LMFDB - Embedded newform 504.2.t.d.457.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (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			457.8
Character	$\chi$	$=$	504.457
Dual form			504.2.t.d.193.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.577666 + 1.63288i) q^{3} +1.85591 q^{5} +(-2.60465 + 0.464545i) q^{7} +(-2.33261 + 1.88652i) q^{9} +O(q^{10})$	\(q+(0.577666 + 1.63288i) q^{3} +1.85591 q^{5} +(-2.60465 + 0.464545i) q^{7} +(-2.33261 + 1.88652i) q^{9} -2.57601 q^{11} +(2.82227 + 4.88832i) q^{13} +(1.07210 + 3.03049i) q^{15} +(3.57951 + 6.19989i) q^{17} +(0.636599 - 1.10262i) q^{19} +(-2.26316 - 3.98473i) q^{21} +0.241277 q^{23} -1.55558 q^{25} +(-4.42793 - 2.71909i) q^{27} +(0.923571 - 1.59967i) q^{29} +(1.49552 - 2.59031i) q^{31} +(-1.48807 - 4.20632i) q^{33} +(-4.83401 + 0.862156i) q^{35} +(0.338260 - 0.585884i) q^{37} +(-6.35171 + 7.43225i) q^{39} +(-0.733933 - 1.27121i) q^{41} +(4.14269 - 7.17535i) q^{43} +(-4.32912 + 3.50122i) q^{45} +(6.15723 + 10.6646i) q^{47} +(6.56840 - 2.41995i) q^{49} +(-8.05593 + 9.42638i) q^{51} +(3.35508 + 5.81117i) q^{53} -4.78085 q^{55} +(2.16819 + 0.402544i) q^{57} +(-1.04139 + 1.80375i) q^{59} +(-6.47973 - 11.2232i) q^{61} +(5.19925 - 5.99732i) q^{63} +(5.23789 + 9.07230i) q^{65} +(2.41551 - 4.18379i) q^{67} +(0.139378 + 0.393977i) q^{69} -1.53621 q^{71} +(-6.55954 - 11.3615i) q^{73} +(-0.898606 - 2.54008i) q^{75} +(6.70960 - 1.19667i) q^{77} +(1.86009 + 3.22177i) q^{79} +(1.88209 - 8.80101i) q^{81} +(-3.00173 + 5.19915i) q^{83} +(6.64326 + 11.5065i) q^{85} +(3.14559 + 0.584007i) q^{87} +(6.60349 - 11.4376i) q^{89} +(-9.62187 - 11.4213i) q^{91} +(5.09357 + 0.945667i) q^{93} +(1.18147 - 2.04637i) q^{95} +(6.40860 - 11.1000i) q^{97} +(6.00881 - 4.85969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9	$ 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9} + 6 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} - 15 q^{21} - 4 q^{23} + 20 q^{25} - 4 q^{27} + 9 q^{29} - 4 q^{31} - 31 q^{33} + 14 q^{35} + 2 q^{37} + 8 q^{39} + 16 q^{41} + 22 q^{45} + 5 q^{47} - 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} - 19 q^{59} - 13 q^{61} + 21 q^{63} + 13 q^{65} + 26 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 8 q^{75} - 4 q^{77} + 10 q^{79} - 8 q^{81} - 28 q^{83} - 20 q^{85} + 9 q^{87} + 6 q^{89} - 37 q^{91} - 32 q^{93} + 12 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9 + 6 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 - 15 * q^21 - 4 * q^23 + 20 * q^25 - 4 * q^27 + 9 * q^29 - 4 * q^31 - 31 * q^33 + 14 * q^35 + 2 * q^37 + 8 * q^39 + 16 * q^41 + 22 * q^45 + 5 * q^47 - 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 - 19 * q^59 - 13 * q^61 + 21 * q^63 + 13 * q^65 + 26 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 8 * q^75 - 4 * q^77 + 10 * q^79 - 8 * q^81 - 28 * q^83 - 20 * q^85 + 9 * q^87 + 6 * q^89 - 37 * q^91 - 32 * q^93 + 12 * q^95 - 29 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.577666	+	1.63288i	0.333515	+	0.942745i
$3$	0.577666	+	1.63288i	0.333515	+	0.942745i
$4$		0			0
$5$	1.85591			0.829990			0.414995	−	0.909824i	$-0.363783\pi$
$5$	1.85591			0.829990			0.414995	+	0.909824i	$0.363783\pi$
$6$		0			0
$7$	−2.60465	+	0.464545i	−0.984465	+	0.175582i
$7$	−2.60465	+	0.464545i	−0.984465	+	0.175582i
$8$		0			0
$9$	−2.33261	+	1.88652i	−0.777535	+	0.628840i
$10$		0			0
$11$	−2.57601			−0.776696			−0.388348	−	0.921513i	$-0.626954\pi$
$11$	−2.57601			−0.776696			−0.388348	+	0.921513i	$0.626954\pi$
$12$		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	0.863876	+	0.503704i	$0.168030\pi$
$17$	3.57951	+	6.19989i	0.868158	+	1.50369i	0.00428199	+	0.999991i	$0.498637\pi$
$18$		0			0
$19$	0.636599	−	1.10262i	0.146046	−	0.252959i	−0.783717	−	0.621118i	$-0.786679\pi$
$19$	0.636599	−	1.10262i	0.146046	−	0.252959i	0.929763	+	0.368160i	$0.120012\pi$
$20$		0			0
$21$	−2.26316	−	3.98473i	−0.493863	−	0.869540i
$22$		0			0
$23$	0.241277			0.0503098			0.0251549	−	0.999684i	$-0.491992\pi$
$23$	0.241277			0.0503098			0.0251549	+	0.999684i	$0.491992\pi$
$24$		0			0
$25$	−1.55558			−0.311116
$26$		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
$31$	1.49552	−	2.59031i	0.268602	−	0.465233i	−0.699899	−	0.714242i	$-0.746772\pi$
$31$	1.49552	−	2.59031i	0.268602	−	0.465233i	0.968501	+	0.249009i	$0.0801049\pi$
$32$		0			0
$33$	−1.48807	−	4.20632i	−0.259040	−	0.732226i
$34$		0			0
$35$	−4.83401	+	0.862156i	−0.817096	+	0.145731i
$36$		0			0
$37$	0.338260	−	0.585884i	0.0556097	−	0.0963188i	−0.836880	−	0.547386i	$-0.815623\pi$
$37$	0.338260	−	0.585884i	0.0556097	−	0.0963188i	0.892490	+	0.451067i	$0.148956\pi$
$38$		0			0
$39$	−6.35171	+	7.43225i	−1.01709	+	1.19011i
$40$		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
$45$	−4.32912	+	3.50122i	−0.645346	+	0.521931i
$46$		0			0
$47$	6.15723	+	10.6646i	0.898124	+	1.55560i	0.829890	+	0.557928i	$0.188403\pi$
$47$	6.15723	+	10.6646i	0.898124	+	1.55560i	0.0682346	+	0.997669i	$0.478263\pi$
$48$		0			0
$49$	6.56840	−	2.41995i	0.938342	−	0.345708i
$50$		0			0
$51$	−8.05593	+	9.42638i	−1.12806	+	1.31996i
$52$		0			0
$53$	3.35508	+	5.81117i	0.460856	+	0.798226i	0.999004	−	0.0446243i	$-0.0142091\pi$
