LMFDB - Embedded newform 122.2.i.a.15.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(15,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("122.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.i (of order $15$, degree $8$, 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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			15.1
Root			$-1.03739i$ of defining polynomial
Character	$\chi$	$=$	122.15
Dual form			122.2.i.a.57.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 + 0.994522i) q^{2} +(-1.03171 + 0.749578i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.51812 + 1.68604i) q^{5} +(-0.853314 - 0.947701i) q^{6} +(-1.54161 + 0.686370i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.424502 + 1.30648i) q^{9} +O(q^{10})$	\(q+(0.104528 + 0.994522i) q^{2} +(-1.03171 + 0.749578i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.51812 + 1.68604i) q^{5} +(-0.853314 - 0.947701i) q^{6} +(-1.54161 + 0.686370i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.424502 + 1.30648i) q^{9} +(-1.51812 + 1.68604i) q^{10} -0.786343 q^{11} +(0.853314 - 0.947701i) q^{12} +(0.135071 - 0.233950i) q^{13} +(-0.843753 - 1.46142i) q^{14} +(-2.83007 - 0.601549i) q^{15} +(0.913545 - 0.406737i) q^{16} +(6.23559 - 1.32542i) q^{17} +(-1.34370 - 0.285612i) q^{18} +(3.66215 + 1.63049i) q^{19} +(-1.83549 - 1.33356i) q^{20} +(1.07600 - 1.86369i) q^{21} +(-0.0821952 - 0.782035i) q^{22} +(1.89716 - 5.83885i) q^{23} +(1.03171 + 0.749578i) q^{24} +(-0.0154081 + 0.146598i) q^{25} +(0.246787 + 0.109877i) q^{26} +(-1.72358 - 5.30463i) q^{27} +(1.36522 - 0.991891i) q^{28} +(1.46703 + 2.54098i) q^{29} +(0.302431 - 2.87744i) q^{30} +(-0.480531 + 4.57195i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.811274 - 0.589425i) q^{33} +(1.96995 + 6.06289i) q^{34} +(-3.49760 - 1.55723i) q^{35} +(0.143593 - 1.36619i) q^{36} +(5.36591 + 3.89856i) q^{37} +(-1.23876 + 3.81252i) q^{38} +(0.0360101 + 0.342613i) q^{39} +(1.13439 - 1.96483i) q^{40} +(-5.19837 - 3.77684i) q^{41} +(1.96595 + 0.875299i) q^{42} +(-1.91436 - 0.406910i) q^{43} +(0.769160 - 0.163490i) q^{44} +(-2.84722 + 1.26767i) q^{45} +(6.00517 + 1.27644i) q^{46} +(-3.91775 - 6.78574i) q^{47} +(-0.637629 + 1.10441i) q^{48} +(-2.77845 + 3.08578i) q^{49} -0.147406 q^{50} +(-5.43979 + 6.04150i) q^{51} +(-0.0834784 + 0.256920i) q^{52} +(-2.25363 - 6.93597i) q^{53} +(5.09541 - 2.26862i) q^{54} +(-1.19376 - 1.32581i) q^{55} +(1.12916 + 1.25406i) q^{56} +(-5.00044 + 1.06288i) q^{57} +(-2.37371 + 1.72460i) q^{58} +(0.495113 + 4.71068i) q^{59} +2.89329 q^{60} +(2.64429 - 7.34899i) q^{61} -4.59713 q^{62} +(-0.242313 - 2.30546i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.599502 - 0.127428i) q^{65} +(0.670998 + 0.745218i) q^{66} +(7.59287 + 8.43274i) q^{67} +(-5.82376 + 2.59291i) q^{68} +(2.41937 + 7.44604i) q^{69} +(1.18310 - 3.64121i) q^{70} +(-6.28668 + 6.98206i) q^{71} +1.37372 q^{72} +(-7.48237 + 8.31001i) q^{73} +(-3.31631 + 5.74402i) q^{74} +(-0.0939903 - 0.162796i) q^{75} +(-3.92112 - 0.833461i) q^{76} +(1.21224 - 0.539723i) q^{77} +(-0.336972 + 0.0716257i) q^{78} +(-0.836660 - 0.177838i) q^{79} +(2.07264 + 0.922800i) q^{80} +(2.42038 + 1.75851i) q^{81} +(3.21277 - 5.56468i) q^{82} +(-1.27811 - 12.1604i) q^{83} +(-0.665006 + 2.04668i) q^{84} +(11.7011 + 8.50132i) q^{85} +(0.204576 - 1.94641i) q^{86} +(-3.41821 - 1.52188i) q^{87} +(0.242993 + 0.747857i) q^{88} +(10.6325 - 7.72495i) q^{89} +(-1.55834 - 2.69912i) q^{90} +(-0.0476510 + 0.453369i) q^{91} +(-0.641735 + 6.10570i) q^{92} +(-2.93126 - 5.07710i) q^{93} +(6.33905 - 4.60559i) q^{94} +(2.81049 + 8.64981i) q^{95} +(-1.16501 - 0.518694i) q^{96} +(0.974518 - 9.27192i) q^{97} +(-3.35930 - 2.44068i) q^{98} +(0.333804 - 1.02734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{11} + q^{12} - 9 q^{13} - 10 q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 24 q^{18} + 10 q^{19} - 7 q^{20} - 6 q^{21} - 11 q^{22} - 11 q^{23} - 3 q^{24} - 28 q^{25} + 4 q^{26} - 33 q^{27} + 5 q^{28} + 15 q^{29} - 12 q^{30} - 12 q^{31} + 8 q^{32} + 15 q^{33} - 11 q^{34} + 19 q^{35} + q^{36} + 16 q^{37} - 10 q^{38} + 24 q^{39} + 4 q^{40} - 20 q^{41} - 19 q^{42} - 21 q^{43} - 4 q^{44} + 17 q^{45} + 2 q^{46} - 11 q^{47} + q^{48} - 10 q^{49} + 4 q^{50} - 56 q^{51} - 2 q^{52} - 8 q^{53} + 41 q^{54} + 35 q^{55} + 10 q^{56} + 49 q^{57} - 10 q^{58} + 35 q^{59} + 6 q^{60} + 15 q^{61} + 16 q^{62} - 26 q^{63} - 4 q^{64} + 24 q^{65} + 10 q^{66} + 22 q^{67} + 12 q^{68} + 46 q^{69} + 28 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 