LMFDB - Embedded newform 990.2.o.a.329.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(329,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.329"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			329.15
Character	$\chi$	$=$	990.329
Dual form			990.2.o.a.659.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.648796 + 1.60595i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.04128 - 0.912789i) q^{5} +(-0.241100 - 1.71519i) q^{6} +(-0.226164 - 0.391728i) q^{7} +1.00000i q^{8} +(-2.15813 - 2.08386i) q^{9} +(2.22419 - 0.230141i) q^{10} +(-3.11718 - 1.13278i) q^{11} +(1.06639 + 1.36485i) q^{12} +(-2.54162 + 4.40222i) q^{13} +(0.391728 + 0.226164i) q^{14} +(2.79026 - 2.68597i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.0435865i q^{17} +(2.91093 + 0.725614i) q^{18} +4.27810i q^{19} +(-1.81114 + 1.31140i) q^{20} +(0.775829 - 0.109056i) q^{21} +(3.26595 - 0.577573i) q^{22} +(4.08759 - 7.07991i) q^{23} +(-1.60595 - 0.648796i) q^{24} +(3.33363 + 3.72651i) q^{25} -5.08325i q^{26} +(4.74676 - 2.11384i) q^{27} -0.452329 q^{28} +(-0.475791 - 0.824095i) q^{29} +(-1.07345 + 3.72125i) q^{30} +(3.81464 - 6.60714i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.84160 - 4.27108i) q^{33} +(0.0217933 + 0.0377470i) q^{34} +(0.104099 + 1.00607i) q^{35} +(-2.88374 + 0.827063i) q^{36} +0.634364i q^{37} +(-2.13905 - 3.70495i) q^{38} +(-5.42074 - 6.93786i) q^{39} +(0.912789 - 2.04128i) q^{40} +(3.73641 - 6.47166i) q^{41} +(-0.617360 + 0.482360i) q^{42} +(5.49060 + 9.51000i) q^{43} +(-2.53961 + 2.13317i) q^{44} +(2.50321 + 6.22366i) q^{45} +8.17517i q^{46} +(0.238156 + 0.412499i) q^{47} +(1.71519 - 0.241100i) q^{48} +(3.39770 - 5.88499i) q^{49} +(-4.75027 - 1.56044i) q^{50} +(0.0699976 + 0.0282787i) q^{51} +(2.54162 + 4.40222i) q^{52} +6.91367 q^{53} +(-3.05389 + 4.20401i) q^{54} +(5.32904 + 5.15765i) q^{55} +(0.391728 - 0.226164i) q^{56} +(-6.87040 - 2.77561i) q^{57} +(0.824095 + 0.475791i) q^{58} +(0.281094 + 0.162290i) q^{59} +(-0.930987 - 3.75942i) q^{60} +(6.16775 - 3.56095i) q^{61} +7.62927i q^{62} +(-0.328216 + 1.31670i) q^{63} -1.00000 q^{64} +(9.20646 - 6.66620i) q^{65} +(-1.19138 + 5.61966i) q^{66} +(-7.59412 - 4.38447i) q^{67} +(-0.0377470 - 0.0217933i) q^{68} +(8.71794 + 11.1579i) q^{69} +(-0.593186 - 0.819230i) q^{70} +3.00346i q^{71} +(2.08386 - 2.15813i) q^{72} +3.24558 q^{73} +(-0.317182 - 0.549376i) q^{74} +(-8.14743 + 2.93589i) q^{75} +(3.70495 + 2.13905i) q^{76} +(0.261253 + 1.47728i) q^{77} +(8.16343 + 3.29799i) q^{78} +(-3.31760 + 1.91542i) q^{79} +(0.230141 + 2.22419i) q^{80} +(0.315035 + 8.99448i) q^{81} +7.47283i q^{82} +(-9.58193 + 5.53213i) q^{83} +(0.293469 - 0.726416i) q^{84} +(-0.0397853 + 0.0889722i) q^{85} +(-9.51000 - 5.49060i) q^{86} +(1.63214 - 0.229426i) q^{87} +(1.13278 - 3.11718i) q^{88} -1.97313i q^{89} +(-5.27968 - 4.13824i) q^{90} +2.29930 q^{91} +(-4.08759 - 7.07991i) q^{92} +(8.13580 + 10.4128i) q^{93} +(-0.412499 - 0.238156i) q^{94} +(3.90501 - 8.73280i) q^{95} +(-1.36485 + 1.06639i) q^{96} +(9.83932 - 5.68074i) q^{97} +6.79540i q^{98} +(4.36671 + 8.94046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.648796	+	1.60595i	−0.374582	+	0.927194i
$3$	−0.648796	+	1.60595i	−0.374582	+	0.927194i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.04128	−	0.912789i	−0.912887	−	0.408212i
$5$	−2.04128	−	0.912789i	−0.912887	−	0.408212i
$6$	−0.241100	−	1.71519i	−0.0984285	−	0.700223i
$7$	−0.226164	−	0.391728i	−0.0854821	−	0.148059i	0.820114	−	0.572200i	$-0.193910\pi$
$7$	−0.226164	−	0.391728i	−0.0854821	−	0.148059i	−0.905597	+	0.424140i	$0.860576\pi$
$8$			1.00000i			0.353553i
$9$	−2.15813	−	2.08386i	−0.719376	−	0.694621i
$10$	2.22419	−	0.230141i	0.703352	−	0.0727769i
$11$	−3.11718	−	1.13278i	−0.939865	−	0.341546i
$11$	−3.11718	−	1.13278i	−0.939865	−	0.341546i
$12$	1.06639	+	1.36485i	0.307841	+	0.393997i
$13$	−2.54162	+	4.40222i	−0.704920	+	1.22096i	0.261801	+	0.965122i	$0.415684\pi$
$13$	−2.54162	+	4.40222i	−0.704920	+	1.22096i	−0.966720	+	0.255835i	$0.917650\pi$
$14$	0.391728	+	0.226164i	0.104694	+	0.0604450i
$15$	2.79026	−	2.68597i	0.720443	−	0.693514i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	0.0435865i		−	0.0105713i	−0.999986	−	0.00528564i	$-0.998318\pi$
$17$		−	0.0435865i		−	0.0105713i	0.999986	−	0.00528564i	$-0.00168248\pi$
$18$	2.91093	+	0.725614i	0.686112	+	0.171029i
$19$			4.27810i			0.981464i	0.871311	+	0.490732i	$0.163271\pi$
$19$			4.27810i			0.981464i	−0.871311	+	0.490732i	$0.836729\pi$
$20$	−1.81114	+	1.31140i	−0.404983	+	0.293239i
$21$	0.775829	−	0.109056i	0.169300	−	0.0237981i
$22$	3.26595	−	0.577573i	0.696302	−	0.123139i
$23$	4.08759	−	7.07991i	0.852320	−	1.47626i	−0.0267883	−	0.999641i	$-0.508528\pi$
$23$	4.08759	−	7.07991i	0.852320	−	1.47626i	0.879109	−	0.476621i	$-0.158139\pi$
$24$	−1.60595	−	0.648796i	−0.327812	−	0.132435i
$25$	3.33363	+	3.72651i	0.666727	+	0.745302i
$26$		−	5.08325i		−	0.996907i
$27$	4.74676	−	2.11384i	0.913514	−	0.406808i
$28$	−0.452329			−0.0854821
$29$	−0.475791	−	0.824095i	−0.0883523	−	0.153031i	0.818463	−	0.574560i	$-0.194827\pi$
$29$	−0.475791	−	0.824095i	−0.0883523	−	0.153031i	−0.906815	+	0.421529i	$0.861493\pi$
$30$	−1.07345	+	3.72125i	−0.195985	+	0.679404i
$31$	3.81464	−	6.60714i	0.685129	−	1.18668i	−0.288268	−	0.957550i	$-0.593079\pi$
$31$	3.81464	−	6.60714i	0.685129	−	1.18668i	0.973396	−	0.229128i	$-0.0735874\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.84160	−	4.27108i	0.668736	−	0.743500i
$34$	0.0217933	+	0.0377470i	0.00373751	+	0.00647356i
$35$	0.104099	+	1.00607i	0.0175960	+	0.170056i
$36$	−2.88374	+	0.827063i	−0.480624	+	0.137844i
$37$			0.634364i			0.104289i	0.998640	+	0.0521444i	$0.0166056\pi$
$37$			0.634364i			0.104289i	−0.998640	+	0.0521444i	$0.983394\pi$
$38$	−2.13905	−	3.70495i	−0.347000	−	0.601022i
$39$	−5.42074	−	6.93786i	−0.868013	−	1.11095i
$40$	0.912789	−	2.04128i	0.144325	−	0.322754i
$41$	3.73641	−	6.47166i	0.583530	−	1.01070i	−0.411527	−	0.911397i	$-0.635004\pi$
$41$	3.73641	−	6.47166i	0.583530	−	1.01070i	0.995057	−	0.0993057i	$-0.0316622\pi$
$42$	−0.617360	+	0.482360i	−0.0952607	+	0.0744298i
$43$	5.49060	+	9.51000i	0.837309	+	1.45026i	0.892137	+	0.451765i	$0.149205\pi$
$43$	5.49060	+	9.51000i	0.837309	+	1.45026i	−0.0548284	+	0.998496i	$0.517461\pi$
$44$	−2.53961	+	2.13317i	−0.382860	+	0.321587i
$45$	2.50321	+	6.22366i	0.373157	+	0.927768i
$46$			8.17517i			1.20536i
$47$	0.238156	+	0.412499i	0.0347386	+	0.0601691i	0.882872	−	0.469614i	$-0.155607\pi$
$47$	0.238156	+	0.412499i	0.0347386	+	0.0601691i	−0.848133	+	0.529783i	$0.822273\pi$
$48$	1.71519	−	0.241100i	0.247566	−	0.0347997i
$49$	3.39770	−	5.88499i	0.485386	−	0.840713i
$50$	−4.75027	−	1.56044i	−0.671789	−	0.220679i
$51$	0.0699976	+	0.0282787i	0.00980163	+	0.00395982i
$52$	2.54162	+	4.40222i	0.352460	+	0.610479i
$53$	6.91367			0.949665			0.474833	−	0.880076i	$-0.342509\pi$
$53$	6.91367			0.949665			0.474833	+	0.880076i	$0.342509\pi$
$54$	−3.05389	+	4.20401i	−0.415582	+	0.572094i
$55$	5.32904	+	5.15765i	0.718568	+	0.695457i
$56$	0.391728	−	0.226164i	0.0523469	−	0.0302225i
$57$	−6.87040	−	2.77561i	−0.910007	−	0.367639i
$58$	0.824095	+	0.475791i	0.108209	+	0.0624745i
$59$	0.281094	+	0.162290i	0.0365954	+	0.0211283i	0.518186	−	0.855268i	$-0.326607\pi$
$59$	0.281094	+	0.162290i	0.0365954	+	0.0211283i	−0.481591	+	0.876396i	$0.659941\pi$
$60$	−0.930987	−	3.75942i	−0.120190	−	0.485339i
$61$	6.16775	−	3.56095i	0.789699	−	0.455933i	−0.0501576	−	0.998741i	$-0.515972\pi$
$61$	6.16775	−	3.56095i	0.789699	−	0.455933i	0.839857	+	0.542808i	$0.182639\pi$
$62$			7.62927i			0.968918i
$63$	−0.328216	+	1.31670i	−0.0413513	+	0.165888i
$64$	−1.00000			−0.125000
$65$	9.20646	−	6.66620i	1.14192	−	0.826840i
$66$	−1.19138	+	5.61966i	−0.146649	+	0.691733i
$67$	−7.59412	−	4.38447i	−0.927769	−	0.535648i	−0.0416637	−	0.999132i	$-0.513266\pi$
$67$	−7.59412	−	4.38447i	−0.927769	−	0.535648i	−0.886105	+	0.463484i	$0.846599\pi$
$68$	−0.0377470	−	0.0217933i	−0.00457750	−	0.00264282i
$69$	8.71794	+	11.1579i	1.04952	+	1.34325i
$70$	−0.593186	−	0.819230i	−0.0708993	−	0.0979167i
$71$			3.00346i			0.356445i	0.983990	+	0.178223i	$0.0570347\pi$
$71$			3.00346i			0.356445i	−0.983990	+	0.178223i	$0.942965\pi$
$72$	2.08386	−	2.15813i	0.245586	−	0.254338i
$73$	3.24558			0.379866			0.189933	−	0.981797i	$-0.439173\pi$
$73$	3.24558			0.379866			0.189933	+	0.981797i	$0.439173\pi$
$74$	−0.317182	−	0.549376i	−0.0368717	−	0.0638636i
$75$	−8.14743	+	2.93589i	−0.940784	+	0.339007i
$76$	3.70495	+	2.13905i	0.424986	+	0.245366i
$77$	0.261253	+	1.47728i	0.0297725	+	0.168352i
$78$	8.16343	+	3.29799i	0.924326	+	0.373424i
$79$	−3.31760	+	1.91542i	−0.373259	+	0.215501i	−0.674881	−	0.737926i	$-0.735805\pi$
$79$	−3.31760	+	1.91542i	−0.373259	+	0.215501i	0.301622	+	0.953428i	$0.402472\pi$
$80$	0.230141	+	2.22419i	0.0257305	+	0.248672i
$81$	0.315035	+	8.99448i	0.0350039	+	0.999387i
