LMFDB - Embedded newform 504.2.q.d.121.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.5
Character	$\chi$	$=$	504.121
Dual form			504.2.q.d.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.455209 - 1.67116i) q^{3} +(0.240694 + 0.416893i) q^{5} +(-1.92765 + 1.81223i) q^{7} +(-2.58557 + 1.52146i) q^{9} +O(q^{10})$	\(q+(-0.455209 - 1.67116i) q^{3} +(0.240694 + 0.416893i) q^{5} +(-1.92765 + 1.81223i) q^{7} +(-2.58557 + 1.52146i) q^{9} +(-1.69080 + 2.92855i) q^{11} +(-2.86067 + 4.95482i) q^{13} +(0.587131 - 0.592012i) q^{15} +(2.75605 + 4.77362i) q^{17} +(2.18023 - 3.77626i) q^{19} +(3.90601 + 2.39647i) q^{21} +(-1.81293 - 3.14008i) q^{23} +(2.38413 - 4.12944i) q^{25} +(3.71958 + 3.62832i) q^{27} +(1.53131 + 2.65231i) q^{29} -9.34918 q^{31} +(5.66374 + 1.49249i) q^{33} +(-1.21948 - 0.367431i) q^{35} +(1.48552 - 2.57299i) q^{37} +(9.58252 + 2.52516i) q^{39} +(-6.29558 + 10.9043i) q^{41} +(1.90827 + 3.30522i) q^{43} +(-1.25662 - 0.711701i) q^{45} -3.76564 q^{47} +(0.431647 - 6.98668i) q^{49} +(6.72291 - 6.77880i) q^{51} +(5.57860 + 9.66242i) q^{53} -1.62786 q^{55} +(-7.30321 - 1.92452i) q^{57} +8.42282 q^{59} -7.28625 q^{61} +(2.22683 - 7.61848i) q^{63} -2.75418 q^{65} +2.57143 q^{67} +(-4.42232 + 4.45909i) q^{69} -3.94304 q^{71} +(-0.862216 - 1.49340i) q^{73} +(-7.98625 - 2.10451i) q^{75} +(-2.04794 - 8.70932i) q^{77} -5.59960 q^{79} +(4.37033 - 7.86767i) q^{81} +(-0.119494 - 0.206970i) q^{83} +(-1.32673 + 2.29796i) q^{85} +(3.73538 - 3.76643i) q^{87} +(0.648116 - 1.12257i) q^{89} +(-3.46492 - 14.7353i) q^{91} +(4.25583 + 15.6240i) q^{93} +2.09907 q^{95} +(-7.02669 - 12.1706i) q^{97} +(-0.0839884 - 10.1444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.455209	−	1.67116i	−0.262815	−	0.964846i
$3$	−0.455209	−	1.67116i	−0.262815	−	0.964846i
$4$		0			0
$5$	0.240694	+	0.416893i	0.107641	+	0.186440i	0.914814	−	0.403875i	$-0.132337\pi$
$5$	0.240694	+	0.416893i	0.107641	+	0.186440i	−0.807173	+	0.590315i	$0.799003\pi$
$6$		0			0
$7$	−1.92765	+	1.81223i	−0.728582	+	0.684958i
$7$	−1.92765	+	1.81223i	−0.728582	+	0.684958i
$8$		0			0
$9$	−2.58557	+	1.52146i	−0.861856	+	0.507153i
$10$		0			0
$11$	−1.69080	+	2.92855i	−0.509794	+	0.882990i	0.490141	+	0.871643i	$0.336945\pi$
$11$	−1.69080	+	2.92855i	−0.509794	+	0.882990i	−0.999936	+	0.0113468i	$0.996388\pi$
$12$		0			0
$13$	−2.86067	+	4.95482i	−0.793406	+	1.37422i	0.130440	+	0.991456i	$0.458361\pi$
$13$	−2.86067	+	4.95482i	−0.793406	+	1.37422i	−0.923846	+	0.382764i	$0.874972\pi$
$14$		0			0
$15$	0.587131	−	0.592012i	0.151596	−	0.152857i
$16$		0			0
$17$	2.75605	+	4.77362i	0.668440	+	1.15777i	0.978340	+	0.207003i	$0.0663711\pi$
$17$	2.75605	+	4.77362i	0.668440	+	1.15777i	−0.309900	+	0.950769i	$0.600296\pi$
$18$		0			0
$19$	2.18023	−	3.77626i	0.500178	−	0.866334i	−0.499822	−	0.866128i	$-0.666601\pi$
$19$	2.18023	−	3.77626i	0.500178	−	0.866334i	1.00000		0.000205746i	$-6.54909e-5\pi$
$20$		0			0
$21$	3.90601	+	2.39647i	0.852362	+	0.522952i
$22$		0			0
$23$	−1.81293	−	3.14008i	−0.378021	−	0.654752i	0.612753	−	0.790274i	$-0.290062\pi$
$23$	−1.81293	−	3.14008i	−0.378021	−	0.654752i	−0.990774	+	0.135523i	$0.956729\pi$
$24$		0			0
$25$	2.38413	−	4.12944i	0.476827	−	0.825888i
$26$		0			0
$27$	3.71958	+	3.62832i	0.715833	+	0.698271i
$28$		0			0
$29$	1.53131	+	2.65231i	0.284358	+	0.492522i	0.972453	−	0.233098i	$-0.0748863\pi$
$29$	1.53131	+	2.65231i	0.284358	+	0.492522i	−0.688095	+	0.725620i	$0.741553\pi$
$30$		0			0
$31$	−9.34918			−1.67916			−0.839581	−	0.543235i	$-0.817199\pi$
$31$	−9.34918			−1.67916			−0.839581	+	0.543235i	$0.817199\pi$
$32$		0			0
$33$	5.66374	+	1.49249i	0.985931	+	0.259810i
$34$		0			0
$35$	−1.21948	−	0.367431i	−0.206130	−	0.0621072i
$36$		0			0
$37$	1.48552	−	2.57299i	0.244218	−	0.422997i	−0.717694	−	0.696359i	$-0.754802\pi$
$37$	1.48552	−	2.57299i	0.244218	−	0.422997i	0.961911	+	0.273361i	$0.0881355\pi$
$38$		0			0
$39$	9.58252	+	2.52516i	1.53443	+	0.404349i
$40$		0			0
$41$	−6.29558	+	10.9043i	−0.983204	+	1.70296i	−0.333545	+	0.942734i	$0.608245\pi$
$41$	−6.29558	+	10.9043i	−0.983204	+	1.70296i	−0.649659	+	0.760226i	$0.725088\pi$
$42$		0			0
$43$	1.90827	+	3.30522i	0.291009	+	0.504042i	0.974049	−	0.226339i	$-0.0726758\pi$
$43$	1.90827	+	3.30522i	0.291009	+	0.504042i	−0.683040	+	0.730381i	$0.739342\pi$
$44$		0			0
$45$	−1.25662	−	0.711701i	−0.187325	−	0.106094i
$46$		0			0
$47$	−3.76564			−0.549276			−0.274638	−	0.961548i	$-0.588558\pi$
$47$	−3.76564			−0.549276			−0.274638	+	0.961548i	$0.588558\pi$
$48$		0			0
$49$	0.431647	−	6.98668i	0.0616639	−	0.998097i
$50$		0			0
$51$	6.72291	−	6.77880i	0.941396	−	0.949222i
$52$		0			0
$53$	5.57860	+	9.66242i	0.766280	+	1.32724i	0.939567	+	0.342364i	$0.111228\pi$
$53$	5.57860	+	9.66242i	0.766280	+	1.32724i	−0.173287	+	0.984871i	$0.555439\pi$
$54$		0			0
$55$	−1.62786			−0.219500
$56$		0			0
$57$	−7.30321	−	1.92452i	−0.967334	−	0.254909i
$58$		0			0
$59$	8.42282			1.09656			0.548279	−	0.836296i	$-0.315283\pi$
$59$	8.42282			1.09656			0.548279	+	0.836296i	$0.315283\pi$
$60$		0			0
$61$	−7.28625			−0.932908			−0.466454	−	0.884545i	$-0.654469\pi$
$61$	−7.28625			−0.932908			−0.466454	+	0.884545i	$0.654469\pi$
$62$		0			0
$63$	2.22683	−	7.61848i	0.280555	−	0.959838i
$64$		0			0
$65$	−2.75418			−0.341614
$66$		0			0
$67$	2.57143			0.314150			0.157075	−	0.987587i	$-0.449794\pi$
$67$	2.57143			0.314150			0.157075	+	0.987587i	$0.449794\pi$
$68$		0			0
$69$	−4.42232	+	4.45909i	−0.532385	+	0.536811i
$70$		0			0
$71$	−3.94304			−0.467953			−0.233977	−	0.972242i	$-0.575174\pi$
$71$	−3.94304			−0.467953			−0.233977	+	0.972242i	$0.575174\pi$
$72$		0			0
$73$	−0.862216	−	1.49340i	−0.100915	−	0.174790i	0.811147	−	0.584842i	$-0.198844\pi$
$73$	−0.862216	−	1.49340i	−0.100915	−	0.174790i	−0.912062	+	0.410053i	$0.865510\pi$
$74$		0			0
$75$	−7.98625	−	2.10451i	−0.922172	−	0.243008i
$76$		0			0
$77$	−2.04794	−	8.70932i	−0.233384	−	0.992519i
$78$		0			0
$79$	−5.59960			−0.630004			−0.315002	−	0.949091i	$-0.602005\pi$
$79$	−5.59960			−0.630004			−0.315002	+	0.949091i	$0.602005\pi$
$80$		0			0
$81$	4.37033	−	7.86767i	0.485592	−	0.874185i
$82$		0			0
$83$	−0.119494	−	0.206970i	−0.0131162	−	0.0227179i	0.859393	−	0.511316i	$-0.170842\pi$
$83$	−0.119494	−	0.206970i	−0.0131162	−	0.0227179i	−0.872509	+	0.488598i	$0.837508\pi$
$84$		0			0
$85$	−1.32673	+	2.29796i	−0.143904	+	0.249249i
$86$		0			0
$87$	3.73538	−	3.76643i	0.400475	−	0.403804i
$88$		0			0
$89$	0.648116	−	1.12257i	0.0687002	−	0.118992i	−0.829629	−	0.558315i	$-0.811448\pi$
