LMFDB - Embedded newform 462.2.bc.b.359.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (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:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			359.1
Character	$\chi$	$=$	462.359
Dual form			462.2.bc.b.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 - 0.406737i) q^{2} +(-1.73195 + 0.0186784i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-3.32022 + 0.348969i) q^{5} +(-1.57462 + 0.721511i) q^{6} +(2.29036 + 1.32448i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.99930 - 0.0647000i) q^{9} +O(q^{10})$	\(q+(0.913545 - 0.406737i) q^{2} +(-1.73195 + 0.0186784i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-3.32022 + 0.348969i) q^{5} +(-1.57462 + 0.721511i) q^{6} +(2.29036 + 1.32448i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.99930 - 0.0647000i) q^{9} +(-2.89123 + 1.66925i) q^{10} +(2.51334 + 2.16405i) q^{11} +(-1.14502 + 1.29959i) q^{12} +(1.75434 - 2.41465i) q^{13} +(2.63106 + 0.278398i) q^{14} +(5.74393 - 0.666413i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(2.48929 + 1.10830i) q^{17} +(2.71368 - 1.27903i) q^{18} +(4.68444 - 4.21789i) q^{19} +(-1.96232 + 2.70091i) q^{20} +(-3.99153 - 2.25115i) q^{21} +(3.17625 + 0.954689i) q^{22} +(0.928949 + 0.536329i) q^{23} +(-0.517438 + 1.65295i) q^{24} +(6.01131 - 1.27774i) q^{25} +(0.620548 - 2.91945i) q^{26} +(-5.19343 + 0.168079i) q^{27} +(2.51683 - 0.815820i) q^{28} +(-0.535164 - 1.64707i) q^{29} +(4.97629 - 2.94506i) q^{30} +(-0.527904 + 5.02267i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.39340 - 3.70108i) q^{33} +2.72486 q^{34} +(-8.06669 - 3.59829i) q^{35} +(1.95884 - 2.27221i) q^{36} +(9.83325 + 2.09012i) q^{37} +(2.56388 - 5.75857i) q^{38} +(-2.99334 + 4.21482i) q^{39} +(-0.694114 + 3.26555i) q^{40} +(-3.40181 + 10.4697i) q^{41} +(-4.56207 - 0.433028i) q^{42} +0.998721i q^{43} +(3.28996 - 0.419746i) q^{44} +(-9.93575 + 1.26148i) q^{45} +(1.06678 + 0.112123i) q^{46} +(6.94657 - 6.25472i) q^{47} +(0.199614 + 1.72051i) q^{48} +(3.49151 + 6.06707i) q^{49} +(4.97190 - 3.61230i) q^{50} +(-4.33202 - 1.87303i) q^{51} +(-0.620548 - 2.91945i) q^{52} +(-6.83748 - 0.718649i) q^{53} +(-4.67607 + 2.26591i) q^{54} +(-9.10002 - 6.30803i) q^{55} +(1.96742 - 1.76898i) q^{56} +(-8.03444 + 7.39267i) q^{57} +(-1.15882 - 1.28700i) q^{58} +(-4.43116 - 3.98984i) q^{59} +(3.34820 - 4.71449i) q^{60} +(-10.1752 + 1.06945i) q^{61} +(1.56064 + 4.80315i) q^{62} +(6.95518 + 3.82433i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.98217 + 8.62936i) q^{65} +(-5.51894 - 1.59415i) q^{66} +(1.86083 + 3.22305i) q^{67} +(2.48929 - 1.10830i) q^{68} +(-1.61891 - 0.911544i) q^{69} +(-8.83285 - 0.00618325i) q^{70} +(-0.722902 - 0.994990i) q^{71} +(0.865302 - 2.87250i) q^{72} +(4.44631 + 4.00348i) q^{73} +(9.83325 - 2.09012i) q^{74} +(-10.3874 + 2.32527i) q^{75} -6.30354i q^{76} +(2.89022 + 8.28533i) q^{77} +(-1.02023 + 5.06793i) q^{78} +(-7.00278 - 15.7285i) q^{79} +(0.694114 + 3.26555i) q^{80} +(8.99163 - 0.388110i) q^{81} +(1.15070 + 10.9482i) q^{82} +(9.70645 - 7.05215i) q^{83} +(-4.34379 + 1.45997i) q^{84} +(-8.65173 - 2.81112i) q^{85} +(0.406216 + 0.912377i) q^{86} +(0.957642 + 2.84264i) q^{87} +(2.83480 - 1.72160i) q^{88} +(11.7595 + 6.78938i) q^{89} +(-8.56367 + 5.19365i) q^{90} +(7.21623 - 3.20682i) q^{91} +(1.02016 - 0.331470i) q^{92} +(0.820487 - 8.70887i) q^{93} +(3.80198 - 8.53939i) q^{94} +(-14.0814 + 15.6390i) q^{95} +(0.882151 + 1.49057i) q^{96} +(-2.77243 - 2.01429i) q^{97} +(5.65735 + 4.12242i) q^{98} +(7.67829 + 6.32803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$3$	−1.73195	+	0.0186784i	−0.999942	+	0.0107840i
$3$	−1.73195	+	0.0186784i	−0.999942	+	0.0107840i
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	−3.32022	+	0.348969i	−1.48485	+	0.156064i	−0.811973	−	0.583695i	$-0.801606\pi$
$5$	−3.32022	+	0.348969i	−1.48485	+	0.156064i	−0.672872	+	0.739759i	$0.734940\pi$
$6$	−1.57462	+	0.721511i	−0.642835	+	0.294556i
$7$	2.29036	+	1.32448i	0.865675	+	0.500606i
$7$	2.29036	+	1.32448i	0.865675	+	0.500606i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	2.99930	−	0.0647000i	0.999767	−	0.0215667i
$10$	−2.89123	+	1.66925i	−0.914287	+	0.527864i
$11$	2.51334	+	2.16405i	0.757801	+	0.652485i
$11$	2.51334	+	2.16405i	0.757801	+	0.652485i
$12$	−1.14502	+	1.29959i	−0.330539	+	0.375159i
$13$	1.75434	−	2.41465i	0.486568	−	0.669703i	−0.493183	−	0.869926i	$-0.664167\pi$
$13$	1.75434	−	2.41465i	0.486568	−	0.669703i	0.979750	+	0.200223i	$0.0641666\pi$
$14$	2.63106	+	0.278398i	0.703181	+	0.0744051i
$15$	5.74393	−	0.666413i	1.48308	−	0.172067i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	2.48929	+	1.10830i	0.603740	+	0.268803i	0.685760	−	0.727828i	$-0.259470\pi$
$17$	2.48929	+	1.10830i	0.603740	+	0.268803i	−0.0820190	+	0.996631i	$0.526137\pi$
$18$	2.71368	−	1.27903i	0.639621	−	0.301471i
$19$	4.68444	−	4.21789i	1.07468	−	0.967651i	0.0751208	−	0.997174i	$-0.476066\pi$
$19$	4.68444	−	4.21789i	1.07468	−	0.967651i	0.999564	+	0.0295238i	$0.00939909\pi$
$20$	−1.96232	+	2.70091i	−0.438789	+	0.603941i
$21$	−3.99153	−	2.25115i	−0.871023	−	0.491242i
$22$	3.17625	+	0.954689i	0.677179	+	0.203540i
$23$	0.928949	+	0.536329i	0.193699	+	0.111832i	0.593713	−	0.804677i	$-0.297661\pi$
$23$	0.928949	+	0.536329i	0.193699	+	0.111832i	−0.400014	+	0.916509i	$0.630995\pi$
$24$	−0.517438	+	1.65295i	−0.105622	+	0.337408i
$25$	6.01131	−	1.27774i	1.20226	−	0.255549i
$26$	0.620548	−	2.91945i	0.121699	−	0.572551i
$27$	−5.19343	+	0.168079i	−0.999477	+	0.0323469i
$28$	2.51683	−	0.815820i	0.475636	−	0.154176i
$29$	−0.535164	−	1.64707i	−0.0993775	−	0.305852i	0.888992	−	0.457922i	$-0.151406\pi$
$29$	−0.535164	−	1.64707i	−0.0993775	−	0.305852i	−0.988370	+	0.152070i	$0.951406\pi$
$30$	4.97629	−	2.94506i	0.908541	−	0.537693i
$31$	−0.527904	+	5.02267i	−0.0948143	+	0.902098i	0.838950	+	0.544209i	$0.183170\pi$
$31$	−0.527904	+	5.02267i	−0.0948143	+	0.902098i	−0.933764	+	0.357889i	$0.883497\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.39340	−	3.70108i	−0.764794	−	0.644275i
$34$	2.72486			0.467310
$35$	−8.06669	−	3.59829i	−1.36352	−	0.608222i
$36$	1.95884	−	2.27221i	0.326474	−	0.378701i
$37$	9.83325	+	2.09012i	1.61658	+	0.343614i	0.925376	−	0.379050i	$-0.123749\pi$
$37$	9.83325	+	2.09012i	1.61658	+	0.343614i	0.691200	+	0.722663i	$0.257082\pi$
$38$	2.56388	−	5.75857i	0.415916	−	0.934163i
$39$	−2.99334	+	4.21482i	−0.479317	+	0.674911i
$40$	−0.694114	+	3.26555i	−0.109749	+	0.516329i
$41$	−3.40181	+	10.4697i	−0.531273	+	1.63509i	0.220293	+	0.975434i	$0.429299\pi$
$41$	−3.40181	+	10.4697i	−0.531273	+	1.63509i	−0.751567	+	0.659657i	$0.770701\pi$
$42$	−4.56207	−	0.433028i	−0.703943	−	0.0668176i
$43$			0.998721i			0.152304i	0.997096	+	0.0761518i	$0.0242633\pi$
$43$			0.998721i			0.152304i	−0.997096	+	0.0761518i	$0.975737\pi$
$44$	3.28996	−	0.419746i	0.495980	−	0.0632790i
$45$	−9.93575	+	1.26148i	−1.48113	+	0.188050i
$46$	1.06678	+	0.112123i	0.157288	+	0.0165317i
$47$	6.94657	−	6.25472i	1.01326	−	0.912344i	0.0170973	−	0.999854i	$-0.494558\pi$
$47$	6.94657	−	6.25472i	1.01326	−	0.912344i	0.996164	+	0.0875096i	$0.0278908\pi$
$48$	0.199614	+	1.72051i	0.0288118	+	0.248334i
$49$	3.49151	+	6.06707i	0.498787	+	0.866725i
$50$	4.97190	−	3.61230i	0.703133	−	0.510856i
$51$	−4.33202	−	1.87303i	−0.606604	−	0.262276i
$52$	−0.620548	−	2.91945i	−0.0860545	−	0.404854i
$53$	−6.83748	−	0.718649i	−0.939201	−	0.0987140i	−0.377459	−	0.926026i	$-0.623202\pi$
$53$	−6.83748	−	0.718649i	−0.939201	−	0.0987140i	−0.561742	+	0.827312i	$0.689869\pi$
$54$	−4.67607	+	2.26591i	−0.636333	+	0.308351i
$55$	−9.10002	−	6.30803i	−1.22705	−	0.850575i
$56$	1.96742	−	1.76898i	0.262907	−	0.236389i
$57$	−8.03444	+	7.39267i	−1.06419	+	0.979184i
$58$	−1.15882	−	1.28700i	−0.152160	−	0.168991i
$59$	−4.43116	−	3.98984i	−0.576888	−	0.519432i	0.328227	−	0.944599i	$-0.393549\pi$
$59$	−4.43116	−	3.98984i	−0.576888	−	0.519432i	−0.905115	+	0.425166i	$0.860216\pi$
$60$	3.34820	−	4.71449i	0.432250	−	0.608638i
$61$	−10.1752	+	1.06945i	−1.30280	+	0.136930i	−0.730385	−	0.683035i	$-0.760659\pi$
$61$	−10.1752	+	1.06945i	−1.30280	+	0.136930i	−0.572414	+	0.819965i	$0.693993\pi$
$62$	1.56064	+	4.80315i	0.198201	+	0.610001i
$63$	6.95518	+	3.82433i	0.876270	+	0.481820i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−4.98217	+	8.62936i	−0.617962	+	1.07034i
$66$	−5.51894	−	1.59415i	−0.679335	−	0.196226i
$67$	1.86083	+	3.22305i	0.227336	+	0.393758i	0.957018	−	0.290029i	$-0.0936650\pi$
$67$	1.86083	+	3.22305i	0.227336	+	0.393758i	−0.729681	+	0.683787i	$0.760332\pi$
$68$	2.48929	−	1.10830i	0.301870	−	0.134401i
$69$	−1.61891	−	0.911544i	−0.194894	−	0.109737i
$70$	−8.83285	−	0.00618325i	−1.05573	−	0.000739039i
$71$	−0.722902	−	0.994990i	−0.0857927	−	0.118084i	0.763963	−	0.645260i	$-0.223251\pi$
$71$	−0.722902	−	0.994990i	−0.0857927	−	0.118084i	−0.849756	+	0.527176i	$0.823251\pi$
$72$	0.865302	−	2.87250i	0.101977	−	0.338527i
$73$	4.44631	+	4.00348i	0.520402	+	0.468572i	0.886975	−	0.461817i	$-0.152802\pi$
$73$	4.44631	+	4.00348i	0.520402	+	0.468572i	−0.366573	+	0.930389i	$0.619469\pi$
$74$	9.83325	−	2.09012i	1.14309	−	0.242972i
$75$	−10.3874	+	2.32527i	−1.19944	+	0.268499i
$76$		−	6.30354i		−	0.723066i
$77$	2.89022	+	8.28533i	0.329371	+	0.944200i
$78$	−1.02023	+	5.06793i	−0.115518	+	0.573830i
