LMFDB - Embedded newform 588.2.n.e.263.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(263,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("588.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.11
Character	$\chi$	$=$	588.263
Dual form			588.2.n.e.275.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29776 + 0.561968i) q^{2} +(1.27809 - 1.16897i) q^{3} +(1.36838 + 1.45860i) q^{4} +(0.432549 - 0.249732i) q^{5} +(2.31558 - 0.798808i) q^{6} +(0.956154 + 2.66191i) q^{8} +(0.267006 - 2.98809i) q^{9} +O(q^{10})$	\(q+(1.29776 + 0.561968i) q^{2} +(1.27809 - 1.16897i) q^{3} +(1.36838 + 1.45860i) q^{4} +(0.432549 - 0.249732i) q^{5} +(2.31558 - 0.798808i) q^{6} +(0.956154 + 2.66191i) q^{8} +(0.267006 - 2.98809i) q^{9} +(0.701688 - 0.0810151i) q^{10} +(0.695249 - 1.20421i) q^{11} +(3.45398 + 0.264615i) q^{12} -2.75054 q^{13} +(0.260904 - 0.824817i) q^{15} +(-0.255045 + 3.99186i) q^{16} +(5.04311 + 2.91164i) q^{17} +(2.02572 - 3.72779i) q^{18} +(2.14907 - 1.24076i) q^{19} +(0.956154 + 0.289187i) q^{20} +(1.57899 - 1.17207i) q^{22} +(-2.53203 - 4.38560i) q^{23} +(4.33375 + 2.28443i) q^{24} +(-2.37527 + 4.11408i) q^{25} +(-3.56955 - 1.54571i) q^{26} +(-3.15174 - 4.13116i) q^{27} +6.32275i q^{29} +(0.802113 - 0.923798i) q^{30} +(-5.98869 - 3.45757i) q^{31} +(-2.57429 + 5.03717i) q^{32} +(-0.519097 - 2.35181i) q^{33} +(4.90852 + 6.61269i) q^{34} +(4.72381 - 3.69941i) q^{36} +(-3.67154 - 6.35929i) q^{37} +(3.48625 - 0.402514i) q^{38} +(-3.51542 + 3.21530i) q^{39} +(1.07835 + 0.912624i) q^{40} +5.74438i q^{41} +3.52627i q^{43} +(2.70783 - 0.633726i) q^{44} +(-0.630730 - 1.35918i) q^{45} +(-0.821409 - 7.11439i) q^{46} +(-2.53203 - 4.38560i) q^{47} +(4.34041 + 5.40008i) q^{48} +(-5.39452 + 4.00429i) q^{50} +(9.84916 - 2.17393i) q^{51} +(-3.76379 - 4.01194i) q^{52} +(4.54223 + 2.62246i) q^{53} +(-1.76864 - 7.13245i) q^{54} -0.694505i q^{55} +(1.29627 - 4.09801i) q^{57} +(-3.55318 + 8.20544i) q^{58} +(-1.57587 + 2.72949i) q^{59} +(1.56010 - 0.748111i) q^{60} +(-2.45426 - 4.25091i) q^{61} +(-5.82886 - 7.85256i) q^{62} +(-6.17154 + 5.09039i) q^{64} +(-1.18974 + 0.686897i) q^{65} +(0.647974 - 3.34381i) q^{66} +(-9.30445 - 5.37193i) q^{67} +(2.65399 + 11.3402i) q^{68} +(-8.36279 - 2.64530i) q^{69} +4.54224 q^{71} +(8.20934 - 2.14633i) q^{72} +(-4.98752 + 8.63864i) q^{73} +(-1.19108 - 10.3162i) q^{74} +(1.77346 + 8.03477i) q^{75} +(4.75054 + 1.43679i) q^{76} +(-6.36908 + 2.19715i) q^{78} +(1.84576 - 1.06565i) q^{79} +(0.886577 + 1.79037i) q^{80} +(-8.85742 - 1.59568i) q^{81} +(-3.22815 + 7.45485i) q^{82} +12.0165 q^{83} +2.90852 q^{85} +(-1.98165 + 4.57626i) q^{86} +(7.39112 + 8.08102i) q^{87} +(3.87026 + 0.699285i) q^{88} +(-2.12318 + 1.22582i) q^{89} +(-0.0547257 - 2.11834i) q^{90} +(2.93206 - 9.69440i) q^{92} +(-11.6959 + 2.58154i) q^{93} +(-0.821409 - 7.11439i) q^{94} +(0.619718 - 1.07338i) q^{95} +(2.59815 + 9.44720i) q^{96} -0.526031 q^{97} +(-3.41265 - 2.39900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{9}+O(q^{10}) $ 24 * q - 2 * q^4 - 2 * q^9	$ 24 q - 2 q^{4} - 2 q^{9} + 10 q^{10} + 12 q^{12} + 24 q^{13} - 10 q^{16} - 10 q^{18} + 28 q^{22} + 14 q^{24} - 12 q^{25} - 14 q^{30} - 10 q^{33} + 8 q^{34} + 44 q^{36} - 8 q^{37} - 34 q^{40} + 18 q^{45} + 24 q^{46} - 8 q^{48} - 16 q^{52} - 38 q^{54} - 4 q^{57} + 14 q^{58} + 14 q^{60} - 4 q^{61} - 68 q^{64} - 30 q^{66} - 36 q^{69} + 20 q^{72} + 24 q^{76} - 104 q^{78} + 26 q^{81} + 68 q^{82} - 40 q^{85} - 34 q^{88} + 40 q^{90} - 6 q^{93} + 24 q^{94} + 62 q^{96} - 72 q^{97}+O(q^{100}) $ 24 * q - 2 * q^4 - 2 * q^9 + 10 * q^10 + 12 * q^12 + 24 * q^13 - 10 * q^16 - 10 * q^18 + 28 * q^22 + 14 * q^24 - 12 * q^25 - 14 * q^30 - 10 * q^33 + 8 * q^34 + 44 * q^36 - 8 * q^37 - 34 * q^40 + 18 * q^45 + 24 * q^46 - 8 * q^48 - 16 * q^52 - 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 - 4 * q^61 - 68 * q^64 - 30 * q^66 - 36 * q^69 + 20 * q^72 + 24 * q^76 - 104 * q^78 + 26 * q^81 + 68 * q^82 - 40 * q^85 - 34 * q^88 + 40 * q^90 - 6 * q^93 + 24 * q^94 + 62 * q^96 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.29776	+	0.561968i	0.917658	+	0.397371i
$2$	1.29776	+	0.561968i	0.917658	+	0.397371i
$3$	1.27809	−	1.16897i	0.737903	−	0.674907i
$3$	1.27809	−	1.16897i	0.737903	−	0.674907i
$4$	1.36838	+	1.45860i	0.684192	+	0.729302i
$5$	0.432549	−	0.249732i	0.193442	−	0.111684i	−0.400151	−	0.916449i	$-0.631042\pi$
$5$	0.432549	−	0.249732i	0.193442	−	0.111684i	0.593593	+	0.804766i	$0.297709\pi$
$6$	2.31558	−	0.798808i	0.945331	−	0.326112i
$7$		0			0
$7$		0			0
$8$	0.956154	+	2.66191i	0.338051	+	0.941128i
$9$	0.267006	−	2.98809i	0.0890021	−	0.996031i
$10$	0.701688	−	0.0810151i	0.221893	−	0.0256192i
$11$	0.695249	−	1.20421i	0.209626	−	0.363082i	−0.741971	−	0.670432i	$-0.766109\pi$
$11$	0.695249	−	1.20421i	0.209626	−	0.363082i	0.951597	+	0.307350i	$0.0994422\pi$
$12$	3.45398	+	0.264615i	0.997078	+	0.0763879i
$13$	−2.75054			−0.762861			−0.381431	−	0.924397i	$-0.624568\pi$
$13$	−2.75054			−0.762861			−0.381431	+	0.924397i	$0.624568\pi$
$14$		0			0
$15$	0.260904	−	0.824817i	0.0673652	−	0.212967i
$16$	−0.255045	+	3.99186i	−0.0637614	+	0.997965i
$17$	5.04311	+	2.91164i	1.22313	+	0.706177i	0.965585	−	0.260088i	$-0.0837515\pi$
$17$	5.04311	+	2.91164i	1.22313	+	0.706177i	0.257550	+	0.966265i	$0.417085\pi$
$18$	2.02572	−	3.72779i	0.477468	−	0.878649i
$19$	2.14907	−	1.24076i	0.493030	−	0.284651i	−0.232801	−	0.972524i	$-0.574789\pi$
$19$	2.14907	−	1.24076i	0.493030	−	0.284651i	0.725831	+	0.687874i	$0.241456\pi$
$20$	0.956154	+	0.289187i	0.213802	+	0.0646643i
$21$		0			0
$22$	1.57899	−	1.17207i	0.336643	−	0.249886i
$23$	−2.53203	−	4.38560i	−0.527964	−	0.914460i	−0.999469	−	0.0325966i	$-0.989622\pi$
$23$	−2.53203	−	4.38560i	−0.527964	−	0.914460i	0.471505	−	0.881863i	$-0.343711\pi$
$24$	4.33375	+	2.28443i	0.884622	+	0.466308i
$25$	−2.37527	+	4.11408i	−0.475054	+	0.822817i
$26$	−3.56955	−	1.54571i	−0.700046	−	0.303139i
$27$	−3.15174	−	4.13116i	−0.606553	−	0.795043i
$28$		0			0
$29$			6.32275i			1.17411i	0.809549	+	0.587053i	$0.199712\pi$
$29$			6.32275i			1.17411i	−0.809549	+	0.587053i	$0.800288\pi$
$30$	0.802113	−	0.923798i	0.146445	−	0.168662i
$31$	−5.98869	−	3.45757i	−1.07560	−	0.620998i	−0.145894	−	0.989300i	$-0.546606\pi$
$31$	−5.98869	−	3.45757i	−1.07560	−	0.620998i	−0.929706	+	0.368302i	$0.879939\pi$
$32$	−2.57429	+	5.03717i	−0.455074	+	0.890454i
$33$	−0.519097	−	2.35181i	−0.0903631	−	0.409397i
$34$	4.90852	+	6.61269i	0.841805	+	1.13407i
$35$		0			0
$36$	4.72381	−	3.69941i	0.787302	−	0.616568i
$37$	−3.67154	−	6.35929i	−0.603598	−	1.04546i	−0.992271	−	0.124086i	$-0.960400\pi$
$37$	−3.67154	−	6.35929i	−0.603598	−	1.04546i	0.388674	−	0.921375i	$-0.372933\pi$
$38$	3.48625	−	0.402514i	0.565545	−	0.0652964i
$39$	−3.51542	+	3.21530i	−0.562918	+	0.514860i
$40$	1.07835	+	0.912624i	0.170502	+	0.144299i
$41$			5.74438i			0.897121i	0.893753	+	0.448560i	$0.148063\pi$
$41$			5.74438i			0.897121i	−0.893753	+	0.448560i	$0.851937\pi$
$42$		0			0
$43$			3.52627i			0.537751i	0.963175	+	0.268875i	$0.0866520\pi$
$43$			3.52627i			0.537751i	−0.963175	+	0.268875i	$0.913348\pi$
$44$	2.70783	−	0.633726i	0.408220	−	0.0955378i
$45$	−0.630730	−	1.35918i	−0.0940237	−	0.202614i
$46$	−0.821409	−	7.11439i	−0.121110	−	1.04896i
$47$	−2.53203	−	4.38560i	−0.369334	−	0.639705i	0.620128	−	0.784501i	$-0.287081\pi$
$47$	−2.53203	−	4.38560i	−0.369334	−	0.639705i	−0.989462	+	0.144796i	$0.953747\pi$
$48$	4.34041	+	5.40008i	0.626484	+	0.779435i
$49$		0			0
$50$	−5.39452	+	4.00429i	−0.762900	+	0.566292i
$51$	9.84916	−	2.17393i	1.37916	−	0.304411i
$52$	−3.76379	−	4.01194i	−0.521944	−	0.556356i
$53$	4.54223	+	2.62246i	0.623923	+	0.360222i	0.778395	−	0.627775i	$-0.216034\pi$
$53$	4.54223	+	2.62246i	0.623923	+	0.360222i	−0.154472	+	0.987997i	$0.549368\pi$
$54$	−1.76864	−	7.13245i	−0.240681	−	0.970604i
$55$		−	0.694505i		−	0.0936470i
$56$		0			0
$57$	1.29627	−	4.09801i	0.171696	−	0.542794i
$58$	−3.55318	+	8.20544i	−0.466556	+	1.07743i
$59$	−1.57587	+	2.72949i	−0.205161	+	0.355349i	−0.950184	−	0.311689i	$-0.899105\pi$
$59$	−1.57587	+	2.72949i	−0.205161	+	0.355349i	0.745023	+	0.667039i	$0.232438\pi$
$60$	1.56010	−	0.748111i	0.201408	−	0.0965807i
$61$	−2.45426	−	4.25091i	−0.314236	−	0.544273i	0.665039	−	0.746809i	$-0.268415\pi$
$61$	−2.45426	−	4.25091i	−0.314236	−	0.544273i	−0.979275	+	0.202536i	$0.935082\pi$
$62$	−5.82886	−	7.85256i	−0.740267	−	0.997276i
$63$		0			0
$64$	−6.17154	+	5.09039i	−0.771443	+	0.636299i
$65$	−1.18974	+	0.686897i	−0.147569	+	0.0851991i
$66$	0.647974	−	3.34381i	0.0797601	−	0.411594i
$67$	−9.30445	−	5.37193i	−1.13672	−	0.656286i	−0.191104	−	0.981570i	$-0.561207\pi$
$67$	−9.30445	−	5.37193i	−1.13672	−	0.656286i	−0.945616	+	0.325284i	$0.894540\pi$
