LMFDB - Embedded newform 462.2.ba.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	462.19
Dual form			462.2.ba.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.993461 - 2.23135i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(2.46197 - 0.968858i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.993461 - 2.23135i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(2.46197 - 0.968858i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(1.22126 + 2.11528i) q^{10} +(-2.48048 + 2.20165i) q^{11} +(0.866025 + 0.500000i) q^{12} +(5.02484 - 3.65076i) q^{13} +(-2.34721 + 1.22090i) q^{14} +(0.754779 - 2.32297i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.161225 - 1.53396i) q^{17} +(-0.207912 - 0.978148i) q^{18} +(-7.08898 - 1.50681i) q^{19} +(-1.43568 - 1.97604i) q^{20} +(2.47790 + 0.927380i) q^{21} +(2.23675 - 2.44886i) q^{22} +(3.67860 - 6.37152i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(-0.646307 + 0.717797i) q^{25} +(-4.61571 + 4.15600i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.20674 - 1.45956i) q^{28} +(4.64640 + 1.50971i) q^{29} +(-0.507828 + 2.38914i) q^{30} +(2.43371 - 5.46619i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.31654 - 0.0236210i) q^{33} +1.54241i q^{34} +(-4.60774 - 4.53100i) q^{35} +(0.309017 + 0.951057i) q^{36} +(3.29811 + 3.66292i) q^{37} +(7.20765 + 0.757555i) q^{38} +(6.17702 + 0.649231i) q^{39} +(1.63436 + 1.81514i) q^{40} +(2.99369 + 9.21364i) q^{41} +(-2.56126 - 0.663290i) q^{42} +5.75946i q^{43} +(-1.96852 + 2.66925i) q^{44} +(2.11528 - 1.22126i) q^{45} +(-2.99244 + 6.72114i) q^{46} +(1.77817 - 8.36563i) q^{47} +(0.951057 + 0.309017i) q^{48} +(5.12263 - 4.77060i) q^{49} +(0.567737 - 0.781422i) q^{50} +(1.14623 - 1.03207i) q^{51} +(4.15600 - 4.61571i) q^{52} +(-3.79648 - 1.69030i) q^{53} +(0.500000 - 0.866025i) q^{54} +(7.37690 + 3.34756i) q^{55} +(-2.04208 + 1.68223i) q^{56} +(-4.25989 - 5.86323i) q^{57} +(-4.77876 - 1.01576i) q^{58} +(-0.230219 - 1.08309i) q^{59} +(0.255313 - 2.42914i) q^{60} +(-0.819338 + 0.364793i) q^{61} +(-1.84900 + 5.69064i) q^{62} +(1.22090 + 2.34721i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-13.1381 - 7.58529i) q^{65} +(3.30084 - 0.323181i) q^{66} +(5.92505 + 10.2625i) q^{67} +(-0.161225 - 1.53396i) q^{68} +(6.99711 - 2.27350i) q^{69} +(5.05611 + 4.02454i) q^{70} +(-7.75211 - 5.63224i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(0.452673 - 0.0962187i) q^{73} +(-3.66292 - 3.29811i) q^{74} +(-0.960600 + 0.100963i) q^{75} -7.24735 q^{76} +(-3.97378 + 7.82362i) q^{77} -6.21105 q^{78} +(-12.8790 + 1.35364i) q^{79} +(-1.81514 - 1.63436i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-3.94038 - 8.85024i) q^{82} +(-3.78062 - 2.74678i) q^{83} +(2.61656 + 0.391931i) q^{84} +(-3.58296 + 1.16418i) q^{85} +(-0.602028 - 5.72791i) q^{86} +(2.44276 + 4.23098i) q^{87} +(1.67873 - 2.86040i) q^{88} +(7.37544 + 4.25821i) q^{89} +(-1.97604 + 1.43568i) q^{90} +(8.83396 - 13.8564i) q^{91} +(2.27350 - 6.99711i) q^{92} +(5.46619 - 2.43371i) q^{93} +(-0.893982 + 8.50567i) q^{94} +(3.68041 + 17.3150i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-1.48280 - 2.04089i) q^{97} +(-4.59590 + 5.27993i) q^{98} +(-2.44886 - 2.23675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 + 10 * q^19 + 20 * q^20 - 4 * q^21 - 2 * q^22 + 4 * q^23 - 8 * q^24 - 12 * q^26 - 10 * q^28 - 20 * q^29 + 18 * q^30 - 16 * q^31 - 14 * q^33 + 42 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 + 18 * q^39 + 18 * q^40 - 28 * q^41 - 6 * q^42 + 6 * q^44 - 12 * q^45 - 42 * q^46 + 24 * q^47 + 116 * q^49 + 26 * q^51 + 32 * q^54 - 14 * q^55 - 4 * q^56 + 20 * q^58 + 30 * q^59 + 2 * q^60 - 32 * q^61 - 8 * q^62 + 4 * q^63 + 16 * q^64 + 12 * q^65 + 4 * q^66 + 16 * q^67 - 30 * q^68 - 20 * q^70 - 24 * q^71 - 64 * q^73 + 4 * q^74 + 12 * q^75 - 48 * q^77 - 60 * q^79 - 18 * q^80 + 8 * q^81 - 68 * q^82 + 8 * q^83 + 2 * q^84 - 80 * q^85 - 18 * q^86 + 10 * q^87 - 8 * q^88 - 24 * q^89 + 4 * q^90 - 172 * q^91 + 8 * q^92 - 104 * q^93 - 6 * q^94 - 118 * q^95 + 8 * q^96 + 120 * q^97 + 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.994522	+	0.104528i	−0.703233	+	0.0739128i
$2$	−0.994522	+	0.104528i	−0.703233	+	0.0739128i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$4$	0.978148	−	0.207912i	0.489074	−	0.103956i
$5$	−0.993461	−	2.23135i	−0.444289	−	0.997890i	−0.987402	−	0.158231i	$-0.949421\pi$
$5$	−0.993461	−	2.23135i	−0.444289	−	0.997890i	0.543113	−	0.839660i	$-0.317246\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	2.46197	−	0.968858i	0.930539	−	0.366194i
$7$	2.46197	−	0.968858i	0.930539	−	0.366194i
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	1.22126	+	2.11528i	0.386196	+	0.668911i
$11$	−2.48048	+	2.20165i	−0.747892	+	0.663821i
$11$	−2.48048	+	2.20165i	−0.747892	+	0.663821i
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	5.02484	−	3.65076i	1.39364	−	1.01254i	0.398185	−	0.917305i	$-0.369640\pi$
$13$	5.02484	−	3.65076i	1.39364	−	1.01254i	0.995455	−	0.0952338i	$-0.0303599\pi$
$14$	−2.34721	+	1.22090i	−0.627319	+	0.326298i
$15$	0.754779	−	2.32297i	0.194883	−	0.599789i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.161225	−	1.53396i	0.0391029	−	0.372039i	−0.957419	−	0.288703i	$-0.906776\pi$
$17$	0.161225	−	1.53396i	0.0391029	−	0.372039i	0.996522	−	0.0833358i	$-0.0265574\pi$
$18$	−0.207912	−	0.978148i	−0.0490053	−	0.230552i
$19$	−7.08898	−	1.50681i	−1.62632	−	0.345686i	−0.697608	−	0.716479i	$-0.745752\pi$
$19$	−7.08898	−	1.50681i	−1.62632	−	0.345686i	−0.928715	+	0.370793i	$0.879086\pi$
$20$	−1.43568	−	1.97604i	−0.321027	−	0.441856i
$21$	2.47790	+	0.927380i	0.540721	+	0.202371i
$22$	2.23675	−	2.44886i	0.476877	−	0.522100i
$23$	3.67860	−	6.37152i	0.767041	−	1.32855i	−0.172120	−	0.985076i	$-0.555062\pi$
$23$	3.67860	−	6.37152i	0.767041	−	1.32855i	0.939161	−	0.343478i	$-0.111605\pi$
$24$	−0.913545	−	0.406737i	−0.186477	−	0.0830248i
$25$	−0.646307	+	0.717797i	−0.129261	+	0.143559i
$26$	−4.61571	+	4.15600i	−0.905214	+	0.815059i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	2.20674	−	1.45956i	0.417034	−	0.275831i
$29$	4.64640	+	1.50971i	0.862816	+	0.280346i	0.706804	−	0.707409i	$-0.250136\pi$
$29$	4.64640	+	1.50971i	0.862816	+	0.280346i	0.156012	+	0.987755i	$0.450136\pi$
$30$	−0.507828	+	2.38914i	−0.0927163	+	0.436196i
$31$	2.43371	−	5.46619i	0.437106	−	0.981757i	−0.551903	−	0.833908i	$-0.686098\pi$
$31$	2.43371	−	5.46619i	0.437106	−	0.981757i	0.989010	−	0.147849i	$-0.0472350\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−3.31654	−	0.0236210i	−0.577336	−	0.00411188i
$34$			1.54241i			0.264520i
$35$	−4.60774	−	4.53100i	−0.778850	−	0.765879i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	3.29811	+	3.66292i	0.542205	+	0.602180i	0.950521	−	0.310661i	$-0.100550\pi$
$37$	3.29811	+	3.66292i	0.542205	+	0.602180i	−0.408315	+	0.912841i	$0.633884\pi$
$38$	7.20765	+	0.757555i	1.16924	+	0.122892i
$39$	6.17702	+	0.649231i	0.989115	+	0.103960i
$40$	1.63436	+	1.81514i	0.258416	+	0.286999i
$41$	2.99369	+	9.21364i	0.467536	+	1.43893i	0.855764	+	0.517366i	$0.173087\pi$
$41$	2.99369	+	9.21364i	0.467536	+	1.43893i	−0.388228	+	0.921563i	$0.626913\pi$
$42$	−2.56126	−	0.663290i	−0.395211	−	0.102348i
$43$			5.75946i			0.878310i	0.898411	+	0.439155i	$0.144722\pi$
$43$			5.75946i			0.878310i	−0.898411	+	0.439155i	$0.855278\pi$
$44$	−1.96852	+	2.66925i	−0.296766	+	0.402405i
$45$	2.11528	−	1.22126i	0.315328	−	0.182054i
$46$	−2.99244	+	6.72114i	−0.441212	+	0.990977i
$47$	1.77817	−	8.36563i	0.259373	−	1.22025i	−0.634852	−	0.772634i	$-0.718939\pi$
$47$	1.77817	−	8.36563i	0.259373	−	1.22025i	0.894225	−	0.447619i	$-0.147728\pi$
$48$	0.951057	+	0.309017i	0.137273	+	0.0446028i
$49$	5.12263	−	4.77060i	0.731804	−	0.681515i
$50$	0.567737	−	0.781422i	0.0802901	−	0.110510i
$51$	1.14623	−	1.03207i	0.160504	−	0.144519i
$52$	4.15600	−	4.61571i	0.576334	−	0.640083i
$53$	−3.79648	−	1.69030i	−0.521487	−	0.232181i	0.129074	−	0.991635i	$-0.458800\pi$
$53$	−3.79648	−	1.69030i	−0.521487	−	0.232181i	−0.650561	+	0.759454i	$0.725466\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	7.37690	+	3.34756i	0.994701	+	0.451385i
$56$	−2.04208	+	1.68223i	−0.272885	+	0.224797i
$57$	−4.25989	−	5.86323i	−0.564236	−	0.776604i
$58$	−4.77876	−	1.01576i	−0.627482	−	0.133375i
$59$	−0.230219	−	1.08309i	−0.0299719	−	0.141007i	0.960617	−	0.277874i	$-0.0896299\pi$
$59$	−0.230219	−	1.08309i	−0.0299719	−	0.141007i	−0.990589	+	0.136868i	$0.956297\pi$
$60$	0.255313	−	2.42914i	0.0329607	−	0.313600i
$61$	−0.819338	+	0.364793i	−0.104906	+	0.0467069i	−0.458518	−	0.888685i	$-0.651620\pi$
$61$	−0.819338	+	0.364793i	−0.104906	+	0.0467069i	0.353613	+	0.935392i	$0.384953\pi$
$62$	−1.84900	+	5.69064i	−0.234823	+	0.722712i
$63$	1.22090	+	2.34721i	0.153819	+	0.295721i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−13.1381	−	7.58529i	−1.62958	−	0.940840i
$66$	3.30084	−	0.323181i	0.406305	−	0.0397809i
$67$	5.92505	+	10.2625i	0.723860	+	1.25376i	0.959441	+	0.281908i	$0.0909673\pi$
$67$	5.92505	+	10.2625i	0.723860	+	1.25376i	−0.235581	+	0.971855i	$0.575699\pi$
$68$	−0.161225	−	1.53396i	−0.0195514	−	0.186019i
$69$	6.99711	−	2.27350i	0.842353	−	0.273697i
$70$	5.05611	+	4.02454i	0.604321	+	0.481025i
$71$	−7.75211	−	5.63224i	−0.920007	−	0.668424i	0.0235190	−	0.999723i	$-0.492513\pi$
$71$	−7.75211	−	5.63224i	−0.920007	−	0.668424i	−0.943526	+	0.331299i	$0.892513\pi$
$72$	−0.406737	−	0.913545i	−0.0479344	−	0.107662i
