.0412362	−	0.999149i	$-0.486870\pi$
$41$	6.19326	−	3.98017i	0.967225	−	0.621597i	0.925988	+	0.377552i	$0.123234\pi$
$42$		0			0
$43$	2.73894	+	5.01600i	0.417685	+	0.764933i	0.998804	−	0.0488854i	$-0.0155669\pi$
$43$	2.73894	+	5.01600i	0.417685	+	0.764933i	−0.581119	+	0.813818i	$0.697385\pi$
$44$		0			0
$45$	−5.12414	−	4.32176i	−0.763862	−	0.644250i
$46$		0			0
$47$	1.83333	+	1.83333i	0.267418	+	0.267418i	0.828059	−	0.560641i	$-0.189445\pi$
$47$	1.83333	+	1.83333i	0.267418	+	0.267418i	−0.560641	+	0.828059i	$0.689445\pi$
$48$		0			0
$49$	−0.377336	+	1.28509i	−0.0539051	+	0.183584i
$50$		0			0
$51$	0.0528390	+	0.0822190i	0.00739893	+	0.0115130i
$52$		0			0
$53$	2.56327	−	1.91884i	0.352092	−	0.263573i	−0.408561	−	0.912731i	$-0.633969\pi$
$53$	2.56327	−	1.91884i	0.352092	−	0.263573i	0.760654	+	0.649158i	$0.224879\pi$
$54$		0			0
$55$	0.409482	+	1.32873i	0.0552145	+	0.179165i
$56$		0			0
$57$	−0.0962940	−	0.0359158i	−0.0127545	−	0.00475717i
$58$		0			0
$59$	−6.13247	+	0.881716i	−0.798379	+	0.114790i	−0.529418	−	0.848361i	$-0.677590\pi$
$59$	−6.13247	+	0.881716i	−0.798379	+	0.114790i	−0.268962	+	0.963151i	$0.586680\pi$
$60$		0			0
$61$	3.88373	+	13.2268i	0.497260	+	1.69351i	0.699884	+	0.714256i	$0.253235\pi$
$61$	3.88373	+	13.2268i	0.497260	+	1.69351i	−0.202624	+	0.979257i	$0.564947\pi$
$62$		0			0
$63$	−8.63501	+	0.617588i	−1.08791	+	0.0778088i
$64$		0			0
$65$	1.73440	−	1.78131i	0.215126	−	0.220944i
$66$		0			0
$67$	4.76778	+	12.7829i	0.582477	+	1.56168i	0.809082	+	0.587695i	$0.199965\pi$
$67$	4.76778	+	12.7829i	0.582477	+	1.56168i	−0.226605	+	0.973987i	$0.572763\pi$
$68$		0			0
$69$	0.123261	−	0.187271i	0.0148389	−	0.0225448i
$70$		0			0
$71$	−0.404054	+	0.884756i	−0.0479524	+	0.105001i	−0.932092	−	0.362222i	$-0.882018\pi$
$71$	−0.404054	+	0.884756i	−0.0479524	+	0.105001i	0.884139	+	0.467223i	$0.154746\pi$
$72$		0			0
$73$	3.80740	+	0.272310i	0.445622	+	0.0318715i	0.292348	−	0.956312i	$-0.405564\pi$
$73$	3.80740	+	0.272310i	0.445622	+	0.0318715i	0.153275	+	0.988184i	$0.451018\pi$
$74$		0			0
$75$	0.226992	−	0.0557611i	0.0262108	−	0.00643873i
$76$		0			0
$77$	1.57599	+	0.860556i	0.179601	+	0.0980695i
$78$		0			0
$79$	0.310067	+	2.15657i	0.0348853	+	0.242633i	0.999801	−	0.0199256i	$-0.00634293\pi$
$79$	0.310067	+	2.15657i	0.0348853	+	0.242633i	−0.964916	+	0.262558i	$0.915434\pi$
$80$		0			0
$81$	−3.73057	−	8.16880i	−0.414507	−	0.907645i
$82$		0			0
$83$	2.23428	+	10.2708i	0.245244	+	1.12737i	0.920792	+	0.390053i	$0.127543\pi$
$83$	2.23428	+	10.2708i	0.245244	+	1.12737i	−0.675548	+	0.737316i	$0.736093\pi$
$84$		0			0
$85$	4.66696	+	0.271261i	0.506203	+	0.0294224i
$86$		0			0
$87$	0.112994	+	0.0245804i	0.0121143	+	0.00263530i
$88$		0			0
$89$	−9.66802	−	2.83879i	−1.02481	−	0.300911i	−0.274210	−	0.961670i	$-0.588416\pi$
$89$	−9.66802	−	2.83879i	−1.02481	−	0.300911i	−0.750598	+	0.660759i	$0.770235\pi$
$90$		0			0
$91$		−	3.21083i		−	0.336587i
$92$		0			0
$93$	0.279582	−	0.279582i	0.0289913	−	0.0289913i
$94$		0			0
$95$	−4.09970	+	2.71268i	−0.420621	+	0.278315i
$96$		0			0
$97$	2.33842	−	10.7495i	0.237430	−	1.09145i	−0.691841	−	0.722050i	$-0.743200\pi$
$97$	2.33842	−	10.7495i	0.237430	−	1.09145i	0.929271	−	0.369399i	$-0.120436\pi$
$98$		0			0
$99$	−0.265282	+	1.84507i	−0.0266618	+	0.185437i
$100$		0			0
$101$	3.59659	+	2.31139i	0.357874	+	0.229991i	0.707206	−	0.707007i	$-0.249955\pi$
$101$	3.59659	+	2.31139i	0.357874	+	0.229991i	−0.349332	+	0.936999i	$0.613592\pi$
$102$		0			0
$103$	1.31849	−	3.53500i	0.129915	−	0.348314i	−0.855664	−	0.517531i	$-0.826851\pi$
$103$	1.31849	−	3.53500i	0.129915	−	0.348314i	0.985579	+	0.169217i	$0.0541239\pi$
$104$		0			0
$105$	0.159799	−	0.256101i	0.0155948	−	0.0249929i
$106$		0			0
$107$	3.94846	−	7.23107i	0.381712	−	0.699054i	−0.614222	−	0.789133i	$-0.710530\pi$
$107$	3.94846	−	7.23107i	0.381712	−	0.699054i	0.995935	+	0.0900793i	$0.0287121\pi$
$108$		0			0
$109$	−9.46629	+	10.9247i	−0.906706	+	1.04639i	0.0920111	+	0.995758i	$0.470670\pi$
$109$	−9.46629	+	10.9247i	−0.906706	+	1.04639i	−0.998717	+	0.0506366i	$0.983875\pi$
$110$		0			0
$111$	0.0317038	−	0.0274715i	0.00300919	−	0.00260748i
$112$		0			0
$113$	12.4213	−	4.63290i	1.16850	−	0.435826i	0.311046	−	0.950395i	$-0.399321\pi$
$113$	12.4213	−	4.63290i	1.16850	−	0.435826i	0.857449	+	0.514569i	$0.172048\pi$
$114$		0			0
$115$	−3.77193	−	10.0386i	−0.351735	−	0.936100i
$116$		0			0
$117$	3.12301	−	1.16482i	0.288722	−	0.107688i
$118$		0			0
$119$	4.56273	−	3.95363i	0.418265	−	0.362429i
$120$		0			0
$121$	−6.95027	+	8.02104i	−0.631843	+	0.729186i
$122$		0			0
$123$	−0.164937	+	0.302059i	−0.0148719	+	0.0272358i
$124$		0			0
$125$	4.23382	−	10.3477i	0.378685	−	0.925526i
$126$		0			0
$127$	2.33011	−	6.24728i	0.206764	−	0.554356i	−0.791630	−	0.611000i	$-0.790767\pi$
$127$	2.33011	−	6.24728i	0.206764	−	0.554356i	0.998394	+	0.0566443i	$0.0180401\pi$
$128$		0			0
$129$	−0.224757	−	0.144442i	−0.0197887	−	0.0127174i
$130$		0			0
$131$	−1.65287	+	11.4959i	−0.144412	+	1.00440i	0.780753	+	0.624839i	$0.214836\pi$
$131$	−1.65287	+	11.4959i	−0.144412	+	1.00440i	−0.925165	+	0.379565i	$0.876074\pi$
$132$		0			0
$133$	−1.34951	+	6.20361i	−0.117018	+	0.537921i
$134$		0			0
$135$	0.614359	+	0.125086i	0.0528756	+	0.0107657i
$136$		0			0
$137$	13.8908	−	13.8908i	1.18677	−	1.18677i	0.208819	−	0.977954i	$-0.433038\pi$
$137$	13.8908	−	13.8908i	1.18677	−	1.18677i	0.977954	−	0.208819i	$-0.0669621\pi$
$138$		0			0
$139$		−	12.3148i		−	1.04453i	−0.852784	−	0.522264i	$-0.825088\pi$
$139$		−	12.3148i		−	1.04453i	0.852784	−	0.522264i	$-0.174912\pi$
$140$		0			0
$141$	−0.116295	−	0.0341473i	−0.00979380	−	0.00287572i
$142$		0			0
$143$	−0.675560	−	0.146959i	−0.0564932	−	0.0122893i
$144$		0			0
$145$	4.13149	−	3.67760i	0.343102	−	0.305408i
$146$		0			0
$147$	−0.0133091	−	0.0611807i	−0.00109771	−	0.00504610i
$148$		0			0
$149$	−3.32109	−	7.27217i	−0.272074	−	0.595759i	0.723439	−	0.690389i	$-0.242561\pi$
$149$	−3.32109	−	7.27217i	−0.272074	−	0.595759i	−0.995513	+	0.0946298i	$0.969833\pi$
$150$		0			0
$151$	3.34577	+	23.2704i	0.272275	+	1.89372i	0.424593	+	0.905384i	$0.360417\pi$
$151$	3.34577	+	23.2704i	0.272275	+	1.89372i	−0.152318	+	0.988332i	$0.548674\pi$
$152$		0			0
$153$	5.50075	+	3.00364i	0.444709	+	0.242830i
$154$		0			0
$155$	−2.94101	−	18.6823i	−0.236228	−	1.50060i