$68$	2.65399	+	11.3402i	0.321844	+	1.37520i
$69$	−8.36279	−	2.64530i	−1.00676	−	0.318457i
$70$		0			0
$71$	4.54224			0.539065			0.269532	−	0.962991i	$-0.413131\pi$
$71$	4.54224			0.539065			0.269532	+	0.962991i	$0.413131\pi$
$72$	8.20934	−	2.14633i	0.967480	−	0.252947i
$73$	−4.98752	+	8.63864i	−0.583745	+	1.01108i	0.411286	+	0.911507i	$0.365080\pi$
$73$	−4.98752	+	8.63864i	−0.583745	+	1.01108i	−0.995031	+	0.0995695i	$0.968253\pi$
$74$	−1.19108	−	10.3162i	−0.138460	−	1.19923i
$75$	1.77346	+	8.03477i	0.204781	+	0.927776i
$76$	4.75054	+	1.43679i	0.544924	+	0.164811i
$77$		0			0
$78$	−6.36908	+	2.19715i	−0.721156	+	0.248778i
$79$	1.84576	−	1.06565i	0.207664	−	0.119895i	−0.392561	−	0.919726i	$-0.628411\pi$
$79$	1.84576	−	1.06565i	0.207664	−	0.119895i	0.600225	+	0.799831i	$0.295078\pi$
$80$	0.886577	+	1.79037i	0.0991223	+	0.200169i
$81$	−8.85742	−	1.59568i	−0.984157	−	0.177298i
$82$	−3.22815	+	7.45485i	−0.356490	+	0.823250i
$83$	12.0165			1.31899			0.659493	−	0.751710i	$-0.270771\pi$
$83$	12.0165			1.31899			0.659493	+	0.751710i	$0.270771\pi$
$84$		0			0
$85$	2.90852			0.315474
$86$	−1.98165	+	4.57626i	−0.213687	+	0.493471i
$87$	7.39112	+	8.08102i	0.792411	+	0.866376i
$88$	3.87026	+	0.699285i	0.412571	+	0.0745440i
$89$	−2.12318	+	1.22582i	−0.225056	+	0.129936i	−0.608289	−	0.793715i	$-0.708144\pi$
$89$	−2.12318	+	1.22582i	−0.225056	+	0.129936i	0.383233	+	0.923652i	$0.374811\pi$
$90$	−0.0547257	−	2.11834i	−0.00576860	−	0.223293i
$91$		0			0
$92$	2.93206	−	9.69440i	0.305688	−	1.01071i
$93$	−11.6959	+	2.58154i	−1.21280	+	0.267693i
$94$	−0.821409	−	7.11439i	−0.0847219	−	0.733793i
$95$	0.619718	−	1.07338i	0.0635817	−	0.110127i
$96$	2.59815	+	9.44720i	0.265173	+	0.964201i
$97$	−0.526031			−0.0534104			−0.0267052	−	0.999643i	$-0.508502\pi$
$97$	−0.526031			−0.0534104			−0.0267052	+	0.999643i	$0.508502\pi$
$98$		0			0
$99$	−3.41265	−	2.39900i	−0.342984	−	0.241109i
$100$	−9.25110	+	2.16508i	−0.925110	+	0.216508i
$101$	−13.9396	−	8.04803i	−1.38704	−	0.800809i	−0.394061	−	0.919084i	$-0.628930\pi$
$101$	−13.9396	−	8.04803i	−1.38704	−	0.800809i	−0.992981	+	0.118275i	$0.962264\pi$
$102$	14.0036	+	2.71366i	1.38656	+	0.268692i
$103$	−1.62521	+	0.938316i	−0.160137	+	0.0924550i	−0.577927	−	0.816089i	$-0.696138\pi$
$103$	−1.62521	+	0.938316i	−0.160137	+	0.0924550i	0.417790	+	0.908544i	$0.362805\pi$
$104$	−2.62993	−	7.32168i	−0.257886	−	0.717950i
$105$		0			0
$106$	4.42101	+	5.95591i	0.429406	+	0.578490i
$107$	3.63924	+	6.30335i	0.351819	+	0.609368i	0.986568	−	0.163350i	$-0.0522300\pi$
$107$	3.63924	+	6.30335i	0.351819	+	0.609368i	−0.634749	+	0.772718i	$0.718897\pi$
$108$	1.71293	−	10.2502i	0.164827	−	0.986323i
$109$	0.921005	−	1.59523i	0.0882163	−	0.152795i	−0.818541	−	0.574448i	$-0.805217\pi$
$109$	0.921005	−	1.59523i	0.0882163	−	0.152795i	0.906757	+	0.421653i	$0.138550\pi$
$110$	0.390289	−	0.901303i	0.0372126	−	0.0859359i
$111$	−12.1264	−	3.83579i	−1.15099	−	0.364077i
$112$		0			0
$113$		−	10.2728i		−	0.966382i	−0.875515	−	0.483191i	$-0.839478\pi$
$113$		−	10.2728i		−	0.966382i	0.875515	−	0.483191i	$-0.160522\pi$
$114$	3.98520	−	4.58978i	0.373248	−	0.429872i
$115$	−2.19045	−	1.26466i	−0.204260	−	0.117930i
$116$	−9.22238	+	8.65196i	−0.856277	+	0.803314i
$117$	−0.734410	+	8.21886i	−0.0678963	+	0.759834i
$118$	−3.57899	+	2.65665i	−0.329473	+	0.244564i
$119$		0			0
$120$	2.44505	−	0.0941473i	0.223202	−	0.00859443i
$121$	4.53326	+	7.85183i	0.412114	+	0.713803i
$122$	−0.796182	−	6.89589i	−0.0720830	−	0.624325i
$123$	6.71502	+	7.34181i	0.605473	+	0.661988i
$124$	−3.15161	−	13.4664i	−0.283023	−	1.20932i
$125$			4.87005i			0.435590i
$126$		0			0
$127$			1.51224i			0.134190i	0.997747	+	0.0670949i	$0.0213730\pi$
$127$			1.51224i			0.134190i	−0.997747	+	0.0670949i	$0.978627\pi$
$128$	−10.8698	+	3.13792i	−0.960767	+	0.277356i
$129$	4.12211	+	4.50687i	0.362931	+	0.396808i
$130$	−1.93002	+	0.222835i	−0.169274	+	0.0195439i
$131$	−3.32518	−	5.75939i	−0.290523	−	0.503200i	0.683411	−	0.730034i	$-0.260496\pi$
$131$	−3.32518	−	5.75939i	−0.290523	−	0.503200i	−0.973933	+	0.226834i	$0.927162\pi$
$132$	2.72003	−	3.97533i	0.236748	−	0.346008i
$133$		0			0
$134$	−9.05614	−	12.2003i	−0.782331	−	1.05395i
$135$	−2.39497	−	0.999839i	−0.206126	−	0.0860524i
$136$	−2.92854	+	16.2083i	−0.251121	+	1.38985i
$137$	10.5583	+	6.09586i	0.902060	+	0.520805i	0.877868	−	0.478903i	$-0.158965\pi$
$137$	10.5583	+	6.09586i	0.902060	+	0.520805i	0.0241922	+	0.999707i	$0.492299\pi$
$138$	−9.36635	−	8.13259i	−0.797317	−	0.692292i
$139$		−	0.0477837i		−	0.00405296i	−0.999998	−	0.00202648i	$-0.999355\pi$
$139$		−	0.0477837i		−	0.00405296i	0.999998	−	0.00202648i	$-0.000645050\pi$
$140$		0			0
$141$	−8.36279	−	2.64530i	−0.704274	−	0.222774i
$142$	5.89476	+	2.55259i	0.494677	+	0.214209i
$143$	−1.91231	+	3.31221i	−0.159915	+	0.276981i
$144$	11.8600	+	1.82795i	0.988330	+	0.152329i
$145$	1.57899	+	2.73490i	0.131128	+	0.227121i
$146$	−11.3273	+	8.40809i	−0.937451	+	0.695859i
$147$		0			0
$148$	4.25161	−	14.0573i	0.349480	−	1.15550i
$149$	1.98650	−	1.14691i	0.162740	−	0.0939583i	−0.416418	−	0.909173i	$-0.636715\pi$
$149$	1.98650	−	1.14691i	0.162740	−	0.0939583i	0.579158	+	0.815215i	$0.303381\pi$
$150$	−2.21376	+	11.4239i	−0.180752	+	0.932755i
$151$	11.3759	+	6.56789i	0.925759	+	0.534487i	0.885468	−	0.464701i	$-0.153838\pi$
$151$	11.3759	+	6.56789i	0.925759	+	0.534487i	0.0402913	+	0.999188i	$0.487171\pi$
$152$	5.35764	+	4.53427i	0.434562	+	0.367777i
$153$	10.0468	−	14.2919i	0.812236	−	1.15543i
$154$		0			0
$155$	−3.45387			−0.277421
$156$	−9.50029	−	0.727834i	−0.760632	−	0.0582733i
$157$	4.20480	−	7.28292i	0.335579	−	0.581241i	−0.648017	−	0.761626i	$-0.724401\pi$
$157$	4.20480	−	7.28292i	0.335579	−	0.581241i	0.983596	+	0.180386i	$0.0577346\pi$
$158$	2.99422	−	0.345705i	0.238207	−	0.0275028i
$159$	8.87093	−	1.95802i	0.703511	−	0.155281i
$160$	0.144439	+	2.82170i	0.0114189	+	0.223075i
$161$		0			0
$162$	−10.5981	−	7.04840i	−0.832667	−	0.553774i
$163$	−10.7040	+	6.17993i	−0.838399	+	0.484050i	−0.856720	−	0.515782i	$-0.827501\pi$
$163$	−10.7040	+	6.17993i	−0.838399	+	0.484050i	0.0183210	+	0.999832i	$0.494168\pi$
$164$	−8.37876	+	7.86052i	−0.654272	+	0.613803i
$165$	−0.811857	−	0.887636i	−0.0632030	−	0.0691024i
$166$	15.5946	+	6.75291i	1.21038	+	0.524127i
$167$	−2.36549			−0.183047			−0.0915237	−	0.995803i	$-0.529174\pi$
$167$	−2.36549			−0.183047			−0.0915237	+	0.995803i	$0.529174\pi$
$168$		0			0
$169$	−5.43456			−0.418043
$170$	3.77458	+	1.63450i	0.289497	+	0.125360i
$171$	−3.13371	−	6.75291i	−0.239641	−	0.516408i
$172$	−5.14342	+	4.82529i	−0.392182	+	0.367925i
$173$	8.28769	−	4.78490i	0.630102	−	0.363789i	−0.150690	−	0.988581i	$-0.548149\pi$
$173$	8.28769	−	4.78490i	0.630102	−	0.363789i	0.780791	+	0.624792i	$0.214816\pi$
$174$	5.05067	+	14.6408i	0.382890	+	1.10992i
$175$		0			0
$176$	4.62971	+	3.08247i	0.348977	+	0.232350i
$177$	1.17660	+	5.33067i	0.0884386	+	0.400678i
$178$	−3.44425	+	0.397665i	−0.258158	+	0.0298062i
$179$	10.3771	−	17.9736i	0.775619	−	1.34341i	−0.158827	−	0.987306i	$-0.550771\pi$
$179$	10.3771	−	17.9736i	0.775619	−	1.34341i	0.934446	−	0.356105i	$-0.115895\pi$
$180$	1.11942	−	2.77986i	0.0834365	−	0.207199i
$181$	6.43456			0.478277			0.239138	−	0.970985i	$-0.423135\pi$
$181$	6.43456			0.478277			0.239138	+	0.970985i	$0.423135\pi$
$182$		0			0
$183$	−8.10595	−	2.56406i	−0.599209	−	0.189541i
$184$	9.25306	−	10.9333i	0.682145	−	0.806016i
$185$	−3.17624	−	1.83380i	−0.233522	−	0.134824i
$186$	−16.6292	−	3.22246i	−1.21931	−	0.236283i
$187$	7.01244	−	4.04864i	0.512801	−	0.296066i
$188$	2.93206	−	9.69440i	0.213842	−	0.707037i
$189$		0			0
$190$	1.40745	−	1.04474i	0.102107	−	0.0757932i
$191$	−8.76689	−	15.1847i	−0.634350	−	1.09873i	−0.986652	−	0.162840i	$-0.947935\pi$
$191$	−8.76689	−	15.1847i	−0.634350	−	1.09873i	0.352303	−	0.935886i	$-0.385399\pi$
$192$	−1.93723	+	13.7203i	−0.139807	+	0.990179i
$193$	1.09255	−	1.89234i	0.0786432	−	0.136214i	−0.824022	−	0.566558i	$-0.808275\pi$
$193$	1.09255	−	1.89234i	0.0786432	−	0.136214i	0.902665	+	0.430344i	$0.141608\pi$
$194$	−0.682665	−	0.295612i	−0.0490125	−	0.0212237i
$195$	−0.717627	+	2.26869i	−0.0513903	+	0.162464i
$196$		0			0
$197$		−	6.27706i		−	0.447222i	−0.974678	−	0.223611i	$-0.928215\pi$
$197$		−	6.27706i		−	0.447222i	0.974678	−	0.223611i	$-0.0717845\pi$
$198$	−3.08065	−	5.03114i	−0.218932	−	0.357547i
$199$	0.749564	+	0.432761i	0.0531352	+	0.0306776i	0.526332	−	0.850279i	$-0.323567\pi$
$199$	0.749564	+	0.432761i	0.0531352	+	0.0306776i	−0.473197	+	0.880957i	$0.656900\pi$
$200$	−13.2224	−	2.38905i	−0.934968	−	0.168932i
$201$	−18.1715	+	4.01087i	−1.28172	+	0.282905i
$202$	−13.5676	−	18.2781i	−0.954612	−	1.28604i
$203$		0			0
$204$	16.6484	+	11.3912i	1.16562	+	0.797547i
