LMFDB - Embedded newform 966.2.be.b.493.14

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			493.14
Character	$\chi$	$=$	966.493
Dual form			966.2.be.b.145.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 + 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(1.26176 - 0.120484i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-2.41166 - 1.08806i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.327068 + 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(1.26176 - 0.120484i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-2.41166 - 1.08806i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(-0.298825 + 1.23177i) q^{10} +(-4.57045 + 1.58185i) q^{11} +(0.189251 - 0.981929i) q^{12} +(0.667036 + 2.27171i) q^{13} +(1.81700 - 1.92315i) q^{14} +(0.685264 + 1.06629i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-3.75873 - 1.50477i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(1.21465 - 0.486271i) q^{19} +(-1.06629 - 0.685264i) q^{20} +(-0.137980 - 2.64215i) q^{21} -4.83645i q^{22} +(0.901466 - 4.71035i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-3.33211 + 0.642212i) q^{25} +(-2.36494 - 0.112656i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(1.22310 + 2.34607i) q^{28} +(0.617399 + 4.29411i) q^{29} +(-1.23177 + 0.298825i) q^{30} +(-7.09328 + 0.337895i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(-3.50030 - 3.33753i) q^{33} +(2.65137 - 3.05984i) q^{34} +(-3.17404 - 1.08231i) q^{35} +(0.959493 - 0.281733i) q^{36} +(1.40547 + 1.00083i) q^{37} +(0.0622546 + 1.30689i) q^{38} +(-1.71353 + 1.63384i) q^{39} +(0.996325 - 0.783519i) q^{40} +(-10.4587 - 4.77635i) q^{41} +(2.54196 + 0.733771i) q^{42} +(-0.853542 + 1.32814i) q^{43} +(4.57045 + 1.58185i) q^{44} +(-0.633752 + 1.09769i) q^{45} +(4.15644 + 2.39249i) q^{46} +(-7.44345 + 4.29748i) q^{47} +(-0.755750 + 0.654861i) q^{48} +(4.63224 + 5.24808i) q^{49} +(0.482936 - 3.35889i) q^{50} +(-0.384858 - 4.03042i) q^{51} +(0.879955 - 2.19802i) q^{52} +(2.65656 + 2.78612i) q^{53} +(0.458227 - 0.888835i) q^{54} +(-5.57624 + 2.54658i) q^{55} +(-2.61707 + 0.388508i) q^{56} +(0.988798 + 0.856799i) q^{57} +(-4.25987 - 0.821022i) q^{58} +(-4.11130 - 0.997391i) q^{59} +(0.120484 - 1.26176i) q^{60} +(7.07366 + 3.64673i) q^{61} +(2.00068 - 6.81367i) q^{62} +(2.28521 - 1.33335i) q^{63} +(0.415415 - 0.909632i) q^{64} +(1.11535 + 2.78600i) q^{65} +(4.29881 - 2.21619i) q^{66} +(-1.75635 - 9.11279i) q^{67} +(2.02438 + 3.50632i) q^{68} +(4.59980 - 1.35715i) q^{69} +(2.06091 - 2.64549i) q^{70} +(-7.47038 - 8.62128i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(8.18830 - 10.4123i) q^{73} +(-1.40547 + 1.00083i) q^{74} +(-2.09768 - 2.66742i) q^{75} +(-1.25537 - 0.368610i) q^{76} +(12.7435 + 1.15804i) q^{77} +(-0.983545 - 2.15366i) q^{78} +(1.70380 - 1.78689i) q^{79} +(0.414560 + 1.19779i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(7.93437 - 8.32133i) q^{82} +(5.60931 + 12.2827i) q^{83} +(-1.52481 + 2.16216i) q^{84} +(-4.92393 - 1.44580i) q^{85} +(-0.975925 - 1.24099i) q^{86} +(-3.53385 + 2.51644i) q^{87} +(-2.98969 + 3.80170i) q^{88} +(-0.436178 + 9.15651i) q^{89} +(-0.830038 - 0.957915i) q^{90} +(0.863100 - 6.20439i) q^{91} +(-3.62034 + 3.14533i) q^{92} +(-3.55066 - 6.14993i) q^{93} +(-1.62661 - 8.43963i) q^{94} +(1.47401 - 0.759905i) q^{95} +(-0.371662 - 0.928368i) q^{96} +(3.46883 - 7.59568i) q^{97} +(-6.47450 + 2.66100i) q^{98} +(1.36258 - 4.64054i) 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
$5$	1.26176	−	0.120484i	0.564278	−	0.0538820i	0.190981	−	0.981594i	$-0.438833\pi$
$5$	1.26176	−	0.120484i	0.564278	−	0.0538820i	0.373297	+	0.927712i	$0.378227\pi$
$6$	−0.989821	+	0.142315i	−0.404093	+	0.0580998i
$7$	−2.41166	−	1.08806i	−0.911523	−	0.411249i
$7$	−2.41166	−	1.08806i	−0.911523	−	0.411249i
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	−0.580057	+	0.814576i	−0.193352	+	0.271525i
$10$	−0.298825	+	1.23177i	−0.0944968	+	0.389521i
$11$	−4.57045	+	1.58185i	−1.37804	+	0.476945i	−0.912861	−	0.408271i	$-0.866132\pi$
$11$	−4.57045	+	1.58185i	−1.37804	+	0.476945i	−0.465181	+	0.885216i	$0.654011\pi$
$12$	0.189251	−	0.981929i	0.0546321	−	0.283458i
$13$	0.667036	+	2.27171i	0.185002	+	0.630060i	0.998803	+	0.0489159i	$0.0155766\pi$
$13$	0.667036	+	2.27171i	0.185002	+	0.630060i	−0.813801	+	0.581144i	$0.802605\pi$
$14$	1.81700	−	1.92315i	0.485613	−	0.513985i
$15$	0.685264	+	1.06629i	0.176934	+	0.275315i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−3.75873	−	1.50477i	−0.911626	−	0.364960i	−0.132032	−	0.991245i	$-0.542150\pi$
$17$	−3.75873	−	1.50477i	−0.911626	−	0.364960i	−0.779594	+	0.626285i	$0.784574\pi$
$18$	−0.580057	−	0.814576i	−0.136721	−	0.191997i
$19$	1.21465	−	0.486271i	0.278659	−	0.111558i	−0.228123	−	0.973632i	$-0.573259\pi$
$19$	1.21465	−	0.486271i	0.278659	−	0.111558i	0.506782	+	0.862074i	$0.330835\pi$
$20$	−1.06629	−	0.685264i	−0.238430	−	0.153230i
$21$	−0.137980	−	2.64215i	−0.0301098	−	0.576565i
$22$		−	4.83645i		−	1.03113i
$23$	0.901466	−	4.71035i	0.187969	−	0.982175i
$23$	0.901466	−	4.71035i	0.187969	−	0.982175i
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−3.33211	+	0.642212i	−0.666422	+	0.128442i
$26$	−2.36494	−	0.112656i	−0.463803	−	0.0220936i
$27$	−0.989821	−	0.142315i	−0.190491	−	0.0273885i
$28$	1.22310	+	2.34607i	0.231144	+	0.443365i
$29$	0.617399	+	4.29411i	0.114648	+	0.797395i	0.963297	+	0.268439i	$0.0865076\pi$
$29$	0.617399	+	4.29411i	0.114648	+	0.797395i	−0.848649	+	0.528957i	$0.822583\pi$
$30$	−1.23177	+	0.298825i	−0.224890	+	0.0545578i
$31$	−7.09328	+	0.337895i	−1.27399	+	0.0606877i	−0.673647	−	0.739054i	$-0.735273\pi$
$31$	−7.09328	+	0.337895i	−1.27399	+	0.0606877i	−0.600345	+	0.799741i	$0.704970\pi$
$32$	−0.995472	−	0.0950560i	−0.175976	−	0.0168037i
$33$	−3.50030	−	3.33753i	−0.609324	−	0.580989i
$34$	2.65137	−	3.05984i	0.454706	−	0.524759i
$35$	−3.17404	−	1.08231i	−0.536511	−	0.182944i
$36$	0.959493	−	0.281733i	0.159915	−	0.0469554i
$37$	1.40547	+	1.00083i	0.231058	+	0.164535i	0.689722	−	0.724074i	$-0.257733\pi$
$37$	1.40547	+	1.00083i	0.231058	+	0.164535i	−0.458665	+	0.888609i	$0.651672\pi$
$38$	0.0622546	+	1.30689i	0.0100990	+	0.212005i
$39$	−1.71353	+	1.63384i	−0.274384	+	0.261625i
$40$	0.996325	−	0.783519i	0.157533	−	0.123885i
$41$	−10.4587	−	4.77635i	−1.63338	−	0.745940i	−0.633762	−	0.773528i	$-0.718490\pi$
$41$	−10.4587	−	4.77635i	−1.63338	−	0.745940i	−0.999619	+	0.0275877i	$0.991217\pi$
$42$	2.54196	+	0.733771i	0.392234	+	0.113223i
$43$	−0.853542	+	1.32814i	−0.130164	+	0.202539i	−0.900218	−	0.435440i	$-0.856593\pi$
$43$	−0.853542	+	1.32814i	−0.130164	+	0.202539i	0.770054	+	0.637979i	$0.220229\pi$
$44$	4.57045	+	1.58185i	0.689021	+	0.238472i
$45$	−0.633752	+	1.09769i	−0.0944741	+	0.163634i
$46$	4.15644	+	2.39249i	0.612834	+	0.352753i
$47$	−7.44345	+	4.29748i	−1.08574	+	0.626852i	−0.932439	−	0.361328i	$-0.882323\pi$
$47$	−7.44345	+	4.29748i	−1.08574	+	0.626852i	−0.153300	+	0.988180i	$0.548990\pi$
$48$	−0.755750	+	0.654861i	−0.109083	+	0.0945210i
$49$	4.63224	+	5.24808i	0.661749	+	0.749725i
$50$	0.482936	−	3.35889i	0.0682975	−	0.475019i
$51$	−0.384858	−	4.03042i	−0.0538909	−	0.564371i
$52$	0.879955	−	2.19802i	0.122028	−	0.304811i
$53$	2.65656	+	2.78612i	0.364906	+	0.382703i	0.880433	−	0.474171i	$-0.157252\pi$
$53$	2.65656	+	2.78612i	0.364906	+	0.382703i	−0.515526	+	0.856874i	$0.672404\pi$
$54$	0.458227	−	0.888835i	0.0623567	−	0.120955i
$55$	−5.57624	+	2.54658i	−0.751900	+	0.343381i
$56$	−2.61707	+	0.388508i	−0.349721	+	0.0519166i
$57$	0.988798	+	0.856799i	0.130970	+	0.113486i
$58$	−4.25987	−	0.821022i	−0.559348	−	0.107805i
$59$	−4.11130	−	0.997391i	−0.535246	−	0.129849i	−0.0409798	−	0.999160i	$-0.513048\pi$
$59$	−4.11130	−	0.997391i	−0.535246	−	0.129849i	−0.494266	+	0.869311i	$0.664563\pi$
$60$	0.120484	−	1.26176i	0.0155544	−	0.162893i
$61$	7.07366	+	3.64673i	0.905689	+	0.466915i	0.847140	−	0.531369i	$-0.178322\pi$
$61$	7.07366	+	3.64673i	0.905689	+	0.466915i	0.0585490	+	0.998285i	$0.481353\pi$
$62$	2.00068	−	6.81367i	0.254086	−	0.865337i
$63$	2.28521	−	1.33335i	0.287910	−	0.167986i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	1.11535	+	2.78600i	0.138342	+	0.345561i
$66$	4.29881	−	2.21619i	0.529146	−	0.272794i
$67$	−1.75635	−	9.11279i	−0.214572	−	1.11330i	−0.916188	−	0.400749i	$-0.868750\pi$
$67$	−1.75635	−	9.11279i	−0.214572	−	1.11330i	0.701616	−	0.712555i	$-0.252462\pi$
$68$	2.02438	+	3.50632i	0.245492	+	0.425204i
$69$	4.59980	−	1.35715i	0.553751	−	0.163382i
$70$	2.06091	−	2.64549i	0.246326	−	0.316196i
$71$	−7.47038	−	8.62128i	−0.886571	−	1.02316i	−0.999563	−	0.0295613i	$-0.990589\pi$
$71$	−7.47038	−	8.62128i	−0.886571	−	1.02316i	0.112992	−	0.993596i	$-0.463956\pi$
$72$	−0.0475819	+	0.998867i	−0.00560758	+	0.117718i
$73$	8.18830	−	10.4123i	0.958368	−	1.21866i	−0.0173977	−	0.999849i	$-0.505538\pi$
$73$	8.18830	−	10.4123i	0.958368	−	1.21866i	0.975766	−	0.218816i	$-0.0702194\pi$
$74$	−1.40547	+	1.00083i	−0.163382	+	0.116344i
$75$	−2.09768	−	2.66742i	−0.242219	−	0.308007i
$76$	−1.25537	−	0.368610i	−0.144001	−	0.0422824i
$77$	12.7435	+	1.15804i	1.45226	+	0.131971i
$78$	−0.983545	−	2.15366i	−0.111365	−	0.243854i
$79$	1.70380	−	1.78689i	0.191692	−	0.201041i	−0.620873	−	0.783911i	$-0.713222\pi$
$79$	1.70380	−	1.78689i	0.191692	−	0.201041i	0.812565	+	0.582870i	$0.198070\pi$
