LMFDB - Embedded newform 462.2.ba.a.19.5

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			19.5
Character	$\chi$	$=$	462.19
Dual form			462.2.ba.a.73.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.994522 - 0.104528i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-1.50643 - 3.38350i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(2.60972 - 0.435184i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(0.994522 - 0.104528i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-1.50643 - 3.38350i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(2.60972 - 0.435184i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-1.85185 - 3.20750i) q^{10} +(-3.11142 - 1.14850i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-4.06672 + 2.95465i) q^{13} +(2.54993 - 0.705590i) q^{14} +(-1.14451 + 3.52243i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.614026 - 5.84206i) q^{17} +(0.207912 + 0.978148i) q^{18} +(0.983042 + 0.208952i) q^{19} +(-2.17698 - 2.99636i) q^{20} +(-2.23059 - 1.42284i) q^{21} +(-3.21443 - 0.816973i) q^{22} +(0.548198 - 0.949506i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(-5.83309 + 6.47830i) q^{25} +(-3.73560 + 3.36355i) q^{26} +(0.587785 - 0.809017i) q^{27} +(2.46221 - 0.968265i) q^{28} +(2.96015 + 0.961810i) q^{29} +(-0.770043 + 3.62277i) q^{30} +(3.98840 - 8.95809i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.54374 + 2.93545i) q^{33} -5.87424i q^{34} +(-5.40380 - 8.17440i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.68834 + 2.98570i) q^{37} +(0.999498 + 0.105051i) q^{38} +(4.99921 + 0.525438i) q^{39} +(-2.47826 - 2.75239i) q^{40} +(-0.499636 - 1.53772i) q^{41} +(-2.36710 - 1.18188i) q^{42} +0.741833i q^{43} +(-3.28222 - 0.476498i) q^{44} +(3.20750 - 1.85185i) q^{45} +(0.445944 - 1.00161i) q^{46} +(0.175756 - 0.826868i) q^{47} +(-0.951057 - 0.309017i) q^{48} +(6.62123 - 2.27141i) q^{49} +(-5.12397 + 7.05254i) q^{50} +(-4.36541 + 3.93064i) q^{51} +(-3.36355 + 3.73560i) q^{52} +(10.8696 + 4.83946i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.801208 + 12.2576i) q^{55} +(2.34751 - 1.22033i) q^{56} +(-0.590726 - 0.813065i) q^{57} +(3.04447 + 0.647121i) q^{58} +(2.92294 + 13.7514i) q^{59} +(-0.387142 + 3.68341i) q^{60} +(-4.64638 + 2.06870i) q^{61} +(3.03018 - 9.32592i) q^{62} +(0.705590 + 2.54993i) q^{63} +(0.809017 - 0.587785i) q^{64} +(16.1233 + 9.30879i) q^{65} +(1.84213 + 2.75800i) q^{66} +(-1.99742 - 3.45963i) q^{67} +(-0.614026 - 5.84206i) q^{68} +(-1.04273 + 0.338805i) q^{69} +(-6.22866 - 7.56477i) q^{70} +(2.10262 + 1.52764i) q^{71} +(0.406737 + 0.913545i) q^{72} +(10.1489 - 2.15723i) q^{73} +(2.98570 + 2.68834i) q^{74} +(8.66966 - 0.911218i) q^{75} +1.00500 q^{76} +(-8.61974 - 1.64321i) q^{77} +5.02675 q^{78} +(-4.66801 + 0.490627i) q^{79} +(-2.75239 - 2.47826i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-0.657635 - 1.47707i) q^{82} +(-9.62798 - 6.99513i) q^{83} +(-2.47767 - 0.927977i) q^{84} +(-20.6916 + 6.72311i) q^{85} +(0.0775426 + 0.737769i) q^{86} +(-1.55624 - 2.69549i) q^{87} +(-3.31404 - 0.130802i) q^{88} +(7.88289 + 4.55119i) q^{89} +(2.99636 - 2.17698i) q^{90} +(-9.32717 + 9.48056i) q^{91} +(0.338805 - 1.04273i) q^{92} +(-8.95809 + 3.98840i) q^{93} +(0.0883622 - 0.840710i) q^{94} +(-0.773896 - 3.64089i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(9.89329 + 13.6169i) q^{97} +(6.34753 - 2.95108i) q^{98} +(0.816973 - 3.21443i) 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
$5$	−1.50643	−	3.38350i	−0.673697	−	1.51315i	−0.848865	−	0.528609i	$-0.822714\pi$
$5$	−1.50643	−	3.38350i	−0.673697	−	1.51315i	0.175169	−	0.984538i	$-0.443953\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	2.60972	−	0.435184i	0.986380	−	0.164484i
$7$	2.60972	−	0.435184i	0.986380	−	0.164484i
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	−1.85185	−	3.20750i	−0.585607	−	1.01430i
$11$	−3.11142	−	1.14850i	−0.938129	−	0.346285i
$11$	−3.11142	−	1.14850i	−0.938129	−	0.346285i
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−4.06672	+	2.95465i	−1.12791	+	0.819472i	−0.985389	−	0.170321i	$-0.945520\pi$
$13$	−4.06672	+	2.95465i	−1.12791	+	0.819472i	−0.142517	+	0.989792i	$0.545520\pi$
$14$	2.54993	−	0.705590i	0.681497	−	0.188577i
$15$	−1.14451	+	3.52243i	−0.295510	+	0.909488i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.614026	−	5.84206i	0.148923	−	1.41691i	−0.623512	−	0.781814i	$-0.714295\pi$
$17$	0.614026	−	5.84206i	0.148923	−	1.41691i	0.772435	−	0.635094i	$-0.219039\pi$
$18$	0.207912	+	0.978148i	0.0490053	+	0.230552i
$19$	0.983042	+	0.208952i	0.225525	+	0.0479369i	0.319288	−	0.947658i	$-0.396556\pi$
$19$	0.983042	+	0.208952i	0.225525	+	0.0479369i	−0.0937629	+	0.995595i	$0.529890\pi$
$20$	−2.17698	−	2.99636i	−0.486788	−	0.670006i
$21$	−2.23059	−	1.42284i	−0.486755	−	0.310488i
$22$	−3.21443	−	0.816973i	−0.685319	−	0.174179i
$23$	0.548198	−	0.949506i	0.114307	−	0.197986i	−0.803195	−	0.595716i	$-0.796869\pi$
$23$	0.548198	−	0.949506i	0.114307	−	0.197986i	0.917503	+	0.397730i	$0.130202\pi$
$24$	−0.913545	−	0.406737i	−0.186477	−	0.0830248i
$25$	−5.83309	+	6.47830i	−1.16662	+	1.29566i
$26$	−3.73560	+	3.36355i	−0.732611	+	0.659646i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	2.46221	−	0.968265i	0.465313	−	0.182985i
$29$	2.96015	+	0.961810i	0.549685	+	0.178604i	0.570675	−	0.821176i	$-0.306682\pi$
$29$	2.96015	+	0.961810i	0.549685	+	0.178604i	−0.0209896	+	0.999780i	$0.506682\pi$
$30$	−0.770043	+	3.62277i	−0.140590	+	0.661424i
$31$	3.98840	−	8.95809i	0.716338	−	1.60892i	−0.0747385	−	0.997203i	$-0.523812\pi$
$31$	3.98840	−	8.95809i	0.716338	−	1.60892i	0.791076	−	0.611718i	$-0.209521\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.54374	+	2.93545i	0.268731	+	0.510996i
$34$		−	5.87424i		−	1.00742i
$35$	−5.40380	−	8.17440i	−0.913410	−	1.38173i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	2.68834	+	2.98570i	0.441960	+	0.490846i	0.922430	−	0.386165i	$-0.126201\pi$
$37$	2.68834	+	2.98570i	0.441960	+	0.490846i	−0.480470	+	0.877011i	$0.659534\pi$
$38$	0.999498	+	0.105051i	0.162140	+	0.0170416i
$39$	4.99921	+	0.525438i	0.800514	+	0.0841374i
$40$	−2.47826	−	2.75239i	−0.391847	−	0.435191i
$41$	−0.499636	−	1.53772i	−0.0780300	−	0.240152i	0.904431	−	0.426620i	$-0.140296\pi$
$41$	−0.499636	−	1.53772i	−0.0780300	−	0.240152i	−0.982461	+	0.186468i	$0.940296\pi$
$42$	−2.36710	−	1.18188i	−0.365251	−	0.182368i
$43$			0.741833i			0.113128i	0.998399	+	0.0565642i	$0.0180146\pi$
$43$			0.741833i			0.113128i	−0.998399	+	0.0565642i	$0.981985\pi$
$44$	−3.28222	−	0.476498i	−0.494813	−	0.0718347i
$45$	3.20750	−	1.85185i	0.478146	−	0.276058i
$46$	0.445944	−	1.00161i	0.0657509	−	0.147679i
$47$	0.175756	−	0.826868i	0.0256367	−	0.120611i	−0.963468	−	0.267822i	$-0.913696\pi$
$47$	0.175756	−	0.826868i	0.0256367	−	0.120611i	0.989105	+	0.147211i	$0.0470295\pi$
$48$	−0.951057	−	0.309017i	−0.137273	−	0.0446028i
$49$	6.62123	−	2.27141i	0.945890	−	0.324488i
$50$	−5.12397	+	7.05254i	−0.724638	+	0.997379i
$51$	−4.36541	+	3.93064i	−0.611280	+	0.550399i
$52$	−3.36355	+	3.73560i	−0.466440	+	0.518034i
$53$	10.8696	+	4.83946i	1.49306	+	0.664751i	0.980966	−	0.194180i	$-0.0622047\pi$
$53$	10.8696	+	4.83946i	1.49306	+	0.664751i	0.512090	+	0.858932i	$0.328871\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	0.801208	+	12.2576i	0.108035	+	1.65282i
$56$	2.34751	−	1.22033i	0.313699	−	0.163074i
$57$	−0.590726	−	0.813065i	−0.0782436	−	0.107693i
$58$	3.04447	+	0.647121i	0.399758	+	0.0849712i
$59$	2.92294	+	13.7514i	0.380535	+	1.79028i	0.584603	+	0.811320i	$0.301250\pi$
$59$	2.92294	+	13.7514i	0.380535	+	1.79028i	−0.204068	+	0.978957i	$0.565416\pi$
$60$	−0.387142	+	3.68341i	−0.0499799	+	0.475527i
$61$	−4.64638	+	2.06870i	−0.594908	+	0.264870i	−0.682026	−	0.731328i	$-0.738901\pi$
$61$	−4.64638	+	2.06870i	−0.594908	+	0.264870i	0.0871180	+	0.996198i	$0.472234\pi$
$62$	3.03018	−	9.32592i	0.384833	−	1.18439i
$63$	0.705590	+	2.54993i	0.0888959	+	0.321261i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	16.1233	+	9.30879i	1.99985	+	1.15461i
$66$	1.84213	+	2.75800i	0.226750	+	0.339487i
$67$	−1.99742	−	3.45963i	−0.244024	−	0.422662i	0.717833	−	0.696215i	$-0.245134\pi$
$67$	−1.99742	−	3.45963i	−0.244024	−	0.422662i	−0.961857	+	0.273554i	$0.911801\pi$
$68$	−0.614026	−	5.84206i	−0.0744615	−	0.708454i
$69$	−1.04273	+	0.338805i	−0.125530	+	0.0407873i
$70$	−6.22866	−	7.56477i	−0.744467	−	0.904163i
$71$	2.10262	+	1.52764i	0.249535	+	0.181298i	0.705521	−	0.708689i	$-0.250713\pi$
$71$	2.10262	+	1.52764i	0.249535	+	0.181298i	−0.455986	+	0.889987i	$0.650713\pi$
$72$	0.406737	+	0.913545i	0.0479344	+	0.107662i
$73$	10.1489	−	2.15723i	1.18784	−	0.252484i	0.428725	−	0.903435i	$-0.358963\pi$
$73$	10.1489	−	2.15723i	1.18784	−	0.252484i	0.759120	+	0.650951i	$0.225630\pi$
$74$	2.98570	+	2.68834i	0.347081	+	0.312513i
$75$	8.66966	−	0.911218i	1.00109	−	0.105218i
$76$	1.00500			0.115282
$77$	−8.61974	−	1.64321i	−0.982310	−	0.187261i
$78$	5.02675			0.569167
$79$	−4.66801	+	0.490627i	−0.525192	+	0.0551999i	−0.363415	−	0.931627i	$-0.618389\pi$
$79$	−4.66801	+	0.490627i	−0.525192	+	0.0551999i	−0.161777	+	0.986827i	$0.551723\pi$
$80$	−2.75239	−	2.47826i	−0.307726	−	0.277078i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−0.657635	−	1.47707i	−0.0726236	−	0.163115i