$205$	1.43456	+	2.48472i	0.100194	+	0.173541i
$206$	−2.63644	+	0.304397i	−0.183690	+	0.0212084i
$207$	−13.7806	+	6.39495i	−0.957821	+	0.444480i
$208$	0.701512	−	10.9798i	0.0486411	−	0.761309i
$209$		−	3.45056i		−	0.238680i
$210$		0			0
$211$		−	3.90417i		−	0.268774i	−0.990929	−	0.134387i	$-0.957094\pi$
$211$		−	3.90417i		−	0.268774i	0.990929	−	0.134387i	$-0.0429065\pi$
$212$	2.39039	+	10.2138i	0.164173	+	0.701489i
$213$	5.80537	−	5.30976i	0.397778	−	0.363818i
$214$	1.18060	+	10.2254i	0.0807041	+	0.698994i
$215$	0.880622	+	1.52528i	0.0600580	+	0.104023i
$216$	7.98324	−	12.3397i	0.543191	−	0.839609i
$217$		0			0
$218$	2.09171	−	1.55265i	0.141669	−	0.105159i
$219$	3.72385	+	16.8712i	0.251635	+	1.14005i
$220$	1.01301	−	0.950350i	0.0682969	−	0.0640726i
$221$	−13.8713	−	8.00858i	−0.933082	−	0.538715i
$222$	−13.5816	−	11.7926i	−0.911537	−	0.791467i
$223$			23.5017i			1.57379i	0.617085	+	0.786896i	$0.288313\pi$
$223$			23.5017i			1.57379i	−0.617085	+	0.786896i	$0.711687\pi$
$224$		0			0
$225$	11.6591	+	8.19601i	0.777271	+	0.546401i
$226$	5.77297	−	13.3316i	0.384012	−	0.886808i
$227$	9.58391	−	16.5998i	0.636107	−	1.10177i	−0.350173	−	0.936685i	$-0.613877\pi$
$227$	9.58391	−	16.5998i	0.636107	−	1.10177i	0.986280	−	0.165084i	$-0.0527895\pi$
$228$	7.75116	−	3.71690i	0.513333	−	0.246158i
$229$	5.73805	+	9.93860i	0.379181	+	0.656761i	0.990943	−	0.134281i	$-0.0428723\pi$
$229$	5.73805	+	9.93860i	0.379181	+	0.656761i	−0.611762	+	0.791042i	$0.709539\pi$
$230$	−2.13199	−	2.87219i	−0.140579	−	0.189386i
$231$		0			0
$232$	−16.8306	+	6.04552i	−1.10498	+	0.396908i
$233$	17.5088	−	10.1087i	1.14704	−	0.662245i	0.198877	−	0.980025i	$-0.436271\pi$
$233$	17.5088	−	10.1087i	1.14704	−	0.662245i	0.948164	+	0.317780i	$0.102937\pi$
$234$	−5.57182	+	10.2534i	−0.364242	+	0.670288i
$235$	−2.19045	−	1.26466i	−0.142889	−	0.0824971i
$236$	−6.13764	+	1.43642i	−0.399526	+	0.0935031i
$237$	1.11332	−	3.51963i	0.0723181	−	0.228625i
$238$		0			0
$239$	6.90774			0.446824			0.223412	−	0.974724i	$-0.428280\pi$
$239$	6.90774			0.446824			0.223412	+	0.974724i	$0.428280\pi$
$240$	3.22601	+	1.25186i	0.208238	+	0.0808072i
$241$	4.03326	−	6.98581i	0.259805	−	0.449995i	−0.706385	−	0.707828i	$-0.749675\pi$
$241$	4.03326	−	6.98581i	0.259805	−	0.449995i	0.966190	+	0.257833i	$0.0830084\pi$
$242$	1.47063	+	12.7374i	0.0945354	+	0.818789i
$243$	−13.1858	+	8.31466i	−0.845872	+	0.533386i
$244$	2.84201	−	9.39667i	0.181941	−	0.601560i
$245$		0			0
$246$	4.58866	+	13.3016i	0.292562	+	0.848076i
$247$	−5.91109	+	3.41277i	−0.376113	+	0.217149i
$248$	3.47764	−	19.2473i	0.220830	−	1.22221i
$249$	15.3582	−	14.0470i	0.973285	−	0.890193i
$250$	−2.73681	+	6.32017i	−0.173091	+	0.399723i
$251$	20.4073			1.28810			0.644048	−	0.764985i	$-0.277254\pi$
$251$	20.4073			1.28810			0.644048	+	0.764985i	$0.277254\pi$
$252$		0			0
$253$	−7.04155			−0.442699
$254$	−0.849832	+	1.96254i	−0.0533232	+	0.123140i
$255$	3.71734	−	3.39999i	0.232789	−	0.212915i
$256$	−15.8699	−	2.03621i	−0.991869	−	0.127263i
$257$	23.5645	−	13.6050i	1.46991	−	0.848655i	0.470484	−	0.882409i	$-0.344080\pi$
$257$	23.5645	−	13.6050i	1.46991	−	0.848655i	0.999430	+	0.0337537i	$0.0107462\pi$
$258$	2.81681	+	8.16535i	0.175367	+	0.508352i
$259$		0			0
$260$	−2.62993	−	0.795420i	−0.163102	−	0.0493299i
$261$	18.8930	+	1.68821i	1.16945	+	0.104498i
$262$	−1.07872	−	9.34297i	−0.0666433	−	0.577211i
$263$	−1.80247	+	3.12196i	−0.111145	+	0.192508i	−0.916232	−	0.400648i	$-0.868785\pi$
$263$	−1.80247	+	3.12196i	−0.111145	+	0.192508i	0.805087	+	0.593156i	$0.202118\pi$
$264$	5.76396	−	3.63048i	0.354747	−	0.223440i
$265$	2.61965			0.160924
$266$		0			0
$267$	−1.28066	+	4.04864i	−0.0783749	+	0.247772i
$268$	−4.89656	−	20.9224i	−0.299105	−	1.27804i
$269$	22.6598	+	13.0827i	1.38160	+	0.797664i	0.992348	−	0.123469i	$-0.0394020\pi$
$269$	22.6598	+	13.0827i	1.38160	+	0.797664i	0.389247	+	0.921134i	$0.372735\pi$
$270$	−2.54623	−	2.64345i	−0.154958	−	0.160875i
$271$	−19.9722	+	11.5309i	−1.21322	+	0.700455i	−0.963460	−	0.267851i	$-0.913686\pi$
$271$	−19.9722	+	11.5309i	−1.21322	+	0.700455i	−0.249764	+	0.968307i	$0.580353\pi$
$272$	−12.9091	+	19.3888i	−0.782729	+	1.17562i
$273$		0			0
$274$	10.2766	+	13.8444i	0.620830	+	0.836373i
$275$	3.30281	+	5.72063i	0.199167	+	0.344967i
$276$	−7.58507	−	15.8178i	−0.456568	−	0.952118i
$277$	10.1455	−	17.5725i	0.609585	−	1.05583i	−0.381724	−	0.924276i	$-0.624670\pi$
$277$	10.1455	−	17.5725i	0.609585	−	1.05583i	0.991309	−	0.131555i	$-0.0419971\pi$
$278$	0.0268529	−	0.0620120i	0.00161053	−	0.00371923i
$279$	−11.9306	+	16.9716i	−0.714264	+	1.01606i
$280$		0			0
$281$			27.6637i			1.65028i	0.564929	+	0.825140i	$0.308904\pi$
$281$			27.6637i			1.65028i	−0.564929	+	0.825140i	$0.691096\pi$
$282$	−9.36635	−	8.13259i	−0.557758	−	0.484289i
$283$	15.0435	+	8.68535i	0.894242	+	0.516291i	0.875328	−	0.483530i	$-0.160646\pi$
$283$	15.0435	+	8.68535i	0.894242	+	0.516291i	0.0189142	+	0.999821i	$0.493979\pi$
$284$	6.21553	+	6.62533i	0.368824	+	0.393141i
$285$	−0.462703	−	2.09631i	−0.0274081	−	0.124175i
$286$	−4.34308	+	3.22382i	−0.256812	+	0.190628i
$287$		0			0
$288$	14.3642	+	9.03716i	0.846417	+	0.532520i
$289$	8.45533	+	14.6451i	0.497373	+	0.861474i
$290$	0.512239	+	4.43660i	0.0300797	+	0.260526i
$291$	−0.672313	+	0.614916i	−0.0394117	+	0.0360470i
$292$	−19.4252	+	4.54617i	−1.13677	+	0.266044i
$293$			19.9672i			1.16650i	0.812294	+	0.583248i	$0.198218\pi$
$293$			19.9672i			1.16650i	−0.812294	+	0.583248i	$0.801782\pi$
$294$		0			0
$295$			1.57418i			0.0916525i
$296$	13.4173	−	15.8538i	0.779866	−	0.921482i
$297$	−7.16602	+	0.923163i	−0.415815	+	0.0535673i
$298$	3.22253	−	0.372066i	0.186676	−	0.0215532i
$299$	6.96442	+	12.0627i	0.402763	+	0.697606i
$300$	−9.29278	+	13.5814i	−0.536519	+	0.784124i
$301$		0			0
$302$	11.0723	+	14.9165i	0.637141	+	0.858346i
$303$	−27.2239	+	6.00894i	−1.56397	+	0.345204i
$304$	4.40485	+	8.89523i	0.252635	+	0.510176i
$305$	−2.12318	−	1.22582i	−0.121573	−	0.0701901i
$306$	21.0700	−	12.9015i	1.20449	−	0.737530i
$307$		−	14.1529i		−	0.807746i	−0.914815	−	0.403873i	$-0.867664\pi$
$307$		−	14.1529i		−	0.807746i	0.914815	−	0.403873i	$-0.132336\pi$
$308$		0			0
$309$	−0.980294	+	3.09908i	−0.0557670	+	0.176300i
$310$	−4.48231	−	1.94096i	−0.254578	−	0.110239i
$311$	−12.2774	+	21.2652i	−0.696190	+	1.20584i	0.273588	+	0.961847i	$0.411790\pi$
$311$	−12.2774	+	21.2652i	−0.696190	+	1.20584i	−0.969778	+	0.243990i	$0.921544\pi$
$312$	−11.9201	−	6.28341i	−0.674844	−	0.355728i
$313$	0.0260312	+	0.0450873i	0.00147137	+	0.00254848i	0.866760	−	0.498725i	$-0.166198\pi$
$313$	0.0260312	+	0.0450873i	0.00147137	+	0.00254848i	−0.865289	+	0.501274i	$0.832865\pi$
$314$	9.54960	−	7.08856i	0.538915	−	0.400031i
$315$		0			0
$316$	4.08007	+	1.23401i	0.229522	+	0.0694185i
$317$	−5.86864	+	3.38826i	−0.329616	+	0.190304i	−0.655671	−	0.755047i	$-0.727614\pi$
$317$	−5.86864	+	3.38826i	−0.329616	+	0.190304i	0.326055	+	0.945351i	$0.394281\pi$
$318$	12.6127	+	2.44414i	0.707286	+	0.137060i
$319$	7.61390	+	4.39589i	0.426297	+	0.246122i
$320$	−1.39826	+	3.74308i	−0.0781650	+	0.209244i
$321$	12.0197	+	3.80205i	0.670875	+	0.212210i
$322$		0			0
$323$	14.4507			0.804056
$324$	−9.79289	−	15.1030i	−0.544049	−	0.839053i
$325$	6.53326	−	11.3159i	0.362400	−	0.627695i
$326$	−17.3641	+	2.00482i	−0.961711	+	0.111037i
$327$	−0.687654	−	3.11547i	−0.0380273	−	0.172286i
$328$	−15.2910	+	5.49251i	−0.844305	+	0.303273i
$329$		0			0
$330$	−0.554776	−	1.60818i	−0.0305394	−	0.0885274i
$331$	15.4949	−	8.94598i	0.851676	−	0.491715i	−0.00953987	−	0.999954i	$-0.503037\pi$
$331$	15.4949	−	8.94598i	0.851676	−	0.491715i	0.861216	+	0.508239i	$0.169703\pi$
$332$	16.4433	+	17.5274i	0.902441	+	0.961939i
$333$	−19.9825	+	9.27294i	−1.09503	+	0.508154i
$334$	−3.06985	−	1.32933i	−0.167975	−	0.0727378i
$335$	−5.36618			−0.293185
$336$		0			0
$337$	7.09362			0.386414			0.193207	−	0.981158i	$-0.438111\pi$
$337$	7.09362			0.386414			0.193207	+	0.981158i	$0.438111\pi$
$338$	−7.05277	−	3.05404i	−0.383620	−	0.166118i
$339$	−12.0086	−	13.1295i	−0.652217	−	0.713096i
$340$	3.97998	+	4.24238i	0.215845	+	0.230076i
$341$	−8.32726	+	4.80775i	−0.450946	+	0.260354i
$342$	−0.271898	−	10.5247i	−0.0147026	−	0.569112i
$343$		0			0
$344$	−9.38661	+	3.37165i	−0.506092	+	0.181787i
$345$	−4.27793	+	0.944236i	−0.230316	+	0.0508359i
$346$	13.4444	−	1.55226i	0.722777	−	0.0834501i
$347$	4.59539	−	7.95946i	0.246694	−	0.427286i	−0.715913	−	0.698190i	$-0.753989\pi$
$347$	4.59539	−	7.95946i	0.246694	−	0.427286i	0.962606	+	0.270904i	$0.0873225\pi$
$348$	−1.67310	+	21.8387i	−0.0896874	+	1.17067i
$349$	22.1330			1.18475			0.592377	−	0.805661i	$-0.298190\pi$
$349$	22.1330			1.18475			0.592377	+	0.805661i	$0.298190\pi$
$350$		0			0
