LMFDB - Embedded newform 512.2.o.a.149.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			149.32
Character	$\chi$	$=$	512.149
Dual form			512.2.o.a.189.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.108327 - 1.41006i) q^{2} +(-1.21659 - 0.211099i) q^{3} +(-1.97653 + 0.305496i) q^{4} +(-1.04138 + 3.15231i) q^{5} +(-0.165872 + 1.73834i) q^{6} +(0.0945912 - 1.92545i) q^{7} +(0.644880 + 2.75393i) q^{8} +(-1.38909 - 0.497025i) q^{9} +O(q^{10})$	\(q+(-0.108327 - 1.41006i) q^{2} +(-1.21659 - 0.211099i) q^{3} +(-1.97653 + 0.305496i) q^{4} +(-1.04138 + 3.15231i) q^{5} +(-0.165872 + 1.73834i) q^{6} +(0.0945912 - 1.92545i) q^{7} +(0.644880 + 2.75393i) q^{8} +(-1.38909 - 0.497025i) q^{9} +(4.55776 + 1.12693i) q^{10} +(0.764080 + 0.338693i) q^{11} +(2.46913 + 0.0455792i) q^{12} +(1.18368 - 1.02105i) q^{13} +(-2.72524 + 0.0751997i) q^{14} +(1.93239 - 3.61525i) q^{15} +(3.81334 - 1.20764i) q^{16} +(2.62273 - 1.40188i) q^{17} +(-0.550358 + 2.01254i) q^{18} +(7.18479 - 4.07014i) q^{19} +(1.09531 - 6.54878i) q^{20} +(-0.521540 + 2.32252i) q^{21} +(0.394807 - 1.11409i) q^{22} +(-0.446748 - 1.78352i) q^{23} +(-0.203205 - 3.48655i) q^{24} +(-4.83656 - 3.58704i) q^{25} +(-1.56796 - 1.55845i) q^{26} +(4.80812 + 2.72377i) q^{27} +(0.401254 + 3.83460i) q^{28} +(-0.719960 + 0.0176740i) q^{29} +(-5.30705 - 2.33316i) q^{30} +(1.17636 - 0.786019i) q^{31} +(-2.11594 - 5.24622i) q^{32} +(-0.858078 - 0.573349i) q^{33} +(-2.26085 - 3.54634i) q^{34} +(5.97111 + 2.30331i) q^{35} +(2.89742 + 0.558023i) q^{36} +(7.92852 + 0.977890i) q^{37} +(-6.51744 - 9.69007i) q^{38} +(-1.65560 + 0.992328i) q^{39} +(-9.35282 - 0.835035i) q^{40} +(-3.78527 + 2.80735i) q^{41} +(3.33139 + 0.483809i) q^{42} +(1.80019 - 2.55607i) q^{43} +(-1.61370 - 0.436014i) q^{44} +(3.01336 - 3.86126i) q^{45} +(-2.46647 + 0.823145i) q^{46} +(0.0188746 + 0.191637i) q^{47} +(-4.89423 + 0.664220i) q^{48} +(3.26789 + 0.321859i) q^{49} +(-4.53400 + 7.20841i) q^{50} +(-3.48674 + 1.15186i) q^{51} +(-2.02765 + 2.37974i) q^{52} +(-5.66513 - 0.139071i) q^{53} +(3.31982 - 7.07479i) q^{54} +(-1.86337 + 2.05591i) q^{55} +(5.36355 - 0.981185i) q^{56} +(-9.60019 + 3.43500i) q^{57} +(0.102913 + 1.01327i) q^{58} +(1.12879 - 1.30859i) q^{59} +(-2.71499 + 7.73600i) q^{60} +(-10.3844 + 2.33190i) q^{61} +(-1.23576 - 1.57359i) q^{62} +(-1.08839 + 2.62761i) q^{63} +(-7.16826 + 3.55191i) q^{64} +(1.98600 + 4.79463i) q^{65} +(-0.715503 + 1.27205i) q^{66} +(11.7662 + 7.45087i) q^{67} +(-4.75564 + 3.57209i) q^{68} +(0.167012 + 2.26413i) q^{69} +(2.60097 - 8.66913i) q^{70} +(8.20435 + 3.88037i) q^{71} +(0.472975 - 4.14598i) q^{72} +(-0.685082 - 13.9452i) q^{73} +(0.520006 - 11.2856i) q^{74} +(5.12692 + 5.38497i) q^{75} +(-12.9576 + 10.2397i) q^{76} +(0.724412 - 1.43916i) q^{77} +(1.57859 + 2.22699i) q^{78} +(-5.87472 - 7.15837i) q^{79} +(-0.164282 + 13.2785i) q^{80} +(-1.85321 - 1.52089i) q^{81} +(4.36857 + 5.03334i) q^{82} +(9.63044 - 1.18780i) q^{83} +(0.321318 - 4.74987i) q^{84} +(1.68789 + 9.72757i) q^{85} +(-3.79922 - 2.26148i) q^{86} +(0.879630 + 0.130481i) q^{87} +(-0.439998 + 2.32264i) q^{88} +(1.23997 - 4.95024i) q^{89} +(-5.77103 - 3.83073i) q^{90} +(-1.85401 - 2.37569i) q^{91} +(1.42787 + 3.38870i) q^{92} +(-1.59708 + 0.707938i) q^{93} +(0.268175 - 0.0473739i) q^{94} +(5.34822 + 26.8873i) q^{95} +(1.46677 + 6.82920i) q^{96} +(1.27266 - 6.39808i) q^{97} +(0.0998380 - 4.64278i) q^{98} +(-0.893038 - 0.850243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{77}{128}\right)$	$1$

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 $

$2$	−0.108327	−	1.41006i	−0.0765990	−	0.997062i
$2$	−0.108327	−	1.41006i	−0.0765990	−	0.997062i
$3$	−1.21659	−	0.211099i	−0.702401	−	0.121878i	−0.191468	−	0.981499i	$-0.561325\pi$
$3$	−1.21659	−	0.211099i	−0.702401	−	0.121878i	−0.510933	+	0.859621i	$0.670700\pi$
$4$	−1.97653	+	0.305496i	−0.988265	+	0.152748i
$5$	−1.04138	+	3.15231i	−0.465721	+	1.40976i	0.403339	+	0.915051i	$0.367850\pi$
$5$	−1.04138	+	3.15231i	−0.465721	+	1.40976i	−0.869060	+	0.494707i	$0.835275\pi$
$6$	−0.165872	+	1.73834i	−0.0677168	+	0.709673i
$7$	0.0945912	−	1.92545i	0.0357521	−	0.727751i	−0.912278	−	0.409571i	$-0.865678\pi$
$7$	0.0945912	−	1.92545i	0.0357521	−	0.727751i	0.948030	−	0.318180i	$-0.103072\pi$
$8$	0.644880	+	2.75393i	0.227999	+	0.973661i
$9$	−1.38909	−	0.497025i	−0.463031	−	0.165675i
$10$	4.55776	+	1.12693i	1.44129	+	0.356367i
$11$	0.764080	+	0.338693i	0.230379	+	0.102120i	0.517201	−	0.855864i	$-0.326974\pi$
$11$	0.764080	+	0.338693i	0.230379	+	0.102120i	−0.286822	+	0.957984i	$0.592599\pi$
$12$	2.46913	+	0.0455792i	0.712776	+	0.0131576i
$13$	1.18368	−	1.02105i	0.328293	−	0.283188i	−0.473494	−	0.880797i	$-0.657008\pi$
$13$	1.18368	−	1.02105i	0.328293	−	0.283188i	0.801787	+	0.597609i	$0.203883\pi$
$14$	−2.72524	+	0.0751997i	−0.728352	+	0.0200980i
$15$	1.93239	−	3.61525i	0.498942	−	0.933454i
$16$	3.81334	−	1.20764i	0.953336	−	0.301911i
$17$	2.62273	−	1.40188i	0.636106	−	0.340006i	−0.121622	−	0.992577i	$-0.538809\pi$
$17$	2.62273	−	1.40188i	0.636106	−	0.340006i	0.757728	+	0.652571i	$0.226309\pi$
$18$	−0.550358	+	2.01254i	−0.129721	+	0.474361i
$19$	7.18479	−	4.07014i	1.64830	−	0.933753i	0.666118	−	0.745846i	$-0.267955\pi$
$19$	7.18479	−	4.07014i	1.64830	−	0.933753i	0.982187	−	0.187907i	$-0.0601704\pi$
$20$	1.09531	−	6.54878i	0.244918	−	1.46435i
$21$	−0.521540	+	2.32252i	−0.113809	+	0.506816i
$22$	0.394807	−	1.11409i	0.0841730	−	0.237524i
$23$	−0.446748	−	1.78352i	−0.0931534	−	0.371889i	0.905466	−	0.424419i	$-0.139522\pi$
$23$	−0.446748	−	1.78352i	−0.0931534	−	0.371889i	−0.998619	+	0.0525297i	$0.983272\pi$
$24$	−0.203205	−	3.48655i	−0.0414790	−	0.711689i
$25$	−4.83656	−	3.58704i	−0.967313	−	0.717408i
$26$	−1.56796	−	1.55845i	−0.307503	−	0.305637i
$27$	4.80812	+	2.72377i	0.925324	+	0.524189i
$28$	0.401254	+	3.83460i	0.0758300	+	0.724672i
$29$	−0.719960	+	0.0176740i	−0.133693	+	0.00328198i	−0.0913329	−	0.995820i	$-0.529113\pi$
$29$	−0.719960	+	0.0176740i	−0.133693	+	0.00328198i	−0.0423603	+	0.999102i	$0.513488\pi$
$30$	−5.30705	−	2.33316i	−0.968930	−	0.425974i
$31$	1.17636	−	0.786019i	0.211281	−	0.141173i	−0.445428	−	0.895318i	$-0.646948\pi$
$31$	1.17636	−	0.786019i	0.211281	−	0.141173i	0.656708	+	0.754145i	$0.271948\pi$
$32$	−2.11594	−	5.24622i	−0.374049	−	0.927409i
$33$	−0.858078	−	0.573349i	−0.149372	−	0.0998073i
$34$	−2.26085	−	3.54634i	−0.387732	−	0.608193i
$35$	5.97111	+	2.30331i	1.00930	+	0.389331i
$36$	2.89742	+	0.558023i	0.482904	+	0.0930038i
$37$	7.92852	+	0.977890i	1.30344	+	0.160764i	0.744041	−	0.668134i	$-0.232907\pi$
$37$	7.92852	+	0.977890i	1.30344	+	0.160764i	0.559400	+	0.828898i	$0.311032\pi$
$38$	−6.51744	−	9.69007i	−1.05727	−	1.57194i
$39$	−1.65560	+	0.992328i	−0.265108	+	0.158900i
$40$	−9.35282	−	0.835035i	−1.47881	−	0.132031i
$41$	−3.78527	+	2.80735i	−0.591160	+	0.438434i	−0.849477	−	0.527626i	$-0.823082\pi$
$41$	−3.78527	+	2.80735i	−0.591160	+	0.438434i	0.258317	+	0.966060i	$0.416832\pi$
$42$	3.33139	+	0.483809i	0.514045	+	0.0746533i
$43$	1.80019	−	2.55607i	0.274526	−	0.389798i	−0.656752	−	0.754107i	$-0.728070\pi$
$43$	1.80019	−	2.55607i	0.274526	−	0.389798i	0.931278	+	0.364309i	$0.118695\pi$
$44$	−1.61370	−	0.436014i	−0.243274	−	0.0657316i
$45$	3.01336	−	3.86126i	0.449205	−	0.575603i
$46$	−2.46647	+	0.823145i	−0.363661	+	0.121366i
$47$	0.0188746	+	0.191637i	0.00275315	+	0.0279532i	0.996463	−	0.0840309i	$-0.0267794\pi$
$47$	0.0188746	+	0.191637i	0.00275315	+	0.0279532i	−0.993710	+	0.111984i	$0.964279\pi$
$48$	−4.89423	+	0.664220i	−0.706421	+	0.0958719i
$49$	3.26789	+	0.321859i	0.466841	+	0.0459798i
$50$	−4.53400	+	7.20841i	−0.641205	+	1.01942i
$51$	−3.48674	+	1.15186i	−0.488241	+	0.161293i
$52$	−2.02765	+	2.37974i	−0.281184	+	0.330011i
$53$	−5.66513	−	0.139071i	−0.778165	−	0.0191029i	−0.366476	−	0.930427i	$-0.619436\pi$
$53$	−5.66513	−	0.139071i	−0.778165	−	0.0191029i	−0.411689	+	0.911324i	$0.635061\pi$
$54$	3.31982	−	7.07479i	0.451770	−	0.962757i
$55$	−1.86337	+	2.05591i	−0.251256	+	0.277219i
$56$	5.36355	−	0.981185i	0.716735	−	0.131116i
$57$	−9.60019	+	3.43500i	−1.27158	+	0.454977i
$58$	0.102913	+	1.01327i	0.0135131	+	0.133049i
$59$	1.12879	−	1.30859i	0.146957	−	0.170363i	−0.678924	−	0.734208i	$-0.737553\pi$
$59$	1.12879	−	1.30859i	0.146957	−	0.170363i	0.825881	+	0.563845i	$0.190678\pi$
$60$	−2.71499	+	7.73600i	−0.350503	+	0.998713i
$61$	−10.3844	+	2.33190i	−1.32959	+	0.298569i	−0.825167	−	0.564888i	$-0.808919\pi$
$61$	−10.3844	+	2.33190i	−1.32959	+	0.298569i	−0.504422	+	0.863457i	$0.668294\pi$
$62$	−1.23576	−	1.57359i	−0.156942	−	0.199846i
$63$	−1.08839	+	2.62761i	−0.137125	+	0.331048i
$64$	−7.16826	+	3.55191i	−0.896033	+	0.443988i
$65$	1.98600	+	4.79463i	0.246333	+	0.594700i
$66$	−0.715503	+	1.27205i	−0.0880723	+	0.156578i
$67$	11.7662	+	7.45087i	1.43747	+	0.910269i	0.999939	+	0.0110659i	$0.00352247\pi$
$67$	11.7662	+	7.45087i	1.43747	+	0.910269i	0.437532	+	0.899203i	$0.355853\pi$
$68$	−4.75564	+	3.57209i	−0.576706	+	0.433180i
$69$	0.167012	+	2.26413i	0.0201059	+	0.272569i
$70$	2.60097	−	8.66913i	0.310875	−	1.03616i
$71$	8.20435	+	3.88037i	0.973677	+	0.460515i	0.847095	−	0.531441i	$-0.178349\pi$
$71$	8.20435	+	3.88037i	0.973677	+	0.460515i	0.126582	+	0.991956i	$0.459599\pi$
$72$	0.472975	−	4.14598i	0.0557406	−	0.488609i
$73$	−0.685082	−	13.9452i	−0.0801828	−	1.63216i	−0.615945	−	0.787789i	$-0.711226\pi$
$73$	−0.685082	−	13.9452i	−0.0801828	−	1.63216i	0.535763	−	0.844369i	$-0.320024\pi$
