LMFDB - Embedded newform 966.2.k.b.229.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (of order $6$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.2
Character	$\chi$	$=$	966.229
Dual form			966.2.k.b.367.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.92123 + 3.32767i) q^{5} +1.00000i q^{6} +(0.661545 - 2.56171i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.92123 + 3.32767i) q^{5} +1.00000i q^{6} +(0.661545 - 2.56171i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.92123 + 3.32767i) q^{10} +(2.74035 - 1.58214i) q^{11} +(0.866025 + 0.500000i) q^{12} -3.31472i q^{13} +(-1.88773 - 1.85377i) q^{14} -3.84247i q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.62917 + 4.55386i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-4.13142 + 7.15583i) q^{19} +3.84247 q^{20} +(0.707941 + 2.54928i) q^{21} -3.16428i q^{22} +(-1.41546 + 4.58219i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.88227 - 8.45634i) q^{25} +(-2.87063 - 1.65736i) q^{26} +1.00000i q^{27} +(-2.54928 + 0.707941i) q^{28} +7.98273 q^{29} +(-3.32767 - 1.92123i) q^{30} +(-5.08400 + 2.93525i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.58214 + 2.74035i) q^{33} +5.25835 q^{34} +(7.25355 + 7.12305i) q^{35} -1.00000 q^{36} +(9.42232 + 5.43998i) q^{37} +(4.13142 + 7.15583i) q^{38} +(1.65736 + 2.87063i) q^{39} +(1.92123 - 3.32767i) q^{40} +10.0431i q^{41} +(2.56171 + 0.661545i) q^{42} +7.75286i q^{43} +(-2.74035 - 1.58214i) q^{44} +(1.92123 + 3.32767i) q^{45} +(3.26057 + 3.51692i) q^{46} +(-2.67069 - 1.54192i) q^{47} -1.00000i q^{48} +(-6.12472 - 3.38937i) q^{49} -9.76454 q^{50} +(-4.55386 - 2.62917i) q^{51} +(-2.87063 + 1.65736i) q^{52} +(-1.30769 + 0.754997i) q^{53} +(0.866025 + 0.500000i) q^{54} +12.1587i q^{55} +(-0.661545 + 2.56171i) q^{56} -8.26284i q^{57} +(3.99136 - 6.91324i) q^{58} +(2.61824 - 1.51164i) q^{59} +(-3.32767 + 1.92123i) q^{60} +(-2.02565 + 3.50853i) q^{61} +5.87050i q^{62} +(-1.88773 - 1.85377i) q^{63} +1.00000 q^{64} +(11.0303 + 6.36835i) q^{65} +(1.58214 + 2.74035i) q^{66} +(-1.02131 + 0.589651i) q^{67} +(2.62917 - 4.55386i) q^{68} +(-1.06527 - 4.67602i) q^{69} +(9.79551 - 2.72024i) q^{70} -7.16483 q^{71} +(-0.500000 + 0.866025i) q^{72} +(11.7881 - 6.80584i) q^{73} +(9.42232 - 5.43998i) q^{74} +(8.45634 + 4.88227i) q^{75} +8.26284 q^{76} +(-2.24013 - 8.06664i) q^{77} +3.31472 q^{78} +(0.906949 + 0.523627i) q^{79} +(-1.92123 - 3.32767i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.69756 + 5.02154i) q^{82} +1.08744 q^{83} +(1.85377 - 1.88773i) q^{84} -20.2050 q^{85} +(6.71417 + 3.87643i) q^{86} +(-6.91324 + 3.99136i) q^{87} +(-2.74035 + 1.58214i) q^{88} +(7.52955 - 13.0416i) q^{89} +3.84247 q^{90} +(-8.49135 - 2.19283i) q^{91} +(4.67602 - 1.06527i) q^{92} +(2.93525 - 5.08400i) q^{93} +(-2.67069 + 1.54192i) q^{94} +(-15.8748 - 27.4960i) q^{95} +(-0.866025 - 0.500000i) q^{96} -5.59968 q^{97} +(-5.99764 + 3.60948i) q^{98} -3.16428i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.92123	+	3.32767i	−0.859201	+	1.48818i	0.0134902	+	0.999909i	$0.495706\pi$
$5$	−1.92123	+	3.32767i	−0.859201	+	1.48818i	−0.872692	+	0.488272i	$0.837628\pi$
$6$			1.00000i			0.408248i
$7$	0.661545	−	2.56171i	0.250040	−	0.968235i
$7$	0.661545	−	2.56171i	0.250040	−	0.968235i
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.92123	+	3.32767i	0.607547	+	1.05230i
$11$	2.74035	−	1.58214i	0.826247	−	0.477034i	−0.0263192	−	0.999654i	$-0.508379\pi$
$11$	2.74035	−	1.58214i	0.826247	−	0.477034i	0.852566	+	0.522620i	$0.175045\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$		−	3.31472i		−	0.919338i	−0.888090	−	0.459669i	$-0.847968\pi$
$13$		−	3.31472i		−	0.919338i	0.888090	−	0.459669i	$-0.152032\pi$
$14$	−1.88773	−	1.85377i	−0.504518	−	0.495441i
$15$		−	3.84247i		−	0.992120i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.62917	+	4.55386i	0.637668	+	1.10447i	0.985943	+	0.167081i	$0.0534343\pi$
$17$	2.62917	+	4.55386i	0.637668	+	1.10447i	−0.348275	+	0.937392i	$0.613232\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−4.13142	+	7.15583i	−0.947813	+	1.64166i	−0.197794	+	0.980244i	$0.563378\pi$
$19$	−4.13142	+	7.15583i	−0.947813	+	1.64166i	−0.750019	+	0.661416i	$0.769956\pi$
$20$	3.84247			0.859201
$21$	0.707941	+	2.54928i	0.154485	+	0.556298i
$22$		−	3.16428i		−	0.674628i
$23$	−1.41546	+	4.58219i	−0.295143	+	0.955453i
$23$	−1.41546	+	4.58219i	−0.295143	+	0.955453i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−4.88227	−	8.45634i	−0.976454	−	1.69127i
$26$	−2.87063	−	1.65736i	−0.562977	−	0.325035i
$27$			1.00000i			0.192450i
$28$	−2.54928	+	0.707941i	−0.481768	+	0.133788i
$29$	7.98273			1.48235			0.741177	−	0.671309i	$-0.234268\pi$
$29$	7.98273			1.48235			0.741177	+	0.671309i	$0.234268\pi$
$30$	−3.32767	−	1.92123i	−0.607547	−	0.350768i
$31$	−5.08400	+	2.93525i	−0.913113	+	0.527186i	−0.881432	−	0.472312i	$-0.843420\pi$
$31$	−5.08400	+	2.93525i	−0.913113	+	0.527186i	−0.0316819	+	0.999498i	$0.510086\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.58214	+	2.74035i	−0.275416	+	0.477034i
$34$	5.25835			0.901799
$35$	7.25355	+	7.12305i	1.22607	+	1.20401i
$36$	−1.00000			−0.166667
$37$	9.42232	+	5.43998i	1.54902	+	0.894327i	0.998217	+	0.0596913i	$0.0190116\pi$
$37$	9.42232	+	5.43998i	1.54902	+	0.894327i	0.550803	+	0.834636i	$0.314322\pi$
$38$	4.13142	+	7.15583i	0.670205	+	1.16083i
$39$	1.65736	+	2.87063i	0.265390	+	0.459669i
$40$	1.92123	−	3.32767i	0.303774	−	0.526151i
$41$			10.0431i			1.56847i	0.620466	+	0.784233i	$0.286943\pi$
$41$			10.0431i			1.56847i	−0.620466	+	0.784233i	$0.713057\pi$
$42$	2.56171	+	0.661545i	0.395280	+	0.102079i
$43$			7.75286i			1.18230i	0.806562	+	0.591150i	$0.201326\pi$
$43$			7.75286i			1.18230i	−0.806562	+	0.591150i	$0.798674\pi$
$44$	−2.74035	−	1.58214i	−0.413123	−	0.238517i
$45$	1.92123	+	3.32767i	0.286400	+	0.496060i
$46$	3.26057	+	3.51692i	0.480744	+	0.518541i
$47$	−2.67069	−	1.54192i	−0.389560	−	0.224913i	0.292409	−	0.956293i	$-0.405543\pi$
$47$	−2.67069	−	1.54192i	−0.389560	−	0.224913i	−0.681969	+	0.731381i	$0.738876\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−6.12472	−	3.38937i	−0.874960	−	0.484196i
$50$	−9.76454			−1.38092
$51$	−4.55386	−	2.62917i	−0.637668	−	0.368158i
$52$	−2.87063	+	1.65736i	−0.398085	+	0.229834i
$53$	−1.30769	+	0.754997i	−0.179626	+	0.103707i	−0.587117	−	0.809502i	$-0.699737\pi$
$53$	−1.30769	+	0.754997i	−0.179626	+	0.103707i	0.407491	+	0.913209i	$0.366404\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$			12.1587i			1.63947i
$56$	−0.661545	+	2.56171i	−0.0884026	+	0.342323i
$57$		−	8.26284i		−	1.09444i
$58$	3.99136	−	6.91324i	0.524092	−	0.907753i
$59$	2.61824	−	1.51164i	0.340866	−	0.196799i	−0.319789	−	0.947489i	$-0.603612\pi$
$59$	2.61824	−	1.51164i	0.340866	−	0.196799i	0.660655	+	0.750690i	$0.270279\pi$
$60$	−3.32767	+	1.92123i	−0.429601	+	0.248030i
$61$	−2.02565	+	3.50853i	−0.259358	+	0.449221i	−0.966070	−	0.258280i	$-0.916844\pi$
$61$	−2.02565	+	3.50853i	−0.259358	+	0.449221i	0.706712	+	0.707501i	$0.250178\pi$
$62$			5.87050i			0.745554i
$63$	−1.88773	−	1.85377i	−0.237832	−	0.233553i
$64$	1.00000			0.125000
$65$	11.0303	+	6.36835i	1.36814	+	0.789896i
$66$	1.58214	+	2.74035i	0.194748	+	0.337314i
$67$	−1.02131	+	0.589651i	−0.124772	+	0.0720374i	−0.561087	−	0.827757i	$-0.689617\pi$
$67$	−1.02131	+	0.589651i	−0.124772	+	0.0720374i	0.436315	+	0.899794i	$0.356283\pi$
$68$	2.62917	−	4.55386i	0.318834	−	0.552237i
$69$	−1.06527	−	4.67602i	−0.128244	−	0.562927i
$70$	9.79551	−	2.72024i	1.17079	−	0.325131i
$71$	−7.16483			−0.850309			−0.425155	−	0.905121i	$-0.639780\pi$
$71$	−7.16483			−0.850309			−0.425155	+	0.905121i	$0.639780\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	11.7881	−	6.80584i	1.37969	−	0.796563i	0.387567	−	0.921842i	$-0.373316\pi$
$73$	11.7881	−	6.80584i	1.37969	−	0.796563i	0.992122	+	0.125278i	$0.0399824\pi$
$74$	9.42232	−	5.43998i	1.09532	−	0.632385i
$75$	8.45634	+	4.88227i	0.976454	+	0.563756i
$76$	8.26284			0.947813
$77$	−2.24013	−	8.06664i	−0.255286	−	0.919279i
$78$	3.31472			0.375318
$79$	0.906949	+	0.523627i	0.102040	+	0.0589127i	0.550151	−	0.835065i	$-0.314570\pi$
$79$	0.906949	+	0.523627i	0.102040	+	0.0589127i	−0.448112	+	0.893978i	$0.647903\pi$
$80$	−1.92123	−	3.32767i	−0.214800	−	0.372045i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	8.69756	+	5.02154i	0.960485	+	0.554536i
$83$	1.08744			0.119362			0.0596811	−	0.998217i	$-0.480992\pi$