$351$	8.66898	+	11.3629i	0.462716	+	0.606507i
$352$	4.27602	+	6.60206i	0.227913	+	0.351891i
$353$	−9.28947	−	5.36328i	−0.494429	−	0.285458i	0.231981	−	0.972720i	$-0.425479\pi$
$353$	−9.28947	−	5.36328i	−0.494429	−	0.285458i	−0.726410	+	0.687262i	$0.758813\pi$
$354$	−1.46872	+	7.57917i	−0.0780614	+	0.402828i
$355$	1.96474	−	1.13434i	0.104278	−	0.0602047i
$356$	−4.69330	−	1.41948i	−0.248745	−	0.0752325i
$357$		0			0
$358$	23.5676	−	17.4939i	1.24559	−	0.924584i
$359$	−1.80247	−	3.12196i	−0.0951305	−	0.164771i	0.814533	−	0.580118i	$-0.196993\pi$
$359$	−1.80247	−	3.12196i	−0.0951305	−	0.164771i	−0.909663	+	0.415347i	$0.863660\pi$
$360$	3.01493	−	2.97853i	0.158901	−	0.156982i
$361$	−6.42101	+	11.1215i	−0.337948	+	0.585342i
$362$	8.35054	+	3.61601i	0.438895	+	0.190053i
$363$	14.9725	+	4.73606i	0.785851	+	0.248579i
$364$		0			0
$365$			4.98218i			0.260779i
$366$	−9.07870	−	7.88283i	−0.474551	−	0.412042i
$367$	13.0134	+	7.51328i	0.679293	+	0.392190i	0.799589	−	0.600548i	$-0.205051\pi$
$367$	13.0134	+	7.51328i	0.679293	+	0.392190i	−0.120295	+	0.992738i	$0.538384\pi$
$368$	18.1525	−	8.98897i	0.946263	−	0.468582i
$369$	17.1647	+	1.53378i	0.893561	+	0.0798456i
$370$	−3.09148	−	4.16479i	−0.160718	−	0.216517i
$371$		0			0
$372$	−19.7699	−	13.5271i	−1.02502	−	0.701346i
$373$	−1.32846	−	2.30096i	−0.0687850	−	0.119139i	0.829582	−	0.558385i	$-0.188579\pi$
$373$	−1.32846	−	2.30096i	−0.0687850	−	0.119139i	−0.898367	+	0.439246i	$0.855246\pi$
$374$	11.3757	−	1.31341i	0.588223	−	0.0679148i
$375$	5.69295	+	6.22434i	0.293983	+	0.321423i
$376$	9.25306	−	10.9333i	0.477190	−	0.563843i
$377$		−	17.3909i		−	0.895679i
$378$		0			0
$379$		−	17.7150i		−	0.909957i	−0.890502	−	0.454979i	$-0.849647\pi$
$379$		−	17.7150i		−	0.909957i	0.890502	−	0.454979i	$-0.150353\pi$
$380$	2.41365	−	0.564879i	0.123818	−	0.0289777i
$381$	1.76777	+	1.93278i	0.0905656	+	0.0990191i
$382$	−2.84405	−	24.6329i	−0.145514	−	1.26033i
$383$	−16.4609	−	28.5111i	−0.841111	−	1.45685i	−0.888956	−	0.457993i	$-0.848569\pi$
$383$	−16.4609	−	28.5111i	−0.841111	−	1.45685i	0.0478445	−	0.998855i	$-0.484765\pi$
$384$	−10.2244	+	16.7171i	−0.521764	+	0.853090i
$385$		0			0
$386$	2.48130	−	1.84184i	0.126295	−	0.0937473i
$387$	10.5368	+	0.941536i	0.535617	+	0.0478609i
$388$	−0.719813	−	0.767271i	−0.0365430	−	0.0389523i
$389$	5.90821	+	3.41111i	0.299558	+	0.172950i	0.642244	−	0.766500i	$-0.278003\pi$
$389$	5.90821	+	3.41111i	0.299558	+	0.172950i	−0.342686	+	0.939450i	$0.611337\pi$
$390$	−2.20624	+	2.54094i	−0.111717	+	0.128665i
$391$		−	29.4894i		−	1.49134i
$392$		0			0
$393$	−10.9824	−	3.47394i	−0.553991	−	0.175237i
$394$	3.52751	−	8.14615i	0.177713	−	0.410397i
$395$	0.532254	−	0.921890i	0.0267806	−	0.0463853i
$396$	−1.17063	−	8.26045i	−0.0588262	−	0.415103i
$397$	−10.4221	−	18.0516i	−0.523069	−	0.905982i	−0.999640	−	0.0268459i	$-0.991454\pi$
$397$	−10.4221	−	18.0516i	−0.523069	−	0.905982i	0.476571	−	0.879136i	$-0.341880\pi$
$398$	0.729560	+	0.982853i	0.0365695	+	0.0492660i
$399$		0			0
$400$	−15.8170	−	10.5310i	−0.790852	−	0.526551i
$401$	−3.31292	+	1.91271i	−0.165439	+	0.0955164i	−0.580434	−	0.814308i	$-0.697117\pi$
$401$	−3.31292	+	1.91271i	−0.165439	+	0.0955164i	0.414994	+	0.909824i	$0.363784\pi$
$402$	−25.8363	−	5.00665i	−1.28860	−	0.249709i
$403$	16.4721	+	9.51017i	0.820534	+	0.473735i
$404$	−7.33586	−	31.3452i	−0.364972	−	1.55948i
$405$	−4.22976	+	1.52177i	−0.210178	+	0.0756175i
$406$		0			0
$407$	−10.2105			−0.506118
$408$	15.2041	+	24.1390i	0.752716	+	1.19506i
$409$	−1.93456	+	3.35075i	−0.0956576	+	0.165684i	−0.909883	−	0.414865i	$-0.863829\pi$
$409$	−1.93456	+	3.35075i	−0.0956576	+	0.165684i	0.814225	+	0.580549i	$0.197162\pi$
$410$	0.465381	+	4.03076i	0.0229836	+	0.199065i
$411$	20.6204	−	4.55138i	1.01713	−	0.224503i
$412$	−3.59255	−	1.08656i	−0.176992	−	0.0535310i
$413$		0			0
$414$	−21.4778	+	0.554862i	−1.05558	+	0.0272700i
$415$	5.19774	−	3.00092i	0.255147	−	0.147309i
$416$	7.08066	−	13.8549i	0.347158	−	0.679293i
$417$	−0.0558579	−	0.0610717i	−0.00273537	−	0.00299069i
$418$	1.93910	−	4.47802i	0.0948447	−	0.219027i
$419$	13.5133			0.660170			0.330085	−	0.943951i	$-0.392923\pi$
$419$	13.5133			0.660170			0.330085	+	0.943951i	$0.392923\pi$
$420$		0			0
$421$	11.3825			0.554749			0.277374	−	0.960762i	$-0.410536\pi$
$421$	11.3825			0.554749			0.277374	+	0.960762i	$0.410536\pi$
$422$	2.19401	−	5.06669i	0.106803	−	0.246642i
$423$	−13.7806	+	6.39495i	−0.670038	+	0.310933i
$424$	−2.63768	+	14.5985i	−0.128097	+	0.708965i
$425$	−23.9575	+	13.8319i	−1.16211	+	0.670944i
$426$	10.5179	−	3.62838i	0.509595	−	0.175796i
$427$		0			0
$428$	−4.21420	+	13.9336i	−0.203701	+	0.673507i
$429$	1.42779	+	6.46873i	0.0689345	+	0.312313i
$430$	0.285681	+	2.47434i	0.0137768	+	0.119323i
$431$	−12.9623	+	22.4513i	−0.624370	+	1.08144i	0.364293	+	0.931284i	$0.381311\pi$
$431$	−12.9623	+	22.4513i	−0.624370	+	1.08144i	−0.988662	+	0.150155i	$0.952023\pi$
$432$	17.2949	−	11.5277i	0.832100	−	0.554626i
$433$	−23.3825			−1.12369			−0.561845	−	0.827242i	$-0.689908\pi$
$433$	−23.3825			−1.12369			−0.561845	+	0.827242i	$0.689908\pi$
$434$		0			0
$435$	5.21511	+	1.64963i	0.250046	+	0.0790939i
$436$	3.58709	−	0.839505i	0.171791	−	0.0402050i
$437$	−10.8830	−	6.28330i	−0.520604	−	0.300571i
$438$	−4.64838	+	23.9875i	−0.222108	+	1.14617i
$439$	15.3054	−	8.83658i	0.730487	−	0.421747i	−0.0881133	−	0.996110i	$-0.528084\pi$
$439$	15.3054	−	8.83658i	0.730487	−	0.421747i	0.818600	+	0.574364i	$0.194750\pi$
$440$	1.84871	−	0.664053i	0.0881338	−	0.0316575i
$441$		0			0
$442$	−13.5011	−	18.1884i	−0.642180	−	0.865136i
$443$	17.5681	+	30.4288i	0.834685	+	1.44572i	0.894286	+	0.447495i	$0.147684\pi$
$443$	17.5681	+	30.4288i	0.834685	+	1.44572i	−0.0596013	+	0.998222i	$0.518983\pi$
$444$	−10.9987	−	22.9364i	−0.521973	−	1.08851i
$445$	−0.612252	+	1.06045i	−0.0290235	+	0.0502702i
$446$	−13.2072	+	30.4997i	−0.625380	+	1.44420i
$447$	1.19822	−	3.78801i	0.0566737	−	0.179167i
$448$		0			0
$449$		−	5.52733i		−	0.260851i	−0.991458	−	0.130425i	$-0.958366\pi$
$449$		−	5.52733i		−	0.260851i	0.991458	−	0.130425i	$-0.0416343\pi$
$450$	10.5248	+	17.1885i	0.496145	+	0.810274i
$451$	6.91742	+	3.99377i	0.325728	+	0.188059i
$452$	14.9839	−	14.0571i	0.704784	−	0.661191i
$453$	22.2171	−	4.90381i	1.04385	−	0.230401i
$454$	21.7662	−	16.1568i	1.02154	−	0.758277i
$455$		0			0
$456$	12.1480	−	0.467760i	0.568880	−	0.0219049i
$457$	−11.9761	−	20.7432i	−0.560219	−	0.970327i	−0.997477	−	0.0709914i	$-0.977384\pi$
$457$	−11.9761	−	20.7432i	−0.560219	−	0.970327i	0.437258	−	0.899336i	$-0.355950\pi$
$458$	1.86147	+	16.1226i	0.0869808	+	0.753358i
$459$	−3.86613	−	30.0107i	−0.180455	−	1.40078i
$460$	−1.15275	−	4.92553i	−0.0537471	−	0.229654i
$461$		−	2.99679i		−	0.139574i	−0.997562	−	0.0697871i	$-0.977768\pi$
$461$		−	2.99679i		−	0.139574i	0.997562	−	0.0697871i	$-0.0222320\pi$
$462$		0			0
$463$		−	22.4152i		−	1.04172i	−0.853642	−	0.520861i	$-0.825611\pi$
$463$		−	22.4152i		−	1.04172i	0.853642	−	0.520861i	$-0.174389\pi$
$464$	−25.2395	−	1.61259i	−1.17172	−	0.0748626i
$465$	−4.41434	+	4.03748i	−0.204710	+	0.187234i
$466$	28.4031	−	3.27935i	1.31575	−	0.151913i
$467$	6.03065	+	10.4454i	0.279065	+	0.483355i	0.971153	−	0.238459i	$-0.0766421\pi$
$467$	6.03065	+	10.4454i	0.279065	+	0.483355i	−0.692088	+	0.721814i	$0.743309\pi$
$468$	−12.9930	+	10.1753i	−0.600602	+	0.470356i
$469$		0			0
$470$	−2.13199	−	2.87219i	−0.0983414	−	0.132484i
$471$	−3.13945	−	14.2235i	−0.144658	−	0.655384i
$472$	−8.77243	−	1.58502i	−0.403784	−	0.0729564i
$473$	4.24635	+	2.45163i	0.195248	+	0.112726i
$474$	3.42275	−	3.94200i	0.157212	−	0.181062i
$475$			11.7886i			0.540898i
$476$		0			0
$477$	9.04895	−	12.8724i	0.414323	−	0.589386i
$478$	8.96461	+	3.88192i	0.410032	+	0.177555i
$479$	6.70352	−	11.6108i	0.306292	−	0.530513i	−0.671256	−	0.741225i	$-0.734245\pi$
$479$	6.70352	−	11.6108i	0.306292	−	0.530513i	0.977548	+	0.210713i	$0.0675784\pi$
$480$	3.48310	+	3.43753i	0.158981	+	0.156901i
$481$	10.0987	+	17.4915i	0.460461	+	0.797542i
$482$	9.16001	−	6.79937i	0.417227	−	0.309703i
$483$		0			0
$484$	−5.24946	+	17.3566i	−0.238612	+	0.788934i
$485$	−0.227534	+	0.131367i	−0.0103318	+	0.00596507i
$486$	−21.7847	+	3.38045i	−0.988173	+	0.153340i
$487$	−10.5727	−	6.10416i	−0.479095	−	0.276606i	0.240944	−	0.970539i	$-0.422543\pi$
$487$	−10.5727	−	6.10416i	−0.479095	−	0.276606i	−0.720039	+	0.693933i	$0.755876\pi$
$488$	8.96888	−	10.5975i	0.406002	−	0.479728i
$489$	−6.45640	+	20.4111i	−0.291969	+	0.923023i
$490$		0			0
$491$	−39.8981			−1.80058			−0.900288	−	0.435294i	$-0.856644\pi$
$491$	−39.8981			−1.80058			−0.900288	+	0.435294i	$0.856644\pi$
$492$	−1.52005	+	19.8410i	−0.0685291	+	0.894500i
$493$	−18.4096	+	31.8864i	−0.829126	+	1.43609i
$494$	−9.58906	+	1.10713i	−0.431432	+	0.0498121i
