LMFDB - Embedded newform 966.2.k.a.229.15

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			229.15
Character	$\chi$	$=$	966.229
Dual form			966.2.k.a.367.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.856094 - 1.48280i) q^{5} +1.00000i q^{6} +(-0.871223 - 2.49819i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.856094 - 1.48280i) q^{5} +1.00000i q^{6} +(-0.871223 - 2.49819i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.856094 + 1.48280i) q^{10} +(-4.71119 + 2.72001i) q^{11} +(-0.866025 - 0.500000i) q^{12} -1.89389i q^{13} +(2.59911 + 0.494596i) q^{14} -1.71219i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.914685 - 1.58428i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.07007 - 1.85341i) q^{19} -1.71219 q^{20} +(-2.00360 - 1.72789i) q^{21} -5.44002i q^{22} +(2.14896 - 4.28742i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.03421 + 1.79130i) q^{25} +(1.64016 + 0.946946i) q^{26} -1.00000i q^{27} +(-1.72789 + 2.00360i) q^{28} -3.17562 q^{29} +(1.48280 + 0.856094i) q^{30} +(-0.763565 + 0.440845i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.72001 + 4.71119i) q^{33} +1.82937 q^{34} +(-4.45017 - 0.846841i) q^{35} -1.00000 q^{36} +(-9.21832 - 5.32220i) q^{37} +(1.07007 + 1.85341i) q^{38} +(-0.946946 - 1.64016i) q^{39} +(0.856094 - 1.48280i) q^{40} +11.9233i q^{41} +(2.49819 - 0.871223i) q^{42} -10.3118i q^{43} +(4.71119 + 2.72001i) q^{44} +(-0.856094 - 1.48280i) q^{45} +(2.63853 + 4.00477i) q^{46} +(-11.4663 - 6.62008i) q^{47} +1.00000i q^{48} +(-5.48194 + 4.35297i) q^{49} -2.06841 q^{50} +(-1.58428 - 0.914685i) q^{51} +(-1.64016 + 0.946946i) q^{52} +(-3.86997 + 2.23433i) q^{53} +(0.866025 + 0.500000i) q^{54} +9.31433i q^{55} +(-0.871223 - 2.49819i) q^{56} -2.14013i q^{57} +(1.58781 - 2.75017i) q^{58} +(11.6337 - 6.71670i) q^{59} +(-1.48280 + 0.856094i) q^{60} +(2.09766 - 3.63326i) q^{61} -0.881689i q^{62} +(-2.59911 - 0.494596i) q^{63} +1.00000 q^{64} +(-2.80826 - 1.62135i) q^{65} +(-2.72001 - 4.71119i) q^{66} +(-2.17591 + 1.25626i) q^{67} +(-0.914685 + 1.58428i) q^{68} +(-0.282652 - 4.78749i) q^{69} +(2.95847 - 3.43054i) q^{70} +8.36466 q^{71} +(0.500000 - 0.866025i) q^{72} +(9.32247 - 5.38233i) q^{73} +(9.21832 - 5.32220i) q^{74} +(1.79130 + 1.03421i) q^{75} -2.14013 q^{76} +(10.8996 + 9.39974i) q^{77} +1.89389 q^{78} +(-9.82902 - 5.67479i) q^{79} +(0.856094 + 1.48280i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.3259 - 5.96165i) q^{82} +4.05428 q^{83} +(-0.494596 + 2.59911i) q^{84} -3.13223 q^{85} +(8.93027 + 5.15590i) q^{86} +(-2.75017 + 1.58781i) q^{87} +(-4.71119 + 2.72001i) q^{88} +(-3.76779 + 6.52601i) q^{89} +1.71219 q^{90} +(-4.73131 + 1.65000i) q^{91} +(-4.78749 + 0.282652i) q^{92} +(-0.440845 + 0.763565i) q^{93} +(11.4663 - 6.62008i) q^{94} +(-1.83216 - 3.17339i) q^{95} +(-0.866025 - 0.500000i) q^{96} +8.00236 q^{97} +(-1.02881 - 6.92398i) q^{98} +5.44002i 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} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 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 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 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
$5$	0.856094	−	1.48280i	0.382857	−	0.663128i	−0.608612	−	0.793468i	$-0.708274\pi$
$5$	0.856094	−	1.48280i	0.382857	−	0.663128i	0.991469	+	0.130340i	$0.0416069\pi$
$6$			1.00000i			0.408248i
$7$	−0.871223	−	2.49819i	−0.329291	−	0.944228i
$7$	−0.871223	−	2.49819i	−0.329291	−	0.944228i
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.856094	+	1.48280i	0.270721	+	0.468902i
$11$	−4.71119	+	2.72001i	−1.42048	+	0.820114i	−0.996340	−	0.0854836i	$-0.972756\pi$
$11$	−4.71119	+	2.72001i	−1.42048	+	0.820114i	−0.424139	+	0.905597i	$0.639423\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$		−	1.89389i		−	0.525271i	−0.964895	−	0.262636i	$-0.915408\pi$
$13$		−	1.89389i		−	0.525271i	0.964895	−	0.262636i	$-0.0845917\pi$
$14$	2.59911	+	0.494596i	0.694641	+	0.132186i
$15$		−	1.71219i		−	0.442085i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.914685	−	1.58428i	−0.221844	−	0.384245i	0.733524	−	0.679663i	$-0.237874\pi$
$17$	−0.914685	−	1.58428i	−0.221844	−	0.384245i	−0.955368	+	0.295419i	$0.904541\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	1.07007	−	1.85341i	0.245490	−	0.425202i	−0.716779	−	0.697300i	$-0.754384\pi$
$19$	1.07007	−	1.85341i	0.245490	−	0.425202i	0.962269	+	0.272099i	$0.0877177\pi$
$20$	−1.71219			−0.382857
$21$	−2.00360	−	1.72789i	−0.437221	−	0.377056i
$22$		−	5.44002i		−	1.15982i
$23$	2.14896	−	4.28742i	0.448090	−	0.893989i
$23$	2.14896	−	4.28742i	0.448090	−	0.893989i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	1.03421	+	1.79130i	0.206841	+	0.358259i
$26$	1.64016	+	0.946946i	0.321662	+	0.185711i
$27$		−	1.00000i		−	0.192450i
$28$	−1.72789	+	2.00360i	−0.326540	+	0.378644i
$29$	−3.17562			−0.589698			−0.294849	−	0.955544i	$-0.595269\pi$
$29$	−3.17562			−0.589698			−0.294849	+	0.955544i	$0.595269\pi$
$30$	1.48280	+	0.856094i	0.270721	+	0.156301i
$31$	−0.763565	+	0.440845i	−0.137140	+	0.0791780i	−0.567000	−	0.823718i	$-0.691896\pi$
$31$	−0.763565	+	0.440845i	−0.137140	+	0.0791780i	0.429860	+	0.902896i	$0.358563\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.72001	+	4.71119i	−0.473493	+	0.820114i
$34$	1.82937			0.313734
$35$	−4.45017	−	0.846841i	−0.752215	−	0.143142i
$36$	−1.00000			−0.166667
$37$	−9.21832	−	5.32220i	−1.51548	−	0.874964i	−0.999835	−	0.0181631i	$-0.994218\pi$
$37$	−9.21832	−	5.32220i	−1.51548	−	0.874964i	−0.515647	−	0.856801i	$-0.672448\pi$
$38$	1.07007	+	1.85341i	0.173588	+	0.300663i
$39$	−0.946946	−	1.64016i	−0.151633	−	0.262636i
$40$	0.856094	−	1.48280i	0.135360	−	0.234451i
$41$			11.9233i			1.86211i	0.364884	+	0.931053i	$0.381109\pi$
$41$			11.9233i			1.86211i	−0.364884	+	0.931053i	$0.618891\pi$
$42$	2.49819	−	0.871223i	0.385480	−	0.134433i
$43$		−	10.3118i		−	1.57253i	−0.617887	−	0.786267i	$-0.712011\pi$
$43$		−	10.3118i		−	1.57253i	0.617887	−	0.786267i	$-0.287989\pi$
$44$	4.71119	+	2.72001i	0.710239	+	0.410057i
$45$	−0.856094	−	1.48280i	−0.127619	−	0.221043i
$46$	2.63853	+	4.00477i	0.389030	+	0.590471i
$47$	−11.4663	−	6.62008i	−1.67253	−	0.965638i	−0.966213	−	0.257746i	$-0.917020\pi$
$47$	−11.4663	−	6.62008i	−1.67253	−	0.965638i	−0.706321	−	0.707892i	$-0.749646\pi$
$48$			1.00000i			0.144338i
$49$	−5.48194	+	4.35297i	−0.783134	+	0.621852i
$50$	−2.06841			−0.292518
$51$	−1.58428	−	0.914685i	−0.221844	−	0.128082i
$52$	−1.64016	+	0.946946i	−0.227449	+	0.131318i
$53$	−3.86997	+	2.23433i	−0.531581	+	0.306908i	−0.741660	−	0.670776i	$-0.765961\pi$
$53$	−3.86997	+	2.23433i	−0.531581	+	0.306908i	0.210079	+	0.977684i	$0.432628\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$			9.31433i			1.25594i
$56$	−0.871223	−	2.49819i	−0.116422	−	0.333835i
$57$		−	2.14013i		−	0.283468i
$58$	1.58781	−	2.75017i	0.208490	−	0.361115i
$59$	11.6337	−	6.71670i	1.51457	−	0.874440i	0.514721	−	0.857358i	$-0.327896\pi$
$59$	11.6337	−	6.71670i	1.51457	−	0.874440i	0.999854	−	0.0170824i	$-0.00543775\pi$
$60$	−1.48280	+	0.856094i	−0.191428	+	0.110521i
$61$	2.09766	−	3.63326i	0.268578	−	0.465191i	−0.699917	−	0.714224i	$-0.746780\pi$
$61$	2.09766	−	3.63326i	0.268578	−	0.465191i	0.968495	+	0.249034i	$0.0801130\pi$
$62$		−	0.881689i		−	0.111975i
$63$	−2.59911	−	0.494596i	−0.327457	−	0.0623132i
$64$	1.00000			0.125000
$65$	−2.80826	−	1.62135i	−0.348322	−	0.201104i
$66$	−2.72001	−	4.71119i	−0.334810	−	0.579908i
$67$	−2.17591	+	1.25626i	−0.265830	+	0.153477i	−0.626991	−	0.779026i	$-0.715714\pi$
$67$	−2.17591	+	1.25626i	−0.265830	+	0.153477i	0.361161	+	0.932503i	$0.382380\pi$
$68$	−0.914685	+	1.58428i	−0.110922	+	0.192122i
$69$	−0.282652	−	4.78749i	−0.0340273	−	0.576347i
$70$	2.95847	−	3.43054i	0.353605	−	0.410028i
$71$	8.36466			0.992703			0.496351	−	0.868122i	$-0.334673\pi$
$71$	8.36466			0.992703			0.496351	+	0.868122i	$0.334673\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	9.32247	−	5.38233i	1.09111	−	0.629954i	0.157240	−	0.987560i	$-0.449740\pi$
$73$	9.32247	−	5.38233i	1.09111	−	0.629954i	0.933872	+	0.357607i	$0.116407\pi$
$74$	9.21832	−	5.32220i	1.07161	−	0.618693i
$75$	1.79130	+	1.03421i	0.206841	+	0.119420i
$76$	−2.14013			−0.245490
$77$	10.8996	+	9.39974i	1.24213	+	1.07120i
$78$	1.89389			0.214441
$79$	−9.82902	−	5.67479i	−1.10585	−	0.638463i	−0.168099	−	0.985770i	$-0.553763\pi$
$79$	−9.82902	−	5.67479i	−1.10585	−	0.638463i	−0.937752	+	0.347307i	$0.887096\pi$