$73$	0.452673	−	0.0962187i	0.0529814	−	0.0112615i	−0.181345	−	0.983420i	$-0.558045\pi$
$73$	0.452673	−	0.0962187i	0.0529814	−	0.0112615i	0.234326	+	0.972158i	$0.424712\pi$
$74$	−3.66292	−	3.29811i	−0.425806	−	0.383397i
$75$	−0.960600	+	0.100963i	−0.110921	+	0.0116582i
$76$	−7.24735			−0.831328
$77$	−3.97378	+	7.82362i	−0.452855	+	0.891584i
$78$	−6.21105			−0.703262
$79$	−12.8790	+	1.35364i	−1.44900	+	0.152296i	−0.796108	−	0.605154i	$-0.793111\pi$
$79$	−12.8790	+	1.35364i	−1.44900	+	0.152296i	−0.652893	+	0.757450i	$0.726445\pi$
$80$	−1.81514	−	1.63436i	−0.202939	−	0.182727i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−3.94038	−	8.85024i	−0.435142	−	0.977346i
$83$	−3.78062	−	2.74678i	−0.414977	−	0.301498i	0.360637	−	0.932706i	$-0.382559\pi$
$83$	−3.78062	−	2.74678i	−0.414977	−	0.301498i	−0.775614	+	0.631208i	$0.782559\pi$
$84$	2.61656	+	0.391931i	0.285490	+	0.0427632i
$85$	−3.58296	+	1.16418i	−0.388627	+	0.126273i
$86$	−0.602028	−	5.72791i	−0.0649183	−	0.617657i
$87$	2.44276	+	4.23098i	0.261891	+	0.453609i
$88$	1.67873	−	2.86040i	0.178953	−	0.304919i
$89$	7.37544	+	4.25821i	0.781795	+	0.451369i	0.837066	−	0.547102i	$-0.184269\pi$
$89$	7.37544	+	4.25821i	0.781795	+	0.451369i	−0.0552713	+	0.998471i	$0.517602\pi$
$90$	−1.97604	+	1.43568i	−0.208293	+	0.151334i
$91$	8.83396	−	13.8564i	0.926051	−	1.45255i
$92$	2.27350	−	6.99711i	0.237029	−	0.729499i
$93$	5.46619	−	2.43371i	0.566818	−	0.252364i
$94$	−0.893982	+	8.50567i	−0.0922072	+	0.877293i
$95$	3.68041	+	17.3150i	0.377602	+	1.77648i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	−1.48280	−	2.04089i	−0.150555	−	0.207221i	0.727077	−	0.686556i	$-0.240878\pi$
$97$	−1.48280	−	2.04089i	−0.150555	−	0.207221i	−0.877632	+	0.479334i	$0.840878\pi$
$98$	−4.59590	+	5.27993i	−0.464256	+	0.533354i
$99$	−2.44886	−	2.23675i	−0.246120	−	0.224802i
$100$	−0.482946	+	0.836486i	−0.0482946	+	0.0836486i
$101$	13.6719	+	6.08713i	1.36041	+	0.605692i	0.951716	−	0.306980i	$-0.0993185\pi$
$101$	13.6719	+	6.08713i	1.36041	+	0.605692i	0.408692	+	0.912673i	$0.365985\pi$
$102$	−1.03207	+	1.14623i	−0.102190	+	0.113494i
$103$	−9.13629	+	8.22635i	−0.900225	+	0.810566i	−0.982542	−	0.186040i	$-0.940435\pi$
$103$	−9.13629	+	8.22635i	−0.900225	+	0.810566i	0.0823170	+	0.996606i	$0.473768\pi$
$104$	−3.65076	+	5.02484i	−0.357987	+	0.492726i
$105$	−0.392382	−	6.45037i	−0.0382926	−	0.629492i
$106$	3.95237	+	1.28420i	0.383888	+	0.124733i
$107$	−2.97822	+	14.0114i	−0.287915	+	1.35453i	0.561792	+	0.827278i	$0.310112\pi$
$107$	−2.97822	+	14.0114i	−0.287915	+	1.35453i	−0.849707	+	0.527255i	$0.823221\pi$
$108$	−0.406737	+	0.913545i	−0.0391383	+	0.0879060i
$109$	−4.18095	+	2.41387i	−0.400462	+	0.231207i	−0.686684	−	0.726956i	$-0.740934\pi$
$109$	−4.18095	+	2.41387i	−0.400462	+	0.231207i	0.286221	+	0.958164i	$0.407601\pi$
$110$	−7.68640	−	2.55813i	−0.732870	−	0.243908i
$111$			4.92894i			0.467835i
$112$	1.85506	−	1.88647i	0.175286	−	0.178255i
$113$	−1.66328	−	5.11904i	−0.156468	−	0.481559i	0.841839	−	0.539729i	$-0.181473\pi$
$113$	−1.66328	−	5.11904i	−0.156468	−	0.481559i	−0.998307	+	0.0581704i	$0.981473\pi$
$114$	4.84943	+	5.38583i	0.454190	+	0.504429i
$115$	−17.8716	−	1.87839i	−1.66654	−	0.175160i
$116$	4.85875	+	0.510676i	0.451124	+	0.0474150i
$117$	4.15600	+	4.61571i	0.384222	+	0.426722i
$118$	0.342172	+	1.05310i	0.0314995	+	0.0969453i
$119$	−1.08925	−	3.93276i	−0.0998516	−	0.360516i
$120$			2.44252i			0.222970i
$121$	1.30552	−	10.9223i	0.118683	−	0.992932i
$122$	0.776719	−	0.448439i	0.0703208	−	0.0405997i
$123$	−3.94038	+	8.85024i	−0.355292	+	0.798000i
$124$	1.24404	−	5.85274i	0.111718	−	0.525591i
$125$	−9.37112	−	3.04486i	−0.838179	−	0.272341i
$126$	−1.45956	−	2.20674i	−0.130028	−	0.196592i
$127$	−12.3890	+	17.0520i	−1.09935	+	1.51312i	−0.263098	+	0.964769i	$0.584744\pi$
$127$	−12.3890	+	17.0520i	−1.09935	+	1.51312i	−0.836248	+	0.548351i	$0.815256\pi$
$128$	−0.743145	+	0.669131i	−0.0656853	+	0.0591433i
$129$	−3.85383	+	4.28011i	−0.339311	+	0.376843i
$130$	13.8590	+	6.17043i	1.21552	+	0.541183i
$131$	−3.94896	+	6.83981i	−0.345023	+	0.597597i	−0.985358	−	0.170499i	$-0.945462\pi$
$131$	−3.94896	+	6.83981i	−0.345023	+	0.597597i	0.640335	+	0.768096i	$0.278795\pi$
$132$	−3.24898	+	0.666443i	−0.282787	+	0.0580064i
$133$	−18.9128	+	3.15849i	−1.63995	+	0.273876i
$134$	−6.96532	−	9.58693i	−0.601712	−	0.828185i
$135$	2.38914	+	0.507828i	0.205625	+	0.0437069i
$136$	0.320684	+	1.50870i	0.0274984	+	0.129370i
$137$	−1.00411	+	9.55344i	−0.0857867	+	0.816206i	0.864039	+	0.503425i	$0.167927\pi$
$137$	−1.00411	+	9.55344i	−0.0857867	+	0.816206i	−0.949825	+	0.312780i	$0.898740\pi$
$138$	−6.72114	+	2.99244i	−0.572141	+	0.254734i
$139$	−3.25192	+	10.0084i	−0.275825	+	0.848901i	0.713175	+	0.700986i	$0.247256\pi$
$139$	−3.25192	+	10.0084i	−0.275825	+	0.848901i	−0.989000	+	0.147915i	$0.952744\pi$
$140$	−5.44910	−	3.47399i	−0.460533	−	0.293606i
$141$	6.91914	−	5.02705i	0.582696	−	0.423354i
$142$	8.29838	+	4.79107i	0.696384	+	0.402058i
$143$	−4.42632	+	20.1185i	−0.370147	+	1.68240i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−1.24733	−	11.8676i	−0.103585	−	0.985550i
$146$	−0.440136	+	0.143009i	−0.0364259	+	0.0118355i
$147$	6.99901	−	0.117542i	0.577269	−	0.00969469i
$148$	3.98760	+	2.89716i	0.327779	+	0.238145i
$149$	−2.33173	−	5.23715i	−0.191023	−	0.429044i	0.792490	−	0.609886i	$-0.208785\pi$
$149$	−2.33173	−	5.23715i	−0.191023	−	0.429044i	−0.983512	+	0.180841i	$0.942118\pi$
$150$	0.944784	−	0.200820i	0.0771413	−	0.0163969i
$151$	−1.86313	−	1.67757i	−0.151619	−	0.136519i	0.589830	−	0.807527i	$-0.299195\pi$
$151$	−1.86313	−	1.67757i	−0.151619	−	0.136519i	−0.741450	+	0.671009i	$0.765861\pi$
$152$	7.20765	−	0.757555i	0.584618	−	0.0614458i
$153$	1.54241			0.124696
$154$	3.13423	−	8.19614i	0.252563	−	0.660463i
$155$	−14.6148			−1.17389
$156$	6.17702	−	0.649231i	0.494557	−	0.0519801i
$157$	7.49951	+	6.75259i	0.598526	+	0.538915i	0.911740	−	0.410767i	$-0.134739\pi$
$157$	7.49951	+	6.75259i	0.598526	+	0.538915i	−0.313214	+	0.949683i	$0.601406\pi$
$158$	12.6670	−	2.69244i	1.00773	−	0.214199i
$159$	−1.69030	−	3.79648i	−0.134050	−	0.301081i
$160$	1.97604	+	1.43568i	0.156220	+	0.113500i
$161$	2.88352	−	19.2506i	0.227253	−	1.51716i
$162$	0.951057	−	0.309017i	0.0747221	−	0.0242787i
$163$	0.114561	+	1.08997i	0.00897308	+	0.0853732i	0.998092	−	0.0617456i	$-0.0196667\pi$
$163$	0.114561	+	1.08997i	0.00897308	+	0.0853732i	−0.989119	+	0.147119i	$0.953000\pi$
$164$	4.84390	+	8.38988i	0.378245	+	0.655139i
$165$	3.24215	+	7.42383i	0.252401	+	0.577945i
$166$	4.04703	+	2.33655i	0.314110	+	0.181352i
$167$	3.24161	−	2.35517i	0.250844	−	0.182248i	−0.455257	−	0.890360i	$-0.650453\pi$
$167$	3.24161	−	2.35517i	0.250844	−	0.182248i	0.706101	+	0.708112i	$0.250453\pi$
$168$	−2.64319	−	0.116279i	−0.203927	−	0.00897115i
$169$	7.90375	−	24.3252i	0.607981	−	1.87117i
$170$	3.44165	−	1.53232i	0.263962	−	0.117524i
$171$	0.757555	−	7.20765i	0.0579317	−	0.551183i
$172$	1.19746	+	5.63360i	0.0913054	+	0.429558i
$173$	16.2179	+	3.44722i	1.23302	+	0.262087i	0.777927	−	0.628355i	$-0.216271\pi$
$173$	16.2179	+	3.44722i	1.23302	+	0.262087i	0.455096	+	0.890442i	$0.349605\pi$
$174$	−2.87164	−	3.95247i	−0.217698	−	0.299636i
$175$	−0.895749	+	2.39338i	−0.0677122	+	0.180922i
$176$	−1.37054	+	3.02020i	−0.103308	+	0.227656i
$177$	0.553645	−	0.958942i	0.0416145	−	0.0720785i
$178$	−7.78014	−	3.46394i	−0.583146	−	0.259633i
$179$	5.21508	−	5.79193i	0.389793	−	0.432909i	−0.516026	−	0.856573i	$-0.672589\pi$
$179$	5.21508	−	5.79193i	0.389793	−	0.432909i	0.905820	+	0.423663i	$0.139256\pi$
$180$	1.81514	−	1.63436i	0.135293	−	0.121818i
$181$	−5.63411	+	7.75469i	−0.418780	+	0.576401i	−0.965332	−	0.261024i	$-0.915940\pi$
$181$	−5.63411	+	7.75469i	−0.418780	+	0.576401i	0.546552	+	0.837425i	$0.315940\pi$
$182$	−7.33717	+	14.7039i	−0.543868	+	1.08993i
$183$	−0.852981	−	0.277150i	−0.0630542	−	0.0204875i
$184$	−1.52965	+	7.19643i	−0.112767	+	0.530528i
$185$	4.89671	−	10.9982i	0.360014	−	0.808604i
$186$	−5.18186	+	2.99175i	−0.379952	+	0.219365i
$187$	2.97731	+	4.15990i	0.217723	+	0.304202i
$188$		−	8.55252i		−	0.623757i
$189$	−0.663290	+	2.56126i	−0.0482472	+	0.186304i
$190$	−5.47015	−	16.8354i	−0.396847	−	1.22137i
$191$	−2.69657	−	2.99484i	−0.195117	−	0.216699i	0.637645	−	0.770330i	$-0.279908\pi$
$191$	−2.69657	−	2.99484i	−0.195117	−	0.216699i	−0.832762	+	0.553631i	$0.813242\pi$
$192$	0.994522	+	0.104528i	0.0717734	+	0.00754369i
$193$	−13.9164	−	1.46267i	−1.00173	−	0.105286i	−0.410558	−	0.911835i	$-0.634666\pi$
$193$	−13.9164	−	1.46267i	−1.00173	−	0.105286i	−0.591167	+	0.806549i	$0.701333\pi$
$194$	1.68800	+	1.87472i	0.121192	+	0.134597i
$195$	−4.68797	−	14.4281i	−0.335712	−	1.03322i
$196$	4.01882	−	5.73141i	0.287059	−	0.409386i
$197$			13.0895i			0.932586i	0.884630	+	0.466293i	$0.154411\pi$
$197$			13.0895i			0.932586i	−0.884630	+	0.466293i	$0.845589\pi$
$198$	2.66925	+	1.96852i	0.189696	+	0.139897i
$199$	21.0523	−	12.1545i	1.49236	−	0.861612i	0.492394	−	0.870372i	$-0.336122\pi$
$199$	21.0523	−	12.1545i	1.49236	−	0.861612i	0.999962	+	0.00876064i	$0.00278863\pi$
$200$	0.392863	−	0.882385i	0.0277796	−	0.0623941i
$201$	−2.46377	+	11.5911i	−0.173781	+	0.817577i
$202$	−14.2333	−	4.62468i	−1.00145	−	0.325392i
$203$	12.9020	−	0.784842i	0.905544	−	0.0550851i
$204$	0.906603	−	1.24783i	0.0634749	−	0.0873657i
$205$	17.5847	−	15.8334i	1.22817	−	1.10585i
$206$	8.22635	−	9.13629i	0.573157	−	0.636555i
