LMFDB - Embedded newform 256.2.m.a.101.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

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("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			101.26
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07805 + 0.915314i) q^{2} +(-1.53503 + 0.384505i) q^{3} +(0.324401 + 1.97352i) q^{4} +(-3.70568 - 1.75266i) q^{5} +(-2.00679 - 0.990517i) q^{6} +(-0.841234 - 2.77318i) q^{7} +(-1.45666 + 2.42449i) q^{8} +(-0.437291 + 0.233737i) q^{9} +O(q^{10})$	\(q+(1.07805 + 0.915314i) q^{2} +(-1.53503 + 0.384505i) q^{3} +(0.324401 + 1.97352i) q^{4} +(-3.70568 - 1.75266i) q^{5} +(-2.00679 - 0.990517i) q^{6} +(-0.841234 - 2.77318i) q^{7} +(-1.45666 + 2.42449i) q^{8} +(-0.437291 + 0.233737i) q^{9} +(-2.39069 - 5.28132i) q^{10} +(-2.18905 + 0.324715i) q^{11} +(-1.25679 - 2.90467i) q^{12} +(-1.41642 + 3.95862i) q^{13} +(1.63143 - 3.75963i) q^{14} +(6.36223 + 1.26553i) q^{15} +(-3.78953 + 1.28042i) q^{16} +(6.74872 - 1.34240i) q^{17} +(-0.685367 - 0.148278i) q^{18} +(-0.903883 - 0.819232i) q^{19} +(2.25677 - 7.88178i) q^{20} +(2.35762 + 3.93345i) q^{21} +(-2.65713 - 1.65361i) q^{22} +(-8.49026 + 0.836218i) q^{23} +(1.30380 - 4.28175i) q^{24} +(7.48828 + 9.12450i) q^{25} +(-5.15035 + 2.97114i) q^{26} +(4.09895 - 3.71507i) q^{27} +(5.20001 - 2.55981i) q^{28} +(-2.29323 - 3.09207i) q^{29} +(5.70048 + 7.18774i) q^{30} +(-1.05672 - 0.437707i) q^{31} +(-5.25730 - 2.08824i) q^{32} +(3.23540 - 1.34015i) q^{33} +(8.50421 + 4.73001i) q^{34} +(-1.74308 + 11.7509i) q^{35} +(-0.603142 - 0.787177i) q^{36} +(-0.350360 + 7.13173i) q^{37} +(-0.224581 - 1.71051i) q^{38} +(0.652133 - 6.62121i) q^{39} +(9.64722 - 6.43133i) q^{40} +(-2.54227 + 3.09777i) q^{41} +(-1.05870 + 6.39843i) q^{42} +(-0.967436 + 3.86222i) q^{43} +(-1.35096 - 4.21478i) q^{44} +(2.03012 - 0.0997335i) q^{45} +(-9.91836 - 6.86976i) q^{46} +(-6.17170 - 4.12380i) q^{47} +(5.32471 - 3.42258i) q^{48} +(-1.16255 + 0.776791i) q^{49} +(-0.279007 + 16.6908i) q^{50} +(-9.84333 + 4.65555i) q^{51} +(-8.27188 - 1.51114i) q^{52} +(-2.30469 + 3.10751i) q^{53} +(7.81934 - 0.253222i) q^{54} +(8.68102 + 2.63336i) q^{55} +(7.94892 + 2.00003i) q^{56} +(1.70249 + 0.909998i) q^{57} +(0.357982 - 5.43244i) q^{58} +(-1.26468 - 3.53455i) q^{59} +(-0.433621 + 12.9665i) q^{60} +(5.53796 - 9.23953i) q^{61} +(-0.738560 - 1.43910i) q^{62} +(1.01606 + 1.01606i) q^{63} +(-3.75626 - 7.06332i) q^{64} +(12.1869 - 12.1869i) q^{65} +(4.71459 + 1.51666i) q^{66} +(-4.17275 - 2.50105i) q^{67} +(4.83855 + 12.8832i) q^{68} +(12.7113 - 4.54817i) q^{69} +(-12.6349 + 11.0726i) q^{70} +(4.35404 - 8.14584i) q^{71} +(0.0702945 - 1.40068i) q^{72} +(0.401340 - 1.32304i) q^{73} +(-6.90548 + 7.36771i) q^{74} +(-15.0032 - 11.1271i) q^{75} +(1.32355 - 2.04959i) q^{76} +(2.74199 + 5.79746i) q^{77} +(6.76352 - 6.54112i) q^{78} +(5.64174 + 8.44347i) q^{79} +(16.2869 + 1.89691i) q^{80} +(-4.03712 + 6.04198i) q^{81} +(-5.57613 + 1.01258i) q^{82} +(-0.0348013 - 0.708396i) q^{83} +(-6.99791 + 5.92882i) q^{84} +(-27.3614 - 6.85366i) q^{85} +(-4.57809 + 3.27818i) q^{86} +(4.70910 + 3.86465i) q^{87} +(2.40144 - 5.78032i) q^{88} +(-10.9294 - 1.07646i) q^{89} +(2.27987 + 1.75068i) q^{90} +(12.1695 + 0.597848i) q^{91} +(-4.40454 - 16.4844i) q^{92} +(1.79040 + 0.265580i) q^{93} +(-2.87886 - 10.0947i) q^{94} +(1.91367 + 4.62001i) q^{95} +(8.87306 + 1.18406i) q^{96} +(-5.66403 + 13.6742i) q^{97} +(-1.96430 - 0.226675i) q^{98} +(0.881354 - 0.653657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{64}\right)$	$1$

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 $

$2$	1.07805	+	0.915314i	0.762299	+	0.647225i
$2$	1.07805	+	0.915314i	0.762299	+	0.647225i
$3$	−1.53503	+	0.384505i	−0.886250	+	0.221994i	−0.659271	−	0.751906i	$-0.729135\pi$
$3$	−1.53503	+	0.384505i	−0.886250	+	0.221994i	−0.226979	+	0.973900i	$0.572885\pi$
$4$	0.324401	+	1.97352i	0.162201	+	0.986758i
$5$	−3.70568	−	1.75266i	−1.65723	−	0.783811i	−0.999534	−	0.0305277i	$-0.990281\pi$
$5$	−3.70568	−	1.75266i	−1.65723	−	0.783811i	−0.657696	−	0.753284i	$-0.728469\pi$
$6$	−2.00679	−	0.990517i	−0.819268	−	0.404377i
$7$	−0.841234	−	2.77318i	−0.317957	−	1.04816i	−0.959649	−	0.281200i	$-0.909267\pi$
$7$	−0.841234	−	2.77318i	−0.317957	−	1.04816i	0.641692	−	0.766962i	$-0.278233\pi$
$8$	−1.45666	+	2.42449i	−0.515009	+	0.857185i
$9$	−0.437291	+	0.233737i	−0.145764	+	0.0779124i
$10$	−2.39069	−	5.28132i	−0.756003	−	1.67010i
$11$	−2.18905	+	0.324715i	−0.660023	+	0.0979052i	−0.468335	−	0.883551i	$-0.655146\pi$
$11$	−2.18905	+	0.324715i	−0.660023	+	0.0979052i	−0.191688	+	0.981456i	$0.561396\pi$
$12$	−1.25679	−	2.90467i	−0.362805	−	0.838506i
$13$	−1.41642	+	3.95862i	−0.392843	+	1.09792i	0.568527	+	0.822664i	$0.307513\pi$
$13$	−1.41642	+	3.95862i	−0.392843	+	1.09792i	−0.961370	+	0.275258i	$0.911237\pi$
$14$	1.63143	−	3.75963i	0.436018	−	1.00480i
$15$	6.36223	+	1.26553i	1.64272	+	0.326758i
$16$	−3.78953	+	1.28042i	−0.947382	+	0.320105i
$17$	6.74872	−	1.34240i	1.63681	−	0.325581i	0.710887	−	0.703306i	$-0.248294\pi$
$17$	6.74872	−	1.34240i	1.63681	−	0.325581i	0.925918	+	0.377725i	$0.123294\pi$
$18$	−0.685367	−	0.148278i	−0.161542	−	0.0349494i
$19$	−0.903883	−	0.819232i	−0.207365	−	0.187945i	0.561269	−	0.827633i	$-0.310313\pi$
$19$	−0.903883	−	0.819232i	−0.207365	−	0.187945i	−0.768634	+	0.639689i	$0.779063\pi$
$20$	2.25677	−	7.88178i	0.504628	−	1.76242i
$21$	2.35762	+	3.93345i	0.514475	+	0.858349i
$22$	−2.65713	−	1.65361i	−0.566502	−	0.352550i
$23$	−8.49026	+	0.836218i	−1.77034	+	0.174363i	−0.929967	−	0.367643i	$-0.880165\pi$
$23$	−8.49026	+	0.836218i	−1.77034	+	0.174363i	−0.840374	+	0.542006i	$0.817665\pi$
$24$	1.30380	−	4.28175i	0.266136	−	0.874009i
$25$	7.48828	+	9.12450i	1.49766	+	1.82490i
$26$	−5.15035	+	2.97114i	−1.01007	+	0.582688i
$27$	4.09895	−	3.71507i	0.788842	−	0.714965i
$28$	5.20001	−	2.55981i	0.982710	−	0.483759i
$29$	−2.29323	−	3.09207i	−0.425843	−	0.574182i	0.537226	−	0.843438i	$-0.319472\pi$
$29$	−2.29323	−	3.09207i	−0.425843	−	0.574182i	−0.963069	+	0.269256i	$0.913222\pi$
$30$	5.70048	+	7.18774i	1.04076	+	1.31230i
$31$	−1.05672	−	0.437707i	−0.189792	−	0.0786145i	0.285763	−	0.958300i	$-0.407753\pi$
$31$	−1.05672	−	0.437707i	−0.189792	−	0.0786145i	−0.475556	+	0.879686i	$0.657753\pi$
$32$	−5.25730	−	2.08824i	−0.929369	−	0.369153i
$33$	3.23540	−	1.34015i	0.563211	−	0.233290i
$34$	8.50421	+	4.73001i	1.45846	+	0.811191i
$35$	−1.74308	+	11.7509i	−0.294634	+	1.98626i
$36$	−0.603142	−	0.787177i	−0.100524	−	0.131196i
$37$	−0.350360	+	7.13173i	−0.0575988	+	1.17245i	0.779862	+	0.625952i	$0.215289\pi$
$37$	−0.350360	+	7.13173i	−0.0575988	+	1.17245i	−0.837460	+	0.546498i	$0.815961\pi$
$38$	−0.224581	−	1.71051i	−0.0364318	−	0.277482i
$39$	0.652133	−	6.62121i	0.104425	−	1.06024i
$40$	9.64722	−	6.43133i	1.52536	−	1.01688i
$41$	−2.54227	+	3.09777i	−0.397036	+	0.483790i	−0.932706	−	0.360638i	$-0.882559\pi$
$41$	−2.54227	+	3.09777i	−0.397036	+	0.483790i	0.535670	+	0.844427i	$0.320059\pi$
$42$	−1.05870	+	6.39843i	−0.163361	+	0.987300i
$43$	−0.967436	+	3.86222i	−0.147533	+	0.588983i	0.850482	+	0.526004i	$0.176310\pi$
$43$	−0.967436	+	3.86222i	−0.147533	+	0.588983i	−0.998015	+	0.0629795i	$0.979940\pi$
$44$	−1.35096	−	4.21478i	−0.203665	−	0.635403i
$45$	2.03012	−	0.0997335i	0.302633	−	0.0148674i
$46$	−9.91836	−	6.86976i	−1.46238	−	1.01289i
$47$	−6.17170	−	4.12380i	−0.900235	−	0.601518i	0.0170041	−	0.999855i	$-0.494587\pi$
$47$	−6.17170	−	4.12380i	−0.900235	−	0.601518i	−0.917239	+	0.398338i	$0.869587\pi$
$48$	5.32471	−	3.42258i	0.768556	−	0.494006i
$49$	−1.16255	+	0.776791i	−0.166079	+	0.110970i
$50$	−0.279007	+	16.6908i	−0.0394575	+	2.36044i
$51$	−9.84333	+	4.65555i	−1.37834	+	0.651907i
$52$	−8.27188	−	1.51114i	−1.14710	−	0.209557i
$53$	−2.30469	+	3.10751i	−0.316573	+	0.426849i	−0.932620	−	0.360860i	$-0.882483\pi$
$53$	−2.30469	+	3.10751i	−0.316573	+	0.426849i	0.616047	+	0.787710i	$0.288733\pi$
$54$	7.81934	−	0.253222i	1.06408	−	0.0344592i
$55$	8.68102	+	2.63336i	1.17055	+	0.355082i
$56$	7.94892	+	2.00003i	1.06222	+	0.267265i
$57$	1.70249	+	0.909998i	0.225500	+	0.120532i
$58$	0.357982	−	5.43244i	0.0470054	−	0.713315i
$59$	−1.26468	−	3.53455i	−0.164647	−	0.460159i	0.830676	−	0.556756i	$-0.187954\pi$
$59$	−1.26468	−	3.53455i	−0.164647	−	0.460159i	−0.995324	+	0.0965972i	$0.969204\pi$
$60$	−0.433621	+	12.9665i	−0.0559803	+	1.67397i
$61$	5.53796	−	9.23953i	0.709063	−	1.18300i	−0.266617	−	0.963803i	$-0.585906\pi$
$61$	5.53796	−	9.23953i	0.709063	−	1.18300i	0.975680	−	0.219198i	$-0.0703441\pi$
$62$	−0.738560	−	1.43910i	−0.0937973	−	0.182766i
$63$	1.01606	+	1.01606i	0.128011	+	0.128011i
$64$	−3.75626	−	7.06332i	−0.469532	−	0.882915i
$65$	12.1869	−	12.1869i	1.51160	−	1.51160i
$66$	4.71459	+	1.51666i	0.580326	+	0.186687i
$67$	−4.17275	−	2.50105i	−0.509783	−	0.305552i	0.235987	−	0.971756i	$-0.424168\pi$
$67$	−4.17275	−	2.50105i	−0.509783	−	0.305552i	−0.745769	+	0.666204i	$0.767918\pi$
$68$	4.83855	+	12.8832i	0.586760	+	1.56232i
$69$	12.7113	−	4.54817i	1.53026	−	0.547535i
$70$	−12.6349	+	11.0726i	−1.51016	+	1.32343i
$71$	4.35404	−	8.14584i	0.516730	−	0.966733i	−0.479295	−	0.877654i	$-0.659108\pi$
$71$	4.35404	−	8.14584i	0.516730	−	0.966733i	0.996025	−	0.0890792i	$-0.0283924\pi$
$72$	0.0702945	−	1.40068i	0.00828429	−	0.165072i
$73$	0.401340	−	1.32304i	0.0469733	−	0.154850i	−0.930316	−	0.366758i	$-0.880468\pi$