$74$	0.520006	−	11.2856i	0.0604494	−	1.31193i
$75$	5.12692	+	5.38497i	0.592005	+	0.621803i
$76$	−12.9576	+	10.2397i	−1.48633	+	1.17457i
$77$	0.724412	−	1.43916i	0.0825544	−	0.164007i
$78$	1.57859	+	2.22699i	0.178740	+	0.252157i
$79$	−5.87472	−	7.15837i	−0.660958	−	0.805380i	0.329359	−	0.944205i	$-0.393167\pi$
$79$	−5.87472	−	7.15837i	−0.660958	−	0.805380i	−0.990317	+	0.138825i	$0.955667\pi$
$80$	−0.164282	+	13.2785i	−0.0183672	+	1.48458i
$81$	−1.85321	−	1.52089i	−0.205912	−	0.168987i
$82$	4.36857	+	5.03334i	0.482428	+	0.555839i
$83$	9.63044	−	1.18780i	1.05708	−	0.130378i	0.424930	−	0.905226i	$-0.360299\pi$
$83$	9.63044	−	1.18780i	1.05708	−	0.130378i	0.632148	+	0.774848i	$0.282174\pi$
$84$	0.321318	−	4.74987i	0.0350587	−	0.518253i
$85$	1.68789	+	9.72757i	0.183078	+	1.05510i
$86$	−3.79922	−	2.26148i	−0.409681	−	0.243862i
$87$	0.879630	+	0.130481i	0.0943063	+	0.0139890i
$88$	−0.439998	+	2.32264i	−0.0469040	+	0.247594i
$89$	1.23997	−	4.95024i	0.131437	−	0.524725i	−0.868159	−	0.496287i	$-0.834697\pi$
$89$	1.23997	−	4.95024i	0.131437	−	0.524725i	0.999596	−	0.0284384i	$-0.00905344\pi$
$90$	−5.77103	−	3.83073i	−0.608320	−	0.403794i
$91$	−1.85401	−	2.37569i	−0.194353	−	0.249040i
$92$	1.42787	+	3.38870i	0.148866	+	0.353296i
$93$	−1.59708	+	0.707938i	−0.165610	+	0.0734097i
$94$	0.268175	−	0.0473739i	0.0276601	−	0.00488624i
$95$	5.34822	+	26.8873i	0.548715	+	2.75858i
$96$	1.46677	+	6.82920i	0.149701	+	0.697002i
$97$	1.27266	−	6.39808i	0.129219	−	0.649627i	−0.860829	−	0.508895i	$-0.830054\pi$
$97$	1.27266	−	6.39808i	0.129219	−	0.649627i	0.990048	−	0.140732i	$-0.0449457\pi$
$98$	0.0998380	−	4.64278i	0.0100852	−	0.468992i
$99$	−0.893038	−	0.850243i	−0.0897537	−	0.0854526i
$100$	10.6554	+	5.61234i	1.06554	+	0.561234i
$101$	15.0438	−	4.16319i	1.49692	−	0.414253i	0.580427	−	0.814312i	$-0.302885\pi$
$101$	15.0438	−	4.16319i	1.49692	−	0.414253i	0.916489	+	0.400059i	$0.131010\pi$
$102$	2.00190	+	4.79173i	0.198218	+	0.474452i
$103$	1.47441	+	9.93964i	0.145278	+	0.979382i	0.932100	+	0.362202i	$0.117975\pi$
$103$	1.47441	+	9.93964i	0.145278	+	0.979382i	−0.786822	+	0.617180i	$0.788275\pi$
$104$	3.57522	+	2.60131i	0.350579	+	0.255080i
$105$	−6.77820	−	4.06270i	−0.661484	−	0.396478i
$106$	0.417590	+	8.00323i	0.0405600	+	0.777342i
$107$	4.98890	−	3.15919i	0.482296	−	0.305410i	−0.271593	−	0.962412i	$-0.587551\pi$
$107$	4.98890	−	3.15919i	0.482296	−	0.305410i	0.753889	+	0.657002i	$0.228176\pi$
$108$	−10.3355	−	3.91475i	−0.994534	−	0.376697i
$109$	1.48329	−	5.35992i	0.142073	−	0.513387i	−0.857927	−	0.513772i	$-0.828248\pi$
$109$	1.48329	−	5.35992i	0.142073	−	0.513387i	1.00000		0.000385162i	$0.000122601\pi$
$110$	3.10081	+	2.40475i	0.295650	+	0.229284i
$111$	−9.43937	−	2.86340i	−0.895945	−	0.271782i
$112$	−1.96455	−	7.45663i	−0.185632	−	0.704585i
$113$	4.78596	+	15.7772i	0.450225	+	1.48419i	0.829287	+	0.558823i	$0.188747\pi$
$113$	4.78596	+	15.7772i	0.450225	+	1.48419i	−0.379061	+	0.925372i	$0.623753\pi$
$114$	5.88352	+	13.1647i	0.551042	+	1.23299i
$115$	6.08744	+	0.449037i	0.567657	+	0.0418729i
$116$	1.41762	−	0.254878i	0.131623	−	0.0236648i
$117$	−2.15172	+	0.830011i	−0.198927	+	0.0767346i
$118$	−1.96746	−	1.44991i	−0.181120	−	0.133475i
$119$	−2.45116	−	5.18254i	−0.224697	−	0.475083i
$120$	11.2023	+	2.99027i	1.02263	+	0.272973i
$121$	−6.91804	−	7.63288i	−0.628913	−	0.693899i
$122$	4.41303	+	14.3900i	0.399537	+	1.30281i
$123$	5.19777	−	2.61634i	0.468667	−	0.235907i
$124$	−2.08499	+	1.91296i	−0.187237	+	0.171789i
$125$	2.77280	−	1.95283i	0.248007	−	0.174666i
$126$	3.82299	+	1.25005i	0.340579	+	0.111364i
$127$	−0.564947	−	0.564947i	−0.0501310	−	0.0501310i	0.681597	−	0.731728i	$-0.261286\pi$
$127$	−0.564947	−	0.564947i	−0.0501310	−	0.0501310i	−0.731728	+	0.681597i	$0.761286\pi$
$128$	5.78492	+	9.72290i	0.511319	+	0.859391i
$129$	−2.72969	+	2.72969i	−0.240336	+	0.240336i
$130$	6.54556	−	3.31976i	0.574084	−	0.291163i
$131$	−6.51572	−	9.25162i	−0.569281	−	0.808317i	0.426064	−	0.904693i	$-0.359900\pi$
$131$	−6.51572	−	9.25162i	−0.569281	−	0.808317i	−0.995345	+	0.0963758i	$0.969275\pi$
$132$	1.87117	+	0.871103i	0.162865	+	0.0758198i
$133$	−7.15722	−	14.2190i	−0.620610	−	1.23294i
$134$	9.23156	−	17.3982i	0.797485	−	1.50297i
$135$	−13.5933	+	12.3202i	−1.16992	+	1.06036i
$136$	5.55203	+	6.31878i	0.476082	+	0.541831i
$137$	−5.74922	+	2.71918i	−0.491189	+	0.232315i	−0.657068	−	0.753831i	$-0.728204\pi$
$137$	−5.74922	+	2.71918i	−0.491189	+	0.232315i	0.165879	+	0.986146i	$0.446954\pi$
$138$	3.17446	−	0.480764i	0.270228	−	0.0409253i
$139$	−5.35401	−	13.8797i	−0.454121	−	1.17726i	−0.950930	−	0.309405i	$-0.899870\pi$
$139$	−5.35401	−	13.8797i	−0.454121	−	1.17726i	0.496809	−	0.867860i	$-0.334505\pi$
$140$	−12.5057	−	2.72842i	−1.05693	−	0.230593i
$141$	0.0174917	−	0.237129i	0.00147307	−	0.0199699i
$142$	4.58279	−	11.9890i	0.384579	−	1.00609i
$143$	1.25025	−	0.379258i	0.104551	−	0.0317151i
$144$	−5.89732	−	0.217799i	−0.491443	−	0.0181499i
$145$	0.694040	−	2.28794i	0.0576369	−	0.190003i
$146$	−19.5893	+	2.47665i	−1.62122	+	0.204969i
$147$	−3.90775	−	1.08142i	−0.322306	−	0.0891941i
$148$	−15.9697	+	0.489303i	−1.31270	+	0.0402204i
$149$	6.42772	+	10.1505i	0.526580	+	0.831560i	0.998752	−	0.0499461i	$-0.0159049\pi$
$149$	6.42772	+	10.1505i	0.526580	+	0.831560i	−0.472172	+	0.881506i	$0.656530\pi$
$150$	7.03774	−	7.81259i	0.574629	−	0.637895i
$151$	8.37203	−	13.9679i	0.681306	−	1.13669i	−0.301751	−	0.953387i	$-0.597571\pi$
$151$	8.37203	−	13.9679i	0.681306	−	1.13669i	0.983056	−	0.183303i	$-0.0586790\pi$
$152$	15.8422	+	17.1617i	1.28497	+	1.39200i
$153$	−4.33999	+	0.643776i	−0.350867	+	0.0520462i
$154$	−2.10777	−	0.865563i	−0.169849	−	0.0697490i
$155$	1.25274	+	4.52680i	0.100622	+	0.363602i
$156$	2.96919	−	2.46714i	0.237725	−	0.197530i
$157$	1.69478	−	1.78008i	0.135258	−	0.142066i	−0.653126	−	0.757249i	$-0.726543\pi$
$157$	1.69478	−	1.78008i	0.135258	−	0.142066i	0.788384	+	0.615183i	$0.210918\pi$
$158$	−9.45733	+	9.05915i	−0.752385	+	0.720707i
$159$	6.86281	+	1.36510i	0.544256	+	0.108259i
$160$	18.7412	−	1.20678i	1.48162	−	0.0954041i
$161$	−3.47633	+	0.691485i	−0.273973	+	0.0544967i
$162$	−1.94379	+	2.77788i	−0.152718	+	0.218251i
$163$	−1.07954	−	2.43541i	−0.0845564	−	0.190756i	0.866943	−	0.498408i	$-0.166082\pi$
$163$	−1.07954	−	2.43541i	−0.0845564	−	0.190756i	−0.951499	+	0.307652i	$0.900457\pi$
$164$	6.62406	−	6.70519i	0.517253	−	0.523587i
$165$	2.70096	−	2.10785i	0.210270	−	0.164096i
$166$	−2.71811	−	13.4508i	−0.210966	−	1.04399i
$167$	−3.93022	−	0.984469i	−0.304130	−	0.0761805i	0.0879113	−	0.996128i	$-0.471981\pi$
$167$	−3.93022	−	0.984469i	−0.304130	−	0.0761805i	−0.392041	+	0.919948i	$0.628231\pi$
$168$	−6.73240	+	0.0614633i	−0.519416	+	0.00474200i
$169$	−1.54894	+	10.4421i	−0.119149	+	0.803239i
$170$	13.5336	−	3.43379i	1.03798	−	0.263360i
$171$	−12.0033	+	2.08277i	−0.917915	+	0.159273i
$172$	−2.77726	+	5.60211i	−0.211764	+	0.427157i
$173$	2.68273	+	21.7510i	0.203964	+	1.65370i	0.650922	+	0.759145i	$0.274383\pi$
$173$	2.68273	+	21.7510i	0.203964	+	1.65370i	−0.446957	+	0.894555i	$0.647492\pi$
$174$	0.0886975	−	1.25446i	0.00672414	−	0.0951007i
$175$	−7.36416	+	8.97325i	−0.556678	+	0.678314i
$176$	3.32272	+	0.368818i	0.250459	+	0.0278007i
$177$	−1.64953	+	1.35373i	−0.123986	+	0.101753i
$178$	−7.11446	−	1.21219i	−0.533251	−	0.0908572i
$179$	−20.9533	−	10.5470i	−1.56612	−	0.788320i	−0.566755	−	0.823886i	$-0.691802\pi$
$179$	−20.9533	−	10.5470i	−1.56612	−	0.788320i	−0.999367	+	0.0355662i	$0.988677\pi$
$180$	−4.77639	+	8.55246i	−0.356011	+	0.637463i
$181$	−14.7377	+	14.0315i	−1.09545	+	1.04295i	−0.0965821	+	0.995325i	$0.530791\pi$
$181$	−14.7377	+	14.0315i	−1.09545	+	1.04295i	−0.998865	+	0.0476275i	$0.984834\pi$
$182$	−3.14903	+	2.87161i	−0.233421	+	0.212858i
$183$	13.1259	−	0.644834i	0.970294	−	0.0476675i
$184$	4.62358	−	2.38047i	0.340855	−	0.175490i
$185$	−11.3392	+	23.9748i	−0.833678	+	1.76266i
$186$	1.17124	+	2.17529i	0.0858796	+	0.159500i
$187$	2.47878	−	0.182846i	0.181267	−	0.0133710i
$188$	−0.0958507	−	0.373011i	−0.00699063	−	0.0272046i
$189$	5.69928	−	9.00015i	0.414562	−	0.654664i
$190$	37.3333	−	10.4539i	2.70844	−	0.758408i
$191$	−4.22267	+	1.74909i	−0.305542	+	0.126560i	−0.530186	−	0.847881i	$-0.677878\pi$
$191$	−4.22267	+	1.74909i	−0.305542	+	0.126560i	0.224644	+	0.974441i	$0.427878\pi$
$192$	9.47067	−	2.80802i	0.683487	−	0.202651i
$193$	−5.43343	−	2.25060i	−0.391107	−	0.162002i	0.178459	−	0.983947i	$-0.442889\pi$
$193$	−5.43343	−	2.25060i	−0.391107	−	0.162002i	−0.569566	+	0.821946i	$0.692889\pi$
$194$	−9.15954	−	1.10143i	−0.657616	−	0.0790784i
$195$	−1.40401	−	6.25236i	−0.100544	−	0.447741i
$196$	−6.55741	+	0.362163i	−0.468386	+	0.0258688i
$197$	12.6830	+	10.9404i	0.903627	+	0.779474i	0.975970	−	0.217906i	$-0.0699226\pi$
$197$	12.6830	+	10.9404i	0.903627	+	0.779474i	−0.0723429	+	0.997380i	$0.523048\pi$
$198$	−1.10215	+	1.35134i	−0.0783265	+	0.0960356i
$199$	−4.28581	−	11.9780i	−0.303813	−	0.849101i	−0.992301	−	0.123853i	$-0.960475\pi$
$199$	−4.28581	−	11.9780i	−0.303813	−	0.849101i	0.688487	−	0.725248i	$-0.258275\pi$
$200$	6.75945	−	15.6328i	0.477966	−	1.10540i
$201$	−12.7418	−	11.5485i	−0.898740	−	0.814570i
$202$	−7.50000	−	20.7617i	−0.527698	−	1.46079i
$203$	−0.0340715	+	1.38792i	−0.00239135	+	0.0974127i
$204$	6.53976	−	3.34188i	0.457874	−	0.233978i
$205$	−4.90772	−	14.8559i	−0.342770	−	1.03758i
$206$	13.8558	−	3.15574i	0.965376	−	0.219870i