$156$		0			0
$157$	6.07076	+	0.434190i	0.484500	+	0.0346521i	0.311453	−	0.950262i	$-0.399184\pi$
$157$	6.07076	+	0.434190i	0.484500	+	0.0346521i	0.173047	+	0.984914i	$0.444639\pi$
$158$		0			0
$159$	−0.0621809	+	0.136157i	−0.00493127	+	0.0107980i
$160$		0			0
$161$	−12.5343	−	5.89042i	−0.987838	−	0.464230i
$162$		0			0
$163$	2.82382	+	7.57095i	0.221179	+	0.593003i	0.999387	−	0.0350031i	$-0.0111441\pi$
$163$	2.82382	+	7.57095i	0.221179	+	0.593003i	−0.778209	+	0.628006i	$0.783871\pi$
$164$		0			0
$165$	−0.0465697	−	0.0453434i	−0.00362545	−	0.00352998i
$166$		0			0
$167$	8.28055	−	0.592237i	0.640768	−	0.0458287i	0.252825	−	0.967512i	$-0.418640\pi$
$167$	8.28055	−	0.592237i	0.640768	−	0.0458287i	0.387943	+	0.921683i	$0.373186\pi$
$168$		0			0
$169$	−3.31423	−	11.2872i	−0.254941	−	0.868249i
$170$		0			0
$171$	−6.52350	+	0.937938i	−0.498864	+	0.0717259i
$172$		0			0
$173$	−2.43148	−	0.906895i	−0.184862	−	0.0689499i	0.255329	−	0.966854i	$-0.417816\pi$
$173$	−2.43148	−	0.906895i	−0.184862	−	0.0689499i	−0.440190	+	0.897904i	$0.645089\pi$
$174$		0			0
$175$	−5.40504	−	13.3891i	−0.408583	−	1.01212i
$176$		0			0
$177$	0.231860	−	0.173568i	0.0174277	−	0.0130462i
$178$		0			0
$179$	−0.0260598	−	0.0405498i	−0.00194780	−	0.00303084i	0.840278	−	0.542155i	$-0.182392\pi$
$179$	−0.0260598	−	0.0405498i	−0.00194780	−	0.00303084i	−0.842226	+	0.539125i	$0.818755\pi$
$180$		0			0
$181$	−1.62901	+	5.54788i	−0.121083	+	0.412371i	−0.997619	−	0.0689653i	$-0.978030\pi$
$181$	−1.62901	+	5.54788i	−0.121083	+	0.412371i	0.876536	+	0.481336i	$0.159848\pi$
$182$		0			0
$183$	−0.455681	−	0.455681i	−0.0336849	−	0.0336849i
$184$		0			0
$185$	−0.169836	−	1.99937i	−0.0124866	−	0.146997i
$186$		0			0
$187$	−0.623010	−	1.14096i	−0.0455590	−	0.0834350i
$188$		0			0
$189$	0.681161	−	0.437756i	0.0495472	−	0.0318420i
$190$		0			0
$191$	8.15000	+	1.17179i	0.589713	+	0.0847880i	0.430710	−	0.902490i	$-0.358263\pi$
$191$	8.15000	+	1.17179i	0.589713	+	0.0847880i	0.159003	+	0.987278i	$0.449172\pi$
$192$		0			0
$193$	15.1665	−	3.29926i	1.09171	−	0.237486i	0.369546	−	0.929212i	$-0.379513\pi$
$193$	15.1665	−	3.29926i	1.09171	−	0.237486i	0.722160	+	0.691726i	$0.243149\pi$
$194$		0			0
$195$	−0.0312538	+	0.111944i	−0.00223813	+	0.00801651i
$196$		0			0
$197$	1.65720	−	2.21376i	0.118070	−	0.157724i	−0.737612	−	0.675225i	$-0.764047\pi$
$197$	1.65720	−	2.21376i	0.118070	−	0.157724i	0.855683	+	0.517501i	$0.173138\pi$
$198$		0			0
$199$	18.4366	−	5.41346i	1.30693	−	0.383750i	0.447173	−	0.894448i	$-0.352431\pi$
$199$	18.4366	−	5.41346i	1.30693	−	0.383750i	0.859760	+	0.510698i	$0.170613\pi$
$200$		0			0
$201$	−0.482010	−	0.417664i	−0.0339983	−	0.0294597i
$202$		0			0
$203$	0.509597	−	7.12509i	0.0357667	−	0.500083i
$204$		0			0
$205$	7.03764	+	14.8816i	0.491530	+	1.03938i
$206$		0			0
$207$	1.18214	−	14.3283i	0.0821641	−	0.995888i
$208$		0			0
$209$	1.24347	+	0.567876i	0.0860129	+	0.0392808i
$210$		0			0
$211$	1.83738	+	2.12045i	0.126490	+	0.145978i	0.815462	−	0.578811i	$-0.196483\pi$
$211$	1.83738	+	2.12045i	0.126490	+	0.145978i	−0.688972	+	0.724788i	$0.741938\pi$
$212$		0			0
$213$	−0.00324377	−	0.0453538i	−0.000222259	−	0.00310759i
$214$		0			0
$215$	−11.9129	+	4.62525i	−0.812454	+	0.315439i
$216$		0			0
$217$	−19.5529	−	14.6371i	−1.32733	−	0.993630i
$218$		0			0
$219$	−0.162318	+	0.0741280i	−0.0109684	+	0.00500911i
$220$		0			0
$221$	−1.25673	+	1.95551i	−0.0845369	+	0.131542i
$222$		0			0
$223$	9.49522	+	12.6841i	0.635847	+	0.849392i	0.996525	−	0.0832984i	$-0.0265455\pi$
$223$	9.49522	+	12.6841i	0.635847	+	0.849392i	−0.360678	+	0.932691i	$0.617455\pi$
$224$		0			0
$225$	11.0621	−	10.1145i	0.737471	−	0.674299i
$226$		0			0
$227$	11.4244	−	6.23822i	0.758267	−	0.414045i	−0.0530949	−	0.998589i	$-0.516909\pi$
$227$	11.4244	−	6.23822i	0.758267	−	0.414045i	0.811362	+	0.584544i	$0.198727\pi$
$228$		0			0
$229$	1.27982			0.0845730			0.0422865	−	0.999106i	$-0.486536\pi$
$229$	1.27982			0.0845730			0.0422865	+	0.999106i	$0.486536\pi$
$230$		0			0
$231$	−0.0839425			−0.00552301
$232$		0			0
$233$	−13.8859	+	7.58228i	−0.909696	+	0.496731i	−0.864719	−	0.502257i	$-0.832503\pi$
$233$	−13.8859	+	7.58228i	−0.909696	+	0.496731i	−0.0449770	+	0.998988i	$0.514321\pi$
$234$		0			0
$235$	−4.59436	+	3.53591i	−0.299703	+	0.230658i
$236$		0			0
$237$	−0.0610377	−	0.0815368i	−0.00396482	−	0.00529638i
$238$		0			0
$239$	−4.50993	+	7.01758i	−0.291723	+	0.453930i	−0.955920	−	0.293628i	$-0.905137\pi$
$239$	−4.50993	+	7.01758i	−0.291723	+	0.453930i	0.664197	+	0.747558i	$0.268774\pi$
$240$		0			0
$241$	−13.2858	+	6.06744i	−0.855816	+	0.390838i	−0.794488	−	0.607280i	$-0.792261\pi$
$241$	−13.2858	+	6.06744i	−0.855816	+	0.390838i	−0.0613278	+	0.998118i	$0.519534\pi$
$242$		0			0
$243$	1.00946	+	0.755673i	0.0647570	+	0.0484765i
$244$		0			0
$245$	−2.74057	−	1.20765i	−0.175089	−	0.0771541i
$246$		0			0
$247$	−0.174381	−	2.43817i	−0.0110956	−	0.155137i
$248$		0			0
$249$	−0.321779	−	0.371353i	−0.0203919	−	0.0235335i
$250$		0			0
$251$	7.92879	+	3.62096i	0.500461	+	0.228553i	0.649618	−	0.760261i	$-0.274929\pi$
$251$	7.92879	+	3.62096i	0.500461	+	0.228553i	−0.149157	+	0.988813i	$0.547656\pi$
$252$		0			0
$253$	−1.81304	+	2.36761i	−0.113985	+	0.148850i
$254$		0			0
$255$	−0.197562	+	0.0934287i	−0.0123718	+	0.00585073i
$256$		0			0
$257$	1.47010	−	20.5547i	0.0917025	−	1.28217i	−0.718297	−	0.695737i	$-0.755078\pi$
$257$	1.47010	−	20.5547i	0.0917025	−	1.28217i	0.809999	−	0.586431i	$-0.199467\pi$
$258$		0			0
$259$	−1.95845	−	1.69701i	−0.121692	−	0.105447i
$260$		0			0
$261$	7.11507	−	2.08917i	0.440412	−	0.129317i
$262$		0			0
$263$	3.43557	−	4.58938i	0.211846	−	0.282993i	−0.682014	−	0.731339i	$-0.738896\pi$
$263$	3.43557	−	4.58938i	0.211846	−	0.282993i	0.893860	+	0.448346i	$0.147987\pi$
$264$		0			0
$265$	3.51482	+	6.23760i	0.215913	+	0.383172i
$266$		0			0
$267$	0.460277	−	0.100127i	0.0281685	−	0.00612769i
$268$		0			0
$269$	5.04128	+	0.724827i	0.307373	+	0.0441935i	0.294275	−	0.955721i	$-0.404922\pi$
$269$	5.04128	+	0.724827i	0.307373	+	0.0441935i	0.0130973	+	0.999914i	$0.495831\pi$
$270$		0			0
$271$	17.3028	−	11.1198i	1.05107	−	0.675481i	0.103369	−	0.994643i	$-0.467038\pi$
$271$	17.3028	−	11.1198i	1.05107	−	0.675481i	0.947700	+	0.319162i	$0.103401\pi$
$272$		0			0