$207$	6.72114	+	2.99244i	0.467151	+	0.207989i
$208$	3.10552	−	5.37892i	0.215329	−	0.372961i
$209$	20.9015	−	11.8698i	1.44579	−	0.821052i
$210$	1.06448	+	6.37402i	0.0734561	+	0.439849i
$211$	5.27200	+	7.25629i	0.362940	+	0.499544i	0.950965	−	0.309299i	$-0.100094\pi$
$211$	5.27200	+	7.25629i	0.362940	+	0.499544i	−0.588025	+	0.808843i	$0.700094\pi$
$212$	−4.06496	−	0.864033i	−0.279182	−	0.0593420i
$213$	−1.99224	−	9.37275i	−0.136506	−	0.642210i
$214$	1.49731	−	14.2460i	0.102354	−	0.973833i
$215$	12.8514	−	5.72180i	0.876457	−	0.390224i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	0.695757	−	15.8155i	0.0472311	−	1.07363i
$218$	3.90573	−	2.83768i	0.264529	−	0.192192i
$219$	0.400785	+	0.231393i	0.0270825	+	0.0156361i
$220$	7.91169	+	1.74067i	0.533406	+	0.117356i
$221$	−4.78997	−	8.29648i	−0.322209	−	0.558082i
$222$	−0.515215	−	4.90194i	−0.0345790	−	0.328997i
$223$	−7.30645	+	2.37401i	−0.489276	+	0.158976i	−0.543257	−	0.839566i	$-0.682809\pi$
$223$	−7.30645	+	2.37401i	−0.489276	+	0.158976i	0.0539807	+	0.998542i	$0.482809\pi$
$224$	−1.64770	+	2.07004i	−0.110092	+	0.138311i
$225$	−0.781422	−	0.567737i	−0.0520948	−	0.0378491i
$226$	2.18925	+	4.91714i	0.145627	+	0.327083i
$227$	23.5633	−	5.00854i	1.56395	−	0.332428i	0.657075	−	0.753825i	$-0.271793\pi$
$227$	23.5633	−	5.00854i	1.56395	−	0.332428i	0.906876	+	0.421397i	$0.138460\pi$
$228$	−5.38583	−	4.84943i	−0.356685	−	0.321161i
$229$	−7.48493	+	0.786698i	−0.494618	+	0.0519865i	−0.348554	−	0.937289i	$-0.613327\pi$
$229$	−7.48493	+	0.786698i	−0.494618	+	0.0519865i	−0.146064	+	0.989275i	$0.546661\pi$
$230$	17.9701			1.18491
$231$	−8.18812	+	3.15510i	−0.538739	+	0.207590i
$232$	−4.88552			−0.320750
$233$	−11.2304	+	1.18036i	−0.735725	+	0.0773278i	−0.464977	−	0.885323i	$-0.653938\pi$
$233$	−11.2304	+	1.18036i	−0.735725	+	0.0773278i	−0.270748	+	0.962650i	$0.587271\pi$
$234$	−4.61571	−	4.15600i	−0.301738	−	0.271686i
$235$	−20.4332	+	4.34321i	−1.33291	+	0.283320i
$236$	−0.450376	−	1.01156i	−0.0293170	−	0.0658470i
$237$	−10.4767	−	7.61179i	−0.680536	−	0.494439i
$238$	1.49437	+	3.79736i	0.0968657	+	0.246146i
$239$	9.36819	−	3.04391i	0.605978	−	0.196894i	0.0100732	−	0.999949i	$-0.496794\pi$
$239$	9.36819	−	3.04391i	0.605978	−	0.196894i	0.595905	+	0.803055i	$0.296794\pi$
$240$	−0.255313	−	2.42914i	−0.0164804	−	0.156800i
$241$	−0.886162	−	1.53488i	−0.0570827	−	0.0988702i	0.836072	−	0.548620i	$-0.184847\pi$
$241$	−0.886162	−	1.53488i	−0.0570827	−	0.0988702i	−0.893155	+	0.449750i	$0.851513\pi$
$242$	−0.156680	+	10.9989i	−0.0100718	+	0.707035i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−0.725589	+	0.527171i	−0.0464511	+	0.0337487i
$245$	−15.7340	−	6.69097i	−1.00521	−	0.427471i
$246$	2.99369	−	9.21364i	0.190871	−	0.587440i
$247$	−41.1220	+	18.3087i	−2.61653	+	1.16495i
$248$	−0.625445	+	5.95071i	−0.0397158	+	0.377871i
$249$	−0.971593	−	4.57099i	−0.0615722	−	0.289674i
$250$	9.63806	+	2.04863i	0.609564	+	0.129567i
$251$	14.4584	+	19.9002i	0.912603	+	1.25609i	0.966270	+	0.257532i	$0.0829092\pi$
$251$	14.4584	+	19.9002i	0.912603	+	1.25609i	−0.0536665	+	0.998559i	$0.517091\pi$
$252$	1.68223	+	2.04208i	0.105971	+	0.128639i
$253$	4.90315	+	23.9034i	0.308259	+	1.50279i
$254$	10.5387	−	18.2536i	0.661258	−	1.14533i
$255$	−3.44165	−	1.53232i	−0.215524	−	0.0959576i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	8.15678	−	7.34440i	0.508806	−	0.458131i	−0.374298	−	0.927309i	$-0.622116\pi$
$257$	8.15678	−	7.34440i	0.508806	−	0.458131i	0.883104	+	0.469178i	$0.155450\pi$
$258$	3.38533	−	4.65950i	0.210761	−	0.290088i
$259$	11.6687	+	5.82261i	0.725058	+	0.361800i
$260$	−14.4281	−	4.68797i	−0.894792	−	0.290735i
$261$	−1.01576	+	4.77876i	−0.0628737	+	0.295798i
$262$	3.21238	−	7.21512i	0.198461	−	0.445751i
$263$	−0.478450	+	0.276234i	−0.0295025	+	0.0170333i	−0.514679	−	0.857383i	$-0.672089\pi$
$263$	−0.478450	+	0.276234i	−0.0295025	+	0.0170333i	0.485176	+	0.874416i	$0.338755\pi$
$264$	3.16152	−	1.00240i	0.194578	−	0.0616936i
$265$			10.1505i			0.623543i
$266$	18.4790	−	5.11811i	1.13302	−	0.313811i
$267$	2.63172	+	8.09960i	0.161059	+	0.495687i
$268$	7.92927	+	8.80634i	0.484357	+	0.537933i
$269$	−6.74649	−	0.709085i	−0.411341	−	0.0432337i	−0.103402	−	0.994640i	$-0.532973\pi$
$269$	−6.74649	−	0.709085i	−0.411341	−	0.0432337i	−0.307939	+	0.951406i	$0.599639\pi$
$270$	−2.42914	−	0.255313i	−0.147833	−	0.0155378i
$271$	5.41668	+	6.01584i	0.329040	+	0.365436i	0.884852	−	0.465872i	$-0.154259\pi$
$271$	5.41668	+	6.01584i	0.329040	+	0.365436i	−0.555812	+	0.831308i	$0.687593\pi$
$272$	−0.476629	−	1.46691i	−0.0288999	−	0.0889448i
$273$	15.8367	−	4.38626i	0.958479	−	0.265469i
$274$		−	9.60607i		−	0.580324i
$275$	0.0228153	−	3.20342i	0.00137581	−	0.193173i
$276$	6.37152	−	3.67860i	0.383521	−	0.221426i
$277$	4.90652	−	11.0202i	0.294804	−	0.662141i	−0.704043	−	0.710158i	$-0.748624\pi$
$277$	4.90652	−	11.0202i	0.294804	−	0.662141i	0.998847	+	0.0480172i	$0.0152902\pi$
$278$	2.18795	−	10.2935i	0.131224	−	0.617362i
$279$	5.69064	+	1.84900i	0.340690	+	0.110697i
$280$	5.78238	+	2.88537i	0.345563	+	0.172434i
$281$	−17.3184	+	23.8367i	−1.03313	+	1.42198i	−0.130555	+	0.991441i	$0.541676\pi$
$281$	−17.3184	+	23.8367i	−1.03313	+	1.42198i	−0.902573	+	0.430537i	$0.858324\pi$
$282$	−6.35576	+	5.72275i	−0.378480	+	0.340785i
$283$	16.1136	−	17.8960i	0.957855	−	1.06381i	−0.0400562	−	0.999197i	$-0.512754\pi$
$283$	16.1136	−	17.8960i	0.957855	−	1.06381i	0.997911	−	0.0646078i	$-0.0205796\pi$
$284$	−8.75372	−	3.89741i	−0.519438	−	0.231269i
$285$	−8.85089	+	15.3302i	−0.524282	+	0.908082i
$286$	2.29911	−	20.4710i	0.135949	−	1.21048i
$287$	16.2971	+	19.7833i	0.961988	+	1.16777i
$288$	−0.587785	−	0.809017i	−0.0346356	−	0.0476718i
$289$	14.3015	+	3.03987i	0.841264	+	0.178816i
$290$	2.48100	+	11.6722i	0.145689	+	0.685415i
$291$	0.263692	−	2.50886i	0.0154579	−	0.147072i
$292$	0.422776	−	0.188232i	0.0247411	−	0.0110155i
$293$	−1.14843	+	3.53450i	−0.0670920	+	0.206488i	−0.978982	−	0.203947i	$-0.934623\pi$
$293$	−1.14843	+	3.53450i	−0.0670920	+	0.206488i	0.911890	+	0.410435i	$0.134623\pi$
$294$	−6.94839	+	0.848494i	−0.405238	+	0.0494852i
$295$	−2.18805	+	1.58971i	−0.127393	+	0.0925565i
$296$	−4.26859	−	2.46447i	−0.248107	−	0.143244i
$297$	−0.323181	−	3.30084i	−0.0187529	−	0.191534i
$298$	2.86639	+	4.96473i	0.166045	+	0.287599i
$299$	−4.77652	−	45.4456i	−0.276233	−	2.62819i
$300$	−0.918617	+	0.298477i	−0.0530364	+	0.0172326i
$301$	5.58010	+	14.1796i	0.321632	+	0.817301i
$302$	2.02828	+	1.47363i	0.116714	+	0.0847979i
$303$	6.08713	+	13.6719i	0.349697	+	0.785432i
$304$	−7.08898	+	1.50681i	−0.406581	+	0.0864214i
$305$	1.62796	+	1.46582i	0.0932168	+	0.0839328i
$306$	−1.53396	+	0.161225i	−0.0876904	+	0.00921663i
$307$	−25.4847			−1.45449			−0.727244	−	0.686379i	$-0.759199\pi$
$307$	−25.4847			−1.45449			−0.727244	+	0.686379i	$0.759199\pi$
$308$	−2.26033	+	8.47885i	−0.128794	+	0.483127i
$309$	−12.2941			−0.699386
$310$	14.5347	−	1.52766i	0.825517	−	0.0867653i
$311$	12.6123	+	11.3561i	0.715176	+	0.643947i	0.944162	−	0.329483i	$-0.106874\pi$
$311$	12.6123	+	11.3561i	0.715176	+	0.643947i	−0.228986	+	0.973430i	$0.573541\pi$
$312$	−6.07532	+	1.29135i	−0.343947	+	0.0731082i
$313$	−6.17033	−	13.8588i	−0.348768	−	0.783345i	−0.999707	−	0.0242149i	$-0.992291\pi$
$313$	−6.17033	−	13.8588i	−0.348768	−	0.783345i	0.650939	−	0.759130i	$-0.274375\pi$
$314$	−8.16427	−	5.93169i	−0.460736	−	0.334744i
$315$	4.02454	−	5.05611i	0.226757	−	0.284880i
$316$	−12.3161	+	4.00175i	−0.692836	+	0.225116i
$317$	−1.39270	−	13.2506i	−0.0782218	−	0.744230i	−0.961393	−	0.275179i	$-0.911263\pi$
$317$	−1.39270	−	13.2506i	−0.0782218	−	0.744230i	0.883171	−	0.469051i	$-0.155404\pi$
$318$	2.07788	+	3.59900i	0.116522	+	0.201822i
$319$	−14.8491	+	6.48494i	−0.831392	+	0.363087i
$320$	−2.11528	−	1.22126i	−0.118248	−	0.0682704i
$321$	−11.5887	+	8.41969i	−0.646818	+	0.469941i
$322$	−0.855491	+	19.4465i	−0.0476746	+	1.08371i
$323$	−3.45430	+	10.6312i	−0.192202	+	0.591538i
$324$	−0.913545	+	0.406737i	−0.0507525	+	0.0225965i
$325$	−0.627086	+	5.96633i	−0.0347845	+	0.330952i
$326$	−0.227866	−	1.07203i	−0.0126203	−	0.0593740i
$327$	−4.72225	−	1.00374i	−0.261141	−	0.0555072i
$328$	−5.69434	−	7.83759i	−0.314418	−	0.432759i
$329$	−3.72730	−	22.3187i	−0.205493	−	1.23047i
$330$	−4.00039	−	7.04427i	−0.220214	−	0.387774i
$331$	−8.49537	+	14.7144i	−0.466948	+	0.808777i	−0.999287	−	0.0377539i	$-0.987980\pi$
$331$	−8.49537	+	14.7144i	−0.466948	+	0.808777i	0.532339	+	0.846531i	$0.321313\pi$
$332$	−4.26909	−	1.90072i	−0.234297	−	0.104316i
$333$	−3.29811	+	3.66292i	−0.180735	+	0.200727i
$334$	−2.97767	+	2.68111i	−0.162931	+	0.146704i
$335$	17.0129	−	23.4163i	0.929514	−	1.27937i
$336$	2.64087	−	0.160647i	0.144071	−	0.00876400i
$337$	29.2150	+	9.49253i	1.59144	+	0.517091i	0.964972	−	0.262354i	$-0.0844988\pi$
$337$	29.2150	+	9.49253i	1.59144	+	0.517091i	0.626471	+	0.779445i	$0.284499\pi$
$338$	−5.31777	+	25.0182i	−0.289249	+	1.36081i
$339$	2.18925	−	4.91714i	0.118904	−	0.267062i
$340$	−3.26262	+	1.88368i	−0.176941	+	0.102157i
$341$	5.99787	+	18.9169i	0.324803	+	1.02441i
$342$			7.24735i			0.391892i
$343$	7.98974	−	16.7082i	0.431406	−	0.902158i
$344$	−1.77977	−	5.47757i	−0.0959589	−	0.295331i
$345$	−12.0243	−	13.3544i	−0.647368	−	0.718976i
$346$	−16.4894	−	1.73310i	−0.886474	−	0.0931722i
$347$	8.91560	+	0.937067i	0.478614	+	0.0503044i	0.340764	−	0.940149i	$-0.389314\pi$
$347$	8.91560	+	0.937067i	0.478614	+	0.0503044i	0.137850	+	0.990453i	$0.455981\pi$