$80$	0.856094	+	1.48280i	0.0957142	+	0.165782i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.3259	−	5.96165i	−1.14030	−	0.658354i
$83$	4.05428			0.445015			0.222507	−	0.974931i	$-0.428576\pi$
$83$	4.05428			0.445015			0.222507	+	0.974931i	$0.428576\pi$
$84$	−0.494596	+	2.59911i	−0.0539648	+	0.283586i
$85$	−3.13223			−0.339738
$86$	8.93027	+	5.15590i	0.962976	+	0.555974i
$87$	−2.75017	+	1.58781i	−0.294849	+	0.170231i
$88$	−4.71119	+	2.72001i	−0.502215	+	0.289954i
$89$	−3.76779	+	6.52601i	−0.399385	+	0.691755i	−0.993650	−	0.112514i	$-0.964110\pi$
$89$	−3.76779	+	6.52601i	−0.399385	+	0.691755i	0.594265	+	0.804269i	$0.297443\pi$
$90$	1.71219			0.180480
$91$	−4.73131	+	1.65000i	−0.495976	+	0.172967i
$92$	−4.78749	+	0.282652i	−0.499131	+	0.0294685i
$93$	−0.440845	+	0.763565i	−0.0457134	+	0.0791780i
$94$	11.4663	−	6.62008i	1.18266	−	0.682809i
$95$	−1.83216	−	3.17339i	−0.187975	−	0.325583i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	8.00236			0.812517			0.406258	−	0.913758i	$-0.366833\pi$
$97$	8.00236			0.812517			0.406258	+	0.913758i	$0.366833\pi$
$98$	−1.02881	−	6.92398i	−0.103925	−	0.699428i
$99$			5.44002i			0.546742i
$100$	1.03421	−	1.79130i	0.103421	−	0.179130i
$101$	−0.973621	+	0.562121i	−0.0968790	+	0.0559331i	−0.547657	−	0.836703i	$-0.684480\pi$
$101$	−0.973621	+	0.562121i	−0.0968790	+	0.0559331i	0.450778	+	0.892636i	$0.351147\pi$
$102$	1.58428	−	0.914685i	0.156867	−	0.0905673i
$103$	5.36817	−	9.29795i	0.528942	−	0.916154i	−0.470488	−	0.882406i	$-0.655922\pi$
$103$	5.36817	−	9.29795i	0.528942	−	0.916154i	0.999430	−	0.0337482i	$-0.0107444\pi$
$104$		−	1.89389i		−	0.185711i
$105$	−4.27738	+	1.49170i	−0.417429	+	0.145575i
$106$		−	4.46865i		−	0.434034i
$107$	4.85433	+	2.80265i	0.469285	+	0.270942i	0.715940	−	0.698161i	$-0.245998\pi$
$107$	4.85433	+	2.80265i	0.469285	+	0.270942i	−0.246655	+	0.969103i	$0.579332\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	12.9848	−	7.49680i	1.24372	−	0.718063i	0.273872	−	0.961766i	$-0.411695\pi$
$109$	12.9848	−	7.49680i	1.24372	−	0.718063i	0.969850	+	0.243703i	$0.0783621\pi$
$110$	−8.06645	−	4.65717i	−0.769106	−	0.444043i
$111$	−10.6444			−1.01032
$112$	2.59911	+	0.494596i	0.245593	+	0.0467349i
$113$			14.2499i			1.34052i	0.742127	+	0.670259i	$0.233817\pi$
$113$			14.2499i			1.34052i	−0.742127	+	0.670259i	$0.766183\pi$
$114$	1.85341	+	1.07007i	0.173588	+	0.100221i
$115$	−4.51766	−	6.85691i	−0.421274	−	0.639410i
$116$	1.58781	+	2.75017i	0.147425	+	0.255347i
$117$	−1.64016	−	0.946946i	−0.151633	−	0.0875452i
$118$			13.4334i			1.23665i
$119$	−3.16095	+	3.66532i	−0.289763	+	0.336000i
$120$		−	1.71219i		−	0.156301i
$121$	9.29690	−	16.1027i	0.845173	−	1.46388i
$122$	2.09766	+	3.63326i	0.189913	+	0.328939i
$123$	5.96165	+	10.3259i	0.537544	+	0.931053i
$124$	0.763565	+	0.440845i	0.0685702	+	0.0395890i
$125$	12.1025			1.08248
$126$	1.72789	−	2.00360i	0.153932	−	0.178495i
$127$	−12.4975			−1.10898			−0.554488	−	0.832192i	$-0.687086\pi$
$127$	−12.4975			−1.10898			−0.554488	+	0.832192i	$0.687086\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.15590	−	8.93027i	−0.453951	−	0.786267i
$130$	2.80826	−	1.62135i	0.246301	−	0.142202i
$131$	11.2479	+	6.49399i	0.982735	+	0.567383i	0.903095	−	0.429441i	$-0.141289\pi$
$131$	11.2479	+	6.49399i	0.982735	+	0.567383i	0.0796406	+	0.996824i	$0.474623\pi$
$132$	5.44002			0.473493
$133$	−5.56245	−	1.05850i	−0.482325	−	0.0917837i
$134$		−	2.51253i		−	0.217049i
$135$	−1.48280	−	0.856094i	−0.127619	−	0.0736808i
$136$	−0.914685	−	1.58428i	−0.0784336	−	0.135851i
$137$	7.97891	−	4.60663i	0.681684	−	0.393571i	−0.118805	−	0.992918i	$-0.537906\pi$
$137$	7.97891	−	4.60663i	0.681684	−	0.393571i	0.800489	+	0.599347i	$0.204573\pi$
$138$	4.28742	+	2.14896i	0.364969	+	0.182932i
$139$			2.51124i			0.213001i	0.994313	+	0.106500i	$0.0339645\pi$
$139$			2.51124i			0.213001i	−0.994313	+	0.106500i	$0.966035\pi$
$140$	1.49170	+	4.27738i	0.126071	+	0.361504i
$141$	−13.2402			−1.11502
$142$	−4.18233	+	7.24401i	−0.350973	+	0.607904i
$143$	5.15141	+	8.92250i	0.430782	+	0.746137i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−2.71863	+	4.70881i	−0.225770	+	0.391045i
$146$			10.7647i			0.890889i
$147$	−2.57102	+	6.51075i	−0.212054	+	0.536998i
$148$			10.6444i			0.874964i
$149$	14.3049	+	8.25893i	1.17190	+	0.676598i	0.954127	−	0.299401i	$-0.0967867\pi$
$149$	14.3049	+	8.25893i	1.17190	+	0.676598i	0.217775	+	0.975999i	$0.430120\pi$
$150$	−1.79130	+	1.03421i	−0.146259	+	0.0844426i
$151$	−7.94635	−	13.7635i	−0.646664	−	1.12006i	−0.983914	−	0.178641i	$-0.942830\pi$
$151$	−7.94635	−	13.7635i	−0.646664	−	1.12006i	0.337250	−	0.941415i	$-0.390503\pi$
$152$	1.07007	−	1.85341i	0.0867939	−	0.150331i
$153$	−1.82937			−0.147896
$154$	−13.5902	+	4.73947i	−1.09513	+	0.381917i
$155$			1.50962i			0.121255i
$156$	−0.946946	+	1.64016i	−0.0758164	+	0.131318i
$157$	4.81872	+	8.34626i	0.384575	+	0.666104i	0.991710	−	0.128495i	$-0.0410145\pi$
$157$	4.81872	+	8.34626i	0.384575	+	0.666104i	−0.607135	+	0.794599i	$0.707681\pi$
$158$	9.82902	−	5.67479i	0.781955	−	0.451462i
$159$	−2.23433	+	3.86997i	−0.177194	+	0.306908i
$160$	−1.71219			−0.135360
$161$	−12.5830	−	1.63323i	−0.991681	−	0.128717i
$162$	1.00000			0.0785674
$163$	4.92012	−	8.52190i	0.385374	−	0.667487i	−0.606447	−	0.795124i	$-0.707406\pi$
$163$	4.92012	−	8.52190i	0.385374	−	0.667487i	0.991821	+	0.127637i	$0.0407392\pi$
$164$	10.3259	−	5.96165i	0.806315	−	0.465526i
$165$	4.65717	+	8.06645i	0.362560	+	0.627972i
$166$	−2.02714	+	3.51111i	−0.157337	+	0.272515i
$167$		−	8.85452i		−	0.685184i	−0.939484	−	0.342592i	$-0.888695\pi$
$167$		−	8.85452i		−	0.685184i	0.939484	−	0.342592i	$-0.111305\pi$
$168$	−2.00360	−	1.72789i	−0.154581	−	0.133309i
$169$	9.41317			0.724090
$170$	1.56611	−	2.71259i	0.120115	−	0.208046i
$171$	−1.07007	−	1.85341i	−0.0818301	−	0.141734i
$172$	−8.93027	+	5.15590i	−0.680927	+	0.393133i
$173$	−20.6321	−	11.9120i	−1.56863	−	0.905650i	−0.996329	−	0.0856079i	$-0.972717\pi$
$173$	−20.6321	−	11.9120i	−1.56863	−	0.905650i	−0.572303	−	0.820042i	$-0.693950\pi$
$174$		−	3.17562i		−	0.240743i
$175$	3.57398	−	4.14427i	0.270168	−	0.313277i
$176$		−	5.44002i		−	0.410057i
$177$	6.71670	−	11.6337i	0.504858	−	0.874440i
$178$	−3.76779	−	6.52601i	−0.282408	−	0.489145i
$179$	5.53038	+	9.57890i	0.413360	+	0.715961i	0.995255	−	0.0973034i	$-0.0310217\pi$
$179$	5.53038	+	9.57890i	0.413360	+	0.715961i	−0.581895	+	0.813264i	$0.697688\pi$
$180$	−0.856094	+	1.48280i	−0.0638095	+	0.110521i
$181$	−14.7799			−1.09858			−0.549291	−	0.835631i	$-0.685102\pi$
$181$	−14.7799			−1.09858			−0.549291	+	0.835631i	$0.685102\pi$
$182$	0.936711	−	4.92244i	0.0694336	−	0.364875i
$183$		−	4.19532i		−	0.310127i
$184$	2.14896	−	4.28742i	0.158424	−	0.316073i
$185$	−15.7835	+	9.11261i	−1.16043	+	0.669972i
$186$	−0.440845	−	0.763565i	−0.0323243	−	0.0559873i
$187$	8.61852	+	4.97590i	0.630248	+	0.363874i
$188$			13.2402i			0.965638i
$189$	−2.49819	+	0.871223i	−0.181717	+	0.0633721i
$190$	3.66431			0.265837
$191$	7.63930	+	4.41055i	0.552760	+	0.319136i	0.750234	−	0.661172i	$-0.229941\pi$
$191$	7.63930	+	4.41055i	0.552760	+	0.319136i	−0.197474	+	0.980308i	$0.563274\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−7.81464	−	13.5353i	−0.562510	−	0.974296i	−0.997277	−	0.0737526i	$-0.976502\pi$
$193$	−7.81464	−	13.5353i	−0.562510	−	0.974296i	0.434767	−	0.900543i	$-0.356831\pi$
$194$	−4.00118	+	6.93025i	−0.287268	+	0.497563i
$195$	−3.24270			−0.232215
$196$	6.51075	+	2.57102i	0.465054	+	0.183644i
$197$	12.1476			0.865482			0.432741	−	0.901518i	$-0.357546\pi$
$197$	12.1476			0.865482			0.432741	+	0.901518i	$0.357546\pi$
$198$	−4.71119	−	2.72001i	−0.334810	−	0.193303i
$199$	9.93403	+	17.2062i	0.704205	+	1.21972i	0.966978	+	0.254861i	$0.0820296\pi$
$199$	9.93403	+	17.2062i	0.704205	+	1.21972i	−0.262773	+	0.964858i	$0.584637\pi$
$200$	1.03421	+	1.79130i	0.0731294	+	0.126664i
$201$	−1.25626	+	2.17591i	−0.0886100	+	0.153477i
$202$		−	1.12424i		−	0.0791013i
$203$	2.76667	+	7.93332i	0.194183	+	0.556810i
$204$			1.82937i			0.128082i
$205$	17.6798	+	10.2075i	1.23481	+	0.712920i
$206$	5.36817	+	9.29795i	0.374018	+	0.647819i
$207$	−2.63853	−	4.00477i	−0.183391	−	0.278350i
$208$	1.64016	+	0.946946i	0.113725	+	0.0656589i
$209$			11.6424i			0.805320i
$210$	0.846841	−	4.45017i	0.0584375	−	0.307091i
$211$	4.16961			0.287048			0.143524	−	0.989647i	$-0.454157\pi$
$211$	4.16961			0.287048			0.143524	+	0.989647i	$0.454157\pi$
$212$	3.86997	+	2.23433i	0.265790	+	0.153454i
$213$	7.24401	−	4.18233i	0.496351	−	0.286569i
$214$	−4.85433	+	2.80265i	−0.331835	+	0.191585i
