LMFDB - Embedded newform 966.2.be.b.493.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.3
Character	$\chi$	$=$	966.493
Dual form			966.2.be.b.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 + 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.81663 + 0.173468i) q^{5} +(0.989821 - 0.142315i) q^{6} +(-1.72602 + 2.00521i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.81663 + 0.173468i) q^{5} +(0.989821 - 0.142315i) q^{6} +(-1.72602 + 2.00521i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(0.430236 - 1.77346i) q^{10} +(-2.76261 + 0.956147i) q^{11} +(-0.189251 + 0.981929i) q^{12} +(-1.18633 - 4.04028i) q^{13} +(-1.33040 - 2.28693i) q^{14} +(0.986614 + 1.53520i) q^{15} +(0.235759 + 0.971812i) q^{16} +(2.93923 + 1.17669i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(5.27622 - 2.11228i) q^{19} +(1.53520 + 0.986614i) q^{20} +(2.57321 + 0.615304i) q^{21} -2.92339i q^{22} +(3.30500 + 3.47519i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.63957 + 0.316002i) q^{25} +(4.20608 + 0.200360i) q^{26} +(0.989821 + 0.142315i) q^{27} +(2.59628 - 0.509249i) q^{28} +(-0.523807 - 3.64316i) q^{29} +(-1.77346 + 0.430236i) q^{30} +(3.49561 - 0.166516i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(2.11576 + 2.01737i) q^{33} +(-2.07330 + 2.39272i) q^{34} +(2.78770 - 3.94214i) q^{35} +(0.959493 - 0.281733i) q^{36} +(0.0262834 + 0.0187163i) q^{37} +(0.270424 + 5.67689i) q^{38} +(-3.04753 + 2.90582i) q^{39} +(-1.43447 + 1.12808i) q^{40} +(-3.07809 - 1.40572i) q^{41} +(-1.42308 + 2.23044i) q^{42} +(4.83994 - 7.53109i) q^{43} +(2.76261 + 0.956147i) q^{44} +(0.912449 - 1.58041i) q^{45} +(-4.36502 + 1.98660i) q^{46} +(6.45267 - 3.72545i) q^{47} +(0.755750 - 0.654861i) q^{48} +(-1.04174 - 6.92205i) q^{49} +(0.237630 - 1.65275i) q^{50} +(-0.300949 - 3.15168i) q^{51} +(-1.56501 + 3.90922i) q^{52} +(2.81184 + 2.94897i) q^{53} +(-0.458227 + 0.888835i) q^{54} +(4.85279 - 2.21619i) q^{55} +(-0.367919 + 2.62005i) q^{56} +(-4.29517 - 3.72179i) q^{57} +(3.61411 + 0.696562i) q^{58} +(3.40675 + 0.826469i) q^{59} +(0.173468 - 1.81663i) q^{60} +(11.3024 + 5.82678i) q^{61} +(-0.985944 + 3.35782i) q^{62} +(-0.632209 - 2.56911i) q^{63} +(0.415415 - 0.909632i) q^{64} +(2.85599 + 7.13392i) q^{65} +(-2.59841 + 1.33957i) q^{66} +(-2.20172 - 11.4236i) q^{67} +(-1.58301 - 2.74185i) q^{68} +(1.57444 - 4.53003i) q^{69} +(2.81356 + 3.92373i) q^{70} +(3.46736 + 4.00155i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(5.72466 - 7.27950i) q^{73} +(-0.0262834 + 0.0187163i) q^{74} +(1.03217 + 1.31251i) q^{75} +(-5.45312 - 1.60118i) q^{76} +(2.85103 - 7.18993i) q^{77} +(-1.74925 - 3.83032i) q^{78} +(9.88737 - 10.3696i) q^{79} +(-0.596866 - 1.72453i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(2.33515 - 2.44903i) q^{82} +(-0.933075 - 2.04315i) q^{83} +(-1.64232 - 2.07431i) q^{84} +(-5.54362 - 1.62775i) q^{85} +(5.53390 + 7.03692i) q^{86} +(-2.99815 + 2.13497i) q^{87} +(-1.80712 + 2.29794i) q^{88} +(-0.726719 + 15.2557i) q^{89} +(1.19505 + 1.37917i) q^{90} +(10.1492 + 4.59474i) q^{91} +(-0.449685 - 4.77470i) q^{92} +(-1.74979 - 3.03072i) q^{93} +(1.41009 + 7.31626i) q^{94} +(-9.21856 + 4.75250i) q^{95} +(0.371662 + 0.928368i) q^{96} +(-4.32963 + 9.48057i) q^{97} +(6.88206 + 1.27954i) q^{98} +(0.823614 - 2.80497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$3$	−0.458227	−	0.888835i	−0.264557	−	0.513169i
$3$	−0.458227	−	0.888835i	−0.264557	−	0.513169i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−1.81663	+	0.173468i	−0.812424	+	0.0775771i	−0.492994	−	0.870033i	$-0.664097\pi$
$5$	−1.81663	+	0.173468i	−0.812424	+	0.0775771i	−0.319430	+	0.947610i	$0.603491\pi$
$6$	0.989821	−	0.142315i	0.404093	−	0.0580998i
$7$	−1.72602	+	2.00521i	−0.652373	+	0.757898i
$7$	−1.72602	+	2.00521i	−0.652373	+	0.757898i
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	−0.580057	+	0.814576i	−0.193352	+	0.271525i
$10$	0.430236	−	1.77346i	0.136053	−	0.560816i
$11$	−2.76261	+	0.956147i	−0.832957	+	0.288289i	−0.710070	−	0.704131i	$-0.751337\pi$
$11$	−2.76261	+	0.956147i	−0.832957	+	0.288289i	−0.122887	+	0.992421i	$0.539215\pi$
$12$	−0.189251	+	0.981929i	−0.0546321	+	0.283458i
$13$	−1.18633	−	4.04028i	−0.329030	−	1.12057i	−0.943428	−	0.331576i	$-0.892420\pi$
$13$	−1.18633	−	4.04028i	−0.329030	−	1.12057i	0.614399	−	0.788995i	$-0.289399\pi$
$14$	−1.33040	−	2.28693i	−0.355565	−	0.611207i
$15$	0.986614	+	1.53520i	0.254743	+	0.396387i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	2.93923	+	1.17669i	0.712868	+	0.285389i	0.699612	−	0.714523i	$-0.253356\pi$
$17$	2.93923	+	1.17669i	0.712868	+	0.285389i	0.0132557	+	0.999912i	$0.495780\pi$
$18$	−0.580057	−	0.814576i	−0.136721	−	0.191997i
$19$	5.27622	−	2.11228i	1.21045	−	0.484590i	0.323398	−	0.946263i	$-0.395175\pi$
$19$	5.27622	−	2.11228i	1.21045	−	0.484590i	0.887050	+	0.461673i	$0.152751\pi$
$20$	1.53520	+	0.986614i	0.343282	+	0.220614i
$21$	2.57321	+	0.615304i	0.561520	+	0.134270i
$22$		−	2.92339i		−	0.623269i
$23$	3.30500	+	3.47519i	0.689140	+	0.724628i
$23$	3.30500	+	3.47519i	0.689140	+	0.724628i
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−1.63957	+	0.316002i	−0.327915	+	0.0632003i
$26$	4.20608	+	0.200360i	0.824880	+	0.0392939i
$27$	0.989821	+	0.142315i	0.190491	+	0.0273885i
$28$	2.59628	−	0.509249i	0.490651	−	0.0962391i
$29$	−0.523807	−	3.64316i	−0.0972685	−	0.676518i	−0.978864	−	0.204512i	$-0.934439\pi$
$29$	−0.523807	−	3.64316i	−0.0972685	−	0.676518i	0.881596	−	0.472006i	$-0.156470\pi$
$30$	−1.77346	+	0.430236i	−0.323787	+	0.0785500i
$31$	3.49561	−	0.166516i	0.627830	−	0.0299072i	0.268744	−	0.963212i	$-0.413391\pi$
$31$	3.49561	−	0.166516i	0.627830	−	0.0299072i	0.359086	+	0.933304i	$0.383088\pi$
$32$	−0.995472	−	0.0950560i	−0.175976	−	0.0168037i
$33$	2.11576	+	2.01737i	0.368306	+	0.351179i
$34$	−2.07330	+	2.39272i	−0.355568	+	0.410347i
$35$	2.78770	−	3.94214i	0.471208	−	0.666344i
$36$	0.959493	−	0.281733i	0.159915	−	0.0469554i
$37$	0.0262834	+	0.0187163i	0.00432097	+	0.00307695i	0.582215	−	0.813035i	$-0.302186\pi$
$37$	0.0262834	+	0.0187163i	0.00432097	+	0.00307695i	−0.577894	+	0.816112i	$0.696125\pi$
$38$	0.270424	+	5.67689i	0.0438685	+	0.920914i
$39$	−3.04753	+	2.90582i	−0.487996	+	0.465303i
$40$	−1.43447	+	1.12808i	−0.226809	+	0.178365i
$41$	−3.07809	−	1.40572i	−0.480717	−	0.219536i	0.160292	−	0.987070i	$-0.448756\pi$
$41$	−3.07809	−	1.40572i	−0.480717	−	0.219536i	−0.641009	+	0.767534i	$0.721484\pi$
$42$	−1.42308	+	2.23044i	−0.219585	+	0.344164i
$43$	4.83994	−	7.53109i	0.738083	−	1.14848i	−0.245739	−	0.969336i	$-0.579031\pi$
$43$	4.83994	−	7.53109i	0.738083	−	1.14848i	0.983823	−	0.179144i	$-0.0573329\pi$
$44$	2.76261	+	0.956147i	0.416479	+	0.144145i
$45$	0.912449	−	1.58041i	0.136020	−	0.235593i
$46$	−4.36502	+	1.98660i	−0.643587	+	0.292909i
$47$	6.45267	−	3.72545i	0.941219	−	0.543413i	0.0508770	−	0.998705i	$-0.483798\pi$
$47$	6.45267	−	3.72545i	0.941219	−	0.543413i	0.890342	+	0.455292i	$0.150465\pi$
$48$	0.755750	−	0.654861i	0.109083	−	0.0945210i
$49$	−1.04174	−	6.92205i	−0.148820	−	0.988864i
$50$	0.237630	−	1.65275i	0.0336059	−	0.233734i
$51$	−0.300949	−	3.15168i	−0.0421413	−	0.441324i
$52$	−1.56501	+	3.90922i	−0.217028	+	0.542111i
$53$	2.81184	+	2.94897i	0.386236	+	0.405072i	0.887934	−	0.459970i	$-0.152140\pi$
$53$	2.81184	+	2.94897i	0.386236	+	0.405072i	−0.501699	+	0.865042i	$0.667291\pi$
$54$	−0.458227	+	0.888835i	−0.0623567	+	0.120955i
$55$	4.85279	−	2.21619i	0.654349	−	0.298831i
$56$	−0.367919	+	2.62005i	−0.0491652	+	0.350118i
$57$	−4.29517	−	3.72179i	−0.568910	−	0.492963i
$58$	3.61411	+	0.696562i	0.474556	+	0.0914631i
$59$	3.40675	+	0.826469i	0.443522	+	0.107597i	0.451299	−	0.892373i	$-0.350961\pi$
$59$	3.40675	+	0.826469i	0.443522	+	0.107597i	−0.00777788	+	0.999970i	$0.502476\pi$
$60$	0.173468	−	1.81663i	0.0223946	−	0.234527i
$61$	11.3024	+	5.82678i	1.44712	+	0.746042i	0.989693	−	0.143205i	$-0.0457409\pi$
$61$	11.3024	+	5.82678i	1.44712	+	0.746042i	0.457427	+	0.889247i	$0.348771\pi$
$62$	−0.985944	+	3.35782i	−0.125215	+	0.426443i
$63$	−0.632209	−	2.56911i	−0.0796508	−	0.323677i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	2.85599	+	7.13392i	0.354242	+	0.884854i
$66$	−2.59841	+	1.33957i	−0.319842	+	0.164890i
$67$	−2.20172	−	11.4236i	−0.268982	−	1.39561i	−0.825324	−	0.564659i	$-0.809008\pi$
$67$	−2.20172	−	11.4236i	−0.268982	−	1.39561i	0.556342	−	0.830954i	$-0.312205\pi$
$68$	−1.58301	−	2.74185i	−0.191968	−	0.332498i
$69$	1.57444	−	4.53003i	0.189540	−	0.545351i
$70$	2.81356	+	3.92373i	0.336285	+	0.468975i
$71$	3.46736	+	4.00155i	0.411500	+	0.474897i	0.923229	−	0.384250i	$-0.125540\pi$
$71$	3.46736	+	4.00155i	0.411500	+	0.474897i	−0.511729	+	0.859147i	$0.670995\pi$
$72$	−0.0475819	+	0.998867i	−0.00560758	+	0.117718i
$73$	5.72466	−	7.27950i	0.670021	−	0.852001i	−0.325598	−	0.945508i	$-0.605565\pi$
$73$	5.72466	−	7.27950i	0.670021	−	0.852001i	0.995619	+	0.0935074i	$0.0298079\pi$
$74$	−0.0262834	+	0.0187163i	−0.00305538	+	0.00217573i
$75$	1.03217	+	1.31251i	0.119185	+	0.151556i
$76$	−5.45312	−	1.60118i	−0.625515	−	0.183668i
$77$	2.85103	−	7.18993i	0.324905	−	0.819369i
$78$	−1.74925	−	3.83032i	−0.198063	−	0.433698i
$79$	9.88737	−	10.3696i	1.11242	−	1.16667i	0.127824	−	0.991797i	$-0.459201\pi$
$79$	9.88737	−	10.3696i	1.11242	−	1.16667i	0.984591	−	0.174871i	$-0.0559509\pi$