$348$	3.26905	+	3.63065i	0.175239	+	0.194623i
$349$	−5.56062	−	17.1138i	−0.297653	−	0.916082i	−0.982317	−	0.187224i	$-0.940051\pi$
$349$	−5.56062	−	17.1138i	−0.297653	−	0.916082i	0.684664	−	0.728859i	$-0.259949\pi$
$350$	0.640665	−	2.47390i	0.0342450	−	0.132235i
$351$			6.21105i			0.331521i
$352$	1.04733	−	3.14692i	0.0558230	−	0.167731i
$353$	−12.5781	+	7.26194i	−0.669462	+	0.386514i	−0.795873	−	0.605464i	$-0.792988\pi$
$353$	−12.5781	+	7.26194i	−0.669462	+	0.386514i	0.126411	+	0.991978i	$0.459654\pi$
$354$	−0.450376	+	1.01156i	−0.0239372	+	0.0537638i
$355$	−4.86608	+	22.8931i	−0.258265	+	1.21504i
$356$	8.09960	+	2.63172i	0.429278	+	0.139481i
$357$	1.82206	−	3.65146i	0.0964336	−	0.193256i
$358$	−4.58109	+	6.30533i	−0.242118	+	0.333247i
$359$	−6.76062	+	6.08729i	−0.356812	+	0.321275i	−0.827968	−	0.560775i	$-0.810503\pi$
$359$	−6.76062	+	6.08729i	−0.356812	+	0.321275i	0.471157	+	0.882050i	$0.343837\pi$
$360$	−1.63436	+	1.81514i	−0.0861385	+	0.0956665i
$361$	30.6258	+	13.6355i	1.61188	+	0.717657i
$362$	4.79266	−	8.30113i	0.251897	−	0.436298i
$363$	8.27860	−	7.24325i	0.434514	−	0.380172i
$364$	5.76000	−	15.3903i	0.301906	−	0.806672i
$365$	−0.664411	−	0.914483i	−0.0347769	−	0.0478662i
$366$	0.877278	+	0.186471i	0.0458561	+	0.00974701i
$367$	0.417648	+	1.96488i	0.0218010	+	0.102566i	0.987703	−	0.156343i	$-0.0499705\pi$
$367$	0.417648	+	1.96488i	0.0218010	+	0.102566i	−0.965902	+	0.258909i	$0.916637\pi$
$368$	0.769037	−	7.31690i	0.0400888	−	0.381420i
$369$	−8.85024	+	3.94038i	−0.460725	+	0.205128i
$370$	−3.72026	+	11.4498i	−0.193407	+	0.595247i
$371$	−10.9845	−	0.483230i	−0.570287	−	0.0250881i
$372$	4.84075	−	3.51701i	0.250981	−	0.182348i
$373$	2.74717	+	1.58608i	0.142243	+	0.0821242i	0.569433	−	0.822038i	$-0.307163\pi$
$373$	2.74717	+	1.58608i	0.142243	+	0.0821242i	−0.427189	+	0.904162i	$0.640496\pi$
$374$	−3.39583	−	3.82590i	−0.175594	−	0.197833i
$375$	−4.92669	−	8.53328i	−0.254413	−	0.440657i
$376$	0.893982	+	8.50567i	0.0461036	+	0.438646i
$377$	28.8590	−	9.37686i	1.48632	−	0.482933i
$378$	0.391931	−	2.61656i	0.0201588	−	0.134581i
$379$	−29.3714	−	21.3396i	−1.50871	−	1.09614i	−0.966747	−	0.255735i	$-0.917683\pi$
$379$	−29.3714	−	21.3396i	−1.50871	−	1.09614i	−0.541960	−	0.840404i	$-0.682317\pi$
$380$	7.19996	+	16.1714i	0.369350	+	0.829575i
$381$	−20.6168	+	4.38224i	−1.05623	+	0.224509i
$382$	2.99484	+	2.69657i	0.153229	+	0.137968i
$383$	−4.13809	+	0.434931i	−0.211447	+	0.0222239i	−0.209659	−	0.977774i	$-0.567236\pi$
$383$	−4.13809	+	0.434931i	−0.211447	+	0.0222239i	−0.00178716	+	0.999998i	$0.500569\pi$
$384$	−1.00000			−0.0510310
$385$	21.4050	+	1.09444i	1.09090	+	0.0557780i
$386$	13.9931			0.712228
$387$	−5.72791	+	0.602028i	−0.291166	+	0.0306028i
$388$	−1.87472	−	1.68800i	−0.0951744	−	0.0856954i
$389$	9.88559	−	2.10125i	0.501219	−	0.106537i	0.0496376	−	0.998767i	$-0.484193\pi$
$389$	9.88559	−	2.10125i	0.501219	−	0.106537i	0.451581	+	0.892230i	$0.350860\pi$
$390$	6.17043	+	13.8590i	0.312452	+	0.701779i
$391$	−9.18055	−	6.67006i	−0.464280	−	0.337319i
$392$	−3.39771	+	6.12009i	−0.171610	+	0.309111i
$393$	−7.51138	+	2.44059i	−0.378899	+	0.123112i
$394$	−1.36822	−	13.0178i	−0.0689300	−	0.655825i
$395$	15.8152	+	27.3928i	0.795751	+	1.37828i
$396$	−2.86040	−	1.67873i	−0.143740	−	0.0843592i
$397$	−1.72152	−	0.993920i	−0.0864006	−	0.0498834i	0.456177	−	0.889889i	$-0.349218\pi$
$397$	−1.72152	−	0.993920i	−0.0864006	−	0.0498834i	−0.542578	+	0.840006i	$0.682552\pi$
$398$	−19.6664	+	14.2885i	−0.985790	+	0.716218i
$399$	−16.1684	−	10.3079i	−0.809431	−	0.516040i
$400$	−0.298477	+	0.918617i	−0.0149238	+	0.0459309i
$401$	−8.03658	+	3.57811i	−0.401328	+	0.178683i	−0.597467	−	0.801893i	$-0.703826\pi$
$401$	−8.03658	+	3.57811i	−0.401328	+	0.178683i	0.196140	+	0.980576i	$0.437159\pi$
$402$	1.23867	−	11.7852i	0.0617794	−	0.587792i
$403$	−7.72678	−	36.3516i	−0.384898	−	1.81080i
$404$	14.6387	+	3.11156i	0.728305	+	0.154806i
$405$	1.43568	+	1.97604i	0.0713393	+	0.0981901i
$406$	−12.7493	+	2.12917i	−0.632737	+	0.105669i
$407$	−16.2453	−	1.82452i	−0.805250	−	0.0904381i
$408$	−0.771203	+	1.33576i	−0.0381802	+	0.0661301i
$409$	−8.11986	−	3.61520i	−0.401501	−	0.178760i	0.196044	−	0.980595i	$-0.437191\pi$
$409$	−8.11986	−	3.61520i	−0.401501	−	0.178760i	−0.597545	+	0.801835i	$0.703857\pi$
$410$	−15.8334	+	17.5847i	−0.781955	+	0.868449i
$411$	−7.13870	+	6.42771i	−0.352126	+	0.317056i
$412$	−7.22628	+	9.94613i	−0.356013	+	0.490010i
$413$	−1.61616	−	2.44350i	−0.0795258	−	0.120237i
$414$	−6.99711	−	2.27350i	−0.343889	−	0.111736i
$415$	−2.37313	+	11.1647i	−0.116493	+	0.548054i
$416$	−2.52626	+	5.67407i	−0.123860	+	0.278194i
$417$	−9.11357	+	5.26172i	−0.446294	+	0.257668i
$418$	−19.5463	+	13.9896i	−0.956039	+	0.684253i
$419$			11.4222i			0.558012i	0.960289	+	0.279006i	$0.0900050\pi$
$419$			11.4222i			0.558012i	−0.960289	+	0.279006i	$0.909995\pi$
$420$	−1.72492	−	6.22783i	−0.0841672	−	0.303887i
$421$	−0.546690	−	1.68254i	−0.0266440	−	0.0820019i	0.936850	−	0.349731i	$-0.113727\pi$
$421$	−0.546690	−	1.68254i	−0.0266440	−	0.0820019i	−0.963494	+	0.267729i	$0.913727\pi$
$422$	−6.00161	−	6.66547i	−0.292154	−	0.324470i
$423$	8.50567	+	0.893982i	0.413560	+	0.0434669i
$424$	4.13300	+	0.434396i	0.200716	+	0.0210961i
$425$	0.996868	+	1.10713i	0.0483552	+	0.0537039i
$426$	2.96104	+	9.11316i	0.143463	+	0.441534i
$427$	−1.66376	+	1.69193i	−0.0805148	+	0.0818784i
$428$			14.3244i			0.692397i
$429$	−16.7513	+	11.9892i	−0.808762	+	0.578844i
$430$	−12.1829	+	7.03379i	−0.587511	+	0.339200i
$431$	−7.61302	+	17.0991i	−0.366706	+	0.823635i	0.632105	+	0.774883i	$0.282191\pi$
$431$	−7.61302	+	17.0991i	−0.366706	+	0.823635i	−0.998811	+	0.0487525i	$0.984475\pi$
$432$	−0.207912	+	0.978148i	−0.0100032	+	0.0470611i
$433$	26.8155	+	8.71289i	1.28867	+	0.418715i	0.871627	−	0.490171i	$-0.163066\pi$
$433$	26.8155	+	8.71289i	1.28867	+	0.418715i	0.417046	+	0.908886i	$0.363066\pi$
$434$	0.961228	+	15.8016i	0.0461404	+	0.758502i
$435$	7.01402	−	9.65397i	0.336296	−	0.462872i
$436$	−3.58771	+	3.23039i	−0.171820	+	0.154708i
$437$	−35.6782	+	39.6246i	−1.70672	+	1.89550i
$438$	−0.422776	−	0.188232i	−0.0202010	−	0.00899408i
$439$	14.9209	−	25.8438i	0.712136	−	1.23346i	−0.251918	−	0.967749i	$-0.581061\pi$
$439$	14.9209	−	25.8438i	0.712136	−	1.23346i	0.964054	−	0.265707i	$-0.0856053\pi$
$440$	−8.05030	−	0.904133i	−0.383783	−	0.0431029i
$441$	5.27993	+	4.59590i	0.251425	+	0.218853i
$442$	5.63095	+	7.75034i	0.267837	+	0.368646i
$443$	5.20292	+	1.10592i	0.247198	+	0.0525436i	0.329844	−	0.944035i	$-0.393004\pi$
$443$	5.20292	+	1.10592i	0.247198	+	0.0525436i	−0.0826460	+	0.996579i	$0.526337\pi$
$444$	1.02478	+	4.82123i	0.0486341	+	0.228806i
$445$	2.17435	−	20.6876i	0.103074	−	0.980684i
$446$	7.01828	−	3.12474i	0.332325	−	0.147961i
$447$	1.77152	−	5.45219i	0.0837903	−	0.257880i
$448$	1.42230	−	2.23093i	0.0671973	−	0.105402i
$449$	18.7125	−	13.5954i	0.883098	−	0.641608i	−0.0509715	−	0.998700i	$-0.516232\pi$
$449$	18.7125	−	13.5954i	0.883098	−	0.641608i	0.934069	+	0.357092i	$0.116232\pi$
$450$	0.836486	+	0.482946i	0.0394323	+	0.0227663i
$451$	−27.7110	−	16.2632i	−1.30486	−	0.765803i
$452$	−2.69124	−	4.66136i	−0.126585	−	0.219252i
$453$	−0.262062	−	2.49336i	−0.0123128	−	0.117148i
$454$	−22.9107	+	7.44414i	−1.07525	+	0.349371i
$455$	−39.6948	−	5.94583i	−1.86092	−	0.278745i
$456$	5.86323	+	4.25989i	0.274571	+	0.199487i
$457$	0.553720	+	1.24368i	0.0259019	+	0.0581767i	0.926033	−	0.377442i	$-0.123196\pi$
$457$	0.553720	+	1.24368i	0.0259019	+	0.0581767i	−0.900131	+	0.435619i	$0.856530\pi$
$458$	7.36170	−	1.56478i	0.343989	−	0.0731172i
$459$	1.14623	+	1.03207i	0.0535015	+	0.0481729i
$460$	−17.8716	+	1.87839i	−0.833270	+	0.0875802i
$461$	9.67739			0.450721			0.225361	−	0.974275i	$-0.427644\pi$
$461$	9.67739			0.450721			0.225361	+	0.974275i	$0.427644\pi$
$462$	7.81347	−	3.99371i	0.363515	−	0.185804i
$463$	25.6318			1.19121			0.595606	−	0.803276i	$-0.296912\pi$
$463$	25.6318			1.19121			0.595606	+	0.803276i	$0.296912\pi$
$464$	4.85875	−	0.510676i	0.225562	−	0.0237075i
$465$	−10.8609	−	9.77920i	−0.503662	−	0.453500i
$466$	11.0455	−	2.34778i	0.511671	−	0.108759i
$467$	6.05733	+	13.6050i	0.280300	+	0.629563i	0.997750	−	0.0670466i	$-0.0213576\pi$
$467$	6.05733	+	13.6050i	0.280300	+	0.629563i	−0.717450	+	0.696610i	$0.754691\pi$
$468$	5.02484	+	3.65076i	0.232273	+	0.168756i
$469$	24.5302	+	19.5254i	1.13270	+	0.901601i
$470$	19.8673	−	6.45527i	0.916409	−	0.297759i
$471$	1.05486	+	10.0363i	0.0486053	+	0.462449i
$472$	0.553645	+	0.958942i	0.0254836	+	0.0441389i
$473$	−12.6803	−	14.2862i	−0.583040	−	0.656880i
$474$	11.2150	+	6.47497i	0.515121	+	0.297405i
$475$	5.66324	−	4.11459i	0.259847	−	0.188790i
$476$	−1.88312	−	3.62035i	−0.0863125	−	0.165939i
$477$	1.28420	−	3.95237i	0.0587996	−	0.180967i
$478$	−8.99870	+	4.00648i	−0.411591	+	0.183252i
$479$	3.70560	−	35.2564i	0.169313	−	1.61091i	−0.498711	−	0.866768i	$-0.666193\pi$
$479$	3.70560	−	35.2564i	0.169313	−	1.61091i	0.668024	−	0.744139i	$-0.267140\pi$
$480$	0.507828	+	2.38914i	0.0231791	+	0.109049i
$481$	29.9449	+	6.36498i	1.36537	+	0.290218i
$482$	1.04175	+	1.43384i	0.0474503	+	0.0653097i
$483$	15.0240	−	12.3765i	0.683616	−	0.563150i
$484$	−0.993875	−	10.9550i	−0.0451761	−	0.497955i
$485$	−3.08085	+	5.33618i	−0.139894	+	0.242304i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	−20.3272	+	22.5756i	−0.921113	+	1.02300i	0.0785470	+	0.996910i	$0.474972\pi$