$80$	0.414560	+	1.19779i	0.0463492	+	0.133917i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	7.93437	−	8.32133i	0.876205	−	0.918937i
$83$	5.60931	+	12.2827i	0.615702	+	1.34820i	0.918605	+	0.395177i	$0.129317\pi$
$83$	5.60931	+	12.2827i	0.615702	+	1.34820i	−0.302903	+	0.953021i	$0.597956\pi$
$84$	−1.52481	+	2.16216i	−0.166370	+	0.235912i
$85$	−4.92393	−	1.44580i	−0.534075	−	0.156819i
$86$	−0.975925	−	1.24099i	−0.105237	−	0.133819i
$87$	−3.53385	+	2.51644i	−0.378868	+	0.269791i
$88$	−2.98969	+	3.80170i	−0.318702	+	0.405263i
$89$	−0.436178	+	9.15651i	−0.0462348	+	0.970588i	0.849938	+	0.526883i	$0.176639\pi$
$89$	−0.436178	+	9.15651i	−0.0462348	+	0.970588i	−0.896173	+	0.443705i	$0.853664\pi$
$90$	−0.830038	−	0.957915i	−0.0874937	−	0.100973i
$91$	0.863100	−	6.20439i	0.0904775	−	0.650397i
$92$	−3.62034	+	3.14533i	−0.377447	+	0.327924i
$93$	−3.55066	−	6.14993i	−0.368187	−	0.637718i
$94$	−1.62661	−	8.43963i	−0.167772	−	0.870482i
$95$	1.47401	−	0.759905i	0.151230	−	0.0779646i
$96$	−0.371662	−	0.928368i	−0.0379326	−	0.0947512i
$97$	3.46883	−	7.59568i	0.352207	−	0.771225i	−0.647750	−	0.761853i	$-0.724290\pi$
$97$	3.46883	−	7.59568i	0.352207	−	0.771225i	0.999956	−	0.00937142i	$-0.00298306\pi$
$98$	−6.47450	+	2.66100i	−0.654023	+	0.268801i
$99$	1.36258	−	4.64054i	0.136945	−	0.466391i
$100$	3.01621	+	1.55496i	0.301621	+	0.155496i
$101$	−0.444631	+	4.65639i	−0.0442425	+	0.463328i	0.946019	+	0.324110i	$0.105065\pi$
$101$	−0.444631	+	4.65639i	−0.0442425	+	0.463328i	−0.990262	+	0.139218i	$0.955541\pi$
$102$	3.93462	+	0.954529i	0.389586	+	0.0945125i
$103$	0.149400	+	0.0287945i	0.0147208	+	0.00283721i	0.196606	−	0.980483i	$-0.437008\pi$
$103$	0.149400	+	0.0287945i	0.0147208	+	0.00283721i	−0.181886	+	0.983320i	$0.558220\pi$
$104$	1.78933	+	1.55046i	0.175458	+	0.152035i
$105$	−0.492435	−	3.31715i	−0.0480568	−	0.323720i
$106$	−3.50176	+	1.59920i	−0.340121	+	0.155328i
$107$	−2.62852	+	5.09862i	−0.254109	+	0.492903i	−0.981039	−	0.193808i	$-0.937916\pi$
$107$	−2.62852	+	5.09862i	−0.254109	+	0.492903i	0.726930	+	0.686711i	$0.240946\pi$
$108$	0.690079	+	0.723734i	0.0664029	+	0.0696413i
$109$	−1.51422	+	3.78234i	−0.145036	+	0.362282i	−0.983043	−	0.183378i	$-0.941297\pi$
$109$	−1.51422	+	3.78234i	−0.145036	+	0.362282i	0.838006	+	0.545660i	$0.183721\pi$
$110$	−0.582714	−	6.10245i	−0.0555596	−	0.581846i
$111$	−0.245550	+	1.70784i	−0.0233066	+	0.162101i
$112$	0.488820	−	2.60020i	0.0461891	−	0.245696i
$113$	−12.4218	+	10.7636i	−1.16855	+	1.01255i	−0.168907	+	0.985632i	$0.554024\pi$
$113$	−12.4218	+	10.7636i	−1.16855	+	1.01255i	−0.999638	+	0.0269181i	$0.991431\pi$
$114$	−1.13308	+	0.654184i	−0.106123	+	0.0612699i
$115$	0.569917	−	6.05196i	0.0531450	−	0.564348i
$116$	2.16913	−	3.75705i	0.201399	−	0.348833i
$117$	−2.23740	−	0.774373i	−0.206848	−	0.0715908i
$118$	2.28721	−	3.55897i	0.210555	−	0.327629i
$119$	7.42751	+	7.71873i	0.680879	+	0.707575i
$120$	1.15296	+	0.526540i	0.105251	+	0.0480663i
$121$	9.74015	−	7.65974i	0.885468	−	0.696340i
$122$	−5.75973	+	5.49189i	−0.521461	+	0.497212i
$123$	−0.547086	−	11.4848i	−0.0493291	−	1.03555i
$124$	5.78457	+	4.11917i	0.519470	+	0.369913i
$125$	−10.2078	+	2.99727i	−0.913010	+	0.268084i
$126$	0.512593	+	2.59562i	0.0456654	+	0.231236i
$127$	4.41240	−	5.09218i	0.391537	−	0.451858i	−0.525420	−	0.850843i	$-0.676092\pi$
$127$	4.41240	−	5.09218i	0.391537	−	0.451858i	0.916958	+	0.398985i	$0.130637\pi$
$128$	0.723734	+	0.690079i	0.0639697	+	0.0609949i
$129$	−1.57161	−	0.150071i	−0.138373	−	0.0132130i
$130$	−2.99757	+	0.142792i	−0.262904	+	0.0125237i
$131$	11.3210	−	2.74644i	0.989118	−	0.239957i	0.291612	−	0.956537i	$-0.405808\pi$
$131$	11.3210	−	2.74644i	0.989118	−	0.239957i	0.697506	+	0.716579i	$0.254293\pi$
$132$	0.688298	+	4.78722i	0.0599087	+	0.416674i
$133$	−3.45841	−	0.148888i	−0.299882	−	0.0129102i
$134$	9.18604	+	1.32075i	0.793553	+	0.114096i
$135$	−1.26607	−	0.0603102i	−0.108966	−	0.00519068i
$136$	−3.97558	+	0.766231i	−0.340904	+	0.0657038i
$137$	14.2319	+	8.21679i	1.21591	+	0.702008i	0.964041	−	0.265753i	$-0.0856205\pi$
$137$	14.2319	+	8.21679i	1.21591	+	0.702008i	0.251872	+	0.967761i	$0.418954\pi$
$138$	−0.221938	+	4.79069i	−0.0188926	+	0.407811i
$139$		−	18.9405i		−	1.60651i	−0.595632	−	0.803257i	$-0.703098\pi$
$139$		−	18.9405i		−	1.60651i	0.595632	−	0.803257i	$-0.296902\pi$
$140$	1.82593	+	2.81282i	0.154319	+	0.237726i
$141$	−7.23054	−	4.64678i	−0.608921	−	0.391330i
$142$	10.5904	−	4.23977i	0.888729	−	0.355794i
$143$	−6.64215	−	9.32760i	−0.555445	−	0.780013i
$144$	−0.928368	−	0.371662i	−0.0773640	−	0.0309719i
$145$	1.29638	+	5.34376i	0.107659	+	0.443775i
$146$	7.16148	+	11.1435i	0.592688	+	0.922241i
$147$	−2.54206	+	6.52211i	−0.209666	+	0.537935i
$148$	−0.486101	−	1.65551i	−0.0399573	−	0.136082i
$149$	2.92873	−	15.1957i	0.239931	−	1.24488i	−0.639476	−	0.768811i	$-0.720849\pi$
$149$	2.92873	−	15.1957i	0.239931	−	1.24488i	0.879407	−	0.476070i	$-0.157939\pi$
$150$	3.20680	−	1.10988i	0.261834	−	0.0906216i
$151$	−3.86333	+	15.9249i	−0.314394	+	1.29595i	0.567060	+	0.823677i	$0.308081\pi$
$151$	−3.86333	+	15.9249i	−0.314394	+	1.29595i	−0.881453	+	0.472271i	$0.843434\pi$
$152$	0.758928	−	1.06576i	0.0615572	−	0.0864449i
$153$	3.40603	−	2.18892i	0.275361	−	0.176964i
$154$	−5.26235	+	11.6639i	−0.424052	+	0.939902i
$155$	−8.90934	+	1.28097i	−0.715615	+	0.102890i
$156$	2.35690	−	0.225057i	0.188703	−	0.0180189i
$157$	14.9856	+	11.7848i	1.19598	+	0.940531i	0.999203	−	0.0399174i	$-0.0127095\pi$
$157$	14.9856	+	11.7848i	1.19598	+	0.940531i	0.196779	+	0.980448i	$0.436952\pi$
$158$	1.13136	+	2.19452i	0.0900058	+	0.174587i
$159$	−1.25910	+	3.63792i	−0.0998528	+	0.288506i
$160$	−1.26750			−0.100205
$161$	−7.29918	+	10.3789i	−0.575256	+	0.817973i
$162$	1.00000			0.0785674
$163$	−5.57402	+	16.1051i	−0.436591	+	1.26145i	0.485419	+	0.874281i	$0.338667\pi$
$163$	−5.57402	+	16.1051i	−0.436591	+	1.26145i	−0.922010	+	0.387165i	$0.873454\pi$
$164$	5.26859	+	10.2196i	0.411407	+	0.798019i
$165$	−4.81867	−	3.78945i	−0.375133	−	0.295008i
$166$	−13.4418	+	1.28353i	−1.04328	+	0.0996214i
$167$	−17.4214	+	2.50482i	−1.34811	+	0.193829i	−0.778272	−	0.627927i	$-0.783903\pi$
$167$	−17.4214	+	2.50482i	−1.34811	+	0.193829i	−0.569839	+	0.821756i	$0.692994\pi$
$168$	−1.54453	−	2.14812i	−0.119163	−	0.165731i
$169$	6.22055	−	3.99770i	0.478503	−	0.307516i
$170$	2.97674	−	4.18025i	0.228305	−	0.320610i
$171$	−0.308459	+	1.27149i	−0.0235885	+	0.0972330i
$172$	1.49193	−	0.516362i	0.113759	−	0.0393722i
$173$	−1.17926	+	6.11859i	−0.0896576	+	0.465188i	0.909154	+	0.416459i	$0.136729\pi$
$173$	−1.17926	+	6.11859i	−0.0896576	+	0.465188i	−0.998812	+	0.0487288i	$0.984483\pi$
$174$	−1.22223	−	4.16253i	−0.0926570	−	0.315561i
$175$	8.73470	+	2.07674i	0.660281	+	0.156987i
$176$	−2.61478	−	4.06868i	−0.197096	−	0.306688i
$177$	−0.997391	−	4.11130i	−0.0749685	−	0.309024i
$178$	−8.51025	−	3.40699i	−0.637870	−	0.255365i
$179$	4.68328	+	6.57675i	0.350045	+	0.491570i	0.951633	−	0.307237i	$-0.0994044\pi$
$179$	4.68328	+	6.57675i	0.350045	+	0.491570i	−0.601588	+	0.798807i	$0.705465\pi$
$180$	1.17671	−	0.471083i	0.0877068	−	0.0351125i
$181$	7.66432	+	4.92556i	0.569685	+	0.366114i	0.793549	−	0.608506i	$-0.208231\pi$
$181$	7.66432	+	4.92556i	0.569685	+	0.366114i	−0.223864	+	0.974620i	$0.571867\pi$
$182$	5.58086	+	2.84489i	0.413681	+	0.210877i
$183$			7.95835i			0.588298i
$184$	−1.78824	−	4.44996i	−0.131831	−	0.328056i
$185$	1.89395	+	1.09348i	0.139246	+	0.0803939i
$186$	6.97300	−	1.34394i	0.511285	−	0.0985421i
$187$	19.5594	+	0.931728i	1.43032	+	0.0681347i
$188$	8.50747	+	1.22319i	0.620471	+	0.0892103i
$189$	2.23227	+	1.42020i	0.162374	+	0.103305i
$190$	0.236009	+	1.64148i	0.0171219	+	0.119086i
$191$	4.18751	−	1.01588i	0.302997	−	0.0735064i	−0.0813778	−	0.996683i	$-0.525932\pi$
$191$	4.18751	−	1.01588i	0.302997	−	0.0735064i	0.384375	+	0.923177i	$0.374417\pi$
$192$	0.998867	−	0.0475819i	0.0720870	−	0.00343393i
$193$	−19.1217	−	1.82590i	−1.37641	−	0.131431i	−0.619524	−	0.784978i	$-0.712674\pi$
$193$	−19.1217	−	1.82590i	−1.37641	−	0.131431i	−0.756887	+	0.653546i	$0.773280\pi$
$194$	6.04338	+	5.76235i	0.433890	+	0.413713i
$195$	−1.96522	+	2.26798i	−0.140732	+	0.162413i
$196$	−0.397043	−	6.98873i	−0.0283602	−	0.499195i
$197$	−20.7517	+	6.09325i	−1.47850	+	0.434126i	−0.918851	−	0.394605i	$-0.870881\pi$
$197$	−20.7517	+	6.09325i	−1.47850	+	0.434126i	−0.559647	+	0.828731i	$0.689063\pi$
$198$	3.93965	+	2.80541i	0.279979	+	0.199372i
$199$	−0.0651216	−	1.36707i	−0.00461634	−	0.0969090i	−1.00000		0.000928604i	$-0.999704\pi$
$199$	−0.0651216	−	1.36707i	−0.00461634	−	0.0969090i	0.995383	−	0.0959804i	$-0.0305986\pi$
$200$	−2.45594	+	2.34174i	−0.173661	+	0.165586i
$201$	7.29497	−	5.73683i	0.514547	−	0.404645i
$202$	−4.25487	−	1.94313i	−0.299371	−	0.136718i
$203$	3.18329	−	11.0277i	0.223423	−	0.773993i
$204$	−2.18892	+	3.40603i	−0.153255	+	0.238470i
$205$	−13.7719	−	4.76652i	−0.961874	−	0.332908i
$206$	−0.0760748	+	0.131765i	−0.00530038	+	0.00918053i
$207$	3.31403	+	3.46658i	0.230341	+	0.240944i
$208$	−2.05042	+	1.18381i	−0.142171	+	0.0820824i
$209$	−4.78227	+	4.14386i	−0.330797	+	0.286637i
$210$	3.29577	+	0.619581i	0.227429	+	0.0427551i
$211$	0.196277	−	1.36514i	0.0135123	−	0.0939801i	−0.981949	−	0.189144i	$-0.939429\pi$
$211$	0.196277	−	1.36514i	0.0135123	−	0.0939801i	0.995462	+	0.0951643i	$0.0303377\pi$
$212$	−0.365932	−	3.83221i	−0.0251323	−	0.263198i