$215$	−15.2903	−	8.82786i	−1.04279	−	0.602055i
$216$		−	1.00000i		−	0.0680414i
$217$	1.76655	+	1.52346i	0.119921	+	0.103419i
$218$			14.9936i			1.01550i
$219$	5.38233	−	9.32247i	0.363704	−	0.629954i
$220$	8.06645	−	4.65717i	0.543840	−	0.313986i
$221$	−3.00046	+	1.73232i	−0.201833	+	0.116528i
$222$	5.32220	−	9.21832i	0.357203	−	0.618693i
$223$			18.8422i			1.26177i	0.775877	+	0.630884i	$0.217307\pi$
$223$			18.8422i			1.26177i	−0.775877	+	0.630884i	$0.782693\pi$
$224$	−1.72789	+	2.00360i	−0.115449	+	0.133871i
$225$	2.06841			0.137894
$226$	−12.3408	−	7.12495i	−0.820897	−	0.473945i
$227$	−6.40004	−	11.0852i	−0.424786	−	0.735750i	0.571615	−	0.820522i	$-0.306317\pi$
$227$	−6.40004	−	11.0852i	−0.424786	−	0.735750i	−0.996400	+	0.0847717i	$0.972984\pi$
$228$	−1.85341	+	1.07007i	−0.122745	+	0.0708669i
$229$	3.31024	−	5.73350i	0.218747	−	0.378881i	−0.735678	−	0.677331i	$-0.763136\pi$
$229$	3.31024	−	5.73350i	0.218747	−	0.378881i	0.954425	+	0.298451i	$0.0964698\pi$
$230$	8.19709	−	0.483954i	0.540500	−	0.0319110i
$231$	14.1392	+	2.69061i	0.930292	+	0.177029i
$232$	−3.17562			−0.208490
$233$	3.38598	−	5.86469i	0.221823	−	0.384209i	−0.733539	−	0.679648i	$-0.762133\pi$
$233$	3.38598	−	5.86469i	0.221823	−	0.384209i	0.955362	+	0.295439i	$0.0954659\pi$
$234$	1.64016	−	0.946946i	0.107221	−	0.0619038i
$235$	−19.6325	+	11.3348i	−1.28068	+	0.739402i
$236$	−11.6337	−	6.71670i	−0.757287	−	0.437220i
$237$	−11.3496			−0.737234
$238$	−1.59379	−	4.57012i	−0.103310	−	0.296237i
$239$	−5.88604			−0.380736			−0.190368	−	0.981713i	$-0.560968\pi$
$239$	−5.88604			−0.380736			−0.190368	+	0.981713i	$0.560968\pi$
$240$	1.48280	+	0.856094i	0.0957142	+	0.0552606i
$241$	10.4424	+	18.0868i	0.672655	+	1.16507i	0.977148	+	0.212559i	$0.0681797\pi$
$241$	10.4424	+	18.0868i	0.672655	+	1.16507i	−0.304493	+	0.952515i	$0.598487\pi$
$242$	9.29690	+	16.1027i	0.597627	+	1.03512i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−4.19532			−0.268578
$245$	1.76152	+	11.8552i	0.112539	+	0.757399i
$246$	−11.9233			−0.760201
$247$	−3.51016	−	2.02659i	−0.223346	−	0.128949i
$248$	−0.763565	+	0.440845i	−0.0484864	+	0.0279937i
$249$	3.51111	−	2.02714i	0.222507	−	0.128465i
$250$	−6.05123	+	10.4810i	−0.382713	+	0.662879i
$251$	−18.3210			−1.15641			−0.578206	−	0.815891i	$-0.696247\pi$
$251$	−18.3210			−1.15641			−0.578206	+	0.815891i	$0.696247\pi$
$252$	0.871223	+	2.49819i	0.0548819	+	0.157371i
$253$	1.53763	+	26.0441i	0.0966701	+	1.63738i
$254$	6.24876	−	10.8232i	0.392082	−	0.679106i
$255$	−2.71259	+	1.56611i	−0.169869	+	0.0980738i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.88100	−	2.24070i	−0.242090	−	0.139771i	0.374047	−	0.927410i	$-0.377970\pi$
$257$	−3.88100	−	2.24070i	−0.242090	−	0.139771i	−0.616137	+	0.787639i	$0.711303\pi$
$258$	10.3118			0.641984
$259$	−5.26467	+	27.6660i	−0.327131	+	1.71908i
$260$			3.24270i			0.201104i
$261$	−1.58781	+	2.75017i	−0.0982830	+	0.170231i
$262$	−11.2479	+	6.49399i	−0.694899	+	0.401200i
$263$	−14.7132	+	8.49468i	−0.907256	+	0.523805i	−0.879547	−	0.475811i	$-0.842155\pi$
$263$	−14.7132	+	8.49468i	−0.907256	+	0.523805i	−0.0277090	+	0.999616i	$0.508821\pi$
$264$	−2.72001	+	4.71119i	−0.167405	+	0.289954i
$265$			7.65117i			0.470008i
$266$	3.69791	−	4.28797i	0.226734	−	0.262912i
$267$			7.53558i			0.461170i
$268$	2.17591	+	1.25626i	0.132915	+	0.0767385i
$269$	−11.0491	+	6.37921i	−0.673676	+	0.388947i	−0.797468	−	0.603361i	$-0.793828\pi$
$269$	−11.0491	+	6.37921i	−0.673676	+	0.388947i	0.123792	+	0.992308i	$0.460495\pi$
$270$	1.48280	−	0.856094i	0.0902402	−	0.0521002i
$271$	7.67265	+	4.42981i	0.466080	+	0.269092i	0.714597	−	0.699536i	$-0.246610\pi$
$271$	7.67265	+	4.42981i	0.466080	+	0.269092i	−0.248517	+	0.968627i	$0.579943\pi$
$272$	1.82937			0.110922
$273$	−3.27243	+	3.79460i	−0.198057	+	0.229660i
$274$			9.21325i			0.556593i
$275$	−9.74469	−	5.62610i	−0.587627	−	0.339267i
$276$	−4.00477	+	2.63853i	−0.241059	+	0.158821i
$277$	11.5967	+	20.0860i	0.696776	+	1.20685i	0.969578	+	0.244782i	$0.0787162\pi$
$277$	11.5967	+	20.0860i	0.696776	+	1.20685i	−0.272802	+	0.962070i	$0.587950\pi$
$278$	−2.17480	−	1.25562i	−0.130436	−	0.0753071i
$279$			0.881689i			0.0527853i
$280$	−4.45017	−	0.846841i	−0.265948	−	0.0506084i
$281$			20.1977i			1.20489i	0.798159	+	0.602447i	$0.205807\pi$
$281$			20.1977i			1.20489i	−0.798159	+	0.602447i	$0.794193\pi$
$282$	6.62008	−	11.4663i	0.394220	−	0.682809i
$283$	−1.39988	−	2.42466i	−0.0832142	−	0.144131i	0.821415	−	0.570331i	$-0.193185\pi$
$283$	−1.39988	−	2.42466i	−0.0832142	−	0.144131i	−0.904629	+	0.426200i	$0.859852\pi$
$284$	−4.18233	−	7.24401i	−0.248176	−	0.429853i
$285$	−3.17339	−	1.83216i	−0.187975	−	0.108528i
$286$	−10.3028			−0.609218
$287$	29.7867	−	10.3878i	1.75825	−	0.613175i
$288$	−1.00000			−0.0589256
$289$	6.82670	−	11.8242i	0.401571	−	0.695541i
$290$	−2.71863	−	4.70881i	−0.159644	−	0.276511i
$291$	6.93025	−	4.00118i	0.406258	−	0.234553i
$292$	−9.32247	−	5.38233i	−0.545556	−	0.314977i
$293$	14.8848			0.869582			0.434791	−	0.900531i	$-0.356822\pi$
$293$	14.8848			0.869582			0.434791	+	0.900531i	$0.356822\pi$
$294$	−4.35297	−	5.48194i	−0.253870	−	0.319713i
$295$		−	23.0005i		−	1.33914i
$296$	−9.21832	−	5.32220i	−0.535804	−	0.309347i
$297$	2.72001	+	4.71119i	0.157831	+	0.273371i
$298$	−14.3049	+	8.25893i	−0.828660	+	0.478427i
$299$	−8.11991	−	4.06991i	−0.469587	−	0.235369i
$300$		−	2.06841i		−	0.119420i
$301$	−25.7608	+	8.98387i	−1.48483	+	0.517822i
$302$	15.8927			0.914522
$303$	−0.562121	+	0.973621i	−0.0322930	+	0.0559331i
$304$	1.07007	+	1.85341i	0.0613726	+	0.106300i
$305$	−3.59159	−	6.22082i	−0.205654	−	0.356203i
$306$	0.914685	−	1.58428i	0.0522891	−	0.0905673i
$307$		−	9.54444i		−	0.544730i	−0.962194	−	0.272365i	$-0.912194\pi$
$307$		−	9.54444i		−	0.544730i	0.962194	−	0.272365i	$-0.0878058\pi$
$308$	2.69061	−	14.1392i	0.153312	−	0.805656i
$309$		−	10.7363i		−	0.610770i
$310$	−1.30737	−	0.754809i	−0.0742535	−	0.0428703i
$311$	7.54011	−	4.35328i	0.427560	−	0.246852i	−0.270747	−	0.962651i	$-0.587271\pi$
$311$	7.54011	−	4.35328i	0.427560	−	0.246852i	0.698307	+	0.715799i	$0.253937\pi$
$312$	−0.946946	−	1.64016i	−0.0536103	−	0.0928557i
$313$	−9.63958	+	16.6962i	−0.544861	+	0.943727i	0.453755	+	0.891127i	$0.350084\pi$
$313$	−9.63958	+	16.6962i	−0.544861	+	0.943727i	−0.998616	+	0.0526004i	$0.983249\pi$
$314$	−9.63743			−0.543872
$315$	−2.95847	+	3.43054i	−0.166691	+	0.193289i
$316$			11.3496i			0.638463i
$317$	15.1154	−	26.1807i	0.848967	−	1.47045i	−0.0331644	−	0.999450i	$-0.510558\pi$
$317$	15.1154	−	26.1807i	0.848967	−	1.47045i	0.882131	−	0.471004i	$-0.156108\pi$
$318$	−2.23433	−	3.86997i	−0.125295	−	0.217017i
$319$	14.9610	−	8.63772i	0.837654	−	0.483620i
$320$	0.856094	−	1.48280i	0.0478571	−	0.0828909i
$321$	5.60529			0.312857
$322$	7.70593	−	10.0806i	0.429435	−	0.561770i
$323$	−3.91510			−0.217842
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	3.39253	−	1.95868i	0.188183	−	0.108648i
$326$	4.92012	+	8.52190i	0.272500	+	0.471984i
$327$	7.49680	−	12.9848i	0.414574	−	0.718063i
$328$			11.9233i			0.658354i
$329$	−6.54852	+	34.4126i	−0.361032	+	1.89723i
$330$	−9.31433			−0.512737
$331$	9.16017	−	15.8659i	0.503489	−	0.872068i	−0.496503	−	0.868035i	$-0.665383\pi$
$331$	9.16017	−	15.8659i	0.503489	−	0.872068i	0.999992	−	0.00403308i	$-0.00128377\pi$
$332$	−2.02714	−	3.51111i	−0.111254	−	0.192697i
$333$	−9.21832	+	5.32220i	−0.505161	+	0.291655i
$334$	7.66824	+	4.42726i	0.419588	+	0.242249i
$335$			4.30192i			0.235039i
$336$	2.49819	−	0.871223i	0.136288	−	0.0475291i
$337$		−	10.5804i		−	0.576353i	−0.957577	−	0.288176i	$-0.906951\pi$
$337$		−	10.5804i		−	0.576353i	0.957577	−	0.288176i	$-0.0930489\pi$
$338$	−4.70658	+	8.15204i	−0.256004	+	0.443413i
$339$	7.12495	+	12.3408i	0.386974	+	0.670259i
$340$	1.56611	+	2.71259i	0.0849344	+	0.147111i
$341$	2.39820	−	4.15381i	0.129870	−	0.224941i
$342$	2.14013			0.115725
$343$	15.6505	+	9.90254i	0.845050	+	0.534687i
$344$		−	10.3118i		−	0.555974i
$345$	−7.34087	−	3.67943i	−0.395219	−	0.198094i
$346$	20.6321	−	11.9120i	1.10919	−	0.640391i
$347$	−8.81206	−	15.2629i	−0.473056	−	0.819358i	0.526468	−	0.850195i	$-0.323516\pi$
$347$	−8.81206	−	15.2629i	−0.473056	−	0.819358i	−0.999524	+	0.0308372i	$0.990183\pi$
$348$	2.75017	+	1.58781i	0.147425	+	0.0851156i
$349$		−	11.5501i		−	0.618260i	−0.951020	−	0.309130i	$-0.899962\pi$
$349$		−	11.5501i		−	0.618260i	0.951020	−	0.309130i	$-0.100038\pi$
$350$	1.80205	+	5.16729i	0.0963235	+	0.276203i
$351$	−1.89389			−0.101089
