LMFDB - Embedded newform 966.2.f.b.461.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(461,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("966.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.f (of order $2$, degree $1$, 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:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.18
Character	$\chi$	$=$	966.461
Dual form			966.2.f.b.461.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.375300 - 1.69090i) q^{3} -1.00000 q^{4} -0.513446 q^{5} +(1.69090 - 0.375300i) q^{6} +(-2.61371 - 0.410499i) q^{7} -1.00000i q^{8} +(-2.71830 + 1.26919i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.375300 - 1.69090i) q^{3} -1.00000 q^{4} -0.513446 q^{5} +(1.69090 - 0.375300i) q^{6} +(-2.61371 - 0.410499i) q^{7} -1.00000i q^{8} +(-2.71830 + 1.26919i) q^{9} -0.513446i q^{10} -3.12460i q^{11} +(0.375300 + 1.69090i) q^{12} +5.94261i q^{13} +(0.410499 - 2.61371i) q^{14} +(0.192696 + 0.868187i) q^{15} +1.00000 q^{16} +5.76481 q^{17} +(-1.26919 - 2.71830i) q^{18} -0.598956i q^{19} +0.513446 q^{20} +(0.286811 + 4.57359i) q^{21} +3.12460 q^{22} -1.00000i q^{23} +(-1.69090 + 0.375300i) q^{24} -4.73637 q^{25} -5.94261 q^{26} +(3.16625 + 4.12005i) q^{27} +(2.61371 + 0.410499i) q^{28} +7.46215i q^{29} +(-0.868187 + 0.192696i) q^{30} +7.72010i q^{31} +1.00000i q^{32} +(-5.28339 + 1.17266i) q^{33} +5.76481i q^{34} +(1.34200 + 0.210769i) q^{35} +(2.71830 - 1.26919i) q^{36} -1.50999 q^{37} +0.598956 q^{38} +(10.0484 - 2.23026i) q^{39} +0.513446i q^{40} -1.20021 q^{41} +(-4.57359 + 0.286811i) q^{42} +5.20634 q^{43} +3.12460i q^{44} +(1.39570 - 0.651660i) q^{45} +1.00000 q^{46} +6.27170 q^{47} +(-0.375300 - 1.69090i) q^{48} +(6.66298 + 2.14585i) q^{49} -4.73637i q^{50} +(-2.16353 - 9.74773i) q^{51} -5.94261i q^{52} +11.4811i q^{53} +(-4.12005 + 3.16625i) q^{54} +1.60431i q^{55} +(-0.410499 + 2.61371i) q^{56} +(-1.01278 + 0.224788i) q^{57} -7.46215 q^{58} +11.2251 q^{59} +(-0.192696 - 0.868187i) q^{60} -0.414953i q^{61} -7.72010 q^{62} +(7.62586 - 2.20144i) q^{63} -1.00000 q^{64} -3.05121i q^{65} +(-1.17266 - 5.28339i) q^{66} -6.23026 q^{67} -5.76481 q^{68} +(-1.69090 + 0.375300i) q^{69} +(-0.210769 + 1.34200i) q^{70} +4.92377i q^{71} +(1.26919 + 2.71830i) q^{72} +3.88420i q^{73} -1.50999i q^{74} +(1.77756 + 8.00874i) q^{75} +0.598956i q^{76} +(-1.28265 + 8.16681i) q^{77} +(2.23026 + 10.0484i) q^{78} -12.9971 q^{79} -0.513446 q^{80} +(5.77831 - 6.90008i) q^{81} -1.20021i q^{82} -11.5826 q^{83} +(-0.286811 - 4.57359i) q^{84} -2.95992 q^{85} +5.20634i q^{86} +(12.6178 - 2.80054i) q^{87} -3.12460 q^{88} +3.08081 q^{89} +(0.651660 + 1.39570i) q^{90} +(2.43944 - 15.5323i) q^{91} +1.00000i q^{92} +(13.0539 - 2.89735i) q^{93} +6.27170i q^{94} +0.307531i q^{95} +(1.69090 - 0.375300i) q^{96} +4.96299i q^{97} +(-2.14585 + 6.66298i) q^{98} +(3.96571 + 8.49360i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9	$ 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9} + 24 q^{16} + 16 q^{18} - 28 q^{21} + 8 q^{22} - 24 q^{25} + 4 q^{28} + 24 q^{30} - 8 q^{36} + 40 q^{37} + 72 q^{39} + 64 q^{43} + 24 q^{46} - 24 q^{51} + 16 q^{58} + 12 q^{63} - 24 q^{64} - 64 q^{67} + 16 q^{70} - 16 q^{72} - 32 q^{78} + 88 q^{79} + 48 q^{81} + 28 q^{84} + 64 q^{85} - 8 q^{88} - 56 q^{91} + 8 q^{93} - 8 q^{99}+O(q^{100}) $ 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9 + 24 * q^16 + 16 * q^18 - 28 * q^21 + 8 * q^22 - 24 * q^25 + 4 * q^28 + 24 * q^30 - 8 * q^36 + 40 * q^37 + 72 * q^39 + 64 * q^43 + 24 * q^46 - 24 * q^51 + 16 * q^58 + 12 * q^63 - 24 * q^64 - 64 * q^67 + 16 * q^70 - 16 * q^72 - 32 * q^78 + 88 * q^79 + 48 * q^81 + 28 * q^84 + 64 * q^85 - 8 * q^88 - 56 * q^91 + 8 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.375300	−	1.69090i	−0.216679	−	0.976243i
$3$	−0.375300	−	1.69090i	−0.216679	−	0.976243i
$4$	−1.00000			−0.500000
$5$	−0.513446			−0.229620			−0.114810	−	0.993387i	$-0.536626\pi$
$5$	−0.513446			−0.229620			−0.114810	+	0.993387i	$0.536626\pi$
$6$	1.69090	−	0.375300i	0.690308	−	0.153215i
$7$	−2.61371	−	0.410499i	−0.987890	−	0.155154i
$7$	−2.61371	−	0.410499i	−0.987890	−	0.155154i
$8$		−	1.00000i		−	0.353553i
$9$	−2.71830	+	1.26919i	−0.906100	+	0.423063i
$10$		−	0.513446i		−	0.162366i
$11$		−	3.12460i		−	0.942103i	−0.882106	−	0.471051i	$-0.843875\pi$
$11$		−	3.12460i		−	0.942103i	0.882106	−	0.471051i	$-0.156125\pi$
$12$	0.375300	+	1.69090i	0.108340	+	0.488121i
$13$			5.94261i			1.64818i	0.566456	+	0.824092i	$0.308314\pi$
$13$			5.94261i			1.64818i	−0.566456	+	0.824092i	$0.691686\pi$
$14$	0.410499	−	2.61371i	0.109711	−	0.698544i
$15$	0.192696	+	0.868187i	0.0497539	+	0.224165i
$16$	1.00000			0.250000
$17$	5.76481			1.39817			0.699086	−	0.715038i	$-0.253590\pi$
$17$	5.76481			1.39817			0.699086	+	0.715038i	$0.253590\pi$
$18$	−1.26919	−	2.71830i	−0.299151	−	0.640710i
$19$		−	0.598956i		−	0.137410i	−0.997637	−	0.0687049i	$-0.978113\pi$
$19$		−	0.598956i		−	0.137410i	0.997637	−	0.0687049i	$-0.0218867\pi$
$20$	0.513446			0.114810
$21$	0.286811	+	4.57359i	0.0625874	+	0.998039i
$22$	3.12460			0.666167
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	−1.69090	+	0.375300i	−0.345154	+	0.0766077i
$25$	−4.73637			−0.947275
$26$	−5.94261			−1.16544
$27$	3.16625	+	4.12005i	0.609346	+	0.792905i
$28$	2.61371	+	0.410499i	0.493945	+	0.0775770i
$29$			7.46215i			1.38569i	0.721088	+	0.692843i	$0.243642\pi$
$29$			7.46215i			1.38569i	−0.721088	+	0.692843i	$0.756358\pi$
$30$	−0.868187	+	0.192696i	−0.158508	+	0.0351813i
$31$			7.72010i			1.38657i	0.720663	+	0.693286i	$0.243838\pi$
$31$			7.72010i			1.38657i	−0.720663	+	0.693286i	$0.756162\pi$
$32$			1.00000i			0.176777i
$33$	−5.28339	+	1.17266i	−0.919721	+	0.204134i
$34$			5.76481i			0.988657i
$35$	1.34200	+	0.210769i	0.226839	+	0.0356265i
$36$	2.71830	−	1.26919i	0.453050	−	0.211532i
$37$	−1.50999			−0.248241			−0.124121	−	0.992267i	$-0.539611\pi$
$37$	−1.50999			−0.248241			−0.124121	+	0.992267i	$0.539611\pi$
$38$	0.598956			0.0971635
$39$	10.0484	−	2.23026i	1.60903	−	0.357127i
$40$			0.513446i			0.0811829i
$41$	−1.20021			−0.187441			−0.0937203	−	0.995599i	$-0.529876\pi$
$41$	−1.20021			−0.187441			−0.0937203	+	0.995599i	$0.529876\pi$
$42$	−4.57359	+	0.286811i	−0.705720	+	0.0442560i
$43$	5.20634			0.793960			0.396980	−	0.917827i	$-0.370058\pi$
$43$	5.20634			0.793960			0.396980	+	0.917827i	$0.370058\pi$
$44$			3.12460i			0.471051i
$45$	1.39570	−	0.651660i	0.208059	−	0.0971438i
$46$	1.00000			0.147442
$47$	6.27170			0.914821			0.457411	−	0.889256i	$-0.348777\pi$
$47$	6.27170			0.914821			0.457411	+	0.889256i	$0.348777\pi$
$48$	−0.375300	−	1.69090i	−0.0541698	−	0.244061i
$49$	6.66298	+	2.14585i	0.951854	+	0.306550i
$50$		−	4.73637i		−	0.669824i
$51$	−2.16353	−	9.74773i	−0.302955	−	1.36496i
$52$		−	5.94261i		−	0.824092i
$53$			11.4811i			1.57705i	0.615003	+	0.788525i	$0.289155\pi$
$53$			11.4811i			1.57705i	−0.615003	+	0.788525i	$0.710845\pi$
$54$	−4.12005	+	3.16625i	−0.560668	+	0.430872i
$55$			1.60431i			0.216326i
$56$	−0.410499	+	2.61371i	−0.0548553	+	0.349272i
$57$	−1.01278	+	0.224788i	−0.134145	+	0.0297739i
$58$	−7.46215			−0.979829
$59$	11.2251			1.46138			0.730692	−	0.682708i	$-0.239198\pi$
$59$	11.2251			1.46138			0.730692	+	0.682708i	$0.239198\pi$
$60$	−0.192696	−	0.868187i	−0.0248770	−	0.112082i
$61$		−	0.414953i		−	0.0531293i	−0.999647	−	0.0265647i	$-0.991543\pi$
$61$		−	0.414953i		−	0.0531293i	0.999647	−	0.0265647i	$-0.00845679\pi$
$62$	−7.72010			−0.980454
$63$	7.62586	−	2.20144i	0.960768	−	0.277355i
$64$	−1.00000			−0.125000
$65$		−	3.05121i		−	0.378456i
$66$	−1.17266	−	5.28339i	−0.144345	−	0.650341i
$67$	−6.23026			−0.761147			−0.380574	−	0.924751i	$-0.624273\pi$