$53$	3.35508	+	5.81117i	0.460856	+	0.798226i	−0.538148	+	0.842851i	$0.680876\pi$
$54$		0			0
$55$	−4.78085			−0.644650
$56$		0			0
$57$	2.16819	+	0.402544i	0.287184	+	0.0533182i
$58$		0			0
$59$	−1.04139	+	1.80375i	−0.135578	+	0.234828i	−0.925818	−	0.377969i	$-0.876622\pi$
$59$	−1.04139	+	1.80375i	−0.135578	+	0.234828i	0.790240	+	0.612797i	$0.209956\pi$
$60$		0			0
$61$	−6.47973	−	11.2232i	−0.829644	−	1.43699i	−0.898317	−	0.439347i	$-0.855210\pi$
$61$	−6.47973	−	11.2232i	−0.829644	−	1.43699i	0.0686730	−	0.997639i	$-0.478123\pi$
$62$		0			0
$63$	5.19925	−	5.99732i	0.655043	−	0.755591i
$64$		0			0
$65$	5.23789	+	9.07230i	0.649681	+	1.12528i
$66$		0			0
$67$	2.41551	−	4.18379i	0.295102	−	0.511131i	−0.679907	−	0.733298i	$-0.737980\pi$
$67$	2.41551	−	4.18379i	0.295102	−	0.511131i	0.975009	+	0.222167i	$0.0713132\pi$
$68$		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	−0.938788	−	0.344496i	$-0.888050\pi$
$73$	−6.55954	−	11.3615i	−0.767736	−	1.32976i	0.171052	−	0.985262i	$-0.445283\pi$
$74$		0			0
$75$	−0.898606	−	2.54008i	−0.103762	−	0.293303i
$76$		0			0
$77$	6.70960	−	1.19667i	0.764630	−	0.136373i
$78$		0			0
$79$	1.86009	+	3.22177i	0.209277	+	0.362478i	0.951487	−	0.307689i	$-0.0995558\pi$
$79$	1.86009	+	3.22177i	0.209277	+	0.362478i	−0.742210	+	0.670167i	$0.766222\pi$
$80$		0			0
$81$	1.88209	−	8.80101i	0.209121	−	0.977890i
$82$		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
$87$	3.14559	+	0.584007i	0.337242	+	0.0626121i
$88$		0			0
$89$	6.60349	−	11.4376i	0.699968	−	1.21238i	−0.268509	−	0.963277i	$-0.586531\pi$
$89$	6.60349	−	11.4376i	0.699968	−	1.21238i	0.968477	−	0.249103i	$-0.0801359\pi$
$90$		0			0
$91$	−9.62187	−	11.4213i	−1.00865	−	1.19728i
$92$		0			0
$93$	5.09357	+	0.945667i	0.528179	+	0.0980611i
$94$		0			0
$95$	1.18147	−	2.04637i	0.121217	−	0.209953i
$96$		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
$101$	12.2013			1.21408			0.607039	−	0.794672i	$-0.292357\pi$
$101$	12.2013			1.21408			0.607039	+	0.794672i	$0.292357\pi$
$102$		0			0
$103$	13.6433			1.34431			0.672155	−	0.740411i	$-0.265369\pi$
$103$	13.6433			1.34431			0.672155	+	0.740411i	$0.265369\pi$
$104$		0			0
$105$	−4.20024	−	7.39532i	−0.409901	−	0.721710i
$106$		0			0
$107$	−6.48002	+	11.2237i	−0.626448	+	1.08504i	0.361811	+	0.932251i	$0.382158\pi$
$107$	−6.48002	+	11.2237i	−0.626448	+	1.08504i	−0.988259	+	0.152788i	$0.951175\pi$
$108$		0			0
$109$	7.70089	+	13.3383i	0.737612	+	1.27758i	0.953568	+	0.301178i	$0.0973799\pi$
$109$	7.70089	+	13.3383i	0.737612	+	1.27758i	−0.215956	+	0.976403i	$0.569287\pi$
$110$		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
$115$	0.447790			0.0417566
$116$		0			0
$117$	−15.8051	−	6.07824i	−1.46119	−	0.561934i
$118$		0			0
$119$	−12.2035	−	14.4857i	−1.11869	−	1.32790i
$120$		0			0
$121$	−4.36418			−0.396744
$122$		0			0
$123$	1.65177	−	1.93276i	0.148935	−	0.174271i
$124$		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
$129$	14.1096	+	2.61957i	1.24228	+	0.230640i
$130$		0			0
$131$	14.0868			1.23077			0.615383	−	0.788229i	$-0.289002\pi$
$131$	14.0868			1.23077			0.615383	+	0.788229i	$0.289002\pi$
$132$		0			0
$133$	−1.14590	+	3.16767i	−0.0993620	+	0.274672i
$134$		0			0
$135$	−8.21785	−	5.04640i	−0.707280	−	0.434325i
$136$		0			0
$137$	13.6964			1.17016			0.585079	−	0.810976i	$-0.301063\pi$
$137$	13.6964			1.17016			0.585079	+	0.810976i	$0.301063\pi$
$138$		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
$147$	7.74583	+	9.32749i	0.638866	+	0.769318i
$148$		0			0
$149$	−3.92029			−0.321163			−0.160581	−	0.987023i	$-0.551337\pi$
$149$	−3.92029			−0.321163			−0.160581	+	0.987023i	$0.551337\pi$
$150$		0			0
$151$	19.5784			1.59327			0.796634	−	0.604462i	$-0.206612\pi$
$151$	19.5784			1.59327			0.796634	+	0.604462i	$0.206612\pi$
$152$		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
$157$	−7.39637	+	12.8109i	−0.590295	+	1.02242i	0.403898	+	0.914804i	$0.367655\pi$
$157$	−7.39637	+	12.8109i	−0.590295	+	1.02242i	−0.994193	+	0.107616i	$0.965678\pi$
$158$		0			0
$159$	−7.55084	+	8.83537i	−0.598821	+	0.700690i
$160$		0			0
$161$	−0.628443	+	0.112084i	−0.0495282	+	0.00883347i
$162$		0			0
$163$	7.54686	−	13.0715i	0.591116	−	1.02384i	−0.402967	−	0.915215i	$-0.632021\pi$
$163$	7.54686	−	13.0715i	0.591116	−	1.02384i	0.994082	−	0.108628i	$-0.0346456\pi$
$164$		0			0
$165$	−2.76173	−	7.80656i	−0.215001	−	0.607740i
$166$		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
$171$	0.595183	+	3.77293i	0.0455147	+	0.288524i
$172$		0			0
$173$	−0.325786	−	0.564277i	−0.0247690	−	0.0429012i	0.853375	−	0.521297i	$-0.174552\pi$
$173$	−0.325786	−	0.564277i	−0.0247690	−	0.0429012i	−0.878144	+	0.478396i	$0.841218\pi$
$174$		0			0
$175$	4.05174	−	0.722638i	0.306283	−	0.0546263i
$176$		0			0
$177$	−3.54688	−	0.658511i	−0.266600	−	0.0494967i
$178$		0			0
$179$	10.9059	+	18.8896i	0.815145	+	1.41187i	0.909223	+	0.416308i	$0.136676\pi$
$179$	10.9059	+	18.8896i	0.815145	+	1.41187i	−0.0940781	+	0.995565i	$0.529990\pi$
$180$		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
$185$	0.627782	−	1.08735i	0.0461555	−	0.0799436i
$186$		0			0
$187$	−9.22085	−	15.9710i	−0.674295	−	1.16791i
$188$		0			0
$189$	12.7963	+	5.02531i	0.930797	+	0.365537i
$190$		0			0