$82$			7.47283i			0.825236i
$83$	−9.58193	+	5.53213i	−1.05175	+	0.607230i	−0.923140	−	0.384465i	$-0.874386\pi$
$83$	−9.58193	+	5.53213i	−1.05175	+	0.607230i	−0.128613	+	0.991695i	$0.541053\pi$
$84$	0.293469	−	0.726416i	0.0320201	−	0.0792585i
$85$	−0.0397853	+	0.0889722i	−0.00431532	+	0.00965039i
$86$	−9.51000	−	5.49060i	−1.02549	−	0.592067i
$87$	1.63214	−	0.229426i	0.174984	−	0.0245971i
$88$	1.13278	−	3.11718i	0.120755	−	0.332292i
$89$		−	1.97313i		−	0.209151i	−0.994517	−	0.104576i	$-0.966652\pi$
$89$		−	1.97313i		−	0.209151i	0.994517	−	0.104576i	$-0.0333484\pi$
$90$	−5.27968	−	4.13824i	−0.556527	−	0.436209i
$91$	2.29930			0.241032
$92$	−4.08759	−	7.07991i	−0.426160	−	0.738131i
$93$	8.13580	+	10.4128i	0.843643	+	1.07976i
$94$	−0.412499	−	0.238156i	−0.0425460	−	0.0245639i
$95$	3.90501	−	8.73280i	0.400645	−	0.895966i
$96$	−1.36485	+	1.06639i	−0.139299	+	0.108838i
$97$	9.83932	−	5.68074i	0.999032	−	0.576791i	0.0910702	−	0.995844i	$-0.470971\pi$
$97$	9.83932	−	5.68074i	0.999032	−	0.576791i	0.907962	+	0.419053i	$0.137638\pi$
$98$			6.79540i			0.686439i
$99$	4.36671	+	8.94046i	0.438871	+	0.898550i
$100$	4.89407	−	1.02375i	0.489407	−	0.102375i
$101$	5.25401	+	9.10020i	0.522793	+	0.905504i	0.999648	+	0.0265223i	$0.00844329\pi$
$101$	5.25401	+	9.10020i	0.522793	+	0.905504i	−0.476855	+	0.878982i	$0.658223\pi$
$102$	−0.0747591	+	0.0105087i	−0.00740225	+	0.00104052i
$103$	4.42543	+	2.55502i	0.436051	+	0.251754i	0.701921	−	0.712255i	$-0.252326\pi$
$103$	4.42543	+	2.55502i	0.436051	+	0.251754i	−0.265870	+	0.964009i	$0.585659\pi$
$104$	−4.40222	−	2.54162i	−0.431674	−	0.249227i
$105$	−1.68323	−	0.485554i	−0.164266	−	0.0473852i
$106$	−5.98741	+	3.45683i	−0.581549	+	0.335757i
$107$			1.47790i			0.142874i	0.997445	+	0.0714368i	$0.0227584\pi$
$107$			1.47790i			0.142874i	−0.997445	+	0.0714368i	$0.977242\pi$
$108$	0.542741	−	5.16773i	0.0522253	−	0.497265i
$109$		−	15.7305i		−	1.50670i	−0.657617	−	0.753352i	$-0.728436\pi$
$109$		−	15.7305i		−	1.50670i	0.657617	−	0.753352i	$-0.271564\pi$
$110$	−7.19391	−	1.80213i	−0.685912	−	0.171827i
$111$	−1.01876	−	0.411573i	−0.0966960	−	0.0390648i
$112$	−0.226164	+	0.391728i	−0.0213705	+	0.0370149i
$113$	−4.32460	+	7.49042i	−0.406824	+	0.704640i	−0.994532	−	0.104433i	$-0.966697\pi$
$113$	−4.32460	+	7.49042i	−0.406824	+	0.704640i	0.587708	+	0.809073i	$0.300030\pi$
$114$	7.33775	−	1.03145i	0.687243	−	0.0966041i
$115$	−14.8064	+	10.7210i	−1.38070	+	0.999734i
$116$	−0.951583			−0.0883523
$117$	14.6588	−	4.20417i	1.35520	−	0.388675i
$118$	−0.324580			−0.0298800
$119$	−0.0170741	+	0.00985772i	−0.00156518	+	0.000903656i
$120$	2.68597	+	2.79026i	0.245194	+	0.254715i
$121$	8.43362	+	7.06216i	0.766692	+	0.642015i
$122$	−3.56095	+	6.16775i	−0.322393	+	0.558401i
$123$	7.96897	+	10.1993i	0.718538	+	0.919637i
$124$	−3.81464	−	6.60714i	−0.342564	−	0.593339i
$125$	−3.40335	−	10.6498i	−0.304405	−	0.952543i
$126$	−0.374104	−	1.30440i	−0.0333279	−	0.116205i
$127$	−16.9227			−1.50165			−0.750825	−	0.660501i	$-0.770344\pi$
$127$	−16.9227			−1.50165			−0.750825	+	0.660501i	$0.770344\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−18.8348	+	2.64756i	−1.65831	+	0.233105i
$130$	−4.63993	+	10.3763i	−0.406949	+	0.910064i
$131$	6.19075	−	10.7227i	0.540888	−	0.936846i	−0.457965	−	0.888970i	$-0.651422\pi$
$131$	6.19075	−	10.7227i	0.540888	−	0.936846i	0.998853	−	0.0478758i	$-0.0152452\pi$
$132$	−1.77807	−	5.46246i	−0.154761	−	0.475446i
$133$	1.67585	−	0.967555i	0.145315	−	0.0838977i
$134$	8.76893			0.757520
$135$	−11.6189	−	0.0178558i	−0.999999	−	0.00153678i
$136$	0.0435865			0.00373751
$137$	−2.48341	−	4.30140i	−0.212172	−	0.367493i	0.740222	−	0.672363i	$-0.234720\pi$
$137$	−2.48341	−	4.30140i	−0.212172	−	0.367493i	−0.952394	+	0.304870i	$0.901387\pi$
$138$	−13.1289	−	5.30402i	−1.11761	−	0.451508i
$139$	9.75453	+	5.63178i	0.827369	+	0.477681i	0.852951	−	0.521991i	$-0.174811\pi$
$139$	9.75453	+	5.63178i	0.827369	+	0.477681i	−0.0255823	+	0.999673i	$0.508144\pi$
$140$	0.923329	+	0.412881i	0.0780356	+	0.0348948i
$141$	−0.816965	+	0.114839i	−0.0688009	+	0.00967117i
$142$	−1.50173	−	2.60107i	−0.126022	−	0.218277i
$143$	12.9095	−	10.8434i	1.07954	−	0.906772i
$144$	−0.725614	+	2.91093i	−0.0604678	+	0.242577i
$145$	0.218998	+	2.11650i	0.0181868	+	0.175766i
$146$	−2.81075	+	1.62279i	−0.232619	+	0.134303i
$147$	7.24656	+	9.27468i	0.597686	+	0.764963i
$148$	0.549376	+	0.317182i	0.0451584	+	0.0260722i
$149$	8.37963	−	14.5139i	0.686486	−	1.18903i	−0.286481	−	0.958086i	$-0.592486\pi$
$149$	8.37963	−	14.5139i	0.686486	−	1.18903i	0.972967	−	0.230943i	$-0.0741811\pi$
$150$	5.58793	−	6.61627i	0.456253	−	0.540216i
$151$	18.5674	−	10.7199i	1.51099	−	0.872373i	0.511077	−	0.859535i	$-0.329247\pi$
$151$	18.5674	−	10.7199i	1.51099	−	0.872373i	0.999918	−	0.0128384i	$-0.00408669\pi$
$152$	−4.27810			−0.347000
$153$	−0.0908283	+	0.0940653i	−0.00734303	+	0.00760473i
$154$	−0.964893	−	1.14874i	−0.0777533	−	0.0925679i
$155$	−13.8177	+	10.0051i	−1.10986	+	0.803626i
$156$	−8.71873	+	1.22557i	−0.698057	+	0.0981241i
$157$	−1.91837	−	1.10757i	−0.153102	−	0.0883938i	0.421492	−	0.906832i	$-0.361507\pi$
$157$	−1.91837	−	1.10757i	−0.153102	−	0.0883938i	−0.574594	+	0.818439i	$0.694840\pi$
$158$	1.91542	−	3.31760i	0.152382	−	0.263934i
$159$	−4.48556	+	11.1030i	−0.355728	+	0.880524i
$160$	−1.31140	−	1.81114i	−0.103676	−	0.143183i
$161$	−3.69787			−0.291433
$162$	−4.77007	−	7.63193i	−0.374772	−	0.599621i
$163$		−	1.15777i		−	0.0906835i	−0.998972	−	0.0453418i	$-0.985562\pi$
$163$		−	1.15777i		−	0.0906835i	0.998972	−	0.0453418i	$-0.0144377\pi$
$164$	−3.73641	−	6.47166i	−0.291765	−	0.505352i
$165$	−11.7404	+	5.21190i	−0.913986	+	0.405745i
$166$	5.53213	−	9.58193i	0.429376	−	0.743702i
$167$	−9.20454	−	5.31425i	−0.712269	−	0.411229i	0.0996316	−	0.995024i	$-0.468234\pi$
$167$	−9.20454	−	5.31425i	−0.712269	−	0.411229i	−0.811901	+	0.583796i	$0.801567\pi$
$168$	0.109056	+	0.775829i	0.00841388	+	0.0598565i
$169$	−6.41971	−	11.1193i	−0.493824	−	0.855328i
$170$	−0.0100310	−	0.0969448i	−0.000769345	−	0.00743533i
$171$	8.91498	−	9.23270i	0.681745	−	0.706042i
$172$	10.9812			0.837309
$173$	2.26248	−	1.30624i	0.172013	−	0.0993119i	−0.411522	−	0.911400i	$-0.635003\pi$
$173$	2.26248	−	1.30624i	0.172013	−	0.0993119i	0.583535	+	0.812088i	$0.301669\pi$
$174$	−1.29876	+	1.01476i	−0.0984591	+	0.0769288i
$175$	0.705831	−	2.14868i	0.0533558	−	0.162425i
$176$	0.577573	+	3.26595i	0.0435362	+	0.246180i
$177$	−0.443002	+	0.346130i	−0.0332980	+	0.0260167i
$178$	0.986564	+	1.70878i	0.0739461	+	0.128078i
$179$		−	12.9132i		−	0.965178i	−0.875847	−	0.482589i	$-0.839696\pi$
$179$		−	12.9132i		−	0.965178i	0.875847	−	0.482589i	$-0.160304\pi$
$180$	6.64145	+	0.943983i	0.495025	+	0.0703603i
$181$	7.90044			0.587235			0.293618	−	0.955923i	$-0.405141\pi$
$181$	7.90044			0.587235			0.293618	+	0.955923i	$0.405141\pi$
$182$	−1.99125	+	1.14965i	−0.147602	+	0.0852178i
$183$	1.71709	+	12.2154i	0.126931	+	0.902988i
$184$	7.07991	+	4.08759i	0.521938	+	0.301341i
$185$	0.579041	−	1.29491i	0.0425719	−	0.0952040i
$186$	−12.2522	−	4.94984i	−0.898375	−	0.362940i
$187$	−0.0493740	+	0.135867i	−0.00361058	+	0.00993558i
$188$	0.476312			0.0347386
$189$	−1.90160	−	1.38136i	−0.138321	−	0.100479i
$190$	0.984566	+	9.51533i	0.0714279	+	0.690314i
$191$	−19.3227	+	11.1560i	−1.39814	+	0.807217i	−0.994198	−	0.107567i	$-0.965694\pi$
$191$	−19.3227	+	11.1560i	−1.39814	+	0.807217i	−0.403943	+	0.914784i	$0.632361\pi$
$192$	0.648796	−	1.60595i	0.0468228	−	0.115899i
$193$	7.11684	−	12.3267i	0.512281	−	0.887297i	−0.487617	−	0.873057i	$-0.662134\pi$
$193$	7.11684	−	12.3267i	0.512281	−	0.887297i	0.999899	−	0.0142396i	$-0.00453275\pi$
$194$	−5.68074	+	9.83932i	−0.407853	+	0.706422i
$195$	4.73244	+	19.1101i	0.338897	+	1.36850i
$196$	−3.39770	−	5.88499i	−0.242693	−	0.420356i
$197$			3.86657i			0.275482i	0.990468	+	0.137741i	$0.0439841\pi$
$197$			3.86657i			0.275482i	−0.990468	+	0.137741i	$0.956016\pi$
$198$	−8.25192	−	5.55931i	−0.586438	−	0.395083i
$199$	−5.56462			−0.394465			−0.197233	−	0.980357i	$-0.563195\pi$
$199$	−5.56462			−0.394465			−0.197233	+	0.980357i	$0.563195\pi$
$200$	−3.72651	+	3.33363i	−0.263504	+	0.235723i
$201$	11.9682	−	9.35112i	0.844175	−	0.659577i
$202$	−9.10020	−	5.25401i	−0.640288	−	0.369671i
$203$	−0.215214	+	0.372762i	−0.0151051	+	0.0261628i
$204$	0.0594889	−	0.0464803i	0.00416506	−	0.00325427i
$205$	−13.5343	+	9.79990i	−0.945278	+	0.684455i
$206$	−5.11005			−0.356034
$207$	−23.5751	+	6.76138i	−1.63858	+	0.469948i
$208$	5.08325			0.352460
$209$	4.84615	−	13.3356i	0.335215	−	0.922444i
$210$	1.70050	−	0.421112i	0.117345	−	0.0290595i
$211$	−8.78713	−	5.07325i	−0.604931	−	0.349257i	0.166048	−	0.986118i	$-0.446899\pi$
$211$	−8.78713	−	5.07325i	−0.604931	−	0.349257i	−0.770979	+	0.636861i	$0.780233\pi$
$212$	3.45683	−	5.98741i	0.237416	−	0.411217i
$213$	−4.82340	−	1.94863i	−0.330494	−	0.133518i
