LMFDB - Embedded newform 504.2.q.d.25.7

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			25.7
Character	$\chi$	$=$	504.25
Dual form			504.2.q.d.121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12528 - 1.31671i) q^{3} +(-0.927957 + 1.60727i) q^{5} +(0.900017 + 2.48796i) q^{7} +(-0.467471 - 2.96335i) q^{9} +O(q^{10})$	\(q+(1.12528 - 1.31671i) q^{3} +(-0.927957 + 1.60727i) q^{5} +(0.900017 + 2.48796i) q^{7} +(-0.467471 - 2.96335i) q^{9} +(1.28800 + 2.23089i) q^{11} +(2.82227 + 4.88832i) q^{13} +(1.07210 + 3.03049i) q^{15} +(3.57951 - 6.19989i) q^{17} +(0.636599 + 1.10262i) q^{19} +(4.28871 + 1.61460i) q^{21} +(-0.120639 + 0.208952i) q^{23} +(0.777791 + 1.34717i) q^{25} +(-4.42793 - 2.71909i) q^{27} +(0.923571 - 1.59967i) q^{29} -2.99103 q^{31} +(4.38681 + 0.814451i) q^{33} +(-4.83401 - 0.862156i) q^{35} +(0.338260 + 0.585884i) q^{37} +(9.61237 + 1.78462i) q^{39} +(-0.733933 - 1.27121i) q^{41} +(4.14269 - 7.17535i) q^{43} +(5.19670 + 1.99851i) q^{45} -12.3145 q^{47} +(-5.37994 + 4.47842i) q^{49} +(-4.13552 - 11.6898i) q^{51} +(3.35508 - 5.81117i) q^{53} -4.78085 q^{55} +(2.16819 + 0.402544i) q^{57} +2.08279 q^{59} +12.9595 q^{61} +(6.95199 - 3.83012i) q^{63} -10.4758 q^{65} -4.83102 q^{67} +(0.139378 + 0.393977i) q^{69} -1.53621 q^{71} +(-6.55954 + 11.3615i) q^{73} +(2.64908 + 0.491825i) q^{75} +(-4.39115 + 5.21235i) q^{77} -3.72018 q^{79} +(-8.56294 + 2.77056i) q^{81} +(-3.00173 + 5.19915i) q^{83} +(6.64326 + 11.5065i) q^{85} +(-1.06703 - 3.01616i) q^{87} +(6.60349 + 11.4376i) q^{89} +(-9.62187 + 11.4213i) q^{91} +(-3.36576 + 3.93833i) q^{93} -2.36294 q^{95} +(6.40860 - 11.1000i) q^{97} +(6.00881 - 4.85969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.12528	−	1.31671i	0.649683	−	0.760205i
$3$	1.12528	−	1.31671i	0.649683	−	0.760205i
$4$		0			0
$5$	−0.927957	+	1.60727i	−0.414995	+	0.718793i	−0.995428	−	0.0955156i	$-0.969550\pi$
$5$	−0.927957	+	1.60727i	−0.414995	+	0.718793i	0.580433	+	0.814308i	$0.302883\pi$
$6$		0			0
$7$	0.900017	+	2.48796i	0.340174	+	0.940362i
$7$	0.900017	+	2.48796i	0.340174	+	0.940362i
$8$		0			0
$9$	−0.467471	−	2.96335i	−0.155824	−	0.987785i
$10$		0			0
$11$	1.28800	+	2.23089i	0.388348	+	0.672638i	0.992227	−	0.124437i	$-0.0397126\pi$
$11$	1.28800	+	2.23089i	0.388348	+	0.672638i	−0.603880	+	0.797076i	$0.706379\pi$
$12$		0			0
$13$	2.82227	+	4.88832i	0.782757	+	1.35578i	0.930330	+	0.366724i	$0.119521\pi$
$13$	2.82227	+	4.88832i	0.782757	+	1.35578i	−0.147573	+	0.989051i	$0.547146\pi$
$14$		0			0
$15$	1.07210	+	3.03049i	0.276814	+	0.782469i
$16$		0			0
$17$	3.57951	−	6.19989i	0.868158	−	1.50369i	0.00428199	−	0.999991i	$-0.498637\pi$
$17$	3.57951	−	6.19989i	0.868158	−	1.50369i	0.863876	−	0.503704i	$-0.168030\pi$
$18$		0			0
$19$	0.636599	+	1.10262i	0.146046	+	0.252959i	0.929763	−	0.368160i	$-0.120012\pi$
$19$	0.636599	+	1.10262i	0.146046	+	0.252959i	−0.783717	+	0.621118i	$0.786679\pi$
$20$		0			0
$21$	4.28871	+	1.61460i	0.935874	+	0.352335i
$22$		0			0
$23$	−0.120639	+	0.208952i	−0.0251549	+	0.0435696i	−0.878329	−	0.478057i	$-0.841341\pi$
$23$	−0.120639	+	0.208952i	−0.0251549	+	0.0435696i	0.853174	+	0.521627i	$0.174675\pi$
$24$		0			0
$25$	0.777791	+	1.34717i	0.155558	+	0.269435i
$26$		0			0
$27$	−4.42793	−	2.71909i	−0.852155	−	0.523289i
$28$		0			0
$29$	0.923571	−	1.59967i	0.171503	−	0.297051i	−0.767443	−	0.641118i	$-0.778471\pi$
$29$	0.923571	−	1.59967i	0.171503	−	0.297051i	0.938945	+	0.344066i	$0.111804\pi$
$30$		0			0
$31$	−2.99103			−0.537205			−0.268602	−	0.963251i	$-0.586562\pi$
$31$	−2.99103			−0.537205			−0.268602	+	0.963251i	$0.586562\pi$
$32$		0			0
$33$	4.38681	+	0.814451i	0.763646	+	0.141778i
$34$		0			0
$35$	−4.83401	−	0.862156i	−0.817096	−	0.145731i
$36$		0			0
$37$	0.338260	+	0.585884i	0.0556097	+	0.0963188i	0.892490	−	0.451067i	$-0.148956\pi$
$37$	0.338260	+	0.585884i	0.0556097	+	0.0963188i	−0.836880	+	0.547386i	$0.815623\pi$
$38$		0			0
$39$	9.61237	+	1.78462i	1.53921	+	0.285768i
$40$		0			0
$41$	−0.733933	−	1.27121i	−0.114621	−	0.198529i	0.803007	−	0.595969i	$-0.203232\pi$
$41$	−0.733933	−	1.27121i	−0.114621	−	0.198529i	−0.917628	+	0.397440i	$0.869899\pi$
$42$		0			0
$43$	4.14269	−	7.17535i	0.631754	−	1.09423i	−0.355439	−	0.934700i	$-0.615669\pi$
$43$	4.14269	−	7.17535i	0.631754	−	1.09423i	0.987193	−	0.159531i	$-0.0509981\pi$
$44$		0			0
$45$	5.19670	+	1.99851i	0.774678	+	0.297921i
$46$		0			0
$47$	−12.3145			−1.79625			−0.898124	−	0.439742i	$-0.855070\pi$
$47$	−12.3145			−1.79625			−0.898124	+	0.439742i	$0.855070\pi$
$48$		0			0
$49$	−5.37994	+	4.47842i	−0.768563	+	0.639774i
$50$		0			0
$51$	−4.13552	−	11.6898i	−0.579088	−	1.63690i
$52$		0			0
$53$	3.35508	−	5.81117i	0.460856	−	0.798226i	−0.538148	−	0.842851i	$-0.680876\pi$
$53$	3.35508	−	5.81117i	0.460856	−	0.798226i	0.999004	+	0.0446243i	$0.0142091\pi$
$54$		0			0
$55$	−4.78085			−0.644650
$56$		0			0
$57$	2.16819	+	0.402544i	0.287184	+	0.0533182i
$58$		0			0
$59$	2.08279			0.271156			0.135578	−	0.990767i	$-0.456711\pi$
$59$	2.08279			0.271156			0.135578	+	0.990767i	$0.456711\pi$
$60$		0			0
$61$	12.9595			1.65929			0.829644	−	0.558292i	$-0.188543\pi$
$61$	12.9595			1.65929			0.829644	+	0.558292i	$0.188543\pi$
$62$		0			0
$63$	6.95199	−	3.83012i	0.875869	−	0.482550i
$64$		0			0
$65$	−10.4758			−1.29936
$66$		0			0
$67$	−4.83102			−0.590203			−0.295102	−	0.955466i	$-0.595354\pi$
$67$	−4.83102			−0.590203			−0.295102	+	0.955466i	$0.595354\pi$
$68$		0			0
$69$	0.139378	+	0.393977i	0.0167791	+	0.0474293i
$70$		0			0
$71$	−1.53621			−0.182314			−0.0911572	−	0.995837i	$-0.529057\pi$
$71$	−1.53621			−0.182314			−0.0911572	+	0.995837i	$0.529057\pi$
$72$		0			0
$73$	−6.55954	+	11.3615i	−0.767736	+	1.32976i	0.171052	+	0.985262i	$0.445283\pi$
$73$	−6.55954	+	11.3615i	−0.767736	+	1.32976i	−0.938788	+	0.344496i	$0.888050\pi$
$74$		0			0
$75$	2.64908	+	0.491825i	0.305889	+	0.0567910i
$76$		0			0
$77$	−4.39115	+	5.21235i	−0.500418	+	0.594002i
$78$		0			0
$79$	−3.72018			−0.418553			−0.209277	−	0.977856i	$-0.567111\pi$
$79$	−3.72018			−0.418553			−0.209277	+	0.977856i	$0.567111\pi$
$80$		0			0
$81$	−8.56294	+	2.77056i	−0.951438	+	0.307840i
$82$		0			0
$83$	−3.00173	+	5.19915i	−0.329483	+	0.570681i	−0.982409	−	0.186740i	$-0.940208\pi$
$83$	−3.00173	+	5.19915i	−0.329483	+	0.570681i	0.652926	+	0.757421i	$0.273541\pi$
$84$		0			0
$85$	6.64326	+	11.5065i	0.720563	+	1.24805i
$86$		0			0
$87$	−1.06703	−	3.01616i	−0.114398	−	0.323367i
$88$		0			0
$89$	6.60349	+	11.4376i	0.699968	+	1.21238i	0.968477	+	0.249103i	$0.0801359\pi$