$79$	−7.00278	−	15.7285i	−0.787874	−	1.76959i	−0.621312	−	0.783564i	$-0.713400\pi$
$79$	−7.00278	−	15.7285i	−0.787874	−	1.76959i	−0.166563	−	0.986031i	$-0.553267\pi$
$80$	0.694114	+	3.26555i	0.0776043	+	0.365100i
$81$	8.99163	−	0.388110i	0.999070	−	0.0431233i
$82$	1.15070	+	10.9482i	0.127074	+	1.20902i
$83$	9.70645	−	7.05215i	1.06542	−	0.774073i	0.0903372	−	0.995911i	$-0.471206\pi$
$83$	9.70645	−	7.05215i	1.06542	−	0.774073i	0.975084	+	0.221838i	$0.0712055\pi$
$84$	−4.34379	+	1.45997i	−0.473946	+	0.159296i
$85$	−8.65173	−	2.81112i	−0.938412	−	0.304908i
$86$	0.406216	+	0.912377i	0.0438034	+	0.0983841i
$87$	0.957642	+	2.84264i	0.102670	+	0.304763i
$88$	2.83480	−	1.72160i	0.302191	−	0.183523i
$89$	11.7595	+	6.78938i	1.24651	+	0.719673i	0.970412	−	0.241457i	$-0.0776252\pi$
$89$	11.7595	+	6.78938i	1.24651	+	0.719673i	0.276098	+	0.961129i	$0.410959\pi$
$90$	−8.56367	+	5.19365i	−0.902690	+	0.547459i
$91$	7.21623	−	3.20682i	0.756467	−	0.336166i
$92$	1.02016	−	0.331470i	0.106359	−	0.0345581i
$93$	0.820487	−	8.70887i	0.0850806	−	0.903068i
$94$	3.80198	−	8.53939i	0.392145	−	0.880771i
$95$	−14.0814	+	15.6390i	−1.44473	+	1.60453i
$96$	0.882151	+	1.49057i	0.0900342	+	0.152131i
$97$	−2.77243	−	2.01429i	−0.281498	−	0.204520i	0.438073	−	0.898940i	$-0.355661\pi$
$97$	−2.77243	−	2.01429i	−0.281498	−	0.204520i	−0.719571	+	0.694419i	$0.755661\pi$
$98$	5.65735	+	4.12242i	0.571479	+	0.416427i
$99$	7.67829	+	6.32803i	0.771697	+	0.635990i
$100$	3.07280	−	5.32225i	0.307280	−	0.532225i
$101$	0.933886	−	8.88533i	0.0929251	−	0.884123i	−0.844411	−	0.535696i	$-0.820049\pi$
$101$	0.933886	−	8.88533i	0.0929251	−	0.884123i	0.937336	−	0.348427i	$-0.113284\pi$
$102$	−4.71933	+	0.0508960i	−0.467283	+	0.00503945i
$103$	10.1931	+	2.16662i	1.00436	+	0.213483i	0.680600	−	0.732656i	$-0.261719\pi$
$103$	10.1931	+	2.16662i	1.00436	+	0.213483i	0.323761	+	0.946139i	$0.395053\pi$
$104$	−1.75434	−	2.41465i	−0.172028	−	0.236776i
$105$	14.0383	+	6.08139i	1.37000	+	0.593483i
$106$	−6.53865	+	2.12454i	−0.635090	+	0.206353i
$107$	−10.2173	−	11.3475i	−0.987744	−	1.09700i	−0.995282	−	0.0970289i	$-0.969066\pi$
$107$	−10.2173	−	11.3475i	−0.987744	−	1.09700i	0.00753794	−	0.999972i	$-0.497601\pi$
$108$	−3.35018	+	3.97194i	−0.322371	+	0.382200i
$109$	−8.40092	+	4.85027i	−0.804662	+	0.464572i	−0.845099	−	0.534610i	$-0.820458\pi$
$109$	−8.40092	+	4.85027i	−0.804662	+	0.464572i	0.0404368	+	0.999182i	$0.487125\pi$
$110$	−10.8790	−	2.06136i	−1.03727	−	0.196543i
$111$	−17.0697	−	3.43632i	−1.62019	−	0.326161i
$112$	1.07782	−	2.41626i	0.101844	−	0.228315i
$113$	−9.74475	−	3.16626i	−0.916709	−	0.297857i	−0.187593	−	0.982247i	$-0.560069\pi$
$113$	−9.74475	−	3.16626i	−0.916709	−	0.297857i	−0.729116	+	0.684390i	$0.760069\pi$
$114$	−4.33295	+	10.0214i	−0.405818	+	0.938594i
$115$	−3.27147	−	1.45655i	−0.305067	−	0.135824i
$116$	−1.58210	−	0.704397i	−0.146895	−	0.0654017i
$117$	5.10558	−	7.35577i	0.472011	−	0.680041i
$118$	−5.67088	−	1.84258i	−0.522047	−	0.169623i
$119$	4.23344	+	5.83542i	0.388079	+	0.534932i
$120$	1.14118	−	5.66873i	0.104175	−	0.517482i
$121$	1.63378	+	10.8780i	0.148525	+	0.988909i
$122$	−8.86051	+	5.11562i	−0.802193	+	0.463146i
$123$	5.69621	−	18.1965i	0.513610	−	1.64073i
$124$	3.37933	+	3.75313i	0.303473	+	0.337041i
$125$	−3.63743	+	1.18187i	−0.325342	+	0.105710i
$126$	7.90937	+	0.664771i	0.704622	+	0.0592225i
$127$	−8.86744	−	12.2050i	−0.786858	−	1.08302i	−0.994492	−	0.104811i	$-0.966576\pi$
$127$	−8.86744	−	12.2050i	−0.786858	−	1.08302i	0.207634	−	0.978207i	$-0.433424\pi$
$128$	−0.978148	−	0.207912i	−0.0864569	−	0.0183770i
$129$	−0.0186545	−	1.72973i	−0.00164244	−	0.152295i
$130$	−1.04156	+	9.90974i	−0.0913505	+	0.869142i
$131$	−1.43436	+	2.48439i	−0.125321	+	0.217062i	−0.921858	−	0.387527i	$-0.873329\pi$
$131$	−1.43436	+	2.48439i	−0.125321	+	0.217062i	0.796537	+	0.604589i	$0.206663\pi$
$132$	−5.69020	+	0.788429i	−0.495268	+	0.0686240i
$133$	16.3156	−	3.45605i	1.41474	−	0.299677i
$134$	3.01088	+	2.18753i	0.260101	+	0.188974i
$135$	17.1847	−	2.37041i	1.47902	−	0.204012i
$136$	1.82329	−	2.02497i	0.156346	−	0.173640i
$137$	−1.92954	+	4.33381i	−0.164852	+	0.370263i	−0.977016	−	0.213166i	$-0.931623\pi$
$137$	−1.92954	+	4.33381i	−0.164852	+	0.370263i	0.812164	+	0.583429i	$0.198289\pi$
$138$	−1.84971	−	0.174266i	−0.157458	−	0.0148345i
$139$	−10.7864	+	3.50472i	−0.914891	+	0.297266i	−0.728369	−	0.685185i	$-0.759721\pi$
$139$	−10.7864	+	3.50472i	−0.914891	+	0.297266i	−0.186522	+	0.982451i	$0.559721\pi$
$140$	−8.07172	+	3.58699i	−0.682185	+	0.303156i
$141$	−11.9143	+	10.9626i	−1.00336	+	0.923218i
$142$	−1.06510	−	0.614937i	−0.0893815	−	0.0516044i
$143$	9.63469	−	2.27235i	0.805693	−	0.190023i
$144$	−0.377858	−	2.97611i	−0.0314882	−	0.248009i
$145$	2.35163	+	5.28186i	0.195293	+	0.438634i
$146$	5.69027	+	1.84888i	0.470930	+	0.153014i
$147$	−6.16044	−	10.4427i	−0.508105	−	0.861295i
$148$	8.13299	−	5.90896i	0.668528	−	0.485714i
$149$	−0.537142	−	5.11056i	−0.0440044	−	0.418674i	−0.994243	−	0.107150i	$-0.965827\pi$
$149$	−0.537142	−	5.11056i	−0.0440044	−	0.418674i	0.950238	−	0.311523i	$-0.100839\pi$
$150$	−8.54362	+	6.34919i	−0.697583	+	0.518409i
$151$	1.78735	+	8.40882i	0.145453	+	0.684300i	0.989081	+	0.147373i	$0.0470817\pi$
$151$	1.78735	+	8.40882i	0.145453	+	0.684300i	−0.843628	+	0.536927i	$0.819585\pi$
$152$	−2.56388	−	5.75857i	−0.207958	−	0.467082i
$153$	7.53783	+	3.16307i	0.609397	+	0.255719i
$154$	6.01030	+	6.39346i	0.484323	+	0.515200i
$155$		−	16.8606i		−	1.35427i
$156$	1.12929	+	5.04475i	0.0904154	+	0.403903i
$157$	−16.4611	+	3.49892i	−1.31374	+	0.279244i	−0.810925	−	0.585151i	$-0.801035\pi$
$157$	−16.4611	+	3.49892i	−1.31374	+	0.279244i	−0.502814	+	0.864394i	$0.667702\pi$
$158$	−12.7947	−	11.5204i	−1.01789	−	0.916515i
$159$	11.8556	+	1.11695i	0.940211	+	0.0885799i
$160$	1.96232	+	2.70091i	0.155135	+	0.213525i
$161$	1.41727	+	2.45876i	0.111697	+	0.193778i
$162$	8.05640	−	4.01178i	0.632971	−	0.315195i
$163$	5.64118	−	2.51161i	0.441851	−	0.196725i	−0.173738	−	0.984792i	$-0.555585\pi$
$163$	5.64118	−	2.51161i	0.441851	−	0.196725i	0.615589	+	0.788067i	$0.288918\pi$
$164$	5.50424	+	9.53363i	0.429809	+	0.744451i
$165$	15.8786	+	10.7552i	1.23615	+	0.837293i
$166$	5.99891	−	10.3904i	0.465606	−	0.806453i
$167$	0.650095	+	0.472322i	0.0503059	+	0.0365494i	0.612654	−	0.790351i	$-0.290102\pi$
$167$	0.650095	+	0.472322i	0.0503059	+	0.0365494i	−0.562348	+	0.826901i	$0.690102\pi$
$168$	−3.37442	+	3.10053i	−0.260342	+	0.239211i
$169$	1.26442	+	3.89149i	0.0972631	+	0.299345i
$170$	−9.04713	+	0.950892i	−0.693883	+	0.0729301i
$171$	13.7772	−	12.9538i	1.05357	−	0.990603i
$172$	0.742194	+	0.668275i	0.0565918	+	0.0509555i
$173$	13.7475	+	15.2682i	1.04520	+	1.16082i	0.986704	+	0.162529i	$0.0519652\pi$
$173$	13.7475	+	15.2682i	1.04520	+	1.16082i	0.0585004	+	0.998287i	$0.481368\pi$
$174$	2.03105	+	2.20737i	0.153974	+	0.167340i
$175$	15.4604	+	5.03536i	1.16870	+	0.380638i
$176$	1.88948	−	2.72578i	0.142425	−	0.205463i
$177$	7.74907	+	6.82743i	0.582456	+	0.513181i
$178$	13.5044	+	1.41937i	1.01220	+	0.106386i
$179$	1.38101	+	6.49716i	0.103222	+	0.485621i	0.999142	+	0.0414063i	$0.0131838\pi$
$179$	1.38101	+	6.49716i	0.103222	+	0.485621i	−0.895921	+	0.444214i	$0.853483\pi$
$180$	−5.71085	+	8.22780i	−0.425662	+	0.613264i
$181$	−9.87038	+	7.17125i	−0.733660	+	0.533035i	−0.890719	−	0.454554i	$-0.849799\pi$
$181$	−9.87038	+	7.17125i	−0.733660	+	0.533035i	0.157060	+	0.987589i	$0.449799\pi$
$182$	5.28803	−	5.86469i	0.391975	−	0.434719i
$183$	17.6029	−	2.04230i	1.30125	−	0.150971i
$184$	0.797141	−	0.717749i	0.0587660	−	0.0529131i
$185$	−33.3779	−	3.50816i	−2.45399	−	0.257925i
$186$	−2.79266	−	8.28967i	−0.204768	−	0.607828i
$187$	3.85801	+	8.17248i	0.282126	+	0.597631i
$188$		−	9.34753i		−	0.681739i
$189$	−12.1175	−	6.49363i	−0.881415	−	0.472342i
$190$	−6.50307	+	20.0144i	−0.471783	+	1.45200i
$191$	−0.375896	+	1.76845i	−0.0271989	+	0.127961i	−0.989652	−	0.143486i	$-0.954169\pi$
$191$	−0.375896	+	1.76845i	−0.0271989	+	0.127961i	0.962453	+	0.271447i	$0.0875021\pi$
$192$	1.41216	+	1.00290i	0.101914	+	0.0723783i
$193$	−1.41399	+	3.17587i	−0.101781	+	0.228604i	−0.957257	−	0.289238i	$-0.906598\pi$
$193$	−1.41399	+	3.17587i	−0.101781	+	0.228604i	0.855476	+	0.517842i	$0.173265\pi$
$194$	−3.35203	−	0.712496i	−0.240662	−	0.0511542i
$195$	8.46768	−	15.0387i	0.606383	−	1.07694i
$196$	6.84499	+	1.46497i	0.488928	+	0.104640i
$197$	−2.52468			−0.179876			−0.0899379	−	0.995947i	$-0.528667\pi$
$197$	−2.52468			−0.179876			−0.0899379	+	0.995947i	$0.528667\pi$
$198$	9.58830	+	2.65790i	0.681411	+	0.188889i
$199$	−7.25141	−	12.5598i	−0.514039	−	0.890342i	−0.999867	−	0.0162876i	$-0.994815\pi$
$199$	−7.25141	−	12.5598i	−0.514039	−	0.890342i	0.485828	−	0.874054i	$-0.338518\pi$
$200$	0.642391	−	6.11194i	0.0454239	−	0.432180i
$201$	−3.28306	−	5.54740i	−0.231569	−	0.391284i
$202$	−2.76084	−	8.49700i	−0.194252	−	0.597847i
$203$	0.955785	−	4.48119i	0.0670830	−	0.314518i
$204$	−4.29062	+	1.96602i	−0.300403	+	0.137649i
$205$	7.64114	−	35.9488i	0.533681	−	2.51077i
$206$	10.1931	−	2.16662i	0.710190	−	0.150956i
$207$	2.82090	+	1.54851i	0.196066	+	0.107629i
$208$	−2.58480	−	1.49233i	−0.179224	−	0.103475i
$209$	20.9013	−	0.463638i	1.44578	−	0.0320705i
$210$	15.2982	−	0.154274i	1.05567	−	0.0106459i
$211$	1.03651	−	1.42663i	0.0713564	−	0.0982136i	−0.771847	−	0.635808i	$-0.780667\pi$