7 q^{74} - 15 q^{75} - 20 q^{76} + 2 q^{77} + 11 q^{78} + 10 q^{79} - 4 q^{80} - 27 q^{81} + 15 q^{82} - 45 q^{83} + 17 q^{84} + 2 q^{85} + 11 q^{86} - 9 q^{87} - 8 q^{88} - 26 q^{89} + 8 q^{90} - 84 q^{91} - 47 q^{92} - 33 q^{93} - 2 q^{94} + 37 q^{95} + 9 q^{96} - 41 q^{97} - 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9 - 6 * q^10 - 2 * q^11 + q^12 - 9 * q^13 - 10 * q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 24 * q^18 + 10 * q^19 - 7 * q^20 - 6 * q^21 - 11 * q^22 - 11 * q^23 - 3 * q^24 - 28 * q^25 + 4 * q^26 - 33 * q^27 + 5 * q^28 + 15 * q^29 - 12 * q^30 - 12 * q^31 + 8 * q^32 + 15 * q^33 - 11 * q^34 + 19 * q^35 + q^36 + 16 * q^37 - 10 * q^38 + 24 * q^39 + 4 * q^40 - 20 * q^41 - 19 * q^42 - 21 * q^43 - 4 * q^44 + 17 * q^45 + 2 * q^46 - 11 * q^47 + q^48 - 10 * q^49 + 4 * q^50 - 56 * q^51 - 2 * q^52 - 8 * q^53 + 41 * q^54 + 35 * q^55 + 10 * q^56 + 49 * q^57 - 10 * q^58 + 35 * q^59 + 6 * q^60 + 15 * q^61 + 16 * q^62 - 26 * q^63 - 4 * q^64 + 24 * q^65 + 10 * q^66 + 22 * q^67 + 12 * q^68 + 46 * q^69 + 28 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 7 * q^74 - 15 * q^75 - 20 * q^76 + 2 * q^77 + 11 * q^78 + 10 * q^79 - 4 * q^80 - 27 * q^81 + 15 * q^82 - 45 * q^83 + 17 * q^84 + 2 * q^85 + 11 * q^86 - 9 * q^87 - 8 * q^88 - 26 * q^89 + 8 * q^90 - 84 * q^91 - 47 * q^92 - 33 * q^93 - 2 * q^94 + 37 * q^95 + 9 * q^96 - 41 * q^97 - 5 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

Coefficient data

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

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

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

$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$3$	−1.03171	+	0.749578i	−0.595655	+	0.432769i	−0.844334	−	0.535817i	$-0.820004\pi$
$3$	−1.03171	+	0.749578i	−0.595655	+	0.432769i	0.248679	+	0.968586i	$0.420004\pi$
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	1.51812	+	1.68604i	0.678922	+	0.754020i	0.979873	−	0.199620i	$-0.0639707\pi$
$5$	1.51812	+	1.68604i	0.678922	+	0.754020i	−0.300951	+	0.953640i	$0.597304\pi$
$6$	−0.853314	−	0.947701i	−0.348364	−	0.386897i
$7$	−1.54161	+	0.686370i	−0.582675	+	0.259424i	−0.676837	−	0.736133i	$-0.736650\pi$
$7$	−1.54161	+	0.686370i	−0.582675	+	0.259424i	0.0941616	+	0.995557i	$0.469983\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.424502	+	1.30648i	−0.141501	+	0.435494i
$10$	−1.51812	+	1.68604i	−0.480071	+	0.533172i
$11$	−0.786343			−0.237091			−0.118546	−	0.992949i	$-0.537823\pi$
$11$	−0.786343			−0.237091			−0.118546	+	0.992949i	$0.537823\pi$
$12$	0.853314	−	0.947701i	0.246331	−	0.273578i
$13$	0.135071	−	0.233950i	0.0374619	−	0.0648860i	−0.846687	−	0.532092i	$-0.821406\pi$
$13$	0.135071	−	0.233950i	0.0374619	−	0.0648860i	0.884148	+	0.467206i	$0.154739\pi$
$14$	−0.843753	−	1.46142i	−0.225502	−	0.390582i
$15$	−2.83007	−	0.601549i	−0.730720	−	0.155319i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	6.23559	−	1.32542i	1.51235	−	0.321461i	0.624294	−	0.781189i	$-0.285387\pi$
$17$	6.23559	−	1.32542i	1.51235	−	0.321461i	0.888060	+	0.459728i	$0.152053\pi$
$18$	−1.34370	−	0.285612i	−0.316713	−	0.0673194i
$19$	3.66215	+	1.63049i	0.840155	+	0.374061i	0.781262	−	0.624203i	$-0.214576\pi$
$19$	3.66215	+	1.63049i	0.840155	+	0.374061i	0.0588930	+	0.998264i	$0.481243\pi$
$20$	−1.83549	−	1.33356i	−0.410428	−	0.298193i
$21$	1.07600	−	1.86369i	0.234803	−	0.406691i
$22$	−0.0821952	−	0.782035i	−0.0175241	−	0.166731i
$23$	1.89716	−	5.83885i	0.395585	−	1.21748i	−0.532920	−	0.846165i	$-0.678906\pi$
$23$	1.89716	−	5.83885i	0.395585	−	1.21748i	0.928505	−	0.371319i	$-0.121094\pi$
$24$	1.03171	+	0.749578i	0.210596	+	0.153007i
$25$	−0.0154081	+	0.146598i	−0.00308162	+	0.0293197i
$26$	0.246787	+	0.109877i	0.0483989	+	0.0215486i
$27$	−1.72358	−	5.30463i	−0.331703	−	1.02088i
$28$	1.36522	−	0.991891i	0.258002	−	0.187450i
$29$	1.46703	+	2.54098i	0.272421	+	0.471848i	0.969481	−	0.245165i	$-0.0788422\pi$
$29$	1.46703	+	2.54098i	0.272421	+	0.471848i	−0.697060	+	0.717013i	$0.745509\pi$
$30$	0.302431	−	2.87744i	0.0552162	−	0.525347i
$31$	−0.480531	+	4.57195i	−0.0863059	+	0.821146i	0.862664	+	0.505778i	$0.168795\pi$
$31$	−0.480531	+	4.57195i	−0.0863059	+	0.821146i	−0.948970	+	0.315368i	$0.897872\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.811274	−	0.589425i	0.141225	−	0.102606i
$34$	1.96995	+	6.06289i	0.337844	+	1.03978i
$35$	−3.49760	−	1.55723i	−0.591202	−	0.263220i
$36$	0.143593	−	1.36619i	0.0239321	−	0.227699i
$37$	5.36591	+	3.89856i	0.882149	+	0.640919i	0.933819	−	0.357745i	$-0.116454\pi$