$67$	−6.23026			−0.761147			−0.380574	+	0.924751i	$0.624273\pi$
$68$	−5.76481			−0.699086
$69$	−1.69090	+	0.375300i	−0.203561	+	0.0451808i
$70$	−0.210769	+	1.34200i	−0.0251917	+	0.160400i
$71$			4.92377i			0.584344i	0.956366	+	0.292172i	$0.0943780\pi$
$71$			4.92377i			0.584344i	−0.956366	+	0.292172i	$0.905622\pi$
$72$	1.26919	+	2.71830i	0.149575	+	0.320355i
$73$			3.88420i			0.454612i	0.973823	+	0.227306i	$0.0729917\pi$
$73$			3.88420i			0.454612i	−0.973823	+	0.227306i	$0.927008\pi$
$74$		−	1.50999i		−	0.175533i
$75$	1.77756	+	8.00874i	0.205255	+	0.924770i
$76$			0.598956i			0.0687049i
$77$	−1.28265	+	8.16681i	−0.146171	+	0.930694i
$78$	2.23026	+	10.0484i	0.252527	+	1.13775i
$79$	−12.9971			−1.46229			−0.731144	−	0.682223i	$-0.761013\pi$
$79$	−12.9971			−1.46229			−0.731144	+	0.682223i	$0.761013\pi$
$80$	−0.513446			−0.0574050
$81$	5.77831	−	6.90008i	0.642035	−	0.766675i
$82$		−	1.20021i		−	0.132541i
$83$	−11.5826			−1.27136			−0.635680	−	0.771953i	$-0.719280\pi$
$83$	−11.5826			−1.27136			−0.635680	+	0.771953i	$0.719280\pi$
$84$	−0.286811	−	4.57359i	−0.0312937	−	0.499020i
$85$	−2.95992			−0.321048
$86$			5.20634i			0.561414i
$87$	12.6178	−	2.80054i	1.35277	−	0.300250i
$88$	−3.12460			−0.333084
$89$	3.08081			0.326565			0.163283	−	0.986579i	$-0.447792\pi$
$89$	3.08081			0.326565			0.163283	+	0.986579i	$0.447792\pi$
$90$	0.651660	+	1.39570i	0.0686910	+	0.147120i
$91$	2.43944	−	15.5323i	0.255722	−	1.62822i
$92$			1.00000i			0.104257i
$93$	13.0539	−	2.89735i	1.35363	−	0.300441i
$94$			6.27170i			0.646876i
$95$			0.307531i			0.0315521i
$96$	1.69090	−	0.375300i	0.172577	−	0.0383039i
$97$			4.96299i			0.503915i	0.967738	+	0.251958i	$0.0810744\pi$
$97$			4.96299i			0.503915i	−0.967738	+	0.251958i	$0.918926\pi$
$98$	−2.14585	+	6.66298i	−0.216764	+	0.673063i
$99$	3.96571	+	8.49360i	0.398569	+	0.853639i
$100$	4.73637			0.473637
$101$	−11.5773			−1.15199			−0.575993	−	0.817455i	$-0.695384\pi$
$101$	−11.5773			−1.15199			−0.575993	+	0.817455i	$0.695384\pi$
$102$	9.74773	−	2.16353i	0.965169	−	0.214222i
$103$			9.68173i			0.953969i	0.878912	+	0.476985i	$0.158270\pi$
$103$			9.68173i			0.953969i	−0.878912	+	0.476985i	$0.841730\pi$
$104$	5.94261			0.582721
$105$	−0.147262	−	2.34829i	−0.0143713	−	0.229170i
$106$	−11.4811			−1.11514
$107$		−	8.90889i		−	0.861255i	−0.902530	−	0.430628i	$-0.858292\pi$
$107$		−	8.90889i		−	0.861255i	0.902530	−	0.430628i	$-0.141708\pi$
$108$	−3.16625	−	4.12005i	−0.304673	−	0.396452i
$109$	0.131905			0.0126342			0.00631710	−	0.999980i	$-0.497989\pi$
$109$	0.131905			0.0126342			0.00631710	+	0.999980i	$0.497989\pi$
$110$	−1.60431			−0.152965
$111$	0.566700	+	2.55325i	0.0537888	+	0.242344i
$112$	−2.61371	−	0.410499i	−0.246973	−	0.0387885i
$113$		−	2.89434i		−	0.272277i	−0.990690	−	0.136138i	$-0.956531\pi$
$113$		−	2.89434i		−	0.272277i	0.990690	−	0.136138i	$-0.0434692\pi$
$114$	−0.224788	−	1.01278i	−0.0210533	−	0.0948551i
$115$			0.513446i			0.0478791i
$116$		−	7.46215i		−	0.692843i
$117$	−7.54230	−	16.1538i	−0.697286	−	1.49342i
$118$			11.2251i			1.03335i
$119$	−15.0676	−	2.36645i	−1.38124	−	0.216932i
$120$	0.868187	−	0.192696i	0.0792542	−	0.0175907i
$121$	1.23687			0.112443
$122$	0.414953			0.0375681
$123$	0.450437	+	2.02943i	0.0406145	+	0.182988i
$124$		−	7.72010i		−	0.693286i
$125$	4.99910			0.447133
$126$	2.20144	+	7.62586i	0.196120	+	0.679365i
$127$	2.86544			0.254267			0.127133	−	0.991886i	$-0.459422\pi$
$127$	2.86544			0.254267			0.127133	+	0.991886i	$0.459422\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−1.95394	−	8.80341i	−0.172035	−	0.775097i
$130$	3.05121			0.267609
$131$	−6.14864			−0.537209			−0.268605	−	0.963251i	$-0.586562\pi$
$131$	−6.14864			−0.537209			−0.268605	+	0.963251i	$0.586562\pi$
$132$	5.28339	−	1.17266i	0.459860	−	0.102067i
$133$	−0.245871	+	1.56550i	−0.0213197	+	0.135746i
$134$		−	6.23026i		−	0.538212i
$135$	−1.62570	−	2.11542i	−0.139918	−	0.182067i
$136$		−	5.76481i		−	0.494328i
$137$		−	5.99665i		−	0.512329i	−0.966633	−	0.256164i	$-0.917541\pi$
$137$		−	5.99665i		−	0.512329i	0.966633	−	0.256164i	$-0.0824588\pi$
$138$	−0.375300	−	1.69090i	−0.0319476	−	0.143939i
$139$			11.1572i			0.946341i	0.880971	+	0.473170i	$0.156891\pi$
$139$			11.1572i			0.946341i	−0.880971	+	0.473170i	$0.843109\pi$
$140$	−1.34200	−	0.210769i	−0.113420	−	0.0178132i
$141$	−2.35377	−	10.6048i	−0.198223	−	0.893087i
$142$	−4.92377			−0.413194
$143$	18.5683			1.55276
$144$	−2.71830	+	1.26919i	−0.226525	+	0.105766i
$145$		−	3.83141i		−	0.318181i
$146$	−3.88420			−0.321459
$147$	1.12781	−	12.0718i	0.0930204	−	0.995664i
$148$	1.50999			0.124121
$149$			19.4811i			1.59595i	0.602688	+	0.797977i	$0.294096\pi$
$149$			19.4811i			1.59595i	−0.602688	+	0.797977i	$0.705904\pi$
$150$	−8.00874	+	1.77756i	−0.653911	+	0.145137i
$151$	−17.5790			−1.43056			−0.715279	−	0.698839i	$-0.753700\pi$
$151$	−17.5790			−1.43056			−0.715279	+	0.698839i	$0.753700\pi$
$152$	−0.598956			−0.0485817
$153$	−15.6705	+	7.31664i	−1.26688	+	0.591515i
$154$	−8.16681	−	1.28265i	−0.658100	−	0.103359i
$155$		−	3.96385i		−	0.318384i
$156$	−10.0484	+	2.23026i	−0.804514	+	0.178564i
$157$		−	20.1823i		−	1.61072i	−0.592787	−	0.805359i	$-0.701972\pi$
$157$		−	20.1823i		−	1.61072i	0.592787	−	0.805359i	$-0.298028\pi$
$158$		−	12.9971i		−	1.03399i
$159$	19.4134	−	4.30885i	1.53958	−	0.341714i
$160$		−	0.513446i		−	0.0405915i
$161$	−0.410499	+	2.61371i	−0.0323519	+	0.205989i
$162$	6.90008	+	5.77831i	0.542121	+	0.453987i
$163$	−12.0967			−0.947490			−0.473745	−	0.880662i	$-0.657098\pi$
$163$	−12.0967			−0.947490			−0.473745	+	0.880662i	$0.657098\pi$
$164$	1.20021			0.0937203
$165$	2.71274	−	0.602098i	0.211186	−	0.0468733i
$166$		−	11.5826i		−	0.898987i
$167$	9.90523			0.766490			0.383245	−	0.923647i	$-0.374807\pi$
$167$	9.90523			0.766490			0.383245	+	0.923647i	$0.374807\pi$
$168$	4.57359	−	0.286811i	0.352860	−	0.0221280i
$169$	−22.3146			−1.71651
$170$		−	2.95992i		−	0.227015i
$171$	0.760189	+	1.62814i	0.0581331	+	0.124507i
$172$	−5.20634			−0.396980
$173$	15.4859			1.17737			0.588686	−	0.808362i	$-0.299646\pi$
$173$	15.4859			1.17737			0.588686	+	0.808362i	$0.299646\pi$
$174$	2.80054	+	12.6178i	0.212309	+	0.956551i
$175$	12.3795	+	1.94428i	0.935803	+	0.146974i
$176$		−	3.12460i		−	0.235526i
$177$	−4.21278	−	18.9805i	−0.316652	−	1.42667i
$178$			3.08081i			0.230917i
$179$		−	1.39837i		−	0.104519i	−0.998634	−	0.0522594i	$-0.983358\pi$
$179$		−	1.39837i		−	0.104519i	0.998634	−	0.0522594i	$-0.0166423\pi$
$180$	−1.39570	+	0.651660i	−0.104029	+	0.0485719i
$181$		−	8.72194i		−	0.648296i	−0.946006	−	0.324148i	$-0.894922\pi$
$181$		−	8.72194i		−	0.648296i	0.946006	−	0.324148i	$-0.105078\pi$
$182$	15.5323	+	2.43944i	1.15133	+	0.180823i
$183$	−0.701645	+	0.155732i	−0.0518671	+	0.0115120i
$184$	−1.00000			−0.0737210
$185$	0.775300			0.0570012
$186$	2.89735	+	13.0539i	0.212444	+	0.957161i
$187$		−	18.0127i		−	1.31722i
$188$	−6.27170			−0.457411
$189$	−6.58440	−	12.0684i	−0.478944	−	0.877845i
$190$	−0.307531			−0.0223107
$191$			2.53346i			0.183314i	0.995791	+	0.0916572i	$0.0292164\pi$
$191$			2.53346i			0.183314i	−0.995791	+	0.0916572i	$0.970784\pi$
$192$	0.375300	+	1.69090i	0.0270849	+	0.122030i
$193$	−20.4444			−1.47162			−0.735811	−	0.677187i	$-0.763199\pi$
$193$	−20.4444			−1.47162			−0.735811	+	0.677187i	$0.763199\pi$
$194$	−4.96299			−0.356322
$195$	−5.15930	+	1.14512i	−0.369465	+	0.0820036i
$196$	−6.66298	−	2.14585i	−0.475927	−	0.153275i
$197$		−	12.1385i		−	0.864830i	−0.901675	−	0.432415i	$-0.857662\pi$
$197$		−	12.1385i		−	0.864830i	0.901675	−	0.432415i	$-0.142338\pi$
$198$	−8.49360	+	3.96571i	−0.603614	+	0.281831i
$199$		−	5.49653i		−	0.389639i	−0.980839	−	0.194819i	$-0.937588\pi$