$273$	0.0719355	+	0.131740i	0.00435373	+	0.00797327i
$274$		0			0
$275$	−3.06447	+	0.524404i	−0.184794	+	0.0316228i
$276$		0			0
$277$	19.5001	+	19.5001i	1.17165	+	1.17165i	0.981817	+	0.189831i	$0.0607940\pi$
$277$	19.5001	+	19.5001i	1.17165	+	1.17165i	0.189831	+	0.981817i	$0.439206\pi$
$278$		0			0
$279$	7.14336	−	24.3280i	0.427662	−	1.45648i
$280$		0			0
$281$	−15.2584	−	23.7425i	−0.910239	−	1.41636i	−0.909200	−	0.416360i	$-0.863306\pi$
$281$	−15.2584	−	23.7425i	−0.910239	−	1.41636i	−0.00103862	−	0.999999i	$-0.500331\pi$
$282$		0			0
$283$	−10.5953	+	7.93155i	−0.629826	+	0.471482i	−0.865876	−	0.500259i	$-0.833238\pi$
$283$	−10.5953	+	7.93155i	−0.629826	+	0.471482i	0.236050	+	0.971741i	$0.424147\pi$
$284$		0			0
$285$	0.107435	−	0.203150i	0.00636392	−	0.0120336i
$286$		0			0
$287$	19.9193	+	7.42952i	1.17580	+	0.438551i
$288$		0			0
$289$	12.5006	−	1.79732i	0.735331	−	0.105725i
$290$		0			0
$291$	0.144887	+	0.493441i	0.00849345	+	0.0289260i
$292$		0			0
$293$	15.8495	−	1.13358i	0.925940	−	0.0662245i	0.399781	−	0.916611i	$-0.369086\pi$
$293$	15.8495	−	1.13358i	0.925940	−	0.0662245i	0.526159	+	0.850386i	$0.323632\pi$
$294$		0			0
$295$	−0.184822	−	13.8524i	−0.0107608	−	0.806517i
$296$		0			0
$297$	−0.0609273	−	0.163352i	−0.00353536	−	0.00947867i
$298$		0			0
$299$	5.26944	+	0.816442i	0.304740	+	0.0472161i
$300$		0			0
$301$	−6.85599	+	15.0125i	−0.395172	+	0.865307i
$302$		0			0
$303$	−0.199352	−	0.0142579i	−0.0114524	−	0.000819095i
$304$		0			0
$305$	−30.4496	+	4.79345i	−1.74354	+	0.274472i
$306$		0			0
$307$	−10.0122	−	5.46708i	−0.571427	−	0.312023i	0.167431	−	0.985884i	$-0.446453\pi$
$307$	−10.0122	−	5.46708i	−0.571427	−	0.312023i	−0.738858	+	0.673861i	$0.764635\pi$
$308$		0			0
$309$	0.0251008	+	0.174580i	0.00142794	+	0.00993151i
$310$		0			0
$311$	4.59387	+	10.0592i	0.260494	+	0.570403i	0.994012	−	0.109267i	$-0.0348503\pi$
$311$	4.59387	+	10.0592i	0.260494	+	0.570403i	−0.733518	+	0.679670i	$0.762123\pi$
$312$		0			0
$313$	3.26733	+	15.0197i	0.184681	+	0.848963i	0.972472	+	0.233021i	$0.0748610\pi$
$313$	3.26733	+	15.0197i	0.184681	+	0.848963i	−0.787791	+	0.615942i	$0.788775\pi$
$314$		0			0
$315$	1.12325	−	19.3252i	0.0632880	−	1.08885i
$316$		0			0
$317$	23.1232	+	5.03014i	1.29873	+	0.282521i	0.808202	−	0.588905i	$-0.200441\pi$
$317$	23.1232	+	5.03014i	1.29873	+	0.282521i	0.490526	+	0.871426i	$0.336805\pi$
$318$		0			0
$319$	−1.47580	−	0.433333i	−0.0826288	−	0.0242620i
$320$		0			0
$321$			0.385151i			0.0214970i
$322$		0			0
$323$	3.25002	−	3.25002i	0.180836	−	0.180836i
$324$		0			0
$325$	3.44913	+	4.36000i	0.191323	+	0.241849i
$326$		0			0
$327$	0.143644	−	0.660320i	0.00794353	−	0.0365158i
$328$		0			0
$329$	−1.06554	+	7.41101i	−0.0587453	+	0.408582i
$330$		0			0
$331$	0.748852	+	0.481258i	0.0411606	+	0.0264523i	0.561059	−	0.827776i	$-0.310394\pi$
$331$	0.748852	+	0.481258i	0.0411606	+	0.0264523i	−0.519899	+	0.854228i	$0.674030\pi$
$332$		0			0
$333$	0.940106	−	2.52052i	0.0515175	−	0.138124i
$334$		0			0
$335$	−29.7206	+	6.88183i	−1.62381	+	0.375995i
$336$		0			0
$337$	5.29012	−	9.68813i	0.288171	−	0.527746i	−0.692987	−	0.720950i	$-0.743706\pi$
$337$	5.29012	−	9.68813i	0.288171	−	0.527746i	0.981159	+	0.193203i	$0.0618877\pi$
$338$		0			0
$339$	−0.405847	+	0.468373i	−0.0220426	+	0.0254385i
$340$		0			0
$341$	−3.97458	+	3.44399i	−0.215235	+	0.186503i
$342$		0			0
$343$	15.3161	−	5.71262i	0.826994	−	0.308453i
$344$		0			0
$345$	0.379665	+	0.327374i	0.0204405	+	0.0176252i
$346$		0			0
$347$	7.53487	−	2.81036i	0.404493	−	0.150868i	−0.138979	−	0.990295i	$-0.544382\pi$
$347$	7.53487	−	2.81036i	0.404493	−	0.150868i	0.543472	+	0.839427i	$0.317109\pi$
$348$		0			0
$349$	−19.0865	+	16.5386i	−1.02168	+	0.885289i	−0.993445	−	0.114313i	$-0.963533\pi$
$349$	−19.0865	+	16.5386i	−1.02168	+	0.885289i	−0.0282326	+	0.999601i	$0.508988\pi$
$350$		0			0
$351$	−0.204154	+	0.235606i	−0.0108969	+	0.0125757i
$352$		0			0
$353$	−13.3304	+	24.4128i	−0.709507	+	1.29936i	0.235360	+	0.971908i	$0.424373\pi$
$353$	−13.3304	+	24.4128i	−0.709507	+	1.29936i	−0.944866	+	0.327456i	$0.893809\pi$
$354$		0			0
$355$	−1.84518	−	1.15133i	−0.0979320	−	0.0611065i
$356$		0			0
$357$	−0.0986311	+	0.264440i	−0.00522011	+	0.0139957i
$358$		0			0
$359$	−15.5908	−	10.0196i	−0.822853	−	0.528816i	0.0601462	−	0.998190i	$-0.480843\pi$
$359$	−15.5908	−	10.0196i	−0.822853	−	0.528816i	−0.883000	+	0.469374i	$0.844480\pi$
$360$		0			0
$361$	2.01614	−	14.0226i	0.106113	−	0.738030i
$362$		0			0
$363$	0.105465	−	0.484816i	0.00553549	−	0.0254462i
$364$		0			0
$365$	−1.70289	+	8.36375i	−0.0891333	+	0.437779i
$366$		0			0
$367$	−14.6761	+	14.6761i	−0.766085	+	0.766085i	−0.977415	−	0.211330i	$-0.932221\pi$
$367$	−14.6761	+	14.6761i	−0.766085	+	0.766085i	0.211330	+	0.977415i	$0.432221\pi$
$368$		0			0
$369$			22.0697i			1.14890i
$370$		0			0
$371$	8.87194	+	2.60504i	0.460608	+	0.135247i
$372$		0			0
$373$	9.80702	+	2.13339i	0.507788	+	0.110463i	0.459159	−	0.888354i	$-0.348151\pi$
$373$	9.80702	+	2.13339i	0.507788	+	0.110463i	0.0486298	+	0.998817i	$0.484515\pi$
$374$		0			0
$375$	0.0581165	+	0.519419i	0.00300112	+	0.0268227i
$376$		0			0
$377$	0.584625	+	2.68748i	0.0301097	+	0.138412i
$378$		0			0
$379$	−9.57218	−	20.9601i	−0.491690	−	1.07665i	−0.979082	−	0.203467i	$-0.934779\pi$
$379$	−9.57218	−	20.9601i	−0.491690	−	1.07665i	0.487392	−	0.873183i	$-0.337948\pi$
$380$		0			0
$381$	0.0443597	+	0.308529i	0.00227262	+	0.0158064i
$382$		0			0
$383$	−21.5957	−	11.7921i	−1.10349	−	0.602549i	−0.179032	−	0.983843i	$-0.557297\pi$
$383$	−21.5957	−	11.7921i	−1.10349	−	0.602549i	−0.924454	+	0.381294i	$0.875479\pi$
$384$		0			0
$385$	−2.36310	+	3.24612i	−0.120435	+	0.165437i
$386$		0			0
$387$	−17.0891	−	1.22224i	−0.868687	−	0.0621297i
$388$		0			0
$389$	−5.42505	+	11.8792i	−0.275061	+	0.602300i	−0.995866	−	0.0908387i	$-0.971045\pi$
$389$	−5.42505	+	11.8792i	−0.275061	+	0.602300i	0.720805	+	0.693138i	$0.243773\pi$
$390$		0			0
$391$	5.32828	+	8.49342i	0.269463	+	0.429531i
$392$		0			0
$393$	−0.189738	−	0.508707i	−0.00957101	−	0.0256609i
$394$		0			0
$395$	−4.87138	+	0.0649952i	−0.245106	+	0.00327026i
$396$		0			0
$397$	−7.22169	+	0.516506i	−0.362446	+	0.0259227i	−0.251375	−	0.967890i	$-0.580883\pi$
$397$	−7.22169	+	0.516506i	−0.362446	+	0.0259227i	−0.111071	+	0.993812i	$0.535428\pi$