$487$	−20.3272	+	22.5756i	−0.921113	+	1.02300i	−0.999660	+	0.0260888i	$0.991695\pi$
$488$	0.666510	−	0.600128i	0.0301715	−	0.0271665i
$489$	−0.644198	+	0.886663i	−0.0291316	+	0.0400963i
$490$	16.3472	+	5.00966i	0.738493	+	0.226314i
$491$	−10.7617	−	3.49668i	−0.485667	−	0.157803i	0.0559408	−	0.998434i	$-0.482184\pi$
$491$	−10.7617	−	3.49668i	−0.485667	−	0.157803i	−0.541608	+	0.840631i	$0.682184\pi$
$492$	−2.01421	+	9.47610i	−0.0908074	+	0.427215i
$493$	3.06494	−	6.88397i	0.138038	−	0.310039i
$494$	38.9830	−	22.5068i	1.75393	−	1.01263i
$495$	−2.55813	+	7.68640i	−0.114979	+	0.345478i
$496$		−	5.98349i		−	0.268667i
$497$	−24.5423	−	6.35573i	−1.10087	−	0.285094i
$498$	1.44407	+	4.44439i	0.0647103	+	0.199158i
$499$	11.0612	+	12.2847i	0.495168	+	0.549940i	0.937987	−	0.346671i	$-0.112688\pi$
$499$	11.0612	+	12.2847i	0.495168	+	0.549940i	−0.442819	+	0.896611i	$0.646021\pi$
$500$	−9.79940	−	1.02996i	−0.438243	−	0.0460612i
$501$	3.98490	+	0.418830i	0.178032	+	0.0187120i
$502$	−16.4593	−	18.2799i	−0.734614	−	0.815872i
$503$	−6.96102	−	21.4238i	−0.310376	−	0.955240i	−0.977616	−	0.210397i	$-0.932524\pi$
$503$	−6.96102	−	21.4238i	−0.310376	−	0.955240i	0.667240	−	0.744843i	$-0.267476\pi$
$504$	−1.88647	−	1.85506i	−0.0840301	−	0.0826307i
$505$		−	36.5542i		−	1.62664i
$506$	−7.37488	−	23.2599i	−0.327853	−	1.03403i
$507$	22.1504	−	12.7885i	0.983734	−	0.567959i
$508$	−8.57296	+	19.2552i	−0.380364	+	0.854311i
$509$	4.37338	−	20.5752i	0.193847	−	0.911978i	−0.768436	−	0.639927i	$-0.778965\pi$
$509$	4.37338	−	20.5752i	0.193847	−	0.911978i	0.962283	−	0.272051i	$-0.0877020\pi$
$510$	3.58296	+	1.16418i	0.158656	+	0.0515506i
$511$	1.02125	−	0.675464i	0.0451773	−	0.0298808i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	5.38583	−	4.84943i	0.237790	−	0.214107i
$514$	−7.34440	+	8.15678i	−0.323948	+	0.359780i
$515$	27.4324	+	12.2137i	1.20882	+	0.538200i
$516$	−2.87973	+	4.98784i	−0.126773	+	0.219577i
$517$	14.0074	+	24.6656i	0.616046	+	1.08479i
$518$	−12.2134	−	4.57100i	−0.536626	−	0.200838i
$519$	9.74560	+	13.4137i	0.427784	+	0.588795i
$520$	14.8391	+	3.15414i	0.650736	+	0.138318i
$521$	1.34934	+	6.34815i	0.0591157	+	0.278117i	0.997770	−	0.0667412i	$-0.0212602\pi$
$521$	1.34934	+	6.34815i	0.0591157	+	0.278117i	−0.938655	+	0.344859i	$0.887927\pi$
$522$	0.510676	−	4.85875i	0.0223517	−	0.212662i
$523$	12.3955	−	5.51884i	0.542018	−	0.241322i	−0.117418	−	0.993083i	$-0.537462\pi$
$523$	12.3955	−	5.51884i	0.542018	−	0.241322i	0.659436	+	0.751761i	$0.270795\pi$
$524$	−2.44059	+	7.51138i	−0.106618	+	0.328136i
$525$	−2.26715	+	1.17925i	−0.0989467	+	0.0514668i
$526$	0.446955	−	0.324732i	0.0194882	−	0.0141590i
$527$	−7.99252	−	4.61449i	−0.348160	−	0.201010i
$528$	−3.03942	+	1.32738i	−0.132274	+	0.0577668i
$529$	−15.5642	−	26.9580i	−0.676704	−	1.17209i
$530$	−1.06102	−	10.0949i	−0.0460878	−	0.438496i
$531$	1.05310	−	0.342172i	0.0457005	−	0.0148490i
$532$	−17.8428	+	7.02165i	−0.773583	+	0.304427i
$533$	48.6796	+	35.3678i	2.10855	+	1.53195i
$534$	−3.46394	−	7.78014i	−0.149899	−	0.336679i
$535$	34.2231	−	7.27434i	1.47959	−	0.314497i
$536$	−8.80634	−	7.92927i	−0.380376	−	0.342492i
$537$	7.75112	−	0.814675i	0.334485	−	0.0351558i
$538$	6.78366			0.292464
$539$	−2.20338	+	23.1116i	−0.0949063	+	0.995486i
$540$	2.44252			0.105109
$541$	9.08921	−	0.955314i	0.390776	−	0.0410722i	0.0928965	−	0.995676i	$-0.470387\pi$
$541$	9.08921	−	0.955314i	0.390776	−	0.0410722i	0.297879	+	0.954604i	$0.403721\pi$
$542$	−6.01584	−	5.41668i	−0.258402	−	0.232666i
$543$	−9.37586	+	1.99290i	−0.402357	+	0.0855235i
$544$	0.627353	+	1.40906i	0.0268975	+	0.0604128i
$545$	9.53981	+	6.93108i	0.408641	+	0.296895i
$546$	−15.2914	+	6.01762i	−0.654413	+	0.257530i
$547$	−11.4897	+	3.73322i	−0.491263	+	0.159621i	−0.544164	−	0.838979i	$-0.683153\pi$
$547$	−11.4897	+	3.73322i	−0.491263	+	0.159621i	0.0529011	+	0.998600i	$0.483153\pi$
$548$	1.00411	+	9.55344i	0.0428933	+	0.408103i
$549$	−0.448439	−	0.776719i	−0.0191389	−	0.0331495i
$550$	0.312158	+	3.18825i	0.0133105	+	0.135948i
$551$	−30.6634	−	17.7035i	−1.30631	−	0.754196i
$552$	−5.95210	+	4.32445i	−0.253338	+	0.184061i
$553$	−30.3963	+	15.8105i	−1.29258	+	0.672333i
$554$	−3.72771	+	11.4727i	−0.158375	+	0.487429i
$555$	10.9982	−	4.89671i	0.466848	−	0.207854i
$556$	−1.10000	+	10.4658i	−0.0466504	+	0.443849i
$557$	−5.47101	−	25.7391i	−0.231814	−	1.09060i	−0.927954	−	0.372694i	$-0.878434\pi$
$557$	−5.47101	−	25.7391i	−0.231814	−	1.09060i	0.696140	−	0.717906i	$-0.254899\pi$
$558$	−5.85274	−	1.24404i	−0.247766	−	0.0526643i
$559$	21.0264	+	28.9404i	0.889323	+	1.22405i
$560$	−6.05230	−	2.26514i	−0.255756	−	0.0957198i
$561$	−0.570944	+	5.08362i	−0.0241053	+	0.214631i
$562$	14.7319	−	25.5164i	0.621427	−	1.07634i
$563$	−29.4289	−	13.1026i	−1.24028	−	0.552209i	−0.321475	−	0.946918i	$-0.604179\pi$
$563$	−29.4289	−	13.1026i	−1.24028	−	0.552209i	−0.918806	+	0.394709i	$0.870845\pi$
$564$	5.72275	−	6.35576i	0.240971	−	0.267626i
$565$	−9.76997	+	8.79692i	−0.411026	+	0.370089i
$566$	−14.1547	+	19.4823i	−0.594966	+	0.818901i
$567$	−2.20674	+	1.45956i	−0.0926742	+	0.0612957i
$568$	9.11316	+	2.96104i	0.382380	+	0.124243i
$569$	5.29250	−	24.8993i	0.221873	−	1.04383i	−0.716334	−	0.697757i	$-0.754181\pi$
$569$	5.29250	−	24.8993i	0.221873	−	1.04383i	0.938207	−	0.346074i	$-0.112485\pi$
$570$	7.19996	−	16.1714i	0.301573	−	0.677345i
$571$	10.5602	−	6.09692i	0.441929	−	0.255148i	−0.262486	−	0.964936i	$-0.584542\pi$
$571$	10.5602	−	6.09692i	0.441929	−	0.255148i	0.704416	+	0.709788i	$0.251209\pi$
$572$	−0.146711	+	20.5992i	−0.00613429	+	0.861295i
$573$		−	4.02995i		−	0.168354i
$574$	−18.2757	−	17.9714i	−0.762815	−	0.750112i
$575$	2.19595	+	6.75845i	0.0915776	+	0.281847i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	1.77759	+	0.186833i	0.0740022	+	0.00777795i	0.141457	−	0.989944i	$-0.454821\pi$
$577$	1.77759	+	0.186833i	0.0740022	+	0.00777795i	−0.0674550	+	0.997722i	$0.521488\pi$
$578$	−14.5409	−	1.52831i	−0.604821	−	0.0635693i
$579$	−9.36319	−	10.3989i	−0.389121	−	0.432162i
$580$	−3.68749	−	11.3489i	−0.153115	−	0.471238i
$581$	−11.9690	−	3.09962i	−0.496559	−	0.128594i
$582$			2.52268i			0.104569i
$583$	13.1385	−	4.16575i	0.544142	−	0.172528i
$584$	−0.400785	+	0.231393i	−0.0165846	+	0.00957512i
$585$	6.17043	−	13.8590i	0.255116	−	0.573000i
$586$	0.772682	−	3.63518i	0.0319192	−	0.150168i
$587$	−4.26798	−	1.38675i	−0.176159	−	0.0572374i	0.219610	−	0.975588i	$-0.429522\pi$
$587$	−4.26798	−	1.38675i	−0.176159	−	0.0572374i	−0.395768	+	0.918350i	$0.629522\pi$
$588$	6.82163	−	1.57015i	0.281319	−	0.0647519i
$589$	−25.4890	+	35.0826i	−1.05026	+	1.44555i
$590$	2.00989	−	1.80972i	0.0827460	−	0.0745048i
$591$	−8.75856	+	9.72737i	−0.360279	+	0.400130i
$592$	4.50281	+	2.00478i	0.185064	+	0.0823960i
$593$	−5.11193	+	8.85412i	−0.209922	+	0.363595i	−0.951690	−	0.307062i	$-0.900654\pi$
$593$	−5.11193	+	8.85412i	−0.209922	+	0.363595i	0.741768	+	0.670657i	$0.233988\pi$
$594$	0.666443	+	3.24898i	0.0273445	+	0.133307i
$595$	−7.69324	+	6.33755i	−0.315392	+	0.259814i
$596$	−3.36964	−	4.63791i	−0.138026	−	0.189976i
$597$	23.7779	+	5.05414i	0.973163	+	0.206852i
$598$	9.50071	+	44.6973i	0.388513	+	1.82781i
$599$	2.20189	−	20.9496i	0.0899668	−	0.855977i	−0.852736	−	0.522343i	$-0.825058\pi$
$599$	2.20189	−	20.9496i	0.0899668	−	0.855977i	0.942702	−	0.333635i	$-0.108275\pi$
$600$	0.882385	−	0.392863i	0.0360232	−	0.0160386i
$601$	−1.36033	+	4.18667i	−0.0554891	+	0.170778i	−0.974960	−	0.222380i	$-0.928617\pi$
$601$	−1.36033	+	4.18667i	−0.0554891	+	0.170778i	0.919471	+	0.393158i	$0.128617\pi$
$602$	−7.03171	−	13.5187i	−0.286591	−	0.550981i
$603$	−9.58693	+	6.96532i	−0.390410	+	0.283650i
$604$	−2.17120	−	1.25354i	−0.0883450	−	0.0510060i
$605$	−25.6684	+	7.93777i	−1.04357	+	0.322716i
$606$	−7.48289	−	12.9608i	−0.303972	−	0.526495i
$607$	4.05175	+	38.5498i	0.164455	+	1.56469i	0.696240	+	0.717809i	$0.254855\pi$
$607$	4.05175	+	38.5498i	0.164455	+	1.56469i	−0.531784	+	0.846880i	$0.678478\pi$
$608$	6.89264	−	2.23956i	0.279534	−	0.0908260i
$609$	10.1132	+	8.04988i	0.409809	+	0.326198i
$610$	−1.77226	−	1.28762i	−0.0717569	−	0.0521344i
$611$	−21.6059	−	48.5276i	−0.874081	−	1.96322i
$612$	1.50870	−	0.320684i	0.0609856	−	0.0129629i
$613$	−30.4022	−	27.3742i	−1.22793	−	1.10563i	−0.990966	−	0.134117i	$-0.957180\pi$
$613$	−30.4022	−	27.3742i	−1.22793	−	1.10563i	−0.236966	−	0.971518i	$-0.576153\pi$
$614$	25.3451	−	2.66388i	1.02284	−	0.107505i
$615$	23.6626			0.954169
$616$	1.36166	−	8.66867i	0.0548629	−	0.349271i
$617$	−4.10456			−0.165244			−0.0826218	−	0.996581i	$-0.526329\pi$
$617$	−4.10456			−0.165244			−0.0826218	+	0.996581i	$0.526329\pi$
$618$	12.2267	−	1.28508i	0.491832	−	0.0516936i
$619$	−29.8470	−	26.8744i	−1.19965	−	1.08017i	−0.994849	−	0.101370i	$-0.967678\pi$
$619$	−29.8470	−	26.8744i	−1.19965	−	1.08017i	−0.204804	−	0.978803i	$-0.565656\pi$
$620$	−14.2954	+	3.03858i	−0.574118	+	0.122032i
$621$	2.99244	+	6.72114i	0.120083	+	0.269710i
$622$	−13.7302	−	9.97558i	−0.550531	−	0.399984i
$623$	22.2837	+	3.33785i	0.892779	+	0.133728i
$624$	5.90705	−	1.91932i	0.236471	−	0.0768342i
$625$	3.02051	+	28.7382i	0.120820	+	1.14953i
$626$	7.58516	+	13.1379i	0.303164	+	0.525096i
$627$	23.4753	+	5.16484i	0.937513	+	0.206264i
$628$	8.73957	+	5.04579i	0.348747	+	0.201349i
$629$	6.15049	−	4.46859i	0.245236	−	0.178175i
$630$	−3.47399	+	5.44910i	−0.138407	+	0.217097i
$631$	14.9668	−	46.0630i	0.595817	−	1.83374i	0.0452025	−	0.998978i	$-0.485607\pi$