$214$	−0.738948	−	1.27990i	−0.0505134	−	0.0874919i
$215$	−2.52722	−	24.4243i	−0.172355	−	1.66572i
$216$	2.11384	+	4.74676i	0.143828	+	0.322976i
$217$	−3.45094			−0.234265
$218$	7.86523	+	13.6230i	0.532700	+	0.922664i
$219$	−2.10572	+	5.21222i	−0.142291	+	0.352209i
$220$	7.13117	−	2.03626i	0.480784	−	0.137285i
$221$	0.191878	+	0.110781i	0.0129071	+	0.00745191i
$222$	1.08805	−	0.152945i	0.0730254	−	0.0102650i
$223$	12.0937	−	6.98228i	0.809851	−	0.467568i	−0.0370530	−	0.999313i	$-0.511797\pi$
$223$	12.0937	−	6.98228i	0.809851	−	0.467568i	0.846904	+	0.531745i	$0.178464\pi$
$224$		−	0.452329i		−	0.0302225i
$225$	0.571131	−	14.9891i	0.0380754	−	0.999275i
$226$		−	8.64920i		−	0.575336i
$227$	19.9940	−	11.5435i	1.32705	−	0.766172i	0.342206	−	0.939625i	$-0.388826\pi$
$227$	19.9940	−	11.5435i	1.32705	−	0.766172i	0.984842	+	0.173453i	$0.0554926\pi$
$228$	−5.83896	+	4.56214i	−0.386694	+	0.302135i
$229$	8.77718	−	15.2025i	0.580012	−	1.00461i	−0.415465	−	0.909609i	$-0.636381\pi$
$229$	8.77718	−	15.2025i	0.580012	−	1.00461i	0.995477	−	0.0950018i	$-0.0302857\pi$
$230$	7.46221	−	16.6878i	0.492043	−	1.10036i
$231$	−2.54194	−	0.538896i	−0.167247	−	0.0354568i
$232$	0.824095	−	0.475791i	0.0541045	−	0.0312372i
$233$			1.72723i			0.113155i	0.998398	+	0.0565774i	$0.0180188\pi$
$233$			1.72723i			0.113155i	−0.998398	+	0.0565774i	$0.981981\pi$
$234$	−10.5928	+	10.9703i	−0.692473	+	0.717151i
$235$	−0.109619	−	1.05941i	−0.00715074	−	0.0691083i
$236$	0.281094	−	0.162290i	0.0182977	−	0.0105642i
$237$	−0.923613	−	6.57061i	−0.0599951	−	0.426807i
$238$	0.00985772	−	0.0170741i	0.000638981	−	0.00110675i
$239$	−9.49102	+	16.4389i	−0.613923	+	1.06335i	0.376650	+	0.926356i	$0.377076\pi$
$239$	−9.49102	+	16.4389i	−0.613923	+	1.06335i	−0.990572	+	0.136990i	$0.956257\pi$
$240$	−3.72125	−	1.07345i	−0.240206	−	0.0692911i
$241$	−12.0607	+	6.96327i	−0.776900	+	0.448543i	−0.835331	−	0.549748i	$-0.814724\pi$
$241$	−12.0607	+	6.96327i	−0.776900	+	0.448543i	0.0584304	+	0.998291i	$0.481390\pi$
$242$	−10.8348	−	1.89920i	−0.696488	−	0.122085i
$243$	−14.6491	−	5.32965i	−0.939737	−	0.341897i
$244$		−	7.12190i		−	0.455933i
$245$	−12.3074	+	8.91151i	−0.786291	+	0.569336i
$246$	−12.0010	−	4.84834i	−0.765153	−	0.309119i
$247$	−18.8332	−	10.8733i	−1.19833	−	0.691854i
$248$	6.60714	+	3.81464i	0.419554	+	0.242230i
$249$	−2.66759	−	18.9773i	−0.169052	−	1.20264i
$250$	8.27227	+	7.52128i	0.523184	+	0.475687i
$251$		−	9.27646i		−	0.585525i	−0.956185	−	0.292763i	$-0.905425\pi$
$251$		−	9.27646i		−	0.585525i	0.956185	−	0.292763i	$-0.0945745\pi$
$252$	0.976184	+	0.942591i	0.0614938	+	0.0593777i
$253$	−20.7617	+	17.4390i	−1.30528	+	1.09638i
$254$	14.6555	−	8.46137i	0.919570	−	0.530914i
$255$	−0.117072	−	0.121618i	−0.00733134	−	0.00761600i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.3295	+	17.8912i	−0.644337	+	1.11602i	0.340118	+	0.940383i	$0.389533\pi$
$257$	−10.3295	+	17.8912i	−0.644337	+	1.11602i	−0.984454	+	0.175641i	$0.943800\pi$
$258$	14.9877	−	11.7103i	0.933091	−	0.729049i
$259$	0.248499	−	0.143471i	0.0154409	−	0.00891483i
$260$	−1.16986	−	11.3061i	−0.0725518	−	0.701176i
$261$	−0.690482	+	2.76999i	−0.0427397	+	0.171458i
$262$			12.3815i			0.764932i
$263$	−6.32611	+	3.65238i	−0.390085	+	0.225216i	−0.682197	−	0.731169i	$-0.738975\pi$
$263$	−6.32611	+	3.65238i	−0.390085	+	0.225216i	0.292112	+	0.956384i	$0.405642\pi$
$264$	4.27108	+	3.84160i	0.262867	+	0.236434i
$265$	−14.1127	−	6.31072i	−0.866938	−	0.387664i
$266$	−0.967555	+	1.67585i	−0.0593246	+	0.102753i
$267$	3.16874	+	1.28016i	0.193924	+	0.0783443i
$268$	−7.59412	+	4.38447i	−0.463885	+	0.267824i
$269$		−	2.45108i		−	0.149445i	−0.997204	−	0.0747225i	$-0.976193\pi$
$269$		−	2.45108i		−	0.149445i	0.997204	−	0.0747225i	$-0.0238071\pi$
$270$	10.0712	−	5.79400i	0.612915	−	0.352612i
$271$			27.6304i			1.67843i	0.543800	+	0.839215i	$0.316985\pi$
$271$			27.6304i			1.67843i	−0.543800	+	0.839215i	$0.683015\pi$
$272$	−0.0377470	+	0.0217933i	−0.00228875	+	0.00132141i
$273$	−1.49178	+	3.69255i	−0.0902864	+	0.223484i
$274$	4.30140	+	2.48341i	0.259857	+	0.150028i
$275$	−6.17021	−	15.3925i	−0.372078	−	0.928202i
$276$	14.0220	−	1.97103i	0.844023	−	0.118642i
$277$	−15.5732	−	26.9736i	−0.935702	−	1.62068i	−0.773377	−	0.633947i	$-0.781434\pi$
$277$	−15.5732	−	26.9736i	−0.935702	−	1.62068i	−0.162326	−	0.986737i	$-0.551899\pi$
$278$	−11.2636			−0.675544
$279$	−22.0008	+	6.30989i	−1.31716	+	0.377763i
$280$	−1.00607	+	0.104099i	−0.0601240	+	0.00622112i
$281$	−9.12301	−	15.8015i	−0.544233	−	0.942640i	−0.998655	−	0.0518528i	$-0.983487\pi$
$281$	−9.12301	−	15.8015i	−0.544233	−	0.942640i	0.454421	−	0.890787i	$-0.349846\pi$
$282$	0.650093	−	0.507936i	0.0387125	−	0.0302471i
$283$	−5.21409	+	9.03107i	−0.309946	+	0.536841i	−0.978350	−	0.206956i	$-0.933644\pi$
$283$	−5.21409	+	9.03107i	−0.309946	+	0.536841i	0.668405	+	0.743798i	$0.266977\pi$
$284$	2.60107	+	1.50173i	0.154345	+	0.0891113i
$285$	11.4909	+	11.9370i	0.680660	+	0.707089i
$286$	−5.75821	+	15.8454i	−0.340490	+	0.936958i
$287$	−3.38018			−0.199525
$288$	−0.827063	−	2.88374i	−0.0487351	−	0.169926i
$289$	16.9981			0.999888
$290$	−1.24791	−	1.72345i	−0.0732798	−	0.101204i
$291$	2.73925	+	19.4871i	0.160578	+	1.14235i
$292$	1.62279	−	2.81075i	0.0949665	−	0.164487i
$293$	20.8248	+	12.0232i	1.21660	+	0.702402i	0.964188	−	0.265219i	$-0.0854444\pi$
$293$	20.8248	+	12.0232i	1.21660	+	0.702402i	0.252407	+	0.967621i	$0.418778\pi$
$294$	−10.9130	−	4.40883i	−0.636462	−	0.257128i
$295$	−0.425655	−	0.587859i	−0.0247826	−	0.0342265i
$296$	−0.634364			−0.0368717
$297$	−17.1910	+	1.21218i	−0.997523	+	0.0703377i
$298$			16.7593i			0.970838i
$299$	20.7782	+	35.9889i	1.20164	+	2.08129i
$300$	−1.53116	+	8.52382i	−0.0884014	+	0.492123i
$301$	2.48356	−	4.30165i	0.143150	−	0.247943i
$302$	−10.7199	+	18.5674i	−0.616861	+	1.06843i
$303$	−18.0232	+	2.53348i	−1.03541	+	0.145545i
$304$	3.70495	−	2.13905i	0.212493	−	0.122683i
$305$	−15.8405	+	1.63904i	−0.907023	+	0.0938511i
$306$	0.0316270	−	0.126877i	0.00180799	−	0.00725308i
$307$	−28.1365			−1.60583			−0.802917	−	0.596091i	$-0.796720\pi$
$307$	−28.1365			−1.60583			−0.802917	+	0.596091i	$0.796720\pi$
$308$	1.40999	+	0.512389i	0.0803417	+	0.0291961i
$309$	−6.97443	+	5.44932i	−0.396762	+	0.310001i
$310$	6.96391	−	15.5735i	0.395524	−	0.884513i
$311$	23.7253	+	13.6978i	1.34534	+	0.776730i	0.987585	−	0.157087i	$-0.0502104\pi$
$311$	23.7253	+	13.6978i	1.34534	+	0.776730i	0.357751	+	0.933817i	$0.383544\pi$
$312$	6.93786	−	5.42074i	0.392779	−	0.306889i
$313$	29.6056	−	17.0928i	1.67341	−	0.966144i	0.707703	−	0.706510i	$-0.249731\pi$
$313$	29.6056	−	17.0928i	1.67341	−	0.966144i	0.965707	−	0.259634i	$-0.0836018\pi$
$314$	2.21514			0.125008
$315$	1.87185	−	2.38815i	0.105467	−	0.134557i
$316$			3.83084i			0.215501i
$317$	−6.33494	−	10.9724i	−0.355806	−	0.616274i	0.631450	−	0.775417i	$-0.282460\pi$
$317$	−6.33494	−	10.9724i	−0.355806	−	0.616274i	−0.987256	+	0.159143i	$0.949127\pi$
$318$	−1.66688	−	11.8582i	−0.0934742	−	0.664977i
$319$	0.549609	+	3.10782i	0.0307722	+	0.174004i
$320$	2.04128	+	0.912789i	0.114111	+	0.0510265i
$321$	−2.37342	−	0.958853i	−0.132472	−	0.0535179i
$322$	3.20245	−	1.84893i	0.178465	−	0.103037i
$323$	0.186468			0.0103753
$324$	7.94697	+	4.22441i	0.441498	+	0.234690i
$325$	−24.8778	+	5.20400i	−1.37997	+	0.288666i
$326$	0.578885	+	1.00266i	0.0320615	+	0.0555321i
$327$	25.2623	+	10.2059i	1.39701	+	0.564385i
$328$	6.47166	+	3.73641i	0.357338	+	0.206309i
$329$	0.107725	−	0.186585i	0.00593907	−	0.0102868i
$330$	7.56151	−	10.3838i	0.416247	−	0.571610i
$331$	8.61667	+	14.9245i	0.473615	+	0.820325i	0.999544	−	0.0302035i	$-0.00961553\pi$
$331$	8.61667	+	14.9245i	0.473615	+	0.820325i	−0.525929	+	0.850529i	$0.676282\pi$
$332$			11.0643i			0.607230i
$333$	1.32193	−	1.36904i	0.0724412	−	0.0750229i
$334$	10.6285			0.581565
$335$	11.4996	+	15.8817i	0.628291	+	0.867712i
$336$	−0.482360	−	0.617360i	−0.0263149	−	0.0336797i
$337$	−0.160378	+	0.277783i	−0.00873636	+	0.0151318i	−0.870361	−	0.492415i	$-0.836114\pi$
$337$	−0.160378	+	0.277783i	−0.00873636	+	0.0151318i	0.861624	+	0.507547i	$0.169448\pi$
$338$	11.1193	+	6.41971i	0.604809	+	0.349186i
$339$	−9.22344	−	11.8048i	−0.500948	−	0.641150i
$340$	0.0571595	+	0.0789412i	0.00309991	+	0.00428119i
$341$	−19.3753	+	16.2745i	−1.04923	+	0.881314i
$342$	−3.10425	+	12.4532i	−0.167859	+	0.673394i
$343$	−6.24006			−0.336931
$344$	−9.51000	+	5.49060i	−0.512745	+	0.296033i
$345$	−7.61098	−	30.7339i	−0.409761	−	1.65466i
$346$	−1.30624	+	2.26248i	−0.0702241	+	0.121632i
$347$	−8.28529	−	4.78352i	−0.444778	−	0.256793i	0.260844	−	0.965381i	$-0.415999\pi$
$347$	−8.28529	−	4.78352i	−0.444778	−	0.256793i	−0.705622	+	0.708588i	$0.749332\pi$
$348$	0.617383	−	1.52819i	0.0330952	−	0.0819196i
$349$	16.5762	−	9.57026i	0.887303	−	0.512284i	0.0142435	−	0.999899i	$-0.495466\pi$
$349$	16.5762	−	9.57026i	0.887303	−	0.512284i	0.873059	+	0.487614i	$0.162133\pi$