$352$	4.71119	+	2.72001i	0.251107	+	0.144977i
$353$	−5.56055	+	3.21039i	−0.295958	+	0.170872i	−0.640626	−	0.767853i	$-0.721325\pi$
$353$	−5.56055	+	3.21039i	−0.295958	+	0.170872i	0.344667	+	0.938725i	$0.387992\pi$
$354$	6.71670	+	11.6337i	0.356989	+	0.618323i
$355$	7.16094	−	12.4031i	0.380063	−	0.658289i
$356$	7.53558			0.399385
$357$	−0.904798	+	4.75474i	−0.0478870	+	0.251647i
$358$	−11.0608			−0.584580
$359$	−22.8748	−	13.2068i	−1.20728	−	0.697026i	−0.245119	−	0.969493i	$-0.578827\pi$
$359$	−22.8748	−	13.2068i	−1.20728	−	0.697026i	−0.962165	+	0.272467i	$0.912160\pi$
$360$	−0.856094	−	1.48280i	−0.0451201	−	0.0781503i
$361$	7.20991	+	12.4879i	0.379469	+	0.657260i
$362$	7.38995	−	12.7998i	0.388407	−	0.672741i
$363$		−	18.5938i		−	0.975921i
$364$	3.79460	+	3.27243i	0.198891	+	0.171522i
$365$		−	18.4311i		−	0.964729i
$366$	3.63326	+	2.09766i	0.189913	+	0.109646i
$367$	2.40046	+	4.15771i	0.125303	+	0.217031i	0.921851	−	0.387544i	$-0.126676\pi$
$367$	2.40046	+	4.15771i	0.125303	+	0.217031i	−0.796548	+	0.604575i	$0.793343\pi$
$368$	2.63853	+	4.00477i	0.137543	+	0.208763i
$369$	10.3259	+	5.96165i	0.537544	+	0.310351i
$370$		−	18.2252i		−	0.947484i
$371$	8.95338	+	7.72133i	0.464836	+	0.400871i
$372$	0.881689			0.0457134
$373$	30.3208	+	17.5057i	1.56995	+	0.906412i	0.996173	+	0.0874008i	$0.0278561\pi$
$373$	30.3208	+	17.5057i	1.56995	+	0.906412i	0.573778	+	0.819011i	$0.305477\pi$
$374$	−8.61852	+	4.97590i	−0.445653	+	0.257298i
$375$	10.4810	−	6.05123i	0.541238	−	0.312484i
$376$	−11.4663	−	6.62008i	−0.591330	−	0.341405i
$377$			6.01429i			0.309752i
$378$	0.494596	−	2.59911i	0.0254392	−	0.133684i
$379$			0.886526i			0.0455378i	0.999741	+	0.0227689i	$0.00724819\pi$
$379$			0.886526i			0.0455378i	−0.999741	+	0.0227689i	$0.992752\pi$
$380$	−1.83216	+	3.17339i	−0.0939877	+	0.162791i
$381$	−10.8232	+	6.24876i	−0.554488	+	0.320134i
$382$	−7.63930	+	4.41055i	−0.390860	+	0.225663i
$383$	10.4297	−	18.0647i	0.532931	−	0.923064i	−0.466329	−	0.884611i	$-0.654424\pi$
$383$	10.4297	−	18.0647i	0.532931	−	0.923064i	0.999260	−	0.0384528i	$-0.0122429\pi$
$384$			1.00000i			0.0510310i
$385$	23.2690	−	8.11486i	1.18590	−	0.413572i
$386$	15.6293			0.795509
$387$	−8.93027	−	5.15590i	−0.453951	−	0.262089i
$388$	−4.00118	−	6.93025i	−0.203129	−	0.351830i
$389$	−3.62461	+	2.09267i	−0.183775	+	0.106102i	−0.589065	−	0.808086i	$-0.700504\pi$
$389$	−3.62461	+	2.09267i	−0.183775	+	0.106102i	0.405290	+	0.914188i	$0.367170\pi$
$390$	1.62135	−	2.80826i	0.0821003	−	0.142202i
$391$	−8.75810	+	0.517075i	−0.442916	+	0.0261496i
$392$	−5.48194	+	4.35297i	−0.276880	+	0.219858i
$393$	12.9880			0.655157
$394$	−6.07381	+	10.5201i	−0.305994	+	0.529997i
$395$	−16.8291	+	9.71630i	−0.846765	+	0.488880i
$396$	4.71119	−	2.72001i	0.236746	−	0.136686i
$397$	2.73023	+	1.57630i	0.137026	+	0.0791121i	0.566946	−	0.823755i	$-0.308125\pi$
$397$	2.73023	+	1.57630i	0.137026	+	0.0791121i	−0.429920	+	0.902867i	$0.641458\pi$
$398$	−19.8681			−0.995896
$399$	−5.34647	+	1.86453i	−0.267658	+	0.0933435i
$400$	−2.06841			−0.103421
$401$	−9.87373	−	5.70060i	−0.493071	−	0.284674i	0.232777	−	0.972530i	$-0.425219\pi$
$401$	−9.87373	−	5.70060i	−0.493071	−	0.284674i	−0.725847	+	0.687856i	$0.758552\pi$
$402$	−1.25626	−	2.17591i	−0.0626567	−	0.108525i
$403$	0.834912	+	1.44611i	0.0415899	+	0.0720359i
$404$	0.973621	+	0.562121i	0.0484395	+	0.0279665i
$405$	−1.71219			−0.0850793
$406$	−8.25379	−	1.57065i	−0.409629	−	0.0779500i
$407$	57.9057			2.87028
$408$	−1.58428	−	0.914685i	−0.0784336	−	0.0452837i
$409$	−25.7800	+	14.8841i	−1.27474	+	0.735972i	−0.975877	−	0.218323i	$-0.929941\pi$
$409$	−25.7800	+	14.8841i	−1.27474	+	0.735972i	−0.298865	+	0.954295i	$0.596608\pi$
$410$	−17.6798	+	10.2075i	−0.873145	+	0.504111i
$411$	4.60663	−	7.97891i	0.227228	−	0.393571i
$412$	−10.7363			−0.528942
$413$	−26.9151	−	23.2114i	−1.32441	−	1.14216i
$414$	4.78749	−	0.282652i	0.235293	−	0.0138916i
$415$	3.47084	−	6.01168i	0.170377	−	0.295102i
$416$	−1.64016	+	0.946946i	−0.0804154	+	0.0464279i
$417$	1.25562	+	2.17480i	0.0614880	+	0.106500i
$418$	−10.0826	−	5.82119i	−0.493156	−	0.284724i
$419$	25.0523			1.22388			0.611942	−	0.790902i	$-0.290388\pi$
$419$	25.0523			1.22388			0.611942	+	0.790902i	$0.290388\pi$
$420$	3.43054	+	2.95847i	0.167393	+	0.144358i
$421$		−	19.2187i		−	0.936664i	−0.883553	−	0.468332i	$-0.844855\pi$
$421$		−	19.2187i		−	0.936664i	0.883553	−	0.468332i	$-0.155145\pi$
$422$	−2.08480	+	3.61099i	−0.101487	+	0.175780i
$423$	−11.4663	+	6.62008i	−0.557511	+	0.321879i
$424$	−3.86997	+	2.23433i	−0.187942	+	0.108508i
$425$	1.89195	−	3.27695i	0.0917728	−	0.158955i
$426$			8.36466i			0.405269i
$427$	−10.9041	−	2.07499i	−0.527687	−	0.100416i
$428$		−	5.60529i		−	0.270942i
$429$	8.92250	+	5.15141i	0.430782	+	0.248712i
$430$	15.2903	−	8.82786i	0.737364	−	0.425717i
$431$	26.1869	−	15.1190i	1.26138	−	0.728258i	0.288039	−	0.957619i	$-0.406997\pi$
$431$	26.1869	−	15.1190i	1.26138	−	0.728258i	0.973342	+	0.229361i	$0.0736635\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−11.9577			−0.574652			−0.287326	−	0.957833i	$-0.592766\pi$
$433$	−11.9577			−0.574652			−0.287326	+	0.957833i	$0.592766\pi$
$434$	−2.20263	+	0.768148i	−0.105730	+	0.0368723i
$435$			5.43726i			0.260697i
$436$	−12.9848	−	7.49680i	−0.621861	−	0.359032i
$437$	−5.64681	−	8.57074i	−0.270124	−	0.409994i
$438$	5.38233	+	9.32247i	0.257178	+	0.445445i
$439$	−16.8912	−	9.75213i	−0.806172	−	0.465444i	0.0394528	−	0.999221i	$-0.487439\pi$
$439$	−16.8912	−	9.75213i	−0.806172	−	0.465444i	−0.845625	+	0.533778i	$0.820772\pi$
$440$			9.31433i			0.444043i
$441$	1.02881	+	6.92398i	0.0489909	+	0.329714i
$442$		−	3.46463i		−	0.164796i
$443$	−7.53611	+	13.0529i	−0.358051	+	0.620163i	−0.987635	−	0.156770i	$-0.949892\pi$
$443$	−7.53611	+	13.0529i	−0.358051	+	0.620163i	0.629584	+	0.776932i	$0.283225\pi$
$444$	5.32220	+	9.21832i	0.252580	+	0.437482i
$445$	6.45117	+	11.1737i	0.305815	+	0.529687i
$446$	−16.3178	−	9.42110i	−0.772671	−	0.446102i
$447$	16.5179			0.781268
$448$	−0.871223	−	2.49819i	−0.0411614	−	0.118029i
$449$	32.2159			1.52036			0.760181	−	0.649711i	$-0.225110\pi$
$449$	32.2159			1.52036			0.760181	+	0.649711i	$0.225110\pi$
$450$	−1.03421	+	1.79130i	−0.0487529	+	0.0844426i
$451$	−32.4315	−	56.1730i	−1.52714	−	2.64508i
$452$	12.3408	−	7.12495i	0.580461	−	0.335130i
$453$	−13.7635	−	7.94635i	−0.646664	−	0.373352i
$454$	12.8001			0.600738
$455$	−1.60383	+	8.42814i	−0.0751885	+	0.395117i
$456$		−	2.14013i		−	0.100221i
$457$	35.7285	+	20.6279i	1.67131	+	0.964931i	0.966907	+	0.255130i	$0.0821184\pi$
$457$	35.7285	+	20.6279i	1.67131	+	0.964931i	0.704403	+	0.709800i	$0.251215\pi$
$458$	3.31024	+	5.73350i	0.154677	+	0.267909i
$459$	−1.58428	+	0.914685i	−0.0739479	+	0.0426938i
$460$	−3.67943	+	7.34087i	−0.171554	+	0.342270i
$461$		−	18.5722i		−	0.864995i	−0.901635	−	0.432498i	$-0.857632\pi$
$461$		−	18.5722i		−	0.864995i	0.901635	−	0.432498i	$-0.142368\pi$
$462$	−9.39974	+	10.8996i	−0.437315	+	0.507096i
$463$	−0.550711			−0.0255937			−0.0127969	−	0.999918i	$-0.504073\pi$
$463$	−0.550711			−0.0255937			−0.0127969	+	0.999918i	$0.504073\pi$
$464$	1.58781	−	2.75017i	0.0737123	−	0.127673i
$465$	0.754809	+	1.30737i	0.0350034	+	0.0606277i
$466$	3.38598	+	5.86469i	0.156853	+	0.271677i
$467$	−2.00679	+	3.47586i	−0.0928631	+	0.160844i	−0.908715	−	0.417418i	$-0.862935\pi$
$467$	−2.00679	+	3.47586i	−0.0928631	+	0.160844i	0.815852	+	0.578261i	$0.196269\pi$
$468$			1.89389i			0.0875452i
$469$	5.03409	+	4.34136i	0.232453	+	0.200466i
$470$		−	22.6696i		−	1.04567i
$471$	8.34626	+	4.81872i	0.384575	+	0.222035i
$472$	11.6337	−	6.71670i	0.535483	−	0.309161i
$473$	28.0482	+	48.5808i	1.28966	+	2.23375i
$474$	5.67479	−	9.82902i	0.260652	−	0.451462i
$475$	4.42668			0.203110
$476$	4.75474	+	0.904798i	0.217933	+	0.0414714i
$477$			4.46865i			0.204605i
$478$	2.94302	−	5.09746i	0.134611	−	0.233152i
$479$	−16.2156	−	28.0863i	−0.740912	−	1.28330i	−0.952081	−	0.305847i	$-0.901060\pi$
$479$	−16.2156	−	28.0863i	−0.740912	−	1.28330i	0.211169	−	0.977450i	$-0.432273\pi$
$480$	−1.48280	+	0.856094i	−0.0676802	+	0.0390752i
$481$	−10.0797	+	17.4585i	−0.459594	+	0.796039i
$482$	−20.8848			−0.951278
$483$	−11.7138	+	4.87710i	−0.532998	+	0.221916i
$484$	−18.5938			−0.845173
$485$	6.85077	−	11.8659i	0.311078	−	0.538802i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−11.0204	−	19.0879i	−0.499383	−	0.864957i	0.500616	−	0.865669i	$-0.333107\pi$
$487$	−11.0204	−	19.0879i	−0.499383	−	0.864957i	−1.00000		0.000711975i	$0.999773\pi$
$488$	2.09766	−	3.63326i	0.0949566	−	0.164470i