$80$	−0.596866	−	1.72453i	−0.0667316	−	0.192808i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	2.33515	−	2.44903i	0.257874	−	0.270450i
$83$	−0.933075	−	2.04315i	−0.102418	−	0.224265i	0.851485	−	0.524379i	$-0.175702\pi$
$83$	−0.933075	−	2.04315i	−0.102418	−	0.224265i	−0.953903	+	0.300114i	$0.902975\pi$
$84$	−1.64232	−	2.07431i	−0.179192	−	0.226326i
$85$	−5.54362	−	1.62775i	−0.601290	−	0.176555i
$86$	5.53390	+	7.03692i	0.596735	+	0.758811i
$87$	−2.99815	+	2.13497i	−0.321435	+	0.228893i
$88$	−1.80712	+	2.29794i	−0.192640	+	0.244961i
$89$	−0.726719	+	15.2557i	−0.0770321	+	1.61710i	0.547983	+	0.836490i	$0.315396\pi$
$89$	−0.726719	+	15.2557i	−0.0770321	+	1.61710i	−0.625015	+	0.780613i	$0.714907\pi$
$90$	1.19505	+	1.37917i	0.125970	+	0.145377i
$91$	10.1492	+	4.59474i	1.06393	+	0.481660i
$92$	−0.449685	−	4.77470i	−0.0468829	−	0.497797i
$93$	−1.74979	−	3.03072i	−0.181444	−	0.314271i
$94$	1.41009	+	7.31626i	0.145440	+	0.754615i
$95$	−9.21856	+	4.75250i	−0.945804	+	0.487596i
$96$	0.371662	+	0.928368i	0.0379326	+	0.0947512i
$97$	−4.32963	+	9.48057i	−0.439607	+	0.962606i	0.552063	+	0.833803i	$0.313841\pi$
$97$	−4.32963	+	9.48057i	−0.439607	+	0.962606i	−0.991670	+	0.128803i	$0.958886\pi$
$98$	6.88206	+	1.27954i	0.695193	+	0.129253i
$99$	0.823614	−	2.80497i	0.0827763	−	0.281910i
$100$	1.48413	+	0.765122i	0.148413	+	0.0765122i
$101$	−1.00629	+	10.5383i	−0.100129	+	1.04860i	0.796147	+	0.605104i	$0.206868\pi$
$101$	−1.00629	+	10.5383i	−0.100129	+	1.04860i	−0.896276	+	0.443497i	$0.853738\pi$
$102$	3.07677	+	0.746417i	0.304646	+	0.0739063i
$103$	−12.5158	−	2.41223i	−1.23322	−	0.237684i	−0.469326	−	0.883025i	$-0.655503\pi$
$103$	−12.5158	−	2.41223i	−1.23322	−	0.237684i	−0.763895	+	0.645341i	$0.776715\pi$
$104$	−3.18235	−	2.75752i	−0.312055	−	0.270397i
$105$	−4.78131	−	0.671414i	−0.466609	−	0.0655233i
$106$	−3.70644	+	1.69268i	−0.360001	+	0.164407i
$107$	−0.610471	+	1.18415i	−0.0590164	+	0.114476i	−0.916499	−	0.400037i	$-0.868997\pi$
$107$	−0.610471	+	1.18415i	−0.0590164	+	0.114476i	0.857482	+	0.514513i	$0.172027\pi$
$108$	−0.690079	−	0.723734i	−0.0664029	−	0.0696413i
$109$	3.86325	−	9.64994i	0.370033	−	0.924297i	−0.620146	−	0.784487i	$-0.712927\pi$
$109$	3.86325	−	9.64994i	0.370033	−	0.924297i	0.990178	−	0.139810i	$-0.0446492\pi$
$110$	0.507113	+	5.31073i	0.0483514	+	0.506358i
$111$	0.00459198	−	0.0319380i	0.000435852	−	0.00303142i
$112$	−2.35561	−	1.20462i	−0.222584	−	0.113826i
$113$	−6.55842	+	5.68291i	−0.616965	+	0.534603i	−0.906305	−	0.422623i	$-0.861109\pi$
$113$	−6.55842	+	5.68291i	−0.616965	+	0.534603i	0.289341	+	0.957226i	$0.406564\pi$
$114$	4.92191	−	2.84167i	0.460979	−	0.266146i
$115$	−6.60681	−	5.73985i	−0.616089	−	0.535243i
$116$	−1.84031	+	3.18751i	−0.170869	+	0.295953i
$117$	3.97925	+	1.37723i	0.367882	+	0.127325i
$118$	−1.89525	+	2.94907i	−0.174472	+	0.271484i
$119$	−7.43267	+	3.86279i	−0.681351	+	0.354101i
$120$	1.65999	+	0.758090i	0.151535	+	0.0692038i
$121$	−1.92881	+	1.51683i	−0.175346	+	0.137894i
$122$	−9.20295	+	8.77499i	−0.833196	+	0.794451i
$123$	0.161012	+	3.38005i	0.0145179	+	0.304769i
$124$	−2.85067	−	2.02995i	−0.255998	−	0.182295i
$125$	11.6786	−	3.42914i	1.04456	−	0.306711i
$126$	2.63458	+	0.242835i	0.234707	+	0.0216335i
$127$	−3.56899	+	4.11884i	−0.316697	+	0.365488i	−0.891671	−	0.452684i	$-0.850467\pi$
$127$	−3.56899	+	4.11884i	−0.316697	+	0.365488i	0.574974	+	0.818172i	$0.305012\pi$
$128$	0.723734	+	0.690079i	0.0639697	+	0.0609949i
$129$	−8.91168	−	0.850963i	−0.784630	−	0.0749231i
$130$	−7.67566	+	0.365637i	−0.673200	+	0.0320685i
$131$	−3.49648	+	0.848237i	−0.305489	+	0.0741108i	−0.385573	−	0.922677i	$-0.625996\pi$
$131$	−3.49648	+	0.848237i	−0.305489	+	0.0741108i	0.0800842	+	0.996788i	$0.474481\pi$
$132$	−0.416042	−	2.89363i	−0.0362118	−	0.251859i
$133$	−4.87128	+	14.2258i	−0.422393	+	1.23353i
$134$	11.5154	+	1.65567i	0.994780	+	0.143028i
$135$	−1.82283	−	0.0868321i	−0.156884	−	0.00747332i
$136$	3.10880	−	0.599173i	0.266578	−	0.0513786i
$137$	1.93565	+	1.11755i	0.165374	+	0.0954787i	0.580403	−	0.814330i	$-0.302895\pi$
$137$	1.93565	+	1.11755i	0.165374	+	0.0954787i	−0.415029	+	0.909808i	$0.636228\pi$
$138$	3.76593	+	2.96947i	0.320577	+	0.252778i
$139$		−	22.0328i		−	1.86880i	−0.356231	−	0.934398i	$-0.615939\pi$
$139$		−	22.0328i		−	1.86880i	0.356231	−	0.934398i	$-0.384061\pi$
$140$	−4.62815	+	1.37549i	−0.391150	+	0.116250i
$141$	−6.26810	−	4.02826i	−0.527869	−	0.339241i
$142$	−4.91553	+	1.96788i	−0.412502	+	0.165141i
$143$	7.14047	+	10.0274i	0.597116	+	0.838532i
$144$	−0.928368	−	0.371662i	−0.0773640	−	0.0309719i
$145$	1.58354	+	6.52742i	0.131506	+	0.542073i
$146$	5.00678	+	7.79070i	0.414364	+	0.644763i
$147$	−5.67521	+	4.09780i	−0.468084	+	0.337981i
$148$	−0.00909049	−	0.0309594i	−0.000747234	−	0.00254484i
$149$	2.41945	−	12.5533i	0.198209	−	1.02840i	−0.737424	−	0.675430i	$-0.763958\pi$
$149$	2.41945	−	12.5533i	0.198209	−	1.02840i	0.935633	−	0.352975i	$-0.114830\pi$
$150$	−1.57791	+	0.546121i	−0.128836	+	0.0445906i
$151$	0.0399442	−	0.164652i	0.00325061	−	0.0133992i	−0.970163	−	0.242453i	$-0.922048\pi$
$151$	0.0399442	−	0.164652i	0.00325061	−	0.0133992i	0.973414	+	0.229054i	$0.0735632\pi$
$152$	3.29665	−	4.62950i	0.267394	−	0.375502i
$153$	−2.66342	+	1.71168i	−0.215325	+	0.138381i
$154$	5.86201	+	5.04582i	0.472374	+	0.406604i
$155$	−6.32136	+	0.908874i	−0.507744	+	0.0730025i
$156$	4.19178	−	0.400266i	0.335611	−	0.0320470i
$157$	−1.45386	−	1.14333i	−0.116031	−	0.0912475i	0.558458	−	0.829533i	$-0.311393\pi$
$157$	−1.45386	−	1.14333i	−0.116031	−	0.0912475i	−0.674488	+	0.738285i	$0.735636\pi$
$158$	6.56541	+	12.7351i	0.522316	+	1.01315i
$159$	1.33269	−	3.85056i	0.105689	−	0.305369i
$160$	1.82490			0.144271
$161$	−12.6730	+	0.628984i	−0.998771	+	0.0495709i
$162$	1.00000			0.0785674
$163$	−3.13837	+	9.06773i	−0.245816	+	0.710240i	0.752830	+	0.658216i	$0.228688\pi$
$163$	−3.13837	+	9.06773i	−0.245816	+	0.710240i	−0.998646	+	0.0520241i	$0.983433\pi$
$164$	1.55059	+	3.00772i	0.121080	+	0.234863i
$165$	−4.19351	−	3.29781i	−0.326464	−	0.256734i
$166$	2.23596	−	0.213508i	0.173544	−	0.0165714i
$167$	16.9842	−	2.44196i	1.31428	−	0.188965i	0.550713	−	0.834694i	$-0.314356\pi$
$167$	16.9842	−	2.44196i	1.31428	−	0.188965i	0.763566	+	0.645729i	$0.223447\pi$
$168$	2.49738	−	0.873555i	0.192677	−	0.0673962i
$169$	−3.98017	+	2.55790i	−0.306167	+	0.196761i
$170$	3.35137	−	4.70634i	0.257038	−	0.360960i
$171$	−1.33990	+	5.52313i	−0.102464	+	0.422364i
$172$	−8.45986	+	2.92798i	−0.645058	+	0.223257i
$173$	0.808755	−	4.19622i	0.0614885	−	0.319033i	−0.938141	−	0.346254i	$-0.887454\pi$
$173$	0.808755	−	4.19622i	0.0614885	−	0.319033i	0.999629	+	0.0272209i	$0.00866576\pi$
$174$	−1.03695	−	3.53153i	−0.0786111	−	0.267725i
$175$	2.19628	−	3.83311i	0.166023	−	0.289756i
$176$	−1.58050	−	2.45931i	−0.119135	−	0.185378i
$177$	−0.826469	−	3.40675i	−0.0621212	−	0.256067i
$178$	−14.1790	−	5.67641i	−1.06276	−	0.425465i
$179$	−12.0622	−	16.9390i	−0.901571	−	1.26608i	−0.963421	−	0.267993i	$-0.913639\pi$
$179$	−12.0622	−	16.9390i	−0.901571	−	1.26608i	0.0618501	−	0.998085i	$-0.480300\pi$
$180$	−1.69418	+	0.678246i	−0.126276	+	0.0505535i
$181$	19.9464	+	12.8188i	1.48260	+	0.952812i	0.996899	+	0.0786885i	$0.0250733\pi$
$181$	19.9464	+	12.8188i	1.48260	+	0.952812i	0.485705	+	0.874123i	$0.338563\pi$
$182$	−7.66152	+	8.08825i	−0.567910	+	0.599541i
$183$		−	12.7159i		−	0.939988i
$184$	4.65918	+	1.13670i	0.343479	+	0.0837986i
$185$	−0.0509940	−	0.0294414i	−0.00374916	−	0.00216458i
$186$	3.43633	−	0.662298i	0.251964	−	0.0485621i
$187$	−9.24502	−	0.440395i	−0.676063	−	0.0322048i
$188$	−7.37507	−	1.06037i	−0.537882	−	0.0773358i
$189$	−1.99382	+	1.73916i	−0.145029	+	0.126505i
$190$	−1.47602	−	10.2659i	−0.107082	−	0.744769i
$191$	6.31818	−	1.53277i	0.457167	−	0.110908i	−0.000560651	−	1.00000i	$-0.500178\pi$
$191$	6.31818	−	1.53277i	0.457167	−	0.110908i	0.457728	+	0.889092i	$0.348663\pi$
$192$	−0.998867	+	0.0475819i	−0.0720870	+	0.00343393i
$193$	3.08278	+	0.294370i	0.221904	+	0.0211892i	0.205416	−	0.978675i	$-0.434145\pi$
$193$	3.08278	+	0.294370i	0.221904	+	0.0211892i	0.0164881	+	0.999864i	$0.494751\pi$
$194$	−7.54306	−	7.19229i	−0.541560	−	0.516377i
$195$	5.03219	−	5.80746i	0.360363	−	0.415881i
$196$	−3.46007	+	6.08506i	−0.247148	+	0.434647i
$197$	−17.8396	+	5.23817i	−1.27102	+	0.373204i	−0.846584	−	0.532255i	$-0.821345\pi$
$197$	−17.8396	+	5.23817i	−1.27102	+	0.373204i	−0.424433	+	0.905459i	$0.639527\pi$
$198$	2.38132	+	1.69573i	0.169233	+	0.120510i
$199$	−0.811391	−	17.0332i	−0.0575180	−	1.20745i	−0.824530	−	0.565818i	$-0.808560\pi$
$199$	−0.811391	−	17.0332i	−0.0575180	−	1.20745i	0.767012	−	0.641633i	$-0.221743\pi$
$200$	−1.20845	+	1.15226i	−0.0854505	+	0.0814769i
$201$	−9.14480	+	7.19155i	−0.645025	+	0.507253i
$202$	−9.62959	−	4.39769i	−0.677535	−	0.309420i
$203$	8.20940	+	5.23781i	0.576187	+	0.367622i
$204$	−1.71168	+	2.66342i	−0.119841	+	0.186477i
$205$	5.83561	+	2.01973i	0.407577	+	0.141064i
$206$	6.37308	−	11.0385i	0.444034	−	0.769089i
$207$	−4.74790	+	0.676365i	−0.330002	+	0.0470106i
$208$	3.64670	−	2.10542i	0.252853	−	0.145985i
$209$	−12.5565	+	10.8802i	−0.868549	+	0.752602i
$210$	2.19830	−	4.29875i	0.151697	−	0.296642i
$211$	−1.24941	+	8.68982i	−0.0860127	+	0.598232i	0.900538	+	0.434777i	$0.143173\pi$
$211$	−1.24941	+	8.68982i	−0.0860127	+	0.598232i	−0.986551	+	0.163455i	$0.947736\pi$
$212$	−0.387321	−	4.05621i	−0.0266013	−	0.278582i