$199$		−	5.49653i		−	0.389639i	0.980839	−	0.194819i	$-0.0624121\pi$
$200$			4.73637i			0.334912i
$201$	2.33821	+	10.5348i	0.164925	+	0.743065i
$202$		−	11.5773i		−	0.814577i
$203$	3.06321	−	19.5039i	0.214995	−	1.36891i
$204$	2.16353	+	9.74773i	0.151477	+	0.682478i
$205$	0.616241			0.0430401
$206$	−9.68173			−0.674558
$207$	1.26919	+	2.71830i	0.0882148	+	0.188935i
$208$			5.94261i			0.412046i
$209$	−1.87150			−0.129454
$210$	2.34829	−	0.147262i	0.162048	−	0.0101621i
$211$	20.5183			1.41254			0.706268	−	0.707944i	$-0.250377\pi$
$211$	20.5183			1.41254			0.706268	+	0.707944i	$0.250377\pi$
$212$		−	11.4811i		−	0.788525i
$213$	8.32562	−	1.84789i	0.570462	−	0.126615i
$214$	8.90889			0.608999
$215$	−2.67317			−0.182309
$216$	4.12005	−	3.16625i	0.280334	−	0.215436i
$217$	3.16909	−	20.1781i	0.215132	−	1.36978i
$218$			0.131905i			0.00893373i
$219$	6.56781	−	1.45774i	0.443812	−	0.0985050i
$220$		−	1.60431i		−	0.108163i
$221$			34.2580i			2.30444i
$222$	−2.55325	+	0.566700i	−0.171363	+	0.0380344i
$223$			13.9302i			0.932837i	0.884564	+	0.466419i	$0.154456\pi$
$223$			13.9302i			0.932837i	−0.884564	+	0.466419i	$0.845544\pi$
$224$	0.410499	−	2.61371i	0.0274276	−	0.174636i
$225$	12.8749	−	6.01136i	0.858326	−	0.400757i
$226$	2.89434			0.192529
$227$	20.1970			1.34052			0.670260	−	0.742126i	$-0.266182\pi$
$227$	20.1970			1.34052			0.670260	+	0.742126i	$0.266182\pi$
$228$	1.01278	−	0.224788i	0.0670727	−	0.0148869i
$229$			5.07556i			0.335402i	0.985838	+	0.167701i	$0.0536344\pi$
$229$			5.07556i			0.335402i	−0.985838	+	0.167701i	$0.946366\pi$
$230$	−0.513446			−0.0338556
$231$	14.2906	−	0.896171i	0.940256	−	0.0589637i
$232$	7.46215			0.489914
$233$			16.3692i			1.07238i	0.844096	+	0.536192i	$0.180138\pi$
$233$			16.3692i			1.07238i	−0.844096	+	0.536192i	$0.819862\pi$
$234$	16.1538	−	7.54230i	1.05601	−	0.493056i
$235$	−3.22018			−0.210061
$236$	−11.2251			−0.730692
$237$	4.87781	+	21.9768i	0.316848	+	1.42755i
$238$	2.36645	−	15.0676i	0.153394	−	0.976685i
$239$		−	17.3203i		−	1.12036i	−0.828372	−	0.560178i	$-0.810733\pi$
$239$		−	17.3203i		−	1.12036i	0.828372	−	0.560178i	$-0.189267\pi$
$240$	0.192696	+	0.868187i	0.0124385	+	0.0560412i
$241$		−	1.31010i		−	0.0843910i	−0.999109	−	0.0421955i	$-0.986565\pi$
$241$		−	1.31010i		−	0.0843910i	0.999109	−	0.0421955i	$-0.0134352\pi$
$242$			1.23687i			0.0795089i
$243$	−13.8360	−	7.18097i	−0.887577	−	0.460659i
$244$			0.414953i			0.0265647i
$245$	−3.42108	−	1.10178i	−0.218565	−	0.0703901i
$246$	−2.02943	+	0.450437i	−0.129392	+	0.0287188i
$247$	3.55936			0.226477
$248$	7.72010			0.490227
$249$	4.34696	+	19.5851i	0.275477	+	1.24116i
$250$			4.99910i			0.316171i
$251$	13.5742			0.856794			0.428397	−	0.903591i	$-0.359078\pi$
$251$	13.5742			0.856794			0.428397	+	0.903591i	$0.359078\pi$
$252$	−7.62586	+	2.20144i	−0.480384	+	0.138678i
$253$	−3.12460			−0.196442
$254$			2.86544i			0.179794i
$255$	1.11086	+	5.00493i	0.0695645	+	0.313421i
$256$	1.00000			0.0625000
$257$	−7.53285			−0.469886			−0.234943	−	0.972009i	$-0.575490\pi$
$257$	−7.53285			−0.469886			−0.234943	+	0.972009i	$0.575490\pi$
$258$	8.80341	−	1.95394i	0.548077	−	0.121647i
$259$	3.94669	+	0.619851i	0.245235	+	0.0385157i
$260$			3.05121i			0.189228i
$261$	−9.47089	−	20.2844i	−0.586233	−	1.25557i
$262$		−	6.14864i		−	0.379864i
$263$		−	11.0572i		−	0.681818i	−0.940096	−	0.340909i	$-0.889265\pi$
$263$		−	11.0572i		−	0.681818i	0.940096	−	0.340909i	$-0.110735\pi$
$264$	1.17266	+	5.28339i	0.0721723	+	0.325170i
$265$		−	5.89492i		−	0.362122i
$266$	−1.56550	−	0.245871i	−0.0959868	−	0.0150753i
$267$	−1.15623	−	5.20935i	−0.0707600	−	0.318807i
$268$	6.23026			0.380574
$269$	−23.5386			−1.43517			−0.717587	−	0.696469i	$-0.754754\pi$
$269$	−23.5386			−1.43517			−0.717587	+	0.696469i	$0.754754\pi$
$270$	2.11542	−	1.62570i	0.128741	−	0.0989369i
$271$			31.8184i			1.93283i	0.256987	+	0.966415i	$0.417270\pi$
$271$			31.8184i			1.93283i	−0.256987	+	0.966415i	$0.582730\pi$
$272$	5.76481			0.349543
$273$	−27.1791	+	1.70441i	−1.64495	+	0.103155i
$274$	5.99665			0.362271
$275$			14.7993i			0.892430i
$276$	1.69090	−	0.375300i	0.101780	−	0.0225904i
$277$	−19.4731			−1.17002			−0.585012	−	0.811024i	$-0.698910\pi$
$277$	−19.4731			−1.17002			−0.585012	+	0.811024i	$0.698910\pi$
$278$	−11.1572			−0.669164
$279$	−9.79828	−	20.9856i	−0.586607	−	1.25637i
$280$	0.210769	−	1.34200i	0.0125959	−	0.0801998i
$281$			30.0501i			1.79264i	0.443412	+	0.896318i	$0.353768\pi$
$281$			30.0501i			1.79264i	−0.443412	+	0.896318i	$0.646232\pi$
$282$	10.6048	−	2.35377i	0.631508	−	0.140165i
$283$		−	13.1776i		−	0.783325i	−0.920109	−	0.391662i	$-0.871900\pi$
$283$		−	13.1776i		−	0.783325i	0.920109	−	0.391662i	$-0.128100\pi$
$284$		−	4.92377i		−	0.292172i
$285$	0.520005	−	0.115416i	0.0308025	−	0.00683668i
$286$			18.5683i			1.09797i
$287$	3.13699	+	0.492683i	0.185171	+	0.0290822i
$288$	−1.26919	−	2.71830i	−0.0747877	−	0.160177i
$289$	16.2330			0.954885
$290$	3.83141			0.224988
$291$	8.39193	−	1.86261i	0.491944	−	0.109188i
$292$		−	3.88420i		−	0.227306i
$293$	22.0715			1.28943			0.644715	−	0.764423i	$-0.276976\pi$
$293$	22.0715			1.28943			0.644715	+	0.764423i	$0.276976\pi$
$294$	12.0718	+	1.12781i	0.704041	+	0.0657754i
$295$	−5.76348			−0.335563
$296$			1.50999i			0.0877666i
$297$	12.8735	−	9.89328i	0.746998	−	0.574066i
$298$	−19.4811			−1.12851
$299$	5.94261			0.343670
$300$	−1.77756	−	8.00874i	−0.102627	−	0.462385i
$301$	−13.6079	−	2.13720i	−0.784345	−	0.123186i
$302$		−	17.5790i		−	1.01156i
$303$	4.34496	+	19.5761i	0.249611	+	1.12462i
$304$		−	0.598956i		−	0.0343525i
$305$			0.213056i			0.0121996i
$306$	−7.31664	−	15.6705i	−0.418264	−	0.895822i
$307$			12.0164i			0.685814i	0.939369	+	0.342907i	$0.111412\pi$
$307$			12.0164i			0.685814i	−0.939369	+	0.342907i	$0.888588\pi$
$308$	1.28265	−	8.16681i	0.0730855	−	0.465347i
$309$	16.3709	−	3.63355i	0.931306	−	0.206705i
$310$	3.96385			0.225132
$311$	−1.75546			−0.0995432			−0.0497716	−	0.998761i	$-0.515849\pi$
$311$	−1.75546			−0.0995432			−0.0497716	+	0.998761i	$0.515849\pi$
$312$	−2.23026	−	10.0484i	−0.126264	−	0.568877i
$313$			11.1277i			0.628975i	0.949262	+	0.314488i	$0.101833\pi$
$313$			11.1277i			0.628975i	−0.949262	+	0.314488i	$0.898167\pi$
$314$	20.1823			1.13895
$315$	−3.91546	+	1.13032i	−0.220611	+	0.0636862i
$316$	12.9971			0.731144
$317$		−	28.4300i		−	1.59679i	−0.602135	−	0.798394i	$-0.705683\pi$
$317$		−	28.4300i		−	1.59679i	0.602135	−	0.798394i	$-0.294317\pi$
$318$	4.30885	+	19.4134i	0.241628	+	1.08865i
$319$	23.3162			1.30546
$320$	0.513446			0.0287025
$321$	−15.0641	+	3.34350i	−0.840794	+	0.186616i
$322$	−2.61371	−	0.410499i	−0.145656	−	0.0228762i
$323$		−	3.45287i		−	0.192123i
$324$	−5.77831	+	6.90008i	−0.321017	+	0.383338i
$325$		−	28.1464i		−	1.56128i
$326$		−	12.0967i		−	0.669977i
$327$	−0.0495039	−	0.223038i	−0.00273757	−	0.0123340i
$328$			1.20021i			0.0662703i
$329$	−16.3924	−	2.57453i	−0.903743	−	0.141938i
$330$	0.602098	+	2.71274i	0.0331444	+	0.149331i
$331$	13.9077			0.764437			0.382219	−	0.924072i	$-0.375160\pi$
$331$	13.9077			0.764437			0.382219	+	0.924072i	$0.375160\pi$
$332$	11.5826			0.635680
$333$	4.10461	−	1.91647i	0.224932	−	0.105022i
$334$			9.90523i			0.541990i
$335$	3.19890			0.174775
$336$	0.286811	+	4.57359i	0.0156468	+	0.249510i
$337$	21.1199			1.15048			0.575238	−	0.817986i	$-0.304910\pi$
$337$	21.1199			1.15048			0.575238	+	0.817986i	$0.304910\pi$
$338$		−	22.3146i		−	1.21376i
$339$	−4.89405	+	1.08625i	−0.265808	+	0.0589967i
$340$	2.95992			0.160524
$341$	24.1222			1.30629
$342$	−1.62814	+	0.760189i	−0.0880398	+	0.0411063i
$343$	−16.5342	−	8.34379i	−0.892765	−	0.450522i
$344$		−	5.20634i		−	0.280707i
$345$	0.868187	−	0.192696i	0.0467416	−	0.0103744i