$83$	1.08744			0.119362			0.0596811	+	0.998217i	$0.480992\pi$
$84$	1.85377	−	1.88773i	0.202263	−	0.205969i
$85$	−20.2050			−2.19154
$86$	6.71417	+	3.87643i	0.724008	+	0.418006i
$87$	−6.91324	+	3.99136i	−0.741177	+	0.427919i
$88$	−2.74035	+	1.58214i	−0.292122	+	0.168657i
$89$	7.52955	−	13.0416i	0.798130	−	1.38240i	−0.122702	−	0.992444i	$-0.539156\pi$
$89$	7.52955	−	13.0416i	0.798130	−	1.38240i	0.920832	−	0.389959i	$-0.127511\pi$
$90$	3.84247			0.405031
$91$	−8.49135	−	2.19283i	−0.890135	−	0.229872i
$92$	4.67602	−	1.06527i	0.487509	−	0.111062i
$93$	2.93525	−	5.08400i	0.304371	−	0.527186i
$94$	−2.67069	+	1.54192i	−0.275461	+	0.159037i
$95$	−15.8748	−	27.4960i	−1.62872	−	2.82103i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	−5.59968			−0.568561			−0.284281	−	0.958741i	$-0.591755\pi$
$97$	−5.59968			−0.568561			−0.284281	+	0.958741i	$0.591755\pi$
$98$	−5.99764	+	3.60948i	−0.605853	+	0.364612i
$99$		−	3.16428i		−	0.318022i
$100$	−4.88227	+	8.45634i	−0.488227	+	0.845634i
$101$	4.70595	−	2.71698i	0.468260	−	0.270350i	−0.247251	−	0.968951i	$-0.579527\pi$
$101$	4.70595	−	2.71698i	0.468260	−	0.270350i	0.715511	+	0.698602i	$0.246194\pi$
$102$	−4.55386	+	2.62917i	−0.450900	+	0.260327i
$103$	−3.82669	+	6.62802i	−0.377055	+	0.653078i	−0.990632	−	0.136556i	$-0.956397\pi$
$103$	−3.82669	+	6.62802i	−0.377055	+	0.653078i	0.613577	+	0.789635i	$0.289730\pi$
$104$			3.31472i			0.325035i
$105$	−9.84328	−	2.54196i	−0.960606	−	0.248070i
$106$			1.50999i			0.146664i
$107$	2.40173	+	1.38664i	0.232184	+	0.134052i	0.611579	−	0.791183i	$-0.290535\pi$
$107$	2.40173	+	1.38664i	0.232184	+	0.134052i	−0.379395	+	0.925235i	$0.623868\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	1.07798	−	0.622372i	0.103252	−	0.0596124i	−0.447485	−	0.894291i	$-0.647680\pi$
$109$	1.07798	−	0.622372i	0.103252	−	0.0596124i	0.550737	+	0.834679i	$0.314347\pi$
$110$	10.5297	+	6.07933i	1.00397	+	0.579641i
$111$	−10.8800			−1.03268
$112$	1.88773	+	1.85377i	0.178374	+	0.175165i
$113$			1.65561i			0.155747i	0.996963	+	0.0778734i	$0.0248130\pi$
$113$			1.65561i			0.155747i	−0.996963	+	0.0778734i	$0.975187\pi$
$114$	−7.15583	−	4.13142i	−0.670205	−	0.386943i
$115$	−12.5286	−	13.5136i	−1.16830	−	1.26015i
$116$	−3.99136	−	6.91324i	−0.370589	−	0.641879i
$117$	−2.87063	−	1.65736i	−0.265390	−	0.153223i
$118$		−	3.02328i		−	0.278316i
$119$	13.4050	−	3.72260i	1.22883	−	0.341250i
$120$			3.84247i			0.350768i
$121$	−0.493654	+	0.855034i	−0.0448776	+	0.0777304i
$122$	2.02565	+	3.50853i	0.183394	+	0.317647i
$123$	−5.02154	−	8.69756i	−0.452777	−	0.784233i
$124$	5.08400	+	2.93525i	0.456557	+	0.263593i
$125$	18.3076			1.63748
$126$	−2.54928	+	0.707941i	−0.227108	+	0.0630684i
$127$	10.7509			0.953986			0.476993	−	0.878907i	$-0.341727\pi$
$127$	10.7509			0.953986			0.476993	+	0.878907i	$0.341727\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.87643	−	6.71417i	−0.341301	−	0.591150i
$130$	11.0303	−	6.36835i	0.967422	−	0.558541i
$131$	13.5437	+	7.81945i	1.18332	+	0.683189i	0.956780	−	0.290814i	$-0.0939260\pi$
$131$	13.5437	+	7.81945i	1.18332	+	0.683189i	0.226538	+	0.974002i	$0.427259\pi$
$132$	3.16428			0.275416
$133$	15.5980	+	15.3174i	1.35252	+	1.32819i
$134$			1.17930i			0.101876i
$135$	−3.32767	−	1.92123i	−0.286400	−	0.165353i
$136$	−2.62917	−	4.55386i	−0.225450	−	0.390490i
$137$	−16.0864	+	9.28751i	−1.37436	+	0.793485i	−0.991473	−	0.130311i	$-0.958402\pi$
$137$	−16.0864	+	9.28751i	−1.37436	+	0.793485i	−0.382884	+	0.923796i	$0.625069\pi$
$138$	−4.58219	−	1.41546i	−0.390062	−	0.120492i
$139$		−	6.69121i		−	0.567541i	−0.958892	−	0.283770i	$-0.908415\pi$
$139$		−	6.69121i		−	0.567541i	0.958892	−	0.283770i	$-0.0915854\pi$
$140$	2.54196	−	9.84328i	0.214835	−	0.831909i
$141$	3.08385			0.259707
$142$	−3.58242	+	6.20493i	−0.300630	+	0.520706i
$143$	−5.24436	−	9.08349i	−0.438555	−	0.759600i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−15.3367	+	26.5639i	−1.27364	+	2.20601i
$146$		−	13.6117i		−	1.12651i
$147$	6.99885	−	0.127077i	0.577255	−	0.0104812i
$148$		−	10.8800i		−	0.894327i
$149$	−5.61769	−	3.24337i	−0.460219	−	0.265708i	0.251917	−	0.967749i	$-0.418939\pi$
$149$	−5.61769	−	3.24337i	−0.460219	−	0.265708i	−0.712136	+	0.702041i	$0.752272\pi$
$150$	8.45634	−	4.88227i	0.690458	−	0.398636i
$151$	0.882910	+	1.52924i	0.0718502	+	0.124448i	0.899712	−	0.436484i	$-0.143776\pi$
$151$	0.882910	+	1.52924i	0.0718502	+	0.124448i	−0.827862	+	0.560932i	$0.810443\pi$
$152$	4.13142	−	7.15583i	0.335102	−	0.580414i
$153$	5.25835			0.425112
$154$	−8.10598	−	2.09331i	−0.653198	−	0.168684i
$155$		−	22.5572i		−	1.81184i
$156$	1.65736	−	2.87063i	0.132695	−	0.229834i
$157$	−2.41790	−	4.18792i	−0.192969	−	0.334232i	0.753264	−	0.657719i	$-0.228478\pi$
$157$	−2.41790	−	4.18792i	−0.192969	−	0.334232i	−0.946233	+	0.323486i	$0.895145\pi$
$158$	0.906949	−	0.523627i	0.0721530	−	0.0416575i
$159$	0.754997	−	1.30769i	0.0598752	−	0.103707i
$160$	−3.84247			−0.303774
$161$	10.8019	+	6.65732i	0.851306	+	0.524670i
$162$	−1.00000			−0.0785674
$163$	1.06878	−	1.85118i	0.0837130	−	0.144995i	−0.821129	−	0.570743i	$-0.806655\pi$
$163$	1.06878	−	1.85118i	0.0837130	−	0.144995i	0.904842	+	0.425747i	$0.139989\pi$
$164$	8.69756	−	5.02154i	0.679166	−	0.392116i
$165$	−6.07933	−	10.5297i	−0.473275	−	0.819736i
$166$	0.543720	−	0.941751i	0.0422009	−	0.0730941i
$167$			8.83236i			0.683468i	0.939797	+	0.341734i	$0.111014\pi$
$167$			8.83236i			0.683468i	−0.939797	+	0.341734i	$0.888986\pi$
$168$	−0.707941	−	2.54928i	−0.0546188	−	0.196681i
$169$	2.01263			0.154818
$170$	−10.1025	+	17.4981i	−0.774827	+	1.34204i
$171$	4.13142	+	7.15583i	0.315938	+	0.547220i
$172$	6.71417	−	3.87643i	0.511951	−	0.295575i
$173$	9.25785	+	5.34502i	0.703861	+	0.406375i	0.808784	−	0.588106i	$-0.200126\pi$
$173$	9.25785	+	5.34502i	0.703861	+	0.406375i	−0.104923	+	0.994480i	$0.533459\pi$
$174$			7.98273i			0.605169i
$175$	−24.8925	+	6.91272i	−1.88170	+	0.522552i
$176$			3.16428i			0.238517i
$177$	−1.51164	+	2.61824i	−0.113622	+	0.196799i
$178$	−7.52955	−	13.0416i	−0.564363	−	0.977506i
$179$	−7.27746	−	12.6049i	−0.543943	−	0.942137i	−0.998673	−	0.0515076i	$-0.983597\pi$
$179$	−7.27746	−	12.6049i	−0.543943	−	0.942137i	0.454729	−	0.890630i	$-0.349736\pi$
$180$	1.92123	−	3.32767i	0.143200	−	0.248030i
$181$	−11.5877			−0.861306			−0.430653	−	0.902518i	$-0.641717\pi$
$181$	−11.5877			−0.861306			−0.430653	+	0.902518i	$0.641717\pi$
$182$	−6.14473	+	6.25731i	−0.455477	+	0.463823i
$183$		−	4.05130i		−	0.299481i
$184$	1.41546	−	4.58219i	0.104349	−	0.337804i
$185$	−36.2049	+	20.9029i	−2.66184	+	1.53681i
$186$	−2.93525	−	5.08400i	−0.215223	−	0.372777i
$187$	14.4097	+	8.31945i	1.05374	+	0.608379i
$188$			3.08385i			0.224913i
$189$	2.56171	+	0.661545i	0.186337	+	0.0481203i
$190$	−31.7497			−2.30336
$191$	−3.89830	−	2.25069i	−0.282071	−	0.162854i	0.352289	−	0.935891i	$-0.385403\pi$
$191$	−3.89830	−	2.25069i	−0.282071	−	0.162854i	−0.634361	+	0.773037i	$0.718737\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	9.37357	+	16.2355i	0.674724	+	1.16866i	0.976549	+	0.215293i	$0.0690707\pi$
$193$	9.37357	+	16.2355i	0.674724	+	1.16866i	−0.301825	+	0.953363i	$0.597596\pi$
$194$	−2.79984	+	4.84946i	−0.201017	+	0.348171i
$195$	−12.7367			−0.912094
$196$	0.127077	+	6.99885i	0.00907695	+	0.499918i
$197$	19.5247			1.39108			0.695539	−	0.718488i	$-0.255166\pi$
$197$	19.5247			1.39108			0.695539	+	0.718488i	$0.255166\pi$
$198$	−2.74035	−	1.58214i	−0.194748	−	0.112438i
$199$	−10.4887	−	18.1670i	−0.743527	−	1.28783i	−0.950880	−	0.309560i	$-0.899818\pi$
$199$	−10.4887	−	18.1670i	−0.743527	−	1.28783i	0.207353	−	0.978266i	$-0.433515\pi$
$200$	4.88227	+	8.45634i	0.345229	+	0.597954i
$201$	0.589651	−	1.02131i	0.0415908	−	0.0720374i
$202$		−	5.43396i		−	0.382332i
$203$	5.28093	−	20.4494i	0.370649	−	1.43527i
$204$			5.25835i			0.368158i
$205$	−33.4201	−	19.2951i	−2.33416	−	1.34763i
$206$	3.82669	+	6.62802i	0.266618	+	0.461796i
$207$	3.26057	+	3.51692i	0.226625	+	0.244443i
$208$	2.87063	+	1.65736i	0.199042	+	0.114917i
$209$			26.1460i			1.80855i
$210$	−7.12305	+	7.25355i	−0.491537	+	0.500543i
$211$	−12.4701			−0.858478			−0.429239	−	0.903191i	$-0.641218\pi$
$211$	−12.4701			−0.858478			−0.429239	+	0.903191i	$0.641218\pi$
$212$	1.30769	+	0.754997i	0.0898128	+	0.0518534i
$213$	6.20493	−	3.58242i	0.425155	−	0.245463i
$214$	2.40173	−	1.38664i	0.164179	−	0.0947888i
$215$	−25.7990	−	14.8951i	−1.75948	−	1.01583i