$73$	0.401340	−	1.32304i	0.0469733	−	0.154850i	0.977290	+	0.211908i	$0.0679677\pi$
$74$	−6.90548	+	7.36771i	−0.802746	+	0.856478i
$75$	−15.0032	−	11.1271i	−1.73242	−	1.28485i
$76$	1.32355	−	2.04959i	0.151821	−	0.235104i
$77$	2.74199	+	5.79746i	0.312479	+	0.660682i
$78$	6.76352	−	6.54112i	0.765818	−	0.740636i
$79$	5.64174	+	8.44347i	0.634746	+	0.949964i	0.999820	+	0.0189856i	$0.00604367\pi$
$79$	5.64174	+	8.44347i	0.634746	+	0.949964i	−0.365074	+	0.930978i	$0.618956\pi$
$80$	16.2869	+	1.89691i	1.82093	+	0.212081i
$81$	−4.03712	+	6.04198i	−0.448569	+	0.671331i
$82$	−5.57613	+	1.01258i	−0.615781	+	0.111821i
$83$	−0.0348013	−	0.708396i	−0.00381994	−	0.0777566i	0.996129	−	0.0879088i	$-0.0280184\pi$
$83$	−0.0348013	−	0.708396i	−0.00381994	−	0.0777566i	−0.999948	+	0.0101522i	$0.996768\pi$
$84$	−6.99791	+	5.92882i	−0.763535	+	0.646887i
$85$	−27.3614	−	6.85366i	−2.96776	−	0.743384i
$86$	−4.57809	+	3.27818i	−0.493669	+	0.353495i
$87$	4.70910	+	3.86465i	0.504868	+	0.414334i
$88$	2.40144	−	5.78032i	0.255995	−	0.616184i
$89$	−10.9294	−	1.07646i	−1.15852	−	0.114104i	−0.499557	−	0.866281i	$-0.666504\pi$
$89$	−10.9294	−	1.07646i	−1.15852	−	0.114104i	−0.658961	+	0.752177i	$0.729004\pi$
$90$	2.27987	+	1.75068i	0.240319	+	0.184538i
$91$	12.1695	+	0.597848i	1.27571	+	0.0626715i
$92$	−4.40454	−	16.4844i	−0.459205	−	1.71862i
$93$	1.79040	+	0.265580i	0.185655	+	0.0275394i
$94$	−2.87886	−	10.0947i	−0.296931	−	1.04119i
$95$	1.91367	+	4.62001i	0.196338	+	0.474003i
$96$	8.87306	+	1.18406i	0.905603	+	0.120847i
$97$	−5.66403	+	13.6742i	−0.575095	+	1.38840i	0.322073	+	0.946715i	$0.395620\pi$
$97$	−5.66403	+	13.6742i	−0.575095	+	1.38840i	−0.897169	+	0.441688i	$0.854380\pi$
$98$	−1.96430	−	0.226675i	−0.198424	−	0.0228977i
$99$	0.881354	−	0.653657i	0.0885795	−	0.0656950i
$100$	−15.5781	+	17.7382i	−1.55781	+	1.77382i
$101$	1.04172	+	1.14936i	0.103655	+	0.114365i	0.790569	−	0.612373i	$-0.209785\pi$
$101$	1.04172	+	1.14936i	0.103655	+	0.114365i	−0.686914	+	0.726739i	$0.741035\pi$
$102$	−14.8729	−	3.99080i	−1.47264	−	0.395148i
$103$	3.14968	−	2.58487i	0.310347	−	0.254695i	−0.466306	−	0.884623i	$-0.654416\pi$
$103$	3.14968	−	2.58487i	0.310347	−	0.254695i	0.776654	+	0.629928i	$0.216916\pi$
$104$	−7.53437	−	9.20046i	−0.738805	−	0.902179i
$105$	−1.84260	−	18.7082i	−0.179819	−	1.82573i
$106$	−5.32892	+	1.24055i	−0.517591	+	0.120493i
$107$	−9.12107	+	5.46696i	−0.881767	+	0.528511i	−0.881872	−	0.471489i	$-0.843717\pi$
$107$	−9.12107	+	5.46696i	−0.881767	+	0.528511i	0.000104830		1.00000i	$0.499967\pi$
$108$	8.66145	+	6.88416i	0.833448	+	0.662429i
$109$	2.33750	−	2.57903i	0.223892	−	0.247027i	−0.618638	−	0.785676i	$-0.712315\pi$
$109$	2.33750	−	2.57903i	0.223892	−	0.247027i	0.842530	+	0.538649i	$0.181065\pi$
$110$	6.94826	+	10.7848i	0.662491	+	1.02829i
$111$	−2.20437	−	11.0821i	−0.209230	−	1.05187i
$112$	6.73872	+	9.43190i	0.636749	+	0.891231i
$113$	0.304300	−	1.52982i	0.0286262	−	0.143913i	−0.963829	−	0.266521i	$-0.914126\pi$
$113$	0.304300	−	1.52982i	0.0286262	−	0.143913i	0.992455	+	0.122608i	$0.0391257\pi$
$114$	1.00244	+	2.53934i	0.0938870	+	0.237831i
$115$	32.9278	+	11.7817i	3.07053	+	1.09865i
$116$	5.35831	−	5.52880i	0.497507	−	0.513336i
$117$	−0.305889	−	2.06214i	−0.0282795	−	0.190645i
$118$	1.87182	−	4.96801i	0.172315	−	0.457343i
$119$	−9.39998	−	17.5861i	−0.861695	−	1.61212i
$120$	−12.3359	+	13.5817i	−1.12611	+	1.23983i
$121$	−5.83985	+	1.77150i	−0.530895	+	0.161045i
$122$	14.4273	−	4.89174i	1.30619	−	0.442877i
$123$	2.71136	−	5.73268i	0.244475	−	0.516898i
$124$	0.521021	−	2.22744i	0.0467891	−	0.200030i
$125$	−6.77689	−	27.0548i	−0.606143	−	2.41986i
$126$	0.165354	+	2.02538i	0.0147309	+	0.180435i
$127$			1.98512i			0.176151i	0.996114	+	0.0880757i	$0.0280717\pi$
$127$			1.98512i			0.176151i	−0.996114	+	0.0880757i	$0.971928\pi$
$128$	2.41571	−	11.0528i	0.213520	−	0.976939i
$129$		−	6.30061i		−	0.554738i
$130$	24.2929	−	1.98329i	2.13063	−	0.173946i
$131$	1.23915	+	4.94696i	0.108265	+	0.432218i	0.999784	−	0.0207646i	$-0.00661006\pi$
$131$	1.23915	+	4.94696i	0.108265	+	0.432218i	−0.891519	+	0.452982i	$0.850360\pi$
$132$	3.69437	+	5.95037i	0.321553	+	0.517913i
$133$	−1.51150	+	3.19579i	−0.131064	+	0.277111i
$134$	−2.20920	−	6.51564i	−0.190846	−	0.562866i
$135$	−21.7006	+	6.58281i	−1.86769	+	0.566558i
$136$	−6.57598	+	18.3176i	−0.563886	+	1.57072i
$137$	1.73161	+	3.23962i	0.147942	+	0.276780i	0.944967	−	0.327167i	$-0.106094\pi$
$137$	1.73161	+	3.23962i	0.147942	+	0.276780i	−0.797025	+	0.603947i	$0.793594\pi$
$138$	17.8664	+	6.73163i	1.52089	+	0.573035i
$139$	−2.42752	−	16.3650i	−0.205899	−	1.38806i	−0.807784	−	0.589478i	$-0.799333\pi$
$139$	−2.42752	−	16.3650i	−0.205899	−	1.38806i	0.601885	−	0.798583i	$-0.294417\pi$
$140$	−23.7560	+	0.372007i	−2.00775	+	0.0314403i
$141$	11.0594	+	3.95710i	0.931366	+	0.333248i
$142$	12.1499	−	4.79634i	1.01960	−	0.402500i
$143$	1.81518	−	9.12554i	0.151793	−	0.763116i
$144$	1.35785	−	1.44567i	0.113154	−	0.120473i
$145$	3.07866	+	15.4775i	0.255669	+	1.28533i
$146$	1.64366	−	1.05896i	0.136030	−	0.0876399i
$147$	1.48587	−	1.63940i	0.122552	−	0.135216i
$148$	−14.1882	+	1.62210i	−1.16627	+	0.133336i
$149$	3.13178	−	1.87711i	0.256565	−	0.153779i	−0.380038	−	0.924971i	$-0.624089\pi$
$149$	3.13178	−	1.87711i	0.256565	−	0.153779i	0.636603	+	0.771192i	$0.280339\pi$
$150$	−5.98943	−	25.7282i	−0.489035	−	2.10070i
$151$	0.761817	+	7.73486i	0.0619958	+	0.629454i	0.975106	+	0.221740i	$0.0711737\pi$
$151$	0.761817	+	7.73486i	0.0619958	+	0.629454i	−0.913110	+	0.407713i	$0.866326\pi$
$152$	3.30287	−	0.998106i	0.267898	−	0.0809571i
$153$	−2.63739	+	2.16445i	−0.213220	+	0.174985i
$154$	−2.35048	+	8.75976i	−0.189407	+	0.705882i
$155$	3.14871	+	3.47407i	0.252910	+	0.279044i
$156$	13.2786	−	0.860935i	1.06314	−	0.0689300i
$157$	−3.85763	+	2.86102i	−0.307873	+	0.228334i	−0.738593	−	0.674151i	$-0.764510\pi$
$157$	−3.85763	+	2.86102i	−0.307873	+	0.228334i	0.430720	+	0.902485i	$0.358260\pi$
$158$	−1.64632	+	14.2665i	−0.130974	+	1.13498i
$159$	2.34291	−	5.65628i	0.185805	−	0.448573i
$160$	15.8219	+	16.9526i	1.25083	+	1.34022i
$161$	9.46128	+	22.8415i	0.745653	+	1.80017i
$162$	−9.88254	+	2.81835i	−0.776446	+	0.221430i
$163$	−6.14286	−	0.911207i	−0.481146	−	0.0713713i	−0.0982482	−	0.995162i	$-0.531324\pi$
$163$	−6.14286	−	0.911207i	−0.481146	−	0.0713713i	−0.382898	+	0.923791i	$0.625074\pi$
$164$	−6.93821	−	4.01229i	−0.541783	−	0.313307i
$165$	−14.3382	−	0.704389i	−1.11622	−	0.0548366i
$166$	0.610887	−	0.795543i	0.0474140	−	0.0617461i
$167$	−14.7439	−	1.45215i	−1.14092	−	0.112371i	−0.490144	−	0.871641i	$-0.663056\pi$
$167$	−14.7439	−	1.45215i	−1.14092	−	0.112371i	−0.650775	+	0.759271i	$0.725556\pi$
$168$	−12.9709	−	0.0137028i	−1.00072	−	0.00105719i
$169$	−3.61528	−	2.96698i	−0.278098	−	0.228229i
$170$	−23.2238	−	32.4329i	−1.78118	−	2.48749i
$171$	0.586746	+	0.146972i	0.0448696	+	0.0112392i
$172$	−7.93599	−	0.656342i	−0.605114	−	0.0500456i
$173$	0.172758	+	3.51657i	0.0131346	+	0.267360i	0.996376	+	0.0850538i	$0.0271062\pi$
$173$	0.172758	+	3.51657i	0.0131346	+	0.267360i	−0.983242	+	0.182306i	$0.941644\pi$
$174$	1.53929	+	8.47661i	0.116693	+	0.642610i
$175$	19.0045	−	28.4422i	1.43660	−	2.15003i
$176$	7.87969	−	4.03342i	0.593954	−	0.304030i
$177$	3.30037	+	4.93936i	0.248071	+	0.371265i
$178$	−10.7972	−	11.1643i	−0.809286	−	0.836803i
$179$	0.238998	+	0.505319i	0.0178635	+	0.0377693i	0.912724	−	0.408577i	$-0.133975\pi$
$179$	0.238998	+	0.505319i	0.0178635	+	0.0377693i	−0.894860	+	0.446346i	$0.852725\pi$
$180$	0.855400	+	3.97412i	0.0637577	+	0.296214i
$181$	−15.7624	−	11.6902i	−1.17161	−	0.868926i	−0.178252	−	0.983985i	$-0.557044\pi$
$181$	−15.7624	−	11.6902i	−1.17161	−	0.868926i	−0.993359	+	0.115059i	$0.963294\pi$
$182$	12.5721	+	11.7834i	0.931909	+	0.873444i
$183$	−4.94829	+	16.3123i	−0.365788	+	1.20584i
$184$	10.3401	−	21.8026i	0.762279	−	1.60731i
$185$	13.7978	−	25.8139i	1.01443	−	1.89787i
$186$	1.68705	+	1.92508i	0.123701	+	0.141154i
$187$	−14.3374	+	5.13000i	−1.04845	+	0.375143i
$188$	6.13627	−	13.5177i	0.447534	−	0.985880i
$189$	−13.7507	−	8.24186i	−1.00022	−	0.599507i
$190$	−2.16572	+	6.73223i	−0.157118	+	0.488407i
$191$	−4.96962	+	4.96962i	−0.359589	+	0.359589i	−0.863661	−	0.504072i	$-0.831834\pi$
$191$	−4.96962	+	4.96962i	−0.359589	+	0.359589i	0.504072	+	0.863661i	$0.331834\pi$
$192$	8.48185	+	9.39811i	0.612125	+	0.678250i
$193$	−0.449902	−	0.449902i	−0.0323846	−	0.0323846i	0.690729	−	0.723114i	$-0.257290\pi$
$193$	−0.449902	−	0.449902i	−0.0323846	−	0.0323846i	−0.723114	+	0.690729i	$0.757290\pi$
$194$	−18.6223	+	9.55714i	−1.33700	+	0.686163i
$195$	−14.0213	+	23.3931i	−1.00409	+	1.67522i
$196$	−1.91014	−	2.04232i	−0.136439	−	0.145880i
$197$	2.85549	+	7.98055i	0.203445	+	0.568590i	0.999320	−	0.0368703i	$-0.0117389\pi$
$197$	2.85549	+	7.98055i	0.203445	+	0.568590i	−0.795875	+	0.605461i	$0.792989\pi$
$198$	1.54845	+	0.102038i	0.110043	+	0.00725155i
$199$	17.7792	+	9.50318i	1.26033	+	0.673662i	0.959954	−	0.280157i	$-0.0903866\pi$
$199$	17.7792	+	9.50318i	1.26033	+	0.673662i	0.300380	+	0.953820i	$0.402887\pi$
$200$	−33.0301	+	4.86390i	−2.33558	+	0.343930i
$201$	7.36696	+	2.23474i	0.519625	+	0.157627i
$202$	0.0710043	+	2.19257i	0.00499585	+	0.154269i
$203$	−6.64570	+	8.96069i	−0.466437	+	0.628917i
$204$	−12.3810	−	17.9157i	−0.866842	−	1.25435i
$205$	14.8502	−	7.02360i	1.03718	−	0.490550i