$89$	6.60349	+	11.4376i	0.699968	+	1.21238i	−0.268509	+	0.963277i	$0.586531\pi$
$90$		0			0
$91$	−9.62187	+	11.4213i	−1.00865	+	1.19728i
$92$		0			0
$93$	−3.36576	+	3.93833i	−0.349013	+	0.408386i
$94$		0			0
$95$	−2.36294			−0.242433
$96$		0			0
$97$	6.40860	−	11.1000i	0.650695	−	1.12704i	−0.332260	−	0.943188i	$-0.607811\pi$
$97$	6.40860	−	11.1000i	0.650695	−	1.12704i	0.982955	−	0.183848i	$-0.0588556\pi$
$98$		0			0
$99$	6.00881	−	4.85969i	0.603908	−	0.488417i
$100$		0			0
$101$	−6.10066	−	10.5667i	−0.607039	−	1.05142i	−0.991726	−	0.128375i	$-0.959024\pi$
$101$	−6.10066	−	10.5667i	−0.607039	−	1.05142i	0.384687	−	0.923047i	$-0.374309\pi$
$102$		0			0
$103$	−6.82163	+	11.8154i	−0.672155	+	1.16421i	0.305137	+	0.952309i	$0.401298\pi$
$103$	−6.82163	+	11.8154i	−0.672155	+	1.16421i	−0.977292	+	0.211898i	$0.932036\pi$
$104$		0			0
$105$	−6.57484	+	5.39483i	−0.641639	+	0.526482i
$106$		0			0
$107$	−6.48002	−	11.2237i	−0.626448	−	1.08504i	−0.988259	−	0.152788i	$-0.951175\pi$
$107$	−6.48002	−	11.2237i	−0.626448	−	1.08504i	0.361811	−	0.932251i	$-0.382158\pi$
$108$		0			0
$109$	7.70089	−	13.3383i	0.737612	−	1.27758i	−0.215956	−	0.976403i	$-0.569287\pi$
$109$	7.70089	−	13.3383i	0.737612	−	1.27758i	0.953568	−	0.301178i	$-0.0973799\pi$
$110$		0			0
$111$	1.15208	+	0.213894i	0.109351	+	0.0203019i
$112$		0			0
$113$	−7.73446	−	13.3965i	−0.727597	−	1.26023i	−0.957896	−	0.287115i	$-0.907304\pi$
$113$	−7.73446	−	13.3965i	−0.727597	−	1.26023i	0.230299	−	0.973120i	$-0.426029\pi$
$114$		0			0
$115$	−0.223895	−	0.387797i	−0.0208783	−	0.0361623i
$116$		0			0
$117$	13.1665	−	10.6485i	1.21724	−	0.984457i
$118$		0			0
$119$	18.6467	+	3.32569i	1.70934	+	0.304865i
$120$		0			0
$121$	2.18209	−	3.77949i	0.198372	−	0.343590i
$122$		0			0
$123$	−2.49970	−	0.464092i	−0.225390	−	0.0418457i
$124$		0			0
$125$	−12.1666			−1.08821
$126$		0			0
$127$	−3.19404			−0.283425			−0.141713	−	0.989908i	$-0.545261\pi$
$127$	−3.19404			−0.283425			−0.141713	+	0.989908i	$0.545261\pi$
$128$		0			0
$129$	−4.78618	−	13.5290i	−0.421399	−	1.19117i
$130$		0			0
$131$	−7.04338	+	12.1995i	−0.615383	+	1.06587i	0.374935	+	0.927051i	$0.377665\pi$
$131$	−7.04338	+	12.1995i	−0.615383	+	1.06587i	−0.990317	+	0.138823i	$0.955668\pi$
$132$		0			0
$133$	−2.17033	+	2.57621i	−0.188192	+	0.223386i
$134$		0			0
$135$	8.47924	−	4.59367i	0.729777	−	0.395360i
$136$		0			0
$137$	−6.84818	−	11.8614i	−0.585079	−	1.01339i	−0.994866	−	0.101206i	$-0.967730\pi$
$137$	−6.84818	−	11.8614i	−0.585079	−	1.01339i	0.409786	−	0.912182i	$-0.365603\pi$
$138$		0			0
$139$	−4.94131	−	8.55859i	−0.419116	−	0.725931i	0.576735	−	0.816932i	$-0.304327\pi$
$139$	−4.94131	−	8.55859i	−0.419116	−	0.725931i	−0.995851	+	0.0910010i	$0.970993\pi$
$140$		0			0
$141$	−13.8573	+	16.2146i	−1.16699	+	1.36552i
$142$		0			0
$143$	−7.27019	+	12.5923i	−0.607964	+	1.05302i
$144$		0			0
$145$	1.71407	+	2.96885i	0.142346	+	0.246550i
$146$		0			0
$147$	−0.157162	+	12.1233i	−0.0129625	+	0.999916i
$148$		0			0
$149$	1.96015	−	3.39507i	0.160581	−	0.278135i	−0.774496	−	0.632579i	$-0.781996\pi$
$149$	1.96015	−	3.39507i	0.160581	−	0.278135i	0.935077	+	0.354444i	$0.115330\pi$
$150$		0			0
$151$	−9.78920	−	16.9554i	−0.796634	−	1.37981i	−0.921796	−	0.387674i	$-0.873278\pi$
$151$	−9.78920	−	16.9554i	−0.796634	−	1.37981i	0.125162	−	0.992136i	$-0.460055\pi$
$152$		0			0
$153$	−20.0458	−	7.70909i	−1.62061	−	0.623243i
$154$		0			0
$155$	2.77555	−	4.80739i	0.222937	−	0.386139i
$156$		0			0
$157$	14.7927			1.18059			0.590295	−	0.807188i	$-0.299012\pi$
$157$	14.7927			1.18059			0.590295	+	0.807188i	$0.299012\pi$
$158$		0			0
$159$	−3.87623	−	10.9569i	−0.307405	−	0.868939i
$160$		0			0
$161$	−0.628443	−	0.112084i	−0.0495282	−	0.00883347i
$162$		0			0
$163$	7.54686	+	13.0715i	0.591116	+	1.02384i	0.994082	+	0.108628i	$0.0346456\pi$
$163$	7.54686	+	13.0715i	0.591116	+	1.02384i	−0.402967	+	0.915215i	$0.632021\pi$
$164$		0			0
$165$	−5.37982	+	6.29501i	−0.418818	+	0.490066i
$166$		0			0
$167$	1.92946	+	3.34192i	0.149306	+	0.258605i	0.930971	−	0.365093i	$-0.118963\pi$
$167$	1.92946	+	3.34192i	0.149306	+	0.258605i	−0.781665	+	0.623698i	$0.785629\pi$
$168$		0			0
$169$	−9.43043	+	16.3340i	−0.725418	+	1.25646i
$170$		0			0
$171$	2.96987	−	2.40191i	0.227111	−	0.183679i
$172$		0			0
$173$	0.651571			0.0495380			0.0247690	−	0.999693i	$-0.492115\pi$
$173$	0.651571			0.0495380			0.0247690	+	0.999693i	$0.492115\pi$
$174$		0			0
$175$	−2.65170	+	3.14760i	−0.200449	+	0.237936i
$176$		0			0
$177$	2.34373	−	2.74244i	0.176165	−	0.206134i
$178$		0			0
$179$	10.9059	−	18.8896i	0.815145	−	1.41187i	−0.0940781	−	0.995565i	$-0.529990\pi$
$179$	10.9059	−	18.8896i	0.815145	−	1.41187i	0.909223	−	0.416308i	$-0.136676\pi$
$180$		0			0
$181$	−25.0338			−1.86075			−0.930374	−	0.366613i	$-0.880517\pi$
$181$	−25.0338			−1.86075			−0.930374	+	0.366613i	$0.880517\pi$
$182$		0			0
$183$	14.5831	−	17.0639i	1.07801	−	1.26140i
$184$		0			0
$185$	−1.25556			−0.0923109
$186$		0			0
$187$	18.4417			1.34859
$188$		0			0
$189$	2.77979	−	13.4638i	0.202200	−	0.979344i
$190$		0			0
$191$	8.66073			0.626668			0.313334	−	0.949643i	$-0.398554\pi$
$191$	8.66073			0.626668			0.313334	+	0.949643i	$0.398554\pi$
$192$		0			0
$193$	1.61664			0.116369			0.0581843	−	0.998306i	$-0.481469\pi$
$193$	1.61664			0.116369			0.0581843	+	0.998306i	$0.481469\pi$
$194$		0			0
$195$	−11.7882	+	13.7936i	−0.844173	+	0.987781i
$196$		0			0
$197$	10.7746			0.767659			0.383829	−	0.923404i	$-0.374605\pi$
$197$	10.7746			0.767659			0.383829	+	0.923404i	$0.374605\pi$
$198$		0			0
$199$	2.38768	−	4.13558i	0.169258	−	0.293163i	−0.768901	−	0.639368i	$-0.779196\pi$
$199$	2.38768	−	4.13558i	0.169258	−	0.293163i	0.938159	+	0.346204i	$0.112530\pi$
$200$		0			0
$201$	−5.43627	+	6.36107i	−0.383445	+	0.448676i
$202$		0			0
$203$	4.81115	+	0.858080i	0.337677	+	0.0602254i
$204$		0			0
$205$	2.72423			0.190269
$206$		0			0
$207$	0.675595	+	0.259816i	0.0469571	+	0.0180585i
$208$		0			0
$209$	−1.63988	+	2.84036i	−0.113433	+	0.196472i
$210$		0			0
$211$	2.42787	+	4.20520i	0.167142	+	0.289498i	0.937414	−	0.348218i	$-0.113213\pi$
$211$	2.42787	+	4.20520i	0.167142	+	0.289498i	−0.770272	+	0.637715i	$0.779880\pi$
$212$		0			0
$213$	−1.72867	+	2.02275i	−0.118447	+	0.138596i
$214$		0			0
$215$	7.68848	+	13.3168i	0.524350	+	0.908200i
$216$		0			0
$217$	−2.69198	−	7.44158i	−0.182743	−	0.505167i
$218$		0			0
$219$	7.57844	+	21.4219i	0.512104	+	1.44756i
$220$		0			0