$191$	−4.33036	−	7.50041i	−0.313334	−	0.542711i	0.665748	−	0.746177i	$-0.268113\pi$
$191$	−4.33036	−	7.50041i	−0.313334	−	0.542711i	−0.979082	+	0.203466i	$0.934779\pi$
$192$		0			0
$193$	−0.808322	+	1.40006i	−0.0581843	+	0.100778i	−0.893650	−	0.448764i	$-0.851864\pi$
$193$	−0.808322	+	1.40006i	−0.0581843	+	0.100778i	0.835466	+	0.549542i	$0.185198\pi$
$194$		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	0.938159	−	0.346204i	$-0.112530\pi$
$199$	2.38768	+	4.13558i	0.169258	+	0.293163i	−0.768901	+	0.639368i	$0.779196\pi$
$200$		0			0
$201$	8.22699	+	1.52741i	0.580287	+	0.107735i
$202$		0			0
$203$	−1.66246	+	4.59562i	−0.116682	+	0.322549i
$204$		0			0
$205$	−1.36212	−	2.35925i	−0.0951343	−	0.164777i
$206$		0			0
$207$	−0.562805	+	0.455174i	−0.0391176	+	0.0316368i
$208$		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
$213$	−0.887415	−	2.50845i	−0.0608046	−	0.171876i
$214$		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
$219$	14.7627	−	17.2741i	0.997570	−	1.16727i
$220$		0			0
$221$	−20.2047	+	34.9955i	−1.35911	+	2.35406i
$222$		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
$227$	−13.9491			−0.925837			−0.462919	−	0.886401i	$-0.653198\pi$
$227$	−13.9491			−0.925837			−0.462919	+	0.886401i	$0.653198\pi$
$228$		0			0
$229$	1.60027			0.105749			0.0528745	−	0.998601i	$-0.483162\pi$
$229$	1.60027			0.105749			0.0528745	+	0.998601i	$0.483162\pi$
$230$		0			0
$231$	5.82993	+	10.2647i	0.383581	+	0.675368i
$232$		0			0
$233$	3.69939	−	6.40753i	0.242355	−	0.419771i	−0.719030	−	0.694979i	$-0.755413\pi$
$233$	3.69939	−	6.40753i	0.242355	−	0.419771i	0.961385	+	0.275208i	$0.0887468\pi$
$234$		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
$241$	4.24297			0.273314			0.136657	−	0.990618i	$-0.456364\pi$
$241$	4.24297			0.273314			0.136657	+	0.990618i	$0.456364\pi$
$242$		0			0
$243$	15.4582	−	2.01080i	0.991645	−	0.128993i
$244$		0			0
$245$	12.1904	−	4.49123i	0.778815	−	0.286934i
$246$		0			0
$247$	7.18661			0.457273
$248$		0			0
$249$	−10.2236	−	1.89810i	−0.647894	−	0.120287i
$250$		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
$255$	−14.9511	+	17.4946i	−0.936275	+	1.09555i
$256$		0			0
$257$	−6.15495			−0.383935			−0.191968	−	0.981401i	$-0.561487\pi$
$257$	−6.15495			−0.383935			−0.191968	+	0.981401i	$0.561487\pi$
$258$		0			0
$259$	−0.608880	+	1.68316i	−0.0378340	+	0.104586i
$260$		0			0
$261$	0.863485	+	5.47373i	0.0534484	+	0.338816i
$262$		0			0
$263$	−25.3411			−1.56260			−0.781300	−	0.624156i	$-0.785443\pi$
$263$	−25.3411			−1.56260			−0.781300	+	0.624156i	$0.785443\pi$
$264$		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	0.652095	−	0.758138i	$-0.273891\pi$
$269$	−5.42092	−	9.38931i	−0.330519	−	0.572476i	−0.982614	+	0.185662i	$0.940557\pi$
$270$		0			0
$271$	−15.0184	+	26.0127i	−0.912306	+	1.58016i	−0.101507	+	0.994835i	$0.532366\pi$
$271$	−15.0184	+	26.0127i	−0.912306	+	1.58016i	−0.810799	+	0.585325i	$0.800967\pi$
$272$		0			0
$273$	13.0914	−	22.3091i	0.792326	−	1.35021i
$274$		0			0
$275$	4.00719			0.241643
$276$		0			0
$277$	19.7629			1.18744			0.593720	−	0.804672i	$-0.297659\pi$
$277$	19.7629			1.18744			0.593720	+	0.804672i	$0.297659\pi$
$278$		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
$283$	−11.6063	+	20.1028i	−0.689926	+	1.19499i	0.281936	+	0.959433i	$0.409023\pi$
$283$	−11.6063	+	20.1028i	−0.689926	+	1.19499i	−0.971861	+	0.235553i	$0.924310\pi$
$284$		0			0
$285$	4.02398	+	0.747087i	0.238360	+	0.0442536i
$286$		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
$291$	21.8270	+	4.05239i	1.27952	+	0.237555i
$292$		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
$297$	11.4064	+	7.00440i	0.661865	+	0.406437i
$298$		0			0
$299$	0.680950	+	1.17944i	0.0393803	+	0.0682088i
$300$		0			0
$301$	−7.45698	+	20.6137i	−0.429813	+	1.18816i
$302$		0			0
$303$	7.04829	+	19.9233i	0.404913	+	1.14456i
$304$		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
$311$	3.46220	−	5.99670i	0.196323	−	0.340042i	−0.751010	−	0.660290i	$-0.770433\pi$
$311$	3.46220	−	5.99670i	0.196323	−	0.340042i	0.947333	+	0.320249i	$0.103767\pi$
$312$		0			0
$313$	−15.1157	−	26.1811i	−0.854388	−	1.47984i	−0.877212	−	0.480104i	$-0.840599\pi$
$313$	−15.1157	−	26.1811i	−0.854388	−	1.47984i	0.0228236	−	0.999740i	$-0.492734\pi$
$314$		0			0
$315$	9.64935	−	11.1305i	0.543679	−	0.627133i
$316$		0			0
$317$	−4.68699	−	8.11811i	−0.263248	−	0.455959i	0.703855	−	0.710343i	$-0.251460\pi$
$317$	−4.68699	−	8.11811i	−0.263248	−	0.455959i	−0.967103	+	0.254385i	$0.918127\pi$
$318$		0			0
$319$	−2.37913	+	4.12077i	−0.133205	+	0.230719i
$320$		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
$327$	−17.3314	+	20.2797i	−0.958428	+	1.12147i
$328$		0			0
$329$	−20.9916	−	24.9173i	−1.15731	−	1.37374i
$330$		0			0
$331$	−13.7720	−	23.8539i	−0.756979	−	1.31113i	−0.944384	−	0.328844i	$-0.893341\pi$
$331$	−13.7720	−	23.8539i	−0.756979	−	1.31113i	0.187405	−	0.982283i	$-0.439992\pi$
$332$		0			0
$333$	0.316254	+	2.00477i	0.0173306	+	0.109861i
$334$		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
$339$	17.4069	−	20.3681i	0.945415	−	1.10625i
$340$		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
$345$	0.258673	+	0.731188i	0.0139265	+	0.0393658i
$346$		0			0