$206$	5.76150	+	0.0963101i	0.401422	+	0.00671024i
$207$	3.51726	−	2.35016i	0.244467	−	0.163347i
$208$	0.298850	−	16.8149i	0.0207215	−	1.16590i
$209$	2.24466	+	1.49983i	0.155266	+	0.103746i
$210$	15.1375	−	21.8550i	1.04458	−	1.50814i
$211$	5.00809	−	0.246032i	0.344771	−	0.0169375i	0.124054	−	0.992275i	$-0.460410\pi$
$211$	5.00809	−	0.246032i	0.344771	−	0.0169375i	0.220717	+	0.975338i	$0.429160\pi$
$212$	−6.88036	−	3.54026i	−0.472545	−	0.243146i
$213$	−3.55147	+	14.1783i	−0.243343	+	0.971478i
$214$	−14.8370	−	2.45496i	−1.01424	−	0.167818i
$215$	10.3542	−	12.6166i	0.706147	−	0.860443i
$216$	3.03634	+	15.3494i	0.206597	+	1.04440i
$217$	−0.324892	+	3.29868i	−0.0220551	+	0.223929i
$218$	4.88058	−	0.640792i	0.330554	−	0.0433999i
$219$	−0.107353	+	2.18522i	−0.00725425	+	0.147664i
$220$	−2.38084	+	17.9864i	−0.160516	+	1.21264i
$221$	−4.24493	+	28.6170i	−0.285545	+	1.92499i
$222$	7.76720	−	13.9648i	0.521300	−	0.937259i
$223$	−22.6509	+	9.38230i	−1.51682	+	0.628286i	−0.976950	−	0.213466i	$-0.931525\pi$
$223$	−22.6509	+	9.38230i	−1.51682	+	0.628286i	−0.539865	+	0.841752i	$0.681525\pi$
$224$	−1.36845	+	16.3361i	−0.0914333	+	1.09150i
$225$	−5.40730	−	2.23978i	−0.360487	−	0.149318i
$226$	1.72832	−	1.37070i	0.114966	−	0.0911776i
$227$	7.41200	+	9.99392i	0.491952	+	0.663320i	0.977511	−	0.210884i	$-0.0676341\pi$
$227$	7.41200	+	9.99392i	0.491952	+	0.663320i	−0.485560	+	0.874204i	$0.661384\pi$
$228$	−1.24361	+	3.65509i	−0.0823599	+	0.242064i
$229$	7.13860	−	6.47005i	0.471732	−	0.427553i	−0.400759	−	0.916184i	$-0.631253\pi$
$229$	7.13860	−	6.47005i	0.471732	−	0.427553i	0.872491	+	0.488631i	$0.162503\pi$
$230$	24.7139	+	42.8406i	1.62959	+	2.82483i
$231$	−6.43819	−	7.84496i	−0.423602	−	0.516161i
$232$	10.8371	−	1.05581i	0.711493	−	0.0693171i
$233$	1.77279	−	0.174604i	0.116139	−	0.0114387i	−0.0397806	−	0.999208i	$-0.512666\pi$
$233$	1.77279	−	0.174604i	0.116139	−	0.0114387i	0.155920	+	0.987770i	$0.450166\pi$
$234$	1.55774	−	2.50308i	0.101833	−	0.163632i
$235$	15.6427	+	26.0983i	1.02042	+	1.70247i
$236$	6.56522	−	3.64248i	0.427359	−	0.237105i
$237$	−11.9068	−	10.7917i	−0.773430	−	0.700996i
$238$	5.96314	−	27.5627i	0.386533	−	1.78663i
$239$	−12.0286	+	2.39265i	−0.778068	+	0.154767i	−0.568121	−	0.822945i	$-0.692329\pi$
$239$	−12.0286	+	2.39265i	−0.778068	+	0.154767i	−0.209947	+	0.977713i	$0.567329\pi$
$240$	−25.7303	+	3.35059i	−1.66088	+	0.216280i
$241$	15.2041	+	3.02428i	0.979380	+	0.194811i	0.658724	−	0.752385i	$-0.271097\pi$
$241$	15.2041	+	3.02428i	0.979380	+	0.194811i	0.320656	+	0.947196i	$0.396097\pi$
$242$	−7.91715	−	3.43552i	−0.508934	−	0.220844i
$243$	−1.71710	+	4.79897i	−0.110152	+	0.307854i
$244$	20.0309	+	7.93194i	1.28235	+	0.507790i
$245$	5.66948	−	0.840988i	0.362210	−	0.0537288i
$246$	8.17019	−	3.69840i	0.520912	−	0.235801i
$247$	4.52330	−	2.41775i	0.287811	−	0.153838i
$248$	2.60050	−	1.92441i	0.165132	−	0.122200i
$249$	0.325803	+	1.07403i	0.0206469	+	0.0680638i
$250$	17.4578	−	35.3696i	1.10413	−	2.23697i
$251$	14.7459	+	6.97430i	0.930754	+	0.440214i	0.831924	−	0.554890i	$-0.187240\pi$
$251$	14.7459	+	6.97430i	0.930754	+	0.440214i	0.0988308	+	0.995104i	$0.468490\pi$
$252$	−1.67560	+	2.33482i	−0.105553	+	0.147080i
$253$	18.3141	−	4.58743i	1.15140	−	0.288409i
$254$	−1.81701	+	2.14007i	−0.114009	+	0.134280i
$255$	44.6358			2.79520
$256$	12.7210	−	9.70438i	0.795065	−	0.606524i
$257$	−16.2017			−1.01064			−0.505319	−	0.862933i	$-0.668625\pi$
$257$	−16.2017			−1.01064			−0.505319	+	0.862933i	$0.668625\pi$
$258$	5.76704	−	6.79240i	0.359040	−	0.422876i
$259$	20.0723	−	5.02785i	1.24723	−	0.312415i
$260$	28.0044	+	20.0975i	1.73676	+	1.24640i
$261$	1.72554	+	0.816121i	0.106808	+	0.0505166i
$262$	−3.19215	+	6.46730i	−0.197212	+	0.399551i
$263$	8.31584	+	27.4136i	0.512777	+	1.69040i	0.705135	+	0.709073i	$0.250886\pi$
$263$	8.31584	+	27.4136i	0.512777	+	1.69040i	−0.192358	+	0.981325i	$0.561614\pi$
$264$	−1.46373	+	9.79633i	−0.0900861	+	0.602922i
$265$	13.9868	−	7.47611i	0.859204	−	0.459254i
$266$	−4.55463	+	2.06174i	−0.279262	+	0.126414i
$267$	17.1909	−	2.55003i	1.05207	−	0.156059i
$268$	3.58222	−	9.04633i	0.218819	−	0.552593i
$269$	−2.69988	+	7.54567i	−0.164615	+	0.460068i	−0.995319	−	0.0966469i	$-0.969188\pi$
$269$	−2.69988	+	7.54567i	−0.164615	+	0.460068i	0.830704	+	0.556714i	$0.187938\pi$
$270$	−29.4198	−	12.7662i	−1.79043	−	0.776929i
$271$	12.6512	+	2.51647i	0.768503	+	0.152865i	0.563746	−	0.825948i	$-0.309360\pi$
$271$	12.6512	+	2.51647i	0.768503	+	0.152865i	0.204757	+	0.978813i	$0.434360\pi$
$272$	−23.8556	+	13.7283i	−1.44646	+	0.832399i
$273$	−18.9104	+	3.76151i	−1.14451	+	0.227657i
$274$	−1.09850	+	5.07746i	−0.0663626	+	0.306740i
$275$	−19.3551	−	17.5424i	−1.16716	−	1.05785i
$276$	13.0994	+	23.6105i	0.788493	+	1.42118i
$277$	4.60510	+	7.68314i	0.276693	+	0.461635i	0.964435	−	0.264321i	$-0.0851477\pi$
$277$	4.60510	+	7.68314i	0.276693	+	0.461635i	−0.687741	+	0.725956i	$0.741398\pi$
$278$	12.3621	−	19.8643i	0.741430	−	1.19138i
$279$	0.564403	−	0.0555888i	0.0337899	−	0.00332801i
$280$	−25.9508	−	21.3432i	−1.55086	−	1.27550i
$281$	−14.9338	−	18.1969i	−0.890876	−	1.08554i	−0.995845	−	0.0910603i	$-0.970974\pi$
$281$	−14.9338	−	18.1969i	−0.890876	−	1.08554i	0.104969	−	0.994475i	$-0.466526\pi$
$282$	8.30060	+	14.3888i	0.494293	+	0.856838i
$283$	−16.7066	+	15.1420i	−0.993105	+	0.900098i	−0.994997	−	0.0999004i	$-0.968148\pi$
$283$	−16.7066	+	15.1420i	−0.993105	+	0.900098i	0.00189254	+	0.999998i	$0.499398\pi$
$284$	17.4884	+	5.95025i	1.03775	+	0.353082i
$285$	−4.71396	−	6.35603i	−0.279231	−	0.376499i
$286$	10.3096	−	8.17636i	0.609619	−	0.483478i
$287$	10.7293	+	4.44422i	0.633331	+	0.262334i
$288$	2.78707	−	0.315656i	0.164230	−	0.0186002i
$289$	28.0372	−	11.6134i	1.64925	−	0.683141i
$290$	−10.8478	+	19.5035i	−0.637003	+	1.14528i
$291$	3.43667	−	23.1681i	0.201461	−	1.35814i
$292$	2.74123	+	0.362855i	0.160419	+	0.0212345i
$293$	−0.225987	+	4.60008i	−0.0132023	+	0.268739i	0.983115	+	0.182991i	$0.0585780\pi$
$293$	−0.225987	+	4.60008i	−0.0132023	+	0.268739i	−0.996317	+	0.0857481i	$0.972672\pi$
$294$	3.10242	−	0.407329i	0.180937	−	0.0237559i
$295$	−1.50834	+	15.3144i	−0.0878190	+	0.891641i
$296$	−16.7804	−	11.2380i	−0.975343	−	0.653195i
$297$	−7.76645	+	9.46345i	−0.450655	+	0.549125i
$298$	5.09437	+	0.842927i	0.295109	+	0.0488295i
$299$	8.71547	−	34.7941i	0.504029	−	2.01220i
$300$	17.0925	−	33.2186i	0.986834	−	1.91788i
$301$	11.5245	−	0.566161i	0.664259	−	0.0326330i
$302$	−6.25854	+	9.03589i	−0.360139	+	0.519957i
$303$	−2.04100	−	1.36375i	−0.117252	−	0.0783455i
$304$	4.47425	+	1.94715i	0.256616	+	0.111677i
$305$	−36.7156	+	24.5326i	−2.10233	+	1.40473i
$306$	−4.82440	−	0.0806454i	−0.275792	−	0.00461019i
$307$	9.99954	−	4.72943i	0.570704	−	0.269923i	−0.120343	−	0.992732i	$-0.538400\pi$
$307$	9.99954	−	4.72943i	0.570704	−	0.269923i	0.691047	+	0.722809i	$0.257150\pi$
$308$	−10.5519	+	7.29207i	−0.601249	+	0.415504i
$309$	−3.84095	+	5.17893i	−0.218504	+	0.294619i
$310$	0.214619	+	6.62729i	0.0121895	+	0.376405i
$311$	−18.9737	−	5.75561i	−1.07590	−	0.326370i	−0.297875	−	0.954605i	$-0.596278\pi$
$311$	−18.9737	−	5.75561i	−1.07590	−	0.326370i	−0.778024	+	0.628234i	$0.783778\pi$
$312$	15.1031	+	11.2260i	0.855045	+	0.635545i
$313$	−27.7092	−	14.8109i	−1.56622	−	0.837159i	−0.999916	−	0.0129598i	$-0.995875\pi$
$313$	−27.7092	−	14.8109i	−1.56622	−	0.837159i	−0.566299	−	0.824200i	$-0.691625\pi$
$314$	−6.77747	−	0.446616i	−0.382475	−	0.0252040i
$315$	−1.98439	−	5.54599i	−0.111808	−	0.312481i
$316$	−14.8331	+	13.8731i	−0.834428	+	0.780425i
$317$	6.49469	−	10.8357i	0.364778	−	0.608596i	−0.619547	−	0.784960i	$-0.712684\pi$
$317$	6.49469	−	10.8357i	0.364778	−	0.608596i	0.984325	+	0.176364i	$0.0564336\pi$
$318$	7.70306	−	3.95328i	0.431966	−	0.221689i
$319$	6.02404	+	6.02404i	0.337281	+	0.337281i
$320$	1.53992	+	32.7578i	0.0860839	+	1.83122i
$321$	11.8990	−	11.8990i	0.664140	−	0.664140i
$322$	−10.7074	+	33.2844i	−0.596701	+	1.85487i
$323$	−7.19980	−	4.31539i	−0.400607	−	0.240115i
$324$	−13.2336	−	6.00730i	−0.735199	−	0.333739i
$325$	−46.7269	+	16.7192i	−2.59194	+	0.927412i
$326$	−5.78830	−	6.60498i	−0.320584	−	0.365816i
$327$	−2.59648	+	4.85768i	−0.143586	+	0.268630i
$328$	−3.80725	−	10.6761i	−0.210220	−	0.589489i
$329$	−6.24418	+	20.5843i	−0.344253	+	1.13485i
$330$	−14.8126	−	13.8833i	−0.815406	−	0.764250i
$331$	2.00231	+	1.48501i	0.110057	+	0.0816237i	0.649328	−	0.760508i	$-0.275050\pi$
$331$	2.00231	+	1.48501i	0.110057	+	0.0816237i	−0.539271	+	0.842132i	$0.681300\pi$
$332$	1.38674	−	0.298485i	0.0761073	−	0.0163815i
$333$	−1.51374	−	3.20054i	−0.0829525	−	0.175388i
$334$	−14.5656	−	15.0608i	−0.796993	−	0.824091i
$335$	11.0794	+	16.5815i	0.605332	+	0.905943i
$336$	−13.9707	−	11.8872i	−0.762166	−	0.648499i
$337$	−3.08813	+	4.62171i	−0.168221	+	0.251761i	−0.905996	−	0.423286i	$-0.860877\pi$
$337$	−3.08813	+	4.62171i	−0.168221	+	0.251761i	0.737775	+	0.675047i	$0.235877\pi$
$338$	−1.18175	−	6.50768i	−0.0642785	−	0.353971i
$339$	0.121114	+	2.46533i	0.00657799	+	0.133898i
$340$	4.64976	−	56.2214i	0.252169	−	3.04903i
$341$	2.45534	+	0.615030i	0.132964	+	0.0333058i
$342$	0.498018	+	0.695500i	0.0269297	+	0.0376083i
$343$	−12.5489	−	10.2986i	−0.677579	−	0.556074i
$344$	−7.95467	−	7.97150i	−0.428887	−	0.429794i
$345$	−55.0752	−	5.42444i	−2.96515	−	0.292042i
$346$	−3.03252	+	3.94918i	−0.163029	+	0.212309i