$221$	40.4094			2.71823
$222$		0			0
$223$	3.86187	−	6.68896i	0.258610	−	0.447926i	−0.707260	−	0.706954i	$-0.750069\pi$
$223$	3.86187	−	6.68896i	0.258610	−	0.447926i	0.965870	+	0.259028i	$0.0834021\pi$
$224$		0			0
$225$	3.62856	−	2.93463i	0.241904	−	0.195642i
$226$		0			0
$227$	6.97457	+	12.0803i	0.462919	+	0.801799i	0.999105	−	0.0423011i	$-0.0134689\pi$
$227$	6.97457	+	12.0803i	0.462919	+	0.801799i	−0.536186	+	0.844100i	$0.680136\pi$
$228$		0			0
$229$	−0.800136	+	1.38588i	−0.0528745	+	0.0915812i	−0.891251	−	0.453510i	$-0.850172\pi$
$229$	−0.800136	+	1.38588i	−0.0528745	+	0.0915812i	0.838377	+	0.545091i	$0.183505\pi$
$230$		0			0
$231$	1.92188	+	11.6473i	0.126450	+	0.766333i
$232$		0			0
$233$	3.69939	+	6.40753i	0.242355	+	0.419771i	0.961385	−	0.275208i	$-0.0887468\pi$
$233$	3.69939	+	6.40753i	0.242355	+	0.419771i	−0.719030	+	0.694979i	$0.755413\pi$
$234$		0			0
$235$	11.4273	−	19.7926i	0.745434	−	1.29113i
$236$		0			0
$237$	−4.18626	+	4.89841i	−0.271927	+	0.318186i
$238$		0			0
$239$	−1.25117	−	2.16709i	−0.0809316	−	0.140178i	0.822719	−	0.568449i	$-0.192456\pi$
$239$	−1.25117	−	2.16709i	−0.0809316	−	0.140178i	−0.903650	+	0.428271i	$0.859123\pi$
$240$		0			0
$241$	−2.12148	−	3.67452i	−0.136657	−	0.236697i	0.789572	−	0.613658i	$-0.210302\pi$
$241$	−2.12148	−	3.67452i	−0.136657	−	0.236697i	−0.926229	+	0.376961i	$0.876969\pi$
$242$		0			0
$243$	−5.98770	+	14.3926i	−0.384111	+	0.923287i
$244$		0			0
$245$	−2.20567	−	12.8028i	−0.140915	−	0.817940i
$246$		0			0
$247$	−3.59331	+	6.22379i	−0.228637	+	0.396010i
$248$		0			0
$249$	3.46800	+	9.80295i	0.219775	+	0.621237i
$250$		0			0
$251$	−13.5381			−0.854516			−0.427258	−	0.904130i	$-0.640520\pi$
$251$	−13.5381			−0.854516			−0.427258	+	0.904130i	$0.640520\pi$
$252$		0			0
$253$	−0.621532			−0.0390754
$254$		0			0
$255$	22.6263	+	4.20077i	1.41691	+	0.263062i
$256$		0			0
$257$	3.07747	−	5.33034i	0.191968	−	0.332497i	−0.753935	−	0.656949i	$-0.771847\pi$
$257$	3.07747	−	5.33034i	0.191968	−	0.332497i	0.945902	+	0.324452i	$0.105180\pi$
$258$		0			0
$259$	−1.15322	+	1.36889i	−0.0716576	+	0.0850584i
$260$		0			0
$261$	−5.17214	−	1.98907i	−0.320147	−	0.123120i
$262$		0			0
$263$	12.6706	+	21.9460i	0.781300	+	1.35325i	0.931185	+	0.364547i	$0.118776\pi$
$263$	12.6706	+	21.9460i	0.781300	+	1.35325i	−0.149885	+	0.988703i	$0.547890\pi$
$264$		0			0
$265$	6.22675	+	10.7850i	0.382506	+	0.662520i
$266$		0			0
$267$	22.4908	+	4.17562i	1.37642	+	0.255544i
$268$		0			0
$269$	−5.42092	+	9.38931i	−0.330519	+	0.572476i	−0.982614	−	0.185662i	$-0.940557\pi$
$269$	−5.42092	+	9.38931i	−0.330519	+	0.572476i	0.652095	+	0.758138i	$0.273891\pi$
$270$		0			0
$271$	−15.0184	−	26.0127i	−0.912306	−	1.58016i	−0.810799	−	0.585325i	$-0.800967\pi$
$271$	−15.0184	−	26.0127i	−0.912306	−	1.58016i	−0.101507	−	0.994835i	$-0.532366\pi$
$272$		0			0
$273$	4.21122	+	25.5214i	0.254875	+	1.54463i
$274$		0			0
$275$	−2.00360	+	3.47033i	−0.120821	+	0.209269i
$276$		0			0
$277$	−9.88147	−	17.1152i	−0.593720	−	1.02835i	−0.993726	−	0.111841i	$-0.964325\pi$
$277$	−9.88147	−	17.1152i	−0.593720	−	1.02835i	0.400006	−	0.916513i	$-0.369008\pi$
$278$		0			0
$279$	1.39822	+	8.86348i	0.0837092	+	0.530643i
$280$		0			0
$281$	−3.98596	+	6.90388i	−0.237782	+	0.411851i	−0.960078	−	0.279734i	$-0.909754\pi$
$281$	−3.98596	+	6.90388i	−0.237782	+	0.411851i	0.722295	+	0.691585i	$0.243087\pi$
$282$		0			0
$283$	23.2127			1.37985			0.689926	−	0.723880i	$-0.257643\pi$
$283$	23.2127			1.37985			0.689926	+	0.723880i	$0.257643\pi$
$284$		0			0
$285$	−2.65898	+	3.11132i	−0.157505	+	0.184299i
$286$		0			0
$287$	2.50217	−	2.97011i	0.147698	−	0.175320i
$288$		0			0
$289$	−17.1258	−	29.6627i	−1.00740	−	1.74486i
$290$		0			0
$291$	−7.40405	−	20.9290i	−0.434033	−	1.22688i
$292$		0			0
$293$	11.8556	+	20.5345i	0.692612	+	1.19964i	0.970979	+	0.239164i	$0.0768735\pi$
$293$	11.8556	+	20.5345i	0.692612	+	1.19964i	−0.278367	+	0.960475i	$0.589793\pi$
$294$		0			0
$295$	−1.93274	+	3.34760i	−0.112528	+	0.194905i
$296$		0			0
$297$	0.362800	−	13.3804i	0.0210518	−	0.776410i
$298$		0			0
$299$	−1.36190			−0.0787607
$300$		0			0
$301$	21.5805	+	3.84893i	1.24388	+	0.221849i
$302$		0			0
$303$	−20.7782	−	3.85767i	−1.19368	−	0.221617i
$304$		0			0
$305$	−12.0258	+	20.8293i	−0.688597	+	1.19268i
$306$		0			0
$307$	3.87810			0.221335			0.110668	−	0.993857i	$-0.464701\pi$
$307$	3.87810			0.221335			0.110668	+	0.993857i	$0.464701\pi$
$308$		0			0
$309$	7.88124	+	22.2778i	0.448348	+	1.26734i
$310$		0			0
$311$	−6.92439			−0.392646			−0.196323	−	0.980539i	$-0.562900\pi$
$311$	−6.92439			−0.392646			−0.196323	+	0.980539i	$0.562900\pi$
$312$		0			0
$313$	30.2313			1.70878			0.854388	−	0.519636i	$-0.173932\pi$
$313$	30.2313			1.70878			0.854388	+	0.519636i	$0.173932\pi$
$314$		0			0
$315$	−0.295116	+	14.7279i	−0.0166279	+	0.829824i
$316$		0			0
$317$	9.37399			0.526496			0.263248	−	0.964728i	$-0.415206\pi$
$317$	9.37399			0.526496			0.263248	+	0.964728i	$0.415206\pi$
$318$		0			0
$319$	4.75825			0.266411
$320$		0			0
$321$	−22.0703	−	4.09755i	−1.23184	−	0.228703i
$322$		0			0
$323$	9.11484			0.507163
$324$		0			0
$325$	−4.39027	+	7.60418i	−0.243529	+	0.421804i
$326$		0			0
$327$	−8.89708	−	25.1493i	−0.492010	−	1.39076i
$328$		0			0
$329$	−11.0832	−	30.6379i	−0.611038	−	1.68912i
$330$		0			0
$331$	27.5441			1.51396			0.756979	−	0.653439i	$-0.226674\pi$
$331$	27.5441			1.51396			0.756979	+	0.653439i	$0.226674\pi$
$332$		0			0
$333$	1.57806	−	1.27627i	0.0864769	−	0.0699391i
$334$		0			0
$335$	4.48298	−	7.76475i	0.244931	−	0.424234i
$336$		0			0
$337$	−3.41673	−	5.91796i	−0.186121	−	0.322372i	0.757832	−	0.652449i	$-0.226258\pi$
$337$	−3.41673	−	5.91796i	−0.186121	−	0.322372i	−0.943954	+	0.330078i	$0.892925\pi$
$338$		0			0
$339$	−26.3428	−	4.89077i	−1.43074	−	0.265630i
$340$		0			0
$341$	−3.85246	−	6.67266i	−0.208622	−	0.361345i
$342$		0			0
$343$	−15.9842	−	9.35445i	−0.863065	−	0.505093i
$344$		0			0
$345$	−0.762564	−	0.141577i	−0.0410551	−	0.00762224i
$346$		0			0
$347$	20.1919			1.08396			0.541979	−	0.840392i	$-0.317675\pi$
$347$	20.1919			1.08396			0.541979	+	0.840392i	$0.317675\pi$
$348$		0			0
$349$	−4.25154	+	7.36388i	−0.227580	+	0.394180i	−0.957090	−	0.289790i	$-0.906415\pi$
$349$	−4.25154	+	7.36388i	−0.227580	+	0.394180i	0.729511	+	0.683970i	$0.239748\pi$
$350$		0			0
$351$	0.794966	−	29.3191i	0.0424321	−	1.56494i
$352$		0			0
$353$	−2.35452	−	4.07815i	−0.125318	−	0.217058i	0.796539	−	0.604587i	$-0.206662\pi$