$347$	−10.0959	+	17.4867i	−0.541979	+	0.938735i	0.456812	+	0.889564i	$0.348991\pi$
$347$	−10.0959	+	17.4867i	−0.541979	+	0.938735i	−0.998790	+	0.0491714i	$0.984342\pi$
$348$		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
$353$	4.70904			0.250637			0.125318	−	0.992117i	$-0.460005\pi$
$353$	4.70904			0.250637			0.125318	+	0.992117i	$0.460005\pi$
$354$		0			0
$355$	−2.85107			−0.151319
$356$		0			0
$357$	16.6039	−	28.2948i	0.878771	−	1.49752i
$358$		0			0
$359$	6.03357	−	10.4504i	0.318440	−	0.551554i	−0.661723	−	0.749748i	$-0.730175\pi$
$359$	6.03357	−	10.4504i	0.318440	−	0.551554i	0.980163	+	0.198195i	$0.0635079\pi$
$360$		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
$367$	0.960711			0.0501487			0.0250744	−	0.999686i	$-0.492018\pi$
$367$	0.960711			0.0501487			0.0250744	+	0.999686i	$0.492018\pi$
$368$		0			0
$369$	4.11013	+	1.58065i	0.213965	+	0.0822854i
$370$		0			0
$371$	−11.4384	−	13.5775i	−0.593850	−	0.704908i
$372$		0			0
$373$	−7.04998			−0.365034			−0.182517	−	0.983203i	$-0.558425\pi$
$373$	−7.04998			−0.365034			−0.182517	+	0.983203i	$0.558425\pi$
$374$		0			0
$375$	−7.02822	−	19.8666i	−0.362936	−	1.02591i
$376$		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
$381$	−1.84509	−	5.21549i	−0.0945267	−	0.267198i
$382$		0			0
$383$	32.1975			1.64522			0.822608	−	0.568609i	$-0.192518\pi$
$383$	32.1975			1.64522			0.822608	+	0.568609i	$0.192518\pi$
$384$		0			0
$385$	12.4524	−	2.22092i	0.634635	−	0.113189i
$386$		0			0
$387$	3.87317	+	24.5525i	0.196884	+	1.24807i
$388$		0			0
$389$	−25.7426			−1.30520			−0.652600	−	0.757702i	$-0.726322\pi$
$389$	−25.7426			−1.30520			−0.652600	+	0.757702i	$0.726322\pi$
$390$		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	−0.525332	−	0.850898i	$-0.676059\pi$
$397$	9.44903	−	16.3662i	0.474233	−	0.821396i	0.999565	+	0.0295016i	$0.00939202\pi$
$398$		0			0
$399$	−5.83438	−	0.0412635i	−0.292084	−	0.00206576i
$400$		0			0
$401$	15.2039			0.759245			0.379622	−	0.925142i	$-0.376054\pi$
$401$	15.2039			0.759245			0.379622	+	0.925142i	$0.376054\pi$
$402$		0			0
$403$	16.8830			0.841002
$404$		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
$409$	14.9729	−	25.9339i	0.740363	−	1.28235i	−0.211967	−	0.977277i	$-0.567987\pi$
$409$	14.9729	−	25.9339i	0.740363	−	1.28235i	0.952330	−	0.305070i	$-0.0986798\pi$
$410$		0			0
$411$	7.91191	+	22.3645i	0.390266	+	1.10316i
$412$		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
$417$	11.1207	−	13.0126i	0.544585	−	0.637229i
$418$		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
$423$	−34.4814	−	13.2606i	−1.67654	−	0.644755i
$424$		0			0
$425$	−5.56822	−	9.64444i	−0.270098	−	0.467824i
$426$		0			0
$427$	22.0911	+	26.2224i	1.06906	+	1.26899i
$428$		0			0
$429$	16.3621	−	19.1455i	0.789968	−	0.924355i
$430$		0			0
$431$	1.36446	+	2.36331i	0.0657237	+	0.113837i	0.897015	−	0.442000i	$-0.145731\pi$
$431$	1.36446	+	2.36331i	0.0657237	+	0.113837i	−0.831291	+	0.555837i	$0.812398\pi$
$432$		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
$437$	0.153597	−	0.266037i	0.00734753	−	0.0127263i
$438$		0			0
$439$	1.44066	+	2.49529i	0.0687587	+	0.119094i	0.898355	−	0.439270i	$-0.144763\pi$
$439$	1.44066	+	2.49529i	0.0687587	+	0.119094i	−0.829596	+	0.558363i	$0.811429\pi$
$440$		0			0
$441$	−10.7562	+	18.0362i	−0.512199	+	0.858867i
$442$		0			0
$443$	−12.4865	−	21.6273i	−0.593254	−	1.02755i	−0.993791	−	0.111265i	$-0.964510\pi$
$443$	−12.4865	−	21.6273i	−0.593254	−	1.02755i	0.400537	−	0.916281i	$-0.368824\pi$
$444$		0			0
$445$	12.2555	−	21.2272i	0.580967	−	1.00626i
$446$		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
$453$	11.3098	+	31.9692i	0.531379	+	1.50205i
$454$		0			0
$455$	−17.8574	−	21.1969i	−0.837166	−	0.993727i
$456$		0			0
$457$	12.8085	+	22.1850i	0.599158	+	1.03777i	0.992946	+	0.118571i	$0.0378312\pi$
$457$	12.8085	+	22.1850i	0.599158	+	1.03777i	−0.393788	+	0.919201i	$0.628835\pi$
$458$		0			0
$459$	1.00826	−	37.1857i	0.0470616	−	1.73568i
$460$		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
$465$	9.45324	+	1.75508i	0.438383	+	0.0813898i
$466$		0			0
$467$	−10.4087	+	18.0283i	−0.481655	+	0.834251i	−0.999778	−	0.0210550i	$-0.993297\pi$
$467$	−10.4087	+	18.0283i	−0.481655	+	0.834251i	0.518123	+	0.855306i	$0.326631\pi$
$468$		0			0
$469$	−4.34800	+	12.0194i	−0.200772	+	0.555005i
$470$		0			0
$471$	−25.1913	−	4.67699i	−1.16075	−	0.215504i
$472$		0			0
$473$	−10.6716	+	18.4838i	−0.490681	+	0.849884i
$474$		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
$479$	27.4873			1.25592			0.627962	−	0.778244i	$-0.283889\pi$
$479$	27.4873			1.25592			0.627962	+	0.778244i	$0.283889\pi$
$480$		0			0
$481$	3.81865			0.174115
$482$		0			0
$483$	−0.546050	−	0.961425i	−0.0248461	−	0.0437464i
$484$		0			0
$485$	11.8938	−	20.6007i	0.540070	−	0.935429i
$486$		0			0
$487$	−6.32927	−	10.9626i	−0.286807	−	0.496763i	0.686239	−	0.727376i	$-0.259260\pi$
$487$	−6.32927	−	10.9626i	−0.286807	−	0.496763i	−0.973046	+	0.230613i	$0.925927\pi$
$488$		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
$493$	13.2237			0.595566
$494$		0			0
$495$	11.1518	−	9.01917i	0.501238	−	0.405381i
$496$		0			0
$497$	4.00128	−	0.713638i	0.179482	−	0.0320110i
$498$		0			0
$499$	−4.24205			−0.189900			−0.0949502	−	0.995482i	$-0.530269\pi$