$350$	0.463074	+	2.21373i	0.0247523	+	0.118329i
$351$	−2.75889	+	26.2689i	−0.147259	+	1.40213i
$352$	−2.13317	−	2.53961i	−0.113698	−	0.135361i
$353$	12.8395	+	22.2387i	0.683378	+	1.18365i	0.973944	+	0.226790i	$0.0728232\pi$
$353$	12.8395	+	22.2387i	0.683378	+	1.18365i	−0.290566	+	0.956855i	$0.593843\pi$
$354$	0.210586	−	0.521258i	0.0111925	−	0.0277045i
$355$	2.74153	−	6.13090i	0.145505	−	0.325394i
$356$	−1.70878	−	0.986564i	−0.0905651	−	0.0522878i
$357$	−0.00475339	−	0.0338157i	−0.000251576	−	0.00178972i
$358$	6.45660	+	11.1832i	0.341242	+	0.591049i
$359$	−12.1567			−0.641607			−0.320804	−	0.947146i	$-0.603953\pi$
$359$	−12.1567			−0.641607			−0.320804	+	0.947146i	$0.603953\pi$
$360$	−6.22366	+	2.50321i	−0.328016	+	0.131931i
$361$	0.697833			0.0367281
$362$	−6.84198	+	3.95022i	−0.359607	+	0.207619i
$363$	−16.8131	+	8.96204i	−0.882461	+	0.470385i
$364$	1.14965	−	1.99125i	0.0602581	−	0.104370i
$365$	−6.62512	−	2.96253i	−0.346775	−	0.155066i
$366$	−7.59474	−	9.72030i	−0.396983	−	0.508088i
$367$	24.6371	−	14.2242i	1.28604	−	0.742498i	0.308098	−	0.951355i	$-0.400308\pi$
$367$	24.6371	−	14.2242i	1.28604	−	0.742498i	0.977946	+	0.208857i	$0.0669743\pi$
$368$	−8.17517			−0.426160
$369$	−21.5497	+	6.18050i	−1.12183	+	0.321744i
$370$	0.145993	+	1.41095i	0.00758982	+	0.0733517i
$371$	−1.56363	−	2.70828i	−0.0811794	−	0.140607i
$372$	13.0856	−	1.83941i	0.678459	−	0.0953692i
$373$	13.7797	−	23.8672i	0.713486	−	1.23579i	−0.250054	−	0.968232i	$-0.580448\pi$
$373$	13.7797	−	23.8672i	0.713486	−	1.23579i	0.963540	−	0.267563i	$-0.0862182\pi$
$374$	−0.0251744	−	0.142351i	−0.00130174	−	0.00736081i
$375$	19.3110	+	1.44391i	0.997216	+	0.0745632i
$376$	−0.412499	+	0.238156i	−0.0212730	+	0.0122820i
$377$	4.83713			0.249125
$378$	2.33751	+	0.245497i	0.120229	+	0.0126270i
$379$	−21.3996			−1.09923			−0.549613	−	0.835420i	$-0.685225\pi$
$379$	−21.3996			−1.09923			−0.549613	+	0.835420i	$0.685225\pi$
$380$	−5.61032	−	7.74823i	−0.287803	−	0.397476i
$381$	10.9794	−	27.1770i	0.562492	−	1.39232i
$382$	11.1560	−	19.3227i	0.570789	−	0.988635i
$383$	17.9090	−	31.0193i	0.915106	−	1.58501i	0.108360	−	0.994112i	$-0.465440\pi$
$383$	17.9090	−	31.0193i	0.915106	−	1.58501i	0.806746	−	0.590898i	$-0.201227\pi$
$384$	0.241100	+	1.71519i	0.0123036	+	0.0875278i
$385$	0.815157	−	3.25401i	0.0415442	−	0.165840i
$386$			14.2337i			0.724475i
$387$	7.96811	−	31.9654i	0.405042	−	1.62489i
$388$		−	11.3615i		−	0.576791i
$389$	8.64619	−	4.99188i	0.438379	−	0.253099i	−0.264531	−	0.964377i	$-0.585217\pi$
$389$	8.64619	−	4.99188i	0.438379	−	0.253099i	0.702910	+	0.711279i	$0.251884\pi$
$390$	−13.6535	−	14.1836i	−0.691370	−	0.718215i
$391$	−0.308588	−	0.178164i	−0.0156060	−	0.00901012i
$392$	5.88499	+	3.39770i	0.297237	+	0.171610i
$393$	13.2035	+	16.8988i	0.666030	+	0.852434i
$394$	−1.93329	−	3.34855i	−0.0973975	−	0.168697i
$395$	8.52052	−	0.881631i	0.428714	−	0.0443597i
$396$	9.92602	+	0.688544i	0.498801	+	0.0346006i
$397$		−	31.9173i		−	1.60188i	−0.598743	−	0.800941i	$-0.704333\pi$
$397$		−	31.9173i		−	1.60188i	0.598743	−	0.800941i	$-0.295667\pi$
$398$	4.81910	−	2.78231i	0.241560	−	0.139465i
$399$	0.466554	+	3.31908i	0.0233569	+	0.166162i
$400$	1.56044	−	4.75027i	0.0780219	−	0.237513i
$401$	−7.69190	−	4.44092i	−0.384115	−	0.221769i	0.295492	−	0.955345i	$-0.404516\pi$
$401$	−7.69190	−	4.44092i	−0.384115	−	0.221769i	−0.679607	+	0.733576i	$0.737850\pi$
$402$	−5.68924	+	14.0824i	−0.283754	+	0.702368i
$403$	19.3907	+	33.5858i	0.965922	+	1.67303i
$404$	10.5080			0.522793
$405$	7.56699	−	18.6478i	0.376007	−	0.926617i
$406$		−	0.430428i		−	0.0213618i
$407$	0.718596	−	1.97743i	0.0356195	−	0.0980174i
$408$	−0.0282787	+	0.0699976i	−0.00140001	+	0.00346540i
$409$	−20.2865	−	11.7124i	−1.00310	−	0.579141i	−0.0939372	−	0.995578i	$-0.529945\pi$
$409$	−20.2865	−	11.7124i	−1.00310	−	0.579141i	−0.909165	+	0.416437i	$0.863279\pi$
$410$	6.82111	−	15.2541i	0.336871	−	0.753347i
$411$	8.51904	−	1.19750i	0.420213	−	0.0590683i
$412$	4.42543	−	2.55502i	0.218025	−	0.125877i
$413$		−	0.146817i		−	0.00722439i
$414$	17.0359	−	17.6431i	0.837270	−	0.867109i
$415$	24.6090	−	2.54634i	1.20801	−	0.124995i
$416$	−4.40222	+	2.54162i	−0.215837	+	0.124613i
$417$	−15.3730	+	12.0114i	−0.752821	+	0.588200i
$418$	2.47092	+	13.9721i	0.120856	+	0.683396i
$419$	−4.20886	−	2.42999i	−0.205616	−	0.118713i	0.393656	−	0.919258i	$-0.371210\pi$
$419$	−4.20886	−	2.42999i	−0.205616	−	0.118713i	−0.599272	+	0.800545i	$0.704543\pi$
$420$	−1.26212	+	1.21494i	−0.0615850	+	0.0592831i
$421$	14.8130	+	25.6569i	0.721942	+	1.25044i	0.960220	+	0.279244i	$0.0900838\pi$
$421$	14.8130	+	25.6569i	0.721942	+	1.25044i	−0.238278	+	0.971197i	$0.576583\pi$
$422$	10.1465			0.493924
$423$	0.345619	−	1.38651i	0.0168046	−	0.0674144i
$424$			6.91367i			0.335757i
$425$	0.162426	−	0.145301i	0.00787880	−	0.00704815i
$426$	5.15150	−	0.724133i	0.249591	−	0.0350844i
$427$	−2.78985	−	1.61072i	−0.135010	−	0.0779482i
$428$	1.27990	+	0.738948i	0.0618661	+	0.0357184i
$429$	9.03835	+	27.7671i	0.436376	+	1.34061i
$430$	14.4008	+	19.8885i	0.694468	+	0.959107i
$431$	22.2647			1.07245			0.536227	−	0.844074i	$-0.319849\pi$
$431$	22.2647			1.07245			0.536227	+	0.844074i	$0.319849\pi$
$432$	−4.20401	−	3.05389i	−0.202266	−	0.146930i
$433$			19.6952i			0.946491i	0.880930	+	0.473246i	$0.156918\pi$
$433$			19.6952i			0.946491i	−0.880930	+	0.473246i	$0.843082\pi$
$434$	2.98860	−	1.72547i	0.143457	−	0.0828252i
$435$	−3.54108	−	1.02148i	−0.169782	−	0.0489762i
$436$	−13.6230	−	7.86523i	−0.652422	−	0.376676i
$437$	30.2886	+	17.4871i	1.44890	+	0.836522i
$438$	−0.782507	−	5.56677i	−0.0373896	−	0.265991i
$439$	20.0721	−	11.5886i	0.957990	−	0.553096i	0.0624358	−	0.998049i	$-0.480113\pi$
$439$	20.0721	−	11.5886i	0.957990	−	0.553096i	0.895554	+	0.444953i	$0.146780\pi$
$440$	−5.15765	+	5.32904i	−0.245881	+	0.254052i
$441$	−19.5962	+	5.62022i	−0.933151	+	0.267630i
$442$	−0.221561			−0.0105386
$443$	−1.77905	−	3.08141i	−0.0845253	−	0.146402i	0.820664	−	0.571412i	$-0.193604\pi$
$443$	−1.77905	−	3.08141i	−0.0845253	−	0.146402i	−0.905189	+	0.425010i	$0.860271\pi$
$444$	−0.865810	+	0.676481i	−0.0410895	+	0.0321044i
$445$	−1.80105	+	4.02770i	−0.0853779	+	0.190931i
$446$	−6.98228	+	12.0937i	−0.330620	+	0.572651i
$447$	17.8720	+	22.8738i	0.845315	+	1.08190i
$448$	0.226164	+	0.391728i	0.0106853	+	0.0185074i
$449$		−	17.9470i		−	0.846969i	−0.905903	−	0.423485i	$-0.860807\pi$
$449$		−	17.9470i		−	0.846969i	0.905903	−	0.423485i	$-0.139193\pi$
$450$	6.99995	+	13.2665i	0.329981	+	0.625390i
$451$	−18.9780	+	15.9408i	−0.893641	+	0.750622i
$452$	4.32460	+	7.49042i	0.203412	+	0.352320i
$453$	5.16913	+	36.7733i	0.242867	+	1.72776i
$454$	−11.5435	+	19.9940i	−0.541765	+	0.938365i
$455$	−4.69351	−	2.09878i	−0.220035	−	0.0983922i
$456$	2.77561	−	6.87040i	0.129980	−	0.321736i
$457$	1.61145	+	2.79112i	0.0753806	+	0.130563i	0.901252	−	0.433296i	$-0.142649\pi$
$457$	1.61145	+	2.79112i	0.0753806	+	0.130563i	−0.825871	+	0.563859i	$0.809316\pi$
$458$			17.5544i			0.820262i
$459$	−0.0921348	−	0.206895i	−0.00430048	−	0.00965701i
$460$	1.88144	+	18.1832i	0.0877226	+	0.847794i
$461$	8.31451	+	14.4012i	0.387245	+	0.670729i	0.992078	−	0.125624i	$-0.0400933\pi$
$461$	8.31451	+	14.4012i	0.387245	+	0.670729i	−0.604833	+	0.796353i	$0.706760\pi$
$462$	2.47083	−	0.804270i	0.114953	−	0.0374180i
$463$	−12.6743	−	7.31752i	−0.589026	−	0.340074i	0.175686	−	0.984446i	$-0.443786\pi$
$463$	−12.6743	−	7.31752i	−0.589026	−	0.340074i	−0.764712	+	0.644372i	$0.777119\pi$
$464$	−0.475791	+	0.824095i	−0.0220881	+	0.0382576i
$465$	−7.10275	−	28.6817i	−0.329382	−	1.33008i
$466$	−0.863616	−	1.49583i	−0.0400062	−	0.0692928i
$467$	10.6726			0.493870			0.246935	−	0.969032i	$-0.420577\pi$
$467$	10.6726			0.493870			0.246935	+	0.969032i	$0.420577\pi$
$468$	3.68848	−	14.7970i	0.170500	−	0.683990i
$469$			3.96644i			0.183153i
$470$	0.624638	+	0.862667i	0.0288124	+	0.0397919i
$471$	3.02333	−	2.36221i	0.139308	−	0.108845i
$472$	−0.162290	+	0.281094i	−0.00747000	+	0.0129384i
$473$	−6.34244	−	35.8640i	−0.291626	−	1.64903i
$474$	4.08518	+	5.22850i	0.187638	+	0.240153i
$475$	−15.9424	+	14.2616i	−0.731488	+	0.654368i
$476$			0.0197154i			0.000903656i
$477$	−14.9206	−	14.4071i	−0.683167	−	0.659657i
$478$		−	18.9820i		−	0.868218i
$479$	18.8864	+	32.7122i	0.862943	+	1.49466i	0.869076	+	0.494679i	$0.164715\pi$
$479$	18.8864	+	32.7122i	0.862943	+	1.49466i	−0.00613280	+	0.999981i	$0.501952\pi$
$480$	3.75942	−	0.930987i	0.171593	−	0.0424935i
$481$	−2.79261	−	1.61232i	−0.127332	−	0.0735153i
$482$	6.96327	−	12.0607i	0.317168	−	0.549351i
$483$	2.39916	−	5.93858i	0.109166	−	0.270215i
$484$	10.3328	−	3.77265i	0.469674	−	0.171484i
$485$	−25.2701	+	2.61474i	−1.14746	+	0.118729i
$486$	15.3513	−	2.70891i	0.696348	−	0.122879i
$487$			26.6224i			1.20638i	0.797599	+	0.603188i	$0.206103\pi$
$487$			26.6224i			1.20638i	−0.797599	+	0.603188i	$0.793897\pi$