$353$	−2.35452	−	4.07815i	−0.125318	−	0.217058i	−0.921857	+	0.387529i	$0.873329\pi$
$354$		0			0
$355$	1.42554	−	2.46910i	0.0756596	−	0.131046i
$356$		0			0
$357$	25.3618	−	20.8101i	1.34229	−	1.10139i
$358$		0			0
$359$	6.03357	+	10.4504i	0.318440	+	0.551554i	0.980163	−	0.198195i	$-0.0635079\pi$
$359$	6.03357	+	10.4504i	0.318440	+	0.551554i	−0.661723	+	0.749748i	$0.730175\pi$
$360$		0			0
$361$	8.68948	−	15.0506i	0.457341	−	0.792138i
$362$		0			0
$363$	−2.52104	−	7.12619i	−0.132320	−	0.374028i
$364$		0			0
$365$	−12.1739	−	21.0859i	−0.637213	−	1.10369i
$366$		0			0
$367$	−0.480356	−	0.832001i	−0.0250744	−	0.0434301i	0.853216	−	0.521558i	$-0.174649\pi$
$367$	−0.480356	−	0.832001i	−0.0250744	−	0.0434301i	−0.878290	+	0.478128i	$0.841316\pi$
$368$		0			0
$369$	−3.42395	+	2.76916i	−0.178244	+	0.144157i
$370$		0			0
$371$	17.4776	+	3.11717i	0.907393	+	0.161836i
$372$		0			0
$373$	3.52499	−	6.10547i	0.182517	−	0.316129i	−0.760220	−	0.649666i	$-0.774909\pi$
$373$	3.52499	−	6.10547i	0.182517	−	0.316129i	0.942737	+	0.333537i	$0.108242\pi$
$374$		0			0
$375$	−13.6909	+	16.0199i	−0.706994	+	0.827266i
$376$		0			0
$377$	10.4263			0.536980
$378$		0			0
$379$	−37.1330			−1.90739			−0.953697	−	0.300769i	$-0.902757\pi$
$379$	−37.1330			−1.90739			−0.953697	+	0.300769i	$0.902757\pi$
$380$		0			0
$381$	−3.59421	+	4.20564i	−0.184137	+	0.215461i
$382$		0			0
$383$	−16.0988	+	27.8839i	−0.822608	+	1.42480i	0.0811254	+	0.996704i	$0.474149\pi$
$383$	−16.0988	+	27.8839i	−0.822608	+	1.42480i	−0.903734	+	0.428095i	$0.859185\pi$
$384$		0			0
$385$	−4.30285	−	11.8946i	−0.219293	−	0.606204i
$386$		0			0
$387$	−23.1997	−	8.92199i	−1.17931	−	0.453530i
$388$		0			0
$389$	12.8713	+	22.2937i	0.652600	+	1.13034i	0.982490	+	0.186317i	$0.0596552\pi$
$389$	12.8713	+	22.2937i	0.652600	+	1.13034i	−0.329889	+	0.944020i	$0.607011\pi$
$390$		0			0
$391$	0.863654	+	1.49589i	0.0436769	+	0.0756506i
$392$		0			0
$393$	8.13743	+	23.0020i	0.410479	+	1.16030i
$394$		0			0
$395$	3.45217	−	5.97933i	0.173697	−	0.300853i
$396$		0			0
$397$	9.44903	+	16.3662i	0.474233	+	0.821396i	0.999565	−	0.0295016i	$-0.00939202\pi$
$397$	9.44903	+	16.3662i	0.474233	+	0.821396i	−0.525332	+	0.850898i	$0.676059\pi$
$398$		0			0
$399$	0.949893	+	5.75668i	0.0475541	+	0.288194i
$400$		0			0
$401$	−7.60193	+	13.1669i	−0.379622	+	0.657525i	−0.991007	−	0.133808i	$-0.957279\pi$
$401$	−7.60193	+	13.1669i	−0.379622	+	0.657525i	0.611385	+	0.791333i	$0.290613\pi$
$402$		0			0
$403$	−8.44150	−	14.6211i	−0.420501	−	0.728329i
$404$		0			0
$405$	3.49300	−	16.3339i	0.173569	−	0.811639i
$406$		0			0
$407$	−0.871362	+	1.50924i	−0.0431918	+	0.0748104i
$408$		0			0
$409$	−29.9458			−1.48073			−0.740363	−	0.672207i	$-0.765346\pi$
$409$	−29.9458			−1.48073			−0.740363	+	0.672207i	$0.765346\pi$
$410$		0			0
$411$	−23.3242	−	4.33035i	−1.15050	−	0.213600i
$412$		0			0
$413$	1.87454	+	5.18191i	0.0922403	+	0.254985i
$414$		0			0
$415$	−5.57096	−	9.64918i	−0.273468	−	0.473660i
$416$		0			0
$417$	−16.8296	−	3.12456i	−0.824149	−	0.153011i
$418$		0			0
$419$	−12.2660	−	21.2453i	−0.599231	−	1.03790i	−0.992935	−	0.118661i	$-0.962140\pi$
$419$	−12.2660	−	21.2453i	−0.599231	−	1.03790i	0.393704	−	0.919237i	$-0.371194\pi$
$420$		0			0
$421$	−2.37791	+	4.11866i	−0.115892	+	0.200731i	−0.918136	−	0.396265i	$-0.870306\pi$
$421$	−2.37791	+	4.11866i	−0.115892	+	0.200731i	0.802244	+	0.596996i	$0.203639\pi$
$422$		0			0
$423$	5.75665	+	36.4921i	0.279898	+	1.77431i
$424$		0			0
$425$	11.1364			0.540197
$426$		0			0
$427$	11.6637	+	32.2427i	0.564448	+	1.56033i
$428$		0			0
$429$	8.39948	+	23.7427i	0.405531	+	1.14631i
$430$		0			0
$431$	1.36446	−	2.36331i	0.0657237	−	0.113837i	−0.831291	−	0.555837i	$-0.812398\pi$
$431$	1.36446	−	2.36331i	0.0657237	−	0.113837i	0.897015	+	0.442000i	$0.145731\pi$
$432$		0			0
$433$	14.5592			0.699672			0.349836	−	0.936811i	$-0.386237\pi$
$433$	14.5592			0.699672			0.349836	+	0.936811i	$0.386237\pi$
$434$		0			0
$435$	5.83794	+	1.08387i	0.279908	+	0.0519674i
$436$		0			0
$437$	−0.307194			−0.0146951
$438$		0			0
$439$	−2.88131			−0.137517			−0.0687587	−	0.997633i	$-0.521904\pi$
$439$	−2.88131			−0.137517			−0.0687587	+	0.997633i	$0.521904\pi$
$440$		0			0
$441$	15.7861	+	13.8491i	0.751720	+	0.659483i
$442$		0			0
$443$	24.9731			1.18651			0.593254	−	0.805016i	$-0.297843\pi$
$443$	24.9731			1.18651			0.593254	+	0.805016i	$0.297843\pi$
$444$		0			0
$445$	−24.5110			−1.16193
$446$		0			0
$447$	−2.26462	−	6.40138i	−0.107113	−	0.302775i
$448$		0			0
$449$	−2.99154			−0.141180			−0.0705898	−	0.997505i	$-0.522488\pi$
$449$	−2.99154			−0.141180			−0.0705898	+	0.997505i	$0.522488\pi$
$450$		0			0
$451$	1.89062	−	3.27464i	0.0890257	−	0.154197i
$452$		0			0
$453$	−33.3410	−	6.19006i	−1.56650	−	0.290834i
$454$		0			0
$455$	−9.42838	−	26.0634i	−0.442009	−	1.22187i
$456$		0			0
$457$	−25.6171			−1.19832			−0.599158	−	0.800631i	$-0.704498\pi$
$457$	−25.6171			−1.19832			−0.599158	+	0.800631i	$0.704498\pi$
$458$		0			0
$459$	−32.7079	+	17.7197i	−1.52667	+	0.827083i
$460$		0			0
$461$	−6.45759	+	11.1849i	−0.300760	+	0.520931i	−0.976308	−	0.216384i	$-0.930574\pi$
$461$	−6.45759	+	11.1849i	−0.300760	+	0.520931i	0.675548	+	0.737316i	$0.263907\pi$
$462$		0			0
$463$	−12.2457	−	21.2102i	−0.569108	−	0.985724i	−0.996654	−	0.0817305i	$-0.973955\pi$
$463$	−12.2457	−	21.2102i	−0.569108	−	0.985724i	0.427547	−	0.903993i	$-0.359378\pi$
$464$		0			0
$465$	−3.20668	−	9.06428i	−0.148706	−	0.420346i
$466$		0			0
$467$	−10.4087	−	18.0283i	−0.481655	−	0.834251i	0.518123	−	0.855306i	$-0.326631\pi$
$467$	−10.4087	−	18.0283i	−0.481655	−	0.834251i	−0.999778	+	0.0210550i	$0.993297\pi$
$468$		0			0
$469$	−4.34800	−	12.0194i	−0.200772	−	0.555005i
$470$		0			0
$471$	16.6460	−	19.4778i	0.767009	−	0.897490i
$472$		0			0
$473$	21.3432			0.981362
$474$		0			0
$475$	−0.990281	+	1.71522i	−0.0454372	+	0.0786996i
$476$		0			0
$477$	−18.7890	−	7.22575i	−0.860288	−	0.330844i
$478$		0			0
$479$	−13.7436	−	23.8047i	−0.627962	−	1.08766i	−0.987960	−	0.154709i	$-0.950556\pi$
$479$	−13.7436	−	23.8047i	−0.627962	−	1.08766i	0.359998	−	0.932953i	$-0.382777\pi$
$480$		0			0
$481$	−1.90932	+	3.30705i	−0.0870577	+	0.150788i
$482$		0			0
$483$	−0.854759	+	0.701353i	−0.0388929	+	0.0319126i
$484$		0			0
$485$	11.8938	+	20.6007i	0.540070	+	0.935429i
$486$		0			0
$487$	−6.32927	+	10.9626i	−0.286807	+	0.496763i	−0.973046	−	0.230613i	$-0.925927\pi$
$487$	−6.32927	+	10.9626i	−0.286807	+	0.496763i	0.686239	+	0.727376i	$0.259260\pi$
$488$		0			0