$499$	−4.24205			−0.189900			−0.0949502	+	0.995482i	$0.530269\pi$
$500$		0			0
$501$	−4.34237	+	5.08108i	−0.194003	+	0.227006i
$502$		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
$507$	−32.1191	−	5.96319i	−1.42646	−	0.264835i
$508$		0			0
$509$	−4.85469			−0.215180			−0.107590	−	0.994195i	$-0.534313\pi$
$509$	−4.85469			−0.215180			−0.107590	+	0.994195i	$0.534313\pi$
$510$		0			0
$511$	22.3632	+	26.5454i	0.989290	+	1.17430i
$512$		0			0
$513$	−5.81694	+	3.15136i	−0.256824	+	0.139136i
$514$		0			0
$515$	25.3207			1.11576
$516$		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	0.985737	−	0.168296i	$-0.0538263\pi$
$521$	7.92316	+	13.7233i	0.347120	+	0.601229i	−0.638617	+	0.769525i	$0.720493\pi$
$522$		0			0
$523$	10.7605	−	18.6377i	0.470524	−	0.814972i	−0.528908	−	0.848679i	$-0.677398\pi$
$523$	10.7605	−	18.6377i	0.470524	−	0.814972i	0.999432	+	0.0337078i	$0.0107316\pi$
$524$		0			0
$525$	3.52054	+	6.19858i	0.153649	+	0.270528i
$526$		0			0
$527$	21.4128			0.932758
$528$		0			0
$529$	−22.9418			−0.997469
$530$		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
$535$	−12.0264	+	20.8303i	−0.519945	+	0.900572i
$536$		0			0
$537$	−24.5445	+	28.7199i	−1.05917	+	1.23936i
$538$		0			0
$539$	−16.9202	+	6.23382i	−0.728806	+	0.268510i
$540$		0			0
$541$	7.55977	−	13.0939i	0.325020	−	0.562951i	−0.656497	−	0.754329i	$-0.727962\pi$
$541$	7.55977	−	13.0939i	0.325020	−	0.562951i	0.981516	+	0.191378i	$0.0612957\pi$
$542$		0			0
$543$	−14.4612	−	40.8772i	−0.620588	−	1.75421i
$544$		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
$549$	36.2875	+	13.9552i	1.54871	+	0.595594i
$550$		0			0
$551$	−1.17589	−	2.03670i	−0.0500945	−	0.0867662i
$552$		0			0
$553$	−6.34154	−	7.52749i	−0.269670	−	0.320101i
$554$		0			0
$555$	2.13816	+	0.396969i	0.0907600	+	0.0168504i
$556$		0			0
$557$	−5.37036	−	9.30173i	−0.227549	−	0.394127i	0.729532	−	0.683947i	$-0.239738\pi$
$557$	−5.37036	−	9.30173i	−0.227549	−	0.394127i	−0.957081	+	0.289820i	$0.906405\pi$
$558$		0			0
$559$	46.7672			1.97804
$560$		0			0
$561$	20.7521	−	24.2824i	0.876156	−	1.02520i
$562$		0			0
$563$	11.7380	−	20.3308i	0.494697	−	0.856840i	−0.505285	−	0.862953i	$-0.668612\pi$
$563$	11.7380	−	20.3308i	0.494697	−	0.856840i	0.999981	+	0.00611281i	$0.00194578\pi$
$564$		0			0
$565$	−14.3545	−	24.8627i	−0.603898	−	1.04598i
$566$		0			0
$567$	−0.813726	+	23.7979i	−0.0341733	+	0.999416i
$568$		0			0
$569$	18.9681	+	32.8537i	0.795183	+	1.37730i	0.922723	+	0.385463i	$0.125958\pi$
$569$	18.9681	+	32.8537i	0.795183	+	1.37730i	−0.127540	+	0.991833i	$0.540708\pi$
$570$		0			0
$571$	2.15815	−	3.73803i	0.0903158	−	0.156432i	−0.817328	−	0.576172i	$-0.804546\pi$
$571$	2.15815	−	3.73803i	0.0903158	−	0.156432i	0.907644	+	0.419741i	$0.137879\pi$
$572$		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	0.741290	−	0.671185i	$-0.234214\pi$
$577$	−5.05923	−	8.76284i	−0.210618	−	0.364802i	−0.951908	+	0.306383i	$0.900881\pi$
$578$		0			0
$579$	−2.75306	−	0.511131i	−0.114413	−	0.0212419i
$580$		0			0
$581$	5.40322	−	14.9364i	0.224163	−	0.619667i
$582$		0			0
$583$	−8.64272	−	14.9696i	−0.357945	−	0.619979i
$584$		0			0
$585$	−29.3330	−	11.2807i	−1.21277	−	0.466400i
$586$		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
$591$	6.22412	+	17.5937i	0.256026	+	0.723706i
$592$		0			0
$593$	21.8434	−	37.8339i	0.897002	−	1.55365i	0.0656957	−	0.997840i	$-0.479073\pi$
$593$	21.8434	−	37.8339i	0.897002	−	1.55365i	0.831307	−	0.555814i	$-0.187593\pi$
$594$		0			0
$595$	−22.6486	−	26.8842i	−0.928504	−	1.10215i
$596$		0			0
$597$	−5.37363	+	6.28778i	−0.219928	+	0.257342i
$598$		0			0
$599$	7.63946	−	13.2319i	0.312140	−	0.540642i	−0.666686	−	0.745339i	$-0.732288\pi$
$599$	7.63946	−	13.2319i	0.312140	−	0.540642i	0.978825	+	0.204697i	$0.0656209\pi$
$600$		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
$605$	−8.09955			−0.329293
$606$		0			0
$607$	−2.66981			−0.108364			−0.0541821	−	0.998531i	$-0.517255\pi$
$607$	−2.66981			−0.108364			−0.0541821	+	0.998531i	$0.517255\pi$
$608$		0			0
$609$	−8.46445	−	0.0598647i	−0.342997	−	0.00242584i
$610$		0			0
$611$	−34.7547	+	60.1970i	−1.40603	+	2.43531i
$612$		0			0
$613$	−13.5875	−	23.5343i	−0.548796	−	0.950542i	−0.998357	−	0.0572929i	$-0.981753\pi$
$613$	−13.5875	−	23.5343i	−0.548796	−	0.950542i	0.449562	−	0.893249i	$-0.351580\pi$
$614$		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
$619$	−31.2681			−1.25677			−0.628385	−	0.777902i	$-0.716284\pi$
$619$	−31.2681			−1.25677			−0.628385	+	0.777902i	$0.716284\pi$
$620$		0			0
$621$	−1.06836	−	0.656055i	−0.0428717	−	0.0263266i
$622$		0			0
$623$	−11.8865	+	32.8585i	−0.476223	+	1.31645i
$624$		0			0
$625$	−14.8023			−0.592090
$626$		0			0
$627$	−5.58528	−	1.03696i	−0.223055	−	0.0414121i
$628$		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
$633$	−5.46409	+	6.39363i	−0.217178	+	0.254124i
$634$		0			0
$635$	−5.92787			−0.235240
$636$		0			0
$637$	30.3673	+	25.2786i	1.20320	+	1.00158i
$638$		0			0
$639$	3.58337	−	2.89809i	0.141756	−	0.114647i
$640$		0			0
$641$	−33.5310			−1.32440			−0.662198	−	0.749329i	$-0.730376\pi$
$641$	−33.5310			−1.32440			−0.662198	+	0.749329i	$0.730376\pi$