$211$	1.03651	−	1.42663i	0.0713564	−	0.0982136i	0.843203	+	0.537595i	$0.180667\pi$
$212$	−5.10923	+	4.60037i	−0.350903	+	0.315955i
$213$	1.27062	+	1.70977i	0.0870611	+	0.117152i
$214$	−13.9494	−	6.21067i	−0.953561	−	0.424553i
$215$	−0.348522	−	3.31597i	−0.0237690	−	0.226147i
$216$	−1.44501	+	4.99119i	−0.0983202	+	0.339607i
$217$	−7.86151	+	10.8045i	−0.533674	+	0.733459i
$218$	−5.70184	+	7.84790i	−0.386177	+	0.531527i
$219$	−7.77557	−	6.85077i	−0.525424	−	0.462932i
$220$	−10.7769	+	2.54174i	−0.726578	+	0.171364i
$221$	7.04322	−	4.06641i	0.473778	−	0.273536i
$222$	−16.9917	+	3.80366i	−1.14041	+	0.255285i
$223$	4.13231	−	12.7179i	0.276720	−	0.851656i	−0.712040	−	0.702139i	$-0.752228\pi$
$223$	4.13231	−	12.7179i	0.276720	−	0.851656i	0.988759	−	0.149516i	$-0.0477716\pi$
$224$	0.00185210	−	2.64575i	0.000123749	−	0.176777i
$225$	17.9471	−	4.22127i	1.19647	−	0.281418i
$226$	−10.1901	+	1.07102i	−0.677836	+	0.0712434i
$227$	4.22526	−	4.69262i	0.280440	−	0.311460i	−0.586424	−	0.810004i	$-0.699465\pi$
$227$	4.22526	−	4.69262i	0.280440	−	0.311460i	0.866865	+	0.498544i	$0.166132\pi$
$228$	0.117740	+	10.9174i	0.00779751	+	0.723024i
$229$	−8.92949	+	3.97566i	−0.590077	+	0.262719i	−0.679979	−	0.733231i	$-0.738011\pi$
$229$	−8.92949	+	3.97566i	−0.590077	+	0.262719i	0.0899021	+	0.995951i	$0.471345\pi$
$230$	−3.58107			−0.236129
$231$	−5.16048	−	14.2958i	−0.339535	−	0.940594i
$232$	−1.73183			−0.113700
$233$	0.457257	−	0.203584i	0.0299559	−	0.0133372i	−0.391704	−	0.920091i	$-0.628114\pi$
$233$	0.457257	−	0.203584i	0.0299559	−	0.0133372i	0.421660	+	0.906754i	$0.361448\pi$
$234$	1.67232	−	8.79645i	0.109323	−	0.575042i
$235$	−20.8814	+	23.1911i	−1.36215	+	1.51282i
$236$	−5.93005	+	0.623274i	−0.386013	+	0.0405717i
$237$	12.4222	+	27.1102i	0.806912	+	1.76100i
$238$	6.24092	+	3.60902i	0.404539	+	0.233938i
$239$	0.201722	−	0.620837i	0.0130483	−	0.0401586i	−0.944320	−	0.329027i	$-0.893279\pi$
$239$	0.201722	−	0.620837i	0.0130483	−	0.0401586i	0.957369	+	0.288869i	$0.0932791\pi$
$240$	−1.26317	−	5.64280i	−0.0815370	−	0.364241i
$241$	3.93195	−	2.27011i	0.253279	−	0.146231i	−0.367986	−	0.929831i	$-0.619953\pi$
$241$	3.93195	−	2.27011i	0.253279	−	0.146231i	0.621265	+	0.783601i	$0.286619\pi$
$242$	5.91701	+	9.27302i	0.380360	+	0.596093i
$243$	−15.5658	+	0.840136i	−0.998547	+	0.0538947i
$244$	−6.01377	+	8.27724i	−0.384992	+	0.529896i
$245$	−13.7098	−	18.9256i	−0.875886	−	1.20911i
$246$	−2.19745	−	18.9402i	−0.140104	−	1.20758i
$247$	−1.96660	−	18.7109i	−0.125132	−	1.19055i
$248$	4.61371	+	2.05416i	0.292971	+	0.130439i
$249$	−16.6794	+	12.3953i	−1.05701	+	0.785518i
$250$	−2.84225	+	2.55917i	−0.179760	+	0.161856i
$251$	−11.5950	+	15.9591i	−0.731869	+	1.00733i	0.267176	+	0.963648i	$0.413909\pi$
$251$	−11.5950	+	15.9591i	−0.731869	+	1.00733i	−0.999045	+	0.0436839i	$0.986091\pi$
$252$	7.49595	−	2.60973i	0.472201	−	0.164398i
$253$	1.17413	+	3.35827i	0.0738166	+	0.211133i
$254$	−13.0650	−	7.54309i	−0.819772	−	0.473296i
$255$	15.0369	+	4.70711i	0.941645	+	0.294771i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	0.935775	−	4.40247i	0.0583720	−	0.274619i	−0.939276	−	0.343162i	$-0.888502\pi$
$257$	0.935775	−	4.40247i	0.0583720	−	0.274619i	0.997648	+	0.0685436i	$0.0218352\pi$
$258$	−0.720588	−	1.57260i	−0.0448619	−	0.0979060i
$259$	19.7534	+	17.8111i	1.22741	+	1.10673i
$260$	3.07915	+	9.47664i	0.190961	+	0.587716i
$261$	−1.71168	−	4.90542i	−0.105951	−	0.303638i
$262$	−0.299863	+	2.85301i	−0.0185256	+	0.176260i
$263$	9.14930	+	15.8471i	0.564170	+	0.977172i	0.997126	+	0.0757566i	$0.0241372\pi$
$263$	9.14930	+	15.8471i	0.564170	+	0.977172i	−0.432956	+	0.901415i	$0.642529\pi$
$264$	−4.87757	+	3.03468i	−0.300194	+	0.186772i
$265$	22.9527			1.40997
$266$	13.4993	−	9.79340i	0.827696	−	0.600472i
$267$	−20.4938	−	11.5392i	−1.25420	−	0.706188i
$268$	3.64033	+	0.773776i	0.222368	+	0.0472659i
$269$	12.9511	−	29.0886i	0.789641	−	1.77356i	0.175310	−	0.984513i	$-0.443907\pi$
$269$	12.9511	−	29.0886i	0.789641	−	1.77356i	0.614331	−	0.789049i	$-0.289426\pi$
$270$	14.7348	−	9.15510i	0.896734	−	0.557162i
$271$	1.23587	−	5.81433i	0.0750740	−	0.353195i	−0.924537	−	0.381093i	$-0.875548\pi$
$271$	1.23587	−	5.81433i	0.0750740	−	0.353195i	0.999611	+	0.0278974i	$0.00888117\pi$
$272$	0.842029	−	2.59150i	0.0510555	−	0.157133i
$273$	−12.4383	+	5.68885i	−0.752798	+	0.344305i
$274$			4.74395i			0.286593i
$275$	17.8736	+	9.79737i	1.07782	+	0.590804i
$276$	−1.76067	+	0.593144i	−0.105980	+	0.0357031i
$277$	2.66540	+	0.280145i	0.160148	+	0.0168323i	0.184263	−	0.982877i	$-0.441010\pi$
$277$	2.66540	+	0.280145i	0.160148	+	0.0168323i	−0.0241150	+	0.999709i	$0.507677\pi$
$278$	−8.42838	+	7.58894i	−0.505500	+	0.455155i
$279$	−1.25838	+	15.0987i	−0.0753370	+	0.903933i
$280$	−5.91492	+	6.55995i	−0.353484	+	0.392032i
$281$	−15.7119	+	11.4154i	−0.937294	+	0.680984i	−0.947768	−	0.318961i	$-0.896666\pi$
$281$	−15.7119	+	11.4154i	−0.937294	+	0.680984i	0.0104735	+	0.999945i	$0.496666\pi$
$282$	−6.42534	+	14.8608i	−0.382624	+	0.884949i
$283$	−3.32141	−	15.6260i	−0.197437	−	0.928869i	−0.959575	−	0.281454i	$-0.909183\pi$
$283$	−3.32141	−	15.6260i	−0.197437	−	0.928869i	0.762137	−	0.647415i	$-0.224150\pi$
$284$	−1.22314	−	0.128557i	−0.0725799	−	0.00762845i
$285$	24.0963	−	27.3490i	1.42734	−	1.62002i
$286$	7.87748	−	5.99467i	0.465805	−	0.354473i
$287$	−21.6583	+	19.4737i	−1.27845	+	1.14950i
$288$	−1.55568	−	2.56512i	−0.0916695	−	0.151151i
$289$	−6.40701	−	7.11570i	−0.376883	−	0.418571i
$290$	4.29665	+	3.86872i	0.252308	+	0.227179i
$291$	4.83934	+	3.43687i	0.283687	+	0.201473i
$292$	5.95033	−	0.625405i	0.348217	−	0.0365990i
$293$	3.37442	+	10.3854i	0.197136	+	0.606722i	0.999945	+	0.0104858i	$0.00333781\pi$
$293$	3.37442	+	10.3854i	0.197136	+	0.606722i	−0.802809	+	0.596236i	$0.796662\pi$
$294$	−9.87525	−	7.03416i	−0.575936	−	0.410240i
$295$	16.1047	+	11.7008i	0.937654	+	0.681246i
$296$	5.02647	−	8.70609i	0.292157	−	0.506031i
$297$	−13.4166	−	10.8164i	−0.778511	−	0.627632i
$298$	−2.56936	−	4.45026i	−0.148839	−	0.257796i
$299$	2.92474	−	1.30218i	0.169142	−	0.0753070i
$300$	−5.22253	+	9.27527i	−0.301523	+	0.535508i
$301$	−1.32279	+	2.28743i	−0.0762441	+	0.131845i
$302$	5.05300	+	6.95486i	0.290768	+	0.400207i
$303$	−1.45148	+	15.4064i	−0.0833853	+	0.885074i
$304$	−4.68444	−	4.21789i	−0.268671	−	0.241913i
$305$	33.4106	−	7.10164i	1.91309	−	0.406639i
$306$	8.17269	−	0.176299i	0.467201	−	0.0100783i
$307$		−	12.4401i		−	0.709997i	−0.934867	−	0.354998i	$-0.884481\pi$
$307$		−	12.4401i		−	0.709997i	0.934867	−	0.354998i	$-0.115519\pi$
$308$	8.09113	+	3.39611i	0.461035	+	0.193511i
$309$	−17.6945	−	3.56209i	−1.00660	−	0.202640i
$310$	−6.85781	−	15.4029i	−0.389497	−	0.874825i
$311$	0.775212	+	3.64709i	0.0439582	+	0.206807i	0.994646	−	0.103343i	$-0.0329539\pi$
$311$	0.775212	+	3.64709i	0.0439582	+	0.206807i	−0.950688	+	0.310150i	$0.899621\pi$
$312$	3.08354	+	4.14928i	0.174571	+	0.234907i
$313$	1.04624	+	9.95430i	0.0591369	+	0.562650i	0.983471	+	0.181066i	$0.0579548\pi$
$313$	1.04624	+	9.95430i	0.0591369	+	0.562650i	−0.924334	+	0.381584i	$0.875379\pi$
$314$	−13.6148	+	9.89175i	−0.768329	+	0.558224i
$315$	−24.4273	−	10.2705i	−1.37632	−	0.578674i
$316$	−16.3743	−	5.32034i	−0.921128	−	0.299293i
$317$	−8.87954	−	19.9438i	−0.498725	−	1.12015i	−0.971082	−	0.238747i	$-0.923263\pi$
$317$	−8.87954	−	19.9438i	−0.498725	−	1.12015i	0.472357	−	0.881407i	$-0.343403\pi$
$318$	11.2849	−	3.80172i	0.632828	−	0.213190i
$319$	2.21928	−	5.29776i	0.124256	−	0.296618i
$320$	2.89123	+	1.66925i	0.161625	+	0.0933140i
$321$	17.9078	+	19.4624i	0.999516	+	1.08628i
$322$	2.29481	+	1.66973i	0.127885	+	0.0930506i
$323$	16.3356	−	5.30776i	0.908938	−	0.295332i
$324$	5.72815	−	6.94178i	0.318231	−	0.385654i
$325$	7.46061	−	16.7568i	0.413840	−	0.929501i
$326$	4.13191	−	4.58895i	0.228845	−	0.254158i
$327$	14.4594	−	8.55734i	0.799605	−	0.473222i
$328$	8.90605	+	6.47062i	0.491754	+	0.357280i
$329$	24.1944	−	5.12498i	1.33388	−	0.282549i
$330$	18.8804	+	3.36697i	1.03933	+	0.185346i
$331$	−11.7817	+	20.4066i	−0.647582	+	1.12165i	0.336116	+	0.941821i	$0.390887\pi$
$331$	−11.7817	+	20.4066i	−0.647582	+	1.12165i	−0.983699	+	0.179825i	$0.942447\pi$
$332$	1.25411	−	11.9321i	0.0688285	−	0.654859i
$333$	29.6281	+	5.63270i	1.62361	+	0.308670i
$334$	0.786002	+	0.167070i	0.0430081	+	0.00914166i
$335$	−7.30309	−	10.0518i	−0.399011	−	0.549191i
$336$	−1.82159	+	4.20497i	−0.0993759	+	0.229400i
$337$	13.0031	−	4.22496i	0.708324	−	0.230148i	0.0673702	−	0.997728i	$-0.478539\pi$
$337$	13.0031	−	4.22496i	0.708324	−	0.230148i	0.640954	+	0.767580i	$0.278539\pi$
$338$	2.73791	+	3.04076i	0.148923	+	0.165396i
$339$	16.9366	+	5.30179i	0.919868	+	0.287954i
$340$	−7.87820	+	4.54848i	−0.427256	+	0.246676i
$341$	−12.1961	+	11.4813i	−0.660456	+	0.621746i
$342$	7.31727	−	17.4376i	0.395673	−	0.942916i
$343$	−0.0388941	+	18.5202i	−0.00210008	+	0.999998i
$344$	0.949840	+	0.308622i	0.0512119	+	0.0166398i
$345$	5.69324	+	2.46157i	0.306514	+	0.132527i
$346$	18.7691	+	8.35654i	1.00903	+	0.449250i
$347$	6.62864	+	2.95126i	0.355844	+	0.158432i	0.576870	−	0.816836i	$-0.304274\pi$
$347$	6.62864	+	2.95126i	0.355844	+	0.158432i	−0.221026	+	0.975268i	$0.570941\pi$
$348$	2.75328	+	1.19043i	0.147591	+	0.0638138i
$349$	−13.9076	−	4.51886i	−0.744458	−	0.241889i	−0.0878629	−	0.996133i	$-0.528004\pi$
$349$	−13.9076	−	4.51886i	−0.744458	−	0.241889i	−0.656595	+	0.754244i	$0.728004\pi$