$37$	5.36591	+	3.89856i	0.882149	+	0.640919i	−0.0516698	+	0.998664i	$0.516454\pi$
$38$	−1.23876	+	3.81252i	−0.200954	+	0.618473i
$39$	0.0360101	+	0.342613i	0.00576623	+	0.0548620i
$40$	1.13439	−	1.96483i	0.179364	−	0.310667i
$41$	−5.19837	−	3.77684i	−0.811849	−	0.589843i	0.102517	−	0.994731i	$-0.467310\pi$
$41$	−5.19837	−	3.77684i	−0.811849	−	0.589843i	−0.914366	+	0.404888i	$0.867310\pi$
$42$	1.96595	+	0.875299i	0.303353	+	0.135062i
$43$	−1.91436	−	0.406910i	−0.291938	−	0.0620532i	0.0596148	−	0.998221i	$-0.481013\pi$
$43$	−1.91436	−	0.406910i	−0.291938	−	0.0620532i	−0.351552	+	0.936168i	$0.614346\pi$
$44$	0.769160	−	0.163490i	0.115955	−	0.0246470i
$45$	−2.84722	+	1.26767i	−0.424439	+	0.188972i
$46$	6.00517	+	1.27644i	0.885414	+	0.188201i
$47$	−3.91775	−	6.78574i	−0.571463	−	0.989802i	−0.996416	−	0.0845870i	$-0.973043\pi$
$47$	−3.91775	−	6.78574i	−0.571463	−	0.989802i	0.424954	−	0.905215i	$-0.360290\pi$
$48$	−0.637629	+	1.10441i	−0.0920338	+	0.159407i
$49$	−2.77845	+	3.08578i	−0.396921	+	0.440826i
$50$	−0.147406			−0.0208464
$51$	−5.43979	+	6.04150i	−0.761724	+	0.845980i
$52$	−0.0834784	+	0.256920i	−0.0115764	+	0.0356284i
$53$	−2.25363	−	6.93597i	−0.309561	−	0.952729i	−0.977936	−	0.208905i	$-0.933010\pi$
$53$	−2.25363	−	6.93597i	−0.309561	−	0.952729i	0.668375	−	0.743824i	$-0.266990\pi$
$54$	5.09541	−	2.26862i	0.693397	−	0.308720i
$55$	−1.19376	−	1.32581i	−0.160967	−	0.178772i
$56$	1.12916	+	1.25406i	0.150891	+	0.167581i
$57$	−5.00044	+	1.06288i	−0.662325	+	0.140782i
$58$	−2.37371	+	1.72460i	−0.311684	+	0.226451i
$59$	0.495113	+	4.71068i	0.0644582	+	0.613279i	0.978298	+	0.207204i	$0.0664362\pi$
$59$	0.495113	+	4.71068i	0.0644582	+	0.613279i	−0.913840	+	0.406075i	$0.866897\pi$
$60$	2.89329			0.373522
$61$	2.64429	−	7.34899i	0.338567	−	0.940942i
$61$	2.64429	−	7.34899i	0.338567	−	0.940942i
$62$	−4.59713			−0.583836
$63$	−0.242313	−	2.30546i	−0.0305286	−	0.290460i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.599502	−	0.127428i	0.0743590	−	0.0158055i
$66$	0.670998	+	0.745218i	0.0825941	+	0.0917300i
$67$	7.59287	+	8.43274i	0.927617	+	1.03022i	0.999462	+	0.0328071i	$0.0104447\pi$
$67$	7.59287	+	8.43274i	0.927617	+	1.03022i	−0.0718448	+	0.997416i	$0.522889\pi$
$68$	−5.82376	+	2.59291i	−0.706235	+	0.314436i
$69$	2.41937	+	7.44604i	0.291257	+	0.896398i
$70$	1.18310	−	3.64121i	0.141408	−	0.435208i
$71$	−6.28668	+	6.98206i	−0.746091	+	0.828618i	−0.989983	−	0.141184i	$-0.954909\pi$
$71$	−6.28668	+	6.98206i	−0.746091	+	0.828618i	0.243892	+	0.969802i	$0.421576\pi$
$72$	1.37372			0.161894
$73$	−7.48237	+	8.31001i	−0.875745	+	0.972613i	−0.999807	−	0.0196611i	$-0.993741\pi$
$73$	−7.48237	+	8.31001i	−0.875745	+	0.972613i	0.124062	+	0.992275i	$0.460408\pi$
$74$	−3.31631	+	5.74402i	−0.385513	+	0.667729i
$75$	−0.0939903	−	0.162796i	−0.0108531	−	0.0187981i
$76$	−3.92112	−	0.833461i	−0.449784	−	0.0956045i
$77$	1.21224	−	0.539723i	0.138147	−	0.0615071i
$78$	−0.336972	+	0.0716257i	−0.0381546	+	0.00811001i
$79$	−0.836660	−	0.177838i	−0.0941316	−	0.0200083i	0.160605	−	0.987019i	$-0.448655\pi$
$79$	−0.836660	−	0.177838i	−0.0941316	−	0.0200083i	−0.254737	+	0.967010i	$0.581989\pi$
$80$	2.07264	+	0.922800i	0.231728	+	0.103172i
$81$	2.42038	+	1.75851i	0.268931	+	0.195390i
$82$	3.21277	−	5.56468i	0.354791	−	0.614516i
$83$	−1.27811	−	12.1604i	−0.140291	−	1.33478i	−0.807483	−	0.589891i	$-0.799171\pi$
$83$	−1.27811	−	12.1604i	−0.140291	−	1.33478i	0.667192	−	0.744886i	$-0.267496\pi$
$84$	−0.665006	+	2.04668i	−0.0725581	+	0.223311i
$85$	11.7011	+	8.50132i	1.26916	+	0.922098i
$86$	0.204576	−	1.94641i	0.0220600	−	0.209887i
$87$	−3.41821	−	1.52188i	−0.366470	−	0.163163i
$88$	0.242993	+	0.747857i	0.0259032	+	0.0797218i
$89$	10.6325	−	7.72495i	1.12704	−	0.818843i	0.141779	−	0.989898i	$-0.454718\pi$
$89$	10.6325	−	7.72495i	1.12704	−	0.818843i	0.985261	+	0.171056i	$0.0547178\pi$
$90$	−1.55834	−	2.69912i	−0.164263	−	0.284512i
$91$	−0.0476510	+	0.453369i	−0.00499518	+	0.0475259i
$92$	−0.641735	+	6.10570i	−0.0669055	+	0.636563i
$93$	−2.93126	−	5.07710i	−0.303958	−	0.526470i
$94$	6.33905	−	4.60559i	0.653823	−	0.475030i
$95$	2.81049	+	8.64981i	0.288351	+	0.887452i
$96$	−1.16501	−	0.518694i	−0.118903	−	0.0529390i
$97$	0.974518	−	9.27192i	0.0989474	−	0.941421i	−0.826600	−	0.562790i	$-0.809728\pi$
$97$	0.974518	−	9.27192i	0.0989474	−	0.941421i	0.925547	−	0.378632i	$-0.123605\pi$
$98$	−3.35930	−	2.44068i	−0.339341	−	0.246545i
$99$	0.333804	−	1.02734i	0.0335486	−	0.103252i
$100$	−0.0154081	−	0.146598i	−0.00154081	−	0.0146598i