$489$	25.7038	+	4.77215i	1.16237	+	0.215804i
$490$		0			0
$491$	−1.40618	−	2.43557i	−0.0634598	−	0.109916i	0.832550	−	0.553950i	$-0.186880\pi$
$491$	−1.40618	−	2.43557i	−0.0634598	−	0.109916i	−0.896010	+	0.444034i	$0.853547\pi$
$492$		0			0
$493$	−6.61186	−	11.4521i	−0.297783	−	0.515776i
$494$		0			0
$495$	2.23491	+	14.1674i	0.100452	+	0.636775i
$496$		0			0
$497$	−1.38261	−	3.82203i	−0.0620187	−	0.171442i
$498$		0			0
$499$	2.12103	−	3.67373i	0.0949502	−	0.164459i	−0.814638	−	0.579970i	$-0.803064\pi$
$499$	2.12103	−	3.67373i	0.0949502	−	0.164459i	0.909588	+	0.415512i	$0.136397\pi$
$500$		0			0
$501$	6.57153	+	1.22006i	0.293594	+	0.0545084i
$502$		0			0
$503$	22.2162			0.990570			0.495285	−	0.868730i	$-0.335064\pi$
$503$	22.2162			0.990570			0.495285	+	0.868730i	$0.335064\pi$
$504$		0			0
$505$	22.6446			1.00767
$506$		0			0
$507$	10.8953	+	30.7975i	0.483876	+	1.36777i
$508$		0			0
$509$	2.42735	−	4.20429i	0.107590	−	0.186352i	−0.807203	−	0.590273i	$-0.799020\pi$
$509$	2.42735	−	4.20429i	0.107590	−	0.186352i	0.914794	+	0.403922i	$0.132353\pi$
$510$		0			0
$511$	−34.1706	−	6.09440i	−1.51162	−	0.269601i
$512$		0			0
$513$	0.179314	−	6.61330i	0.00791693	−	0.291984i
$514$		0			0
$515$	−12.6604	−	21.9284i	−0.557882	−	0.966280i
$516$		0			0
$517$	−15.8611	−	27.4722i	−0.697569	−	1.20823i
$518$		0			0
$519$	0.733203	−	0.857933i	0.0321840	−	0.0376591i
$520$		0			0
$521$	7.92316	−	13.7233i	0.347120	−	0.601229i	−0.638617	−	0.769525i	$-0.720493\pi$
$521$	7.92316	−	13.7233i	0.347120	−	0.601229i	0.985737	+	0.168296i	$0.0538263\pi$
$522$		0			0
$523$	10.7605	+	18.6377i	0.470524	+	0.814972i	0.999432	−	0.0337078i	$-0.0107316\pi$
$523$	10.7605	+	18.6377i	0.470524	+	0.814972i	−0.528908	+	0.848679i	$0.677398\pi$
$524$		0			0
$525$	1.16057	+	7.03346i	0.0506515	+	0.306965i
$526$		0			0
$527$	−10.7064	+	18.5441i	−0.466379	+	0.807792i
$528$		0			0
$529$	11.4709	+	19.8682i	0.498734	+	0.863833i
$530$		0			0
$531$	−0.973643	−	6.17204i	−0.0422525	−	0.267844i
$532$		0			0
$533$	4.14271	−	7.17539i	0.179441	−	0.310801i
$534$		0			0
$535$	24.0527			1.03989
$536$		0			0
$537$	−12.5999	−	35.6161i	−0.543727	−	1.53695i
$538$		0			0
$539$	−16.9202	−	6.23382i	−0.728806	−	0.268510i
$540$		0			0
$541$	7.55977	+	13.0939i	0.325020	+	0.562951i	0.981516	−	0.191378i	$-0.0612957\pi$
$541$	7.55977	+	13.0939i	0.325020	+	0.562951i	−0.656497	+	0.754329i	$0.727962\pi$
$542$		0			0
$543$	−28.1701	+	32.9623i	−1.20890	+	1.41455i
$544$		0			0
$545$	14.2922	+	24.7548i	0.612211	+	1.06038i
$546$		0			0
$547$	−19.4532	+	33.6939i	−0.831757	+	1.44065i	0.0648863	+	0.997893i	$0.479332\pi$
$547$	−19.4532	+	33.6939i	−0.831757	+	1.44065i	−0.896644	+	0.442753i	$0.854002\pi$
$548$		0			0
$549$	−6.05817	−	38.4035i	−0.258556	−	1.63902i
$550$		0			0
$551$	2.35177			0.100189
$552$		0			0
$553$	−3.34823	−	9.25568i	−0.142381	−	0.393592i
$554$		0			0
$555$	−1.41287	+	1.65322i	−0.0599729	+	0.0701753i
$556$		0			0
$557$	−5.37036	+	9.30173i	−0.227549	+	0.394127i	−0.957081	−	0.289820i	$-0.906405\pi$
$557$	−5.37036	+	9.30173i	−0.227549	+	0.394127i	0.729532	+	0.683947i	$0.239738\pi$
$558$		0			0
$559$	46.7672			1.97804
$560$		0			0
$561$	20.7521	−	24.2824i	0.876156	−	1.02520i
$562$		0			0
$563$	−23.4760			−0.989394			−0.494697	−	0.869066i	$-0.664721\pi$
$563$	−23.4760			−0.989394			−0.494697	+	0.869066i	$0.664721\pi$
$564$		0			0
$565$	28.7090			1.20780
$566$		0			0
$567$	−14.5999	−	18.8107i	−0.613136	−	0.789977i
$568$		0			0
$569$	−37.9361			−1.59037			−0.795183	−	0.606370i	$-0.792625\pi$
$569$	−37.9361			−1.59037			−0.795183	+	0.606370i	$0.792625\pi$
$570$		0			0
$571$	−4.31630			−0.180632			−0.0903158	−	0.995913i	$-0.528788\pi$
$571$	−4.31630			−0.180632			−0.0903158	+	0.995913i	$0.528788\pi$
$572$		0			0
$573$	9.74578	−	11.4037i	0.407136	−	0.476396i
$574$		0			0
$575$	−0.375326			−0.0156522
$576$		0			0
$577$	−5.05923	+	8.76284i	−0.210618	+	0.364802i	−0.951908	−	0.306383i	$-0.900881\pi$
$577$	−5.05923	+	8.76284i	−0.210618	+	0.364802i	0.741290	+	0.671185i	$0.234214\pi$
$578$		0			0
$579$	1.81918	−	2.12866i	0.0756027	−	0.0884640i
$580$		0			0
$581$	−15.6369	−	2.78888i	−0.648729	−	0.115702i
$582$		0			0
$583$	17.2854			0.715890
$584$		0			0
$585$	4.89712	+	31.0435i	0.202471	+	1.28349i
$586$		0			0
$587$	−4.10992	+	7.11859i	−0.169635	+	0.293816i	−0.938291	−	0.345846i	$-0.887592\pi$
$587$	−4.10992	+	7.11859i	−0.169635	+	0.293816i	0.768657	+	0.639661i	$0.220925\pi$
$588$		0			0
$589$	−1.90409	−	3.29797i	−0.0784565	−	0.135891i
$590$		0			0
$591$	12.1245	−	14.1871i	0.498735	−	0.583578i
$592$		0			0
$593$	21.8434	+	37.8339i	0.897002	+	1.55365i	0.831307	+	0.555814i	$0.187593\pi$
$593$	21.8434	+	37.8339i	0.897002	+	1.55365i	0.0656957	+	0.997840i	$0.479073\pi$
$594$		0			0
$595$	−22.6486	+	26.8842i	−0.928504	+	1.10215i
$596$		0			0
$597$	−2.75856	−	7.79759i	−0.112900	−	0.319134i
$598$		0			0
$599$	−15.2789			−0.624280			−0.312140	−	0.950036i	$-0.601046\pi$
$599$	−15.2789			−0.624280			−0.312140	+	0.950036i	$0.601046\pi$
$600$		0			0
$601$	7.65696	−	13.2622i	0.312334	−	0.540978i	−0.666533	−	0.745475i	$-0.732223\pi$
$601$	7.65696	−	13.2622i	0.312334	−	0.540978i	0.978867	+	0.204497i	$0.0655559\pi$
$602$		0			0
$603$	2.25836	+	14.3160i	0.0919676	+	0.582994i
$604$		0			0
$605$	4.04977	+	7.01441i	0.164647	+	0.285176i
$606$		0			0
$607$	1.33490	−	2.31212i	0.0541821	−	0.0938461i	−0.837662	−	0.546189i	$-0.816078\pi$
$607$	1.33490	−	2.31212i	0.0541821	−	0.0938461i	0.891844	+	0.452342i	$0.149412\pi$
$608$		0			0
$609$	6.54376	−	5.36933i	0.265167	−	0.217576i
$610$		0			0
$611$	−34.7547	−	60.1970i	−1.40603	−	2.43531i
$612$		0			0
$613$	−13.5875	+	23.5343i	−0.548796	+	0.950542i	0.449562	+	0.893249i	$0.351580\pi$
$613$	−13.5875	+	23.5343i	−0.548796	+	0.950542i	−0.998357	+	0.0572929i	$0.981753\pi$
$614$		0			0
$615$	3.06554	−	3.58703i	0.123614	−	0.144643i
$616$		0			0
$617$	−17.6058	−	30.4942i	−0.708785	−	1.22765i	−0.965308	−	0.261113i	$-0.915910\pi$
$617$	−17.6058	−	30.4942i	−0.708785	−	1.22765i	0.256524	−	0.966538i	$-0.417423\pi$
$618$		0			0
$619$	15.6340	+	27.0790i	0.628385	+	1.08840i	0.987876	+	0.155247i	$0.0496172\pi$
$619$	15.6340	+	27.0790i	0.628385	+	1.08840i	−0.359490	+	0.933149i	$0.617049\pi$
$620$		0			0
$621$	1.10234	−	0.597198i	0.0442354	−	0.0239647i
$622$		0			0
$623$	−22.5130	+	26.7233i	−0.901966	+	1.07064i
$624$		0			0
$625$	7.40113	−	12.8191i	0.296045	−	0.512765i
$626$		0			0
$627$	1.89461	+	5.35547i	0.0756634	+	0.213877i
$628$		0			0
$629$	4.84322			0.193112
$630$		0			0