$83$	−9.62798	−	6.99513i	−1.05681	−	0.767816i	−0.0833126	−	0.996523i	$-0.526550\pi$
$83$	−9.62798	−	6.99513i	−1.05681	−	0.767816i	−0.973495	+	0.228708i	$0.926550\pi$
$84$	−2.47767	−	0.927977i	−0.270336	−	0.101251i
$85$	−20.6916	+	6.72311i	−2.24432	+	0.729224i
$86$	0.0775426	+	0.737769i	0.00836163	+	0.0795556i
$87$	−1.55624	−	2.69549i	−0.166846	−	0.288987i
$88$	−3.31404	−	0.130802i	−0.353278	−	0.0139436i
$89$	7.88289	+	4.55119i	0.835585	+	0.482425i	0.855761	−	0.517371i	$-0.173089\pi$
$89$	7.88289	+	4.55119i	0.835585	+	0.482425i	−0.0201762	+	0.999796i	$0.506423\pi$
$90$	2.99636	−	2.17698i	0.315844	−	0.229474i
$91$	−9.32717	+	9.48056i	−0.977753	+	0.993833i
$92$	0.338805	−	1.04273i	0.0353229	−	0.108713i
$93$	−8.95809	+	3.98840i	−0.928911	+	0.413578i
$94$	0.0883622	−	0.840710i	0.00911387	−	0.0867126i
$95$	−0.773896	−	3.64089i	−0.0794001	−	0.373548i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	9.89329	+	13.6169i	1.00451	+	1.38259i	0.922516	+	0.385958i	$0.126129\pi$
$97$	9.89329	+	13.6169i	1.00451	+	1.38259i	0.0819947	+	0.996633i	$0.473871\pi$
$98$	6.34753	−	2.95108i	0.641197	−	0.298104i
$99$	0.816973	−	3.21443i	0.0821088	−	0.323062i
$100$	−4.35871	+	7.54950i	−0.435871	+	0.754950i
$101$	−9.59256	−	4.27088i	−0.954495	−	0.424969i	−0.130426	−	0.991458i	$-0.541635\pi$
$101$	−9.59256	−	4.27088i	−0.954495	−	0.424969i	−0.824069	+	0.566489i	$0.808301\pi$
$102$	−3.93064	+	4.36541i	−0.389191	+	0.432240i
$103$	8.33311	−	7.50317i	0.821086	−	0.739309i	−0.147212	−	0.989105i	$-0.547030\pi$
$103$	8.33311	−	7.50317i	0.821086	−	0.739309i	0.968299	+	0.249796i	$0.0803634\pi$
$104$	−2.95465	+	4.06672i	−0.289727	+	0.398775i
$105$	−1.45393	+	9.69061i	−0.141889	+	0.945707i
$106$	11.3159	+	3.67677i	1.09910	+	0.357119i
$107$	2.97578	−	13.9999i	0.287679	−	1.35342i	−0.562442	−	0.826837i	$-0.690138\pi$
$107$	2.97578	−	13.9999i	0.287679	−	1.35342i	0.850121	−	0.526587i	$-0.176529\pi$
$108$	0.406737	−	0.913545i	0.0391383	−	0.0879060i
$109$	7.37614	−	4.25862i	0.706506	−	0.407902i	−0.103260	−	0.994654i	$-0.532927\pi$
$109$	7.37614	−	4.25862i	0.706506	−	0.407902i	0.809766	+	0.586753i	$0.199594\pi$
$110$	2.07809	+	12.1067i	0.198138	+	1.15433i
$111$		−	4.01766i		−	0.381339i
$112$	2.20709	−	1.45903i	0.208550	−	0.137865i
$113$	0.0799653	+	0.246108i	0.00752251	+	0.0231519i	0.954747	−	0.297418i	$-0.0961255\pi$
$113$	0.0799653	+	0.246108i	0.00752251	+	0.0231519i	−0.947225	+	0.320570i	$0.896126\pi$
$114$	−0.672479	−	0.746863i	−0.0629834	−	0.0699502i
$115$	−4.03848	−	0.424461i	−0.376590	−	0.0395812i
$116$	3.09543	+	0.325343i	0.287404	+	0.0302073i
$117$	−3.36355	−	3.73560i	−0.310960	−	0.345356i
$118$	4.34434	+	13.3705i	0.399929	+	1.23086i
$119$	−0.939941	−	15.5133i	−0.0861642	−	1.42211i
$120$			3.70370i			0.338100i
$121$	8.36191	+	7.14692i	0.760174	+	0.649720i
$122$	−4.40469	+	2.54305i	−0.398782	+	0.230237i
$123$	−0.657635	+	1.47707i	−0.0592969	+	0.133183i
$124$	2.03875	−	9.59157i	0.183085	−	0.861349i
$125$	13.0943	+	4.25461i	1.17119	+	0.380544i
$126$	0.968265	+	2.46221i	0.0862599	+	0.219351i
$127$	−8.50527	+	11.7065i	−0.754721	+	1.03878i	0.242914	+	0.970048i	$0.421897\pi$
$127$	−8.50527	+	11.7065i	−0.754721	+	1.03878i	−0.997635	+	0.0687361i	$0.978103\pi$
$128$	0.743145	−	0.669131i	0.0656853	−	0.0591433i
$129$	0.496383	−	0.551289i	0.0437041	−	0.0485383i
$130$	17.0080	+	7.57245i	1.49170	+	0.664148i
$131$	5.25134	−	9.09559i	0.458812	−	0.794685i	−0.540087	−	0.841609i	$-0.681609\pi$
$131$	5.25134	−	9.09559i	0.458812	−	0.794685i	0.998898	+	0.0469240i	$0.0149419\pi$
$132$	2.12032	+	2.55034i	0.184550	+	0.221979i
$133$	2.65639	+	0.117501i	0.230338	+	0.0101886i
$134$	−2.34811	−	3.23189i	−0.202846	−	0.279193i
$135$	−3.62277	−	0.770043i	−0.311798	−	0.0662748i
$136$	−1.22132	−	5.74588i	−0.104728	−	0.492705i
$137$	0.0647523	−	0.616077i	0.00553216	−	0.0526350i	−0.991408	−	0.130809i	$-0.958242\pi$
$137$	0.0647523	−	0.616077i	0.00553216	−	0.0526350i	0.996940	+	0.0781744i	$0.0249091\pi$
$138$	−1.00161	+	0.445944i	−0.0852625	+	0.0379613i
$139$	−4.80277	+	14.7814i	−0.407366	+	1.25374i	0.511538	+	0.859261i	$0.329076\pi$
$139$	−4.80277	+	14.7814i	−0.407366	+	1.25374i	−0.918904	+	0.394482i	$0.870924\pi$
$140$	−6.98527	−	6.87226i	−0.590363	−	0.580812i
$141$	−0.683895	+	0.496879i	−0.0575944	+	0.0418448i
$142$	2.25079	+	1.29949i	0.188882	+	0.109051i
$143$	16.0467	−	4.52254i	1.34189	−	0.378194i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−1.20497	−	11.4646i	−0.100068	−	0.952079i
$146$	9.86786	−	3.20626i	0.816670	−	0.265352i
$147$	−6.44040	−	2.74248i	−0.531196	−	0.226196i
$148$	3.25035	+	2.36152i	0.267177	+	0.194116i
$149$	5.27966	+	11.8583i	0.432526	+	0.971470i	0.989973	+	0.141257i	$0.0451144\pi$
$149$	5.27966	+	11.8583i	0.432526	+	0.971470i	−0.557447	+	0.830213i	$0.688219\pi$
$150$	8.52692	−	1.81245i	0.696220	−	0.147986i
$151$	3.50679	+	3.15752i	0.285378	+	0.256956i	0.799370	−	0.600840i	$-0.205167\pi$
$151$	3.50679	+	3.15752i	0.285378	+	0.256956i	−0.513991	+	0.857795i	$0.671834\pi$
$152$	0.999498	−	0.105051i	0.0810700	−	0.00852080i
$153$	5.87424			0.474904
$154$	−8.74428	−	0.733197i	−0.704634	−	0.0590827i
$155$	−36.3180			−2.91713
$156$	4.99921	−	0.525438i	0.400257	−	0.0420687i
$157$	4.63366	+	4.17217i	0.369807	+	0.332975i	0.832991	−	0.553287i	$-0.186627\pi$
$157$	4.63366	+	4.17217i	0.369807	+	0.332975i	−0.463184	+	0.886262i	$0.653293\pi$
$158$	−4.59115	+	0.975879i	−0.365252	+	0.0776368i
$159$	−4.83946	−	10.8696i	−0.383794	−	0.862016i
$160$	−2.99636	−	2.17698i	−0.236883	−	0.172106i
$161$	1.01743	−	2.71651i	0.0801847	−	0.214091i
$162$	−0.951057	+	0.309017i	−0.0747221	+	0.0242787i
$163$	−2.25731	−	21.4769i	−0.176806	−	1.68220i	−0.619088	−	0.785322i	$-0.712497\pi$
$163$	−2.25731	−	21.4769i	−0.176806	−	1.68220i	0.442281	−	0.896876i	$-0.354169\pi$
$164$	−0.808428	−	1.40024i	−0.0631276	−	0.109340i
$165$	7.60655	−	9.64531i	0.592169	−	0.750886i
$166$	−10.3064	−	5.95042i	−0.799934	−	0.461842i
$167$	−17.6530	+	12.8257i	−1.36603	+	0.992480i	−0.367996	+	0.929828i	$0.619956\pi$
$167$	−17.6530	+	12.8257i	−1.36603	+	0.992480i	−0.998035	+	0.0626520i	$0.980044\pi$
$168$	−2.56110	−	0.663906i	−0.197593	−	0.0512215i
$169$	3.79107	−	11.6677i	0.291621	−	0.897517i
$170$	−19.8755	+	8.84914i	−1.52438	+	0.678698i
$171$	−0.105051	+	0.999498i	−0.00803349	+	0.0764335i
$172$	0.154236	+	0.725622i	0.0117604	+	0.0553281i
$173$	2.78224	+	0.591384i	0.211530	+	0.0449621i	0.312458	−	0.949932i	$-0.398848\pi$
$173$	2.78224	+	0.591384i	0.211530	+	0.0449621i	−0.100928	+	0.994894i	$0.532181\pi$
$174$	−1.82947	−	2.51805i	−0.138692	−	0.190893i
$175$	−12.4034	+	19.4450i	−0.937613	+	1.46990i
$176$	−3.30956	+	0.216326i	−0.249468	+	0.0163062i
$177$	7.02929	−	12.1751i	0.528354	−	0.915136i
$178$	8.31544	+	3.70227i	0.623268	+	0.277497i
$179$	6.25982	−	6.95224i	0.467881	−	0.519635i	−0.462306	−	0.886720i	$-0.652978\pi$
$179$	6.25982	−	6.95224i	0.467881	−	0.519635i	0.930187	+	0.367086i	$0.119645\pi$
$180$	2.75239	−	2.47826i	0.205151	−	0.184719i
$181$	−1.43215	+	1.97118i	−0.106451	+	0.146517i	−0.858919	−	0.512112i	$-0.828863\pi$
$181$	−1.43215	+	1.97118i	−0.106451	+	0.146517i	0.752468	+	0.658629i	$0.228863\pi$
$182$	−8.28509	+	10.4036i	−0.614132	+	0.771165i
$183$	4.83716	+	1.57169i	0.357574	+	0.116183i
$184$	0.227953	−	1.07244i	0.0168050	−	0.0790611i
$185$	6.05232	−	13.5937i	0.444976	−	0.999432i
$186$	−8.49212	+	4.90293i	−0.622672	+	0.359500i
$187$	−8.62008	+	17.4719i	−0.630363	+	1.27767i
$188$		−	0.845341i		−	0.0616528i
$189$	1.18188	−	2.36710i	0.0859692	−	0.172181i
$190$	−1.15023	−	3.54006i	−0.0834467	−	0.256823i
$191$	−11.2371	−	12.4800i	−0.813087	−	0.903024i	0.183712	−	0.982980i	$-0.441189\pi$
$191$	−11.2371	−	12.4800i	−0.813087	−	0.903024i	−0.996798	+	0.0799558i	$0.974522\pi$
$192$	−0.994522	−	0.104528i	−0.0717734	−	0.00754369i
$193$	−3.08364	−	0.324103i	−0.221965	−	0.0233295i	−0.00710691	−	0.999975i	$-0.502262\pi$
$193$	−3.08364	−	0.324103i	−0.221965	−	0.0233295i	−0.214858	+	0.976645i	$0.568929\pi$
$194$	11.2624	+	12.5082i	0.808597	+	0.898038i
$195$	−5.75315	−	17.7064i	−0.411991	−	1.26798i
$196$	6.00429	−	3.59841i	0.428878	−	0.257029i
$197$		−	2.34016i		−	0.166729i	−0.996519	−	0.0833646i	$-0.973433\pi$
$197$		−	2.34016i		−	0.166729i	0.996519	−	0.0833646i	$-0.0265666\pi$
$198$	0.476498	−	3.28222i	0.0338632	−	0.233257i
$199$	4.03474	−	2.32946i	0.286015	−	0.165131i	−0.350128	−	0.936702i	$-0.613862\pi$
$199$	4.03474	−	2.32946i	0.286015	−	0.165131i	0.636143	+	0.771571i	$0.280529\pi$
$200$	−3.54569	+	7.96375i	−0.250718	+	0.563122i
$201$	−0.830574	+	3.90754i	−0.0585842	+	0.275617i
$202$	−9.98644	−	3.24479i	−0.702643	−	0.228303i
$203$	8.14370	+	1.22184i	0.571576	+	0.0857564i
$204$	−3.45279	+	4.75236i	−0.241744	+	0.332732i
$205$	−4.45021	+	4.00699i	−0.310816	+	0.279860i
$206$	7.50317	−	8.33311i	0.522771	−	0.580596i
$207$	1.00161	+	0.445944i	0.0696165	+	0.0309953i
$208$	−2.51337	+	4.35329i	−0.174271	+	0.301846i
$209$	−2.81868	−	1.77916i	−0.194972	−	0.123067i
$210$	−0.433023	+	9.78950i	−0.0298814	+	0.675540i
$211$	−2.54981	−	3.50951i	−0.175536	−	0.241605i	0.712179	−	0.701998i	$-0.247708\pi$
$211$	−2.54981	−	3.50951i	−0.175536	−	0.241605i	−0.887715	+	0.460393i	$0.847708\pi$
$212$	11.6383	+	2.47379i	0.799319	+	0.169901i