$216$		−	1.00000i		−	0.0680414i
$217$	4.15596	+	14.9655i	0.282125	+	1.01593i
$218$		−	1.24474i		−	0.0843047i
$219$	−6.80584	+	11.7881i	−0.459896	+	0.796563i
$220$	10.5297	−	6.07933i	0.709912	−	0.409868i
$221$	15.0948	−	8.71497i	1.01538	−	0.586233i
$222$	−5.43998	+	9.42232i	−0.365107	+	0.632385i
$223$		−	28.5966i		−	1.91497i	−0.288488	−	0.957483i	$-0.593153\pi$
$223$		−	28.5966i		−	1.91497i	0.288488	−	0.957483i	$-0.406847\pi$
$224$	2.54928	−	0.707941i	0.170331	−	0.0473013i
$225$	−9.76454			−0.650970
$226$	1.43380	+	0.827805i	0.0953750	+	0.0550648i
$227$	10.7833	+	18.6772i	0.715712	+	1.23965i	0.962684	+	0.270627i	$0.0872309\pi$
$227$	10.7833	+	18.6772i	0.715712	+	1.23965i	−0.246973	+	0.969022i	$0.579436\pi$
$228$	−7.15583	+	4.13142i	−0.473906	+	0.273610i
$229$	6.40165	−	11.0880i	0.423033	−	0.732715i	−0.573202	−	0.819414i	$-0.694299\pi$
$229$	6.40165	−	11.0880i	0.423033	−	0.732715i	0.996234	+	0.0866999i	$0.0276321\pi$
$230$	−17.9675	+	4.09328i	−1.18474	+	0.269903i
$231$	5.97333	+	5.86585i	0.393016	+	0.385945i
$232$	−7.98273			−0.524092
$233$	−12.0170	+	20.8140i	−0.787257	+	1.36357i	0.140384	+	0.990097i	$0.455166\pi$
$233$	−12.0170	+	20.8140i	−0.787257	+	1.36357i	−0.927641	+	0.373472i	$0.878167\pi$
$234$	−2.87063	+	1.65736i	−0.187659	+	0.108345i
$235$	10.2620	−	5.92479i	0.669421	−	0.386490i
$236$	−2.61824	−	1.51164i	−0.170433	−	0.0983994i
$237$	−1.04725			−0.0680265
$238$	3.47863	−	13.4704i	0.225486	−	0.873154i
$239$	12.2248			0.790758			0.395379	−	0.918518i	$-0.370613\pi$
$239$	12.2248			0.790758			0.395379	+	0.918518i	$0.370613\pi$
$240$	3.32767	+	1.92123i	0.214800	+	0.124015i
$241$	2.39058	+	4.14061i	0.153991	+	0.266720i	0.932691	−	0.360676i	$-0.117454\pi$
$241$	2.39058	+	4.14061i	0.153991	+	0.266720i	−0.778700	+	0.627396i	$0.784121\pi$
$242$	0.493654	+	0.855034i	0.0317333	+	0.0549637i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.05130			0.259358
$245$	23.0457	−	13.8693i	1.47234	−	0.886076i
$246$	−10.0431			−0.640324
$247$	23.7196	+	13.6945i	1.50924	+	0.871360i
$248$	5.08400	−	2.93525i	0.322834	−	0.186389i
$249$	−0.941751	+	0.543720i	−0.0596811	+	0.0344569i
$250$	9.15380	−	15.8548i	0.578937	−	1.00275i
$251$	−16.4306			−1.03709			−0.518546	−	0.855050i	$-0.673527\pi$
$251$	−16.4306			−1.03709			−0.518546	+	0.855050i	$0.673527\pi$
$252$	−0.661545	+	2.56171i	−0.0416734	+	0.161373i
$253$	3.37083	+	14.7963i	0.211922	+	0.930233i
$254$	5.37544	−	9.31053i	0.337285	−	0.584195i
$255$	17.4981	−	10.1025i	1.09577	−	0.632644i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.31244	+	1.33509i	0.144246	+	0.0832805i	0.570386	−	0.821377i	$-0.306794\pi$
$257$	2.31244	+	1.33509i	0.144246	+	0.0832805i	−0.426140	+	0.904657i	$0.640127\pi$
$258$	−7.75286			−0.482672
$259$	20.1689	−	20.5385i	1.25324	−	1.27620i
$260$		−	12.7367i		−	0.789896i
$261$	3.99136	−	6.91324i	0.247059	−	0.427919i
$262$	13.5437	−	7.81945i	0.836732	−	0.483087i
$263$	−20.5853	+	11.8849i	−1.26934	+	0.732855i	−0.974864	−	0.222803i	$-0.928479\pi$
$263$	−20.5853	+	11.8849i	−1.26934	+	0.732855i	−0.294479	+	0.955658i	$0.595146\pi$
$264$	1.58214	−	2.74035i	0.0973741	−	0.168657i
$265$		−	5.80210i		−	0.356420i
$266$	21.0643	−	5.84960i	1.29153	−	0.358662i
$267$			15.0591i			0.921602i
$268$	1.02131	+	0.589651i	0.0623862	+	0.0360187i
$269$	19.6022	−	11.3173i	1.19517	−	0.690029i	0.235692	−	0.971828i	$-0.424264\pi$
$269$	19.6022	−	11.3173i	1.19517	−	0.690029i	0.959473	+	0.281799i	$0.0909311\pi$
$270$	−3.32767	+	1.92123i	−0.202516	+	0.116923i
$271$	−15.1425	−	8.74250i	−0.919838	−	0.531069i	−0.0362549	−	0.999343i	$-0.511543\pi$
$271$	−15.1425	−	8.74250i	−0.919838	−	0.531069i	−0.883584	+	0.468274i	$0.844876\pi$
$272$	−5.25835			−0.318834
$273$	8.45014	−	2.34662i	0.511426	−	0.142024i
$274$			18.5750i			1.12216i
$275$	−26.7583	−	15.4489i	−1.61358	−	0.931603i
$276$	−3.51692	+	3.26057i	−0.211694	+	0.196263i
$277$	−12.0748	−	20.9141i	−0.725502	−	1.25661i	−0.958767	−	0.284193i	$-0.908274\pi$
$277$	−12.0748	−	20.9141i	−0.725502	−	1.25661i	0.233266	−	0.972413i	$-0.425059\pi$
$278$	−5.79476	−	3.34560i	−0.347546	−	0.200656i
$279$			5.87050i			0.351458i
$280$	−7.25355	−	7.12305i	−0.433483	−	0.425683i
$281$			20.6153i			1.22981i	0.788603	+	0.614903i	$0.210805\pi$
$281$			20.6153i			1.22981i	−0.788603	+	0.614903i	$0.789195\pi$
$282$	1.54192	−	2.67069i	0.0918202	−	0.159037i
$283$	−1.91637	−	3.31924i	−0.113916	−	0.197309i	0.803430	−	0.595399i	$-0.203006\pi$
$283$	−1.91637	−	3.31924i	−0.113916	−	0.197309i	−0.917346	+	0.398091i	$0.869673\pi$
$284$	3.58242	+	6.20493i	0.212577	+	0.368195i
$285$	27.4960	+	15.8748i	1.62872	+	0.940344i
$286$	−10.4887			−0.620211
$287$	25.7275	+	6.64395i	1.51864	+	0.392180i
$288$	1.00000			0.0589256
$289$	−5.32511	+	9.22336i	−0.313242	+	0.542550i
$290$	15.3367	+	26.5639i	0.900601	+	1.55989i
$291$	4.84946	−	2.79984i	0.284281	−	0.164129i
$292$	−11.7881	−	6.80584i	−0.689844	−	0.398282i
$293$	4.96236			0.289904			0.144952	−	0.989439i	$-0.453697\pi$
$293$	4.96236			0.289904			0.144952	+	0.989439i	$0.453697\pi$
$294$	3.38937	−	6.12472i	0.197672	−	0.357201i
$295$			11.6169i			0.676359i
$296$	−9.42232	−	5.43998i	−0.547661	−	0.316192i
$297$	1.58214	+	2.74035i	0.0918052	+	0.159011i
$298$	−5.61769	+	3.24337i	−0.325424	+	0.187884i
$299$	15.1887	+	4.69185i	0.878384	+	0.271336i
$300$		−	9.76454i		−	0.563756i
$301$	19.8606	+	5.12886i	1.14474	+	0.295623i
$302$	1.76582			0.101611
$303$	−2.71698	+	4.70595i	−0.156087	+	0.270350i
$304$	−4.13142	−	7.15583i	−0.236953	−	0.410415i
$305$	−7.78350	−	13.4814i	−0.445682	−	0.771943i
$306$	2.62917	−	4.55386i	0.150300	−	0.260327i
$307$		−	25.1691i		−	1.43648i	−0.695797	−	0.718239i	$-0.744949\pi$
$307$		−	25.1691i		−	1.43648i	0.695797	−	0.718239i	$-0.255051\pi$
$308$	−5.86585	+	5.97333i	−0.334238	+	0.340362i
$309$		−	7.65338i		−	0.435386i
$310$	−19.5351	−	11.2786i	−1.10952	−	0.640581i
$311$	−0.268515	+	0.155027i	−0.0152261	+	0.00879078i	−0.507594	−	0.861597i	$-0.669465\pi$
$311$	−0.268515	+	0.155027i	−0.0152261	+	0.00879078i	0.492368	+	0.870387i	$0.336132\pi$
$312$	−1.65736	−	2.87063i	−0.0938295	−	0.162517i
$313$	3.01528	−	5.22262i	0.170434	−	0.295200i	−0.768138	−	0.640285i	$-0.778816\pi$
$313$	3.01528	−	5.22262i	0.170434	−	0.295200i	0.938572	+	0.345085i	$0.112150\pi$
$314$	−4.83579			−0.272900
$315$	9.79551	−	2.72024i	0.551915	−	0.153268i
$316$		−	1.04725i		−	0.0589127i
$317$	−4.50761	+	7.80741i	−0.253173	+	0.438508i	−0.964398	−	0.264457i	$-0.914807\pi$
$317$	−4.50761	+	7.80741i	−0.253173	+	0.438508i	0.711225	+	0.702964i	$0.248141\pi$
$318$	−0.754997	−	1.30769i	−0.0423381	−	0.0733318i
$319$	21.8755	−	12.6298i	1.22479	−	0.707133i
$320$	−1.92123	+	3.32767i	−0.107400	+	0.186023i
$321$	−2.77328			−0.154789
$322$	11.1663	−	6.02602i	0.622276	−	0.335817i
$323$	−43.4489			−2.41756
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−28.0304	+	16.1834i	−1.55485	+	0.897691i
$326$	−1.06878	−	1.85118i	−0.0591941	−	0.102527i
$327$	−0.622372	+	1.07798i	−0.0344172	+	0.0596124i
$328$		−	10.0431i		−	0.554536i
$329$	−5.71674	+	5.82148i	−0.315174	+	0.320949i
$330$	−12.1587			−0.669312
$331$	−3.34029	+	5.78556i	−0.183599	+	0.318003i	−0.943104	−	0.332499i	$-0.892108\pi$
$331$	−3.34029	+	5.78556i	−0.183599	+	0.318003i	0.759504	+	0.650502i	$0.225441\pi$
$332$	−0.543720	−	0.941751i	−0.0298405	−	0.0516853i
$333$	9.42232	−	5.43998i	0.516340	−	0.298109i
$334$	7.64904	+	4.41618i	0.418537	+	0.241642i
$335$		−	4.53143i		−	0.247578i
$336$	−2.56171	−	0.661545i	−0.139753	−	0.0360902i
$337$		−	10.3992i		−	0.566480i	−0.959049	−	0.283240i	$-0.908591\pi$
$337$		−	10.3992i		−	0.566480i	0.959049	−	0.283240i	$-0.0914093\pi$
$338$	1.00632	−	1.74299i	0.0547364	−	0.0948063i
$339$	−0.827805	−	1.43380i	−0.0449602	−	0.0778734i
$340$	10.1025	+	17.4981i	0.547886	+	0.948966i
$341$	−9.28796	+	16.0872i	−0.502971	+	0.871172i
$342$	8.26284			0.446803
$343$	−12.7344	+	13.4475i	−0.687591	+	0.726098i
$344$		−	7.75286i		−	0.418006i
$345$	17.6069	+	5.43885i	0.947924	+	0.292818i
$346$	9.25785	−	5.34502i	0.497705	−	0.287350i
$347$	−3.25758	−	5.64230i	−0.174876	−	0.302895i	0.765242	−	0.643742i	$-0.222619\pi$
$347$	−3.25758	−	5.64230i	−0.174876	−	0.302895i	−0.940118	+	0.340848i	$0.889286\pi$
$348$	6.91324	+	3.99136i	0.370589	+	0.213960i
$349$			7.54524i			0.403887i	0.979397	+	0.201944i	$0.0647258\pi$
$349$			7.54524i			0.403887i	−0.979397	+	0.201944i	$0.935274\pi$
$350$	−6.45968	+	25.0139i	−0.345284	+	1.33705i
$351$	3.31472			0.176927