$213$	1.96788	−	4.91553i	0.134837	−	0.336807i
$214$	−0.919355	−	0.964192i	−0.0628458	−	0.0659108i
$215$	−7.48600	+	14.5208i	−0.510541	+	0.990311i
$216$	0.909632	−	0.415415i	0.0618926	−	0.0282654i
$217$	−5.69958	+	7.29684i	−0.386912	+	0.495342i
$218$	7.85566	+	6.80697i	0.532052	+	0.461026i
$219$	−9.09347	−	1.75262i	−0.614480	−	0.118431i
$220$	−5.18451	−	1.25775i	−0.349539	−	0.0847973i
$221$	1.26725	−	13.2712i	0.0852445	−	0.892721i
$222$	0.0286795	+	0.0147853i	0.00192484	+	0.000992325i
$223$	−0.801828	+	2.73077i	−0.0536943	+	0.182866i	−0.981974	−	0.189017i	$-0.939470\pi$
$223$	−0.801828	+	2.73077i	−0.0536943	+	0.182866i	0.928279	+	0.371884i	$0.121288\pi$
$224$	1.90881	−	1.83206i	0.127538	−	0.122410i
$225$	0.693638	−	1.51886i	0.0462425	−	0.101257i
$226$	−3.22530	−	8.05641i	−0.214544	−	0.535905i
$227$	23.4953	−	12.1127i	1.55944	−	0.803945i	0.559742	−	0.828667i	$-0.310900\pi$
$227$	23.4953	−	12.1127i	1.55944	−	0.803945i	0.999694	+	0.0247216i	$0.00786994\pi$
$228$	1.07558	+	5.58063i	0.0712318	+	0.369586i
$229$	13.8903	+	24.0587i	0.917897	+	1.58984i	0.802603	+	0.596514i	$0.203448\pi$
$229$	13.8903	+	24.0587i	0.917897	+	1.58984i	0.115294	+	0.993331i	$0.463219\pi$
$230$	7.58504	−	4.36612i	0.500142	−	0.287894i
$231$	−7.69708	+	0.760524i	−0.506431	+	0.0500388i
$232$	−2.41029	−	2.78163i	−0.158244	−	0.182623i
$233$	0.541270	−	11.3627i	0.0354598	−	0.744392i	−0.909204	−	0.416351i	$-0.863309\pi$
$233$	0.541270	−	11.3627i	0.0354598	−	0.744392i	0.944664	−	0.328041i	$-0.106388\pi$
$234$	−2.60297	+	3.30995i	−0.170162	+	0.216378i
$235$	−11.0759	+	7.88712i	−0.722513	+	0.514499i
$236$	−2.16700	−	2.75556i	−0.141060	−	0.179372i
$237$	−13.7475	−	4.03663i	−0.892996	−	0.262207i
$238$	−1.21935	−	8.28727i	−0.0790387	−	0.537184i
$239$	−0.209842	−	0.459490i	−0.0135735	−	0.0297219i	0.902724	−	0.430221i	$-0.141564\pi$
$239$	−0.209842	−	0.459490i	−0.0135735	−	0.0297219i	−0.916297	+	0.400499i	$0.868837\pi$
$240$	−1.25932	+	1.32074i	−0.0812890	+	0.0852535i
$241$	−2.28275	−	6.59557i	−0.147045	−	0.424858i	0.847293	−	0.531126i	$-0.178231\pi$
$241$	−2.28275	−	6.59557i	−0.147045	−	0.424858i	−0.994337	+	0.106268i	$0.966110\pi$
$242$	−0.802556	−	2.31883i	−0.0515903	−	0.149060i
$243$	−0.690079	+	0.723734i	−0.0442686	+	0.0464276i
$244$	−5.28239	−	11.5668i	−0.338170	−	0.740489i
$245$	3.09321	+	12.3941i	0.197618	+	0.791832i
$246$	−3.24681	−	0.953351i	−0.207009	−	0.0607834i
$247$	−14.7936	−	18.8115i	−0.941291	−	1.19695i
$248$	2.85067	−	2.02995i	0.181018	−	0.128902i
$249$	−1.38846	+	1.76557i	−0.0879903	+	0.111889i
$250$	−0.579148	+	12.1578i	−0.0366286	+	0.768928i
$251$	14.5057	+	16.7405i	0.915591	+	1.05665i	0.998194	+	0.0600662i	$0.0191312\pi$
$251$	14.5057	+	16.7405i	0.915591	+	1.05665i	−0.0826031	+	0.996583i	$0.526323\pi$
$252$	−1.09117	+	2.41026i	−0.0687371	+	0.151832i
$253$	−12.4532	−	6.44052i	−0.782927	−	0.404912i
$254$	−2.72500	−	4.71984i	−0.170982	−	0.296149i
$255$	1.09343	+	5.67325i	0.0684732	+	0.355273i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−0.721129	−	1.80129i	−0.0449828	−	0.112362i	0.904175	−	0.427162i	$-0.140487\pi$
$257$	−0.721129	−	1.80129i	−0.0449828	−	0.112362i	−0.949158	+	0.314801i	$0.898062\pi$
$258$	3.71889	−	8.14323i	0.231528	−	0.506975i
$259$	−0.0828958	+	0.0203991i	−0.00515089	+	0.00126754i
$260$	2.16494	−	7.37310i	0.134264	−	0.457260i
$261$	3.27147	+	1.68656i	0.202499	+	0.104395i
$262$	0.342002	−	3.58161i	0.0211290	−	0.221272i
$263$	−25.7093	−	6.23700i	−1.58530	−	0.384590i	−0.656250	−	0.754543i	$-0.727858\pi$
$263$	−25.7093	−	6.23700i	−1.58530	−	0.384590i	−0.929050	+	0.369954i	$0.879374\pi$
$264$	2.87056	+	0.553255i	0.176671	+	0.0340505i
$265$	−5.61963	−	4.86944i	−0.345211	−	0.299127i
$266$	−11.8501	−	9.25615i	−0.726577	−	0.567531i
$267$	13.8928	−	6.34464i	0.850227	−	0.388286i
$268$	−5.33093	+	10.3406i	−0.325638	+	0.631650i
$269$	0.0635910	+	0.0666923i	0.00387721	+	0.00406630i	0.725670	−	0.688043i	$-0.241530\pi$
$269$	0.0635910	+	0.0666923i	0.00387721	+	0.00406630i	−0.721793	+	0.692109i	$0.756682\pi$
$270$	0.678246	−	1.69418i	0.0412767	−	0.103104i
$271$	0.671301	+	7.03018i	0.0407786	+	0.427053i	0.992691	+	0.120683i	$0.0385084\pi$
$271$	0.671301	+	7.03018i	0.0407786	+	0.427053i	−0.951912	+	0.306370i	$0.900886\pi$
$272$	−0.450571	+	3.13379i	−0.0273199	+	0.190014i
$273$	−0.566683	−	11.1264i	−0.0342972	−	0.673402i
$274$	−1.68918	+	1.46368i	−0.102047	+	0.0884241i
$275$	4.22735	−	2.44066i	0.254919	−	0.147177i
$276$	−4.03787	+	2.58759i	−0.243051	+	0.155755i
$277$	−0.506201	+	0.876766i	−0.0304147	+	0.0526798i	−0.880832	−	0.473429i	$-0.843016\pi$
$277$	−0.506201	+	0.876766i	−0.0304147	+	0.0526798i	0.850417	+	0.526109i	$0.176349\pi$
$278$	20.8210	+	7.20621i	1.24876	+	0.432200i
$279$	−1.89201	+	2.94403i	−0.113272	+	0.176254i
$280$	0.213881	−	4.82349i	0.0127818	−	0.288258i
$281$	1.94975	+	0.890419i	0.116312	+	0.0531180i	0.472721	−	0.881212i	$-0.343272\pi$
$281$	1.94975	+	0.890419i	0.116312	+	0.0531180i	−0.356409	+	0.934330i	$0.615999\pi$
$282$	5.85681	−	4.60584i	0.348768	−	0.274274i
$283$	1.55242	−	1.48023i	0.0922819	−	0.0879906i	−0.642534	−	0.766257i	$-0.722117\pi$
$283$	1.55242	−	1.48023i	0.0922819	−	0.0879906i	0.734816	+	0.678266i	$0.237268\pi$
$284$	−0.251937	−	5.28881i	−0.0149497	−	0.313833i
$285$	8.44837	+	6.01606i	0.500438	+	0.356361i
$286$	−11.8113	+	3.46811i	−0.698417	+	0.205074i
$287$	8.13159	−	3.74593i	0.479993	−	0.221115i
$288$	0.654861	−	0.755750i	0.0385880	−	0.0445330i
$289$	−5.04901	−	4.81422i	−0.297001	−	0.283190i
$290$	−6.68635	−	0.638469i	−0.392636	−	0.0374922i
$291$	10.4106	−	0.495919i	0.610281	−	0.0290713i
$292$	−8.99978	+	2.18332i	−0.526672	+	0.127769i
$293$	−2.43836	−	16.9592i	−0.142451	−	0.990766i	−0.928163	−	0.372174i	$-0.878612\pi$
$293$	−2.43836	−	16.9592i	−0.142451	−	0.990766i	0.785712	−	0.618592i	$-0.212297\pi$
$294$	−2.01624	−	6.70334i	−0.117590	−	0.390947i
$295$	−6.33219	−	0.910432i	−0.368674	−	0.0530074i
$296$	0.0322298	+	0.00153530i	0.00187332	+	8.92373e-5i
$297$	−2.87056	+	0.553255i	−0.166567	+	0.0321031i
$298$	11.0715	+	6.39216i	0.641357	+	0.370288i
$299$	10.1199	−	17.4759i	0.585250	−	1.01066i
$300$		−	1.66975i		−	0.0964029i
$301$	6.74761	+	22.7039i	0.388926	+	1.30863i
$302$	0.142532	+	0.0915997i	0.00820179	+	0.00527097i
$303$	9.82793	−	3.93451i	0.564600	−	0.226032i
$304$	3.29665	+	4.62950i	0.189076	+	0.265520i
$305$	−21.5430	−	8.62453i	−1.23355	−	0.493839i
$306$	−0.746417	−	3.07677i	−0.0426698	−	0.175887i
$307$	−14.9082	−	23.1977i	−0.850858	−	1.32396i	−0.944553	−	0.328360i	$-0.893504\pi$
$307$	−14.9082	−	23.1977i	−0.850858	−	1.32396i	0.0936951	−	0.995601i	$-0.470132\pi$
$308$	−6.68558	+	3.88928i	−0.380946	+	0.221612i
$309$	3.59101	+	12.2299i	0.204285	+	0.695732i
$310$	1.20863	−	6.27095i	0.0686454	−	0.356166i
$311$	7.04482	−	2.43824i	0.399475	−	0.138260i	−0.119941	−	0.992781i	$-0.538271\pi$
$311$	7.04482	−	2.43824i	0.399475	−	0.138260i	0.519416	+	0.854521i	$0.326149\pi$
$312$	−0.992745	+	4.09215i	−0.0562031	+	0.231672i
$313$	1.66401	−	2.33677i	0.0940553	−	0.132082i	−0.764867	−	0.644188i	$-0.777195\pi$
$313$	1.66401	−	2.33677i	0.0940553	−	0.132082i	0.858922	+	0.512106i	$0.171135\pi$
$314$	1.55596	−	0.999952i	0.0878077	−	0.0564306i
$315$	1.59415	+	4.55746i	0.0898201	+	0.256784i
$316$	−14.1820	+	2.03907i	−0.797802	+	0.114707i
$317$	−28.1051	+	2.68371i	−1.57854	+	0.150732i	−0.847197	−	0.531278i	$-0.821712\pi$
$317$	−28.1051	+	2.68371i	−1.57854	+	0.150732i	−0.731342	+	0.682010i	$0.761106\pi$
$318$	3.20290	+	2.51879i	0.179610	+	0.141247i
$319$	4.93047	+	9.56377i	0.276053	+	0.535469i
$320$	−0.596866	+	1.72453i	−0.0333658	+	0.0964042i
$321$	1.33225			0.0743588
$322$	3.55053	−	12.1817i	0.197864	−	0.678859i
$323$	17.9935			1.00119
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	3.22181	+	6.24945i	0.178714	+	0.346657i
$326$	−7.54255	−	5.93153i	−0.417743	−	0.328517i
$327$	−10.3475	+	0.988062i	−0.572216	+	0.0546400i
$328$	−3.34944	+	0.481577i	−0.184942	+	0.0265906i
$329$	−3.66710	+	19.3692i	−0.202174	+	1.06786i
$330$	4.48799	−	2.88426i	0.247056	−	0.158773i
$331$	8.79724	−	12.3540i	0.483540	−	0.679037i	−0.498677	−	0.866788i	$-0.666180\pi$
$331$	8.79724	−	12.3540i	0.483540	−	0.679037i	0.982217	+	0.187751i	$0.0601199\pi$
$332$	−0.529544	+	2.18281i	−0.0290625	+	0.119797i
$333$	−0.0304918	+	0.0105533i	−0.00167094	+	0.000578317i
$334$	−3.24734	+	16.8488i	−0.177687	+	0.921926i
$335$	5.98133	+	20.3706i	0.326795	+	1.11296i
$336$	0.00869753	+	2.64574i	0.000474489	+	0.144337i
$337$	−10.5796	−	16.4622i	−0.576307	−	0.896751i	0.423652	−	0.905825i	$-0.360748\pi$
$337$	−10.5796	−	16.4622i	−0.576307	−	0.896751i	−0.999959	+	0.00907376i	$0.997112\pi$
$338$	−1.11543	−	4.59787i	−0.0606714	−	0.250091i
$339$	8.05641	+	3.22530i	0.437564	+	0.175174i
$340$	3.35137	+	4.70634i	0.181754	+	0.255237i
$341$	−9.49778	+	3.80234i	−0.514333	+	0.205908i
$342$	−4.78112	−	3.07264i	−0.258533	−	0.166149i
$343$	15.6782	+	9.85867i	0.846544	+	0.532318i
$344$		−	8.95222i		−	0.482671i
$345$	−2.07436	+	8.50252i	−0.111680	+	0.457760i
$346$	3.70091	+	2.13672i	0.198962	+	0.114871i
$347$	−10.3537	+	1.99550i	−0.555813	+	0.107124i	−0.459420	−	0.888219i	$-0.651943\pi$
$347$	−10.3537	+	1.99550i	−0.555813	+	0.107124i	−0.0963932	+	0.995343i	$0.530731\pi$
$348$	3.67645	+	0.175131i	0.197079	+	0.00938801i
$349$	−14.8840	−	2.13999i	−0.796720	−	0.114551i	−0.268079	−	0.963397i	$-0.586389\pi$