$101$	−3.46013	+	5.99313i	−0.344296	+	0.596338i	−0.985226	−	0.171261i	$-0.945216\pi$
$101$	−3.46013	+	5.99313i	−0.344296	+	0.596338i	0.640929	+	0.767600i	$0.278549\pi$
$102$	−6.57702	−	4.77849i	−0.651222	−	0.473141i
$103$	−12.7577	−	5.68011i	−1.25706	−	0.559677i	−0.333359	−	0.942800i	$-0.608182\pi$
$103$	−12.7577	−	5.68011i	−1.25706	−	0.559677i	−0.923697	+	0.383123i	$0.874849\pi$
$104$	−0.264239	−	0.0561656i	−0.0259107	−	0.00550749i
$105$	4.77575	−	1.01512i	0.466066	−	0.0990653i
$106$	6.66241	−	2.96630i	0.647110	−	0.288112i
$107$	17.7776	+	3.77875i	1.71863	+	0.365306i	0.958638	−	0.284629i	$-0.0918705\pi$
$107$	17.7776	+	3.77875i	1.71863	+	0.365306i	0.759990	+	0.649935i	$0.225204\pi$
$108$	2.78881	+	4.83036i	0.268353	+	0.464801i
$109$	−2.60824	+	4.51761i	−0.249824	+	0.432709i	−0.963477	−	0.267791i	$-0.913706\pi$
$109$	−2.60824	+	4.51761i	−0.249824	+	0.432709i	0.713653	+	0.700500i	$0.247040\pi$
$110$	1.19376	−	1.32581i	0.113821	−	0.126411i
$111$	−8.45831			−0.802827
$112$	−1.12916	+	1.25406i	−0.106696	+	0.118498i
$113$	5.48251	−	16.8734i	0.515751	−	1.58732i	−0.266160	−	0.963929i	$-0.585755\pi$
$113$	5.48251	−	16.8734i	0.515751	−	1.58732i	0.781911	−	0.623390i	$-0.214245\pi$
$114$	−1.57974	−	4.86195i	−0.147957	−	0.455363i
$115$	12.7246	−	5.66537i	1.18658	−	0.528299i
$116$	−1.96328	−	2.18044i	−0.182286	−	0.202449i
$117$	0.248313	+	0.275780i	0.0229566	+	0.0254959i
$118$	−4.63312	+	0.984801i	−0.426514	+	0.0906583i
$119$	−8.70315	+	6.32321i	−0.797816	+	0.579647i
$120$	0.302431	+	2.87744i	0.0276081	+	0.262673i
$121$	−10.3817			−0.943788
$122$	7.58514	+	1.86163i	0.686726	+	0.168544i
$123$	8.19422			0.738848
$124$	−0.480531	−	4.57195i	−0.0431530	−	0.410573i
$125$	8.90688	−	6.47123i	0.796656	−	0.578804i
$126$	2.26750	−	0.481972i	0.202005	−	0.0429374i
$127$	5.18769	+	5.76151i	0.460333	+	0.511251i	0.927963	−	0.372673i	$-0.121559\pi$
$127$	5.18769	+	5.76151i	0.460333	+	0.511251i	−0.467630	+	0.883924i	$0.654892\pi$
$128$	−0.669131	−	0.743145i	−0.0591433	−	0.0656853i
$129$	2.28007	−	1.01515i	0.200749	−	0.0893792i
$130$	0.189395	+	0.582898i	0.0166110	+	0.0511235i
$131$	0.281158	−	0.865315i	0.0245649	−	0.0756029i	−0.938023	−	0.346574i	$-0.887345\pi$
$131$	0.281158	−	0.865315i	0.0245649	−	0.0756029i	0.962587	+	0.270971i	$0.0873449\pi$
$132$	−0.670998	+	0.745218i	−0.0584029	+	0.0648629i
$133$	−6.76474			−0.586578
$134$	−7.59287	+	8.43274i	−0.655924	+	0.728478i
$135$	6.32722	−	10.9591i	0.544560	−	0.943206i
$136$	−3.18745	−	5.52083i	−0.273322	−	0.473407i
$137$	−7.24401	−	1.53976i	−0.618898	−	0.131551i	−0.112216	−	0.993684i	$-0.535795\pi$
$137$	−7.24401	−	1.53976i	−0.618898	−	0.131551i	−0.506682	+	0.862133i	$0.669128\pi$
$138$	−7.15236	+	3.18444i	−0.608849	+	0.271077i
$139$	14.1326	−	3.00398i	1.19871	−	0.254794i	0.435047	−	0.900408i	$-0.356732\pi$
$139$	14.1326	−	3.00398i	1.19871	−	0.254794i	0.763664	+	0.645614i	$0.223398\pi$
$140$	3.74493	+	0.796010i	0.316504	+	0.0672751i
$141$	9.12841	+	4.06423i	0.768750	+	0.342270i
$142$	−7.60095	−	5.52241i	−0.637858	−	0.463431i
$143$	−0.106212	+	0.183965i	−0.00888190	+	0.0153839i
$144$	0.143593	+	1.36619i	0.0119660	+	0.113849i
$145$	−2.05706	+	6.33098i	−0.170829	+	0.525759i
$146$	−9.04661	−	6.57275i	−0.748703	−	0.543964i
$147$	0.553508	−	5.26628i	0.0456526	−	0.434355i
$148$	−6.05920	−	2.69773i	−0.498063	−	0.221752i
$149$	−1.35599	−	4.17332i	−0.111087	−	0.341892i	0.880024	−	0.474930i	$-0.157527\pi$
$149$	−1.35599	−	4.17332i	−0.111087	−	0.341892i	−0.991111	+	0.133038i	$0.957527\pi$
$150$	0.152080	−	0.110492i	0.0124172	−	0.00902165i
$151$	−5.14298	−	8.90791i	−0.418530	−	0.724915i	0.577262	−	0.816559i	$-0.304121\pi$
$151$	−5.14298	−	8.90791i	−0.418530	−	0.724915i	−0.995792	+	0.0916439i	$0.970788\pi$
$152$	0.419026	−	3.98676i	0.0339875	−	0.323369i
$153$	−0.915388	+	8.70934i	−0.0740048	+	0.704108i
$154$	0.663479	+	1.14918i	0.0534647	+	0.0926035i
$155$	−8.43798	+	6.13055i	−0.677755	+	0.492418i
$156$	−0.106457	−	0.327639i	−0.00852334	−	0.0262321i
$157$	−19.3080	−	8.59648i	−1.54095	−	0.686074i	−0.551932	−	0.833889i	$-0.686109\pi$
$157$	−19.3080	−	8.59648i	−1.54095	−	0.686074i	−0.989015	+	0.147815i	$0.952776\pi$
$158$	0.0894086	−	0.850666i	0.00711297	−	0.0676754i
$159$	7.52414	+	5.46661i	0.596703	+	0.433530i
$160$	−0.701095	+	2.15775i	−0.0554264	+	0.170585i
$161$	1.08293	+	10.3034i	0.0853469	+	0.812022i
$162$	−1.49588	+	2.59093i	−0.117527	+	0.203563i
$163$	6.21531	+	4.51569i	0.486821	+	0.353696i	0.803960	−	0.594683i	$-0.202722\pi$
$163$	6.21531	+	4.51569i	0.486821	+	0.353696i	−0.317140	+	0.948379i	$0.602722\pi$