$495$	−2.07525	−	0.185437i	−0.0932753	−	0.00833478i
$496$	15.3295	−	23.0242i	0.688316	−	1.03382i
$497$		0			0
$498$	27.8253	−	9.59891i	1.24688	−	0.430138i
$499$	7.33971	−	4.23758i	0.328571	−	0.189700i	−0.326636	−	0.945150i	$-0.605915\pi$
$499$	7.33971	−	4.23758i	0.328571	−	0.189700i	0.655206	+	0.755450i	$0.272582\pi$
$500$	−7.10346	+	6.66410i	−0.317677	+	0.298028i
$501$	−3.02330	+	2.76520i	−0.135071	+	0.123540i
$502$	26.4838	+	11.4682i	1.18203	+	0.511852i
$503$	−42.5519			−1.89730			−0.948648	−	0.316334i	$-0.897548\pi$
$503$	−42.5519			−1.89730			−0.948648	+	0.316334i	$0.897548\pi$
$504$		0			0
$505$	−8.03941			−0.357749
$506$	−9.13828	−	3.95712i	−0.406246	−	0.175916i
$507$	−6.94583	+	6.35285i	−0.308475	+	0.282140i
$508$	−2.20576	+	2.06933i	−0.0978649	+	0.0918117i
$509$	−14.9018	+	8.60356i	−0.660511	+	0.381346i	−0.792472	−	0.609909i	$-0.791206\pi$
$509$	−14.9018	+	8.60356i	−0.660511	+	0.381346i	0.131961	+	0.991255i	$0.457873\pi$
$510$	6.73492	−	2.32335i	0.298227	−	0.102880i
$511$		0			0
$512$	−19.4511	−	11.5609i	−0.859626	−	0.510924i
$513$	−11.8991	−	4.96758i	−0.525359	−	0.219324i
$514$	38.2267	−	4.41356i	1.68611	−	0.194674i
$515$	−0.468656	+	0.811735i	−0.0206514	+	0.0357693i
$516$	−0.933104	+	12.1797i	−0.0410776	+	0.536179i
$517$	−7.04155			−0.309687
$518$		0			0
$519$	4.99896	−	15.8036i	0.219430	−	0.693701i
$520$	−2.96603	−	2.51021i	−0.130069	−	0.110080i
$521$	9.47744	+	5.47180i	0.415214	+	0.239724i	0.693028	−	0.720911i	$-0.256276\pi$
$521$	9.47744	+	5.47180i	0.415214	+	0.239724i	−0.277814	+	0.960635i	$0.589610\pi$
$522$	23.5699	+	12.8081i	1.03163	+	0.560597i
$523$	−4.79287	+	2.76716i	−0.209578	+	0.121000i	−0.601115	−	0.799162i	$-0.705277\pi$
$523$	−4.79287	+	2.76716i	−0.209578	+	0.121000i	0.391537	+	0.920162i	$0.371943\pi$
$524$	3.85053	−	12.7312i	0.168211	−	0.556164i
$525$		0			0
$526$	−4.09362	+	3.03864i	−0.178490	+	0.132491i
$527$	−20.1344	−	34.8739i	−0.877069	−	1.51913i
$528$	9.52048	−	1.47234i	0.414326	−	0.0640756i
$529$	−1.32230	+	2.29030i	−0.0574915	+	0.0995782i
$530$	3.39968	+	1.47216i	0.147673	+	0.0639464i
$531$	7.73521	+	5.43764i	0.335679	+	0.235974i
$532$		0			0
$533$		−	15.8001i		−	0.684379i
$534$	−3.93719	+	4.53449i	−0.170379	+	0.196226i
$535$	3.14830	+	1.81767i	0.136113	+	0.0785848i
$536$	5.40311	−	29.9040i	0.233379	−	1.29166i
$537$	−7.74788	−	35.1023i	−0.334346	−	1.51478i
$538$	22.0551	+	29.7123i	0.950863	+	1.28099i
$539$		0			0
$540$	−1.81887	−	4.86147i	−0.0782717	−	0.209204i
$541$	−6.26409	−	10.8497i	−0.269314	−	0.466466i	0.699371	−	0.714759i	$-0.253464\pi$
$541$	−6.26409	−	10.8497i	−0.269314	−	0.466466i	−0.968685	+	0.248293i	$0.920130\pi$
$542$	−32.3992	+	3.74073i	−1.39167	+	0.160678i
$543$	8.22391	−	7.52182i	0.352922	−	0.322792i
$544$	−27.6488	+	17.9076i	−1.18543	+	0.767782i
$545$		−	0.920019i		−	0.0394093i
$546$		0			0
$547$			37.4911i			1.60300i	0.597992	+	0.801502i	$0.295966\pi$
$547$			37.4911i			1.60300i	−0.597992	+	0.801502i	$0.704034\pi$
$548$	5.55644	+	23.7419i	0.237359	+	1.01420i
$549$	−13.3574	+	6.19855i	−0.570081	+	0.264548i
$550$	1.07146	+	9.28010i	0.0456871	+	0.395705i
$551$	7.84505	+	13.5880i	0.334210	+	0.578869i
$552$	−0.954556	−	24.7903i	−0.0406286	−	1.05515i
$553$		0			0
$554$	23.0417	−	17.1036i	0.978947	−	0.726661i
$555$	−6.20318	+	1.36918i	−0.263310	+	0.0581185i
$556$	0.0696975	−	0.0653865i	0.00295583	−	0.00277301i
$557$	26.0411	+	15.0348i	1.10340	+	0.637046i	0.937111	−	0.349031i	$-0.113489\pi$
$557$	26.0411	+	15.0348i	1.10340	+	0.637046i	0.166286	+	0.986078i	$0.446823\pi$
$558$	−25.0205	+	15.3205i	−1.05920	+	0.648569i
$559$		−	9.69912i		−	0.410229i
$560$		0			0
$561$	4.22976	−	13.3719i	0.178581	−	0.564560i
$562$	−15.5461	+	35.9010i	−0.655773	+	1.51439i
$563$	3.41956	−	5.92285i	0.144117	−	0.249618i	−0.784926	−	0.619589i	$-0.787299\pi$
$563$	3.41956	−	5.92285i	0.144117	−	0.249618i	0.929043	+	0.369971i	$0.120632\pi$
$564$	−7.58507	−	15.8178i	−0.319389	−	0.666049i
$565$	−2.56544	−	4.44348i	−0.107929	−	0.186939i
$566$	14.6420	+	19.7255i	0.615449	+	0.829124i
$567$		0			0
$568$	4.34308	+	12.0910i	0.182232	+	0.507329i
$569$	−29.0006	+	16.7435i	−1.21577	+	0.701924i	−0.964010	−	0.265866i	$-0.914342\pi$
$569$	−29.0006	+	16.7435i	−1.21577	+	0.701924i	−0.251759	+	0.967790i	$0.581009\pi$
$570$	0.577579	−	2.98054i	0.0241921	−	0.124841i
$571$	−24.2464	−	13.9986i	−1.01468	−	0.585825i	−0.102121	−	0.994772i	$-0.532563\pi$
$571$	−24.2464	−	13.9986i	−1.01468	−	0.585825i	−0.912558	+	0.408947i	$0.865896\pi$
$572$	−7.44798	+	1.74309i	−0.311416	+	0.0728821i
$573$	−28.9553	−	9.15909i	−1.20963	−	0.382627i
$574$		0			0
$575$	24.0570			1.00324
$576$	13.5627	+	19.8003i	0.565114	+	0.825013i
$577$	18.8181	−	32.5939i	0.783409	−	1.35690i	−0.146537	−	0.989205i	$-0.546813\pi$
$577$	18.8181	−	32.5939i	0.783409	−	1.35690i	0.929945	−	0.367698i	$-0.119854\pi$
$578$	2.74298	+	23.7575i	0.114093	+	0.988180i
$579$	−0.815732	−	3.69573i	−0.0339007	−	0.153589i
$580$	−1.82846	+	6.04552i	−0.0759227	+	0.251027i
$581$		0			0
$582$	−1.21807	+	0.420198i	−0.0504905	+	0.0174178i
$583$	6.31596	−	3.64652i	0.261580	−	0.151023i
$584$	−27.7641	−	5.01647i	−1.14889	−	0.207583i
$585$	1.73485	+	3.73846i	0.0717270	+	0.154566i
$586$	−11.2209	+	25.9127i	−0.463531	+	1.07044i
$587$	−19.7791			−0.816373			−0.408186	−	0.912899i	$-0.633839\pi$
$587$	−19.7791			−0.816373			−0.408186	+	0.912899i	$0.633839\pi$
$588$		0			0
$589$	−17.1601			−0.707071
$590$	−0.884640	+	2.04292i	−0.0364201	+	0.0841057i
$591$	−7.33771	−	8.02262i	−0.301833	−	0.330007i
$592$	26.3218	−	13.0344i	1.08182	−	0.535709i
$593$	−19.5061	+	11.2619i	−0.801020	+	0.462469i	−0.843828	−	0.536614i	$-0.819703\pi$
$593$	−19.5061	+	11.2619i	−0.801020	+	0.462469i	0.0428074	+	0.999083i	$0.486370\pi$
$594$	−9.81860	−	2.82902i	−0.402862	−	0.116076i
$595$		0			0
$596$	4.39118	+	1.32811i	0.179870	+	0.0544013i
$597$	1.46389	−	0.323114i	0.0599132	−	0.0132242i
$598$	2.25932	+	19.5684i	0.0923903	+	0.800210i
$599$	−13.3658	+	23.1503i	−0.546113	+	0.945895i	0.452423	+	0.891803i	$0.350560\pi$
$599$	−13.3658	+	23.1503i	−0.546113	+	0.945895i	−0.998536	+	0.0540915i	$0.982774\pi$
$600$	−19.6922	+	12.4033i	−0.803929	+	0.506361i
$601$	−31.1478			−1.27055			−0.635273	−	0.772288i	$-0.719112\pi$
$601$	−31.1478			−1.27055			−0.635273	+	0.772288i	$0.719112\pi$
$602$		0			0
$603$	−18.5362	+	26.3682i	−0.754851	+	1.07380i
$604$	5.98669	+	25.5804i	0.243595	+	1.04085i
$605$	3.92171	+	2.26420i	0.159440	+	0.0920529i
$606$	−38.7071	−	7.50079i	−1.57237	−	0.304699i
$607$	−10.8934	+	6.28933i	−0.442151	+	0.255276i	−0.704510	−	0.709694i	$-0.748833\pi$
$607$	−10.8934	+	6.28933i	−0.442151	+	0.255276i	0.262358	+	0.964970i	$0.415500\pi$
$608$	0.717627	+	14.0193i	0.0291036	+	0.568558i
$609$		0			0
$610$	−2.06651	−	2.78398i	−0.0836707	−	0.112720i
$611$	6.96442	+	12.0627i	0.281750	+	0.488006i
$612$	34.5941	−	4.90248i	1.39838	−	0.198171i
$613$	−2.27131	+	3.93403i	−0.0917374	+	0.158894i	−0.908242	−	0.418445i	$-0.862575\pi$
$613$	−2.27131	+	3.93403i	−0.0917374	+	0.158894i	0.816505	+	0.577339i	$0.195909\pi$
$614$	7.95344	−	18.3671i	0.320975	−	0.741234i
$615$	4.73806	+	1.49873i	0.191057	+	0.0604348i
$616$		0			0
$617$		−	35.4652i		−	1.42777i	−0.700261	−	0.713887i	$-0.746933\pi$
$617$		−	35.4652i		−	1.42777i	0.700261	−	0.713887i	$-0.253067\pi$
$618$	−3.01377	+	3.47098i	−0.121232	+	0.139623i
$619$	−35.9030	−	20.7286i	−1.44306	−	0.833153i	−0.445011	−	0.895525i	$-0.646800\pi$
$619$	−35.9030	−	20.7286i	−1.44306	−	0.833153i	−0.998053	+	0.0623719i	$0.980134\pi$
$620$	−4.72622	−	5.03782i	−0.189810	−	0.202324i
$621$	−10.1373	+	24.2825i	−0.406797	+	0.974423i
$622$	−27.8836	+	20.6976i	−1.11803	+	0.829900i
$623$		0			0
$624$	−11.9384	−	14.8531i	−0.477920	−	0.594600i
$625$	−10.6601	−	18.4639i	−0.426405	−	0.738556i
$626$	0.00844472	+	0.0731414i	0.000337519	+	0.00292332i
$627$	−4.03361	−	4.41012i	−0.161087	−	0.176123i
$628$	16.3767	−	3.83271i	0.653500	−	0.152942i
$629$		−	42.7609i		−	1.70499i
$630$		0			0
$631$			22.2919i			0.887428i	0.896168	+	0.443714i	$0.146339\pi$
$631$			22.2919i			0.887428i	−0.896168	+	0.443714i	$0.853661\pi$
$632$	4.60149	+	3.89432i	0.183037	+	0.154908i
$633$	−4.56386	−	4.98986i	−0.181397	−	0.198329i
$634$	−9.52021	+	1.09918i	−0.378096	+	0.0436540i
$635$	0.377656	+	0.654119i	0.0149868	+	0.0259579i
$636$	14.9948	+	10.2599i	0.594583	+	0.406830i
$637$		0			0
$638$	7.41070	+	9.98359i	0.293393	+	0.395254i
$639$	1.21281	−	13.5726i	0.0479779	−	0.536926i
$640$	−3.91810	+	4.07186i	−0.154876	+	0.160954i
$641$	−29.5411	−	17.0555i	−1.16680	−	0.673653i	−0.213877	−	0.976861i	$-0.568609\pi$
$641$	−29.5411	−	17.0555i	−1.16680	−	0.673653i	−0.952925	+	0.303207i	$0.901943\pi$
$642$	13.4621	+	11.6888i	0.531307	+	0.461322i