$207$	−0.265879	+	2.69952i	−0.0184799	+	0.187629i
$208$	3.28071	−	5.32307i	0.227476	−	0.369088i
$209$	6.86828	−	0.676467i	0.475089	−	0.0467922i
$210$	−4.99437	+	9.99776i	−0.344645	+	0.689911i
$211$	10.1525	+	7.92307i	0.698925	+	0.545446i	0.900944	−	0.433935i	$-0.142875\pi$
$211$	10.1525	+	7.92307i	0.698925	+	0.545446i	−0.202019	+	0.979382i	$0.564750\pi$
$212$	11.2398	−	1.45580i	0.771952	−	0.0999845i
$213$	−9.16223	−	6.45277i	−0.627785	−	0.442136i
$214$	−4.99508	−	6.69242i	−0.341456	−	0.457484i
$215$	6.18286	+	8.33662i	0.421667	+	0.568553i
$216$	−4.40040	+	14.9977i	−0.299410	+	1.02047i
$217$	−1.40217	−	2.33937i	−0.0951852	−	0.158807i
$218$	−7.71848	−	1.51090i	−0.522762	−	0.102331i
$219$	−2.11035	+	17.1102i	−0.142604	+	1.15620i
$220$	3.05493	−	4.63282i	0.205963	−	0.312345i
$221$	1.67308	−	4.33731i	0.112544	−	0.291759i
$222$	−3.01502	+	13.6202i	−0.202355	+	0.914131i
$223$	−13.5898	+	20.3386i	−0.910039	+	1.36197i	0.0220557	+	0.999757i	$0.492979\pi$
$223$	−13.5898	+	20.3386i	−0.910039	+	1.36197i	−0.932095	+	0.362214i	$0.882021\pi$
$224$	−10.3015	+	3.57789i	−0.688296	+	0.239058i
$225$	4.93558	+	7.38662i	0.329039	+	0.492441i
$226$	21.7283	−	8.45759i	1.44535	−	0.562591i
$227$	−0.490195	−	19.9683i	−0.0325354	−	1.32534i	−0.764775	−	0.644297i	$-0.777150\pi$
$227$	−0.490195	−	19.9683i	−0.0325354	−	1.32534i	0.732240	−	0.681047i	$-0.238475\pi$
$228$	17.9257	−	9.72220i	1.18716	−	0.643869i
$229$	1.42029	−	2.50716i	0.0938553	−	0.165678i	−0.819207	−	0.573498i	$-0.805586\pi$
$229$	1.42029	−	2.50716i	0.0938553	−	0.165678i	0.913062	+	0.407820i	$0.133711\pi$
$230$	−0.0262688	−	8.63229i	−0.00173211	−	0.569197i
$231$	−1.18512	+	1.59795i	−0.0779752	+	0.105137i
$232$	−0.512960	−	1.97132i	−0.0336775	−	0.129424i
$233$	8.85002	−	2.21681i	0.579784	−	0.145228i	0.0580159	−	0.998316i	$-0.481523\pi$
$233$	8.85002	−	2.21681i	0.579784	−	0.145228i	0.521768	+	0.853087i	$0.325273\pi$
$234$	1.40345	+	2.94414i	0.0917467	+	0.192465i
$235$	−0.623756	−	0.140069i	−0.0406894	−	0.00913710i
$236$	−1.83133	+	2.93130i	−0.119209	+	0.190812i
$237$	5.63603	+	9.94899i	0.366100	+	0.646256i
$238$	−7.04216	+	4.01769i	−0.456475	+	0.260428i
$239$	−8.79927	−	16.4623i	−0.569177	−	1.06486i	−0.987657	−	0.156630i	$-0.949937\pi$
$239$	−8.79927	−	16.4623i	−0.569177	−	1.06486i	0.418480	−	0.908226i	$-0.362563\pi$
$240$	3.00294	−	16.1198i	0.193839	−	1.04053i
$241$	−10.3426	−	5.52826i	−0.666229	−	0.356107i	0.103362	−	0.994644i	$-0.467040\pi$
$241$	−10.3426	−	5.52826i	−0.666229	−	0.356107i	−0.769591	+	0.638537i	$0.779540\pi$
$242$	−10.0134	+	10.5817i	−0.643686	+	0.680217i
$243$	−8.89480	−	10.3116i	−0.570602	−	0.661486i
$244$	19.8127	−	7.78147i	1.26838	−	0.498158i
$245$	−4.41773	+	9.96623i	−0.282238	+	0.636719i
$246$	−4.25225	−	7.04574i	−0.271113	−	0.449220i
$247$	4.34868	−	12.1537i	0.276700	−	0.773324i
$248$	2.92325	+	2.73273i	0.185627	+	0.173528i
$249$	−11.9671	−	0.587905i	−0.758384	−	0.0372570i
$250$	−3.05397	−	3.69827i	−0.193150	−	0.233899i
$251$	−7.73721	−	2.55603i	−0.488368	−	0.161335i	0.0589477	−	0.998261i	$-0.481225\pi$
$251$	−7.73721	−	2.55603i	−0.488368	−	0.161335i	−0.547316	+	0.836926i	$0.684350\pi$
$252$	1.34852	−	5.52605i	0.0849485	−	0.348109i
$253$	0.262714	−	1.51406i	0.0165167	−	0.0951882i
$254$	−0.735410	+	0.857808i	−0.0461437	+	0.0538237i
$255$		−	12.1908i		−	0.763419i
$256$	13.0832	−	9.21033i	0.817699	−	0.575645i
$257$		−	16.2759i		−	1.01526i	−0.861574	−	0.507632i	$-0.830521\pi$
$257$		−	16.2759i		−	1.01526i	0.861574	−	0.507632i	$-0.169479\pi$
$258$	4.14472	+	3.55332i	0.258039	+	0.221220i
$259$	2.63284	−	15.1735i	0.163597	−	0.942833i
$260$	−5.39013	−	8.87001i	−0.334281	−	0.550094i
$261$	1.00887	+	0.333287i	0.0624478	+	0.0206300i
$262$	−12.3395	+	10.1898i	−0.762336	+	0.629525i
$263$	9.38279	+	0.460947i	0.578568	+	0.0284232i	0.336248	−	0.941773i	$-0.390842\pi$
$263$	9.38279	+	0.460947i	0.578568	+	0.0284232i	0.242319	+	0.970197i	$0.422092\pi$
$264$	1.02561	−	2.73283i	0.0631217	−	0.168194i
$265$	6.33797	−	17.7134i	0.389338	−	1.08813i
$266$	−19.2742	+	11.6324i	−1.18178	+	0.713228i
$267$	−2.55354	+	5.76069i	−0.156274	+	0.352548i
$268$	−25.5325	−	11.1323i	−1.55964	−	0.680016i
$269$	14.2510	+	16.5209i	0.868901	+	1.00730i	0.999873	+	0.0159115i	$0.00506500\pi$
$269$	14.2510	+	16.5209i	0.868901	+	1.00730i	−0.130973	+	0.991386i	$0.541810\pi$
$270$	18.8448	+	17.8327i	1.14686	+	1.08526i
$271$	7.35409	+	3.93084i	0.446729	+	0.238782i	0.679392	−	0.733776i	$-0.262244\pi$
$271$	7.35409	+	3.93084i	0.446729	+	0.238782i	−0.232663	+	0.972558i	$0.574744\pi$
$272$	8.30841	−	8.51318i	0.503771	−	0.516187i
$273$	1.75407	+	3.28164i	0.106161	+	0.198614i
$274$	4.45700	+	7.81218i	0.269257	+	0.471951i
$275$	−2.48061	−	4.37890i	−0.149587	−	0.264057i
$276$	−1.02179	−	4.42409i	−0.0615043	−	0.266299i
$277$	−20.4520	−	4.59265i	−1.22884	−	0.275945i	−0.444218	−	0.895919i	$-0.646518\pi$
$277$	−20.4520	−	4.59265i	−1.22884	−	0.275945i	−0.784623	+	0.619973i	$0.787143\pi$
$278$	−18.9913	+	9.05302i	−1.13902	+	0.542964i
$279$	−2.02474	+	0.507172i	−0.121218	+	0.0303636i
$280$	−2.49251	+	17.9294i	−0.148956	+	1.07149i
$281$	15.3149	−	20.6498i	0.913613	−	1.23186i	−0.0587221	−	0.998274i	$-0.518703\pi$
$281$	15.3149	−	20.6498i	0.913613	−	1.23186i	0.972335	−	0.233590i	$-0.0750474\pi$
$282$	−0.336261	+	0.00102327i	−0.0200241	+	6.09349e-5i
$283$	−1.23025	+	2.17170i	−0.0731309	+	0.129094i	−0.904255	−	0.426993i	$-0.859573\pi$
$283$	−1.23025	+	2.17170i	−0.0731309	+	0.129094i	0.831124	+	0.556087i	$0.187698\pi$
$284$	−17.4016	−	5.16327i	−1.03259	−	0.306384i
$285$	−0.830724	−	33.8400i	−0.0492079	−	2.00451i
$286$	−0.670212	−	1.72184i	−0.0396305	−	0.101814i
$287$	5.04735	+	7.55389i	0.297936	+	0.445892i
$288$	0.331732	+	8.33915i	0.0195475	+	0.491389i
$289$	−4.53123	+	6.78147i	−0.266543	+	0.398910i
$290$	−3.30132	−	0.730790i	−0.193860	−	0.0429135i
$291$	−2.89894	+	7.51522i	−0.169939	+	0.440550i
$292$	5.61428	+	27.3537i	0.328551	+	1.60076i
$293$	−2.59994	+	21.0797i	−0.151890	+	1.23149i	0.702433	+	0.711750i	$0.252097\pi$
$293$	−2.59994	+	21.0797i	−0.151890	+	1.23149i	−0.854323	+	0.519742i	$0.826028\pi$
$294$	−1.10155	+	5.62731i	−0.0642437	+	0.328191i
$295$	2.94957	+	4.92105i	0.171730	+	0.286515i
$296$	2.41990	+	22.4652i	0.140654	+	1.30576i
$297$	2.75127	+	3.70965i	0.159645	+	0.215256i
$298$	13.6165	−	10.1630i	0.788782	−	0.588729i
$299$	−2.34986	−	1.65496i	−0.135896	−	0.0957088i
$300$	−11.7786	−	9.07730i	−0.680037	−	0.524078i
$301$	−4.75131	−	3.70796i	−0.273861	−	0.213723i
$302$	−20.6025	−	10.2919i	−1.18554	−	0.592235i
$303$	−19.1811	+	1.88917i	−1.10192	+	0.108530i
$304$	22.4828	−	24.1975i	1.28948	−	1.38782i
$305$	3.46329	−	35.1634i	0.198307	−	2.01345i
$306$	1.37790	+	6.04990i	0.0787694	+	0.345850i
$307$	1.41392	+	4.28001i	0.0806968	+	0.244273i	0.981989	−	0.188940i	$-0.0605050\pi$
$307$	1.41392	+	4.28001i	0.0806968	+	0.244273i	−0.901292	+	0.433212i	$0.857380\pi$
$308$	−0.992165	+	3.06585i	−0.0565338	+	0.174693i
$309$	0.304495	−	12.4038i	0.0173221	−	0.705625i
$310$	6.24735	−	2.25681i	0.354826	−	0.128178i
$311$	−10.6144	−	9.62038i	−0.601890	−	0.545521i	0.312727	−	0.949843i	$-0.398758\pi$
$311$	−10.6144	−	9.62038i	−0.601890	−	0.545521i	−0.914617	+	0.404322i	$0.867508\pi$
$312$	−3.80046	−	3.91947i	−0.215159	−	0.221896i
$313$	8.27410	+	23.1246i	0.467680	+	1.30708i	0.911625	+	0.411023i	$0.134829\pi$
$313$	8.27410	+	23.1246i	0.467680	+	1.30708i	−0.443945	+	0.896054i	$0.646421\pi$
$314$	−2.69361	−	2.19691i	−0.152009	−	0.123979i
$315$	−7.14962	−	6.16730i	−0.402835	−	0.347488i
$316$	13.7984	+	12.3540i	0.776222	+	0.694969i
$317$	0.934298	+	4.16062i	0.0524754	+	0.233684i	0.994919	−	0.100683i	$-0.0321027\pi$
$317$	0.934298	+	4.16062i	0.0524754	+	0.233684i	−0.942443	+	0.334366i	$0.891478\pi$
$318$	1.18144	−	9.82484i	0.0662517	−	0.550950i
$319$	−0.556093	−	0.230341i	−0.0311352	−	0.0128966i
$320$	−3.73181	−	26.2955i	−0.208615	−	1.46996i
$321$	−6.73638	+	2.79030i	−0.375988	+	0.155739i
$322$	1.35162	+	4.82692i	0.0753226	+	0.268994i
$323$	13.1380	−	20.7471i	0.731015	−	1.15440i
$324$	4.12754	+	2.43993i	0.229308	+	0.135552i
$325$	−9.38747	+	0.692461i	−0.520723	+	0.0384108i
$326$	−3.31713	+	1.78604i	−0.183719	+	0.0989197i
$327$	−2.93604	+	6.20773i	−0.162363	+	0.343288i
$328$	−10.1723	−	8.61396i	−0.561670	−	0.475627i
$329$	0.370773	−	0.0182149i	0.0204414	−	0.00100422i
$330$	−3.26479	−	3.58018i	−0.179721	−	0.197082i
$331$	20.5443	−	19.5598i	1.12921	−	1.07510i	0.132745	−	0.991150i	$-0.457621\pi$
$331$	20.5443	−	19.5598i	1.12921	−	1.07510i	0.996470	−	0.0839514i	$-0.0267541\pi$
$332$	−18.6720	+	5.28979i	−1.02476	+	0.290315i
$333$	−10.5274	−	5.29905i	−0.576898	−	0.290386i
$334$	−0.962408	+	5.64849i	−0.0526606	+	0.309071i
$335$	−35.7406	+	29.3316i	−1.95272	+	1.60255i
$336$	0.815970	+	9.48641i	0.0445148	+	0.517526i
$337$	13.3939	−	16.3205i	0.729611	−	0.889034i	−0.267610	−	0.963527i	$-0.586234\pi$
$337$	13.3939	−	16.3205i	0.729611	−	0.889034i	0.997221	+	0.0744936i	$0.0237340\pi$
$338$	14.8918	+	1.05293i	0.810006	+	0.0572719i
$339$	−2.49202	−	20.2048i	−0.135348	−	1.09737i
$340$	−6.30791	−	18.7112i	−0.342094	−	1.01476i
$341$	1.16505	−	0.202156i	0.0630911	−	0.0109473i
$342$	4.23711	+	16.6997i	0.229117	+	0.903018i
$343$	2.90888	−	19.6100i	0.157065	−	1.05884i
$344$	8.20015	+	3.30924i	0.442123	+	0.178422i
$345$	−7.31116	−	1.83135i	−0.393620	−	0.0985966i
$346$	30.3796	−	6.13905i	1.63322	−	0.330037i
$347$	−4.52654	+	3.53255i	−0.242998	+	0.189637i	−0.729380	−	0.684109i	$-0.760191\pi$