$349$	−14.8840	−	2.13999i	−0.796720	−	0.114551i	−0.528641	+	0.848846i	$0.677298\pi$
$350$	2.90396	+	3.32917i	0.155223	+	0.177952i
$351$	−0.599266	−	4.16799i	−0.0319865	−	0.222471i
$352$	2.84098	−	0.689215i	0.151425	−	0.0367353i
$353$	−2.47620	+	0.117956i	−0.131795	+	0.00627816i	−0.113376	−	0.993552i	$-0.536166\pi$
$353$	−2.47620	+	0.117956i	−0.131795	+	0.00627816i	−0.0184192	+	0.999830i	$0.505863\pi$
$354$	3.48970	+	0.333226i	0.185475	+	0.0177107i
$355$	−6.99307	−	6.66788i	−0.371154	−	0.353894i
$356$	10.0017	−	11.5426i	0.530089	−	0.611755i
$357$	6.83923	+	4.83639i	0.361970	+	0.255969i
$358$	19.9525	−	5.85858i	1.05452	−	0.309636i
$359$	27.2341	+	19.3933i	1.43736	+	1.02354i	0.991733	+	0.128321i	$0.0409588\pi$
$359$	27.2341	+	19.3933i	1.43736	+	1.02354i	0.445628	+	0.895218i	$0.352981\pi$
$360$	−0.0868321	−	1.82283i	−0.00457646	−	0.0960716i
$361$	9.62584	−	9.17822i	0.506623	−	0.483064i
$362$	−18.6376	+	14.6567i	−0.979569	+	0.770342i
$363$	2.23205	+	1.01934i	0.117152	+	0.0535016i
$364$	−5.13756	−	9.88555i	−0.269281	−	0.518144i
$365$	−9.13686	+	14.2172i	−0.478245	+	0.744164i
$366$	12.0166	+	4.15897i	0.628116	+	0.217393i
$367$	14.5001	−	25.1148i	0.756897	−	1.31098i	−0.187528	−	0.982259i	$-0.560048\pi$
$367$	14.5001	−	25.1148i	0.756897	−	1.31098i	0.944426	−	0.328725i	$-0.106619\pi$
$368$	−2.59805	+	4.03115i	−0.135433	+	0.210138i
$369$	2.93053	−	1.69194i	0.152557	−	0.0880790i
$370$	0.0445007	−	0.0385601i	0.00231348	−	0.00200464i
$371$	−10.7666	+	0.548355i	−0.558973	+	0.0284692i
$372$	−0.498041	+	3.46395i	−0.0258222	+	0.179598i
$373$	3.59841	+	37.6842i	0.186319	+	1.95122i	0.291031	+	0.956714i	$0.406002\pi$
$373$	3.59841	+	37.6842i	0.186319	+	1.95122i	−0.104712	+	0.994503i	$0.533392\pi$
$374$	3.43992	−	8.59251i	0.177874	−	0.444308i
$375$	−8.39937	−	8.80901i	−0.433742	−	0.454895i
$376$	3.41420	−	6.62263i	0.176074	−	0.341536i
$377$	−14.0980	+	6.43832i	−0.726082	+	0.331591i
$378$	−0.991396	−	2.45298i	−0.0509919	−	0.126168i
$379$	14.5559	+	12.6127i	0.747686	+	0.647873i	0.942972	−	0.332873i	$-0.108018\pi$
$379$	14.5559	+	12.6127i	0.747686	+	0.647873i	−0.195286	+	0.980746i	$0.562564\pi$
$380$	10.1841	+	1.96282i	0.522432	+	0.100690i
$381$	5.29638	+	1.28489i	0.271342	+	0.0658268i
$382$	−0.618002	+	6.47201i	−0.0316197	+	0.331137i
$383$	3.33630	+	1.71998i	0.170477	+	0.0878869i	0.541353	−	0.840795i	$-0.317912\pi$
$383$	3.33630	+	1.71998i	0.170477	+	0.0878869i	−0.370876	+	0.928682i	$0.620943\pi$
$384$	0.281733	−	0.959493i	0.0143771	−	0.0489639i
$385$	−3.93205	+	13.5560i	−0.200396	+	0.690880i
$386$	−1.28646	+	2.81695i	−0.0654791	+	0.143379i
$387$	3.32720	+	8.31095i	0.169131	+	0.422470i
$388$	9.26382	−	4.77583i	0.470299	−	0.242456i
$389$	−5.51879	−	28.6342i	−0.279814	−	1.45181i	−0.801151	−	0.598462i	$-0.795779\pi$
$389$	−5.51879	−	28.6342i	−0.279814	−	1.45181i	0.521337	−	0.853351i	$-0.325433\pi$
$390$	3.84218	+	6.65486i	0.194557	+	0.336982i
$391$	5.62493	+	14.1033i	0.284465	+	0.713237i
$392$	−4.61871	−	5.25999i	−0.233280	−	0.265670i
$393$	2.35612	+	2.71911i	0.118851	+	0.137161i
$394$	0.884677	−	18.5717i	0.0445694	−	0.935626i
$395$	−16.1629	+	20.5529i	−0.813246	+	1.03413i
$396$	−2.38132	+	1.69573i	−0.119666	+	0.0852138i
$397$	11.4931	+	14.6147i	0.576824	+	0.733491i	0.983665	−	0.180008i	$-0.0576122\pi$
$397$	11.4931	+	14.6147i	0.576824	+	0.733491i	−0.406841	+	0.913499i	$0.633370\pi$
$398$	16.3618	+	4.80425i	0.820141	+	0.240815i
$399$	14.8765	−	2.18886i	0.744757	−	0.109580i
$400$	−0.693638	−	1.51886i	−0.0346819	−	0.0759428i
$401$	7.47663	−	7.84126i	0.373365	−	0.391574i	−0.510066	−	0.860135i	$-0.670379\pi$
$401$	7.47663	−	7.84126i	0.373365	−	0.391574i	0.883431	+	0.468561i	$0.155228\pi$
$402$	−3.80505	−	10.9940i	−0.189779	−	0.548330i
$403$	−4.81973	−	13.9257i	−0.240088	−	0.693688i
$404$	7.30535	−	7.66163i	0.363455	−	0.381180i
$405$	0.758090	+	1.65999i	0.0376698	+	0.0824853i
$406$	−7.63476	+	6.04477i	−0.378907	+	0.299997i
$407$	−0.0905063	−	0.0265750i	−0.00448623	−	0.00131728i
$408$	−1.95710	−	2.48866i	−0.0968910	−	0.123207i
$409$	6.80595	−	4.84649i	0.336532	−	0.239644i	−0.399280	−	0.916829i	$-0.630740\pi$
$409$	6.80595	−	4.84649i	0.336532	−	0.239644i	0.735812	+	0.677185i	$0.236800\pi$
$410$	−3.81728	+	4.85407i	−0.188522	+	0.239725i
$411$	0.106350	−	2.23257i	0.00524587	−	0.110124i
$412$	8.34696	+	9.63291i	0.411225	+	0.474579i
$413$	−7.53736	+	5.40476i	−0.370889	+	0.265951i
$414$	0.913720	−	4.70798i	0.0449069	−	0.231385i
$415$	2.04948	+	3.54980i	0.100605	+	0.174253i
$416$	0.796908	+	4.13475i	0.0390716	+	0.202723i
$417$	−19.5835	+	10.0960i	−0.959009	+	0.494403i
$418$	−6.17502	−	15.4245i	−0.302030	−	0.754435i
$419$	6.59072	−	14.4317i	0.321978	−	0.705033i	−0.677559	−	0.735468i	$-0.736962\pi$
$419$	6.59072	−	14.4317i	0.321978	−	0.705033i	0.999537	+	0.0304357i	$0.00968948\pi$
$420$	3.34333	+	3.48338i	0.163138	+	0.169972i
$421$	1.08584	−	3.69803i	0.0529206	−	0.180231i	−0.928791	−	0.370603i	$-0.879151\pi$
$421$	1.08584	−	3.69803i	0.0529206	−	0.180231i	0.981712	+	0.190372i	$0.0609693\pi$
$422$	−7.80324	−	4.02285i	−0.379856	−	0.195829i
$423$	−0.708254	+	7.41717i	−0.0344365	+	0.360635i
$424$	3.95980	+	0.960638i	0.192305	+	0.0466527i
$425$	−5.19091	−	1.00047i	−0.251796	−	0.0485298i
$426$	4.00155	+	3.46736i	0.193876	+	0.167994i
$427$	−31.1920	+	12.6065i	−1.50949	+	0.610072i
$428$	1.21185	−	0.553435i	0.0585772	−	0.0267513i
$429$	5.64074	−	10.9415i	0.272338	−	0.528261i
$430$	−11.2737	−	11.8236i	−0.543668	−	0.570183i
$431$	5.72270	−	14.2946i	0.275653	−	0.688547i	−0.724347	−	0.689436i	$-0.757859\pi$
$431$	5.72270	−	14.2946i	0.275653	−	0.688547i	1.00000		0.000888586i	$0.000282846\pi$
$432$	0.0950560	+	0.995472i	0.00457339	+	0.0478947i
$433$	4.36818	−	30.3814i	0.209921	−	1.46003i	−0.563486	−	0.826126i	$-0.690540\pi$
$433$	4.36818	−	30.3814i	0.209921	−	1.46003i	0.773407	−	0.633909i	$-0.218551\pi$
$434$	−5.03137	−	7.77267i	−0.241514	−	0.373100i
$435$	5.07619	−	4.39854i	0.243385	−	0.210894i
$436$	−9.00192	+	5.19726i	−0.431114	+	0.248904i
$437$	24.7785	+	11.3548i	1.18532	+	0.543174i
$438$	4.63041	−	8.02011i	0.221250	−	0.383216i
$439$	27.0568	+	9.36444i	1.29135	+	0.446940i	0.884494	−	0.466552i	$-0.154504\pi$
$439$	27.0568	+	9.36444i	1.29135	+	0.446940i	0.406856	+	0.913492i	$0.366625\pi$
$440$	2.88426	−	4.48799i	0.137502	−	0.213957i
$441$	6.24280	+	3.16661i	0.297276	+	0.150791i
$442$	12.1269	+	5.53815i	0.576816	+	0.263423i
$443$	26.7884	−	21.0666i	1.27275	−	1.00091i	0.273517	−	0.961867i	$-0.411813\pi$
$443$	26.7884	−	21.0666i	1.27275	−	1.00091i	0.999238	−	0.0390380i	$-0.0124293\pi$
$444$	−0.0233523	+	0.0222663i	−0.00110825	+	0.00105671i
$445$	−1.32619	−	27.8401i	−0.0628674	−	1.31975i
$446$	−2.31833	−	1.65088i	−0.109776	−	0.0781713i
$447$	−12.2665	+	3.60176i	−0.580183	+	0.170357i
$448$	1.10699	+	2.40303i	0.0523004	+	0.113533i
$449$	−18.1559	+	20.9530i	−0.856830	+	0.988834i	−1.00000		0.000864046i	$-0.999725\pi$
$449$	−18.1559	+	20.9530i	−0.856830	+	0.988834i	0.143170	+	0.989698i	$0.454270\pi$
$450$	1.20845	+	1.15226i	0.0569670	+	0.0543179i
$451$	9.84762	+	0.940334i	0.463706	+	0.0442786i
$452$	8.66821	−	0.412918i	0.407718	−	0.0194220i
$453$	−0.164652	+	0.0399442i	−0.00773603	+	0.00187674i
$454$	3.76192	+	26.1647i	0.176556	+	1.22797i
$455$	−19.2345	−	6.58640i	−0.901727	−	0.308775i
$456$	−5.62548	−	0.808822i	−0.263437	−	0.0378766i
$457$	6.01637	+	0.286595i	0.281434	+	0.0134064i	0.187824	−	0.982203i	$-0.439856\pi$
$457$	6.01637	+	0.286595i	0.281434	+	0.0134064i	0.0936096	+	0.995609i	$0.470159\pi$
$458$	−27.2786	+	5.25752i	−1.27464	+	0.245668i
$459$	2.74185	+	1.58301i	0.127979	+	0.0738885i
$460$	1.64517	+	8.59588i	0.0767064	+	0.400785i
$461$			17.4425i			0.812379i	0.913789	+	0.406190i	$0.133143\pi$
$461$			17.4425i			0.812379i	−0.913789	+	0.406190i	$0.866857\pi$
$462$	1.79877	−	7.52249i	0.0836865	−	0.349978i
$463$	13.4639	+	8.65271i	0.625719	+	0.402125i	0.814722	−	0.579851i	$-0.196889\pi$
$463$	13.4639	+	8.65271i	0.625719	+	0.402125i	−0.189003	+	0.981976i	$0.560526\pi$
$464$	3.41697	−	1.36795i	0.158629	−	0.0635054i
$465$	3.70445	+	5.20218i	0.171790	+	0.241245i
$466$	10.5607	+	4.22786i	0.489214	+	0.195852i
$467$	0.600555	+	2.47552i	0.0277904	+	0.114553i	0.984017	−	0.178072i	$-0.0569861\pi$
$467$	0.600555	+	2.47552i	0.0277904	+	0.114553i	−0.956227	+	0.292626i	$0.905471\pi$
$468$	−2.27656	−	3.54239i	−0.105234	−	0.163747i
$469$	26.7069	+	15.3024i	1.23321	+	0.706599i
$470$	−3.83076	−	13.0464i	−0.176700	−	0.601784i
$471$	−0.350033	+	1.81614i	−0.0161287	+	0.0836835i
$472$	3.31277	−	1.14656i	0.152482	−	0.0527747i
$473$	−6.17001	+	25.4331i	−0.283697	+	1.16942i
$474$	8.31098	−	11.6711i	0.381736	−	0.536073i
$475$	−7.98326	+	5.13053i	−0.366297	+	0.235405i
$476$	8.23029	+	1.55821i	0.377235	+	0.0714206i
$477$	−4.03319	+	0.579885i	−0.184667	+	0.0265511i
$478$	0.502851	−	0.0480164i	0.0229998	−	0.00219622i
$479$	24.2605	+	19.0787i	1.10849	+	0.871727i	0.992587	−	0.121534i	$-0.0387813\pi$
$479$	24.2605	+	19.0787i	1.10849	+	0.871727i	0.115903	+	0.993260i	$0.463024\pi$
$480$	−0.836217	−	1.62203i	−0.0381679	−	0.0740354i
$481$	0.0444383	−	0.128396i	0.00202621	−	0.00585436i
$482$	6.97943			0.317904
$483$	6.36616	+	10.9760i	0.289670	+	0.499424i
$484$	2.45379			0.111536
$485$	6.22079	−	17.9738i	0.282471	−	0.816147i
$486$	−0.458227	−	0.888835i	−0.0207856	−	0.0403184i
$487$	17.2986	+	13.6037i	0.783872	+	0.616444i	0.927772	−	0.373148i	$-0.121722\pi$