$213$	−0.540359	−	2.54219i	−0.0370248	−	0.174188i
$214$	1.49608	−	14.2343i	0.102270	−	0.973036i
$215$	2.50999	−	1.11752i	0.171180	−	0.0762142i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	6.51017	−	25.1138i	0.441939	−	1.70483i
$218$	6.89059	−	5.00631i	0.466690	−	0.339070i
$219$	−8.98560	−	5.18784i	−0.607191	−	0.350562i
$220$	3.33221	+	11.8232i	0.224657	+	0.797120i
$221$	14.7642	+	25.5723i	0.993145	+	1.72018i
$222$	−0.419959	−	3.99565i	−0.0281858	−	0.268170i
$223$	8.82999	−	2.86904i	0.591300	−	0.192125i	0.00194330	−	0.999998i	$-0.499381\pi$
$223$	8.82999	−	2.86904i	0.591300	−	0.192125i	0.589356	+	0.807873i	$0.299381\pi$
$224$	2.04249	−	1.68174i	0.136469	−	0.112366i
$225$	−7.05254	−	5.12397i	−0.470169	−	0.341598i
$226$	0.105253	+	0.236401i	0.00700130	+	0.0157252i
$227$	0.0791919	−	0.0168328i	0.00525615	−	0.00111723i	−0.205283	−	0.978703i	$-0.565811\pi$
$227$	0.0791919	−	0.0168328i	0.00525615	−	0.00111723i	0.210539	+	0.977585i	$0.432478\pi$
$228$	−0.746863	−	0.672479i	−0.0494622	−	0.0445360i
$229$	−29.3270	+	3.08240i	−1.93798	+	0.203690i	−0.992524	−	0.122046i	$-0.961054\pi$
$229$	−29.3270	+	3.08240i	−1.93798	+	0.203690i	−0.945461	+	0.325737i	$0.894388\pi$
$230$	−4.06072			−0.267756
$231$	5.30619	+	6.98887i	0.349122	+	0.459834i
$232$	3.11248			0.204344
$233$	23.1288	−	2.43094i	1.51522	−	0.159256i	0.689892	−	0.723912i	$-0.257658\pi$
$233$	23.1288	−	2.43094i	1.51522	−	0.159256i	0.825326	+	0.564656i	$0.190991\pi$
$234$	−3.73560	−	3.36355i	−0.244204	−	0.219882i
$235$	−3.06247	+	0.650949i	−0.199774	+	0.0424632i
$236$	5.71814	+	12.8432i	0.372219	+	0.836018i
$237$	3.79730	+	2.75890i	0.246661	+	0.179210i
$238$	−2.55638	−	15.3301i	−0.165705	−	0.993703i
$239$	−9.74990	+	3.16793i	−0.630669	+	0.204917i	−0.606871	−	0.794800i	$-0.707576\pi$
$239$	−9.74990	+	3.16793i	−0.630669	+	0.204917i	−0.0237973	+	0.999717i	$0.507576\pi$
$240$	0.387142	+	3.68341i	0.0249899	+	0.237763i
$241$	10.0961	+	17.4870i	0.650349	+	1.12644i	0.983038	+	0.183401i	$0.0587106\pi$
$241$	10.0961	+	17.4870i	0.650349	+	1.12644i	−0.332690	+	0.943036i	$0.607956\pi$
$242$	9.06316	+	6.23371i	0.582602	+	0.400718i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−4.11474	+	2.98953i	−0.263419	+	0.191385i
$245$	−17.6598	−	18.9812i	−1.12824	−	1.21266i
$246$	−0.499636	+	1.53772i	−0.0318556	+	0.0980415i
$247$	−4.61514	+	2.05479i	−0.293654	+	0.130743i
$248$	1.02499	−	9.75214i	0.0650870	−	0.619261i
$249$	2.47432	+	11.6408i	0.156804	+	0.737704i
$250$	13.4673	+	2.86257i	0.851749	+	0.181045i
$251$	3.57029	+	4.91408i	0.225354	+	0.310174i	0.906690	−	0.421797i	$-0.138601\pi$
$251$	3.57029	+	4.91408i	0.225354	+	0.310174i	−0.681336	+	0.731971i	$0.738601\pi$
$252$	1.22033	+	2.34751i	0.0768736	+	0.147879i
$253$	−2.79618	+	2.32471i	−0.175794	+	0.146153i
$254$	−7.23502	+	12.5314i	−0.453965	+	0.786291i
$255$	19.8755	+	8.84914i	1.24465	+	0.554155i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−19.9920	+	18.0009i	−1.24707	+	1.12286i	−0.259487	+	0.965747i	$0.583554\pi$
$257$	−19.9920	+	18.0009i	−1.24707	+	1.12286i	−0.987580	+	0.157118i	$0.949780\pi$
$258$	0.436038	−	0.600155i	0.0271466	−	0.0373640i
$259$	8.31512	+	6.62191i	0.516677	+	0.411465i
$260$	17.7064	+	5.75315i	1.09810	+	0.356795i
$261$	−0.647121	+	3.04447i	−0.0400558	+	0.188448i
$262$	4.27183	−	9.59468i	0.263914	−	0.592761i
$263$	−13.9067	+	8.02901i	−0.857521	+	0.495090i	−0.863181	−	0.504894i	$-0.831532\pi$
$263$	−13.9067	+	8.02901i	−0.857521	+	0.495090i	0.00566047	+	0.999984i	$0.498198\pi$
$264$	2.37529	+	2.31473i	0.146189	+	0.142462i
$265$		−	44.0677i		−	2.70705i
$266$	2.65412	−	0.160811i	0.162735	−	0.00985997i
$267$	−2.81279	−	8.65688i	−0.172140	−	0.529792i
$268$	−2.67307	−	2.96875i	−0.163284	−	0.181345i
$269$	−30.2443	−	3.17880i	−1.84403	−	0.193815i	−0.882832	−	0.469688i	$-0.844366\pi$
$269$	−30.2443	−	3.17880i	−1.84403	−	0.193815i	−0.961194	+	0.275873i	$0.911033\pi$
$270$	−3.68341	−	0.387142i	−0.224165	−	0.0235607i
$271$	−17.2992	−	19.2127i	−1.05085	−	1.16709i	−0.985579	−	0.169219i	$-0.945876\pi$
$271$	−17.2992	−	19.2127i	−1.05085	−	1.16709i	−0.0652707	−	0.997868i	$-0.520791\pi$
$272$	−1.81524	−	5.58674i	−0.110065	−	0.338746i
$273$	13.2752	−	0.804332i	0.803450	−	0.0486804i
$274$		−	0.619470i		−	0.0374236i
$275$	25.5895	−	13.4575i	1.54311	−	0.811515i
$276$	−0.949506	+	0.548198i	−0.0571536	+	0.0329976i
$277$	7.50734	−	16.8618i	0.451073	−	1.01313i	−0.534700	−	0.845042i	$-0.679575\pi$
$277$	7.50734	−	16.8618i	0.451073	−	1.01313i	0.985773	−	0.168084i	$-0.0537579\pi$
$278$	−3.23138	+	15.2025i	−0.193806	+	0.911783i
$279$	9.32592	+	3.03018i	0.558328	+	0.181412i
$280$	−7.66535	−	6.10445i	−0.458092	−	0.364811i
$281$	−7.54553	+	10.3855i	−0.450129	+	0.619549i	−0.972425	−	0.233215i	$-0.925075\pi$
$281$	−7.54553	+	10.3855i	−0.450129	+	0.619549i	0.522296	+	0.852764i	$0.325075\pi$
$282$	−0.628211	+	0.565644i	−0.0374094	+	0.0336836i
$283$	−12.8834	+	14.3084i	−0.765837	+	0.850549i	−0.992350	−	0.123460i	$-0.960601\pi$
$283$	−12.8834	+	14.3084i	−0.765837	+	0.850549i	0.226512	+	0.974008i	$0.427268\pi$
$284$	2.37429	+	1.05710i	0.140888	+	0.0627275i
$285$	−1.86112	+	3.22355i	−0.110243	+	0.190947i
$286$	15.4861	−	6.17510i	0.915710	−	0.365141i
$287$	−1.97310	−	3.79558i	−0.116468	−	0.224046i
$288$	0.587785	+	0.809017i	0.0346356	+	0.0476718i
$289$	−17.1242	−	3.63985i	−1.00730	−	0.214109i
$290$	−2.39674	−	11.2758i	−0.140742	−	0.662138i
$291$	1.75937	−	16.7393i	0.103136	−	0.981273i
$292$	9.47866	−	4.22017i	0.554696	−	0.246967i
$293$	−4.20754	+	12.9495i	−0.245807	+	0.756516i	0.749696	+	0.661783i	$0.230200\pi$
$293$	−4.20754	+	12.9495i	−0.245807	+	0.756516i	−0.995503	+	0.0947331i	$0.969800\pi$
$294$	−6.69179	−	2.05425i	−0.390273	−	0.119806i
$295$	42.1246	−	30.6053i	2.45259	−	1.78191i
$296$	3.47939	+	2.00883i	0.202236	+	0.116761i
$297$	−2.75800	+	1.84213i	−0.160036	+	0.106891i
$298$	6.49026	+	11.2415i	0.375971	+	0.651201i
$299$	0.576088	+	5.48111i	0.0333160	+	0.316981i
$300$	8.29075	−	2.69383i	0.478667	−	0.155528i
$301$	0.322834	+	1.93597i	0.0186078	+	0.111588i
$302$	3.81763	+	2.77367i	0.219680	+	0.159607i
$303$	4.27088	+	9.59256i	0.245356	+	0.551078i
$304$	0.983042	−	0.208952i	0.0563813	−	0.0119842i
$305$	13.9989	+	12.6047i	0.801575	+	0.721742i
$306$	5.84206	−	0.614026i	0.333968	−	0.0351015i
$307$	11.0131			0.628551			0.314276	−	0.949332i	$-0.398238\pi$
$307$	11.0131			0.628551			0.314276	+	0.949332i	$0.398238\pi$
$308$	−8.77302	+	0.184845i	−0.499889	+	0.0105325i
$309$	−11.2133			−0.637903
$310$	−36.1190	+	3.79626i	−2.05142	+	0.215613i
$311$	−21.7655	−	19.5978i	−1.23421	−	1.11129i	−0.989926	−	0.141585i	$-0.954780\pi$
$311$	−21.7655	−	19.5978i	−1.23421	−	1.11129i	−0.244284	−	0.969704i	$-0.578553\pi$
$312$	4.91690	−	1.04512i	0.278365	−	0.0591682i
$313$	1.18589	+	2.66356i	0.0670307	+	0.150553i	0.943954	−	0.330077i	$-0.107075\pi$
$313$	1.18589	+	2.66356i	0.0670307	+	0.150553i	−0.876923	+	0.480630i	$0.840408\pi$
$314$	5.04439	+	3.66496i	0.284671	+	0.206826i
$315$	7.56477	−	6.22866i	0.426226	−	0.350945i
$316$	−4.46399	+	1.45044i	−0.251119	+	0.0815936i
$317$	0.921042	+	8.76313i	0.0517309	+	0.492186i	0.989459	+	0.144815i	$0.0462588\pi$
$317$	0.921042	+	8.76313i	0.0517309	+	0.492186i	−0.937728	+	0.347371i	$0.887075\pi$
$318$	−5.94914	−	10.3042i	−0.333611	−	0.577831i
$319$	−8.10563	−	6.39231i	−0.453828	−	0.357901i
$320$	−3.20750	−	1.85185i	−0.179305	−	0.103522i
$321$	−11.5792	+	8.41279i	−0.646289	+	0.469556i
$322$	0.727904	−	2.80798i	0.0405645	−	0.156482i
$323$	1.82432	−	5.61469i	0.101508	−	0.312410i
$324$	−0.913545	+	0.406737i	−0.0507525	+	0.0225965i
$325$	4.58046	−	43.5802i	0.254078	−	2.41739i
$326$	−4.48989	−	21.1233i	−0.248672	−	1.16991i
$327$	−8.33111	−	1.77083i	−0.460712	−	0.0979273i
$328$	−0.950364	−	1.30806i	−0.0524751	−	0.0722258i
$329$	0.0988340	−	2.23438i	0.00544889	−	0.123185i
$330$	6.55667	−	10.3876i	0.360933	−	0.571817i
$331$	−2.31939	+	4.01730i	−0.127485	+	0.220811i	−0.922702	−	0.385515i	$-0.874024\pi$
$331$	−2.31939	+	4.01730i	−0.127485	+	0.220811i	0.795217	+	0.606326i	$0.207357\pi$
$332$	−10.8720	−	4.84051i	−0.596676	−	0.265657i
$333$	−2.68834	+	2.98570i	−0.147320	+	0.163615i
$334$	−16.2157	+	14.6006i	−0.887281	+	0.798912i
$335$	−8.69670	+	11.9700i	−0.475151	+	0.653990i
$336$	−2.61647	−	0.392562i	−0.142740	−	0.0214160i
$337$	0.640551	+	0.208127i	0.0348930	+	0.0113374i	0.326412	−	0.945228i	$-0.394160\pi$
$337$	0.640551	+	0.208127i	0.0348930	+	0.0113374i	−0.291518	+	0.956565i	$0.594160\pi$
$338$	2.55070	−	12.0001i	0.138740	−	0.652718i
$339$	0.105253	−	0.236401i	0.00571653	−	0.0128395i
$340$	−18.8416	+	10.8782i	−1.02183	+	0.589955i
$341$	−22.6979	+	23.2918i	−1.22916	+	1.26132i
$342$			1.00500i			0.0543444i
$343$	16.2910	−	8.80920i	0.879634	−	0.475652i
$344$	0.229239	+	0.705525i	0.0123597	+	0.0380393i
$345$	2.71715	+	3.01771i	0.146287	+	0.162468i
$346$	2.82882	+	0.297321i	0.152078	+	0.0159841i
$347$	12.7063	+	1.33549i	0.682112	+	0.0716929i	0.439246	−	0.898367i	$-0.355246\pi$
$347$	12.7063	+	1.33549i	0.682112	+	0.0716929i	0.242866	+	0.970060i	$0.421912\pi$
$348$	−2.08266	−	2.31302i	−0.111642	−	0.123991i
$349$	0.0215856	+	0.0664336i	0.00115545	+	0.00355611i	0.951633	−	0.307238i	$-0.0994049\pi$
$349$	0.0215856	+	0.0664336i	0.00115545	+	0.00355611i	−0.950477	+	0.310795i	$0.899405\pi$