$398$		0			0
$399$	−0.0836153	−	0.284768i	−0.00418600	−	0.0142562i
$400$		0			0
$401$	−37.5899	+	5.40462i	−1.87715	+	0.269894i	−0.983774	−	0.179413i	$-0.942580\pi$
$401$	−37.5899	+	5.40462i	−1.87715	+	0.269894i	−0.893377	+	0.449307i	$0.851671\pi$
$402$		0			0
$403$	8.81108	+	3.28636i	0.438911	+	0.163705i
$404$		0			0
$405$	19.1900	−	5.91391i	0.953561	−	0.293865i
$406$		0			0
$407$	−0.446689	+	0.334387i	−0.0221416	+	0.0165750i
$408$		0			0
$409$	8.61194	+	13.4004i	0.425833	+	0.662609i	0.986185	−	0.165645i	$-0.0529707\pi$
$409$	8.61194	+	13.4004i	0.425833	+	0.662609i	−0.560352	+	0.828254i	$0.689334\pi$
$410$		0			0
$411$	−0.258728	+	0.881148i	−0.0127621	+	0.0434638i
$412$		0			0
$413$	−12.6511	−	12.6511i	−0.622521	−	0.622521i
$414$		0			0
$415$	−23.4190	+	1.98932i	−1.14959	+	0.0976520i
$416$		0			0
$417$	0.275901	+	0.505274i	0.0135109	+	0.0247434i
$418$		0			0
$419$	10.2159	−	6.56534i	0.499078	−	0.320738i	−0.266770	−	0.963760i	$-0.585956\pi$
$419$	10.2159	−	6.56534i	0.499078	−	0.320738i	0.765847	+	0.643023i	$0.222320\pi$
$420$		0			0
$421$	24.3000	+	3.49382i	1.18431	+	0.170278i	0.706194	−	0.708018i	$-0.250410\pi$
$421$	24.3000	+	3.49382i	1.18431	+	0.170278i	0.478117	+	0.878296i	$0.341320\pi$
$422$		0			0
$423$	−7.59485	+	1.65216i	−0.369274	+	0.0803307i
$424$		0			0
$425$	−1.94869	+	10.2700i	−0.0945254	+	0.498169i
$426$		0			0
$427$	−23.8564	+	31.8685i	−1.15449	+	1.54222i
$428$		0			0
$429$	0.0310106	−	0.00910553i	0.00149721	−	0.000439619i
$430$		0			0
$431$	−4.43914	−	3.84653i	−0.213826	−	0.185281i	0.541362	−	0.840790i	$-0.317909\pi$
$431$	−4.43914	−	3.84653i	−0.213826	−	0.185281i	−0.755188	+	0.655509i	$0.772454\pi$
$432$		0			0
$433$	−1.16911	+	16.3463i	−0.0561840	+	0.785555i	0.888770	+	0.458353i	$0.151560\pi$
$433$	−1.16911	+	16.3463i	−0.0561840	+	0.785555i	−0.944954	+	0.327202i	$0.893894\pi$
$434$		0			0
$435$	−0.0871215	+	0.243453i	−0.00417716	+	0.0116727i
$436$		0			0
$437$	−9.83787	−	3.79218i	−0.470609	−	0.181405i
$438$		0			0
$439$	8.36448	+	3.81993i	0.399215	+	0.182315i	0.604897	−	0.796303i	$-0.293214\pi$
$439$	8.36448	+	3.81993i	0.399215	+	0.182315i	−0.205682	+	0.978619i	$0.565941\pi$
$440$		0			0
$441$	−2.62933	−	3.03440i	−0.125206	−	0.144495i
$442$		0			0
$443$	−1.94384	−	27.1784i	−0.0923546	−	1.29129i	−0.806477	−	0.591265i	$-0.798629\pi$
$443$	−1.94384	−	27.1784i	−0.0923546	−	1.29129i	0.714122	−	0.700021i	$-0.246826\pi$
$444$		0			0
$445$	9.08547	−	20.6180i	0.430692	−	0.977386i
$446$		0			0
$447$	0.299189	+	0.223970i	0.0141512	+	0.0105934i
$448$		0			0
$449$	−9.78375	+	4.46809i	−0.461724	+	0.210862i	−0.632675	−	0.774417i	$-0.718043\pi$
$449$	−9.78375	+	4.46809i	−0.461724	+	0.210862i	0.170951	+	0.985279i	$0.445316\pi$
$450$		0			0
$451$	2.47488	−	3.85098i	0.116537	−	0.181336i
$452$		0			0
$453$	−0.658626	−	0.879821i	−0.0309449	−	0.0413376i
$454$		0			0
$455$	7.11957	+	0.926870i	0.333770	+	0.0434523i
$456$		0			0
$457$	−19.2356	+	10.5034i	−0.899804	+	0.491330i	−0.861397	−	0.507932i	$-0.830410\pi$
$457$	−19.2356	+	10.5034i	−0.899804	+	0.491330i	−0.0384067	+	0.999262i	$0.512228\pi$
$458$		0			0
$459$	−0.586190			−0.0273610
$460$		0			0
$461$	5.44735			0.253709			0.126854	−	0.991921i	$-0.459512\pi$
$461$	5.44735			0.253709			0.126854	+	0.991921i	$0.459512\pi$
$462$		0			0
$463$	−14.0218	+	7.65647i	−0.651647	+	0.355826i	−0.770825	−	0.637046i	$-0.780156\pi$
$463$	−14.0218	+	7.65647i	−0.651647	+	0.355826i	0.119178	+	0.992873i	$0.461974\pi$
$464$		0			0
$465$	0.539227	+	0.700641i	0.0250060	+	0.0324914i
$466$		0			0
$467$	20.4468	+	27.3138i	0.946166	+	1.26393i	0.964496	+	0.264098i	$0.0850741\pi$
$467$	20.4468	+	27.3138i	0.946166	+	1.26393i	−0.0183300	+	0.999832i	$0.505835\pi$
$468$		0			0
$469$	−21.3004	+	33.1441i	−0.983562	+	1.53045i
$470$		0			0
$471$	−0.258810	+	0.118195i	−0.0119253	+	0.00544612i
$472$		0			0
$473$	2.84484	+	2.12962i	0.130806	+	0.0979200i
$474$		0			0
$475$	−4.83152	−	9.87357i	−0.221685	−	0.453030i
$476$		0			0
$477$	0.684768	+	9.57431i	0.0313534	+	0.438378i
$478$		0			0
$479$	−7.08995	−	8.18224i	−0.323948	−	0.373856i	0.570293	−	0.821441i	$-0.306830\pi$
$479$	−7.08995	−	8.18224i	−0.323948	−	0.373856i	−0.894241	+	0.447585i	$0.852284\pi$
$480$		0			0
$481$	0.907585	+	0.414480i	0.0413823	+	0.0188987i
$482$		0			0
$483$	0.646248	−	0.0391346i	0.0294053	−	0.00178068i
$484$		0			0
$485$	23.1605	+	8.28816i	1.05166	+	0.376346i
$486$		0			0
$487$	1.24307	−	17.3804i	0.0563289	−	0.787581i	−0.888263	−	0.459335i	$-0.848088\pi$
$487$	1.24307	−	17.3804i	0.0563289	−	0.787581i	0.944592	−	0.328246i	$-0.106458\pi$
$488$		0			0
$489$	−0.285480	−	0.247370i	−0.0129099	−	0.0111865i
$490$		0			0
$491$	8.92733	−	2.62130i	0.402885	−	0.118298i	−0.0740112	−	0.997257i	$-0.523580\pi$
$491$	8.92733	−	2.62130i	0.402885	−	0.118298i	0.476896	+	0.878960i	$0.341762\pi$
$492$		0			0
$493$	−3.09915	+	4.13997i	−0.139579	+	0.186455i
$494$		0			0
$495$	−4.01461	−	1.12084i	−0.180443	−	0.0503780i
$496$		0			0
$497$	−2.74463	+	0.597057i	−0.123113	+	0.0267817i
$498$		0			0
$499$	−8.96005	−	1.28826i	−0.401107	−	0.0576705i	−0.0611905	−	0.998126i	$-0.519490\pi$
$499$	−8.96005	−	1.28826i	−0.401107	−	0.0576705i	−0.339916	+	0.940456i	$0.610399\pi$
$500$		0			0
$501$	−0.326481	+	0.209817i	−0.0145861	+	0.00937392i
$502$		0			0
$503$	2.60394	+	4.76877i	0.116104	+	0.212629i	0.929268	−	0.369406i	$-0.120439\pi$
$503$	2.60394	+	4.76877i	0.116104	+	0.212629i	−0.813164	+	0.582034i	$0.802257\pi$
$504$		0			0
$505$	−6.16339	+	7.30769i	−0.274267	+	0.325188i
$506$		0			0
$507$	0.388862	+	0.388862i	0.0172699	+	0.0172699i
$508$		0			0
$509$	−7.09233	+	24.1543i	−0.314362	+	1.07062i	0.639104	+	0.769120i	$0.279305\pi$
$509$	−7.09233	+	24.1543i	−0.314362	+	1.07062i	−0.953466	+	0.301499i	$0.902513\pi$
$510$		0			0
$511$	5.95951	+	9.27318i	0.263633	+	0.410222i
$512$		0			0
$513$	0.493469	−	0.369406i	0.0217872	−	0.0163097i
$514$		0			0
$515$	7.45776	+	3.94401i	0.328628	+	0.173794i
$516$		0			0
$517$	1.51051	+	0.563391i	0.0664321	+	0.0247779i
$518$		0			0
$519$	0.120081	−	0.0172651i	0.00527098	−	0.000757853i
$520$		0			0
$521$	−10.1091	−	34.4283i	−0.442886	−	1.50833i	−0.814621	−	0.579994i	$-0.803055\pi$
$521$	−10.1091	−	34.4283i	−0.442886	−	1.50833i	0.371735	−	0.928339i	$-0.378763\pi$
$522$		0			0
$523$	40.2388	−	2.87793i	1.75952	−	0.125843i	0.846142	−	0.532958i	$-0.178920\pi$