$352$	2.74035	+	1.58214i	0.146061	+	0.0843284i
$353$	−3.08609	+	1.78176i	−0.164256	+	0.0948333i	−0.579875	−	0.814706i	$-0.696898\pi$
$353$	−3.08609	+	1.78176i	−0.164256	+	0.0948333i	0.415619	+	0.909539i	$0.363565\pi$
$354$	1.51164	+	2.61824i	0.0803428	+	0.139158i
$355$	13.7653	−	23.8422i	0.730587	−	1.26541i
$356$	−15.0591			−0.798130
$357$	−9.74776	+	9.92636i	−0.515906	+	0.525359i
$358$	−14.5549			−0.769252
$359$	−2.53871	−	1.46572i	−0.133988	−	0.0773579i	0.431508	−	0.902109i	$-0.357982\pi$
$359$	−2.53871	−	1.46572i	−0.133988	−	0.0773579i	−0.565496	+	0.824751i	$0.691315\pi$
$360$	−1.92123	−	3.32767i	−0.101258	−	0.175384i
$361$	−24.6373	−	42.6730i	−1.29670	−	2.24595i
$362$	−5.79384	+	10.0352i	−0.304518	+	0.527440i
$363$		−	0.987308i		−	0.0518202i
$364$	2.34662	+	8.45014i	0.122997	+	0.442908i
$365$			52.3024i			2.73763i
$366$	−3.50853	−	2.02565i	−0.183394	−	0.105882i
$367$	−5.73898	−	9.94021i	−0.299572	−	0.518875i	0.676466	−	0.736474i	$-0.263511\pi$
$367$	−5.73898	−	9.94021i	−0.299572	−	0.518875i	−0.976038	+	0.217599i	$0.930177\pi$
$368$	−3.26057	−	3.51692i	−0.169969	−	0.183332i
$369$	8.69756	+	5.02154i	0.452777	+	0.261411i
$370$			41.8059i			2.17338i
$371$	1.06899	+	3.84940i	0.0554990	+	0.199851i
$372$	−5.87050			−0.304371
$373$	−0.499769	−	0.288542i	−0.0258771	−	0.0149401i	0.487006	−	0.873399i	$-0.338089\pi$
$373$	−0.499769	−	0.288542i	−0.0258771	−	0.0149401i	−0.512883	+	0.858459i	$0.671422\pi$
$374$	14.4097	−	8.31945i	0.745108	−	0.430189i
$375$	−15.8548	+	9.15380i	−0.818741	+	0.472700i
$376$	2.67069	+	1.54192i	0.137730	+	0.0795186i
$377$		−	26.4605i		−	1.36278i
$378$	1.85377	−	1.88773i	0.0953476	−	0.0970945i
$379$		−	18.5894i		−	0.954872i	−0.878667	−	0.477436i	$-0.841566\pi$
$379$		−	18.5894i		−	0.954872i	0.878667	−	0.477436i	$-0.158434\pi$
$380$	−15.8748	+	27.4960i	−0.814362	+	1.41052i
$381$	−9.31053	+	5.37544i	−0.476993	+	0.275392i
$382$	−3.89830	+	2.25069i	−0.199455	+	0.115155i
$383$	4.47528	−	7.75141i	0.228676	−	0.396079i	−0.728740	−	0.684791i	$-0.759894\pi$
$383$	4.47528	−	7.75141i	0.228676	−	0.396079i	0.957416	+	0.288712i	$0.0932270\pi$
$384$			1.00000i			0.0510310i
$385$	31.1469	+	8.04349i	1.58740	+	0.409934i
$386$	18.7471			0.954204
$387$	6.71417	+	3.87643i	0.341301	+	0.197050i
$388$	2.79984	+	4.84946i	0.142140	+	0.246194i
$389$	27.9893	−	16.1596i	1.41911	−	0.819324i	0.422891	−	0.906181i	$-0.361015\pi$
$389$	27.9893	−	16.1596i	1.41911	−	0.819324i	0.996221	+	0.0868564i	$0.0276821\pi$
$390$	−6.36835	+	11.0303i	−0.322474	+	0.558541i
$391$	−24.5882	+	5.60158i	−1.24348	+	0.283284i
$392$	6.12472	+	3.38937i	0.309345	+	0.171189i
$393$	−15.6389			−0.788878
$394$	9.76235	−	16.9089i	0.491820	−	0.851858i
$395$	−3.48492	+	2.01202i	−0.175345	+	0.101236i
$396$	−2.74035	+	1.58214i	−0.137708	+	0.0795056i
$397$	6.31851	+	3.64799i	0.317117	+	0.183087i	0.650107	−	0.759843i	$-0.274724\pi$
$397$	6.31851	+	3.64799i	0.317117	+	0.183087i	−0.332990	+	0.942930i	$0.608058\pi$
$398$	−20.9775			−1.05151
$399$	−21.1670	−	5.46624i	−1.05968	−	0.273654i
$400$	9.76454			0.488227
$401$	3.63684	+	2.09973i	0.181615	+	0.104856i	0.588051	−	0.808824i	$-0.299895\pi$
$401$	3.63684	+	2.09973i	0.181615	+	0.104856i	−0.406436	+	0.913679i	$0.633229\pi$
$402$	−0.589651	−	1.02131i	−0.0294091	−	0.0509381i
$403$	9.72953	+	16.8520i	0.484662	+	0.839460i
$404$	−4.70595	−	2.71698i	−0.234130	−	0.135175i
$405$	3.84247			0.190934
$406$	−15.0693	−	14.7981i	−0.747875	−	0.734419i
$407$	34.4273			1.70650
$408$	4.55386	+	2.62917i	0.225450	+	0.130163i
$409$	−26.3826	+	15.2320i	−1.30454	+	0.753174i	−0.981179	−	0.193103i	$-0.938145\pi$
$409$	−26.3826	+	15.2320i	−1.30454	+	0.753174i	−0.323357	+	0.946277i	$0.604812\pi$
$410$	−33.4201	+	19.2951i	−1.65050	+	0.952917i
$411$	9.28751	−	16.0864i	0.458119	−	0.793485i
$412$	7.65338			0.377055
$413$	−2.14030	−	7.70718i	−0.105317	−	0.379246i
$414$	4.67602	−	1.06527i	0.229814	−	0.0523553i
$415$	−2.08923	+	3.61865i	−0.102556	+	0.177632i
$416$	2.87063	−	1.65736i	0.140744	−	0.0812587i
$417$	3.34560	+	5.79476i	0.163835	+	0.283770i
$418$	22.6431	+	13.0730i	1.10751	+	0.639421i
$419$	16.5543			0.808730			0.404365	−	0.914598i	$-0.367493\pi$
$419$	16.5543			0.808730			0.404365	+	0.914598i	$0.367493\pi$
$420$	2.72024	+	9.79551i	0.132734	+	0.477972i
$421$			6.17026i			0.300720i	0.988631	+	0.150360i	$0.0480432\pi$
$421$			6.17026i			0.300720i	−0.988631	+	0.150360i	$0.951957\pi$
$422$	−6.23505	+	10.7994i	−0.303518	+	0.525708i
$423$	−2.67069	+	1.54192i	−0.129853	+	0.0749709i
$424$	1.30769	−	0.754997i	0.0635072	−	0.0366659i
$425$	25.6727	−	44.4664i	1.24531	−	2.15694i
$426$		−	7.16483i		−	0.347137i
$427$	7.64778	+	7.51018i	0.370102	+	0.363443i
$428$		−	2.77328i		−	0.134052i
$429$	9.08349	+	5.24436i	0.438555	+	0.253200i
$430$	−25.7990	+	14.8951i	−1.24414	+	0.718303i
$431$	11.5358	−	6.66019i	0.555659	−	0.320810i	−0.195742	−	0.980655i	$-0.562712\pi$
$431$	11.5358	−	6.66019i	0.555659	−	0.320810i	0.751401	+	0.659845i	$0.229378\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−40.0511			−1.92473			−0.962367	−	0.271755i	$-0.912396\pi$
$433$	−40.0511			−1.92473			−0.962367	+	0.271755i	$0.912396\pi$
$434$	15.0385	+	3.88360i	0.721872	+	0.186419i
$435$		−	30.6734i		−	1.47067i
$436$	−1.07798	−	0.622372i	−0.0516259	−	0.0298062i
$437$	−26.9415	−	29.0597i	−1.28879	−	1.39012i
$438$	6.80584	+	11.7881i	0.325196	+	0.563255i
$439$	27.2080	+	15.7085i	1.29857	+	0.749727i	0.980156	−	0.198226i	$-0.0635179\pi$
$439$	27.2080	+	15.7085i	1.29857	+	0.749727i	0.318410	+	0.947953i	$0.396851\pi$
$440$		−	12.1587i		−	0.579641i
$441$	−5.99764	+	3.60948i	−0.285602	+	0.171880i
$442$		−	17.4299i		−	0.829058i
$443$	−5.94122	+	10.2905i	−0.282276	+	0.488916i	−0.971945	−	0.235209i	$-0.924423\pi$
$443$	−5.94122	+	10.2905i	−0.282276	+	0.488916i	0.689669	+	0.724125i	$0.257756\pi$
$444$	5.43998	+	9.42232i	0.258170	+	0.447163i
$445$	28.9320	+	50.1117i	1.37151	+	2.37552i
$446$	−24.7653	−	14.2983i	−1.17267	−	0.677043i
$447$	6.48675			0.306813
$448$	0.661545	−	2.56171i	0.0312550	−	0.121029i
$449$	−27.8402			−1.31386			−0.656931	−	0.753950i	$-0.728146\pi$
$449$	−27.8402			−1.31386			−0.656931	+	0.753950i	$0.728146\pi$
$450$	−4.88227	+	8.45634i	−0.230153	+	0.398636i
$451$	15.8896	+	27.5216i	0.748211	+	1.29594i
$452$	1.43380	−	0.827805i	0.0674403	−	0.0389367i
$453$	−1.52924	−	0.882910i	−0.0718502	−	0.0414827i
$454$	21.5666			1.01217
$455$	23.6109	−	24.0435i	1.10690	−	1.12718i
$456$			8.26284i			0.386943i
$457$	19.9389	+	11.5117i	0.932702	+	0.538496i	0.887665	−	0.460490i	$-0.152326\pi$
$457$	19.9389	+	11.5117i	0.932702	+	0.538496i	0.0450367	+	0.998985i	$0.485660\pi$
$458$	−6.40165	−	11.0880i	−0.299129	−	0.518107i
$459$	−4.55386	+	2.62917i	−0.212556	+	0.122719i
$460$	−5.43885	+	17.6069i	−0.253588	+	0.820927i
$461$			3.84382i			0.179024i	0.995986	+	0.0895122i	$0.0285308\pi$
$461$			3.84382i			0.179024i	−0.995986	+	0.0895122i	$0.971469\pi$
$462$	8.06664	−	2.24013i	0.375294	−	0.104220i
$463$	−9.42551			−0.438041			−0.219020	−	0.975720i	$-0.570286\pi$
$463$	−9.42551			−0.438041			−0.219020	+	0.975720i	$0.570286\pi$
$464$	−3.99136	+	6.91324i	−0.185294	+	0.320939i
$465$	11.2786	+	19.5351i	0.523032	+	0.905919i
$466$	12.0170	+	20.8140i	0.556675	+	0.964189i
$467$	−11.2398	+	19.4679i	−0.520117	+	0.900868i	0.479610	+	0.877482i	$0.340778\pi$
$467$	−11.2398	+	19.4679i	−0.520117	+	0.900868i	−0.999726	+	0.0233865i	$0.992555\pi$
$468$			3.31472i			0.153223i
$469$	0.834876	+	3.00637i	0.0385510	+	0.138821i
$470$		−	11.8496i		−	0.546580i
$471$	4.18792	+	2.41790i	0.192969	+	0.111411i
$472$	−2.61824	+	1.51164i	−0.120514	+	0.0695789i
$473$	12.2661	+	21.2456i	0.563997	+	0.976871i
$474$	−0.523627	+	0.906949i	−0.0240510	+	0.0416575i
$475$	80.6829			3.70198
$476$	−9.92636	−	9.74776i	−0.454974	−	0.446788i
$477$			1.50999i			0.0691379i
$478$	6.11241	−	10.5870i	0.279575	−	0.484238i
$479$	−8.79390	−	15.2315i	−0.401804	−	0.695944i	0.592140	−	0.805835i	$-0.298283\pi$
$479$	−8.79390	−	15.2315i	−0.401804	−	0.695944i	−0.993944	+	0.109891i	$0.964950\pi$
$480$	3.32767	−	1.92123i	0.151887	−	0.0876919i
$481$	18.0320	−	31.2323i	0.822188	−	1.42407i
$482$	4.78116			0.217776
$483$	−12.6833	−	0.364477i	−0.577112	−	0.0165843i
$484$	0.987308			0.0448776
$485$	10.7583	−	18.6339i	0.488509	−	0.846122i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	2.32828	+	4.03269i	0.105504	+	0.182739i	0.913944	−	0.405840i	$-0.133021\pi$
$487$	2.32828	+	4.03269i	0.105504	+	0.182739i	−0.808440	+	0.588579i	$0.799688\pi$