$631$	15.5090			0.617403			0.308702	−	0.951159i	$-0.400106\pi$
$631$	15.5090			0.617403			0.308702	+	0.951159i	$0.400106\pi$
$632$		0			0
$633$	8.26909	+	1.53523i	0.328667	+	0.0610199i
$634$		0			0
$635$	2.96393	−	5.13369i	0.117620	−	0.203724i
$636$		0			0
$637$	−37.0756	−	13.6595i	−1.46899	−	0.541210i
$638$		0			0
$639$	0.718133	+	4.55233i	0.0284089	+	0.180087i
$640$		0			0
$641$	16.7655	+	29.0387i	0.662198	+	1.14696i	0.980037	+	0.198816i	$0.0637096\pi$
$641$	16.7655	+	29.0387i	0.662198	+	1.14696i	−0.317839	+	0.948145i	$0.602957\pi$
$642$		0			0
$643$	−10.2721	−	17.7918i	−0.405093	−	0.701641i	0.589239	−	0.807958i	$-0.299427\pi$
$643$	−10.2721	−	17.7918i	−0.405093	−	0.701641i	−0.994332	+	0.106317i	$0.966094\pi$
$644$		0			0
$645$	26.1862	+	4.86170i	1.03108	+	0.191429i
$646$		0			0
$647$	−16.8855	+	29.2465i	−0.663836	+	1.14980i	0.315763	+	0.948838i	$0.397739\pi$
$647$	−16.8855	+	29.2465i	−0.663836	+	1.14980i	−0.979599	+	0.200960i	$0.935594\pi$
$648$		0			0
$649$	2.68264	+	4.64647i	0.105303	+	0.182390i
$650$		0			0
$651$	−12.8277	−	4.82933i	−0.502756	−	0.189276i
$652$		0			0
$653$	−9.00576	+	15.5984i	−0.352423	+	0.610414i	−0.986673	−	0.162714i	$-0.947975\pi$
$653$	−9.00576	+	15.5984i	−0.352423	+	0.610414i	0.634251	+	0.773127i	$0.281309\pi$
$654$		0			0
$655$	−13.0719	−	22.6412i	−0.510762	−	0.884665i
$656$		0			0
$657$	36.7344	+	14.1271i	1.43315	+	0.551150i
$658$		0			0
$659$	1.42710	−	2.47180i	0.0555918	−	0.0962878i	−0.836890	−	0.547371i	$-0.815629\pi$
$659$	1.42710	−	2.47180i	0.0555918	−	0.0962878i	0.892482	+	0.451083i	$0.148962\pi$
$660$		0			0
$661$	14.0549			0.546673			0.273337	−	0.961918i	$-0.411873\pi$
$661$	14.0549			0.546673			0.273337	+	0.961918i	$0.411873\pi$
$662$		0			0
$663$	45.4720	−	53.2076i	1.76599	−	2.06641i
$664$		0			0
$665$	−2.12669	−	5.87892i	−0.0824695	−	0.227975i
$666$		0			0
$667$	0.222837	+	0.385964i	0.00862827	+	0.0149446i
$668$		0			0
$669$	−4.46174	−	12.6120i	−0.172501	−	0.487607i
$670$		0			0
$671$	16.6918	+	28.9111i	0.644381	+	1.11610i
$672$		0			0
$673$	−7.54157	+	13.0624i	−0.290706	+	0.503518i	−0.973977	−	0.226647i	$-0.927223\pi$
$673$	−7.54157	+	13.0624i	−0.290706	+	0.503518i	0.683271	+	0.730165i	$0.260557\pi$
$674$		0			0
$675$	0.219085	−	8.08007i	0.00843258	−	0.311002i
$676$		0			0
$677$	−36.2187			−1.39200			−0.695998	−	0.718043i	$-0.745038\pi$
$677$	−36.2187			−1.39200			−0.695998	+	0.718043i	$0.745038\pi$
$678$		0			0
$679$	33.3843	+	5.95417i	1.28117	+	0.228500i
$680$		0			0
$681$	23.7547	+	4.41027i	0.910282	+	0.169002i
$682$		0			0
$683$	8.84350	−	15.3174i	0.338387	−	0.586104i	−0.645742	−	0.763555i	$-0.723452\pi$
$683$	8.84350	−	15.3174i	0.338387	−	0.586104i	0.984130	+	0.177452i	$0.0567853\pi$
$684$		0			0
$685$	25.4193			0.971220
$686$		0			0
$687$	0.924422	+	2.61305i	0.0352689	+	0.0996942i
$688$		0			0
$689$	37.8758			1.44295
$690$		0			0
$691$	22.4097			0.852506			0.426253	−	0.904604i	$-0.359833\pi$
$691$	22.4097			0.852506			0.426253	+	0.904604i	$0.359833\pi$
$692$		0			0
$693$	17.4988	+	10.5759i	0.664723	+	0.401745i
$694$		0			0
$695$	18.3413			0.695725
$696$		0			0
$697$	−10.5085			−0.398037
$698$		0			0
$699$	12.5997	+	2.33925i	0.476566	+	0.0884787i
$700$		0			0
$701$	−31.1776			−1.17756			−0.588781	−	0.808293i	$-0.700392\pi$
$701$	−31.1776			−1.17756			−0.588781	+	0.808293i	$0.700392\pi$
$702$		0			0
$703$	−0.430672	+	0.745946i	−0.0162431	+	0.0281339i
$704$		0			0
$705$	−13.2023	−	37.3188i	−0.497228	−	1.40551i
$706$		0			0
$707$	20.7988	−	24.6884i	0.782218	−	0.928503i
$708$		0			0
$709$	−8.04985			−0.302318			−0.151159	−	0.988509i	$-0.548301\pi$
$709$	−8.04985			−0.302318			−0.151159	+	0.988509i	$0.548301\pi$
$710$		0			0
$711$	1.73908	+	11.0242i	0.0652205	+	0.413440i
$712$		0			0
$713$	0.360834	−	0.624982i	0.0135133	−	0.0234058i
$714$		0			0
$715$	−13.4929	−	23.3703i	−0.504604	−	0.874000i
$716$		0			0
$717$	−4.26137	−	0.791161i	−0.159144	−	0.0295464i
$718$		0			0
$719$	−20.9980	−	36.3696i	−0.783093	−	1.35636i	−0.930132	−	0.367226i	$-0.880308\pi$
$719$	−20.9980	−	36.3696i	−0.783093	−	1.35636i	0.147039	−	0.989131i	$-0.453026\pi$
$720$		0			0
$721$	−35.5359	−	6.33791i	−1.32343	−	0.236036i
$722$		0			0
$723$	−7.22556	−	1.34149i	−0.268722	−	0.0498906i
$724$		0			0
$725$	2.87338			0.106715
$726$		0			0
$727$	0.668774	−	1.15835i	0.0248035	−	0.0429609i	−0.853357	−	0.521327i	$-0.825437\pi$
$727$	0.668774	−	1.15835i	0.0248035	−	0.0429609i	0.878161	+	0.478366i	$0.158771\pi$
$728$		0			0
$729$	12.2131	+	24.0799i	0.452337	+	0.891847i
$730$		0			0
$731$	−29.6576	−	51.3684i	−1.09693	−	1.89993i
$732$		0			0
$733$	−14.7374	+	25.5260i	−0.544340	+	0.942824i	0.454308	+	0.890845i	$0.349886\pi$
$733$	−14.7374	+	25.5260i	−0.544340	+	0.942824i	−0.998648	+	0.0519798i	$0.983447\pi$
$734$		0			0
$735$	−19.3396	−	11.5025i	−0.713353	−	0.424278i
$736$		0			0
$737$	−6.22238	−	10.7775i	−0.229204	−	0.396993i
$738$		0			0
$739$	9.52146	−	16.4916i	0.350252	−	0.606655i	−0.636041	−	0.771655i	$-0.719429\pi$
$739$	9.52146	−	16.4916i	0.350252	−	0.606655i	0.986294	+	0.165000i	$0.0527625\pi$
$740$		0			0
$741$	4.15146	+	11.7349i	0.152508	+	0.431092i
$742$		0			0
$743$	21.6613	+	37.5185i	0.794676	+	1.37642i	0.923045	+	0.384693i	$0.125693\pi$
$743$	21.6613	+	37.5185i	0.794676	+	1.37642i	−0.128369	+	0.991726i	$0.540974\pi$
$744$		0			0
$745$	3.63786	+	6.30097i	0.133281	+	0.230850i
$746$		0			0
$747$	16.8102	+	6.46475i	0.615052	+	0.236533i
$748$		0			0
$749$	22.0921	−	26.2236i	0.807228	−	0.958190i
$750$		0			0
$751$	−17.4381	+	30.2037i	−0.636327	+	1.10215i	0.349906	+	0.936785i	$0.386214\pi$
$751$	−17.4381	+	30.2037i	−0.636327	+	1.10215i	−0.986232	+	0.165365i	$0.947120\pi$
$752$		0			0
$753$	−15.2342	+	17.8258i	−0.555165	+	0.649608i
$754$		0			0
$755$	36.3358			1.32240
$756$		0			0
$757$	8.67255			0.315209			0.157605	−	0.987502i	$-0.449623\pi$
$757$	8.67255			0.315209			0.157605	+	0.987502i	$0.449623\pi$
$758$		0			0
$759$	−0.699400	+	0.818380i	−0.0253866	+	0.0297053i
$760$		0			0
$761$	2.74489	−	4.75428i	0.0995021	−	0.172343i	−0.811977	−	0.583690i	$-0.801608\pi$
$761$	2.74489	−	4.75428i	0.0995021	−	0.172343i	0.911479	+	0.411347i	$0.134942\pi$
$762$		0			0
$763$	40.1163	+	7.15482i	1.45231	+	0.259022i
$764$		0			0
$765$	30.9922	−	25.0653i	1.12053	−	0.906237i
$766$		0			0
$767$	5.87819	+	10.1813i	0.212249	+	0.367627i
$768$		0			0
$769$	1.81365	+	3.14134i	0.0654021	+	0.113280i	0.896872	−	0.442290i	$-0.145834\pi$
$769$	1.81365	+	3.14134i	0.0654021	+	0.113280i	−0.831470	+	0.555569i	$0.812500\pi$