$523$	40.2388	−	2.87793i	1.75952	−	0.125843i	0.913377	+	0.407115i	$0.133465\pi$
$524$		0			0
$525$	0.521738	+	0.428260i	0.0227705	+	0.0186908i
$526$		0			0
$527$	6.17938	+	16.5676i	0.269178	+	0.721694i
$528$		0			0
$529$	12.8542	−	19.0727i	0.558879	−	0.829250i
$530$		0			0
$531$	7.71552	−	16.8946i	0.334825	−	0.733165i
$532$		0			0
$533$	−8.16463	−	0.583946i	−0.353649	−	0.0252935i
$534$		0			0
$535$	14.8941	+	10.8425i	0.643926	+	0.468764i
$536$		0			0
$537$	0.00197771	+	0.00107991i	8.53444e−5	+	4.66015e-5i
$538$		0			0
$539$	0.118520	+	0.824327i	0.00510503	+	0.0355063i
$540$		0			0
$541$	9.00737	+	19.7234i	0.387257	+	0.847975i	0.998405	+	0.0564583i	$0.0179808\pi$
$541$	9.00737	+	19.7234i	0.387257	+	0.847975i	−0.611148	+	0.791516i	$0.709292\pi$
$542$		0			0
$543$	−0.0574569	−	0.264125i	−0.00246571	−	0.0113347i
$544$		0			0
$545$	−21.4913	−	24.1438i	−0.920585	−	1.03420i
$546$		0			0
$547$	10.6625	+	2.31948i	0.455895	+	0.0991738i	0.434648	−	0.900600i	$-0.356873\pi$
$547$	10.6625	+	2.31948i	0.455895	+	0.0991738i	0.0212467	+	0.999774i	$0.493236\pi$
$548$		0			0
$549$	−39.6514	−	11.6427i	−1.69228	−	0.496898i
$550$		0			0
$551$		−	5.43816i		−	0.231673i
$552$		0			0
$553$	−4.44894	+	4.44894i	−0.189188	+	0.189188i
$554$		0			0
$555$	0.0517622	+	0.0782288i	0.00219718	+	0.00332063i
$556$		0			0
$557$	2.20022	−	10.1142i	0.0932263	−	0.428554i	−0.906750	−	0.421669i	$-0.861445\pi$
$557$	2.20022	−	10.1142i	0.0932263	−	0.428554i	0.999976	−	0.00688568i	$-0.00219180\pi$
$558$		0			0
$559$	0.904324	−	6.28971i	0.0382488	−	0.266027i
$560$		0			0
$561$	0.0511240	+	0.0328554i	0.00215846	+	0.00138716i
$562$		0			0
$563$	−5.77770	+	15.4906i	−0.243501	+	0.652851i	−0.999999	−	0.00114429i	$-0.999636\pi$
$563$	−5.77770	+	15.4906i	−0.243501	+	0.652851i	0.756498	+	0.653996i	$0.226908\pi$
$564$		0			0
$565$	6.68714	+	28.8798i	0.281330	+	1.21498i
$566$		0			0
$567$	12.4285	−	22.7611i	0.521949	−	0.955878i
$568$		0			0
$569$	−3.37859	+	3.89910i	−0.141638	+	0.163459i	−0.822136	−	0.569291i	$-0.807218\pi$
$569$	−3.37859	+	3.89910i	−0.141638	+	0.163459i	0.680498	+	0.732750i	$0.261763\pi$
$570$		0			0
$571$	−13.9138	+	12.0564i	−0.582275	+	0.504544i	−0.895456	−	0.445149i	$-0.853151\pi$
$571$	−13.9138	+	12.0564i	−0.582275	+	0.504544i	0.313182	+	0.949693i	$0.398605\pi$
$572$		0			0
$573$	−0.360646	+	0.134514i	−0.0150662	+	0.00561940i
$574$		0			0
$575$	23.3479	−	5.46590i	0.973674	−	0.227944i
$576$		0			0
$577$	29.6682	−	11.0657i	1.23510	−	0.460670i	0.354738	−	0.934966i	$-0.384570\pi$
$577$	29.6682	−	11.0657i	1.23510	−	0.460670i	0.880365	+	0.474296i	$0.157297\pi$
$578$		0			0
$579$	−0.548361	+	0.475158i	−0.0227891	+	0.0197469i
$580$		0			0
$581$	−19.8774	+	22.9398i	−0.824654	+	0.951702i
$582$		0			0
$583$	0.954166	−	1.74743i	0.0395175	−	0.0723710i
$584$		0			0
$585$	1.68131	+	7.26107i	0.0695135	+	0.300208i
$586$		0			0
$587$	−6.12545	+	16.4230i	−0.252824	+	0.677848i	0.747089	+	0.664723i	$0.231451\pi$
$587$	−6.12545	+	16.4230i	−0.252824	+	0.677848i	−0.999914	+	0.0131249i	$0.995822\pi$
$588$		0			0
$589$	−15.6425	−	10.0528i	−0.644539	−	0.414220i
$590$		0			0
$591$	−0.0183976	+	0.127958i	−0.000756775	+	0.00526349i
$592$		0			0
$593$	−0.0135628	+	0.0623474i	−0.000556959	+	0.00256030i	−0.977425	−	0.211285i	$-0.932235\pi$
$593$	−0.0135628	+	0.0623474i	−0.000556959	+	0.00256030i	0.976868	+	0.213845i	$0.0685988\pi$
$594$		0			0
$595$	7.44949	+	11.2585i	0.305399	+	0.461553i
$596$		0			0
$597$	−0.635166	+	0.635166i	−0.0259956	+	0.0259956i
$598$		0			0
$599$			22.7964i			0.931437i	0.884933	+	0.465719i	$0.154204\pi$
$599$			22.7964i			0.931437i	−0.884933	+	0.465719i	$0.845796\pi$
$600$		0			0
$601$	35.2693	+	10.3560i	1.43867	+	0.422430i	0.905777	−	0.423755i	$-0.139288\pi$
$601$	35.2693	+	10.3560i	1.43867	+	0.422430i	0.532888	+	0.846186i	$0.321107\pi$
$602$		0			0
$603$	−39.9649	−	8.69382i	−1.62749	−	0.354040i
$604$		0			0
$605$	−15.7792	−	17.7267i	−0.641515	−	0.720691i
$606$		0			0
$607$	6.27596	+	28.8501i	0.254733	+	1.17099i	0.909678	+	0.415313i	$0.136328\pi$
$607$	6.27596	+	28.8501i	0.254733	+	1.17099i	−0.654945	+	0.755676i	$0.727308\pi$
$608$		0			0
$609$	0.138722	+	0.303758i	0.00562129	+	0.0123089i
$610$		0			0
$611$	−0.410258	−	2.85341i	−0.0165973	−	0.115437i
$612$		0			0
$613$	−22.4381	−	12.2521i	−0.906267	−	0.494859i	−0.0426970	−	0.999088i	$-0.513595\pi$
$613$	−22.4381	−	12.2521i	−0.906267	−	0.494859i	−0.863570	+	0.504229i	$0.831777\pi$
$614$		0			0
$615$	−0.622161	−	0.452919i	−0.0250879	−	0.0182635i
$616$		0			0
$617$	−30.0344	−	2.14810i	−1.20914	−	0.0864793i	−0.547828	−	0.836591i	$-0.684545\pi$
$617$	−30.0344	−	2.14810i	−1.20914	−	0.0864793i	−0.661311	+	0.750112i	$0.730000\pi$
$618$		0			0
$619$	−14.7832	+	32.3707i	−0.594188	+	1.30109i	0.338691	+	0.940898i	$0.390016\pi$
$619$	−14.7832	+	32.3707i	−0.594188	+	1.30109i	−0.932878	+	0.360192i	$0.882711\pi$
$620$		0			0
$621$	0.545216	+	1.22920i	0.0218788	+	0.0493259i
$622$		0			0
$623$	−10.1687	−	27.2633i	−0.407399	−	1.09228i
$624$		0			0
$625$	21.7223	+	12.3750i	0.868894	+	0.494998i
$626$		0			0
$627$	−0.0637422	+	0.00455893i	−0.00254562	+	0.000182066i
$628$		0			0
$629$	0.528552	+	1.80008i	0.0210748	+	0.0717740i
$630$		0			0
$631$	−44.0286	+	6.33036i	−1.75275	+	0.252008i	−0.942531	−	0.334118i	$-0.891562\pi$
$631$	−44.0286	+	6.33036i	−1.75275	+	0.252008i	−0.810220	+	0.586125i	$0.800653\pi$
$632$		0			0
$633$	−0.122894	−	0.0458371i	−0.00488459	−	0.00182186i
$634$		0			0
$635$	13.1798	+	6.97009i	0.523025	+	0.276600i
$636$		0			0
$637$	1.19214	−	0.892423i	0.0472342	−	0.0353591i
$638$		0			0
$639$	−1.57642	−	2.45295i	−0.0623621	−	0.0970373i
$640$		0			0
$641$	3.57248	−	12.1667i	0.141104	−	0.480557i	−0.858368	−	0.513034i	$-0.828521\pi$
$641$	3.57248	−	12.1667i	0.141104	−	0.480557i	0.999472	+	0.0324770i	$0.0103396\pi$
$642$		0			0
$643$	25.5764	+	25.5764i	1.00863	+	1.00863i	0.999962	+	0.00867061i	$0.00275998\pi$
$643$	25.5764	+	25.5764i	1.00863	+	1.00863i	0.00867061	+	0.999962i	$0.497240\pi$
$644$		0			0
$645$	0.385161	−	0.456670i	0.0151657	−	0.0179814i
$646$		0			0
$647$	4.19382	+	7.68042i	0.164876	+	0.301948i	0.947035	−	0.321131i	$-0.104063\pi$
$647$	4.19382	+	7.68042i	0.164876	+	0.301948i	−0.782158	+	0.623080i	$0.785881\pi$
$648$		0			0
$649$	−3.24084	+	2.08276i	−0.127214	+	0.0817555i