$487$	17.2986	+	13.6037i	0.783872	+	0.616444i	−0.143899	+	0.989592i	$0.545964\pi$
$488$	12.6583	−	1.20873i	0.573017	−	0.0547164i
$489$	9.49781	−	1.36558i	0.429506	−	0.0617536i
$490$	−12.7242	−	1.13064i	−0.574819	−	0.0510771i
$491$	4.49551	−	2.88909i	0.202880	−	0.130383i	−0.435256	−	0.900307i	$-0.643342\pi$
$491$	4.49551	−	2.88909i	0.202880	−	0.130383i	0.638136	+	0.769924i	$0.279706\pi$
$492$	1.96285	−	2.75643i	0.0884919	−	0.124270i
$493$	2.74728	−	11.3244i	0.123731	−	0.510027i
$494$	22.6154	−	7.82727i	1.01752	−	0.352166i
$495$	−1.00963	+	5.23848i	−0.0453797	+	0.235452i
$496$	0.985944	+	3.35782i	0.0442702	+	0.150770i
$497$	−14.0087	+	0.0460518i	−0.628375	+	0.00206571i
$498$	−1.21435	−	1.88956i	−0.0544162	−	0.0846733i
$499$	7.61950	+	31.4080i	0.341095	+	1.40601i	0.841516	+	0.540232i	$0.181664\pi$
$499$	7.61950	+	31.4080i	0.341095	+	1.40601i	−0.500421	+	0.865782i	$0.666821\pi$
$500$	−11.2997	−	4.52373i	−0.505339	−	0.202307i
$501$	−9.95313	−	13.9772i	−0.444673	−	0.624456i
$502$	−20.5641	+	8.23262i	−0.917821	+	0.367440i
$503$	10.0498	+	6.45864i	0.448100	+	0.287977i	0.745164	−	0.666881i	$-0.232371\pi$
$503$	10.0498	+	6.45864i	0.448100	+	0.287977i	−0.297064	+	0.954858i	$0.596007\pi$
$504$	−1.92081	−	1.81947i	−0.0855598	−	0.0810458i
$505$		−	19.3188i		−	0.859676i
$506$	10.1593	−	9.66181i	0.451638	−	0.429520i
$507$	4.09737	+	2.36562i	0.181971	+	0.105061i
$508$	5.35152	−	1.03142i	0.237435	−	0.0457619i
$509$	15.4848	+	0.737632i	0.686352	+	0.0326950i	0.387861	−	0.921718i	$-0.373214\pi$
$509$	15.4848	+	0.737632i	0.686352	+	0.0326950i	0.298490	+	0.954413i	$0.403517\pi$
$510$	−5.71885	−	0.822246i	−0.253235	−	0.0364097i
$511$	4.71607	+	24.0437i	0.208627	+	1.06363i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	5.52313	−	1.33990i	0.243852	−	0.0591578i
$514$	1.93808	−	0.0923222i	0.0854851	−	0.00407216i
$515$	23.1551	+	2.21105i	1.02034	+	0.0974303i
$516$	6.47903	+	6.17774i	0.285223	+	0.271960i
$517$	−14.2641	+	16.4617i	−0.627335	+	0.723983i
$518$	0.00783541	−	0.0850085i	0.000344268	−	0.00373506i
$519$	−4.10034	+	1.20397i	−0.179985	+	0.0528484i
$520$	6.25950	+	4.45737i	0.274497	+	0.195469i
$521$	−1.23461	−	25.9177i	−0.0540893	−	1.13547i	−0.848878	−	0.528588i	$-0.822722\pi$
$521$	−1.23461	−	25.9177i	−0.0540893	−	1.13547i	0.794789	−	0.606886i	$-0.207581\pi$
$522$	−2.66379	+	2.53992i	−0.116591	+	0.111169i
$523$	−11.4547	+	9.00811i	−0.500881	+	0.393897i	−0.836386	−	0.548141i	$-0.815336\pi$
$523$	−11.4547	+	9.00811i	−0.500881	+	0.393897i	0.335505	+	0.942038i	$0.391093\pi$
$524$	3.27276	+	1.49462i	0.142971	+	0.0652928i
$525$	−4.41340	−	0.195697i	−0.192617	−	0.00854092i
$526$	14.3026	−	22.2553i	0.623625	−	0.970379i
$527$	10.4703	+	3.62382i	0.456095	+	0.157856i
$528$	−1.46170	+	2.53173i	−0.0636121	+	0.110179i
$529$	−1.15393	+	22.9710i	−0.0501709	+	0.998741i
$530$	6.43963	−	3.71792i	0.279720	−	0.161496i
$531$	−2.64933	+	2.29566i	−0.114971	+	0.0996232i
$532$	12.6229	−	8.17098i	0.547271	−	0.354257i
$533$	−2.02785	+	14.1040i	−0.0878358	+	0.610912i
$534$	1.45179	+	15.2039i	0.0628252	+	0.657935i
$535$	0.903591	−	2.25706i	0.0390656	−	0.0975813i
$536$	−8.02826	−	8.41979i	−0.346768	−	0.363680i
$537$	−9.52875	+	18.4832i	−0.411196	+	0.797609i
$538$	−0.0838229	+	0.0382806i	−0.00361386	+	0.00165039i
$539$	9.49641	+	18.1268i	0.409039	+	0.780778i
$540$	1.37917	+	1.19505i	0.0593499	+	0.0514269i
$541$	43.0875	+	8.30444i	1.85248	+	0.357036i	0.989067	−	0.147468i	$-0.0471123\pi$
$541$	43.0875	+	8.30444i	1.85248	+	0.357036i	0.863410	+	0.504504i	$0.168324\pi$
$542$	−6.86309	−	1.66497i	−0.294795	−	0.0715164i
$543$	2.25381	−	23.6030i	0.0967202	−	1.01290i
$544$	−2.81407	−	1.45075i	−0.120652	−	0.0622005i
$545$	−5.34417	+	18.2006i	−0.228919	+	0.779627i
$546$	10.6998	+	3.10358i	0.457911	+	0.132821i
$547$	−2.02452	+	4.43308i	−0.0865622	+	0.189545i	−0.947963	−	0.318382i	$-0.896861\pi$
$547$	−2.02452	+	4.43308i	−0.0865622	+	0.189545i	0.861400	+	0.507927i	$0.169588\pi$
$548$	−0.830702	−	2.07499i	−0.0354858	−	0.0886394i
$549$	−11.3024	+	5.82678i	−0.482373	+	0.248681i
$550$	0.923796	+	4.79311i	0.0393908	+	0.204379i
$551$	−10.4591	−	18.1157i	−0.445572	−	0.771754i
$552$	−1.12462	−	4.66211i	−0.0478670	−	0.198432i
$553$	3.72742	+	37.7243i	0.158506	+	1.60420i
$554$	−0.662983	−	0.765123i	−0.0281674	−	0.0325070i
$555$	−0.00280176	+	0.0588162i	−0.000118928	+	0.00249661i
$556$	−13.6198	+	17.3189i	−0.577606	+	0.734486i
$557$	−0.368296	+	0.262262i	−0.0156052	+	0.0111124i	−0.587833	−	0.808982i	$-0.700019\pi$
$557$	−0.368296	+	0.262262i	−0.0156052	+	0.0111124i	0.572228	+	0.820095i	$0.306079\pi$
$558$	−2.16329	−	2.75085i	−0.0915795	−	0.116453i
$559$	−36.1695	−	10.6203i	−1.52981	−	0.449191i
$560$	4.48825	+	1.77973i	0.189663	+	0.0752071i
$561$	3.84487	+	8.41910i	0.162331	+	0.355455i
$562$	−1.47915	+	1.55128i	−0.0623940	+	0.0654370i
$563$	−15.0979	−	43.6224i	−0.636299	−	1.83847i	−0.537323	−	0.843377i	$-0.680564\pi$
$563$	−15.0979	−	43.6224i	−0.636299	−	1.83847i	−0.0989770	−	0.995090i	$-0.531557\pi$
$564$	2.43695	+	7.04111i	0.102614	+	0.296484i
$565$	10.9285	−	11.4614i	0.459764	−	0.482186i
$566$	0.891072	+	1.95118i	0.0374546	+	0.0820140i
$567$	2.45945	+	0.975247i	0.103287	+	0.0409565i
$568$	5.08033	+	1.49172i	0.213166	+	0.0625912i
$569$	−16.7866	−	21.3458i	−0.703729	−	0.894864i	0.294420	−	0.955676i	$-0.404873\pi$
$569$	−16.7866	−	21.3458i	−0.703729	−	0.894864i	−0.998149	+	0.0608119i	$0.980631\pi$
$570$	−8.44837	+	6.01606i	−0.353863	+	0.251985i
$571$	4.61115	−	5.86355i	0.192971	−	0.245382i	−0.679934	−	0.733274i	$-0.737991\pi$
$571$	4.61115	−	5.86355i	0.192971	−	0.245382i	0.872904	+	0.487892i	$0.162234\pi$
$572$	0.585731	−	12.2960i	0.0244906	−	0.514122i
$573$	−4.25754	−	4.91346i	−0.177861	−	0.205263i
$574$	0.880323	+	8.90953i	0.0367440	+	0.371877i
$575$	−6.51696	−	4.65345i	−0.271776	−	0.194062i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	2.70047	+	14.0114i	0.112422	+	0.583302i	0.993827	+	0.110940i	$0.0353862\pi$
$577$	2.70047	+	14.0114i	0.112422	+	0.583302i	−0.881405	+	0.472362i	$0.843402\pi$
$578$	6.20082	−	3.19674i	0.257920	−	0.132967i
$579$	−1.15097	−	2.87498i	−0.0478326	−	0.119480i
$580$	2.79024	−	6.10978i	0.115859	−	0.253695i
$581$	5.70744	+	1.65550i	0.236785	+	0.0686816i
$582$	−2.93634	+	10.0002i	−0.121715	+	0.414523i
$583$	−10.5877	−	5.45831i	−0.438496	−	0.226060i
$584$	0.880297	−	9.21889i	0.0364270	−	0.381480i
$585$	−7.46776	−	1.81166i	−0.308754	−	0.0749028i
$586$	16.8240	+	3.24255i	0.694991	+	0.133949i
$587$	−3.59173	−	3.11225i	−0.148246	−	0.128456i	0.577580	−	0.816334i	$-0.303997\pi$
$587$	−3.59173	−	3.11225i	−0.148246	−	0.128456i	−0.725827	+	0.687878i	$0.758543\pi$
$588$	6.99411	+	0.287096i	0.288432	+	0.0118396i
$589$	18.0919	−	8.26228i	0.745463	−	0.340441i
$590$	2.93142	−	5.68615i	0.120684	−	0.234095i
$591$	12.8304	+	13.4562i	0.527774	+	0.553513i
$592$	−0.0119922	+	0.0299551i	−0.000492876	+	0.00123115i
$593$	−3.13651	−	32.8471i	−0.128801	−	1.34887i	−0.796592	−	0.604518i	$-0.793366\pi$
$593$	−3.13651	−	32.8471i	−0.128801	−	1.34887i	0.667790	−	0.744349i	$-0.267240\pi$
$594$	0.416042	−	2.89363i	0.0170704	−	0.118727i
$595$	12.8324	−	8.30660i	0.526076	−	0.340537i
$596$	−9.66174	+	8.37194i	−0.395760	+	0.342928i
$597$	−14.7679	+	8.52626i	−0.604410	+	0.348956i
$598$	13.2048	+	15.2791i	0.539985	+	0.624810i
$599$	15.8238	−	27.4076i	0.646543	−	1.11984i	−0.337400	−	0.941361i	$-0.609548\pi$
$599$	15.8238	−	27.4076i	0.646543	−	1.11984i	0.983943	−	0.178483i	$-0.0571191\pi$
$600$	1.57791	+	0.546121i	0.0644180	+	0.0222953i
$601$	−13.3940	+	20.8415i	−0.546354	+	0.850143i	−0.999140	−	0.0414760i	$-0.986794\pi$
$601$	−13.3940	+	20.8415i	−0.546354	+	0.850143i	0.452785	+	0.891620i	$0.350430\pi$
$602$	−23.6621	−	1.04921i	−0.964395	−	0.0427628i
$603$	10.5825	+	4.83286i	0.430953	+	0.196809i
$604$	−0.133179	+	0.104733i	−0.00541899	+	0.00426154i
$605$	3.24082	−	3.09012i	0.131758	−	0.125631i
$606$	0.503714	+	10.5743i	0.0204620	+	0.429550i
$607$	−5.80967	−	4.13705i	−0.235807	−	0.167918i	0.456045	−	0.889957i	$-0.349266\pi$
$607$	−5.80967	−	4.13705i	−0.235807	−	0.167918i	−0.691852	+	0.722039i	$0.743205\pi$
$608$	−5.45312	+	1.60118i	−0.221153	+	0.0649364i
$609$	0.893784	−	9.69691i	0.0362180	−	0.392938i
$610$	15.1962	−	17.5374i	0.615277	−	0.710068i
$611$	−22.7069	−	21.6510i	−0.918622	−	0.875905i
$612$	3.15168	+	0.300949i	0.127399	+	0.0121651i
$613$	31.2096	−	1.48670i	1.26055	−	0.0600472i	0.593359	−	0.804938i	$-0.297802\pi$
$613$	31.2096	−	1.48670i	1.26055	−	0.0600472i	0.667186	+	0.744891i	$0.267499\pi$
$614$	26.7978	−	6.50108i	1.08147	−	0.262362i
$615$	−0.878829	−	6.11239i	−0.0354378	−	0.246475i
$616$	−1.48873	−	7.58994i	−0.0599828	−	0.305807i
$617$	−34.4879	−	4.95861i	−1.38843	−	0.199626i	−0.592772	−	0.805371i	$-0.701966\pi$
$617$	−34.4879	−	4.95861i	−1.38843	−	0.199626i	−0.795659	+	0.605744i	$0.792875\pi$
$618$	−12.7317	−	0.606487i	−0.512145	−	0.0243965i
$619$	11.5646	−	2.22889i	0.464819	−	0.0895866i	0.0485357	−	0.998821i	$-0.484545\pi$
$619$	11.5646	−	2.22889i	0.464819	−	0.0895866i	0.416283	+	0.909235i	$0.363332\pi$
$620$	5.53075	+	3.19318i	0.222120	+	0.128241i
$621$	2.77679	+	3.91017i	0.111429	+	0.156910i
$622$			7.45483i			0.298912i
$623$	−29.3366	−	27.7888i	−1.17535	−	1.11334i
$624$	−3.54239	−	2.27656i	−0.141809	−	0.0911352i
$625$	−12.8702	+	5.15243i	−0.514806	+	0.206097i
$626$	1.66401	+	2.33677i	0.0665071	+	0.0933962i