$350$	16.1719	−	1.68829i	0.864423	−	0.0902427i
$351$	−8.70522	+	12.8352i	−0.464650	+	0.685091i
$352$	0.617451	−	3.25864i	0.0329102	−	0.173686i
$353$	5.90086	−	3.40686i	0.314071	−	0.181329i	−0.334676	−	0.942333i	$-0.608627\pi$
$353$	5.90086	−	3.40686i	0.314071	−	0.181329i	0.648747	+	0.761004i	$0.275293\pi$
$354$	9.85610	+	3.08533i	0.523846	+	0.163984i
$355$	2.74741	+	3.05131i	0.145817	+	0.161947i
$356$	12.9142	−	4.19607i	0.684449	−	0.222391i
$357$	−7.44111	−	10.0276i	−0.393825	−	0.530716i
$358$	3.90425	+	5.37374i	0.206346	+	0.284011i
$359$	6.94845	+	1.47694i	0.366725	+	0.0779498i	0.387589	−	0.921832i	$-0.373308\pi$
$359$	6.94845	+	1.47694i	0.366725	+	0.0779498i	−0.0208633	+	0.999782i	$0.506641\pi$
$360$	−1.87058	+	9.83928i	−0.0985880	+	0.518576i
$361$	2.16736	−	20.6210i	0.114071	−	1.08532i
$362$	−6.10023	+	10.5659i	−0.320621	+	0.555332i
$363$	−3.03281	−	18.8096i	−0.159181	−	0.987249i
$364$	2.44547	−	7.50849i	0.128177	−	0.393552i
$365$	−16.1598	−	11.7408i	−0.845843	−	0.614541i
$366$	15.2504	−	9.02549i	0.797151	−	0.471770i
$367$	−5.87201	+	6.52153i	−0.306516	+	0.340421i	−0.876648	−	0.481132i	$-0.840226\pi$
$367$	−5.87201	+	6.52153i	−0.306516	+	0.340421i	0.570131	+	0.821554i	$0.306892\pi$
$368$	0.436290	−	0.979922i	0.0227432	−	0.0510820i
$369$	−9.52566	+	31.6219i	−0.495886	+	1.64617i
$370$	−31.9191	+	10.3712i	−1.65940	+	0.539171i
$371$	−14.7085	−	10.7021i	−0.763626	−	0.555624i
$372$	−5.92294	−	6.43711i	−0.307090	−	0.333749i
$373$	5.86734	+	3.38751i	0.303799	+	0.175399i	0.644148	−	0.764901i	$-0.277212\pi$
$373$	5.86734	+	3.38751i	0.303799	+	0.175399i	−0.340349	+	0.940299i	$0.610545\pi$
$374$	6.84851	+	5.89674i	0.354128	+	0.304913i
$375$	6.27778	−	2.11489i	0.324183	−	0.109212i
$376$	−3.80198	−	8.53939i	−0.196072	−	0.440385i
$377$	−4.91595	−	1.59729i	−0.253184	−	0.0822645i
$378$	−13.7110	−	1.00362i	−0.705220	−	0.0516204i
$379$	−25.4883	+	18.5184i	−1.30925	+	0.951224i	−0.309247	+	0.950982i	$0.600077\pi$
$379$	−25.4883	+	18.5184i	−1.30925	+	0.951224i	−1.00000		0.000242201i	$0.999923\pi$
$380$	2.19974	+	20.9291i	0.112844	+	1.07364i
$381$	15.5859	+	20.9728i	0.798492	+	1.07447i
$382$	0.375896	+	1.76845i	0.0192325	+	0.0904820i
$383$	−11.4024	−	25.6103i	−0.582637	−	1.30862i	−0.928846	−	0.370467i	$-0.879198\pi$
$383$	−11.4024	−	25.6103i	−0.582637	−	1.30862i	0.346208	−	0.938158i	$-0.387469\pi$
$384$	1.69799	+	0.341822i	0.0866500	+	0.0174436i
$385$	−12.4875	−	26.5005i	−0.636421	−	1.35059i
$386$			3.47642i			0.176945i
$387$	0.0646173	+	2.99547i	0.00328468	+	0.152268i
$388$	−3.35203	+	0.712496i	−0.170174	+	0.0361715i
$389$	−3.26130	−	2.93648i	−0.165354	−	0.148886i	0.582300	−	0.812974i	$-0.302153\pi$
$389$	−3.26130	−	2.93648i	−0.165354	−	0.148886i	−0.747654	+	0.664089i	$0.768820\pi$
$390$	1.61883	−	17.1826i	0.0819724	−	0.870077i
$391$	1.71801	+	2.36463i	0.0868833	+	0.119585i
$392$	6.84906	−	1.44579i	0.345930	−	0.0730236i
$393$	2.43784	−	4.32963i	0.122973	−	0.218401i
$394$	−2.30641	+	1.02688i	−0.116195	+	0.0517334i
$395$	28.7395	+	49.7783i	1.44604	+	2.50462i
$396$	9.84042	−	1.47180i	0.494500	−	0.0739609i
$397$	−18.5435	+	32.1184i	−0.930674	+	1.61197i	−0.148502	+	0.988912i	$0.547445\pi$
$397$	−18.5435	+	32.1184i	−0.930674	+	1.61197i	−0.782172	+	0.623062i	$0.785888\pi$
$398$	−11.7330	−	8.52455i	−0.588124	−	0.427297i
$399$	−28.1932	+	6.29045i	−1.41143	+	0.314916i
$400$	−1.89910	−	5.84482i	−0.0949549	−	0.292241i
$401$	−28.1005	+	2.95348i	−1.40327	+	0.147490i	−0.775716	−	0.631082i	$-0.782611\pi$
$401$	−28.1005	+	2.95348i	−1.40327	+	0.147490i	−0.627555	+	0.778572i	$0.715944\pi$
$402$	−5.25556	−	3.73246i	−0.262123	−	0.186158i
$403$	11.2018	+	10.0862i	0.558004	+	0.502429i
$404$	−5.97819	−	6.63946i	−0.297426	−	0.330325i
$405$	−29.7187	+	4.42640i	−1.47673	+	0.219950i
$406$	−0.949510	−	4.48252i	−0.0471234	−	0.222464i
$407$	20.1912	+	26.5328i	1.00084	+	1.31518i
$408$	−3.12002	+	3.54120i	−0.154464	+	0.175315i
$409$	−26.3232	−	2.76668i	−1.30160	−	0.136803i	−0.571758	−	0.820422i	$-0.693739\pi$
$409$	−26.3232	−	2.76668i	−1.30160	−	0.136803i	−0.729839	+	0.683619i	$0.760405\pi$
$410$	−7.64114	−	35.9488i	−0.377369	−	1.77538i
$411$	3.26092	−	7.54199i	0.160849	−	0.372019i
$412$	8.43066	−	6.12523i	0.415349	−	0.301768i
$413$	−4.86451	−	15.0071i	−0.239367	−	0.738453i
$414$	3.20686	+	0.267271i	0.157608	+	0.0131357i
$415$	−29.7665	+	26.8019i	−1.46118	+	1.31565i
$416$	−2.96832	−	0.311983i	−0.145534	−	0.0152962i
$417$	18.6161	−	6.27147i	0.911632	−	0.307115i
$418$	18.9057	−	8.92489i	0.924710	−	0.436531i
$419$			33.9103i			1.65663i	0.560264	+	0.828314i	$0.310700\pi$
$419$			33.9103i			1.65663i	−0.560264	+	0.828314i	$0.689300\pi$
$420$	13.9128	−	6.36326i	0.678876	−	0.310495i
$421$	4.92289	−	15.1511i	0.239927	−	0.738420i	−0.756502	−	0.653991i	$-0.773093\pi$
$421$	4.92289	−	15.1511i	0.239927	−	0.738420i	0.996430	−	0.0844289i	$-0.0269066\pi$
$422$	0.366635	−	1.72488i	0.0178475	−	0.0839660i
$423$	20.4302	−	19.2092i	0.993349	−	0.933985i
$424$	−2.79637	+	6.28076i	−0.135804	+	0.305021i
$425$	16.3800	+	3.48168i	0.794547	+	0.168886i
$426$	1.85619	+	1.04515i	0.0899328	+	0.0506375i
$427$	−24.7213	−	11.0274i	−1.19635	−	0.533652i
$428$	−15.2695			−0.738080
$429$	−16.6444	+	4.11556i	−0.803597	+	0.198701i
$430$	−1.66712	−	2.88753i	−0.0803955	−	0.139249i
$431$	0.540037	−	5.13811i	0.0260127	−	0.247494i	−0.973787	−	0.227463i	$-0.926957\pi$
$431$	0.540037	−	5.13811i	0.0260127	−	0.247494i	0.999799	−	0.0200310i	$-0.00637648\pi$
$432$	0.710020	+	5.14741i	0.0341609	+	0.247655i
$433$	−0.666032	−	2.04984i	−0.0320074	−	0.0985088i	0.933777	−	0.357857i	$-0.116492\pi$
$433$	−0.666032	−	2.04984i	−0.0320074	−	0.0985088i	−0.965784	+	0.259348i	$0.916492\pi$
$434$	−2.78725	+	13.0680i	−0.133792	+	0.627283i
$435$	−4.17157	−	9.10399i	−0.200011	−	0.436503i
$436$	−2.01686	+	9.48856i	−0.0965899	+	0.454420i
$437$	6.61379	−	1.40580i	0.316380	−	0.0672487i
$438$	−9.88980	−	3.09588i	−0.472553	−	0.147927i
$439$	−18.5718	−	10.7224i	−0.886383	−	0.511753i	−0.0136252	−	0.999907i	$-0.504337\pi$
$439$	−18.5718	−	10.7224i	−0.886383	−	0.511753i	−0.872758	+	0.488154i	$0.837670\pi$
$440$	−8.81136	+	6.70535i	−0.420065	+	0.319665i
$441$	10.8646	+	17.9711i	0.517363	+	0.855766i
$442$	4.78035	−	6.57958i	0.227378	−	0.312959i
$443$	9.19482	−	8.27905i	0.436859	−	0.393350i	−0.421144	−	0.906994i	$-0.638371\pi$
$443$	9.19482	−	8.27905i	0.436859	−	0.393350i	0.858003	+	0.513644i	$0.171705\pi$
$444$	−13.9756	+	10.3859i	−0.663251	+	0.492895i
$445$	−41.4135	−	18.4385i	−1.96319	−	0.874068i
$446$	−1.39780	−	13.2992i	−0.0661877	−	0.629734i
$447$	1.02576	+	8.84121i	0.0485168	+	0.418175i
$448$	−1.07443	−	2.41777i	−0.0507621	−	0.114229i
$449$	7.18781	−	9.89317i	0.339214	−	0.466887i	−0.604998	−	0.796227i	$-0.706826\pi$
$449$	7.18781	−	9.89317i	0.339214	−	0.466887i	0.944212	+	0.329340i	$0.106826\pi$
$450$	14.6785	−	11.1561i	0.691952	−	0.525902i
$451$	−31.2068	+	18.9522i	−1.46947	+	0.892426i
$452$	−8.87350	+	5.12312i	−0.417374	+	0.240971i
$453$	−3.25266	−	14.5303i	−0.152824	−	0.682692i
$454$	1.95130	−	6.00549i	0.0915792	−	0.281852i
$455$	−22.8404	+	13.1656i	−1.07077	+	0.617212i
$456$	4.54807	+	9.92567i	0.212983	+	0.464812i
$457$	−15.9931	+	1.68094i	−0.748123	+	0.0786309i	−0.470915	−	0.882179i	$-0.656076\pi$
$457$	−15.9931	+	1.68094i	−0.748123	+	0.0786309i	−0.277209	+	0.960810i	$0.589409\pi$
$458$	−6.54045	+	7.26390i	−0.305615	+	0.339420i
$459$	−13.1142	−	5.33749i	−0.612119	−	0.249133i
$460$	−3.27147	+	1.45655i	−0.152533	+	0.0679122i
$461$	−17.8529			−0.831491			−0.415745	−	0.909481i	$-0.636479\pi$
$461$	−17.8529			−0.831491			−0.415745	+	0.909481i	$0.636479\pi$
$462$	−10.5290	−	10.9609i	−0.489851	−	0.509947i
$463$	−25.1200			−1.16742			−0.583712	−	0.811961i	$-0.698400\pi$
$463$	−25.1200			−1.16742			−0.583712	+	0.811961i	$0.698400\pi$
$464$	−1.58210	+	0.704397i	−0.0734473	+	0.0327008i
$465$	0.314928	+	29.2016i	0.0146044	+	1.35419i
$466$	0.334920	−	0.371967i	0.0155149	−	0.0172310i
$467$	−10.7061	+	1.12525i	−0.495418	+	0.0520705i	−0.348943	−	0.937144i	$-0.613459\pi$
$467$	−10.7061	+	1.12525i	−0.495418	+	0.0520705i	−0.146475	+	0.989214i	$0.546793\pi$
$468$	−2.05010	−	8.71615i	−0.0947658	−	0.402904i
$469$	−0.00689288	+	9.84657i	−0.000318284	+	0.454673i
$470$	−9.64342	+	29.6794i	−0.444818	+	1.36901i
$471$	28.4445	−	6.36741i	1.31065	−	0.293395i
$472$	−5.16386	+	2.98136i	−0.237686	+	0.137228i
$473$	−2.16128	+	2.51013i	−0.0993758	+	0.115416i
$474$	22.3750	+	19.7138i	1.02772	+	0.905485i
$475$	22.7703	−	31.3406i	1.04477	−	1.43800i
$476$	7.16929	+	0.758597i	0.328604	+	0.0347702i
$477$	−20.5542	−	1.71306i	−0.941111	−	0.0784356i
$478$	−0.0682348	−	0.649211i	−0.00312099	−	0.0296942i
$479$	−20.8775	−	9.29526i	−0.953917	−	0.424711i	−0.130058	−	0.991506i	$-0.541516\pi$
$479$	−20.8775	−	9.29526i	−0.953917	−	0.424711i	−0.823859	+	0.566795i	$0.808183\pi$
$480$	−3.44909	−	4.64118i	−0.157429	−	0.211840i
$481$	22.2978	−	20.0770i	1.01669	−	0.915435i
$482$	2.66867	−	3.67312i	0.121555	−	0.167306i
$483$	−2.50057	−	4.23198i	−0.113780	−	0.192562i
$484$	9.17714	+	6.06466i	0.417143	+	0.275667i
$485$	9.90800	+	5.72039i	0.449899	+	0.259749i
$486$	−13.8784	+	7.09868i	−0.629535	+	0.322003i
$487$	−12.9944	+	2.76204i	−0.588831	+	0.125160i	−0.492685	−	0.870207i	$-0.663985\pi$
$487$	−12.9944	+	2.76204i	−0.588831	+	0.125160i	−0.0961453	+	0.995367i	$0.530651\pi$