$643$		−	24.2299i		−	0.955533i	−0.878487	−	0.477766i	$-0.841447\pi$
$643$		−	24.2299i		−	0.955533i	0.878487	−	0.477766i	$-0.158553\pi$
$644$		0			0
$645$	2.90852	+	0.920019i	0.114523	+	0.0362257i
$646$	18.7536	+	8.12080i	0.737849	+	0.319509i
$647$	−0.714092	+	1.23684i	−0.0280738	+	0.0486253i	−0.879721	−	0.475490i	$-0.842271\pi$
$647$	−0.714092	+	1.23684i	−0.0280738	+	0.0486253i	0.851647	+	0.524116i	$0.175604\pi$
$648$	−4.22149	−	25.1034i	−0.165836	−	0.986153i
$649$	2.19125	+	3.79535i	0.0860140	+	0.148981i
$650$	14.8378	−	11.0139i	0.581987	−	0.432002i
$651$		0			0
$652$	−23.6612	−	7.15630i	−0.926644	−	0.280262i
$653$	4.35426	−	2.51393i	0.170395	−	0.0983778i	−0.412377	−	0.911013i	$-0.635301\pi$
$653$	4.35426	−	2.51393i	0.170395	−	0.0983778i	0.582772	+	0.812636i	$0.301968\pi$
$654$	0.858379	−	4.42958i	0.0335653	−	0.173210i
$655$	−2.87661	−	1.66081i	−0.112398	−	0.0648933i
$656$	−22.9307	−	1.46508i	−0.895295	−	0.0572017i
$657$	24.4814	+	17.2097i	0.955109	+	0.671416i
$658$		0			0
$659$	19.7930			0.771025			0.385512	−	0.922703i	$-0.374025\pi$
$659$	19.7930			0.771025			0.385512	+	0.922703i	$0.374025\pi$
$660$	0.183777	−	2.39880i	0.00715349	−	0.0933734i
$661$	−11.3306	+	19.6252i	−0.440709	+	0.763331i	−0.997742	−	0.0671595i	$-0.978606\pi$
$661$	−11.3306	+	19.6252i	−0.440709	+	0.763331i	0.557033	+	0.830490i	$0.311940\pi$
$662$	25.1361	−	2.90215i	0.976941	−	0.112795i
$663$	−27.0905	+	5.97948i	−1.05211	+	0.232224i
$664$	11.4897	+	31.9870i	0.445885	+	1.24134i
$665$		0			0
$666$	−31.1437	+	0.804573i	−1.20679	+	0.0311766i
$667$	27.7290	−	16.0094i	1.07367	−	0.619885i
$668$	−3.23691	−	3.45032i	−0.125240	−	0.133497i
$669$	27.4729	+	30.0372i	1.06216	+	1.16131i
$670$	−6.96403	−	3.01562i	−0.269044	−	0.116503i
$671$	−6.82530			−0.263488
$672$		0			0
$673$	−11.2766			−0.434680			−0.217340	−	0.976096i	$-0.569738\pi$
$673$	−11.2766			−0.434680			−0.217340	+	0.976096i	$0.569738\pi$
$674$	9.20584	+	3.98638i	0.354596	+	0.153550i
$675$	24.4822	−	3.15392i	0.942320	−	0.121394i
$676$	−7.43656	−	7.92686i	−0.286022	−	0.304879i
$677$	8.73729	−	5.04448i	0.335801	−	0.193875i	−0.322612	−	0.946531i	$-0.604561\pi$
$677$	8.73729	−	5.04448i	0.335801	−	0.193875i	0.658414	+	0.752656i	$0.271228\pi$
$678$	−8.20598	−	23.7874i	−0.315149	−	0.913551i
$679$		0			0
$680$	2.78100	+	7.74223i	0.106646	+	0.296901i
$681$	−7.15568	−	32.4193i	−0.274206	−	1.24231i
$682$	−13.5086	+	1.55967i	−0.517272	+	0.0597229i
$683$	3.11743	−	5.39955i	0.119285	−	0.206608i	−0.800199	−	0.599734i	$-0.795273\pi$
$683$	3.11743	−	5.39955i	0.119285	−	0.206608i	0.919485	+	0.393126i	$0.128606\pi$
$684$	5.56170	−	13.8114i	0.212657	−	0.528093i
$685$	6.08933			0.232662
$686$		0			0
$687$	18.9517	+	5.99476i	0.723052	+	0.228714i
$688$	−14.0764	−	0.899358i	−0.536656	−	0.0342877i
$689$	−12.4936	−	7.21316i	−0.475967	−	0.274799i
$690$	−6.08238	−	1.17866i	−0.231552	−	0.0448709i
$691$	14.7810	−	8.53381i	0.562295	−	0.324641i	−0.191771	−	0.981440i	$-0.561423\pi$
$691$	14.7810	−	8.53381i	0.562295	−	0.324641i	0.754066	+	0.656798i	$0.228090\pi$
$692$	18.3200	+	5.54087i	0.696423	+	0.210632i
$693$		0			0
$694$	10.4367	−	7.74704i	0.396172	−	0.294074i
$695$	−0.0119331	−	0.0206688i	−0.000452650	−	0.000784012i
$696$	−14.4439	+	27.4012i	−0.547495	+	1.03864i
$697$	−16.7256	+	28.9695i	−0.633526	+	1.09730i
$698$	28.7235	+	12.4380i	1.08720	+	0.470787i
$699$	10.5610	−	33.3872i	0.399452	−	1.26282i
$700$		0			0
$701$			21.4324i			0.809489i	0.914430	+	0.404744i	$0.132640\pi$
$701$			21.4324i			0.809489i	−0.914430	+	0.404744i	$0.867360\pi$
$702$	4.86471	+	19.6181i	0.183607	+	0.740436i
$703$	−15.7808	−	9.11104i	−0.595183	−	0.343629i
$704$	1.83913	+	10.9709i	0.0693147	+	0.413481i
$705$	−4.27793	+	0.944236i	−0.161116	+	0.0355620i
$706$	−9.04155	−	12.1807i	−0.340283	−	0.458425i
$707$		0			0
$708$	−6.16529	+	9.01060i	−0.231706	+	0.338639i
$709$	4.27131	+	7.39813i	0.160412	+	0.277843i	0.935017	−	0.354604i	$-0.115384\pi$
$709$	4.27131	+	7.39813i	0.160412	+	0.277843i	−0.774604	+	0.632446i	$0.782051\pi$
$710$	3.18724	−	0.367990i	0.119615	−	0.0138104i
$711$	−2.69143	−	5.79983i	−0.100937	−	0.217511i
$712$	−5.29310	−	4.47964i	−0.198367	−	0.167882i
$713$			35.0186i			1.31146i
$714$		0			0
$715$			1.91026i			0.0714396i
$716$	40.4162	−	9.45880i	1.51042	−	0.353492i
$717$	8.82868	−	8.07495i	0.329713	−	0.301565i
$718$	−0.584734	−	5.06450i	−0.0218221	−	0.189005i
$719$	13.7366	+	23.7924i	0.512287	+	0.887308i	0.999899	+	0.0142470i	$0.00453511\pi$
$719$	13.7366	+	23.7924i	0.512287	+	0.887308i	−0.487611	+	0.873061i	$0.662132\pi$
$720$	5.58651	−	2.17114i	0.208197	−	0.0809134i
$721$		0			0
$722$	−14.5829	+	10.8247i	−0.542719	+	0.402854i
$723$	−3.01137	−	13.6432i	−0.111994	−	0.507397i
$724$	8.80495	+	9.38546i	0.327233	+	0.348808i
$725$	−26.0123	−	15.0182i	−0.966074	−	0.557763i
$726$	16.7692	+	14.5603i	0.622364	+	0.540385i
$727$			45.7930i			1.69837i	0.528096	+	0.849185i	$0.322906\pi$
$727$			45.7930i			1.69837i	−0.528096	+	0.849185i	$0.677094\pi$
$728$		0			0
$729$	−7.13303	+	26.0407i	−0.264186	+	0.964472i
$730$	−2.79982	+	6.46569i	−0.103626	+	0.239306i
$731$	−10.2672	+	17.7834i	−0.379747	+	0.657741i
$732$	−7.35212	−	15.3320i	−0.271742	−	0.566686i
$733$	−21.6466	−	37.4930i	−0.799535	−	1.38483i	−0.919919	−	0.392107i	$-0.871746\pi$
$733$	−21.6466	−	37.4930i	−0.799535	−	1.38483i	0.120385	−	0.992727i	$-0.461587\pi$
$734$	12.6661	+	17.0636i	0.467514	+	0.629828i
$735$		0			0
$736$	28.6091	−	1.46446i	1.05455	−	0.0539807i
$737$	−12.9378	+	7.46966i	−0.476571	+	0.275148i
$738$	21.4138	+	11.6365i	0.788255	+	0.428346i
$739$	−4.48246	−	2.58795i	−0.164890	−	0.0951993i	0.415284	−	0.909692i	$-0.363682\pi$
$739$	−4.48246	−	2.58795i	−0.164890	−	0.0951993i	−0.580174	+	0.814492i	$0.697016\pi$
$740$	−1.67153	−	7.14223i	−0.0614466	−	0.262553i
$741$	−3.56544	+	11.2717i	−0.130980	+	0.414077i
$742$		0			0
$743$	−49.5492			−1.81778			−0.908891	−	0.417034i	$-0.863070\pi$
$743$	−49.5492			−1.81778			−0.908891	+	0.417034i	$0.863070\pi$
$744$	−18.0549	−	28.6650i	−0.661924	−	1.05091i
$745$	0.572839	−	0.992187i	0.0209872	−	0.0363509i
$746$	−0.430963	−	3.73265i	−0.0157787	−	0.136662i
$747$	3.20849	−	35.9066i	0.117393	−	1.31375i
$748$	15.5011	+	4.68828i	0.566775	+	0.171420i
$749$		0			0
$750$	3.89023	+	11.2770i	0.142051	+	0.411777i
$751$	−26.4899	+	15.2939i	−0.966630	+	0.558084i	−0.898207	−	0.439572i	$-0.855130\pi$
$751$	−26.4899	+	15.2939i	−0.966630	+	0.558084i	−0.0684228	+	0.997656i	$0.521797\pi$
$752$	18.1525	−	8.98897i	0.661953	−	0.327794i
$753$	26.0822	−	23.8555i	0.950489	−	0.869344i
$754$	9.77315	−	22.5694i	0.355917	−	0.821927i
$755$	6.56086			0.238774
$756$		0			0
$757$	46.4533			1.68837			0.844187	−	0.536049i	$-0.180084\pi$
$757$	46.4533			1.68837			0.844187	+	0.536049i	$0.180084\pi$
$758$	9.95524	−	22.9899i	0.361591	−	0.835030i
$759$	−8.99971	+	8.23138i	−0.326669	+	0.298780i
$760$	3.44980	+	0.623315i	0.125137	+	0.0226100i
$761$	34.1633	−	19.7242i	1.23842	−	0.715002i	0.269649	−	0.962959i	$-0.413092\pi$
$761$	34.1633	−	19.7242i	1.23842	−	0.715002i	0.968771	+	0.247956i	$0.0797589\pi$
$762$	1.20799	+	3.50172i	0.0437609	+	0.126854i
$763$		0			0
$764$	10.1520	−	33.5659i	0.367285	−	1.21437i
$765$	0.776595	−	8.69095i	0.0280778	−	0.314222i
$766$	−5.34004	−	46.2511i	−0.192943	−	1.67112i
$767$	4.33449	−	7.50756i	0.156509	−	0.271082i
$768$	−22.6634	+	15.9490i	−0.817794	+	0.575511i
$769$	−39.7256			−1.43254			−0.716270	−	0.697823i	$-0.754152\pi$
$769$	−39.7256			−1.43254			−0.716270	+	0.697823i	$0.754152\pi$
$770$		0			0
$771$	14.2136	−	44.9346i	0.511891	−	1.61828i
$772$	4.25520	−	0.995865i	0.153148	−	0.0358420i
$773$	18.9935	+	10.9659i	0.683149	+	0.394416i	0.801040	−	0.598610i	$-0.204280\pi$
$773$	18.9935	+	10.9659i	0.683149	+	0.394416i	−0.117891	+	0.993026i	$0.537613\pi$
$774$	13.1452	+	7.14324i	0.472494	+	0.256758i
$775$	28.4495	−	16.4253i	1.02194	−	0.590015i
$776$	−0.502967	−	1.40025i	−0.0180554	−	0.0502660i
$777$		0			0
$778$	5.75054	+	7.74704i	0.206167	+	0.277745i
$779$	7.12742	+	12.3451i	0.255366	+	0.442307i
$780$	−4.29111	+	2.05771i	−0.153646	+	0.0736777i
$781$	3.15799	−	5.46980i	0.113002	−	0.195725i
$782$	16.5721	−	38.2703i	0.592617	−	1.36854i
$783$	26.1203	−	19.9277i	0.933464	−	0.712157i
$784$		0			0
$785$		−	4.20029i		−	0.149915i
$786$	−12.3004	−	10.6801i	−0.438740	−	0.380948i
$787$	−4.36864	−	2.52223i	−0.155725	−	0.0899080i	0.420112	−	0.907472i	$-0.361991\pi$
$787$	−4.36864	−	2.52223i	−0.155725	−	0.0899080i	−0.575838	+	0.817564i	$0.695324\pi$
$788$	9.15574	−	8.58944i	0.326160	−	0.305986i
$789$	1.34578	+	6.09717i	0.0479111	+	0.217065i
$790$	1.20881	−	0.897287i	0.0430076	−	0.0319240i
$791$		0			0
$792$	3.12291	−	11.3780i	0.110968	−	0.404299i
$793$	6.75054	+	11.6923i	0.239719	+	0.415205i
$794$	−3.38101	−	29.2835i	−0.119987	−	1.03923i