$770$		0			0
$771$	−3.55550	−	10.0503i	−0.128048	−	0.361953i
$772$		0			0
$773$	−6.96717	+	12.0675i	−0.250592	+	0.434037i	−0.963689	−	0.267028i	$-0.913958\pi$
$773$	−6.96717	+	12.0675i	−0.250592	+	0.434037i	0.713097	+	0.701065i	$0.247292\pi$
$774$		0			0
$775$	−2.32640	−	4.02944i	−0.0835666	−	0.144742i
$776$		0			0
$777$	0.504731	+	3.05884i	0.0181071	+	0.109735i
$778$		0			0
$779$	0.934441	−	1.61850i	0.0334798	−	0.0579888i
$780$		0			0
$781$	−1.97864	−	3.42711i	−0.0708014	−	0.122632i
$782$		0			0
$783$	−8.43916	+	4.57196i	−0.301591	+	0.163388i
$784$		0			0
$785$	−13.7270	+	23.7759i	−0.489939	+	0.848599i
$786$		0			0
$787$	17.5785			0.626604			0.313302	−	0.949654i	$-0.398565\pi$
$787$	17.5785			0.626604			0.313302	+	0.949654i	$0.398565\pi$
$788$		0			0
$789$	43.1546	+	8.01204i	1.53635	+	0.285236i
$790$		0			0
$791$	26.3688	−	31.3001i	0.937567	−	1.11290i
$792$		0			0
$793$	36.5751	+	63.3499i	1.29882	+	2.24962i
$794$		0			0
$795$	21.2077	+	3.93739i	0.752159	+	0.139645i
$796$		0			0
$797$	5.57971	+	9.66434i	0.197644	+	0.342329i	0.947764	−	0.318973i	$-0.103338\pi$
$797$	5.57971	+	9.66434i	0.197644	+	0.342329i	−0.750120	+	0.661301i	$0.770004\pi$
$798$		0			0
$799$	−44.0797	+	76.3483i	−1.55943	+	2.70101i
$800$		0			0
$801$	30.8067	−	24.9152i	1.08850	−	0.880336i
$802$		0			0
$803$	−33.7949			−1.19259
$804$		0			0
$805$	0.763317	−	0.906067i	0.0269034	−	0.0319347i
$806$		0			0
$807$	6.26296	+	17.7034i	0.220466	+	0.623190i
$808$		0			0
$809$	14.3481	−	24.8517i	0.504453	−	0.873738i	−0.495534	−	0.868589i	$-0.665028\pi$
$809$	14.3481	−	24.8517i	0.504453	−	0.873738i	0.999987	−	0.00514935i	$-0.00163910\pi$
$810$		0			0
$811$	47.1695			1.65635			0.828173	−	0.560473i	$-0.189380\pi$
$811$	47.1695			1.65635			0.828173	+	0.560473i	$0.189380\pi$
$812$		0			0
$813$	−51.1513	−	9.49670i	−1.79396	−	0.333064i
$814$		0			0
$815$	−28.0126			−0.981240
$816$		0			0
$817$	10.5489			0.369060
$818$		0			0
$819$	38.3432	+	23.1739i	1.33982	+	0.809761i
$820$		0			0
$821$	−38.7707			−1.35311			−0.676554	−	0.736393i	$-0.736528\pi$
$821$	−38.7707			−1.35311			−0.676554	+	0.736393i	$0.736528\pi$
$822$		0			0
$823$	−22.7840			−0.794202			−0.397101	−	0.917775i	$-0.629984\pi$
$823$	−22.7840			−0.794202			−0.397101	+	0.917775i	$0.629984\pi$
$824$		0			0
$825$	2.31482	+	6.54327i	0.0805916	+	0.227807i
$826$		0			0
$827$	−1.55152			−0.0539515			−0.0269758	−	0.999636i	$-0.508588\pi$
$827$	−1.55152			−0.0539515			−0.0269758	+	0.999636i	$0.508588\pi$
$828$		0			0
$829$	−23.8972	+	41.3911i	−0.829983	+	1.43757i	0.0680673	+	0.997681i	$0.478317\pi$
$829$	−23.8972	+	41.3911i	−0.829983	+	1.43757i	−0.898051	+	0.439892i	$0.855017\pi$
$830$		0			0
$831$	−33.6553	−	6.24841i	−1.16749	−	0.216755i
$832$		0			0
$833$	8.50818	+	49.3856i	0.294791	+	1.71111i
$834$		0			0
$835$	−7.16181			−0.247845
$836$		0			0
$837$	13.2441	+	8.13288i	0.457782	+	0.281114i
$838$		0			0
$839$	19.5804	−	33.9142i	0.675990	−	1.17085i	−0.300188	−	0.953880i	$-0.597049\pi$
$839$	19.5804	−	33.9142i	0.675990	−	1.17085i	0.976178	−	0.216970i	$-0.0696173\pi$
$840$		0			0
$841$	12.7940	+	22.1599i	0.441174	+	0.764135i
$842$		0			0
$843$	4.60510	+	13.0172i	0.158608	+	0.448336i
$844$		0			0
$845$	−17.5021	−	30.3145i	−0.602089	−	1.04285i
$846$		0			0
$847$	11.3672	+	2.02736i	0.390580	+	0.0696609i
$848$		0			0
$849$	26.1209	−	30.5645i	0.896466	−	1.04897i
$850$		0			0
$851$	−0.163229			−0.00559542
$852$		0			0
$853$	14.5234	−	25.1552i	0.497270	−	0.861298i	−0.502725	−	0.864447i	$-0.667669\pi$
$853$	14.5234	−	25.1552i	0.497270	−	0.861298i	0.999995	+	0.00314895i	$0.00100234\pi$
$854$		0			0
$855$	1.10461	+	7.00224i	0.0377768	+	0.239472i
$856$		0			0
$857$	24.1292	+	41.7930i	0.824239	+	1.42762i	0.902500	+	0.430690i	$0.141730\pi$
$857$	24.1292	+	41.7930i	0.824239	+	1.42762i	−0.0782612	+	0.996933i	$0.524937\pi$
$858$		0			0
$859$	5.07528	−	8.79063i	0.173166	−	0.299933i	−0.766359	−	0.642413i	$-0.777934\pi$
$859$	5.07528	−	8.79063i	0.173166	−	0.299933i	0.939525	+	0.342480i	$0.111267\pi$
$860$		0			0
$861$	−1.09513	−	6.63686i	−0.0373219	−	0.226184i
$862$		0			0
$863$	25.7981	+	44.6837i	0.878179	+	1.52105i	0.853338	+	0.521359i	$0.174575\pi$
$863$	25.7981	+	44.6837i	0.878179	+	1.52105i	0.0248411	+	0.999691i	$0.492092\pi$
$864$		0			0
$865$	−0.604630	+	1.04725i	−0.0205580	+	0.0356076i
$866$		0			0
$867$	−58.3287	−	10.8292i	−1.98094	−	0.367780i
$868$		0			0
$869$	−4.79161	−	8.29931i	−0.162544	−	0.281535i
$870$		0			0
$871$	−13.6345	−	23.6156i	−0.461986	−	0.800183i
$872$		0			0
$873$	−35.8891	−	13.8020i	−1.21466	−	0.467128i
$874$		0			0
$875$	−10.9501	−	30.2701i	−0.370182	−	1.02332i
$876$		0			0
$877$	5.19891	−	9.00477i	0.175555	−	0.304069i	−0.764798	−	0.644270i	$-0.777161\pi$
$877$	5.19891	−	9.00477i	0.175555	−	0.304069i	0.940353	+	0.340200i	$0.110495\pi$
$878$		0			0
$879$	40.3790	+	7.49672i	1.36195	+	0.252858i
$880$		0			0
$881$	23.6562			0.796996			0.398498	−	0.917169i	$-0.369532\pi$
$881$	23.6562			0.796996			0.398498	+	0.917169i	$0.369532\pi$
$882$		0			0
$883$	41.8601			1.40871			0.704353	−	0.709850i	$-0.251237\pi$
$883$	41.8601			1.40871			0.704353	+	0.709850i	$0.251237\pi$
$884$		0			0
$885$	2.23295	+	6.31187i	0.0750599	+	0.212171i
$886$		0			0
$887$	−21.1252	+	36.5900i	−0.709316	+	1.22857i	0.255795	+	0.966731i	$0.417663\pi$
$887$	−21.1252	+	36.5900i	−0.709316	+	1.22857i	−0.965111	+	0.261840i	$0.915671\pi$
$888$		0			0
$889$	−2.87469	−	7.94667i	−0.0964141	−	0.266523i
$890$		0			0
$891$	−17.2099	−	15.5345i	−0.576554	−	0.520424i
$892$		0			0
$893$	−7.83937	−	13.5782i	−0.262334	−	0.454377i
$894$		0			0
$895$	20.2404	+	35.0574i	0.676563	+	1.17184i
$896$		0			0
$897$	−1.53252	+	1.79323i	−0.0511695	+	0.0598743i
$898$		0			0
$899$	−2.76243	+	4.78467i	−0.0921321	+	0.159578i
$900$		0			0
$901$	−24.0191	−	41.6023i	−0.800192	−	1.38597i
$902$		0			0
$903$	29.3521	−	24.0842i	0.976778	−	0.801472i
$904$		0			0
$905$	23.2303	−	40.2360i	0.772201	−	1.33749i
$906$		0			0
$907$	20.4404	+	35.4037i	0.678711	+	1.17556i	0.975369	+	0.220578i	$0.0707945\pi$
$907$	20.4404	+	35.4037i	0.678711	+	1.17556i	−0.296658	+	0.954984i	$0.595872\pi$
$908$		0			0
$909$	−28.4609	+	23.0180i	−0.943988	+	0.763460i
$910$		0			0
$911$	14.4235	−	24.9823i	0.477873	−	0.827701i	−0.521805	−	0.853065i	$-0.674741\pi$
$911$	14.4235	−	24.9823i	0.477873	−	0.827701i	0.999678	+	0.0253641i	$0.00807452\pi$
$912$		0			0
$913$	−15.4650			−0.511816
$914$		0			0
$915$	13.8938	+	39.2735i	0.459315	+	1.29834i
$916$		0			0