$213$	4.23977	−	10.5904i	0.290504	−	0.725645i
$214$	−3.95850	−	4.15155i	−0.270597	−	0.283794i
$215$	−0.916950	+	1.77863i	−0.0625354	+	0.121302i
$216$	−0.909632	+	0.415415i	−0.0618926	+	0.0282654i
$217$	17.4743	+	6.90304i	1.18623	+	0.468609i
$218$	−3.07906	−	2.66802i	−0.208540	−	0.180701i
$219$	13.0069	+	2.50687i	0.878925	+	0.169399i
$220$	5.95741	+	1.44525i	0.401649	+	0.0974389i
$221$	0.911198	−	9.54250i	0.0612938	−	0.641898i
$222$	−1.53360	−	0.790624i	−0.102928	−	0.0530632i
$223$	−1.48501	+	5.05748i	−0.0994436	+	0.338674i	−0.994154	−	0.107973i	$-0.965564\pi$
$223$	−1.48501	+	5.05748i	−0.0994436	+	0.338674i	0.894710	+	0.446647i	$0.147382\pi$
$224$	2.29732	+	1.31238i	0.153496	+	0.0876869i
$225$	1.40968	−	3.08678i	0.0939789	−	0.205785i
$226$	−6.10879	−	15.2590i	−0.406351	−	1.01502i
$227$	2.47939	−	1.27821i	0.164563	−	0.0848379i	−0.373978	−	0.927438i	$-0.622006\pi$
$227$	2.47939	−	1.27821i	0.164563	−	0.0848379i	0.538540	+	0.842600i	$0.318976\pi$
$228$	−0.247610	−	1.28472i	−0.0163984	−	0.0850829i
$229$	10.1554	+	17.5897i	0.671087	+	1.16236i	0.977596	+	0.210489i	$0.0675057\pi$
$229$	10.1554	+	17.5897i	0.671087	+	1.16236i	−0.306509	+	0.951868i	$0.599161\pi$
$230$	5.53270	+	2.51797i	0.364816	+	0.166030i
$231$	4.81011	+	11.8575i	0.316482	+	0.780169i
$232$	2.84096	+	3.27864i	0.186518	+	0.215253i
$233$	−0.470541	+	9.87788i	−0.0308262	+	0.647121i	0.929597	+	0.368577i	$0.120155\pi$
$233$	−0.470541	+	9.87788i	−0.0308262	+	0.647121i	−0.960423	+	0.278544i	$0.910148\pi$
$234$	1.46357	−	1.86107i	0.0956763	−	0.121662i
$235$	−8.87410	+	6.31922i	−0.578883	+	0.412220i
$236$	2.61515	+	3.32544i	0.170232	+	0.216468i
$237$	2.36898	+	0.695594i	0.153881	+	0.0451837i
$238$	−9.72350	+	4.49446i	−0.630281	+	0.291332i
$239$	−3.91329	−	8.56892i	−0.253130	−	0.554277i	0.739821	−	0.672804i	$-0.234910\pi$
$239$	−3.91329	−	8.56892i	−0.253130	−	0.554277i	−0.992951	+	0.118527i	$0.962183\pi$
$240$	−0.874678	+	0.917335i	−0.0564602	+	0.0592137i
$241$	6.68231	+	19.3073i	0.430445	+	1.24369i	0.926795	+	0.375567i	$0.122552\pi$
$241$	6.68231	+	19.3073i	0.430445	+	1.24369i	−0.496350	+	0.868123i	$0.665327\pi$
$242$	4.05277	+	11.7097i	0.260522	+	0.752728i
$243$	0.690079	−	0.723734i	0.0442686	−	0.0464276i
$244$	−3.30602	−	7.23917i	−0.211646	−	0.463440i
$245$	6.47711	+	6.06373i	0.413807	+	0.387397i
$246$	11.0320	+	3.23930i	0.703377	+	0.206530i
$247$	1.91488	+	2.43497i	0.121841	+	0.154933i
$248$	−5.78457	+	4.11917i	−0.367321	+	0.261568i
$249$	−8.34694	+	10.6140i	−0.528966	+	0.672635i
$250$	0.506210	−	10.6267i	0.0320155	−	0.672089i
$251$	7.90751	+	9.12575i	0.499118	+	0.576013i	0.948279	−	0.317438i	$-0.102823\pi$
$251$	7.90751	+	9.12575i	0.499118	+	0.576013i	−0.449161	+	0.893451i	$0.648277\pi$
$252$	−2.62052	−	0.364543i	−0.165077	−	0.0229641i
$253$	3.33094	+	22.9544i	0.209415	+	1.44313i
$254$	3.36896	+	5.83521i	0.211387	+	0.366134i
$255$	−0.971201	−	5.03907i	−0.0608189	−	0.315559i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	1.12942	+	2.82116i	0.0704515	+	0.175979i	0.959414	−	0.282000i	$-0.0909977\pi$
$257$	1.12942	+	2.82116i	0.0704515	+	0.175979i	−0.888963	+	0.457979i	$0.848573\pi$
$258$	0.655841	−	1.43609i	0.0408309	−	0.0894071i
$259$	−2.30055	−	3.94290i	−0.142949	−	0.245000i
$260$	0.845470	−	2.87941i	0.0524338	−	0.178573i
$261$	−3.85600	−	1.98791i	−0.238681	−	0.123048i
$262$	−1.10734	+	11.5966i	−0.0684117	+	0.716440i
$263$	−11.2158	−	2.72094i	−0.691599	−	0.167780i	−0.125471	−	0.992097i	$-0.540044\pi$
$263$	−11.2158	−	2.72094i	−0.691599	−	0.167780i	−0.566128	+	0.824317i	$0.691559\pi$
$264$	−4.74905	−	0.915304i	−0.292284	−	0.0563330i
$265$	3.68763	+	3.19535i	0.226530	+	0.196289i
$266$	1.27183	−	3.21951i	0.0779812	−	0.197401i
$267$	−8.33850	+	3.80806i	−0.510308	+	0.233050i
$268$	−4.25257	+	8.24884i	−0.259767	+	0.503878i
$269$	−9.09961	−	9.54339i	−0.554813	−	0.581871i	0.385276	−	0.922802i	$-0.374106\pi$
$269$	−9.09961	−	9.54339i	−0.554813	−	0.581871i	−0.940088	+	0.340931i	$0.889258\pi$
$270$	0.471083	−	1.17671i	0.0286692	−	0.0716123i
$271$	−1.78040	−	18.6452i	−0.108151	−	1.13261i	−0.872771	−	0.488130i	$-0.837679\pi$
$271$	−1.78040	−	18.6452i	−0.108151	−	1.13261i	0.764619	−	0.644482i	$-0.222927\pi$
$272$	0.576197	−	4.00754i	0.0349371	−	0.242993i
$273$	5.91017	−	2.07586i	0.357700	−	0.125637i
$274$	−12.4197	+	10.7617i	−0.750300	+	0.650138i
$275$	14.2134	−	8.20608i	0.857097	−	0.494845i
$276$	−4.45462	−	1.77661i	−0.268137	−	0.106940i
$277$	−14.5444	+	25.1916i	−0.873887	+	1.51362i	−0.0159435	+	0.999873i	$0.505075\pi$
$277$	−14.5444	+	25.1916i	−0.873887	+	1.51362i	−0.857944	+	0.513744i	$0.828258\pi$
$278$	17.8988	+	6.19484i	1.07350	+	0.371542i
$279$	3.83927	−	5.97402i	0.229851	−	0.357655i
$280$	−3.25532	+	0.805520i	−0.194542	+	0.0481391i
$281$	−17.1468	−	7.83068i	−1.02289	−	0.467139i	−0.167913	−	0.985802i	$-0.553703\pi$
$281$	−17.1468	−	7.83068i	−1.02289	−	0.467139i	−0.854979	+	0.518663i	$0.826430\pi$
$282$	6.75609	−	5.31305i	0.402319	−	0.316388i
$283$	−5.44557	+	5.19234i	−0.323705	+	0.308652i	−0.834454	−	0.551078i	$-0.814217\pi$
$283$	−5.44557	+	5.19234i	−0.323705	+	0.308652i	0.510749	+	0.859730i	$0.329368\pi$
$284$	0.542795	+	11.3947i	0.0322089	+	0.676149i
$285$	1.35086	+	0.961943i	0.0800181	+	0.0569806i
$286$	10.9870	−	3.22608i	0.649676	−	0.190762i
$287$	20.0260	+	22.8987i	1.18210	+	1.35167i
$288$	0.654861	−	0.755750i	0.0385880	−	0.0445330i
$289$	−0.439753	−	0.419303i	−0.0258678	−	0.0246649i
$290$	−5.47387	−	0.522691i	−0.321436	−	0.0306935i
$291$	8.34082	−	0.397322i	0.488948	−	0.0232915i
$292$	−12.8729	+	3.12293i	−0.753328	+	0.182756i
$293$	−1.61960	−	11.2646i	−0.0946181	−	0.658083i	−0.980839	−	0.194820i	$-0.937588\pi$
$293$	−1.61960	−	11.2646i	−0.0946181	−	0.658083i	0.886221	−	0.463263i	$-0.153321\pi$
$294$	−5.33197	−	4.53542i	−0.310967	−	0.264511i
$295$	−5.30766	−	0.763126i	−0.309024	−	0.0444309i
$296$	1.72345	+	0.0820978i	0.100173	+	0.00477184i
$297$	4.74905	−	0.915304i	0.275568	−	0.0531113i
$298$	13.4021	+	7.73768i	0.776360	+	0.448232i
$299$	11.3019	−	1.09409i	0.653604	−	0.0632731i
$300$			3.39343i			0.195920i
$301$	3.50355	−	2.27431i	0.201941	−	0.131089i
$302$	−13.7854	−	8.85937i	−0.793263	−	0.509799i
$303$	−4.34251	+	1.73848i	−0.249470	+	0.0998729i
$304$	0.758928	+	1.06576i	0.0435275	+	0.0611258i
$305$	9.36466	+	3.74905i	0.536219	+	0.214670i
$306$	0.954529	+	3.93462i	0.0545668	+	0.224927i
$307$	7.98774	+	12.4292i	0.455884	+	0.709370i	0.990770	−	0.135555i	$-0.0432817\pi$
$307$	7.98774	+	12.4292i	0.455884	+	0.709370i	−0.534886	+	0.844925i	$0.679645\pi$
$308$	−9.30123	−	8.78781i	−0.529987	−	0.500732i
$309$	0.0428655	+	0.145986i	0.00243853	+	0.00830488i
$310$	1.70344	−	8.83830i	0.0967490	−	0.501982i
$311$	4.77561	−	1.65285i	0.270800	−	0.0937248i	−0.188293	−	0.982113i	$-0.560296\pi$
$311$	4.77561	−	1.65285i	0.270800	−	0.0937248i	0.459093	+	0.888388i	$0.348174\pi$
$312$	−0.558188	+	2.30088i	−0.0316011	+	0.130262i
$313$	10.6658	−	14.9780i	0.602865	−	0.846605i	−0.394519	−	0.918888i	$-0.629089\pi$
$313$	10.6658	−	14.9780i	0.602865	−	0.846605i	0.997384	+	0.0722823i	$0.0230283\pi$
$314$	−16.0380	+	10.3070i	−0.905075	+	0.581656i
$315$	2.72275	−	1.95770i	0.153410	−	0.110304i
$316$	−2.44386	+	0.351373i	−0.137478	+	0.0197663i
$317$	20.3911	−	1.94712i	1.14528	−	0.109361i	0.494886	−	0.868958i	$-0.335210\pi$
$317$	20.3911	−	1.94712i	1.14528	−	0.109361i	0.650394	+	0.759597i	$0.274604\pi$
$318$	−3.02603	−	2.37969i	−0.169691	−	0.133447i
$319$	−9.61441	−	18.6493i	−0.538303	−	1.04416i
$320$	0.414560	−	1.19779i	0.0231746	−	0.0669586i
$321$	−5.73630			−0.320169
$322$	−7.42076	−	10.2923i	−0.413543	−	0.573570i
$323$	−5.29725			−0.294747
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	−3.68156	−	7.14123i	−0.204216	−	0.396124i
$326$	−13.3962	−	10.5349i	−0.741948	−	0.583475i
$327$	−4.05573	+	0.387276i	−0.224283	+	0.0214164i
$328$	−11.3807	+	1.63630i	−0.628397	+	0.0903498i
$329$	22.6270	−	2.26514i	1.24747	−	0.124881i
$330$	5.15706	−	3.31424i	0.283887	−	0.182443i
$331$	0.275324	−	0.386638i	0.0151332	−	0.0212515i	−0.806940	−	0.590633i	$-0.798878\pi$
$331$	0.275324	−	0.386638i	0.0151332	−	0.0212515i	0.822073	+	0.569382i	$0.192817\pi$
$332$	3.18343	−	13.1223i	0.174713	−	0.720179i
$333$	−1.63050	+	0.564323i	−0.0893511	+	0.0309247i
$334$	3.33093	−	17.2825i	0.182260	−	0.945657i
$335$	−3.31404	−	11.2866i	−0.181065	−	0.616652i
$336$	2.53514	−	0.757002i	0.138303	−	0.0412978i
$337$	9.82359	+	15.2858i	0.535125	+	0.832671i	0.998570	−	0.0534547i	$-0.0170233\pi$
$337$	9.82359	+	15.2858i	0.535125	+	0.832671i	−0.463445	+	0.886126i	$0.653387\pi$
$338$	1.74329	+	7.18594i	0.0948225	+	0.390864i
$339$	−15.2590	−	6.10879i	−0.828757	−	0.331784i
$340$	2.97674	+	4.18025i	0.161436	+	0.226706i
$341$	31.8850	−	12.7648i	1.72667	−	0.691254i
$342$	−1.10067	−	0.707357i	−0.0595174	−	0.0382495i
$343$	−5.46118	−	17.6968i	−0.294876	−	0.955535i
$344$			1.57876i			0.0851210i
$345$	5.64035	−	2.26661i	0.303666	−	0.122030i
$346$	−5.39638	−	3.11560i	−0.290111	−	0.167496i
$347$	−35.1864	+	6.78162i	−1.88890	+	0.364057i	−0.996238	−	0.0866603i	$-0.972381\pi$
$347$	−35.1864	+	6.78162i	−1.88890	+	0.364057i	−0.892667	+	0.450717i	$0.851168\pi$
$348$	4.33335	+	0.206423i	0.232292	+	0.0110654i
$349$	−11.8516	−	1.70400i	−0.634400	−	0.0912129i	−0.182391	−	0.983226i	$-0.558384\pi$
$349$	−11.8516	−	1.70400i	−0.634400	−	0.0912129i	−0.452009	+	0.892013i	$0.649293\pi$
$350$	−4.81936	+	7.57506i	−0.257606	+	0.404904i