$89$	0.648116	−	1.12257i	0.0687002	−	0.118992i	0.898329	+	0.439323i	$0.144781\pi$
$90$		0			0
$91$	−3.46492	−	14.7353i	−0.363222	−	1.54468i
$92$		0			0
$93$	4.25583	+	15.6240i	0.441309	+	1.62013i
$94$		0			0
$95$	2.09907			0.215360
$96$		0			0
$97$	−7.02669	−	12.1706i	−0.713452	−	1.23574i	−0.963553	−	0.267516i	$-0.913797\pi$
$97$	−7.02669	−	12.1706i	−0.713452	−	1.23574i	0.250101	−	0.968220i	$-0.419536\pi$
$98$		0			0
$99$	−0.0839884	−	10.1444i	−0.00844115	−	1.01955i
$100$		0			0
$101$	−5.30322	+	9.18545i	−0.527690	+	0.913986i	0.471789	+	0.881712i	$0.343609\pi$
$101$	−5.30322	+	9.18545i	−0.527690	+	0.913986i	−0.999479	+	0.0322748i	$0.989725\pi$
$102$		0			0
$103$	0.0797078	+	0.138058i	0.00785385	+	0.0136033i	0.869926	−	0.493183i	$-0.164167\pi$
$103$	0.0797078	+	0.138058i	0.00785385	+	0.0136033i	−0.862072	+	0.506786i	$0.830833\pi$
$104$		0			0
$105$	−0.0589194	+	2.20521i	−0.00574995	+	0.215206i
$106$		0			0
$107$	−3.99030	+	6.91140i	−0.385757	+	0.668150i	−0.991874	−	0.127225i	$-0.959393\pi$
$107$	−3.99030	+	6.91140i	−0.385757	+	0.668150i	0.606117	+	0.795375i	$0.292726\pi$
$108$		0			0
$109$	−6.85612	−	11.8751i	−0.656697	−	1.13743i	−0.981466	−	0.191639i	$-0.938620\pi$
$109$	−6.85612	−	11.8751i	−0.656697	−	1.13743i	0.324769	−	0.945793i	$-0.394714\pi$
$110$		0			0
$111$	−4.97611	−	1.31129i	−0.472312	−	0.124462i
$112$		0			0
$113$	8.98656	−	15.5652i	0.845384	−	1.46425i	−0.0399031	−	0.999204i	$-0.512705\pi$
$113$	8.98656	−	15.5652i	0.845384	−	1.46425i	0.885287	−	0.465045i	$-0.153962\pi$
$114$		0			0
$115$	0.872719	−	1.51159i	0.0813814	−	0.140957i
$116$		0			0
$117$	−0.142100	−	17.1634i	−0.0131372	−	1.58676i
$118$		0			0
$119$	−13.9636	−	4.20726i	−1.28004	−	0.385679i
$120$		0			0
$121$	−0.217588	−	0.376874i	−0.0197807	−	0.0342613i
$122$		0			0
$123$	21.0886	+	5.55721i	1.90150	+	0.501077i
$124$		0			0
$125$	4.70232			0.420588
$126$		0			0
$127$	18.9684			1.68317			0.841587	−	0.540121i	$-0.181622\pi$
$127$	18.9684			1.68317			0.841587	+	0.540121i	$0.181622\pi$
$128$		0			0
$129$	4.65490	−	4.69360i	0.409841	−	0.413249i
$130$		0			0
$131$	2.44116	+	4.22821i	0.213285	+	0.369420i	0.952741	−	0.303785i	$-0.0982504\pi$
$131$	2.44116	+	4.22821i	0.213285	+	0.369420i	−0.739456	+	0.673205i	$0.764917\pi$
$132$		0			0
$133$	2.64075	+	11.2304i	0.228982	+	0.973797i
$134$		0			0
$135$	−0.617346	+	2.42398i	−0.0531326	+	0.208623i
$136$		0			0
$137$	3.23741	−	5.60736i	0.276591	−	0.479069i	−0.693945	−	0.720028i	$-0.744129\pi$
$137$	3.23741	−	5.60736i	0.276591	−	0.479069i	0.970535	+	0.240959i	$0.0774621\pi$
$138$		0			0
$139$	−11.3740	+	19.7003i	−0.964727	+	1.67096i	−0.254381	+	0.967104i	$0.581872\pi$
$139$	−11.3740	+	19.7003i	−0.964727	+	1.67096i	−0.710346	+	0.703852i	$0.751462\pi$
$140$		0			0
$141$	1.71416	+	6.29300i	0.144358	+	0.529967i
$142$		0			0
$143$	−9.67362	−	16.7552i	−0.808948	−	1.40114i
$144$		0			0
$145$	−0.737155	+	1.27679i	−0.0612174	+	0.106032i
$146$		0			0
$147$	−11.8724	+	2.45905i	−0.979216	+	0.202819i
$148$		0			0
$149$	7.10230	+	12.3016i	0.581843	+	1.00778i	0.995261	+	0.0972407i	$0.0310017\pi$
$149$	7.10230	+	12.3016i	0.581843	+	1.00778i	−0.413418	+	0.910542i	$0.635665\pi$
$150$		0			0
$151$	−1.26129	+	2.18462i	−0.102643	+	0.177782i	−0.912773	−	0.408468i	$-0.866063\pi$
$151$	−1.26129	+	2.18462i	−0.102643	+	0.177782i	0.810130	+	0.586250i	$0.199396\pi$
$152$		0			0
$153$	−14.3888	−	8.14930i	−1.16327	−	0.658832i
$154$		0			0
$155$	−2.25029	−	3.89761i	−0.180747	−	0.313064i
$156$		0			0
$157$	17.4813			1.39516			0.697579	−	0.716508i	$-0.254261\pi$
$157$	17.4813			1.39516			0.697579	+	0.716508i	$0.254261\pi$
$158$		0			0
$159$	13.6080	−	13.7212i	1.07919	−	1.08816i
$160$		0			0
$161$	9.18523	+	2.76753i	0.723897	+	0.218112i
$162$		0			0
$163$	0.881184	−	1.52625i	0.0690196	−	0.119546i	−0.829450	−	0.558580i	$-0.811346\pi$
$163$	0.881184	−	1.52625i	0.0690196	−	0.119546i	0.898470	+	0.439035i	$0.144680\pi$
$164$		0			0
$165$	0.741015	+	2.72041i	0.0576879	+	0.211784i
$166$		0			0
$167$	−3.57220	+	6.18723i	−0.276425	+	0.478782i	−0.970494	−	0.241127i	$-0.922483\pi$
$167$	−3.57220	+	6.18723i	−0.276425	+	0.478782i	0.694069	+	0.719909i	$0.255816\pi$
$168$		0			0
$169$	−9.86684	−	17.0899i	−0.758988	−	1.31461i
$170$		0			0
$171$	0.108300	+	13.0809i	0.00828193	+	1.00032i
$172$		0			0
$173$	9.89382			0.752213			0.376107	−	0.926576i	$-0.377263\pi$
$173$	9.89382			0.752213			0.376107	+	0.926576i	$0.377263\pi$
$174$		0			0
$175$	2.88773	+	12.2807i	0.218292	+	0.928334i
$176$		0			0
$177$	−3.83415	−	14.0759i	−0.288192	−	1.05801i
$178$		0			0
$179$	2.02967	+	3.51550i	0.151705	+	0.262761i	0.931854	−	0.362833i	$-0.118190\pi$
$179$	2.02967	+	3.51550i	0.151705	+	0.262761i	−0.780149	+	0.625593i	$0.784857\pi$
$180$		0			0
$181$	4.58084			0.340491			0.170246	−	0.985402i	$-0.445544\pi$
$181$	4.58084			0.340491			0.170246	+	0.985402i	$0.445544\pi$
$182$		0			0
$183$	3.31677	+	12.1765i	0.245183	+	0.900113i
$184$		0			0
$185$	1.43022			0.105152
$186$		0			0
$187$	−18.6397			−1.36307
$188$		0			0
$189$	−13.7454	−	0.253396i	−0.999830	−	0.0184319i
$190$		0			0
$191$	11.1925			0.809860			0.404930	−	0.914348i	$-0.367296\pi$
$191$	11.1925			0.809860			0.404930	+	0.914348i	$0.367296\pi$
$192$		0			0
$193$	16.2936			1.17284			0.586419	−	0.810008i	$-0.300537\pi$
$193$	16.2936			1.17284			0.586419	+	0.810008i	$0.300537\pi$
$194$		0			0
$195$	1.25373	+	4.60268i	0.0897813	+	0.329605i
$196$		0			0
$197$	−3.17438			−0.226165			−0.113082	−	0.993586i	$-0.536072\pi$
$197$	−3.17438			−0.226165			−0.113082	+	0.993586i	$0.536072\pi$
$198$		0			0
$199$	1.44140	+	2.49658i	0.102178	+	0.176978i	0.912582	−	0.408894i	$-0.134085\pi$
$199$	1.44140	+	2.49658i	0.102178	+	0.176978i	−0.810404	+	0.585872i	$0.800752\pi$
$200$		0			0
$201$	−1.17054	−	4.29727i	−0.0825633	−	0.303106i
$202$		0			0
$203$	−7.75844	−	2.33763i	−0.544536	−	0.164070i
$204$		0			0
$205$	−6.06122			−0.423334
$206$		0			0
$207$	9.46494	+	5.36060i	0.657859	+	0.372587i
$208$		0			0
$209$	7.37264	+	12.7698i	0.509976	+	0.883305i
$210$		0			0
$211$	−0.242718	+	0.420400i	−0.0167094	+	0.0289415i	−0.874259	−	0.485459i	$-0.838652\pi$
$211$	−0.242718	+	0.420400i	−0.0167094	+	0.0289415i	0.857550	+	0.514401i	$0.171986\pi$
$212$		0			0
$213$	1.79491	+	6.58946i	0.122985	+	0.451503i
$214$		0			0
$215$	−0.918617	+	1.59109i	−0.0626492	+	0.108512i
$216$		0			0
$217$	18.0219	−	16.9429i	1.22341	−	1.15016i
$218$		0			0
$219$	−2.10323	+	2.12071i	−0.142123	+	0.143305i
$220$		0			0
$221$	−31.5366			−2.12138
$222$		0			0