$795$	3.34813	−	3.06230i	0.118746	−	0.108608i
$796$	0.394466	+	1.68550i	0.0139815	+	0.0597410i
$797$		−	28.3335i		−	1.00362i	−0.864977	−	0.501812i	$-0.832667\pi$
$797$		−	28.3335i		−	1.00362i	0.864977	−	0.501812i	$-0.167333\pi$
$798$		0			0
$799$		−	29.4894i		−	1.04326i
$800$	−14.6087	−	22.5554i	−0.516496	−	0.797455i
$801$	3.09595	+	6.67155i	0.109390	+	0.235728i
$802$	−5.37427	+	0.620500i	−0.189772	+	0.0219106i
$803$	6.93514	+	12.0120i	0.244736	+	0.423895i
$804$	−30.7159	−	21.0166i	−1.08327	−	0.741200i
$805$		0			0
$806$	16.0325	+	21.5987i	0.564721	+	0.760783i
$807$	44.2545	−	9.76797i	1.55783	−	0.343849i
$808$	8.09475	−	44.8011i	0.284772	−	1.57610i
$809$	−17.5088	−	10.1087i	−0.615577	−	0.355404i	0.159568	−	0.987187i	$-0.448990\pi$
$809$	−17.5088	−	10.1087i	−0.615577	−	0.355404i	−0.775145	+	0.631783i	$0.782323\pi$
$810$	−6.34442	−	0.402085i	−0.222920	−	0.0141278i
$811$			1.33368i			0.0468317i	0.999726	+	0.0234158i	$0.00745418\pi$
$811$			1.33368i			0.0468317i	−0.999726	+	0.0234158i	$0.992546\pi$
$812$		0			0
$813$	−12.0468	+	38.0845i	−0.422500	+	1.33568i
$814$	−13.2509	−	5.73799i	−0.464443	−	0.201117i
$815$	−3.08666	+	5.34625i	−0.108121	+	0.187271i
$816$	6.16605	+	39.8709i	0.215855	+	1.39576i
$817$	4.37527	+	7.57819i	0.153071	+	0.265127i
$818$	−4.39361	+	3.26133i	−0.153619	+	0.114030i
$819$		0			0
$820$	−1.66120	+	5.49251i	−0.0580117	+	0.191807i
$821$	4.59977	−	2.65568i	0.160533	−	0.0926838i	−0.417581	−	0.908640i	$-0.637122\pi$
$821$	4.59977	−	2.65568i	0.160533	−	0.0926838i	0.578114	+	0.815956i	$0.303789\pi$
$822$	29.3181	+	5.68136i	1.02259	+	0.198160i
$823$	−13.2508	−	7.65035i	−0.461894	−	0.266675i	0.250946	−	0.968001i	$-0.419258\pi$
$823$	−13.2508	−	7.65035i	−0.461894	−	0.266675i	−0.712840	+	0.701326i	$0.752592\pi$
$824$	−4.05167	−	3.42899i	−0.141146	−	0.119455i
$825$	10.9085	+	3.45056i	0.379786	+	0.120133i
$826$		0			0
$827$	0.288306			0.0100254			0.00501270	−	0.999987i	$-0.498404\pi$
$827$	0.288306			0.0100254			0.00501270	+	0.999987i	$0.498404\pi$
$828$	−28.1849	−	11.3497i	−0.979493	−	0.394431i
$829$	−20.5551	+	35.6025i	−0.713908	+	1.23653i	0.249471	+	0.968382i	$0.419743\pi$
$829$	−20.5551	+	35.6025i	−0.713908	+	1.23653i	−0.963379	+	0.268143i	$0.913590\pi$
$830$	8.43186	−	0.973522i	0.292674	−	0.0337914i
$831$	−7.57498	−	34.3190i	−0.262773	−	1.19051i
$832$	16.9750	−	14.0013i	0.588504	−	0.485408i
$833$		0			0
$834$	−0.0381700	−	0.110647i	−0.00132172	−	0.00383139i
$835$	−1.02319	+	0.590740i	−0.0354090	+	0.0204434i
$836$	5.03300	−	4.72170i	0.174070	−	0.163303i
$837$	4.59102	+	35.6376i	0.158689	+	1.23182i
$838$	17.5371	+	7.59406i	0.605810	+	0.262333i
$839$	−25.7705			−0.889695			−0.444848	−	0.895606i	$-0.646742\pi$
$839$	−25.7705			−0.889695			−0.444848	+	0.895606i	$0.646742\pi$
$840$		0			0
$841$	−10.9772			−0.378523
$842$	14.7718	+	6.39659i	0.509070	+	0.220441i
$843$	32.3381	+	35.3566i	1.11378	+	1.21775i
$844$	5.69463	−	5.34240i	0.196017	−	0.183893i
$845$	−2.35071	+	1.35718i	−0.0808669	+	0.0466885i
$846$	−21.4778	+	0.554862i	−0.738421	+	0.0190766i
$847$		0			0
$848$	−11.6270	+	17.4631i	−0.399271	+	0.599685i
$849$	29.3798	−	6.48478i	1.00831	−	0.222557i
$850$	−38.8642	+	4.48717i	−1.33303	+	0.153909i
$851$	−18.5929	+	32.2038i	−0.637355	+	1.10393i
$852$	15.6888	+	1.20195i	0.537490	+	0.0411780i
$853$	51.4656			1.76215			0.881074	−	0.472978i	$-0.156821\pi$
$853$	51.4656			1.76215			0.881074	+	0.472978i	$0.156821\pi$
$854$		0			0
$855$	−3.04190	−	2.13838i	−0.104031	−	0.0731309i
$856$	−13.2993	+	15.7143i	−0.454560	+	0.537104i
$857$	30.8099	+	17.7881i	1.05245	+	0.607631i	0.923334	−	0.383999i	$-0.125453\pi$
$857$	30.8099	+	17.7881i	1.05245	+	0.607631i	0.129114	+	0.991630i	$0.458787\pi$
$858$	−1.78227	+	9.19726i	−0.0608459	+	0.313989i
$859$	−44.4334	+	25.6536i	−1.51605	+	0.875290i	−0.516225	+	0.856453i	$0.672663\pi$
$859$	−44.4334	+	25.6536i	−1.51605	+	0.875290i	−0.999823	+	0.0188372i	$0.994004\pi$
$860$	−1.01975	+	3.37165i	−0.0347732	+	0.114972i
$861$		0			0
$862$	−29.4388	+	21.8521i	−1.00269	+	0.744286i
$863$	5.89152	+	10.2044i	0.200550	+	0.347362i	0.948706	−	0.316161i	$-0.102394\pi$
$863$	5.89152	+	10.2044i	0.200550	+	0.347362i	−0.748156	+	0.663523i	$0.769061\pi$
$864$	28.9228	−	5.24106i	0.983975	−	0.178305i
$865$	2.38989	−	4.13941i	0.0812587	−	0.140744i
$866$	−30.3450	−	13.1402i	−1.03116	−	0.446522i
$867$	27.9263	+	8.83360i	0.948428	+	0.300005i
$868$		0			0
$869$		−	2.96357i		−	0.100532i
$870$	5.84095	+	5.07156i	0.198027	+	0.171942i
$871$	25.5922	+	14.7757i	0.867160	+	0.500655i
$872$	5.12698	+	0.926351i	0.173621	+	0.0313702i
$873$	−0.140454	+	1.57183i	−0.00475364	+	0.0531984i
$874$	−10.5925	−	14.2701i	−0.358298	−	0.482694i
$875$		0			0
$876$	−19.5127	+	28.5179i	−0.659273	+	0.963531i
$877$	−0.664314	−	1.15063i	−0.0224323	−	0.0388539i	0.854591	−	0.519301i	$-0.173808\pi$
$877$	−0.664314	−	1.15063i	−0.0224323	−	0.0388539i	−0.877024	+	0.480447i	$0.840474\pi$
$878$	24.8287	−	2.86666i	0.837927	−	0.0967450i
$879$	23.3411	+	25.5198i	0.787275	+	0.860760i
$880$	2.77237	+	0.177130i	0.0934564	+	0.00597106i
$881$			23.8258i			0.802713i	0.915922	+	0.401356i	$0.131461\pi$
$881$			23.8258i			0.802713i	−0.915922	+	0.401356i	$0.868539\pi$
$882$		0			0
$883$		−	30.2235i		−	1.01710i	−0.861032	−	0.508551i	$-0.830181\pi$
$883$		−	30.2235i		−	1.01710i	0.861032	−	0.508551i	$-0.169819\pi$
$884$	−7.29989	−	31.1915i	−0.245522	−	1.04908i
$885$	1.84018	+	2.01194i	0.0618569	+	0.0676307i
$886$	5.69923	+	49.3621i	0.191469	+	1.65835i
$887$	−10.9556	−	18.9756i	−0.367852	−	0.637138i	0.621377	−	0.783511i	$-0.286573\pi$
$887$	−10.9556	−	18.9756i	−0.367852	−	0.637138i	−0.989229	+	0.146373i	$0.953240\pi$
$888$	−1.38415	−	35.9470i	−0.0464489	−	1.20630i
$889$		0			0
$890$	−1.39050	+	1.03215i	−0.0466096	+	0.0345978i
$891$	−8.07964	+	9.55676i	−0.270678	+	0.320164i
$892$	−34.2797	+	32.1594i	−1.14777	+	1.07678i
$893$	−10.8830	−	6.28330i	−0.364185	−	0.210262i
$894$	3.68374	−	4.24259i	0.123203	−	0.141893i
$895$		−	10.3660i		−	0.346496i
$896$		0			0
$897$	23.0021	+	7.27599i	0.768019	+	0.242938i
$898$	3.10618	−	7.17317i	0.103655	−	0.239372i
$899$	21.8614	−	37.8650i	0.729117	−	1.26287i
$900$	3.99936	+	28.2212i	0.133312	+	0.940708i
$901$	15.2713	+	26.4507i	0.508761	+	0.881200i
$902$	6.73281	+	9.07034i	0.224178	+	0.302009i
$903$		0			0
$904$	27.3452	−	9.82235i	0.909489	−	0.326687i
$905$	2.78326	−	1.60692i	0.0925187	−	0.0534157i
$906$	31.5883	+	6.12129i	1.04945	+	0.203366i
$907$	42.4039	+	24.4819i	1.40800	+	0.812907i	0.995195	−	0.0979134i	$-0.0312168\pi$
$907$	42.4039	+	24.4819i	1.40800	+	0.812907i	0.412802	+	0.910821i	$0.364550\pi$
$908$	37.3270	−	8.73583i	1.23874	−	0.289909i
$909$	−27.7702	+	39.5040i	−0.921081	+	1.31026i
$910$		0			0
$911$	51.8251			1.71704			0.858522	−	0.512777i	$-0.171383\pi$
$911$	51.8251			1.71704			0.858522	+	0.512777i	$0.171383\pi$
$912$	16.0281	+	6.21972i	0.530742	+	0.205955i
$913$	8.35449	−	14.4704i	0.276493	−	0.478900i
$914$	−3.88515	−	33.6500i	−0.128509	−	1.11304i
$915$	−4.14655	+	0.915237i	−0.137081	+	0.0302568i
$916$	−6.64461	+	21.9694i	−0.219544	+	0.725889i
$917$		0			0
$918$	11.8477	−	41.1194i	0.391033	−	1.35714i
$919$	−43.7375	+	25.2518i	−1.44277	+	0.832981i	−0.998034	−	0.0626826i	$-0.980034\pi$
$919$	−43.7375	+	25.2518i	−1.44277	+	0.832981i	−0.444732	+	0.895664i	$0.646701\pi$
$920$	1.27200	−	7.03999i	0.0419365	−	0.232102i
$921$	−16.5443	−	18.0886i	−0.545153	−	0.596038i
$922$	1.68410	−	3.88912i	0.0554628	−	0.128081i
$923$	−12.4936			−0.411232
$924$		0			0
$925$	34.8836			1.14696
$926$	12.5966	−	29.0896i	0.413950	−	0.955944i
$927$	2.36984	+	5.10682i	0.0778356	+	0.167730i
$928$	−31.8488	−	16.2766i	−1.04549	−	0.534304i
$929$	1.07011	−	0.617830i	0.0351093	−	0.0202703i	−0.482343	−	0.875983i	$-0.660214\pi$
$929$	1.07011	−	0.617830i	0.0351093	−	0.0202703i	0.517452	+	0.855712i	$0.326881\pi$
$930$	−7.99770	+	2.75898i	−0.262255	+	0.0904705i
$931$		0			0
$932$	38.7034	+	11.7058i	1.26777	+	0.383436i
$933$	9.16676	+	41.5307i	0.300106	+	1.35965i
$934$	1.95639	+	16.9447i	0.0640151	+	0.554447i
$935$	2.02215	−	3.50247i	0.0661314	−	0.114543i
$936$	−22.5801	+	5.90356i	−0.738053	+	0.192964i
$937$	29.4139			0.960909			0.480455	−	0.877020i	$-0.340472\pi$
$937$	29.4139			0.960909			0.480455	+	0.877020i	$0.340472\pi$
$938$		0			0
$939$	0.0859759	+	0.0271957i	0.00280572	+	0.000887499i
$940$	−1.15275	−	4.92553i	−0.0375984	−	0.160653i
$941$	−38.8530	−	22.4318i	−1.26657	−	0.731256i	−0.292235	−	0.956346i	$-0.594399\pi$
$941$	−38.8530	−	22.4318i	−1.26657	−	0.731256i	−0.974338	+	0.225090i	$0.927732\pi$
$942$	3.91888	−	20.2230i	0.127684	−	0.658901i
$943$	25.1925	−	14.5449i	0.820381	−	0.473647i
$944$	−10.4938	−	6.98680i	−0.341545	−	0.227401i
$945$		0			0
$946$	4.13303	+	5.56796i	0.134376	+	0.181030i