$351$	−0.336947	−	2.34352i	−0.0179849	−	0.125088i
$352$	4.70011	−	1.14024i	0.250517	−	0.0607748i
$353$	7.90490	−	0.376557i	0.420735	−	0.0200421i	0.163853	−	0.986485i	$-0.447608\pi$
$353$	7.90490	−	0.376557i	0.420735	−	0.0200421i	0.256882	+	0.966443i	$0.417305\pi$
$354$	4.21140	+	0.402140i	0.223833	+	0.0213735i
$355$	−10.4646	−	9.97796i	−0.555402	−	0.529575i
$356$	6.00304	−	6.92787i	0.318160	−	0.367177i
$357$	−3.45719	+	10.1388i	−0.182974	+	0.536600i
$358$	−7.74679	+	2.27466i	−0.409431	+	0.120220i
$359$	−15.4783	−	11.0220i	−0.816913	−	0.581721i	0.0934062	−	0.995628i	$-0.470224\pi$
$359$	−15.4783	−	11.0220i	−0.816913	−	0.581721i	−0.910319	+	0.413907i	$0.864164\pi$
$360$	0.0603102	+	1.26607i	0.00317863	+	0.0667276i
$361$	−12.5120	+	11.9302i	−0.658528	+	0.627906i
$362$	−7.16142	+	5.63180i	−0.376396	+	0.296001i
$363$	11.2714	+	5.14750i	0.591597	+	0.270173i
$364$	−4.51374	+	4.34344i	−0.236584	+	0.227658i
$365$	9.07720	−	14.1244i	0.475122	−	0.739305i
$366$	−7.52064	−	2.60292i	−0.393110	−	0.136057i
$367$	1.91627	−	3.31908i	0.100029	−	0.173255i	−0.811668	−	0.584120i	$-0.801440\pi$
$367$	1.91627	−	3.31908i	0.100029	−	0.173255i	0.911696	+	0.410865i	$0.134773\pi$
$368$	4.79010	−	0.234451i	0.249701	−	0.0122216i
$369$	9.95737	−	5.74889i	0.518360	−	0.299275i
$370$	−1.65279	+	1.43215i	−0.0859243	+	0.0744538i
$371$	−3.37526	−	9.60968i	−0.175235	−	0.498910i
$372$	−1.01062	+	7.02905i	−0.0523984	+	0.364439i
$373$	−3.26012	−	34.1415i	−0.168803	−	1.76778i	−0.542333	−	0.840164i	$-0.682459\pi$
$373$	−3.26012	−	34.1415i	−0.168803	−	1.76778i	0.373531	−	0.927618i	$-0.378147\pi$
$374$	−7.27773	+	18.1789i	−0.376323	+	0.940008i
$375$	−7.34155	−	7.69959i	−0.379116	−	0.397605i
$376$	−3.93844	+	7.63950i	−0.203109	+	0.393977i
$377$	−9.34316	+	4.26688i	−0.481197	+	0.219755i
$378$	−2.07220	+	1.64499i	−0.106582	+	0.0846093i
$379$	16.1158	+	13.9644i	0.827813	+	0.717304i	0.961822	−	0.273676i	$-0.0882396\pi$
$379$	16.1158	+	13.9644i	0.827813	+	0.717304i	−0.134009	+	0.990980i	$0.542785\pi$
$380$	−1.62839	−	0.313847i	−0.0835347	−	0.0161000i
$381$	6.54799	+	1.58853i	0.335464	+	0.0813826i
$382$	−0.409594	+	4.28946i	−0.0209566	+	0.219468i
$383$	17.7043	+	9.12718i	0.904645	+	0.466377i	0.846778	−	0.531947i	$-0.178540\pi$
$383$	17.7043	+	9.12718i	0.904645	+	0.466377i	0.0578678	+	0.998324i	$0.481570\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	16.2188	−	0.0742099i	0.826589	−	0.00378209i
$386$	7.97958	−	17.4728i	0.406150	−	0.889344i
$387$	−0.586766	−	1.46567i	−0.0298270	−	0.0745042i
$388$	−7.42203	+	3.82632i	−0.376796	+	0.194252i
$389$	−3.53916	−	18.3629i	−0.179443	−	0.931036i	−0.954289	−	0.298887i	$-0.903385\pi$
$389$	−3.53916	−	18.3629i	−0.179443	−	0.931036i	0.774846	−	0.632150i	$-0.217827\pi$
$390$	−1.50048	−	2.59891i	−0.0759799	−	0.131601i
$391$	−10.4763	+	16.3484i	−0.529812	+	0.826775i
$392$	6.73422	+	1.91058i	0.340129	+	0.0964991i
$393$	7.62870	+	8.80399i	0.384817	+	0.444102i
$394$	1.02909	−	21.6033i	0.0518449	−	1.08836i
$395$	1.93450	−	2.45991i	0.0973351	−	0.123772i
$396$	−3.93965	+	2.80541i	−0.197975	+	0.140977i
$397$	17.6832	+	22.4861i	0.887496	+	1.12854i	0.990993	+	0.133913i	$0.0427544\pi$
$397$	17.6832	+	22.4861i	0.887496	+	1.12854i	−0.103497	+	0.994630i	$0.533003\pi$
$398$	1.31318	+	0.385585i	0.0658238	+	0.0193276i
$399$	−1.45240	−	3.14218i	−0.0727109	−	0.157306i
$400$	−1.40968	−	3.08678i	−0.0704842	−	0.154339i
$401$	2.78245	−	2.91815i	0.138949	−	0.145725i	−0.650583	−	0.759436i	$-0.725475\pi$
$401$	2.78245	−	2.91815i	0.138949	−	0.145725i	0.789531	+	0.613710i	$0.210324\pi$
$402$	3.03536	+	8.77008i	0.151390	+	0.437412i
$403$	−5.49907	−	15.8885i	−0.273928	−	0.791464i
$404$	3.22789	−	3.38532i	0.160594	−	0.168426i
$405$	−0.526540	−	1.15296i	−0.0261640	−	0.0572911i
$406$	9.38004	+	6.61502i	0.465524	+	0.328298i
$407$	−8.00678	−	2.35100i	−0.396881	−	0.116535i
$408$	−2.50277	−	3.18253i	−0.123906	−	0.157559i
$409$	26.9575	−	19.1963i	1.33296	−	0.949198i	0.332981	−	0.942933i	$-0.391945\pi$
$409$	26.9575	−	19.1963i	1.33296	−	0.949198i	0.999980	−	0.00626421i	$-0.00199397\pi$
$410$	9.00872	−	11.4555i	0.444909	−	0.565748i
$411$	−0.781941	+	16.4150i	−0.0385703	+	0.809690i
$412$	−0.0996368	−	0.114987i	−0.00490875	−	0.00566500i
$413$	8.82985	+	6.87872i	0.434489	+	0.338480i
$414$	−4.35984	+	1.99796i	−0.214274	+	0.0981942i
$415$	8.55749	+	14.8220i	0.420071	+	0.727584i
$416$	−0.448075	−	2.32483i	−0.0219687	−	0.113984i
$417$	16.8350	−	8.67905i	0.824414	−	0.425015i
$418$	−2.35182	−	5.87457i	−0.115031	−	0.287335i
$419$	−12.7066	+	27.8236i	−0.620758	+	1.35927i	0.294209	+	0.955741i	$0.404944\pi$
$419$	−12.7066	+	27.8236i	−0.620758	+	1.35927i	−0.914967	+	0.403529i	$0.867783\pi$
$420$	−1.66344	+	2.91186i	−0.0811677	+	0.142084i
$421$	3.51252	−	11.9625i	0.171190	−	0.583019i	−0.828544	−	0.559925i	$-0.810830\pi$
$421$	3.51252	−	11.9625i	0.171190	−	0.583019i	0.999733	−	0.0230942i	$-0.00735176\pi$
$422$	1.22586	+	0.631976i	0.0596740	+	0.0307641i
$423$	0.817003	−	8.55604i	0.0397240	−	0.416009i
$424$	3.74113	+	0.907588i	0.181685	+	0.0440764i
$425$	13.4909	+	2.60016i	0.654404	+	0.126126i
$426$	8.62128	+	7.47038i	0.417702	+	0.361941i
$427$	−13.0914	−	16.4913i	−0.633539	−	0.798068i
$428$	5.21792	−	2.38294i	0.252218	−	0.115184i
$429$	5.24709	−	10.1779i	0.253332	−	0.491395i
$430$	−1.38091	−	1.44825i	−0.0665932	−	0.0698409i
$431$	0.0687429	−	0.171711i	0.00331123	−	0.00827105i	−0.926703	−	0.375794i	$-0.877370\pi$
$431$	0.0687429	−	0.171711i	0.00331123	−	0.00827105i	0.930014	+	0.367523i	$0.119794\pi$
$432$	−0.0950560	−	0.995472i	−0.00457339	−	0.0478947i
$433$	0.446408	−	3.10484i	0.0214530	−	0.149209i	−0.976279	−	0.216514i	$-0.930531\pi$
$433$	0.446408	−	3.10484i	0.0214530	−	0.149209i	0.997732	+	0.0673056i	$0.0214402\pi$
$434$	−12.2387	+	14.2554i	−0.587474	+	0.684283i
$435$	−4.15569	+	3.60092i	−0.199250	+	0.172651i
$436$	3.52835	−	2.03709i	0.168977	−	0.0975590i
$437$	−1.19554	−	6.15976i	−0.0571906	−	0.294661i
$438$	−6.62314	+	11.4716i	−0.316466	+	0.548135i
$439$	−0.679193	−	0.235071i	−0.0324161	−	0.0112193i	0.310812	−	0.950471i	$-0.399399\pi$
$439$	−0.679193	−	0.235071i	−0.0324161	−	0.0112193i	−0.343228	+	0.939252i	$0.611520\pi$
$440$	−3.31424	+	5.15706i	−0.158000	+	0.245853i
$441$	−6.96192	+	0.729131i	−0.331520	+	0.0347205i
$442$	8.71964	+	3.98213i	0.414751	+	0.189411i
$443$	−27.6023	+	21.7067i	−1.31142	+	1.03131i	−0.314803	+	0.949157i	$0.601939\pi$
$443$	−27.6023	+	21.7067i	−1.31142	+	1.03131i	−0.996619	+	0.0821574i	$0.973819\pi$
$444$	1.24873	−	1.19066i	0.0592621	−	0.0565063i
$445$	0.552857	+	11.6059i	0.0262080	+	0.550173i
$446$	−4.29362	−	3.05748i	−0.203309	−	0.144776i
$447$	14.8485	−	4.35991i	0.702310	−	0.206217i
$448$	−1.99158	+	1.74173i	−0.0940932	+	0.0822890i
$449$	11.0168	−	12.7141i	0.519917	−	0.600016i	−0.433693	−	0.901061i	$-0.642790\pi$
$449$	11.0168	−	12.7141i	0.519917	−	0.600016i	0.953610	+	0.301045i	$0.0973353\pi$
$450$	2.45594	+	2.34174i	0.115774	+	0.110391i
$451$	55.3566	+	5.28591i	2.60664	+	0.248904i
$452$	16.4178	−	0.782076i	0.772228	−	0.0367857i
$453$	−15.9249	+	3.86333i	−0.748216	+	0.181515i
$454$	0.396984	+	2.76108i	0.0186314	+	0.129584i
$455$	0.341500	−	7.93246i	0.0160098	−	0.371880i
$456$	1.29505	+	0.186200i	0.0606463	+	0.00871962i
$457$	−19.6210	−	0.934663i	−0.917831	−	0.0437217i	−0.416653	−	0.909066i	$-0.636797\pi$
$457$	−19.6210	−	0.934663i	−0.917831	−	0.0437217i	−0.501178	+	0.865344i	$0.667100\pi$
$458$	−19.9437	+	3.84384i	−0.931910	+	0.179611i
$459$	3.50632	+	2.02438i	0.163661	+	0.0944898i
$460$	−4.18906	+	4.40486i	−0.195316	+	0.205378i
$461$		−	16.2620i		−	0.757398i	−0.925520	−	0.378699i	$-0.876372\pi$
$461$		−	16.2620i		−	0.757398i	0.925520	−	0.378699i	$-0.123628\pi$
$462$	−12.7786	+	0.667335i	−0.594515	+	0.0310472i
$463$	−15.9648	−	10.2600i	−0.741947	−	0.476821i	0.114261	−	0.993451i	$-0.463550\pi$
$463$	−15.9648	−	10.2600i	−0.741947	−	0.476821i	−0.856209	+	0.516630i	$0.827186\pi$
$464$	−4.02750	+	1.61237i	−0.186972	+	0.0748524i
$465$	−5.22107	−	7.33196i	−0.242121	−	0.340012i
$466$	−9.18070	−	3.67540i	−0.425288	−	0.170260i
$467$	−3.06392	−	12.6296i	−0.141781	−	0.584430i	−0.997728	−	0.0673664i	$-0.978540\pi$
$467$	−3.06392	−	12.6296i	−0.141781	−	0.584430i	0.855947	−	0.517063i	$-0.172975\pi$
$468$	1.28003	+	1.99177i	0.0591695	+	0.0920695i
$469$	−5.67956	+	23.8880i	−0.262258	+	1.10305i
$470$	−3.06923	−	10.4528i	−0.141573	−	0.482154i
$471$	−3.60796	+	18.7199i	−0.166246	+	0.862565i
$472$	−3.99788	+	1.38368i	−0.184017	+	0.0636890i
$473$	1.80016	−	7.42035i	0.0827714	−	0.341188i
$474$	−1.43215	+	2.01118i	−0.0657810	+	0.0923764i
$475$	−3.73505	+	2.40037i	−0.171376	+	0.110137i
$476$	−1.06702	−	10.6587i	−0.0489067	−	0.488541i
$477$	−3.81046	+	0.547862i	−0.174469	+	0.0250849i
$478$	9.37755	−	0.895447i	0.428919	−	0.0409568i
$479$	−21.0444	−	16.5495i	−0.961542	−	0.756165i	0.00828344	−	0.999966i	$-0.497363\pi$
$479$	−21.0444	−	16.5495i	−0.961542	−	0.756165i	−0.969825	+	0.243801i	$0.921606\pi$
$480$	−0.580804	−	1.12660i	−0.0265099	−	0.0514221i
$481$	−1.33610	+	3.86041i	−0.0609210	+	0.176020i
$482$	−20.4309			−0.930604
$483$	−12.5698	−	1.73187i	−0.571947	−	0.0788030i
$484$	−12.3912			−0.563237
$485$	3.46169	−	10.0019i	0.157187	−	0.454163i
$486$	0.458227	+	0.888835i	0.0207856	+	0.0403184i
$487$	−29.3966	−	23.1177i	−1.33209	−	1.04756i	−0.994331	−	0.106331i	$-0.966090\pi$