$164$	5.87002	+	2.61350i	0.458372	+	0.204080i
$165$	2.22540	+	0.473024i	0.173247	+	0.0368249i
$166$	11.9602	−	2.54222i	0.928291	−	0.197314i
$167$	−13.6123	+	6.06057i	−1.05335	+	0.468981i	−0.859013	−	0.511954i	$-0.828922\pi$
$167$	−13.6123	+	6.06057i	−1.05335	+	0.468981i	−0.194336	+	0.980935i	$0.562255\pi$
$168$	−2.10498	−	0.447427i	−0.162403	−	0.0345197i
$169$	6.46351	+	11.1951i	0.497193	+	0.861164i
$170$	−7.23166	+	12.5256i	−0.554643	+	0.960669i
$171$	−3.68480	+	4.09239i	−0.281784	+	0.312953i
$172$	1.95713			0.149230
$173$	−11.3935	+	12.6538i	−0.866232	+	0.962048i	−0.999579	−	0.0290215i	$-0.990761\pi$
$173$	−11.3935	+	12.6538i	−0.866232	+	0.962048i	0.133347	+	0.991069i	$0.457428\pi$
$174$	1.15625	−	3.55856i	0.0876549	−	0.269774i
$175$	−0.0768675	−	0.236574i	−0.00581064	−	0.0178833i
$176$	−0.718360	+	0.319835i	−0.0541484	+	0.0241084i
$177$	−4.04183	−	4.48891i	−0.303803	−	0.337407i
$178$	8.79402	+	9.76675i	0.659140	+	0.732049i
$179$	24.1653	−	5.13650i	1.80620	−	0.383920i	0.823234	−	0.567702i	$-0.192167\pi$
$179$	24.1653	−	5.13650i	1.80620	−	0.383920i	0.982967	+	0.183782i	$0.0588339\pi$
$180$	2.52144	−	1.83194i	0.187937	−	0.136544i
$181$	−0.366063	−	3.48286i	−0.0272093	−	0.258879i	−0.999667	−	0.0258000i	$-0.991787\pi$
$181$	−0.366063	−	3.48286i	−0.0272093	−	0.258879i	0.972458	−	0.233079i	$-0.0748800\pi$
$182$	−0.455866			−0.0337910
$183$	2.78051	+	9.56410i	0.205542	+	0.706999i
$184$	−6.13933			−0.452598
$185$	1.57295	+	14.9656i	0.115645	+	1.10029i
$186$	4.74288	−	3.44591i	0.347765	−	0.252666i
$187$	−4.90332	+	1.04223i	−0.358566	+	0.0762156i
$188$	5.24297	+	5.82291i	0.382383	+	0.424679i
$189$	6.29803	+	6.99467i	0.458114	+	0.508788i
$190$	−8.30865	+	3.69925i	−0.602773	+	0.268372i
$191$	0.696153	+	2.14254i	0.0503719	+	0.155029i	0.973078	−	0.230475i	$-0.0740279\pi$
$191$	0.696153	+	2.14254i	0.0503719	+	0.155029i	−0.922706	+	0.385503i	$0.874028\pi$
$192$	0.394076	−	1.21284i	0.0284400	−	0.0875294i
$193$	−1.97575	+	2.19429i	−0.142218	+	0.157949i	−0.810045	−	0.586367i	$-0.800558\pi$
$193$	−1.97575	+	2.19429i	−0.142218	+	0.157949i	0.667828	+	0.744316i	$0.267224\pi$
$194$	9.32300			0.669352
$195$	−0.522992	+	0.580841i	−0.0374522	+	0.0415949i
$196$	2.07616	−	3.59602i	0.148297	−	0.256858i
$197$	4.24253	+	7.34828i	0.302268	+	0.523543i	0.976649	−	0.214840i	$-0.0689230\pi$
$197$	4.24253	+	7.34828i	0.302268	+	0.523543i	−0.674381	+	0.738383i	$0.735590\pi$
$198$	1.05661	+	0.224589i	0.0750898	+	0.0159608i
$199$	−20.4559	+	9.10756i	−1.45008	+	0.645618i	−0.972486	−	0.232962i	$-0.925158\pi$
$199$	−20.4559	+	9.10756i	−1.45008	+	0.645618i	−0.477595	+	0.878580i	$0.658491\pi$
$200$	0.144185	−	0.0306474i	0.0101954	−	0.00216710i
$201$	−14.1546	−	3.00865i	−0.998388	−	0.212214i
$202$	−6.32198	−	2.81473i	−0.444813	−	0.198043i
$203$	−4.00565	−	2.91028i	−0.281142	−	0.204261i
$204$	4.06482	−	7.04048i	0.284594	−	0.492932i
$205$	−1.52384	−	14.4983i	−0.106429	−	1.01261i
$206$	4.31544	−	13.2816i	0.300671	−	0.925371i
$207$	6.82301	+	4.95721i	0.474232	+	0.344550i
$208$	0.0282375	−	0.268662i	0.00195792	−	0.0186284i
$209$	−2.87971	−	1.28213i	−0.199194	−	0.0886867i
$210$	1.50876	+	4.64348i	0.104114	+	0.320431i
$211$	7.68370	−	5.58254i	0.528968	−	0.384318i	−0.291004	−	0.956722i	$-0.593989\pi$
$211$	7.68370	−	5.58254i	0.528968	−	0.384318i	0.819972	+	0.572404i	$0.193989\pi$
$212$	3.64646	+	6.31585i	0.250440	+	0.433774i
$213$	1.25240	−	11.9158i	0.0858130	−	0.816456i
$214$	−1.89978	+	18.0752i	−0.129866	+	1.23560i
$215$	−2.22016	−	3.84543i	−0.151414	−	0.262256i
$216$	−4.51239	+	3.27844i	−0.307029	+	0.223070i
$217$	−2.39726	−	7.37799i	−0.162736	−	0.500851i
$218$	−4.76550	−	2.12174i	−0.322760	−	0.143702i
$219$	1.49060	−	14.1821i	0.100725	−	0.958338i
$220$	1.44332	+	1.04864i	0.0973089	+	0.0706991i
$221$	0.532167	−	1.63784i	0.0357974	−	0.110173i
$222$	−0.884134	−	8.41197i	−0.0593392	−	0.564575i
$223$	8.99719	−	15.5836i	0.602496	−	1.04355i	−0.389946	−	0.920838i	$-0.627506\pi$
$223$	8.99719	−	15.5836i	0.602496	−	1.04355i	0.992442	−	0.122716i	$-0.0391605\pi$
$224$	−1.36522	−	0.991891i	−0.0912176	−	0.0662735i
$225$	−0.184988	−	0.0823618i	−0.0123325	−	0.00549078i
$226$	17.3541	+	3.68872i	1.15438	+	0.245370i
$227$	−7.60819	+	1.61717i	−0.504974	+	0.107335i	−0.453353	−	0.891331i	$-0.649772\pi$
$227$	−7.60819	+	1.61717i	−0.504974	+	0.107335i	−0.0516211	+	0.998667i	$0.516439\pi$
$228$	4.67019	−	2.07930i	0.309291	−	0.137705i
$229$	−19.1308	−	4.06637i	−1.26420	−	0.268714i	−0.473431	−	0.880831i	$-0.656985\pi$
$229$	−19.1308	−	4.06637i	−1.26420	−	0.268714i	−0.790767	+	0.612117i	$0.790318\pi$