$347$	−4.52654	+	3.53255i	−0.242998	+	0.189637i	0.486382	+	0.873746i	$0.338316\pi$
$348$	−1.77848	+	0.0108242i	−0.0953364	+	0.000580239i
$349$	9.22241	+	20.8054i	0.493664	+	1.11369i	0.971886	+	0.235450i	$0.0756563\pi$
$349$	9.22241	+	20.8054i	0.493664	+	1.11369i	−0.478222	+	0.878239i	$0.658719\pi$
$350$	13.4505	+	9.41184i	0.718962	+	0.503084i
$351$	8.47236	−	1.68526i	0.452221	−	0.0899524i
$352$	0.160113	−	4.72518i	0.00853403	−	0.251853i
$353$	−13.1614	−	2.61797i	−0.700513	−	0.139341i	−0.168030	−	0.985782i	$-0.553741\pi$
$353$	−13.1614	−	2.61797i	−0.700513	−	0.139341i	−0.532482	+	0.846441i	$0.678741\pi$
$354$	2.08753	+	2.17928i	0.110951	+	0.115828i
$355$	−20.7760	+	21.8217i	−1.10268	+	1.15818i
$356$	−0.938562	+	10.1631i	−0.0497437	+	0.538644i
$357$	1.88804	+	6.82249i	0.0999256	+	0.361085i
$358$	−12.6021	+	30.6879i	−0.666040	+	1.62191i
$359$	34.1265	−	5.06218i	1.80113	−	0.267172i	0.839862	−	0.542800i	$-0.182636\pi$
$359$	34.1265	−	5.06218i	1.80113	−	0.267172i	0.961264	+	0.275629i	$0.0888860\pi$
$360$	12.5769	+	5.80852i	0.662860	+	0.306136i
$361$	25.2873	−	42.1893i	1.33091	−	2.22049i
$362$	21.3817	+	19.2611i	1.12380	+	1.01234i
$363$	6.80516	+	10.7465i	0.357178	+	0.564046i
$364$	4.39027	+	4.12924i	0.230113	+	0.216431i
$365$	44.6729	+	12.3627i	2.33829	+	0.647092i
$366$	−2.33115	−	18.4384i	−0.121851	−	0.963792i
$367$	−0.150107	+	0.494838i	−0.00783554	+	0.0258303i	−0.960771	−	0.277343i	$-0.910546\pi$
$367$	−0.150107	+	0.494838i	−0.00783554	+	0.0258303i	0.952935	+	0.303173i	$0.0980461\pi$
$368$	−3.85746	−	6.26166i	−0.201084	−	0.326411i
$369$	6.65341	−	2.01829i	0.346363	−	0.105068i
$370$	35.0343	+	13.3919i	1.82134	+	0.696210i
$371$	−0.803646	+	10.8948i	−0.0417232	+	0.565628i
$372$	2.94041	−	1.88716i	0.152453	−	0.0978448i
$373$	6.19269	+	16.0539i	0.320645	+	0.831242i	0.995628	+	0.0934082i	$0.0297762\pi$
$373$	6.19269	+	16.0539i	0.320645	+	0.831242i	−0.674982	+	0.737834i	$0.735849\pi$
$374$	−0.526344	−	3.47542i	−0.0272166	−	0.179710i
$375$	−3.78561	+	1.79046i	−0.195488	+	0.0924591i
$376$	−0.515584	+	0.175562i	−0.0265892	+	0.00905394i
$377$	−0.834154	+	0.756033i	−0.0429611	+	0.0389377i
$378$	−13.3081	−	7.06136i	−0.684496	−	0.363197i
$379$	15.4962	+	30.7857i	0.795987	+	1.58135i	0.813540	+	0.581509i	$0.197537\pi$
$379$	15.4962	+	30.7857i	0.795987	+	1.58135i	−0.0175528	+	0.999846i	$0.505588\pi$
$380$	−18.7849	−	51.5097i	−0.963644	−	2.64239i
$381$	0.568052	+	0.806572i	0.0291022	+	0.0413219i
$382$	2.92375	+	5.76474i	0.149592	+	0.294950i
$383$	0.0323013	−	0.0323013i	0.00165052	−	0.00165052i	−0.706281	−	0.707932i	$-0.749629\pi$
$383$	0.0323013	−	0.0323013i	0.00165052	−	0.00165052i	0.707932	+	0.706281i	$0.249629\pi$
$384$	−4.98540	−	13.0500i	−0.254410	−	0.665956i
$385$	3.78229	+	3.78229i	0.192763	+	0.192763i
$386$	−2.58489	+	7.90526i	−0.131567	+	0.402367i
$387$	−3.77106	+	2.65588i	−0.191694	+	0.135006i
$388$	−0.560858	+	13.0348i	−0.0284733	+	0.661742i
$389$	17.4937	−	8.80561i	0.886968	−	0.446462i	0.0532041	−	0.998584i	$-0.483057\pi$
$389$	17.4937	−	8.80561i	0.886968	−	0.446462i	0.833764	+	0.552122i	$0.186182\pi$
$390$	−8.66410	+	2.65704i	−0.438724	+	0.134545i
$391$	−3.67198	−	4.05140i	−0.185700	−	0.204888i
$392$	1.22102	+	9.20709i	0.0616707	+	0.465029i
$393$	5.97399	+	12.6309i	0.301348	+	0.637146i
$394$	14.0527	−	19.0689i	0.707967	−	0.960679i
$395$	28.6833	−	11.0644i	1.44321	−	0.556708i
$396$	2.02486	+	1.40771i	0.101753	+	0.0707402i
$397$	−17.5901	−	1.29752i	−0.882820	−	0.0651207i	−0.375443	−	0.926845i	$-0.622510\pi$
$397$	−17.5901	−	1.29752i	−0.882820	−	0.0651207i	−0.507376	+	0.861725i	$0.669385\pi$
$398$	−16.4255	+	7.34080i	−0.823334	+	0.367961i
$399$	5.70583	+	18.8096i	0.285649	+	0.941657i
$400$	−22.7753	−	7.83777i	−1.13877	−	0.391888i
$401$	−12.7898	−	3.87974i	−0.638691	−	0.193745i	−0.0457016	−	0.998955i	$-0.514552\pi$
$401$	−12.7898	−	3.87974i	−0.638691	−	0.193745i	−0.592989	+	0.805210i	$0.702052\pi$
$402$	−14.9038	+	19.2178i	−0.743334	+	0.958495i
$403$	0.589869	−	2.13151i	0.0293835	−	0.106178i
$404$	−28.4627	+	12.8245i	−1.41607	+	0.638042i
$405$	6.72421	−	4.25806i	0.334129	−	0.211585i
$406$	1.96074	−	0.102307i	0.0973097	−	0.00507740i
$407$	5.72682	+	3.43252i	0.283868	+	0.170144i
$408$	−5.42068	−	8.85942i	−0.268363	−	0.438607i
$409$	−2.31867	−	15.6312i	−0.114651	−	0.772912i	−0.967887	−	0.251387i	$-0.919113\pi$
$409$	−2.31867	−	15.6312i	−0.114651	−	0.772912i	0.853236	−	0.521525i	$-0.174637\pi$
$410$	−20.4160	+	8.52947i	−1.00828	+	0.421241i
$411$	7.56849	−	2.09448i	0.373326	−	0.103313i
$412$	−5.95073	−	19.1956i	−0.293171	−	0.945698i
$413$	−2.41284	−	2.29722i	−0.118728	−	0.113039i
$414$	3.83528	+	0.0824735i	0.188494	+	0.00405335i
$415$	−6.28466	+	31.5951i	−0.308502	+	1.55094i
$416$	−7.86123	−	4.04936i	−0.385428	−	0.198536i
$417$	3.58366	+	18.0163i	0.175492	+	0.882260i
$418$	−1.69788	−	9.61140i	−0.0830461	−	0.470109i
$419$	4.31936	−	1.91464i	0.211014	−	0.0935363i	−0.297026	−	0.954869i	$-0.595995\pi$
$419$	4.31936	−	1.91464i	0.211014	−	0.0935363i	0.508041	+	0.861333i	$0.330370\pi$
$420$	14.6384	+	5.95933i	0.714283	+	0.290785i
$421$	22.0061	+	28.1982i	1.07251	+	1.37430i	0.922672	+	0.385585i	$0.126000\pi$
$421$	22.0061	+	28.1982i	1.07251	+	1.37430i	0.149838	+	0.988711i	$0.452125\pi$
$422$	10.0722	−	15.1739i	0.490307	−	0.738652i
$423$	0.0690299	−	0.275583i	0.00335635	−	0.0133993i
$424$	−3.27033	−	15.6911i	−0.158821	−	0.762025i
$425$	−17.7136	−	2.62757i	−0.859236	−	0.127456i
$426$	−8.10626	+	13.6183i	−0.392750	+	0.659808i
$427$	3.50768	+	20.2152i	0.169748	+	0.978284i
$428$	−8.89560	+	7.76832i	−0.429985	+	0.375496i
$429$	−1.60110	+	0.197477i	−0.0773020	+	0.00953430i
$430$	11.0853	−	9.62127i	0.534583	−	0.463979i
$431$	−26.3482	−	21.6234i	−1.26915	−	1.04156i	−0.996847	−	0.0793491i	$-0.974716\pi$
$431$	−26.3482	−	21.6234i	−1.26915	−	1.04156i	−0.272300	−	0.962213i	$-0.587784\pi$
$432$	21.6244	+	4.58016i	1.04040	+	0.220363i
$433$	19.4338	+	23.6802i	0.933929	+	1.13800i	0.990211	+	0.139581i	$0.0445756\pi$
$433$	19.4338	+	23.6802i	0.933929	+	1.13800i	−0.0562813	+	0.998415i	$0.517924\pi$
$434$	−3.14676	+	2.23055i	−0.151049	+	0.107070i
$435$	−1.32735	+	2.63699i	−0.0636415	+	0.126434i
$436$	−1.29433	+	11.0472i	−0.0619873	+	0.529064i
$437$	−10.4690	−	10.9959i	−0.500798	−	0.526005i
$438$	24.3550	+	1.12220i	1.16373	+	0.0536210i
$439$	−0.129927	−	2.64472i	−0.00620107	−	0.126226i	−0.999900	−	0.0141433i	$-0.995498\pi$
$439$	−0.129927	−	2.64472i	−0.00620107	−	0.126226i	0.993699	−	0.112082i	$-0.0357521\pi$
$440$	−6.86348	−	3.80577i	−0.327204	−	0.181433i
$441$	−4.37942	−	2.07131i	−0.208544	−	0.0986340i
$442$	−6.29710	−	1.88930i	−0.299522	−	0.0898647i
$443$	2.75396	+	37.3345i	0.130845	+	1.77382i	0.521473	+	0.853268i	$0.325383\pi$
$443$	2.75396	+	37.3345i	0.130845	+	1.77382i	−0.390628	+	0.920549i	$0.627742\pi$
$444$	19.5319	+	2.77591i	0.926945	+	0.131739i
$445$	14.3134	+	9.06388i	0.678522	+	0.429669i
$446$	30.1507	+	16.9592i	1.42768	+	0.803040i
$447$	−5.67718	−	13.7059i	−0.268521	−	0.648268i
$448$	6.16096	+	14.1381i	0.291078	+	0.667962i
$449$	−11.6562	+	28.1406i	−0.550091	+	1.32804i	0.367320	+	0.930095i	$0.380276\pi$
$449$	−11.6562	+	28.1406i	−0.550091	+	1.32804i	−0.917411	+	0.397942i	$0.869724\pi$
$450$	9.88091	−	7.75963i	0.465790	−	0.365793i
$451$	−3.84308	+	0.862992i	−0.180963	+	0.0406367i
$452$	−14.2795	−	29.7220i	−0.671650	−	1.39801i
$453$	−13.1340	+	15.2259i	−0.617088	+	0.715376i
$454$	−28.1034	+	2.85432i	−1.31896	+	0.133960i
$455$	9.41966	−	3.37041i	0.441601	−	0.158007i
$456$	−15.6507	−	24.2231i	−0.732912	−	1.13435i
$457$	−0.0238542	+	0.0263190i	−0.00111585	+	0.00123115i	−0.741509	−	0.670943i	$-0.765889\pi$
$457$	−0.0238542	+	0.0263190i	−0.00111585	+	0.00123115i	0.740393	+	0.672174i	$0.234639\pi$
$458$	−3.68910	−	1.73110i	−0.172380	−	0.0808888i
$459$	16.4288	+	0.403305i	0.766831	+	0.0188247i
$460$	−12.1692	+	0.972155i	−0.567392	+	0.0453269i
$461$	−29.8570	+	9.86342i	−1.39058	+	0.459385i	−0.908919	−	0.416973i	$-0.863091\pi$
$461$	−29.8570	+	9.86342i	−1.39058	+	0.459385i	−0.481660	+	0.876358i	$0.659966\pi$
$462$	2.38159	+	1.49799i	0.110801	+	0.0696927i
$463$	0.0165958	+	0.00163454i	0.000771271	+	7.59636e-5i	0.0984028	−	0.995147i	$-0.468627\pi$
$463$	0.0165958	+	0.00163454i	0.000771271	+	7.59636e-5i	−0.0976315	+	0.995223i	$0.531127\pi$
$464$	−2.72411	+	0.936852i	−0.126464	+	0.0434923i
$465$	−0.568467	−	5.77174i	−0.0263620	−	0.267658i
$466$	−4.08454	−	12.2389i	−0.189213	−	0.566956i
$467$	14.5108	−	18.5939i	0.671479	−	0.860421i	−0.324873	−	0.945758i	$-0.605322\pi$
$467$	14.5108	−	18.5939i	0.671479	−	0.860421i	0.996352	+	0.0853367i	$0.0271966\pi$
$468$	3.99938	−	2.29789i	0.184871	−	0.106220i
$469$	15.4592	−	21.9504i	0.713842	−	1.01358i
$470$	−0.129936	+	0.894706i	−0.00599349	+	0.0412697i
$471$	−2.43764	+	1.80787i	−0.112320	+	0.0833025i
$472$	4.33169	+	2.26474i	0.199382	+	0.104243i
$473$	2.24121	−	1.34333i	0.103051	−	0.0617665i
$474$	13.4181	−	9.02488i	0.616315	−	0.414527i
$475$	−49.3495	−	6.08667i	−2.26431	−	0.279276i
$476$	6.42804	+	9.49463i	0.294629	+	0.435186i
$477$	7.80026	+	3.00889i	0.357149	+	0.137768i
$478$	−22.2596	+	14.1908i	−1.01813	+	0.649072i
$479$	0.605575	+	0.404633i	0.0276694	+	0.0184881i	0.569328	−	0.822110i	$-0.307203\pi$
$479$	0.605575	+	0.404633i	0.0276694	+	0.0184881i	−0.541659	+	0.840599i	$0.682203\pi$
$480$	−23.0552	−	2.48810i	−1.05232	−	0.113566i
$481$	10.3833	−	6.93789i	0.473437	−	0.316340i