$627$	15.4245	+	6.17502i	0.615993	+	0.246607i
$628$	0.436052	+	1.79743i	0.0174004	+	0.0717254i
$629$	0.0552296	+	0.0859390i	0.00220215	+	0.00342661i
$630$	−4.82820	+	0.0158721i	−0.192360	+	0.000632360i
$631$	8.27927	+	28.1966i	0.329593	+	1.12249i	0.943019	+	0.332738i	$0.107972\pi$
$631$	8.27927	+	28.1966i	0.329593	+	1.12249i	−0.613427	+	0.789752i	$0.710209\pi$
$632$	2.71157	−	14.0690i	0.107860	−	0.559633i
$633$	8.29633	−	2.87139i	0.329749	−	0.114127i
$634$	6.65617	−	27.4371i	0.264350	−	1.08967i
$635$	5.76907	−	8.10153i	0.228939	−	0.321499i
$636$	−3.42782	+	2.20293i	−0.135922	+	0.0873518i
$637$	−26.7312	+	12.4208i	−1.05913	+	0.492128i
$638$	−10.6504	+	1.53129i	−0.421652	+	0.0606244i
$639$	−5.27084	+	0.503304i	−0.208511	+	0.0199104i
$640$	−1.43447	−	1.12808i	−0.0567023	−	0.0445912i
$641$	0.554430	+	1.07544i	0.0218987	+	0.0424775i	0.899531	−	0.436857i	$-0.143908\pi$
$641$	0.554430	+	1.07544i	0.0218987	+	0.0424775i	−0.877632	+	0.479334i	$0.840878\pi$
$642$	−0.435735	+	1.25897i	−0.0171971	+	0.0496877i
$643$	−35.4648			−1.39860			−0.699298	−	0.714830i	$-0.746504\pi$
$643$	−35.4648			−1.39860			−0.699298	+	0.714830i	$0.746504\pi$
$644$	10.3504	+	7.33950i	0.407865	+	0.289217i
$645$	16.3369			0.643264
$646$	−5.88510	+	17.0039i	−0.231546	+	0.669009i
$647$	1.02255	+	1.98346i	0.0402004	+	0.0779779i	0.908080	−	0.418796i	$-0.137548\pi$
$647$	1.02255	+	1.98346i	0.0402004	+	0.0779779i	−0.867880	+	0.496774i	$0.834518\pi$
$648$	−0.786053	−	0.618159i	−0.0308791	−	0.0242836i
$649$	−10.2017	+	0.974148i	−0.400453	+	0.0382387i
$650$	−6.95948	+	1.00062i	−0.272973	+	0.0392477i
$651$	9.09739	+	1.72238i	0.356555	+	0.0675054i
$652$	8.07223	−	5.18771i	0.316133	−	0.203166i
$653$	21.8486	−	30.6821i	0.855003	−	1.20068i	−0.123065	−	0.992399i	$-0.539272\pi$
$653$	21.8486	−	30.6821i	0.855003	−	1.20068i	0.978068	−	0.208285i	$-0.0667881\pi$
$654$	2.45060	−	10.1015i	0.0958261	−	0.395001i
$655$	6.20469	−	2.14746i	0.242437	−	0.0839083i
$656$	0.640405	−	3.32273i	0.0250036	−	0.129731i
$657$	2.60908	+	8.88570i	0.101790	+	0.346664i
$658$	−17.1045	−	9.80045i	−0.666802	−	0.382061i
$659$	1.07141	+	1.66714i	0.0417361	+	0.0649426i	0.861495	−	0.507767i	$-0.169529\pi$
$659$	1.07141	+	1.66714i	0.0417361	+	0.0649426i	−0.819759	+	0.572709i	$0.805892\pi$
$660$	1.25775	+	5.18451i	0.0489578	+	0.201807i
$661$	−6.47837	−	2.59355i	−0.251979	−	0.100877i	0.242234	−	0.970218i	$-0.422120\pi$
$661$	−6.47837	−	2.59355i	−0.251979	−	0.100877i	−0.494214	+	0.869340i	$0.664544\pi$
$662$	8.79724	+	12.3540i	0.341914	+	0.480152i
$663$	−12.3766	+	4.95486i	−0.480669	+	0.192431i
$664$	−1.88956	−	1.21435i	−0.0733292	−	0.0471258i
$665$	6.38162	−	26.6880i	0.247469	−	1.03492i
$666$		−	0.0322664i		−	0.00125030i
$667$	10.9295	−	13.8610i	0.423192	−	0.536699i
$668$	−14.8600	−	8.57944i	−0.574952	−	0.331949i
$669$	2.79463	−	0.538620i	0.108047	−	0.0208243i
$670$	−21.2065	−	1.01019i	−0.819278	−	0.0390270i
$671$	−36.7952	−	5.29036i	−1.42046	−	0.204232i
$672$	−2.50307	−	0.857117i	−0.0965580	−	0.0330640i
$673$	−4.39561	−	30.5721i	−0.169438	−	1.17847i	−0.880049	−	0.474884i	$-0.842490\pi$
$673$	−4.39561	−	30.5721i	−0.169438	−	1.17847i	0.710610	−	0.703586i	$-0.248419\pi$
$674$	19.0170	−	4.61348i	0.732508	−	0.177704i
$675$	−1.66786	+	0.0794498i	−0.0641958	+	0.00305802i
$676$	4.70981	+	0.449732i	0.181147	+	0.0172974i
$677$	2.66805	+	2.54398i	0.102542	+	0.0977731i	0.739616	−	0.673029i	$-0.235007\pi$
$677$	2.66805	+	2.54398i	0.102542	+	0.0977731i	−0.637074	+	0.770802i	$0.719856\pi$
$678$	−5.68291	+	6.55842i	−0.218251	+	0.251875i
$679$	−11.5375	−	25.0454i	−0.442769	−	0.961156i
$680$	−5.54362	+	1.62775i	−0.212588	+	0.0624215i
$681$	−21.5323	−	15.3331i	−0.825120	−	0.587565i
$682$	−0.486792	−	10.2190i	−0.0186402	−	0.391307i
$683$	−29.9789	+	28.5848i	−1.14711	+	1.09377i	−0.152691	+	0.988274i	$0.548794\pi$
$683$	−29.9789	+	28.5848i	−1.14711	+	1.09377i	−0.994420	+	0.105494i	$0.966358\pi$
$684$	4.46740	−	3.51320i	0.170815	−	0.134331i
$685$	−3.71023	−	1.69441i	−0.141761	−	0.0647399i
$686$	−14.4443	+	11.5915i	−0.551486	+	0.442565i
$687$	15.0193	−	23.3705i	0.573023	−	0.891642i
$688$	8.45986	+	2.92798i	0.322529	+	0.111628i
$689$	8.57889	−	14.8591i	0.326830	−	0.566085i
$690$	−7.35643	−	4.74117i	−0.280055	−	0.180493i
$691$	36.2886	−	20.9512i	1.38048	−	0.797022i	0.388266	−	0.921548i	$-0.373074\pi$
$691$	36.2886	−	20.9512i	1.38048	−	0.797022i	0.992216	+	0.124526i	$0.0397410\pi$
$692$	−3.22966	+	2.79851i	−0.122773	+	0.106384i
$693$	4.20299	+	6.49295i	0.159658	+	0.246647i
$694$	1.50060	−	10.4369i	0.0569619	−	0.396178i
$695$	3.82197	+	40.0255i	0.144976	+	1.51825i
$696$	−1.36795	+	3.41697i	−0.0518520	+	0.129520i
$697$	−7.39312	−	7.75368i	−0.280034	−	0.293692i
$698$	6.89036	−	13.3654i	0.260804	−	0.505889i
$699$	−10.3476	+	4.72557i	−0.391380	+	0.178737i
$700$	−4.09586	+	1.65538i	−0.154809	+	0.0625675i
$701$	−18.6307	−	16.1436i	−0.703674	−	0.609737i	0.227730	−	0.973724i	$-0.426870\pi$
$701$	−18.6307	−	16.1436i	−0.703674	−	0.609737i	−0.931404	+	0.363988i	$0.881415\pi$
$702$	4.13475	+	0.796908i	0.156056	+	0.0300774i
$703$	0.178211	+	0.0432336i	0.00672137	+	0.00163059i
$704$	−0.277886	+	2.91015i	−0.0104732	+	0.109681i
$705$	12.0856	+	6.23057i	0.455171	+	0.234657i
$706$	0.698418	−	2.37859i	0.0262853	−	0.0895195i
$707$	−19.3947	−	20.2071i	−0.729411	−	0.759967i
$708$	−1.45627	+	3.18878i	−0.0547298	+	0.119842i
$709$	−11.0113	−	27.5049i	−0.413538	−	1.03297i	−0.978204	−	0.207647i	$-0.933419\pi$
$709$	−11.0113	−	27.5049i	−0.413538	−	1.03297i	0.564666	−	0.825319i	$-0.309005\pi$
$710$	8.58836	−	4.42761i	0.322316	−	0.166165i
$711$	2.71157	+	14.0690i	0.101692	+	0.527627i
$712$	7.63651	+	13.2268i	0.286190	+	0.495696i
$713$	12.1317	+	11.5976i	0.454335	+	0.434333i
$714$	−6.80728	+	4.88125i	−0.254756	+	0.182676i
$715$	−14.7111	−	16.9775i	−0.550162	−	0.634921i
$716$	−0.989459	+	20.7713i	−0.0369778	+	0.776260i
$717$	−0.312255	+	0.397065i	−0.0116614	+	0.0148287i
$718$	−27.2341	+	19.3933i	−1.01637	+	0.723752i
$719$	21.6319	+	27.5072i	0.806733	+	1.02584i	0.999009	+	0.0445036i	$0.0141706\pi$
$719$	21.6319	+	27.5072i	0.806733	+	1.02584i	−0.192276	+	0.981341i	$0.561587\pi$
$720$	1.75098	+	0.514133i	0.0652551	+	0.0191606i
$721$	26.4395	−	20.9333i	0.984660	−	0.779597i
$722$	5.52512	+	12.0983i	0.205624	+	0.450253i
$723$	−4.81636	+	5.05125i	−0.179122	+	0.187858i
$724$	−7.75489	−	22.4063i	−0.288208	−	0.832723i
$725$	2.01006	+	5.80770i	0.0746519	+	0.215693i
$726$	−1.69331	+	1.77589i	−0.0628446	+	0.0659095i
$727$	−1.12877	−	2.47166i	−0.0418637	−	0.0916688i	0.887545	−	0.460722i	$-0.152409\pi$
$727$	−1.12877	−	2.47166i	−0.0418637	−	0.0916688i	−0.929408	+	0.369053i	$0.879682\pi$
$728$	11.0222	−	1.62175i	0.408509	−	0.0601061i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	−10.4469	−	13.2843i	−0.386658	−	0.491676i
$731$	23.0874	−	16.4405i	0.853919	−	0.608073i
$732$	−7.86046	+	9.99539i	−0.290531	+	0.369440i
$733$	−1.14745	+	24.0879i	−0.0423819	+	0.889706i	0.873148	+	0.487456i	$0.162075\pi$
$733$	−1.14745	+	24.0879i	−0.0423819	+	0.889706i	−0.915530	+	0.402250i	$0.868228\pi$
$734$	18.9910	+	21.9168i	0.700972	+	0.808965i
$735$	9.59895	−	8.42867i	0.354063	−	0.310896i
$736$	−2.95970	−	3.77362i	−0.109096	−	0.139097i
$737$	17.0051	+	29.4537i	0.626391	+	1.08494i
$738$	0.640405	+	3.32273i	0.0235736	+	0.122312i
$739$	24.1056	−	12.4273i	0.886739	−	0.457146i	0.0462225	−	0.998931i	$-0.485282\pi$
$739$	24.1056	−	12.4273i	0.886739	−	0.457146i	0.840517	+	0.541785i	$0.182251\pi$
$740$	0.0218845	+	0.0546649i	0.000804492	+	0.00200952i
$741$	−9.94156	+	21.7690i	−0.365212	+	0.799703i
$742$	3.00321	−	10.3538i	0.110251	−	0.380099i
$743$	−13.4017	+	45.6419i	−0.491659	+	1.67444i	0.222883	+	0.974845i	$0.428453\pi$
$743$	−13.4017	+	45.6419i	−0.491659	+	1.67444i	−0.714542	+	0.699592i	$0.753365\pi$
$744$	−3.11054	−	1.60360i	−0.114038	−	0.0587907i
$745$	−2.21766	+	23.2244i	−0.0812489	+	0.850877i
$746$	−36.7886	−	8.92481i	−1.34693	−	0.326761i
$747$	2.20554	+	0.425082i	0.0806963	+	0.0155529i
$748$	6.99484	+	6.06107i	0.255757	+	0.221614i
$749$	−1.32078	−	3.26798i	−0.0482604	−	0.119409i
$750$	11.0717	−	5.05627i	0.404281	−	0.184629i
$751$	−14.6033	+	28.3264i	−0.532881	+	1.03365i	0.456693	+	0.889624i	$0.349034\pi$
$751$	−14.6033	+	28.3264i	−0.532881	+	1.03365i	−0.989575	+	0.144021i	$0.953997\pi$
$752$	5.14171	+	5.39247i	0.187499	+	0.196643i
$753$	8.23262	−	20.5641i	0.300013	−	0.749397i
$754$	−1.47323	−	15.4284i	−0.0536519	−	0.561868i
$755$	−0.0440022	+	0.306042i	−0.00160140	+	0.0111380i
$756$	2.64233	−	0.134577i	0.0961005	−	0.00489452i
$757$	12.3965	−	10.7416i	0.450558	−	0.390411i	−0.399811	−	0.916598i	$-0.630924\pi$
$757$	12.3965	−	10.7416i	0.450558	−	0.390411i	0.850369	+	0.526187i	$0.176379\pi$
$758$	−16.6798	+	9.63010i	−0.605838	+	0.349781i
$759$	−0.0181708	+	14.0201i	−0.000659559	+	0.508896i
$760$	−5.18575	+	8.98198i	−0.188107	+	0.325811i
$761$	−21.9028	−	7.58062i	−0.793975	−	0.274797i	−0.100179	−	0.994969i	$-0.531942\pi$
$761$	−21.9028	−	7.58062i	−0.793975	−	0.274797i	−0.693795	+	0.720172i	$0.744063\pi$
$762$	−2.94650	+	4.58484i	−0.106740	+	0.166091i
$763$	12.6821	+	24.4026i	0.459124	+	0.883433i
$764$	−5.91392	−	2.70080i	−0.213958	−	0.0977114i
$765$	4.54155	−	3.57151i	0.164200	−	0.129128i
$766$	−2.71658	+	2.59025i	−0.0981539	+	0.0935896i
$767$	−0.702377	−	14.7447i	−0.0253613	−	0.532400i
$768$	0.814576	+	0.580057i	0.0293935	+	0.0209310i