$223$	2.14795	+	3.72037i	0.143838	+	0.249134i	0.928939	−	0.370234i	$-0.120722\pi$
$223$	2.14795	+	3.72037i	0.143838	+	0.249134i	−0.785101	+	0.619368i	$0.787389\pi$
$224$		0			0
$225$	0.118429	+	14.3043i	0.00789527	+	0.953621i
$226$		0			0
$227$	8.69137	−	15.0539i	0.576866	−	0.999162i	−0.418970	−	0.908000i	$-0.637609\pi$
$227$	8.69137	−	15.0539i	0.576866	−	0.999162i	0.995836	−	0.0911616i	$-0.0290580\pi$
$228$		0			0
$229$	−3.66563	−	6.34905i	−0.242231	−	0.419557i	0.719118	−	0.694888i	$-0.244546\pi$
$229$	−3.66563	−	6.34905i	−0.242231	−	0.419557i	−0.961350	+	0.275331i	$0.911213\pi$
$230$		0			0
$231$	−13.6224	+	7.38700i	−0.896291	+	0.486029i
$232$		0			0
$233$	−2.16624	+	3.75205i	−0.141915	+	0.245805i	−0.928218	−	0.372037i	$-0.878659\pi$
$233$	−2.16624	+	3.75205i	−0.141915	+	0.245805i	0.786302	+	0.617842i	$0.211993\pi$
$234$		0			0
$235$	−0.906366	−	1.56987i	−0.0591248	−	0.102407i
$236$		0			0
$237$	2.54899	+	9.35784i	0.165575	+	0.607857i
$238$		0			0
$239$	1.77960	−	3.08236i	0.115113	−	0.199381i	−0.802712	−	0.596367i	$-0.796610\pi$
$239$	1.77960	−	3.08236i	0.115113	−	0.199381i	0.917825	+	0.396986i	$0.129944\pi$
$240$		0			0
$241$	−8.00925	+	13.8724i	−0.515921	+	0.893602i	0.483908	+	0.875119i	$0.339217\pi$
$241$	−8.00925	+	13.8724i	−0.515921	+	0.893602i	−0.999829	+	0.0184829i	$0.994116\pi$
$242$		0			0
$243$	−15.1376	−	3.72210i	−0.971076	−	0.238773i
$244$		0			0
$245$	3.01659	−	1.50170i	0.192723	−	0.0959399i
$246$		0			0
$247$	12.4738	+	21.6053i	0.793689	+	1.37471i
$248$		0			0
$249$	−0.291486	+	0.293909i	−0.0184722	+	0.0186257i
$250$		0			0
$251$	−12.8007			−0.807972			−0.403986	−	0.914765i	$-0.632375\pi$
$251$	−12.8007			−0.807972			−0.403986	+	0.914765i	$0.632375\pi$
$252$		0			0
$253$	12.2612			0.770852
$254$		0			0
$255$	4.44420	+	1.17112i	0.278307	+	0.0733386i
$256$		0			0
$257$	−8.20769	−	14.2161i	−0.511981	−	0.886778i	−0.999904	−	0.0138906i	$-0.995578\pi$
$257$	−8.20769	−	14.2161i	−0.511981	−	0.886778i	0.487922	−	0.872887i	$-0.337755\pi$
$258$		0			0
$259$	1.79930	+	7.65192i	0.111803	+	0.475467i
$260$		0			0
$261$	−7.99470	−	4.52791i	−0.494860	−	0.280271i
$262$		0			0
$263$	−12.8264	+	22.2160i	−0.790910	+	1.36990i	0.134494	+	0.990914i	$0.457059\pi$
$263$	−12.8264	+	22.2160i	−0.790910	+	1.36990i	−0.925404	+	0.378982i	$0.876274\pi$
$264$		0			0
$265$	−2.68547	+	4.65136i	−0.164967	+	0.285731i
$266$		0			0
$267$	−2.17103	−	0.572103i	−0.132865	−	0.0350121i
$268$		0			0
$269$	5.35397	+	9.27335i	0.326437	+	0.565406i	0.981802	−	0.189906i	$-0.0608184\pi$
$269$	5.35397	+	9.27335i	0.326437	+	0.565406i	−0.655365	+	0.755313i	$0.727485\pi$
$270$		0			0
$271$	−12.7513	+	22.0859i	−0.774587	+	1.34162i	0.160439	+	0.987046i	$0.448709\pi$
$271$	−12.7513	+	22.0859i	−0.774587	+	1.34162i	−0.935026	+	0.354578i	$0.884624\pi$
$272$		0			0
$273$	−23.0479	+	12.4981i	−1.39492	+	0.756420i
$274$		0			0
$275$	8.06217	+	13.9641i	0.486167	+	0.842066i
$276$		0			0
$277$	6.39123	−	11.0699i	0.384012	−	0.665128i	−0.607620	−	0.794228i	$-0.707876\pi$
$277$	6.39123	−	11.0699i	0.384012	−	0.665128i	0.991632	+	0.129100i	$0.0412089\pi$
$278$		0			0
$279$	24.1729	−	14.2244i	1.44720	−	0.851591i
$280$		0			0
$281$	−10.4763	−	18.1454i	−0.624961	−	1.08246i	−0.988548	−	0.150904i	$-0.951781\pi$
$281$	−10.4763	−	18.1454i	−0.624961	−	1.08246i	0.363587	−	0.931560i	$-0.381552\pi$
$282$		0			0
$283$	15.0617			0.895325			0.447663	−	0.894203i	$-0.352257\pi$
$283$	15.0617			0.895325			0.447663	+	0.894203i	$0.352257\pi$
$284$		0			0
$285$	−0.955514	−	3.50788i	−0.0565998	−	0.207789i
$286$		0			0
$287$	−7.62537	−	32.4286i	−0.450112	−	1.91420i
$288$		0			0
$289$	−6.69162	+	11.5902i	−0.393625	+	0.681778i
$290$		0			0
$291$	−17.1404	+	17.2829i	−1.00479	+	1.01314i
$292$		0			0
$293$	0.134459	−	0.232890i	0.00785519	−	0.0136056i	−0.862071	−	0.506787i	$-0.830833\pi$
$293$	0.134459	−	0.232890i	0.00785519	−	0.0136056i	0.869926	+	0.493182i	$0.164166\pi$
$294$		0			0
$295$	2.02732	+	3.51142i	0.118035	+	0.204443i
$296$		0			0
$297$	−16.9148	+	4.75820i	−0.981494	+	0.276099i
$298$		0			0
$299$	20.7447			1.19970
$300$		0			0
$301$	−9.66830	−	2.91308i	−0.557272	−	0.167907i
$302$		0			0
$303$	17.7645	+	4.68124i	1.02054	+	0.268930i
$304$		0			0
$305$	−1.75375	−	3.03759i	−0.100420	−	0.173932i
$306$		0			0
$307$	−5.03514			−0.287371			−0.143685	−	0.989623i	$-0.545895\pi$
$307$	−5.03514			−0.287371			−0.143685	+	0.989623i	$0.545895\pi$
$308$		0			0
$309$	0.194434	−	0.196050i	0.0110609	−	0.0111529i
$310$		0			0
$311$	4.47630			0.253828			0.126914	−	0.991914i	$-0.459493\pi$
$311$	4.47630			0.253828			0.126914	+	0.991914i	$0.459493\pi$
$312$		0			0
$313$	10.9779			0.620508			0.310254	−	0.950654i	$-0.399586\pi$
$313$	10.9779			0.620508			0.310254	+	0.950654i	$0.399586\pi$
$314$		0			0
$315$	3.71208	−	0.905366i	0.209152	−	0.0510116i
$316$		0			0
$317$	24.9652			1.40218			0.701092	−	0.713071i	$-0.252696\pi$
$317$	24.9652			1.40218			0.701092	+	0.713071i	$0.252696\pi$
$318$		0			0
$319$	−10.3566			−0.579856
$320$		0			0
$321$	13.3665	+	3.52230i	0.746045	+	0.196596i
$322$		0			0
$323$	24.0352			1.33736
$324$		0			0
$325$	13.6404	+	23.6259i	0.756635	+	1.31053i
$326$		0			0
$327$	−16.7243	+	16.8634i	−0.924857	+	0.932546i
$328$		0			0
$329$	7.25883	−	6.82421i	0.400193	−	0.376231i
$330$		0			0
$331$	12.0241			0.660905			0.330453	−	0.943823i	$-0.392799\pi$
$331$	12.0241			0.660905			0.330453	+	0.943823i	$0.392799\pi$
$332$		0			0
$333$	0.0737914	+	8.91280i	0.00404374	+	0.488419i
$334$		0			0
$335$	0.618925	+	1.07201i	0.0338155	+	0.0585702i
$336$		0			0
$337$	−14.1286	+	24.4715i	−0.769636	+	1.33305i	0.168125	+	0.985766i	$0.446229\pi$
$337$	−14.1286	+	24.4715i	−0.769636	+	1.33305i	−0.937761	+	0.347282i	$0.887105\pi$
$338$		0			0
$339$	−30.1027	−	7.93258i	−1.63495	−	0.430839i
$340$		0			0
$341$	15.8076	−	27.3795i	0.856027	−	1.48268i
$342$		0			0
$343$	11.8294	+	14.2501i	0.638728	+	0.769433i
$344$		0			0
$345$	−2.92339	−	0.770363i	−0.157390	−	0.0414750i
$346$		0			0
$347$	19.6059			1.05250			0.526249	−	0.850331i	$-0.323598\pi$
$347$	19.6059			1.05250			0.526249	+	0.850331i	$0.323598\pi$
$348$		0			0
$349$	−8.22904	−	14.2531i	−0.440490	−	0.762952i	0.557236	−	0.830354i	$-0.311862\pi$
$349$	−8.22904	−	14.2531i	−0.440490	−	0.762952i	−0.997726	+	0.0674029i	$0.978529\pi$
$350$		0			0
$351$	−28.6182	+	8.05042i	−1.52753	+	0.429700i
$352$		0			0
$353$	13.6854	−	23.7039i	0.728402	−	1.26163i	−0.229156	−	0.973390i	$-0.573597\pi$
$353$	13.6854	−	23.7039i	0.728402	−	1.26163i	0.957558	−	0.288240i	$-0.0930700\pi$