$347$	21.8388	+	1.07287i	1.17237	+	0.0575949i	0.625914	−	0.779892i	$-0.284726\pi$
$347$	21.8388	+	1.07287i	1.17237	+	0.0575949i	0.546457	+	0.837487i	$0.315976\pi$
$348$	−6.09932	+	10.5472i	−0.326958	+	0.565388i
$349$	−6.34846	−	0.941705i	−0.339825	−	0.0504083i	−0.0253631	−	0.999678i	$-0.508074\pi$
$349$	−6.34846	−	0.941705i	−0.339825	−	0.0504083i	−0.314462	+	0.949270i	$0.601824\pi$
$350$	46.5214	−	13.2672i	2.48667	−	0.709160i
$351$	8.90072	+	21.4882i	0.475085	+	1.14696i
$352$	12.1866	+	2.86414i	0.649547	+	0.152659i
$353$	13.1257	−	31.6882i	0.698610	−	1.68659i	−0.0280599	−	0.999606i	$-0.508933\pi$
$353$	13.1257	−	31.6882i	0.698610	−	1.68659i	0.726670	−	0.686987i	$-0.241067\pi$
$354$	−0.963082	+	8.34577i	−0.0511872	+	0.443573i
$355$	−30.4115	+	22.5547i	−1.61408	+	1.19708i
$356$	−1.42112	−	21.9186i	−0.0753192	−	1.16168i
$357$	21.1912	+	23.3809i	1.12156	+	1.23745i
$358$	−0.204873	+	0.763519i	−0.0108279	+	0.0403532i
$359$	10.6694	−	8.75613i	0.563108	−	0.462131i	−0.309262	−	0.950977i	$-0.600082\pi$
$359$	10.6694	−	8.75613i	0.563108	−	0.462131i	0.872370	+	0.488846i	$0.162582\pi$
$360$	−2.71540	+	5.06728i	−0.143114	+	0.267069i
$361$	−1.71646	−	17.4275i	−0.0903401	−	0.917238i
$362$	−6.29253	−	27.0302i	−0.330728	−	1.42068i
$363$	8.28319	−	4.96475i	0.434755	−	0.260582i
$364$	2.76793	+	24.2106i	0.145079	+	1.26898i
$365$	−3.80607	+	4.19935i	−0.199219	+	0.219804i
$366$	−20.2654	+	13.0563i	−1.05929	+	0.682465i
$367$	−5.51278	−	27.7146i	−0.287765	−	1.44669i	−0.806235	−	0.591596i	$-0.798498\pi$
$367$	−5.51278	−	27.7146i	−0.287765	−	1.44669i	0.518470	−	0.855096i	$-0.326502\pi$
$368$	31.1034	−	14.0400i	1.62137	−	0.731884i
$369$	0.387650	−	1.94885i	0.0201803	−	0.101453i
$370$	38.5025	−	15.1994i	2.00165	−	0.790180i
$371$	10.5565	+	3.77716i	0.548064	+	0.196100i
$372$	0.0566798	+	3.61953i	0.00293871	+	0.187664i
$373$	3.96602	+	26.7367i	0.205353	+	1.38437i	0.809321	+	0.587366i	$0.199835\pi$
$373$	3.96602	+	26.7367i	0.205353	+	1.38437i	−0.603969	+	0.797008i	$0.706415\pi$
$374$	−20.1520	−	7.59279i	−1.04204	−	0.392614i
$375$	20.8054	+	38.9242i	1.07439	+	2.01004i
$376$	18.9882	−	8.95620i	0.979240	−	0.461881i
$377$	15.4885	−	4.69838i	0.797697	−	0.241979i
$378$	−7.28012	−	21.4714i	−0.374449	−	1.10437i
$379$	1.50176	−	3.17520i	0.0771400	−	0.163099i	−0.861733	−	0.507361i	$-0.830621\pi$
$379$	1.50176	−	3.17520i	0.0771400	−	0.163099i	0.938873	+	0.344262i	$0.111871\pi$
$380$	−8.49686	+	5.27539i	−0.435880	+	0.270622i
$381$	−0.763290	−	3.04723i	−0.0391045	−	0.156114i
$382$	−9.90628	+	0.808757i	−0.506849	+	0.0413796i
$383$			24.5135i			1.25258i	0.779589	+	0.626292i	$0.215428\pi$
$383$			24.5135i			1.25258i	−0.779589	+	0.626292i	$0.784572\pi$
$384$	0.541674	+	17.8952i	0.0276422	+	0.913212i
$385$		−	26.2893i		−	1.33983i
$386$	−0.0732171	−	0.896819i	−0.00372665	−	0.0456469i
$387$	−0.479693	−	1.91504i	−0.0243842	−	0.0973471i
$388$	−28.8236	−	6.74214i	−1.46330	−	0.342280i
$389$	15.9134	−	33.6460i	0.806840	−	1.70592i	0.103994	−	0.994578i	$-0.466838\pi$
$389$	15.9134	−	33.6460i	0.806840	−	1.70592i	0.702846	−	0.711342i	$-0.251912\pi$
$390$	−36.5278	+	12.3852i	−1.84966	+	0.627147i
$391$	−56.1758	+	17.0408i	−2.84093	+	0.861788i
$392$	−0.189874	−	3.95011i	−0.00959006	−	0.199511i
$393$	−3.80426	−	7.11727i	−0.191900	−	0.359019i
$394$	−4.22634	+	11.2171i	−0.212920	+	0.565111i
$395$	−6.10800	−	41.1768i	−0.307327	−	2.07183i
$396$	1.57591	+	1.52732i	0.0791927	+	0.0767507i
$397$	−12.6956	−	4.54256i	−0.637175	−	0.227985i	−0.00156911	−	0.999999i	$-0.500499\pi$
$397$	−12.6956	−	4.54256i	−0.637175	−	0.227985i	−0.635605	+	0.772014i	$0.719249\pi$
$398$	10.4685	+	26.5185i	0.524741	+	1.32925i
$399$	1.09140	−	5.48682i	0.0546381	−	0.274685i
$400$	−40.0603	−	24.9894i	−2.00301	−	1.24947i
$401$	−3.50513	−	17.6215i	−0.175038	−	0.879976i	−0.964075	−	0.265630i	$-0.914420\pi$
$401$	−3.50513	−	17.6215i	−0.175038	−	0.879976i	0.789037	−	0.614346i	$-0.210580\pi$
$402$	5.89649	+	9.15226i	0.294090	+	0.456473i
$403$	3.22947	−	3.56317i	0.160871	−	0.177494i
$404$	−1.93034	+	2.42870i	−0.0960380	+	0.120832i
$405$	25.5498	−	15.3139i	1.26958	−	0.760956i
$406$	−15.3663	+	3.57721i	−0.762615	+	0.177534i
$407$	−1.54882	−	15.7255i	−0.0767724	−	0.779483i
$408$	3.05112	−	30.6466i	0.151053	−	1.51723i
$409$	−11.4360	+	9.38526i	−0.565472	+	0.464071i	−0.873172	−	0.487413i	$-0.837941\pi$
$409$	−11.4360	+	9.38526i	−0.565472	+	0.464071i	0.307700	+	0.951484i	$0.400441\pi$
$410$	22.4381	+	6.02073i	1.10814	+	0.297343i
$411$	−3.90373	−	4.30710i	−0.192557	−	0.212454i
$412$	6.12305	+	5.37740i	0.301661	+	0.264926i
$413$	−8.73803	+	6.48056i	−0.429970	+	0.318888i
$414$	5.94293	+	0.685800i	0.292079	+	0.0337052i
$415$	−1.11261	+	2.68608i	−0.0546160	+	0.131855i
$416$	15.7131	−	17.8538i	0.770397	−	0.875356i
$417$	10.0187	+	24.1874i	0.490620	+	1.18446i
$418$	1.04705	+	3.67147i	0.0512127	+	0.179578i
$419$	−16.6652	−	2.47204i	−0.814146	−	0.120767i	−0.273343	−	0.961917i	$-0.588130\pi$
$419$	−16.6652	−	2.47204i	−0.814146	−	0.120767i	−0.540803	+	0.841149i	$0.681880\pi$
$420$	36.3232	−	9.70535i	1.77239	−	0.473573i
$421$	24.7196	+	1.21439i	1.20476	+	0.0591859i	0.641518	−	0.767108i	$-0.278305\pi$
$421$	24.7196	+	1.21439i	1.20476	+	0.0591859i	0.563239	+	0.826294i	$0.309555\pi$
$422$	5.62419	+	4.31874i	0.273781	+	0.210233i
$423$	3.66272	+	0.360746i	0.178087	+	0.0175401i
$424$	−4.17696	−	10.1143i	−0.202851	−	0.491193i
$425$	62.7851	+	51.5264i	3.04553	+	2.49940i
$426$	−16.8062	+	12.0342i	−0.814264	+	0.583060i
$427$	−30.2816	−	7.58514i	−1.46543	−	0.367071i
$428$	−13.7480	−	16.2271i	−0.664535	−	0.784366i
$429$	0.722455	+	14.7059i	0.0348805	+	0.710008i
$430$	22.7105	−	4.12405i	1.09520	−	0.198879i
$431$	−19.5024	+	29.1874i	−0.939396	+	1.40591i	−0.0256268	+	0.999672i	$0.508158\pi$
$431$	−19.5024	+	29.1874i	−0.939396	+	1.40591i	−0.913769	+	0.406234i	$0.866842\pi$
$432$	−10.7762	+	19.3267i	−0.518471	+	0.929858i
$433$	5.93251	+	8.87864i	0.285098	+	0.426680i	0.946183	−	0.323631i	$-0.104904\pi$
$433$	5.93251	+	8.87864i	0.285098	+	0.426680i	−0.661085	+	0.750311i	$0.729904\pi$
$434$	−3.36958	+	3.25878i	−0.161745	+	0.156426i
$435$	−10.6770	−	22.5746i	−0.511922	−	1.08237i
$436$	5.84805	+	3.77645i	0.280071	+	0.180859i
$437$	8.35926	+	6.19965i	0.399878	+	0.296569i
$438$	−2.11590	+	2.25753i	−0.101101	+	0.107869i
$439$	−1.79932	+	5.93157i	−0.0858770	+	0.283098i	−0.989352	−	0.145542i	$-0.953507\pi$
$439$	−1.79932	+	5.93157i	−0.0858770	+	0.283098i	0.903475	+	0.428641i	$0.141007\pi$
$440$	−19.0299	+	17.2111i	−0.907214	+	0.820507i
$441$	0.326808	−	0.611415i	0.0155623	−	0.0291150i
$442$	−30.7698	+	26.9652i	−1.46357	+	1.28261i
$443$	−17.8033	+	6.37012i	−0.845860	+	0.302654i	−0.723920	−	0.689884i	$-0.757662\pi$
$443$	−17.8033	+	6.37012i	−0.845860	+	0.302654i	−0.121940	+	0.992537i	$0.538912\pi$
$444$	21.1557	−	7.94543i	1.00400	−	0.377073i
$445$	38.6143	+	23.1445i	1.83049	+	1.09716i
$446$	−33.0066	−	10.6180i	−1.56291	−	0.502779i
$447$	−4.08561	+	4.08561i	−0.193243	+	0.193243i
$448$	−16.4280	+	16.3587i	−0.776148	+	0.772875i
$449$	0.819619	+	0.819619i	0.0386802	+	0.0386802i	0.726182	−	0.687502i	$-0.241293\pi$
$449$	0.819619	+	0.819619i	0.0386802	+	0.0386802i	−0.687502	+	0.726182i	$0.741293\pi$
$450$	−3.77926	−	7.36397i	−0.178156	−	0.347141i
$451$	4.55927	−	7.60668i	0.214687	−	0.358184i
$452$	3.11784	+	0.104266i	0.146651	+	0.00490425i
$453$	−4.14350	−	11.5803i	−0.194679	−	0.544091i
$454$	−1.15704	+	17.5583i	−0.0543026	+	0.824051i
$455$	−44.0484	−	23.5443i	−2.06502	−	1.10378i
$456$	−4.68623	+	2.80209i	−0.219453	+	0.131220i
$457$	−0.235274	−	0.0713695i	−0.0110056	−	0.00333852i	0.284777	−	0.958594i	$-0.408080\pi$
$457$	−0.235274	−	0.0713695i	−0.0110056	−	0.00333852i	−0.295783	+	0.955255i	$0.595580\pi$
$458$	13.6179	−	0.441004i	0.636324	−	0.0206068i
$459$	22.6755	−	30.5744i	1.05840	−	1.42709i
$460$	−12.5697	+	68.8055i	−0.586063	+	3.20807i
$461$	35.5541	−	16.8158i	1.65592	−	0.783191i	0.656330	−	0.754474i	$-0.272108\pi$
$461$	35.5541	−	16.8158i	1.65592	−	0.783191i	0.999588	−	0.0287170i	$-0.00914215\pi$
$462$	0.239881	−	14.3503i	0.0111603	−	0.667635i
$463$	−9.75114	+	6.51550i	−0.453174	+	0.302801i	−0.761130	−	0.648599i	$-0.775355\pi$
$463$	−9.75114	+	6.51550i	−0.453174	+	0.302801i	0.307956	+	0.951401i	$0.400355\pi$
$464$	12.6494	+	8.78117i	0.587234	+	0.407656i
$465$	−6.16916	−	4.12210i	−0.286088	−	0.191158i
$466$	2.07098	+	1.43442i	0.0959362	+	0.0664484i
$467$	1.53914	−	0.0756129i	0.0712227	−	0.00349895i	−0.0134251	−	0.999910i	$-0.504273\pi$
$467$	1.53914	−	0.0756129i	0.0712227	−	0.00349895i	0.0846479	+	0.996411i	$0.473023\pi$
$468$	3.97043	−	1.27264i	0.183533	−	0.0588277i
$469$	−3.42560	+	13.6757i	−0.158179	+	0.631487i
$470$	−7.02444	+	42.4534i	−0.324013	+	1.95823i
$471$	4.82151	−	5.87503i	0.222163	−	0.270707i
$472$	10.4117	+	2.08245i	0.479236	+	0.0958524i
$473$	0.863645	−	8.76874i	0.0397104	−	0.403187i
$474$	−2.95839	−	22.5325i	−0.135883	−	1.03495i
$475$	0.706549	−	14.3821i	0.0324187	−	0.659897i
$476$	31.6571	−	24.2560i	1.45100	−	1.11177i
$477$	0.281479	−	1.89758i	0.0128880	−	0.0868842i
$478$	−15.1575	−	8.43058i	−0.693290	−	0.385606i
$479$	−7.03657	+	2.91464i	−0.321509	+	0.133173i	−0.537600	−	0.843200i	$-0.680669\pi$
$479$	−7.03657	+	2.91464i	−0.321509	+	0.133173i	0.216091	+	0.976373i	$0.430669\pi$
$480$	−30.8055	−	19.9391i	−1.40607	−	0.910093i
$481$	−27.7355	−	11.4884i	−1.26463	−	0.523828i