$769$	−19.8357	+	5.82428i	−0.715293	+	0.210029i	−0.619075	−	0.785331i	$-0.712493\pi$
$769$	−19.8357	+	5.82428i	−0.715293	+	0.210029i	−0.0962172	+	0.995360i	$0.530674\pi$
$770$	−11.5244	−	8.14954i	−0.415311	−	0.293689i
$771$	−1.27061	+	1.46637i	−0.0457600	+	0.0528098i
$772$	−2.24126	−	2.13704i	−0.0806649	−	0.0769138i
$773$	−34.7329	−	3.31659i	−1.24925	−	0.119289i	−0.550612	−	0.834761i	$-0.685606\pi$
$773$	−34.7329	−	3.31659i	−1.24925	−	0.119289i	−0.698642	+	0.715472i	$0.746212\pi$
$774$	−8.94208	+	0.425964i	−0.321416	+	0.0153110i
$775$	−5.67869	+	1.37763i	−0.203984	+	0.0494861i
$776$	1.48327	+	10.3163i	0.0532461	+	0.370335i
$777$	0.0561165	+	0.0643333i	0.00201317	+	0.00230794i
$778$	28.8644	+	4.15007i	1.03484	+	0.148787i
$779$	−19.2100	−	0.915083i	−0.688268	−	0.0327863i
$780$	−7.54550	+	1.45428i	−0.270172	+	0.0520714i
$781$	−13.4050	−	7.73940i	−0.479670	−	0.276937i
$782$	−15.1674	+	0.702812i	−0.542385	+	0.0251325i
$783$		−	3.68062i		−	0.131535i
$784$	6.48133	−	2.64431i	0.231476	−	0.0944395i
$785$	2.83946	+	1.82481i	0.101345	+	0.0651303i
$786$	−3.34017	+	1.33720i	−0.119140	+	0.0476965i
$787$	0.866465	+	1.21678i	0.0308862	+	0.0433735i	0.829730	−	0.558165i	$-0.188494\pi$
$787$	0.866465	+	1.21678i	0.0308862	+	0.0433735i	−0.798844	+	0.601538i	$0.794555\pi$
$788$	17.2609	+	6.91021i	0.614893	+	0.246166i
$789$	6.23700	+	25.7093i	0.222043	+	0.915274i
$790$	−14.1361	−	21.9962i	−0.502939	−	0.782589i
$791$	−0.0754775	−	22.9598i	−0.00268367	−	0.816357i
$792$	−0.823614	−	2.80497i	−0.0292659	−	0.0996703i
$793$	10.1334	−	52.5772i	0.359848	−	1.86707i
$794$	−17.5700	+	6.08102i	−0.623534	+	0.215807i
$795$	−1.75307	+	7.22624i	−0.0621748	+	0.256288i
$796$	−9.89143	+	13.8906i	−0.350592	+	0.492338i
$797$	28.1560	−	18.0948i	0.997337	−	0.640950i	0.0632510	−	0.997998i	$-0.479853\pi$
$797$	28.1560	−	18.0948i	0.997337	−	0.640950i	0.934086	+	0.357048i	$0.116217\pi$
$798$	−2.79716	+	14.7742i	−0.0990183	+	0.523002i
$799$	23.3496	−	3.35716i	0.826049	−	0.118768i
$800$	1.66219	−	0.158720i	0.0587672	−	0.00561158i
$801$	−12.0054	−	9.44115i	−0.424190	−	0.333587i
$802$	4.96463	+	9.63005i	0.175307	+	0.340049i
$803$	−8.85471	+	25.5840i	−0.312476	+	0.902840i
$804$	11.6338			0.410293
$805$	22.9131	−	3.34098i	0.807579	−	0.117754i
$806$	14.7362			0.519059
$807$	0.0301394	−	0.0870821i	0.00106096	−	0.00306544i
$808$	4.85090	+	9.40943i	0.170654	+	0.331023i
$809$	18.6872	+	14.6958i	0.657007	+	0.516676i	0.890092	−	0.455780i	$-0.150640\pi$
$809$	18.6872	+	14.6958i	0.657007	+	0.516676i	−0.233085	+	0.972456i	$0.574882\pi$
$810$	−1.81663	+	0.173468i	−0.0638300	+	0.00609503i
$811$	31.5219	−	4.53217i	1.10688	−	0.159146i	0.435452	−	0.900212i	$-0.356589\pi$
$811$	31.5219	−	4.53217i	1.10688	−	0.159146i	0.671432	+	0.741066i	$0.265679\pi$
$812$	−3.21523	−	9.19191i	−0.112832	−	0.322573i
$813$	5.94106	−	3.81809i	0.208362	−	0.133906i
$814$	0.0547151	−	0.0768367i	0.00191776	−	0.00269312i
$815$	4.12832	−	17.0172i	0.144609	−	0.596085i
$816$	2.99189	−	1.03550i	0.104737	−	0.0362498i
$817$	9.62881	−	49.9590i	0.336869	−	1.74784i
$818$	2.35393	+	8.01676i	0.0823033	+	0.280299i
$819$	−9.62990	+	5.60211i	−0.336496	+	0.195754i
$820$	−3.33859	−	5.19495i	−0.116589	−	0.181415i
$821$	1.06088	+	4.37301i	0.0370250	+	0.152619i	0.987323	−	0.158721i	$-0.0507372\pi$
$821$	1.06088	+	4.37301i	0.0370250	+	0.152619i	−0.950298	+	0.311341i	$0.899222\pi$
$822$	2.07499	+	0.830702i	0.0723737	+	0.0289741i
$823$	−15.0657	−	21.1568i	−0.525158	−	0.737481i	0.463757	−	0.885962i	$-0.346501\pi$
$823$	−15.0657	−	21.1568i	−0.525158	−	0.737481i	−0.988915	+	0.148481i	$0.952562\pi$
$824$	−11.8331	+	4.73727i	−0.412227	+	0.165031i
$825$	−4.10643	−	2.63904i	−0.142968	−	0.0918797i
$826$	−2.64227	−	8.89053i	−0.0919364	−	0.309341i
$827$		−	3.47612i		−	0.120877i	−0.998172	−	0.0604383i	$-0.980750\pi$
$827$		−	3.47612i		−	0.120877i	0.998172	−	0.0604383i	$-0.0192498\pi$
$828$	4.15020	+	2.40330i	0.144229	+	0.0835203i
$829$	−39.9951	−	23.0912i	−1.38909	−	0.801989i	−0.395874	−	0.918305i	$-0.629558\pi$
$829$	−39.9951	−	23.0912i	−1.38909	−	0.801989i	−0.993212	+	0.116316i	$0.962892\pi$
$830$	−4.02488	+	0.775732i	−0.139706	+	0.0269260i
$831$	1.01126	+	0.0481721i	0.0350801	+	0.00167107i
$832$	−4.16799	−	0.599266i	−0.144499	−	0.0207758i
$833$	5.08320	−	21.5713i	0.176123	−	0.747401i
$834$	−3.13559	−	21.8085i	−0.108577	−	0.755167i
$835$	−30.4306	+	7.38237i	−1.05309	+	0.255478i
$836$	16.5958	−	0.790554i	0.573977	−	0.0273419i
$837$	3.48373	+	0.332656i	0.120415	+	0.0114983i
$838$	11.4823	+	10.9484i	0.396650	+	0.378205i
$839$	24.8186	−	28.6422i	0.856833	−	0.988838i	−0.143166	−	0.989699i	$-0.545728\pi$
$839$	24.8186	−	28.6422i	0.856833	−	0.988838i	1.00000		0.000860407i	$0.000273876\pi$
$840$	−4.38529	+	2.02014i	−0.151307	+	0.0697016i
$841$	14.8271	−	4.35362i	0.511278	−	0.150125i
$842$	3.13950	+	2.23563i	0.108194	+	0.0770448i
$843$	−0.101989	−	2.14102i	−0.00351270	−	0.0737406i
$844$	6.35379	−	6.05833i	0.218706	−	0.208536i
$845$	6.78680	−	5.33720i	0.233473	−	0.183605i
$846$	−6.77758	−	3.09522i	−0.233018	−	0.106416i
$847$	0.287588	−	6.48575i	0.00988164	−	0.222853i
$848$	−2.20293	+	3.42782i	−0.0756489	+	0.117712i
$849$	−2.02704	−	0.701566i	−0.0695679	−	0.0240777i
$850$	2.64322	−	4.57820i	0.0906618	−	0.157031i
$851$	0.0218238	+	0.153197i	0.000748112	+	0.00525154i
$852$	−4.58544	+	2.64741i	−0.157095	+	0.0906986i
$853$	−22.8965	+	19.8399i	−0.783961	+	0.679306i	−0.951872	−	0.306496i	$-0.900843\pi$
$853$	−22.8965	+	19.8399i	−0.783961	+	0.679306i	0.167911	+	0.985802i	$0.446298\pi$
$854$	−1.71127	−	33.5996i	−0.0585585	−	1.14976i
$855$	1.47602	−	10.2659i	0.0504788	−	0.351087i
$856$	0.126638	+	1.32621i	0.00432840	+	0.0453291i
$857$	−0.821478	+	2.05195i	−0.0280611	+	0.0700933i	−0.941737	−	0.336351i	$-0.890807\pi$
$857$	−0.821478	+	2.05195i	−0.0280611	+	0.0700933i	0.913676	+	0.406444i	$0.133231\pi$
$858$	8.49484	+	8.90913i	0.290009	+	0.304153i
$859$	−12.2612	+	23.7834i	−0.418346	+	0.811478i	−0.999998	−	0.00195954i	$-0.999376\pi$
$859$	−12.2612	+	23.7834i	−0.418346	+	0.811478i	0.581652	+	0.813438i	$0.302407\pi$
$860$	14.8606	−	6.78659i	0.506741	−	0.231421i
$861$	−7.05563	−	5.51116i	−0.240455	−	0.187820i
$862$	11.6367	+	10.0833i	0.396348	+	0.343437i
$863$	−53.4147	−	10.2948i	−1.81826	−	0.350441i	−0.837618	−	0.546256i	$-0.816053\pi$
$863$	−53.4147	−	10.2948i	−1.81826	−	0.350441i	−0.980641	+	0.195815i	$0.937265\pi$
$864$	−0.971812	−	0.235759i	−0.0330617	−	0.00802068i
$865$	−0.741305	+	7.76329i	−0.0252051	+	0.263960i
$866$	27.2817	+	14.0647i	0.927070	+	0.477938i
$867$	−1.96546	+	6.69375i	−0.0667506	+	0.227332i
$868$	8.99078	−	2.21246i	0.305167	−	0.0750958i
$869$	−17.4001	+	38.1008i	−0.590257	+	1.29248i
$870$	2.49637	+	6.23562i	0.0846348	+	0.211407i
$871$	−43.5425	+	22.4477i	−1.47538	+	0.760612i
$872$	−1.96718	−	10.2067i	−0.0666170	−	0.345642i
$873$	−5.21121	−	9.02608i	−0.176373	−	0.305487i
$874$	−18.8345	+	19.7019i	−0.637088	+	0.666427i
$875$	−13.2813	+	29.3367i	−0.448989	+	0.991763i
$876$	6.06455	+	6.99886i	0.204902	+	0.236470i
$877$	−0.178155	+	3.73994i	−0.00601588	+	0.126289i	0.993862	+	0.110631i	$0.0352872\pi$
$877$	−0.178155	+	3.73994i	−0.00601588	+	0.126289i	−0.999877	+	0.0156577i	$0.995016\pi$
$878$	−17.6988	+	22.5059i	−0.597306	+	0.759536i
$879$	−13.9566	+	9.93845i	−0.470745	+	0.335216i
$880$	3.29781	+	4.19351i	0.111169	+	0.141363i
$881$	−12.1199	−	3.55871i	−0.408328	−	0.119896i	0.0711166	−	0.997468i	$-0.477344\pi$
$881$	−12.1199	−	3.55871i	−0.408328	−	0.119896i	−0.479445	+	0.877572i	$0.659162\pi$
$882$	−5.03427	+	4.86376i	−0.169513	+	0.163771i
$883$	2.31928	+	5.07851i	0.0780500	+	0.170906i	0.944634	−	0.328125i	$-0.106417\pi$
$883$	2.31928	+	5.07851i	0.0780500	+	0.170906i	−0.866584	+	0.499031i	$0.833689\pi$
$884$	−9.19987	+	9.64854i	−0.309425	+	0.324516i
$885$	2.09235	+	6.04546i	0.0703337	+	0.203216i
$886$	11.1463	+	32.2053i	0.374469	+	1.08196i
$887$	−4.23215	+	4.43855i	−0.142102	+	0.149032i	−0.790939	−	0.611896i	$-0.790407\pi$
$887$	−4.23215	+	4.43855i	−0.142102	+	0.149032i	0.648837	+	0.760928i	$0.275256\pi$
$888$	−0.0134039	−	0.0293505i	−0.000449807	−	0.000984939i
$889$	−2.09900	−	14.2658i	−0.0703981	−	0.478458i
$890$	26.7427	+	7.85236i	0.896417	+	0.263212i
$891$	1.80712	+	2.29794i	0.0605408	+	0.0769839i
$892$	2.31833	−	1.65088i	0.0776235	−	0.0552754i
$893$	26.1765	−	33.2862i	0.875964	−	1.11388i
$894$	0.608302	−	12.7698i	0.0203447	−	0.427087i
$895$	24.8510	+	28.6795i	0.830676	+	0.958651i
$896$	−2.63293	+	0.260151i	−0.0879600	+	0.00869105i
$897$	−20.1704	−	0.987036i	−0.673469	−	0.0329562i
$898$	−13.8624	−	24.0104i	−0.462595	−	0.801237i
$899$	−2.43767	−	12.6478i	−0.0813009	−	0.421829i
$900$	−1.48413	+	0.765122i	−0.0494710	+	0.0255041i
$901$	4.79461	+	11.9764i	0.159732	+	0.398990i
$902$	−4.10946	+	8.99846i	−0.136830	+	0.299616i
$903$	17.0881	−	16.4010i	0.568655	−	0.545792i
$904$	−2.44489	+	8.32652i	−0.0813157	+	0.276936i
$905$	−38.4590	−	19.8270i	−1.27842	−	0.659071i
$906$	0.0161052	−	0.168661i	0.000535058	−	0.00560338i
$907$	18.7137	+	4.53988i	0.621377	+	0.150744i	0.534074	−	0.845437i	$-0.320660\pi$
$907$	18.7137	+	4.53988i	0.621377	+	0.150744i	0.0873024	+	0.996182i	$0.472175\pi$
$908$	−25.9561	−	5.00263i	−0.861383	−	0.166018i
$909$	−8.00055	−	6.93252i	−0.265362	−	0.229937i
$910$	12.5151	−	16.0224i	0.414873	−	0.531138i
$911$	−32.2534	+	14.7296i	−1.06860	+	0.488015i	−0.870501	−	0.492166i	$-0.836205\pi$