$354$		0			0
$355$	−0.949065	−	1.64383i	−0.0503711	−	0.0872453i
$356$		0			0
$357$	−0.674654	+	25.2506i	−0.0357065	+	1.33640i
$358$		0			0
$359$	7.88714	−	13.6609i	0.416267	−	0.720996i	−0.579293	−	0.815119i	$-0.696671\pi$
$359$	7.88714	−	13.6609i	0.416267	−	0.720996i	0.995561	+	0.0941231i	$0.0300047\pi$
$360$		0			0
$361$	−0.00677168	−	0.0117289i	−0.000356404	−	0.000617310i
$362$		0			0
$363$	−0.530769	+	0.535182i	−0.0278582	+	0.0280898i
$364$		0			0
$365$	0.415060	−	0.718905i	0.0217252	−	0.0376292i
$366$		0			0
$367$	−9.40684	+	16.2931i	−0.491033	+	0.850494i	−0.999947	−	0.0103233i	$-0.996714\pi$
$367$	−9.40684	+	16.2931i	−0.491033	+	0.850494i	0.508914	+	0.860818i	$0.330047\pi$
$368$		0			0
$369$	−0.312726	−	37.7722i	−0.0162798	−	1.96634i
$370$		0			0
$371$	−28.2641	−	8.51603i	−1.46740	−	0.442130i
$372$		0			0
$373$	8.78687	+	15.2193i	0.454967	+	0.788026i	0.998686	−	0.0512414i	$-0.0163178\pi$
$373$	8.78687	+	15.2193i	0.454967	+	0.788026i	−0.543719	+	0.839267i	$0.682984\pi$
$374$		0			0
$375$	−2.14054	−	7.85834i	−0.110537	−	0.405803i
$376$		0			0
$377$	−17.5223			−0.902446
$378$		0			0
$379$	34.4618			1.77018			0.885091	−	0.465419i	$-0.154096\pi$
$379$	34.4618			1.77018			0.885091	+	0.465419i	$0.154096\pi$
$380$		0			0
$381$	−8.63460	−	31.6993i	−0.442364	−	1.62400i
$382$		0			0
$383$	11.3705	+	19.6943i	0.581005	+	1.00633i	0.995361	+	0.0962145i	$0.0306735\pi$
$383$	11.3705	+	19.6943i	0.581005	+	1.00633i	−0.414356	+	0.910115i	$0.635993\pi$
$384$		0			0
$385$	3.13793	−	2.95005i	0.159924	−	0.150348i
$386$		0			0
$387$	−9.96273	−	5.64253i	−0.506434	−	0.286826i
$388$		0			0
$389$	−7.88189	+	13.6518i	−0.399628	+	0.692175i	−0.993680	−	0.112251i	$-0.964194\pi$
$389$	−7.88189	+	13.6518i	−0.399628	+	0.692175i	0.594052	+	0.804426i	$0.297527\pi$
$390$		0			0
$391$	9.99303	−	17.3084i	0.505369	−	0.875325i
$392$		0			0
$393$	5.95479	−	6.00429i	0.300379	−	0.302877i
$394$		0			0
$395$	−1.34779	−	2.33444i	−0.0678145	−	0.117458i
$396$		0			0
$397$	−5.39875	+	9.35091i	−0.270955	+	0.469308i	−0.969107	−	0.246642i	$-0.920673\pi$
$397$	−5.39875	+	9.35091i	−0.270955	+	0.469308i	0.698151	+	0.715950i	$0.254006\pi$
$398$		0			0
$399$	17.5657	−	9.52529i	0.879384	−	0.476861i
$400$		0			0
$401$	−6.16473	−	10.6776i	−0.307852	−	0.533215i	0.670040	−	0.742325i	$-0.266277\pi$
$401$	−6.16473	−	10.6776i	−0.307852	−	0.533215i	−0.977892	+	0.209110i	$0.932943\pi$
$402$		0			0
$403$	26.7449	−	46.3235i	1.33226	−	2.30754i
$404$		0			0
$405$	4.33189	−	0.0717346i	0.215253	−	0.00356452i
$406$		0			0
$407$	5.02342	+	8.70082i	0.249002	+	0.431284i
$408$		0			0
$409$	18.6354			0.921462			0.460731	−	0.887540i	$-0.347587\pi$
$409$	18.6354			0.921462			0.460731	+	0.887540i	$0.347587\pi$
$410$		0			0
$411$	−10.8445	−	2.85772i	−0.534920	−	0.140961i
$412$		0			0
$413$	−16.2362	+	15.2641i	−0.798932	+	0.751096i
$414$		0			0
$415$	0.0575230	−	0.0996328i	0.00282369	−	0.00489078i
$416$		0			0
$417$	38.0999	+	10.0400i	1.86576	+	0.491660i
$418$		0			0
$419$	−5.90976	+	10.2360i	−0.288711	+	0.500062i	−0.973502	−	0.228677i	$-0.926560\pi$
$419$	−5.90976	+	10.2360i	−0.288711	+	0.500062i	0.684791	+	0.728739i	$0.259893\pi$
$420$		0			0
$421$	4.81800	+	8.34503i	0.234815	+	0.406712i	0.959219	−	0.282664i	$-0.0912182\pi$
$421$	4.81800	+	8.34503i	0.234815	+	0.406712i	−0.724404	+	0.689376i	$0.757885\pi$
$422$		0			0
$423$	9.73633	−	5.72927i	0.473397	−	0.278567i
$424$		0			0
$425$	26.2832			1.27492
$426$		0			0
$427$	14.0453	−	13.2044i	0.679700	−	0.639003i
$428$		0			0
$429$	−23.5971	+	23.7933i	−1.13928	+	1.14875i
$430$		0			0
$431$	−18.2913	−	31.6815i	−0.881062	−	1.52604i	−0.850162	−	0.526522i	$-0.823496\pi$
$431$	−18.2913	−	31.6815i	−0.881062	−	1.52604i	−0.0309004	−	0.999522i	$-0.509837\pi$
$432$		0			0
$433$	−7.69388			−0.369744			−0.184872	−	0.982763i	$-0.559187\pi$
$433$	−7.69388			−0.369744			−0.184872	+	0.982763i	$0.559187\pi$
$434$		0			0
$435$	2.46928	+	0.650699i	0.118393	+	0.0311986i
$436$		0			0
$437$	−15.8104			−0.756312
$438$		0			0
$439$	−20.5434			−0.980482			−0.490241	−	0.871587i	$-0.663091\pi$
$439$	−20.5434			−0.980482			−0.490241	+	0.871587i	$0.663091\pi$
$440$		0			0
$441$	9.51388	+	18.7213i	0.453042	+	0.891489i
$442$		0			0
$443$	−33.6802			−1.60020			−0.800098	−	0.599870i	$-0.795219\pi$
$443$	−33.6802			−1.60020			−0.800098	+	0.599870i	$0.795219\pi$
$444$		0			0
$445$	0.623990			0.0295799
$446$		0			0
$447$	17.3249	−	17.4689i	0.819438	−	0.826250i
$448$		0			0
$449$	−22.5141			−1.06250			−0.531252	−	0.847214i	$-0.678278\pi$
$449$	−22.5141			−1.06250			−0.531252	+	0.847214i	$0.678278\pi$
$450$		0			0
$451$	−21.2891	−	36.8738i	−1.00246	−	1.73632i
$452$		0			0
$453$	4.22501	+	1.11336i	0.198508	+	0.0523104i
$454$		0			0
$455$	5.30908	−	4.99120i	0.248894	−	0.233991i
$456$		0			0
$457$	−23.7117			−1.10919			−0.554594	−	0.832121i	$-0.687126\pi$
$457$	−23.7117			−1.10919			−0.554594	+	0.832121i	$0.687126\pi$
$458$		0			0
$459$	−7.06889	+	27.7557i	−0.329947	+	1.29552i
$460$		0			0
$461$	−5.57340	−	9.65342i	−0.259579	−	0.449605i	0.706550	−	0.707663i	$-0.250251\pi$
$461$	−5.57340	−	9.65342i	−0.259579	−	0.449605i	−0.966129	+	0.258059i	$0.916917\pi$
$462$		0			0
$463$	10.3208	−	17.8761i	0.479647	−	0.830773i	−0.520080	−	0.854117i	$-0.674098\pi$
$463$	10.3208	−	17.8761i	0.479647	−	0.830773i	0.999727	+	0.0233441i	$0.00743133\pi$
$464$		0			0
$465$	−5.48919	+	5.53482i	−0.254555	+	0.256671i
$466$		0			0
$467$	−8.68477	+	15.0425i	−0.401883	+	0.696082i	−0.993953	−	0.109804i	$-0.964978\pi$
$467$	−8.68477	+	15.0425i	−0.401883	+	0.696082i	0.592070	+	0.805887i	$0.298311\pi$
$468$		0			0
$469$	−4.95680	+	4.66001i	−0.228884	+	0.215179i
$470$		0			0
$471$	−7.95764	−	29.2141i	−0.366669	−	1.34611i
$472$		0			0
$473$	−12.9060			−0.593419
$474$		0			0
$475$	−10.3959	−	18.0062i	−0.476997	−	0.826182i
$476$		0			0
$477$	−29.1248	−	16.4952i	−1.33353	−	0.755266i
$478$		0			0
$479$	2.04517	−	3.54233i	0.0934461	−	0.161853i	−0.815513	−	0.578739i	$-0.803545\pi$
$479$	2.04517	−	3.54233i	0.0934461	−	0.161853i	0.908959	+	0.416886i	$0.136878\pi$
$480$		0			0
$481$	8.49915	+	14.7210i	0.387528	+	0.671218i
$482$		0			0
$483$	0.443787	−	16.6098i	0.0201930	−	0.755772i
$484$		0			0
$485$	3.38256	−	5.85876i	0.153594	−	0.266033i
$486$		0			0
$487$	−0.843065	−	1.46023i	−0.0382029	−	0.0661694i	0.846292	−	0.532720i	$-0.178830\pi$
$487$	−0.843065	−	1.46023i	−0.0382029	−	0.0661694i	−0.884495	+	0.466550i	$0.845497\pi$
$488$		0			0
$489$	−2.95174	−	0.777835i	−0.133482	−	0.0351749i
$490$		0			0