$489$		−	9.84024i		−	0.444991i
$490$	−11.1476	−	4.40206i	−0.503599	−	0.198865i
$491$	−8.61008			−0.388568			−0.194284	−	0.980945i	$-0.562238\pi$
$491$	−8.61008			−0.388568			−0.194284	+	0.980945i	$0.562238\pi$
$492$	5.96165	−	10.3259i	0.268772	−	0.465526i
$493$	2.90469	+	5.03108i	0.130821	+	0.226588i
$494$	3.51016	−	2.02659i	0.157930	−	0.0911807i
$495$	8.06645	+	4.65717i	0.362560	+	0.209324i
$496$		−	0.881689i		−	0.0395890i
$497$	−7.28749	−	20.8965i	−0.326888	−	0.937338i
$498$			4.05428i			0.181677i
$499$	−4.48145	+	7.76211i	−0.200617	+	0.347480i	−0.948728	−	0.316095i	$-0.897628\pi$
$499$	−4.48145	+	7.76211i	−0.200617	+	0.347480i	0.748110	+	0.663575i	$0.230961\pi$
$500$	−6.05123	−	10.4810i	−0.270619	−	0.468726i
$501$	−4.42726	−	7.66824i	−0.197795	−	0.342592i
$502$	9.16051	−	15.8665i	0.408853	−	0.708155i
$503$	−36.5643			−1.63032			−0.815161	−	0.579234i	$-0.803352\pi$
$503$	−36.5643			−1.63032			−0.815161	+	0.579234i	$0.803352\pi$
$504$	−2.59911	−	0.494596i	−0.115774	−	0.0220310i
$505$			1.92491i			0.0856575i
$506$	−23.3236	−	11.6904i	−1.03686	−	0.519702i
$507$	8.15204	−	4.70658i	0.362045	−	0.209027i
$508$	6.24876	+	10.8232i	0.277244	+	0.480200i
$509$	−34.1740	−	19.7304i	−1.51474	−	0.874533i	−0.999851	−	0.0172740i	$-0.994501\pi$
$509$	−34.1740	−	19.7304i	−1.51474	−	0.874533i	−0.514885	−	0.857259i	$-0.672165\pi$
$510$		−	3.13223i		−	0.138697i
$511$	−21.5680	−	18.6001i	−0.954114	−	0.822821i
$512$	1.00000			0.0441942
$513$	−1.85341	−	1.07007i	−0.0818301	−	0.0472446i
$514$	3.88100	−	2.24070i	0.171184	−	0.0988329i
$515$	−9.19132	−	15.9198i	−0.405018	−	0.701512i
$516$	−5.15590	+	8.93027i	−0.226976	+	0.393133i
$517$	72.0267			3.16773
$518$	−21.3271	−	18.3923i	−0.937059	−	0.808112i
$519$	−23.8239			−1.04575
$520$	−2.80826	−	1.62135i	−0.123150	−	0.0711009i
$521$	7.96692	+	13.7991i	0.349037	+	0.604550i	0.986079	−	0.166279i	$-0.0531753\pi$
$521$	7.96692	+	13.7991i	0.349037	+	0.604550i	−0.637041	+	0.770830i	$0.719842\pi$
$522$	−1.58781	−	2.75017i	−0.0694966	−	0.120372i
$523$	13.7829	−	23.8727i	0.602686	−	1.04388i	−0.389727	−	0.920930i	$-0.627431\pi$
$523$	13.7829	−	23.8727i	0.602686	−	1.04388i	0.992413	−	0.122952i	$-0.0392361\pi$
$524$		−	12.9880i		−	0.567383i
$525$	1.02303	−	5.37603i	0.0446486	−	0.234629i
$526$		−	16.9894i		−	0.740772i
$527$	1.39684	+	0.806468i	0.0608474	+	0.0351303i
$528$	−2.72001	−	4.71119i	−0.118373	−	0.205028i
$529$	−13.7639	−	18.4270i	−0.598431	−	0.801174i
$530$	−6.62611	−	3.82559i	−0.287820	−	0.166173i
$531$		−	13.4334i		−	0.582960i
$532$	1.86453	+	5.34647i	0.0808378	+	0.231799i
$533$	22.5814			0.978111
$534$	−6.52601	−	3.76779i	−0.282408	−	0.163048i
$535$	8.31152	−	4.79866i	0.359338	−	0.207464i
$536$	−2.17591	+	1.25626i	−0.0939851	+	0.0542623i
$537$	9.57890	+	5.53038i	0.413360	+	0.238654i
$538$		−	12.7584i		−	0.550054i
$539$	13.9864	−	35.4186i	0.602436	−	1.52559i
$540$			1.71219i			0.0736808i
$541$	0.561420	−	0.972408i	0.0241373	−	0.0418071i	−0.853704	−	0.520758i	$-0.825649\pi$
$541$	0.561420	−	0.972408i	0.0241373	−	0.0418071i	0.877842	+	0.478951i	$0.158983\pi$
$542$	−7.67265	+	4.42981i	−0.329568	+	0.190276i
$543$	−12.7998	+	7.38995i	−0.549291	+	0.317133i
$544$	−0.914685	+	1.58428i	−0.0392168	+	0.0679255i
$545$		−	25.6719i		−	1.09966i
$546$	−1.65000	−	4.73131i	−0.0706136	−	0.202481i
$547$	4.98856			0.213295			0.106648	−	0.994297i	$-0.465988\pi$
$547$	4.98856			0.213295			0.106648	+	0.994297i	$0.465988\pi$
$548$	−7.97891	−	4.60663i	−0.340842	−	0.196785i
$549$	−2.09766	−	3.63326i	−0.0895260	−	0.155064i
$550$	9.74469	−	5.62610i	0.415515	−	0.239898i
$551$	−3.39813	+	5.88573i	−0.144765	+	0.250741i
$552$	−0.282652	−	4.78749i	−0.0120305	−	0.203769i
$553$	−5.61345	+	29.4988i	−0.238708	+	1.25442i
$554$	−23.1933			−0.985390
$555$	−9.11261	+	15.7835i	−0.386809	+	0.669972i
$556$	2.17480	−	1.25562i	0.0922319	−	0.0532501i
$557$	16.3698	−	9.45111i	0.693611	−	0.400457i	−0.111352	−	0.993781i	$-0.535518\pi$
$557$	16.3698	−	9.45111i	0.693611	−	0.400457i	0.804963	+	0.593324i	$0.202185\pi$
$558$	−0.763565	−	0.440845i	−0.0323243	−	0.0186624i
$559$	−19.5294			−0.826007
$560$	2.95847	−	3.43054i	0.125018	−	0.144967i
$561$	9.95181			0.420166
$562$	−17.4917	−	10.0988i	−0.737844	−	0.425994i
$563$	8.42080	+	14.5852i	0.354894	+	0.614695i	0.987100	−	0.160106i	$-0.0511835\pi$
$563$	8.42080	+	14.5852i	0.354894	+	0.614695i	−0.632206	+	0.774801i	$0.717850\pi$
$564$	6.62008	+	11.4663i	0.278756	+	0.482819i
$565$	21.1297	+	12.1993i	0.888935	+	0.513227i
$566$	2.79976			0.117683
$567$	−1.72789	+	2.00360i	−0.0725645	+	0.0841432i
$568$	8.36466			0.350973
$569$	−34.2575	−	19.7786i	−1.43615	−	0.829162i	−0.438571	−	0.898697i	$-0.644515\pi$
$569$	−34.2575	−	19.7786i	−1.43615	−	0.829162i	−0.997580	+	0.0695349i	$0.977848\pi$
$570$	3.17339	−	1.83216i	0.132919	−	0.0767406i
$571$	22.8808	−	13.2102i	0.957532	−	0.552831i	0.0621193	−	0.998069i	$-0.480214\pi$
$571$	22.8808	−	13.2102i	0.957532	−	0.552831i	0.895413	+	0.445237i	$0.146881\pi$
$572$	5.15141	−	8.92250i	0.215391	−	0.373068i
$573$	8.82110			0.368507
$574$	−5.89721	+	30.9900i	−0.246145	+	1.29350i
$575$	9.90251	−	0.584641i	0.412963	−	0.0243812i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−2.65486	+	1.53278i	−0.110523	+	0.0638106i	−0.554243	−	0.832355i	$-0.686992\pi$
$577$	−2.65486	+	1.53278i	−0.110523	+	0.0638106i	0.443719	+	0.896166i	$0.353659\pi$
$578$	6.82670	+	11.8242i	0.283953	+	0.491822i
$579$	−13.5353	−	7.81464i	−0.562510	−	0.324765i
$580$	5.43726			0.225770
$581$	−3.53218	−	10.1284i	−0.146540	−	0.420196i
$582$			8.00236i			0.331709i
$583$	12.1548	−	21.0527i	0.503399	−	0.871913i
$584$	9.32247	−	5.38233i	0.385766	−	0.222722i
$585$	−2.80826	+	1.62135i	−0.116107	+	0.0670346i
$586$	−7.44242	+	12.8907i	−0.307444	+	0.532508i
$587$			37.5601i			1.55027i	0.631795	+	0.775136i	$0.282318\pi$
$587$			37.5601i			1.55027i	−0.631795	+	0.775136i	$0.717682\pi$
$588$	6.92398	−	1.02881i	0.285540	−	0.0424274i
$589$			1.88693i			0.0777497i
$590$	19.9190	+	11.5003i	0.820054	+	0.473458i
$591$	10.5201	−	6.07381i	0.432741	−	0.249843i
$592$	9.21832	−	5.32220i	0.378871	−	0.218741i
$593$	−36.2565	−	20.9327i	−1.48887	−	0.859602i	−0.488955	−	0.872309i	$-0.662622\pi$
$593$	−36.2565	−	20.9327i	−1.48887	−	0.859602i	−0.999919	+	0.0127072i	$0.995955\pi$
$594$	−5.44002			−0.223207
$595$	2.72887	+	7.82491i	0.111873	+	0.320790i
$596$		−	16.5179i		−	0.676598i
$597$	17.2062	+	9.93403i	0.704205	+	0.406573i
$598$	7.58460	−	4.99710i	0.310157	−	0.204346i
$599$	2.85422	+	4.94365i	0.116620	+	0.201992i	0.918426	−	0.395592i	$-0.129461\pi$
$599$	2.85422	+	4.94365i	0.116620	+	0.201992i	−0.801806	+	0.597584i	$0.796127\pi$
$600$	1.79130	+	1.03421i	0.0731294	+	0.0422213i
$601$		−	34.1894i		−	1.39462i	−0.716772	−	0.697308i	$-0.754381\pi$
$601$		−	34.1894i		−	1.39462i	0.716772	−	0.697308i	$-0.245619\pi$
$602$	5.10017	−	26.8015i	0.207867	−	1.09235i
$603$			2.51253i			0.102318i
$604$	−7.94635	+	13.7635i	−0.323332	+	0.560028i
$605$	−15.9180	−	27.5709i	−0.647160	−	1.12091i
$606$	−0.562121	−	0.973621i	−0.0228346	−	0.0395507i
$607$	34.9401	+	20.1726i	1.41817	+	0.818783i	0.996138	−	0.0877971i	$-0.0279827\pi$
$607$	34.9401	+	20.1726i	1.41817	+	0.818783i	0.422035	+	0.906580i	$0.361316\pi$
$608$	−2.14013			−0.0867939
$609$	6.36267	+	5.48712i	0.257828	+	0.222349i
$610$	7.18318			0.290838
$611$	−12.5377	+	21.7160i	−0.507222	+	0.878534i
$612$	0.914685	+	1.58428i	0.0369740	+	0.0640408i
$613$	−0.000864587	0	0.000499169i	−3.49203e−5	0	2.01613e-5i	−0.500017	−	0.866015i	$-0.666673\pi$
$613$	−0.000864587	0	0.000499169i	−3.49203e−5	0	2.01613e-5i	0.499983	+	0.866035i	$0.333340\pi$
$614$	8.26573	+	4.77222i	0.333578	+	0.192591i
$615$	20.4149			0.823209
$616$	10.8996	+	9.39974i	0.439158	+	0.378726i
$617$		−	2.41321i		−	0.0971522i	−0.998819	−	0.0485761i	$-0.984532\pi$
$617$		−	2.41321i		−	0.0971522i	0.998819	−	0.0485761i	$-0.0154683\pi$
$618$	9.29795	+	5.36817i	0.374018	+	0.215940i
$619$	−6.95107	−	12.0396i	−0.279387	−	0.483913i	0.691846	−	0.722046i	$-0.256798\pi$
$619$	−6.95107	−	12.0396i	−0.279387	−	0.483913i	−0.971233	+	0.238133i	$0.923465\pi$
$620$	1.30737	−	0.754809i	0.0525051	−	0.0303138i
$621$	−4.28742	−	2.14896i	−0.172048	−	0.0862349i
$622$			8.70656i			0.349101i
$623$	19.5858	+	3.72707i	0.784689	+	0.149322i
$624$	1.89389			0.0758164
$625$	5.18981	−	8.98901i	0.207592	−	0.359560i
$626$	−9.63958	−	16.6962i	−0.385275	−	0.667316i
$627$	5.82119	+	10.0826i	0.232476	+	0.402660i
$628$	4.81872	−	8.34626i	0.192288	−	0.333052i
$629$			19.4725i			0.776421i