$488$	2.02565	−	3.50853i	0.0916969	−	0.158824i
$489$			2.13755i			0.0966635i
$490$	−0.488290	−	26.8928i	−0.0220587	−	1.21489i
$491$	26.8348			1.21104			0.605518	−	0.795832i	$-0.292966\pi$
$491$	26.8348			1.21104			0.605518	+	0.795832i	$0.292966\pi$
$492$	−5.02154	+	8.69756i	−0.226389	+	0.392116i
$493$	20.9880	+	36.3522i	0.945251	+	1.63722i
$494$	23.7196	−	13.6945i	1.06719	−	0.616145i
$495$	10.5297	+	6.07933i	0.473275	+	0.273245i
$496$		−	5.87050i		−	0.263593i
$497$	−4.73986	+	18.3542i	−0.212612	+	0.823299i
$498$			1.08744i			0.0487294i
$499$	−4.87269	+	8.43974i	−0.218131	+	0.377815i	−0.954237	−	0.299052i	$-0.903329\pi$
$499$	−4.87269	+	8.43974i	−0.218131	+	0.377815i	0.736105	+	0.676867i	$0.236663\pi$
$500$	−9.15380	−	15.8548i	−0.409370	−	0.709050i
$501$	−4.41618	−	7.64904i	−0.197300	−	0.341734i
$502$	−8.21532	+	14.2293i	−0.366668	+	0.635087i
$503$	32.1926			1.43540			0.717699	−	0.696353i	$-0.245195\pi$
$503$	32.1926			1.43540			0.717699	+	0.696353i	$0.245195\pi$
$504$	1.88773	+	1.85377i	0.0840863	+	0.0825735i
$505$			20.8798i			0.929140i
$506$	14.4994	+	4.47891i	0.644575	+	0.199112i
$507$	−1.74299	+	1.00632i	−0.0774090	+	0.0446921i
$508$	−5.37544	−	9.31053i	−0.238497	−	0.413088i
$509$	−15.4153	−	8.90000i	−0.683269	−	0.394486i	0.117817	−	0.993035i	$-0.462411\pi$
$509$	−15.4153	−	8.90000i	−0.683269	−	0.394486i	−0.801086	+	0.598550i	$0.795744\pi$
$510$		−	20.2050i		−	0.894693i
$511$	−9.63626	−	34.7000i	−0.426283	−	1.53504i
$512$	−1.00000			−0.0441942
$513$	−7.15583	−	4.13142i	−0.315938	−	0.182407i
$514$	2.31244	−	1.33509i	0.101997	−	0.0588882i
$515$	−14.7039	−	25.4680i	−0.647932	−	1.12225i
$516$	−3.87643	+	6.71417i	−0.170650	+	0.295575i
$517$	−9.75816			−0.429164
$518$	−7.70236	−	27.7360i	−0.338422	−	1.21865i
$519$	−10.6900			−0.469241
$520$	−11.0303	−	6.36835i	−0.483711	−	0.279271i
$521$	−9.48176	−	16.4229i	−0.415403	−	0.719500i	0.580067	−	0.814569i	$-0.303026\pi$
$521$	−9.48176	−	16.4229i	−0.415403	−	0.719500i	−0.995471	+	0.0950687i	$0.969693\pi$
$522$	−3.99136	−	6.91324i	−0.174697	−	0.302584i
$523$	−13.8411	+	23.9735i	−0.605230	+	1.04829i	0.386785	+	0.922170i	$0.373586\pi$
$523$	−13.8411	+	23.9735i	−0.605230	+	1.04829i	−0.992015	+	0.126119i	$0.959748\pi$
$524$		−	15.6389i		−	0.683189i
$525$	18.1012	−	18.4329i	0.790002	−	0.804476i
$526$			23.7698i			1.03641i
$527$	−26.7334	−	15.4346i	−1.16453	−	0.672340i
$528$	−1.58214	−	2.74035i	−0.0688539	−	0.119258i
$529$	−18.9930	−	12.9718i	−0.825781	−	0.563991i
$530$	−5.02477	−	2.90105i	−0.218262	−	0.126014i
$531$		−	3.02328i		−	0.131199i
$532$	5.46624	−	21.1670i	0.236991	−	0.917706i
$533$	33.2900			1.44195
$534$	13.0416	+	7.52955i	0.564363	+	0.325835i
$535$	−9.22857	+	5.32812i	−0.398986	+	0.230355i
$536$	1.02131	−	0.589651i	0.0441137	−	0.0254691i
$537$	12.6049	+	7.27746i	0.543943	+	0.314046i
$538$		−	22.6346i		−	0.975848i
$539$	−22.1463	+	0.402109i	−0.953910	+	0.0173200i
$540$			3.84247i			0.165353i
$541$	14.5490	−	25.1996i	0.625511	−	1.08342i	−0.362931	−	0.931816i	$-0.618224\pi$
$541$	14.5490	−	25.1996i	0.625511	−	1.08342i	0.988442	−	0.151600i	$-0.0484427\pi$
$542$	−15.1425	+	8.74250i	−0.650424	+	0.375522i
$543$	10.0352	−	5.79384i	0.430653	−	0.248638i
$544$	−2.62917	+	4.55386i	−0.112725	+	0.195245i
$545$			4.78289i			0.204876i
$546$	2.19283	−	8.49135i	0.0938447	−	0.363396i
$547$	−37.4883			−1.60288			−0.801442	−	0.598073i	$-0.795933\pi$
$547$	−37.4883			−1.60288			−0.801442	+	0.598073i	$0.795933\pi$
$548$	16.0864	+	9.28751i	0.687179	+	0.396743i
$549$	2.02565	+	3.50853i	0.0864527	+	0.149740i
$550$	−26.7583	+	15.4489i	−1.14098	+	0.658743i
$551$	−32.9800	+	57.1230i	−1.40499	+	2.43352i
$552$	1.06527	+	4.67602i	0.0453410	+	0.199025i
$553$	1.94137	−	1.97694i	0.0825554	−	0.0840679i
$554$	−24.1495			−1.02601
$555$	20.9029	−	36.2049i	0.887280	−	1.53681i
$556$	−5.79476	+	3.34560i	−0.245752	+	0.141885i
$557$	20.5052	−	11.8387i	0.868831	−	0.501620i	0.00187163	−	0.999998i	$-0.499404\pi$
$557$	20.5052	−	11.8387i	0.868831	−	0.501620i	0.866960	+	0.498378i	$0.166071\pi$
$558$	5.08400	+	2.93525i	0.215223	+	0.124259i
$559$	25.6986			1.08693
$560$	−9.79551	+	2.72024i	−0.413936	+	0.114951i
$561$	−16.6389			−0.702495
$562$	17.8534	+	10.3077i	0.753100	+	0.434802i
$563$	1.85680	+	3.21607i	0.0782546	+	0.135541i	0.902497	−	0.430696i	$-0.141732\pi$
$563$	1.85680	+	3.21607i	0.0782546	+	0.135541i	−0.824242	+	0.566237i	$0.808399\pi$
$564$	−1.54192	−	2.67069i	−0.0649267	−	0.112456i
$565$	−5.50933	−	3.18081i	−0.231779	−	0.133818i
$566$	−3.83273			−0.161102
$567$	−2.54928	+	0.707941i	−0.107060	+	0.0297307i
$568$	7.16483			0.300630
$569$	2.32692	+	1.34345i	0.0975496	+	0.0563203i	0.547981	−	0.836491i	$-0.315397\pi$
$569$	2.32692	+	1.34345i	0.0975496	+	0.0563203i	−0.450432	+	0.892811i	$0.648730\pi$
$570$	27.4960	−	15.8748i	1.15168	−	0.664924i
$571$	7.71055	−	4.45169i	0.322676	−	0.186297i	−0.329909	−	0.944013i	$-0.607018\pi$
$571$	7.71055	−	4.45169i	0.322676	−	0.186297i	0.652585	+	0.757716i	$0.273685\pi$
$572$	−5.24436	+	9.08349i	−0.219278	+	0.379800i
$573$	4.50137			0.188048
$574$	18.6176	−	18.9587i	0.777082	−	0.791319i
$575$	45.6592	−	10.4019i	1.90412	−	0.433789i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	27.9620	−	16.1439i	1.16407	−	0.672078i	0.211796	−	0.977314i	$-0.432069\pi$
$577$	27.9620	−	16.1439i	1.16407	−	0.672078i	0.952277	+	0.305236i	$0.0987353\pi$
$578$	5.32511	+	9.22336i	0.221495	+	0.383641i
$579$	−16.2355	−	9.37357i	−0.674724	−	0.389552i
$580$	30.6734			1.27364
$581$	0.719390	−	2.78571i	0.0298453	−	0.115571i
$582$		−	5.59968i		−	0.232114i
$583$	−2.38903	+	4.13791i	−0.0989433	+	0.171375i
$584$	−11.7881	+	6.80584i	−0.487793	+	0.281628i
$585$	11.0303	−	6.36835i	0.456047	−	0.263299i
$586$	2.48118	−	4.29753i	0.102497	−	0.177529i
$587$			20.5857i			0.849663i	0.905272	+	0.424832i	$0.139667\pi$
$587$			20.5857i			0.849663i	−0.905272	+	0.424832i	$0.860333\pi$
$588$	−3.60948	−	5.99764i	−0.148852	−	0.247339i
$589$		−	48.5070i		−	1.99870i
$590$	10.0605	+	5.80843i	0.414184	+	0.239129i
$591$	−16.9089	+	9.76235i	−0.695539	+	0.401570i
$592$	−9.42232	+	5.43998i	−0.387255	+	0.223582i
$593$	33.7874	+	19.5072i	1.38748	+	0.801064i	0.993031	−	0.117852i	$-0.0376009\pi$
$593$	33.7874	+	19.5072i	1.38748	+	0.801064i	0.394452	+	0.918916i	$0.370934\pi$
$594$	3.16428			0.129832
$595$	−13.3665	+	51.7594i	−0.547974	+	2.12193i
$596$			6.48675i			0.265708i
$597$	18.1670	+	10.4887i	0.743527	+	0.429275i
$598$	11.6576	−	10.8079i	0.476715	−	0.441966i
$599$	6.85299	+	11.8697i	0.280006	+	0.484984i	0.971386	−	0.237507i	$-0.0763303\pi$
$599$	6.85299	+	11.8697i	0.280006	+	0.484984i	−0.691380	+	0.722491i	$0.742997\pi$
$600$	−8.45634	−	4.88227i	−0.345229	−	0.199318i
$601$		−	11.1704i		−	0.455648i	−0.973702	−	0.227824i	$-0.926839\pi$
$601$		−	11.1704i		−	0.455648i	0.973702	−	0.227824i	$-0.0731611\pi$
$602$	14.3720	−	14.6353i	0.585760	−	0.596492i
$603$			1.17930i			0.0480249i
$604$	0.882910	−	1.52924i	0.0359251	−	0.0622241i
$605$	−1.89685	−	3.28544i	−0.0771179	−	0.133572i
$606$	2.71698	+	4.70595i	0.110370	+	0.191166i
$607$	−8.20963	−	4.73983i	−0.333219	−	0.192384i	0.324050	−	0.946040i	$-0.394955\pi$
$607$	−8.20963	−	4.73983i	−0.333219	−	0.192384i	−0.657269	+	0.753656i	$0.728289\pi$
$608$	−8.26284			−0.335102
$609$	5.65130	+	20.3502i	0.229002	+	0.824631i
$610$	−15.5670			−0.630289
$611$	−5.11104	+	8.85259i	−0.206771	+	0.358137i
$612$	−2.62917	−	4.55386i	−0.106278	−	0.184079i
$613$	30.1837	−	17.4266i	1.21911	−	0.703853i	0.254381	−	0.967104i	$-0.418128\pi$
$613$	30.1837	−	17.4266i	1.21911	−	0.703853i	0.964727	+	0.263251i	$0.0847948\pi$
$614$	−21.7971	−	12.5846i	−0.879659	−	0.507871i
$615$	38.5902			1.55611
$616$	2.24013	+	8.06664i	0.0902572	+	0.325014i
$617$			32.0777i			1.29140i	0.763592	+	0.645699i	$0.223434\pi$
$617$			32.0777i			1.29140i	−0.763592	+	0.645699i	$0.776566\pi$
$618$	−6.62802	−	3.82669i	−0.266618	−	0.153932i
$619$	8.24184	+	14.2753i	0.331268	+	0.573772i	0.982761	−	0.184882i	$-0.0591904\pi$
$619$	8.24184	+	14.2753i	0.331268	+	0.573772i	−0.651493	+	0.758655i	$0.725857\pi$
$620$	−19.5351	+	11.2786i	−0.784548	+	0.452959i
$621$	−4.58219	−	1.41546i	−0.183877	−	0.0568004i
$622$			0.310054i			0.0124320i
$623$	−28.4276	−	27.9161i	−1.13893	−	1.11843i
$624$	−3.31472			−0.132695
$625$	−10.7618	+	18.6400i	−0.430472	+	0.745599i
$626$	−3.01528	−	5.22262i	−0.120515	−	0.208738i
$627$	−13.0730	−	22.6431i	−0.522085	−	0.904277i