$230$	6.96443	+	12.0627i	0.459221	+	0.795394i
$231$	−0.846107	+	1.46550i	−0.0556698	+	0.0964229i
$232$	1.96328	−	2.18044i	0.128895	−	0.143153i
$233$	−22.1667			−1.45219			−0.726093	−	0.687596i	$-0.758666\pi$
$233$	−22.1667			−1.45219			−0.726093	+	0.687596i	$0.758666\pi$
$234$	−0.248313	+	0.275780i	−0.0162327	+	0.0180283i
$235$	5.49343	−	16.9070i	0.358352	−	1.10289i
$236$	−1.46370	−	4.50480i	−0.0952787	−	0.293238i
$237$	0.996490	−	0.443666i	0.0647290	−	0.0288192i
$238$	−7.19829	−	7.99452i	−0.466596	−	0.518208i
$239$	7.42313	+	8.24422i	0.480162	+	0.533274i	0.933744	−	0.357940i	$-0.116521\pi$
$239$	7.42313	+	8.24422i	0.480162	+	0.533274i	−0.453582	+	0.891214i	$0.649854\pi$
$240$	−2.83007	+	0.601549i	−0.182680	+	0.0388298i
$241$	−8.07191	+	5.86458i	−0.519957	+	0.377771i	−0.816588	−	0.577221i	$-0.804137\pi$
$241$	−8.07191	+	5.86458i	−0.519957	+	0.377771i	0.296631	+	0.954992i	$0.404137\pi$
$242$	−1.08518	−	10.3248i	−0.0697580	−	0.663703i
$243$	12.9176			0.828664
$244$	−1.05857	+	7.73818i	−0.0677677	+	0.495386i
$245$	−9.42075			−0.601870
$246$	0.856529	+	8.14933i	0.0546103	+	0.519582i
$247$	0.876104	−	0.636527i	0.0557452	−	0.0405012i
$248$	4.49667	−	0.955797i	0.285539	−	0.0606932i
$249$	10.4338	+	11.5879i	0.661215	+	0.734354i
$250$	7.36680	+	8.18166i	0.465918	+	0.517454i
$251$	13.0803	−	5.82374i	0.825623	−	0.367591i	0.0499702	−	0.998751i	$-0.484087\pi$
$251$	13.0803	−	5.82374i	0.825623	−	0.367591i	0.775653	+	0.631160i	$0.217421\pi$
$252$	0.716349	+	2.20470i	0.0451258	+	0.138883i
$253$	−1.49182	+	4.59134i	−0.0937897	+	0.288655i
$254$	−5.18769	+	5.76151i	−0.325504	+	0.361509i
$255$	−18.4445			−1.15504
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	15.1309	−	26.2075i	0.943840	−	1.63478i	0.185782	−	0.982591i	$-0.440518\pi$
$257$	15.1309	−	26.2075i	0.943840	−	1.63478i	0.758058	−	0.652187i	$-0.226149\pi$
$258$	1.24792	+	2.16147i	0.0776923	+	0.134567i
$259$	−10.9480	−	2.32707i	−0.680276	−	0.144597i
$260$	−0.559907	+	0.249287i	−0.0347240	+	0.0154601i
$261$	−3.94250	+	0.838005i	−0.244035	+	0.0518712i
$262$	0.889963	+	0.189168i	0.0549821	+	0.0116868i
$263$	11.8610	+	5.28085i	0.731379	+	0.325631i	0.738417	−	0.674344i	$-0.235574\pi$
$263$	11.8610	+	5.28085i	0.731379	+	0.325631i	−0.00703791	+	0.999975i	$0.502240\pi$
$264$	−0.811274	−	0.589425i	−0.0499305	−	0.0362766i
$265$	8.27305	−	14.3293i	0.508209	−	0.880244i
$266$	−0.707108	−	6.72769i	−0.0433556	−	0.412501i
$267$	−5.17913	+	15.9397i	−0.316958	+	0.975496i
$268$	−9.18021	−	6.66982i	−0.560771	−	0.407424i
$269$	1.71974	−	16.3622i	0.104854	−	0.997621i	−0.807958	−	0.589241i	$-0.799427\pi$
$269$	1.71974	−	16.3622i	0.104854	−	0.997621i	0.912812	−	0.408381i	$-0.133906\pi$
$270$	11.5604	+	5.14702i	0.703544	+	0.313238i
$271$	−4.08385	−	12.5688i	−0.248076	−	0.763499i	−0.995115	−	0.0987194i	$-0.968525\pi$
$271$	−4.08385	−	12.5688i	−0.248076	−	0.763499i	0.747039	−	0.664780i	$-0.231475\pi$
$272$	5.15740	−	3.74707i	0.312714	−	0.227200i
$273$	−0.290673	−	0.503461i	−0.0175923	−	0.0304708i
$274$	0.774122	−	7.36528i	0.0467664	−	0.444953i
$275$	0.0121161	−	0.115277i	0.000730626	−	0.00695145i
$276$	−3.91462	−	6.78031i	−0.235632	−	0.408127i
$277$	−20.0853	+	14.5928i	−1.20681	+	0.876797i	−0.994937	−	0.100501i	$-0.967955\pi$
$277$	−20.0853	+	14.5928i	−1.20681	+	0.876797i	−0.211870	+	0.977298i	$0.567955\pi$
$278$	4.46478	+	13.7412i	0.267780	+	0.824141i
$279$	−5.76918	−	2.56861i	−0.345392	−	0.153778i
$280$	−0.400197	+	3.80762i	−0.0239164	+	0.227549i
$281$	−1.02076	−	0.741624i	−0.0608933	−	0.0442416i	0.556922	−	0.830565i	$-0.311982\pi$
$281$	−1.02076	−	0.741624i	−0.0608933	−	0.0442416i	−0.617815	+	0.786323i	$0.711982\pi$
$282$	−3.08779	+	9.50323i	−0.183875	+	0.565909i
$283$	0.200562	+	1.90822i	0.0119222	+	0.113432i	0.998864	−	0.0476425i	$-0.0151708\pi$
$283$	0.200562	+	1.90822i	0.0119222	+	0.113432i	−0.986942	+	0.161074i	$0.948504\pi$
$284$	4.69765	−	8.13656i	0.278754	−	0.482816i
$285$	−9.38331	−	6.81737i	−0.555819	−	0.403826i
$286$	−0.194059	−	0.0864007i	−0.0114750	−	0.00510898i
$287$	10.6062	+	2.25441i	0.626063	+	0.133074i
$288$	−1.34370	+	0.285612i	−0.0791782	+	0.0168298i
$289$	21.5956	−	9.61500i	1.27033	−	0.565588i
$290$	−6.51132	−	1.38402i	−0.382358	−	0.0812726i
$291$	5.94461	+	10.2964i	0.348479	+	0.603584i
$292$	5.59111	−	9.68409i	0.327195	−	0.566719i
$293$	12.2470	−	13.6017i	0.715477	−	0.794618i	−0.270282	−	0.962781i	$-0.587117\pi$
$293$	12.2470	−	13.6017i	0.715477	−	0.794618i	0.985759	+	0.168163i	$0.0537835\pi$
$294$	5.29529			0.308827