$346$			15.4859i			0.832527i
$347$			19.1370i			1.02733i	0.857991	+	0.513664i	$0.171712\pi$
$347$			19.1370i			1.02733i	−0.857991	+	0.513664i	$0.828288\pi$
$348$	−12.6178	+	2.80054i	−0.676383	+	0.150125i
$349$			14.1011i			0.754815i	0.926047	+	0.377408i	$0.123184\pi$
$349$			14.1011i			0.754815i	−0.926047	+	0.377408i	$0.876816\pi$
$350$	−1.94428	+	12.3795i	−0.103926	+	0.661713i
$351$	−24.4839	+	18.8158i	−1.30685	+	1.00431i
$352$	3.12460			0.166542
$353$	−18.6428			−0.992255			−0.496127	−	0.868250i	$-0.665245\pi$
$353$	−18.6428			−0.992255			−0.496127	+	0.868250i	$0.665245\pi$
$354$	18.9805	−	4.21278i	1.00880	−	0.223906i
$355$		−	2.52809i		−	0.134177i
$356$	−3.08081			−0.163283
$357$	1.65341	+	26.3659i	0.0875079	+	1.39543i
$358$	1.39837			0.0739060
$359$			31.3788i			1.65611i	0.560647	+	0.828055i	$0.310552\pi$
$359$			31.3788i			1.65611i	−0.560647	+	0.828055i	$0.689448\pi$
$360$	−0.651660	−	1.39570i	−0.0343455	−	0.0735598i
$361$	18.6413			0.981119
$362$	8.72194			0.458415
$363$	−0.464196	−	2.09142i	−0.0243640	−	0.109771i
$364$	−2.43944	+	15.5323i	−0.127861	+	0.814112i
$365$		−	1.99433i		−	0.104388i
$366$	−0.155732	−	0.701645i	−0.00814023	−	0.0366756i
$367$		−	37.8630i		−	1.97643i	−0.153060	−	0.988217i	$-0.548913\pi$
$367$		−	37.8630i		−	1.97643i	0.153060	−	0.988217i	$-0.451087\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	3.26252	−	1.52329i	0.169840	−	0.0792993i
$370$			0.775300i			0.0403059i
$371$	4.71298	−	30.0083i	0.244686	−	1.55795i
$372$	−13.0539	+	2.89735i	−0.676815	+	0.150221i
$373$	29.9205			1.54922			0.774612	−	0.632437i	$-0.217945\pi$
$373$	29.9205			1.54922			0.774612	+	0.632437i	$0.217945\pi$
$374$	18.0127			0.931416
$375$	−1.87616	−	8.45299i	−0.0968845	−	0.436511i
$376$		−	6.27170i		−	0.323438i
$377$	−44.3447			−2.28387
$378$	12.0684	−	6.58440i	0.620730	−	0.338665i
$379$	4.96883			0.255232			0.127616	−	0.991824i	$-0.459268\pi$
$379$	4.96883			0.255232			0.127616	+	0.991824i	$0.459268\pi$
$380$		−	0.307531i		−	0.0157760i
$381$	−1.07540	−	4.84518i	−0.0550944	−	0.248226i
$382$	−2.53346			−0.129623
$383$	−8.23658			−0.420869			−0.210435	−	0.977608i	$-0.567488\pi$
$383$	−8.23658			−0.420869			−0.210435	+	0.977608i	$0.567488\pi$
$384$	−1.69090	+	0.375300i	−0.0862885	+	0.0191519i
$385$	0.658569	−	4.19321i	0.0335638	−	0.213706i
$386$		−	20.4444i		−	1.04059i
$387$	−14.1524	+	6.60784i	−0.719407	+	0.335895i
$388$		−	4.96299i		−	0.251958i
$389$		−	4.16289i		−	0.211067i	−0.994416	−	0.105533i	$-0.966345\pi$
$389$		−	4.16289i		−	0.211067i	0.994416	−	0.105533i	$-0.0336550\pi$
$390$	−1.14512	−	5.15930i	−0.0579853	−	0.261251i
$391$		−	5.76481i		−	0.291539i
$392$	2.14585	−	6.66298i	0.108382	−	0.336531i
$393$	2.30758	+	10.3967i	0.116402	+	0.524447i
$394$	12.1385			0.611527
$395$	6.67331			0.335771
$396$	−3.96571	−	8.49360i	−0.199285	−	0.426820i
$397$			22.7412i			1.14135i	0.821176	+	0.570675i	$0.193318\pi$
$397$			22.7412i			1.14135i	−0.821176	+	0.570675i	$0.806682\pi$
$398$	5.49653			0.275516
$399$	2.73938	−	0.171787i	0.137140	−	0.00860012i
$400$	−4.73637			−0.236819
$401$		−	3.51834i		−	0.175698i	−0.996134	−	0.0878488i	$-0.972001\pi$
$401$		−	3.51834i		−	0.175698i	0.996134	−	0.0878488i	$-0.0279992\pi$
$402$	−10.5348	+	2.33821i	−0.525426	+	0.116620i
$403$	−45.8776			−2.28532
$404$	11.5773			0.575993
$405$	−2.96685	+	3.54282i	−0.147424	+	0.176044i
$406$	19.5039	+	3.06321i	0.967963	+	0.152024i
$407$			4.71813i			0.233869i
$408$	−9.74773	+	2.16353i	−0.482585	+	0.107111i
$409$		−	18.0529i		−	0.892659i	−0.894869	−	0.446329i	$-0.852731\pi$
$409$		−	18.0529i		−	0.892659i	0.894869	−	0.446329i	$-0.147269\pi$
$410$			0.616241i			0.0304340i
$411$	−10.1398	+	2.25054i	−0.500157	+	0.111011i
$412$		−	9.68173i		−	0.476985i
$413$	−29.3392	−	4.60789i	−1.44369	−	0.226740i
$414$	−2.71830	+	1.26919i	−0.133597	+	0.0623773i
$415$	5.94706			0.291930
$416$	−5.94261			−0.291360
$417$	18.8657	−	4.18729i	0.923858	−	0.205053i
$418$		−	1.87150i		−	0.0915380i
$419$	−27.0100			−1.31952			−0.659762	−	0.751474i	$-0.729343\pi$
$419$	−27.0100			−1.31952			−0.659762	+	0.751474i	$0.729343\pi$
$420$	0.147262	+	2.34829i	0.00718565	+	0.114585i
$421$	−26.3099			−1.28227			−0.641133	−	0.767430i	$-0.721535\pi$
$421$	−26.3099			−1.28227			−0.641133	+	0.767430i	$0.721535\pi$
$422$			20.5183i			0.998814i
$423$	−17.0484	+	7.95997i	−0.828919	+	0.387027i
$424$	11.4811			0.557571
$425$	−27.3043			−1.32445
$426$	1.84789	+	8.32562i	0.0895306	+	0.403377i
$427$	−0.170338	+	1.08457i	−0.00824323	+	0.0524859i
$428$			8.90889i			0.430628i
$429$	−6.96867	−	31.3972i	−0.336451	−	1.51587i
$430$		−	2.67317i		−	0.128912i
$431$			15.9844i			0.769940i	0.922929	+	0.384970i	$0.125788\pi$
$431$			15.9844i			0.769940i	−0.922929	+	0.384970i	$0.874212\pi$
$432$	3.16625	+	4.12005i	0.152336	+	0.198226i
$433$			40.7682i			1.95920i	0.200967	+	0.979598i	$0.435592\pi$
$433$			40.7682i			1.95920i	−0.200967	+	0.979598i	$0.564408\pi$
$434$	20.1781	+	3.16909i	0.968581	+	0.152121i
$435$	−6.47854	+	1.43793i	−0.310622	+	0.0689433i
$436$	−0.131905			−0.00631710
$437$	−0.598956			−0.0286519
$438$	1.45774	+	6.56781i	0.0696535	+	0.313822i
$439$			29.4214i			1.40421i	0.712075	+	0.702104i	$0.247756\pi$
$439$			29.4214i			1.40421i	−0.712075	+	0.702104i	$0.752244\pi$
$440$	1.60431			0.0764826
$441$	−20.8355	+	2.62352i	−0.992166	+	0.124929i
$442$	−34.2580			−1.62949
$443$		−	41.1411i		−	1.95467i	−0.211692	−	0.977336i	$-0.567897\pi$
$443$		−	41.1411i		−	1.95467i	0.211692	−	0.977336i	$-0.432103\pi$
$444$	−0.566700	−	2.55325i	−0.0268944	−	0.121172i
$445$	−1.58183			−0.0749859
$446$	−13.9302			−0.659616
$447$	32.9406	−	7.31125i	1.55804	−	0.345810i
$448$	2.61371	+	0.410499i	0.123486	+	0.0193943i
$449$			37.3241i			1.76143i	0.473643	+	0.880717i	$0.342939\pi$
$449$			37.3241i			1.76143i	−0.473643	+	0.880717i	$0.657061\pi$
$450$	6.01136	+	12.8749i	0.283378	+	0.606928i
$451$			3.75016i			0.176588i
$452$			2.89434i			0.136138i
$453$	6.59739	+	29.7244i	0.309972	+	1.39657i
$454$			20.1970i			0.947891i
$455$	−1.25252	+	7.97498i	−0.0587190	+	0.373873i
$456$	0.224788	+	1.01278i	0.0105267	+	0.0474276i
$457$	−18.9154			−0.884827			−0.442414	−	0.896811i	$-0.645878\pi$
$457$	−18.9154			−0.884827			−0.442414	+	0.896811i	$0.645878\pi$
$458$	−5.07556			−0.237165
$459$	18.2529	+	23.7513i	0.851970	+	1.10862i
$460$		−	0.513446i		−	0.0239395i
$461$	−41.5200			−1.93378			−0.966890	−	0.255193i	$-0.917861\pi$
$461$	−41.5200			−1.93378			−0.966890	+	0.255193i	$0.917861\pi$
$462$	0.896171	+	14.2906i	0.0416937	+	0.664861i
$463$	−25.5118			−1.18563			−0.592817	−	0.805337i	$-0.701984\pi$
$463$	−25.5118			−1.18563			−0.592817	+	0.805337i	$0.701984\pi$
$464$			7.46215i			0.346422i
$465$	−6.70249	+	1.48763i	−0.310820	+	0.0689873i
$466$	−16.3692			−0.758290
$467$	5.49956			0.254489			0.127245	−	0.991871i	$-0.459387\pi$
$467$	5.49956			0.254489			0.127245	+	0.991871i	$0.459387\pi$
$468$	7.54230	+	16.1538i	0.348643	+	0.746710i
$469$	16.2841	+	2.55752i	0.751930	+	0.118095i
$470$		−	3.22018i		−	0.148536i
$471$	−34.1262	+	7.57439i	−1.57245	+	0.349010i
$472$		−	11.2251i		−	0.516677i
$473$		−	16.2677i		−	0.747991i
$474$	−21.9768	+	4.87781i	−1.00943	+	0.224045i
$475$			2.83688i			0.130165i
$476$	15.0676	+	2.36645i	0.690620	+	0.108466i
$477$	−14.5717	−	31.2091i	−0.667192	−	1.42896i
$478$	17.3203			0.792212
$479$	34.8057			1.59031			0.795156	−	0.606406i	$-0.207389\pi$
$479$	34.8057			1.59031			0.795156	+	0.606406i	$0.207389\pi$
$480$	−0.868187	+	0.192696i	−0.0396271	+	0.00879533i
$481$		−	8.97330i		−	0.409147i
$482$	1.31010			0.0596734
$483$	4.57359	−	0.286811i	0.208106	−	0.0130504i
$484$	−1.23687			−0.0562213
$485$		−	2.54823i		−	0.115709i
$486$	7.18097	−	13.8360i	0.325735	−	0.627612i