$350$	−10.3029	+	20.6350i	−0.550716	+	1.10299i
$351$			5.02675i			0.268308i
$352$	−3.26882	+	0.561085i	−0.174229	+	0.0299059i
$353$	3.31580	−	1.91438i	0.176482	−	0.101892i	−0.409157	−	0.912464i	$-0.634177\pi$
$353$	3.31580	−	1.91438i	0.176482	−	0.101892i	0.585639	+	0.810572i	$0.300844\pi$
$354$	5.71814	−	12.8432i	0.303916	−	0.682606i
$355$	2.00133	−	9.41551i	0.106220	−	0.499724i
$356$	8.65688	+	2.81279i	0.458814	+	0.149078i
$357$	−9.68194	+	12.1576i	−0.512422	+	0.643448i
$358$	5.49882	−	7.56848i	0.290622	−	0.400007i
$359$	−2.75427	+	2.47995i	−0.145365	+	0.130887i	−0.738605	−	0.674139i	$-0.764515\pi$
$359$	−2.75427	+	2.47995i	−0.145365	+	0.130887i	0.593240	+	0.805025i	$0.297848\pi$
$360$	2.47826	−	2.75239i	0.130616	−	0.145064i
$361$	−16.4347	−	7.31718i	−0.864982	−	0.385115i
$362$	−1.21826	+	2.11008i	−0.0640301	+	0.110903i
$363$	−1.43189	−	10.9064i	−0.0751547	−	0.572438i
$364$	−7.15223	+	11.2126i	−0.374879	+	0.587701i
$365$	−22.5877	−	31.0893i	−1.18229	−	1.62729i
$366$	4.97495	+	1.05746i	0.260045	+	0.0552743i
$367$	−0.774662	−	3.64450i	−0.0404370	−	0.190241i	0.953293	−	0.302047i	$-0.0976699\pi$
$367$	−0.774662	−	3.64450i	−0.0404370	−	0.190241i	−0.993730	+	0.111806i	$0.964337\pi$
$368$	0.114605	−	1.09039i	0.00597418	−	0.0568405i
$369$	1.47707	−	0.657635i	0.0768933	−	0.0342351i
$370$	4.59824	−	14.1519i	0.239051	−	0.735723i
$371$	30.4726	+	7.89934i	1.58206	+	0.410113i
$372$	−7.93310	+	5.76374i	−0.411312	+	0.298836i
$373$	28.9662	+	16.7237i	1.49981	+	0.865918i	1.00000		0.000214021i	$-6.81251e-5\pi$
$373$	28.9662	+	16.7237i	1.49981	+	0.865918i	0.499815	+	0.866132i	$0.333401\pi$
$374$	−6.74655	+	18.2773i	−0.348856	+	0.945094i
$375$	−6.88410	−	11.9236i	−0.355493	−	0.615733i
$376$	−0.0883622	−	0.840710i	−0.00455693	−	0.0433563i
$377$	−14.8799	+	4.83477i	−0.766354	+	0.249003i
$378$	0.927977	−	2.47767i	0.0477300	−	0.127438i
$379$	15.3097	+	11.1232i	0.786409	+	0.571359i	0.906895	−	0.421356i	$-0.138446\pi$
$379$	15.3097	+	11.1232i	0.786409	+	0.571359i	−0.120487	+	0.992715i	$0.538446\pi$
$380$	−1.51397	−	3.40043i	−0.0776650	−	0.174438i
$381$	14.1538	−	3.00849i	0.725122	−	0.154130i
$382$	−12.4800	−	11.2371i	−0.638535	−	0.574939i
$383$	−2.53172	+	0.266095i	−0.129365	+	0.0135968i	−0.168990	−	0.985618i	$-0.554050\pi$
$383$	−2.53172	+	0.266095i	−0.129365	+	0.0135968i	0.0396246	+	0.999215i	$0.487384\pi$
$384$	−1.00000			−0.0510310
$385$	7.42525	+	31.6403i	0.378426	+	1.61254i
$386$	−3.10062			−0.157817
$387$	−0.737769	+	0.0775426i	−0.0375029	+	0.00394171i
$388$	12.5082	+	11.2624i	0.635008	+	0.571764i
$389$	−7.16250	+	1.52244i	−0.363153	+	0.0771906i	−0.385875	−	0.922551i	$-0.626100\pi$
$389$	−7.16250	+	1.52244i	−0.363153	+	0.0771906i	0.0227215	+	0.999742i	$0.492767\pi$
$390$	−7.57245	−	17.0080i	−0.383446	−	0.861233i
$391$	−5.21047	−	3.78563i	−0.263505	−	0.191447i
$392$	5.59526	−	4.20631i	0.282603	−	0.212451i
$393$	−9.98865	+	3.24551i	−0.503861	+	0.163714i
$394$	−0.244613	−	2.32734i	−0.0123234	−	0.117250i
$395$	8.69207	+	15.0551i	0.437345	+	0.757505i
$396$	0.130802	−	3.31404i	0.00657306	−	0.166537i
$397$	26.5956	+	15.3550i	1.33479	+	0.770644i	0.986030	−	0.166567i	$-0.0532681\pi$
$397$	26.5956	+	15.3550i	1.33479	+	0.770644i	0.348764	+	0.937211i	$0.386601\pi$
$398$	3.76914	−	2.73844i	0.188930	−	0.137266i
$399$	−1.89546	−	1.86479i	−0.0948917	−	0.0933565i
$400$	−2.69383	+	8.29075i	−0.134691	+	0.414538i
$401$	−7.63467	+	3.39917i	−0.381257	+	0.169747i	−0.588412	−	0.808562i	$-0.700246\pi$
$401$	−7.63467	+	3.39917i	−0.381257	+	0.169747i	0.207154	+	0.978308i	$0.433580\pi$
$402$	−0.417575	+	3.97296i	−0.0208267	+	0.198153i
$403$	10.2483	+	48.2144i	0.510503	+	2.40173i
$404$	−10.2709	−	2.18315i	−0.510997	−	0.108616i
$405$	2.17698	+	2.99636i	0.108175	+	0.148890i
$406$	8.22681	+	0.363899i	0.408290	+	0.0180600i
$407$	−4.93549	−	12.3773i	−0.244643	−	0.613521i
$408$	−2.93712	+	5.08724i	−0.145409	+	0.251856i
$409$	−25.3361	−	11.2804i	−1.25279	−	0.557778i	−0.330328	−	0.943866i	$-0.607159\pi$
$409$	−25.3361	−	11.2804i	−1.25279	−	0.557778i	−0.922462	+	0.386088i	$0.873826\pi$
$410$	−4.00699	+	4.45021i	−0.197891	+	0.219780i
$411$	−0.460356	+	0.414507i	−0.0227077	+	0.0204461i
$412$	6.59102	−	9.07176i	0.324716	−	0.446934i
$413$	13.6124	+	34.6152i	0.669824	+	1.70330i
$414$	1.04273	+	0.338805i	0.0512476	+	0.0166514i
$415$	−9.16416	+	43.1140i	−0.449851	+	2.11638i
$416$	−2.04456	+	4.59216i	−0.100243	+	0.225149i
$417$	13.4599	−	7.77105i	0.659132	−	0.380550i
$418$	−2.98921	−	1.47478i	−0.146207	−	0.0721338i
$419$			5.11093i			0.249685i	0.992177	+	0.124843i	$0.0398426\pi$
$419$			5.11093i			0.249685i	−0.992177	+	0.124843i	$0.960157\pi$
$420$	0.592631	+	9.78114i	0.0289175	+	0.477271i
$421$	−6.46148	−	19.8864i	−0.314913	−	0.969203i	−0.975790	−	0.218709i	$-0.929815\pi$
$421$	−6.46148	−	19.8864i	−0.314913	−	0.969203i	0.660877	−	0.750494i	$-0.270185\pi$
$422$	−2.90268	−	3.22376i	−0.141300	−	0.156930i
$423$	0.840710	+	0.0883622i	0.0408767	+	0.00429632i
$424$	11.8331	+	1.24371i	0.574666	+	0.0603998i
$425$	34.2650	+	38.0551i	1.66210	+	1.84594i
$426$	−0.803130	−	2.47178i	−0.0389118	−	0.119758i
$427$	−11.2255	+	7.42075i	−0.543238	+	0.359115i
$428$		−	14.3127i		−	0.691830i
$429$	−14.9512	−	7.37643i	−0.721850	−	0.356138i
$430$	2.37943	−	1.37376i	0.114746	−	0.0662488i
$431$	−4.60569	+	10.3446i	−0.221848	+	0.498279i	−0.989841	−	0.142179i	$-0.954589\pi$
$431$	−4.60569	+	10.3446i	−0.221848	+	0.498279i	0.767993	+	0.640459i	$0.221256\pi$
$432$	0.207912	−	0.978148i	0.0100032	−	0.0470611i
$433$	34.7568	+	11.2932i	1.67031	+	0.542715i	0.982992	−	0.183646i	$-0.0587900\pi$
$433$	34.7568	+	11.2932i	1.67031	+	0.542715i	0.687313	+	0.726361i	$0.258790\pi$
$434$	3.84940	−	25.6567i	0.184777	−	1.23156i
$435$	−6.77581	+	9.32611i	−0.324875	+	0.447153i
$436$	6.32954	−	5.69914i	0.303130	−	0.272939i
$437$	0.737303	−	0.818858i	0.0352700	−	0.0391713i
$438$	−9.47866	−	4.22017i	−0.452908	−	0.201647i
$439$	13.7054	−	23.7384i	0.654122	−	1.13297i	−0.327992	−	0.944681i	$-0.606372\pi$
$439$	13.7054	−	23.7384i	0.654122	−	1.13297i	0.982113	−	0.188291i	$-0.0602949\pi$
$440$	4.54981	+	11.4101i	0.216904	+	0.543956i
$441$	2.95108	+	6.34753i	0.140527	+	0.302263i
$442$	17.3563	+	23.8889i	0.825556	+	1.13628i
$443$	31.7443	+	6.74745i	1.50822	+	0.320581i	0.886524	−	0.462682i	$-0.153113\pi$
$443$	31.7443	+	6.74745i	1.50822	+	0.320581i	0.621691	+	0.783263i	$0.286446\pi$
$444$	−0.835318	−	3.92986i	−0.0396424	−	0.186503i
$445$	3.52392	−	33.5278i	0.167050	−	1.58937i
$446$	8.48172	−	3.77630i	0.401621	−	0.178813i
$447$	4.01120	−	12.3452i	0.189723	−	0.583909i
$448$	1.85551	−	1.88602i	0.0876646	−	0.0891062i
$449$	−14.1874	+	10.3077i	−0.669543	+	0.486452i	−0.869872	−	0.493277i	$-0.835799\pi$
$449$	−14.1874	+	10.3077i	−0.669543	+	0.486452i	0.200329	+	0.979729i	$0.435799\pi$
$450$	−7.54950	−	4.35871i	−0.355887	−	0.205471i
$451$	−0.211488	+	5.35833i	−0.00995860	+	0.252314i
$452$	0.129387	+	0.224104i	0.00608584	+	0.0105410i
$453$	−0.493254	−	4.69300i	−0.0231751	−	0.220496i
$454$	0.0769986	−	0.0250184i	0.00361372	−	0.00117417i
$455$	46.1282	+	17.2767i	2.16252	+	0.809943i
$456$	−0.813065	−	0.590726i	−0.0380753	−	0.0276633i
$457$	−1.71809	−	3.85890i	−0.0803689	−	0.180512i	0.868892	−	0.495002i	$-0.164833\pi$
$457$	−1.71809	−	3.85890i	−0.0803689	−	0.180512i	−0.949260	+	0.314491i	$0.898166\pi$
$458$	−28.8442	+	6.13102i	−1.34780	+	0.286484i
$459$	−4.36541	−	3.93064i	−0.203760	−	0.183466i
$460$	−4.03848	+	0.424461i	−0.188295	+	0.0197906i
$461$	−22.3624			−1.04152			−0.520761	−	0.853702i	$-0.674352\pi$
$461$	−22.3624			−1.04152			−0.520761	+	0.853702i	$0.674352\pi$
$462$	6.00766	+	6.39594i	0.279502	+	0.297566i
$463$	35.8049			1.66399			0.831997	−	0.554780i	$-0.187198\pi$
$463$	35.8049			1.66399			0.831997	+	0.554780i	$0.187198\pi$
$464$	3.09543	−	0.325343i	0.143702	−	0.0151037i
$465$	26.9895	+	24.3015i	1.25161	+	1.12695i
$466$	22.7480	−	4.83524i	1.05378	−	0.223988i
$467$	2.60077	+	5.84143i	0.120349	+	0.270309i	0.963667	−	0.267106i	$-0.0860674\pi$
$467$	2.60077	+	5.84143i	0.120349	+	0.270309i	−0.843318	+	0.537415i	$0.819401\pi$
$468$	−4.06672	−	2.95465i	−0.187984	−	0.136579i
$469$	−6.71828	−	8.15941i	−0.310221	−	0.376767i
$470$	−2.97766	+	0.967499i	−0.137349	+	0.0446274i
$471$	−0.651757	−	6.20105i	−0.0300314	−	0.285729i
$472$	7.02929	+	12.1751i	0.323549	+	0.560404i
$473$	0.851992	−	2.30816i	0.0391746	−	0.106129i
$474$	4.06488	+	2.34686i	0.186706	+	0.107795i
$475$	−7.08782	+	5.14961i	−0.325212	+	0.236280i
$476$	−4.14480	−	14.9789i	−0.189977	−	0.686557i
$477$	−3.67677	+	11.3159i	−0.168348	+	0.518121i
$478$	−9.36535	+	4.16972i	−0.428361	+	0.190719i
$479$	−3.32486	+	31.6339i	−0.151917	+	1.44539i	0.607259	+	0.794504i	$0.292269\pi$
$479$	−3.32486	+	31.6339i	−0.151917	+	1.44539i	−0.759176	+	0.650885i	$0.774398\pi$
$480$	0.770043	+	3.62277i	0.0351475	+	0.165356i
$481$	−19.7544	−	4.19893i	−0.900723	−	0.191455i
$482$	11.8687	+	16.3359i	0.540605	+	0.744079i
$483$	−2.57380	+	1.33797i	−0.117112	+	0.0608795i
$484$	9.66511	+	5.25220i	0.439323	+	0.238736i
$485$	31.1694	−	53.9869i	1.41533	−	2.45142i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	1.96322	−	2.18038i	0.0889620	−	0.0988023i	−0.697020	−	0.717052i	$-0.745491\pi$
$487$	1.96322	−	2.18038i	0.0889620	−	0.0988023i	0.785982	+	0.618249i	$0.212158\pi$