$487$	−29.3966	−	23.1177i	−1.33209	−	1.04756i	−0.337756	−	0.941234i	$-0.609668\pi$
$488$	7.92231	−	0.756489i	0.358626	−	0.0342446i
$489$	−16.8689	+	2.42539i	−0.762839	+	0.109680i
$490$	−7.84868	+	4.13762i	−0.354567	+	0.186919i
$491$	26.5812	−	17.0827i	1.19959	−	0.770931i	0.220707	−	0.975340i	$-0.429164\pi$
$491$	26.5812	−	17.0827i	1.19959	−	0.770931i	0.978886	+	0.204409i	$0.0655273\pi$
$492$	−6.66936	+	9.36581i	−0.300678	+	0.422243i
$493$	4.14100	−	17.0694i	0.186501	−	0.768768i
$494$	−2.92735	+	1.01316i	−0.131707	+	0.0455844i
$495$	1.16015	−	6.01943i	0.0521449	−	0.270553i
$496$	−2.00068	−	6.81367i	−0.0898330	−	0.305943i
$497$	8.63556	+	28.9199i	0.387358	+	1.29723i
$498$	−7.30022	−	11.3594i	−0.327131	−	0.509025i
$499$	−3.22653	−	13.3000i	−0.144440	−	0.595388i	−0.997312	−	0.0732690i	$-0.976657\pi$
$499$	−3.22653	−	13.3000i	−0.144440	−	0.595388i	0.852873	−	0.522119i	$-0.174858\pi$
$500$	9.87664	+	3.95401i	0.441697	+	0.176829i
$501$	−10.2093	−	14.3370i	−0.456120	−	0.640530i
$502$	−11.2101	+	4.48786i	−0.500333	+	0.200303i
$503$	−34.4509	−	22.1402i	−1.53609	−	0.987184i	−0.988633	−	0.150348i	$-0.951961\pi$
$503$	−34.4509	−	22.1402i	−1.53609	−	0.987184i	−0.547455	−	0.836835i	$-0.684403\pi$
$504$	1.20158	−	2.35716i	0.0535227	−	0.104996i
$505$			5.92884i			0.263830i
$506$	−22.7813	−	4.35989i	−1.01275	−	0.193821i
$507$	6.40372	+	3.69719i	0.284399	+	0.164198i
$508$	−6.61616	+	1.27516i	−0.293545	+	0.0565761i
$509$	33.8890	+	1.61433i	1.50211	+	0.0715541i	0.782422	−	0.622749i	$-0.213984\pi$
$509$	33.8890	+	1.61433i	1.50211	+	0.0715541i	0.719683	+	0.694303i	$0.244287\pi$
$510$	5.07957	+	0.730332i	0.224927	+	0.0323396i
$511$	−31.0766	+	16.2015i	−1.37475	+	0.716713i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	−1.27149	+	0.308459i	−0.0561375	+	0.0136188i
$514$	−3.03540	+	0.144594i	−0.133886	+	0.00637776i
$515$	0.191977	+	0.0183316i	0.00845951	+	0.000807786i
$516$	1.14260	+	1.08947i	0.0503003	+	0.0479612i
$517$	27.2219	−	31.4158i	1.19722	−	1.38166i
$518$	4.47848	−	0.884428i	0.196773	−	0.0388596i
$519$	−5.97879	+	1.75553i	−0.262440	+	0.0770593i
$520$	2.44452	+	1.74073i	0.107199	+	0.0763361i
$521$	−0.744110	−	15.6208i	−0.0326001	−	0.684359i	−0.954729	−	0.297477i	$-0.903855\pi$
$521$	−0.744110	−	15.6208i	−0.0326001	−	0.684359i	0.922129	−	0.386883i	$-0.126448\pi$
$522$	3.13975	−	2.99374i	0.137423	−	0.131033i
$523$	−0.594430	+	0.467465i	−0.0259926	+	0.0204408i	−0.631071	−	0.775725i	$-0.717384\pi$
$523$	−0.594430	+	0.467465i	−0.0259926	+	0.0204408i	0.605078	+	0.796166i	$0.293142\pi$
$524$	−10.5966	−	4.83931i	−0.462915	−	0.211406i
$525$	2.15659	+	8.71533i	0.0941212	+	0.380368i
$526$	6.23963	−	9.70905i	0.272061	−	0.423335i
$527$	27.1702	+	9.40370i	1.18355	+	0.409631i
$528$	2.41822	−	4.18849i	0.105240	−	0.182280i
$529$	−21.3747	−	8.49243i	−0.929336	−	0.369236i
$530$	−4.22572	+	2.43972i	−0.183553	+	0.105975i
$531$	3.19724	−	2.77042i	0.138748	−	0.120226i
$532$	2.62646	+	2.25488i	0.113871	+	0.0977615i
$533$	3.87415	−	26.9453i	0.167808	−	1.16713i
$534$	−0.871368	−	9.12538i	−0.0377078	−	0.394894i
$535$	−2.70227	+	6.74996i	−0.116830	+	0.291826i
$536$	−6.40428	−	6.71662i	−0.276623	−	0.290114i
$537$	−3.69965	+	7.17631i	−0.159652	+	0.309681i
$538$	11.9947	−	5.47780i	0.517128	−	0.236165i
$539$	−29.4731	−	16.6586i	−1.26950	−	0.717535i
$540$	0.957915	+	0.830038i	0.0412221	+	0.0357192i
$541$	−29.5392	−	5.69321i	−1.26999	−	0.244770i	−0.490641	−	0.871362i	$-0.663237\pi$
$541$	−29.5392	−	5.69321i	−1.26999	−	0.244770i	−0.779348	+	0.626592i	$0.784449\pi$
$542$	18.2020	+	4.41576i	0.781843	+	0.189673i
$543$	−0.866018	+	9.06935i	−0.0371644	+	0.389203i
$544$	3.59867	+	1.85525i	0.154292	+	0.0795430i
$545$	−1.45488	+	4.95486i	−0.0623201	+	0.212243i
$546$	0.0286615	+	6.26407i	0.00122660	+	0.268077i
$547$	7.46788	−	16.3524i	0.319304	−	0.699177i	−0.680121	−	0.733100i	$-0.738073\pi$
$547$	7.46788	−	16.3524i	0.319304	−	0.699177i	0.999424	+	0.0339226i	$0.0108000\pi$
$548$	−6.10774	−	15.2564i	−0.260910	−	0.651721i
$549$	−7.07366	+	3.64673i	−0.301896	+	0.155638i
$550$	3.10602	+	16.1156i	0.132441	+	0.687171i
$551$	2.83802	+	4.91560i	0.120904	+	0.209411i
$552$	3.13587	−	3.62855i	0.133471	−	0.154441i
$553$	−6.05323	+	2.45554i	−0.257409	+	0.104420i
$554$	−19.0491	−	21.9838i	−0.809318	−	0.934003i
$555$	−0.104059	+	2.18447i	−0.00441707	+	0.0927257i
$556$	−11.7083	+	14.8883i	−0.496541	+	0.631403i
$557$	−16.9387	+	12.0620i	−0.717714	+	0.511082i	−0.879592	−	0.475729i	$-0.842184\pi$
$557$	−16.9387	+	12.0620i	−0.717714	+	0.511082i	0.161878	+	0.986811i	$0.448245\pi$
$558$	4.38975	+	5.58202i	0.185833	+	0.236306i
$559$	−3.58649	−	1.05309i	−0.151692	−	0.0445409i
$560$	0.303493	−	3.33974i	0.0128249	−	0.141130i
$561$	8.13448	+	17.8120i	0.343438	+	0.752024i
$562$	13.0082	−	13.6426i	0.548716	−	0.575477i
$563$	4.45236	+	12.8642i	0.187644	+	0.542163i	0.999107	−	0.0422408i	$-0.0134497\pi$
$563$	4.45236	+	12.8642i	0.187644	+	0.542163i	−0.811463	+	0.584404i	$0.801328\pi$
$564$	2.81114	+	8.12224i	0.118370	+	0.342008i
$565$	−14.3766	+	15.0777i	−0.604826	+	0.634323i
$566$	−3.12569	−	6.84431i	−0.131383	−	0.287688i
$567$	−0.239441	+	2.63489i	−0.0100556	+	0.110655i
$568$	−10.9455	−	3.21389i	−0.459263	−	0.134852i
$569$	−22.1776	−	28.2011i	−0.929733	−	1.18225i	−0.982988	−	0.183671i	$-0.941202\pi$
$569$	−22.1776	−	28.2011i	−0.929733	−	1.18225i	0.0532544	−	0.998581i	$-0.483041\pi$
$570$	−1.35086	+	0.961943i	−0.0565813	+	0.0402914i
$571$	5.27260	−	6.70466i	0.220652	−	0.280581i	−0.663107	−	0.748525i	$-0.730762\pi$
$571$	5.27260	−	6.70466i	0.220652	−	0.280581i	0.883758	+	0.467943i	$0.155005\pi$
$572$	−0.544854	+	11.4379i	−0.0227815	+	0.478242i
$573$	2.82178	+	3.25650i	0.117881	+	0.136042i
$574$	−28.1892	+	11.4352i	−1.17659	+	0.477295i
$575$	0.0212547	+	16.2743i	0.000886381	+	0.678686i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	3.54395	+	18.3877i	0.147536	+	0.765492i	0.978030	+	0.208464i	$0.0668463\pi$
$577$	3.54395	+	18.3877i	0.147536	+	0.765492i	−0.830494	+	0.557028i	$0.811942\pi$
$578$	0.540071	−	0.278426i	0.0224640	−	0.0115810i
$579$	−7.13915	−	17.8327i	−0.296693	−	0.741103i
$580$	2.28427	−	5.00185i	0.0948491	−	0.207691i
$581$	−0.163461	−	35.7250i	−0.00678149	−	1.48212i
$582$	−2.35255	+	8.01204i	−0.0975162	+	0.332110i
$583$	−16.5489	−	8.53154i	−0.685384	−	0.353340i
$584$	1.25914	−	13.1863i	0.0521035	−	0.545653i
$585$	−2.91637	−	0.707505i	−0.120577	−	0.0292517i
$586$	11.1747	+	2.15376i	0.461624	+	0.0889708i
$587$	19.5717	+	16.9590i	0.807811	+	0.699972i	0.957397	−	0.288776i	$-0.0932484\pi$
$587$	19.5717	+	16.9590i	0.807811	+	0.699972i	−0.149585	+	0.988749i	$0.547794\pi$
$588$	6.02990	−	3.55533i	0.248669	−	0.146619i
$589$	−8.45152	+	3.85968i	−0.348239	+	0.159035i
$590$	2.45712	−	4.76615i	0.101158	−	0.196219i
$591$	−14.9249	−	15.6528i	−0.613928	−	0.643869i
$592$	−0.641266	+	1.60181i	−0.0263559	+	0.0658338i
$593$	−4.44437	−	46.5436i	−0.182509	−	1.91132i	−0.369970	−	0.929044i	$-0.620632\pi$
$593$	−4.44437	−	46.5436i	−0.182509	−	1.91132i	0.187461	−	0.982272i	$-0.439974\pi$
$594$	−0.688298	+	4.78722i	−0.0282412	+	0.196422i
$595$	10.3018	+	8.84432i	0.422331	+	0.362582i
$596$	−11.6955	+	10.1342i	−0.479066	+	0.415113i
$597$	1.18526	−	0.684310i	0.0485094	−	0.0280069i
$598$	−2.66256	+	11.0381i	−0.108880	+	0.451382i
$599$	7.08352	−	12.2690i	0.289425	−	0.501299i	−0.684248	−	0.729250i	$-0.739869\pi$
$599$	7.08352	−	12.2690i	0.289425	−	0.501299i	0.973673	+	0.227951i	$0.0732026\pi$
$600$	−3.20680	−	1.10988i	−0.130917	−	0.0453108i
$601$	6.25755	−	9.73694i	0.255251	−	0.397178i	−0.689852	−	0.723950i	$-0.742325\pi$
$601$	6.25755	−	9.73694i	0.255251	−	0.397178i	0.945103	+	0.326772i	$0.105961\pi$
$602$	1.00333	+	4.05471i	0.0408927	+	0.165258i
$603$	8.44184	+	3.85526i	0.343778	+	0.156998i
$604$	12.8809	−	10.1296i	0.524116	−	0.412169i
$605$	11.3669	−	10.8383i	0.462130	−	0.440640i
$606$	−0.222568	−	4.67227i	−0.00904120	−	0.189798i
$607$	−17.4424	−	12.4207i	−0.707967	−	0.504141i	0.168440	−	0.985712i	$-0.446127\pi$
$607$	−17.4424	−	12.4207i	−0.707967	−	0.504141i	−0.876407	+	0.481571i	$0.840066\pi$
$608$	−1.25537	+	0.368610i	−0.0509120	+	0.0149491i
$609$	11.2605	−	2.22376i	0.456298	−	0.0901115i
$610$	−6.60573	+	7.62342i	−0.267458	+	0.308663i
$611$	−14.7277	−	14.0428i	−0.595819	−	0.568112i
$612$	−4.03042	−	0.384858i	−0.162920	−	0.0155570i
$613$	−11.5163	+	0.548589i	−0.465139	+	0.0221573i	−0.278844	−	0.960336i	$-0.589951\pi$
$613$	−11.5163	+	0.548589i	−0.465139	+	0.0221573i	−0.186295	+	0.982494i	$0.559648\pi$
$614$	−14.3581	+	3.48324i	−0.579446	+	0.140572i
$615$	−2.07402	−	14.4251i	−0.0836326	−	0.581678i
$616$	11.3466	−	5.91546i	0.457168	−	0.238341i
$617$	33.9189	+	4.87681i	1.36552	+	0.196333i	0.785801	−	0.618480i	$-0.212251\pi$
$617$	33.9189	+	4.87681i	1.36552	+	0.196333i	0.579724	+	0.814813i	$0.303160\pi$
$618$	−0.151977	−	0.00723957i	−0.00611342	−	0.000291218i
$619$	8.12129	−	1.56525i	0.326422	−	0.0629128i	−0.0234075	−	0.999726i	$-0.507452\pi$
$619$	8.12129	−	1.56525i	0.326422	−	0.0629128i	0.349830	+	0.936813i	$0.386239\pi$
$620$	7.79506	+	4.50048i	0.313057	+	0.180744i
$621$	−1.56264	+	4.53411i	−0.0627067	+	0.181948i
$622$			5.05355i			0.202629i
$623$	11.0148	−	21.6078i	0.441297	−	0.865699i
$624$	−1.99177	−	1.28003i	−0.0797346	−	0.0512423i
$625$	3.23311	−	1.29434i	0.129324	−	0.0517737i
$626$	10.6658	+	14.9780i	0.426290	+	0.598640i
$627$	−5.87457	−	2.35182i	−0.234608	−	0.0939228i