$487$	16.0666			0.728048			0.364024	−	0.931390i	$-0.381403\pi$
$487$	16.0666			0.728048			0.364024	+	0.931390i	$0.381403\pi$
$488$	−0.414953			−0.0187841
$489$	4.53990	+	20.4544i	0.205302	+	0.924981i
$490$	1.10178	−	3.42108i	0.0497733	−	0.154549i
$491$			0.917569i			0.0414093i	0.999786	+	0.0207047i	$0.00659097\pi$
$491$			0.917569i			0.0414093i	−0.999786	+	0.0207047i	$0.993409\pi$
$492$	−0.450437	−	2.02943i	−0.0203073	−	0.0914938i
$493$			43.0179i			1.93743i
$494$			3.55936i			0.160143i
$495$	−2.03618	−	4.36101i	−0.0915194	−	0.196013i
$496$			7.72010i			0.346643i
$497$	2.02120	−	12.8693i	0.0906634	−	0.577268i
$498$	−19.5851	+	4.34696i	−0.877629	+	0.194792i
$499$	23.2826			1.04227			0.521137	−	0.853473i	$-0.325508\pi$
$499$	23.2826			1.04227			0.521137	+	0.853473i	$0.325508\pi$
$500$	−4.99910			−0.223567
$501$	−3.71743	−	16.7488i	−0.166082	−	0.748280i
$502$			13.5742i			0.605845i
$503$	−27.6132			−1.23121			−0.615605	−	0.788055i	$-0.711088\pi$
$503$	−27.6132			−1.23121			−0.615605	+	0.788055i	$0.711088\pi$
$504$	−2.20144	−	7.62586i	−0.0980598	−	0.339683i
$505$	5.94432			0.264519
$506$		−	3.12460i		−	0.138905i
$507$	8.37467	+	37.7318i	0.371932	+	1.67573i
$508$	−2.86544			−0.127133
$509$	−0.853514			−0.0378314			−0.0189157	−	0.999821i	$-0.506021\pi$
$509$	−0.853514			−0.0378314			−0.0189157	+	0.999821i	$0.506021\pi$
$510$	−5.00493	+	1.11086i	−0.221622	+	0.0491895i
$511$	1.59446	−	10.1522i	0.0705349	−	0.449107i
$512$			1.00000i			0.0441942i
$513$	2.46773	−	1.89645i	0.108953	−	0.0837301i
$514$		−	7.53285i		−	0.332260i
$515$		−	4.97104i		−	0.219050i
$516$	1.95394	+	8.80341i	0.0860173	+	0.387549i
$517$		−	19.5966i		−	0.861855i
$518$	−0.619851	+	3.94669i	−0.0272347	+	0.173407i
$519$	−5.81185	−	26.1851i	−0.255112	−	1.14940i
$520$	−3.05121			−0.133804
$521$	−23.9342			−1.04857			−0.524287	−	0.851541i	$-0.675668\pi$
$521$	−23.9342			−1.04857			−0.524287	+	0.851541i	$0.675668\pi$
$522$	20.2844	−	9.47089i	0.887823	−	0.414530i
$523$			0.0538713i			0.00235563i	0.999999	+	0.00117781i	$0.000374910\pi$
$523$			0.0538713i			0.00235563i	−0.999999	+	0.00117781i	$0.999625\pi$
$524$	6.14864			0.268605
$525$	−1.35845	−	21.6622i	−0.0592874	−	0.945418i
$526$	11.0572			0.482118
$527$			44.5049i			1.93866i
$528$	−5.28339	+	1.17266i	−0.229930	+	0.0510335i
$529$	−1.00000			−0.0434783
$530$	5.89492			0.256059
$531$	−30.5132	+	14.2468i	−1.32416	+	0.618258i
$532$	0.245871	−	1.56550i	0.0106599	−	0.0678729i
$533$		−	7.13236i		−	0.308937i
$534$	5.20935	−	1.15623i	0.225431	−	0.0500349i
$535$			4.57423i			0.197761i
$536$			6.23026i			0.269106i
$537$	−2.36450	+	0.524807i	−0.102036	+	0.0226471i
$538$		−	23.5386i		−	1.01482i
$539$	6.70493	−	20.8192i	0.288802	−	0.896745i
$540$	1.62570	+	2.11542i	0.0699590	+	0.0910334i
$541$	29.4600			1.26658			0.633291	−	0.773914i	$-0.281704\pi$
$541$	29.4600			1.26658			0.633291	+	0.773914i	$0.281704\pi$
$542$	−31.8184			−1.36672
$543$	−14.7479	+	3.27334i	−0.632895	+	0.140472i
$544$			5.76481i			0.247164i
$545$	−0.0677260			−0.00290106
$546$	−1.70441	−	27.1791i	−0.0729419	−	1.16316i
$547$	−0.939855			−0.0401853			−0.0200926	−	0.999798i	$-0.506396\pi$
$547$	−0.939855			−0.0401853			−0.0200926	+	0.999798i	$0.506396\pi$
$548$			5.99665i			0.256164i
$549$	0.526655	+	1.12797i	0.0224771	+	0.0481405i
$550$	−14.7993			−0.631043
$551$	4.46950			0.190407
$552$	0.375300	+	1.69090i	0.0159738	+	0.0719696i
$553$	33.9707	+	5.33530i	1.44458	+	0.226880i
$554$		−	19.4731i		−	0.827333i
$555$	−0.290970	−	1.31096i	−0.0123510	−	0.0556470i
$556$		−	11.1572i		−	0.473170i
$557$		−	2.58809i		−	0.109661i	−0.998496	−	0.0548305i	$-0.982538\pi$
$557$		−	2.58809i		−	0.109661i	0.998496	−	0.0548305i	$-0.0174619\pi$
$558$	20.9856	−	9.79828i	0.888389	−	0.414794i
$559$			30.9393i			1.30859i
$560$	1.34200	+	0.210769i	0.0567098	+	0.00890662i
$561$	−30.4578	+	6.76017i	−1.28593	+	0.285415i
$562$	−30.0501			−1.26759
$563$	14.1978			0.598366			0.299183	−	0.954196i	$-0.403286\pi$
$563$	14.1978			0.598366			0.299183	+	0.954196i	$0.403286\pi$
$564$	2.35377	+	10.6048i	0.0991114	+	0.446544i
$565$			1.48609i			0.0625202i
$566$	13.1776			0.553894
$567$	−17.9353	+	15.6628i	−0.753213	+	0.657777i
$568$	4.92377			0.206597
$569$			33.1988i			1.39177i	0.718155	+	0.695883i	$0.244987\pi$
$569$			33.1988i			1.39177i	−0.718155	+	0.695883i	$0.755013\pi$
$570$	0.115416	+	0.520005i	0.00483426	+	0.0217806i
$571$	40.4709			1.69366			0.846828	−	0.531867i	$-0.178510\pi$
$571$	40.4709			1.69366			0.846828	+	0.531867i	$0.178510\pi$
$572$	−18.5683			−0.776379
$573$	4.28383	−	0.950805i	0.178959	−	0.0397205i
$574$	−0.492683	+	3.13699i	−0.0205642	+	0.130936i
$575$			4.73637i			0.197520i
$576$	2.71830	−	1.26919i	0.113263	−	0.0528829i
$577$		−	9.49368i		−	0.395227i	−0.980280	−	0.197614i	$-0.936681\pi$
$577$		−	9.49368i		−	0.395227i	0.980280	−	0.197614i	$-0.0633191\pi$
$578$			16.2330i			0.675206i
$579$	7.67279	+	34.5695i	0.318870	+	1.43666i
$580$			3.83141i			0.159091i
$581$	30.2737	+	4.75466i	1.25596	+	0.197257i
$582$	1.86261	+	8.39193i	0.0772076	+	0.347857i
$583$	35.8738			1.48574
$584$	3.88420			0.160730
$585$	3.87256	+	8.29410i	0.160111	+	0.342919i
$586$			22.0715i			0.911765i
$587$	−13.6279			−0.562484			−0.281242	−	0.959637i	$-0.590746\pi$
$587$	−13.6279			−0.562484			−0.281242	+	0.959637i	$0.590746\pi$
$588$	−1.12781	+	12.0718i	−0.0465102	+	0.497832i
$589$	4.62400			0.190529
$590$		−	5.76348i		−	0.237279i
$591$	−20.5249	+	4.55556i	−0.844284	+	0.187391i
$592$	−1.50999			−0.0620603
$593$	29.6556			1.21781			0.608905	−	0.793243i	$-0.291609\pi$
$593$	29.6556			1.21781			0.608905	+	0.793243i	$0.291609\pi$
$594$	9.89328	+	12.8735i	0.405926	+	0.528207i
$595$	7.73637	+	1.21504i	0.317160	+	0.0498119i
$596$		−	19.4811i		−	0.797977i
$597$	−9.29410	+	2.06285i	−0.380382	+	0.0844267i
$598$			5.94261i			0.243011i
$599$		−	26.8065i		−	1.09528i	−0.836713	−	0.547641i	$-0.815526\pi$
$599$		−	26.8065i		−	1.09528i	0.836713	−	0.547641i	$-0.184474\pi$
$600$	8.00874	−	1.77756i	0.326956	−	0.0725686i
$601$		−	22.5267i		−	0.918883i	−0.888208	−	0.459442i	$-0.848050\pi$
$601$		−	22.5267i		−	0.918883i	0.888208	−	0.459442i	$-0.151950\pi$
$602$	2.13720	−	13.6079i	0.0871057	−	0.554616i
$603$	16.9357	−	7.90738i	0.689676	−	0.322014i
$604$	17.5790			0.715279
$605$	−0.635065			−0.0258191
$606$	−19.5761	+	4.34496i	−0.795225	+	0.176502i
$607$		−	12.1355i		−	0.492565i	−0.969198	−	0.246282i	$-0.920791\pi$
$607$		−	12.1355i		−	0.492565i	0.969198	−	0.246282i	$-0.0792091\pi$
$608$	0.598956			0.0242909
$609$	−34.1288	+	2.14023i	−1.38297	+	0.0867265i
$610$	−0.213056			−0.00862639
$611$			37.2703i			1.50779i
$612$	15.6705	−	7.31664i	0.633442	−	0.295758i
$613$	−25.0619			−1.01224			−0.506120	−	0.862463i	$-0.668921\pi$
$613$	−25.0619			−1.01224			−0.506120	+	0.862463i	$0.668921\pi$
$614$	−12.0164			−0.484944
$615$	−0.231275	−	1.04200i	−0.00932590	−	0.0420176i
$616$	8.16681	+	1.28265i	0.329050	+	0.0516793i
$617$		−	26.2335i		−	1.05612i	−0.849207	−	0.528061i	$-0.822919\pi$
$617$		−	26.2335i		−	1.05612i	0.849207	−	0.528061i	$-0.177081\pi$
$618$	3.63355	+	16.3709i	0.146163	+	0.658533i
$619$			45.7540i			1.83901i	0.393082	+	0.919503i	$0.371409\pi$
$619$			45.7540i			1.83901i	−0.393082	+	0.919503i	$0.628591\pi$
$620$			3.96385i			0.159192i
$621$	4.12005	−	3.16625i	0.165332	−	0.127057i
$622$		−	1.75546i		−	0.0703877i
$623$	−8.05235	−	1.26467i	−0.322611	−	0.0506679i
$624$	10.0484	−	2.23026i	0.402257	−	0.0892818i
$625$	21.1151			0.844604
$626$	−11.1277			−0.444753
$627$	0.702372	+	3.16452i	0.0280501	+	0.126379i
$628$			20.1823i			0.805359i
$629$	−8.70482			−0.347084
$630$	−1.13032	−	3.91546i	−0.0450330	−	0.155996i
$631$	−4.90036			−0.195080			−0.0975402	−	0.995232i	$-0.531097\pi$