$482$	−6.67478	+	15.1826i	−0.304028	+	0.691549i
$483$	4.37526	−	0.107407i	0.199081	−	0.00488717i
$484$	16.0055	+	12.9732i	0.727525	+	0.589691i
$485$	18.8434	+	10.6747i	0.855637	+	0.484712i
$486$	−13.5763	+	13.6592i	−0.615835	+	0.619595i
$487$	10.9766	+	8.14083i	0.497399	+	0.368896i	0.815124	−	0.579287i	$-0.196669\pi$
$487$	10.9766	+	8.14083i	0.497399	+	0.368896i	−0.317725	+	0.948183i	$0.602919\pi$
$488$	−13.1186	−	27.0942i	−0.593851	−	1.22650i
$489$	0.799254	+	3.19080i	0.0361435	+	0.144293i
$490$	14.5315	+	5.14964i	0.656467	+	0.232637i
$491$	−4.00720	+	17.8449i	−0.180842	+	0.805328i	0.798317	+	0.602237i	$0.205724\pi$
$491$	−4.00720	+	17.8449i	−0.180842	+	0.805328i	−0.979160	+	0.203091i	$0.934901\pi$
$492$	−9.47426	+	6.75916i	−0.427133	+	0.304727i
$493$	−1.86349	+	1.05565i	−0.0839271	+	0.0475441i
$494$	−17.6086	−	4.81531i	−0.792247	−	0.216651i
$495$	3.61023	−	1.92971i	0.162268	−	0.0867339i
$496$	3.53664	−	4.41799i	0.158800	−	0.198373i
$497$	8.24751	−	15.4300i	0.369951	−	0.692130i
$498$	0.467383	+	16.9380i	0.0209439	+	0.759009i
$499$	−11.4945	+	9.91519i	−0.514563	+	0.443865i	−0.871595	−	0.490227i	$-0.836914\pi$
$499$	−11.4945	+	9.91519i	−0.514563	+	0.443865i	0.357032	+	0.934092i	$0.383789\pi$
$500$	−4.88394	+	4.70690i	−0.218417	+	0.210499i
$501$	4.57366	+	2.02737i	0.204336	+	0.0905760i
$502$	−2.76600	+	11.1868i	−0.123453	+	0.499292i
$503$	−15.5266	−	5.55550i	−0.692296	−	0.247708i	−0.0328511	−	0.999460i	$-0.510459\pi$
$503$	−15.5266	−	5.55550i	−0.692296	−	0.247708i	−0.659445	+	0.751753i	$0.729209\pi$
$504$	−7.93814	−	1.30286i	−0.353593	−	0.0580341i
$505$	−2.54272	+	51.7583i	−0.113150	+	2.30322i
$506$	−2.16337	−	0.206428i	−0.0961737	−	0.00917686i
$507$	4.08876	−	12.3768i	0.181588	−	0.549675i
$508$	1.28922	+	0.944046i	0.0572001	+	0.0418853i
$509$	−25.3261	−	4.39449i	−1.12256	−	0.194782i	−0.420769	−	0.907168i	$-0.638240\pi$
$509$	−25.3261	−	4.39449i	−1.12256	−	0.194782i	−0.701788	+	0.712385i	$0.747615\pi$
$510$	−17.1898	+	1.32060i	−0.761176	+	0.0584772i
$511$	−26.9155			−1.19067
$512$	−14.4044	−	17.4503i	−0.636589	−	0.771203i
$513$	45.6315			2.01468
$514$	−22.9500	+	1.76313i	−1.01228	+	0.0777682i
$515$	−32.8683	−	5.70319i	−1.44835	−	0.251313i
$516$	4.56140	−	6.22922i	0.200804	−	0.274226i
$517$	−0.0504845	+	0.152819i	−0.00222031	+	0.00672096i
$518$	−21.6807	−	2.06876i	−0.952594	−	0.0908963i
$519$	1.32783	−	27.0285i	0.0582851	−	1.18642i
$520$	−11.9233	+	8.56126i	−0.522873	+	0.375436i
$521$	−32.5299	−	11.6394i	−1.42516	−	0.509930i	−0.492381	−	0.870380i	$-0.663873\pi$
$521$	−32.5299	−	11.6394i	−1.42516	−	0.509930i	−0.932779	+	0.360449i	$0.882623\pi$
$522$	0.360666	−	1.45868i	0.0157859	−	0.0638445i
$523$	9.83966	+	4.36162i	0.430258	+	0.190720i	0.608991	−	0.793177i	$-0.291575\pi$
$523$	9.83966	+	4.36162i	0.430258	+	0.190720i	−0.178732	+	0.983898i	$0.557200\pi$
$524$	15.7049	+	16.2956i	0.686070	+	0.711875i
$525$	10.8534	−	9.36224i	0.473683	−	0.408602i
$526$	−0.366451	−	13.2802i	−0.0159780	−	0.579045i
$527$	1.98337	−	3.71063i	0.0863972	−	0.161638i
$528$	−3.96455	−	1.15013i	−0.172535	−	0.0500528i
$529$	17.3028	−	9.24856i	0.752297	−	0.402111i
$530$	−25.6636	−	7.01806i	−1.11475	−	0.304845i
$531$	−2.21840	+	1.25671i	−0.0962703	+	0.0545365i
$532$	18.4903	+	25.9177i	0.801656	+	1.12367i
$533$	−1.61410	+	7.18793i	−0.0699146	+	0.311344i
$534$	8.39952	+	2.97660i	0.363483	+	0.128810i
$535$	4.76339	+	19.0165i	0.205939	+	0.822156i
$536$	−12.9314	+	37.2082i	−0.558551	+	1.60715i
$537$	23.2652	+	17.2547i	1.00397	+	0.744593i
$538$	21.7517	−	21.8845i	0.937781	−	0.943506i
$539$	2.38792	+	1.35274i	0.102855	+	0.0582665i
$540$	23.1037	−	28.5040i	0.994226	−	1.22662i
$541$	−26.8335	+	0.658725i	−1.15366	+	0.0283208i	−0.596874	−	0.802335i	$-0.703591\pi$
$541$	−26.8335	+	0.658725i	−1.15366	+	0.0283208i	−0.556787	+	0.830656i	$0.687966\pi$
$542$	4.74607	−	10.7955i	0.203861	−	0.463707i
$543$	20.8919	−	13.9595i	0.896557	−	0.599060i
$544$	−12.9041	−	10.7931i	−0.553259	−	0.462752i
$545$	15.3515	+	10.2575i	0.657585	+	0.439384i
$546$	4.43728	−	2.82883i	0.189898	−	0.121063i
$547$	−13.1563	−	5.07496i	−0.562524	−	0.216990i	0.0618899	−	0.998083i	$-0.480287\pi$
$547$	−13.1563	−	5.07496i	−0.562524	−	0.216990i	−0.624414	+	0.781093i	$0.714662\pi$
$548$	10.5328	−	7.13090i	0.449939	−	0.304617i
$549$	15.5839	+	1.92209i	0.665106	+	0.0820330i
$550$	−5.90578	+	3.97217i	−0.251823	+	0.169374i
$551$	−5.10083	+	3.05732i	−0.217303	+	0.130246i
$552$	−6.12754	+	1.92003i	−0.260806	+	0.0817219i
$553$	−14.3388	+	10.6344i	−0.609747	+	0.452219i
$554$	−4.26039	+	29.3360i	−0.181007	+	1.24637i
$555$	18.8563	−	26.7739i	0.800407	−	1.13649i
$556$	14.8226	+	25.7981i	0.628617	+	1.09408i
$557$	22.5768	−	28.9294i	0.956608	−	1.22578i	−0.0175346	−	0.999846i	$-0.505582\pi$
$557$	22.5768	−	28.9294i	0.956608	−	1.22578i	0.974143	−	0.225934i	$-0.0725433\pi$
$558$	0.934477	+	2.80007i	0.0395596	+	0.118536i
$559$	−0.479027	−	4.86365i	−0.0202607	−	0.205710i
$560$	25.5515	+	1.57234i	1.07975	+	0.0664436i
$561$	−3.05428	−	0.300820i	−0.128952	−	0.0127006i
$562$	−30.7765	−	19.3580i	−1.29823	−	0.816569i
$563$	−40.4178	+	13.3522i	−1.70341	+	0.562729i	−0.990376	−	0.138404i	$-0.955803\pi$
$563$	−40.4178	+	13.3522i	−1.70341	+	0.562729i	−0.713031	+	0.701133i	$0.752678\pi$
$564$	0.0378692	+	0.474037i	0.00159458	+	0.0199606i
$565$	−54.7187	−	1.34327i	−2.30203	−	0.0565118i
$566$	3.19549	+	1.49947i	0.134317	+	0.0630276i
$567$	−3.10369	+	3.42439i	−0.130343	+	0.143811i
$568$	−5.39544	+	25.0966i	−0.226388	+	1.05303i
$569$	35.2346	−	12.6071i	1.47711	−	0.528519i	0.529602	−	0.848246i	$-0.322341\pi$
$569$	35.2346	−	12.6071i	1.47711	−	0.528519i	0.947509	+	0.319728i	$0.103591\pi$
$570$	−47.6263	+	4.83716i	−1.99485	+	0.202607i
$571$	−7.18007	+	8.32369i	−0.300476	+	0.348336i	−0.887144	−	0.461492i	$-0.847314\pi$
$571$	−7.18007	+	8.32369i	−0.300476	+	0.348336i	0.586668	+	0.809828i	$0.300439\pi$
$572$	−2.35529	+	1.13156i	−0.0984795	+	0.0473129i
$573$	5.50651	−	1.23653i	0.230038	−	0.0516567i
$574$	10.1047	−	7.93535i	0.421760	−	0.331215i
$575$	−4.23682	+	10.2286i	−0.176688	+	0.426562i
$576$	11.7228	−	1.37112i	0.488448	−	0.0571300i
$577$	8.23046	+	19.8701i	0.342638	+	0.827202i	0.997447	+	0.0714076i	$0.0227491\pi$
$577$	8.23046	+	19.8701i	0.342638	+	0.827202i	−0.654809	+	0.755795i	$0.727251\pi$
$578$	10.0531	+	5.65469i	0.418155	+	0.235204i
$579$	6.13518	+	3.88506i	0.254970	+	0.161458i
$580$	−0.672834	+	4.73422i	−0.0279379	+	0.196578i
$581$	−1.37610	−	18.6553i	−0.0570901	−	0.773951i
$582$	10.9109	+	3.27357i	0.452273	+	0.135694i
$583$	−4.28151	−	2.02500i	−0.177322	−	0.0838670i
$584$	37.9622	−	10.8796i	1.57089	−	0.450202i
$585$	−0.375686	−	7.64727i	−0.0155327	−	0.316176i
$586$	30.0053	+	1.38255i	1.23951	+	0.0571127i
$587$	30.7580	+	32.3061i	1.26952	+	1.33342i	0.917662	+	0.397362i	$0.130074\pi$
$587$	30.7580	+	32.3061i	1.26952	+	1.33342i	0.351856	+	0.936054i	$0.385551\pi$
$588$	8.05416	+	0.943658i	0.332148	+	0.0389158i
$589$	5.25270	−	10.4353i	0.216434	−	0.429980i
$590$	6.61946	−	4.69215i	0.272519	−	0.193173i
$591$	−13.1206	−	15.9875i	−0.539708	−	0.657636i
$592$	31.4151	−	5.84580i	1.29115	−	0.240261i
$593$	10.8862	+	8.93408i	0.447043	+	0.366879i	0.830814	−	0.556549i	$-0.187875\pi$
$593$	10.8862	+	8.93408i	0.447043	+	0.366879i	−0.383772	+	0.923428i	$0.625375\pi$
$594$	4.93279	−	4.28131i	0.202395	−	0.175664i
$595$	18.8896	−	2.32981i	0.774398	−	0.0955129i
$596$	−15.8055	−	18.0991i	−0.647420	−	0.741368i
$597$	2.68554	+	15.4772i	0.109912	+	0.633438i
$598$	−2.07904	+	3.49272i	−0.0850181	+	0.142828i
$599$	−8.19323	−	1.21535i	−0.334766	−	0.0496579i	−0.0227686	−	0.999741i	$-0.507248\pi$
$599$	−8.19323	−	1.21535i	−0.334766	−	0.0496579i	−0.311998	+	0.950083i	$0.600998\pi$
$600$	−11.5236	+	17.5918i	−0.470448	+	0.718183i
$601$	1.13806	−	4.54340i	0.0464226	−	0.185329i	−0.942384	−	0.334534i	$-0.891421\pi$
$601$	1.13806	−	4.54340i	0.0464226	−	0.185329i	0.988806	+	0.149204i	$0.0476712\pi$
$602$	−4.71374	+	7.10129i	−0.192118	+	0.289427i
$603$	−12.6411	−	16.1980i	−0.514784	−	0.659635i
$604$	−12.2804	+	30.1656i	−0.499684	+	1.22742i
$605$	31.2656	−	13.8591i	1.27113	−	0.563452i
$606$	4.74168	+	26.8418i	0.192618	+	1.09037i
$607$	−3.57173	−	17.9563i	−0.144972	−	0.728823i	−0.983059	−	0.183287i	$-0.941326\pi$
$607$	−3.57173	−	17.9563i	−0.144972	−	0.728823i	0.838087	−	0.545536i	$-0.183674\pi$
$608$	−36.5554	−	29.0808i	−1.48252	−	1.17938i
$609$	0.334439	−	1.68134i	0.0135522	−	0.0681314i
$610$	−49.9576	−	1.07428i	−2.02272	−	0.0434965i
$611$	0.218012	+	0.207565i	0.00881983	+	0.00839717i
$612$	8.38144	−	2.59829i	0.338800	−	0.105030i
$613$	−19.0424	+	5.26975i	−0.769116	+	0.212843i	−0.629119	−	0.777309i	$-0.716584\pi$
$613$	−19.0424	+	5.26975i	−0.769116	+	0.212843i	−0.139997	+	0.990152i	$0.544709\pi$
$614$	5.88189	−	2.45736i	0.237374	−	0.0991708i
$615$	2.83464	+	19.1096i	0.114304	+	0.770574i
$616$	4.43050	+	1.06689i	0.178510	+	0.0429864i
$617$	7.90370	+	4.73729i	0.318191	+	0.190716i	0.664277	−	0.747486i	$-0.268740\pi$
$617$	7.90370	+	4.73729i	0.318191	+	0.190716i	−0.346086	+	0.938203i	$0.612490\pi$
$618$	−17.5230	+	0.914311i	−0.704879	+	0.0367790i
$619$	22.8036	−	14.4402i	0.916552	−	0.580400i	0.00882509	−	0.999961i	$-0.497191\pi$
$619$	22.8036	−	14.4402i	0.916552	−	0.580400i	0.907727	+	0.419561i	$0.137816\pi$
$620$	−3.85899	−	8.56466i	−0.154981	−	0.343965i
$621$	2.70987	−	9.79221i	0.108743	−	0.392948i
$622$	−12.4155	+	16.0091i	−0.497814	+	0.641908i
$623$	−9.41415	−	2.85575i	−0.377170	−	0.114413i