$488$	3.56095	+	6.16775i	0.161197	+	0.279201i
$489$	1.85932	+	0.751156i	0.0840812	+	0.0339684i
$490$	6.20276	−	13.8713i	0.280212	−	0.626641i
$491$	1.97541	−	3.42151i	0.0891490	−	0.154411i	−0.818003	−	0.575214i	$-0.804919\pi$
$491$	1.97541	−	3.42151i	0.0891490	−	0.154411i	0.907152	+	0.420804i	$0.138252\pi$
$492$	12.8173	−	1.80170i	0.577849	−	0.0812267i
$493$	−0.0359194	+	0.0207381i	−0.00161773	+	0.000933997i
$494$	21.7467			0.978429
$495$	−0.752927	−	22.2359i	−0.0338415	−	0.999427i
$496$	−7.62927			−0.342564
$497$	1.17654	−	0.679276i	0.0527751	−	0.0304697i
$498$	11.7988	+	15.1010i	0.528719	+	0.676693i
$499$	−17.5821	+	30.4531i	−0.787083	+	1.36327i	0.140664	+	0.990057i	$0.455076\pi$
$499$	−17.5821	+	30.4531i	−0.787083	+	1.36327i	−0.927747	+	0.373210i	$0.878257\pi$
$500$	−10.9246	−	2.37749i	−0.488564	−	0.106324i
$501$	14.5063	−	11.3341i	0.648092	−	0.506372i
$502$	4.63823	+	8.03365i	0.207014	+	0.358559i
$503$		−	34.7627i		−	1.54999i	−0.631965	−	0.774997i	$-0.717751\pi$
$503$		−	34.7627i		−	1.54999i	0.631965	−	0.774997i	$-0.282249\pi$
$504$	−1.31670	−	0.328216i	−0.0586503	−	0.0146199i
$505$	−2.41832	−	23.3718i	−0.107614	−	1.04003i
$506$	9.26067	−	25.4835i	0.411687	−	1.13288i
$507$	22.0220	−	3.09558i	0.978033	−	0.137480i
$508$	−8.46137	+	14.6555i	−0.375413	+	0.650234i
$509$	32.9611	+	19.0301i	1.46097	+	0.843494i	0.999057	−	0.0434292i	$-0.0138283\pi$
$509$	32.9611	+	19.0301i	1.46097	+	0.843494i	0.461918	+	0.886923i	$0.347162\pi$
$510$	0.162196	+	0.0467881i	0.00718217	+	0.00207181i
$511$	−0.734034	−	1.27138i	−0.0324717	−	0.0562427i
$512$		−	1.00000i		−	0.0441942i
$513$	9.04321	+	20.3071i	0.399268	+	0.896581i
$514$		−	20.6590i		−	0.911230i
$515$	−6.70134	−	9.25500i	−0.295296	−	0.407824i
$516$	−7.12455	+	17.6352i	−0.313641	+	0.776347i
$517$	−0.275105	−	1.55561i	−0.0120991	−	0.0684157i
$518$	−0.143471	+	0.248499i	−0.00630374	+	0.0109184i
$519$	0.629870	+	4.48091i	0.0276482	+	0.196690i
$520$	6.66620	+	9.20646i	0.292332	+	0.403730i
$521$		−	14.7532i		−	0.646351i	−0.946339	−	0.323176i	$-0.895250\pi$
$521$		−	14.7532i		−	0.646351i	0.946339	−	0.323176i	$-0.104750\pi$
$522$	−0.787019	−	2.74412i	−0.0344469	−	0.120107i
$523$	−8.77407			−0.383663			−0.191832	−	0.981428i	$-0.561443\pi$
$523$	−8.77407			−0.383663			−0.191832	+	0.981428i	$0.561443\pi$
$524$	−6.19075	−	10.7227i	−0.270444	−	0.468423i
$525$	2.99273	+	2.52758i	0.130613	+	0.110313i
$526$	3.65238	−	6.32611i	0.159251	−	0.275832i
$527$	−0.287982	−	0.166267i	−0.0125447	−	0.00724269i
$528$	−5.61966	−	1.19138i	−0.244564	−	0.0518482i
$529$	−21.9167	−	37.9609i	−0.952900	−	1.65047i
$530$	15.3773	−	1.59112i	0.667949	−	0.0691137i
$531$	−0.268448	−	0.936004i	−0.0116496	−	0.0406191i
$532$		−	1.93511i		−	0.0838977i
$533$	18.9931	+	32.8971i	0.822683	+	1.42493i
$534$	−3.38428	+	0.475720i	−0.146452	+	0.0205864i
$535$	1.34901	−	3.01680i	0.0583227	−	0.130428i
$536$	4.38447	−	7.59412i	0.189380	−	0.328016i
$537$	20.7379	+	8.37803i	0.894907	+	0.361539i
$538$	1.22554	+	2.12270i	0.0528368	+	0.0915160i
$539$	−17.2576	+	14.4957i	−0.743339	+	0.624375i
$540$	−5.82493	+	10.0534i	−0.250665	+	0.432628i
$541$		−	39.4333i		−	1.69537i	−0.530499	−	0.847685i	$-0.677996\pi$
$541$		−	39.4333i		−	1.69537i	0.530499	−	0.847685i	$-0.322004\pi$
$542$	−13.8152	−	23.9287i	−0.593415	−	1.02782i
$543$	−5.12577	+	12.6877i	−0.219968	+	0.544481i
$544$	0.0217933	−	0.0377470i	0.000934378	−	0.00161839i
$545$	−14.3586	+	32.1102i	−0.615054	+	1.37545i
$546$	−0.554361	−	3.94373i	−0.0237244	−	0.168776i
$547$	13.6574	+	23.6553i	0.583947	+	1.01143i	0.995006	+	0.0998168i	$0.0318257\pi$
$547$	13.6574	+	23.6553i	0.583947	+	1.01143i	−0.411059	+	0.911609i	$0.634841\pi$
$548$	−4.96683			−0.212172
$549$	−20.7313	−	5.16775i	−0.884791	−	0.220554i
$550$	13.0398	+	10.2452i	0.556019	+	0.436856i
$551$	3.52556	−	2.03548i	0.150194	−	0.0867146i
$552$	−11.1579	+	8.71794i	−0.474910	+	0.371060i
$553$	1.50065	+	0.866399i	0.0638140	+	0.0368430i
$554$	26.9736	+	15.5732i	1.14600	+	0.661641i
$555$	1.70388	+	1.77004i	0.0723258	+	0.0751341i
$556$	9.75453	−	5.63178i	0.413684	−	0.238841i
$557$			27.6984i			1.17362i	0.809726	+	0.586809i	$0.199616\pi$
$557$			27.6984i			1.17362i	−0.809726	+	0.586809i	$0.800384\pi$
$558$	15.8984	−	16.4649i	0.673031	−	0.697017i
$559$	−55.8202			−2.36094
$560$	0.819230	−	0.593186i	0.0346188	−	0.0250667i
$561$	−0.186161	−	0.167442i	−0.00785974	−	0.00706940i
$562$	15.8015	+	9.12301i	0.666547	+	0.384831i
$563$	−5.99074	−	3.45876i	−0.252480	−	0.145769i	0.368419	−	0.929660i	$-0.379899\pi$
$563$	−5.99074	−	3.45876i	−0.252480	−	0.145769i	−0.620899	+	0.783890i	$0.713232\pi$
$564$	−0.309029	+	0.764932i	−0.0130125	+	0.0322094i
$565$	15.6649	−	11.3426i	0.659027	−	0.477186i
$566$		−	10.4282i		−	0.438329i
$567$	3.45215	−	2.15764i	0.144976	−	0.0906124i
$568$	−3.00346			−0.126022
$569$	9.75720	+	16.9000i	0.409043	+	0.708483i	0.994783	−	0.102016i	$-0.0325293\pi$
$569$	9.75720	+	16.9000i	0.409043	+	0.708483i	−0.585740	+	0.810499i	$0.699196\pi$
$570$	−15.9199	−	4.59234i	−0.666811	−	0.192352i
$571$	−32.1837	−	18.5813i	−1.34684	−	0.777601i	−0.359044	−	0.933321i	$-0.616897\pi$
$571$	−32.1837	−	18.5813i	−1.34684	−	0.777601i	−0.987801	+	0.155720i	$0.950230\pi$
$572$	−2.93595	−	16.6016i	−0.122758	−	0.694149i
$573$	−5.37940	−	38.2692i	−0.224728	−	1.59872i
$574$	2.92732	−	1.69009i	0.122184	−	0.0705429i
$575$	40.0099	−	8.36937i	1.66853	−	0.349027i
$576$	2.15813	+	2.08386i	0.0899220	+	0.0868276i
$577$		−	19.1514i		−	0.797284i	−0.917107	−	0.398642i	$-0.869482\pi$
$577$		−	19.1514i		−	0.797284i	0.917107	−	0.398642i	$-0.130518\pi$
$578$	−14.7208	+	8.49905i	−0.612304	+	0.353514i
$579$	15.1787	+	19.4268i	0.630805	+	0.807350i
$580$	1.94245	+	0.868594i	0.0806557	+	0.0360664i
$581$	4.33418	+	2.50234i	0.179812	+	0.103815i
$582$	−12.1158	−	15.5067i	−0.502216	−	0.642772i
$583$	−21.5511	−	7.83167i	−0.892557	−	0.324355i
$584$			3.24558i			0.134303i
$585$	−33.7602	−	4.79850i	−1.39581	−	0.198394i
$586$	−24.0464			−0.993346
$587$	3.37971	+	5.85383i	0.139496	+	0.241614i	0.927306	−	0.374305i	$-0.122119\pi$
$587$	3.37971	+	5.85383i	0.139496	+	0.241614i	−0.787810	+	0.615918i	$0.788785\pi$
$588$	11.6554	−	1.63837i	0.480660	−	0.0675652i
$589$	28.2660	+	16.3194i	1.16468	+	0.672429i
$590$	0.662558	+	0.296273i	0.0272771	+	0.0121974i
$591$	−6.20951	−	2.50861i	−0.255425	−	0.103191i
$592$	0.549376	−	0.317182i	0.0225792	−	0.0130361i
$593$		−	5.83465i		−	0.239600i	−0.992798	−	0.119800i	$-0.961775\pi$
$593$		−	5.83465i		−	0.239600i	0.992798	−	0.119800i	$-0.0382254\pi$
$594$	14.2818	−	9.64528i	0.585988	−	0.395751i
$595$	0.0438510	−	0.00453733i	0.00179771	−	0.000186012i
$596$	−8.37963	−	14.5139i	−0.343243	−	0.594515i
$597$	3.61030	−	8.93648i	0.147760	−	0.365746i
$598$	−35.9889	−	20.7782i	−1.47170	−	0.849684i
$599$	31.8448	+	18.3856i	1.30114	+	0.751215i	0.980600	−	0.196019i	$-0.0628014\pi$
$599$	31.8448	+	18.3856i	1.30114	+	0.751215i	0.320543	+	0.947234i	$0.396135\pi$
$600$	−2.93589	−	8.14743i	−0.119857	−	0.332617i
$601$	−28.0731	+	16.2080i	−1.14512	+	0.661138i	−0.947694	−	0.319179i	$-0.896593\pi$
$601$	−28.0731	+	16.2080i	−1.14512	+	0.661138i	−0.197430	+	0.980317i	$0.563259\pi$
$602$			4.96711i			0.202444i
$603$	7.25246	+	25.2873i	0.295343	+	1.02978i
$604$		−	21.4398i		−	0.872373i
$605$	−10.7691	−	22.1139i	−0.437826	−	0.899060i
$606$	14.3418	−	11.2057i	0.582597	−	0.455199i
$607$	−2.51599	+	4.35782i	−0.102121	+	0.176879i	−0.912558	−	0.408947i	$-0.865896\pi$
$607$	−2.51599	+	4.35782i	−0.102121	+	0.176879i	0.810437	+	0.585825i	$0.199230\pi$
$608$	−2.13905	+	3.70495i	−0.0867500	+	0.150255i
$609$	−0.459006	−	0.587469i	−0.0185999	−	0.0238054i
$610$	12.8987	−	9.33969i	0.522255	−	0.378153i
$611$	−2.42121			−0.0979518
$612$	0.0360488	+	0.125692i	0.00145719	+	0.00508081i
$613$	30.9881			1.25160			0.625799	−	0.779985i	$-0.284773\pi$
$613$	30.9881			1.25160			0.625799	+	0.779985i	$0.284773\pi$
$614$	24.3669	−	14.0682i	0.983369	−	0.567748i
$615$	−6.95710	−	28.0935i	−0.280538	−	1.13284i
$616$	−1.47728	+	0.261253i	−0.0595214	+	0.0105262i
$617$	−20.5693	+	35.6271i	−0.828089	+	1.43429i	0.0714465	+	0.997444i	$0.477238\pi$
$617$	−20.5693	+	35.6271i	−0.828089	+	1.43429i	−0.899535	+	0.436848i	$0.856095\pi$
$618$	3.31538	−	8.20646i	0.133364	−	0.330112i
$619$	−22.9204	−	39.6993i	−0.921249	−	1.59565i	−0.797485	−	0.603338i	$-0.793837\pi$
$619$	−22.9204	−	39.6993i	−0.921249	−	1.59565i	−0.123763	−	0.992312i	$-0.539496\pi$
$620$	1.75581	+	16.9690i	0.0705149	+	0.681490i
$621$	4.43700	−	42.2471i	0.178051	−	1.69532i
$622$	−27.3956			−1.09846
$623$	−0.772930	+	0.446251i	−0.0309668	+	0.0178787i
$624$	−3.29799	+	8.16343i	−0.132025	+	0.326799i
$625$	−2.77378	+	24.8456i	−0.110951	+	0.993826i
$626$	−17.0928	+	29.6056i	−0.683167	+	1.18328i
$627$	18.2721	+	16.4348i	0.729718	+	0.656341i
$628$	−1.91837	+	1.10757i	−0.0765512	+	0.0441969i
$629$	0.0276497			0.00110247
$630$	−0.426991	+	3.00412i	−0.0170117	+	0.119687i