$631$	−4.90036			−0.195080			−0.0975402	+	0.995232i	$0.531097\pi$
$632$			12.9971i			0.516997i
$633$	−7.70050	−	34.6944i	−0.306068	−	1.37898i
$634$	28.4300			1.12910
$635$	−1.47125			−0.0583848
$636$	−19.4134	+	4.30885i	−0.769792	+	0.170857i
$637$	−12.7520	+	39.5955i	−0.505251	+	1.56883i
$638$			23.3162i			0.923099i
$639$	−6.24920	−	13.3843i	−0.247215	−	0.529474i
$640$			0.513446i			0.0202957i
$641$		−	31.1335i		−	1.22970i	−0.788645	−	0.614849i	$-0.789217\pi$
$641$		−	31.1335i		−	1.22970i	0.788645	−	0.614849i	$-0.210783\pi$
$642$	−3.34350	−	15.0641i	−0.131958	−	0.594531i
$643$		−	5.88939i		−	0.232255i	−0.993234	−	0.116127i	$-0.962952\pi$
$643$		−	5.88939i		−	0.232255i	0.993234	−	0.116127i	$-0.0370481\pi$
$644$	0.410499	−	2.61371i	0.0161759	−	0.102995i
$645$	1.00324	+	4.52008i	0.0395026	+	0.177978i
$646$	3.45287			0.135851
$647$	2.41417			0.0949109			0.0474554	−	0.998873i	$-0.484889\pi$
$647$	2.41417			0.0949109			0.0474554	+	0.998873i	$0.484889\pi$
$648$	−6.90008	−	5.77831i	−0.271061	−	0.226994i
$649$		−	35.0740i		−	1.37677i
$650$	28.1464			1.10399
$651$	−35.3086	+	2.21421i	−1.38385	+	0.0867818i
$652$	12.0967			0.473745
$653$		−	8.82490i		−	0.345345i	−0.984979	−	0.172673i	$-0.944760\pi$
$653$		−	8.82490i		−	0.345345i	0.984979	−	0.172673i	$-0.0552403\pi$
$654$	0.223038	−	0.0495039i	0.00872149	−	0.00193575i
$655$	3.15699			0.123354
$656$	−1.20021			−0.0468602
$657$	−4.92979	−	10.5584i	−0.192330	−	0.411924i
$658$	2.57453	−	16.3924i	0.100365	−	0.639043i
$659$		−	10.9303i		−	0.425785i	−0.977076	−	0.212893i	$-0.931712\pi$
$659$		−	10.9303i		−	0.425785i	0.977076	−	0.212893i	$-0.0682884\pi$
$660$	−2.71274	+	0.602098i	−0.105593	+	0.0234366i
$661$			1.21755i			0.0473572i	0.999720	+	0.0236786i	$0.00753784\pi$
$661$			1.21755i			0.0473572i	−0.999720	+	0.0236786i	$0.992462\pi$
$662$			13.9077i			0.540539i
$663$	57.9270	−	12.8570i	2.24970	−	0.499325i
$664$			11.5826i			0.449493i
$665$	0.126241	−	0.803798i	0.00489543	−	0.0311700i
$666$	1.91647	+	4.10461i	0.0742616	+	0.159051i
$667$	7.46215			0.288936
$668$	−9.90523			−0.383245
$669$	23.5547	−	5.22801i	0.910676	−	0.202127i
$670$			3.19890i			0.123584i
$671$	−1.29656			−0.0500533
$672$	−4.57359	+	0.286811i	−0.176430	+	0.0110640i
$673$	−0.236971			−0.00913456			−0.00456728	−	0.999990i	$-0.501454\pi$
$673$	−0.236971			−0.00913456			−0.00456728	+	0.999990i	$0.501454\pi$
$674$			21.1199i			0.813509i
$675$	−14.9966	−	19.5141i	−0.577218	−	0.751098i
$676$	22.3146			0.858255
$677$	49.8520			1.91597			0.957985	−	0.286819i	$-0.0925978\pi$
$677$	49.8520			1.91597			0.957985	+	0.286819i	$0.0925978\pi$
$678$	−1.08625	−	4.89405i	−0.0417170	−	0.187955i
$679$	2.03730	−	12.9718i	0.0781845	−	0.497813i
$680$			2.95992i			0.113508i
$681$	−7.57992	−	34.1511i	−0.290463	−	1.30867i
$682$			24.1222i			0.923688i
$683$		−	17.3214i		−	0.662784i	−0.943493	−	0.331392i	$-0.892482\pi$
$683$		−	17.3214i		−	0.662784i	0.943493	−	0.331392i	$-0.107518\pi$
$684$	−0.760189	−	1.62814i	−0.0290665	−	0.0622536i
$685$			3.07896i			0.117641i
$686$	8.34379	−	16.5342i	0.318567	−	0.631280i
$687$	8.58227	−	1.90485i	0.327434	−	0.0726747i
$688$	5.20634			0.198490
$689$	−68.2277			−2.59927
$690$	0.192696	+	0.868187i	0.00733581	+	0.0330513i
$691$		−	10.6840i		−	0.406438i	−0.979133	−	0.203219i	$-0.934860\pi$
$691$		−	10.6840i		−	0.406438i	0.979133	−	0.203219i	$-0.0651403\pi$
$692$	−15.4859			−0.588686
$693$	−6.87861	−	23.8278i	−0.261297	−	0.905142i
$694$	−19.1370			−0.726431
$695$		−	5.72861i		−	0.217299i
$696$	−2.80054	−	12.6178i	−0.106154	−	0.478275i
$697$	−6.91896			−0.262074
$698$	−14.1011			−0.533735
$699$	27.6788	−	6.14337i	1.04691	−	0.232363i
$700$	−12.3795	−	1.94428i	−0.467902	−	0.0734868i
$701$			34.4386i			1.30073i	0.759622	+	0.650365i	$0.225384\pi$
$701$			34.4386i			1.30073i	−0.759622	+	0.650365i	$0.774616\pi$
$702$	−18.8158	−	24.4839i	−0.710157	−	0.924084i
$703$			0.904419i			0.0341108i
$704$			3.12460i			0.117763i
$705$	1.20853	+	5.44500i	0.0455159	+	0.205071i
$706$		−	18.6428i		−	0.701630i
$707$	30.2598	+	4.75248i	1.13804	+	0.178735i
$708$	4.21278	+	18.9805i	0.158326	+	0.713333i
$709$	13.2555			0.497820			0.248910	−	0.968527i	$-0.419928\pi$
$709$	13.2555			0.497820			0.248910	+	0.968527i	$0.419928\pi$
$710$	2.52809			0.0948775
$711$	35.3300	−	16.4958i	1.32498	−	0.618641i
$712$		−	3.08081i		−	0.115458i
$713$	7.72010			0.289120
$714$	−26.3659	+	1.65341i	−0.986719	+	0.0618774i
$715$	−9.53381			−0.356544
$716$			1.39837i			0.0522594i
$717$	−29.2869	+	6.50030i	−1.09374	+	0.242758i
$718$	−31.3788			−1.17105
$719$	42.5915			1.58839			0.794197	−	0.607661i	$-0.207892\pi$
$719$	42.5915			1.58839			0.794197	+	0.607661i	$0.207892\pi$
$720$	1.39570	−	0.651660i	0.0520147	−	0.0242859i
$721$	3.97434	−	25.3053i	0.148012	−	0.942417i
$722$			18.6413i			0.693756i
$723$	−2.21525	+	0.491680i	−0.0823861	+	0.0182858i
$724$			8.72194i			0.324148i
$725$		−	35.3435i		−	1.31263i
$726$	2.09142	−	0.464196i	0.0776200	−	0.0172279i
$727$		−	15.2086i		−	0.564054i	−0.959406	−	0.282027i	$-0.908993\pi$
$727$		−	15.2086i		−	0.564054i	0.959406	−	0.282027i	$-0.0910068\pi$
$728$	−15.5323	−	2.43944i	−0.575664	−	0.0904115i
$729$	−6.94968	+	26.0903i	−0.257396	+	0.966306i
$730$	1.99433			0.0738134
$731$	30.0136			1.11009
$732$	0.701645	−	0.155732i	0.0259336	−	0.00575601i
$733$		−	40.0252i		−	1.47836i	−0.673506	−	0.739182i	$-0.735212\pi$
$733$		−	40.0252i		−	1.47836i	0.673506	−	0.739182i	$-0.264788\pi$
$734$	37.8630			1.39755
$735$	−0.579071	+	6.19821i	−0.0213594	+	0.228624i
$736$	1.00000			0.0368605
$737$			19.4671i			0.717079i
$738$	1.52329	+	3.26252i	0.0560730	+	0.120095i
$739$	−40.8452			−1.50252			−0.751258	−	0.660008i	$-0.770553\pi$
$739$	−40.8452			−1.50252			−0.751258	+	0.660008i	$0.770553\pi$
$740$	−0.775300			−0.0285006
$741$	−1.33583	−	6.01853i	−0.0490728	−	0.221096i
$742$	30.0083	+	4.71298i	1.10164	+	0.173019i
$743$		−	0.856157i		−	0.0314094i	−0.999877	−	0.0157047i	$-0.995001\pi$
$743$		−	0.856157i		−	0.0314094i	0.999877	−	0.0157047i	$-0.00499916\pi$
$744$	−2.89735	−	13.0539i	−0.106222	−	0.478581i
$745$		−	10.0025i		−	0.366463i
$746$			29.9205i			1.09547i
$747$	31.4851	−	14.7006i	1.15198	−	0.537866i
$748$			18.0127i			0.658611i
$749$	−3.65709	+	23.2853i	−0.133627	+	0.850826i
$750$	8.45299	−	1.87616i	0.308660	−	0.0685077i
$751$	2.12709			0.0776186			0.0388093	−	0.999247i	$-0.487644\pi$
$751$	2.12709			0.0776186			0.0388093	+	0.999247i	$0.487644\pi$
$752$	6.27170			0.228705
$753$	−5.09438	−	22.9526i	−0.185650	−	0.836439i
$754$		−	44.3447i		−	1.61494i
$755$	9.02586			0.328485
$756$	6.58440	+	12.0684i	0.239472	+	0.438923i
$757$	21.5544			0.783408			0.391704	−	0.920091i	$-0.371886\pi$
$757$	21.5544			0.783408			0.391704	+	0.920091i	$0.371886\pi$
$758$			4.96883i			0.180476i
$759$	1.17266	+	5.28339i	0.0425649	+	0.191775i
$760$	0.307531			0.0111553
$761$	−31.0013			−1.12380			−0.561898	−	0.827206i	$-0.689929\pi$
$761$	−31.0013			−1.12380			−0.561898	+	0.827206i	$0.689929\pi$
$762$	4.84518	−	1.07540i	0.175522	−	0.0389576i
$763$	−0.344762	−	0.0541469i	−0.0124812	−	0.00196025i
$764$		−	2.53346i		−	0.0916572i
$765$	8.04595	−	3.75670i	0.290902	−	0.135824i
$766$		−	8.23658i		−	0.297600i
$767$			66.7064i			2.40863i
$768$	−0.375300	−	1.69090i	−0.0135425	−	0.0610152i
$769$			29.8396i			1.07604i	0.842931	+	0.538021i	$0.180828\pi$
$769$			29.8396i			1.07604i	−0.842931	+	0.538021i	$0.819172\pi$
$770$	4.19321	+	0.658569i	0.151113	+	0.0237332i
$771$	2.82708	+	12.7373i	0.101815	+	0.458723i
$772$	20.4444			0.735811
$773$	42.9528			1.54490			0.772452	−	0.635073i	$-0.219030\pi$
$773$	42.9528			1.54490			0.772452	+	0.635073i	$0.219030\pi$
$774$	−6.60784	−	14.1524i	−0.237514	−	0.508697i
$775$		−	36.5653i		−	1.31346i