$947$	−8.77882	−	15.2054i	−0.285273	−	0.494108i	0.687402	−	0.726277i	$-0.258751\pi$
$947$	−8.77882	−	15.2054i	−0.285273	−	0.494108i	−0.972675	+	0.232169i	$0.925418\pi$
$948$	6.65720	−	3.19231i	0.216216	−	0.103682i
$949$	13.7183	−	23.7609i	0.445316	−	0.771311i
$950$	−6.62481	+	15.2988i	−0.214937	+	0.496359i
$951$	−3.53984	+	11.1908i	−0.114787	+	0.362886i
$952$		0			0
$953$			37.1546i			1.20356i	0.798663	+	0.601778i	$0.205541\pi$
$953$			37.1546i			1.20356i	−0.798663	+	0.601778i	$0.794459\pi$
$954$	18.9773	−	11.6201i	0.614412	−	0.376215i
$955$	−7.58422	−	4.37875i	−0.245420	−	0.141693i
$956$	9.45244	+	10.0756i	0.305714	+	0.325870i
$957$	14.8699	−	3.28212i	0.480675	−	0.106096i
$958$	15.2245	−	11.3010i	0.491881	−	0.365118i
$959$		0			0
$960$	2.58846	+	6.41850i	0.0835422	+	0.207156i
$961$	8.40960	+	14.5658i	0.271277	+	0.469866i
$962$	3.27610	+	28.3749i	0.105626	+	0.914845i
$963$	19.8067	−	9.19136i	0.638262	−	0.296187i
$964$	15.7086	−	3.67635i	0.505939	−	0.118407i
$965$		−	1.09138i		−	0.0351326i
$966$		0			0
$967$			53.9045i			1.73345i	0.498786	+	0.866725i	$0.333779\pi$
$967$			53.9045i			1.73345i	−0.498786	+	0.866725i	$0.666221\pi$
$968$	−16.5664	+	19.5747i	−0.532464	+	0.629154i
$969$	18.4692	−	16.8924i	0.593316	−	0.542663i
$970$	−0.369110	+	0.0426165i	−0.0118514	+	0.00136833i
$971$	19.1783	+	33.2177i	0.615460	+	1.06601i	0.990304	+	0.138920i	$0.0443631\pi$
$971$	19.1783	+	33.2177i	0.615460	+	1.06601i	−0.374844	+	0.927088i	$0.622304\pi$
$972$	−30.1711	−	7.85526i	−0.967738	−	0.251957i
$973$		0			0
$974$	−10.2906	−	13.8633i	−0.329731	−	0.444208i
$975$	−4.87795	−	22.0999i	−0.156220	−	0.707764i
$976$	17.5950	−	8.71290i	0.563202	−	0.278893i
$977$	15.5907	+	9.00127i	0.498789	+	0.287976i	0.728214	−	0.685350i	$-0.240351\pi$
$977$	15.5907	+	9.00127i	0.498789	+	0.287976i	−0.229424	+	0.973327i	$0.573684\pi$
$978$	−19.8493	+	22.8605i	−0.634710	+	0.730999i
$979$			3.40899i			0.108952i
$980$		0			0
$981$	−4.52078	−	3.17799i	−0.144337	−	0.101465i
$982$	−51.7783	−	22.4214i	−1.65231	−	0.715497i
$983$	−6.87845	+	11.9138i	−0.219388	+	0.379992i	−0.954621	−	0.297823i	$-0.903740\pi$
$983$	−6.87845	+	11.9138i	−0.219388	+	0.379992i	0.735233	+	0.677815i	$0.237073\pi$
$984$	−13.1226	+	24.8947i	−0.418335	+	0.793613i
$985$	−1.56758	−	2.71514i	−0.0499474	−	0.0865114i
$986$	−41.8104	+	31.0354i	−1.33151	+	0.988368i
$987$		0			0
$988$	−13.0665	−	3.95195i	−0.415701	−	0.125728i
$989$	15.4648	−	8.92860i	0.491751	−	0.283913i
$990$	−2.58897	−	1.40687i	−0.0822829	−	0.0447134i
$991$	1.60779	+	0.928258i	0.0510731	+	0.0294871i	0.525319	−	0.850905i	$-0.323946\pi$
$991$	1.60779	+	0.928258i	0.0510731	+	0.0294871i	−0.474246	+	0.880392i	$0.657279\pi$
$992$	32.8330	−	21.2653i	1.04245	−	0.675172i
$993$	9.34619	−	29.5468i	0.296593	−	0.937640i
$994$		0			0
$995$	0.432298			0.0137048
$996$	41.5049	+	3.17976i	1.31513	+	0.100755i
$997$	30.1748	−	52.2642i	0.955644	−	1.65522i	0.222756	−	0.974874i	$-0.428495\pi$
$997$	30.1748	−	52.2642i	0.955644	−	1.65522i	0.732888	−	0.680350i	$-0.238172\pi$
$998$	11.9066	−	1.37471i	0.376897	−	0.0435156i
$999$	−14.6995	+	35.2106i	−0.465073	+	1.11401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.e.263.11		24
3.2	odd	2	inner	588.2.n.e.263.2		24
4.3	odd	2	inner	588.2.n.e.263.7		24
7.2	even	3	inner	588.2.n.e.275.6		24
7.3	odd	6		588.2.e.e.491.4		12
7.4	even	3		588.2.e.d.491.4		12
7.5	odd	6		84.2.n.a.23.6	yes	24
7.6	odd	2		84.2.n.a.11.11	yes	24
12.11	even	2	inner	588.2.n.e.263.6		24
21.2	odd	6	inner	588.2.n.e.275.7		24
21.5	even	6		84.2.n.a.23.7	yes	24
21.11	odd	6		588.2.e.d.491.9		12
21.17	even	6		588.2.e.e.491.9		12
21.20	even	2		84.2.n.a.11.2	✓	24
28.3	even	6		588.2.e.e.491.10		12
28.11	odd	6		588.2.e.d.491.10		12
28.19	even	6		84.2.n.a.23.2	yes	24
28.23	odd	6	inner	588.2.n.e.275.2		24
28.27	even	2		84.2.n.a.11.7	yes	24
84.11	even	6		588.2.e.d.491.3		12
84.23	even	6	inner	588.2.n.e.275.11		24
84.47	odd	6		84.2.n.a.23.11	yes	24
84.59	odd	6		588.2.e.e.491.3		12
84.83	odd	2		84.2.n.a.11.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.2	✓	24	21.20	even	2
84.2.n.a.11.6	yes	24	84.83	odd	2
84.2.n.a.11.7	yes	24	28.27	even	2
84.2.n.a.11.11	yes	24	7.6	odd	2
84.2.n.a.23.2	yes	24	28.19	even	6
84.2.n.a.23.6	yes	24	7.5	odd	6
84.2.n.a.23.7	yes	24	21.5	even	6
84.2.n.a.23.11	yes	24	84.47	odd	6
588.2.e.d.491.3		12	84.11	even	6
588.2.e.d.491.4		12	7.4	even	3
588.2.e.d.491.9		12	21.11	odd	6
588.2.e.d.491.10		12	28.11	odd	6
588.2.e.e.491.3		12	84.59	odd	6
588.2.e.e.491.4		12	7.3	odd	6
588.2.e.e.491.9		12	21.17	even	6
588.2.e.e.491.10		12	28.3	even	6
588.2.n.e.263.2		24	3.2	odd	2	inner
588.2.n.e.263.6		24	12.11	even	2	inner
588.2.n.e.263.7		24	4.3	odd	2	inner
588.2.n.e.263.11		24	1.1	even	1	trivial
588.2.n.e.275.2		24	28.23	odd	6	inner
588.2.n.e.275.6		24	7.2	even	3	inner
588.2.n.e.275.7		24	21.2	odd	6	inner
588.2.n.e.275.11		24	84.23	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.29776 + 0.561968i) q^{2} +(1.27809 - 1.16897i) q^{3} +(1.36838 + 1.45860i) q^{4} +(0.432549 - 0.249732i) q^{5} +(2.31558 - 0.798808i) q^{6} +(0.956154 + 2.66191i) q^{8} +(0.267006 - 2.98809i) q^{9} +O(q^{10})\)	\(q+(1.29776 + 0.561968i) q^{2} +(1.27809 - 1.16897i) q^{3} +(1.36838 + 1.45860i) q^{4} +(0.432549 - 0.249732i) q^{5} +(2.31558 - 0.798808i) q^{6} +(0.956154 + 2.66191i) q^{8} +(0.267006 - 2.98809i) q^{9} +(0.701688 - 0.0810151i) q^{10} +(0.695249 - 1.20421i) q^{11} +(3.45398 + 0.264615i) q^{12} -2.75054 q^{13} +(0.260904 - 0.824817i) q^{15} +(-0.255045 + 3.99186i) q^{16} +(5.04311 + 2.91164i) q^{17} +(2.02572 - 3.72779i) q^{18} +(2.14907 - 1.24076i) q^{19} +(0.956154 + 0.289187i) q^{20} +(1.57899 - 1.17207i) q^{22} +(-2.53203 - 4.38560i) q^{23} +(4.33375 + 2.28443i) q^{24} +(-2.37527 + 4.11408i) q^{25} +(-3.56955 - 1.54571i) q^{26} +(-3.15174 - 4.13116i) q^{27} +6.32275i q^{29} +(0.802113 - 0.923798i) q^{30} +(-5.98869 - 3.45757i) q^{31} +(-2.57429 + 5.03717i) q^{32} +(-0.519097 - 2.35181i) q^{33} +(4.90852 + 6.61269i) q^{34} +(4.72381 - 3.69941i) q^{36} +(-3.67154 - 6.35929i) q^{37} +(3.48625 - 0.402514i) q^{38} +(-3.51542 + 3.21530i) q^{39} +(1.07835 + 0.912624i) q^{40} +5.74438i q^{41} +3.52627i q^{43} +(2.70783 - 0.633726i) q^{44} +(-0.630730 - 1.35918i) q^{45} +(-0.821409 - 7.11439i) q^{46} +(-2.53203 - 4.38560i) q^{47} +(4.34041 + 5.40008i) q^{48} +(-5.39452 + 4.00429i) q^{50} +(9.84916 - 2.17393i) q^{51} +(-3.76379 - 4.01194i) q^{52} +(4.54223 + 2.62246i) q^{53} +(-1.76864 - 7.13245i) q^{54} -0.694505i q^{55} +(1.29627 - 4.09801i) q^{57} +(-3.55318 + 8.20544i) q^{58} +(-1.57587 + 2.72949i) q^{59} +(1.56010 - 0.748111i) q^{60} +(-2.45426 - 4.25091i) q^{61} +(-5.82886 - 7.85256i) q^{62} +(-6.17154 + 5.09039i) q^{64} +(-1.18974 + 0.686897i) q^{65} +(0.647974 - 3.34381i) q^{66} +(-9.30445 - 5.37193i) q^{67} +(2.65399 + 11.3402i) q^{68} +(-8.36279 - 2.64530i) q^{69} +4.54224 q^{71} +(8.20934 - 2.14633i) q^{72} +(-4.98752 + 8.63864i) q^{73} +(-1.19108 - 10.3162i) q^{74} +(1.77346 + 8.03477i) q^{75} +(4.75054 + 1.43679i) q^{76} +(-6.36908 + 2.19715i) q^{78} +(1.84576 - 1.06565i) q^{79} +(0.886577 + 1.79037i) q^{80} +(-8.85742 - 1.59568i) q^{81} +(-3.22815 + 7.45485i) q^{82} +12.0165 q^{83} +2.90852 q^{85} +(-1.98165 + 4.57626i) q^{86} +(7.39112 + 8.08102i) q^{87} +(3.87026 + 0.699285i) q^{88} +(-2.12318 + 1.22582i) q^{89} +(-0.0547257 - 2.11834i) q^{90} +(2.93206 - 9.69440i) q^{92} +(-11.6959 + 2.58154i) q^{93} +(-0.821409 - 7.11439i) q^{94} +(0.619718 - 1.07338i) q^{95} +(2.59815 + 9.44720i) q^{96} -0.526031 q^{97} +(-3.41265 - 2.39900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9}+O(q^{10}) \) 24 * q - 2 * q^4 - 2 * q^9	\( 24 q - 2 q^{4} - 2 q^{9} + 10 q^{10} + 12 q^{12} + 24 q^{13} - 10 q^{16} - 10 q^{18} + 28 q^{22} + 14 q^{24} - 12 q^{25} - 14 q^{30} - 10 q^{33} + 8 q^{34} + 44 q^{36} - 8 q^{37} - 34 q^{40} + 18 q^{45} + 24 q^{46} - 8 q^{48} - 16 q^{52} - 38 q^{54} - 4 q^{57} + 14 q^{58} + 14 q^{60} - 4 q^{61} - 68 q^{64} - 30 q^{66} - 36 q^{69} + 20 q^{72} + 24 q^{76} - 104 q^{78} + 26 q^{81} + 68 q^{82} - 40 q^{85} - 34 q^{88} + 40 q^{90} - 6 q^{93} + 24 q^{94} + 62 q^{96} - 72 q^{97}+O(q^{100}) \) 24 * q - 2 * q^4 - 2 * q^9 + 10 * q^10 + 12 * q^12 + 24 * q^13 - 10 * q^16 - 10 * q^18 + 28 * q^22 + 14 * q^24 - 12 * q^25 - 14 * q^30 - 10 * q^33 + 8 * q^34 + 44 * q^36 - 8 * q^37 - 34 * q^40 + 18 * q^45 + 24 * q^46 - 8 * q^48 - 16 * q^52 - 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 - 4 * q^61 - 68 * q^64 - 30 * q^66 - 36 * q^69 + 20 * q^72 + 24 * q^76 - 104 * q^78 + 26 * q^81 + 68 * q^82 - 40 * q^85 - 34 * q^88 + 40 * q^90 - 6 * q^93 + 24 * q^94 + 62 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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