$631$	18.9601			0.754791			0.377396	−	0.926052i	$-0.376820\pi$
$631$	18.9601			0.754791			0.377396	+	0.926052i	$0.376820\pi$
$632$	−1.91542	−	3.31760i	−0.0761912	−	0.131967i
$633$	13.8484	−	10.8202i	0.550425	−	0.430062i
$634$	10.9724	+	6.33494i	0.435771	+	0.251593i
$635$	34.5440	+	15.4469i	1.37084	+	0.612991i
$636$	7.37268	+	9.43610i	0.292346	+	0.374166i
$637$	17.2714	+	29.9149i	0.684316	+	1.18527i
$638$	−2.02988	−	2.41665i	−0.0803639	−	0.0956759i
$639$	6.25880	−	6.48185i	0.247594	−	0.256418i
$640$	−2.22419	+	0.230141i	−0.0879190	+	0.00909711i
$641$	5.14147	−	2.96843i	0.203076	−	0.117246i	−0.395014	−	0.918675i	$-0.629260\pi$
$641$	5.14147	−	2.96843i	0.203076	−	0.117246i	0.598089	+	0.801429i	$0.295927\pi$
$642$	2.53487	−	0.356320i	0.100043	−	0.0140628i
$643$	−40.6531	−	23.4711i	−1.60320	−	0.925608i	−0.990842	−	0.135028i	$-0.956888\pi$
$643$	−40.6531	−	23.4711i	−1.60320	−	0.925608i	−0.612358	−	0.790580i	$-0.709779\pi$
$644$	−1.84893	+	3.20245i	−0.0728582	+	0.126194i
$645$	40.8638	+	11.7878i	1.60901	+	0.464144i
$646$	−0.161486	+	0.0932338i	−0.00635357	+	0.00366823i
$647$	−1.34715			−0.0529618			−0.0264809	−	0.999649i	$-0.508430\pi$
$647$	−1.34715			−0.0529618			−0.0264809	+	0.999649i	$0.508430\pi$
$648$	−8.99448	+	0.315035i	−0.353337	+	0.0123757i
$649$	−0.692383	−	0.824305i	−0.0271784	−	0.0323568i
$650$	18.9428	−	16.9457i	0.742997	−	0.664665i
$651$	2.23896	−	5.54203i	0.0877516	−	0.217209i
$652$	−1.00266	−	0.578885i	−0.0392671	−	0.0226709i
$653$	3.28263	−	5.68568i	0.128459	−	0.222498i	−0.794621	−	0.607106i	$-0.792330\pi$
$653$	3.28263	−	5.68568i	0.128459	−	0.222498i	0.923080	+	0.384609i	$0.125664\pi$
$654$	−26.9807	+	3.79261i	−1.05503	+	0.148303i
$655$	−22.4246	+	16.2372i	−0.876201	+	0.634438i
$656$	−7.47283			−0.291765
$657$	−7.00437	−	6.76333i	−0.273266	−	0.263863i
$658$			0.215450i			0.00839911i
$659$	15.1380	+	26.2197i	0.589691	+	1.02137i	0.994273	+	0.106873i	$0.0340838\pi$
$659$	15.1380	+	26.2197i	0.589691	+	1.02137i	−0.404582	+	0.914502i	$0.632583\pi$
$660$	−1.35655	+	12.7734i	−0.0528036	+	0.497204i
$661$	−21.9336	+	37.9901i	−0.853118	+	1.47764i	0.0252616	+	0.999681i	$0.491958\pi$
$661$	−21.9336	+	37.9901i	−0.853118	+	1.47764i	−0.878380	+	0.477963i	$0.841375\pi$
$662$	−14.9245	−	8.61667i	−0.580057	−	0.334896i
$663$	−0.302397	+	0.236271i	−0.0117441	+	0.00917601i
$664$	−5.53213	−	9.58193i	−0.214688	−	0.371851i
$665$	−4.30406	+	0.445348i	−0.166904	+	0.0172698i
$666$	−0.460303	+	1.84659i	−0.0178364	+	0.0715538i
$667$	−7.77935			−0.301218
$668$	−9.20454	+	5.31425i	−0.356134	+	0.205614i
$669$	3.36685	+	23.9518i	0.130170	+	0.926032i
$670$	−17.8998	−	8.00418i	−0.691531	−	0.309229i
$671$	−23.2597	+	4.11342i	−0.897933	+	0.158797i
$672$	0.726416	+	0.293469i	0.0280221	+	0.0113208i
$673$	6.10841	+	10.5801i	0.235462	+	0.407832i	0.959407	−	0.282026i	$-0.0910064\pi$
$673$	6.10841	+	10.5801i	0.235462	+	0.407832i	−0.723945	+	0.689858i	$0.757673\pi$
$674$		−	0.320757i		−	0.0123551i
$675$	23.7012	+	10.6421i	0.912259	+	0.409614i
$676$	−12.8394			−0.493824
$677$	−6.99557	+	4.03889i	−0.268862	+	0.155227i	−0.628370	−	0.777914i	$-0.716278\pi$
$677$	−6.99557	+	4.03889i	−0.268862	+	0.155227i	0.359509	+	0.933142i	$0.382944\pi$
$678$	13.8901	+	5.61156i	0.533448	+	0.215511i
$679$	−4.45061	−	2.56956i	−0.170799	−	0.0986107i
$680$	−0.0889722	−	0.0397853i	−0.00341193	−	0.00152570i
$681$	5.56629	+	39.5987i	0.213301	+	1.51742i
$682$	8.64229	−	23.7818i	0.330930	−	0.910652i
$683$	11.1579			0.426945			0.213473	−	0.976949i	$-0.431523\pi$
$683$	11.1579			0.426945			0.213473	+	0.976949i	$0.431523\pi$
$684$	−3.53826	−	12.3369i	−0.135289	−	0.471715i
$685$	1.14307	+	11.0472i	0.0436744	+	0.422091i
$686$	5.40405	−	3.12003i	0.206328	−	0.119123i
$687$	18.7198	+	23.9590i	0.714207	+	0.914094i
$688$	5.49060	−	9.51000i	0.209327	−	0.362565i
$689$	−17.5720	+	30.4355i	−0.669438	+	1.15950i
$690$	21.9583	+	22.8109i	0.835937	+	0.868395i
$691$	21.3402	+	36.9623i	0.811819	+	1.40611i	0.911589	+	0.411102i	$0.134856\pi$
$691$	21.3402	+	36.9623i	0.811819	+	1.40611i	−0.0997701	+	0.995011i	$0.531811\pi$
$692$		−	2.61249i		−	0.0993119i
$693$	2.51464	−	3.73258i	0.0955231	−	0.141789i
$694$	9.56703			0.363160
$695$	−14.7711	−	20.3999i	−0.560299	−	0.773811i
$696$	0.229426	+	1.63214i	0.00869638	+	0.0618663i
$697$	−0.282077	−	0.162857i	−0.0106844	−	0.00616866i
$698$	−9.57026	+	16.5762i	−0.362240	+	0.627418i
$699$	−2.77384	−	1.12062i	−0.104916	−	0.0423858i
$700$	−1.50790	−	1.68561i	−0.0569932	−	0.0637100i
$701$	29.2723			1.10560			0.552799	−	0.833314i	$-0.313560\pi$
$701$	29.2723			1.10560			0.552799	+	0.833314i	$0.313560\pi$
$702$	−10.7452	−	24.1289i	−0.405550	−	0.910688i
$703$	−2.71388			−0.102356
$704$	3.11718	+	1.13278i	0.117483	+	0.0426933i
$705$	1.77248	+	0.511299i	0.0667553	+	0.0192566i
$706$	−22.2387	−	12.8395i	−0.836964	−	0.483221i
$707$	2.37654	−	4.11629i	0.0893789	−	0.154809i
$708$	0.0782561	+	0.556716i	0.00294104	+	0.0209227i
$709$	12.9676	+	22.4606i	0.487010	+	0.843526i	0.999888	−	0.0149353i	$-0.00475423\pi$
$709$	12.9676	+	22.4606i	0.487010	+	0.843526i	−0.512879	+	0.858461i	$0.671421\pi$
$710$	0.691219	+	6.68028i	0.0259410	+	0.250706i
$711$	11.1513	+	2.77971i	0.418206	+	0.104247i
$712$	1.97313			0.0739461
$713$	−31.1853	−	54.0145i	−1.16790	−	2.02286i
$714$	0.0210244	+	0.0269086i	0.000786818	+	0.00100703i
$715$	−36.2495	+	10.3508i	−1.35566	+	0.387099i
$716$	−11.1832	−	6.45660i	−0.417934	−	0.241295i
$717$	−20.2423	−	25.9076i	−0.755963	−	0.967536i
$718$	10.5280	−	6.07836i	0.392902	−	0.226842i
$719$			17.7887i			0.663408i	0.943383	+	0.331704i	$0.107624\pi$
$719$			17.7887i			0.663408i	−0.943383	+	0.331704i	$0.892376\pi$
$720$	4.13824	−	5.27968i	0.154223	−	0.196762i
$721$		−	2.31142i		−	0.0860819i
$722$	−0.604341	+	0.348917i	−0.0224913	+	0.0129853i
$723$	−3.35768	−	23.8866i	−0.124874	−	0.888353i
$724$	3.95022	−	6.84198i	0.146809	−	0.254280i
$725$	1.48489	−	4.52027i	0.0551473	−	0.167879i
$726$	10.0796	−	16.1679i	0.374089	−	0.600048i
$727$	16.5788	−	9.57175i	0.614872	−	0.354997i	−0.159998	−	0.987117i	$-0.551149\pi$
$727$	16.5788	−	9.57175i	0.614872	−	0.354997i	0.774870	+	0.632121i	$0.217815\pi$
$728$			2.29930i			0.0852178i
$729$	18.0634	−	20.0677i	0.669014	−	0.743250i
$730$	7.21879	−	0.746939i	0.267179	−	0.0276455i
$731$	0.414508	−	0.239316i	0.0153311	−	0.00885142i
$732$	11.4374	+	4.62066i	0.422738	+	0.170784i
$733$	14.8406	−	25.7047i	0.548150	−	0.949424i	−0.450251	−	0.892902i	$-0.648665\pi$
$733$	14.8406	−	25.7047i	0.548150	−	0.949424i	0.998401	−	0.0565222i	$-0.0180012\pi$
$734$	−14.2242	+	24.6371i	−0.525025	+	0.909370i
$735$	−6.32643	−	25.5468i	−0.233354	−	0.942307i
$736$	7.07991	−	4.08759i	0.260969	−	0.150670i
$737$	18.7056	+	22.2696i	0.689029	+	0.820312i
$738$	15.5723	−	16.1273i	0.573226	−	0.593655i
$739$		−	40.9671i		−	1.50700i	−0.657448	−	0.753500i	$-0.728364\pi$
$739$		−	40.9671i		−	1.50700i	0.657448	−	0.753500i	$-0.271636\pi$
$740$	−0.831908	−	1.14892i	−0.0305815	−	0.0422352i
$741$	29.6809	−	23.1905i	1.09035	−	0.851924i
$742$	2.70828	+	1.56363i	0.0994241	+	0.0574025i
$743$	−27.7734	−	16.0350i	−1.01891	−	0.588267i	−0.105121	−	0.994459i	$-0.533523\pi$
$743$	−27.7734	−	16.0350i	−1.01891	−	0.588267i	−0.913788	+	0.406192i	$0.866856\pi$
$744$	−10.4128	+	8.13580i	−0.381751	+	0.298273i
$745$	−30.3533	+	21.9782i	−1.11206	+	0.805218i
$746$			27.5594i			1.00902i
$747$	32.2072	+	8.02837i	1.17840	+	0.293743i
$748$	0.0929773	+	0.110693i	0.00339959	+	0.00404732i
$749$	0.578934	−	0.334248i	0.0211538	−	0.0122131i
$750$	−17.4458	+	8.40504i	−0.637030	+	0.306909i
$751$	−0.451775	+	0.782496i	−0.0164855	+	0.0285537i	−0.874150	−	0.485655i	$-0.838581\pi$
$751$	−0.451775	+	0.782496i	−0.0164855	+	0.0285537i	0.857665	+	0.514209i	$0.171914\pi$
$752$	0.238156	−	0.412499i	0.00868466	−	0.0150423i
$753$	14.8975	+	6.01853i	0.542895	+	0.219327i
$754$	−4.18908	+	2.41857i	−0.152557	+	0.0880790i
$755$	−47.6863	+	4.93417i	−1.73548	+	0.179573i
$756$	−2.14710	+	0.956150i	−0.0780891	+	0.0347748i
$757$			44.8155i			1.62885i	0.580270	+	0.814424i	$0.302947\pi$
$757$			44.8155i			1.62885i	−0.580270	+	0.814424i	$0.697053\pi$
$758$	18.5326	−	10.6998i	0.673135	−	0.388635i
$759$	−14.5360	−	44.6566i	−0.527623	−	1.62093i
$760$	8.73280	+	3.90501i	0.316772	+	0.141649i
$761$	9.20997	−	15.9521i	0.333861	−	0.578264i	−0.649404	−	0.760443i	$-0.724982\pi$
$761$	9.20997	−	15.9521i	0.333861	−	0.578264i	0.983265	+	0.182179i	$0.0583150\pi$
$762$	4.08007	+	29.0257i	0.147805	+	1.05149i
$763$	−6.16207	+	3.55767i	−0.223082	+	0.128796i
$764$			22.3119i			0.807217i
$765$	0.271268	−	0.109106i	0.00980770	−	0.00394475i
$766$			35.8180i			1.29416i
$767$	−1.42887	+	0.824960i	−0.0515936	+	0.0297876i
$768$	−1.06639	−	1.36485i	−0.0384801	−	0.0492497i
$769$	−14.5848	−	8.42053i	−0.525941	−	0.303652i	0.213421	−	0.976960i	$-0.431539\pi$
$769$	−14.5848	−	8.42053i	−0.525941	−	0.303652i	−0.739362	+	0.673308i	$0.764873\pi$