$650$		0			0
$651$	1.13018	+	0.162495i	0.0442952	+	0.00636869i
$652$		0			0
$653$	17.1798	−	3.73723i	0.672296	−	0.146249i	0.136556	−	0.990632i	$-0.456397\pi$
$653$	17.1798	−	3.73723i	0.672296	−	0.146249i	0.535740	+	0.844383i	$0.320033\pi$
$654$		0			0
$655$	−25.0135	−	6.98352i	−0.977357	−	0.272869i
$656$		0			0
$657$	−6.85755	+	9.16062i	−0.267539	+	0.357390i
$658$		0			0
$659$	45.1308	−	13.2516i	1.75805	−	0.516210i	0.766085	−	0.642739i	$-0.222202\pi$
$659$	45.1308	−	13.2516i	1.75805	−	0.516210i	0.991963	+	0.126529i	$0.0403838\pi$
$660$		0			0
$661$	−5.93565	−	5.14327i	−0.230870	−	0.200050i	0.531742	−	0.846907i	$-0.321538\pi$
$661$	−5.93565	−	5.14327i	−0.230870	−	0.200050i	−0.762612	+	0.646857i	$0.776083\pi$
$662$		0			0
$663$	0.00775221	−	0.108390i	0.000301071	−	0.00420952i
$664$		0			0
$665$	−13.3661	−	4.78315i	−0.518314	−	0.185482i
$666$		0			0
$667$	11.5637	+	2.64807i	0.447749	+	0.102534i
$668$		0			0
$669$	−0.673762	−	0.307697i	−0.0260492	−	0.0118963i
$670$		0			0
$671$	5.61323	+	6.47801i	0.216696	+	0.250081i
$672$		0			0
$673$	−1.86113	−	26.0220i	−0.0717412	−	1.00307i	−0.898061	−	0.439872i	$-0.855024\pi$
$673$	−1.86113	−	26.0220i	−0.0717412	−	1.00307i	0.826319	−	0.563202i	$-0.190431\pi$
$674$		0			0
$675$	−0.454706	+	1.32614i	−0.0175016	+	0.0510433i
$676$		0			0
$677$	−38.9391	−	29.1494i	−1.49655	−	1.12030i	−0.961262	−	0.275635i	$-0.911112\pi$
$677$	−38.9391	−	29.1494i	−1.49655	−	1.12030i	−0.535289	−	0.844669i	$-0.679797\pi$
$678$		0			0
$679$	28.8976	−	13.1971i	1.10899	−	0.506457i
$680$		0			0
$681$	−0.328982	+	0.511906i	−0.0126066	+	0.0196163i
$682$		0			0
$683$	−25.4505	−	33.9979i	−0.973837	−	1.30089i	−0.953593	−	0.301098i	$-0.902647\pi$
$683$	−25.4505	−	33.9979i	−0.973837	−	1.30089i	−0.0202434	−	0.999795i	$-0.506444\pi$
$684$		0			0
$685$	26.7911	+	34.8108i	1.02363	+	1.33005i
$686$		0			0
$687$	−0.0525109	+	0.0286731i	−0.00200341	+	0.00109395i
$688$		0			0
$689$	−3.56011			−0.135629
$690$		0			0
$691$	18.2417			0.693947			0.346974	−	0.937875i	$-0.387209\pi$
$691$	18.2417			0.693947			0.346974	+	0.937875i	$0.387209\pi$
$692$		0			0
$693$	−4.72453	+	2.57979i	−0.179470	+	0.0979980i
$694$		0			0
$695$	27.3063	+	3.55491i	1.03579	+	0.134845i
$696$		0			0
$697$	−9.22363	−	12.3213i	−0.349370	−	0.466703i
$698$		0			0
$699$	0.399863	−	0.622199i	0.0151242	−	0.0235337i
$700$		0			0
$701$	−5.66689	+	2.58798i	−0.214036	+	0.0977468i	−0.519548	−	0.854441i	$-0.673900\pi$
$701$	−5.66689	+	2.58798i	−0.214036	+	0.0977468i	0.305512	+	0.952188i	$0.401172\pi$
$702$		0			0
$703$	−1.57933	−	1.18227i	−0.0595655	−	0.0445902i
$704$		0			0
$705$	0.109287	−	0.248010i	0.00411600	−	0.00934060i
$706$		0			0
$707$	0.880760	+	12.3146i	0.0331244	+	0.463139i
$708$		0			0
$709$	21.3230	+	24.6080i	0.800801	+	0.924174i	0.998425	−	0.0561043i	$-0.0178679\pi$
$709$	21.3230	+	24.6080i	0.800801	+	0.924174i	−0.197624	+	0.980278i	$0.563322\pi$
$710$		0			0
$711$	−5.94123	−	2.71327i	−0.222814	−	0.101756i
$712$		0			0
$713$	28.9934	−	28.3672i	1.08581	−	1.06236i
$714$		0			0
$715$	0.520874	−	1.45554i	0.0194796	−	0.0544339i
$716$		0			0
$717$	0.0278197	−	0.388971i	0.00103895	−	0.0145264i
$718$		0			0
$719$	−30.4326	−	26.3700i	−1.13494	−	0.983435i	−0.134972	−	0.990849i	$-0.543094\pi$
$719$	−30.4326	−	26.3700i	−1.13494	−	0.983435i	−0.999973	+	0.00741457i	$0.997640\pi$
$720$		0			0
$721$	10.4540	−	3.06956i	0.389326	−	0.114316i
$722$		0			0
$723$	0.409181	−	0.546602i	0.0152176	−	0.0203283i
$724$		0			0
$725$	6.96191	+	10.2226i	0.258559	+	0.379658i
$726$		0			0
$727$	−47.3516	+	10.3007i	−1.75617	+	0.382032i	−0.971344	−	0.237679i	$-0.923613\pi$
$727$	−47.3516	+	10.3007i	−1.75617	+	0.382032i	−0.784830	+	0.619711i	$0.787250\pi$
$728$		0			0
$729$	26.6084	+	3.82572i	0.985498	+	0.141693i
$730$		0			0
$731$	10.0515	−	6.45970i	0.371768	−	0.238920i
$732$		0			0
$733$	10.9886	+	20.1241i	0.405873	+	0.743301i	0.998044	−	0.0625110i	$-0.0199108\pi$
$733$	10.9886	+	20.1241i	0.405873	+	0.743301i	−0.592171	+	0.805812i	$0.701729\pi$
$734$		0			0
$735$	0.139501	−	0.0118499i	0.00514559	−	0.000437090i
$736$		0			0
$737$	5.99861	+	5.99861i	0.220962	+	0.220962i
$738$		0			0
$739$	12.6529	−	43.0918i	0.465444	−	1.58516i	−0.308060	−	0.951367i	$-0.599680\pi$
$739$	12.6529	−	43.0918i	0.465444	−	1.58516i	0.773504	−	0.633791i	$-0.218502\pi$
$740$		0			0
$741$	0.0617794	+	0.0961307i	0.00226952	+	0.00353145i
$742$		0			0
$743$	−8.95832	+	6.70612i	−0.328649	+	0.246024i	−0.750841	−	0.660483i	$-0.770352\pi$
$743$	−8.95832	+	6.70612i	−0.328649	+	0.246024i	0.422192	+	0.906506i	$0.361261\pi$
$744$		0			0
$745$	17.0837	−	5.26478i	0.625898	−	0.192887i
$746$		0			0
$747$	−29.5234	−	11.0117i	−1.08020	−	0.402895i
$748$		0			0
$749$	23.5499	−	3.38597i	0.860495	−	0.123721i
$750$		0			0
$751$	−11.4649	−	39.0458i	−0.418359	−	1.42480i	−0.851918	−	0.523675i	$-0.824561\pi$
$751$	−11.4649	−	39.0458i	−0.418359	−	1.42480i	0.433559	−	0.901125i	$-0.357258\pi$
$752$		0			0
$753$	−0.406441	+	0.0290692i	−0.0148115	+	0.00105934i
$754$		0			0
$755$	−52.5645	+	0.701329i	−1.91302	+	0.0255240i
$756$		0			0
$757$	−2.14697	−	5.75625i	−0.0780330	−	0.209215i	0.892075	−	0.451887i	$-0.149249\pi$
$757$	−2.14697	−	5.75625i	−0.0780330	−	0.209215i	−0.970108	+	0.242672i	$0.921976\pi$
$758$		0			0
$759$	0.0213447	−	0.137762i	0.000774763	−	0.00500044i
$760$		0			0
$761$	4.22538	−	9.25230i	0.153170	−	0.335396i	−0.817455	−	0.575992i	$-0.804616\pi$
$761$	4.22538	−	9.25230i	0.153170	−	0.335396i	0.970625	+	0.240597i	$0.0773431\pi$
$762$		0			0
$763$	−41.6379	−	2.97800i	−1.50739	−	0.107811i
$764$		0			0
$765$	−8.24803	+	11.3301i	−0.298208	+	0.409639i
$766$		0			0
$767$	6.04597	+	3.30135i	0.218307	+	0.119205i
$768$		0			0
$769$	−2.92270	−	20.3278i	−0.105395	−	0.733039i	−0.972159	−	0.234321i	$-0.924713\pi$
$769$	−2.92270	−	20.3278i	−0.105395	−	0.733039i	0.866764	−	0.498718i	$-0.166196\pi$
$770$		0			0
$771$	0.400189	+	0.876293i	0.0144125	+	0.0315589i
$772$		0			0
$773$	−4.28263	−	19.6869i	−0.154036	−	0.708090i	−0.987769	−	0.155923i	$-0.950165\pi$
$773$	−4.28263	−	19.6869i	−0.154036	−	0.708090i	0.833734	−	0.552167i	$-0.186199\pi$
$774$		0			0
$775$	42.2743	−	1.12827i	1.51854	−	0.0405286i
$776$		0			0
$777$	0.118375	+	0.0257509i	0.00424667	+	0.000923807i
$778$		0			0
$779$	15.5293	+	4.55983i	0.556397	+	0.163373i