$628$	−4.49460	−	18.5270i	−0.179354	−	0.739307i
$629$	−3.77676	−	5.87676i	−0.150589	−	0.234322i
$630$	0.959502	+	3.21330i	0.0382275	+	0.128021i
$631$	7.50068	+	25.5450i	0.298597	+	1.01693i	0.962988	+	0.269544i	$0.0868729\pi$
$631$	7.50068	+	25.5450i	0.298597	+	1.01693i	−0.664391	+	0.747385i	$0.731309\pi$
$632$	0.467259	−	2.42437i	0.0185866	−	0.0964362i
$633$	1.30332	−	0.451085i	0.0518025	−	0.0179290i
$634$	−4.82926	+	19.9065i	−0.191794	+	0.790587i
$635$	4.95388	−	6.95676i	0.196589	−	0.276070i
$636$	3.23853	−	2.08128i	0.128416	−	0.0825279i
$637$	−8.83226	+	14.0238i	−0.349947	+	0.555643i
$638$	20.7682	−	2.98602i	0.822221	−	0.118218i
$639$	11.3559	−	1.08436i	0.449234	−	0.0428966i
$640$	0.996325	+	0.783519i	0.0393832	+	0.0309713i
$641$	−11.1736	−	21.6738i	−0.441332	−	0.856065i	−0.999650	−	0.0264380i	$-0.991584\pi$
$641$	−11.1736	−	21.6738i	−0.441332	−	0.856065i	0.558318	−	0.829627i	$-0.311447\pi$
$642$	1.87616	−	5.42081i	0.0740461	−	0.213942i
$643$	0.319561			0.0126023			0.00630113	−	0.999980i	$-0.497994\pi$
$643$	0.319561			0.0126023			0.00630113	+	0.999980i	$0.497994\pi$
$644$	12.1534	−	3.64633i	0.478910	−	0.143685i
$645$	−2.00108			−0.0787926
$646$	1.73256	−	5.00591i	0.0681667	−	0.196955i
$647$	22.2390	+	43.1377i	0.874307	+	1.69592i	0.703600	+	0.710597i	$0.251575\pi$
$647$	22.2390	+	43.1377i	0.874307	+	1.69592i	0.170707	+	0.985322i	$0.445395\pi$
$648$	−0.786053	−	0.618159i	−0.0308791	−	0.0242836i
$649$	20.3682	−	1.94493i	0.799521	−	0.0763450i
$650$	7.95259	−	1.14341i	0.311926	−	0.0448482i
$651$	1.87150	+	18.6949i	0.0733500	+	0.732711i
$652$	14.3370	−	9.21381i	0.561479	−	0.360841i
$653$	−28.3500	+	39.8120i	−1.10942	+	1.55796i	−0.316548	+	0.948576i	$0.602524\pi$
$653$	−28.3500	+	39.8120i	−1.10942	+	1.55796i	−0.792873	+	0.609387i	$0.791415\pi$
$654$	0.960525	−	3.95934i	0.0375595	−	0.154822i
$655$	13.9535	−	4.82935i	0.545208	−	0.188698i
$656$	2.17597	−	11.2900i	0.0849573	−	0.440800i
$657$	3.73191	+	12.7097i	0.145596	+	0.495853i
$658$	−5.26002	+	22.1234i	−0.205057	+	0.862460i
$659$	7.18145	+	11.1746i	0.279750	+	0.435299i	0.952486	−	0.304584i	$-0.0985174\pi$
$659$	7.18145	+	11.1746i	0.279750	+	0.435299i	−0.672736	+	0.739883i	$0.734881\pi$
$660$	1.44525	+	5.95741i	0.0562564	+	0.231892i
$661$	0.190471	+	0.0762530i	0.00740845	+	0.00296590i	0.375364	−	0.926878i	$-0.377518\pi$
$661$	0.190471	+	0.0762530i	0.00740845	+	0.00296590i	−0.367955	+	0.929843i	$0.619942\pi$
$662$	0.275324	+	0.386638i	0.0107008	+	0.0150271i
$663$	8.89924	−	3.56272i	0.345618	−	0.138365i
$664$	11.3594	+	7.30022i	0.440829	+	0.283304i
$665$	−4.38164	+	0.228821i	−0.169913	+	0.00887331i
$666$		−	1.72540i		−	0.0668579i
$667$	20.7833	+	0.962827i	0.804732	+	0.0372808i
$668$	15.2425	+	8.80029i	0.589752	+	0.340493i
$669$	−5.17574	+	0.997542i	−0.200106	+	0.0385672i
$670$	11.7497	+	0.559709i	0.453932	+	0.0216235i
$671$	−38.0983	−	5.47771i	−1.47077	−	0.211465i
$672$	−0.113797	+	2.64330i	−0.00438980	+	0.101968i
$673$	6.16922	+	42.9079i	0.237806	+	1.65398i	0.662811	+	0.748786i	$0.269363\pi$
$673$	6.16922	+	42.9079i	0.237806	+	1.65398i	−0.425005	+	0.905191i	$0.639728\pi$
$674$	−17.6581	+	4.28380i	−0.680164	+	0.165006i
$675$	3.38959	−	0.161466i	0.130465	−	0.00621483i
$676$	−7.36089	−	0.702880i	−0.283111	−	0.0270339i
$677$	10.2286	+	9.75293i	0.393116	+	0.374835i	0.860699	−	0.509114i	$-0.170027\pi$
$677$	10.2286	+	9.75293i	0.393116	+	0.374835i	−0.467583	+	0.883949i	$0.654875\pi$
$678$	10.7636	−	12.4218i	0.413372	−	0.477057i
$679$	−16.6302	+	14.5439i	−0.638210	+	0.558145i
$680$	−4.92393	+	1.44580i	−0.188824	+	0.0554438i
$681$	2.27224	+	1.61806i	0.0870725	+	0.0620040i
$682$	1.63421	+	34.3063i	0.0625771	+	1.31366i
$683$	−1.55417	+	1.48189i	−0.0594685	+	0.0567031i	−0.719231	−	0.694771i	$-0.755506\pi$
$683$	−1.55417	+	1.48189i	−0.0594685	+	0.0567031i	0.659762	+	0.751475i	$0.270657\pi$
$684$	1.02845	−	0.808779i	0.0393236	−	0.0309244i
$685$	18.9473	+	8.65294i	0.723939	+	0.330612i
$686$	18.5096	+	0.627224i	0.706701	+	0.0239475i
$687$	−10.9808	+	17.0865i	−0.418945	+	0.651891i
$688$	−1.49193	−	0.516362i	−0.0568793	−	0.0196861i
$689$	−4.55725	+	7.89339i	−0.173617	+	0.300714i
$690$	0.297167	+	6.07146i	0.0113130	+	0.231137i
$691$	−7.31761	+	4.22482i	−0.278375	+	0.160720i	−0.632688	−	0.774407i	$-0.718048\pi$
$691$	−7.31761	+	4.22482i	−0.278375	+	0.160720i	0.354313	+	0.935127i	$0.384715\pi$
$692$	4.70923	−	4.08057i	0.179018	−	0.155120i
$693$	−8.33529	+	9.70884i	−0.316631	+	0.368808i
$694$	5.09971	−	35.4692i	0.193582	−	1.34639i
$695$	−2.28203	−	23.8985i	−0.0865623	−	0.906521i
$696$	−1.61237	+	4.02750i	−0.0611167	+	0.152662i
$697$	32.1243	+	33.6910i	1.21679	+	1.27614i
$698$	5.48655	−	10.6424i	0.207669	−	0.402821i
$699$	−8.99542	+	4.10807i	−0.340238	+	0.155382i
$700$	−5.58218	−	7.03186i	−0.210987	−	0.265779i
$701$	−16.5537	−	14.3439i	−0.625226	−	0.541762i	0.283597	−	0.958944i	$-0.408472\pi$
$701$	−16.5537	−	14.3439i	−0.625226	−	0.541762i	−0.908823	+	0.417182i	$0.863018\pi$
$702$	2.32483	+	0.448075i	0.0877452	+	0.0169115i
$703$	2.19382	+	0.532216i	0.0827416	+	0.0200729i
$704$	−0.459733	+	4.81455i	−0.0173269	+	0.181455i
$705$	−9.68310	−	4.99198i	−0.364686	−	0.188009i
$706$	−2.22959	+	7.59330i	−0.0839118	+	0.285777i
$707$	6.13874	−	10.7459i	0.230871	−	0.404140i
$708$	−1.75744	+	3.84825i	−0.0660485	+	0.144626i
$709$	−13.8331	−	34.5535i	−0.519514	−	1.29768i	−0.923739	−	0.383023i	$-0.874883\pi$
$709$	−13.8331	−	34.5535i	−0.519514	−	1.29768i	0.404225	−	0.914660i	$-0.367541\pi$
$710$	12.8518	−	6.62557i	0.482320	−	0.248653i
$711$	0.467259	+	2.42437i	0.0175236	+	0.0909209i
$712$	4.58345	+	7.93876i	0.171772	+	0.297518i
$713$	−4.80275	+	33.7164i	−0.179865	+	1.26269i
$714$	−8.45040	−	6.58312i	−0.316248	−	0.246367i
$715$	−9.50466	−	10.9690i	−0.355454	−	0.410216i
$716$	0.384169	−	8.06469i	0.0143571	−	0.301392i
$717$	5.82318	−	7.40478i	0.217471	−	0.276537i
$718$	15.4783	−	11.0220i	0.577645	−	0.411339i
$719$	8.86942	+	11.2784i	0.330774	+	0.420613i	0.922784	−	0.385317i	$-0.125908\pi$
$719$	8.86942	+	11.2784i	0.330774	+	0.420613i	−0.592011	+	0.805930i	$0.701666\pi$
$720$	−1.21616	−	0.357097i	−0.0453236	−	0.0133082i
$721$	−0.328973	−	0.231999i	−0.0122516	−	0.00864010i
$722$	−7.18177	−	15.7259i	−0.267278	−	0.585257i
$723$	−14.0990	+	14.7866i	−0.524346	+	0.549918i
$724$	−2.97979	−	8.60952i	−0.110743	−	0.319970i
$725$	−4.81497	−	13.9119i	−0.178823	−	0.516676i
$726$	−8.55092	+	8.96794i	−0.317354	+	0.332832i
$727$	8.47441	+	18.5564i	0.314298	+	0.688217i	0.999182	−	0.0404349i	$-0.0128743\pi$
$727$	8.47441	+	18.5564i	0.314298	+	0.688217i	−0.684884	+	0.728652i	$0.740147\pi$
$728$	−2.62826	−	5.68609i	−0.0974098	−	0.210741i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	10.3787	+	13.1976i	0.384133	+	0.488465i
$731$	5.20677	−	3.70773i	0.192580	−	0.137135i
$732$	4.91952	−	6.25568i	0.181831	−	0.231217i
$733$	−1.06976	+	22.4570i	−0.0395125	+	0.829469i	0.888941	+	0.458021i	$0.151442\pi$
$733$	−1.06976	+	22.4570i	−0.0395125	+	0.829469i	−0.928454	+	0.371448i	$0.878861\pi$
$734$	2.50978	+	2.89644i	0.0926377	+	0.106910i
$735$	−2.42167	+	8.53564i	−0.0893247	+	0.314842i
$736$	−1.34513	+	4.60333i	−0.0495822	+	0.169681i
$737$	22.4423	+	38.8713i	0.826674	+	1.43184i
$738$	2.17597	+	11.2900i	0.0800985	+	0.415590i
$739$	−20.8685	+	10.7585i	−0.767660	+	0.395756i	−0.797129	−	0.603809i	$-0.793649\pi$
$739$	−20.8685	+	10.7585i	−0.767660	+	0.395756i	0.0294685	+	0.999566i	$0.490619\pi$
$740$	−0.812807	−	2.03029i	−0.0298794	−	0.0746351i
$741$	−1.28684	+	2.81778i	−0.0472732	+	0.103514i
$742$	10.1851	−	0.0466023i	0.373907	−	0.00171082i
$743$	1.34559	−	4.58267i	0.0493650	−	0.168122i	−0.931121	−	0.364710i	$-0.881168\pi$
$743$	1.34559	−	4.58267i	0.0493650	−	0.168122i	0.980486	+	0.196588i	$0.0629863\pi$
$744$	−6.31191	−	3.25402i	−0.231406	−	0.119298i
$745$	1.86453	−	19.5263i	0.0683111	−	0.715387i
$746$	33.3301	+	8.08578i	1.22030	+	0.296042i
$747$	−13.2589	−	2.55544i	−0.485117	−	0.0934987i
$748$	−14.7988	−	12.8232i	−0.541096	−	0.468863i
$749$	11.8867	−	9.43617i	0.434332	−	0.344790i
$750$	9.67731	−	4.41948i	0.353365	−	0.161377i
$751$	1.49204	−	2.89416i	0.0544455	−	0.105609i	−0.860043	−	0.510222i	$-0.829563\pi$
$751$	1.49204	−	2.89416i	0.0544455	−	0.105609i	0.914488	+	0.404612i	$0.132594\pi$
$752$	−5.93120	−	6.22046i	−0.216289	−	0.226837i
$753$	−4.48786	+	11.2101i	−0.163547	+	0.408520i
$754$	−0.976355	−	10.2248i	−0.0355567	−	0.372367i
$755$	−2.95592	+	20.5589i	−0.107577	+	0.748215i
$756$	−0.876771	−	2.49625i	−0.0318879	−	0.0907878i
$757$	25.3749	−	21.9875i	0.922266	−	0.799148i	−0.0576957	−	0.998334i	$-0.518375\pi$
$757$	25.3749	−	21.9875i	0.922266	−	0.799148i	0.979962	+	0.199186i	$0.0638299\pi$
$758$	−18.4674	+	10.6621i	−0.670764	+	0.387266i
$759$	−18.8763	+	13.4790i	−0.685167	+	0.489255i
$760$	0.829180	−	1.43618i	0.0300775	−	0.0520958i
$761$	−1.74362	−	0.603472i	−0.0632061	−	0.0218759i	0.295282	−	0.955410i	$-0.404586\pi$
$761$	−1.74362	−	0.603472i	−0.0632061	−	0.0218759i	−0.358488	+	0.933534i	$0.616708\pi$
$762$	−3.64280	+	5.66830i	−0.131965	+	0.205341i
$763$	7.76721	−	7.47417i	0.281192	−	0.270583i
$764$	−3.91958	−	1.79001i	−0.141805	−	0.0647603i
$765$	4.03387	−	3.17227i	0.145845	−	0.114694i
$766$	−14.4157	+	13.7453i	−0.520860	+	0.496639i
$767$	−0.476597	−	10.0050i	−0.0172089	−	0.361259i
$768$	−0.814576	−	0.580057i	−0.0293935	−	0.0209310i
$769$	42.7457	−	12.5513i	1.54145	−	0.452610i	0.602917	−	0.797804i	$-0.294005\pi$