$917$	−36.6910	−	6.54393i	−1.21165	−	0.216100i
$918$		0			0
$919$	21.8195	+	37.7925i	0.719760	+	1.24666i	0.961095	+	0.276219i	$0.0890815\pi$
$919$	21.8195	+	37.7925i	0.719760	+	1.24666i	−0.241335	+	0.970442i	$0.577585\pi$
$920$		0			0
$921$	4.36397	−	5.10635i	0.143798	−	0.168260i
$922$		0			0
$923$	−4.33560	−	7.50947i	−0.142708	−	0.247177i
$924$		0			0
$925$	−0.526192	+	0.911391i	−0.0173011	+	0.0299663i
$926$		0			0
$927$	38.2021	+	14.6915i	1.25472	+	0.482534i
$928$		0			0
$929$	−27.4754			−0.901438			−0.450719	−	0.892666i	$-0.648832\pi$
$929$	−27.4754			−0.901438			−0.450719	+	0.892666i	$0.648832\pi$
$930$		0			0
$931$	−8.36286	−	3.08108i	−0.274082	−	0.100978i
$932$		0			0
$933$	−7.79191	+	9.11744i	−0.255096	+	0.298492i
$934$		0			0
$935$	−17.1131	+	29.6408i	−0.559658	+	0.969356i
$936$		0			0
$937$	−3.11920			−0.101900			−0.0509500	−	0.998701i	$-0.516225\pi$
$937$	−3.11920			−0.101900			−0.0509500	+	0.998701i	$0.516225\pi$
$938$		0			0
$939$	34.0188	−	39.8060i	1.11016	−	1.29902i
$940$		0			0
$941$	−26.1215			−0.851538			−0.425769	−	0.904832i	$-0.639996\pi$
$941$	−26.1215			−0.851538			−0.425769	+	0.904832i	$0.639996\pi$
$942$		0			0
$943$	0.354163			0.0115331
$944$		0			0
$945$	19.0604	+	16.9617i	0.620033	+	0.551763i
$946$		0			0
$947$	−7.18031			−0.233329			−0.116664	−	0.993171i	$-0.537220\pi$
$947$	−7.18031			−0.233329			−0.116664	+	0.993171i	$0.537220\pi$
$948$		0			0
$949$	−74.0512			−2.40380
$950$		0			0
$951$	10.5484	−	12.3429i	0.342055	−	0.400245i
$952$		0			0
$953$	−32.1187			−1.04043			−0.520214	−	0.854036i	$-0.674148\pi$
$953$	−32.1187			−1.04043			−0.520214	+	0.854036i	$0.674148\pi$
$954$		0			0
$955$	−8.03678	+	13.9201i	−0.260064	+	0.450444i
$956$		0			0
$957$	5.35438	−	6.26526i	0.173083	−	0.202527i
$958$		0			0
$959$	23.3473	−	27.7135i	0.753922	−	0.894915i
$960$		0			0
$961$	−22.0537			−0.711411
$962$		0			0
$963$	−30.2307	+	24.4494i	−0.974170	+	0.787870i
$964$		0			0
$965$	−1.50018	+	2.59838i	−0.0482924	+	0.0836449i
$966$		0			0
$967$	−27.4860	−	47.6071i	−0.883890	−	1.53094i	−0.846981	−	0.531623i	$-0.821582\pi$
$967$	−27.4860	−	47.6071i	−0.883890	−	1.53094i	−0.0369085	−	0.999319i	$-0.511751\pi$
$968$		0			0
$969$	10.2568	−	12.0016i	0.329495	−	0.385548i
$970$		0			0
$971$	20.8518	+	36.1163i	0.669165	+	1.15903i	0.978138	+	0.207957i	$0.0666813\pi$
$971$	20.8518	+	36.1163i	0.669165	+	1.15903i	−0.308973	+	0.951071i	$0.599985\pi$
$972$		0			0
$973$	16.8462	−	19.9967i	0.540065	−	0.641064i
$974$		0			0
$975$	5.07222	+	14.3376i	0.162441	+	0.459170i
$976$		0			0
$977$	5.22874			0.167282			0.0836412	−	0.996496i	$-0.473345\pi$
$977$	5.22874			0.167282			0.0836412	+	0.996496i	$0.473345\pi$
$978$		0			0
$979$	−17.0106	+	29.4633i	−0.543662	+	0.941651i
$980$		0			0
$981$	−43.1262	−	16.5852i	−1.37691	−	0.529525i
$982$		0			0
$983$	−3.45349	−	5.98162i	−0.110149	−	0.190784i	0.805681	−	0.592349i	$-0.201800\pi$
$983$	−3.45349	−	5.98162i	−0.110149	−	0.190784i	−0.915830	+	0.401566i	$0.868466\pi$
$984$		0			0
$985$	−9.99837	+	17.3177i	−0.318575	+	0.551788i
$986$		0			0
$987$	−52.8132	−	19.8830i	−1.68106	−	0.632882i
$988$		0			0
$989$	0.999537	+	1.73125i	0.0317834	+	0.0550505i
$990$		0			0
$991$	2.19861	−	3.80811i	0.0698412	−	0.120968i	−0.828990	−	0.559263i	$-0.811084\pi$
$991$	2.19861	−	3.80811i	0.0698412	−	0.120968i	0.898831	+	0.438295i	$0.144417\pi$
$992$		0			0
$993$	30.9949	−	36.2676i	0.983593	−	1.15092i
$994$		0			0
$995$	4.43133	+	7.67528i	0.140482	+	0.243323i
$996$		0			0
$997$	14.0180	+	24.2798i	0.443954	+	0.768950i	0.997979	−	0.0635498i	$-0.0202422\pi$
$997$	14.0180	+	24.2798i	0.443954	+	0.768950i	−0.554025	+	0.832500i	$0.686909\pi$
$998$		0			0
$999$	0.0952798	−	3.51401i	0.00301452	−	0.111178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.d.25.7	✓	22
3.2	odd	2		1512.2.q.c.1369.9		22
4.3	odd	2		1008.2.q.k.529.5		22
7.2	even	3		504.2.t.d.457.8	yes	22
9.4	even	3		504.2.t.d.193.8	yes	22
9.5	odd	6		1512.2.t.d.361.3		22
12.11	even	2		3024.2.q.k.2881.9		22
21.2	odd	6		1512.2.t.d.289.3		22
28.23	odd	6		1008.2.t.k.961.4		22
36.23	even	6		3024.2.t.l.1873.3		22
36.31	odd	6		1008.2.t.k.193.4		22
63.23	odd	6		1512.2.q.c.793.9		22
63.58	even	3	inner	504.2.q.d.121.7	yes	22
84.23	even	6		3024.2.t.l.289.3		22
252.23	even	6		3024.2.q.k.2305.9		22
252.247	odd	6		1008.2.q.k.625.5		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.7	✓	22	1.1	even	1	trivial
504.2.q.d.121.7	yes	22	63.58	even	3	inner
504.2.t.d.193.8	yes	22	9.4	even	3
504.2.t.d.457.8	yes	22	7.2	even	3
1008.2.q.k.529.5		22	4.3	odd	2
1008.2.q.k.625.5		22	252.247	odd	6
1008.2.t.k.193.4		22	36.31	odd	6
1008.2.t.k.961.4		22	28.23	odd	6
1512.2.q.c.793.9		22	63.23	odd	6
1512.2.q.c.1369.9		22	3.2	odd	2
1512.2.t.d.289.3		22	21.2	odd	6
1512.2.t.d.361.3		22	9.5	odd	6
3024.2.q.k.2305.9		22	252.23	even	6
3024.2.q.k.2881.9		22	12.11	even	2
3024.2.t.l.289.3		22	84.23	even	6
3024.2.t.l.1873.3		22	36.23	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)

\(f(q)\)	\(=\)	\(q+(1.12528 - 1.31671i) q^{3} +(-0.927957 + 1.60727i) q^{5} +(0.900017 + 2.48796i) q^{7} +(-0.467471 - 2.96335i) q^{9} +O(q^{10})\)	\(q+(1.12528 - 1.31671i) q^{3} +(-0.927957 + 1.60727i) q^{5} +(0.900017 + 2.48796i) q^{7} +(-0.467471 - 2.96335i) q^{9} +(1.28800 + 2.23089i) q^{11} +(2.82227 + 4.88832i) q^{13} +(1.07210 + 3.03049i) q^{15} +(3.57951 - 6.19989i) q^{17} +(0.636599 + 1.10262i) q^{19} +(4.28871 + 1.61460i) q^{21} +(-0.120639 + 0.208952i) q^{23} +(0.777791 + 1.34717i) q^{25} +(-4.42793 - 2.71909i) q^{27} +(0.923571 - 1.59967i) q^{29} -2.99103 q^{31} +(4.38681 + 0.814451i) q^{33} +(-4.83401 - 0.862156i) q^{35} +(0.338260 + 0.585884i) q^{37} +(9.61237 + 1.78462i) q^{39} +(-0.733933 - 1.27121i) q^{41} +(4.14269 - 7.17535i) q^{43} +(5.19670 + 1.99851i) q^{45} -12.3145 q^{47} +(-5.37994 + 4.47842i) q^{49} +(-4.13552 - 11.6898i) q^{51} +(3.35508 - 5.81117i) q^{53} -4.78085 q^{55} +(2.16819 + 0.402544i) q^{57} +2.08279 q^{59} +12.9595 q^{61} +(6.95199 - 3.83012i) q^{63} -10.4758 q^{65} -4.83102 q^{67} +(0.139378 + 0.393977i) q^{69} -1.53621 q^{71} +(-6.55954 + 11.3615i) q^{73} +(2.64908 + 0.491825i) q^{75} +(-4.39115 + 5.21235i) q^{77} -3.72018 q^{79} +(-8.56294 + 2.77056i) q^{81} +(-3.00173 + 5.19915i) q^{83} +(6.64326 + 11.5065i) q^{85} +(-1.06703 - 3.01616i) q^{87} +(6.60349 + 11.4376i) q^{89} +(-9.62187 + 11.4213i) q^{91} +(-3.36576 + 3.93833i) q^{93} -2.36294 q^{95} +(6.40860 - 11.1000i) q^{97} +(6.00881 - 4.85969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more