$642$		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	−0.979599	−	0.200960i	$-0.935594\pi$
$647$	−16.8855	−	29.2465i	−0.663836	−	1.14980i	0.315763	−	0.948838i	$-0.397739\pi$
$648$		0			0
$649$	2.68264	−	4.64647i	0.105303	−	0.182390i
$650$		0			0
$651$	−13.7063	−	0.0969374i	−0.537191	−	0.00379928i
$652$		0			0
$653$	18.0115			0.704845			0.352423	−	0.935841i	$-0.385358\pi$
$653$	18.0115			0.704845			0.352423	+	0.935841i	$0.385358\pi$
$654$		0			0
$655$	26.1438			1.02152
$656$		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
$661$	−7.02746	+	12.1719i	−0.273337	+	0.473433i	−0.969714	−	0.244243i	$-0.921461\pi$
$661$	−7.02746	+	12.1719i	−0.273337	+	0.473433i	0.696378	+	0.717676i	$0.254794\pi$
$662$		0			0
$663$	−68.8151	−	12.7761i	−2.67256	−	0.496184i
$664$		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
$669$	13.1532	+	2.44200i	0.508530	+	0.0944132i
$670$		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
$675$	6.88800	+	4.22977i	0.265119	+	0.162804i
$676$		0			0
$677$	18.1093	+	31.3663i	0.695998	+	1.20550i	0.969843	+	0.243731i	$0.0783713\pi$
$677$	18.1093	+	31.3663i	0.695998	+	1.20550i	−0.273845	+	0.961774i	$0.588295\pi$
$678$		0			0
$679$	−11.5357	+	31.8887i	−0.442699	+	1.22378i
$680$		0			0
$681$	−8.05794	−	22.7773i	−0.308781	−	0.872828i
$682$		0			0
$683$	8.84350	+	15.3174i	0.338387	+	0.586104i	0.984130	−	0.177452i	$-0.0567853\pi$
$683$	8.84350	+	15.3174i	0.338387	+	0.586104i	−0.645742	+	0.763555i	$0.723452\pi$
$684$		0			0
$685$	25.4193			0.971220
$686$		0			0
$687$	0.924422	+	2.61305i	0.0352689	+	0.0996942i
$688$		0			0
$689$	−18.9379	+	32.8014i	−0.721477	+	1.24963i
$690$		0			0
$691$	−11.2049	−	19.4074i	−0.426253	−	0.738292i	0.570283	−	0.821448i	$-0.306833\pi$
$691$	−11.2049	−	19.4074i	−0.426253	−	0.738292i	−0.996537	+	0.0831559i	$0.973500\pi$
$692$		0			0
$693$	−13.3933	+	15.4491i	−0.508769	+	0.586865i
$694$		0			0
$695$	−9.17064	−	15.8840i	−0.347862	−	0.602515i
$696$		0			0
$697$	5.25424	−	9.10061i	0.199018	−	0.344710i
$698$		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
$705$	−25.7179	+	30.0929i	−0.968592	+	1.13337i
$706$		0			0
$707$	−31.7802	+	5.66806i	−1.19522	+	0.213170i
$708$		0			0
$709$	4.02492	+	6.97137i	0.151159	+	0.261815i	0.931654	−	0.363347i	$-0.118366\pi$
$709$	4.02492	+	6.97137i	0.151159	+	0.261815i	−0.780495	+	0.625162i	$0.785033\pi$
$710$		0			0
$711$	−10.4168	−	4.00602i	−0.390660	−	0.150238i
$712$		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
$717$	2.81585	−	3.29487i	0.105160	−	0.123049i
$718$		0			0
$719$	−20.9980	+	36.3696i	−0.783093	+	1.35636i	0.147039	+	0.989131i	$0.453026\pi$
$719$	−20.9980	+	36.3696i	−0.783093	+	1.35636i	−0.930132	+	0.367226i	$0.880308\pi$
$720$		0			0
$721$	−35.5359	+	6.33791i	−1.32343	+	0.236036i
$722$		0			0
$723$	2.45102	+	6.92827i	0.0911543	+	0.257665i
$724$		0			0
$725$	−1.43669	+	2.48842i	−0.0533573	+	0.0924176i
$726$		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
$731$	59.3152			2.19385
$732$		0			0
$733$	29.4749			1.08868			0.544340	−	0.838865i	$-0.316780\pi$
$733$	29.4749			1.08868			0.544340	+	0.838865i	$0.316780\pi$
$734$		0			0
$735$	14.3756	+	17.3110i	0.530252	+	0.638527i
$736$		0			0
$737$	−6.22238	+	10.7775i	−0.229204	+	0.396993i
$738$		0			0
$739$	9.52146	+	16.4916i	0.350252	+	0.606655i	0.986294	−	0.165000i	$-0.0527625\pi$
$739$	9.52146	+	16.4916i	0.350252	+	0.606655i	−0.636041	+	0.771655i	$0.719429\pi$
$740$		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
$745$	−7.27573			−0.266562
$746$		0			0
$747$	−2.80645	−	17.7904i	−0.102682	−	0.650917i
$748$		0			0
$749$	11.6643	−	32.2441i	0.426203	−	1.17818i
$750$		0			0
$751$	34.8763			1.27265			0.636327	−	0.771420i	$-0.280453\pi$
$751$	34.8763			1.27265			0.636327	+	0.771420i	$0.280453\pi$
$752$		0			0
$753$	−7.82049	−	22.1061i	−0.284994	−	0.805591i
$754$		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
$759$	−0.359038	−	1.01489i	−0.0130322	−	0.0368381i
$760$		0			0
$761$	−5.48977			−0.199004			−0.0995021	−	0.995037i	$-0.531725\pi$
$761$	−5.48977			−0.199004			−0.0995021	+	0.995037i	$0.531725\pi$
$762$		0			0
$763$	−26.2544	−	31.1643i	−0.950473	−	1.12822i
$764$		0			0
$765$	−37.2033	−	14.3074i	−1.34509	−	0.517285i
$766$		0			0
$767$	−11.7564			−0.424499
$768$		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	0.713097	−	0.701065i	$-0.247292\pi$
$773$	−6.96717	−	12.0675i	−0.250592	−	0.434037i	−0.963689	+	0.267028i	$0.913958\pi$
$774$		0			0
$775$	−2.32640	+	4.02944i	−0.0835666	+	0.144742i
$776$		0			0
$777$	−3.10013	−	0.0219256i	−0.111217	−	0.000786577i
$778$		0			0
$779$	−1.86888			−0.0669597
$780$		0			0
$781$	3.95729			0.141603
$782$		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
$787$	−8.78923	+	15.2234i	−0.313302	+	0.542655i	−0.979075	−	0.203499i	$-0.934769\pi$
$787$	−8.78923	+	15.2234i	−0.313302	+	0.542655i	0.665773	+	0.746154i	$0.268102\pi$
$788$		0			0
$789$	−14.6387	−	41.3790i	−0.521151	−	1.47313i
$790$		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
$795$	−14.0137	+	16.3977i	−0.497015	+	0.581566i
$796$		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
$801$	6.17388	+	39.1370i	0.218143	+	1.38284i
$802$		0			0
$803$	16.8974	+	29.2672i	0.596297	+	1.03282i
$804$		0			0
$805$	−1.16634	+	0.208019i	−0.0411079	+	0.00733169i