$491$	6.85070	−	11.8658i	0.309168	−	0.535494i	−0.669013	−	0.743251i	$-0.733283\pi$
$491$	6.85070	−	11.8658i	0.309168	−	0.535494i	0.978181	+	0.207757i	$0.0666162\pi$
$492$		0			0
$493$	−8.44076	+	14.6198i	−0.380153	+	0.658444i
$494$		0			0
$495$	4.20893	−	2.47671i	0.189177	−	0.111320i
$496$		0			0
$497$	7.60079	−	7.14570i	0.340942	−	0.320528i
$498$		0			0
$499$	3.27827	+	5.67813i	0.146756	+	0.254188i	0.930027	−	0.367492i	$-0.119784\pi$
$499$	3.27827	+	5.67813i	0.146756	+	0.254188i	−0.783271	+	0.621680i	$0.786450\pi$
$500$		0			0
$501$	11.9660	+	3.15324i	0.534600	+	0.140876i
$502$		0			0
$503$	26.8584			1.19756			0.598779	−	0.800914i	$-0.295653\pi$
$503$	26.8584			1.19756			0.598779	+	0.800914i	$0.295653\pi$
$504$		0			0
$505$	−5.10580			−0.227205
$506$		0			0
$507$	−24.0685	+	24.2686i	−1.06892	+	1.07780i
$508$		0			0
$509$	19.8669	+	34.4104i	0.880584	+	1.52522i	0.850693	+	0.525662i	$0.176183\pi$
$509$	19.8669	+	34.4104i	0.880584	+	1.52522i	0.0298904	+	0.999553i	$0.490484\pi$
$510$		0			0
$511$	4.36844	+	1.31622i	0.193248	+	0.0582261i
$512$		0			0
$513$	21.8110	−	6.13554i	0.962980	−	0.270891i
$514$		0			0
$515$	−0.0383703	+	0.0664593i	−0.00169080	+	0.00292855i
$516$		0			0
$517$	6.36694	−	11.0279i	0.280018	−	0.485005i
$518$		0			0
$519$	−4.50376	−	16.5342i	−0.197693	−	0.725770i
$520$		0			0
$521$	11.7585	+	20.3663i	0.515148	+	0.892262i	0.999845	+	0.0175802i	$0.00559623\pi$
$521$	11.7585	+	20.3663i	0.515148	+	0.892262i	−0.484698	+	0.874682i	$0.661070\pi$
$522$		0			0
$523$	−10.9289	+	18.9294i	−0.477887	+	0.827725i	−0.999679	−	0.0253481i	$-0.991931\pi$
$523$	−10.9289	+	18.9294i	−0.477887	+	0.827725i	0.521791	+	0.853073i	$0.325264\pi$
$524$		0			0
$525$	19.2085	−	10.4162i	0.838329	−	0.454598i
$526$		0			0
$527$	−25.7668	−	44.6294i	−1.12242	−	1.94409i
$528$		0			0
$529$	4.92660	−	8.53312i	0.214200	−	0.371005i
$530$		0			0
$531$	−21.7778	+	12.8150i	−0.945075	+	0.556122i
$532$		0			0
$533$	−36.0191	−	62.3869i	−1.56016	−	2.70228i
$534$		0			0
$535$	−3.84175			−0.166094
$536$		0			0
$537$	4.95104	−	4.99220i	0.213653	−	0.215429i
$538$		0			0
$539$	19.7310	+	13.0772i	0.849874	+	0.563273i
$540$		0			0
$541$	14.0063	−	24.2596i	0.602178	−	1.04300i	−0.390313	−	0.920682i	$-0.627633\pi$
$541$	14.0063	−	24.2596i	0.602178	−	1.04300i	0.992491	−	0.122320i	$-0.0390334\pi$
$542$		0			0
$543$	−2.08524	−	7.65533i	−0.0894863	−	0.328522i
$544$		0			0
$545$	3.30045	−	5.71654i	0.141376	−	0.244870i
$546$		0			0
$547$	−2.02714	−	3.51112i	−0.0866744	−	0.150124i	0.819429	−	0.573181i	$-0.194291\pi$
$547$	−2.02714	−	3.51112i	−0.0866744	−	0.150124i	−0.906103	+	0.423056i	$0.860957\pi$
$548$		0			0
$549$	18.8391	−	11.0857i	0.804033	−	0.473127i
$550$		0			0
$551$	13.3544			0.568919
$552$		0			0
$553$	10.7941	−	10.1478i	0.459010	−	0.431527i
$554$		0			0
$555$	−0.651049	−	2.39013i	−0.0276355	−	0.101455i
$556$		0			0
$557$	−0.926620	−	1.60495i	−0.0392621	−	0.0680040i	0.845727	−	0.533616i	$-0.179167\pi$
$557$	−0.926620	−	1.60495i	−0.0392621	−	0.0680040i	−0.884989	+	0.465612i	$0.845834\pi$
$558$		0			0
$559$	−21.8357			−0.923553
$560$		0			0
$561$	8.48496	+	31.1499i	0.358235	+	1.31515i
$562$		0			0
$563$	44.4662			1.87403			0.937013	−	0.349295i	$-0.113579\pi$
$563$	44.4662			1.87403			0.937013	+	0.349295i	$0.113579\pi$
$564$		0			0
$565$	8.65202			0.363993
$566$		0			0
$567$	5.83357	+	23.0861i	0.244987	+	0.969526i
$568$		0			0
$569$	15.2623			0.639830			0.319915	−	0.947446i	$-0.396346\pi$
$569$	15.2623			0.639830			0.319915	+	0.947446i	$0.396346\pi$
$570$		0			0
$571$	−25.5267			−1.06826			−0.534130	−	0.845402i	$-0.679361\pi$
$571$	−25.5267			−1.06826			−0.534130	+	0.845402i	$0.679361\pi$
$572$		0			0
$573$	−5.09493	−	18.7045i	−0.212844	−	0.781390i
$574$		0			0
$575$	−17.2890			−0.721002
$576$		0			0
$577$	−3.26981	−	5.66348i	−0.136124	−	0.235774i	0.789902	−	0.613233i	$-0.210131\pi$
$577$	−3.26981	−	5.66348i	−0.136124	−	0.235774i	−0.926026	+	0.377459i	$0.876798\pi$
$578$		0			0
$579$	−7.41699	−	27.2292i	−0.308240	−	1.13161i
$580$		0			0
$581$	0.605420	+	0.182414i	0.0251171	+	0.00756783i
$582$		0			0
$583$	−37.7291			−1.56258
$584$		0			0
$585$	7.12111	−	4.19036i	0.294422	−	0.173250i
$586$		0			0
$587$	15.2055	+	26.3366i	0.627597	+	1.08703i	0.988033	+	0.154245i	$0.0492947\pi$
$587$	15.2055	+	26.3366i	0.627597	+	1.08703i	−0.360436	+	0.932784i	$0.617372\pi$
$588$		0			0
$589$	−20.3833	+	35.3049i	−0.839880	+	1.45471i
$590$		0			0
$591$	1.44501	+	5.30490i	0.0594396	+	0.218214i
$592$		0			0
$593$	−21.3291	+	36.9432i	−0.875883	+	1.51707i	−0.0200633	+	0.999799i	$0.506387\pi$
$593$	−21.3291	+	36.9432i	−0.875883	+	1.51707i	−0.855819	+	0.517275i	$0.826947\pi$
$594$		0			0
$595$	−1.60697	−	6.83399i	−0.0658792	−	0.280166i
$596$		0			0
$597$	3.51605	−	3.54528i	0.143902	−	0.145099i
$598$		0			0
$599$	−44.5574			−1.82057			−0.910284	−	0.413985i	$-0.864137\pi$
$599$	−44.5574			−1.82057			−0.910284	+	0.413985i	$0.864137\pi$
$600$		0			0
$601$	14.1961	+	24.5884i	0.579071	+	1.00298i	0.995586	+	0.0938518i	$0.0299180\pi$
$601$	14.1961	+	24.5884i	0.579071	+	1.00298i	−0.416515	+	0.909129i	$0.636749\pi$
$602$		0			0
$603$	−6.64860	+	3.91232i	−0.270752	+	0.159322i
$604$		0			0
$605$	0.104744	−	0.181422i	0.00425845	−	0.00737586i
$606$		0			0
$607$	−7.01391	−	12.1484i	−0.284686	−	0.493090i	0.687847	−	0.725856i	$-0.258556\pi$
$607$	−7.01391	−	12.1484i	−0.284686	−	0.493090i	−0.972533	+	0.232765i	$0.925223\pi$
$608$		0			0
$609$	−0.374851	+	14.0297i	−0.0151897	+	0.568513i
$610$		0			0
$611$	10.7723	−	18.6581i	0.435799	−	0.754826i
$612$		0			0
$613$	−9.97062	−	17.2696i	−0.402709	−	0.697513i	0.591342	−	0.806421i	$-0.298598\pi$
$613$	−9.97062	−	17.2696i	−0.402709	−	0.697513i	−0.994052	+	0.108907i	$0.965265\pi$
$614$		0			0
$615$	2.75912	+	10.1293i	0.111259	+	0.408452i
$616$		0			0
$617$	−1.51584	+	2.62551i	−0.0610254	+	0.105699i	−0.894924	−	0.446219i	$-0.852770\pi$
$617$	−1.51584	+	2.62551i	−0.0610254	+	0.105699i	0.833899	+	0.551918i	$0.186104\pi$
$618$		0			0
$619$	−1.27715	+	2.21209i	−0.0513331	+	0.0889116i	−0.890550	−	0.454885i	$-0.849680\pi$
$619$	−1.27715	+	2.21209i	−0.0513331	+	0.0889116i	0.839217	+	0.543797i	$0.183014\pi$
$620$		0			0
$621$	4.64990	−	18.2577i	0.186594	−	0.732654i
$622$		0			0
$623$	0.785016	+	3.33846i	0.0314510	+	0.133752i
$624$		0			0
$625$	−10.7888	−	18.6868i	−0.431554	−	0.747473i
$626$		0			0
$627$	17.9843	−	18.1338i	0.718223	−	0.724194i
$628$		0			0
$629$	16.3766			0.652980
$630$		0			0
$631$	37.1162			1.47757			0.738786	−	0.673941i	$-0.235400\pi$