$630$	−1.49170	−	4.27738i	−0.0594307	−	0.170415i
$631$			24.1283i			0.960533i	0.877123	+	0.480267i	$0.159460\pi$
$631$			24.1283i			0.960533i	−0.877123	+	0.480267i	$0.840540\pi$
$632$	−9.82902	−	5.67479i	−0.390977	−	0.225731i
$633$	3.61099	−	2.08480i	0.143524	−	0.0828635i
$634$	15.1154	+	26.1807i	0.600310	+	1.03977i
$635$	−10.6990	+	18.5313i	−0.424579	+	0.735392i
$636$	4.46865			0.177194
$637$	8.24405	+	10.3822i	0.326641	+	0.411358i
$638$			17.2754i			0.683941i
$639$	4.18233	−	7.24401i	0.165450	−	0.286569i
$640$	0.856094	+	1.48280i	0.0338401	+	0.0586128i
$641$	−19.9602	+	11.5240i	−0.788379	+	0.455171i	−0.839392	−	0.543527i	$-0.817089\pi$
$641$	−19.9602	+	11.5240i	−0.788379	+	0.455171i	0.0510124	+	0.998698i	$0.483755\pi$
$642$	−2.80265	+	4.85433i	−0.110612	+	0.191585i
$643$	−29.0451			−1.14543			−0.572714	−	0.819755i	$-0.694110\pi$
$643$	−29.0451			−1.14543			−0.572714	+	0.819755i	$0.694110\pi$
$644$	4.87710	+	11.7138i	0.192184	+	0.461590i
$645$	−17.6557			−0.695193
$646$	1.95755	−	3.39058i	0.0770188	−	0.133400i
$647$	−30.5437	+	17.6344i	−1.20080	+	0.693280i	−0.960732	−	0.277478i	$-0.910502\pi$
$647$	−30.5437	+	17.6344i	−1.20080	+	0.693280i	−0.240063	+	0.970757i	$0.577168\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−36.5390	+	63.2874i	−1.43428	+	2.48425i
$650$			3.91735i			0.153651i
$651$	2.29161	+	0.436079i	0.0898152	+	0.0170913i
$652$	−9.84024			−0.385374
$653$	−3.69462	+	6.39927i	−0.144582	+	0.250423i	−0.929217	−	0.369535i	$-0.879517\pi$
$653$	−3.69462	+	6.39927i	−0.144582	+	0.250423i	0.784635	+	0.619958i	$0.212850\pi$
$654$	7.49680	+	12.9848i	0.293148	+	0.507748i
$655$	19.2586	−	11.1189i	0.752494	−	0.434453i
$656$	−10.3259	−	5.96165i	−0.403158	−	0.232763i
$657$		−	10.7647i		−	0.419969i
$658$	−26.5280	−	22.8775i	−1.03417	−	0.891858i
$659$		−	8.57331i		−	0.333969i	−0.985960	−	0.166984i	$-0.946597\pi$
$659$		−	8.57331i		−	0.333969i	0.985960	−	0.166984i	$-0.0534030\pi$
$660$	4.65717	−	8.06645i	0.181280	−	0.313986i
$661$	13.0308	+	22.5700i	0.506840	+	0.877873i	0.999969	+	0.00791620i	$0.00251983\pi$
$661$	13.0308	+	22.5700i	0.506840	+	0.877873i	−0.493129	+	0.869956i	$0.664147\pi$
$662$	9.16017	+	15.8659i	0.356020	+	0.616645i
$663$	−1.73232	+	3.00046i	−0.0672776	+	0.116528i
$664$	4.05428			0.157337
$665$	−6.33152	+	7.34181i	−0.245526	+	0.284703i
$666$		−	10.6444i		−	0.412462i
$667$	−6.82430	+	13.6152i	−0.264238	+	0.527183i
$668$	−7.66824	+	4.42726i	−0.296693	+	0.171296i
$669$	9.42110	+	16.3178i	0.364241	+	0.630884i
$670$	−3.72557	−	2.15096i	−0.143931	−	0.0830988i
$671$			22.8226i			0.881058i
$672$	−0.494596	+	2.59911i	−0.0190794	+	0.100263i
$673$	2.95257			0.113813			0.0569066	−	0.998380i	$-0.481876\pi$
$673$	2.95257			0.113813			0.0569066	+	0.998380i	$0.481876\pi$
$674$	9.16292	+	5.29021i	0.352943	+	0.203771i
$675$	1.79130	−	1.03421i	0.0689471	−	0.0398066i
$676$	−4.70658	−	8.15204i	−0.181022	−	0.313540i
$677$	3.50477	−	6.07044i	0.134699	−	0.233306i	−0.790783	−	0.612096i	$-0.790327\pi$
$677$	3.50477	−	6.07044i	0.134699	−	0.233306i	0.925483	+	0.378790i	$0.123660\pi$
$678$	−14.2499			−0.547264
$679$	−6.97184	−	19.9914i	−0.267555	−	0.767201i
$680$	−3.13223			−0.120115
$681$	−11.0852	−	6.40004i	−0.424786	−	0.245250i
$682$	2.39820	+	4.15381i	0.0918319	+	0.159058i
$683$	−19.4468	−	33.6828i	−0.744110	−	1.28884i	−0.950610	−	0.310389i	$-0.899541\pi$
$683$	−19.4468	−	33.6828i	−0.744110	−	1.28884i	0.206500	−	0.978447i	$-0.433793\pi$
$684$	−1.07007	+	1.85341i	−0.0409150	+	0.0708669i
$685$		−	15.7748i		−	0.602725i
$686$	−16.4011	+	8.60250i	−0.626198	+	0.328445i
$687$		−	6.62048i		−	0.252587i
$688$	8.93027	+	5.15590i	0.340463	+	0.196567i
$689$	4.23157	+	7.32930i	0.161210	+	0.279224i
$690$	6.85691	−	4.51766i	0.261038	−	0.171984i
$691$	−6.75382	−	3.89932i	−0.256928	−	0.148337i	0.366005	−	0.930613i	$-0.380725\pi$
$691$	−6.75382	−	3.89932i	−0.256928	−	0.148337i	−0.622932	+	0.782276i	$0.714059\pi$
$692$			23.8239i			0.905650i
$693$	13.5902	−	4.73947i	0.516250	−	0.180038i
$694$	17.6241			0.669003
$695$	3.72366	+	2.14986i	0.141247	+	0.0815487i
$696$	−2.75017	+	1.58781i	−0.104245	+	0.0601858i
$697$	18.8898	−	10.9061i	0.715504	−	0.413096i
$698$	10.0026	+	5.77503i	0.378606	+	0.218588i
$699$		−	6.77196i		−	0.256139i
$700$	−5.37603	−	1.02303i	−0.203195	−	0.0386668i
$701$			41.8152i			1.57934i	0.613534	+	0.789669i	$0.289748\pi$
$701$			41.8152i			1.57934i	−0.613534	+	0.789669i	$0.710252\pi$
$702$	0.946946	−	1.64016i	0.0357402	−	0.0619038i
$703$	−19.7284	+	11.3902i	−0.744072	+	0.429590i
$704$	−4.71119	+	2.72001i	−0.177560	+	0.102514i
$705$	−11.3348	+	19.6325i	−0.426894	+	0.739402i
$706$		−	6.42077i		−	0.241649i
$707$	2.25253	+	1.94256i	0.0847150	+	0.0730576i
$708$	−13.4334			−0.504858
$709$	−20.2717	−	11.7039i	−0.761321	−	0.439549i	0.0684487	−	0.997655i	$-0.478195\pi$
$709$	−20.2717	−	11.7039i	−0.761321	−	0.439549i	−0.829770	+	0.558106i	$0.811528\pi$
$710$	7.16094	+	12.4031i	0.268745	+	0.465480i
$711$	−9.82902	+	5.67479i	−0.368617	+	0.212821i
$712$	−3.76779	+	6.52601i	−0.141204	+	0.244572i
$713$	0.249211	+	4.22108i	0.00933303	+	0.158081i
$714$	−3.66532	−	3.16095i	−0.137171	−	0.118295i
$715$	17.6404			0.659712
$716$	5.53038	−	9.57890i	0.206680	−	0.357980i
$717$	−5.09746	+	2.94302i	−0.190368	+	0.109909i
$718$	22.8748	−	13.2068i	0.853679	−	0.492872i
$719$	24.6409	+	14.2265i	0.918952	+	0.530557i	0.883301	−	0.468807i	$-0.155316\pi$
$719$	24.6409	+	14.2265i	0.918952	+	0.530557i	0.0356514	+	0.999364i	$0.488649\pi$
$720$	1.71219			0.0638095
$721$	−27.9050	−	5.31015i	−1.03923	−	0.197760i
$722$	−14.4198			−0.536650
$723$	18.0868	+	10.4424i	0.672655	+	0.388358i
$724$	7.38995	+	12.7998i	0.274645	+	0.475700i
$725$	−3.28425	−	5.68848i	−0.121974	−	0.211265i
$726$	16.1027	+	9.29690i	0.597627	+	0.345040i
$727$	14.9860			0.555800			0.277900	−	0.960610i	$-0.410362\pi$
$727$	14.9860			0.555800			0.277900	+	0.960610i	$0.410362\pi$
$728$	−4.73131	+	1.65000i	−0.175354	+	0.0611532i
$729$	−1.00000			−0.0370370
$730$	15.9618	+	9.21556i	0.590773	+	0.341083i
$731$	−16.3368	+	9.43204i	−0.604237	+	0.348857i
$732$	−3.63326	+	2.09766i	−0.134289	+	0.0775318i
$733$	23.1759	−	40.1419i	0.856022	−	1.48267i	−0.0196710	−	0.999807i	$-0.506262\pi$
$733$	23.1759	−	40.1419i	0.856022	−	1.48267i	0.875693	−	0.482868i	$-0.160405\pi$
$734$	−4.80091			−0.177205
$735$	7.45310	+	9.38611i	0.274912	+	0.346212i
$736$	−4.78749	+	0.282652i	−0.176469	+	0.0104187i
$737$	6.83409	−	11.8370i	0.251737	−	0.436021i
$738$	−10.3259	+	5.96165i	−0.380101	+	0.219451i
$739$	−0.319810	−	0.553927i	−0.0117644	−	0.0203765i	0.860083	−	0.510154i	$-0.170411\pi$
$739$	−0.319810	−	0.553927i	−0.0117644	−	0.0203765i	−0.871848	+	0.489777i	$0.837078\pi$
$740$	15.7835	+	9.11261i	0.580213	+	0.334986i
$741$	−4.05319			−0.148898
$742$	−11.1636	+	3.89319i	−0.409827	+	0.142924i
$743$		−	29.0373i		−	1.06527i	−0.846344	−	0.532637i	$-0.821201\pi$
$743$		−	29.0373i		−	1.06527i	0.846344	−	0.532637i	$-0.178799\pi$
$744$	−0.440845	+	0.763565i	−0.0161621	+	0.0279937i
$745$	24.4927	−	14.1408i	0.897342	−	0.518081i
$746$	−30.3208	+	17.5057i	−1.11012	+	0.640930i
$747$	2.02714	−	3.51111i	0.0741692	−	0.128465i
$748$		−	9.95181i		−	0.363874i
$749$	2.77235	−	14.5688i	0.101300	−	0.532331i
$750$			12.1025i			0.441919i
$751$	14.3436	+	8.28131i	0.523407	+	0.302189i	0.738328	−	0.674442i	$-0.235616\pi$
$751$	14.3436	+	8.28131i	0.523407	+	0.302189i	−0.214920	+	0.976632i	$0.568949\pi$
$752$	11.4663	−	6.62008i	0.418133	−	0.241409i
$753$	−15.8665	+	9.16051i	−0.578206	+	0.333827i
$754$	−5.20853	−	3.00714i	−0.189683	−	0.109514i
$755$	−27.2113			−0.990320
$756$	2.00360	+	1.72789i	0.0728702	+	0.0628427i
$757$			6.66666i			0.242304i	0.992634	+	0.121152i	$0.0386588\pi$
$757$			6.66666i			0.242304i	−0.992634	+	0.121152i	$0.961341\pi$
$758$	−0.767754	−	0.443263i	−0.0278861	−	0.0161000i
$759$	14.3537	+	21.7860i	0.521005	+	0.790782i
$760$	−1.83216	−	3.17339i	−0.0664593	−	0.115111i
$761$	−15.0046	−	8.66293i	−0.543918	−	0.314031i	0.202748	−	0.979231i	$-0.435013\pi$
$761$	−15.0046	−	8.66293i	−0.543918	−	0.314031i	−0.746665	+	0.665200i	$0.768346\pi$
$762$		−	12.4975i		−	0.452737i
$763$	−30.0412	−	25.9073i	−1.08756	−	0.937906i
$764$		−	8.82110i		−	0.319136i
$765$	−1.56611	+	2.71259i	−0.0566229	+	0.0980738i
$766$	10.4297	+	18.0647i	0.376839	+	0.652705i
$767$	−12.7207	−	22.0329i	−0.459318	−	0.795563i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−2.24359			−0.0809059			−0.0404529	−	0.999181i	$-0.512880\pi$
$769$	−2.24359			−0.0809059			−0.0404529	+	0.999181i	$0.512880\pi$