$624$	−5.11499	+	5.78346i	−0.204763	+	0.231524i
$625$	−5.47146	−	18.0370i	−0.218859	−	0.721480i
$626$	31.7107	−	14.1720i	1.26741	−	0.566427i
$627$	−8.49872	−	0.626903i	−0.339406	−	0.0250361i
$628$	−2.80598	+	4.03614i	−0.111971	+	0.161060i
$629$	22.1653	−	8.55009i	0.883787	−	0.340914i
$630$	−7.92176	+	10.7495i	−0.315610	+	0.428269i
$631$	3.32555	+	7.03128i	0.132388	+	0.279911i	0.959284	−	0.282445i	$-0.0911453\pi$
$631$	3.32555	+	7.03128i	0.132388	+	0.279911i	−0.826896	+	0.562355i	$0.809895\pi$
$632$	15.9252	−	20.7949i	0.633469	−	0.827175i
$633$	−10.6789	−	11.7823i	−0.424448	−	0.468306i
$634$	5.76550	−	1.76812i	0.228977	−	0.0702212i
$635$	2.36922	−	1.19256i	0.0940196	−	0.0473255i
$636$	−13.9816	−	0.601596i	−0.554406	−	0.0238548i
$637$	4.19676	−	2.95569i	0.166282	−	0.117109i
$638$	−0.264554	+	0.809076i	−0.0104738	+	0.0320316i
$639$	−9.46795	−	9.46795i	−0.374546	−	0.374546i
$640$	−36.6739	+	8.11060i	−1.44966	+	0.320600i
$641$	−1.82469	+	1.82469i	−0.0720710	+	0.0720710i	−0.742223	−	0.670152i	$-0.766229\pi$
$641$	−1.82469	+	1.82469i	−0.0720710	+	0.0720710i	0.670152	+	0.742223i	$0.266229\pi$
$642$	4.66422	+	9.19642i	0.184082	+	0.362954i
$643$	−25.0756	−	35.6046i	−0.988886	−	1.40411i	−0.913446	−	0.406960i	$-0.866589\pi$
$643$	−25.0756	−	35.6046i	−0.988886	−	1.40411i	−0.0754398	−	0.997150i	$-0.524036\pi$
$644$	6.65983	−	2.42875i	0.262434	−	0.0957060i
$645$	−5.76218	−	11.4475i	−0.226886	−	0.450744i
$646$	−30.6778	−	16.2778i	−1.20700	−	0.640442i
$647$	−32.9614	+	29.8744i	−1.29584	+	1.17449i	−0.322135	+	0.946694i	$0.604400\pi$
$647$	−32.9614	+	29.8744i	−1.29584	+	1.17449i	−0.973710	+	0.227791i	$0.926850\pi$
$648$	2.99332	−	6.08439i	0.117589	−	0.239017i
$649$	1.30570	−	0.617549i	0.0512531	−	0.0242409i
$650$	1.99333	+	13.1619i	0.0781849	+	0.516251i
$651$	1.21203	+	3.14206i	0.0475031	+	0.123147i
$652$	2.87776	+	4.48387i	0.112702	+	0.175602i
$653$	−2.42901	+	32.9292i	−0.0950543	+	1.28862i	0.713691	+	0.700461i	$0.247022\pi$
$653$	−2.42901	+	32.9292i	−0.0950543	+	1.28862i	−0.808745	+	0.588159i	$0.799853\pi$
$654$	9.07132	+	3.46752i	0.354717	+	0.135591i
$655$	35.9494	−	10.9051i	1.40466	−	0.426098i
$656$	−11.0443	+	15.2766i	−0.431206	+	0.596452i
$657$	−5.97945	+	19.7116i	−0.233281	+	0.769023i
$658$	−0.0658490	−	0.520838i	−0.00256706	−	0.0203044i
$659$	−29.8863	−	8.27066i	−1.16421	−	0.322179i	−0.369533	−	0.929217i	$-0.620482\pi$
$659$	−29.8863	−	8.27066i	−1.16421	−	0.322179i	−0.794673	+	0.607038i	$0.792357\pi$
$660$	−4.69460	+	4.99137i	−0.182737	+	0.194289i
$661$	1.23084	+	1.94371i	0.0478741	+	0.0756015i	0.867945	−	0.496661i	$-0.165441\pi$
$661$	1.23084	+	1.94371i	0.0478741	+	0.0756015i	−0.820070	+	0.572263i	$0.806066\pi$
$662$	−29.8059	−	26.8498i	−1.15844	−	1.04355i
$663$	−2.95107	+	4.92356i	−0.114610	+	0.191215i
$664$	9.48160	+	25.7556i	0.367957	+	0.999510i
$665$	52.2760	−	7.75441i	2.02718	−	0.300703i
$666$	−6.33157	+	15.4183i	−0.245343	+	0.597447i
$667$	0.353162	+	1.27617i	0.0136745	+	0.0494133i
$668$	8.06895	+	0.745166i	0.312197	+	0.0288313i
$669$	20.8267	−	21.8750i	0.805207	−	0.845736i
$670$	45.2309	+	47.2189i	1.74742	+	1.82423i
$671$	−8.72433	−	1.73538i	−0.336799	−	0.0669935i
$672$	13.2880	−	2.17820i	0.512596	−	0.0840260i
$673$	−15.0359	+	2.99082i	−0.579590	+	0.115288i	−0.476175	−	0.879351i	$-0.657977\pi$
$673$	−15.0359	+	2.99082i	−0.579590	+	0.115288i	−0.103415	+	0.994638i	$0.532977\pi$
$674$	−24.4638	−	17.1182i	−0.942309	−	0.659368i
$675$	−13.4845	−	30.4206i	−0.519020	−	1.17089i
$676$	−0.128495	−	21.1123i	−0.00494210	−	0.812013i
$677$	−17.2439	+	13.4573i	−0.662738	+	0.517206i	−0.889611	−	0.456719i	$-0.849025\pi$
$677$	−17.2439	+	13.4573i	−0.662738	+	0.517206i	0.226873	+	0.973924i	$0.427150\pi$
$678$	−28.2200	+	5.70263i	−1.08378	+	0.219008i
$679$	−12.1988	−	3.05564i	−0.468147	−	0.117265i
$680$	−25.7006	+	10.9215i	−0.985571	+	0.418819i
$681$	−3.61893	+	24.3968i	−0.138678	+	0.934888i
$682$	−0.411259	−	1.62089i	−0.0157479	−	0.0620672i
$683$	13.8233	−	2.39857i	0.528934	−	0.0917788i	0.0997790	−	0.995010i	$-0.468186\pi$
$683$	13.8233	−	2.39857i	0.528934	−	0.0917788i	0.429155	+	0.903231i	$0.358811\pi$
$684$	23.0886	−	7.78362i	0.882815	−	0.297614i
$685$	−2.58456	−	20.9551i	−0.0987509	−	0.800651i
$686$	−27.9664	−	1.97738i	−1.06776	−	0.0754967i
$687$	−2.25717	+	2.75037i	−0.0861166	+	0.104933i
$688$	3.77792	−	11.9212i	0.144032	−	0.454491i
$689$	−6.84768	+	5.61975i	−0.260876	+	0.214095i
$690$	−1.79031	+	10.5076i	−0.0681560	+	0.400016i
$691$	14.9675	+	7.53399i	0.569389	+	0.286606i	0.710857	−	0.703336i	$-0.248307\pi$
$691$	14.9675	+	7.53399i	0.569389	+	0.286606i	−0.141468	+	0.989943i	$0.545182\pi$
$692$	−11.9474	−	42.1720i	−0.454170	−	1.60314i
$693$	−1.72157	+	1.63907i	−0.0653971	+	0.0622632i
$694$	5.47145	+	6.00002i	0.207693	+	0.227758i
$695$	49.3289	−	2.42337i	1.87115	−	0.0919238i
$696$	0.207921	+	2.50658i	0.00788121	+	0.0950119i
$697$	−5.99218	+	12.6694i	−0.226970	+	0.479888i
$698$	28.3378	−	15.2579i	1.07260	−	0.577521i
$699$	−11.2349	+	0.828733i	−0.424941	+	0.0313456i
$700$	11.8142	−	19.9856i	0.446534	−	0.755386i
$701$	15.9339	−	25.1624i	0.601815	−	0.950370i	−0.397645	−	0.917539i	$-0.630173\pi$
$701$	15.9339	−	25.1624i	0.601815	−	0.950370i	0.999461	−	0.0328313i	$-0.0104524\pi$
$702$	−3.29410	−	11.7640i	−0.124328	−	0.444002i
$703$	60.9449	−	25.2442i	2.29858	−	0.952104i
$704$	−6.68013	+	0.286099i	−0.251767	+	0.0107827i
$705$	0.729290	+	0.302082i	0.0274667	+	0.0113771i
$706$	−2.26575	+	18.8420i	−0.0852726	+	0.709128i
$707$	−6.59299	−	29.3599i	−0.247955	−	1.10419i
$708$	2.84678	−	3.17962i	0.106989	−	0.119497i
$709$	−23.5917	−	20.3503i	−0.886005	−	0.764273i	0.0867202	−	0.996233i	$-0.472361\pi$
$709$	−23.5917	−	20.3503i	−0.886005	−	0.764273i	−0.972725	+	0.231959i	$0.925486\pi$
$710$	33.0205	+	26.9315i	1.23924	+	1.01072i
$711$	4.60264	+	12.8635i	0.172613	+	0.482420i
$712$	14.4323	+	0.222483i	0.540872	+	0.00833791i
$713$	−1.92742	−	1.74691i	−0.0721823	−	0.0654222i
$714$	9.41559	−	3.40131i	0.352370	−	0.127291i
$715$	−0.106446	+	4.33612i	−0.00398085	+	0.162162i
$716$	44.6369	+	14.4453i	1.66816	+	0.539847i
$717$	7.22997	+	21.8854i	0.270008	+	0.817326i
$718$	−10.8348	−	47.5719i	−0.404351	−	1.77537i
$719$	2.38357	−	24.2008i	0.0888923	−	0.902539i	−0.842542	−	0.538630i	$-0.818942\pi$
$719$	2.38357	−	24.2008i	0.0888923	−	0.902539i	0.931435	−	0.363909i	$-0.118558\pi$
$720$	6.82794	−	18.3634i	0.254462	−	0.684363i
$721$	19.2777	−	1.89869i	0.717940	−	0.0707110i
$722$	−62.2288	−	31.0863i	−2.31591	−	1.15691i
$723$	11.4158	+	8.90898i	0.424558	+	0.331328i
$724$	24.8430	−	32.2360i	0.923284	−	1.19804i
$725$	3.54553	+	2.49704i	0.131678	+	0.0927378i
$726$	14.4160	−	10.7598i	0.535029	−	0.399334i
$727$	−10.9126	−	14.7139i	−0.404726	−	0.545710i	0.553079	−	0.833129i	$-0.313453\pi$
$727$	−10.9126	−	14.7139i	−0.404726	−	0.545710i	−0.957805	+	0.287419i	$0.907203\pi$
$728$	5.34688	−	6.63785i	0.198169	−	0.246015i
$729$	12.3421	+	20.5916i	0.457116	+	0.762652i
$730$	12.5928	−	64.3307i	0.466080	−	2.38099i
$731$	1.13811	−	9.22755i	0.0420945	−	0.341293i
$732$	−25.7467	+	5.28444i	−0.951627	+	0.195319i
$733$	18.5601	−	48.1152i	0.685532	−	1.77717i	0.0583570	−	0.998296i	$-0.481414\pi$
$733$	18.5601	−	48.1152i	0.685532	−	1.77717i	0.627175	−	0.778879i	$-0.284211\pi$
$734$	0.714011	+	0.158056i	0.0263546	+	0.00583394i
$735$	7.47845	−	11.1923i	0.275847	−	0.412834i
$736$	−8.41143	+	6.11755i	−0.310049	+	0.225496i
$737$	6.46676	+	9.67819i	0.238206	+	0.356501i
$738$	−3.56665	−	9.16306i	−0.131290	−	0.337297i
$739$	0.766354	+	31.2178i	0.0281908	+	1.14836i	0.832455	+	0.554093i	$0.186935\pi$
$739$	0.766354	+	31.2178i	0.0281908	+	1.14836i	−0.804264	+	0.594272i	$0.797440\pi$
$740$	15.0882	−	50.8511i	0.554652	−	1.86932i
$741$	−7.85623	+	13.8682i	−0.288606	+	0.509460i
$742$	15.4493	−	0.0470136i	0.567162	−	0.00172592i
$743$	4.79547	−	6.46594i	0.175929	−	0.237212i	−0.706438	−	0.707775i	$-0.749699\pi$
$743$	4.79547	−	6.46594i	0.175929	−	0.237212i	0.882367	+	0.470563i	$0.155949\pi$
$744$	−2.97954	−	3.94172i	−0.109235	−	0.144510i
$745$	−38.6912	+	9.69165i	−1.41754	+	0.355075i
$746$	21.9662	−	10.4711i	0.804239	−	0.383376i
$747$	−13.9679	−	3.13660i	−0.511060	−	0.114762i
$748$	−4.84353	+	1.11866i	−0.177097	+	0.0409022i
$749$	−5.61095	−	9.90471i	−0.205020	−	0.361910i
$750$	2.93474	+	5.14398i	0.107162	+	0.187832i
$751$	4.44890	+	8.32331i	0.162343	+	0.303722i	0.949919	−	0.312495i	$-0.101165\pi$
$751$	4.44890	+	8.32331i	0.162343	+	0.303722i	−0.787577	+	0.616216i	$0.788665\pi$
$752$	0.303405	+	0.707985i	0.0110640	+	0.0258176i
$753$	8.87348	+	4.74297i	0.323367	+	0.172843i
$754$	1.15641	+	1.09431i	0.0421141	+	0.0398523i
$755$	35.3127	+	40.9372i	1.28516	+	1.48986i
$756$	−8.51529	+	19.5302i	−0.309698	+	0.710306i
$757$	−2.62947	+	5.93200i	−0.0955698	+	0.215602i	−0.955617	−	0.294613i	$-0.904809\pi$
$757$	−2.62947	+	5.93200i	−0.0955698	+	0.215602i	0.860047	+	0.510215i	$0.170434\pi$
$758$	41.7310	−	25.1855i	1.51574	−	0.914779i
$759$	−0.639234	+	1.78654i	−0.0232027	+	0.0648473i
$760$	−70.5968	+	32.0677i	−2.56081	+	1.16322i
$761$	16.5711	+	0.814087i	0.600702	+	0.0295106i	0.347148	−	0.937810i	$-0.387150\pi$
$761$	16.5711	+	0.814087i	0.600702	+	0.0295106i	0.253555	+	0.967321i	$0.418400\pi$
$762$	1.07578	−	0.888361i	0.0389713	−	0.0321819i
$763$	−10.1799	−	3.36300i	−0.368539	−	0.121749i
$764$	7.81190	−	4.74713i	0.282625	−	0.171745i
$765$	2.49021	−	14.3514i	0.0900336	−	0.518876i
$766$	−0.0490458	−	0.0420476i	−0.00177210	−	0.00151924i