$780$		0			0
$781$			0.604797i			0.0216413i
$782$		0			0
$783$	−0.490427	+	0.490427i	−0.0175264	+	0.0175264i
$784$		0			0
$785$	−2.71520	+	13.3357i	−0.0969095	+	0.475972i
$786$		0			0
$787$	9.13827	−	42.0079i	0.325744	−	1.49742i	−0.465020	−	0.885300i	$-0.653953\pi$
$787$	9.13827	−	42.0079i	0.325744	−	1.49742i	0.790764	−	0.612121i	$-0.209683\pi$
$788$		0			0
$789$	−0.0381403	+	0.265272i	−0.00135783	+	0.00944393i
$790$		0			0
$791$	32.2064	+	20.6978i	1.14513	+	0.735930i
$792$		0			0
$793$	5.35632	−	14.3608i	0.190208	−	0.509969i
$794$		0			0
$795$	−0.283959	−	0.177182i	−0.0100710	−	0.00628399i
$796$		0			0
$797$	24.1007	−	44.1371i	0.853690	−	1.56342i	0.0277795	−	0.999614i	$-0.491156\pi$
$797$	24.1007	−	44.1371i	0.853690	−	1.56342i	0.825910	−	0.563802i	$-0.190662\pi$
$798$		0			0
$799$	3.54965	−	4.09651i	0.125577	−	0.144924i
$800$		0			0
$801$	22.8286	−	19.7811i	0.806607	−	0.698929i
$802$		0			0
$803$	2.22385	−	0.829452i	0.0784778	−	0.0292707i
$804$		0			0
$805$	16.6794	−	26.0925i	0.587872	−	0.919642i
$806$		0			0
$807$	−0.223082	+	0.0832053i	−0.00785286	+	0.00292897i
$808$		0			0
$809$	34.4294	−	29.8333i	1.21047	−	1.04888i	0.213057	−	0.977040i	$-0.431658\pi$
$809$	34.4294	−	29.8333i	1.21047	−	1.04888i	0.997416	−	0.0718416i	$-0.0228876\pi$
$810$		0			0
$811$	−34.8890	+	40.2641i	−1.22512	+	1.41386i	−0.345344	+	0.938476i	$0.612238\pi$
$811$	−34.8890	+	40.2641i	−1.22512	+	1.41386i	−0.879776	+	0.475388i	$0.842308\pi$
$812$		0			0
$813$	−0.460802	+	0.843896i	−0.0161610	+	0.0295967i
$814$		0			0
$815$	−17.6026	+	4.07591i	−0.616594	+	0.142773i
$816$		0			0
$817$	−4.39080	+	11.7722i	−0.153615	+	0.411857i
$818$		0			0
$819$	8.09747	+	5.20393i	0.282949	+	0.181840i
$820$		0			0
$821$	0.848233	−	5.89959i	0.0296035	−	0.205897i	−0.969651	−	0.244492i	$-0.921379\pi$
$821$	0.848233	−	5.89959i	0.0296035	−	0.205897i	0.999255	+	0.0385944i	$0.0122880\pi$
$822$		0			0
$823$	−0.239309	+	1.10009i	−0.00834179	+	0.0383466i	−0.981130	−	0.193351i	$-0.938064\pi$
$823$	−0.239309	+	1.10009i	−0.00834179	+	0.0383466i	0.972788	+	0.231698i	$0.0744280\pi$
$824$		0			0
$825$	0.113986	−	0.0901724i	0.00396847	−	0.00313940i
$826$		0			0
$827$	2.56413	−	2.56413i	0.0891635	−	0.0891635i	−0.661118	−	0.750282i	$-0.729918\pi$
$827$	2.56413	−	2.56413i	0.0891635	−	0.0891635i	0.750282	+	0.661118i	$0.229918\pi$
$828$		0			0
$829$		−	6.22752i		−	0.216291i	−0.994135	−	0.108145i	$-0.965509\pi$
$829$		−	6.22752i		−	0.216291i	0.994135	−	0.108145i	$-0.0344912\pi$
$830$		0			0
$831$	−1.23697	−	0.363206i	−0.0429099	−	0.0125995i
$832$		0			0
$833$	2.73610	+	0.595202i	0.0948002	+	0.0206225i
$834$		0			0
$835$	−1.07714	+	18.5319i	−0.0372760	+	0.641323i
$836$		0			0
$837$	0.504092	+	2.31728i	0.0174240	+	0.0800968i
$838$		0			0
$839$	15.7581	+	34.5054i	0.544030	+	1.19126i	0.959514	+	0.281659i	$0.0908848\pi$
$839$	15.7581	+	34.5054i	0.544030	+	1.19126i	−0.415484	+	0.909600i	$0.636388\pi$
$840$		0			0
$841$	−3.25634	−	22.6483i	−0.112287	−	0.780976i
$842$		0			0
$843$	1.15798	+	0.632302i	0.0398828	+	0.0217777i
$844$		0			0
$845$	25.9846	−	4.09055i	0.893896	−	0.140719i
$846$		0			0
$847$	−30.5711	−	2.18649i	−1.05043	−	0.0751286i
$848$		0			0
$849$	0.257026	−	0.562808i	0.00882110	−	0.0193155i
$850$		0			0
$851$	3.28303	−	2.78259i	0.112541	−	0.0953861i
$852$		0			0
$853$	−9.59827	−	25.7340i	−0.328638	−	0.881114i	−0.991232	−	0.132134i	$-0.957817\pi$
$853$	−9.59827	−	25.7340i	−0.328638	−	0.881114i	0.662593	−	0.748979i	$-0.269456\pi$
$854$		0			0
$855$	−0.196607	−	14.7357i	−0.00672382	−	0.503950i
$856$		0			0
$857$	12.2424	−	0.875592i	0.418192	−	0.0299097i	0.139342	−	0.990244i	$-0.455501\pi$
$857$	12.2424	−	0.875592i	0.418192	−	0.0299097i	0.278850	+	0.960335i	$0.410047\pi$
$858$		0			0
$859$	−5.72595	−	19.5008i	−0.195367	−	0.665359i	−0.997656	−	0.0684234i	$-0.978203\pi$
$859$	−5.72595	−	19.5008i	−0.195367	−	0.665359i	0.802289	−	0.596935i	$-0.203615\pi$
$860$		0			0
$861$	−0.983737	+	0.141440i	−0.0335257	+	0.00482026i
$862$		0			0
$863$	18.0898	+	6.74716i	0.615785	+	0.229676i	0.637949	−	0.770078i	$-0.279783\pi$
$863$	18.0898	+	6.74716i	0.615785	+	0.229676i	−0.0221643	+	0.999754i	$0.507056\pi$
$864$		0			0
$865$	2.71280	−	5.12966i	0.0922381	−	0.174414i
$866$		0			0
$867$	−0.472632	+	0.353808i	−0.0160514	+	0.0120159i
$868$		0			0
$869$	0.732431	+	1.13969i	0.0248460	+	0.0386612i
$870$		0			0
$871$	4.27369	−	14.5548i	0.144808	−	0.493172i
$872$		0			0
$873$	23.3195	+	23.3195i	0.789246	+	0.789246i
$874$		0			0
$875$	31.2488	−	8.11987i	1.05640	−	0.274502i
$876$		0			0
$877$	5.16978	+	9.46774i	0.174571	+	0.319703i	0.950285	−	0.311382i	$-0.100792\pi$
$877$	5.16978	+	9.46774i	0.174571	+	0.319703i	−0.775714	+	0.631085i	$0.782610\pi$
$878$		0			0
$879$	−0.624907	+	0.401604i	−0.0210776	+	0.0135458i
$880$		0			0
$881$	−0.0444367	−	0.00638903i	−0.00149711	−	0.000215252i	0.141566	−	0.989929i	$-0.454786\pi$
$881$	−0.0444367	−	0.00638903i	−0.00149711	−	0.000215252i	−0.143063	+	0.989714i	$0.545695\pi$
$882$		0			0
$883$	−26.3106	+	5.72351i	−0.885421	+	0.192612i	−0.632208	−	0.774799i	$-0.717851\pi$
$883$	−26.3106	+	5.72351i	−0.885421	+	0.192612i	−0.253213	+	0.967411i	$0.581487\pi$
$884$		0			0
$885$	0.317932	+	0.564221i	0.0106872	+	0.0189661i
$886$		0			0
$887$	−25.3893	+	33.9162i	−0.852490	+	1.13879i	0.136475	+	0.990644i	$0.456423\pi$
$887$	−25.3893	+	33.9162i	−0.852490	+	1.13879i	−0.988965	+	0.148150i	$0.952668\pi$
$888$		0			0
$889$	18.4749	−	5.42472i	0.619628	−	0.181939i
$890$		0			0
$891$	−4.22010	−	3.65674i	−0.141379	−	0.122505i
$892$		0			0
$893$	−0.406632	+	5.68546i	−0.0136074	+	0.190257i
$894$		0			0
$895$	0.0974361	−	0.0460784i	0.00325693	−	0.00154023i
$896$		0			0
$897$	−0.234496	+	0.0845580i	−0.00782959	+	0.00282331i
$898$		0			0
$899$	19.0309	+	8.69111i	0.634716	+	0.289865i
$900$		0			0
$901$	−4.38370	−	5.05906i	−0.146042	−	0.168542i
$902$		0			0
$903$	−0.0550402	−	0.769562i	−0.00183162	−	0.0256094i
$904$		0			0
$905$	−11.8314	−	5.21359i	−0.393289	−	0.173306i
$906$		0			0
$907$	8.90444	+	6.66578i	0.295667	+	0.221334i	0.736804	−	0.676106i	$-0.236334\pi$
$907$	8.90444	+	6.66578i	0.295667	+	0.221334i	−0.441137	+	0.897440i	$0.645425\pi$
$908$		0			0
$909$	−11.6583	+	5.32415i	−0.386680	+	0.176591i
$910$		0			0
$911$	12.2990	−	19.1376i	0.407485	−	0.634059i	−0.575488	−	0.817810i	$-0.695188\pi$