$770$	0.921060	+	3.22564i	0.0331927	+	0.116244i
$771$	−22.0306	−	28.1964i	−0.793413	−	1.01547i
$772$	−7.11684	−	12.3267i	−0.256141	−	0.443648i
$773$	−40.5836			−1.45969			−0.729845	−	0.683613i	$-0.760408\pi$
$773$	−40.5836			−1.45969			−0.729845	+	0.683613i	$0.760408\pi$
$774$	9.08214	+	31.6669i	0.326451	+	1.13824i
$775$	37.3382	−	7.81050i	1.34123	−	0.280562i
$776$	5.68074	+	9.83932i	0.203927	+	0.353211i
$777$	0.0691815	+	0.492158i	0.00248187	+	0.0176561i
$778$	−4.99188	+	8.64619i	−0.178968	+	0.309981i
$779$	27.6864	+	15.9848i	0.991969	+	0.572714i
$780$	18.9160	+	5.45663i	0.677303	+	0.195379i
$781$	3.40226	−	9.36233i	0.121743	−	0.335010i
$782$	0.356327			0.0127422
$783$	−4.00047	−	2.90603i	−0.142965	−	0.103853i
$784$	−6.79540			−0.242693
$785$	2.90495	+	4.01193i	0.103682	+	0.143192i
$786$	−19.8840	−	8.03306i	−0.709240	−	0.286530i
$787$	−1.34717	+	2.33337i	−0.0480216	+	0.0831758i	−0.889037	−	0.457835i	$-0.848625\pi$
$787$	−1.34717	+	2.33337i	−0.0480216	+	0.0831758i	0.841015	+	0.541011i	$0.181958\pi$
$788$	3.34855	+	1.93329i	0.119287	+	0.0688704i
$789$	−1.76118	−	12.5290i	−0.0626995	−	0.446046i
$790$	−6.93817	+	5.02377i	−0.246849	+	0.178738i
$791$	3.91228			0.139105
$792$	−8.94046	+	4.36671i	−0.317685	+	0.155164i
$793$			36.2024i			1.28558i
$794$	15.9586	+	27.6412i	0.566351	+	0.980949i
$795$	19.2910	−	18.5699i	0.684180	−	0.658607i
$796$	−2.78231	+	4.81910i	−0.0986163	+	0.170808i
$797$	−8.75854	+	15.1702i	−0.310243	+	0.537357i	−0.978415	−	0.206650i	$-0.933744\pi$
$797$	−8.75854	+	15.1702i	−0.310243	+	0.537357i	0.668172	+	0.744007i	$0.267077\pi$
$798$	−2.06359	−	2.64113i	−0.0730502	−	0.0934949i
$799$	0.0179794	−	0.0103804i	0.000636064	−	0.000367232i
$800$	1.02375	+	4.89407i	0.0361952	+	0.173032i
$801$	−4.11173	+	4.25826i	−0.145281	+	0.150458i
$802$	8.88184			0.313629
$803$	−10.1170	−	3.67652i	−0.357023	−	0.129742i
$804$	−2.11419	−	15.0404i	−0.0745616	−	0.530433i
$805$	7.54837	+	3.37537i	0.266045	+	0.118966i
$806$	−33.5858	−	19.3907i	−1.18301	−	0.683010i
$807$	3.93630	+	1.59025i	0.138564	+	0.0559795i
$808$	−9.10020	+	5.25401i	−0.320144	+	0.184835i
$809$	−53.5346			−1.88218			−0.941089	−	0.338159i	$-0.890196\pi$
$809$	−53.5346			−1.88218			−0.941089	+	0.338159i	$0.890196\pi$
$810$	2.77070	+	19.9330i	0.0973523	+	0.700373i
$811$		−	21.1038i		−	0.741053i	−0.928822	−	0.370527i	$-0.879177\pi$
$811$		−	21.1038i		−	0.741053i	0.928822	−	0.370527i	$-0.120823\pi$
$812$	0.215214	+	0.372762i	0.00755254	+	0.0130814i
$813$	−44.3730	−	17.9265i	−1.55623	−	0.628710i
$814$	0.366392	+	2.07180i	0.0128420	+	0.0726166i
$815$	−1.05680	+	2.36333i	−0.0370181	+	0.0827838i
$816$	−0.0105087	−	0.0747591i	−0.000367878	−	0.00261709i
$817$	−40.6847	+	23.4893i	−1.42338	+	0.821788i
$818$	23.4248			0.819029
$819$	−4.96219	−	4.79143i	−0.173393	−	0.167426i
$820$	1.71980	+	16.6210i	0.0600581	+	0.580431i
$821$	−4.98597	−	8.63596i	−0.174012	−	0.301397i	0.765807	−	0.643070i	$-0.222340\pi$
$821$	−4.98597	−	8.63596i	−0.174012	−	0.301397i	−0.939819	+	0.341673i	$0.889006\pi$
$822$	−6.77896	+	5.29659i	−0.236443	+	0.184740i
$823$	30.5871	+	17.6595i	1.06620	+	0.615571i	0.927141	−	0.374713i	$-0.122259\pi$
$823$	30.5871	+	17.6595i	1.06620	+	0.615571i	0.139060	+	0.990284i	$0.455592\pi$
$824$	−2.55502	+	4.42543i	−0.0890085	+	0.154167i
$825$	28.7227	+	0.0775462i	0.999996	+	0.00269981i
$826$	0.0734084	+	0.127147i	0.00255421	+	0.00442401i
$827$		−	16.5709i		−	0.576228i	−0.957596	−	0.288114i	$-0.906972\pi$
$827$		−	16.5709i		−	0.576228i	0.957596	−	0.288114i	$-0.0930283\pi$
$828$	−5.93202	+	23.7973i	−0.206152	+	0.827014i
$829$	−23.3717			−0.811731			−0.405866	−	0.913933i	$-0.633030\pi$
$829$	−23.3717			−0.811731			−0.405866	+	0.913933i	$0.633030\pi$
$830$	−20.0389	+	14.5097i	−0.695560	+	0.503639i
$831$	53.4219	−	7.50938i	1.85319	−	0.260498i
$832$	2.54162	−	4.40222i	0.0881150	−	0.152620i
$833$	−0.256506	−	0.148094i	−0.00888741	−	0.00513115i
$834$	7.30775	−	18.0887i	0.253047	−	0.626360i
$835$	13.9382	+	19.2497i	0.482353	+	0.666162i
$836$	−9.12591	−	10.8647i	−0.315626	−	0.375763i
$837$	4.14072	−	39.4260i	0.143124	−	1.36276i
$838$	4.85997			0.167885
$839$	25.4155	−	14.6736i	0.877440	−	0.506590i	0.00762677	−	0.999971i	$-0.497572\pi$
$839$	25.4155	−	14.6736i	0.877440	−	0.506590i	0.869814	+	0.493380i	$0.164239\pi$
$840$	0.485554	−	1.68323i	0.0167532	−	0.0580769i
$841$	14.0472	−	24.3305i	0.484388	−	0.838984i
$842$	−25.6569	−	14.8130i	−0.884195	−	0.510490i
$843$	31.2954	−	4.39911i	1.07787	−	0.151513i
$844$	−8.78713	+	5.07325i	−0.302465	+	0.174628i
$845$	2.95487	+	28.5574i	0.101651	+	0.982403i
$846$	0.393940	+	1.37356i	0.0135439	+	0.0472240i
$847$	0.859064	−	4.90090i	0.0295178	−	0.168397i
$848$	−3.45683	−	5.98741i	−0.118708	−	0.205609i
$849$	−11.1205	−	14.2329i	−0.381656	−	0.488471i
$850$	−0.0680140	+	0.207048i	−0.00233286	+	0.00710167i
$851$	4.49124	+	2.59302i	0.153958	+	0.0888875i
$852$	−4.09926	+	3.20287i	−0.140438	+	0.109728i
$853$	−4.56943	−	7.91448i	−0.156454	−	0.270987i	0.777133	−	0.629336i	$-0.216673\pi$
$853$	−4.56943	−	7.91448i	−0.156454	−	0.270987i	−0.933588	+	0.358349i	$0.883340\pi$
$854$	3.22144			0.110235
$855$	−26.6255	+	10.7090i	−0.910571	+	0.366240i
$856$	−1.47790			−0.0505134
$857$	6.33846	−	3.65951i	0.216518	−	0.125007i	−0.387819	−	0.921735i	$-0.626771\pi$
$857$	6.33846	−	3.65951i	0.216518	−	0.125007i	0.604337	+	0.796729i	$0.293438\pi$
$858$	−21.7110	−	19.5278i	−0.741200	−	0.666668i
$859$	16.5101	−	28.5964i	0.563318	−	0.975696i	−0.433886	−	0.900968i	$-0.642858\pi$
$859$	16.5101	−	28.5964i	0.563318	−	0.975696i	0.997204	−	0.0747278i	$-0.0238088\pi$
$860$	−22.4157	−	10.0235i	−0.764368	−	0.341799i
$861$	2.19304	−	5.42838i	0.0747387	−	0.184999i
$862$	−19.2818	+	11.1324i	−0.656741	+	0.379169i
$863$	−28.8079			−0.980633			−0.490317	−	0.871544i	$-0.663119\pi$
$863$	−28.8079			−0.980633			−0.490317	+	0.871544i	$0.663119\pi$
$864$	5.16773	+	0.542741i	0.175810	+	0.0184644i
$865$	−5.81068	+	0.601240i	−0.197569	+	0.0204428i
$866$	−9.84761	−	17.0566i	−0.334635	−	0.579605i
$867$	−11.0283	+	27.2980i	−0.374541	+	0.927090i
$868$	−1.72547	+	2.98860i	−0.0585663	+	0.101440i
$869$	12.5113	−	2.21259i	0.424417	−	0.0750569i
$870$	3.57740	−	0.885911i	0.121285	−	0.0300352i
$871$	38.6028	−	22.2873i	1.30801	−	0.755177i
$872$	15.7305			0.532700
$873$	−33.0724	−	8.24404i	−1.11933	−	0.279018i
$874$	−34.9742			−1.18302
$875$	−3.40209	+	3.74179i	−0.115012	+	0.126495i
$876$	3.46106	+	4.42971i	0.116938	+	0.149666i
$877$	−2.59338	+	4.49186i	−0.0875722	+	0.151679i	−0.906484	−	0.422239i	$-0.861244\pi$
$877$	−2.59338	+	4.49186i	−0.0875722	+	0.151679i	0.818912	+	0.573919i	$0.194578\pi$
$878$	−11.5886	+	20.0721i	−0.391098	+	0.677401i
$879$	−32.8196	+	25.6429i	−1.10698	+	0.864912i
$880$	1.80213	−	7.19391i	0.0607499	−	0.242507i
$881$			12.8415i			0.432642i	0.976322	+	0.216321i	$0.0694058\pi$
$881$			12.8415i			0.432642i	−0.976322	+	0.216321i	$0.930594\pi$
$882$	14.1607	−	14.6653i	0.476815	−	0.493808i
$883$			8.11713i			0.273163i	0.990629	+	0.136582i	$0.0436116\pi$
$883$			8.11713i			0.273163i	−0.990629	+	0.136582i	$0.956388\pi$
$884$	0.191878	−	0.110781i	0.00645354	−	0.00372595i
$885$	1.22023	−	0.302180i	0.0410177	−	0.0101577i
$886$	3.08141	+	1.77905i	0.103522	+	0.0597684i
$887$	−29.8155	−	17.2140i	−1.00111	−	0.577989i	−0.0925304	−	0.995710i	$-0.529496\pi$
$887$	−29.8155	−	17.2140i	−1.00111	−	0.577989i	−0.908575	+	0.417721i	$0.862829\pi$
$888$	0.411573	−	1.01876i	0.0138115	−	0.0341872i
$889$	3.82732	+	6.62912i	0.128364	+	0.222334i
$890$	−0.454097	−	4.38862i	−0.0152214	−	0.147107i
$891$	9.20676	−	28.3943i	0.308438	−	0.951244i
$892$		−	13.9646i		−	0.467568i
$893$	−1.76471	+	1.01886i	−0.0590538	+	0.0340947i
$894$	−26.9145	−	10.8733i	−0.900155	−	0.363659i
$895$	−11.7870	+	26.3594i	−0.393997	+	0.881099i
$896$	−0.391728	−	0.226164i	−0.0130867	−	0.00755563i
$897$	−71.2771	+	10.0192i	−2.37987	+	0.334533i
$898$	8.97348	+	15.5425i	0.299449	+	0.518661i
$899$	−7.25988			−0.242131
$900$	−12.6954	−	7.98918i	−0.423180	−	0.266306i
$901$		−	0.301343i		−	0.0100392i
$902$	8.46507	−	23.2941i	0.281856	−	0.775610i
$903$	5.29689	+	6.77935i	0.176270	+	0.225603i
$904$	−7.49042	−	4.32460i	−0.249128	−	0.143834i
$905$	−16.1270	−	7.21144i	−0.536080	−	0.239716i
$906$	−22.8632	−	29.2620i	−0.759581	−	0.972166i
$907$	−29.9795	+	17.3087i	−0.995453	+	0.574725i	−0.906900	−	0.421347i	$-0.861558\pi$
$907$	−29.9795	+	17.3087i	−0.995453	+	0.574725i	−0.0885529	+	0.996071i	$0.528224\pi$
$908$		−	23.0871i		−	0.766172i
$909$	7.62476	−	30.5880i	0.252897	−	1.01454i
$910$	5.11409	−	0.529163i	0.169530	−	0.0175416i
$911$	−18.3466	+	10.5924i	−0.607850	+	0.350943i	−0.772124	−	0.635472i	$-0.780805\pi$
$911$	−18.3466	+	10.5924i	−0.607850	+	0.350943i	0.164273	+	0.986415i	$0.447472\pi$
$912$	1.03145	+	7.33775i	0.0341547	+	0.242977i
$913$	36.1353	−	6.39042i	1.19590	−	0.211492i
$914$	−2.79112	−	1.61145i	−0.0923220	−	0.0533021i
$915$	7.64503	−	26.5024i	0.252737	−	0.876141i