$631$	14.9668	−	46.0630i	0.595817	−	1.83374i	0.550615	−	0.834759i	$-0.314393\pi$
$632$	11.8304	−	5.26722i	0.470587	−	0.209519i
$633$	−0.937544	+	8.92013i	−0.0372640	+	0.354543i
$634$	2.77014	+	13.0325i	0.110016	+	0.517586i
$635$	50.3570	+	10.7037i	1.99836	+	0.424764i
$636$	−2.44270	−	3.36209i	−0.0968593	−	0.133315i
$637$	8.32406	−	42.6730i	0.329811	−	1.69077i
$638$	14.0899	−	8.00157i	0.557826	−	0.316785i
$639$	4.79107	−	8.29838i	0.189532	−	0.328279i
$640$	2.23135	+	0.993461i	0.0882019	+	0.0392700i
$641$	−8.76872	+	9.73865i	−0.346344	+	0.384654i	−0.890998	−	0.454007i	$-0.849994\pi$
$641$	−8.76872	+	9.73865i	−0.346344	+	0.384654i	0.544654	+	0.838661i	$0.316661\pi$
$642$	10.6451	−	9.58491i	0.420129	−	0.378286i
$643$	−9.05854	+	12.4680i	−0.357234	+	0.491691i	−0.949376	−	0.314144i	$-0.898283\pi$
$643$	−9.05854	+	12.4680i	−0.357234	+	0.491691i	0.592141	+	0.805834i	$0.298283\pi$
$644$	−1.18191	−	19.4294i	−0.0465738	−	0.765626i
$645$	13.3791	+	4.34712i	0.526800	+	0.171168i
$646$	2.32411	−	10.9341i	0.0914409	−	0.430196i
$647$	−20.1376	+	45.2298i	−0.791691	+	1.77817i	−0.185854	+	0.982577i	$0.559505\pi$
$647$	−20.1376	+	45.2298i	−0.791691	+	1.77817i	−0.605837	+	0.795589i	$0.707161\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	2.95564	+	2.17973i	0.116019	+	0.0855618i
$650$		−	5.99919i		−	0.235308i
$651$	11.0997	−	11.2877i	0.435032	−	0.442399i
$652$	0.338675	+	1.04233i	0.0132635	+	0.0408210i
$653$	−12.8832	−	14.3082i	−0.504157	−	0.559923i	0.436315	−	0.899794i	$-0.356283\pi$
$653$	−12.8832	−	14.3082i	−0.504157	−	0.559923i	−0.940472	+	0.339871i	$0.889617\pi$
$654$	4.80130	+	0.504637i	0.187746	+	0.0197329i
$655$	19.1852	+	2.01644i	0.749626	+	0.0787889i
$656$	6.48240	+	7.19944i	0.253095	+	0.281091i
$657$	0.143009	+	0.440136i	0.00557931	+	0.0171713i
$658$	6.03982	+	21.8069i	0.235457	+	0.850121i
$659$			33.1527i			1.29145i	0.763572	+	0.645723i	$0.223444\pi$
$659$			33.1527i			1.29145i	−0.763572	+	0.645723i	$0.776556\pi$
$660$	4.71480	+	6.58752i	0.183523	+	0.256419i
$661$	−11.3551	+	6.55588i	−0.441663	+	0.254994i	−0.704303	−	0.709900i	$-0.748740\pi$
$661$	−11.3551	+	6.55588i	−0.441663	+	0.254994i	0.262640	+	0.964894i	$0.415407\pi$
$662$	6.91076	−	15.5218i	0.268594	−	0.603272i
$663$	1.99178	−	9.37060i	0.0773545	−	0.363924i
$664$	4.44439	+	1.44407i	0.172476	+	0.0560407i
$665$	25.8368	+	39.0632i	1.00191	+	1.51481i
$666$	2.89716	−	3.98760i	0.112263	−	0.154516i
$667$	26.7114	−	24.0510i	1.03427	−	0.931260i
$668$	2.68111	−	2.97767i	0.103735	−	0.115210i
$669$	−7.01828	−	3.12474i	−0.271342	−	0.120809i
$670$	−14.4720	+	25.0663i	−0.559104	+	0.968396i
$671$	1.22920	−	2.70875i	0.0474529	−	0.104570i
$672$	−2.60961	+	0.435813i	−0.100668	+	0.0168118i
$673$	17.3388	+	23.8648i	0.668361	+	0.919919i	0.999722	−	0.0235846i	$-0.00750790\pi$
$673$	17.3388	+	23.8648i	0.668361	+	0.919919i	−0.331361	+	0.943504i	$0.607508\pi$
$674$	−30.0472	−	6.38673i	−1.15737	−	0.246008i
$675$	−0.200820	−	0.944784i	−0.00772957	−	0.0363648i
$676$	2.67353	−	25.4370i	0.102828	−	0.978345i
$677$	−26.1435	+	11.6398i	−1.00478	+	0.447356i	−0.842099	−	0.539324i	$-0.818680\pi$
$677$	−26.1435	+	11.6398i	−1.00478	+	0.447356i	−0.162678	+	0.986679i	$0.552013\pi$
$678$	−1.66328	+	5.11904i	−0.0638778	+	0.196596i
$679$	−5.62794	−	3.58801i	−0.215980	−	0.137695i
$680$	3.04785	−	2.21439i	0.116880	−	0.0849181i
$681$	20.8623	+	12.0449i	0.799446	+	0.461560i
$682$	−7.94237	−	18.1863i	−0.304129	−	0.696391i
$683$	3.20726	+	5.55514i	0.122722	+	0.212562i	0.920840	−	0.389940i	$-0.127504\pi$
$683$	3.20726	+	5.55514i	0.122722	+	0.212562i	−0.798118	+	0.602501i	$0.794171\pi$
$684$	−0.757555	−	7.20765i	−0.0289658	−	0.275591i
$685$	22.3146	−	7.25046i	0.852598	−	0.277026i
$686$	−6.19949	+	17.4518i	−0.236698	+	0.666314i
$687$	−6.08879	−	4.42377i	−0.232302	−	0.168777i
$688$	2.34258	+	5.26153i	0.0893102	+	0.200594i
$689$	−25.2476	+	5.36655i	−0.961858	+	0.204449i
$690$	13.3544	+	12.0243i	0.508392	+	0.457759i
$691$	−30.9447	+	3.25242i	−1.17719	+	0.123728i	−0.672852	−	0.739777i	$-0.734931\pi$
$691$	−30.9447	+	3.25242i	−1.17719	+	0.123728i	−0.504340	+	0.863505i	$0.668264\pi$
$692$	16.5802			0.630285
$693$	−8.19614	−	3.13423i	−0.311345	−	0.119059i
$694$	−8.96471			−0.340296
$695$	25.5629	−	2.68677i	0.969656	−	0.101915i
$696$	−3.63065	−	3.26905i	−0.137619	−	0.123913i
$697$	14.6160	−	3.10672i	0.553620	−	0.117676i
$698$	7.31904	+	16.4388i	0.277030	+	0.622219i
$699$	−9.13560	−	6.63740i	−0.345540	−	0.251049i
$700$	−0.378563	+	2.52731i	−0.0143083	+	0.0955234i
$701$	−13.9653	+	4.53760i	−0.527462	+	0.171383i	−0.560629	−	0.828067i	$-0.689441\pi$
$701$	−13.9653	+	4.53760i	−0.527462	+	0.171383i	0.0331671	+	0.999450i	$0.489441\pi$
$702$	−0.649231	−	6.17702i	−0.0245036	−	0.233137i
$703$	−17.8609	−	30.9360i	−0.673636	−	1.16677i
$704$	−0.712652	+	3.23916i	−0.0268591	+	0.122080i
$705$	−18.0910	−	10.4448i	−0.681346	−	0.393375i
$706$	11.7501	−	8.53693i	0.442220	−	0.321291i
$707$	39.5575	+	1.74021i	1.48771	+	0.0654474i
$708$	0.342172	−	1.05310i	0.0128596	−	0.0395778i
$709$	0.378331	−	0.168444i	0.0142085	−	0.00632605i	−0.399620	−	0.916681i	$-0.630858\pi$
$709$	0.378331	−	0.168444i	0.0142085	−	0.00632605i	0.413829	+	0.910355i	$0.364191\pi$
$710$	2.44644	−	23.2763i	0.0918133	−	0.873545i
$711$	−2.69244	−	12.6670i	−0.100975	−	0.475048i
$712$	−8.33032	−	1.77066i	−0.312192	−	0.0663584i
$713$	−25.8753	−	35.6143i	−0.969039	−	1.33377i
$714$	−1.43040	+	3.82192i	−0.0535312	+	0.143032i
$715$	49.2889	−	10.1103i	1.84330	−	0.378105i
$716$	3.89691	−	6.74964i	0.145634	−	0.252246i
$717$	8.99870	+	4.00648i	0.336063	+	0.149625i
$718$	6.08729	−	6.76062i	0.227175	−	0.252304i
$719$	2.50358	−	2.25423i	0.0933678	−	0.0840687i	−0.621125	−	0.783711i	$-0.713324\pi$
$719$	2.50358	−	2.25423i	0.0933678	−	0.0840687i	0.714493	+	0.699643i	$0.246657\pi$
$720$	1.43568	−	1.97604i	0.0535045	−	0.0736426i
$721$	−14.5231	+	29.1048i	−0.540870	+	1.08392i
$722$	−31.8833	−	10.3595i	−1.18658	−	0.385542i
$723$	0.368487	−	1.73360i	0.0137042	−	0.0644731i
$724$	−3.89870	+	8.75662i	−0.144894	+	0.325437i
$725$	−4.08667	+	2.35944i	−0.151775	+	0.0876274i
$726$	−7.47613	+	8.06892i	−0.277465	+	0.299466i
$727$		−	36.2102i		−	1.34296i	−0.741023	−	0.671480i	$-0.765659\pi$
$727$		−	36.2102i		−	1.34296i	0.741023	−	0.671480i	$-0.234341\pi$
$728$	−4.11972	+	15.9081i	−0.152687	+	0.589593i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	0.756361	+	0.840024i	0.0279942	+	0.0310907i
$731$	8.83476	+	0.928571i	0.326765	+	0.0343444i
$732$	−0.891964	−	0.0937492i	−0.0329679	−	0.00346507i
$733$	−0.974510	−	1.08230i	−0.0359943	−	0.0399758i	0.724879	−	0.688876i	$-0.241896\pi$
$733$	−0.974510	−	1.08230i	−0.0359943	−	0.0399758i	−0.760873	+	0.648901i	$0.775229\pi$
$734$	−0.620745	−	1.91046i	−0.0229121	−	0.0705163i
$735$	−7.21553	−	15.5005i	−0.266149	−	0.571744i
$736$			7.35720i			0.271190i
$737$	−37.2913	−	12.4110i	−1.37364	−	0.457165i
$738$	8.38988	−	4.84390i	0.308836	−	0.178306i
$739$	−6.86493	+	15.4189i	−0.252531	+	0.567193i	−0.994677	−	0.103045i	$-0.967141\pi$
$739$	−6.86493	+	15.4189i	−0.252531	+	0.567193i	0.742146	+	0.670238i	$0.233808\pi$
$740$	2.50305	−	11.7759i	0.0920141	−	0.432892i
$741$	−42.8105	−	13.9100i	−1.57268	−	0.510996i
$742$	10.9748	−	0.667611i	0.402899	−	0.0245088i
$743$	13.1588	−	18.1115i	0.482749	−	0.664447i	−0.496281	−	0.868162i	$-0.665301\pi$
$743$	13.1588	−	18.1115i	0.482749	−	0.664447i	0.979030	+	0.203715i	$0.0653015\pi$
$744$	−4.44660	+	4.00374i	−0.163020	+	0.146784i
$745$	−9.36944	+	10.4058i	−0.343270	+	0.381239i
$746$	−2.89792	−	1.29024i	−0.106100	−	0.0472389i
$747$	2.33655	−	4.04703i	0.0854900	−	0.148073i
$748$	3.77714	+	3.44998i	0.138106	+	0.126144i
$749$	6.24277	+	37.3812i	0.228106	+	1.36588i
$750$	5.79167	+	7.97155i	0.211482	+	0.291080i
$751$	47.3057	+	10.0551i	1.72621	+	0.366917i	0.960932	−	0.276784i	$-0.0892687\pi$
$751$	47.3057	+	10.0551i	1.72621	+	0.366917i	0.765277	+	0.643701i	$0.222602\pi$
$752$	−1.77817	−	8.36563i	−0.0648432	−	0.305063i
$753$	−2.57119	+	24.4633i	−0.0936995	+	0.891491i
$754$	−27.7208	+	12.3421i	−1.00953	+	0.449472i
$755$	−1.89230	+	5.82390i	−0.0688678	+	0.211953i
$756$	−0.116279	+	2.64319i	−0.00422904	+	0.0961321i
$757$	2.03585	−	1.47913i	0.0739944	−	0.0537601i	−0.550173	−	0.835051i	$-0.685438\pi$
$757$	2.03585	−	1.47913i	0.0739944	−	0.0537601i	0.624167	+	0.781291i	$0.285438\pi$
$758$	31.4411	+	18.1525i	1.14199	+	0.659329i
$759$	−12.3507	+	21.0445i	−0.448303	+	0.763868i
$760$	−8.85089	−	15.3302i	−0.321056	−	0.556085i
$761$	0.693172	+	6.59509i	0.0251275	+	0.239072i	0.999876	+	0.0157653i	$0.00501845\pi$
$761$	0.693172	+	6.59509i	0.0251275	+	0.239072i	−0.974748	+	0.223307i	$0.928315\pi$
$762$	20.0458	−	6.51328i	0.726184	−	0.235951i
$763$	−7.95469	+	9.99364i	−0.287979	+	0.361794i
$764$	−3.26030	−	2.36875i	−0.117954	−	0.0856983i
$765$	−1.53232	−	3.44165i	−0.0554011	−	0.124433i
$766$	4.06996	−	0.865097i	0.147054	−	0.0312572i
$767$	−5.11093	−	4.60190i	−0.184545	−	0.166165i
$768$	0.994522	−	0.104528i	0.0358867	−	0.00377185i
$769$	−21.3952			−0.771531			−0.385765	−	0.922597i	$-0.626063\pi$
$769$	−21.3952			−0.771531			−0.385765	+	0.922597i	$0.626063\pi$
$770$	−21.4022	+	1.14899i	−0.771281	+	0.0414067i
$771$	10.9760			0.395292
$772$	−13.9164	+	1.46267i	−0.500863	+	0.0526428i
$773$	12.0702	+	10.8681i	0.434136	+	0.390898i	0.857017	−	0.515287i	$-0.172315\pi$
$773$	12.0702	+	10.8681i	0.434136	+	0.390898i	−0.422882	+	0.906185i	$0.638981\pi$