$631$	37.1162			1.47757			0.738786	+	0.673941i	$0.235400\pi$
$632$		0			0
$633$	0.813044	+	0.214251i	0.0323156	+	0.00851572i
$634$		0			0
$635$	4.56557	+	7.90780i	0.181179	+	0.313812i
$636$		0			0
$637$	33.3830	+	22.1253i	1.32268	+	0.876636i
$638$		0			0
$639$	10.1950	−	5.99917i	0.403308	−	0.237324i
$640$		0			0
$641$	−10.5484	+	18.2704i	−0.416638	+	0.721638i	−0.995599	−	0.0937176i	$-0.970125\pi$
$641$	−10.5484	+	18.2704i	−0.416638	+	0.721638i	0.578961	+	0.815355i	$0.303458\pi$
$642$		0			0
$643$	9.31948	−	16.1418i	0.367524	−	0.636571i	−0.621654	−	0.783292i	$-0.713539\pi$
$643$	9.31948	−	16.1418i	0.367524	−	0.636571i	0.989178	+	0.146722i	$0.0468722\pi$
$644$		0			0
$645$	3.07714	+	0.810879i	0.121162	+	0.0319283i
$646$		0			0
$647$	4.78509	+	8.28801i	0.188121	+	0.325835i	0.944624	−	0.328155i	$-0.106427\pi$
$647$	4.78509	+	8.28801i	0.188121	+	0.325835i	−0.756503	+	0.653991i	$0.773094\pi$
$648$		0			0
$649$	−14.2413	+	24.6666i	−0.559019	+	0.968249i
$650$		0			0
$651$	−36.5180	−	22.4050i	−1.43125	−	0.878121i
$652$		0			0
$653$	16.4280	+	28.4541i	0.642877	+	1.11350i	0.984788	+	0.173763i	$0.0555926\pi$
$653$	16.4280	+	28.4541i	0.642877	+	1.11350i	−0.341911	+	0.939732i	$0.611074\pi$
$654$		0			0
$655$	−1.17514	+	2.03541i	−0.0459166	+	0.0795299i
$656$		0			0
$657$	4.50147	+	2.54947i	0.175619	+	0.0994642i
$658$		0			0
$659$	24.8011	+	42.9568i	0.966114	+	1.67336i	0.706593	+	0.707620i	$0.250231\pi$
$659$	24.8011	+	42.9568i	0.966114	+	1.67336i	0.259521	+	0.965738i	$0.416435\pi$
$660$		0			0
$661$	−3.31789			−0.129051			−0.0645255	−	0.997916i	$-0.520553\pi$
$661$	−3.31789			−0.129051			−0.0645255	+	0.997916i	$0.520553\pi$
$662$		0			0
$663$	14.3557	+	52.7027i	0.557531	+	2.04680i
$664$		0			0
$665$	−4.04626	+	3.80399i	−0.156907	+	0.147512i
$666$		0			0
$667$	5.55232	−	9.61690i	0.214987	−	0.372368i
$668$		0			0
$669$	5.23957	−	5.28313i	0.202573	−	0.204257i
$670$		0			0
$671$	12.3196	−	21.3381i	0.475591	−	0.823748i
$672$		0			0
$673$	21.8005	+	37.7597i	0.840349	+	1.45553i	0.889600	+	0.456741i	$0.150983\pi$
$673$	21.8005	+	37.7597i	0.840349	+	1.45553i	−0.0492503	+	0.998786i	$0.515683\pi$
$674$		0			0
$675$	23.8509	−	6.70937i	0.918022	−	0.258244i
$676$		0			0
$677$	−18.2808			−0.702587			−0.351294	−	0.936265i	$-0.614258\pi$
$677$	−18.2808			−0.702587			−0.351294	+	0.936265i	$0.614258\pi$
$678$		0			0
$679$	35.6009	+	10.7266i	1.36624	+	0.411650i
$680$		0			0
$681$	−29.1139	−	7.67202i	−1.11565	−	0.293992i
$682$		0			0
$683$	22.5380	+	39.0369i	0.862391	+	1.49371i	0.869614	+	0.493732i	$0.164367\pi$
$683$	22.5380	+	39.0369i	0.862391	+	1.49371i	−0.00722317	+	0.999974i	$0.502299\pi$
$684$		0			0
$685$	3.11689			0.119090
$686$		0			0
$687$	−8.94167	+	9.01601i	−0.341146	+	0.343982i
$688$		0			0
$689$	−63.8341			−2.43189
$690$		0			0
$691$	41.7955			1.58998			0.794988	−	0.606625i	$-0.207477\pi$
$691$	41.7955			1.58998			0.794988	+	0.606625i	$0.207477\pi$
$692$		0			0
$693$	18.5459	+	19.4027i	0.704502	+	0.737047i
$694$		0			0
$695$	−10.9506			−0.415378
$696$		0			0
$697$	−69.4037			−2.62885
$698$		0			0
$699$	7.25637	+	1.91218i	0.274461	+	0.0723253i
$700$		0			0
$701$	19.3967			0.732604			0.366302	−	0.930496i	$-0.380624\pi$
$701$	19.3967			0.732604			0.366302	+	0.930496i	$0.380624\pi$
$702$		0			0
$703$	−6.47753	−	11.2194i	−0.244305	−	0.423148i
$704$		0			0
$705$	−2.21093	+	2.22931i	−0.0832683	+	0.0839605i
$706$		0			0
$707$	−6.42340	−	27.3170i	−0.241577	−	1.02736i
$708$		0			0
$709$	−17.2308			−0.647118			−0.323559	−	0.946208i	$-0.604879\pi$
$709$	−17.2308			−0.647118			−0.323559	+	0.946208i	$0.604879\pi$
$710$		0			0
$711$	14.4782	−	8.51956i	0.542973	−	0.319508i
$712$		0			0
$713$	16.9494	+	29.3572i	0.634759	+	1.09943i
$714$		0			0
$715$	4.65675	−	8.06573i	0.174153	−	0.301641i
$716$		0			0
$717$	−5.96121	−	1.57088i	−0.222626	−	0.0586657i
$718$		0			0
$719$	5.08444	−	8.80650i	0.189617	−	0.328427i	−0.755505	−	0.655143i	$-0.772609\pi$
$719$	5.08444	−	8.80650i	0.189617	−	0.328427i	0.945123	+	0.326715i	$0.105942\pi$
$720$		0			0
$721$	−0.403841	−	0.121678i	−0.0150398	−	0.00453153i
$722$		0			0
$723$	26.8290	+	7.06990i	0.997780	+	0.262932i
$724$		0			0
$725$	14.6034			0.542358
$726$		0			0
$727$	−0.0914356	−	0.158371i	−0.00339116	−	0.00587366i	0.864325	−	0.502934i	$-0.167746\pi$
$727$	−0.0914356	−	0.158371i	−0.00339116	−	0.00587366i	−0.867716	+	0.497060i	$0.834413\pi$
$728$		0			0
$729$	0.670536	+	26.9917i	0.0248347	+	0.999692i
$730$		0			0
$731$	−10.5186	+	18.2187i	−0.389044	+	0.673844i
$732$		0			0
$733$	−20.9672	−	36.3162i	−0.774440	−	1.34137i	−0.935109	−	0.354361i	$-0.884698\pi$
$733$	−20.9672	−	36.3162i	−0.774440	−	1.34137i	0.160669	−	0.987008i	$-0.448635\pi$
$734$		0			0
$735$	−3.88276	−	4.35763i	−0.143218	−	0.160734i
$736$		0			0
$737$	−4.34776	+	7.53054i	−0.160152	+	0.277391i
$738$		0			0
$739$	−11.8013	−	20.4404i	−0.434116	−	0.751911i	0.563107	−	0.826384i	$-0.309606\pi$
$739$	−11.8013	−	20.4404i	−0.434116	−	0.751911i	−0.997223	+	0.0744729i	$0.976273\pi$
$740$		0			0
$741$	30.4277	−	30.6807i	1.11779	−	1.12708i
$742$		0			0
$743$	−11.1821	+	19.3680i	−0.410233	+	0.710544i	−0.994915	−	0.100718i	$-0.967886\pi$
$743$	−11.1821	+	19.3680i	−0.410233	+	0.710544i	0.584682	+	0.811263i	$0.301219\pi$
$744$		0			0
$745$	−3.41896	+	5.92181i	−0.125261	+	0.216958i
$746$		0			0
$747$	0.623857	+	0.353330i	0.0228257	+	0.0129277i
$748$		0			0
$749$	−4.83315	−	20.5541i	−0.176600	−	0.751029i
$750$		0			0
$751$	−15.5231	−	26.8868i	−0.566445	−	0.981112i	−0.996914	−	0.0785064i	$-0.974985\pi$
$751$	−15.5231	−	26.8868i	−0.566445	−	0.981112i	0.430468	−	0.902606i	$-0.358348\pi$
$752$		0			0
$753$	5.82699	+	21.3920i	0.212347	+	0.779568i
$754$		0			0
$755$	−1.21434			−0.0441943
$756$		0			0
$757$	−44.0639			−1.60153			−0.800764	−	0.598980i	$-0.795573\pi$
$757$	−44.0639			−1.60153			−0.800764	+	0.598980i	$0.795573\pi$
$758$		0			0
$759$	−5.58139	−	20.4904i	−0.202592	−	0.743754i
$760$		0			0
$761$	−2.87470	−	4.97913i	−0.104208	−	0.180493i	0.809206	−	0.587524i	$-0.199897\pi$
$761$	−2.87470	−	4.97913i	−0.104208	−	0.180493i	−0.913414	+	0.407031i	$0.866564\pi$
$762$		0			0
$763$	34.7367	+	10.4662i	1.25755	+	0.378903i
$764$		0			0
$765$	−0.0659036	−	7.96009i	−0.00238275	−	0.287798i
$766$		0			0
$767$	−24.0949	+	41.7336i	−0.870016	+	1.50691i
$768$		0			0
$769$	−7.48401	+	12.9627i	−0.269880	+	0.467446i	−0.968831	−	0.247724i	$-0.920317\pi$
$769$	−7.48401	+	12.9627i	−0.269880	+	0.467446i	0.698950	+	0.715170i	$0.253651\pi$
$770$		0			0