$488$	−2.12719	+	10.0077i	−0.0962935	+	0.453025i
$489$	−9.72333	+	4.45536i	−0.439704	+	0.201478i
$490$	−20.2222	−	11.7131i	−0.913547	−	0.529143i
$491$	−7.50139	−	23.0869i	−0.338533	−	1.04190i	−0.964956	−	0.262413i	$-0.915482\pi$
$491$	−7.50139	−	23.0869i	−0.338533	−	1.04190i	0.626423	−	0.779484i	$-0.284518\pi$
$492$	−9.71114	−	16.4090i	−0.437812	−	0.739773i
$493$	0.493269	−	4.69314i	0.0222157	−	0.211368i
$494$	−9.40699	−	16.2934i	−0.423240	−	0.733074i
$495$	−27.7019	−	18.3309i	−1.24511	−	0.823914i
$496$	5.05033			0.226767
$497$	−0.337864	−	3.23636i	−0.0151553	−	0.145170i
$498$	−10.1957	+	18.1077i	−0.456882	+	0.811427i
$499$	38.1694	+	8.11316i	1.70870	+	0.363195i	0.955589	−	0.294703i	$-0.0952206\pi$
$499$	38.1694	+	8.11316i	1.70870	+	0.363195i	0.753108	+	0.657897i	$0.228554\pi$
$500$	−1.55561	+	3.49397i	−0.0695692	+	0.156255i
$501$	−1.13475	−	0.805895i	−0.0506971	−	0.0360047i
$502$	−4.10139	+	19.2955i	−0.183054	+	0.861200i
$503$	13.1616	−	40.5071i	0.586845	−	1.80612i	−0.00488488	−	0.999988i	$-0.501555\pi$
$503$	13.1616	−	40.5071i	0.586845	−	1.80612i	0.591730	−	0.806136i	$-0.298445\pi$
$504$	5.78642	−	5.43299i	0.257748	−	0.242004i
$505$			29.8271i			1.32729i
$506$	2.43855	+	2.59037i	0.108407	+	0.115156i
$507$	−2.26260	−	6.71624i	−0.100486	−	0.298279i
$508$	−15.0035	−	1.57694i	−0.665675	−	0.0699652i
$509$	−26.5793	+	23.9321i	−1.17811	+	1.06077i	−0.181099	+	0.983465i	$0.557965\pi$
$509$	−26.5793	+	23.9321i	−1.17811	+	1.06077i	−0.997007	+	0.0773067i	$0.975368\pi$
$510$	15.6514	−	1.81588i	0.693056	−	0.0804086i
$511$	4.88114	+	15.0585i	0.215929	+	0.666147i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−23.6194	+	22.6927i	−1.04282	+	1.00191i
$514$	−0.935775	−	4.40247i	−0.0412753	−	0.194185i
$515$	−34.5995	−	3.63656i	−1.52464	−	0.160246i
$516$	−1.29793	−	1.14356i	−0.0571380	−	0.0503422i
$517$	30.9946	−	0.687530i	1.36314	−	0.0302375i
$518$	25.2900	+	8.23680i	1.11118	+	0.361904i
$519$	−24.0952	−	26.1869i	−1.05766	−	1.14948i
$520$	6.66744	+	7.40494i	0.292387	+	0.324728i
$521$	2.41414	+	2.17370i	0.105765	+	0.0952315i	0.720317	−	0.693645i	$-0.243996\pi$
$521$	2.41414	+	2.17370i	0.105765	+	0.0952315i	−0.614552	+	0.788877i	$0.710663\pi$
$522$	−3.55892	−	3.78512i	−0.155770	−	0.165670i
$523$	12.8721	−	1.35291i	0.562858	−	0.0591587i	0.181173	−	0.983451i	$-0.442011\pi$
$523$	12.8721	−	1.35291i	0.562858	−	0.0591587i	0.381685	+	0.924293i	$0.375344\pi$
$524$	0.886485	+	2.72832i	0.0387263	+	0.119187i
$525$	−26.8707	−	8.43222i	−1.17274	−	0.368012i
$526$	14.8039	+	10.7557i	0.645480	+	0.468969i
$527$	−6.88073	+	11.9178i	−0.299729	+	0.519146i
$528$	−3.22157	+	4.75621i	−0.140201	+	0.206987i
$529$	−10.9247	−	18.9221i	−0.474987	−	0.822702i
$530$	20.9683	−	9.33571i	0.910806	−	0.405517i
$531$	−13.5485	−	11.6800i	−0.587956	−	0.506870i
$532$	8.34891	−	14.4374i	0.361971	−	0.625940i
$533$	19.3127	+	26.5816i	0.836525	+	1.15138i
$534$	−23.4154	−	2.20603i	−1.01328	−	0.0954644i
$535$	37.8835	+	34.1105i	1.63785	+	1.47473i
$536$	3.64033	−	0.773776i	0.157238	−	0.0334220i
$537$	−2.51320	−	11.2270i	−0.108453	−	0.484479i
$538$		−	31.8414i		−	1.37278i
$539$	−4.35409	+	22.8044i	−0.187544	+	0.982256i
$540$	9.73723	−	14.3568i	0.419024	−	0.617818i
$541$	15.0775	+	33.8646i	0.648232	+	1.45595i	0.876036	+	0.482245i	$0.160179\pi$
$541$	15.0775	+	33.8646i	0.648232	+	1.45595i	−0.227804	+	0.973707i	$0.573155\pi$
$542$	−1.23587	−	5.81433i	−0.0530853	−	0.249747i
$543$	16.9611	−	12.6046i	0.727869	−	0.540916i
$544$	−0.284826	−	2.70994i	−0.0122118	−	0.116188i
$545$	26.2003	−	19.0356i	1.12230	−	0.815396i
$546$	−9.04905	+	10.2561i	−0.387264	+	0.438921i
$547$	26.0099	+	8.45114i	1.11211	+	0.361345i	0.806750	−	0.590894i	$-0.201225\pi$
$547$	26.0099	+	8.45114i	1.11211	+	0.361345i	0.305356	+	0.952238i	$0.401225\pi$
$548$	1.92954	+	4.33381i	0.0824258	+	0.185131i
$549$	−30.4493	+	3.86595i	−1.29954	+	0.164995i
$550$	20.3133	+	1.68050i	0.866161	+	0.0716568i
$551$	−9.45409	−	5.45832i	−0.402758	−	0.232532i
$552$	−1.36720	+	1.25799i	−0.0581920	+	0.0535438i
$553$	4.79318	−	45.2990i	0.203827	−	1.92631i
$554$	2.54891	−	0.828190i	0.108293	−	0.0351864i
$555$	57.8744	+	5.45251i	2.45663	+	0.231446i
$556$	−4.61300	+	10.3610i	−0.195635	+	0.439403i
$557$	24.8415	−	27.5893i	1.05257	−	1.16899i	0.0673422	−	0.997730i	$-0.478548\pi$
$557$	24.8415	−	27.5893i	1.05257	−	1.16899i	0.985225	−	0.171264i	$-0.0547852\pi$
$558$	4.99159	+	14.3051i	0.211311	+	0.605584i
$559$	2.41156	+	1.75210i	0.101998	+	0.0741060i
$560$	−2.73538	+	8.39863i	−0.115591	+	0.354907i
$561$	−6.83453	−	14.0823i	−0.288554	−	0.594554i
$562$	−9.71050	+	16.8191i	−0.409613	+	0.709470i
$563$	−2.17353	+	20.6797i	−0.0916033	+	0.871547i	0.848164	+	0.529733i	$0.177708\pi$
$563$	−2.17353	+	20.6797i	−0.0916033	+	0.871547i	−0.939768	+	0.341814i	$0.888959\pi$
$564$	0.174597	+	16.1895i	0.00735184	+	0.681699i
$565$	33.4596	+	7.11206i	1.40766	+	0.299206i
$566$	−9.38992	−	12.9241i	−0.394688	−	0.543241i
$567$	21.1081	+	11.0203i	0.886458	+	0.462810i
$568$	−1.16968	+	0.380052i	−0.0490787	+	0.0159466i
$569$	−12.0790	−	13.4151i	−0.506380	−	0.562392i	0.434700	−	0.900575i	$-0.356854\pi$
$569$	−12.0790	−	13.4151i	−0.506380	−	0.562392i	−0.941080	+	0.338183i	$0.890188\pi$
$570$	10.8892	−	34.7854i	0.456097	−	1.45700i
$571$	14.9901	−	8.65456i	0.627317	−	0.362182i	−0.152395	−	0.988320i	$-0.548699\pi$
$571$	14.9901	−	8.65456i	0.627317	−	0.362182i	0.779712	+	0.626138i	$0.215365\pi$
$572$	4.75818	−	8.68047i	0.198949	−	0.362949i
$573$	0.618002	−	3.06989i	0.0258174	−	0.128247i
$574$	−11.8651	+	26.5994i	−0.495240	+	1.11024i
$575$	6.26950	+	2.03708i	0.261456	+	0.0849522i
$576$	−2.46452	−	1.71060i	−0.102688	−	0.0712751i
$577$	10.1319	+	4.51101i	0.421797	+	0.187796i	0.606648	−	0.794970i	$-0.292514\pi$
$577$	10.1319	+	4.51101i	0.421797	+	0.187796i	−0.184851	+	0.982766i	$0.559180\pi$
$578$	−8.74731	−	3.89455i	−0.363840	−	0.161992i
$579$	2.38964	−	5.52686i	0.0993100	−	0.229689i
$580$	5.49873	+	1.78665i	0.228323	+	0.0741865i
$581$	31.5717	−	3.29597i	1.30981	−	0.136740i
$582$	5.81886	+	1.17140i	0.241199	+	0.0485560i
$583$	−15.6297	−	16.6029i	−0.647318	−	0.687620i
$584$	5.18152	−	2.99155i	0.214413	−	0.123791i
$585$	−14.3847	+	26.2044i	−0.594734	+	1.08342i
$586$	7.30682	+	8.11504i	0.301842	+	0.335229i
$587$	17.3402	−	5.63418i	0.715708	−	0.232548i	0.0715467	−	0.997437i	$-0.477206\pi$
$587$	17.3402	−	5.63418i	0.715708	−	0.232548i	0.644161	+	0.764890i	$0.277206\pi$
$588$	−11.8825	−	2.40940i	−0.490028	−	0.0993618i
$589$	18.7121	+	25.7550i	0.771020	+	1.06122i
$590$	19.4715	+	4.13881i	0.801631	+	0.170392i
$591$	4.37262	−	0.0471569i	0.179865	−	0.00193977i
$592$	1.05082	−	9.99786i	0.0431883	−	0.410910i
$593$	6.16209	−	10.6730i	0.253047	−	0.438290i	−0.711317	−	0.702872i	$-0.751901\pi$
$593$	6.16209	−	10.6730i	0.253047	−	0.438290i	0.964363	+	0.264582i	$0.0852341\pi$
$594$	−16.6561	−	4.42425i	−0.683408	−	0.181529i
$595$	−16.0923	−	17.8975i	−0.659721	−	0.733726i
$596$	−4.15731	−	3.02046i	−0.170290	−	0.123723i
$597$	12.7937	+	21.6175i	0.523611	+	0.884747i
$598$	2.14224	−	2.37920i	0.0876028	−	0.0972928i
$599$	−8.76998	+	19.6977i	−0.358332	+	0.804826i	0.640974	+	0.767563i	$0.278531\pi$
$599$	−8.76998	+	19.6977i	−0.358332	+	0.804826i	−0.999305	+	0.0372632i	$0.988136\pi$
$600$	−0.998428	+	10.5976i	−0.0407607	+	0.432644i
$601$	17.0063	−	5.52569i	0.693702	−	0.225398i	0.0591179	−	0.998251i	$-0.481171\pi$
$601$	17.0063	−	5.52569i	0.693702	−	0.225398i	0.634585	+	0.772853i	$0.281171\pi$
$602$	−0.278042	+	2.62770i	−0.0113322	+	0.107097i
$603$	5.78972	+	9.54650i	0.235776	+	0.388764i
$604$	7.44494	+	4.29834i	0.302930	+	0.174897i
$605$	−9.22058	−	35.5471i	−0.374870	−	1.44520i
$606$	4.94035	+	14.6648i	0.200688	+	0.595717i
$607$	−8.20506	−	18.4289i	−0.333033	−	0.748005i	−0.999996	−	0.00291373i	$-0.999073\pi$
$607$	−8.20506	−	18.4289i	−0.333033	−	0.748005i	0.666962	−	0.745091i	$-0.267594\pi$
$608$	−5.99502	−	1.94790i	−0.243130	−	0.0789978i
$609$	−1.57167	+	7.77905i	−0.0636873	+	0.315223i
$610$	27.6336	−	20.0770i	1.11885	−	0.812893i
$611$	−2.91627	−	27.7464i	−0.117980	−	1.12250i
$612$	7.39441	−	3.48519i	0.298901	−	0.140880i
$613$	2.23682	+	10.5234i	0.0903444	+	0.425037i	0.999954	+	0.00957323i	$0.00304730\pi$
$613$	2.23682	+	10.5234i	0.0903444	+	0.425037i	−0.909610	+	0.415464i	$0.863619\pi$
$614$	−5.05986	−	11.3646i	−0.204200	−	0.458640i
$615$	−12.5626	+	62.4042i	−0.506573	+	2.51638i
$616$	8.77294	−	0.188459i	0.353472	−	0.00759324i
$617$		−	44.5484i		−	1.79345i	−0.442589	−	0.896725i	$-0.645940\pi$
$617$		−	44.5484i		−	1.79345i	0.442589	−	0.896725i	$-0.354060\pi$
$618$	−17.6135	+	3.94287i	−0.708521	+	0.158605i
$619$	−15.3636	+	3.26563i	−0.617515	+	0.131257i	−0.506040	−	0.862510i	$-0.668891\pi$
$619$	−15.3636	+	3.26563i	−0.617515	+	0.131257i	−0.111476	+	0.993767i	$0.535558\pi$
$620$	−12.5298	−	11.2819i	−0.503210	−	0.453093i
$621$	−4.91458	−	2.62925i	−0.197215	−	0.105508i
$622$	2.19160	+	3.01647i	0.0878750	+	0.120950i
$623$	17.9412	+	31.1254i	0.718800	+	1.24701i
$624$	4.50462	+	2.53637i	0.180329	+	0.101536i
$625$	−16.4068	+	7.30480i	−0.656274	+	0.292192i
$626$	5.00457	+	8.66816i	0.200023	+	0.346450i
$627$	−36.1914	+	1.19340i	−1.44535	+	0.0476599i
$628$	−8.41443	+	14.5742i	−0.335772	+	0.581575i
$629$	22.1613	+	16.1011i	0.883628	+	0.641994i
$630$	−26.4928	+	0.552940i	−1.05550	+	0.0220297i
$631$	−6.45028	−	19.8519i	−0.256782	−	0.790293i	−0.993473	−	0.114064i	$-0.963613\pi$