$295$	−7.19076	+	7.98615i	−0.418662	+	0.464971i
$296$	2.04959	−	6.30800i	0.119130	−	0.366645i
$297$	1.35532	+	4.17126i	0.0786439	+	0.242041i
$298$	4.00872	−	1.78480i	0.232219	−	0.103390i
$299$	−1.10975	−	1.23250i	−0.0641783	−	0.0712772i
$300$	0.125784	+	0.139697i	0.00726212	+	0.00806540i
$301$	3.23050	−	0.686663i	0.186203	−	0.0395786i
$302$	8.32152	−	6.04594i	0.478850	−	0.347905i
$303$	−0.922477	−	8.77678i	−0.0529949	−	0.504213i
$304$	4.00872			0.229916
$305$	16.4050	−	6.69825i	0.939350	−	0.383541i
$306$	−8.75731			−0.500622
$307$	2.44360	+	23.2493i	0.139464	+	1.32691i	0.810611	+	0.585585i	$0.199135\pi$
$307$	2.44360	+	23.2493i	0.139464	+	1.32691i	−0.671147	+	0.741324i	$0.734198\pi$
$308$	−1.07353	+	0.779967i	−0.0611702	+	0.0444427i
$309$	17.4199	−	3.70271i	0.990983	−	0.210640i
$310$	−6.97898	−	7.75094i	−0.396379	−	0.440224i
$311$	12.8487	+	14.2700i	0.728585	+	0.809176i	0.987649	−	0.156684i	$-0.0500805\pi$
$311$	12.8487	+	14.2700i	0.728585	+	0.809176i	−0.259063	+	0.965860i	$0.583414\pi$
$312$	0.314717	−	0.140121i	0.0178173	−	0.00793279i
$313$	−2.41191	−	7.42309i	−0.136329	−	0.419578i	0.859465	−	0.511194i	$-0.170797\pi$
$313$	−2.41191	−	7.42309i	−0.136329	−	0.419578i	−0.995794	+	0.0916164i	$0.970797\pi$
$314$	6.53115	−	20.1008i	0.368574	−	1.13435i
$315$	3.51923	−	3.90850i	0.198286	−	0.220219i
$316$	0.855352			0.0481173
$317$	−9.42090	+	10.4630i	−0.529130	+	0.587659i	−0.947155	−	0.320777i	$-0.896056\pi$
$317$	−9.42090	+	10.4630i	−0.529130	+	0.587659i	0.418024	+	0.908436i	$0.362723\pi$
$318$	−4.65017	+	8.05434i	−0.260769	+	0.451665i
$319$	−1.15359	−	1.99808i	−0.0645888	−	0.111871i
$320$	−2.21921	−	0.471708i	−0.124058	−	0.0263693i
$321$	−21.1737	+	9.42715i	−1.18180	+	0.526172i
$322$	−10.1338	+	2.15400i	−0.564733	+	0.120038i
$323$	24.9968	+	5.31323i	1.39086	+	0.295636i
$324$	−2.73310	−	1.21685i	−0.151839	−	0.0676030i
$325$	0.0322155	+	0.0234059i	0.00178699	+	0.00129833i
$326$	−3.84127	+	6.65328i	−0.212748	+	0.368491i
$327$	−0.695362	−	6.61592i	−0.0384536	−	0.365861i
$328$	−1.98560	+	6.11105i	−0.109636	+	0.337426i
$329$	10.6972	+	7.77196i	0.589755	+	0.428482i
$330$	−0.237815	+	2.26266i	−0.0130913	+	0.124555i
$331$	4.56773	+	2.03368i	0.251065	+	0.111781i	0.528411	−	0.848989i	$-0.322788\pi$
$331$	4.56773	+	2.03368i	0.251065	+	0.111781i	−0.277346	+	0.960770i	$0.589455\pi$
$332$	3.77847	+	11.6289i	0.207370	+	0.638221i
$333$	−7.37124	+	5.35552i	−0.403941	+	0.293480i
$334$	−7.45024	−	12.9042i	−0.407659	−	0.706087i
$335$	−2.69106	+	25.6038i	−0.147028	+	1.39888i
$336$	0.224946	−	2.14022i	0.0122718	−	0.116758i
$337$	13.8982	+	24.0724i	0.757083	+	1.31131i	0.944332	+	0.328993i	$0.106709\pi$
$337$	13.8982	+	24.0724i	0.757083	+	1.31131i	−0.187249	+	0.982312i	$0.559957\pi$
$338$	−10.4582	+	7.59831i	−0.568850	+	0.413294i
$339$	6.99161	+	21.5180i	0.379732	+	1.16870i
$340$	−13.2129	−	5.88276i	−0.716570	−	0.319037i
$341$	0.377862	−	3.59512i	0.0204624	−	0.194687i
$342$	−4.45514	−	3.23685i	−0.240906	−	0.175029i
$343$	5.81558	−	17.8985i	0.314012	−	0.966429i
$344$	0.204576	+	1.94641i	0.0110300	+	0.104943i
$345$	−8.88144	+	15.3831i	−0.478161	+	0.828199i
$346$	−13.7754	−	10.0084i	−0.740570	−	0.538055i
$347$	−19.3944	−	8.63494i	−1.04115	−	0.463548i	−0.186334	−	0.982486i	$-0.559661\pi$
$347$	−19.3944	−	8.63494i	−1.04115	−	0.463548i	−0.854812	+	0.518939i	$0.826327\pi$
$348$	3.65993	+	0.777942i	0.196193	+	0.0417021i
$349$	−20.9788	+	4.45918i	−1.12297	+	0.238694i	−0.731730	−	0.681595i	$-0.761287\pi$
$349$	−20.9788	+	4.45918i	−1.12297	+	0.238694i	−0.391239	+	0.920289i	$0.627953\pi$
$350$	0.227243	−	0.101175i	0.0121466	−	0.00540804i
$351$	−1.47382	−	0.313270i	−0.0786668	−	0.0167211i
$352$	−0.393172	−	0.680993i	−0.0209561	−	0.0362971i
$353$	1.19940	−	2.07742i	0.0638376	−	0.110570i	−0.832340	−	0.554265i	$-0.812999\pi$
$353$	1.19940	−	2.07742i	0.0638376	−	0.110570i	0.896178	+	0.443695i	$0.146333\pi$
$354$	4.04183	−	4.48891i	0.214821	−	0.238583i
$355$	−21.3159			−1.13133
$356$	−8.79402	+	9.76675i	−0.466082	+	0.517637i
$357$	4.23935	−	13.0474i	0.224370	−	0.690540i
$358$	7.63433	+	23.4960i	0.403487	+	1.24180i
$359$	−8.83292	+	3.93267i	−0.466184	+	0.207558i	−0.626366	−	0.779529i	$-0.715458\pi$
$359$	−8.83292	+	3.93267i	−0.466184	+	0.207558i	0.160182	+	0.987087i	$0.448792\pi$
$360$	2.08546	+	2.31614i	0.109914	+	0.122071i
$361$	−1.96064	−	2.17751i	−0.103192	−	0.114606i
$362$	3.42551	−	0.728116i	0.180041	−	0.0382689i
$363$	10.7108	−	7.78187i	0.562172	−	0.408442i
$364$	−0.0476510	−	0.453369i	−0.00249759	−	0.0237630i
$365$	−25.3701			−1.32793