$482$	13.6226	+	17.1768i	0.620495	+	0.782383i
$483$	−23.3060	−	31.4245i	−1.06046	−	1.42987i
$484$	−5.39053	−	10.9504i	−0.245024	−	0.497743i
$485$	44.9552	−	40.7450i	2.04131	−	1.85014i
$486$	−6.24369	+	3.60187i	−0.283220	+	0.163384i
$487$	−20.1728	−	24.5806i	−0.914115	−	1.11385i	−0.993134	−	0.116979i	$-0.962679\pi$
$487$	−20.1728	−	24.5806i	−0.914115	−	1.11385i	0.0790192	−	0.996873i	$-0.474821\pi$
$488$	14.3342	+	26.8856i	0.648877	+	1.21705i
$489$	9.77984	−	0.963230i	0.442260	−	0.0435588i
$490$	6.88178	+	4.28273i	0.310887	+	0.193474i
$491$	0.115027	+	0.191910i	0.00519108	+	0.00866080i	0.860313	−	0.509766i	$-0.170268\pi$
$491$	0.115027	+	0.191910i	0.00519108	+	0.00866080i	−0.855122	+	0.518427i	$0.826518\pi$
$492$	12.1931	+	3.49122i	0.549707	+	0.157396i
$493$	−19.6272	−	17.7890i	−0.883964	−	0.801179i
$494$	7.08937	+	1.53377i	0.318966	+	0.0690076i
$495$	−4.41165	+	0.877532i	−0.198289	+	0.0394421i
$496$	4.56491	+	0.305659i	0.204971	+	0.0137245i
$497$	−26.2526	−	5.22197i	−1.17759	−	0.234237i
$498$	−0.631840	+	1.45607i	−0.0283134	+	0.0652481i
$499$	11.6696	−	32.6145i	0.522405	−	1.46002i	−0.333430	−	0.942775i	$-0.608206\pi$
$499$	11.6696	−	32.6145i	0.522405	−	1.46002i	0.855835	−	0.517249i	$-0.173044\pi$
$500$	51.1947	−	22.1509i	2.28950	−	0.990619i
$501$	23.1907	−	3.44002i	1.03609	−	0.153689i
$502$	9.51323	+	21.0158i	0.424596	+	0.937982i
$503$	24.7226	−	13.2145i	1.10232	−	0.589205i	0.183162	−	0.983083i	$-0.441367\pi$
$503$	24.7226	−	13.2145i	1.10232	−	0.589205i	0.919163	+	0.393878i	$0.128867\pi$
$504$	−3.94348	+	0.983363i	−0.175656	+	0.0438025i
$505$	−1.84584	−	6.08492i	−0.0821388	−	0.270775i
$506$	23.9425	+	11.8176i	1.06437	+	0.525357i
$507$	6.69038	+	3.16431i	0.297130	+	0.140532i
$508$	−3.91767	+	0.643977i	−0.173819	+	0.0285718i
$509$	−38.3016	+	9.59406i	−1.69769	+	0.425249i	−0.966446	−	0.256868i	$-0.917309\pi$
$509$	−38.3016	+	9.59406i	−1.69769	+	0.425249i	−0.731243	+	0.682117i	$0.761059\pi$
$510$	48.1198	+	40.8557i	2.13078	+	1.80912i
$511$	−4.00664			−0.177244
$512$	22.5965	+	1.18190i	0.998635	+	0.0522329i
$513$	−6.74847			−0.297952
$514$	−17.4664	−	14.8297i	−0.770408	−	0.654109i
$515$	−16.2021	+	4.05841i	−0.713949	+	0.178835i
$516$	12.4344	−	2.04393i	0.547392	−	0.0899788i
$517$	14.8492	+	7.02315i	0.653067	+	0.308878i
$518$	26.2411	+	12.9522i	1.15297	+	0.569085i
$519$	−1.61733	−	5.33161i	−0.0709928	−	0.234032i
$520$	11.7947	+	47.2991i	0.517232	+	2.07420i
$521$	−33.8910	+	18.1151i	−1.48479	+	0.793638i	−0.996855	−	0.0792412i	$-0.974750\pi$
$521$	−33.8910	+	18.1151i	−1.48479	+	0.793638i	−0.487937	+	0.872879i	$0.662250\pi$
$522$	1.11322	+	2.45923i	0.0487244	+	0.107638i
$523$	18.1509	−	2.69244i	0.793685	−	0.117732i	0.262438	−	0.964949i	$-0.415474\pi$
$523$	18.1509	−	2.69244i	0.793685	−	0.117732i	0.531247	+	0.847217i	$0.321724\pi$
$524$	−9.36092	+	4.05028i	−0.408934	+	0.176937i
$525$	−18.2363	+	50.9669i	−0.795895	+	2.22438i
$526$	−16.1272	+	37.1650i	−0.703178	+	1.62047i
$527$	−7.71908	−	1.53542i	−0.336248	−	0.0668840i
$528$	−10.5447	+	9.22120i	−0.458899	+	0.401301i
$529$	48.8272	−	9.71233i	2.12292	−	0.422275i
$530$	21.9215	+	4.74268i	0.952211	+	0.206009i
$531$	1.37919	+	1.25002i	0.0598517	+	0.0542464i
$532$	−6.79728	−	1.94625i	−0.294700	−	0.0843805i
$533$	−8.66196	−	14.4516i	−0.375191	−	0.625968i
$534$	20.8668	+	12.9860i	0.902995	+	0.561959i
$535$	43.3814	−	4.27270i	1.87554	−	0.184725i
$536$	12.1421	−	6.47358i	0.524457	−	0.279616i
$537$	−0.561167	−	0.683784i	−0.0242161	−	0.0295074i
$538$	−9.81728	+	5.66340i	−0.423253	+	0.244166i
$539$	2.29264	−	2.07793i	0.0987511	−	0.0895028i
$540$	−20.0310	−	40.6910i	−0.861996	−	1.75106i
$541$	−16.2434	−	21.9016i	−0.698356	−	0.941624i	0.301574	−	0.953443i	$-0.402488\pi$
$541$	−16.2434	−	21.9016i	−0.698356	−	0.941624i	−0.999930	+	0.0118184i	$0.996238\pi$
$542$	11.3353	+	14.2927i	0.486891	+	0.613923i
$543$	28.6907	+	11.8841i	1.23124	+	0.509995i
$544$	−38.2833	−	7.03555i	−1.64138	−	0.301647i
$545$	−13.1822	+	5.46024i	−0.564663	+	0.233891i
$546$	−23.8294	−	13.2538i	−1.01980	−	0.567212i
$547$	−1.25832	+	8.48290i	−0.0538019	+	0.362703i	0.945509	+	0.325595i	$0.105565\pi$
$547$	−1.25832	+	8.48290i	−0.0538019	+	0.362703i	−0.999311	+	0.0371079i	$0.988185\pi$
$548$	−5.83171	+	4.46830i	−0.249118	+	0.190876i
$549$	−0.262082	+	5.33479i	−0.0111854	+	0.227683i
$550$	−4.80900	−	36.6277i	−0.205056	−	1.56181i
$551$	−0.460305	+	4.67356i	−0.0196097	+	0.199100i
$552$	−7.48909	+	37.4434i	−0.318757	+	1.59370i
$553$	18.6692	−	22.7485i	0.793895	−	0.967364i
$554$	−2.06794	+	12.4979i	−0.0878584	+	0.530987i
$555$	−11.2545	+	44.9303i	−0.477726	+	1.90719i
$556$	31.5091	−	10.0996i	1.33628	−	0.428317i
$557$	26.7320	−	1.31326i	1.13267	−	0.0556445i	0.525918	−	0.850535i	$-0.323722\pi$
$557$	26.7320	−	1.31326i	1.13267	−	0.0556445i	0.606752	+	0.794891i	$0.292472\pi$
$558$	0.659338	+	0.456678i	0.0279120	+	0.0193327i
$559$	−13.9188	−	9.30022i	−0.588701	−	0.393358i
$560$	−8.44064	−	46.7622i	−0.356682	−	1.97606i
$561$	20.0358	−	13.3875i	0.845912	−	0.565220i
$562$	0.556420	−	33.2864i	0.0234712	−	1.40410i
$563$	30.6751	−	14.5082i	1.29280	−	0.611449i	0.347510	−	0.937676i	$-0.387027\pi$
$563$	30.6751	−	14.5082i	1.29280	−	0.611449i	0.945291	+	0.326227i	$0.105777\pi$
$564$	−4.22173	+	23.1095i	−0.177767	+	0.973086i
$565$	−3.80889	+	5.13569i	−0.160241	+	0.216060i
$566$	−31.8703	+	1.03209i	−1.33961	+	0.0433820i
$567$	20.1516	+	6.11293i	0.846289	+	0.256719i
$568$	13.4071	+	22.4221i	0.562549	+	0.940809i
$569$	30.8453	+	16.4872i	1.29310	+	0.691178i	0.967150	−	0.254208i	$-0.0818146\pi$
$569$	30.8453	+	16.4872i	1.29310	+	0.691178i	0.325954	+	0.945386i	$0.394315\pi$
$570$	0.735866	−	11.1669i	0.0308220	−	0.467730i
$571$	4.77873	+	13.3557i	0.199984	+	0.558917i	0.999107	−	0.0422502i	$-0.0134527\pi$
$571$	4.77873	+	13.3557i	0.199984	+	0.558917i	−0.799123	+	0.601167i	$0.794703\pi$
$572$	18.5982	+	0.621956i	0.777631	+	0.0260053i
$573$	5.71767	−	9.53935i	0.238859	−	0.398512i
$574$	7.49891	+	14.6118i	0.312998	+	0.609884i
$575$	−71.2075	−	71.2075i	−2.96956	−	2.96956i
$576$	3.29354	+	2.21075i	0.137231	+	0.0921147i
$577$	−13.2440	+	13.2440i	−0.551356	+	0.551356i	−0.926832	−	0.375476i	$-0.877479\pi$
$577$	−13.2440	+	13.2440i	−0.551356	+	0.551356i	0.375476	+	0.926832i	$0.377479\pi$
$578$	40.8556	+	13.1430i	1.69937	+	0.546676i
$579$	0.863602	+	0.517623i	0.0358901	+	0.0215117i
$580$	−29.5463	+	11.0967i	−1.22684	+	0.460765i
$581$	−1.93523	+	0.692437i	−0.0802870	+	0.0287271i
$582$	24.9110	−	21.8309i	1.03260	−	0.904919i
$583$	4.03602	−	7.55086i	0.167155	−	0.312725i
$584$	2.62307	+	2.90027i	0.108544	+	0.120014i
$585$	−2.48069	+	8.17774i	−0.102564	+	0.338108i
$586$	−4.45414	+	4.75228i	−0.183999	+	0.196315i
$587$	−16.7603	−	12.4303i	−0.691771	−	0.513052i	0.191750	−	0.981444i	$-0.438584\pi$
$587$	−16.7603	−	12.4303i	−0.691771	−	0.513052i	−0.883521	+	0.468392i	$0.844834\pi$
$588$	3.71741	+	2.40056i	0.153303	+	0.0989975i
$589$	0.596567	+	1.26133i	0.0245811	+	0.0519724i
$590$	−15.6436	+	15.1292i	−0.644036	+	0.622859i
$591$	−7.45181	−	11.1524i	−0.306527	−	0.458750i
$592$	−7.80393	−	27.4745i	−0.320739	−	1.12920i
$593$	−0.335104	+	0.501519i	−0.0137611	+	0.0205949i	−0.838286	−	0.545230i	$-0.816442\pi$
$593$	−0.335104	+	0.501519i	−0.0137611	+	0.0205949i	0.824525	+	0.565825i	$0.191442\pi$
$594$	−17.0347	+	3.09337i	−0.698942	+	0.126922i
$595$	4.01089	+	81.6434i	0.164430	+	3.34705i
$596$	4.72047	+	5.57167i	0.193358	+	0.228225i
$597$	−30.9456	−	7.75147i	−1.26652	−	0.317247i
$598$	41.2433	−	29.5325i	1.68656	−	1.20768i
$599$	27.0687	+	22.2147i	1.10600	+	0.907667i	0.996270	−	0.0862949i	$-0.0275027\pi$
$599$	27.0687	+	22.2147i	1.10600	+	0.907667i	0.109726	+	0.993962i	$0.465003\pi$
$600$	48.8320	−	20.1665i	1.99356	−	0.823293i
$601$	11.9168	+	1.17371i	0.486098	+	0.0478765i	0.338098	−	0.941111i	$-0.390216\pi$
$601$	11.9168	+	1.17371i	0.486098	+	0.0478765i	0.148000	+	0.988987i	$0.452716\pi$
$602$	12.9422	+	9.93815i	0.527485	+	0.405049i
$603$	2.40930	+	0.118361i	0.0981141	+	0.00482004i
$604$	−15.0177	+	4.01265i	−0.611063	+	0.163273i
$605$	24.7454	+	3.67064i	1.00604	+	0.149233i
$606$	−0.952047	−	3.33835i	−0.0386743	−	0.135611i
$607$	−7.28590	−	17.5897i	−0.295726	−	0.713945i	−0.999992	−	0.00400890i	$-0.998724\pi$
$607$	−7.28590	−	17.5897i	−0.295726	−	0.713945i	0.704266	−	0.709936i	$-0.251276\pi$
$608$	3.04123	+	6.19448i	0.123338	+	0.251219i
$609$	6.75592	−	16.3102i	0.273764	−	0.660924i
$610$	−62.0364	−	7.15885i	−2.51178	−	0.289853i
$611$	25.0662	−	18.5904i	1.01407	−	0.752086i
$612$	−5.12715	−	4.50278i	−0.207253	−	0.182014i
$613$	2.31219	+	2.55111i	0.0933884	+	0.103038i	0.785852	−	0.618415i	$-0.212225\pi$
$613$	2.31219	+	2.55111i	0.0933884	+	0.103038i	−0.692464	+	0.721453i	$0.743475\pi$
$614$	15.1090	+	4.05414i	0.609748	+	0.163612i
$615$	−20.0948	+	16.4914i	−0.810302	+	0.664997i
$616$	−18.0500	−	1.79703i	−0.727256	−	0.0724043i
$617$	−0.996842	−	10.1211i	−0.0401313	−	0.407460i	−0.994174	−	0.107789i	$-0.965623\pi$
$617$	−0.996842	−	10.1211i	−0.0401313	−	0.407460i	0.954042	−	0.299671i	$-0.0968771\pi$
$618$	−8.88110	+	2.06748i	−0.357250	+	0.0831664i
$619$	−9.18977	+	5.50814i	−0.369368	+	0.221391i	−0.686728	−	0.726914i	$-0.740954\pi$
$619$	−9.18977	+	5.50814i	−0.369368	+	0.221391i	0.317360	+	0.948305i	$0.397204\pi$
$620$	−5.83468	+	7.34102i	−0.234326	+	0.294822i
$621$	−31.6945	+	34.9695i	−1.27186	+	1.40328i
$622$	−15.1865	−	23.5717i	−0.608922	−	0.945141i