$488$	−3.77971	+	3.40326i	−0.171099	+	0.154058i
$489$	−12.6933	+	17.4709i	−0.574012	+	0.790060i
$490$	−19.5471	−	17.0313i	−0.883048	−	0.769395i
$491$	38.3588	+	12.4635i	1.73111	+	0.562472i	0.993609	−	0.112874i	$-0.0360058\pi$
$491$	38.3588	+	12.4635i	1.73111	+	0.562472i	0.737501	+	0.675346i	$0.236006\pi$
$492$	−0.336163	+	1.58152i	−0.0151554	+	0.0713006i
$493$	7.43656	−	16.7028i	0.334926	−	0.752255i
$494$	−4.37507	+	2.52595i	−0.196844	+	0.113648i
$495$	−12.1067	+	2.07809i	−0.544157	+	0.0934032i
$496$		−	9.80585i		−	0.440296i
$497$	6.15205	+	3.07169i	0.275957	+	0.137784i
$498$	3.67756	+	11.3184i	0.164795	+	0.507188i
$499$	−11.4804	−	12.7503i	−0.513934	−	0.570782i	0.429194	−	0.903213i	$-0.358798\pi$
$499$	−11.4804	−	12.7503i	−0.513934	−	0.570782i	−0.943128	+	0.332431i	$0.892131\pi$
$500$	13.6928	+	1.43917i	0.612359	+	0.0643616i
$501$	21.7008	+	2.28084i	0.969520	+	0.101901i
$502$	4.06439	+	4.51396i	0.181402	+	0.201468i
$503$	9.60684	+	29.5668i	0.428348	+	1.31832i	0.899752	+	0.436401i	$0.143747\pi$
$503$	9.60684	+	29.5668i	0.428348	+	1.31832i	−0.471404	+	0.881917i	$0.656253\pi$
$504$	1.45903	+	2.20709i	0.0649902	+	0.0983115i
$505$			38.8902i			1.73059i
$506$	−2.53786	+	2.60426i	−0.112822	+	0.115773i
$507$	−10.6245	+	6.13408i	−0.471853	+	0.272424i
$508$	−5.88549	+	13.2190i	−0.261126	+	0.586500i
$509$	3.71005	−	17.4544i	0.164445	−	0.773653i	−0.816186	−	0.577789i	$-0.803916\pi$
$509$	3.71005	−	17.4544i	0.164445	−	0.773653i	0.980631	−	0.195864i	$-0.0627510\pi$
$510$	20.6916	+	6.72311i	0.916240	+	0.297704i
$511$	25.5471	−	10.0464i	1.13014	−	0.444427i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	0.746863	−	0.672479i	0.0329748	−	0.0296907i
$514$	−18.0009	+	19.9920i	−0.793985	+	0.881810i
$515$	−37.9402	−	16.8921i	−1.67185	−	0.744354i
$516$	0.370916	−	0.642446i	0.0163287	−	0.0282821i
$517$	−1.49651	+	2.37088i	−0.0658163	+	0.104271i
$518$	8.96175	+	5.71646i	0.393757	+	0.251167i
$519$	−1.67190	−	2.30117i	−0.0733881	−	0.101010i
$520$	18.2107	+	3.87081i	0.798593	+	0.169746i
$521$	6.66532	+	31.3579i	0.292013	+	1.37381i	0.842377	+	0.538888i	$0.181155\pi$
$521$	6.66532	+	31.3579i	0.292013	+	1.37381i	−0.550364	+	0.834925i	$0.685511\pi$
$522$	−0.325343	+	3.09543i	−0.0142399	+	0.135483i
$523$	7.68589	−	3.42198i	0.336080	−	0.149633i	−0.231756	−	0.972774i	$-0.574447\pi$
$523$	7.68589	−	3.42198i	0.336080	−	0.149633i	0.567837	+	0.823141i	$0.307781\pi$
$524$	3.24551	−	9.98865i	0.141781	−	0.436356i
$525$	22.2288	−	6.15092i	0.970144	−	0.268448i
$526$	−12.9912	+	9.43867i	−0.566444	+	0.411545i
$527$	−49.8848	−	28.8010i	−2.17301	−	1.25459i
$528$	2.60423	+	2.05377i	0.113335	+	0.0893788i
$529$	10.8990	+	18.8775i	0.473868	+	0.820763i
$530$	−4.60632	−	43.8263i	−0.200086	−	1.90369i
$531$	−13.3705	+	4.34434i	−0.580231	+	0.188528i
$532$	2.62277	−	0.437362i	0.113712	−	0.0189620i
$533$	6.57531	+	4.77724i	0.284808	+	0.206925i
$534$	−3.70227	−	8.31544i	−0.160213	−	0.359844i
$535$	−51.8516	+	11.0214i	−2.24174	+	0.476496i
$536$	−2.96875	−	2.67307i	−0.128230	−	0.115459i
$537$	−9.30391	+	0.977880i	−0.401493	+	0.0421986i
$538$	−30.4109			−1.31111
$539$	−23.2102	−	0.537130i	−0.999732	−	0.0231358i
$540$	−3.70370			−0.159382
$541$	−10.9964	+	1.15577i	−0.472771	+	0.0496903i	−0.337918	−	0.941175i	$-0.609723\pi$
$541$	−10.9964	+	1.15577i	−0.472771	+	0.0496903i	−0.134853	+	0.990866i	$0.543056\pi$
$542$	−19.2127	−	17.2992i	−0.825255	−	0.743063i
$543$	2.38327	−	0.506580i	0.102276	−	0.0217394i
$544$	−2.38927	−	5.36639i	−0.102439	−	0.230082i
$545$	−25.5207	−	18.5419i	−1.09319	−	0.794246i
$546$	13.1184	−	2.18756i	0.561415	−	0.0936189i
$547$	−20.8230	+	6.76579i	−0.890326	+	0.289284i	−0.718238	−	0.695797i	$-0.755051\pi$
$547$	−20.8230	+	6.76579i	−0.890326	+	0.289284i	−0.172088	+	0.985082i	$0.555051\pi$
$548$	−0.0647523	−	0.616077i	−0.00276608	−	0.0263175i
$549$	−2.54305	−	4.40469i	−0.108535	−	0.187988i
$550$	24.0426	−	16.0586i	1.02518	−	0.684740i
$551$	2.70897	+	1.56403i	0.115406	+	0.0666298i
$552$	−0.887003	+	0.644445i	−0.0377533	+	0.0274294i
$553$	−11.9687	+	3.31184i	−0.508959	+	0.140834i
$554$	5.70368	−	17.5541i	0.242326	−	0.745804i
$555$	−13.5937	+	6.05232i	−0.577022	+	0.256907i
$556$	−1.62459	+	15.4570i	−0.0688980	+	0.655521i
$557$	−3.79747	−	17.8657i	−0.160904	−	0.756994i	−0.982401	−	0.186782i	$-0.940194\pi$
$557$	−3.79747	−	17.8657i	−0.160904	−	0.756994i	0.821497	−	0.570212i	$-0.193139\pi$
$558$	9.59157	+	2.03875i	0.406044	+	0.0863072i
$559$	−2.19185	−	3.01683i	−0.0927055	−	0.127598i
$560$	−8.26145	−	5.26976i	−0.349110	−	0.222688i
$561$	18.0970	−	7.21621i	0.764055	−	0.304669i
$562$	−6.41862	+	11.1174i	−0.270753	+	0.468958i
$563$	10.3567	+	4.61112i	0.436485	+	0.194335i	0.613202	−	0.789926i	$-0.289881\pi$
$563$	10.3567	+	4.61112i	0.436485	+	0.194335i	−0.176717	+	0.984262i	$0.556548\pi$
$564$	−0.565644	+	0.628211i	−0.0238179	+	0.0264525i
$565$	0.712244	−	0.641308i	0.0299643	−	0.0269800i
$566$	−11.3172	+	15.5767i	−0.475696	+	0.654739i
$567$	−2.46221	+	0.968265i	−0.103403	+	0.0406633i
$568$	2.47178	+	0.803130i	0.103714	+	0.0336986i
$569$	−7.13727	+	33.5782i	−0.299210	+	1.40767i	0.529651	+	0.848216i	$0.322323\pi$
$569$	−7.13727	+	33.5782i	−0.299210	+	1.40767i	−0.828860	+	0.559456i	$0.811010\pi$
$570$	−1.51397	+	3.40043i	−0.0634132	+	0.142428i
$571$	8.57705	−	4.95196i	0.358938	−	0.207233i	−0.309677	−	0.950842i	$-0.600221\pi$
$571$	8.57705	−	4.95196i	0.358938	−	0.207233i	0.668615	+	0.743609i	$0.266887\pi$
$572$	14.7557	−	7.76001i	0.616969	−	0.324462i
$573$			16.7936i			0.701561i
$574$	−2.35904	−	3.56854i	−0.0984643	−	0.148948i
$575$	2.95350	+	9.08995i	0.123170	+	0.379077i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	35.1095	+	3.69016i	1.46163	+	0.153623i	0.801710	−	0.597713i	$-0.203924\pi$
$577$	35.1095	+	3.69016i	1.46163	+	0.153623i	0.659919	+	0.751336i	$0.270590\pi$
$578$	−17.4108	−	1.82995i	−0.724195	−	0.0761159i
$579$	2.07472	+	2.30421i	0.0862224	+	0.0957597i
$580$	−3.56226	−	10.9635i	−0.147915	−	0.455234i
$581$	−28.1705	−	14.0654i	−1.16871	−	0.583530i
$582$		−	16.8315i		−	0.697687i
$583$	−28.2619	−	27.5413i	−1.17049	−	1.14065i
$584$	8.98560	−	5.18784i	0.371827	−	0.214674i
$585$	−7.57245	+	17.0080i	−0.313082	+	0.703194i
$586$	−2.83090	+	13.3183i	−0.116943	+	0.550175i
$587$	0.163138	+	0.0530069i	0.00673344	+	0.00218783i	0.312382	−	0.949957i	$-0.398873\pi$
$587$	0.163138	+	0.0530069i	0.00673344	+	0.00218783i	−0.305648	+	0.952144i	$0.598873\pi$
$588$	−6.86986	−	1.34351i	−0.283308	−	0.0554056i
$589$	5.79258	−	7.97280i	0.238679	−	0.328513i
$590$	38.6947	−	34.8408i	1.59303	−	1.43438i
$591$	−1.56587	+	1.73908i	−0.0644113	+	0.0715360i
$592$	3.67031	+	1.63413i	0.150849	+	0.0671622i
$593$	−2.24729	+	3.89242i	−0.0922851	+	0.159842i	−0.908472	−	0.417945i	$-0.862750\pi$
$593$	−2.24729	+	3.89242i	−0.0922851	+	0.159842i	0.816187	+	0.577788i	$0.196084\pi$
$594$	−2.55034	+	2.12032i	−0.104642	+	0.0869979i
$595$	−51.0734	+	26.5501i	−2.09381	+	1.08845i
$596$	7.62976	+	10.5015i	0.312527	+	0.430157i
$597$	−4.55710	−	0.968642i	−0.186510	−	0.0396439i
$598$	1.14586	+	5.39087i	0.0468579	+	0.220449i
$599$	4.01318	−	38.1829i	0.163974	−	1.56011i	−0.534932	−	0.844895i	$-0.679663\pi$
$599$	4.01318	−	38.1829i	0.163974	−	1.56011i	0.698906	−	0.715214i	$-0.253671\pi$
$600$	7.96375	−	3.54569i	0.325119	−	0.144752i
$601$	−3.98200	+	12.2553i	−0.162429	+	0.499906i	−0.998838	−	0.0482011i	$-0.984651\pi$
$601$	−3.98200	+	12.2553i	−0.162429	+	0.499906i	0.836409	+	0.548107i	$0.184651\pi$
$602$	0.523429	+	1.89162i	0.0213334	+	0.0770967i
$603$	3.23189	−	2.34811i	0.131613	−	0.0956224i
$604$	4.08664	+	2.35942i	0.166283	+	0.0960036i
$605$	11.5850	−	39.0589i	0.470995	−	1.58797i
$606$	5.25018	+	9.09358i	0.213274	+	0.369401i
$607$	−0.837957	−	7.97263i	−0.0340116	−	0.323599i	−0.998278	−	0.0586637i	$-0.981316\pi$
$607$	−0.837957	−	7.97263i	−0.0340116	−	0.323599i	0.964266	−	0.264935i	$-0.0853506\pi$
$608$	0.955815	−	0.310563i	0.0387634	−	0.0125950i
$609$	−5.23438	−	6.35720i	−0.212108	−	0.257607i
$610$	15.2398	+	11.0723i	0.617040	+	0.448306i
$611$	1.72835	+	3.88194i	0.0699216	+	0.157047i
$612$	5.74588	−	1.22132i	0.232263	−	0.0493691i
$613$	−24.4125	−	21.9811i	−0.986011	−	0.887809i	0.00767870	−	0.999971i	$-0.497556\pi$
$613$	−24.4125	−	21.9811i	−0.986011	−	0.887809i	−0.993690	+	0.112162i	$0.964222\pi$
$614$	10.9528	−	1.15118i	0.442018	−	0.0464580i
$615$	5.98835			0.241474
$616$	−8.70564	+	1.10086i	−0.350760	+	0.0443550i
$617$	20.5979			0.829242			0.414621	−	0.909994i	$-0.363914\pi$
$617$	20.5979			0.829242			0.414621	+	0.909994i	$0.363914\pi$
$618$	−11.1519	+	1.17211i	−0.448595	+	0.0471492i
$619$	11.4268	+	10.2887i	0.459282	+	0.413539i	0.866023	−	0.500004i	$-0.166668\pi$
$619$	11.4268	+	10.2887i	0.459282	+	0.413539i	−0.406741	+	0.913543i	$0.633335\pi$
$620$	−35.5243	+	7.55093i	−1.42669	+	0.303253i
$621$	−0.445944	−	1.00161i	−0.0178951	−	0.0401931i
$622$	−23.6948	−	17.2153i	−0.950076	−	0.690271i
$623$	22.5527	+	8.44680i	0.903555	+	0.338414i
$624$	4.78072	−	1.55335i	0.191382	−	0.0621838i
$625$	−0.774163	−	7.36567i	−0.0309665	−	0.294627i
$626$	1.45782	+	2.52501i	0.0582661	+	0.100920i
$627$	0.904197	+	3.20824i	0.0361102	+	0.128125i
$628$	5.39985	+	3.11761i	0.215477	+	0.124406i
$629$	19.0934	−	13.8721i	0.761302	−	0.553118i