$911$	12.2990	−	19.1376i	0.407485	−	0.634059i	0.982973	+	0.183752i	$0.0588242\pi$
$912$		0			0
$913$	3.91675	+	5.23216i	0.129625	+	0.173159i
$914$		0			0
$915$	1.14195	−	0.878866i	0.0377516	−	0.0290544i
$916$		0			0
$917$	−29.4367	+	16.0736i	−0.972085	+	0.530799i
$918$		0			0
$919$	17.6471			0.582125			0.291063	−	0.956704i	$-0.405991\pi$
$919$	17.6471			0.582125			0.291063	+	0.956704i	$0.405991\pi$
$920$		0			0
$921$	0.533283			0.0175723
$922$		0			0
$923$	0.949173	−	0.518288i	0.0312424	−	0.0170596i
$924$		0			0
$925$	4.48234	+	0.200570i	0.147379	+	0.00659471i
$926$		0			0
$927$	6.77808	+	9.05445i	0.222621	+	0.297387i
$928$		0			0
$929$	4.94656	−	7.69700i	0.162292	−	0.252531i	−0.750578	−	0.660782i	$-0.770225\pi$
$929$	4.94656	−	7.69700i	0.162292	−	0.252531i	0.912870	+	0.408251i	$0.133861\pi$
$930$		0			0
$931$	−2.67840	+	1.22318i	−0.0877810	+	0.0400882i
$932$		0			0
$933$	−0.413851	−	0.309805i	−0.0135489	−	0.0101426i
$934$		0			0
$935$	2.70975	−	1.05208i	0.0886184	−	0.0344065i
$936$		0			0
$937$	0.587675	+	8.21678i	0.0191985	+	0.268430i	0.997980	+	0.0635248i	$0.0202342\pi$
$937$	0.587675	+	8.21678i	0.0191985	+	0.268430i	−0.978782	+	0.204906i	$0.934311\pi$
$938$		0			0
$939$	−0.470559	−	0.543054i	−0.0153561	−	0.0177219i
$940$		0			0
$941$	−28.3568	−	12.9501i	−0.924405	−	0.422162i	−0.104411	−	0.994534i	$-0.533296\pi$
$941$	−28.3568	−	12.9501i	−0.924405	−	0.422162i	−0.819994	+	0.572373i	$0.806023\pi$
$942$		0			0
$943$	−17.2579	+	30.8013i	−0.561996	+	1.00303i
$944$		0			0
$945$	0.774030	+	1.63674i	0.0251792	+	0.0532433i
$946$		0			0
$947$	2.30311	−	32.2017i	0.0748411	−	1.04641i	−0.811794	−	0.583944i	$-0.801509\pi$
$947$	2.30311	−	32.2017i	0.0748411	−	1.04641i	0.886635	−	0.462470i	$-0.153037\pi$
$948$		0			0
$949$	−3.20750	−	2.77931i	−0.104120	−	0.0902203i
$950$		0			0
$951$	−1.06144	+	0.311666i	−0.0344194	+	0.0101065i
$952$		0			0
$953$	23.2659	−	31.0797i	0.753658	−	1.00677i	−0.245642	−	0.969361i	$-0.578999\pi$
$953$	23.2659	−	31.0797i	0.753658	−	1.00677i	0.999300	−	0.0374085i	$-0.0119103\pi$
$954$		0			0
$955$	−4.95094	+	17.7332i	−0.160209	+	0.573833i
$956$		0			0
$957$	0.0702601	−	0.0152841i	0.00227119	−	0.000494066i
$958$		0			0
$959$	56.1521	+	8.07345i	1.81325	+	0.260705i
$960$		0			0
$961$	34.1006	−	21.9151i	1.10002	−	0.706940i
$962$		0			0
$963$	11.8368	+	21.6774i	0.381434	+	0.698544i
$964$		0			0
$965$	2.93755	+	34.5819i	0.0945630	+	1.11323i
$966$		0			0
$967$	10.2193	+	10.2193i	0.328630	+	0.328630i	0.852065	−	0.523435i	$-0.175350\pi$
$967$	10.2193	+	10.2193i	0.328630	+	0.328630i	−0.523435	+	0.852065i	$0.675350\pi$
$968$		0			0
$969$	−0.0605343	+	0.206161i	−0.00194464	+	0.00662284i
$970$		0			0
$971$	−4.46633	−	6.94974i	−0.143331	−	0.223028i	0.762164	−	0.647384i	$-0.224137\pi$
$971$	−4.46633	−	6.94974i	−0.143331	−	0.223028i	−0.905495	+	0.424356i	$0.860501\pi$
$972$		0			0
$973$	28.4693	−	21.3119i	0.912684	−	0.683227i
$974$		0			0
$975$	−0.239199	−	0.101616i	−0.00766049	−	0.00325431i
$976$		0			0
$977$	−14.7228	−	5.49131i	−0.471024	−	0.175683i	0.102732	−	0.994709i	$-0.467241\pi$
$977$	−14.7228	−	5.49131i	−0.471024	−	0.175683i	−0.573756	+	0.819026i	$0.694514\pi$
$978$		0			0
$979$	−6.20162	+	0.891658i	−0.198205	+	0.0284975i
$980$		0			0
$981$	−12.2088	−	41.5793i	−0.389797	−	1.32753i
$982$		0			0
$983$	1.22934	−	0.0879238i	0.0392097	−	0.00280433i	−0.0517205	−	0.998662i	$-0.516471\pi$
$983$	1.22934	−	0.0879238i	0.0392097	−	0.00280433i	0.0909303	+	0.995857i	$0.471016\pi$
$984$		0			0
$985$	4.43031	+	4.31364i	0.141161	+	0.137444i
$986$		0			0
$987$	−0.122317	−	0.327945i	−0.00389340	−	0.0104386i
$988$		0			0
$989$	−22.8944	−	15.0690i	−0.727999	−	0.479166i
$990$		0			0
$991$	23.7777	−	52.0659i	0.755323	−	1.65393i	−0.00123431	−	0.999999i	$-0.500393\pi$
$991$	23.7777	−	52.0659i	0.755323	−	1.65393i	0.756557	−	0.653927i	$-0.226880\pi$
$992$		0			0
$993$	−0.0415074	−	0.00296867i	−0.00131720	−	9.42078e-5i
$994$		0			0
$995$	6.68150	+	42.4431i	0.211818	+	1.34554i
$996$		0			0
$997$	−48.8369	−	26.6669i	−1.54668	−	0.844551i	−0.999974	−	0.00722554i	$-0.997700\pi$
$997$	−48.8369	−	26.6669i	−1.54668	−	0.844551i	−0.546705	−	0.837325i	$-0.684118\pi$
$998$		0			0
$999$	0.0358077	+	0.249048i	0.00113291	+	0.00787954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.18	✓	720
5.3	odd	4	inner	920.2.bv.a.753.18	yes	720
23.19	odd	22	inner	920.2.bv.a.617.18	yes	720
115.88	even	44	inner	920.2.bv.a.433.18	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.18	✓	720	1.1	even	1	trivial
920.2.bv.a.433.18	yes	720	115.88	even	44	inner
920.2.bv.a.617.18	yes	720	23.19	odd	22	inner
920.2.bv.a.753.18	yes	720	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0410298 + 0.0224040i) q^{3} +(-0.288669 + 2.21736i) q^{5} +(1.73059 + 2.31180i) q^{7} +(-1.62074 + 2.52192i) q^{9} +(0.565611 - 0.258306i) q^{11} +(-0.890094 - 0.666316i) q^{13} +(-0.0378336 - 0.0974451i) q^{15} +(-0.149145 - 2.08532i) q^{17} +(1.43969 + 1.66149i) q^{19} +(-0.122799 - 0.0560805i) q^{21} +(-4.23404 + 2.25231i) q^{23} +(-4.83334 - 1.28017i) q^{25} +(0.0200025 - 0.279672i) q^{27} +(-1.86944 - 1.61988i) q^{29} +(-8.11526 + 2.38286i) q^{31} +(-0.0174198 + 0.0232702i) q^{33} +(-5.62564 + 3.16999i) q^{35} +(-0.876858 + 0.190749i) q^{37} +(0.0514485 + 0.00739718i) q^{39} +(6.19326 - 3.98017i) q^{41} +(2.73894 + 5.01600i) q^{43} +(-5.12414 - 4.32176i) q^{45} +(1.83333 + 1.83333i) q^{47} +(-0.377336 + 1.28509i) q^{49} +(0.0528390 + 0.0822190i) q^{51} +(2.56327 - 1.91884i) q^{53} +(0.409482 + 1.32873i) q^{55} +(-0.0962940 - 0.0359158i) q^{57} +(-6.13247 + 0.881716i) q^{59} +(3.88373 + 13.2268i) q^{61} +(-8.63501 + 0.617588i) q^{63} +(1.73440 - 1.78131i) q^{65} +(4.76778 + 12.7829i) q^{67} +(0.123261 - 0.187271i) q^{69} +(-0.404054 + 0.884756i) q^{71} +(3.80740 + 0.272310i) q^{73} +(0.226992 - 0.0557611i) q^{75} +(1.57599 + 0.860556i) q^{77} +(0.310067 + 2.15657i) q^{79} +(-3.73057 - 8.16880i) q^{81} +(2.23428 + 10.2708i) q^{83} +(4.66696 + 0.271261i) q^{85} +(0.112994 + 0.0245804i) q^{87} +(-9.66802 - 2.83879i) q^{89} -3.21083i q^{91} +(0.279582 - 0.279582i) q^{93} +(-4.09970 + 2.71268i) q^{95} +(2.33842 - 10.7495i) q^{97} +(-0.265282 + 1.84507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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