$916$	−8.77718	−	15.2025i	−0.290006	−	0.502306i
$917$	−5.60051			−0.184945
$918$	0.183238	+	0.133109i	0.00604777	+	0.00439324i
$919$			20.8953i			0.689272i	0.938736	+	0.344636i	$0.111998\pi$
$919$			20.8953i			0.689272i	−0.938736	+	0.344636i	$0.888002\pi$
$920$	−10.7210	−	14.8064i	−0.353459	−	0.488151i
$921$	18.2548	−	45.1857i	0.601517	−	1.48892i
$922$	−14.4012	−	8.31451i	−0.474277	−	0.273824i
$923$	−13.2219	−	7.63367i	−0.435204	−	0.251265i
$924$	−1.73767	+	1.93193i	−0.0571650	+	0.0635559i
$925$	−2.36397	+	2.11474i	−0.0777267	+	0.0695321i
$926$	14.6350			0.480937
$927$	−4.22633	−	14.7361i	−0.138811	−	0.483996i
$928$		−	0.951583i		−	0.0312372i
$929$	27.5138	−	15.8851i	0.902697	−	0.521173i	0.0246231	−	0.999697i	$-0.492161\pi$
$929$	27.5138	−	15.8851i	0.902697	−	0.521173i	0.878074	+	0.478524i	$0.158828\pi$
$930$	20.4920	+	21.2877i	0.671959	+	0.698050i
$931$	25.1766	+	14.5357i	0.825129	+	0.476389i
$932$	1.49583	+	0.863616i	0.0489974	+	0.0282887i
$933$	−37.3907	+	29.2144i	−1.22412	+	0.956437i
$934$	−9.24276	+	5.33631i	−0.302432	+	0.174609i
$935$	0.224804	−	0.232274i	0.00735187	−	0.00759618i
$936$	4.20417	+	14.6588i	0.137417	+	0.479137i
$937$	33.6507			1.09932			0.549661	−	0.835388i	$-0.314757\pi$
$937$	33.6507			1.09932			0.549661	+	0.835388i	$0.314757\pi$
$938$	−1.98322	−	3.43504i	−0.0647544	−	0.112158i
$939$	8.24215	+	58.6348i	0.268972	+	1.91348i
$940$	−0.972286	−	0.434773i	−0.0317125	−	0.0141807i
$941$	3.26725	−	5.65905i	0.106509	−	0.184480i	−0.807845	−	0.589396i	$-0.799366\pi$
$941$	3.26725	−	5.65905i	0.106509	−	0.184480i	0.914354	+	0.404916i	$0.132699\pi$
$942$	−1.43717	+	3.55740i	−0.0468257	+	0.115906i
$943$	−30.5458	−	52.9069i	−0.994709	−	1.72289i
$944$		−	0.324580i		−	0.0105642i
$945$	2.62080	+	4.55551i	0.0852545	+	0.148191i
$946$	23.4247	+	27.8879i	0.761603	+	0.906715i
$947$	−12.1710	−	21.0807i	−0.395503	−	0.685032i	0.597662	−	0.801748i	$-0.296097\pi$
$947$	−12.1710	−	21.0807i	−0.395503	−	0.685032i	−0.993165	+	0.116716i	$0.962763\pi$
$948$	−6.15212	−	2.48543i	−0.199812	−	0.0807230i
$949$	−8.24904	+	14.2877i	−0.267775	+	0.463800i
$950$	6.67571	−	20.3221i	0.216589	−	0.659337i
$951$	21.7312	−	3.05471i	0.704684	−	0.0990556i
$952$	−0.00985772	−	0.0170741i	−0.000319491	−	0.000553374i
$953$			8.34837i			0.270430i	0.990816	+	0.135215i	$0.0431725\pi$
$953$			8.34837i			0.270430i	−0.990816	+	0.135215i	$0.956827\pi$
$954$	20.1252	+	5.01665i	0.651576	+	0.162420i
$955$	49.6260	−	5.13488i	1.60586	−	0.166161i
$956$	9.49102	+	16.4389i	0.306961	+	0.531673i
$957$	−5.34757	−	1.13370i	−0.172863	−	0.0366472i
$958$	−32.7122	−	18.8864i	−1.05688	−	0.610193i
$959$	−1.12332	+	1.94565i	−0.0362739	+	0.0628282i
$960$	−2.79026	+	2.68597i	−0.0900553	+	0.0866893i
$961$	−13.6029	−	23.5609i	−0.438803	−	0.760029i
$962$	3.22463			0.103966
$963$	3.07973	−	3.18949i	0.0992430	−	0.102780i
$964$			13.9265i			0.448543i
$965$	−25.7791	+	18.6661i	−0.829860	+	0.600883i
$966$	0.891554	+	6.34254i	0.0286853	+	0.204068i
$967$	13.4811	−	23.3499i	0.433522	−	0.750881i	−0.563652	−	0.826012i	$-0.690604\pi$
$967$	13.4811	−	23.3499i	0.433522	−	0.750881i	0.997174	+	0.0751309i	$0.0239375\pi$
$968$	−7.06216	+	8.43362i	−0.226986	+	0.271067i
$969$	−0.120979	+	0.299457i	−0.00388642	+	0.00961994i
$970$	20.5772	−	14.8995i	0.660694	−	0.478394i
$971$			0.0469022i			0.00150516i	1.00000		0.000752582i	$0.000239554\pi$
$971$			0.0469022i			0.00150516i	−1.00000		0.000752582i	$0.999760\pi$
$972$	−11.9401	+	10.0216i	−0.382980	+	0.321444i
$973$		−	5.09484i		−	0.163333i
$974$	−13.3112	−	23.0557i	−0.426518	−	0.738751i
$975$	7.78325	−	43.3287i	0.249264	−	1.38763i
$976$	−6.16775	−	3.56095i	−0.197425	−	0.113983i
$977$	−3.14616	+	5.44931i	−0.100655	+	0.174339i	−0.911955	−	0.410291i	$-0.865427\pi$
$977$	−3.14616	+	5.44931i	−0.100655	+	0.174339i	0.811300	+	0.584630i	$0.198760\pi$
$978$	−1.98579	+	0.279138i	−0.0634987	+	0.00892585i
$979$	−2.23512	+	6.15059i	−0.0714348	+	0.196574i
$980$	1.56390	+	15.1143i	0.0499569	+	0.482808i
$981$	−32.7801	+	33.9483i	−1.04659	+	1.08389i
$982$			3.95082i			0.126076i
$983$	−6.29553	−	10.9042i	−0.200796	−	0.347789i	0.747989	−	0.663711i	$-0.231020\pi$
$983$	−6.29553	−	10.9042i	−0.200796	−	0.347789i	−0.948785	+	0.315922i	$0.897686\pi$
$984$	−10.1993	+	7.96897i	−0.325141	+	0.254041i
$985$	3.52936	−	7.89275i	0.112455	−	0.251484i
$986$	0.0207381	−	0.0359194i	0.000660435	−	0.00114391i
$987$	0.229754	+	0.294056i	0.00731315	+	0.00935991i
$988$	−18.8332	+	10.8733i	−0.599163	+	0.345927i
$989$	89.7732			2.85462
$990$	11.7700	+	18.8803i	0.374075	+	0.600057i
$991$	−23.5442			−0.747905			−0.373952	−	0.927448i	$-0.621998\pi$
$991$	−23.5442			−0.747905			−0.373952	+	0.927448i	$0.621998\pi$
$992$	6.60714	−	3.81464i	0.209777	−	0.121115i
$993$	−29.5584	+	4.15495i	−0.938008	+	0.131853i
$994$	−0.679276	+	1.17654i	−0.0215453	+	0.0373176i
$995$	11.3589	+	5.07932i	0.360102	+	0.161025i
$996$	−17.7686	−	7.17844i	−0.563020	−	0.227458i
$997$	2.12890	+	3.68736i	0.0674229	+	0.116780i	0.897766	−	0.440472i	$-0.145189\pi$
$997$	2.12890	+	3.68736i	0.0674229	+	0.116780i	−0.830343	+	0.557252i	$0.811856\pi$
$998$		−	35.1642i		−	1.11310i
$999$	1.34094	+	3.01117i	0.0424256	+	0.0952693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.o.a.329.15	✓	144
5.4	even	2	inner	990.2.o.a.329.58	yes	144
9.2	odd	6	inner	990.2.o.a.659.22	yes	144
11.10	odd	2	inner	990.2.o.a.329.51	yes	144
45.29	odd	6	inner	990.2.o.a.659.51	yes	144
55.54	odd	2	inner	990.2.o.a.329.22	yes	144
99.65	even	6	inner	990.2.o.a.659.58	yes	144
495.164	even	6	inner	990.2.o.a.659.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.o.a.329.15	✓	144	1.1	even	1	trivial
990.2.o.a.329.22	yes	144	55.54	odd	2	inner
990.2.o.a.329.51	yes	144	11.10	odd	2	inner
990.2.o.a.329.58	yes	144	5.4	even	2	inner
990.2.o.a.659.15	yes	144	495.164	even	6	inner
990.2.o.a.659.22	yes	144	9.2	odd	6	inner
990.2.o.a.659.51	yes	144	45.29	odd	6	inner
990.2.o.a.659.58	yes	144	99.65	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.648796 + 1.60595i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.04128 - 0.912789i) q^{5} +(-0.241100 - 1.71519i) q^{6} +(-0.226164 - 0.391728i) q^{7} +1.00000i q^{8} +(-2.15813 - 2.08386i) q^{9} +(2.22419 - 0.230141i) q^{10} +(-3.11718 - 1.13278i) q^{11} +(1.06639 + 1.36485i) q^{12} +(-2.54162 + 4.40222i) q^{13} +(0.391728 + 0.226164i) q^{14} +(2.79026 - 2.68597i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.0435865i q^{17} +(2.91093 + 0.725614i) q^{18} +4.27810i q^{19} +(-1.81114 + 1.31140i) q^{20} +(0.775829 - 0.109056i) q^{21} +(3.26595 - 0.577573i) q^{22} +(4.08759 - 7.07991i) q^{23} +(-1.60595 - 0.648796i) q^{24} +(3.33363 + 3.72651i) q^{25} -5.08325i q^{26} +(4.74676 - 2.11384i) q^{27} -0.452329 q^{28} +(-0.475791 - 0.824095i) q^{29} +(-1.07345 + 3.72125i) q^{30} +(3.81464 - 6.60714i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.84160 - 4.27108i) q^{33} +(0.0217933 + 0.0377470i) q^{34} +(0.104099 + 1.00607i) q^{35} +(-2.88374 + 0.827063i) q^{36} +0.634364i q^{37} +(-2.13905 - 3.70495i) q^{38} +(-5.42074 - 6.93786i) q^{39} +(0.912789 - 2.04128i) q^{40} +(3.73641 - 6.47166i) q^{41} +(-0.617360 + 0.482360i) q^{42} +(5.49060 + 9.51000i) q^{43} +(-2.53961 + 2.13317i) q^{44} +(2.50321 + 6.22366i) q^{45} +8.17517i q^{46} +(0.238156 + 0.412499i) q^{47} +(1.71519 - 0.241100i) q^{48} +(3.39770 - 5.88499i) q^{49} +(-4.75027 - 1.56044i) q^{50} +(0.0699976 + 0.0282787i) q^{51} +(2.54162 + 4.40222i) q^{52} +6.91367 q^{53} +(-3.05389 + 4.20401i) q^{54} +(5.32904 + 5.15765i) q^{55} +(0.391728 - 0.226164i) q^{56} +(-6.87040 - 2.77561i) q^{57} +(0.824095 + 0.475791i) q^{58} +(0.281094 + 0.162290i) q^{59} +(-0.930987 - 3.75942i) q^{60} +(6.16775 - 3.56095i) q^{61} +7.62927i q^{62} +(-0.328216 + 1.31670i) q^{63} -1.00000 q^{64} +(9.20646 - 6.66620i) q^{65} +(-1.19138 + 5.61966i) q^{66} +(-7.59412 - 4.38447i) q^{67} +(-0.0377470 - 0.0217933i) q^{68} +(8.71794 + 11.1579i) q^{69} +(-0.593186 - 0.819230i) q^{70} +3.00346i q^{71} +(2.08386 - 2.15813i) q^{72} +3.24558 q^{73} +(-0.317182 - 0.549376i) q^{74} +(-8.14743 + 2.93589i) q^{75} +(3.70495 + 2.13905i) q^{76} +(0.261253 + 1.47728i) q^{77} +(8.16343 + 3.29799i) q^{78} +(-3.31760 + 1.91542i) q^{79} +(0.230141 + 2.22419i) q^{80} +(0.315035 + 8.99448i) q^{81} +7.47283i q^{82} +(-9.58193 + 5.53213i) q^{83} +(0.293469 - 0.726416i) q^{84} +(-0.0397853 + 0.0889722i) q^{85} +(-9.51000 - 5.49060i) q^{86} +(1.63214 - 0.229426i) q^{87} +(1.13278 - 3.11718i) q^{88} -1.97313i q^{89} +(-5.27968 - 4.13824i) q^{90} +2.29930 q^{91} +(-4.08759 - 7.07991i) q^{92} +(8.13580 + 10.4128i) q^{93} +(-0.412499 - 0.238156i) q^{94} +(3.90501 - 8.73280i) q^{95} +(-1.36485 + 1.06639i) q^{96} +(9.83932 - 5.68074i) q^{97} +6.79540i q^{98} +(4.36671 + 8.94046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Introduction

L-functions

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