$911$	−32.2534	+	14.7296i	−1.06860	+	0.488015i	−0.198103	+	0.980181i	$0.563478\pi$
$912$	2.60425	−	5.05155i	0.0862354	−	0.167273i
$913$	4.53127	+	4.75226i	0.149963	+	0.157277i
$914$	−2.23859	+	5.59174i	−0.0740461	+	0.184958i
$915$	2.20580	+	23.1002i	0.0729215	+	0.763669i
$916$	3.95359	−	27.4978i	0.130630	−	0.908555i
$917$	4.33409	−	8.47525i	0.143124	−	0.279877i
$918$	−2.39272	+	2.07330i	−0.0789714	+	0.0684291i
$919$	32.7736	−	18.9219i	1.08110	−	0.624174i	0.149908	−	0.988700i	$-0.452102\pi$
$919$	32.7736	−	18.9219i	1.08110	−	0.624174i	0.931193	+	0.364526i	$0.118769\pi$
$920$	−8.66120	−	1.25675i	−0.285551	−	0.0414339i
$921$	−13.7876	+	23.8807i	−0.454315	+	0.786897i
$922$	−16.4832	−	5.70489i	−0.542845	−	0.187881i
$923$	12.0539	−	18.7563i	0.396760	−	0.617371i
$924$	6.52044	+	4.16021i	0.214507	+	0.136861i
$925$	−0.0490080	−	0.0223812i	−0.00161137	−	0.000735889i
$926$	−12.5804	+	9.89335i	−0.413418	+	0.325116i
$927$	9.22483	−	8.79586i	0.302983	−	0.288894i
$928$	0.175131	+	3.67645i	0.00574896	+	0.120685i
$929$	22.8431	+	16.2665i	0.749457	+	0.533686i	0.889763	−	0.456422i	$-0.150869\pi$
$929$	22.8431	+	16.2665i	0.749457	+	0.533686i	−0.140307	+	0.990108i	$0.544809\pi$
$930$	−6.12767	+	1.79925i	−0.200934	+	0.0589996i
$931$	−20.1177	−	34.3218i	−0.659332	−	1.12485i
$932$	−7.44939	+	8.59706i	−0.244013	+	0.281606i
$933$	−5.39532	−	5.14442i	−0.176635	−	0.168421i
$934$	−2.53579	−	0.242139i	−0.0829737	−	0.00792302i
$935$	16.8712	−	0.803675i	0.551748	−	0.0262830i
$936$	4.09215	−	0.992745i	0.133756	−	0.0324489i
$937$	2.56965	+	17.8723i	0.0839470	+	0.583864i	0.987765	+	0.155948i	$0.0498431\pi$
$937$	2.56965	+	17.8723i	0.0839470	+	0.583864i	−0.903818	+	0.427916i	$0.859248\pi$
$938$	−23.1957	+	20.2331i	−0.757368	+	0.660634i
$939$	−2.83950	−	0.408258i	−0.0926635	−	0.0133230i
$940$	13.5817	+	0.646978i	0.442988	+	0.0211021i
$941$	13.5324	−	2.60816i	0.441145	−	0.0850237i	0.0361577	−	0.999346i	$-0.488488\pi$
$941$	13.5324	−	2.60816i	0.441145	−	0.0850237i	0.404987	+	0.914322i	$0.367276\pi$
$942$	−1.60177	−	0.924784i	−0.0521886	−	0.0301311i
$943$	−5.28796	−	15.3429i	−0.172200	−	0.499632i
$944$			3.50557i			0.114097i
$945$	3.32035	−	3.50529i	0.108011	−	0.114027i
$946$	−22.0163	−	14.1490i	−0.715812	−	0.460024i
$947$	−36.5465	+	14.6310i	−1.18760	+	0.475444i	−0.879495	−	0.475908i	$-0.842119\pi$
$947$	−36.5465	+	14.6310i	−1.18760	+	0.475444i	−0.308106	+	0.951352i	$0.599695\pi$
$948$	8.31098	+	11.6711i	0.269928	+	0.379061i
$949$	−36.2026	−	14.4933i	−1.17518	−	0.470473i
$950$	−2.23729	−	9.22222i	−0.0725872	−	0.299208i
$951$	15.2639	+	23.7511i	0.494965	+	0.770181i
$952$	−4.16438	+	7.26799i	−0.134968	+	0.235557i
$953$	9.18851	+	31.2932i	0.297645	+	1.01369i	0.963523	+	0.267626i	$0.0862390\pi$
$953$	9.18851	+	31.2932i	0.297645	+	1.01369i	−0.665878	+	0.746061i	$0.731943\pi$
$954$	0.771135	−	4.00103i	0.0249664	−	0.129538i
$955$	−11.2119	+	3.88049i	−0.362810	+	0.125570i
$956$	−0.119091	+	0.490899i	−0.00385167	+	0.0158768i
$957$	6.24135	−	8.76475i	0.201754	−	0.283324i
$958$	−25.9642	+	16.6862i	−0.838865	+	0.539106i
$959$	−5.58189	+	1.95248i	−0.180249	+	0.0630489i
$960$	1.80632	−	0.259710i	0.0582988	−	0.00838211i
$961$	−18.6681	+	1.78259i	−0.602196	+	0.0575027i
$962$	0.106800	+	0.0839885i	0.00344337	+	0.00270790i
$963$	−0.610471	−	1.18415i	−0.0196721	−	0.0381586i
$964$	−2.28275	+	6.59557i	−0.0735224	+	0.212429i
$965$	−5.65136			−0.181924
$966$	−12.4545	+	2.42613i	−0.400716	+	0.0780596i
$967$	−46.4631			−1.49415			−0.747076	−	0.664738i	$-0.768543\pi$
$967$	−46.4631			−1.49415			−0.747076	+	0.664738i	$0.768543\pi$
$968$	−0.802556	+	2.31883i	−0.0257951	+	0.0745302i
$969$	−8.24511	−	15.9933i	−0.264871	−	0.513778i
$970$	14.9506	+	11.7573i	0.480035	+	0.377504i
$971$	−31.3863	+	2.99703i	−1.00724	+	0.0961794i	−0.585612	−	0.810592i	$-0.699146\pi$
$971$	−31.3863	+	2.99703i	−1.00724	+	0.0961794i	−0.421624	+	0.906771i	$0.638540\pi$
$972$	0.989821	−	0.142315i	0.0317485	−	0.00456475i
$973$	44.1803	+	38.0289i	1.41636	+	1.21915i
$974$	−18.5133	+	11.8978i	−0.593206	+	0.381230i
$975$	4.07841	−	5.72732i	0.130614	−	0.183421i
$976$	−2.99789	+	12.3575i	−0.0959602	+	0.395553i
$977$	−32.5176	+	11.2544i	−1.04033	+	0.360062i	−0.793226	−	0.608927i	$-0.791600\pi$
$977$	−32.5176	+	11.2544i	−1.04033	+	0.360062i	−0.247104	+	0.968989i	$0.579479\pi$
$978$	−1.81596	+	9.42207i	−0.0580679	+	0.301285i
$979$	−12.5791	−	42.8404i	−0.402029	−	1.36918i
$980$	5.23012	−	11.6545i	0.167070	−	0.372291i
$981$	5.61970	+	8.74443i	0.179423	+	0.279188i
$982$	1.25985	+	5.19319i	0.0402036	+	0.165721i
$983$	5.16796	+	2.06894i	0.164832	+	0.0659890i	0.452611	−	0.891708i	$-0.350493\pi$
$983$	5.16796	+	2.06894i	0.164832	+	0.0659890i	−0.287779	+	0.957697i	$0.592917\pi$
$984$	1.96285	+	2.75643i	0.0625733	+	0.0878718i
$985$	31.4993	−	12.6104i	1.00365	−	0.401802i
$986$	9.80305	+	6.30004i	0.312193	+	0.200634i
$987$	18.8964	−	5.61601i	0.601478	−	0.178760i
$988$			23.9316i			0.761367i
$989$	42.1680	−	8.07054i	1.34086	−	0.256628i
$990$	−4.62015	−	2.66744i	−0.146838	−	0.0847769i
$991$	−2.56797	+	0.494935i	−0.0815741	+	0.0157221i	−0.229875	−	0.973220i	$-0.573832\pi$
$991$	−2.56797	+	0.494935i	−0.0815741	+	0.0157221i	0.148301	+	0.988942i	$0.452620\pi$
$992$	−3.49561	−	0.166516i	−0.110986	−	0.00528690i
$993$	−15.0118	−	2.15837i	−0.476385	−	0.0684938i
$994$	4.53827	−	13.2533i	0.143945	−	0.420368i
$995$	4.42871	+	30.8023i	0.140400	+	0.976500i
$996$	2.18281	−	0.529544i	0.0691650	−	0.0167793i
$997$	−42.6320	+	2.03081i	−1.35017	+	0.0643164i	−0.710154	−	0.704046i	$-0.751375\pi$
$997$	−42.6320	+	2.03081i	−1.35017	+	0.0643164i	−0.640014	+	0.768363i	$0.721072\pi$
$998$	−32.1727	−	3.07212i	−1.01841	−	0.0972462i
$999$	0.0233523	+	0.0222663i	0.000738833	+	0.000704476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.493.3	yes	320
7.5	odd	6	inner	966.2.be.b.355.3	yes	320
23.7	odd	22	inner	966.2.be.b.283.3	yes	320
161.145	even	66	inner	966.2.be.b.145.3	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.145.3	✓	320	161.145	even	66	inner
966.2.be.b.283.3	yes	320	23.7	odd	22	inner
966.2.be.b.355.3	yes	320	7.5	odd	6	inner
966.2.be.b.493.3	yes	320	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.81663 + 0.173468i) q^{5} +(0.989821 - 0.142315i) q^{6} +(-1.72602 + 2.00521i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.81663 + 0.173468i) q^{5} +(0.989821 - 0.142315i) q^{6} +(-1.72602 + 2.00521i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(0.430236 - 1.77346i) q^{10} +(-2.76261 + 0.956147i) q^{11} +(-0.189251 + 0.981929i) q^{12} +(-1.18633 - 4.04028i) q^{13} +(-1.33040 - 2.28693i) q^{14} +(0.986614 + 1.53520i) q^{15} +(0.235759 + 0.971812i) q^{16} +(2.93923 + 1.17669i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(5.27622 - 2.11228i) q^{19} +(1.53520 + 0.986614i) q^{20} +(2.57321 + 0.615304i) q^{21} -2.92339i q^{22} +(3.30500 + 3.47519i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.63957 + 0.316002i) q^{25} +(4.20608 + 0.200360i) q^{26} +(0.989821 + 0.142315i) q^{27} +(2.59628 - 0.509249i) q^{28} +(-0.523807 - 3.64316i) q^{29} +(-1.77346 + 0.430236i) q^{30} +(3.49561 - 0.166516i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(2.11576 + 2.01737i) q^{33} +(-2.07330 + 2.39272i) q^{34} +(2.78770 - 3.94214i) q^{35} +(0.959493 - 0.281733i) q^{36} +(0.0262834 + 0.0187163i) q^{37} +(0.270424 + 5.67689i) q^{38} +(-3.04753 + 2.90582i) q^{39} +(-1.43447 + 1.12808i) q^{40} +(-3.07809 - 1.40572i) q^{41} +(-1.42308 + 2.23044i) q^{42} +(4.83994 - 7.53109i) q^{43} +(2.76261 + 0.956147i) q^{44} +(0.912449 - 1.58041i) q^{45} +(-4.36502 + 1.98660i) q^{46} +(6.45267 - 3.72545i) q^{47} +(0.755750 - 0.654861i) q^{48} +(-1.04174 - 6.92205i) q^{49} +(0.237630 - 1.65275i) q^{50} +(-0.300949 - 3.15168i) q^{51} +(-1.56501 + 3.90922i) q^{52} +(2.81184 + 2.94897i) q^{53} +(-0.458227 + 0.888835i) q^{54} +(4.85279 - 2.21619i) q^{55} +(-0.367919 + 2.62005i) q^{56} +(-4.29517 - 3.72179i) q^{57} +(3.61411 + 0.696562i) q^{58} +(3.40675 + 0.826469i) q^{59} +(0.173468 - 1.81663i) q^{60} +(11.3024 + 5.82678i) q^{61} +(-0.985944 + 3.35782i) q^{62} +(-0.632209 - 2.56911i) q^{63} +(0.415415 - 0.909632i) q^{64} +(2.85599 + 7.13392i) q^{65} +(-2.59841 + 1.33957i) q^{66} +(-2.20172 - 11.4236i) q^{67} +(-1.58301 - 2.74185i) q^{68} +(1.57444 - 4.53003i) q^{69} +(2.81356 + 3.92373i) q^{70} +(3.46736 + 4.00155i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(5.72466 - 7.27950i) q^{73} +(-0.0262834 + 0.0187163i) q^{74} +(1.03217 + 1.31251i) q^{75} +(-5.45312 - 1.60118i) q^{76} +(2.85103 - 7.18993i) q^{77} +(-1.74925 - 3.83032i) q^{78} +(9.88737 - 10.3696i) q^{79} +(-0.596866 - 1.72453i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(2.33515 - 2.44903i) q^{82} +(-0.933075 - 2.04315i) q^{83} +(-1.64232 - 2.07431i) q^{84} +(-5.54362 - 1.62775i) q^{85} +(5.53390 + 7.03692i) q^{86} +(-2.99815 + 2.13497i) q^{87} +(-1.80712 + 2.29794i) q^{88} +(-0.726719 + 15.2557i) q^{89} +(1.19505 + 1.37917i) q^{90} +(10.1492 + 4.59474i) q^{91} +(-0.449685 - 4.77470i) q^{92} +(-1.74979 - 3.03072i) q^{93} +(1.41009 + 7.31626i) q^{94} +(-9.21856 + 4.75250i) q^{95} +(0.371662 + 0.928368i) q^{96} +(-4.32963 + 9.48057i) q^{97} +(6.88206 + 1.27954i) q^{98} +(0.823614 - 2.80497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Introduction

L-functions

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