$770$	−4.60683	+	24.2090i	−0.166019	+	0.872431i
$771$	−4.48139			−0.161393
$772$	−7.81464	+	13.5353i	−0.281255	+	0.487148i
$773$	15.9829	+	27.6831i	0.574863	+	0.995693i	0.996056	+	0.0887215i	$0.0282781\pi$
$773$	15.9829	+	27.6831i	0.574863	+	0.995693i	−0.421193	+	0.906971i	$0.638389\pi$
$774$	8.93027	−	5.15590i	0.320992	−	0.185325i
$775$	−1.57937	−	0.911848i	−0.0567325	−	0.0327545i
$776$	8.00236			0.287268
$777$	9.27364	+	26.5918i	0.332690	+	0.953974i
$778$		−	4.18534i		−	0.150052i
$779$	22.0988	+	12.7587i	0.791770	+	0.457129i
$780$	1.62135	+	2.80826i	0.0580537	+	0.100552i
$781$	−39.4075	+	22.7520i	−1.41011	+	0.814129i
$782$	3.93125	−	7.84328i	0.140581	−	0.280475i
$783$			3.17562i			0.113487i
$784$	−1.02881	−	6.92398i	−0.0367432	−	0.247285i
$785$	16.5011			0.588949
$786$	−6.49399	+	11.2479i	−0.231633	+	0.401200i
$787$	−2.21604	−	3.83829i	−0.0789933	−	0.136820i	0.823823	−	0.566848i	$-0.191837\pi$
$787$	−2.21604	−	3.83829i	−0.0789933	−	0.136820i	−0.902816	+	0.430027i	$0.858504\pi$
$788$	−6.07381	−	10.5201i	−0.216370	−	0.374765i
$789$	−8.49468	+	14.7132i	−0.302419	+	0.523805i
$790$		−	19.4326i		−	0.691381i
$791$	35.5990	−	12.4148i	1.26576	−	0.441421i
$792$			5.44002i			0.193303i
$793$	−6.88100	−	3.97274i	−0.244351	−	0.141076i
$794$	−2.73023	+	1.57630i	−0.0968922	+	0.0559407i
$795$	3.82559	+	6.62611i	0.135680	+	0.235004i
$796$	9.93403	−	17.2062i	0.352102	−	0.609859i
$797$	12.3429			0.437207			0.218604	−	0.975814i	$-0.429850\pi$
$797$	12.3429			0.437207			0.218604	+	0.975814i	$0.429850\pi$
$798$	1.05850	−	5.56245i	0.0374705	−	0.196908i
$799$			24.2212i			0.856883i
$800$	1.03421	−	1.79130i	0.0365647	−	0.0633319i
$801$	3.76779	+	6.52601i	0.133128	+	0.230585i
$802$	9.87373	−	5.70060i	0.348654	−	0.201295i
$803$	−29.2800	+	50.7144i	−1.03327	+	1.78967i
$804$	2.51253			0.0886100
$805$	−13.1940	+	17.2599i	−0.465028	+	0.608331i
$806$	−1.66982			−0.0588171
$807$	−6.37921	+	11.0491i	−0.224559	+	0.388947i
$808$	−0.973621	+	0.562121i	−0.0342519	+	0.0197753i
$809$	10.4719	+	18.1379i	0.368173	+	0.637695i	0.989280	−	0.146031i	$-0.0466500\pi$
$809$	10.4719	+	18.1379i	0.368173	+	0.637695i	−0.621107	+	0.783726i	$0.713317\pi$
$810$	0.856094	−	1.48280i	0.0300801	−	0.0521002i
$811$			0.197733i			0.00694333i	0.999994	+	0.00347166i	$0.00110507\pi$
$811$			0.197733i			0.00694333i	−0.999994	+	0.00347166i	$0.998895\pi$
$812$	5.48712	−	6.36267i	0.192560	−	0.223286i
$813$	8.85961			0.310720
$814$	−28.9529	+	50.1478i	−1.01480	+	1.75768i
$815$	−8.42417	−	14.5911i	−0.295086	−	0.511104i
$816$	1.58428	−	0.914685i	0.0554609	−	0.0320204i
$817$	−19.1120	−	11.0343i	−0.668644	−	0.386042i
$818$		−	29.7682i		−	1.04082i
$819$	−0.936711	+	4.92244i	−0.0327313	+	0.172004i
$820$		−	20.4149i		−	0.712920i
$821$	−19.3471	+	33.5102i	−0.675219	+	1.16951i	0.301186	+	0.953565i	$0.402617\pi$
$821$	−19.3471	+	33.5102i	−0.675219	+	1.16951i	−0.976405	+	0.215948i	$0.930716\pi$
$822$	4.60663	+	7.97891i	0.160675	+	0.278297i
$823$	0.950300	+	1.64597i	0.0331254	+	0.0573748i	0.882113	−	0.471038i	$-0.156121\pi$
$823$	0.950300	+	1.64597i	0.0331254	+	0.0573748i	−0.848987	+	0.528413i	$0.822787\pi$
$824$	5.36817	−	9.29795i	0.187009	−	0.323909i
$825$	−11.2522			−0.391751
$826$	33.5592	−	11.7035i	1.16768	−	0.407217i
$827$		−	38.6944i		−	1.34554i	−0.739854	−	0.672768i	$-0.765105\pi$
$827$		−	38.6944i		−	1.34554i	0.739854	−	0.672768i	$-0.234895\pi$
$828$	−2.14896	+	4.28742i	−0.0746816	+	0.148998i
$829$	−3.14575	+	1.81620i	−0.109257	+	0.0630793i	−0.553633	−	0.832761i	$-0.686759\pi$
$829$	−3.14575	+	1.81620i	−0.109257	+	0.0630793i	0.444376	+	0.895840i	$0.353425\pi$
$830$	3.47084	+	6.01168i	0.120475	+	0.208668i
$831$	20.0860	+	11.5967i	0.696776	+	0.402284i
$832$		−	1.89389i		−	0.0656589i
$833$	11.9106	+	4.70334i	0.412677	+	0.162961i
$834$	−2.51124			−0.0869571
$835$	−13.1295	−	7.58030i	−0.454364	−	0.262327i
$836$	10.0826	−	5.82119i	0.348714	−	0.201330i
$837$	0.440845	+	0.763565i	0.0152378	+	0.0263927i
$838$	−12.5261	+	21.6959i	−0.432709	+	0.749473i
$839$	16.4052			0.566369			0.283184	−	0.959065i	$-0.408609\pi$
$839$	16.4052			0.566369			0.283184	+	0.959065i	$0.408609\pi$
$840$	−4.27738	+	1.49170i	−0.147584	+	0.0514685i
$841$	−18.9154			−0.652256
$842$	16.6439	+	9.60937i	0.573587	+	0.331161i
$843$	10.0988	+	17.4917i	0.347823	+	0.602447i
$844$	−2.08480	−	3.61099i	−0.0717619	−	0.124295i
$845$	8.05856	−	13.9578i	0.277223	−	0.480164i
$846$		−	13.2402i		−	0.455206i
$847$	−48.3273	−	9.19641i	−1.66055	−	0.315992i
$848$		−	4.46865i		−	0.153454i
$849$	−2.42466	−	1.39988i	−0.0832142	−	0.0480437i
$850$	1.89195	+	3.27695i	0.0648932	+	0.112398i
$851$	−42.6283	+	28.0856i	−1.46128	+	0.962761i
$852$	−7.24401	−	4.18233i	−0.248176	−	0.143284i
$853$			41.0989i			1.40720i	0.710596	+	0.703600i	$0.248425\pi$
$853$			41.0989i			1.40720i	−0.710596	+	0.703600i	$0.751575\pi$
$854$	7.24904	−	8.40574i	0.248057	−	0.287638i
$855$	−3.66431			−0.125317
$856$	4.85433	+	2.80265i	0.165917	+	0.0957925i
$857$	−7.16132	+	4.13459i	−0.244626	+	0.141235i	−0.617301	−	0.786727i	$-0.711774\pi$
$857$	−7.16132	+	4.13459i	−0.244626	+	0.141235i	0.372675	+	0.927962i	$0.378441\pi$
$858$	−8.92250	+	5.15141i	−0.304609	+	0.175866i
$859$	30.3121	+	17.5007i	1.03424	+	0.597116i	0.918195	−	0.396128i	$-0.129646\pi$
$859$	30.3121	+	17.5007i	1.03424	+	0.597116i	0.116041	+	0.993244i	$0.462980\pi$
$860$			17.6557i			0.602055i
$861$	20.6021	−	23.8895i	0.702118	−	0.814152i
$862$			30.2381i			1.02991i
$863$	9.52936	−	16.5053i	0.324383	−	0.561848i	−0.657004	−	0.753887i	$-0.728177\pi$
$863$	9.52936	−	16.5053i	0.324383	−	0.561848i	0.981387	+	0.192039i	$0.0615100\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−35.3261	+	20.3955i	−1.20112	+	0.693469i
$866$	5.97887	−	10.3557i	0.203170	−	0.351901i
$867$		−	13.6534i		−	0.463694i
$868$	0.436079	−	2.29161i	0.0148015	−	0.0777822i
$869$	61.7419			2.09445
$870$	−4.70881	−	2.71863i	−0.159644	−	0.0921702i
$871$	2.37923	+	4.12094i	0.0806171	+	0.139633i
$872$	12.9848	−	7.49680i	0.439722	−	0.253874i
$873$	4.00118	−	6.93025i	0.135419	−	0.234553i
$874$	10.2459	−	0.604914i	0.346572	−	0.0204615i
$875$	−10.5439	−	30.2343i	−0.356450	−	1.02210i
$876$	−10.7647			−0.363704
$877$	6.68787	−	11.5837i	0.225833	−	0.391155i	−0.730736	−	0.682660i	$-0.760823\pi$
$877$	6.68787	−	11.5837i	0.225833	−	0.391155i	0.956569	+	0.291506i	$0.0941562\pi$
$878$	16.8912	−	9.75213i	0.570050	−	0.329118i
$879$	12.8907	−	7.44242i	0.434791	−	0.251027i
$880$	−8.06645	−	4.65717i	−0.271920	−	0.156993i
$881$	−2.06962			−0.0697274			−0.0348637	−	0.999392i	$-0.511100\pi$
$881$	−2.06962			−0.0697274			−0.0348637	+	0.999392i	$0.511100\pi$
$882$	−6.51075	−	2.57102i	−0.219228	−	0.0865706i
$883$	2.31798			0.0780063			0.0390031	−	0.999239i	$-0.487582\pi$
$883$	2.31798			0.0780063			0.0390031	+	0.999239i	$0.487582\pi$
$884$	3.00046	+	1.73232i	0.100916	+	0.0582641i
$885$	−11.5003	−	19.9190i	−0.386577	−	0.669571i
$886$	−7.53611	−	13.0529i	−0.253180	−	0.438521i
$887$	−7.99444	−	4.61559i	−0.268427	−	0.154976i	0.359746	−	0.933050i	$-0.382863\pi$
$887$	−7.99444	−	4.61559i	−0.268427	−	0.154976i	−0.628173	+	0.778074i	$0.716197\pi$
$888$	−10.6444			−0.357203
$889$	10.8881	+	31.2212i	0.365176	+	1.04713i
$890$	−12.9023			−0.432487
$891$	4.71119	+	2.72001i	0.157831	+	0.0911237i
$892$	16.3178	−	9.42110i	0.546361	−	0.315442i
$893$	−24.5395	+	14.1679i	−0.821182	+	0.474109i
$894$	−8.25893	+	14.3049i	−0.276220	+	0.478427i
$895$	18.9381			0.633031
$896$	2.59911	+	0.494596i	0.0868302	+	0.0165233i
$897$	−9.06700	+	0.535313i	−0.302738	+	0.0178736i
$898$	−16.1080	+	27.8998i	−0.537529	+	0.931028i
$899$	2.42479	−	1.39996i	0.0808714	−	0.0466911i
$900$	−1.03421	−	1.79130i	−0.0344735	−	0.0597099i
$901$	7.07960	+	4.08741i	0.235856	+	0.136171i
$902$	64.8629			2.15970
$903$	−17.8176	+	20.6607i	−0.592933	+	0.687544i
$904$			14.2499i			0.473945i
$905$	−12.6530	+	21.9156i	−0.420600	+	0.728500i
$906$	13.7635	−	7.94635i	0.457261	−	0.264000i
$907$	1.60507	−	0.926687i	0.0532954	−	0.0307701i	−0.473116	−	0.881000i	$-0.656871\pi$
$907$	1.60507	−	0.926687i	0.0532954	−	0.0307701i	0.526411	+	0.850230i	$0.323537\pi$
$908$	−6.40004	+	11.0852i	−0.212393	+	0.367875i
$909$			1.12424i			0.0372887i
$910$	−6.49707	−	5.60302i	−0.215376	−	0.185738i
$911$			44.7825i			1.48371i	0.670560	+	0.741855i	$0.266054\pi$
$911$			44.7825i			1.48371i	−0.670560	+	0.741855i	$0.733946\pi$
$912$	1.85341	+	1.07007i	0.0613726	+	0.0354335i
$913$	−19.1005	+	11.0277i	−0.632134	+	0.364963i
$914$	−35.7285	+	20.6279i	−1.18179	+	0.682309i
$915$	−6.22082	−	3.59159i	−0.205654	−	0.118734i