$628$	−2.41790	+	4.18792i	−0.0964846	+	0.167116i
$629$			57.2106i			2.28114i
$630$	2.54196	−	9.84328i	0.101274	−	0.392166i
$631$		−	20.6601i		−	0.822466i	−0.911530	−	0.411233i	$-0.865098\pi$
$631$		−	20.6601i		−	0.822466i	0.911530	−	0.411233i	$-0.134902\pi$
$632$	−0.906949	−	0.523627i	−0.0360765	−	0.0208288i
$633$	10.7994	−	6.23505i	0.429239	−	0.247821i
$634$	4.50761	+	7.80741i	0.179020	+	0.310072i
$635$	−20.6549	+	35.7754i	−0.819666	+	1.41970i
$636$	−1.50999			−0.0598752
$637$	−11.2348	+	20.3017i	−0.445140	+	0.804383i
$638$		−	25.2596i		−	1.00004i
$639$	−3.58242	+	6.20493i	−0.141718	+	0.245463i
$640$	1.92123	+	3.32767i	0.0759434	+	0.131538i
$641$	9.33182	−	5.38773i	0.368585	−	0.212803i	−0.304255	−	0.952591i	$-0.598408\pi$
$641$	9.33182	−	5.38773i	0.368585	−	0.212803i	0.672840	+	0.739788i	$0.265074\pi$
$642$	−1.38664	+	2.40173i	−0.0547263	+	0.0947888i
$643$	3.41922			0.134841			0.0674204	−	0.997725i	$-0.478523\pi$
$643$	3.41922			0.134841			0.0674204	+	0.997725i	$0.478523\pi$
$644$	0.364477	−	12.6833i	0.0143624	−	0.499794i
$645$	29.7901			1.17298
$646$	−21.7244	+	37.6278i	−0.854737	+	1.48045i
$647$	−2.66787	+	1.54030i	−0.104885	+	0.0605553i	−0.551525	−	0.834158i	$-0.685954\pi$
$647$	−2.66787	+	1.54030i	−0.104885	+	0.0605553i	0.446640	+	0.894714i	$0.352620\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	4.78326	−	8.28485i	0.187759	−	0.325209i
$650$			32.3667i			1.26953i
$651$	−11.0819	−	10.8826i	−0.434335	−	0.426521i
$652$	−2.13755			−0.0837130
$653$	0.861247	−	1.49172i	0.0337032	−	0.0583756i	−0.848682	−	0.528904i	$-0.822603\pi$
$653$	0.861247	−	1.49172i	0.0337032	−	0.0583756i	0.882385	+	0.470528i	$0.155937\pi$
$654$	0.622372	+	1.07798i	0.0243367	+	0.0421523i
$655$	−52.0412	+	30.0460i	−2.03342	+	1.17399i
$656$	−8.69756	−	5.02154i	−0.339583	−	0.196058i
$657$		−	13.6117i		−	0.531042i
$658$	2.18318	+	7.86158i	0.0851092	+	0.306476i
$659$		−	50.7513i		−	1.97699i	−0.151260	−	0.988494i	$-0.548333\pi$
$659$		−	50.7513i		−	1.97699i	0.151260	−	0.988494i	$-0.451667\pi$
$660$	−6.07933	+	10.5297i	−0.236637	+	0.409868i
$661$	11.8485	+	20.5222i	0.460852	+	0.798219i	0.999004	−	0.0446288i	$-0.0142105\pi$
$661$	11.8485	+	20.5222i	0.460852	+	0.798219i	−0.538151	+	0.842848i	$0.680877\pi$
$662$	3.34029	+	5.78556i	0.129824	+	0.224862i
$663$	−8.71497	+	15.0948i	−0.338462	+	0.586233i
$664$	−1.08744			−0.0422009
$665$	−80.9388	+	22.4769i	−3.13867	+	0.871616i
$666$		−	10.8800i		−	0.421590i
$667$	−11.2992	+	36.5784i	−0.437507	+	1.41632i
$668$	7.64904	−	4.41618i	0.295950	−	0.170867i
$669$	14.2983	+	24.7653i	0.552803	+	0.957483i
$670$	−3.92433	−	2.26571i	−0.151610	−	0.0875322i
$671$			12.8195i			0.494890i
$672$	−1.85377	+	1.88773i	−0.0715107	+	0.0728209i
$673$	33.8366			1.30430			0.652152	−	0.758088i	$-0.273866\pi$
$673$	33.8366			1.30430			0.652152	+	0.758088i	$0.273866\pi$
$674$	−9.00596	−	5.19960i	−0.346897	−	0.200281i
$675$	8.45634	−	4.88227i	0.325485	−	0.187919i
$676$	−1.00632	−	1.74299i	−0.0387045	−	0.0670382i
$677$	9.21263	−	15.9567i	0.354070	−	0.613267i	−0.632888	−	0.774243i	$-0.718131\pi$
$677$	9.21263	−	15.9567i	0.354070	−	0.613267i	0.986958	+	0.160976i	$0.0514641\pi$
$678$	−1.65561			−0.0635833
$679$	−3.70444	+	14.3447i	−0.142163	+	0.550501i
$680$	20.2050			0.774827
$681$	−18.6772	−	10.7833i	−0.715712	−	0.413216i
$682$	9.28796	+	16.0872i	0.355654	+	0.616012i
$683$	8.34771	+	14.4587i	0.319416	+	0.553245i	0.980366	−	0.197185i	$-0.0631799\pi$
$683$	8.34771	+	14.4587i	0.319416	+	0.553245i	−0.660950	+	0.750430i	$0.729847\pi$
$684$	4.13142	−	7.15583i	0.157969	−	0.273610i
$685$		−	71.3739i		−	2.72706i
$686$	5.27872	+	17.7520i	0.201543	+	0.677776i
$687$			12.8033i			0.488476i
$688$	−6.71417	−	3.87643i	−0.255975	−	0.147788i
$689$	2.50260	+	4.33464i	0.0953416	+	0.165137i
$690$	13.5136	−	12.5286i	0.514455	−	0.476956i
$691$	16.5739	+	9.56893i	0.630500	+	0.364019i	0.780946	−	0.624599i	$-0.214738\pi$
$691$	16.5739	+	9.56893i	0.630500	+	0.364019i	−0.150446	+	0.988618i	$0.548071\pi$
$692$		−	10.6900i		−	0.406375i
$693$	−8.10598	−	2.09331i	−0.307921	−	0.0795185i
$694$	−6.51517			−0.247312
$695$	22.2662	+	12.8554i	0.844603	+	0.487632i
$696$	6.91324	−	3.99136i	0.262046	−	0.151292i
$697$	−45.7348	+	26.4050i	−1.73233	+	1.00016i
$698$	6.53437	+	3.77262i	0.247329	+	0.142796i
$699$		−	24.0339i		−	0.909046i
$700$	18.4329	+	18.1012i	0.696697	+	0.684162i
$701$			18.7657i			0.708770i	0.935100	+	0.354385i	$0.115310\pi$
$701$			18.7657i			0.708770i	−0.935100	+	0.354385i	$0.884690\pi$
$702$	1.65736	−	2.87063i	0.0625530	−	0.108345i
$703$	−77.8551	+	44.9497i	−2.93636	+	1.69531i
$704$	2.74035	−	1.58214i	0.103281	−	0.0596292i
$705$	−5.92479	+	10.2620i	−0.223140	+	0.386490i
$706$			3.56351i			0.134115i
$707$	−3.84692	−	13.8527i	−0.144678	−	0.520984i
$708$	3.02328			0.113622
$709$	−15.4892	−	8.94271i	−0.581710	−	0.335851i	0.180102	−	0.983648i	$-0.442357\pi$
$709$	−15.4892	−	8.94271i	−0.581710	−	0.335851i	−0.761813	+	0.647797i	$0.775690\pi$
$710$	−13.7653	−	23.8422i	−0.516603	−	0.894783i
$711$	0.906949	−	0.523627i	0.0340132	−	0.0196376i
$712$	−7.52955	+	13.0416i	−0.282182	+	0.488753i
$713$	−6.25368	−	27.4506i	−0.234202	−	1.02803i
$714$	3.72260	+	13.4050i	0.139315	+	0.501669i
$715$	40.3025			1.50723
$716$	−7.27746	+	12.6049i	−0.271972	+	0.471069i
$717$	−10.5870	+	6.11241i	−0.395379	+	0.228272i
$718$	−2.53871	+	1.46572i	−0.0947437	+	0.0547003i
$719$	5.85392	+	3.37976i	0.218314	+	0.126044i	0.605170	−	0.796097i	$-0.293105\pi$
$719$	5.85392	+	3.37976i	0.218314	+	0.126044i	−0.386855	+	0.922141i	$0.626439\pi$
$720$	−3.84247			−0.143200
$721$	14.4475	+	14.1876i	0.538055	+	0.528374i
$722$	−49.2745			−1.83381
$723$	−4.14061	−	2.39058i	−0.153991	−	0.0889066i
$724$	5.79384	+	10.0352i	0.215326	+	0.372956i
$725$	−38.9738	−	67.5047i	−1.44745	−	2.50706i
$726$	−0.855034	−	0.493654i	−0.0317333	−	0.0183212i
$727$	−2.39234			−0.0887271			−0.0443636	−	0.999015i	$-0.514126\pi$
$727$	−2.39234			−0.0887271			−0.0443636	+	0.999015i	$0.514126\pi$
$728$	8.49135	+	2.19283i	0.314710	+	0.0812719i
$729$	−1.00000			−0.0370370
$730$	45.2952	+	26.1512i	1.67645	+	0.967900i
$731$	−35.3055	+	20.3836i	−1.30582	+	0.753915i
$732$	−3.50853	+	2.02565i	−0.129679	+	0.0748702i
$733$	18.1850	−	31.4973i	0.671678	−	1.16338i	−0.305750	−	0.952112i	$-0.598907\pi$
$733$	18.1850	−	31.4973i	0.671678	−	1.16338i	0.977428	−	0.211268i	$-0.0677594\pi$
$734$	−11.4780			−0.423659
$735$	−13.0235	+	23.5340i	−0.480381	+	0.868065i
$736$	−4.67602	+	1.06527i	−0.172361	+	0.0392665i
$737$	−1.86582	+	3.23170i	−0.0687285	+	0.119041i
$738$	8.69756	−	5.02154i	0.320162	−	0.184845i
$739$	4.04206	+	7.00105i	0.148690	+	0.257538i	0.930743	−	0.365673i	$-0.119161\pi$
$739$	4.04206	+	7.00105i	0.148690	+	0.257538i	−0.782054	+	0.623211i	$0.785828\pi$
$740$	36.2049	+	20.9029i	1.33092	+	0.768407i
$741$	−27.3890			−1.00616
$742$	3.86817	+	0.998929i	0.142005	+	0.0366718i
$743$			2.68703i			0.0985774i	0.998785	+	0.0492887i	$0.0156954\pi$
$743$			2.68703i			0.0985774i	−0.998785	+	0.0492887i	$0.984305\pi$
$744$	−2.93525	+	5.08400i	−0.107611	+	0.186389i
$745$	21.5858	−	12.4626i	0.790842	−	0.456593i
$746$	−0.499769	+	0.288542i	−0.0182978	+	0.0105643i
$747$	0.543720	−	0.941751i	0.0198937	−	0.0344569i
$748$		−	16.6389i		−	0.608379i
$749$	5.14102	−	5.23521i	0.187849	−	0.191291i
$750$			18.3076i			0.668499i
$751$	6.53812	+	3.77479i	0.238580	+	0.137744i	0.614524	−	0.788898i	$-0.289348\pi$
$751$	6.53812	+	3.77479i	0.238580	+	0.137744i	−0.375944	+	0.926642i	$0.622682\pi$
$752$	2.67069	−	1.54192i	0.0973900	−	0.0562281i
$753$	14.2293	−	8.21532i	0.518546	−	0.299383i
$754$	−22.9155	−	13.2302i	−0.834532	−	0.481817i
$755$	−6.78510			−0.246935
$756$	−0.707941	−	2.54928i	−0.0257476	−	0.0927164i
$757$			54.2699i			1.97247i	0.165342	+	0.986236i	$0.447127\pi$
$757$			54.2699i			1.97247i	−0.165342	+	0.986236i	$0.552873\pi$
$758$	−16.0989	−	9.29468i	−0.584737	−	0.337598i
$759$	−10.3174	−	11.1285i	−0.374496	−	0.403940i
$760$	15.8748	+	27.4960i	0.575841	+	0.997386i
$761$	−11.8731	−	6.85496i	−0.430401	−	0.248492i	0.269116	−	0.963108i	$-0.413268\pi$
$761$	−11.8731	−	6.85496i	−0.430401	−	0.248492i	−0.699518	+	0.714615i	$0.746602\pi$
$762$			10.7509i			0.389463i
$763$	−0.881205	−	3.17320i	−0.0319018	−	0.114878i
$764$			4.50137i			0.162854i
$765$	−10.1025	+	17.4981i	−0.365257	+	0.632644i
$766$	−4.47528	−	7.75141i	−0.161698	−	0.280070i