$771$	−20.0212	+	20.1877i	−0.721048	+	0.727042i
$772$		0			0
$773$	−10.0605	−	17.4253i	−0.361850	−	0.626743i	0.626415	−	0.779490i	$-0.284521\pi$
$773$	−10.0605	−	17.4253i	−0.361850	−	0.626743i	−0.988265	+	0.152747i	$0.951188\pi$
$774$		0			0
$775$	−22.2897	+	38.6069i	−0.800669	+	1.38680i
$776$		0			0
$777$	11.9685	−	6.49015i	0.429369	−	0.232833i
$778$		0			0
$779$	27.4516	+	47.5475i	0.983555	+	1.70357i
$780$		0			0
$781$	6.66688	−	11.5474i	0.238560	−	0.413198i
$782$		0			0
$783$	−3.92761	+	15.4216i	−0.140361	+	0.551123i
$784$		0			0
$785$	4.20763	+	7.28783i	0.150177	+	0.260114i
$786$		0			0
$787$	−24.1145			−0.859588			−0.429794	−	0.902927i	$-0.641414\pi$
$787$	−24.1145			−0.859588			−0.429794	+	0.902927i	$0.641414\pi$
$788$		0			0
$789$	42.9652	+	11.3221i	1.52960	+	0.403077i
$790$		0			0
$791$	10.8848	+	46.2899i	0.387017	+	1.64588i
$792$		0			0
$793$	20.8435	−	36.1021i	0.740175	−	1.28202i
$794$		0			0
$795$	8.99564	+	2.37051i	0.319042	+	0.0840732i
$796$		0			0
$797$	−1.54611	+	2.67794i	−0.0547661	+	0.0948576i	−0.892109	−	0.451821i	$-0.850775\pi$
$797$	−1.54611	+	2.67794i	−0.0547661	+	0.0948576i	0.837343	+	0.546678i	$0.184108\pi$
$798$		0			0
$799$	−10.3783	−	17.9758i	−0.367158	−	0.635936i
$800$		0			0
$801$	0.0321944	+	3.88856i	0.00113753	+	0.137396i
$802$		0			0
$803$	5.83133			0.205783
$804$		0			0
$805$	1.05706	+	4.49539i	0.0372565	+	0.158442i
$806$		0			0
$807$	13.0601	−	13.1687i	0.459737	−	0.463559i
$808$		0			0
$809$	−3.32067	−	5.75157i	−0.116749	−	0.202215i	0.801729	−	0.597688i	$-0.203914\pi$
$809$	−3.32067	−	5.75157i	−0.116749	−	0.202215i	−0.918477	+	0.395473i	$0.870581\pi$
$810$		0			0
$811$	−23.7806			−0.835049			−0.417525	−	0.908666i	$-0.637102\pi$
$811$	−23.7806			−0.835049			−0.417525	+	0.908666i	$0.637102\pi$
$812$		0			0
$813$	42.7137	+	11.2558i	1.49803	+	0.394758i
$814$		0			0
$815$	0.848381			0.0297175
$816$		0			0
$817$	16.6419			0.582225
$818$		0			0
$819$	31.3780	+	32.8275i	1.09644	+	1.14709i
$820$		0			0
$821$	−49.8303			−1.73909			−0.869544	−	0.493856i	$-0.835587\pi$
$821$	−49.8303			−1.73909			−0.869544	+	0.493856i	$0.835587\pi$
$822$		0			0
$823$	−9.45383			−0.329540			−0.164770	−	0.986332i	$-0.552688\pi$
$823$	−9.45383			−0.329540			−0.164770	+	0.986332i	$0.552688\pi$
$824$		0			0
$825$	19.6663	−	19.8298i	0.684692	−	0.690384i
$826$		0			0
$827$	−7.95385			−0.276582			−0.138291	−	0.990392i	$-0.544161\pi$
$827$	−7.95385			−0.276582			−0.138291	+	0.990392i	$0.544161\pi$
$828$		0			0
$829$	6.22333	+	10.7791i	0.216145	+	0.374374i	0.953626	−	0.300993i	$-0.0973182\pi$
$829$	6.22333	+	10.7791i	0.216145	+	0.374374i	−0.737481	+	0.675368i	$0.763985\pi$
$830$		0			0
$831$	−21.4090	−	5.64164i	−0.742670	−	0.195706i
$832$		0			0
$833$	34.5414	−	17.1951i	1.19679	−	0.595775i
$834$		0			0
$835$	−3.43922			−0.119019
$836$		0			0
$837$	−34.7750	−	33.9218i	−1.20200	−	1.17251i
$838$		0			0
$839$	−22.5163	−	38.9994i	−0.777350	−	1.34641i	−0.933464	−	0.358671i	$-0.883230\pi$
$839$	−22.5163	−	38.9994i	−0.777350	−	1.34641i	0.156114	−	0.987739i	$-0.450103\pi$
$840$		0			0
$841$	9.81015	−	16.9917i	0.338281	−	0.585920i
$842$		0			0
$843$	−25.5550	+	25.7675i	−0.880162	+	0.887480i
$844$		0			0
$845$	4.74977	−	8.22684i	0.163397	−	0.283012i
$846$		0			0
$847$	1.10242	+	0.332160i	0.0378794	+	0.0114131i
$848$		0			0
$849$	−6.85623	−	25.1705i	−0.235305	−	0.863851i
$850$		0			0
$851$	−10.7725			−0.369278
$852$		0			0
$853$	−1.15007	−	1.99198i	−0.0393777	−	0.0682042i	0.845665	−	0.533714i	$-0.179204\pi$
$853$	−1.15007	−	1.99198i	−0.0393777	−	0.0682042i	−0.885043	+	0.465510i	$0.845871\pi$
$854$		0			0
$855$	−5.42728	+	3.19364i	−0.185609	+	0.109220i
$856$		0			0
$857$	−6.33473	+	10.9721i	−0.216390	+	0.374799i	−0.953702	−	0.300754i	$-0.902762\pi$
$857$	−6.33473	+	10.9721i	−0.216390	+	0.374799i	0.737312	+	0.675553i	$0.236095\pi$
$858$		0			0
$859$	−23.7374	−	41.1144i	−0.809910	−	1.40280i	−0.912926	−	0.408125i	$-0.866183\pi$
$859$	−23.7374	−	41.1144i	−0.809910	−	1.40280i	0.103016	−	0.994680i	$-0.467151\pi$
$860$		0			0
$861$	−50.7223	+	27.5050i	−1.72861	+	0.937369i
$862$		0			0
$863$	−16.1445	+	27.9630i	−0.549564	+	0.951873i	0.448740	+	0.893662i	$0.351873\pi$
$863$	−16.1445	+	27.9630i	−0.549564	+	0.951873i	−0.998304	+	0.0582109i	$0.981460\pi$
$864$		0			0
$865$	2.38138	+	4.12467i	0.0809693	+	0.140243i
$866$		0			0
$867$	22.4152	+	5.90681i	0.761262	+	0.200606i
$868$		0			0
$869$	9.46779	−	16.3987i	0.321173	−	0.556287i
$870$		0			0
$871$	−7.35599	+	12.7410i	−0.249248	+	0.431711i
$872$		0			0
$873$	36.6850	+	20.7771i	1.24160	+	0.703197i
$874$		0			0
$875$	−9.06441	+	8.52168i	−0.306433	+	0.288085i
$876$		0			0
$877$	−13.8795	−	24.0399i	−0.468676	−	0.811771i	0.530683	−	0.847570i	$-0.321936\pi$
$877$	−13.8795	−	24.0399i	−0.468676	−	0.811771i	−0.999359	+	0.0357996i	$0.988602\pi$
$878$		0			0
$879$	−0.450404	−	0.118689i	−0.0151918	−	0.00400329i
$880$		0			0
$881$	−22.7696			−0.767126			−0.383563	−	0.923515i	$-0.625303\pi$
$881$	−22.7696			−0.767126			−0.383563	+	0.923515i	$0.625303\pi$
$882$		0			0
$883$	4.65312			0.156590			0.0782950	−	0.996930i	$-0.475052\pi$
$883$	4.65312			0.156590			0.0782950	+	0.996930i	$0.475052\pi$
$884$		0			0
$885$	4.94530	−	4.98641i	0.166234	−	0.167616i
$886$		0			0
$887$	23.6434	+	40.9515i	0.793866	+	1.37502i	0.923557	+	0.383462i	$0.125268\pi$
$887$	23.6434	+	40.9515i	0.793866	+	1.37502i	−0.129691	+	0.991554i	$0.541398\pi$
$888$		0			0
$889$	−36.5644	+	34.3751i	−1.22633	+	1.15290i
$890$		0			0
$891$	15.6515	+	26.1013i	0.524345	+	0.874428i
$892$		0			0
$893$	−8.20996	+	14.2201i	−0.274736	+	0.475856i
$894$		0			0
$895$	−0.977058	+	1.69231i	−0.0326595	+	0.0565678i
$896$		0			0
$897$	−9.44319	−	34.6678i	−0.315299	−	1.15752i
$898$		0			0
$899$	−14.3165	−	24.7970i	−0.477483	−	0.827025i
$900$		0			0
$901$	−30.7498	+	53.2602i	−1.02442	+	1.77436i
$902$		0			0
$903$	−0.467126	+	17.4834i	−0.0155450	+	0.581810i
$904$		0			0
$905$	1.10258	+	1.90972i	0.0366510	+	0.0634813i
$906$		0			0
$907$	3.03306	−	5.25342i	0.100711	−	0.174437i	−0.811267	−	0.584676i	$-0.801222\pi$
$907$	3.03306	−	5.25342i	0.100711	−	0.174437i	0.911978	+	0.410239i	$0.134555\pi$
$908$		0			0
$909$	−0.263431	−	31.8182i	−0.00873747	−	1.05534i
$910$		0			0
$911$	11.3223	+	19.6109i	0.375126	+	0.649737i	0.990346	−	0.138618i	$-0.0442661\pi$
$911$	11.3223	+	19.6109i	0.375126	+	0.649737i	−0.615220	+	0.788356i	$0.710933\pi$
$912$		0			0
$913$	0.808162			0.0267463
$914$		0			0
$915$	−4.27798	+	4.31354i	−0.141426	+	0.142601i
$916$		0			0
$917$	−12.3682	−	3.72656i	−0.408433	−	0.123062i