$623$	6.20901	+	31.2148i	0.248759	+	1.25059i
$624$	6.00667	+	25.9263i	0.240459	+	1.03788i
$625$	−10.7908	+	54.2489i	−0.431631	+	2.16996i
$626$	−16.3154	−	41.3295i	−0.652095	−	1.65186i
$627$	−4.02232	−	1.43921i	−0.160636	−	0.0574764i
$628$	−6.89768	−	6.68499i	−0.275248	−	0.266760i
$629$	7.20919	+	48.6004i	0.287449	+	1.93783i
$630$	2.93704	−	7.79521i	0.117015	−	0.310569i
$631$	−17.3647	−	32.4871i	−0.691278	−	1.29329i	−0.945335	−	0.326101i	$-0.894265\pi$
$631$	−17.3647	−	32.4871i	−0.691278	−	1.29329i	0.254056	−	0.967189i	$-0.418235\pi$
$632$	−28.6892	+	1.37903i	−1.14119	+	0.0548549i
$633$	−7.59297	+	2.30330i	−0.301794	+	0.0915481i
$634$	16.9197	−	5.73683i	0.671968	−	0.227839i
$635$	3.47924	−	7.35623i	0.138069	−	0.291923i
$636$	11.9228	+	2.78886i	0.472770	+	0.110586i
$637$	−1.42836	−	5.70235i	−0.0565938	−	0.225935i
$638$	0.980353	+	12.0081i	0.0388126	+	0.475406i
$639$			4.57981i			0.181174i
$640$	−28.3236	+	36.7242i	−1.11959	+	1.45165i
$641$			7.07226i			0.279338i	0.990198	+	0.139669i	$0.0446038\pi$
$641$			7.07226i			0.279338i	−0.990198	+	0.139669i	$0.955396\pi$
$642$	23.7192	−	1.93645i	0.936121	−	0.0764257i
$643$	9.78575	+	39.0669i	0.385912	+	1.54065i	0.782499	+	0.622651i	$0.213944\pi$
$643$	9.78575	+	39.0669i	0.385912	+	1.54065i	−0.396587	+	0.917997i	$0.629806\pi$
$644$	−42.0089	+	26.0818i	−1.65538	+	1.02777i
$645$	−11.0428	+	23.3480i	−0.434810	+	0.919328i
$646$	−3.81183	−	11.2423i	−0.149975	−	0.442322i
$647$	25.3354	−	7.68541i	0.996038	−	0.302145i	0.250143	−	0.968209i	$-0.419522\pi$
$647$	25.3354	−	7.68541i	0.996038	−	0.302145i	0.745895	+	0.666064i	$0.232022\pi$
$648$	−8.76796	−	18.5891i	−0.344438	−	0.730248i
$649$	3.91617	+	7.32663i	0.153723	+	0.287595i
$650$	−65.6774	−	24.7456i	−2.57608	−	0.970604i
$651$	−0.769641	−	5.18850i	−0.0301646	−	0.203353i
$652$	−0.194469	−	12.4186i	−0.00761599	−	0.486351i
$653$	−16.6605	−	5.96122i	−0.651975	−	0.233280i	−0.00993400	−	0.999951i	$-0.503162\pi$
$653$	−16.6605	−	5.96122i	−0.651975	−	0.233280i	−0.642041	+	0.766670i	$0.721912\pi$
$654$	−7.24545	+	2.86024i	−0.283319	+	0.111844i
$655$	4.07843	−	20.5036i	0.159357	−	0.801143i
$656$	5.66756	−	14.9943i	0.221281	−	0.585427i
$657$	0.133741	+	0.672362i	0.00521774	+	0.0262313i
$658$	−25.5726	+	16.4756i	−0.996925	+	0.642286i
$659$	−24.9084	+	27.4822i	−0.970293	+	1.07055i	0.0271892	+	0.999630i	$0.491344\pi$
$659$	−24.9084	+	27.4822i	−0.970293	+	1.07055i	−0.997482	+	0.0709227i	$0.977406\pi$
$660$	−3.26120	−	28.5251i	−0.126942	−	1.11034i
$661$	−35.3670	+	21.1981i	−1.37562	+	0.824512i	−0.994967	−	0.100207i	$-0.968049\pi$
$661$	−35.3670	+	21.1981i	−1.37562	+	0.824512i	−0.380649	+	0.924720i	$0.624299\pi$
$662$	0.799344	+	3.43366i	0.0310674	+	0.133453i
$663$	−4.48728	−	45.5601i	−0.174272	−	1.76941i
$664$	1.76819	+	0.947520i	0.0686191	+	0.0367709i
$665$	11.2023	−	9.19345i	0.434405	−	0.356507i
$666$	1.29760	−	4.83590i	0.0502810	−	0.187387i
$667$	22.0558	+	24.3348i	0.854003	+	0.942247i
$668$	−1.91711	−	29.5685i	−0.0741750	−	1.14404i
$669$	31.1622	−	23.1115i	1.20480	−	0.893542i
$670$	−3.23308	+	28.0169i	−0.124905	+	1.08239i
$671$	−9.12266	+	22.0240i	−0.352176	+	0.850229i
$672$	−4.18072	−	25.6026i	−0.161275	−	0.987643i
$673$	8.93783	+	21.5778i	0.344528	+	0.831764i	0.997246	+	0.0741634i	$0.0236286\pi$
$673$	8.93783	+	21.5778i	0.344528	+	0.831764i	−0.652718	+	0.757601i	$0.726371\pi$
$674$	−7.55948	+	2.15585i	−0.291180	+	0.0830401i
$675$	64.5922	+	9.58135i	2.48616	+	0.368786i
$676$	4.68259	−	8.09730i	0.180099	−	0.311435i
$677$	25.9348	+	1.27409i	0.996754	+	0.0489674i	0.540900	−	0.841087i	$-0.318084\pi$
$677$	25.9348	+	1.27409i	0.996754	+	0.0489674i	0.455854	+	0.890054i	$0.349334\pi$
$678$	−2.12598	+	2.76861i	−0.0816477	+	0.106328i
$679$	42.6857	+	4.20418i	1.63813	+	0.161341i
$680$	56.4729	−	56.3537i	2.16564	−	2.16107i
$681$	−15.2203	−	12.4910i	−0.583245	−	0.478657i
$682$	2.08404	+	2.91044i	0.0798021	+	0.111447i
$683$	−20.0834	−	5.03062i	−0.768469	−	0.192491i	−0.161129	−	0.986933i	$-0.551513\pi$
$683$	−20.0834	−	5.03062i	−0.768469	−	0.192491i	−0.607340	+	0.794442i	$0.707763\pi$
$684$	−0.0997108	+	1.20563i	−0.00381254	+	0.0460984i
$685$	−0.738864	−	15.0399i	−0.0282305	−	0.574646i
$686$	−4.10194	−	22.5887i	−0.156613	−	0.862441i
$687$	−8.47020	+	12.6766i	−0.323158	+	0.483641i
$688$	−1.27915	−	15.8747i	−0.0487669	−	0.605218i
$689$	−9.03705	−	13.5249i	−0.344284	−	0.515258i
$690$	−54.4090	−	56.2590i	−2.07132	−	2.14174i
$691$	−15.8627	−	33.5388i	−0.603445	−	1.27588i	−0.942215	−	0.335008i	$-0.891261\pi$
$691$	−15.8627	−	33.5388i	−0.603445	−	1.27588i	0.338770	−	0.940869i	$-0.389989\pi$
$692$	−6.88396	+	1.48172i	−0.261689	+	0.0563265i
$693$	−2.55413	−	1.89427i	−0.0970235	−	0.0719575i
$694$	22.5614	+	21.1460i	0.856420	+	0.802691i
$695$	−19.6866	+	64.8980i	−0.746755	+	2.46172i
$696$	−16.2294	+	5.78763i	−0.615173	+	0.219380i
$697$	−12.9986	+	24.3187i	−0.492358	+	0.921137i
$698$	−5.98203	−	6.82604i	−0.226423	−	0.258370i
$699$	−2.65415	+	0.949668i	−0.100389	+	0.0359198i
$700$	62.2962	+	28.2789i	2.35457	+	1.06884i
$701$	18.2788	+	10.9559i	0.690381	+	0.413799i	0.815823	−	0.578302i	$-0.196285\pi$
$701$	18.2788	+	10.9559i	0.690381	+	0.413799i	−0.125441	+	0.992101i	$0.540035\pi$
$702$	−10.0730	+	31.3124i	−0.380182	+	1.18181i
$703$	6.15923	−	6.15923i	0.232300	−	0.232300i
$704$	10.5162	+	14.2422i	0.396344	+	0.536775i
$705$	−34.0470	−	34.0470i	−1.28228	−	1.28228i
$706$	43.1549	−	22.1475i	1.62415	−	0.833531i
$707$	2.31104	−	3.85574i	0.0869158	−	0.145010i
$708$	−8.67725	+	8.11567i	−0.326111	+	0.305006i
$709$	−6.55132	−	18.3097i	−0.246040	−	0.687636i	−0.999544	−	0.0301927i	$-0.990388\pi$
$709$	−6.55132	−	18.3097i	−0.246040	−	0.687636i	0.753504	−	0.657443i	$-0.228362\pi$
$710$	−53.4299	−	3.52088i	−2.00519	−	0.132136i
$711$	−4.44064	−	2.37357i	−0.166537	−	0.0890158i
$712$	18.5304	−	24.9302i	0.694455	−	0.934299i
$713$	9.33783	+	2.83260i	0.349705	+	0.106082i
$714$	1.44441	+	44.6025i	0.0540557	+	1.66920i
$715$	−22.7204	+	30.6349i	−0.849695	+	1.14568i
$716$	−0.919723	+	0.635592i	−0.0343717	+	0.0237532i
$717$	17.5443	−	8.29785i	0.655205	−	0.309889i
$718$	19.5168	+	0.326245i	0.728359	+	0.0121754i
$719$	−4.64072	+	3.10083i	−0.173070	+	0.115642i	−0.639088	−	0.769134i	$-0.720688\pi$
$719$	−4.64072	+	3.10083i	−0.173070	+	0.115642i	0.466018	+	0.884775i	$0.345688\pi$
$720$	−7.56550	+	2.97735i	−0.281950	+	0.110959i
$721$	−9.81793	−	6.56013i	−0.365639	−	0.244312i
$722$	14.1012	−	20.3589i	0.524793	−	0.757681i
$723$	−24.5015	+	1.20368i	−0.911222	+	0.0447655i
$724$	17.9574	−	34.8997i	0.667383	−	1.29704i
$725$	11.0412	−	44.0789i	0.410059	−	1.63705i
$726$	13.4740	+	2.22945i	0.500068	+	0.0827425i
$727$	12.6872	−	15.4594i	0.470544	−	0.573359i	−0.482614	−	0.875833i	$-0.660313\pi$
$727$	12.6872	−	15.4594i	0.470544	−	0.573359i	0.953158	+	0.302474i	$0.0978126\pi$
$728$	−19.1763	+	28.6339i	−0.710722	+	1.06124i
$729$	2.92733	−	29.7217i	0.108420	−	1.10080i
$730$	−7.94687	+	1.04338i	−0.294127	+	0.0386172i
$731$	−1.34430	+	27.3638i	−0.0497206	+	1.01209i
$732$	−33.7979	−	4.47379i	−1.24920	−	0.165356i
$733$	3.39708	−	22.9013i	0.125474	−	0.845877i	−0.831463	−	0.555581i	$-0.812496\pi$
$733$	3.39708	−	22.9013i	0.125474	−	0.845877i	0.956937	−	0.290297i	$-0.0937539\pi$
$734$	19.4245	−	34.9238i	0.716972	−	1.28906i
$735$	−8.37946	+	3.47089i	−0.309081	+	0.128026i
$736$	46.3821	+	13.3335i	1.70967	+	0.491479i
$737$	9.94648	+	4.11997i	0.366383	+	0.151761i
$738$	2.20172	−	1.74614i	0.0810464	−	0.0642765i
$739$	−16.5913	−	22.3707i	−0.610319	−	0.822920i	0.384654	−	0.923061i	$-0.374321\pi$
$739$	−16.5913	−	22.3707i	−0.610319	−	0.822920i	−0.994973	+	0.100141i	$0.968071\pi$
$740$	55.4201	+	18.8561i	2.03728	+	0.693165i
$741$	−6.01376	+	5.45056i	−0.220921	+	0.200231i
$742$	7.92315	+	13.7345i	0.290868	+	0.504208i
$743$	31.3450	+	38.1940i	1.14994	+	1.40120i	0.901624	+	0.432522i	$0.142376\pi$
$743$	31.3450	+	38.1940i	1.14994	+	1.40120i	0.248313	+	0.968680i	$0.420124\pi$
$744$	−3.25190	+	3.95393i	−0.119220	+	0.144958i
$745$	−14.8953	+	1.46706i	−0.545721	+	0.0537488i
$746$	−20.1969	+	32.4538i	−0.739461	+	1.18822i
$747$	0.180797	+	0.301641i	0.00661501	+	0.0110365i
$748$	−14.7752	−	26.6309i	−0.540235	−	0.973721i
$749$	22.8338	+	20.6953i	0.834329	+	0.756192i
$750$	−13.1985	+	61.0060i	−0.481941	+	2.22762i
$751$	−12.3629	+	2.45913i	−0.451128	+	0.0897349i	−0.415425	−	0.909628i	$-0.636367\pi$
$751$	−12.3629	+	2.45913i	−0.451128	+	0.0897349i	−0.0357030	+	0.999362i	$0.511367\pi$
$752$	28.6680	+	7.72487i	1.04541	+	0.281697i
$753$	−25.3171	−	5.03588i	−0.922606	−	0.183518i
$754$	20.9979	+	9.11171i	0.764699	+	0.331829i
$755$	10.7335	−	29.9981i	0.390632	−	1.09174i
$756$	11.8047	−	29.8109i	0.429333	−	1.08421i
$757$	−16.8218	+	2.49528i	−0.611399	+	0.0906925i	−0.445247	−	0.895408i	$-0.646884\pi$
$757$	−16.8218	+	2.49528i	−0.611399	+	0.0906925i	−0.166152	+	0.986100i	$0.553134\pi$
$758$	4.52528	−	2.04846i	0.164365	−	0.0744032i
$759$	−26.3487	+	14.0837i	−0.956398	+	0.511206i
$760$	−13.9887	−	2.09014i	−0.507424	−	0.0758172i
$761$	3.99229	+	13.1608i	0.144720	+	0.477079i	0.999093	−	0.0425818i	$-0.0135583\pi$
$761$	3.99229	+	13.1608i	0.144720	+	0.477079i	−0.854373	+	0.519661i	$0.826058\pi$
$762$	1.96630	−	3.98372i	0.0712315	−	0.144315i
$763$	−9.11851	−	4.31273i	−0.330112	−	0.156131i
$764$	−11.4198	−	8.19547i	−0.413153	−	0.296502i
$765$	13.5668	−	3.39832i	0.490510	−	0.122866i