$776$	4.96299			0.178161
$777$	−0.433083	−	6.90609i	−0.0155368	−	0.247755i
$778$	4.16289			0.149247
$779$			0.718870i			0.0257562i
$780$	5.15930	−	1.14512i	0.184732	−	0.0410018i
$781$	15.3848			0.550512
$782$	5.76481			0.206149
$783$	−30.7445	+	23.6271i	−1.09872	+	0.844362i
$784$	6.66298	+	2.14585i	0.237964	+	0.0766376i
$785$			10.3625i			0.369853i
$786$	−10.3967	+	2.30758i	−0.370840	+	0.0823087i
$787$		−	1.68231i		−	0.0599678i	−0.999550	−	0.0299839i	$-0.990454\pi$
$787$		−	1.68231i		−	0.0599678i	0.999550	−	0.0299839i	$-0.00954560\pi$
$788$			12.1385i			0.432415i
$789$	−18.6967	+	4.14977i	−0.665620	+	0.147736i
$790$			6.67331i			0.237426i
$791$	−1.18812	+	7.56497i	−0.0422448	+	0.268980i
$792$	8.49360	−	3.96571i	0.301807	−	0.140915i
$793$	2.46591			0.0875669
$794$	−22.7412			−0.807056
$795$	−9.96773	+	2.21236i	−0.353519	+	0.0784644i
$796$			5.49653i			0.194819i
$797$	44.4870			1.57581			0.787905	−	0.615796i	$-0.211166\pi$
$797$	44.4870			1.57581			0.787905	+	0.615796i	$0.211166\pi$
$798$	0.171787	+	2.73938i	0.00608121	+	0.0969730i
$799$	36.1551			1.27908
$800$		−	4.73637i		−	0.167456i
$801$	−8.37457	+	3.91014i	−0.295901	+	0.138158i
$802$	3.51834			0.124237
$803$	12.1366			0.428291
$804$	−2.33821	−	10.5348i	−0.0824625	−	0.371532i
$805$	0.210769	−	1.34200i	0.00742863	−	0.0472993i
$806$		−	45.8776i		−	1.61597i
$807$	8.83403	+	39.8015i	0.310973	+	1.40108i
$808$			11.5773i			0.407288i
$809$		−	13.4852i		−	0.474116i	−0.971495	−	0.237058i	$-0.923817\pi$
$809$		−	13.4852i		−	0.474116i	0.971495	−	0.237058i	$-0.0761831\pi$
$810$	−3.54282	−	2.96685i	−0.124482	−	0.104245i
$811$			4.32003i			0.151697i	0.997119	+	0.0758484i	$0.0241665\pi$
$811$			4.32003i			0.151697i	−0.997119	+	0.0758484i	$0.975833\pi$
$812$	−3.06321	+	19.5039i	−0.107497	+	0.684453i
$813$	53.8018	−	11.9414i	1.88691	−	0.418804i
$814$	−4.71813			−0.165370
$815$	6.21102			0.217563
$816$	−2.16353	−	9.74773i	−0.0757387	−	0.341239i
$817$		−	3.11837i		−	0.109098i
$818$	18.0529			0.631205
$819$	13.0823	+	45.3175i	0.457132	+	1.58352i
$820$	−0.616241			−0.0215201
$821$			10.9091i			0.380731i	0.981713	+	0.190366i	$0.0609674\pi$
$821$			10.9091i			0.380731i	−0.981713	+	0.190366i	$0.939033\pi$
$822$	−2.25054	−	10.1398i	−0.0784967	−	0.353664i
$823$	−7.05276			−0.245844			−0.122922	−	0.992416i	$-0.539226\pi$
$823$	−7.05276			−0.245844			−0.122922	+	0.992416i	$0.539226\pi$
$824$	9.68173			0.337279
$825$	25.0241	−	5.55416i	0.871228	−	0.193371i
$826$	4.60789	−	29.3392i	0.160329	−	1.02084i
$827$		−	40.5742i		−	1.41090i	−0.708758	−	0.705452i	$-0.750744\pi$
$827$		−	40.5742i		−	1.41090i	0.708758	−	0.705452i	$-0.249256\pi$
$828$	−1.26919	−	2.71830i	−0.0441074	−	0.0944675i
$829$			11.2741i			0.391564i	0.980647	+	0.195782i	$0.0627245\pi$
$829$			11.2741i			0.391564i	−0.980647	+	0.195782i	$0.937275\pi$
$830$			5.94706i			0.206425i
$831$	7.30825	+	32.9271i	0.253520	+	1.14223i
$832$		−	5.94261i		−	0.206023i
$833$	38.4108	+	12.3704i	1.33086	+	0.428610i
$834$	4.18729	+	18.8657i	0.144994	+	0.653267i
$835$	−5.08580			−0.176001
$836$	1.87150			0.0647271
$837$	−31.8072	+	24.4438i	−1.09942	+	0.844901i
$838$		−	27.0100i		−	0.933045i
$839$	−47.6605			−1.64542			−0.822712	−	0.568459i	$-0.807540\pi$
$839$	−47.6605			−1.64542			−0.822712	+	0.568459i	$0.807540\pi$
$840$	−2.34829	+	0.147262i	−0.0810238	+	0.00508103i
$841$	−26.6837			−0.920128
$842$		−	26.3099i		−	0.906698i
$843$	50.8117	−	11.2778i	1.75005	−	0.388427i
$844$	−20.5183			−0.706268
$845$	11.4573			0.394145
$846$	−7.95997	−	17.0484i	−0.273670	−	0.586135i
$847$	−3.23282	−	0.507733i	−0.111081	−	0.0174459i
$848$			11.4811i			0.394262i
$849$	−22.2820	+	4.94553i	−0.764715	+	0.169730i
$850$		−	27.3043i		−	0.936530i
$851$			1.50999i			0.0517619i
$852$	−8.32562	+	1.84789i	−0.285231	+	0.0633077i
$853$		−	54.6638i		−	1.87165i	−0.352460	−	0.935827i	$-0.614655\pi$
$853$		−	54.6638i		−	1.87165i	0.352460	−	0.935827i	$-0.385345\pi$
$854$	−1.08457	−	0.170338i	−0.0371132	−	0.00582884i
$855$	−0.390316	−	0.835963i	−0.0133485	−	0.0285893i
$856$	−8.90889			−0.304500
$857$	−15.7189			−0.536947			−0.268473	−	0.963287i	$-0.586519\pi$
$857$	−15.7189			−0.536947			−0.268473	+	0.963287i	$0.586519\pi$
$858$	31.3972	−	6.96867i	1.07188	−	0.237907i
$859$			14.1743i			0.483620i	0.970324	+	0.241810i	$0.0777410\pi$
$859$			14.1743i			0.483620i	−0.970324	+	0.241810i	$0.922259\pi$
$860$	2.67317			0.0911545
$861$	−0.344233	−	5.48925i	−0.0117314	−	0.187073i
$862$	−15.9844			−0.544430
$863$		−	20.9276i		−	0.712383i	−0.934413	−	0.356191i	$-0.884075\pi$
$863$		−	20.9276i		−	0.712383i	0.934413	−	0.356191i	$-0.115925\pi$
$864$	−4.12005	+	3.16625i	−0.140167	+	0.107718i
$865$	−7.95117			−0.270348
$866$	−40.7682			−1.38536
$867$	−6.09225	−	27.4485i	−0.206904	−	0.932199i
$868$	−3.16909	+	20.1781i	−0.107566	+	0.684890i
$869$			40.6108i			1.37763i
$870$	−1.43793	−	6.47854i	−0.0487503	−	0.219643i
$871$		−	37.0240i		−	1.25451i
$872$		−	0.131905i		−	0.00446686i
$873$	−6.29898	−	13.4909i	−0.213188	−	0.456598i
$874$		−	0.598956i		−	0.0202600i
$875$	−13.0662	−	2.05213i	−0.441718	−	0.0693745i
$876$	−6.56781	+	1.45774i	−0.221906	+	0.0492525i
$877$	−2.57116			−0.0868218			−0.0434109	−	0.999057i	$-0.513822\pi$
$877$	−2.57116			−0.0868218			−0.0434109	+	0.999057i	$0.513822\pi$
$878$	−29.4214			−0.992925
$879$	−8.28342	−	37.3207i	−0.279393	−	1.25880i
$880$			1.60431i			0.0540814i
$881$	−10.0693			−0.339245			−0.169622	−	0.985509i	$-0.554255\pi$
$881$	−10.0693			−0.339245			−0.169622	+	0.985509i	$0.554255\pi$
$882$	−2.62352	−	20.8355i	−0.0883384	−	0.701567i
$883$	18.4902			0.622246			0.311123	−	0.950370i	$-0.399295\pi$
$883$	18.4902			0.622246			0.311123	+	0.950370i	$0.399295\pi$
$884$		−	34.2580i		−	1.15222i
$885$	2.16303	+	9.74548i	0.0727095	+	0.327591i
$886$	41.1411			1.38216
$887$	15.8796			0.533186			0.266593	−	0.963809i	$-0.414102\pi$
$887$	15.8796			0.533186			0.266593	+	0.963809i	$0.414102\pi$
$888$	2.55325	−	0.566700i	0.0856815	−	0.0190172i
$889$	−7.48944	−	1.17626i	−0.251188	−	0.0394506i
$890$		−	1.58183i		−	0.0530231i
$891$	−21.5600	−	18.0549i	−0.722287	−	0.604863i
$892$		−	13.9302i		−	0.466419i
$893$		−	3.75647i		−	0.125705i
$894$	7.31125	+	32.9406i	0.244525	+	1.10170i
$895$			0.717986i			0.0239996i
$896$	−0.410499	+	2.61371i	−0.0137138	+	0.0873180i
$897$	−2.23026	−	10.0484i	−0.0744662	−	0.335505i
$898$	−37.3241			−1.24552
$899$	−57.6086			−1.92135
$900$	−12.8749	+	6.01136i	−0.429163	+	0.200379i
$901$			66.1863i			2.20499i
$902$	−3.75016			−0.124867
$903$	1.49324	+	23.8117i	0.0496918	+	0.792403i
$904$	−2.89434			−0.0962644
$905$			4.47824i			0.148862i
$906$	−29.7244	+	6.59739i	−0.987526	+	0.219184i
$907$	−16.7086			−0.554800			−0.277400	−	0.960755i	$-0.589473\pi$
$907$	−16.7086			−0.554800			−0.277400	+	0.960755i	$0.589473\pi$
$908$	−20.1970			−0.670260
$909$	31.4706	−	14.6938i	1.04381	−	0.487363i
$910$	−7.97498	−	1.25252i	−0.264368	−	0.0415206i
$911$		−	3.78903i		−	0.125536i	−0.998028	−	0.0627681i	$-0.980007\pi$
$911$		−	3.78903i		−	0.125536i	0.998028	−	0.0627681i	$-0.0199929\pi$
$912$	−1.01278	+	0.224788i	−0.0335364	+	0.00744347i
$913$			36.1911i			1.19775i
$914$		−	18.9154i		−	0.625667i
$915$	0.360257	−	0.0799599i	0.0119097	−	0.00264339i
$916$		−	5.07556i		−	0.167701i
$917$	16.0708	+	2.52401i	0.530704	+	0.0833502i
$918$	−23.7513	+	18.2529i	−0.783911	+	0.602434i
$919$	−57.2674			−1.88908			−0.944539	−	0.328399i	$-0.893491\pi$
$919$	−57.2674			−1.88908			−0.944539	+	0.328399i	$0.893491\pi$
$920$	0.513446			0.0169278
$921$	20.3186	−	4.50976i	0.669521	−	0.148602i
$922$		−	41.5200i		−	1.36739i
$923$	−29.2601			−0.963107
$924$	−14.2906	+	0.896171i	−0.470128	+	0.0294819i
$925$	7.15189			0.235153
$926$		−	25.5118i		−	0.838370i