$806$		0			0
$807$	12.2001	−	14.2756i	0.429466	−	0.502525i
$808$		0			0
$809$	14.3481	+	24.8517i	0.504453	+	0.873738i	0.999987	+	0.00514935i	$0.00163910\pi$
$809$	14.3481	+	24.8517i	0.504453	+	0.873738i	−0.495534	+	0.868589i	$0.665028\pi$
$810$		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
$815$	14.0063	−	24.2597i	0.490620	−	0.849779i
$816$		0			0
$817$	−5.27446	−	9.13563i	−0.184530	−	0.319615i
$818$		0			0
$819$	43.9905	+	8.48949i	1.53715	+	0.296647i
$820$		0			0
$821$	19.3854	+	33.5765i	0.676554	+	1.17183i	0.976012	+	0.217717i	$0.0698609\pi$
$821$	19.3854	+	33.5765i	0.676554	+	1.17183i	−0.299458	+	0.954110i	$0.596806\pi$
$822$		0			0
$823$	11.3920	−	19.7316i	0.397101	−	0.687799i	−0.596266	−	0.802787i	$-0.703350\pi$
$823$	11.3920	−	19.7316i	0.397101	−	0.687799i	0.993367	+	0.114988i	$0.0366830\pi$
$824$		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	−0.898051	−	0.439892i	$-0.855017\pi$
$829$	−23.8972	−	41.3911i	−0.829983	−	1.43757i	0.0680673	−	0.997681i	$-0.478317\pi$
$830$		0			0
$831$	11.4164	+	32.2706i	0.396030	+	1.11945i
$832$		0			0
$833$	38.5151	+	32.0611i	1.33447	+	1.11085i
$834$		0			0
$835$	3.58090	+	6.20231i	0.123922	+	0.214640i
$836$		0			0
$837$	−13.6653	+	7.40326i	−0.472342	+	0.255894i
$838$		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
$843$	−13.5758	−	2.52046i	−0.467574	−	0.0868093i
$844$		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
$849$	−39.5301	−	7.33911i	−1.35667	−	0.251877i
$850$		0			0
$851$	0.0816145	−	0.141361i	0.00279771	−	0.00484578i
$852$		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
$857$	−48.2584			−1.64848			−0.824239	−	0.566243i	$-0.808397\pi$
$857$	−48.2584			−1.64848			−0.824239	+	0.566243i	$0.808397\pi$
$858$		0			0
$859$	−10.1506			−0.346332			−0.173166	−	0.984893i	$-0.555400\pi$
$859$	−10.1506			−0.346332			−0.173166	+	0.984893i	$0.555400\pi$
$860$		0			0
$861$	−3.40442	+	5.80148i	−0.116022	+	0.197714i
$862$		0			0
$863$	25.7981	−	44.6837i	0.878179	−	1.52105i	0.0248411	−	0.999691i	$-0.492092\pi$
$863$	25.7981	−	44.6837i	0.878179	−	1.52105i	0.853338	−	0.521359i	$-0.174575\pi$
$864$		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
$871$	27.2689			0.923972
$872$		0			0
$873$	5.99167	+	37.9819i	0.202787	+	1.28549i
$874$		0			0
$875$	31.6897	−	5.65193i	1.07131	−	0.191070i
$876$		0			0
$877$	−10.3978			−0.351109			−0.175555	−	0.984470i	$-0.556172\pi$
$877$	−10.3978			−0.351109			−0.175555	+	0.984470i	$0.556172\pi$
$878$		0			0
$879$	−26.6819	+	31.2209i	−0.899957	+	1.05305i
$880$		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
$885$	−6.58271	−	1.22214i	−0.221276	−	0.0410818i
$886$		0			0
$887$	42.2505			1.41863			0.709316	−	0.704891i	$-0.249004\pi$
$887$	42.2505			1.41863			0.709316	+	0.704891i	$0.249004\pi$
$888$		0			0
$889$	8.31936	−	1.48378i	0.279022	−	0.0497643i
$890$		0			0
$891$	−4.84829	+	22.6715i	−0.162424	+	0.759523i
$892$		0			0
$893$	15.6787			0.524669
$894$		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
$903$	−37.9674	−	0.268524i	−1.26348	−	0.00893592i
$904$		0			0
$905$	−46.4606			−1.54440
$906$		0			0
$907$	−40.8807			−1.35742			−0.678711	−	0.734405i	$-0.737461\pi$
$907$	−40.8807			−1.35742			−0.678711	+	0.734405i	$0.737461\pi$
$908$		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
$913$	7.73249	−	13.3931i	0.255908	−	0.443246i
$914$		0			0
$915$	27.0649	−	31.6691i	0.894739	−	1.04695i
$916$		0			0
$917$	−36.6910	+	6.54393i	−1.21165	+	0.216100i
$918$		0			0
$919$	21.8195	−	37.7925i	0.719760	−	1.24666i	−0.241335	−	0.970442i	$-0.577585\pi$
$919$	21.8195	−	37.7925i	0.719760	−	1.24666i	0.961095	−	0.276219i	$-0.0890815\pi$
$920$		0			0
$921$	2.24025	+	6.33248i	0.0738186	+	0.208662i
$922$		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
$927$	−31.8243	+	25.7383i	−1.04525	+	0.845355i
$928$		0			0
$929$	13.7377	+	23.7944i	0.450719	+	0.780668i	0.998431	−	0.0559990i	$-0.0178344\pi$
$929$	13.7377	+	23.7944i	0.450719	+	0.780668i	−0.547712	+	0.836667i	$0.684501\pi$
$930$		0			0
$931$	1.51314	−	8.78299i	0.0495911	−	0.287851i
$932$		0			0
$933$	11.7919	+	2.18927i	0.386049	+	0.0716735i
$934$		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
$941$	13.0608	−	22.6219i	0.425769	−	0.737454i	−0.570723	−	0.821143i	$-0.693337\pi$
$941$	13.0608	−	22.6219i	0.425769	−	0.737454i	0.996492	+	0.0836892i	$0.0266703\pi$
$942$		0			0
$943$	−0.177081	−	0.306714i	−0.00576656	−	0.00998797i
$944$		0			0
$945$	23.7489	+	9.32654i	0.772552	+	0.303392i
$946$		0			0
$947$	3.59015	+	6.21833i	0.116664	+	0.202068i	0.918444	−	0.395551i	$-0.129447\pi$
$947$	3.59015	+	6.21833i	0.116664	+	0.202068i	−0.801780	+	0.597620i	$0.796113\pi$
$948$		0			0
$949$	37.0256	−	64.1302i	1.20190	−	2.08176i
$950$		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
$957$	−8.10306	−	1.50441i	−0.261935	−	0.0486305i
$958$		0			0
$959$	−35.6742	+	6.36257i	−1.15198	+	0.205458i
$960$		0			0
$961$	11.0269	+	19.0991i	0.355705	+	0.616100i
$962$		0			0
$963$	−6.05844	−	38.4052i	−0.195231	−	1.23759i
$964$		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
$969$	5.26533	+	14.8835i	0.169147	+	0.478126i
$970$		0			0
$971$	20.8518	−	36.1163i	0.669165	−	1.15903i	−0.308973	−	0.951071i	$-0.599985\pi$