$766$	−22.4376	+	26.4269i	−0.810703	+	0.954843i
$767$	15.7832			0.569899
$768$	−15.7958	+	19.7878i	−0.569982	+	0.714032i
$769$	−10.2624			−0.370070			−0.185035	−	0.982732i	$-0.559240\pi$
$769$	−10.2624			−0.370070			−0.185035	+	0.982732i	$0.559240\pi$
$770$	24.0630	−	28.3413i	0.867169	−	1.02135i
$771$	24.8702	−	6.22965i	0.895677	−	0.224355i
$772$	0.741939	−	1.03384i	0.0267030	−	0.0372086i
$773$	−18.9266	−	8.95161i	−0.680742	−	0.321967i	0.0557195	−	0.998446i	$-0.482255\pi$
$773$	−18.9266	−	8.95161i	−0.680742	−	0.321967i	−0.736461	+	0.676479i	$0.763505\pi$
$774$	1.23573	−	2.50359i	0.0444174	−	0.0899897i
$775$	−3.91915	−	12.9197i	−0.140780	−	0.464090i
$776$	−24.9023	−	33.6511i	−0.893939	−	1.20800i
$777$	−28.8783	+	15.4358i	−1.03600	+	0.553756i
$778$	47.9521	−	21.7065i	1.71917	−	0.778215i
$779$	4.83571	−	0.717309i	0.173257	−	0.0257003i
$780$	−50.7152	−	20.0825i	−1.81590	−	0.719069i
$781$	−6.88614	+	19.2455i	−0.246405	+	0.688657i
$782$	−76.1582	−	33.0477i	−2.72341	−	1.18178i
$783$	−20.8871	−	4.15470i	−0.746443	−	0.148477i
$784$	3.41090	−	4.43223i	0.121818	−	0.158294i
$785$	19.3095	−	3.84090i	0.689187	−	0.137088i
$786$	2.41334	−	11.1549i	0.0860809	−	0.397882i
$787$	−24.3950	−	22.1103i	−0.869587	−	0.788148i	0.108987	−	0.994043i	$-0.465239\pi$
$787$	−24.3950	−	22.1103i	−0.869587	−	0.788148i	−0.978574	+	0.205895i	$0.933989\pi$
$788$	−14.8234	+	8.22424i	−0.528062	+	0.292977i
$789$	−23.3057	−	38.8833i	−0.829706	−	1.38428i
$790$	31.1049	−	49.9816i	1.10666	−	1.77826i
$791$	−4.49845	+	0.443059i	−0.159947	+	0.0157534i
$792$	0.300944	+	3.08899i	0.0106936	+	0.109762i
$793$	28.7317	+	35.0097i	1.02029	+	1.24323i
$794$	−9.52869	−	16.5176i	−0.338160	−	0.586188i
$795$	−18.5956	+	16.8541i	−0.659518	+	0.597752i
$796$	−12.9871	+	38.1704i	−0.460315	+	1.35291i
$797$	33.1205	+	44.6578i	1.17319	+	1.58186i	0.726490	+	0.687177i	$0.241150\pi$
$797$	33.1205	+	44.6578i	1.17319	+	1.58186i	0.446699	+	0.894685i	$0.352600\pi$
$798$	6.19875	−	4.91612i	0.219433	−	0.174029i
$799$	−47.1869	−	19.5454i	−1.66935	−	0.691468i
$800$	−20.3140	−	63.6076i	−0.718208	−	2.24887i
$801$	5.03096	−	2.08389i	0.177760	−	0.0736306i
$802$	12.3505	−	22.2052i	0.436110	−	0.784094i
$803$	−0.448942	+	3.02652i	−0.0158428	+	0.106804i
$804$	−2.02045	+	15.2638i	−0.0712558	+	0.538312i
$805$	4.97290	−	101.226i	0.175272	−	3.56774i
$806$	6.74296	−	0.885312i	0.237511	−	0.0311838i
$807$	1.24305	−	12.6209i	0.0437576	−	0.444278i
$808$	−4.30403	+	0.851399i	−0.151415	+	0.0299521i
$809$	−0.217814	+	0.265408i	−0.00765794	+	0.00933123i	−0.776825	−	0.629716i	$-0.783171\pi$
$809$	−0.217814	+	0.265408i	−0.00765794	+	0.00933123i	0.769167	+	0.639047i	$0.220671\pi$
$810$	41.5611	+	6.87680i	1.46031	+	0.241626i
$811$	10.3792	−	41.4363i	0.364465	−	1.45502i	−0.459396	−	0.888232i	$-0.651934\pi$
$811$	10.3792	−	41.4363i	0.364465	−	1.45502i	0.823860	−	0.566793i	$-0.191816\pi$
$812$	−19.8399	−	10.2085i	−0.696245	−	0.358250i
$813$	−20.3875	+	1.00157i	−0.715021	+	0.0351267i
$814$	12.7240	−	18.3706i	0.445977	−	0.643888i
$815$	21.1664	+	14.1430i	0.741428	+	0.495406i
$816$	31.3405	−	30.2459i	1.09714	−	1.05882i
$817$	4.03851	−	2.69844i	0.141289	−	0.0944066i
$818$	−20.9190	−	0.349686i	−0.731417	−	0.0122265i
$819$	−5.46135	+	2.58303i	−0.190835	+	0.0902583i
$820$	18.6786	+	27.0286i	0.652285	+	0.943878i
$821$	−12.5733	+	16.9532i	−0.438813	+	0.591671i	−0.966149	−	0.257986i	$-0.916941\pi$
$821$	−12.5733	+	16.9532i	−0.438813	+	0.591671i	0.527336	+	0.849657i	$0.323191\pi$
$822$	−0.266082	−	8.21643i	−0.00928066	−	0.286581i
$823$	27.2916	+	8.27881i	0.951324	+	0.288581i	0.727546	−	0.686059i	$-0.240661\pi$
$823$	27.2916	+	8.27881i	0.951324	+	0.288581i	0.223778	+	0.974640i	$0.428161\pi$
$824$	1.67897	+	11.4016i	0.0584896	+	0.397195i
$825$	36.4558	+	19.4860i	1.26923	+	0.678416i
$826$	−15.3518	−	1.01164i	−0.534158	−	0.0351995i
$827$	6.51436	+	18.2064i	0.226527	+	0.633099i	1.00000		0.000729732i	$-0.000232281\pi$
$827$	6.51436	+	18.2064i	0.226527	+	0.633099i	−0.773473	+	0.633829i	$0.781482\pi$
$828$	5.77908	+	6.17898i	0.200837	+	0.214734i
$829$	−0.665360	+	1.11009i	−0.0231089	+	0.0385549i	−0.869066	−	0.494695i	$-0.835280\pi$
$829$	−0.665360	+	1.11009i	−0.0231089	+	0.0385549i	0.845957	+	0.533250i	$0.179030\pi$
$830$	−3.65806	+	1.87735i	−0.126973	+	0.0651639i
$831$	−10.0232	−	10.0232i	−0.347700	−	0.347700i
$832$	33.2814	−	4.86499i	1.15383	−	0.168663i
$833$	−6.80296	+	6.80296i	−0.235709	+	0.235709i
$834$	−11.3383	+	35.2456i	−0.392613	+	1.22045i
$835$	52.0911	+	31.2222i	1.80269	+	1.08049i
$836$	−2.23178	+	4.91642i	−0.0771876	+	0.170038i
$837$	−5.95754	+	2.13164i	−0.205923	+	0.0736804i
$838$	−15.7032	−	17.9188i	−0.542460	−	0.618996i
$839$	13.5572	−	25.3638i	0.468047	−	0.875655i	−0.531543	−	0.847031i	$-0.678388\pi$
$839$	13.5572	−	25.3638i	0.468047	−	0.875655i	0.999590	−	0.0286237i	$-0.00911245\pi$
$840$	48.0418	+	22.7842i	1.65760	+	0.786130i
$841$	4.11630	−	13.5696i	0.141941	−	0.467918i
$842$	25.5375	+	23.9353i	0.880079	+	0.824866i
$843$	29.9206	+	22.1907i	1.03052	+	0.764287i
$844$	2.11018	+	9.80374i	0.0726354	+	0.337459i
$845$	8.19696	+	17.3310i	0.281984	+	0.596205i
$846$	3.61841	+	3.74144i	0.124403	+	0.128633i
$847$	9.82536	+	14.7047i	0.337603	+	0.505259i
$848$	4.75475	−	14.7270i	0.163279	−	0.505726i
$849$	19.8230	−	29.6672i	0.680323	−	1.01817i
$850$	20.5229	+	113.016i	0.703930	+	3.87643i
$851$	−2.98904	−	60.8432i	−0.102463	−	2.08568i
$852$	−29.1331	−	2.40944i	−0.998084	−	0.0825459i
$853$	−9.20257	−	2.30512i	−0.315090	−	0.0789259i	0.0822091	−	0.996615i	$-0.473802\pi$
$853$	−9.20257	−	2.30512i	−0.315090	−	0.0789259i	−0.397299	+	0.917689i	$0.630052\pi$
$854$	−25.7024	−	35.8943i	−0.879518	−	1.22828i
$855$	−1.91670	−	1.57299i	−0.0655497	−	0.0537953i
$856$	0.0317746	−	30.0774i	0.00108603	−	1.02803i
$857$	−15.8589	−	1.56197i	−0.541730	−	0.0533557i	−0.176548	−	0.984292i	$-0.556493\pi$
$857$	−15.8589	−	1.56197i	−0.541730	−	0.0533557i	−0.365182	+	0.930936i	$0.618993\pi$
$858$	−12.6817	+	16.5150i	−0.432946	+	0.563814i
$859$	−20.0150	−	0.983272i	−0.682902	−	0.0335488i	−0.295339	−	0.955392i	$-0.595433\pi$
$859$	−20.0150	−	0.983272i	−0.682902	−	0.0335488i	−0.387562	+	0.921844i	$0.626683\pi$
$860$	28.2579	+	16.3413i	0.963587	+	0.557232i
$861$	−18.1786	−	2.69654i	−0.619526	−	0.0918980i
$862$	−47.7402	+	13.6148i	−1.62604	+	0.463721i
$863$	14.5409	+	35.1049i	0.494979	+	1.19499i	0.952157	+	0.305610i	$0.0988604\pi$
$863$	14.5409	+	35.1049i	0.494979	+	1.19499i	−0.457178	+	0.889375i	$0.651140\pi$
$864$	−29.3074	+	10.9716i	−0.997057	+	0.373263i
$865$	5.52315	−	13.3341i	0.187793	−	0.453372i
$866$	−1.73117	+	15.0018i	−0.0588274	+	0.509781i
$867$	−38.5726	+	28.6074i	−1.30999	+	0.971557i
$868$	−6.61540	+	0.428917i	−0.224541	+	0.0145584i
$869$	−15.0918	−	16.6512i	−0.511953	−	0.564853i
$870$	9.15247	−	34.1094i	0.310298	−	1.15642i
$871$	15.8110	−	12.9758i	0.535737	−	0.439668i
$872$	2.84788	+	9.42402i	0.0964413	+	0.319138i
$873$	−0.719332	−	7.30350i	−0.0243457	−	0.247186i
$874$	3.33711	+	14.3349i	0.112879	+	0.484885i
$875$	−69.3269	+	41.5530i	−2.34368	+	1.40475i
$876$	−4.34740	+	0.497026i	−0.146885	+	0.0167929i
$877$	7.00586	−	7.72978i	0.236571	−	0.261016i	−0.611081	−	0.791568i	$-0.709265\pi$
$877$	7.00586	−	7.72978i	0.236571	−	0.261016i	0.847653	+	0.530552i	$0.178015\pi$
$878$	−7.36901	+	4.74761i	−0.248692	+	0.160224i
$879$	−1.42186	−	7.14815i	−0.0479580	−	0.241101i
$880$	−36.2688	+	1.13618i	−1.22262	+	0.0383005i
$881$	6.39368	−	32.1432i	0.215408	−	1.08293i	−0.710070	−	0.704131i	$-0.751337\pi$
$881$	6.39368	−	32.1432i	0.215408	−	1.08293i	0.925478	−	0.378800i	$-0.123663\pi$
$882$	0.911954	−	0.360007i	0.0307071	−	0.0121221i
$883$	26.5943	+	9.51559i	0.894969	+	0.320225i	0.743894	−	0.668297i	$-0.232977\pi$
$883$	26.5943	+	9.51559i	0.894969	+	0.320225i	0.151075	+	0.988522i	$0.451727\pi$
$884$	−57.8532	+	0.905949i	−1.94581	+	0.0304704i
$885$	−3.57313	−	24.0881i	−0.120109	−	0.809712i
$886$	−25.0236	−	9.42827i	−0.840683	−	0.316749i
$887$	15.7774	+	29.5175i	0.529755	+	0.991101i	0.994408	+	0.105608i	$0.0336790\pi$
$887$	15.7774	+	29.5175i	0.529755	+	0.991101i	−0.464653	+	0.885493i	$0.653821\pi$
$888$	30.0795	+	10.7985i	1.00940	+	0.362373i
$889$	5.50510	−	1.66995i	0.184635	−	0.0560085i
$890$	20.4438	+	60.2953i	0.685278	+	2.02110i
$891$	6.87553	−	14.5371i	0.230339	−	0.487011i
$892$	−25.8641	−	41.6582i	−0.865994	−	1.39482i
$893$	2.20015	+	8.78348i	0.0736252	+	0.293928i
$894$	−8.14412	+	0.664893i	−0.272380	+	0.0222373i
$895$		−	2.29143i		−	0.0765941i
$896$	−32.6835	+	2.59881i	−1.09188	+	0.0868201i
$897$			56.7611i			1.89520i
$898$	0.133385	+	1.63380i	0.00445111	+	0.0545207i
$899$	1.06988	+	4.27121i	0.0356826	+	0.142453i
$900$	2.66610	−	11.3980i	0.0888700	−	0.379932i
$901$	−11.3822	+	24.0655i	−0.379195	+	0.801740i
$902$	11.8776	−	4.02725i	0.395482	−	0.134093i
$903$	−17.4727	+	5.30029i	−0.581455	+	0.176383i
$904$	3.26576	+	2.96621i	0.108618	+	0.0986546i
$905$	37.9215	+	70.9462i	1.26055	+	2.35833i
$906$	6.13270	−	16.2768i	0.203745	−	0.540761i
$907$	4.19612	+	28.2880i	0.139330	+	0.939286i	0.940243	+	0.340505i	$0.110598\pi$
$907$	4.19612	+	28.2880i	0.139330	+	0.939286i	−0.800913	+	0.598781i	$0.795652\pi$
$908$	−17.3187	+	17.8697i	−0.574741	+	0.593028i
$909$	−0.724181	−	0.259116i	−0.0240196	−	0.00859434i
$910$	−25.9361	−	65.7002i	−0.859772	−	2.17794i
$911$	−4.66979	+	23.4766i	−0.154717	+	0.777816i	0.823025	+	0.568005i	$0.192285\pi$