$631$	−6.45028	−	19.8519i	−0.256782	−	0.790293i	0.736692	−	0.676229i	$-0.236387\pi$
$632$	−17.1227	+	1.79967i	−0.681103	+	0.0715868i
$633$	−1.76854	+	2.49022i	−0.0702931	+	0.0989774i
$634$	−16.2237	−	14.6079i	−0.644327	−	0.580154i
$635$	33.7010	+	37.4287i	1.33738	+	1.48531i
$636$	8.76300	−	8.06305i	0.347476	−	0.319721i
$637$	20.7752	+	2.21297i	0.823142	+	0.0876810i
$638$	−0.127379	−	5.74241i	−0.00504300	−	0.227344i
$639$	−2.23258	−	2.93750i	−0.0883194	−	0.116206i
$640$	3.32022	+	0.348969i	0.131243	+	0.0137942i
$641$	7.37927	+	34.7167i	0.291463	+	1.37123i	0.843375	+	0.537325i	$0.180565\pi$
$641$	7.37927	+	34.7167i	0.291463	+	1.37123i	−0.551912	+	0.833903i	$0.686101\pi$
$642$	24.2757	+	10.4960i	0.958084	+	0.414245i
$643$	16.1761	−	11.7527i	0.637925	−	0.463480i	−0.221212	−	0.975226i	$-0.571001\pi$
$643$	16.1761	−	11.7527i	0.637925	−	0.463480i	0.859137	+	0.511746i	$0.171001\pi$
$644$	2.77556	+	0.591994i	0.109372	+	0.0233278i
$645$	0.665560	+	5.73658i	0.0262064	+	0.225878i
$646$	12.7645	−	11.4932i	0.502211	−	0.452193i
$647$	−0.961375	−	0.101045i	−0.0377956	−	0.00397247i	0.0856118	−	0.996329i	$-0.472716\pi$
$647$	−0.961375	−	0.101045i	−0.0377956	−	0.00397247i	−0.123407	+	0.992356i	$0.539382\pi$
$648$	2.40945	−	8.67148i	0.0946522	−	0.340648i
$649$	−2.50282	−	19.6171i	−0.0982444	−	0.770038i
$650$		−	18.3426i		−	0.719456i
$651$	13.4139	−	18.8597i	0.525733	−	0.739171i
$652$	1.90819	−	5.87281i	0.0747305	−	0.229997i
$653$	6.09098	−	28.6558i	0.238358	−	1.12139i	−0.682316	−	0.731057i	$-0.739027\pi$
$653$	6.09098	−	28.6558i	0.238358	−	1.12139i	0.920675	−	0.390331i	$-0.127639\pi$
$654$	9.72871	−	13.6987i	0.380423	−	0.535661i
$655$	3.89542	−	8.74926i	0.152207	−	0.341862i
$656$	10.7679	+	2.28879i	0.420417	+	0.0893623i
$657$	13.5949	+	11.7200i	0.530386	+	0.457239i
$658$	20.0182	−	14.5226i	0.780389	−	0.566152i
$659$	−32.4424			−1.26378			−0.631888	−	0.775060i	$-0.717720\pi$
$659$	−32.4424			−1.26378			−0.631888	+	0.775060i	$0.717720\pi$
$660$	18.6176	−	4.60346i	0.724687	−	0.179189i
$661$	22.4002	+	38.7983i	0.871268	+	1.50908i	0.860686	+	0.509136i	$0.170035\pi$
$661$	22.4002	+	38.7983i	0.871268	+	1.50908i	0.0105814	+	0.999944i	$0.496632\pi$
$662$	−2.46305	+	23.4344i	−0.0957293	+	0.910803i
$663$	−12.1226	+	7.17437i	−0.470801	+	0.278629i
$664$	−3.70753	−	11.4106i	−0.143880	−	0.442818i
$665$	−52.9652	+	17.1684i	−2.05390	+	0.665764i
$666$	29.3577	−	6.90512i	1.13759	−	0.267568i
$667$	0.386229	−	1.81706i	0.0149548	−	0.0703570i
$668$	0.786002	−	0.167070i	0.0304113	−	0.00646413i
$669$	−6.91940	+	22.1040i	−0.267519	+	0.854590i
$670$	−10.7602	−	6.21238i	−0.415701	−	0.240005i
$671$	−27.8881	−	19.3317i	−1.07661	−	0.746292i
$672$	0.0462106	+	4.58234i	0.00178261	+	0.176768i
$673$	−2.27193	+	3.12705i	−0.0875765	+	0.120539i	−0.850557	−	0.525883i	$-0.823735\pi$
$673$	−2.27193	+	3.12705i	−0.0875765	+	0.120539i	0.762981	+	0.646421i	$0.223735\pi$
$674$	10.1605	−	9.14853i	0.391367	−	0.352388i
$675$	−31.0046	+	7.64626i	−1.19337	+	0.294305i
$676$	3.73800	+	1.66426i	0.143769	+	0.0640102i
$677$	−2.30535	−	21.9339i	−0.0886018	−	0.842989i	−0.945087	−	0.326818i	$-0.894024\pi$
$677$	−2.30535	−	21.9339i	−0.0886018	−	0.842989i	0.856485	−	0.516171i	$-0.172643\pi$
$678$	17.6288	−	2.04529i	0.677028	−	0.0785490i
$679$	−3.68199	−	8.28548i	−0.141302	−	0.317968i
$680$	−5.34706	+	7.35960i	−0.205050	+	0.282228i
$681$	−7.23028	+	8.20631i	−0.277065	+	0.314467i
$682$	−6.47184	+	15.4493i	−0.247820	+	0.591583i
$683$	−8.58069	+	4.95407i	−0.328331	+	0.189562i	−0.655100	−	0.755542i	$-0.727373\pi$
$683$	−8.58069	+	4.95407i	−0.328331	+	0.189562i	0.326769	+	0.945104i	$0.394040\pi$
$684$	−0.407839	−	18.9062i	−0.0155941	−	0.722897i
$685$	4.89412	−	15.0625i	0.186995	−	0.575510i
$686$	7.49732	+	16.9349i	0.286249	+	0.646577i
$687$	15.3912	−	7.05244i	0.587210	−	0.269067i
$688$	0.993250	−	0.104395i	0.0378673	−	0.00398001i
$689$	−13.7306	+	15.2494i	−0.523094	+	0.580954i
$690$	6.20224	−	0.0668886i	0.236115	−	0.00254641i
$691$	37.9697	−	16.9052i	1.44444	−	0.643105i	0.473143	−	0.880986i	$-0.343120\pi$
$691$	37.9697	−	16.9052i	1.44444	−	0.643105i	0.971294	+	0.237881i	$0.0764529\pi$
$692$	20.5453			0.781017
$693$	9.20471	+	24.6632i	0.349658	+	0.936877i
$694$	7.25595			0.275432
$695$	34.5902	−	15.4005i	1.31208	−	0.584175i
$696$	2.99944	−	0.0323477i	0.113693	−	0.00122614i
$697$	−20.0716	+	22.2918i	−0.760268	+	0.844363i
$698$	−14.5432	+	1.52855i	−0.550469	+	0.0578566i
$699$	−0.788145	+	0.361138i	−0.0298104	+	0.0136595i
$700$	14.0870	−	8.12002i	0.532440	−	0.306908i
$701$	−13.0745	+	40.2391i	−0.493816	+	1.51981i	0.324978	+	0.945722i	$0.394643\pi$
$701$	−13.0745	+	40.2391i	−0.493816	+	1.51981i	−0.818794	+	0.574088i	$0.805357\pi$
$702$	−2.73207	+	15.2663i	−0.103115	+	0.576188i
$703$	54.8792	−	31.6845i	2.06981	−	1.19500i
$704$	−0.761340	−	3.22806i	−0.0286941	−	0.121662i
$705$	35.7324	−	40.5559i	1.34576	−	1.52742i
$706$	4.00501	−	5.51242i	0.150730	−	0.207463i
$707$	13.9074	−	19.1137i	0.523040	−	0.718845i
$708$	10.2589	−	1.19024i	0.385554	−	0.0447320i
$709$	0.423388	+	4.02827i	0.0159007	+	0.151285i	0.999591	−	0.0285832i	$-0.00909956\pi$
$709$	0.423388	+	4.02827i	0.0159007	+	0.151285i	−0.983691	+	0.179868i	$0.942433\pi$
$710$	3.75097	+	1.67004i	0.140771	+	0.0626754i
$711$	−22.0211	−	46.7214i	−0.825855	−	1.75219i
$712$	10.0910	−	9.08596i	0.378176	−	0.340511i
$713$	−3.18420	+	4.38267i	−0.119249	+	0.164132i
$714$	−10.8764	−	6.13408i	−0.407038	−	0.229562i
$715$	−31.1963	+	10.9069i	−1.16667	+	0.407895i
$716$	5.75241	+	3.32116i	0.214978	+	0.124117i
$717$	−0.337777	+	1.07903i	−0.0126145	+	0.0402970i
$718$	6.94845	−	1.47694i	0.259314	−	0.0551189i
$719$	2.24117	−	10.5439i	0.0835816	−	0.393221i	−0.916393	−	0.400279i	$-0.868913\pi$
$719$	2.24117	−	10.5439i	0.0835816	−	0.393221i	0.999975	+	0.00705800i	$0.00224665\pi$
$720$	2.29314	+	9.74946i	0.0854602	+	0.363341i
$721$	20.4763	+	18.4630i	0.762579	+	0.687596i
$722$	−6.40735	−	19.7198i	−0.238457	−	0.733894i
$723$	−6.76753	+	4.00516i	−0.251687	+	0.148953i
$724$	−1.27530	+	12.1336i	−0.0473960	+	0.450943i
$725$	−5.32157	−	9.21722i	−0.197638	−	0.342319i
$726$	−10.4212	−	15.9499i	−0.386766	−	0.591956i
$727$	1.55296			0.0575962			0.0287981	−	0.999585i	$-0.490832\pi$
$727$	1.55296			0.0575962			0.0287981	+	0.999585i	$0.490832\pi$
$728$	−0.819931	−	7.85401i	−0.0303887	−	0.291089i
$729$	26.9435	−	1.74582i	0.997907	−	0.0646599i
$730$	−19.5381	−	4.15296i	−0.723138	−	0.153708i
$731$	−1.10688	+	2.48610i	−0.0409396	+	0.0919518i
$732$	10.2609	−	14.4481i	0.379255	−	0.534017i
$733$	−4.30849	+	20.2698i	−0.159138	+	0.748684i	0.824113	+	0.566425i	$0.191674\pi$
$733$	−4.30849	+	20.2698i	−0.159138	+	0.748684i	−0.983251	+	0.182258i	$0.941659\pi$
$734$	−2.71180	+	8.34608i	−0.100095	+	0.308059i
$735$	24.0982	+	32.5220i	0.888874	+	1.19959i
$736$		−	1.07266i		−	0.0395387i
$737$	−2.29794	+	12.1275i	−0.0846457	+	0.446724i
$738$	4.15964	+	32.7624i	0.153119	+	1.20600i
$739$	19.9611	+	2.09800i	0.734281	+	0.0771760i	0.464285	−	0.885686i	$-0.346311\pi$
$739$	19.9611	+	2.09800i	0.734281	+	0.0771760i	0.269995	+	0.962862i	$0.412978\pi$
$740$	−24.9412	+	22.4572i	−0.916858	+	0.825543i
$741$	3.75554	+	32.3696i	0.137963	+	1.18913i
$742$	−17.7898	−	3.79435i	−0.653083	−	0.139295i
$743$	18.9719	−	13.7839i	0.696012	−	0.505683i	−0.182619	−	0.983184i	$-0.558457\pi$
$743$	18.9719	−	13.7839i	0.696012	−	0.505683i	0.878631	+	0.477501i	$0.158457\pi$
$744$	−8.02908	−	3.47152i	−0.294360	−	0.127272i
$745$	3.56685	+	16.7807i	0.130679	+	0.614798i
$746$	6.73790	+	0.708182i	0.246692	+	0.0259284i
$747$	28.6563	−	21.7795i	1.04848	−	0.796871i
$748$	8.65485	+	2.60140i	0.316453	+	0.0951165i
$749$	−8.37183	−	39.5224i	−0.305900	−	1.44412i
$750$	4.87483	−	4.48545i	0.178004	−	0.163785i
$751$	−27.4421	−	30.4775i	−1.00138	−	1.11214i	−0.993689	−	0.112170i	$-0.964220\pi$
$751$	−27.4421	−	30.4775i	−1.00138	−	1.11214i	−0.00768699	−	0.999970i	$-0.502447\pi$
$752$	−6.94657	−	6.25472i	−0.253315	−	0.228086i
$753$	19.7839	−	27.8570i	0.720964	−	1.01517i
$754$	−5.14061	+	0.540300i	−0.187210	+	0.0196766i
$755$	−8.86880	−	27.2954i	−0.322769	−	0.993380i
$756$	−12.9339	+	4.65994i	−0.470400	+	0.169480i
$757$	−15.5750	−	11.3159i	−0.566084	−	0.411284i	0.267597	−	0.963531i	$-0.413771\pi$
$757$	−15.5750	−	11.3159i	−0.566084	−	0.411284i	−0.833680	+	0.552247i	$0.813771\pi$
$758$	−15.7527	+	27.2844i	−0.572162	+	0.991014i
$759$	−2.09625	−	5.79443i	−0.0760892	−	0.210324i
$760$	10.5222	+	18.2250i	0.381680	+	0.661089i
$761$	−18.4371	+	8.20873i	−0.668345	+	0.297566i	−0.712720	−	0.701449i	$-0.752537\pi$
$761$	−18.4371	+	8.20873i	−0.668345	+	0.297566i	0.0443753	+	0.999015i	$0.485870\pi$
$762$	22.7689	+	12.8202i	0.824829	+	0.464428i
$763$	−25.6652	−	0.0179664i	−0.929143	−	0.000650427i
$764$	1.06269	+	1.46267i	0.0384469	+	0.0529176i
$765$	−26.1310	−	7.87162i	−0.944769	−	0.284599i
$766$	−20.8333	−	18.7584i	−0.752737	−	0.677768i
$767$	−17.4078	+	3.70015i	−0.628560	+	0.133605i
$768$	1.69022	−	0.378363i	0.0609905	−	0.0136530i
$769$		−	21.3254i		−	0.769014i	−0.923122	−	0.384507i	$-0.874371\pi$
$769$		−	21.3254i		−	0.769014i	0.923122	−	0.384507i	$-0.125629\pi$
$770$	−22.1866	−	19.1303i	−0.799549	−	0.689407i
$771$	−1.53848	+	7.64234i	−0.0554072	+	0.275232i
$772$	1.41399	+	3.17587i	0.0508906	+	0.114302i
$773$	−5.79364	−	27.2569i	−0.208383	−	0.980363i	−0.950651	−	0.310261i	$-0.899584\pi$