$767$		−	2.70150i		−	0.0975454i
$768$	−17.8612	+	8.44338i	−0.644512	+	0.304674i
$769$		−	5.33297i		−	0.192312i	−0.995366	−	0.0961560i	$-0.969345\pi$
$769$		−	5.33297i		−	0.192312i	0.995366	−	0.0961560i	$-0.0306548\pi$
$770$	4.92352	−	5.74298i	0.177432	−	0.206962i
$771$	−3.43583	+	19.8012i	−0.123738	+	0.713122i
$772$	11.4269	+	2.78849i	0.411263	+	0.100360i
$773$	27.3839	+	9.04643i	0.984932	+	0.325377i	0.760661	−	0.649149i	$-0.224875\pi$
$773$	27.3839	+	9.04643i	0.984932	+	0.325377i	0.224271	+	0.974527i	$0.428000\pi$
$774$	4.15346	+	5.02971i	0.149293	+	0.180789i
$775$	−8.50902	−	0.418021i	−0.305653	−	0.0150158i
$776$	18.4406	−	0.621183i	0.661978	−	0.0222992i
$777$	−6.40621	+	17.9042i	−0.229822	+	0.642308i
$778$	−14.3115	−	23.7133i	−0.513091	−	0.850163i
$779$	−15.7701	+	35.5768i	−0.565022	+	1.27467i
$780$	4.68515	+	11.9291i	0.167755	+	0.427129i
$781$	4.95452	+	5.74367i	0.177287	+	0.205525i
$782$	−5.31494	+	5.61658i	−0.190062	+	0.200849i
$783$	−3.50979	−	1.87602i	−0.125430	−	0.0670436i
$784$	12.8503	−	2.71909i	0.458938	−	0.0971103i
$785$	3.84647	+	7.19623i	0.137286	+	0.256845i
$786$	17.1632	−	9.79195i	0.612191	−	0.349267i
$787$	26.6273	+	47.0038i	0.949162	+	1.67551i	0.709574	+	0.704631i	$0.248888\pi$
$787$	26.6273	+	47.0038i	0.949162	+	1.67551i	0.239589	+	0.970874i	$0.422987\pi$
$788$	−28.4106	−	17.7495i	−1.01209	−	0.632300i
$789$	−11.3177	−	2.54149i	−0.402923	−	0.0904793i
$790$	−18.7086	−	39.2465i	−0.665621	−	1.39633i
$791$	30.8309	−	7.72274i	1.09622	−	0.274589i
$792$	1.76561	−	3.00767i	0.0627381	−	0.106873i
$793$	−9.91083	+	13.3632i	−0.351944	+	0.474541i
$794$	0.0759054	+	24.9436i	0.00269378	+	0.885214i
$795$	−11.4500	+	20.2121i	−0.406091	+	0.716851i
$796$	12.1303	+	22.3657i	0.429946	+	0.792730i
$797$	0.535220	+	21.8024i	0.0189584	+	0.772282i	0.931593	+	0.363504i	$0.118420\pi$
$797$	0.535220	+	21.8024i	0.0189584	+	0.772282i	−0.912634	+	0.408777i	$0.865955\pi$
$798$	25.9045	−	10.0831i	0.917010	−	0.356939i
$799$	0.318155	+	0.476153i	0.0112555	+	0.0168451i
$800$	−8.58452	+	32.9636i	−0.303509	+	1.16544i
$801$	−4.18283	+	6.26005i	−0.147793	+	0.221188i
$802$	−4.08517	+	18.4546i	−0.144252	+	0.651655i
$803$	4.19967	−	10.8872i	0.148203	−	0.384203i
$804$	28.7127	+	18.9334i	1.01262	+	0.667731i
$805$	1.44042	−	11.6786i	0.0507680	−	0.411616i
$806$	−3.06946	−	0.600849i	−0.108117	−	0.0211640i
$807$	−13.8502	−	23.1076i	−0.487550	−	0.813427i
$808$	21.1666	+	38.7449i	0.744638	+	1.36304i
$809$	1.53781	+	2.07349i	0.0540664	+	0.0729001i	0.829413	−	0.558636i	$-0.188675\pi$
$809$	1.53781	+	2.07349i	0.0540664	+	0.0729001i	−0.775347	+	0.631536i	$0.782425\pi$
$810$	−6.73253	−	9.02027i	−0.236557	−	0.316940i
$811$	−32.9330	−	23.1941i	−1.15644	−	0.814454i	−0.171129	−	0.985249i	$-0.554741\pi$
$811$	−32.9330	−	23.1941i	−1.15644	−	0.814454i	−0.985307	+	0.170795i	$0.945366\pi$
$812$	−0.356660	−	2.75367i	−0.0125163	−	0.0966349i
$813$	−8.11715	−	6.33468i	−0.284681	−	0.222167i
$814$	4.21969	−	8.44698i	0.147900	−	0.296067i
$815$	8.80140	−	0.866862i	0.308300	−	0.0303649i
$816$	−11.9051	+	8.60319i	−0.416762	+	0.301172i
$817$	2.53043	−	25.6919i	0.0885285	−	0.898845i
$818$	−21.7897	+	4.96274i	−0.761859	+	0.173518i
$819$	1.39461	+	4.22154i	0.0487316	+	0.147513i
$820$	14.2387	+	27.8638i	0.497236	+	0.973046i
$821$	0.760904	−	30.9958i	0.0265557	−	1.08176i	−0.827464	−	0.561519i	$-0.810217\pi$
$821$	0.760904	−	30.9958i	0.0265557	−	1.08176i	0.854019	−	0.520241i	$-0.174158\pi$
$822$	−3.77322	−	10.4451i	−0.131606	−	0.364316i
$823$	24.0308	+	21.7803i	0.837662	+	0.759212i	0.972808	−	0.231613i	$-0.0744004\pi$
$823$	24.0308	+	21.7803i	0.837662	+	0.759212i	−0.135146	+	0.990826i	$0.543150\pi$
$824$	−26.4223	+	10.4703i	−0.920463	+	0.364750i
$825$	2.09352	+	5.85100i	0.0728870	+	0.203706i
$826$	−2.97783	+	3.65110i	−0.103612	+	0.127038i
$827$	−6.04130	−	5.21126i	−0.210076	−	0.181213i	0.541820	−	0.840495i	$-0.317736\pi$
$827$	−6.04130	−	5.21126i	−0.210076	−	0.181213i	−0.751896	+	0.659282i	$0.770861\pi$
$828$	−0.299173	−	5.41690i	−0.0103970	−	0.188250i
$829$	−4.07055	−	18.1270i	−0.141376	−	0.629576i	−0.994216	−	0.107403i	$-0.965747\pi$
$829$	−4.07055	−	18.1270i	−0.141376	−	0.629576i	0.852840	−	0.522173i	$-0.174878\pi$
$830$	45.2318	+	5.43912i	1.57002	+	0.188795i
$831$	23.9123	+	9.90479i	0.829508	+	0.343593i
$832$	−4.85824	+	11.5234i	−0.168429	+	0.399504i
$833$	9.02200	−	3.73704i	0.312594	−	0.129481i
$834$	25.0158	−	7.00482i	0.866225	−	0.242557i
$835$	7.19622	−	11.3641i	0.249036	−	0.393270i
$836$	−13.3687	+	3.43529i	−0.462367	+	0.118812i
$837$	7.79702	−	0.575143i	0.269504	−	0.0198798i
$838$	−3.16766	−	5.88314i	−0.109425	−	0.203230i
$839$	3.46002	−	7.31560i	0.119453	−	0.252563i	−0.835399	−	0.549644i	$-0.814763\pi$
$839$	3.46002	−	7.31560i	0.119453	−	0.252563i	0.954852	+	0.297082i	$0.0960133\pi$
$840$	6.81726	−	21.2866i	0.235218	−	0.734459i
$841$	−28.4470	+	1.39751i	−0.980932	+	0.0481901i
$842$	37.3772	−	34.0845i	1.28810	−	1.17463i
$843$	−22.9912	+	21.8895i	−0.791860	+	0.753914i
$844$	−22.4871	−	12.5586i	−0.774039	−	0.432286i
$845$	−31.3038	−	15.7570i	−1.07688	−	0.542057i
$846$	−0.396066	−	0.0674830i	−0.0136170	−	0.00232011i
$847$	−15.3511	+	12.5983i	−0.527471	+	0.432884i
$848$	−21.7710	+	6.31113i	−0.747620	+	0.216725i
$849$	1.95516	−	2.38237i	0.0671010	−	0.0817628i
$850$	−1.78615	+	25.2619i	−0.0612645	+	0.866475i
$851$	−1.79797	−	14.5775i	−0.0616335	−	0.499711i
$852$	20.0807	+	9.95507i	0.687954	+	0.341055i
$853$	32.0590	−	5.56276i	1.09768	−	0.190465i	0.406858	−	0.913492i	$-0.366625\pi$
$853$	32.0590	−	5.56276i	1.09768	−	0.190465i	0.690820	+	0.723026i	$0.257250\pi$
$854$	28.1247	−	7.13590i	0.962408	−	0.244185i
$855$	5.93450	−	40.0071i	0.202956	−	1.36821i
$856$	11.9174	+	11.7018i	0.407329	+	0.399959i
$857$	−5.00002	−	1.25244i	−0.170797	−	0.0427825i	0.156638	−	0.987656i	$-0.449934\pi$
$857$	−5.00002	−	1.25244i	−0.170797	−	0.0427825i	−0.327435	+	0.944874i	$0.606184\pi$
$858$	0.451898	+	2.23626i	0.0154275	+	0.0763446i
$859$	−37.2107	+	29.0395i	−1.26961	+	0.990815i	−0.270002	+	0.962860i	$0.587025\pi$
$859$	−37.2107	+	29.0395i	−1.26961	+	0.990815i	−0.999609	+	0.0279550i	$0.991100\pi$
$860$	−14.7674	−	14.5887i	−0.503564	−	0.497472i
$861$	−4.54596	−	10.2555i	−0.154926	−	0.349507i
$862$	−27.6360	+	39.4949i	−0.941286	+	1.34520i
$863$	−28.0598	+	5.58144i	−0.955166	+	0.189994i	−0.647982	−	0.761656i	$-0.724387\pi$
$863$	−28.0598	+	5.58144i	−0.955166	+	0.189994i	−0.307184	+	0.951650i	$0.599387\pi$
$864$	4.11579	−	30.9878i	0.140022	−	1.05423i
$865$	−71.3598	−	14.1944i	−2.42631	−	0.482622i
$866$	31.2852	−	29.9680i	1.06311	−	1.01835i
$867$	6.94424	−	7.29376i	0.235839	−	0.247709i
$868$	3.48609	+	4.19548i	0.118326	+	0.142404i
$869$	−2.06427	−	7.45930i	−0.0700254	−	0.253039i
$870$	3.86210	+	1.58598i	0.130937	+	0.0537698i
$871$	21.5351	−	3.19443i	0.729689	−	0.108239i
$872$	15.7174	+	0.628372i	0.532258	+	0.0212794i
$873$	−4.94785	+	8.25498i	−0.167459	+	0.279389i
$874$	−14.3708	+	15.9530i	−0.486098	+	0.539618i
$875$	−3.49778	−	5.52360i	−0.118247	−	0.186732i
$876$	−1.05594	−	34.4636i	−0.0356771	−	1.16442i
$877$	−4.20244	−	1.16297i	−0.141906	−	0.0392708i	0.195036	−	0.980796i	$-0.437518\pi$
$877$	−4.20244	−	1.16297i	−0.141906	−	0.0392708i	−0.336942	+	0.941525i	$0.609393\pi$
$878$	−3.71514	+	0.469701i	−0.125380	+	0.0158516i
$879$	7.61299	−	25.0967i	0.256780	−	0.846489i
$880$	−4.62286	+	10.0902i	−0.155836	+	0.340140i
$881$	−24.0337	+	7.29055i	−0.809716	+	0.245625i	−0.667883	−	0.744266i	$-0.732800\pi$
$881$	−24.0337	+	7.29055i	−0.809716	+	0.245625i	−0.141833	+	0.989891i	$0.545300\pi$
$882$	−2.44626	+	6.39963i	−0.0823699	+	0.215487i
$883$	−4.14772	+	56.2293i	−0.139582	+	1.89227i	0.245518	+	0.969392i	$0.421042\pi$
$883$	−4.14772	+	56.2293i	−0.139582	+	1.89227i	−0.385100	+	0.922875i	$0.625833\pi$
$884$	−1.98187	+	9.08394i	−0.0666576	+	0.305526i
$885$	−2.54960	−	6.60958i	−0.0857038	−	0.222179i
$886$	52.3455	−	7.92760i	1.75858	−	0.266333i
$887$	−6.09929	+	2.88475i	−0.204794	+	0.0968604i	−0.527200	−	0.849741i	$-0.676758\pi$
$887$	−6.09929	+	2.88475i	−0.204794	+	0.0968604i	0.322406	+	0.946601i	$0.395508\pi$
$888$	1.79835	−	27.8419i	0.0603486	−	0.934313i
$889$	−1.14122	+	1.03434i	−0.0382752	+	0.0346906i
$890$	11.2301	−	21.1647i	0.376433	−	0.709441i
$891$	−0.900883	−	1.78975i	−0.0301807	−	0.0599588i
$892$	20.6473	−	44.3514i	0.691322	−	1.48499i
$893$	0.915600	+	1.30005i	0.0306394	+	0.0435046i
$894$	−18.7112	+	9.48988i	−0.625795	+	0.317389i
$895$	55.0679	−	55.0679i	1.84072	−	1.84072i
$896$	19.2681	−	10.2189i	0.643703	−	0.341388i
$897$	2.50947	+	2.50947i	0.0837887	+	0.0837887i
$898$	40.9426	+	13.3876i	1.36627	+	0.446748i
$899$	−0.833040	+	0.586693i	−0.0277834	+	0.0195673i
$900$	−12.0119	−	13.0921i	−0.400397	−	0.436403i
$901$	−15.0531	+	7.57708i	−0.501491	+	0.252429i
$902$	1.63318	+	5.32548i	0.0543789	+	0.177319i
$903$	4.99767	+	5.51408i	0.166312	+	0.183497i
$904$	−40.3629	+	23.3546i	−1.34245	+	0.776763i
$905$	−28.8840	−	61.0701i	−0.960137	−	2.03004i
$906$	22.8922	+	16.8703i	0.760543	+	0.560478i
$907$	28.2240	−	10.8872i	0.937162	−	0.361503i	0.157369	−	0.987540i	$-0.449699\pi$
$907$	28.2240	−	10.8872i	0.937162	−	0.361503i	0.779794	+	0.626037i	$0.215324\pi$
$908$	7.06912	+	39.3182i	0.234597	+	1.30482i
$909$	−22.9665	−	1.69411i	−0.761750	−	0.0561900i
$910$	−5.77288	−	12.9172i	−0.191369	−	0.428200i
$911$	12.8031	+	42.2062i	0.424186	+	1.39835i	0.865459	+	0.500980i	$0.167027\pi$