$774$	5.63360	−	1.19746i	0.202496	−	0.0430418i
$775$	2.35069	+	5.27975i	0.0844395	+	0.189654i
$776$	2.04089	+	1.48280i	0.0732638	+	0.0532292i
$777$	4.77544	+	12.1349i	0.171318	+	0.435338i
$778$	−9.61179	+	3.12306i	−0.344599	+	0.111967i
$779$	−7.33904	−	69.8263i	−0.262948	−	2.50179i
$780$	−7.58529	−	13.1381i	−0.271597	−	0.470420i
$781$	31.6291	−	3.09677i	1.13178	−	0.110811i
$782$	9.82747	+	5.67389i	0.351430	+	0.202898i
$783$	−3.95247	+	2.87164i	−0.141250	+	0.102624i
$784$	2.73938	−	6.44173i	0.0978348	−	0.230062i
$785$	7.61692	−	23.4425i	0.271860	−	0.836698i
$786$	7.21512	−	3.21238i	0.257355	−	0.114582i
$787$	1.34801	−	12.8255i	0.0480514	−	0.457178i	−0.943869	−	0.330319i	$-0.892844\pi$
$787$	1.34801	−	12.8255i	0.0480514	−	0.457178i	0.991921	−	0.126859i	$-0.0404897\pi$
$788$	2.72145	+	12.8034i	0.0969477	+	0.456103i
$789$	−0.540394	−	0.114864i	−0.0192385	−	0.00408928i
$790$	−18.5919	−	25.5896i	−0.661471	−	0.910436i
$791$	−9.05457	−	10.9915i	−0.321943	−	0.390811i
$792$	3.02020	+	1.37054i	0.107318	+	0.0486999i
$793$	−2.78527	+	4.82423i	−0.0989079	+	0.171314i
$794$	1.81598	+	0.808527i	0.0644468	+	0.0286936i
$795$	−6.79204	+	7.54332i	−0.240889	+	0.267534i
$796$	18.0652	−	16.2659i	0.640302	−	0.576531i
$797$	−5.32056	+	7.32312i	−0.188464	+	0.259398i	−0.892785	−	0.450483i	$-0.851252\pi$
$797$	−5.32056	+	7.32312i	−0.188464	+	0.259398i	0.704321	+	0.709882i	$0.251252\pi$
$798$	17.1573	+	8.56138i	0.607361	+	0.303069i
$799$	−12.5458	−	4.07638i	−0.443839	−	0.144212i
$800$	0.200820	−	0.944784i	0.00710006	−	0.0334032i
$801$	−3.46394	+	7.78014i	−0.122392	+	0.274898i
$802$	7.61854	−	4.39856i	0.269020	−	0.155319i
$803$	−0.911006	+	1.23529i	−0.0321487	+	0.0435926i
$804$			11.8501i			0.417921i
$805$	−45.8194	+	12.6905i	−1.61492	+	0.447283i
$806$	11.4842	+	35.3448i	0.404515	+	1.24497i
$807$	−4.53915	−	5.04124i	−0.159786	−	0.177460i
$808$	−14.8838	−	1.56435i	−0.523610	−	0.0550337i
$809$	17.3223	+	1.82065i	0.609021	+	0.0640106i	0.404018	−	0.914751i	$-0.367613\pi$
$809$	17.3223	+	1.82065i	0.609021	+	0.0640106i	0.205002	+	0.978762i	$0.434280\pi$
$810$	−1.63436	−	1.81514i	−0.0574257	−	0.0637777i
$811$	−0.943116	−	2.90261i	−0.0331173	−	0.101925i	0.933131	−	0.359535i	$-0.117065\pi$
$811$	−0.943116	−	2.90261i	−0.0331173	−	0.101925i	−0.966249	+	0.257611i	$0.917065\pi$
$812$	12.4569	−	3.45017i	0.437151	−	0.121077i
$813$			8.09511i			0.283908i
$814$	16.3470	+	0.116426i	0.572963	+	0.00408074i
$815$	2.31830	−	1.33847i	0.0812064	−	0.0468845i
$816$	0.627353	−	1.40906i	0.0219617	−	0.0493269i
$817$	8.67841	−	40.8287i	0.303619	−	1.42842i
$818$	8.45327	+	2.74664i	0.295562	+	0.0960339i
$819$	14.7039	+	7.33717i	0.513797	+	0.256382i
$820$	13.9085	−	19.1435i	0.485707	−	0.668519i
$821$	−17.2073	+	15.4935i	−0.600538	+	0.540727i	−0.912347	−	0.409418i	$-0.865732\pi$
$821$	−17.2073	+	15.4935i	−0.600538	+	0.540727i	0.311809	+	0.950145i	$0.399065\pi$
$822$	6.42771	−	7.13870i	0.224192	−	0.248991i
$823$	4.98016	+	2.21731i	0.173598	+	0.0772906i	0.491695	−	0.870767i	$-0.336377\pi$
$823$	4.98016	+	2.21731i	0.173598	+	0.0772906i	−0.318098	+	0.948058i	$0.603044\pi$
$824$	6.14704	−	10.6470i	0.214142	−	0.370906i
$825$	2.16046	−	2.36534i	0.0752175	−	0.0823504i
$826$	1.86272	+	2.26118i	0.0648122	+	0.0786765i
$827$	15.2211	+	20.9500i	0.529288	+	0.728503i	0.987022	−	0.160587i	$-0.0513386\pi$
$827$	15.2211	+	20.9500i	0.529288	+	0.728503i	−0.457733	+	0.889089i	$0.651339\pi$
$828$	7.19643	+	1.52965i	0.250093	+	0.0531589i
$829$	−4.79785	−	22.5721i	−0.166636	−	0.783962i	−0.979490	−	0.201494i	$-0.935420\pi$
$829$	−4.79785	−	22.5721i	−0.166636	−	0.783962i	0.812853	−	0.582468i	$-0.197913\pi$
$830$	1.19310	−	11.3516i	0.0414132	−	0.394020i
$831$	11.0202	−	4.90652i	0.382287	−	0.170205i
$832$	1.91932	−	5.90705i	0.0665404	−	0.204790i
$833$	−6.49200	−	8.62703i	−0.224934	−	0.298909i
$834$	8.51365	−	6.18553i	0.294804	−	0.214187i
$835$	−8.47563	−	4.89340i	−0.293311	−	0.169343i
$836$	17.9769	−	15.9561i	0.621743	−	0.551853i
$837$	2.99175	+	5.18186i	0.103410	+	0.179111i
$838$	−1.19395	−	11.3597i	−0.0412442	−	0.392413i
$839$	−36.6006	+	11.8923i	−1.26359	+	0.410566i	−0.862773	−	0.505591i	$-0.831274\pi$
$839$	−36.6006	+	11.8923i	−1.26359	+	0.410566i	−0.400819	+	0.916157i	$0.631274\pi$
$840$	2.36645	+	6.01341i	0.0816503	+	0.207482i
$841$	−4.15164	−	3.01635i	−0.143160	−	0.104012i
$842$	0.719568	+	1.61618i	0.0247979	+	0.0556971i
$843$	−28.8199	+	6.12587i	−0.992611	+	0.210986i
$844$	6.66547	+	6.00161i	0.229435	+	0.206584i
$845$	−62.1302	+	6.53015i	−2.13734	+	0.224644i
$846$	−8.55252			−0.294042
$847$	−7.36796	−	28.1552i	−0.253166	−	0.967423i
$848$	−4.15577			−0.142710
$849$	23.9495	−	2.51719i	0.821944	−	0.0863898i
$850$	−1.10713	−	0.996868i	−0.0379744	−	0.0341923i
$851$	35.4708	−	7.53955i	1.21592	−	0.258452i
$852$	−3.89741	−	8.75372i	−0.133523	−	0.299898i
$853$	44.4431	+	32.2898i	1.52170	+	1.10558i	0.960636	+	0.277811i	$0.0896091\pi$
$853$	44.4431	+	32.2898i	1.52170	+	1.10558i	0.561067	+	0.827770i	$0.310391\pi$
$854$	1.47779	−	1.85657i	0.0505688	−	0.0635307i
$855$	−16.8354	+	5.47015i	−0.575758	+	0.187075i
$856$	−1.49731	−	14.2460i	−0.0511770	−	0.486917i
$857$	−21.7343	−	37.6448i	−0.742428	−	1.28592i	−0.951387	−	0.307998i	$-0.900341\pi$
$857$	−21.7343	−	37.6448i	−0.742428	−	1.28592i	0.208959	−	0.977924i	$-0.432992\pi$
$858$	15.4063	−	13.6745i	0.525964	−	0.466840i
$859$	−1.87385	−	1.08187i	−0.0639351	−	0.0369129i	0.467692	−	0.883892i	$-0.345086\pi$
$859$	−1.87385	−	1.08187i	−0.0639351	−	0.0369129i	−0.531627	+	0.846979i	$0.678419\pi$
$860$	11.3809	−	8.26872i	0.388086	−	0.281961i
$861$	−1.12649	+	25.6067i	−0.0383907	+	0.872675i
$862$	5.78397	−	17.8012i	0.197003	−	0.606312i
$863$	−5.34988	+	2.38192i	−0.182112	+	0.0810815i	−0.495767	−	0.868455i	$-0.665113\pi$
$863$	−5.34988	+	2.38192i	−0.182112	+	0.0810815i	0.313655	+	0.949537i	$0.398446\pi$
$864$	0.104528	−	0.994522i	0.00355613	−	0.0338343i
$865$	−8.41989	−	39.6125i	−0.286285	−	1.34686i
$866$	−27.5794	−	5.86218i	−0.937185	−	0.199205i
$867$	8.59400	+	11.8286i	0.291868	+	0.401721i
$868$	−2.60768	−	15.6146i	−0.0885105	−	0.529994i
$869$	28.9658	−	31.7127i	0.982598	−	1.07578i
$870$	−5.96648	+	10.3342i	−0.202283	+	0.350364i
$871$	67.2383	+	29.9364i	2.27828	+	1.01436i
$872$	3.23039	−	3.58771i	0.109395	−	0.121495i
$873$	1.87472	−	1.68800i	0.0634496	−	0.0571303i
$874$	31.3408	−	43.1370i	1.06012	−	1.45913i
$875$	−26.0215	+	1.58291i	−0.879687	+	0.0535122i
$876$	0.440136	+	0.143009i	0.0148708	+	0.00483182i
$877$	−4.99936	+	23.5202i	−0.168817	+	0.794219i	0.809503	+	0.587116i	$0.199737\pi$
$877$	−4.99936	+	23.5202i	−0.168817	+	0.794219i	−0.978319	+	0.207103i	$0.933596\pi$
$878$	−12.1378	+	27.2618i	−0.409629	+	0.920043i
$879$	−3.21849	+	1.85820i	−0.108557	+	0.0626755i
$880$	8.10071	+	0.0576946i	0.273075	+	0.00194489i
$881$			14.3965i			0.485031i	0.970147	+	0.242516i	$0.0779726\pi$
$881$			14.3965i			0.485031i	−0.970147	+	0.242516i	$0.922027\pi$
$882$	−5.73141	−	4.01882i	−0.192987	−	0.135321i
$883$	12.7206	+	39.1499i	0.428082	+	1.31750i	0.900012	+	0.435864i	$0.143557\pi$
$883$	12.7206	+	39.1499i	0.428082	+	1.31750i	−0.471931	+	0.881636i	$0.656443\pi$
$884$	−6.41024	−	7.11929i	−0.215600	−	0.239448i
$885$	−2.68976	−	0.282705i	−0.0904153	−	0.00950303i
$886$	−5.29002	−	0.556004i	−0.177722	−	0.0186793i
$887$	−21.1974	−	23.5421i	−0.711740	−	0.790467i	0.273459	−	0.961884i	$-0.411832\pi$
$887$	−21.1974	−	23.5421i	−0.711740	−	0.790467i	−0.985199	+	0.171417i	$0.945166\pi$
$888$	−1.52313	−	4.68770i	−0.0511128	−	0.157309i
$889$	−13.9804	+	53.9848i	−0.468889	+	1.81059i
$890$			20.8015i			0.697268i
$891$	1.96852	−	2.66925i	0.0659480	−	0.0894234i
$892$	−6.65321	+	3.84123i	−0.222766	+	0.128614i
$893$	−25.2108	+	56.6244i	−0.843648	+	1.89486i
$894$	−1.19191	+	5.60750i	−0.0398635	+	0.187543i
$895$	−18.1048	−	5.88261i	−0.605177	−	0.196634i
$896$	−1.18131	+	2.36738i	−0.0394648	+	0.0790887i
$897$	26.8594	−	36.9688i	0.896808	−	1.23435i
$898$	−17.1889	+	15.4769i	−0.573601	+	0.516472i
$899$	19.5603	−	21.7240i	0.652374	−	0.724534i
$900$	−0.882385	−	0.392863i	−0.0294128	−	0.0130954i
$901$	−3.20494	+	5.55112i	−0.106772	+	0.184935i
$902$	29.2591	+	13.2775i	0.974222	+	0.442092i
$903$	−5.34121	+	14.2713i	−0.177744	+	0.474921i
$904$	3.16374	+	4.35452i	0.105224	+	0.144829i
$905$	22.9007	+	4.86769i	0.761245	+	0.161808i
$906$	0.521253	+	2.45230i	0.0173175	+	0.0814723i
$907$	−3.35926	+	31.9612i	−0.111542	+	1.06126i	0.785364	+	0.619034i	$0.212476\pi$
$907$	−3.35926	+	31.9612i	−0.111542	+	1.06126i	−0.896906	+	0.442221i	$0.854191\pi$
$908$	22.0071	−	9.79818i	0.730330	−	0.325164i
$909$	−4.62468	+	14.2333i	−0.153391	+	0.472089i
$910$	40.0988	+	1.76403i	1.32926	+	0.0584769i
$911$	−4.78727	+	3.47816i	−0.158609	+	0.115236i	−0.664259	−	0.747502i	$-0.731253\pi$
$911$	−4.78727	+	3.47816i	−0.158609	+	0.115236i	0.505650	+	0.862739i	$0.331253\pi$
$912$	−6.27639	−	3.62368i	−0.207832	−	0.119992i
$913$	15.4252	−	1.51026i	0.510499	−	0.0499823i
$914$	−0.680686	−	1.17898i	−0.0225151	−	0.0389973i
$915$	0.228984	+	2.17864i	0.00756998	+	0.0720235i
$916$	−7.15780	+	2.32571i	−0.236501	+	0.0768437i
$917$	−3.09545	+	20.6654i	−0.102221	+	0.682432i
$918$	−1.24783	−	0.906603i	−0.0411846	−	0.0299224i
$919$	0.746649	+	1.67700i	0.0246297	+	0.0553192i	0.925441	−	0.378891i	$-0.123694\pi$
$919$	0.746649	+	1.67700i	0.0246297	+	0.0553192i	−0.900812	+	0.434210i	$0.857028\pi$
$920$	17.5774	−	3.73619i	0.579510	−	0.123179i
$921$	−18.9388	−	17.0526i	−0.624056	−	0.561902i