$916$	−6.62048			−0.218747
$917$	6.42380	−	33.7572i	0.212132	−	1.11476i
$918$		−	1.82937i		−	0.0603782i
$919$	−40.9790	−	23.6592i	−1.35177	−	0.780446i	−0.363274	−	0.931682i	$-0.618341\pi$
$919$	−40.9790	−	23.6592i	−1.35177	−	0.780446i	−0.988498	+	0.151237i	$0.951674\pi$
$920$	−4.51766	−	6.85691i	−0.148943	−	0.226066i
$921$	−4.77222	−	8.26573i	−0.157250	−	0.272365i
$922$	16.0840	+	9.28612i	0.529699	+	0.305822i
$923$		−	15.8418i		−	0.521438i
$924$	−4.73947	−	13.5902i	−0.155917	−	0.447085i
$925$		−	22.0170i		−	0.723914i
$926$	0.275356	−	0.476930i	0.00904875	−	0.0156729i
$927$	−5.36817	−	9.29795i	−0.176314	−	0.305385i
$928$	1.58781	+	2.75017i	0.0521225	+	0.0902787i
$929$	5.59681	+	3.23132i	0.183625	+	0.106016i	0.588995	−	0.808137i	$-0.299524\pi$
$929$	5.59681	+	3.23132i	0.183625	+	0.106016i	−0.405370	+	0.914153i	$0.632857\pi$
$930$	−1.50962			−0.0495023
$931$	2.20179	+	14.8183i	0.0721608	+	0.485649i
$932$	−6.77196			−0.221823
$933$	4.35328	−	7.54011i	0.142520	−	0.246852i
$934$	−2.00679	−	3.47586i	−0.0656641	−	0.113734i
$935$	14.7565	−	8.51968i	0.482590	−	0.278623i
$936$	−1.64016	−	0.946946i	−0.0536103	−	0.0309519i
$937$	30.3346			0.990988			0.495494	−	0.868611i	$-0.334987\pi$
$937$	30.3346			0.990988			0.495494	+	0.868611i	$0.334987\pi$
$938$	−6.27678	+	2.18897i	−0.204944	+	0.0714724i
$939$			19.2792i			0.629151i
$940$	19.6325	+	11.3348i	0.640341	+	0.369701i
$941$	0.505518	+	0.875583i	0.0164794	+	0.0285432i	0.874148	−	0.485661i	$-0.161421\pi$
$941$	0.505518	+	0.875583i	0.0164794	+	0.0285432i	−0.857668	+	0.514204i	$0.828088\pi$
$942$	−8.34626	+	4.81872i	−0.271936	+	0.157002i
$943$	51.1201	+	25.6227i	1.66470	+	0.834391i
$944$			13.4334i			0.437220i
$945$	−0.846841	+	4.45017i	−0.0275477	+	0.144764i
$946$	−56.0963			−1.82385
$947$	−0.218762	+	0.378907i	−0.00710880	+	0.0123128i	−0.869558	−	0.493831i	$-0.835596\pi$
$947$	−0.218762	+	0.378907i	−0.00710880	+	0.0123128i	0.862449	+	0.506144i	$0.168929\pi$
$948$	5.67479	+	9.82902i	0.184308	+	0.319232i
$949$	−10.1936	−	17.6558i	−0.330897	−	0.573130i
$950$	−2.21334	+	3.83362i	−0.0718102	+	0.124379i
$951$		−	30.2308i		−	0.980302i
$952$	−3.16095	+	3.66532i	−0.102447	+	0.118794i
$953$		−	29.7004i		−	0.962091i	−0.876696	−	0.481046i	$-0.840257\pi$
$953$		−	29.7004i		−	0.962091i	0.876696	−	0.481046i	$-0.159743\pi$
$954$	−3.86997	−	2.23433i	−0.125295	−	0.0723390i
$955$	13.0799	−	7.55169i	0.423256	−	0.244367i
$956$	2.94302	+	5.09746i	0.0951841	+	0.164864i
$957$	8.63772	−	14.9610i	0.279218	−	0.483620i
$958$	32.4313			1.04781
$959$	−18.4597	−	15.9195i	−0.596093	−	0.514066i
$960$		−	1.71219i		−	0.0552606i
$961$	−15.1113	+	26.1736i	−0.487462	+	0.844308i
$962$	−10.0797	−	17.4585i	−0.324982	−	0.562885i
$963$	4.85433	−	2.80265i	0.156428	−	0.0903140i
$964$	10.4424	−	18.0868i	0.336328	−	0.582537i
$965$	−26.7603			−0.861443
$966$	1.63323	−	12.5830i	0.0525483	−	0.404852i
$967$	5.66751			0.182255			0.0911273	−	0.995839i	$-0.470953\pi$
$967$	5.66751			0.182255			0.0911273	+	0.995839i	$0.470953\pi$
$968$	9.29690	−	16.1027i	0.298814	−	0.517560i
$969$	−3.39058	+	1.95755i	−0.108921	+	0.0628855i
$970$	6.85077	+	11.8659i	0.219965	+	0.380991i
$971$	9.28294	−	16.0785i	0.297904	−	0.515984i	−0.677752	−	0.735290i	$-0.737046\pi$
$971$	9.28294	−	16.0785i	0.297904	−	0.515984i	0.975656	+	0.219306i	$0.0703792\pi$
$972$			1.00000i			0.0320750i
$973$	6.27356	−	2.18785i	0.201121	−	0.0701392i
$974$	22.0409			0.706235
$975$	1.95868	−	3.39253i	0.0627278	−	0.108648i
$976$	2.09766	+	3.63326i	0.0671445	+	0.116298i
$977$	28.1320	−	16.2420i	0.900022	−	0.519628i	0.0228147	−	0.999740i	$-0.492737\pi$
$977$	28.1320	−	16.2420i	0.900022	−	0.519628i	0.877207	+	0.480112i	$0.159404\pi$
$978$	8.52190	+	4.92012i	0.272500	+	0.157328i
$979$		−	40.9937i		−	1.31016i
$980$	9.38611	−	7.45310i	0.299828	−	0.238080i
$981$		−	14.9936i		−	0.478709i
$982$	4.30504	−	7.45655i	0.137379	−	0.237948i
$983$	15.9027	+	27.5443i	0.507218	+	0.878527i	0.999965	+	0.00835445i	$0.00265933\pi$
$983$	15.9027	+	27.5443i	0.507218	+	0.878527i	−0.492747	+	0.870172i	$0.664007\pi$
$984$	5.96165	+	10.3259i	0.190050	+	0.329177i
$985$	10.3995	−	18.0125i	0.331356	−	0.573925i
$986$	−5.80939			−0.185009
$987$	11.5351	+	33.0765i	0.367167	+	1.05284i
$988$			4.05319i			0.128949i
$989$	−44.2110	−	22.1597i	−1.40583	−	0.704636i
$990$	−8.06645	+	4.65717i	−0.256369	+	0.148014i
$991$	8.95124	+	15.5040i	0.284346	+	0.492501i	0.972450	−	0.233110i	$-0.0748904\pi$
$991$	8.95124	+	15.5040i	0.284346	+	0.492501i	−0.688105	+	0.725611i	$0.741557\pi$
$992$	0.763565	+	0.440845i	0.0242432	+	0.0139968i
$993$		−	18.3203i		−	0.581379i
$994$	21.7407	+	4.13712i	0.689573	+	0.131222i
$995$	34.0179			1.07844
$996$	−3.51111	−	2.02714i	−0.111254	−	0.0642324i
$997$	13.7087	−	7.91475i	0.434160	−	0.250663i	−0.266957	−	0.963708i	$-0.586018\pi$
$997$	13.7087	−	7.91475i	0.434160	−	0.250663i	0.701117	+	0.713046i	$0.252685\pi$
$998$	−4.48145	−	7.76211i	−0.141858	−	0.245705i
$999$	−5.32220	+	9.21832i	−0.168387	+	0.291655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.a.229.15	yes	32
7.3	odd	6	inner	966.2.k.a.367.10	yes	32
23.22	odd	2	inner	966.2.k.a.229.10	✓	32
161.45	even	6	inner	966.2.k.a.367.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.a.229.10	✓	32	23.22	odd	2	inner
966.2.k.a.229.15	yes	32	1.1	even	1	trivial
966.2.k.a.367.10	yes	32	7.3	odd	6	inner
966.2.k.a.367.15	yes	32	161.45	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.856094 - 1.48280i) q^{5} +1.00000i q^{6} +(-0.871223 - 2.49819i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.856094 - 1.48280i) q^{5} +1.00000i q^{6} +(-0.871223 - 2.49819i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.856094 + 1.48280i) q^{10} +(-4.71119 + 2.72001i) q^{11} +(-0.866025 - 0.500000i) q^{12} -1.89389i q^{13} +(2.59911 + 0.494596i) q^{14} -1.71219i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.914685 - 1.58428i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.07007 - 1.85341i) q^{19} -1.71219 q^{20} +(-2.00360 - 1.72789i) q^{21} -5.44002i q^{22} +(2.14896 - 4.28742i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.03421 + 1.79130i) q^{25} +(1.64016 + 0.946946i) q^{26} -1.00000i q^{27} +(-1.72789 + 2.00360i) q^{28} -3.17562 q^{29} +(1.48280 + 0.856094i) q^{30} +(-0.763565 + 0.440845i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.72001 + 4.71119i) q^{33} +1.82937 q^{34} +(-4.45017 - 0.846841i) q^{35} -1.00000 q^{36} +(-9.21832 - 5.32220i) q^{37} +(1.07007 + 1.85341i) q^{38} +(-0.946946 - 1.64016i) q^{39} +(0.856094 - 1.48280i) q^{40} +11.9233i q^{41} +(2.49819 - 0.871223i) q^{42} -10.3118i q^{43} +(4.71119 + 2.72001i) q^{44} +(-0.856094 - 1.48280i) q^{45} +(2.63853 + 4.00477i) q^{46} +(-11.4663 - 6.62008i) q^{47} +1.00000i q^{48} +(-5.48194 + 4.35297i) q^{49} -2.06841 q^{50} +(-1.58428 - 0.914685i) q^{51} +(-1.64016 + 0.946946i) q^{52} +(-3.86997 + 2.23433i) q^{53} +(0.866025 + 0.500000i) q^{54} +9.31433i q^{55} +(-0.871223 - 2.49819i) q^{56} -2.14013i q^{57} +(1.58781 - 2.75017i) q^{58} +(11.6337 - 6.71670i) q^{59} +(-1.48280 + 0.856094i) q^{60} +(2.09766 - 3.63326i) q^{61} -0.881689i q^{62} +(-2.59911 - 0.494596i) q^{63} +1.00000 q^{64} +(-2.80826 - 1.62135i) q^{65} +(-2.72001 - 4.71119i) q^{66} +(-2.17591 + 1.25626i) q^{67} +(-0.914685 + 1.58428i) q^{68} +(-0.282652 - 4.78749i) q^{69} +(2.95847 - 3.43054i) q^{70} +8.36466 q^{71} +(0.500000 - 0.866025i) q^{72} +(9.32247 - 5.38233i) q^{73} +(9.21832 - 5.32220i) q^{74} +(1.79130 + 1.03421i) q^{75} -2.14013 q^{76} +(10.8996 + 9.39974i) q^{77} +1.89389 q^{78} +(-9.82902 - 5.67479i) q^{79} +(0.856094 + 1.48280i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.3259 - 5.96165i) q^{82} +4.05428 q^{83} +(-0.494596 + 2.59911i) q^{84} -3.13223 q^{85} +(8.93027 + 5.15590i) q^{86} +(-2.75017 + 1.58781i) q^{87} +(-4.71119 + 2.72001i) q^{88} +(-3.76779 + 6.52601i) q^{89} +1.71219 q^{90} +(-4.73131 + 1.65000i) q^{91} +(-4.78749 + 0.282652i) q^{92} +(-0.440845 + 0.763565i) q^{93} +(11.4663 - 6.62008i) q^{94} +(-1.83216 - 3.17339i) q^{95} +(-0.866025 - 0.500000i) q^{96} +8.00236 q^{97} +(-1.02881 - 6.92398i) q^{98} +5.44002i 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	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9} - 16 q^{16} + 16 q^{18} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 24 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9 - 16 * q^16 + 16 * q^18 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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