$971$	20.8518	−	36.1163i	0.669165	−	1.15903i	0.978138	−	0.207957i	$-0.0666813\pi$
$972$		0			0
$973$	16.8462	+	19.9967i	0.540065	+	0.641064i
$974$		0			0
$975$	9.88061	−	11.5615i	0.316433	−	0.370263i
$976$		0			0
$977$	−2.61437	+	4.52823i	−0.0836412	+	0.144871i	−0.904811	−	0.425813i	$-0.859988\pi$
$977$	−2.61437	+	4.52823i	−0.0836412	+	0.144871i	0.821170	+	0.570683i	$0.193322\pi$
$978$		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
$983$	6.90697			0.220298			0.110149	−	0.993915i	$-0.464867\pi$
$983$	6.90697			0.220298			0.110149	+	0.993915i	$0.464867\pi$
$984$		0			0
$985$	19.9967			0.637149
$986$		0			0
$987$	28.5609	−	48.6707i	0.909103	−	1.54921i
$988$		0			0
$989$	0.999537	−	1.73125i	0.0317834	−	0.0550505i
$990$		0			0
$991$	2.19861	+	3.80811i	0.0698412	+	0.120968i	0.898831	−	0.438295i	$-0.144417\pi$
$991$	2.19861	+	3.80811i	0.0698412	+	0.120968i	−0.828990	+	0.559263i	$0.811084\pi$
$992$		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
$997$	−28.0359			−0.887907			−0.443954	−	0.896050i	$-0.646425\pi$
$997$	−28.0359			−0.887907			−0.443954	+	0.896050i	$0.646425\pi$
$998$		0			0
$999$	−3.09086	+	1.67449i	−0.0977906	+	0.0529786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.d.457.8	yes	22
3.2	odd	2		1512.2.t.d.289.3		22
4.3	odd	2		1008.2.t.k.961.4		22
7.4	even	3		504.2.q.d.25.7	✓	22
9.4	even	3		504.2.q.d.121.7	yes	22
9.5	odd	6		1512.2.q.c.793.9		22
12.11	even	2		3024.2.t.l.289.3		22
21.11	odd	6		1512.2.q.c.1369.9		22
28.11	odd	6		1008.2.q.k.529.5		22
36.23	even	6		3024.2.q.k.2305.9		22
36.31	odd	6		1008.2.q.k.625.5		22
63.4	even	3	inner	504.2.t.d.193.8	yes	22
63.32	odd	6		1512.2.t.d.361.3		22
84.11	even	6		3024.2.q.k.2881.9		22
252.67	odd	6		1008.2.t.k.193.4		22
252.95	even	6		3024.2.t.l.1873.3		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.7	✓	22	7.4	even	3
504.2.q.d.121.7	yes	22	9.4	even	3
504.2.t.d.193.8	yes	22	63.4	even	3	inner
504.2.t.d.457.8	yes	22	1.1	even	1	trivial
1008.2.q.k.529.5		22	28.11	odd	6
1008.2.q.k.625.5		22	36.31	odd	6
1008.2.t.k.193.4		22	252.67	odd	6
1008.2.t.k.961.4		22	4.3	odd	2
1512.2.q.c.793.9		22	9.5	odd	6
1512.2.q.c.1369.9		22	21.11	odd	6
1512.2.t.d.289.3		22	3.2	odd	2
1512.2.t.d.361.3		22	63.32	odd	6
3024.2.q.k.2305.9		22	36.23	even	6
3024.2.q.k.2881.9		22	84.11	even	6
3024.2.t.l.289.3		22	12.11	even	2
3024.2.t.l.1873.3		22	252.95	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.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.577666 + 1.63288i) q^{3} +1.85591 q^{5} +(-2.60465 + 0.464545i) q^{7} +(-2.33261 + 1.88652i) q^{9} +O(q^{10})\)	\(q+(0.577666 + 1.63288i) q^{3} +1.85591 q^{5} +(-2.60465 + 0.464545i) q^{7} +(-2.33261 + 1.88652i) q^{9} -2.57601 q^{11} +(2.82227 + 4.88832i) q^{13} +(1.07210 + 3.03049i) q^{15} +(3.57951 + 6.19989i) q^{17} +(0.636599 - 1.10262i) q^{19} +(-2.26316 - 3.98473i) q^{21} +0.241277 q^{23} -1.55558 q^{25} +(-4.42793 - 2.71909i) q^{27} +(0.923571 - 1.59967i) q^{29} +(1.49552 - 2.59031i) q^{31} +(-1.48807 - 4.20632i) q^{33} +(-4.83401 + 0.862156i) q^{35} +(0.338260 - 0.585884i) q^{37} +(-6.35171 + 7.43225i) q^{39} +(-0.733933 - 1.27121i) q^{41} +(4.14269 - 7.17535i) q^{43} +(-4.32912 + 3.50122i) q^{45} +(6.15723 + 10.6646i) q^{47} +(6.56840 - 2.41995i) q^{49} +(-8.05593 + 9.42638i) q^{51} +(3.35508 + 5.81117i) q^{53} -4.78085 q^{55} +(2.16819 + 0.402544i) q^{57} +(-1.04139 + 1.80375i) q^{59} +(-6.47973 - 11.2232i) q^{61} +(5.19925 - 5.99732i) q^{63} +(5.23789 + 9.07230i) q^{65} +(2.41551 - 4.18379i) q^{67} +(0.139378 + 0.393977i) q^{69} -1.53621 q^{71} +(-6.55954 - 11.3615i) q^{73} +(-0.898606 - 2.54008i) q^{75} +(6.70960 - 1.19667i) q^{77} +(1.86009 + 3.22177i) q^{79} +(1.88209 - 8.80101i) q^{81} +(-3.00173 + 5.19915i) q^{83} +(6.64326 + 11.5065i) q^{85} +(3.14559 + 0.584007i) q^{87} +(6.60349 - 11.4376i) q^{89} +(-9.62187 - 11.4213i) q^{91} +(5.09357 + 0.945667i) q^{93} +(1.18147 - 2.04637i) q^{95} +(6.40860 - 11.1000i) q^{97} +(6.00881 - 4.85969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9	\( 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9} + 6 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} - 15 q^{21} - 4 q^{23} + 20 q^{25} - 4 q^{27} + 9 q^{29} - 4 q^{31} - 31 q^{33} + 14 q^{35} + 2 q^{37} + 8 q^{39} + 16 q^{41} + 22 q^{45} + 5 q^{47} - 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} - 19 q^{59} - 13 q^{61} + 21 q^{63} + 13 q^{65} + 26 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 8 q^{75} - 4 q^{77} + 10 q^{79} - 8 q^{81} - 28 q^{83} - 20 q^{85} + 9 q^{87} + 6 q^{89} - 37 q^{91} - 32 q^{93} + 12 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9 + 6 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 - 15 * q^21 - 4 * q^23 + 20 * q^25 - 4 * q^27 + 9 * q^29 - 4 * q^31 - 31 * q^33 + 14 * q^35 + 2 * q^37 + 8 * q^39 + 16 * q^41 + 22 * q^45 + 5 * q^47 - 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 - 19 * q^59 - 13 * q^61 + 21 * q^63 + 13 * q^65 + 26 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 8 * q^75 - 4 * q^77 + 10 * q^79 - 8 * q^81 - 28 * q^83 - 20 * q^85 + 9 * q^87 + 6 * q^89 - 37 * q^91 - 32 * q^93 + 12 * q^95 - 29 * q^97 - 56 * q^99

Introduction

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