$922$	−9.62438	+	1.01156i	−0.316962	+	0.0333140i
$923$	−59.5151			−1.95896
$924$	−7.35321	+	4.78856i	−0.241903	+	0.157532i
$925$	−4.76082			−0.156535
$926$	−25.4914	+	2.67926i	−0.837700	+	0.0880459i
$927$	−9.13629	−	8.22635i	−0.300075	−	0.270189i
$928$	−4.77876	+	1.01576i	−0.156870	+	0.0333438i
$929$	8.09833	+	18.1892i	0.265698	+	0.596767i	0.996291	−	0.0860458i	$-0.0274232\pi$
$929$	8.09833	+	18.1892i	0.265698	+	0.596767i	−0.730593	+	0.682813i	$0.760756\pi$
$930$	11.8236	+	8.59036i	0.387711	+	0.281689i
$931$	−43.5026	+	26.0999i	−1.42574	+	0.855390i
$932$	−10.7395	+	3.48949i	−0.351785	+	0.114302i
$933$	1.77400	+	16.8785i	0.0580782	+	0.552577i
$934$	−7.44625	−	12.8973i	−0.243649	−	0.422012i
$935$	6.32435	−	10.7761i	0.206828	−	0.352417i
$936$	−5.37892	−	3.10552i	−0.175816	−	0.101507i
$937$	45.7830	−	33.2633i	1.49566	−	1.08666i	0.523595	−	0.851967i	$-0.324590\pi$
$937$	45.7830	−	33.2633i	1.49566	−	1.08666i	0.972069	−	0.234697i	$-0.0754097\pi$
$938$	−26.4368	−	16.8544i	−0.863192	−	0.550315i
$939$	4.68789	−	14.4278i	0.152983	−	0.470835i
$940$	−19.0837	+	8.49660i	−0.622441	+	0.277129i
$941$	2.14320	−	20.3911i	0.0698662	−	0.664732i	−0.902407	−	0.430885i	$-0.858202\pi$
$941$	2.14320	−	20.3911i	0.0698662	−	0.664732i	0.972273	−	0.233848i	$-0.0751317\pi$
$942$	−2.09816	−	9.87106i	−0.0683617	−	0.321617i
$943$	69.7175	+	14.8189i	2.27032	+	0.482570i
$944$	−0.650849	−	0.895817i	−0.0211833	−	0.0291564i
$945$	6.37402	−	1.06448i	0.207347	−	0.0346275i
$946$	14.1041	+	12.8825i	0.458565	+	0.418846i
$947$	−12.5514	+	21.7396i	−0.407865	+	0.706443i	−0.994650	−	0.103300i	$-0.967060\pi$
$947$	−12.5514	+	21.7396i	−0.407865	+	0.706443i	0.586785	+	0.809742i	$0.300393\pi$
$948$	−11.8304	−	5.26722i	−0.384232	−	0.171071i
$949$	1.92334	−	2.13609i	0.0624343	−	0.0693403i
$950$	−5.20213	+	4.68402i	−0.168779	+	0.151970i
$951$	7.83144	−	10.7790i	0.253952	−	0.349535i
$952$	2.25123	+	3.40368i	0.0729628	+	0.110314i
$953$	−1.08809	−	0.353541i	−0.0352466	−	0.0114523i	0.291341	−	0.956619i	$-0.405899\pi$
$953$	−1.08809	−	0.353541i	−0.0352466	−	0.0114523i	−0.326587	+	0.945167i	$0.605899\pi$
$954$	−0.864033	+	4.06496i	−0.0279741	+	0.131608i
$955$	−4.00360	+	8.99224i	−0.129554	+	0.290982i
$956$	8.53061	−	4.92515i	0.275900	−	0.159291i
$957$	−15.3743	−	5.11676i	−0.496981	−	0.165401i
$958$			35.4506i			1.14536i
$959$	6.78384	+	24.4932i	0.219062	+	0.790926i
$960$	−0.754779	−	2.32297i	−0.0243604	−	0.0749736i
$961$	−3.21329	−	3.56872i	−0.103654	−	0.115120i
$962$	−30.4462	−	3.20002i	−0.981624	−	0.103173i
$963$	−14.2460	−	1.49731i	−0.459069	−	0.0482501i
$964$	−1.18592	−	1.31709i	−0.0381958	−	0.0424207i
$965$	10.5617	+	32.5055i	0.339992	+	1.04639i
$966$	−13.6480	+	13.8791i	−0.439118	+	0.446554i
$967$			4.91179i			0.157953i	0.996876	+	0.0789763i	$0.0251651\pi$
$967$			4.91179i			0.157953i	−0.996876	+	0.0789763i	$0.974835\pi$
$968$	2.13354	+	10.7911i	0.0685746	+	0.346839i
$969$	−9.68074	+	5.58918i	−0.310990	+	0.179550i
$970$	2.50619	−	5.62899i	0.0804688	−	0.180736i
$971$	4.20665	−	19.7907i	0.134998	−	0.635114i	−0.857666	−	0.514207i	$-0.828086\pi$
$971$	4.20665	−	19.7907i	0.134998	−	0.635114i	0.992664	−	0.120907i	$-0.0385804\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	1.69056	+	27.7911i	0.0541968	+	0.890940i
$974$	17.8560	−	24.5767i	0.572144	−	0.787489i
$975$	−4.45827	+	4.01424i	−0.142779	+	0.128559i
$976$	−0.600128	+	0.666510i	−0.0192096	+	0.0213345i
$977$	11.0894	+	4.93734i	0.354783	+	0.157959i	0.576386	−	0.817177i	$-0.304462\pi$
$977$	11.0894	+	4.93734i	0.354783	+	0.157959i	−0.221603	+	0.975137i	$0.571129\pi$
$978$	0.547988	−	0.949143i	0.0175227	−	0.0303502i
$979$	−27.6697	+	5.67571i	−0.884326	+	0.181396i
$980$	−16.7813	−	3.27347i	−0.536060	−	0.104567i
$981$	−2.83768	−	3.90573i	−0.0906001	−	0.124700i
$982$	11.0682	+	2.35262i	0.353201	+	0.0750751i
$983$	−4.19693	−	19.7450i	−0.133861	−	0.629768i	−0.993009	−	0.118040i	$-0.962339\pi$
$983$	−4.19693	−	19.7450i	−0.133861	−	0.629768i	0.859147	−	0.511728i	$-0.170994\pi$
$984$	1.01265	−	9.63473i	0.0322821	−	0.307144i
$985$	29.2072	−	13.0039i	0.930618	−	0.414338i
$986$	−2.32858	+	7.16664i	−0.0741571	+	0.228232i
$987$	12.1642	−	19.0801i	0.387192	−	0.607327i
$988$	−36.4168	+	26.4584i	−1.15857	+	0.841752i
$989$	36.6965	+	21.1868i	1.16688	+	0.673700i
$990$	1.74067	−	7.91169i	0.0553220	−	0.251450i
$991$	−0.435258	−	0.753888i	−0.0138264	−	0.0239481i	0.859029	−	0.511926i	$-0.171068\pi$
$991$	−0.435258	−	0.753888i	−0.0138264	−	0.0239481i	−0.872856	+	0.487978i	$0.837735\pi$
$992$	0.625445	+	5.95071i	0.0198579	+	0.188935i
$993$	−16.1592	+	5.25043i	−0.512795	+	0.166617i
$994$	25.0722	+	3.75554i	0.795243	+	0.119119i
$995$	−48.0356	−	34.8999i	−1.52283	−	1.10640i
$996$	−1.90072	−	4.26909i	−0.0602267	−	0.135271i
$997$	3.99734	−	0.849660i	0.126597	−	0.0269090i	−0.144177	−	0.989552i	$-0.546054\pi$
$997$	3.99734	−	0.849660i	0.126597	−	0.0269090i	0.270774	+	0.962643i	$0.412720\pi$
$998$	−12.2847	−	11.0612i	−0.388866	−	0.350137i
$999$	−4.90194	+	0.515215i	−0.155091	+	0.0163007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.a.19.1	✓	64
7.3	odd	6		462.2.ba.b.283.5	yes	64
11.7	odd	10		462.2.ba.b.271.5	yes	64
77.73	even	30	inner	462.2.ba.a.73.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.19.1	✓	64	1.1	even	1	trivial
462.2.ba.a.73.1	yes	64	77.73	even	30	inner
462.2.ba.b.271.5	yes	64	11.7	odd	10
462.2.ba.b.283.5	yes	64	7.3	odd	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.993461 - 2.23135i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(2.46197 - 0.968858i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.993461 - 2.23135i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(2.46197 - 0.968858i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(1.22126 + 2.11528i) q^{10} +(-2.48048 + 2.20165i) q^{11} +(0.866025 + 0.500000i) q^{12} +(5.02484 - 3.65076i) q^{13} +(-2.34721 + 1.22090i) q^{14} +(0.754779 - 2.32297i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.161225 - 1.53396i) q^{17} +(-0.207912 - 0.978148i) q^{18} +(-7.08898 - 1.50681i) q^{19} +(-1.43568 - 1.97604i) q^{20} +(2.47790 + 0.927380i) q^{21} +(2.23675 - 2.44886i) q^{22} +(3.67860 - 6.37152i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(-0.646307 + 0.717797i) q^{25} +(-4.61571 + 4.15600i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.20674 - 1.45956i) q^{28} +(4.64640 + 1.50971i) q^{29} +(-0.507828 + 2.38914i) q^{30} +(2.43371 - 5.46619i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.31654 - 0.0236210i) q^{33} +1.54241i q^{34} +(-4.60774 - 4.53100i) q^{35} +(0.309017 + 0.951057i) q^{36} +(3.29811 + 3.66292i) q^{37} +(7.20765 + 0.757555i) q^{38} +(6.17702 + 0.649231i) q^{39} +(1.63436 + 1.81514i) q^{40} +(2.99369 + 9.21364i) q^{41} +(-2.56126 - 0.663290i) q^{42} +5.75946i q^{43} +(-1.96852 + 2.66925i) q^{44} +(2.11528 - 1.22126i) q^{45} +(-2.99244 + 6.72114i) q^{46} +(1.77817 - 8.36563i) q^{47} +(0.951057 + 0.309017i) q^{48} +(5.12263 - 4.77060i) q^{49} +(0.567737 - 0.781422i) q^{50} +(1.14623 - 1.03207i) q^{51} +(4.15600 - 4.61571i) q^{52} +(-3.79648 - 1.69030i) q^{53} +(0.500000 - 0.866025i) q^{54} +(7.37690 + 3.34756i) q^{55} +(-2.04208 + 1.68223i) q^{56} +(-4.25989 - 5.86323i) q^{57} +(-4.77876 - 1.01576i) q^{58} +(-0.230219 - 1.08309i) q^{59} +(0.255313 - 2.42914i) q^{60} +(-0.819338 + 0.364793i) q^{61} +(-1.84900 + 5.69064i) q^{62} +(1.22090 + 2.34721i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-13.1381 - 7.58529i) q^{65} +(3.30084 - 0.323181i) q^{66} +(5.92505 + 10.2625i) q^{67} +(-0.161225 - 1.53396i) q^{68} +(6.99711 - 2.27350i) q^{69} +(5.05611 + 4.02454i) q^{70} +(-7.75211 - 5.63224i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(0.452673 - 0.0962187i) q^{73} +(-3.66292 - 3.29811i) q^{74} +(-0.960600 + 0.100963i) q^{75} -7.24735 q^{76} +(-3.97378 + 7.82362i) q^{77} -6.21105 q^{78} +(-12.8790 + 1.35364i) q^{79} +(-1.81514 - 1.63436i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-3.94038 - 8.85024i) q^{82} +(-3.78062 - 2.74678i) q^{83} +(2.61656 + 0.391931i) q^{84} +(-3.58296 + 1.16418i) q^{85} +(-0.602028 - 5.72791i) q^{86} +(2.44276 + 4.23098i) q^{87} +(1.67873 - 2.86040i) q^{88} +(7.37544 + 4.25821i) q^{89} +(-1.97604 + 1.43568i) q^{90} +(8.83396 - 13.8564i) q^{91} +(2.27350 - 6.99711i) q^{92} +(5.46619 - 2.43371i) q^{93} +(-0.893982 + 8.50567i) q^{94} +(3.68041 + 17.3150i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-1.48280 - 2.04089i) q^{97} +(-4.59590 + 5.27993i) q^{98} +(-2.44886 - 2.23675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 + 10 * q^19 + 20 * q^20 - 4 * q^21 - 2 * q^22 + 4 * q^23 - 8 * q^24 - 12 * q^26 - 10 * q^28 - 20 * q^29 + 18 * q^30 - 16 * q^31 - 14 * q^33 + 42 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 + 18 * q^39 + 18 * q^40 - 28 * q^41 - 6 * q^42 + 6 * q^44 - 12 * q^45 - 42 * q^46 + 24 * q^47 + 116 * q^49 + 26 * q^51 + 32 * q^54 - 14 * q^55 - 4 * q^56 + 20 * q^58 + 30 * q^59 + 2 * q^60 - 32 * q^61 - 8 * q^62 + 4 * q^63 + 16 * q^64 + 12 * q^65 + 4 * q^66 + 16 * q^67 - 30 * q^68 - 20 * q^70 - 24 * q^71 - 64 * q^73 + 4 * q^74 + 12 * q^75 - 48 * q^77 - 60 * q^79 - 18 * q^80 + 8 * q^81 - 68 * q^82 + 8 * q^83 + 2 * q^84 - 80 * q^85 - 18 * q^86 + 10 * q^87 - 8 * q^88 - 24 * q^89 + 4 * q^90 - 172 * q^91 + 8 * q^92 - 104 * q^93 - 6 * q^94 - 118 * q^95 + 8 * q^96 + 120 * q^97 + 40 * q^98 + 8 * q^99

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