$769$	42.7457	−	12.5513i	1.54145	−	0.452610i	0.938531	+	0.345194i	$0.112187\pi$
$770$	−5.23454	+	15.3511i	−0.188640	+	0.553215i
$771$	−1.99002	+	2.29660i	−0.0716687	+	0.0827101i
$772$	13.9020	+	13.2555i	0.500343	+	0.477076i
$773$	−16.6957	−	1.59425i	−0.600504	−	0.0573412i	−0.209623	−	0.977782i	$-0.567224\pi$
$773$	−16.6957	−	1.59425i	−0.600504	−	0.0573412i	−0.390881	+	0.920441i	$0.627830\pi$
$774$	1.57697	−	0.0751204i	0.0566831	−	0.00270015i
$775$	23.4186	−	5.68129i	0.841221	−	0.204078i
$776$	−1.18837	−	8.26529i	−0.0426600	−	0.296707i
$777$	2.45042	−	3.85156i	0.0879082	−	0.138174i
$778$	18.5105	+	2.66141i	0.663634	+	0.0954162i
$779$	−15.0263	−	0.715790i	−0.538372	−	0.0256458i
$780$	2.94673	−	0.567937i	0.105510	−	0.0203354i
$781$	47.7805	+	27.5861i	1.70972	+	0.987108i
$782$	−12.0228	−	15.2472i	−0.429934	−	0.545239i
$783$		−	4.33826i		−	0.155037i
$784$	−4.00805	+	5.73895i	−0.143145	+	0.204962i
$785$	20.3282	+	13.0641i	0.725544	+	0.466279i
$786$	−10.8149	+	4.32962i	−0.385754	+	0.154433i
$787$	−24.2639	−	34.0739i	−0.864915	−	1.21460i	−0.975337	−	0.220719i	$-0.929160\pi$
$787$	−24.2639	−	34.0739i	−0.864915	−	1.21460i	0.110422	−	0.993885i	$-0.464780\pi$
$788$	20.0785	+	8.03824i	0.715268	+	0.286350i
$789$	−2.72094	−	11.2158i	−0.0968679	−	0.399295i
$790$	1.69191	+	2.63266i	0.0601954	+	0.0936658i
$791$	41.6686	−	12.4424i	1.48157	−	0.442400i
$792$	−1.36258	−	4.64054i	−0.0484173	−	0.164894i
$793$	−3.56594	+	18.5018i	−0.126630	+	0.657019i
$794$	−27.0330	+	9.35620i	−0.959364	+	0.332039i
$795$	−1.15037	+	4.74189i	−0.0407995	+	0.168178i
$796$	−0.793877	+	1.11484i	−0.0281382	+	0.0395146i
$797$	−11.0914	+	7.12804i	−0.392879	+	0.252488i	−0.722134	−	0.691753i	$-0.756839\pi$
$797$	−11.0914	+	7.12804i	−0.392879	+	0.252488i	0.329255	+	0.944241i	$0.393202\pi$
$798$	3.44440	−	0.344811i	0.121930	−	0.0122062i
$799$	34.4446	−	4.95239i	1.21856	−	0.175203i
$800$	3.37807	−	0.322567i	0.119433	−	0.0114044i
$801$	−7.20566	−	5.66660i	−0.254600	−	0.200219i
$802$	1.84760	+	3.58385i	0.0652411	+	0.126550i
$803$	−20.9536	+	60.5414i	−0.739436	+	2.13646i
$804$	−9.28050			−0.327298
$805$	−7.95935	+	13.9752i	−0.280530	+	0.492560i
$806$	16.8132			0.592221
$807$	4.31282	−	12.4611i	0.151819	−	0.438651i
$808$	2.14339	+	4.15759i	0.0754041	+	0.146264i
$809$	12.3998	+	9.75132i	0.435954	+	0.342838i	0.811893	−	0.583806i	$-0.198437\pi$
$809$	12.3998	+	9.75132i	0.435954	+	0.342838i	−0.375939	+	0.926644i	$0.622680\pi$
$810$	1.26176	−	0.120484i	0.0443339	−	0.00423337i
$811$	29.0669	−	4.17919i	1.02068	−	0.146751i	0.388398	−	0.921492i	$-0.373028\pi$
$811$	29.0669	−	4.17919i	1.02068	−	0.146751i	0.632280	+	0.774740i	$0.282119\pi$
$812$	−9.31911	+	6.70058i	−0.327037	+	0.235144i
$813$	15.7567	−	10.1262i	0.552610	−	0.355141i
$814$	4.84046	−	6.79748i	0.169658	−	0.238251i
$815$	−5.09270	+	20.9924i	−0.178389	+	0.735331i
$816$	3.82607	−	1.32422i	0.133939	−	0.0463569i
$817$	−0.390917	+	2.02827i	−0.0136765	+	0.0709602i
$818$	9.32362	+	31.7533i	0.325993	+	1.11023i
$819$	4.55330	+	4.30196i	0.159105	+	0.150323i
$820$	7.87901	+	12.2600i	0.275147	+	0.428137i
$821$	−7.60420	−	31.3449i	−0.265388	−	1.09395i	−0.935961	−	0.352102i	$-0.885467\pi$
$821$	−7.60420	−	31.3449i	−0.265388	−	1.09395i	0.670573	−	0.741844i	$-0.266048\pi$
$822$	−15.2564	−	6.10774i	−0.532128	−	0.213032i
$823$	−2.76491	−	3.88277i	−0.0963787	−	0.135345i	0.763571	−	0.645724i	$-0.223444\pi$
$823$	−2.76491	−	3.88277i	−0.0963787	−	0.135345i	−0.859949	+	0.510379i	$0.829505\pi$
$824$	0.141251	−	0.0565483i	0.00492071	−	0.00196995i
$825$	13.8068	+	8.87309i	0.480691	+	0.308921i
$826$	−9.38836	+	6.09441i	−0.326663	+	0.212052i
$827$			8.99547i			0.312803i	0.987694	+	0.156402i	$0.0499894\pi$
$827$			8.99547i			0.312803i	−0.987694	+	0.156402i	$0.950011\pi$
$828$	−0.462107	−	4.77352i	−0.0160593	−	0.165891i
$829$	−23.0903	−	13.3312i	−0.801959	−	0.463011i	0.0421964	−	0.999109i	$-0.486564\pi$
$829$	−23.0903	−	13.3312i	−0.801959	−	0.463011i	−0.844156	+	0.536098i	$0.819898\pi$
$830$	−16.8057	+	3.23903i	−0.583334	+	0.112428i
$831$	−29.0558	−	1.38410i	−1.00793	−	0.0480139i
$832$	2.34352	+	0.336947i	0.0812470	+	0.0116816i
$833$	−9.51421	−	26.6966i	−0.329648	−	0.924981i
$834$	2.69552	+	18.7477i	0.0933382	+	0.649181i
$835$	−21.6799	+	5.25950i	−0.750265	+	0.182012i
$836$	6.32068	−	0.301091i	0.218605	−	0.0104135i
$837$	7.06917	+	0.675024i	0.244346	+	0.0233322i
$838$	−22.1374	−	21.1079i	−0.764723	−	0.729162i
$839$	−19.1578	+	22.1093i	−0.661402	+	0.763298i	−0.983006	−	0.183576i	$-0.941233\pi$
$839$	−19.1578	+	22.1093i	−0.661402	+	0.763298i	0.321604	+	0.946874i	$0.395778\pi$
$840$	−2.20765	−	2.52433i	−0.0761711	−	0.0870977i
$841$	9.76713	−	2.86789i	0.336798	−	0.0988927i
$842$	10.1558	+	7.23190i	0.349991	+	0.249228i
$843$	−0.896931	−	18.8289i	−0.0308920	−	0.648502i
$844$	−0.998158	+	0.951742i	−0.0343580	+	0.0327603i
$845$	7.36720	−	5.79363i	0.253439	−	0.199307i
$846$	7.81825	+	3.57047i	0.268797	+	0.122755i
$847$	−31.8242	+	7.87483i	−1.09349	+	0.270582i
$848$	−2.08128	+	3.23853i	−0.0714713	+	0.111211i
$849$	−7.11044	−	2.46095i	−0.244030	−	0.0844594i
$850$	−6.86959	+	11.8985i	−0.235625	+	0.408114i
$851$	5.98124	−	5.71803i	0.205034	−	0.196012i
$852$	−9.87926	+	5.70379i	−0.338458	+	0.195409i
$853$	18.6313	−	16.1441i	0.637925	−	0.552765i	−0.274717	−	0.961525i	$-0.588584\pi$
$853$	18.6313	−	16.1441i	0.637925	−	0.552765i	0.912642	+	0.408760i	$0.134039\pi$
$854$	19.8660	−	6.97765i	0.679802	−	0.238770i
$855$	−0.236009	+	1.64148i	−0.00807135	+	0.0561375i
$856$	0.545270	+	5.71032i	0.0186369	+	0.195175i
$857$	−4.84099	+	12.0922i	−0.165365	+	0.413062i	−0.987786	−	0.155818i	$-0.950199\pi$
$857$	−4.84099	+	12.0922i	−0.165365	+	0.413062i	0.822421	+	0.568880i	$0.192623\pi$
$858$	7.90200	+	8.28738i	0.269770	+	0.282927i
$859$	−4.59809	+	8.91905i	−0.156885	+	0.304314i	−0.954157	−	0.299305i	$-0.903245\pi$
$859$	−4.59809	+	8.91905i	−0.156885	+	0.304314i	0.797273	+	0.603619i	$0.206275\pi$
$860$	1.82025	−	0.831280i	0.0620700	−	0.0283464i
$861$	−11.1767	+	28.2926i	−0.380902	+	0.964210i
$862$	0.139784	+	0.121123i	0.00476106	+	0.00412548i
$863$	33.7781	+	6.51019i	1.14982	+	0.221609i	0.728332	−	0.685225i	$-0.240296\pi$
$863$	33.7781	+	6.51019i	1.14982	+	0.221609i	0.421487	+	0.906834i	$0.361508\pi$
$864$	0.971812	+	0.235759i	0.0330617	+	0.00802068i
$865$	−0.750759	+	7.86230i	−0.0255266	+	0.267326i
$866$	2.78807	+	1.43735i	0.0947424	+	0.0488431i
$867$	0.171185	−	0.583004i	0.00581376	−	0.0197998i
$868$	−9.46852	−	16.2280i	−0.321383	−	0.550815i
$869$	−4.96052	+	10.8620i	−0.168274	+	0.368469i
$870$	−2.04368	−	5.10488i	−0.0692874	−	0.173072i
$871$	19.5301	−	10.0685i	0.661753	−	0.341157i
$872$	0.771044	+	4.00056i	0.0261108	+	0.135476i
$873$	4.17514	+	7.23156i	0.141307	+	0.244751i
$874$	6.21200	+	0.884872i	0.210124	+	0.0299312i
$875$	27.8789	+	3.87827i	0.942479	+	0.131109i
$876$	−8.67447	−	10.0109i	−0.293083	−	0.338236i
$877$	−0.244153	+	5.12541i	−0.00824447	+	0.173073i	0.990990	+	0.133939i	$0.0427627\pi$
$877$	−0.244153	+	5.12541i	−0.00824447	+	0.173073i	−0.999234	+	0.0391333i	$0.987540\pi$
$878$	0.444285	−	0.564954i	0.0149939	−	0.0190663i
$879$	9.27020	−	6.60128i	0.312676	−	0.222656i
$880$	−3.78945	−	4.81867i	−0.127742	−	0.162437i
$881$	−21.1642	−	6.21438i	−0.713041	−	0.209368i	−0.0949588	−	0.995481i	$-0.530272\pi$
$881$	−21.1642	−	6.21438i	−0.713041	−	0.209368i	−0.618082	+	0.786113i	$0.712090\pi$
$882$	1.58799	−	6.81750i	0.0534705	−	0.229557i
$883$	12.0601	+	26.4080i	0.405855	+	0.888698i	0.996643	+	0.0818715i	$0.0260897\pi$
$883$	12.0601	+	26.4080i	0.405855	+	0.888698i	−0.590788	+	0.806827i	$0.701183\pi$
$884$	−6.61503	+	6.93764i	−0.222488	+	0.233338i
$885$	−1.75382	−	5.06732i	−0.0589539	−	0.170336i
$886$	−11.4850	−	33.1837i	−0.385846	−	1.11483i
$887$	−12.4953	+	13.1047i	−0.419552	+	0.440013i	−0.899260	−	0.437415i	$-0.855894\pi$
$887$	−12.4953	+	13.1047i	−0.419552	+	0.440013i	0.479708	+	0.877428i	$0.340743\pi$
$888$	0.716757	+	1.56948i	0.0240528	+	0.0526683i
$889$	−16.1818	+	7.47967i	−0.542721	+	0.250860i
$890$	−11.1484	−	3.27347i	−0.373696	−	0.109727i
$891$	2.98969	+	3.80170i	0.100158	+	0.127362i
$892$	4.29362	−	3.05748i	0.143761	−	0.102372i
$893$	−6.95142	+	8.83945i	−0.232620	+	0.295801i
$894$	−0.736347	+	15.4578i	−0.0246271	+	0.516987i
$895$	6.70159	+	7.73405i	0.224010	+	0.258521i
$896$	−0.994555	−	2.45171i	−0.0332257	−	0.0819057i
$897$	6.15129	+	9.54416i	0.205386	+	0.318670i
$898$	8.41159	+	14.5693i	0.280698	+	0.486184i
$899$	−5.83034	−	30.2507i	−0.194453	−	1.00892i
$900$	−3.01621	+	1.55496i	−0.100540	+	0.0518321i
$901$	−5.79283	−	14.4698i	−0.192987	−	0.482058i
$902$	−23.1006	+	50.5832i	−0.769164	+	1.68423i
$903$	3.62691	+	2.07193i	0.120696	+	0.0689495i
$904$	−4.63067	+	15.7706i	−0.154014	+	0.524523i
$905$	10.2640	+	5.29147i	0.341188	+	0.175894i
$906$	1.55766	−	16.3126i	0.0517499	−	0.541950i
$907$	−26.1502	−	6.34397i	−0.868303	−	0.210648i	−0.223227	−	0.974767i	$-0.571659\pi$
$907$	−26.1502	−	6.34397i	−0.868303	−	0.210648i	−0.645076	+	0.764119i	$0.723174\pi$
$908$	−2.73907	−	0.527912i	−0.0908992	−	0.0175194i
$909$	−3.53507	−	3.06316i	−0.117251	−	0.101599i
$910$	7.38449	+	2.91717i	0.244793	+	0.0967033i
$911$	31.3289	−	14.3074i	1.03797	−	0.474026i	0.177820	−	0.984063i	$-0.443095\pi$
$911$	31.3289	−	14.3074i	1.03797	−	0.474026i	0.860153	+	0.510037i	$0.170368\pi$
$912$	−0.599529	+	1.16292i	−0.0198524	+	0.0385082i