$918$		0			0
$919$	−22.3902	+	38.7810i	−0.738585	+	1.27927i	0.214548	+	0.976713i	$0.431172\pi$
$919$	−22.3902	+	38.7810i	−0.738585	+	1.27927i	−0.953133	+	0.302553i	$0.902161\pi$
$920$		0			0
$921$	2.29204	+	8.41454i	0.0755254	+	0.277268i
$922$		0			0
$923$	11.2797	−	19.5371i	0.371277	−	0.643071i
$924$		0			0
$925$	−7.08335	−	12.2687i	−0.232899	−	0.403393i
$926$		0			0
$927$	−0.416140	−	0.235686i	−0.0136678	−	0.00774096i
$928$		0			0
$929$	−1.10524			−0.0362618			−0.0181309	−	0.999836i	$-0.505772\pi$
$929$	−1.10524			−0.0362618			−0.0181309	+	0.999836i	$0.505772\pi$
$930$		0			0
$931$	−25.4424	−	16.8626i	−0.833842	−	0.552648i
$932$		0			0
$933$	−2.03766	−	7.48063i	−0.0667098	−	0.244905i
$934$		0			0
$935$	−4.48645	−	7.77076i	−0.146723	−	0.254131i
$936$		0			0
$937$	44.7012			1.46033			0.730163	−	0.683273i	$-0.239444\pi$
$937$	44.7012			1.46033			0.730163	+	0.683273i	$0.239444\pi$
$938$		0			0
$939$	−4.99725	−	18.3459i	−0.163079	−	0.598695i
$940$		0			0
$941$	−1.49932			−0.0488765			−0.0244383	−	0.999701i	$-0.507780\pi$
$941$	−1.49932			−0.0488765			−0.0244383	+	0.999701i	$0.507780\pi$
$942$		0			0
$943$	45.6537			1.48669
$944$		0			0
$945$	−3.20279	−	5.79135i	−0.104187	−	0.188393i
$946$		0			0
$947$	9.50893			0.308999			0.154499	−	0.987993i	$-0.450624\pi$
$947$	9.50893			0.308999			0.154499	+	0.987993i	$0.450624\pi$
$948$		0			0
$949$	9.86606			0.320266
$950$		0			0
$951$	−11.3644	−	41.7209i	−0.368515	−	1.35289i
$952$		0			0
$953$	15.2064			0.492585			0.246292	−	0.969196i	$-0.420788\pi$
$953$	15.2064			0.492585			0.246292	+	0.969196i	$0.420788\pi$
$954$		0			0
$955$	2.69396	+	4.66607i	0.0871745	+	0.150991i
$956$		0			0
$957$	4.71441	+	17.3075i	0.152395	+	0.559472i
$958$		0			0
$959$	3.92124	+	16.6759i	0.126623	+	0.538494i
$960$		0			0
$961$	56.4071			1.81958
$962$		0			0
$963$	−0.198213	−	23.9410i	−0.00638734	−	0.771487i
$964$		0			0
$965$	3.92176	+	6.79268i	0.126246	+	0.218664i
$966$		0			0
$967$	−17.9319	+	31.0589i	−0.576649	+	0.998786i	0.419211	+	0.907889i	$0.362307\pi$
$967$	−17.9319	+	31.0589i	−0.576649	+	0.998786i	−0.995860	+	0.0908973i	$0.971027\pi$
$968$		0			0
$969$	−10.9411	−	40.1668i	−0.351478	−	1.29034i
$970$		0			0
$971$	−3.72746	+	6.45615i	−0.119620	+	0.207188i	−0.919617	−	0.392816i	$-0.871501\pi$
$971$	−3.72746	+	6.45615i	−0.119620	+	0.207188i	0.799997	+	0.600004i	$0.204834\pi$
$972$		0			0
$973$	−13.7765	−	58.5874i	−0.441653	−	1.87823i
$974$		0			0
$975$	33.2735	−	33.5501i	1.06560	−	1.07446i
$976$		0			0
$977$	−39.9512			−1.27815			−0.639076	−	0.769143i	$-0.720683\pi$
$977$	−39.9512			−1.27815			−0.639076	+	0.769143i	$0.720683\pi$
$978$		0			0
$979$	2.19167	+	3.79608i	0.0700460	+	0.121323i
$980$		0			0
$981$	35.7945	+	20.2727i	1.14283	+	0.647258i
$982$		0			0
$983$	−4.19208	+	7.26090i	−0.133707	+	0.231587i	−0.925103	−	0.379717i	$-0.876021\pi$
$983$	−4.19208	+	7.26090i	−0.133707	+	0.231587i	0.791396	+	0.611304i	$0.209355\pi$
$984$		0			0
$985$	−0.764052	−	1.32338i	−0.0243447	−	0.0421663i
$986$		0			0
$987$	−14.7087	−	9.02425i	−0.468182	−	0.287245i
$988$		0			0
$989$	6.91911	−	11.9843i	0.220015	−	0.381077i
$990$		0			0
$991$	−21.2345	−	36.7792i	−0.674536	−	1.16833i	−0.976604	−	0.215044i	$-0.931010\pi$
$991$	−21.2345	−	36.7792i	−0.674536	−	1.16833i	0.302068	−	0.953286i	$-0.402323\pi$
$992$		0			0
$993$	−5.47349	−	20.0942i	−0.173696	−	0.637672i
$994$		0			0
$995$	−0.693871	+	1.20182i	−0.0219972	+	0.0381003i
$996$		0			0
$997$	15.4816	−	26.8149i	0.490306	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$997$	15.4816	−	26.8149i	0.490306	−	0.849236i	0.999938	+	0.0111572i	$0.00355152\pi$
$998$		0			0
$999$	14.8612	−	4.18051i	0.470186	−	0.132265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.d.121.5	yes	22
3.2	odd	2		1512.2.q.c.793.6		22
4.3	odd	2		1008.2.q.k.625.7		22
7.4	even	3		504.2.t.d.193.3	yes	22
9.2	odd	6		1512.2.t.d.289.6		22
9.7	even	3		504.2.t.d.457.3	yes	22
12.11	even	2		3024.2.q.k.2305.6		22
21.11	odd	6		1512.2.t.d.361.6		22
28.11	odd	6		1008.2.t.k.193.9		22
36.7	odd	6		1008.2.t.k.961.9		22
36.11	even	6		3024.2.t.l.289.6		22
63.11	odd	6		1512.2.q.c.1369.6		22
63.25	even	3	inner	504.2.q.d.25.5	✓	22
84.11	even	6		3024.2.t.l.1873.6		22
252.11	even	6		3024.2.q.k.2881.6		22
252.151	odd	6		1008.2.q.k.529.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.5	✓	22	63.25	even	3	inner
504.2.q.d.121.5	yes	22	1.1	even	1	trivial
504.2.t.d.193.3	yes	22	7.4	even	3
504.2.t.d.457.3	yes	22	9.7	even	3
1008.2.q.k.529.7		22	252.151	odd	6
1008.2.q.k.625.7		22	4.3	odd	2
1008.2.t.k.193.9		22	28.11	odd	6
1008.2.t.k.961.9		22	36.7	odd	6
1512.2.q.c.793.6		22	3.2	odd	2
1512.2.q.c.1369.6		22	63.11	odd	6
1512.2.t.d.289.6		22	9.2	odd	6
1512.2.t.d.361.6		22	21.11	odd	6
3024.2.q.k.2305.6		22	12.11	even	2
3024.2.q.k.2881.6		22	252.11	even	6
3024.2.t.l.289.6		22	36.11	even	6
3024.2.t.l.1873.6		22	84.11	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.455209 - 1.67116i) q^{3} +(0.240694 + 0.416893i) q^{5} +(-1.92765 + 1.81223i) q^{7} +(-2.58557 + 1.52146i) q^{9} +O(q^{10})\)	\(q+(-0.455209 - 1.67116i) q^{3} +(0.240694 + 0.416893i) q^{5} +(-1.92765 + 1.81223i) q^{7} +(-2.58557 + 1.52146i) q^{9} +(-1.69080 + 2.92855i) q^{11} +(-2.86067 + 4.95482i) q^{13} +(0.587131 - 0.592012i) q^{15} +(2.75605 + 4.77362i) q^{17} +(2.18023 - 3.77626i) q^{19} +(3.90601 + 2.39647i) q^{21} +(-1.81293 - 3.14008i) q^{23} +(2.38413 - 4.12944i) q^{25} +(3.71958 + 3.62832i) q^{27} +(1.53131 + 2.65231i) q^{29} -9.34918 q^{31} +(5.66374 + 1.49249i) q^{33} +(-1.21948 - 0.367431i) q^{35} +(1.48552 - 2.57299i) q^{37} +(9.58252 + 2.52516i) q^{39} +(-6.29558 + 10.9043i) q^{41} +(1.90827 + 3.30522i) q^{43} +(-1.25662 - 0.711701i) q^{45} -3.76564 q^{47} +(0.431647 - 6.98668i) q^{49} +(6.72291 - 6.77880i) q^{51} +(5.57860 + 9.66242i) q^{53} -1.62786 q^{55} +(-7.30321 - 1.92452i) q^{57} +8.42282 q^{59} -7.28625 q^{61} +(2.22683 - 7.61848i) q^{63} -2.75418 q^{65} +2.57143 q^{67} +(-4.42232 + 4.45909i) q^{69} -3.94304 q^{71} +(-0.862216 - 1.49340i) q^{73} +(-7.98625 - 2.10451i) q^{75} +(-2.04794 - 8.70932i) q^{77} -5.59960 q^{79} +(4.37033 - 7.86767i) q^{81} +(-0.119494 - 0.206970i) q^{83} +(-1.32673 + 2.29796i) q^{85} +(3.73538 - 3.76643i) q^{87} +(0.648116 - 1.12257i) q^{89} +(-3.46492 - 14.7353i) q^{91} +(4.25583 + 15.6240i) q^{93} +2.09907 q^{95} +(-7.02669 - 12.1706i) q^{97} +(-0.0839884 - 10.1444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

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