$767$	−5.01066	−	8.67873i	−0.180925	−	0.313371i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	25.6420			0.924674			0.462337	−	0.886704i	$-0.347011\pi$
$769$	25.6420			0.924674			0.462337	+	0.886704i	$0.347011\pi$
$770$	22.5393	−	22.9523i	0.812261	−	0.827143i
$771$	−2.67018			−0.0961640
$772$	9.37357	−	16.2355i	0.337362	−	0.584328i
$773$	7.29750	+	12.6396i	0.262473	+	0.454616i	0.966898	−	0.255161i	$-0.0821286\pi$
$773$	7.29750	+	12.6396i	0.262473	+	0.454616i	−0.704426	+	0.709778i	$0.748795\pi$
$774$	6.71417	−	3.87643i	0.241336	−	0.139335i
$775$	49.6429	+	28.6614i	1.78323	+	1.02955i
$776$	5.59968			0.201017
$777$	−7.19758	+	27.8713i	−0.258212	+	0.999877i
$778$		−	32.3192i		−	1.15870i
$779$	−71.8666	−	41.4922i	−2.57489	−	1.48661i
$780$	6.36835	+	11.0303i	0.228023	+	0.394948i
$781$	−19.6341	+	11.3358i	−0.702565	+	0.405626i
$782$	−7.44297	+	24.0948i	−0.266160	+	0.861627i
$783$			7.98273i			0.285279i
$784$	5.99764	−	3.60948i	0.214201	−	0.128910i
$785$	18.5814			0.663198
$786$	−7.81945	+	13.5437i	−0.278911	+	0.483087i
$787$	8.47508	+	14.6793i	0.302104	+	0.523259i	0.976612	−	0.215008i	$-0.0689777\pi$
$787$	8.47508	+	14.6793i	0.302104	+	0.523259i	−0.674508	+	0.738267i	$0.735644\pi$
$788$	−9.76235	−	16.9089i	−0.347769	−	0.602354i
$789$	11.8849	−	20.5853i	0.423114	−	0.732855i
$790$			4.02404i			0.143169i
$791$	4.24119	+	1.09526i	0.150800	+	0.0389430i
$792$			3.16428i			0.112438i
$793$	11.6298	+	6.71447i	0.412986	+	0.238438i
$794$	6.31851	−	3.64799i	0.224235	−	0.129462i
$795$	2.90105	+	5.02477i	0.102890	+	0.178210i
$796$	−10.4887	+	18.1670i	−0.371763	+	0.643913i
$797$	12.6258			0.447227			0.223614	−	0.974678i	$-0.428215\pi$
$797$	12.6258			0.447227			0.223614	+	0.974678i	$0.428215\pi$
$798$	−15.3174	+	15.5980i	−0.542230	+	0.552165i
$799$		−	16.2159i		−	0.573678i
$800$	4.88227	−	8.45634i	0.172614	−	0.298977i
$801$	−7.52955	−	13.0416i	−0.266043	−	0.460801i
$802$	3.63684	−	2.09973i	0.128421	−	0.0741441i
$803$	21.5356	−	37.3008i	0.759975	−	1.31632i
$804$	−1.17930			−0.0415908
$805$	−42.9063	+	23.1548i	−1.51225	+	0.816099i
$806$	19.4591			0.685416
$807$	−11.3173	+	19.6022i	−0.398388	+	0.690029i
$808$	−4.70595	+	2.71698i	−0.165555	+	0.0955831i
$809$	−3.20899	−	5.55813i	−0.112822	−	0.195413i	0.804085	−	0.594514i	$-0.202656\pi$
$809$	−3.20899	−	5.55813i	−0.112822	−	0.195413i	−0.916907	+	0.399101i	$0.869322\pi$
$810$	1.92123	−	3.32767i	0.0675052	−	0.116923i
$811$		−	25.3306i		−	0.889479i	−0.895660	−	0.444739i	$-0.853296\pi$
$811$		−	25.3306i		−	0.889479i	0.895660	−	0.444739i	$-0.146704\pi$
$812$	−20.3502	+	5.65130i	−0.714152	+	0.198322i
$813$	17.4850			0.613226
$814$	17.2136	−	29.8149i	0.603338	−	1.04501i
$815$	4.10674	+	7.11308i	0.143853	+	0.249160i
$816$	4.55386	−	2.62917i	0.159417	−	0.0920395i
$817$	−55.4781	−	32.0303i	−1.94093	−	1.12060i
$818$			30.4640i			1.06515i
$819$	−6.14473	+	6.25731i	−0.214714	+	0.218648i
$820$			38.5902i			1.34763i
$821$	17.1333	−	29.6758i	0.597957	−	1.03569i	−0.395165	−	0.918610i	$-0.629313\pi$
$821$	17.1333	−	29.6758i	0.597957	−	1.03569i	0.993122	−	0.117082i	$-0.0373540\pi$
$822$	−9.28751	−	16.0864i	−0.323939	−	0.561079i
$823$	−8.68006	−	15.0343i	−0.302568	−	0.524063i	0.674149	−	0.738595i	$-0.264511\pi$
$823$	−8.68006	−	15.0343i	−0.302568	−	0.524063i	−0.976717	+	0.214533i	$0.931177\pi$
$824$	3.82669	−	6.62802i	0.133309	−	0.230898i
$825$	30.8978			1.07572
$826$	−7.74477	−	2.00004i	−0.269475	−	0.0695901i
$827$			8.08668i			0.281201i	0.990066	+	0.140601i	$0.0449034\pi$
$827$			8.08668i			0.281201i	−0.990066	+	0.140601i	$0.955097\pi$
$828$	1.41546	−	4.58219i	0.0491906	−	0.159242i
$829$	19.5904	−	11.3105i	0.680404	−	0.392831i	−0.119603	−	0.992822i	$-0.538162\pi$
$829$	19.5904	−	11.3105i	0.680404	−	0.392831i	0.800007	+	0.599990i	$0.204829\pi$
$830$	2.08923	+	3.61865i	0.0725181	+	0.125605i
$831$	20.9141	+	12.0748i	0.725502	+	0.418869i
$832$		−	3.31472i		−	0.114917i
$833$	−0.668216	−	36.8024i	−0.0231523	−	1.27513i
$834$	6.69121			0.231698
$835$	−29.3912	−	16.9690i	−1.01712	−	0.587237i
$836$	22.6431	−	13.0730i	0.783127	−	0.452139i
$837$	−2.93525	−	5.08400i	−0.101457	−	0.175729i
$838$	8.27714	−	14.3364i	0.285929	−	0.495244i
$839$	−37.7138			−1.30202			−0.651012	−	0.759067i	$-0.725655\pi$
$839$	−37.7138			−1.30202			−0.651012	+	0.759067i	$0.725655\pi$
$840$	9.84328	+	2.54196i	0.339626	+	0.0877060i
$841$	34.7239			1.19738
$842$	5.34360	+	3.08513i	0.184153	+	0.106321i
$843$	−10.3077	−	17.8534i	−0.355015	−	0.614903i
$844$	6.23505	+	10.7994i	0.214619	+	0.371732i
$845$	−3.86674	+	6.69739i	−0.133020	+	0.230397i
$846$			3.08385i			0.106025i
$847$	1.86377	+	1.83024i	0.0640401	+	0.0628879i
$848$		−	1.50999i		−	0.0518534i
$849$	3.31924	+	1.91637i	0.113916	+	0.0657695i
$850$	−25.6727	−	44.4664i	−0.880566	−	1.52518i
$851$	−38.2639	+	35.4748i	−1.31167	+	1.21606i
$852$	−6.20493	−	3.58242i	−0.212577	−	0.122732i
$853$		−	49.0763i		−	1.68034i	−0.542322	−	0.840171i	$-0.682455\pi$
$853$		−	49.0763i		−	1.68034i	0.542322	−	0.840171i	$-0.317545\pi$
$854$	10.3279	−	2.86808i	0.353413	−	0.0981437i
$855$	−31.7497			−1.08582
$856$	−2.40173	−	1.38664i	−0.0820895	−	0.0473944i
$857$	−48.7693	+	28.1570i	−1.66593	+	0.961825i	−0.696131	+	0.717915i	$0.745097\pi$
$857$	−48.7693	+	28.1570i	−1.66593	+	0.961825i	−0.969798	+	0.243910i	$0.921570\pi$
$858$	9.08349	−	5.24436i	0.310105	−	0.179039i
$859$	15.9142	+	9.18809i	0.542987	+	0.313494i	0.746289	−	0.665623i	$-0.231834\pi$
$859$	15.9142	+	9.18809i	0.542987	+	0.313494i	−0.203302	+	0.979116i	$0.565167\pi$
$860$			29.7901i			1.01583i
$861$	−25.6026	+	7.10991i	−0.872535	+	0.242305i
$862$		−	13.3204i		−	0.453694i
$863$	15.0371	−	26.0450i	0.511869	−	0.886583i	−0.488036	−	0.872823i	$-0.662287\pi$
$863$	15.0371	−	26.0450i	0.511869	−	0.886583i	0.999905	−	0.0137598i	$-0.00438002\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−35.5730	+	20.5381i	−1.20952	+	0.698315i
$866$	−20.0256	+	34.6853i	−0.680496	+	1.17865i
$867$		−	10.6502i		−	0.361700i
$868$	10.8826	−	11.0819i	0.369378	−	0.376145i
$869$	3.31381			0.112413
$870$	−26.5639	−	15.3367i	−0.900601	−	0.519962i
$871$	1.95453	+	3.38534i	0.0662267	+	0.114708i
$872$	−1.07798	+	0.622372i	−0.0365050	+	0.0210762i
$873$	−2.79984	+	4.84946i	−0.0947602	+	0.164129i
$874$	−38.6372	+	8.80218i	−1.30692	+	0.297738i
$875$	12.1113	−	46.8988i	0.409436	−	1.58547i
$876$	13.6117			0.459896
$877$	−1.58559	+	2.74632i	−0.0535414	+	0.0927365i	−0.891554	−	0.452915i	$-0.850384\pi$
$877$	−1.58559	+	2.74632i	−0.0535414	+	0.0927365i	0.838012	+	0.545651i	$0.183718\pi$
$878$	27.2080	−	15.7085i	0.918225	−	0.530137i
$879$	−4.29753	+	2.48118i	−0.144952	+	0.0836882i
$880$	−10.5297	−	6.07933i	−0.354956	−	0.204934i
$881$	7.17622			0.241773			0.120886	−	0.992666i	$-0.461426\pi$
$881$	7.17622			0.241773			0.120886	+	0.992666i	$0.461426\pi$
$882$	0.127077	+	6.99885i	0.00427891	+	0.235663i
$883$	−31.1613			−1.04866			−0.524330	−	0.851515i	$-0.675684\pi$
$883$	−31.1613			−1.04866			−0.524330	+	0.851515i	$0.675684\pi$
$884$	−15.0948	−	8.71497i	−0.507692	−	0.293116i
$885$	−5.80843	−	10.0605i	−0.195248	−	0.338180i
$886$	5.94122	+	10.2905i	0.199599	+	0.345716i
$887$	−21.6396	−	12.4936i	−0.726588	−	0.419496i	0.0905848	−	0.995889i	$-0.471126\pi$
$887$	−21.6396	−	12.4936i	−0.726588	−	0.419496i	−0.817173	+	0.576393i	$0.804460\pi$
$888$	10.8800			0.365107
$889$	7.11219	−	27.5406i	0.238535	−	0.923683i
$890$	57.8641			1.93961
$891$	−2.74035	−	1.58214i	−0.0918052	−	0.0530037i
$892$	−24.7653	+	14.2983i	−0.829205	+	0.478742i
$893$	22.0675	−	12.7407i	0.738460	−	0.426350i
$894$	3.24337	−	5.61769i	0.108475	−	0.187884i
$895$	55.9268			1.86943
$896$	−1.88773	−	1.85377i	−0.0630648	−	0.0619301i
$897$	−15.4997	+	3.53108i	−0.517520	+	0.117899i
$898$	−13.9201	+	24.1104i	−0.464521	+	0.804573i
$899$	−40.5842	+	23.4313i	−1.35356	+	0.781477i
$900$	4.88227	+	8.45634i	0.162742	+	0.281878i
$901$	−6.87631	−	3.97004i	−0.229083	−	0.132261i
$902$	31.7792			1.05813
$903$	−19.7642	+	5.48856i	−0.657711	+	0.182648i
$904$		−	1.65561i		−	0.0550648i
$905$	22.2626	−	38.5600i	0.740035	−	1.28178i
$906$	−1.52924	+	0.882910i	−0.0508057	+	0.0293327i
$907$	38.5055	−	22.2312i	1.27855	−	0.738173i	0.301971	−	0.953317i	$-0.402355\pi$
$907$	38.5055	−	22.2312i	1.27855	−	0.738173i	0.976582	+	0.215144i	$0.0690219\pi$
$908$	10.7833	−	18.6772i	0.357856	−	0.619825i
$909$		−	5.43396i		−	0.180233i
$910$	−9.01683	−	32.4694i	−0.298905	−	1.07635i
$911$		−	36.5152i		−	1.20980i	−0.796301	−	0.604901i	$-0.793213\pi$
$911$		−	36.5152i		−	1.20980i	0.796301	−	0.604901i	$-0.206787\pi$