$630$	6.87226	−	6.98527i	0.273797	−	0.278300i
$631$	−0.380862	+	1.17217i	−0.0151619	+	0.0466635i	−0.958351	−	0.285592i	$-0.907810\pi$
$631$	−0.380862	+	1.17217i	−0.0151619	+	0.0466635i	0.943189	+	0.332256i	$0.107810\pi$
$632$	−4.28793	+	1.90911i	−0.170565	+	0.0759402i
$633$	−0.453444	+	4.31423i	−0.0180228	+	0.171475i
$634$	1.83199	+	8.61885i	0.0727577	+	0.342298i
$635$	52.4216	+	11.1425i	2.08029	+	0.442178i
$636$	−6.99363	−	9.62590i	−0.277315	−	0.381692i
$637$	−20.2155	+	28.8006i	−0.800966	+	1.14112i
$638$	−8.72941	−	5.51003i	−0.345600	−	0.218144i
$639$	−1.29949	+	2.25079i	−0.0514071	+	0.0890397i
$640$	−3.38350	−	1.50643i	−0.133745	−	0.0595469i
$641$	21.4682	−	23.8429i	0.847943	−	0.941736i	−0.150961	−	0.988540i	$-0.548237\pi$
$641$	21.4682	−	23.8429i	0.847943	−	0.941736i	0.998904	+	0.0468036i	$0.0149035\pi$
$642$	−10.6364	+	9.57706i	−0.419785	+	0.377977i
$643$	11.2064	−	15.4243i	0.441937	−	0.608274i	−0.528704	−	0.848806i	$-0.677322\pi$
$643$	11.2064	−	15.4243i	0.441937	−	0.608274i	0.970641	+	0.240532i	$0.0773218\pi$
$644$	0.430403	−	2.86868i	0.0169603	−	0.113042i
$645$	−2.61305	−	0.849033i	−0.102889	−	0.0334306i
$646$	1.22743	−	5.77463i	0.0482928	−	0.227200i
$647$	6.71336	−	15.0785i	0.263930	−	0.592796i	−0.732161	−	0.681131i	$-0.761488\pi$
$647$	6.71336	−	15.0785i	0.263930	−	0.592796i	0.996091	+	0.0883359i	$0.0281549\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	6.69888	−	46.1433i	0.262954	−	1.81128i
$650$		−	43.8202i		−	1.71877i
$651$	−21.6424	+	14.3070i	−0.848232	+	0.560736i
$652$	−6.67327	−	20.5382i	−0.261346	−	0.804339i
$653$	−16.0171	−	17.7888i	−0.626797	−	0.696129i	0.343195	−	0.939264i	$-0.388491\pi$
$653$	−16.0171	−	17.7888i	−0.626797	−	0.696129i	−0.969992	+	0.243135i	$0.921824\pi$
$654$	−8.47058	−	0.890294i	−0.331226	−	0.0348132i
$655$	−38.6857	−	4.06603i	−1.51158	−	0.158873i
$656$	−1.08189	−	1.20156i	−0.0422406	−	0.0469130i
$657$	3.20626	+	9.86786i	0.125088	+	0.384982i
$658$	−0.135263	−	2.23247i	−0.00527312	−	0.0870307i
$659$		−	31.8124i		−	1.23924i	−0.784904	−	0.619618i	$-0.787288\pi$
$659$		−	31.8124i		−	1.23924i	0.784904	−	0.619618i	$-0.212712\pi$
$660$	5.43495	−	11.0160i	0.211555	−	0.428798i
$661$	−21.9372	+	12.6655i	−0.853259	+	0.492629i	−0.861749	−	0.507335i	$-0.830631\pi$
$661$	−21.9372	+	12.6655i	−0.853259	+	0.492629i	0.00849033	+	0.999964i	$0.497297\pi$
$662$	−1.88676	+	4.23773i	−0.0733310	+	0.164704i
$663$	6.13928	−	28.8831i	0.238430	−	1.12172i
$664$	−11.3184	−	3.67756i	−0.439238	−	0.142717i
$665$	−3.60411	−	9.16491i	−0.139761	−	0.355400i
$666$	−2.36152	+	3.25035i	−0.0915070	+	0.125949i
$667$	2.53599	−	2.28342i	0.0981939	−	0.0884142i
$668$	−14.6006	+	16.2157i	−0.564916	+	0.627403i
$669$	−8.48172	−	3.77630i	−0.327922	−	0.146000i
$670$	−7.39785	+	12.8135i	−0.285804	+	0.495027i
$671$	16.8328	−	1.10026i	0.649821	−	0.0424749i
$672$	−2.64317	−	0.116916i	−0.101962	−	0.00451014i
$673$	−1.01305	−	1.39434i	−0.0390502	−	0.0537480i	0.789045	−	0.614335i	$-0.210576\pi$
$673$	−1.01305	−	1.39434i	−0.0390502	−	0.0537480i	−0.828096	+	0.560587i	$0.810576\pi$
$674$	0.658797	+	0.140032i	0.0253759	+	0.00539381i
$675$	1.81245	+	8.52692i	0.0697613	+	0.328201i
$676$	1.28237	−	12.2010i	0.0493220	−	0.469268i
$677$	32.7171	−	14.5666i	1.25742	−	0.559839i	0.333617	−	0.942709i	$-0.391731\pi$
$677$	32.7171	−	14.5666i	1.25742	−	0.559839i	0.923802	+	0.382870i	$0.125064\pi$
$678$	0.0799653	−	0.246108i	0.00307105	−	0.00945172i
$679$	31.7445	+	31.2309i	1.21824	+	1.19853i
$680$	−17.6013	+	12.7881i	−0.674980	+	0.490402i
$681$	−0.0701144	−	0.0404806i	−0.00268679	−	0.00155122i
$682$	−20.1389	+	25.5367i	−0.771160	+	0.977852i
$683$	−5.76562	−	9.98635i	−0.220615	−	0.382117i	0.734380	−	0.678739i	$-0.237473\pi$
$683$	−5.76562	−	9.98635i	−0.220615	−	0.382117i	−0.954995	+	0.296622i	$0.904140\pi$
$684$	0.105051	+	0.999498i	0.00401674	+	0.0382168i
$685$	−2.18204	+	0.708988i	−0.0833715	+	0.0270890i
$686$	15.2810	−	10.4638i	0.583431	−	0.399510i
$687$	23.8568	+	17.3329i	0.910192	+	0.661293i
$688$	0.301730	+	0.677698i	0.0115034	+	0.0258370i
$689$	−58.5026	+	12.4351i	−2.22877	+	0.473740i
$690$	3.01771	+	2.71715i	0.114882	+	0.103440i
$691$	44.7255	−	4.70084i	1.70144	−	0.178829i	0.796578	−	0.604535i	$-0.206641\pi$
$691$	44.7255	−	4.70084i	1.70144	−	0.178829i	0.904861	+	0.425707i	$0.139974\pi$
$692$	2.84440			0.108128
$693$	0.733197	−	8.74428i	0.0278519	−	0.332168i
$694$	12.7763			0.484983
$695$	57.2480	−	6.01701i	2.17154	−	0.228238i
$696$	−2.31302	−	2.08266i	−0.0876750	−	0.0789429i
$697$	−9.29025	+	1.97470i	−0.351893	+	0.0747973i
$698$	0.0284115	+	0.0638133i	0.00107539	+	0.00241537i
$699$	−18.8147	−	13.6697i	−0.711636	−	0.517034i
$700$	−8.08956	+	21.5989i	−0.305757	+	0.816361i
$701$	13.5326	−	4.39701i	0.511120	−	0.166073i	−0.0420917	−	0.999114i	$-0.513402\pi$
$701$	13.5326	−	4.39701i	0.511120	−	0.166073i	0.553211	+	0.833041i	$0.313402\pi$
$702$	0.525438	+	4.99921i	0.0198314	+	0.188683i
$703$	2.01888	+	3.49680i	0.0761435	+	0.131884i
$704$	−3.19226	+	0.899696i	−0.120313	+	0.0339086i
$705$	2.71143	+	1.56545i	0.102118	+	0.0589581i
$706$	3.09752	−	2.25048i	0.116577	−	0.0846981i
$707$	−26.8925	−	6.97126i	−1.01140	−	0.262181i
$708$	4.34434	−	13.3705i	0.163270	−	0.502495i
$709$	9.51855	−	4.23793i	0.357476	−	0.159159i	−0.220137	−	0.975469i	$-0.570651\pi$
$709$	9.51855	−	4.23793i	0.357476	−	0.159159i	0.577614	+	0.816310i	$0.303984\pi$
$710$	1.00618	−	9.57313i	0.0377611	−	0.359273i
$711$	−0.975879	−	4.59115i	−0.0365983	−	0.172182i
$712$	8.90347	+	1.89249i	0.333672	+	0.0709241i
$713$	−6.31933	−	8.69782i	−0.236661	−	0.325736i
$714$	−8.35808	+	13.1030i	−0.312793	+	0.490369i
$715$	−39.4753	−	47.4811i	−1.47629	−	1.77569i
$716$	4.67758	−	8.10180i	0.174809	−	0.302779i
$717$	9.36535	+	4.16972i	0.349755	+	0.155721i
$718$	−2.47995	+	2.75427i	−0.0925510	+	0.102788i
$719$	−21.6375	+	19.4825i	−0.806944	+	0.726576i	−0.965395	−	0.260791i	$-0.916017\pi$
$719$	−21.6375	+	19.4825i	−0.806944	+	0.726576i	0.158451	+	0.987367i	$0.449350\pi$
$720$	2.17698	−	2.99636i	0.0811313	−	0.111668i
$721$	18.4818	−	23.2076i	0.688298	−	0.864295i
$722$	−17.1095	−	5.55921i	−0.636749	−	0.206892i
$723$	4.19821	−	19.7510i	0.156133	−	0.734548i
$724$	−0.991019	+	2.22587i	−0.0368309	+	0.0827236i
$725$	−23.4977	+	13.5664i	−0.872682	+	0.503843i
$726$	−2.56408	−	10.6970i	−0.0951618	−	0.397002i
$727$			18.6027i			0.689936i	0.938614	+	0.344968i	$0.112110\pi$
$727$			18.6027i			0.689936i	−0.938614	+	0.344968i	$0.887890\pi$
$728$	−5.94101	+	11.8988i	−0.220189	+	0.440999i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−25.7136	−	28.5579i	−0.951705	−	1.05698i
$731$	4.33383	+	0.455504i	0.160293	+	0.0168474i
$732$	5.05823	+	0.531642i	0.186958	+	0.0196500i
$733$	−24.2441	−	26.9258i	−0.895477	−	0.994528i	−1.00000		5.89591e-6i	$-0.999998\pi$
$733$	−24.2441	−	26.9258i	−0.895477	−	0.994528i	0.104523	−	0.994523i	$-0.466669\pi$
$734$	−1.15137	−	3.54356i	−0.0424979	−	0.130795i
$735$	0.422851	+	25.9225i	0.0155971	+	0.956165i
$736$		−	1.09640i		−	0.0404137i
$737$	2.24144	+	13.0584i	0.0825646	+	0.481013i
$738$	1.40024	−	0.808428i	0.0515435	−	0.0297586i
$739$	−19.3982	+	43.5690i	−0.713573	+	1.60271i	0.0818425	+	0.996645i	$0.473920\pi$
$739$	−19.3982	+	43.5690i	−0.713573	+	1.60271i	−0.795415	+	0.606065i	$0.792747\pi$
$740$	3.09377	−	14.5550i	0.113729	−	0.535054i
$741$	4.80464	+	1.56112i	0.176503	+	0.0573493i
$742$	31.1314	+	4.67081i	1.14287	+	0.171471i
$743$	−4.03853	+	5.55856i	−0.148159	+	0.203924i	−0.876646	−	0.481137i	$-0.840224\pi$
$743$	−4.03853	+	5.55856i	−0.148159	+	0.203924i	0.728486	+	0.685060i	$0.240224\pi$
$744$	−7.28717	+	6.56140i	−0.267161	+	0.240552i
$745$	32.1691	−	35.7274i	1.17859	−	1.30895i
$746$	30.5557	+	13.6043i	1.11872	+	0.498087i
$747$	5.95042	−	10.3064i	0.217714	−	0.377092i
$748$	−4.79909	+	18.8823i	−0.175472	+	0.690407i
$749$	1.67338	−	37.8308i	0.0611441	−	1.38231i
$750$	−8.09274	−	11.1387i	−0.295505	−	0.406728i
$751$	−8.37244	−	1.77962i	−0.305514	−	0.0649391i	0.0526034	−	0.998615i	$-0.483248\pi$
$751$	−8.37244	−	1.77962i	−0.305514	−	0.0649391i	−0.358118	+	0.933676i	$0.616581\pi$
$752$	−0.175756	−	0.826868i	−0.00640917	−	0.0301528i
$753$	0.634920	−	6.04086i	0.0231378	−	0.220141i
$754$	−14.2930	+	6.36366i	−0.520521	+	0.231751i
$755$	5.40075	−	16.6218i	0.196554	−	0.604930i
$756$	0.663906	−	2.56110i	0.0241460	−	0.0931463i
$757$	15.0402	−	10.9273i	0.546645	−	0.397161i	−0.279902	−	0.960029i	$-0.590302\pi$
$757$	15.0402	−	10.9273i	0.546645	−	0.397161i	0.826547	+	0.562867i	$0.190302\pi$
$758$	16.3886	+	9.46194i	0.595259	+	0.343673i
$759$	3.63350	+	0.143411i	0.131888	+	0.00520549i
$760$	−1.86112	−	3.22355i	−0.0675098	−	0.116930i
$761$	2.31303	+	22.0070i	0.0838474	+	0.797755i	0.952951	+	0.303125i	$0.0980298\pi$
$761$	2.31303	+	22.0070i	0.0838474	+	0.797755i	−0.869104	+	0.494630i	$0.835303\pi$
$762$	13.7618	−	4.47149i	0.498538	−	0.161985i
$763$	17.3963	−	14.3238i	0.629790	−	0.518555i
$764$	−13.5863	−	9.87100i	−0.491534	−	0.357120i
$765$	−8.84914	−	19.8755i	−0.319941	−	0.718600i
$766$	−2.49004	+	0.529274i	−0.0899688	+	0.0191235i
$767$	−52.5173	−	47.2868i	−1.89629	−	1.70743i
$768$	−0.994522	+	0.104528i	−0.0358867	+	0.00377185i
$769$	31.2444			1.12670			0.563351	−	0.826217i	$-0.309512\pi$
$769$	31.2444			1.12670			0.563351	+	0.826217i	$0.309512\pi$