$911$	12.8031	+	42.2062i	0.424186	+	1.39835i	−0.441273	+	0.897373i	$0.645473\pi$
$912$	−32.4606	+	24.6925i	−1.07488	+	0.817649i
$913$	7.76073	+	2.35419i	0.256843	+	0.0779123i
$914$	0.0396954	+	0.0307847i	0.00131301	+	0.00101827i
$915$	−11.6364	+	42.0485i	−0.384687	+	1.39008i
$916$	−2.04132	+	5.38937i	−0.0674469	+	0.178070i
$917$	−18.4298	+	11.6706i	−0.608607	+	0.385396i
$918$	−1.21101	−	23.2093i	−0.0399692	−	0.766020i
$919$	−20.2564	−	12.1412i	−0.668196	−	0.400501i	0.139401	−	0.990236i	$-0.455482\pi$
$919$	−20.2564	−	12.1412i	−0.668196	−	0.400501i	−0.807597	+	0.589735i	$0.799232\pi$
$920$	2.68905	+	17.0540i	0.0886554	+	0.562253i
$921$	−0.816665	−	5.50551i	−0.0269100	−	0.181413i
$922$	17.1423	+	41.0316i	0.564553	+	1.35131i
$923$	13.6733	−	3.78392i	0.450064	−	0.124549i
$924$	1.85426	−	3.52045i	0.0610007	−	0.115814i
$925$	−34.8391	−	33.1695i	−1.14550	−	1.09061i
$926$	0.000507022	−	0.0235781i	1.66618e−5	−	0.000774824i
$927$	2.89216	−	14.5399i	0.0949911	−	0.477553i
$928$	1.61611	+	3.73967i	0.0530515	+	0.122761i
$929$	4.70561	+	23.6567i	0.154386	+	0.776151i	0.977936	+	0.208907i	$0.0669905\pi$
$929$	4.70561	+	23.6567i	0.154386	+	0.776151i	−0.823549	+	0.567244i	$0.808009\pi$
$930$	−8.07691	+	1.42681i	−0.264852	+	0.0467869i
$931$	24.7891	−	10.9883i	0.812430	−	0.360126i
$932$	−16.8151	+	7.08525i	−0.550797	+	0.232085i
$933$	10.8826	+	13.9448i	0.356281	+	0.456532i
$934$	−27.7903	−	18.4468i	−0.909328	−	0.603599i
$935$	−2.00498	+	8.00432i	−0.0655698	+	0.261769i
$936$	−3.67340	−	5.39044i	−0.120069	−	0.176192i
$937$	−29.0398	−	4.30764i	−0.948688	−	0.140725i	−0.345585	−	0.938388i	$-0.612319\pi$
$937$	−29.0398	−	4.30764i	−0.948688	−	0.140725i	−0.603103	+	0.797663i	$0.706069\pi$
$938$	−32.6261	−	19.4206i	−1.06528	−	0.634105i
$939$	−5.18465	−	29.8799i	−0.169195	−	0.975093i
$940$	1.27566	+	0.0862959i	0.0416076	+	0.00281466i
$941$	−56.0257	+	6.91011i	−1.82639	+	0.225263i	−0.961136	−	0.276077i	$-0.910966\pi$
$941$	−56.0257	+	6.91011i	−1.82639	+	0.225263i	−0.865250	+	0.501340i	$0.832841\pi$
$942$	2.81327	+	3.24137i	0.0916614	+	0.105609i
$943$	6.69801	+	5.49692i	0.218117	+	0.179004i
$944$	2.72417	−	6.35327i	0.0886643	−	0.206781i
$945$	22.4361	+	27.3385i	0.729848	+	0.889322i
$946$	−2.13696	−	3.01472i	−0.0694786	−	0.0980171i
$947$	5.44696	−	10.8213i	0.177002	−	0.351643i	−0.787248	−	0.616637i	$-0.788495\pi$
$947$	5.44696	−	10.8213i	0.177002	−	0.351643i	0.964250	+	0.264993i	$0.0853698\pi$
$948$	−14.1792	−	17.9427i	−0.460518	−	0.582751i
$949$	−15.0496	−	15.8071i	−0.488530	−	0.513119i
$950$	−3.23667	+	70.2450i	−0.105011	+	2.27905i
$951$	−0.258359	−	5.25902i	−0.00837786	−	0.170535i
$952$	12.6917	−	10.0924i	0.411339	−	0.327098i
$953$	3.93256	+	1.85996i	0.127388	+	0.0602500i	0.490186	−	0.871618i	$-0.336929\pi$
$953$	3.93256	+	1.85996i	0.127388	+	0.0602500i	−0.362799	+	0.931868i	$0.618179\pi$
$954$	3.39773	−	11.3248i	0.110006	−	0.366653i
$955$	−1.11625	−	15.1327i	−0.0361211	−	0.489681i
$956$	22.4212	+	29.8500i	0.725153	+	0.965419i
$957$	0.627915	+	0.397623i	0.0202976	+	0.0128533i
$958$	0.504955	−	0.897730i	0.0163144	−	0.0290043i
$959$	4.69181	+	11.3270i	0.151507	+	0.365769i
$960$	−1.01085	+	32.7788i	−0.0326252	+	1.05793i
$961$	−11.0972	+	26.7910i	−0.357974	+	0.864225i
$962$	−10.9076	−	13.8895i	−0.351676	−	0.447815i
$963$	−8.50024	+	1.90879i	−0.273916	+	0.0615100i
$964$	22.1314	+	7.76714i	0.712805	+	0.250163i
$965$	12.7529	−	14.7841i	0.410530	−	0.475918i
$966$	−0.625410	−	6.15774i	−0.0201222	−	0.198122i
$967$	−1.50606	+	0.538877i	−0.0484316	+	0.0173291i	−0.360994	−	0.932568i	$-0.617563\pi$
$967$	−1.50606	+	0.538877i	−0.0484316	+	0.0173291i	0.312563	+	0.949897i	$0.398813\pi$
$968$	16.5591	−	23.9741i	0.532230	−	0.770557i
$969$	−20.3633	+	22.4674i	−0.654162	+	0.721757i
$970$	13.0107	−	27.7267i	0.417747	−	0.890251i
$971$	−29.4739	−	0.723544i	−0.945863	−	0.0232196i	−0.451310	−	0.892367i	$-0.649043\pi$
$971$	−29.4739	−	0.723544i	−0.945863	−	0.0232196i	−0.494553	+	0.869148i	$0.664668\pi$
$972$	20.7310	+	17.6638i	0.664947	+	0.566566i
$973$	−27.2312	+	8.99597i	−0.872992	+	0.288397i
$974$	10.2900	−	16.3596i	0.329712	−	0.524195i
$975$	11.5669	+	1.13924i	0.370438	+	0.0364850i
$976$	−36.7833	+	21.4330i	−1.17740	+	0.686054i
$977$	−3.04954	−	30.9625i	−0.0975636	−	0.990579i	−0.911962	−	0.410274i	$-0.865433\pi$
$977$	−3.04954	−	30.9625i	−0.0975636	−	0.990579i	0.814399	−	0.580306i	$-0.197067\pi$
$978$	4.41263	−	1.47265i	0.141100	−	0.0470900i
$979$	2.62405	−	3.36241i	0.0838651	−	0.107463i
$980$	5.68713	−	21.0482i	0.181669	−	0.672359i
$981$	−4.72444	+	6.70819i	−0.150840	+	0.214176i
$982$	25.5964	+	3.71730i	0.816814	+	0.118624i
$983$	−18.4982	+	13.7192i	−0.590000	+	0.437574i	−0.849067	−	0.528286i	$-0.822835\pi$
$983$	−18.4982	+	13.7192i	−0.590000	+	0.437574i	0.259067	+	0.965859i	$0.416585\pi$
$984$	10.5571	+	12.6271i	0.336549	+	0.402536i
$985$	−47.6956	+	28.5876i	−1.51971	+	0.910877i
$986$	1.69040	+	2.51327i	0.0538332	+	0.0800387i
$987$	−0.454926	−	0.0561097i	−0.0144804	−	0.00178599i
$988$	−4.88238	+	25.3507i	−0.155329	+	0.806515i
$989$	−5.36303	−	2.06875i	−0.170535	−	0.0657824i
$990$	−3.11209	−	4.88159i	−0.0989086	−	0.155147i
$991$	16.5533	+	11.0606i	0.525833	+	0.351350i	0.789980	−	0.613132i	$-0.210091\pi$
$991$	16.5533	+	11.0606i	0.525833	+	0.351350i	−0.264148	+	0.964482i	$0.585091\pi$
$992$	−6.61273	−	4.50828i	−0.209954	−	0.143138i
$993$	−29.1231	+	19.4594i	−0.924193	+	0.617526i
$994$	−22.6506	−	9.95798i	−0.718435	−	0.315848i
$995$	42.2217	−	1.03649i	1.33852	−	0.0328588i
$996$	23.8329	−	2.49389i	0.755175	−	0.0790218i
$997$	−13.3808	−	7.58011i	−0.423773	−	0.240064i	0.266173	−	0.963925i	$-0.414241\pi$
$997$	−13.3808	−	7.58011i	−0.423773	−	0.240064i	−0.689946	+	0.723861i	$0.742366\pi$
$998$	15.2262	+	15.1338i	0.481976	+	0.479051i
$999$	35.4577	+	26.2973i	1.12183	+	0.832008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.149.32	✓	4032
512.189	even	128	inner	512.2.o.a.189.32	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.149.32	✓	4032	1.1	even	1	trivial
512.2.o.a.189.32	yes	4032	512.189	even	128	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.108327 - 1.41006i) q^{2} +(-1.21659 - 0.211099i) q^{3} +(-1.97653 + 0.305496i) q^{4} +(-1.04138 + 3.15231i) q^{5} +(-0.165872 + 1.73834i) q^{6} +(0.0945912 - 1.92545i) q^{7} +(0.644880 + 2.75393i) q^{8} +(-1.38909 - 0.497025i) q^{9} +O(q^{10})\)	\(q+(-0.108327 - 1.41006i) q^{2} +(-1.21659 - 0.211099i) q^{3} +(-1.97653 + 0.305496i) q^{4} +(-1.04138 + 3.15231i) q^{5} +(-0.165872 + 1.73834i) q^{6} +(0.0945912 - 1.92545i) q^{7} +(0.644880 + 2.75393i) q^{8} +(-1.38909 - 0.497025i) q^{9} +(4.55776 + 1.12693i) q^{10} +(0.764080 + 0.338693i) q^{11} +(2.46913 + 0.0455792i) q^{12} +(1.18368 - 1.02105i) q^{13} +(-2.72524 + 0.0751997i) q^{14} +(1.93239 - 3.61525i) q^{15} +(3.81334 - 1.20764i) q^{16} +(2.62273 - 1.40188i) q^{17} +(-0.550358 + 2.01254i) q^{18} +(7.18479 - 4.07014i) q^{19} +(1.09531 - 6.54878i) q^{20} +(-0.521540 + 2.32252i) q^{21} +(0.394807 - 1.11409i) q^{22} +(-0.446748 - 1.78352i) q^{23} +(-0.203205 - 3.48655i) q^{24} +(-4.83656 - 3.58704i) q^{25} +(-1.56796 - 1.55845i) q^{26} +(4.80812 + 2.72377i) q^{27} +(0.401254 + 3.83460i) q^{28} +(-0.719960 + 0.0176740i) q^{29} +(-5.30705 - 2.33316i) q^{30} +(1.17636 - 0.786019i) q^{31} +(-2.11594 - 5.24622i) q^{32} +(-0.858078 - 0.573349i) q^{33} +(-2.26085 - 3.54634i) q^{34} +(5.97111 + 2.30331i) q^{35} +(2.89742 + 0.558023i) q^{36} +(7.92852 + 0.977890i) q^{37} +(-6.51744 - 9.69007i) q^{38} +(-1.65560 + 0.992328i) q^{39} +(-9.35282 - 0.835035i) q^{40} +(-3.78527 + 2.80735i) q^{41} +(3.33139 + 0.483809i) q^{42} +(1.80019 - 2.55607i) q^{43} +(-1.61370 - 0.436014i) q^{44} +(3.01336 - 3.86126i) q^{45} +(-2.46647 + 0.823145i) q^{46} +(0.0188746 + 0.191637i) q^{47} +(-4.89423 + 0.664220i) q^{48} +(3.26789 + 0.321859i) q^{49} +(-4.53400 + 7.20841i) q^{50} +(-3.48674 + 1.15186i) q^{51} +(-2.02765 + 2.37974i) q^{52} +(-5.66513 - 0.139071i) q^{53} +(3.31982 - 7.07479i) q^{54} +(-1.86337 + 2.05591i) q^{55} +(5.36355 - 0.981185i) q^{56} +(-9.60019 + 3.43500i) q^{57} +(0.102913 + 1.01327i) q^{58} +(1.12879 - 1.30859i) q^{59} +(-2.71499 + 7.73600i) q^{60} +(-10.3844 + 2.33190i) q^{61} +(-1.23576 - 1.57359i) q^{62} +(-1.08839 + 2.62761i) q^{63} +(-7.16826 + 3.55191i) q^{64} +(1.98600 + 4.79463i) q^{65} +(-0.715503 + 1.27205i) q^{66} +(11.7662 + 7.45087i) q^{67} +(-4.75564 + 3.57209i) q^{68} +(0.167012 + 2.26413i) q^{69} +(2.60097 - 8.66913i) q^{70} +(8.20435 + 3.88037i) q^{71} +(0.472975 - 4.14598i) q^{72} +(-0.685082 - 13.9452i) q^{73} +(0.520006 - 11.2856i) q^{74} +(5.12692 + 5.38497i) q^{75} +(-12.9576 + 10.2397i) q^{76} +(0.724412 - 1.43916i) q^{77} +(1.57859 + 2.22699i) q^{78} +(-5.87472 - 7.15837i) q^{79} +(-0.164282 + 13.2785i) q^{80} +(-1.85321 - 1.52089i) q^{81} +(4.36857 + 5.03334i) q^{82} +(9.63044 - 1.18780i) q^{83} +(0.321318 - 4.74987i) q^{84} +(1.68789 + 9.72757i) q^{85} +(-3.79922 - 2.26148i) q^{86} +(0.879630 + 0.130481i) q^{87} +(-0.439998 + 2.32264i) q^{88} +(1.23997 - 4.95024i) q^{89} +(-5.77103 - 3.83073i) q^{90} +(-1.85401 - 2.37569i) q^{91} +(1.42787 + 3.38870i) q^{92} +(-1.59708 + 0.707938i) q^{93} +(0.268175 - 0.0473739i) q^{94} +(5.34822 + 26.8873i) q^{95} +(1.46677 + 6.82920i) q^{96} +(1.27266 - 6.39808i) q^{97} +(0.0998380 - 4.64278i) q^{98} +(-0.893038 - 0.850243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

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