$912$	7.15583	+	4.13142i	0.236953	+	0.136805i
$913$	2.97997	−	1.72049i	0.0986225	−	0.0569397i
$914$	19.9389	−	11.5117i	0.659520	−	0.380774i
$915$	13.4814	+	7.78350i	0.445682	+	0.257314i
$916$	−12.8033			−0.423033
$917$	28.9909	−	29.5221i	0.957365	−	0.974905i
$918$			5.25835i			0.173551i
$919$	20.2679	+	11.7017i	0.668577	+	0.386003i	0.795537	−	0.605905i	$-0.207189\pi$
$919$	20.2679	+	11.7017i	0.668577	+	0.386003i	−0.126960	+	0.991908i	$0.540522\pi$
$920$	12.5286	+	13.5136i	0.413056	+	0.445531i
$921$	12.5846	+	21.7971i	0.414675	+	0.718239i
$922$	3.32884	+	1.92191i	0.109630	+	0.0632947i
$923$			23.7494i			0.781721i
$924$	2.09331	−	8.10598i	0.0688650	−	0.266667i
$925$		−	106.238i		−	3.49308i
$926$	−4.71276	+	8.16273i	−0.154871	+	0.268244i
$927$	3.82669	+	6.62802i	0.125685	+	0.217693i
$928$	3.99136	+	6.91324i	0.131023	+	0.226938i
$929$	−38.0309	−	21.9572i	−1.24775	−	0.720391i	−0.277092	−	0.960843i	$-0.589371\pi$
$929$	−38.0309	−	21.9572i	−1.24775	−	0.720391i	−0.970661	+	0.240452i	$0.922704\pi$
$930$	22.5572			0.739679
$931$	49.5575	−	29.8245i	1.62418	−	0.977459i
$932$	24.0339			0.787257
$933$	0.155027	−	0.268515i	0.00507536	−	0.00879078i
$934$	11.2398	+	19.4679i	0.367778	+	0.637010i
$935$	−55.3688	+	31.9672i	−1.81075	+	1.04544i
$936$	2.87063	+	1.65736i	0.0938295	+	0.0541725i
$937$	−46.8749			−1.53134			−0.765668	−	0.643236i	$-0.777591\pi$
$937$	−46.8749			−1.53134			−0.765668	+	0.643236i	$0.777591\pi$
$938$	3.02103	+	0.780161i	0.0986402	+	0.0254732i
$939$			6.03056i			0.196800i
$940$	−10.2620	−	5.92479i	−0.334711	−	0.193245i
$941$	−12.0581	−	20.8852i	−0.393082	−	0.680838i	0.599772	−	0.800171i	$-0.295258\pi$
$941$	−12.0581	−	20.8852i	−0.393082	−	0.680838i	−0.992854	+	0.119333i	$0.961925\pi$
$942$	4.18792	−	2.41790i	0.136450	−	0.0787793i
$943$	−46.0193	−	14.2156i	−1.49860	−	0.462922i
$944$			3.02328i			0.0983994i
$945$	−7.12305	+	7.25355i	−0.231713	+	0.235958i
$946$	24.5322			0.797612
$947$	0.0204261	−	0.0353790i	0.000663759	−	0.00114966i	−0.865693	−	0.500575i	$-0.833122\pi$
$947$	0.0204261	−	0.0353790i	0.000663759	−	0.00114966i	0.866357	+	0.499425i	$0.166455\pi$
$948$	0.523627	+	0.906949i	0.0170066	+	0.0294563i
$949$	−22.5595	−	39.0741i	−0.732311	−	1.26840i
$950$	40.3414	−	69.8734i	1.30885	−	2.26699i
$951$		−	9.01522i		−	0.292338i
$952$	−13.4050	+	3.72260i	−0.434458	+	0.120650i
$953$			36.3545i			1.17764i	0.808265	+	0.588819i	$0.200407\pi$
$953$			36.3545i			1.17764i	−0.808265	+	0.588819i	$0.799593\pi$
$954$	1.30769	+	0.754997i	0.0423381	+	0.0244439i
$955$	14.9791	−	8.64819i	0.484712	−	0.279849i
$956$	−6.11241	−	10.5870i	−0.197689	−	0.342408i
$957$	−12.6298	+	21.8755i	−0.408264	+	0.707133i
$958$	−17.5878			−0.568236
$959$	13.1500	+	47.3529i	0.424636	+	1.52910i
$960$		−	3.84247i		−	0.124015i
$961$	1.73138	−	2.99883i	0.0558508	−	0.0967364i
$962$	−18.0320	−	31.2323i	−0.581375	−	1.00697i
$963$	2.40173	−	1.38664i	0.0773947	−	0.0446839i
$964$	2.39058	−	4.14061i	0.0769954	−	0.133360i
$965$	−72.0352			−2.31890
$966$	−6.65732	+	10.8019i	−0.214196	+	0.347544i
$967$	17.3961			0.559420			0.279710	−	0.960085i	$-0.409762\pi$
$967$	17.3961			0.559420			0.279710	+	0.960085i	$0.409762\pi$
$968$	0.493654	−	0.855034i	0.0158666	−	0.0274818i
$969$	37.6278	−	21.7244i	1.20878	−	0.697890i
$970$	−10.7583	−	18.6339i	−0.345428	−	0.598298i
$971$	−6.04254	+	10.4660i	−0.193914	+	0.335870i	−0.946544	−	0.322574i	$-0.895452\pi$
$971$	−6.04254	+	10.4660i	−0.193914	+	0.335870i	0.752630	+	0.658444i	$0.228785\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−17.1409	−	4.42653i	−0.549513	−	0.141908i
$974$	4.65655			0.149206
$975$	16.1834	−	28.0304i	0.518282	−	0.897691i
$976$	−2.02565	−	3.50853i	−0.0648395	−	0.112305i
$977$	26.8202	−	15.4847i	0.858054	−	0.495398i	−0.00530597	−	0.999986i	$-0.501689\pi$
$977$	26.8202	−	15.4847i	0.858054	−	0.495398i	0.863360	+	0.504588i	$0.168356\pi$
$978$	1.85118	+	1.06878i	0.0591941	+	0.0341757i
$979$		−	47.6512i		−	1.52294i
$980$	−23.5340	−	13.0235i	−0.751767	−	0.416022i
$981$		−	1.24474i		−	0.0397416i
$982$	13.4174	−	23.2396i	0.428166	−	0.741605i
$983$	−4.01636	−	6.95654i	−0.128102	−	0.221879i	0.794839	−	0.606820i	$-0.207555\pi$
$983$	−4.01636	−	6.95654i	−0.128102	−	0.221879i	−0.922941	+	0.384941i	$0.874222\pi$
$984$	5.02154	+	8.69756i	0.160081	+	0.277268i
$985$	−37.5115	+	64.9718i	−1.19522	+	2.07018i
$986$	41.9759			1.33679
$987$	2.04010	−	7.89992i	0.0649372	−	0.251457i
$988$		−	27.3890i		−	0.871360i
$989$	−35.5251	−	10.9738i	−1.12963	−	0.348948i
$990$	10.5297	−	6.07933i	0.334656	−	0.193214i
$991$	−2.20324	−	3.81613i	−0.0699883	−	0.121223i	0.828908	−	0.559386i	$-0.188963\pi$
$991$	−2.20324	−	3.81613i	−0.0699883	−	0.121223i	−0.898896	+	0.438162i	$0.855630\pi$
$992$	−5.08400	−	2.93525i	−0.161417	−	0.0931943i
$993$		−	6.68058i		−	0.212002i
$994$	13.5253	+	13.2819i	0.428996	+	0.421278i
$995$	80.6052			2.55536
$996$	0.941751	+	0.543720i	0.0298405	+	0.0172284i
$997$	2.70337	−	1.56079i	0.0856167	−	0.0494308i	−0.456580	−	0.889682i	$-0.650926\pi$
$997$	2.70337	−	1.56079i	0.0856167	−	0.0494308i	0.542197	+	0.840251i	$0.317593\pi$
$998$	4.87269	+	8.43974i	0.154242	+	0.267155i
$999$	−5.43998	+	9.42232i	−0.172113	+	0.298109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.b.229.2	✓	32
7.3	odd	6	inner	966.2.k.b.367.7	yes	32
23.22	odd	2	inner	966.2.k.b.229.7	yes	32
161.45	even	6	inner	966.2.k.b.367.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.b.229.2	✓	32	1.1	even	1	trivial
966.2.k.b.229.7	yes	32	23.22	odd	2	inner
966.2.k.b.367.2	yes	32	161.45	even	6	inner
966.2.k.b.367.7	yes	32	7.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.92123 + 3.32767i) q^{5} +1.00000i q^{6} +(0.661545 - 2.56171i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.92123 + 3.32767i) q^{5} +1.00000i q^{6} +(0.661545 - 2.56171i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.92123 + 3.32767i) q^{10} +(2.74035 - 1.58214i) q^{11} +(0.866025 + 0.500000i) q^{12} -3.31472i q^{13} +(-1.88773 - 1.85377i) q^{14} -3.84247i q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.62917 + 4.55386i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-4.13142 + 7.15583i) q^{19} +3.84247 q^{20} +(0.707941 + 2.54928i) q^{21} -3.16428i q^{22} +(-1.41546 + 4.58219i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.88227 - 8.45634i) q^{25} +(-2.87063 - 1.65736i) q^{26} +1.00000i q^{27} +(-2.54928 + 0.707941i) q^{28} +7.98273 q^{29} +(-3.32767 - 1.92123i) q^{30} +(-5.08400 + 2.93525i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.58214 + 2.74035i) q^{33} +5.25835 q^{34} +(7.25355 + 7.12305i) q^{35} -1.00000 q^{36} +(9.42232 + 5.43998i) q^{37} +(4.13142 + 7.15583i) q^{38} +(1.65736 + 2.87063i) q^{39} +(1.92123 - 3.32767i) q^{40} +10.0431i q^{41} +(2.56171 + 0.661545i) q^{42} +7.75286i q^{43} +(-2.74035 - 1.58214i) q^{44} +(1.92123 + 3.32767i) q^{45} +(3.26057 + 3.51692i) q^{46} +(-2.67069 - 1.54192i) q^{47} -1.00000i q^{48} +(-6.12472 - 3.38937i) q^{49} -9.76454 q^{50} +(-4.55386 - 2.62917i) q^{51} +(-2.87063 + 1.65736i) q^{52} +(-1.30769 + 0.754997i) q^{53} +(0.866025 + 0.500000i) q^{54} +12.1587i q^{55} +(-0.661545 + 2.56171i) q^{56} -8.26284i q^{57} +(3.99136 - 6.91324i) q^{58} +(2.61824 - 1.51164i) q^{59} +(-3.32767 + 1.92123i) q^{60} +(-2.02565 + 3.50853i) q^{61} +5.87050i q^{62} +(-1.88773 - 1.85377i) q^{63} +1.00000 q^{64} +(11.0303 + 6.36835i) q^{65} +(1.58214 + 2.74035i) q^{66} +(-1.02131 + 0.589651i) q^{67} +(2.62917 - 4.55386i) q^{68} +(-1.06527 - 4.67602i) q^{69} +(9.79551 - 2.72024i) q^{70} -7.16483 q^{71} +(-0.500000 + 0.866025i) q^{72} +(11.7881 - 6.80584i) q^{73} +(9.42232 - 5.43998i) q^{74} +(8.45634 + 4.88227i) q^{75} +8.26284 q^{76} +(-2.24013 - 8.06664i) q^{77} +3.31472 q^{78} +(0.906949 + 0.523627i) q^{79} +(-1.92123 - 3.32767i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.69756 + 5.02154i) q^{82} +1.08744 q^{83} +(1.85377 - 1.88773i) q^{84} -20.2050 q^{85} +(6.71417 + 3.87643i) q^{86} +(-6.91324 + 3.99136i) q^{87} +(-2.74035 + 1.58214i) q^{88} +(7.52955 - 13.0416i) q^{89} +3.84247 q^{90} +(-8.49135 - 2.19283i) q^{91} +(4.67602 - 1.06527i) q^{92} +(2.93525 - 5.08400i) q^{93} +(-2.67069 + 1.54192i) q^{94} +(-15.8748 - 27.4960i) q^{95} +(-0.866025 - 0.500000i) q^{96} -5.59968 q^{97} +(-5.99764 + 3.60948i) q^{98} -3.16428i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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