$773$	−5.79364	−	27.2569i	−0.208383	−	0.980363i	0.742269	−	0.670102i	$-0.233750\pi$
$774$	1.27740	+	2.71021i	0.0459151	+	0.0974166i
$775$	3.24429	+	30.8673i	0.116538	+	1.10879i
$776$	−2.77243	+	2.01429i	−0.0995246	+	0.0723088i
$777$	−34.5445	−	30.4789i	−1.23928	−	1.09343i
$778$	−4.17372	−	1.35612i	−0.149635	−	0.0486194i
$779$	28.2244	+	63.3931i	1.01125	+	2.27129i
$780$	−5.50994	−	16.3556i	−0.197287	−	0.585623i
$781$	0.336306	−	4.06515i	0.0120340	−	0.145462i
$782$	2.53126	+	1.46142i	0.0905177	+	0.0522604i
$783$	3.05618	+	8.46397i	0.109219	+	0.302478i
$784$	5.66887	−	4.10656i	0.202460	−	0.146663i
$785$	53.4334	−	17.3616i	1.90712	−	0.619661i
$786$	0.466059	−	4.94687i	0.0166238	−	0.176449i
$787$	2.91945	−	6.55719i	0.104067	−	0.233739i	−0.854006	−	0.520264i	$-0.825834\pi$
$787$	2.91945	−	6.55719i	0.104067	−	0.233739i	0.958073	+	0.286525i	$0.0925002\pi$
$788$	−1.68934	+	1.87620i	−0.0601802	+	0.0668369i
$789$	−16.1421	−	27.2754i	−0.574675	−	0.971031i
$790$	46.5015	+	33.7853i	1.65445	+	1.20203i
$791$	−18.1254	−	20.1586i	−0.644463	−	0.716757i
$792$	8.39103	−	5.34702i	0.298162	−	0.189998i
$793$	−15.2684	+	26.4457i	−0.542198	+	0.939114i
$794$	−3.87666	+	36.8839i	−0.137577	+	1.30896i
$795$	−39.7529	+	0.428719i	−1.40989	+	0.0152051i
$796$	−14.1859	−	3.01531i	−0.502806	−	0.106875i
$797$	−2.00296	−	2.75684i	−0.0709485	−	0.0976523i	0.772068	−	0.635540i	$-0.219222\pi$
$797$	−2.00296	−	2.75684i	−0.0709485	−	0.0976523i	−0.843017	+	0.537888i	$0.819222\pi$
$798$	−23.1972	+	17.2138i	−0.821173	+	0.609363i
$799$	24.2241	−	7.87089i	0.856987	−	0.278452i
$800$	−4.11222	−	4.56708i	−0.145389	−	0.161471i
$801$	35.7097	+	19.6026i	1.26174	+	0.692622i
$802$	−24.4698	+	14.1276i	−0.864058	+	0.498864i
$803$	2.51138	+	19.6842i	0.0886247	+	0.694639i
$804$	−6.31932	−	1.27215i	−0.222865	−	0.0448651i
$805$	−5.56368	−	7.66904i	−0.196094	−	0.270298i
$806$	14.3358	+	4.65799i	0.504958	+	0.164071i
$807$	−21.8873	+	50.6219i	−0.770469	+	1.78197i
$808$	−8.16186	−	3.63389i	−0.287133	−	0.127840i
$809$	29.5065	+	13.1372i	1.03739	+	0.461878i	0.853514	−	0.521071i	$-0.174467\pi$
$809$	29.5065	+	13.1372i	1.03739	+	0.461878i	0.183881	+	0.982948i	$0.441134\pi$
$810$	−25.3490	+	16.1314i	−0.890673	+	0.566800i
$811$	38.3203	+	12.4510i	1.34561	+	0.437214i	0.891212	−	0.453586i	$-0.149856\pi$
$811$	38.3203	+	12.4510i	1.34561	+	0.437214i	0.454395	+	0.890800i	$0.349856\pi$
$812$	−2.69063	−	3.70879i	−0.0944225	−	0.130153i
$813$	−2.03187	+	10.0932i	−0.0712608	+	0.353984i
$814$	29.2375	+	16.0264i	1.02477	+	0.561727i
$815$	−17.8535	+	10.3077i	−0.625379	+	0.361063i
$816$	−1.40995	+	4.50407i	−0.0493580	+	0.157674i
$817$	4.21250	+	4.67845i	0.147377	+	0.163678i
$818$	−25.1727	+	8.17912i	−0.880144	+	0.285976i
$819$	21.4362	−	10.0851i	0.749041	−	0.352403i
$820$	−21.6022	−	29.7329i	−0.754382	−	1.03832i
$821$	−7.76292	−	1.65006i	−0.270928	−	0.0575875i	0.0704443	−	0.997516i	$-0.477558\pi$
$821$	−7.76292	−	1.65006i	−0.270928	−	0.0575875i	−0.341372	+	0.939928i	$0.610892\pi$
$822$	−0.0886093	−	8.21629i	−0.00309060	−	0.286576i
$823$	−0.802045	+	7.63095i	−0.0279575	+	0.265998i	0.971610	+	0.236589i	$0.0760294\pi$
$823$	−0.802045	+	7.63095i	−0.0279575	+	0.265998i	−0.999567	+	0.0294096i	$0.990637\pi$
$824$	5.21043	−	9.02473i	0.181514	−	0.314392i
$825$	−31.1392	−	16.6347i	−1.08413	−	0.579146i
$826$	−10.5479	−	11.7311i	−0.367009	−	0.408179i
$827$	27.4136	+	19.9172i	0.953265	+	0.692587i	0.951577	−	0.307411i	$-0.0994627\pi$
$827$	27.4136	+	19.9172i	0.953265	+	0.692587i	0.00168792	+	0.999999i	$0.499463\pi$
$828$	3.03832	−	1.06018i	0.105589	−	0.0368439i
$829$	7.58651	−	8.42567i	0.263490	−	0.292636i	−0.596853	−	0.802351i	$-0.703582\pi$
$829$	7.58651	−	8.42567i	0.263490	−	0.292636i	0.860343	+	0.509715i	$0.170249\pi$
$830$	−16.2918	+	36.5919i	−0.565495	+	1.27012i
$831$	−4.62157	−	0.435411i	−0.160320	−	0.0151042i
$832$	−2.83859	+	0.922314i	−0.0984104	+	0.0319755i
$833$	1.96722	+	18.9723i	0.0681601	+	0.657352i
$834$	14.4558	−	13.3011i	0.500563	−	0.460579i
$835$	−2.32328	−	1.34135i	−0.0804005	−	0.0464192i
$836$	13.6412	−	15.8430i	0.471790	−	0.547940i
$837$	1.89743	−	26.1736i	0.0655846	−	0.904692i
$838$	13.7926	+	30.9786i	0.476457	+	1.07014i
$839$	33.7690	+	10.9722i	1.16584	+	0.378803i	0.827087	−	0.562074i	$-0.189996\pi$
$839$	33.7690	+	10.9722i	1.16584	+	0.378803i	0.338748	+	0.940877i	$0.389996\pi$
$840$	10.1218	−	11.4720i	0.349236	−	0.395821i
$841$	21.0351	−	15.2829i	0.725347	−	0.526996i
$842$	−1.66522	−	15.8435i	−0.0573874	−	0.546005i
$843$	26.9990	−	20.0643i	0.929896	−	0.691052i
$844$	−0.366635	−	1.72488i	−0.0126201	−	0.0593729i
$845$	−5.55615	−	12.4793i	−0.191138	−	0.429302i
$846$	10.8508	−	25.8582i	0.373058	−	0.889023i
$847$	−10.6657	+	27.0784i	−0.366479	+	0.930426i
$848$			6.87515i			0.236094i
$849$	6.04438	+	27.0014i	0.207443	+	0.926686i
$850$	16.3800	−	3.48168i	0.561829	−	0.119421i
$851$	8.01360	+	7.21548i	0.274703	+	0.247343i
$852$	2.12081	+	0.199808i	0.0726579	+	0.00684531i
$853$	−17.7455	−	24.4246i	−0.607594	−	0.836281i	0.388783	−	0.921329i	$-0.372896\pi$
$853$	−17.7455	−	24.4246i	−0.607594	−	0.836281i	−0.996377	+	0.0850483i	$0.972896\pi$
$854$	−27.0693	−	0.0189493i	−0.926292	−	0.000648431i
$855$	−41.2227	+	47.8173i	−1.40979	+	1.63532i
$856$	−13.9494	+	6.21067i	−0.476781	+	0.212276i
$857$	−5.38178	−	9.32152i	−0.183838	−	0.318417i	0.759346	−	0.650687i	$-0.225519\pi$
$857$	−5.38178	−	9.32152i	−0.183838	−	0.318417i	−0.943184	+	0.332270i	$0.892186\pi$
$858$	−13.5314	+	10.5296i	−0.461955	+	0.359475i
$859$	3.62893	−	6.28549i	0.123818	−	0.214458i	−0.797453	−	0.603382i	$-0.793820\pi$
$859$	3.62893	−	6.28549i	0.123818	−	0.214458i	0.921270	+	0.388923i	$0.127153\pi$
$860$	−2.69745	−	1.95981i	−0.0919823	−	0.0668291i
$861$	37.1473	−	34.1321i	1.26598	−	1.16322i
$862$	−1.59651	−	4.91355i	−0.0543773	−	0.167356i
$863$	−48.8626	+	5.13567i	−1.66330	+	0.174820i	−0.888972	−	0.457961i	$-0.848580\pi$
$863$	−48.8626	+	5.13567i	−1.66330	+	0.174820i	−0.774331	+	0.632781i	$0.781913\pi$
$864$	2.74228	+	4.41361i	0.0932942	+	0.150154i
$865$	−50.9728	−	45.8961i	−1.73313	−	1.56052i
$866$	−1.44219	−	1.60172i	−0.0490077	−	0.0544286i
$867$	11.2295	+	12.2044i	0.381375	+	0.414482i
$868$	2.76895	+	13.0719i	0.0939843	+	0.443688i
$869$	16.4369	−	54.6855i	0.557583	−	1.85508i
$870$	−7.51384	−	6.62018i	−0.254743	−	0.224445i
$871$	11.0471	+	1.16109i	0.374315	+	0.0393421i
$872$	2.01686	+	9.48856i	0.0682994	+	0.321323i
$873$	−8.44569	−	5.86209i	−0.285843	−	0.198402i
$874$	5.47020	−	3.97434i	0.185032	−	0.134434i
$875$	−9.89640	−	2.11079i	−0.334559	−	0.0713576i
$876$	−10.2940	+	1.19431i	−0.347802	+	0.0403521i
$877$	−13.5773	+	12.2251i	−0.458474	+	0.412812i	−0.865737	−	0.500499i	$-0.833150\pi$
$877$	−13.5773	+	12.2251i	−0.458474	+	0.412812i	0.407263	+	0.913311i	$0.366483\pi$
$878$	−21.3274	−	2.24160i	−0.719764	−	0.0756502i
$879$	−6.03832	−	17.9240i	−0.203667	−	0.604561i
$880$	−5.32227	+	9.70954i	−0.179414	+	0.327309i
$881$			40.1624i			1.35311i	0.736393	+	0.676554i	$0.236527\pi$
$881$			40.1624i			1.35311i	−0.736393	+	0.676554i	$0.763473\pi$
$882$	17.2348	+	11.9984i	0.580327	+	0.404006i
$883$	−7.24539	+	22.2990i	−0.243827	+	0.750421i	0.752001	+	0.659163i	$0.229089\pi$
$883$	−7.24539	+	22.2990i	−0.243827	+	0.750421i	−0.995827	+	0.0912589i	$0.970911\pi$
$884$	1.69091	−	7.95509i	0.0568714	−	0.267559i
$885$	−28.1112	−	19.9644i	−0.944946	−	0.671094i
$886$	5.03249	−	11.3032i	0.169070	−	0.379737i
$887$	18.1595	+	3.85992i	0.609735	+	0.129603i	0.502423	−	0.864622i	$-0.332442\pi$
$887$	18.1595	+	3.85992i	0.609735	+	0.129603i	0.107313	+	0.994225i	$0.465775\pi$
$888$	−8.54297	+	15.1724i	−0.286683	+	0.509153i
$889$	−4.14439	−	39.6986i	−0.138998	−	1.33145i
$890$	−45.3327			−1.51956
$891$	23.4389	+	18.4829i	0.785234	+	0.619200i
$892$	−6.68621	−	11.5809i	−0.223871	−	0.387756i
$893$	6.15908	−	58.5997i	0.206106	−	1.96097i
$894$	4.53312	+	7.65963i	0.151610	+	0.256176i
$895$	−6.85257	−	21.0900i	−0.229056	−	0.704962i
$896$	−1.96494	−	1.77173i	−0.0656439	−	0.0591893i
$897$	−5.04119	+	2.30994i	−0.168320	+	0.0771267i
$898$	2.54247	−	11.9614i	0.0848435	−	0.399157i
$899$	8.55517	−	1.81846i	0.285331	−	0.0606490i
$900$	8.87192	−	16.1619i	0.295731	−	0.538729i
$901$	−16.2240	−	9.36692i	−0.540499	−	0.312057i
$902$	−20.8003	+	30.0067i	−0.692574	+	0.999113i
$903$	2.24827	−	3.98643i	0.0748178	−	0.132660i
$904$	−6.02259	+	8.28938i	−0.200308	+	0.275701i
$905$	30.2692	−	27.2545i	1.00618	−	0.905972i
$906$	−8.88145	−	11.9511i	−0.295066	−	0.397048i
$907$	33.2753	+	14.8151i	1.10489	+	0.491928i	0.876383	−	0.481615i	$-0.159950\pi$
$907$	33.2753	+	14.8151i	1.10489	+	0.491928i	0.228505	+	0.973543i	$0.426616\pi$
$908$	−0.660050	−	6.27996i	−0.0219045	−	0.208408i
$909$	2.22612	−	26.7102i	0.0738359	−	0.885922i
$910$	−15.5108	+	21.3174i	−0.514178	+	0.706664i
$911$	27.6833	−	38.1027i	0.917187	−	1.26240i	−0.0474648	−	0.998873i	$-0.515114\pi$
$911$	27.6833	−	38.1027i	0.917187	−	1.26240i	0.964652	−	0.263527i	$-0.0848858\pi$
$912$	8.19200	+	7.21768i	0.271264	+	0.239001i
$913$	39.6568	+	3.28077i	1.31245	+	0.108578i
$914$	−13.9267	+	8.04057i	−0.460654	+	0.265959i
$915$	−57.7328	+	12.9237i	−1.90859	+	0.427246i
$916$	−3.02050	+	9.29614i	−0.0998001	+	0.307153i
$917$	−6.57573	+	3.79037i	−0.217150	+	0.125169i
$918$	−14.1514	+	0.457993i	−0.467066	+	0.0151160i
$919$	40.5886	−	4.26604i	1.33890	−	0.140724i	0.592147	−	0.805830i	$-0.298281\pi$