$913$	−45.0663	−	47.2642i	−1.49148	−	1.56422i
$914$	7.30065	−	18.2361i	0.241484	−	0.603198i
$915$	0.958852	+	10.0416i	0.0316987	+	0.331964i
$916$	2.89053	−	20.1040i	0.0955057	−	0.664256i
$917$	−30.2907	−	5.69443i	−1.00029	−	0.188047i
$918$	−3.05984	+	2.65137i	−0.100990	+	0.0875082i
$919$	−16.6102	+	9.58988i	−0.547919	+	0.316341i	−0.748282	−	0.663381i	$-0.769121\pi$
$919$	−16.6102	+	9.58988i	−0.547919	+	0.316341i	0.200363	+	0.979722i	$0.435788\pi$
$920$	−2.79249	−	5.39935i	−0.0920657	−	0.178011i
$921$	−7.38729	+	12.7952i	−0.243419	+	0.421615i
$922$	15.3676	+	5.31879i	0.506106	+	0.175165i
$923$	14.6021	−	22.7213i	0.480633	−	0.747880i
$924$	3.54885	−	12.2941i	0.116748	−	0.404445i
$925$	−5.32592	−	2.43227i	−0.175115	−	0.0799725i
$926$	14.9172	−	11.7310i	0.490211	−	0.385506i
$927$	−0.110116	+	0.104995i	−0.00361668	+	0.00344850i
$928$	−0.206423	−	4.33335i	−0.00677616	−	0.142249i
$929$	4.81000	+	3.42519i	0.157811	+	0.112377i	0.656235	−	0.754557i	$-0.272148\pi$
$929$	4.81000	+	3.42519i	0.157811	+	0.112377i	−0.498424	+	0.866934i	$0.666088\pi$
$930$	8.63636	−	2.53586i	0.283197	−	0.0831542i
$931$	8.17853	+	4.12203i	0.268040	+	0.135094i
$932$	6.47597	−	7.47367i	0.212127	−	0.244808i
$933$	3.65743	+	3.48735i	0.119739	+	0.114171i
$934$	12.9371	+	1.23535i	0.423316	+	0.0404217i
$935$	24.7916	−	1.18097i	0.810772	−	0.0386218i
$936$	−2.30088	+	0.558188i	−0.0752066	+	0.0182449i
$937$	6.82036	+	47.4366i	0.222811	+	1.54969i	0.727331	+	0.686287i	$0.240761\pi$
$937$	6.82036	+	47.4366i	0.222811	+	1.54969i	−0.504520	+	0.863400i	$0.668330\pi$
$938$	−20.7166	−	13.1802i	−0.676420	−	0.430349i
$939$	18.2003	+	2.61681i	0.593944	+	0.0853963i
$940$	10.8818	+	0.518364i	0.354925	+	0.0169072i
$941$	−39.9651	+	7.70265i	−1.30283	+	0.251099i	−0.793023	−	0.609192i	$-0.791494\pi$
$941$	−39.9651	+	7.70265i	−1.30283	+	0.251099i	−0.509803	+	0.860291i	$0.670282\pi$
$942$	−16.5102	−	9.53219i	−0.537932	−	0.310575i
$943$	−31.9265	+	44.9586i	−1.03967	+	1.46405i
$944$		−	4.23055i		−	0.137693i
$945$	2.98771	+	1.52301i	0.0971902	+	0.0495434i
$946$	6.42347	+	4.12811i	0.208845	+	0.134216i
$947$	26.4521	−	10.5898i	0.859578	−	0.344123i	0.100353	−	0.994952i	$-0.468003\pi$
$947$	26.4521	−	10.5898i	0.859578	−	0.344123i	0.759224	+	0.650829i	$0.225578\pi$
$948$	−1.43215	−	2.01118i	−0.0465142	−	0.0653200i
$949$	29.1156	+	11.6561i	0.945133	+	0.378374i
$950$	−1.04674	−	4.31471i	−0.0339606	−	0.139988i
$951$	11.0744	+	17.2321i	0.359113	+	0.558791i
$952$	10.4215	+	2.47779i	0.337762	+	0.0803056i
$953$	−10.5375	−	35.8875i	−0.341344	−	1.16251i	−0.934065	−	0.357102i	$-0.883765\pi$
$953$	−10.5375	−	35.8875i	−0.341344	−	1.16251i	0.592722	−	0.805407i	$-0.298053\pi$
$954$	0.728550	−	3.78008i	0.0235877	−	0.122385i
$955$	5.16125	−	1.78633i	0.167014	−	0.0578041i
$956$	−2.22090	+	9.15466i	−0.0718289	+	0.296083i
$957$	12.1706	−	17.0913i	0.393420	−	0.552482i
$958$	22.5222	−	14.4741i	0.727660	−	0.467638i
$959$	−25.3822	−	35.3013i	−0.819633	−	1.13994i
$960$	1.25460	−	0.180385i	0.0404921	−	0.00582189i
$961$	19.3409	−	1.84683i	0.623899	−	0.0595752i
$962$	−3.21110	−	2.52524i	−0.103530	−	0.0814169i
$963$	−2.62852	−	5.09862i	−0.0847030	−	0.164301i
$964$	6.68231	−	19.3073i	0.215223	−	0.621845i
$965$	−24.3471			−0.783760
$966$	5.74781	−	11.3121i	0.184933	−	0.363960i
$967$	−26.7109			−0.858964			−0.429482	−	0.903075i	$-0.641304\pi$
$967$	−26.7109			−0.858964			−0.429482	+	0.903075i	$0.641304\pi$
$968$	4.05277	−	11.7097i	0.130261	−	0.376364i
$969$	−2.42734	−	4.70839i	−0.0779775	−	0.151255i
$970$	8.31959	+	6.54260i	0.267126	+	0.210070i
$971$	−52.2994	+	4.99399i	−1.67837	+	0.160265i	−0.890316	−	0.455344i	$-0.849516\pi$
$971$	−52.2994	+	4.99399i	−1.67837	+	0.160265i	−0.788052	+	0.615609i	$0.788910\pi$
$972$	−0.989821	+	0.142315i	−0.0317485	+	0.00456475i
$973$	−20.6085	+	45.6782i	−0.660677	+	1.46438i
$974$	31.4610	−	20.2187i	1.00807	−	0.647850i
$975$	4.66039	−	6.54460i	0.149252	−	0.209595i
$976$	−1.87625	+	7.73401i	−0.0600573	+	0.247560i
$977$	41.7073	−	14.4350i	1.33434	−	0.461818i	0.435533	−	0.900173i	$-0.356560\pi$
$977$	41.7073	−	14.4350i	1.33434	−	0.461818i	0.898802	+	0.438355i	$0.144439\pi$
$978$	3.22529	−	16.7344i	0.103134	−	0.535108i
$979$	−12.4907	−	42.5393i	−0.399203	−	1.35956i
$980$	−1.34300	−	8.77029i	−0.0429007	−	0.280157i
$981$	−2.20267	−	3.42742i	−0.0703258	−	0.109429i
$982$	7.44930	+	30.7064i	0.237717	+	0.979882i
$983$	10.7389	+	4.29922i	0.342519	+	0.137124i	0.536543	−	0.843873i	$-0.319730\pi$
$983$	10.7389	+	4.29922i	0.342519	+	0.137124i	−0.194024	+	0.980997i	$0.562154\pi$
$984$	−6.66936	−	9.36581i	−0.212612	−	0.298571i
$985$	−25.4496	+	10.1885i	−0.810892	+	0.324632i
$986$	14.7762	+	9.49611i	0.470571	+	0.302418i
$987$	12.3816	+	19.0738i	0.394112	+	0.607124i
$988$		−	3.09772i		−	0.0985515i
$989$	5.48655	+	5.21775i	0.174462	+	0.165915i
$990$	5.30892	+	3.06511i	0.168729	+	0.0974155i
$991$	26.6602	−	5.13833i	0.846888	−	0.163224i	0.252694	−	0.967546i	$-0.418683\pi$
$991$	26.6602	−	5.13833i	0.846888	−	0.163224i	0.594194	+	0.804322i	$0.297471\pi$
$992$	7.09328	+	0.337895i	0.225212	+	0.0107282i
$993$	0.469818	+	0.0675496i	0.0149092	+	0.00214362i
$994$	−30.1537	−	1.29815i	−0.956417	−	0.0411747i
$995$	−0.246878	−	1.71707i	−0.00782656	−	0.0544349i
$996$	13.1223	−	3.18343i	0.415795	−	0.100871i
$997$	−43.0127	+	2.04895i	−1.36223	+	0.0648908i	−0.715917	−	0.698185i	$-0.753991\pi$
$997$	−43.0127	+	2.04895i	−1.36223	+	0.0648908i	−0.646309	+	0.763076i	$0.723688\pi$
$998$	13.6238	+	1.30091i	0.431253	+	0.0411797i
$999$	−1.24873	−	1.19066i	−0.0395081	−	0.0376709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.493.14	yes	320
7.5	odd	6	inner	966.2.be.b.355.14	yes	320
23.7	odd	22	inner	966.2.be.b.283.14	yes	320
161.145	even	66	inner	966.2.be.b.145.14	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.145.14	✓	320	161.145	even	66	inner
966.2.be.b.283.14	yes	320	23.7	odd	22	inner
966.2.be.b.355.14	yes	320	7.5	odd	6	inner
966.2.be.b.493.14	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)

\(f(q)\)	\(=\)	\(q+(-0.327068 + 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(1.26176 - 0.120484i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-2.41166 - 1.08806i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.327068 + 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(1.26176 - 0.120484i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-2.41166 - 1.08806i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(-0.298825 + 1.23177i) q^{10} +(-4.57045 + 1.58185i) q^{11} +(0.189251 - 0.981929i) q^{12} +(0.667036 + 2.27171i) q^{13} +(1.81700 - 1.92315i) q^{14} +(0.685264 + 1.06629i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-3.75873 - 1.50477i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(1.21465 - 0.486271i) q^{19} +(-1.06629 - 0.685264i) q^{20} +(-0.137980 - 2.64215i) q^{21} -4.83645i q^{22} +(0.901466 - 4.71035i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-3.33211 + 0.642212i) q^{25} +(-2.36494 - 0.112656i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(1.22310 + 2.34607i) q^{28} +(0.617399 + 4.29411i) q^{29} +(-1.23177 + 0.298825i) q^{30} +(-7.09328 + 0.337895i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(-3.50030 - 3.33753i) q^{33} +(2.65137 - 3.05984i) q^{34} +(-3.17404 - 1.08231i) q^{35} +(0.959493 - 0.281733i) q^{36} +(1.40547 + 1.00083i) q^{37} +(0.0622546 + 1.30689i) q^{38} +(-1.71353 + 1.63384i) q^{39} +(0.996325 - 0.783519i) q^{40} +(-10.4587 - 4.77635i) q^{41} +(2.54196 + 0.733771i) q^{42} +(-0.853542 + 1.32814i) q^{43} +(4.57045 + 1.58185i) q^{44} +(-0.633752 + 1.09769i) q^{45} +(4.15644 + 2.39249i) q^{46} +(-7.44345 + 4.29748i) q^{47} +(-0.755750 + 0.654861i) q^{48} +(4.63224 + 5.24808i) q^{49} +(0.482936 - 3.35889i) q^{50} +(-0.384858 - 4.03042i) q^{51} +(0.879955 - 2.19802i) q^{52} +(2.65656 + 2.78612i) q^{53} +(0.458227 - 0.888835i) q^{54} +(-5.57624 + 2.54658i) q^{55} +(-2.61707 + 0.388508i) q^{56} +(0.988798 + 0.856799i) q^{57} +(-4.25987 - 0.821022i) q^{58} +(-4.11130 - 0.997391i) q^{59} +(0.120484 - 1.26176i) q^{60} +(7.07366 + 3.64673i) q^{61} +(2.00068 - 6.81367i) q^{62} +(2.28521 - 1.33335i) q^{63} +(0.415415 - 0.909632i) q^{64} +(1.11535 + 2.78600i) q^{65} +(4.29881 - 2.21619i) q^{66} +(-1.75635 - 9.11279i) q^{67} +(2.02438 + 3.50632i) q^{68} +(4.59980 - 1.35715i) q^{69} +(2.06091 - 2.64549i) q^{70} +(-7.47038 - 8.62128i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(8.18830 - 10.4123i) q^{73} +(-1.40547 + 1.00083i) q^{74} +(-2.09768 - 2.66742i) q^{75} +(-1.25537 - 0.368610i) q^{76} +(12.7435 + 1.15804i) q^{77} +(-0.983545 - 2.15366i) q^{78} +(1.70380 - 1.78689i) q^{79} +(0.414560 + 1.19779i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(7.93437 - 8.32133i) q^{82} +(5.60931 + 12.2827i) q^{83} +(-1.52481 + 2.16216i) q^{84} +(-4.92393 - 1.44580i) q^{85} +(-0.975925 - 1.24099i) q^{86} +(-3.53385 + 2.51644i) q^{87} +(-2.98969 + 3.80170i) q^{88} +(-0.436178 + 9.15651i) q^{89} +(-0.830038 - 0.957915i) q^{90} +(0.863100 - 6.20439i) q^{91} +(-3.62034 + 3.14533i) q^{92} +(-3.55066 - 6.14993i) q^{93} +(-1.62661 - 8.43963i) q^{94} +(1.47401 - 0.759905i) q^{95} +(-0.371662 - 0.928368i) q^{96} +(3.46883 - 7.59568i) q^{97} +(-6.47450 + 2.66100i) q^{98} +(1.36258 - 4.64054i) 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

Modular forms

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