$770$	10.6919	+	30.6908i	0.385309	+	1.10602i
$771$	26.9019			0.968848
$772$	−3.08364	+	0.324103i	−0.110982	+	0.0116647i
$773$	23.7426	+	21.3779i	0.853962	+	0.768911i	0.974639	−	0.223781i	$-0.0718401\pi$
$773$	23.7426	+	21.3779i	0.853962	+	0.768911i	−0.120678	+	0.992692i	$0.538507\pi$
$774$	−0.725622	+	0.154236i	−0.0260819	+	0.00554389i
$775$	34.7685	+	78.0914i	1.24892	+	2.80513i
$776$	13.6169	+	9.89329i	0.488820	+	0.355148i
$777$	−1.74842	−	10.4849i	−0.0627242	−	0.376145i
$778$	−6.96412	+	2.26278i	−0.249676	+	0.0811246i
$779$	−0.169853	−	1.61604i	−0.00608562	−	0.0579008i
$780$	−9.30879	−	16.1233i	−0.333308	−	0.577306i
$781$	−4.78765	−	7.16800i	−0.171316	−	0.256491i
$782$	−5.57763	−	3.22025i	−0.199456	−	0.115156i
$783$	2.51805	−	1.82947i	0.0899878	−	0.0653799i
$784$	5.12493	−	4.76814i	0.183033	−	0.170291i
$785$	7.13624	−	21.9631i	0.254703	−	0.783897i
$786$	−9.59468	+	4.27183i	−0.342231	+	0.152371i
$787$	−0.722385	+	6.87304i	−0.0257503	+	0.244997i	0.974074	+	0.226231i	$0.0726405\pi$
$787$	−0.722385	+	6.87304i	−0.0257503	+	0.244997i	−0.999824	+	0.0187662i	$0.994026\pi$
$788$	−0.486546	−	2.28902i	−0.0173325	−	0.0815429i
$789$	15.7071	+	3.33865i	0.559188	+	0.118859i
$790$	10.2181	+	14.0641i	0.363545	+	0.500377i
$791$	0.315789	+	0.607472i	0.0112282	+	0.0215992i
$792$	−0.216326	−	3.30956i	−0.00768682	−	0.117600i
$793$	12.7833	−	22.1412i	0.453947	−	0.786259i
$794$	28.0549	+	12.4909i	0.995632	+	0.443284i
$795$	−29.4870	+	32.7487i	−1.04580	+	1.16148i
$796$	3.46225	−	3.11742i	0.122716	−	0.110494i
$797$	12.6703	−	17.4392i	0.448807	−	0.617729i	−0.523334	−	0.852128i	$-0.675312\pi$
$797$	12.6703	−	17.4392i	0.448807	−	0.617729i	0.972141	+	0.234398i	$0.0753120\pi$
$798$	−2.08000	−	1.65645i	−0.0736312	−	0.0586376i
$799$	−4.72270	−	1.53450i	−0.167077	−	0.0542866i
$800$	−1.81245	+	8.52692i	−0.0640799	+	0.301472i
$801$	−3.70227	+	8.31544i	−0.130813	+	0.293812i
$802$	−7.23754	+	4.17859i	−0.255566	+	0.147551i
$803$	−34.0552	−	4.94399i	−1.20178	−	0.174470i
$804$			3.99484i			0.140887i
$805$	−10.7240	+	0.649759i	−0.377971	+	0.0229010i
$806$	15.2319	+	46.8790i	0.536521	+	1.65124i
$807$	20.3488	+	22.5997i	0.716313	+	0.795547i
$808$	−10.4428	−	1.09759i	−0.367378	−	0.0386130i
$809$	−31.0357	−	3.26198i	−1.09116	−	0.114685i	−0.458183	−	0.888858i	$-0.651499\pi$
$809$	−31.0357	−	3.26198i	−1.09116	−	0.114685i	−0.632974	+	0.774173i	$0.718166\pi$
$810$	2.47826	+	2.75239i	0.0870772	+	0.0967090i
$811$	−2.53213	−	7.79308i	−0.0889150	−	0.273652i	0.896705	−	0.442628i	$-0.145954\pi$
$811$	−2.53213	−	7.79308i	−0.0889150	−	0.273652i	−0.985620	+	0.168976i	$0.945954\pi$
$812$	8.21978	−	0.498030i	0.288458	−	0.0174774i
$813$			25.8532i			0.906711i
$814$	−6.20223	−	11.7936i	−0.217388	−	0.413366i
$815$	−69.2665	+	39.9910i	−2.42630	+	1.40083i
$816$	−2.38927	+	5.36639i	−0.0836412	+	0.187861i
$817$	−0.155007	+	0.729252i	−0.00542302	+	0.0255133i
$818$	−26.3764	−	8.57022i	−0.922231	−	0.299651i
$819$	−10.4036	−	8.28509i	−0.363530	−	0.289504i
$820$	−3.51987	+	4.84468i	−0.122919	+	0.169184i
$821$	−29.0325	+	26.1410i	−1.01324	+	0.912326i	−0.996162	−	0.0875283i	$-0.972103\pi$
$821$	−29.0325	+	26.1410i	−1.01324	+	0.912326i	−0.0170784	+	0.999854i	$0.505437\pi$
$822$	−0.414507	+	0.460356i	−0.0144576	+	0.0160568i
$823$	−15.6356	−	6.96142i	−0.545023	−	0.242660i	0.115707	−	0.993283i	$-0.463087\pi$
$823$	−15.6356	−	6.96142i	−0.545023	−	0.242660i	−0.660730	+	0.750624i	$0.729753\pi$
$824$	5.60666	−	9.71101i	0.195317	−	0.338299i
$825$	−28.0215	−	7.12189i	−0.975584	−	0.247952i
$826$	17.1561	+	33.0026i	0.596938	+	1.14831i
$827$	−1.55062	−	2.13424i	−0.0539203	−	0.0742149i	0.781205	−	0.624274i	$-0.214605\pi$
$827$	−1.55062	−	2.13424i	−0.0539203	−	0.0742149i	−0.835126	+	0.550059i	$0.814605\pi$
$828$	1.07244	+	0.227953i	0.0372698	+	0.00792193i
$829$	−7.24967	−	34.1070i	−0.251791	−	1.18459i	−0.904331	−	0.426831i	$-0.859630\pi$
$829$	−7.24967	−	34.1070i	−0.251791	−	1.18459i	0.652540	−	0.757754i	$-0.273703\pi$
$830$	−4.60732	+	43.8357i	−0.159922	+	1.52156i
$831$	−16.8618	+	7.50734i	−0.584928	+	0.260427i
$832$	−1.55335	+	4.78072i	−0.0538527	+	0.165742i
$833$	−9.20413	−	40.0763i	−0.318904	−	1.38856i
$834$	12.5738	−	9.13542i	0.435396	−	0.316334i
$835$	69.9887	+	40.4080i	2.42206	+	1.39838i
$836$	−3.12699	−	1.15424i	−0.108149	−	0.0399203i
$837$	−4.90293	−	8.49212i	−0.169470	−	0.293531i
$838$	0.534238	+	5.08294i	0.0184549	+	0.175587i
$839$	−25.5909	+	8.31498i	−0.883495	+	0.287065i	−0.715408	−	0.698707i	$-0.753759\pi$
$839$	−25.5909	+	8.31498i	−0.883495	+	0.287065i	−0.168087	+	0.985772i	$0.553759\pi$
$840$	1.61179	+	9.66561i	0.0556121	+	0.333495i
$841$	−15.6241	−	11.3516i	−0.538762	−	0.391434i
$842$	−8.50478	−	19.1020i	−0.293094	−	0.658300i
$843$	12.5567	−	2.66901i	0.432476	−	0.0919256i
$844$	−3.22376	−	2.90268i	−0.110966	−	0.0999145i
$845$	−45.1887	+	4.74953i	−1.55454	+	0.163389i
$846$	0.845341			0.0290634
$847$	24.9324	+	15.0125i	0.856689	+	0.515834i
$848$	11.8983			0.408588
$849$	19.1484	−	2.01258i	0.657172	−	0.0690716i
$850$	38.0551	+	34.2650i	1.30528	+	1.17528i
$851$	4.30868	−	0.915839i	0.147700	−	0.0313945i
$852$	−1.05710	−	2.37429i	−0.0362157	−	0.0813418i
$853$	0.946340	+	0.687557i	0.0324021	+	0.0235415i	0.603868	−	0.797084i	$-0.293625\pi$
$853$	0.946340	+	0.687557i	0.0324021	+	0.0235415i	−0.571466	+	0.820626i	$0.693625\pi$
$854$	−10.3883	+	8.55348i	−0.355480	+	0.292694i
$855$	3.54006	−	1.15023i	0.121067	−	0.0393372i
$856$	−1.49608	−	14.2343i	−0.0511351	−	0.486518i
$857$	−23.9243	−	41.4380i	−0.817237	−	1.41550i	−0.907710	−	0.419598i	$-0.862171\pi$
$857$	−23.9243	−	41.4380i	−0.817237	−	1.41550i	0.0904727	−	0.995899i	$-0.471162\pi$
$858$	−15.6403	−	5.77320i	−0.533952	−	0.197094i
$859$	−21.1731	−	12.2243i	−0.722417	−	0.417087i	0.0932249	−	0.995645i	$-0.470282\pi$
$859$	−21.1731	−	12.2243i	−0.722417	−	0.417087i	−0.815641	+	0.578558i	$0.803616\pi$
$860$	2.22280	−	1.61496i	0.0757967	−	0.0550695i
$861$	−1.07344	+	4.14093i	−0.0365828	+	0.141122i
$862$	−3.49916	+	10.7693i	−0.119182	+	0.366804i
$863$	33.0620	−	14.7201i	1.12544	−	0.501080i	0.242308	−	0.970199i	$-0.422095\pi$
$863$	33.0620	−	14.7201i	1.12544	−	0.501080i	0.883135	+	0.469120i	$0.155429\pi$
$864$	0.104528	−	0.994522i	0.00355613	−	0.0338343i
$865$	−2.19031	−	10.3046i	−0.0744728	−	0.350367i
$866$	35.7469	+	7.59823i	1.21473	+	0.258198i
$867$	10.2902	+	14.1632i	0.349473	+	0.481009i
$868$	1.14646	−	25.9185i	0.0389135	−	0.879731i
$869$	15.0876	+	3.83464i	0.511813	+	0.130081i
$870$	−5.76385	+	9.98328i	−0.195413	+	0.338465i
$871$	18.3449	+	8.16770i	0.621595	+	0.276752i
$872$	5.69914	−	6.32954i	0.192997	−	0.214345i
$873$	−12.5082	+	11.2624i	−0.423339	+	0.381176i
$874$	0.647670	−	0.891441i	0.0219078	−	0.0301534i
$875$	36.0240	+	5.40487i	1.21783	+	0.182718i
$876$	−9.86786	−	3.20626i	−0.333404	−	0.108330i
$877$	−3.23943	+	15.2403i	−0.109388	+	0.514629i	0.889002	+	0.457903i	$0.151399\pi$
$877$	−3.23943	+	15.2403i	−0.109388	+	0.514629i	−0.998390	+	0.0567256i	$0.981934\pi$
$878$	11.1490	−	25.0410i	0.376259	−	0.845091i
$879$	11.7917	−	6.80793i	0.397724	−	0.229626i
$880$	5.71757	+	10.8720i	0.192739	+	0.366496i
$881$		−	13.0963i		−	0.441227i	−0.975361	−	0.220613i	$-0.929194\pi$
$881$		−	13.0963i		−	0.441227i	0.975361	−	0.220613i	$-0.0708059\pi$
$882$	3.59841	+	6.00429i	0.121165	+	0.202175i
$883$	4.88380	+	15.0308i	0.164353	+	0.505826i	0.998988	−	0.0449772i	$-0.0143215\pi$
$883$	4.88380	+	15.0308i	0.164353	+	0.505826i	−0.834635	+	0.550803i	$0.814322\pi$
$884$	19.7583	+	21.9438i	0.664544	+	0.738050i
$885$	−51.7836	−	5.44267i	−1.74069	−	0.182954i
$886$	32.2757	+	3.39231i	1.08432	+	0.113967i
$887$	−31.0079	−	34.4378i	−1.04114	−	1.15631i	−0.987479	−	0.157749i	$-0.949576\pi$
$887$	−31.0079	−	34.4378i	−1.04114	−	1.15631i	−0.0536647	−	0.998559i	$-0.517090\pi$
$888$	−1.24152	−	3.82102i	−0.0416628	−	0.128225i
$889$	−17.1019	+	34.2520i	−0.573578	+	1.14877i
$890$		−	33.7125i		−	1.13005i
$891$	3.28222	+	0.476498i	0.109958	+	0.0159633i
$892$	8.04052	−	4.64220i	0.269217	−	0.155432i
$893$	0.345552	−	0.776122i	0.0115634	−	0.0259719i
$894$	2.69880	−	12.6969i	0.0902615	−	0.424647i
$895$	−32.9529	−	10.7070i	−1.10149	−	0.357897i
$896$	1.64820	−	2.06965i	0.0550625	−	0.0691420i
$897$	3.23946	−	4.45874i	0.108162	−	0.148873i
$898$	−13.0322	+	11.7342i	−0.434890	+	0.391577i
$899$	20.4222	−	22.6812i	0.681119	−	0.756459i
$900$	−7.96375	−	3.54569i	−0.265458	−	0.118190i
$901$	34.9467	−	60.5294i	1.16424	−	2.01653i
$902$	0.349768	+	5.35109i	0.0116460	+	0.178172i
$903$	1.05551	−	1.65473i	0.0351250	−	0.0550658i
$904$	0.152103	+	0.209352i	0.00505887	+	0.00696294i
$905$	8.82692	+	1.87622i	0.293417	+	0.0623677i
$906$	−0.981103	−	4.61573i	−0.0325950	−	0.153347i
$907$	1.52077	−	14.4691i	0.0504963	−	0.480440i	−0.939826	−	0.341653i	$-0.889013\pi$
$907$	1.52077	−	14.4691i	0.0504963	−	0.480440i	0.990322	−	0.138787i	$-0.0443202\pi$
$908$	0.0739617	−	0.0329299i	0.00245450	−	0.00109282i
$909$	3.24479	−	9.98644i	0.107623	−	0.331229i
$910$	47.6814	+	12.3603i	1.58062	+	0.409741i
$911$	−16.9453	+	12.3115i	−0.561422	+	0.407897i	−0.831979	−	0.554807i	$-0.812792\pi$
$911$	−16.9453	+	12.3115i	−0.561422	+	0.407897i	0.270557	+	0.962704i	$0.412792\pi$
$912$	−0.870359	−	0.502502i	−0.0288205	−	0.0166395i
$913$	21.9228	+	32.8225i	0.725540	+	1.08627i