$927$	−12.2880	−	26.3179i	−0.403589	−	0.864392i
$928$	−7.46215			−0.244957
$929$	15.9314			0.522692			0.261346	−	0.965245i	$-0.415834\pi$
$929$	15.9314			0.522692			0.261346	+	0.965245i	$0.415834\pi$
$930$	−1.48763	−	6.70249i	−0.0487814	−	0.219783i
$931$	1.28527	−	3.99083i	0.0421231	−	0.130794i
$932$		−	16.3692i		−	0.536192i
$933$	0.658825	+	2.96832i	0.0215690	+	0.0971783i
$934$			5.49956i			0.179951i
$935$			9.24856i			0.302460i
$936$	−16.1538	+	7.54230i	−0.528003	+	0.246528i
$937$		−	16.3168i		−	0.533047i	−0.963828	−	0.266524i	$-0.914125\pi$
$937$		−	16.3168i		−	0.533047i	0.963828	−	0.266524i	$-0.0858751\pi$
$938$	−2.55752	+	16.2841i	−0.0835059	+	0.531695i
$939$	18.8159	−	4.17622i	0.614032	−	0.136286i
$940$	3.22018			0.105031
$941$	49.1465			1.60213			0.801064	−	0.598578i	$-0.204267\pi$
$941$	49.1465			1.60213			0.801064	+	0.598578i	$0.204267\pi$
$942$	−7.57439	−	34.1262i	−0.246787	−	1.11189i
$943$			1.20021i			0.0390841i
$944$	11.2251			0.365346
$945$	3.38073	+	6.19646i	0.109975	+	0.201571i
$946$	16.2677			0.528910
$947$		−	49.9998i		−	1.62477i	−0.583118	−	0.812387i	$-0.698168\pi$
$947$		−	49.9998i		−	1.62477i	0.583118	−	0.812387i	$-0.301832\pi$
$948$	−4.87781	−	21.9768i	−0.158424	−	0.713774i
$949$	−23.0823			−0.749284
$950$	−2.83688			−0.0920405
$951$	−48.0724	+	10.6698i	−1.55885	+	0.345991i
$952$	−2.36645	+	15.0676i	−0.0766971	+	0.488342i
$953$			8.16151i			0.264377i	0.991225	+	0.132189i	$0.0422005\pi$
$953$			8.16151i			0.264377i	−0.991225	+	0.132189i	$0.957800\pi$
$954$	31.2091	−	14.5717i	1.01043	−	0.471776i
$955$		−	1.30079i		−	0.0420927i
$956$			17.3203i			0.560178i
$957$	−8.75058	−	39.4255i	−0.282866	−	1.27445i
$958$			34.8057i			1.12452i
$959$	−2.46162	+	15.6735i	−0.0794899	+	0.506124i
$960$	−0.192696	−	0.868187i	−0.00621924	−	0.0280206i
$961$	−28.6000			−0.922580
$962$	8.97330			0.289311
$963$	11.3071	+	24.2170i	0.364365	+	0.780383i
$964$			1.31010i			0.0421955i
$965$	10.4971			0.337914
$966$	0.286811	+	4.57359i	0.00922800	+	0.147153i
$967$	−31.1128			−1.00052			−0.500260	−	0.865875i	$-0.666762\pi$
$967$	−31.1128			−1.00052			−0.500260	+	0.865875i	$0.666762\pi$
$968$		−	1.23687i		−	0.0397545i
$969$	−5.83846	+	1.29586i	−0.187558	+	0.0416290i
$970$	2.54823			0.0818186
$971$	−27.6668			−0.887871			−0.443935	−	0.896059i	$-0.646418\pi$
$971$	−27.6668			−0.887871			−0.443935	+	0.896059i	$0.646418\pi$
$972$	13.8360	+	7.18097i	0.443789	+	0.230330i
$973$	4.58002	−	29.1617i	0.146829	−	0.934881i
$974$			16.0666i			0.514808i
$975$	−47.5928	+	10.5633i	−1.52419	+	0.338298i
$976$		−	0.414953i		−	0.0132823i
$977$		−	2.19604i		−	0.0702576i	−0.999383	−	0.0351288i	$-0.988816\pi$
$977$		−	2.19604i		−	0.0702576i	0.999383	−	0.0351288i	$-0.0111842\pi$
$978$	−20.4544	+	4.53990i	−0.654060	+	0.145170i
$979$		−	9.62631i		−	0.307658i
$980$	3.42108	+	1.10178i	0.109282	+	0.0351950i
$981$	−0.358557	+	0.167412i	−0.0114479	+	0.00534507i
$982$	−0.917569			−0.0292808
$983$	−23.5613			−0.751489			−0.375744	−	0.926723i	$-0.622613\pi$
$983$	−23.5613			−0.751489			−0.375744	+	0.926723i	$0.622613\pi$
$984$	2.02943	−	0.450437i	0.0646959	−	0.0143594i
$985$			6.23244i			0.198582i
$986$	−43.0179			−1.36997
$987$	1.79879	+	28.6842i	0.0572562	+	0.913028i
$988$	−3.55936			−0.113238
$989$		−	5.20634i		−	0.165552i
$990$	4.36101	−	2.03618i	0.138602	−	0.0647140i
$991$	−13.7191			−0.435801			−0.217901	−	0.975971i	$-0.569921\pi$
$991$	−13.7191			−0.435801			−0.217901	+	0.975971i	$0.569921\pi$
$992$	−7.72010			−0.245113
$993$	−5.21956	−	23.5166i	−0.165638	−	0.746276i
$994$	12.8693	+	2.02120i	0.408190	+	0.0641087i
$995$			2.82217i			0.0894689i
$996$	−4.34696	−	19.5851i	−0.137739	−	0.620578i
$997$			25.1593i			0.796804i	0.917211	+	0.398402i	$0.130435\pi$
$997$			25.1593i			0.796804i	−0.917211	+	0.398402i	$0.869565\pi$
$998$			23.2826i			0.736998i
$999$	−4.78102	−	6.22125i	−0.151265	−	0.196832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.b.461.18	yes	24
3.2	odd	2	inner	966.2.f.b.461.7	yes	24
7.6	odd	2	inner	966.2.f.b.461.19	yes	24
21.20	even	2	inner	966.2.f.b.461.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.b.461.6	✓	24	21.20	even	2	inner
966.2.f.b.461.7	yes	24	3.2	odd	2	inner
966.2.f.b.461.18	yes	24	1.1	even	1	trivial
966.2.f.b.461.19	yes	24	7.6	odd	2	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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.375300 - 1.69090i) q^{3} -1.00000 q^{4} -0.513446 q^{5} +(1.69090 - 0.375300i) q^{6} +(-2.61371 - 0.410499i) q^{7} -1.00000i q^{8} +(-2.71830 + 1.26919i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.375300 - 1.69090i) q^{3} -1.00000 q^{4} -0.513446 q^{5} +(1.69090 - 0.375300i) q^{6} +(-2.61371 - 0.410499i) q^{7} -1.00000i q^{8} +(-2.71830 + 1.26919i) q^{9} -0.513446i q^{10} -3.12460i q^{11} +(0.375300 + 1.69090i) q^{12} +5.94261i q^{13} +(0.410499 - 2.61371i) q^{14} +(0.192696 + 0.868187i) q^{15} +1.00000 q^{16} +5.76481 q^{17} +(-1.26919 - 2.71830i) q^{18} -0.598956i q^{19} +0.513446 q^{20} +(0.286811 + 4.57359i) q^{21} +3.12460 q^{22} -1.00000i q^{23} +(-1.69090 + 0.375300i) q^{24} -4.73637 q^{25} -5.94261 q^{26} +(3.16625 + 4.12005i) q^{27} +(2.61371 + 0.410499i) q^{28} +7.46215i q^{29} +(-0.868187 + 0.192696i) q^{30} +7.72010i q^{31} +1.00000i q^{32} +(-5.28339 + 1.17266i) q^{33} +5.76481i q^{34} +(1.34200 + 0.210769i) q^{35} +(2.71830 - 1.26919i) q^{36} -1.50999 q^{37} +0.598956 q^{38} +(10.0484 - 2.23026i) q^{39} +0.513446i q^{40} -1.20021 q^{41} +(-4.57359 + 0.286811i) q^{42} +5.20634 q^{43} +3.12460i q^{44} +(1.39570 - 0.651660i) q^{45} +1.00000 q^{46} +6.27170 q^{47} +(-0.375300 - 1.69090i) q^{48} +(6.66298 + 2.14585i) q^{49} -4.73637i q^{50} +(-2.16353 - 9.74773i) q^{51} -5.94261i q^{52} +11.4811i q^{53} +(-4.12005 + 3.16625i) q^{54} +1.60431i q^{55} +(-0.410499 + 2.61371i) q^{56} +(-1.01278 + 0.224788i) q^{57} -7.46215 q^{58} +11.2251 q^{59} +(-0.192696 - 0.868187i) q^{60} -0.414953i q^{61} -7.72010 q^{62} +(7.62586 - 2.20144i) q^{63} -1.00000 q^{64} -3.05121i q^{65} +(-1.17266 - 5.28339i) q^{66} -6.23026 q^{67} -5.76481 q^{68} +(-1.69090 + 0.375300i) q^{69} +(-0.210769 + 1.34200i) q^{70} +4.92377i q^{71} +(1.26919 + 2.71830i) q^{72} +3.88420i q^{73} -1.50999i q^{74} +(1.77756 + 8.00874i) q^{75} +0.598956i q^{76} +(-1.28265 + 8.16681i) q^{77} +(2.23026 + 10.0484i) q^{78} -12.9971 q^{79} -0.513446 q^{80} +(5.77831 - 6.90008i) q^{81} -1.20021i q^{82} -11.5826 q^{83} +(-0.286811 - 4.57359i) q^{84} -2.95992 q^{85} +5.20634i q^{86} +(12.6178 - 2.80054i) q^{87} -3.12460 q^{88} +3.08081 q^{89} +(0.651660 + 1.39570i) q^{90} +(2.43944 - 15.5323i) q^{91} +1.00000i q^{92} +(13.0539 - 2.89735i) q^{93} +6.27170i q^{94} +0.307531i q^{95} +(1.69090 - 0.375300i) q^{96} +4.96299i q^{97} +(-2.14585 + 6.66298i) q^{98} +(3.96571 + 8.49360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9	\( 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9} + 24 q^{16} + 16 q^{18} - 28 q^{21} + 8 q^{22} - 24 q^{25} + 4 q^{28} + 24 q^{30} - 8 q^{36} + 40 q^{37} + 72 q^{39} + 64 q^{43} + 24 q^{46} - 24 q^{51} + 16 q^{58} + 12 q^{63} - 24 q^{64} - 64 q^{67} + 16 q^{70} - 16 q^{72} - 32 q^{78} + 88 q^{79} + 48 q^{81} + 28 q^{84} + 64 q^{85} - 8 q^{88} - 56 q^{91} + 8 q^{93} - 8 q^{99}+O(q^{100}) \) 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9 + 24 * q^16 + 16 * q^18 - 28 * q^21 + 8 * q^22 - 24 * q^25 + 4 * q^28 + 24 * q^30 - 8 * q^36 + 40 * q^37 + 72 * q^39 + 64 * q^43 + 24 * q^46 - 24 * q^51 + 16 * q^58 + 12 * q^63 - 24 * q^64 - 64 * q^67 + 16 * q^70 - 16 * q^72 - 32 * q^78 + 88 * q^79 + 48 * q^81 + 28 * q^84 + 64 * q^85 - 8 * q^88 - 56 * q^91 + 8 * q^93 - 8 * q^99

Introduction

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