$911$	−4.66979	+	23.4766i	−0.154717	+	0.777816i	−0.977742	+	0.209810i	$0.932715\pi$
$912$	−7.61680	−	1.26856i	−0.252218	−	0.0420063i
$913$	0.306208	+	1.53941i	0.0101340	+	0.0509471i
$914$	−0.188312	−	0.292289i	−0.00622882	−	0.00966808i
$915$	46.9267	−	51.7756i	1.55135	−	1.71165i
$916$	15.0845	+	11.9893i	0.498407	+	0.396136i
$917$	12.6764	−	7.59793i	0.418611	−	0.250906i
$918$	52.4306	−	12.2056i	1.73047	−	0.402846i
$919$	1.31210	+	13.3220i	0.0432823	+	0.439453i	0.992266	+	0.124128i	$0.0396134\pi$
$919$	1.31210	+	13.3220i	0.0432823	+	0.439453i	−0.948984	+	0.315324i	$0.897887\pi$
$920$	−76.5294	+	62.6709i	−2.52310	+	2.06620i
$921$	−13.5311	+	11.1047i	−0.445865	+	0.365912i
$922$	53.7210	+	14.4148i	1.76921	+	0.474725i
$923$	26.0791	+	28.7739i	0.858405	+	0.947104i
$924$	13.3936	−	15.2508i	0.440617	−	0.501714i
$925$	−67.6971	+	50.2076i	−2.22587	+	1.65082i
$926$	−16.4760	−	1.90129i	−0.541435	−	0.0624802i
$927$	−0.773146	+	1.86654i	−0.0253935	+	0.0613052i
$928$	5.59923	+	21.0448i	0.183804	+	0.690828i
$929$	−12.6735	−	30.5964i	−0.415803	−	1.00384i	−0.983550	−	0.180634i	$-0.942185\pi$
$929$	−12.6735	−	30.5964i	−0.415803	−	1.00384i	0.567748	−	0.823203i	$-0.307815\pi$
$930$	−2.87767	−	10.0906i	−0.0943626	−	0.330883i
$931$	1.68718	+	0.250270i	0.0552952	+	0.00820226i
$932$	0.919679	+	3.44198i	0.0301251	+	0.112746i
$933$	31.3382	+	1.53955i	1.02597	+	0.0504026i
$934$	1.72848	+	1.32728i	0.0565577	+	0.0434299i
$935$	62.1208	+	6.11837i	2.03157	+	0.200092i
$936$	5.44520	+	2.26222i	0.177982	+	0.0739429i
$937$	−16.8630	−	13.8391i	−0.550890	−	0.452103i	0.317308	−	0.948323i	$-0.397221\pi$
$937$	−16.8630	−	13.8391i	−0.550890	−	0.452103i	−0.868197	+	0.496219i	$0.834721\pi$
$938$	−16.2106	+	11.6077i	−0.529294	+	0.379005i
$939$	48.2293	+	12.0808i	1.57390	+	0.394242i
$940$	−46.4309	+	39.3375i	−1.51441	+	1.28305i
$941$	1.45106	+	29.5371i	0.0473033	+	0.962881i	0.898756	+	0.438450i	$0.144472\pi$
$941$	1.45106	+	29.5371i	0.0473033	+	0.962881i	−0.851452	+	0.524432i	$0.824278\pi$
$942$	10.5753	−	1.92040i	0.344563	−	0.0625701i
$943$	18.9941	−	28.4267i	0.618534	−	0.925702i
$944$	9.31825	+	11.7749i	0.303283	+	0.383242i
$945$	36.5106	+	54.6419i	1.18769	+	1.77750i
$946$	8.95720	−	8.66266i	0.291224	−	0.281648i
$947$	3.32490	+	7.02992i	0.108045	+	0.228442i	0.950767	−	0.309908i	$-0.100298\pi$
$947$	3.32490	+	7.02992i	0.108045	+	0.228442i	−0.842722	+	0.538349i	$0.819048\pi$
$948$	17.4350	−	26.9991i	0.566262	−	0.876890i
$949$	4.66894	+	3.46272i	0.151560	+	0.112405i
$950$	13.9259	−	14.8580i	0.451815	−	0.482057i
$951$	−5.80315	+	19.1304i	−0.188180	+	0.620346i
$952$	56.3299	+	2.82697i	1.82566	+	0.0916225i
$953$	−0.435998	+	0.815695i	−0.0141234	+	0.0264230i	−0.888884	−	0.458132i	$-0.848519\pi$
$953$	−0.435998	+	0.815695i	−0.0141234	+	0.0264230i	0.874761	+	0.484555i	$0.161019\pi$
$954$	2.04033	−	1.78805i	0.0660581	−	0.0578903i
$955$	27.1258	−	9.70578i	0.877771	−	0.314072i
$956$	−8.62403	−	22.9625i	−0.278921	−	0.742661i
$957$	−11.5634	−	6.93081i	−0.373790	−	0.224041i
$958$	−10.2536	−	3.29853i	−0.331279	−	0.106571i
$959$	7.52735	−	7.52735i	0.243071	−	0.243071i
$960$	−14.9594	−	49.6921i	−0.482811	−	1.60381i
$961$	−20.9952	−	20.9952i	−0.677266	−	0.677266i
$962$	−19.3849	−	37.7719i	−0.624994	−	1.21781i
$963$	2.71073	−	4.52259i	0.0873522	−	0.145738i
$964$	−1.03624	+	30.9865i	−0.0333751	+	0.998010i
$965$	0.878668	+	2.45571i	0.0282853	+	0.0790522i
$966$	3.63816	−	55.2097i	0.117056	−	1.77634i
$967$	−15.9880	−	8.54577i	−0.514140	−	0.274813i	0.193856	−	0.981030i	$-0.437900\pi$
$967$	−15.9880	−	8.54577i	−0.514140	−	0.274813i	−0.707996	+	0.706217i	$0.750400\pi$
$968$	4.21173	−	16.7391i	0.135370	−	0.538015i
$969$	12.7112	+	3.85590i	0.408342	+	0.123869i
$970$	85.7586	−	2.77722i	2.75354	−	0.0891710i
$971$	−14.6404	+	19.7402i	−0.469831	+	0.633494i	−0.973031	−	0.230676i	$-0.925906\pi$
$971$	−14.6404	+	19.7402i	−0.469831	+	0.633494i	0.503199	+	0.864170i	$0.332156\pi$
$972$	−10.0279	−	1.83193i	−0.321644	−	0.0587592i
$973$	−43.3409	+	20.4987i	−1.38945	+	0.657159i
$974$	0.751619	−	44.9636i	0.0240834	−	1.44073i
$975$	65.2986	−	43.6311i	2.09123	−	1.39732i
$976$	−9.15577	+	42.1044i	−0.293069	+	1.34773i
$977$	−44.7792	−	29.9205i	−1.43261	−	0.957241i	−0.998407	−	0.0564274i	$-0.982029\pi$
$977$	−44.7792	−	29.9205i	−1.43261	−	0.957241i	−0.434206	−	0.900814i	$-0.642971\pi$
$978$	11.4249	+	7.91321i	0.365327	+	0.253037i
$979$	24.2746	−	1.19253i	0.775820	−	0.0381136i
$980$	3.49889	+	10.9160i	0.111768	+	0.348699i
$981$	−0.419353	+	1.67415i	−0.0133889	+	0.0534515i
$982$	−0.0516533	+	0.312175i	−0.00164832	+	0.00996191i
$983$	−28.5227	+	34.7551i	−0.909734	+	1.10851i	0.0839691	+	0.996468i	$0.473240\pi$
$983$	−28.5227	+	34.7551i	−0.909734	+	1.10851i	−0.993703	+	0.112046i	$0.964260\pi$
$984$	9.94926	+	14.9242i	0.317171	+	0.475767i
$985$	3.40564	−	34.5780i	0.108513	−	1.10175i
$986$	−4.87661	−	37.1426i	−0.155303	−	1.18286i
$987$	1.67023	−	33.9984i	0.0531642	−	1.08218i
$988$	6.23884	+	8.14248i	0.198484	+	0.259047i
$989$	4.98413	−	33.6003i	0.158486	−	1.06843i
$990$	−5.55922	−	3.09202i	−0.176683	−	0.0982708i
$991$	−12.4967	+	5.17630i	−0.396971	+	0.164431i	−0.572233	−	0.820091i	$-0.693923\pi$
$991$	−12.4967	+	5.17630i	−0.396971	+	0.164431i	0.175262	+	0.984522i	$0.443923\pi$
$992$	4.64145	+	4.50785i	0.147366	+	0.143124i
$993$	−3.64460	−	1.50964i	−0.115658	−	0.0479070i
$994$	−23.5220	−	29.6590i	−0.746073	−	0.940725i
$995$	−49.2282	−	66.3765i	−1.56064	−	2.10428i
$996$	−2.01392	+	0.991393i	−0.0638135	+	0.0314135i
$997$	−27.2565	+	24.7039i	−0.863223	+	0.782380i	−0.977470	−	0.211073i	$-0.932304\pi$
$997$	−27.2565	+	24.7039i	−0.863223	+	0.782380i	0.114247	+	0.993452i	$0.463554\pi$
$998$	42.4330	−	24.4788i	1.34319	−	0.774862i
$999$	25.0588	+	30.5342i	0.792824	+	0.966059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.26	✓	992
256.109	even	64	inner	256.2.m.a.109.26	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.26	✓	992	1.1	even	1	trivial
256.2.m.a.109.26	yes	992	256.109	even	64	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07805 + 0.915314i) q^{2} +(-1.53503 + 0.384505i) q^{3} +(0.324401 + 1.97352i) q^{4} +(-3.70568 - 1.75266i) q^{5} +(-2.00679 - 0.990517i) q^{6} +(-0.841234 - 2.77318i) q^{7} +(-1.45666 + 2.42449i) q^{8} +(-0.437291 + 0.233737i) q^{9} +O(q^{10})\)	\(q+(1.07805 + 0.915314i) q^{2} +(-1.53503 + 0.384505i) q^{3} +(0.324401 + 1.97352i) q^{4} +(-3.70568 - 1.75266i) q^{5} +(-2.00679 - 0.990517i) q^{6} +(-0.841234 - 2.77318i) q^{7} +(-1.45666 + 2.42449i) q^{8} +(-0.437291 + 0.233737i) q^{9} +(-2.39069 - 5.28132i) q^{10} +(-2.18905 + 0.324715i) q^{11} +(-1.25679 - 2.90467i) q^{12} +(-1.41642 + 3.95862i) q^{13} +(1.63143 - 3.75963i) q^{14} +(6.36223 + 1.26553i) q^{15} +(-3.78953 + 1.28042i) q^{16} +(6.74872 - 1.34240i) q^{17} +(-0.685367 - 0.148278i) q^{18} +(-0.903883 - 0.819232i) q^{19} +(2.25677 - 7.88178i) q^{20} +(2.35762 + 3.93345i) q^{21} +(-2.65713 - 1.65361i) q^{22} +(-8.49026 + 0.836218i) q^{23} +(1.30380 - 4.28175i) q^{24} +(7.48828 + 9.12450i) q^{25} +(-5.15035 + 2.97114i) q^{26} +(4.09895 - 3.71507i) q^{27} +(5.20001 - 2.55981i) q^{28} +(-2.29323 - 3.09207i) q^{29} +(5.70048 + 7.18774i) q^{30} +(-1.05672 - 0.437707i) q^{31} +(-5.25730 - 2.08824i) q^{32} +(3.23540 - 1.34015i) q^{33} +(8.50421 + 4.73001i) q^{34} +(-1.74308 + 11.7509i) q^{35} +(-0.603142 - 0.787177i) q^{36} +(-0.350360 + 7.13173i) q^{37} +(-0.224581 - 1.71051i) q^{38} +(0.652133 - 6.62121i) q^{39} +(9.64722 - 6.43133i) q^{40} +(-2.54227 + 3.09777i) q^{41} +(-1.05870 + 6.39843i) q^{42} +(-0.967436 + 3.86222i) q^{43} +(-1.35096 - 4.21478i) q^{44} +(2.03012 - 0.0997335i) q^{45} +(-9.91836 - 6.86976i) q^{46} +(-6.17170 - 4.12380i) q^{47} +(5.32471 - 3.42258i) q^{48} +(-1.16255 + 0.776791i) q^{49} +(-0.279007 + 16.6908i) q^{50} +(-9.84333 + 4.65555i) q^{51} +(-8.27188 - 1.51114i) q^{52} +(-2.30469 + 3.10751i) q^{53} +(7.81934 - 0.253222i) q^{54} +(8.68102 + 2.63336i) q^{55} +(7.94892 + 2.00003i) q^{56} +(1.70249 + 0.909998i) q^{57} +(0.357982 - 5.43244i) q^{58} +(-1.26468 - 3.53455i) q^{59} +(-0.433621 + 12.9665i) q^{60} +(5.53796 - 9.23953i) q^{61} +(-0.738560 - 1.43910i) q^{62} +(1.01606 + 1.01606i) q^{63} +(-3.75626 - 7.06332i) q^{64} +(12.1869 - 12.1869i) q^{65} +(4.71459 + 1.51666i) q^{66} +(-4.17275 - 2.50105i) q^{67} +(4.83855 + 12.8832i) q^{68} +(12.7113 - 4.54817i) q^{69} +(-12.6349 + 11.0726i) q^{70} +(4.35404 - 8.14584i) q^{71} +(0.0702945 - 1.40068i) q^{72} +(0.401340 - 1.32304i) q^{73} +(-6.90548 + 7.36771i) q^{74} +(-15.0032 - 11.1271i) q^{75} +(1.32355 - 2.04959i) q^{76} +(2.74199 + 5.79746i) q^{77} +(6.76352 - 6.54112i) q^{78} +(5.64174 + 8.44347i) q^{79} +(16.2869 + 1.89691i) q^{80} +(-4.03712 + 6.04198i) q^{81} +(-5.57613 + 1.01258i) q^{82} +(-0.0348013 - 0.708396i) q^{83} +(-6.99791 + 5.92882i) q^{84} +(-27.3614 - 6.85366i) q^{85} +(-4.57809 + 3.27818i) q^{86} +(4.70910 + 3.86465i) q^{87} +(2.40144 - 5.78032i) q^{88} +(-10.9294 - 1.07646i) q^{89} +(2.27987 + 1.75068i) q^{90} +(12.1695 + 0.597848i) q^{91} +(-4.40454 - 16.4844i) q^{92} +(1.79040 + 0.265580i) q^{93} +(-2.87886 - 10.0947i) q^{94} +(1.91367 + 4.62001i) q^{95} +(8.87306 + 1.18406i) q^{96} +(-5.66403 + 13.6742i) q^{97} +(-1.96430 - 0.226675i) q^{98} +(0.881354 - 0.653657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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