$914$	−2.11204	−	3.65817i	−0.0698602	−	0.121001i
$915$	−1.96904	−	18.7342i	−0.0650946	−	0.619333i
$916$	−28.0453	+	9.11247i	−0.926643	+	0.301085i
$917$	9.74625	−	26.0222i	0.321850	−	0.859329i
$918$	−4.75236	−	3.45279i	−0.156851	−	0.113959i
$919$	5.37210	+	12.0659i	0.177209	+	0.398018i	0.980210	−	0.197959i	$-0.0634314\pi$
$919$	5.37210	+	12.0659i	0.177209	+	0.398018i	−0.803001	+	0.595978i	$0.796765\pi$
$920$	−3.97199	+	0.844272i	−0.130953	+	0.0278348i
$921$	−8.18433	−	7.36921i	−0.269683	−	0.242824i
$922$	−22.2399	+	2.33751i	−0.732433	+	0.0769819i
$923$	−13.0644			−0.430021
$924$	6.64331	+	5.73293i	0.218549	+	0.188599i
$925$	−35.0236			−1.15157
$926$	35.6087	−	3.74263i	1.17018	−	0.122990i
$927$	8.33311	+	7.50317i	0.273695	+	0.246436i
$928$	3.04447	−	0.647121i	0.0999395	−	0.0212428i
$929$	3.29135	+	7.39249i	0.107986	+	0.242540i	0.959453	−	0.281867i	$-0.0909538\pi$
$929$	3.29135	+	7.39249i	0.107986	+	0.242540i	−0.851468	+	0.524407i	$0.824287\pi$
$930$	29.3818	+	21.3472i	0.963469	+	0.700001i
$931$	6.98356	−	0.849375i	0.228877	−	0.0278371i
$932$	22.1180	−	7.18656i	0.724498	−	0.235404i
$933$	3.06147	+	29.1280i	0.100228	+	0.953607i
$934$	3.19712	+	5.53758i	0.104613	+	0.181195i
$935$	72.1018	+	2.84579i	2.35798	+	0.0930674i
$936$	−4.35329	−	2.51337i	−0.142292	−	0.0821522i
$937$	−45.0986	+	32.7660i	−1.47331	+	1.07042i	−0.493667	+	0.869651i	$0.664344\pi$
$937$	−45.0986	+	32.7660i	−1.47331	+	1.07042i	−0.979639	+	0.200769i	$0.935656\pi$
$938$	−7.53436	−	7.41246i	−0.246006	−	0.242026i
$939$	0.900980	−	2.77293i	0.0294024	−	0.0904912i
$940$	−2.86021	+	1.27345i	−0.0932898	+	0.0415353i
$941$	−4.31502	+	41.0547i	−0.140666	+	1.33835i	0.665386	+	0.746500i	$0.268267\pi$
$941$	−4.31502	+	41.0547i	−0.140666	+	1.33835i	−0.806052	+	0.591845i	$0.798400\pi$
$942$	−1.29637	−	6.09896i	−0.0422381	−	0.198715i
$943$	−1.73398	−	0.368568i	−0.0564660	−	0.0120022i
$944$	8.26343	+	11.3736i	0.268952	+	0.370180i
$945$	−9.78950	−	0.433023i	−0.318453	−	0.0140862i
$946$	0.606057	−	2.38457i	0.0197046	−	0.0775290i
$947$	−21.8248	+	37.8017i	−0.709211	+	1.22839i	0.255939	+	0.966693i	$0.417615\pi$
$947$	−21.8248	+	37.8017i	−0.709211	+	1.22839i	−0.965150	+	0.261697i	$0.915718\pi$
$948$	4.28793	+	1.90911i	0.139265	+	0.0620049i
$949$	−34.8991	+	38.7594i	−1.13287	+	1.25818i
$950$	−6.51072	+	5.86228i	−0.211236	+	0.190197i
$951$	5.17921	−	7.12857i	0.167947	−	0.231160i
$952$	−5.68782	−	14.4636i	−0.184343	−	0.468768i
$953$	2.24724	+	0.730174i	0.0727954	+	0.0236527i	0.345188	−	0.938533i	$-0.387815\pi$
$953$	2.24724	+	0.730174i	0.0727954	+	0.0236527i	−0.272393	+	0.962186i	$0.587815\pi$
$954$	−2.47379	+	11.6383i	−0.0800919	+	0.376803i
$955$	−25.2983	+	56.8210i	−0.818635	+	1.83868i
$956$	−8.87819	+	5.12583i	−0.287141	+	0.165781i
$957$	1.74637	+	10.1741i	0.0564520	+	0.328883i
$958$			31.8081i			1.02767i
$959$	−0.0991218	−	1.63596i	−0.00320081	−	0.0528280i
$960$	1.14451	+	3.52243i	0.0369388	+	0.113686i
$961$	−43.5970	−	48.4194i	−1.40636	−	1.56192i
$962$	−20.0851	−	2.11103i	−0.647570	−	0.0680623i
$963$	14.2343	+	1.49608i	0.458694	+	0.0482106i
$964$	13.5113	+	15.0058i	0.435168	+	0.483303i
$965$	3.54868	+	10.9217i	0.114236	+	0.351583i
$966$	−2.41984	+	1.59967i	−0.0778571	+	0.0514686i
$967$			3.75060i			0.120611i	0.998180	+	0.0603056i	$0.0192075\pi$
$967$			3.75060i			0.120611i	−0.998180	+	0.0603056i	$0.980792\pi$
$968$	10.1612	+	4.21315i	0.326592	+	0.135416i
$969$	−5.11270	+	2.95182i	−0.164244	+	0.0948260i
$970$	25.3555	−	56.9493i	0.814114	−	1.82853i
$971$	−4.83107	+	22.7284i	−0.155036	+	0.729389i	0.830100	+	0.557615i	$0.188283\pi$
$971$	−4.83107	+	22.7284i	−0.155036	+	0.729389i	−0.985136	+	0.171774i	$0.945050\pi$
$972$	0.951057	+	0.309017i	0.0305052	+	0.00991172i
$973$	−6.10123	+	40.6654i	−0.195597	+	1.30367i
$974$	1.72455	−	2.37364i	0.0552583	−	0.0760565i
$975$	−32.5648	+	29.3215i	−1.04291	+	0.939038i
$976$	−3.40326	+	3.77971i	−0.108936	+	0.120985i
$977$	35.8394	+	15.9567i	1.14660	+	0.510501i	0.889975	−	0.456009i	$-0.150721\pi$
$977$	35.8394	+	15.9567i	1.14660	+	0.510501i	0.256629	+	0.966510i	$0.417388\pi$
$978$	−10.7976	+	18.7020i	−0.345269	+	0.598023i
$979$	−19.3000	−	23.2142i	−0.616830	−	0.741928i
$980$	−21.2203	−	14.8948i	−0.677857	−	0.475795i
$981$	5.00631	+	6.89059i	0.159839	+	0.220000i
$982$	39.4515	+	8.38568i	1.25895	+	0.267598i
$983$	8.41109	+	39.5711i	0.268272	+	1.26212i	0.881488	+	0.472206i	$0.156542\pi$
$983$	8.41109	+	39.5711i	0.268272	+	1.26212i	−0.613216	+	0.789915i	$0.710124\pi$
$984$	−0.169007	+	1.60800i	−0.00538776	+	0.0512611i
$985$	−7.91792	+	3.52529i	−0.252286	+	0.112325i
$986$	5.64990	−	17.3886i	0.179930	−	0.553766i
$987$	−1.56854	+	1.59433i	−0.0499271	+	0.0507482i
$988$	−4.08707	+	2.96943i	−0.130027	+	0.0944702i
$989$	0.704375	+	0.406671i	0.0223978	+	0.0129314i
$990$	−11.8232	+	3.33221i	−0.375766	+	0.105904i
$991$	−13.4370	−	23.2736i	−0.426841	−	0.739311i	0.569749	−	0.821819i	$-0.307040\pi$
$991$	−13.4370	−	23.2736i	−0.426841	−	0.739311i	−0.996590	+	0.0825080i	$0.973707\pi$
$992$	−1.02499	−	9.75214i	−0.0325435	−	0.309631i
$993$	4.41174	−	1.43346i	0.140002	−	0.0454895i
$994$	6.43943	+	2.41180i	0.204246	+	0.0764976i
$995$	−13.9598	−	10.1424i	−0.442554	−	0.321535i
$996$	4.84051	+	10.8720i	0.153377	+	0.344491i
$997$	33.4767	−	7.11569i	1.06022	−	0.225356i	0.355378	−	0.934723i	$-0.384352\pi$
$997$	33.4767	−	7.11569i	1.06022	−	0.225356i	0.704840	+	0.709367i	$0.251019\pi$
$998$	−12.7503	−	11.4804i	−0.403604	−	0.363406i
$999$	3.99565	−	0.419959i	0.126417	−	0.0132869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.a.19.5	✓	64
7.3	odd	6		462.2.ba.b.283.1	yes	64
11.7	odd	10		462.2.ba.b.271.1	yes	64
77.73	even	30	inner	462.2.ba.a.73.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.19.5	✓	64	1.1	even	1	trivial
462.2.ba.a.73.5	yes	64	77.73	even	30	inner
462.2.ba.b.271.1	yes	64	11.7	odd	10
462.2.ba.b.283.1	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)

\(f(q)\)	\(=\)	\(q+(0.994522 - 0.104528i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-1.50643 - 3.38350i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(2.60972 - 0.435184i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.994522 - 0.104528i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-1.50643 - 3.38350i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(2.60972 - 0.435184i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-1.85185 - 3.20750i) q^{10} +(-3.11142 - 1.14850i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-4.06672 + 2.95465i) q^{13} +(2.54993 - 0.705590i) q^{14} +(-1.14451 + 3.52243i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.614026 - 5.84206i) q^{17} +(0.207912 + 0.978148i) q^{18} +(0.983042 + 0.208952i) q^{19} +(-2.17698 - 2.99636i) q^{20} +(-2.23059 - 1.42284i) q^{21} +(-3.21443 - 0.816973i) q^{22} +(0.548198 - 0.949506i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(-5.83309 + 6.47830i) q^{25} +(-3.73560 + 3.36355i) q^{26} +(0.587785 - 0.809017i) q^{27} +(2.46221 - 0.968265i) q^{28} +(2.96015 + 0.961810i) q^{29} +(-0.770043 + 3.62277i) q^{30} +(3.98840 - 8.95809i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.54374 + 2.93545i) q^{33} -5.87424i q^{34} +(-5.40380 - 8.17440i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.68834 + 2.98570i) q^{37} +(0.999498 + 0.105051i) q^{38} +(4.99921 + 0.525438i) q^{39} +(-2.47826 - 2.75239i) q^{40} +(-0.499636 - 1.53772i) q^{41} +(-2.36710 - 1.18188i) q^{42} +0.741833i q^{43} +(-3.28222 - 0.476498i) q^{44} +(3.20750 - 1.85185i) q^{45} +(0.445944 - 1.00161i) q^{46} +(0.175756 - 0.826868i) q^{47} +(-0.951057 - 0.309017i) q^{48} +(6.62123 - 2.27141i) q^{49} +(-5.12397 + 7.05254i) q^{50} +(-4.36541 + 3.93064i) q^{51} +(-3.36355 + 3.73560i) q^{52} +(10.8696 + 4.83946i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.801208 + 12.2576i) q^{55} +(2.34751 - 1.22033i) q^{56} +(-0.590726 - 0.813065i) q^{57} +(3.04447 + 0.647121i) q^{58} +(2.92294 + 13.7514i) q^{59} +(-0.387142 + 3.68341i) q^{60} +(-4.64638 + 2.06870i) q^{61} +(3.03018 - 9.32592i) q^{62} +(0.705590 + 2.54993i) q^{63} +(0.809017 - 0.587785i) q^{64} +(16.1233 + 9.30879i) q^{65} +(1.84213 + 2.75800i) q^{66} +(-1.99742 - 3.45963i) q^{67} +(-0.614026 - 5.84206i) q^{68} +(-1.04273 + 0.338805i) q^{69} +(-6.22866 - 7.56477i) q^{70} +(2.10262 + 1.52764i) q^{71} +(0.406737 + 0.913545i) q^{72} +(10.1489 - 2.15723i) q^{73} +(2.98570 + 2.68834i) q^{74} +(8.66966 - 0.911218i) q^{75} +1.00500 q^{76} +(-8.61974 - 1.64321i) q^{77} +5.02675 q^{78} +(-4.66801 + 0.490627i) q^{79} +(-2.75239 - 2.47826i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-0.657635 - 1.47707i) q^{82} +(-9.62798 - 6.99513i) q^{83} +(-2.47767 - 0.927977i) q^{84} +(-20.6916 + 6.72311i) q^{85} +(0.0775426 + 0.737769i) q^{86} +(-1.55624 - 2.69549i) q^{87} +(-3.31404 - 0.130802i) q^{88} +(7.88289 + 4.55119i) q^{89} +(2.99636 - 2.17698i) q^{90} +(-9.32717 + 9.48056i) q^{91} +(0.338805 - 1.04273i) q^{92} +(-8.95809 + 3.98840i) q^{93} +(0.0883622 - 0.840710i) q^{94} +(-0.773896 - 3.64089i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(9.89329 + 13.6169i) q^{97} +(6.34753 - 2.95108i) q^{98} +(0.816973 - 3.21443i) 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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