$919$	40.5886	−	4.26604i	1.33890	−	0.140724i	0.746748	+	0.665107i	$0.231614\pi$
$920$	−2.39621	+	2.66126i	−0.0790006	+	0.0877391i
$921$	0.232362	+	21.5457i	0.00765658	+	0.709955i
$922$	−16.3094	+	7.26141i	−0.537122	+	0.239142i
$923$	−3.67077			−0.120825
$924$	−14.0769	−	5.73076i	−0.463095	−	0.188528i
$925$	61.7814			2.03136
$926$	−22.9482	+	10.2172i	−0.754126	+	0.335758i
$927$	30.7125	+	5.83885i	1.00873	+	0.191773i
$928$	−1.15882	+	1.28700i	−0.0380401	+	0.0422478i
$929$	46.9803	−	4.93783i	1.54137	−	0.162005i	0.704620	−	0.709585i	$-0.251117\pi$
$929$	46.9803	−	4.93783i	1.54137	−	0.162005i	0.836754	+	0.547580i	$0.184451\pi$
$930$	12.1651	+	26.5489i	0.398909	+	0.870574i
$931$	41.9460	+	13.6940i	1.37473	+	0.448804i
$932$	0.154672	−	0.476033i	0.00506647	−	0.0155930i
$933$	−1.41075	−	6.30209i	−0.0461859	−	0.206321i
$934$	−9.32280	+	5.38252i	−0.305051	+	0.176121i
$935$	−15.6614	−	25.7881i	−0.512181	−	0.843360i
$936$	−5.41804	−	7.12875i	−0.177094	−	0.233011i
$937$	−15.0324	+	20.6903i	−0.491086	+	0.675921i	−0.980588	−	0.196081i	$-0.937179\pi$
$937$	−15.0324	+	20.6903i	−0.491086	+	0.675921i	0.489502	+	0.872002i	$0.337179\pi$
$938$	3.99867	+	8.99810i	0.130561	+	0.293798i
$939$	−1.99796	−	17.2208i	−0.0652011	−	0.561980i
$940$	3.26199	+	31.0358i	0.106395	+	1.01228i
$941$	−50.4612	−	22.4668i	−1.64499	−	0.732395i	−0.645479	−	0.763778i	$-0.723342\pi$
$941$	−50.4612	−	22.4668i	−1.64499	−	0.732395i	−0.999507	+	0.0313823i	$0.990009\pi$
$942$	23.3954	−	17.3863i	0.762265	−	0.566477i
$943$	−8.77531	+	7.90132i	−0.285763	+	0.257303i
$944$	−3.50480	+	4.82394i	−0.114071	+	0.157006i
$945$	42.4986	+	17.3316i	1.38248	+	0.563798i
$946$	−0.953468	+	3.17219i	−0.0309999	+	0.103137i
$947$	43.5771	+	25.1592i	1.41606	+	0.817565i	0.995950	−	0.0899056i	$-0.0286566\pi$
$947$	43.5771	+	25.1592i	1.41606	+	0.817565i	0.420115	+	0.907471i	$0.361990\pi$
$948$	28.4589	+	8.90872i	0.924302	+	0.289342i
$949$	17.4674	−	3.71280i	0.567014	−	0.120523i
$950$	8.05431	−	37.8926i	0.261316	−	1.22940i
$951$	15.7514	+	34.3758i	0.510776	+	1.11471i
$952$	6.85802	−	2.22300i	0.222270	−	0.0720478i
$953$	2.88825	+	8.88913i	0.0935597	+	0.287947i	0.986876	−	0.161482i	$-0.0516274\pi$
$953$	2.88825	+	8.88913i	0.0935597	+	0.287947i	−0.893316	+	0.449429i	$0.851627\pi$
$954$	−19.4739	+	6.79518i	−0.630492	+	0.220002i
$955$	0.630922	−	6.00282i	0.0204162	−	0.194247i
$956$	−0.326394	−	0.565330i	−0.0105563	−	0.0182841i
$957$	−3.74473	+	9.21691i	−0.121050	+	0.297940i
$958$	−22.8533			−0.738355
$959$	−10.1594	+	7.37037i	−0.328064	+	0.238002i
$960$	−5.03864	−	2.83706i	−0.162622	−	0.0915656i
$961$	5.37408	+	1.14230i	0.173357	+	0.0368483i
$962$	12.2040	−	27.4106i	0.393473	−	0.883754i
$963$	−31.3790	−	33.3734i	−1.01117	−	1.07544i
$964$	0.943965	−	4.44101i	0.0304031	−	0.143035i
$965$	3.58647	−	11.0380i	0.115452	−	0.355326i
$966$	−4.00569	−	2.84903i	−0.128881	−	0.0916661i
$967$			10.5980i			0.340810i	0.985374	+	0.170405i	$0.0545076\pi$
$967$			10.5980i			0.340810i	−0.985374	+	0.170405i	$0.945492\pi$
$968$	10.8505	+	1.80767i	0.348747	+	0.0581007i
$969$	−28.1933	+	9.49790i	−0.905700	+	0.305117i
$970$	11.3781	+	1.19589i	0.365329	+	0.0383976i
$971$	−15.9890	+	14.3965i	−0.513110	+	0.462006i	−0.884546	−	0.466452i	$-0.845532\pi$
$971$	−15.9890	+	14.3965i	−0.513110	+	0.462006i	0.371437	+	0.928458i	$0.378865\pi$
$972$	−9.79121	+	12.1298i	−0.314053	+	0.389064i
$973$	−29.3467	−	6.25931i	−0.940812	−	0.200664i
$974$	−10.7475	+	7.80853i	−0.344373	+	0.250201i
$975$	−12.6084	+	29.1613i	−0.403793	+	0.933909i
$976$	2.12719	+	10.0077i	0.0680898	+	0.320337i
$977$	34.4648	+	3.62240i	1.10263	+	0.115891i	0.638311	−	0.769778i	$-0.279633\pi$
$977$	34.4648	+	3.62240i	1.10263	+	0.115891i	0.464317	+	0.885669i	$0.346300\pi$
$978$	−7.07054	+	8.02500i	−0.226091	+	0.256611i
$979$	14.8632	+	42.5123i	0.475031	+	1.35870i
$980$	−23.2381	−	2.47532i	−0.742313	−	0.0790711i
$981$	−24.8831	+	15.0910i	−0.794455	+	0.481818i
$982$	−16.2431	−	18.0398i	−0.518340	−	0.575674i
$983$	−40.5060	−	36.4717i	−1.29194	−	1.16327i	−0.976784	−	0.214228i	$-0.931276\pi$
$983$	−40.5060	−	36.4717i	−1.29194	−	1.16327i	−0.315156	−	0.949040i	$-0.602057\pi$
$984$	−15.5457	−	11.0404i	−0.495579	−	0.351957i
$985$	8.38247	−	0.881034i	0.267088	−	0.0280721i
$986$	−1.45825	−	4.48803i	−0.0464401	−	0.142928i
$987$	−41.8078	+	9.32812i	−1.33076	+	0.296917i
$988$	−15.2208	−	11.0586i	−0.484239	−	0.351820i
$989$	−0.535643	+	0.927761i	−0.0170325	+	0.0295011i
$990$	−32.7628	−	5.47878i	−1.04127	−	0.174127i
$991$	−25.1880	−	43.6270i	−0.800124	−	1.38586i	−0.919534	−	0.393011i	$-0.871434\pi$
$991$	−25.1880	−	43.6270i	−0.800124	−	1.38586i	0.119410	−	0.992845i	$-0.461900\pi$
$992$	4.61371	−	2.05416i	0.146485	−	0.0652195i
$993$	20.0242	−	35.5632i	0.635449	−	1.12856i
$994$	−1.62500	−	2.81914i	−0.0515418	−	0.0894176i
$995$	28.4592	+	39.1708i	0.902219	+	1.24180i
$996$	−1.94919	+	20.6892i	−0.0617625	+	0.655563i
$997$	−23.4445	−	21.1096i	−0.742496	−	0.668546i	0.208405	−	0.978043i	$-0.433173\pi$
$997$	−23.4445	−	21.1096i	−0.742496	−	0.668546i	−0.950901	+	0.309496i	$0.899840\pi$
$998$	38.1694	−	8.11316i	1.20823	−	0.256817i
$999$	−51.4196	−	9.20214i	−1.62685	−	0.291143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.b.359.1	yes	128
3.2	odd	2		462.2.bc.a.359.3	yes	128
7.4	even	3	inner	462.2.bc.b.95.12	yes	128
11.8	odd	10		462.2.bc.a.107.14	yes	128
21.11	odd	6		462.2.bc.a.95.14	✓	128
33.8	even	10	inner	462.2.bc.b.107.12	yes	128
77.74	odd	30		462.2.bc.a.305.3	yes	128
231.74	even	30	inner	462.2.bc.b.305.1	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.14	✓	128	21.11	odd	6
462.2.bc.a.107.14	yes	128	11.8	odd	10
462.2.bc.a.305.3	yes	128	77.74	odd	30
462.2.bc.a.359.3	yes	128	3.2	odd	2
462.2.bc.b.95.12	yes	128	7.4	even	3	inner
462.2.bc.b.107.12	yes	128	33.8	even	10	inner
462.2.bc.b.305.1	yes	128	231.74	even	30	inner
462.2.bc.b.359.1	yes	128	1.1	even	1	trivial

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.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 - 0.406737i) q^{2} +(-1.73195 + 0.0186784i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-3.32022 + 0.348969i) q^{5} +(-1.57462 + 0.721511i) q^{6} +(2.29036 + 1.32448i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.99930 - 0.0647000i) q^{9} +O(q^{10})\)	\(q+(0.913545 - 0.406737i) q^{2} +(-1.73195 + 0.0186784i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-3.32022 + 0.348969i) q^{5} +(-1.57462 + 0.721511i) q^{6} +(2.29036 + 1.32448i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.99930 - 0.0647000i) q^{9} +(-2.89123 + 1.66925i) q^{10} +(2.51334 + 2.16405i) q^{11} +(-1.14502 + 1.29959i) q^{12} +(1.75434 - 2.41465i) q^{13} +(2.63106 + 0.278398i) q^{14} +(5.74393 - 0.666413i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(2.48929 + 1.10830i) q^{17} +(2.71368 - 1.27903i) q^{18} +(4.68444 - 4.21789i) q^{19} +(-1.96232 + 2.70091i) q^{20} +(-3.99153 - 2.25115i) q^{21} +(3.17625 + 0.954689i) q^{22} +(0.928949 + 0.536329i) q^{23} +(-0.517438 + 1.65295i) q^{24} +(6.01131 - 1.27774i) q^{25} +(0.620548 - 2.91945i) q^{26} +(-5.19343 + 0.168079i) q^{27} +(2.51683 - 0.815820i) q^{28} +(-0.535164 - 1.64707i) q^{29} +(4.97629 - 2.94506i) q^{30} +(-0.527904 + 5.02267i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.39340 - 3.70108i) q^{33} +2.72486 q^{34} +(-8.06669 - 3.59829i) q^{35} +(1.95884 - 2.27221i) q^{36} +(9.83325 + 2.09012i) q^{37} +(2.56388 - 5.75857i) q^{38} +(-2.99334 + 4.21482i) q^{39} +(-0.694114 + 3.26555i) q^{40} +(-3.40181 + 10.4697i) q^{41} +(-4.56207 - 0.433028i) q^{42} +0.998721i q^{43} +(3.28996 - 0.419746i) q^{44} +(-9.93575 + 1.26148i) q^{45} +(1.06678 + 0.112123i) q^{46} +(6.94657 - 6.25472i) q^{47} +(0.199614 + 1.72051i) q^{48} +(3.49151 + 6.06707i) q^{49} +(4.97190 - 3.61230i) q^{50} +(-4.33202 - 1.87303i) q^{51} +(-0.620548 - 2.91945i) q^{52} +(-6.83748 - 0.718649i) q^{53} +(-4.67607 + 2.26591i) q^{54} +(-9.10002 - 6.30803i) q^{55} +(1.96742 - 1.76898i) q^{56} +(-8.03444 + 7.39267i) q^{57} +(-1.15882 - 1.28700i) q^{58} +(-4.43116 - 3.98984i) q^{59} +(3.34820 - 4.71449i) q^{60} +(-10.1752 + 1.06945i) q^{61} +(1.56064 + 4.80315i) q^{62} +(6.95518 + 3.82433i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.98217 + 8.62936i) q^{65} +(-5.51894 - 1.59415i) q^{66} +(1.86083 + 3.22305i) q^{67} +(2.48929 - 1.10830i) q^{68} +(-1.61891 - 0.911544i) q^{69} +(-8.83285 - 0.00618325i) q^{70} +(-0.722902 - 0.994990i) q^{71} +(0.865302 - 2.87250i) q^{72} +(4.44631 + 4.00348i) q^{73} +(9.83325 - 2.09012i) q^{74} +(-10.3874 + 2.32527i) q^{75} -6.30354i q^{76} +(2.89022 + 8.28533i) q^{77} +(-1.02023 + 5.06793i) q^{78} +(-7.00278 - 15.7285i) q^{79} +(0.694114 + 3.26555i) q^{80} +(8.99163 - 0.388110i) q^{81} +(1.15070 + 10.9482i) q^{82} +(9.70645 - 7.05215i) q^{83} +(-4.34379 + 1.45997i) q^{84} +(-8.65173 - 2.81112i) q^{85} +(0.406216 + 0.912377i) q^{86} +(0.957642 + 2.84264i) q^{87} +(2.83480 - 1.72160i) q^{88} +(11.7595 + 6.78938i) q^{89} +(-8.56367 + 5.19365i) q^{90} +(7.21623 - 3.20682i) q^{91} +(1.02016 - 0.331470i) q^{92} +(0.820487 - 8.70887i) q^{93} +(3.80198 - 8.53939i) q^{94} +(-14.0814 + 15.6390i) q^{95} +(0.882151 + 1.49057i) q^{96} +(-2.77243 - 2.01429i) q^{97} +(5.65735 + 4.12242i) q^{98} +(7.67829 + 6.32803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

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