$366$	−9.22106	+	3.76500i	−0.481993	+	0.196800i
$367$	−6.03572			−0.315062			−0.157531	−	0.987514i	$-0.550353\pi$
$367$	−6.03572			−0.315062			−0.157531	+	0.987514i	$0.550353\pi$
$368$	−0.641735	−	6.10570i	−0.0334527	−	0.318282i
$369$	7.14109	−	5.18830i	0.371750	−	0.270092i
$370$	−14.7192	+	3.12866i	−0.765214	+	0.162651i
$371$	8.23488	+	9.14576i	0.427534	+	0.474824i
$372$	3.92280	+	4.35671i	0.203388	+	0.225885i
$373$	26.2649	−	11.6939i	1.35994	−	0.605486i	0.408345	−	0.912828i	$-0.366106\pi$
$373$	26.2649	−	11.6939i	1.35994	−	0.605486i	0.951599	+	0.307341i	$0.0994394\pi$
$374$	−1.54906	−	4.76751i	−0.0800999	−	0.246522i
$375$	−4.33859	+	13.3528i	−0.224044	+	0.689536i
$376$	−5.24297	+	5.82291i	−0.270386	+	0.300294i
$377$	0.792615			0.0408217
$378$	−6.29803	+	6.99467i	−0.323936	+	0.359767i
$379$	−7.58897	+	13.1445i	−0.389819	+	0.675187i	−0.992425	−	0.122852i	$-0.960796\pi$
$379$	−7.58897	+	13.1445i	−0.389819	+	0.675187i	0.602606	+	0.798039i	$0.294129\pi$
$380$	−4.54748	−	7.87646i	−0.233281	−	0.404054i
$381$	−9.67086	−	2.05561i	−0.495453	−	0.105312i
$382$	−2.05803	+	0.916296i	−0.105298	+	0.0468818i
$383$	−14.4717	+	3.07605i	−0.739468	+	0.157179i	−0.562220	−	0.826987i	$-0.690053\pi$
$383$	−14.4717	+	3.07605i	−0.739468	+	0.157179i	−0.177248	+	0.984166i	$0.556719\pi$
$384$	1.24739	+	0.265141i	0.0636556	+	0.0135304i
$385$	2.75031	+	1.22452i	0.140169	+	0.0624072i
$386$	−2.38879	−	1.73556i	−0.121586	−	0.0883377i
$387$	1.34427	−	2.32835i	0.0683332	−	0.118357i
$388$	0.974518	+	9.27192i	0.0494737	+	0.470711i
$389$	−0.382590	+	1.17749i	−0.0193981	+	0.0597012i	−0.960287	−	0.279014i	$-0.909992\pi$
$389$	−0.382590	+	1.17749i	−0.0193981	+	0.0597012i	0.940889	+	0.338715i	$0.109992\pi$
$390$	−0.632327	−	0.459412i	−0.0320191	−	0.0232633i
$391$	4.09100	−	38.9232i	0.206891	−	1.96843i
$392$	3.79334	+	1.68890i	0.191592	+	0.0853025i
$393$	0.358549	+	1.10350i	0.0180864	+	0.0556642i
$394$	−6.86456	+	4.98739i	−0.345831	+	0.251261i
$395$	−0.970307	−	1.68062i	−0.0488214	−	0.0845612i
$396$	−0.112913	+	1.07430i	−0.00567409	+	0.0539854i
$397$	−2.19397	+	20.8742i	−0.110112	+	1.04765i	0.790333	+	0.612678i	$0.209908\pi$
$397$	−2.19397	+	20.8742i	−0.110112	+	1.04765i	−0.900445	+	0.434970i	$0.856759\pi$
$398$	−11.1959	−	19.3918i	−0.561199	−	0.972026i
$399$	6.97922	−	5.07070i	0.349398	−	0.253853i
$400$	0.0455510	+	0.140191i	0.00227755	+	0.00700957i
$401$	21.5597	+	9.59900i	1.07664	+	0.479351i	0.866939	−	0.498414i	$-0.166084\pi$
$401$	21.5597	+	9.59900i	1.07664	+	0.479351i	0.209701	+	0.977765i	$0.432751\pi$
$402$	1.51261	−	14.3915i	0.0754423	−	0.717785i
$403$	1.00470	+	0.729957i	0.0500477	+	0.0363617i
$404$	2.13848	−	6.58157i	0.106393	−	0.327445i
$405$	0.709503	+	6.75047i	0.0352555	+	0.335433i
$406$	2.47563	−	4.28791i	0.122863	−	0.212806i
$407$	−4.21944	−	3.06560i	−0.209150	−	0.151956i
$408$	7.42680	+	3.30662i	0.367681	+	0.163702i
$409$	−6.20379	−	1.31866i	−0.306758	−	0.0652033i	0.0519610	−	0.998649i	$-0.483453\pi$
$409$	−6.20379	−	1.31866i	−0.306758	−	0.0652033i	−0.358718	+	0.933446i	$0.616786\pi$
$410$	14.2596	−	3.03098i	0.704233	−	0.149689i
$411$	8.62786	−	3.84137i	0.425581	−	0.189481i
$412$	13.6599	+	2.90350i	0.672975	+	0.143045i
$413$	−3.99655	−	6.92222i	−0.196657	−	0.340620i
$414$	−4.21685	+	7.30380i	−0.207247	+	0.358962i
$415$	18.5626	−	20.6158i	0.911202	−	1.01199i
$416$	0.270142			0.0132448
$417$	−12.3290	+	13.6927i	−0.603752	+	0.670534i
$418$	0.974093	−	2.99795i	0.0476445	−	0.146635i
$419$	−7.54092	−	23.2086i	−0.368398	−	1.13381i	−0.947826	−	0.318789i	$-0.896724\pi$
$419$	−7.54092	−	23.2086i	−0.368398	−	1.13381i	0.579428	−	0.815024i	$-0.303276\pi$
$420$	−4.46034	+	1.98587i	−0.217642	+	0.0969005i
$421$	18.4630	+	20.5053i	0.899834	+	0.999366i	0.999990	+	0.00439470i	$0.00139888\pi$
$421$	18.4630	+	20.5053i	0.899834	+	0.999366i	−0.100157	+	0.994972i	$0.531934\pi$
$422$	6.35512	+	7.05808i	0.309362	+	0.343582i
$423$	10.5285	−	2.23791i	0.511915	−	0.108811i
$424$	−5.90009	+	4.28667i	−0.286534	+	0.208179i
$425$	0.0982252	+	0.934551i	0.00476462	+	0.0453324i
$426$	11.9814			0.580502
$427$	0.967658	+	13.1443i	0.0468283	+	0.636096i
$428$	−18.1748			−0.878511
$429$	−0.0283163	−	0.269412i	−0.00136712	−	0.0130073i
$430$	3.59229	−	2.60995i	0.173236	−	0.125863i
$431$	−35.4614	+	7.53755i	−1.70812	+	0.363071i	−0.955409	−	0.295286i	$-0.904585\pi$
$431$	−35.4614	+	7.53755i	−1.70812	+	0.363071i	−0.752706	+	0.658357i	$0.771252\pi$
$432$	−3.73215	−	4.14498i	−0.179563	−	0.199425i
$433$	20.3756	+	22.6294i	0.979187	+	1.08750i	0.996152	+	0.0876415i	$0.0279330\pi$
$433$	20.3756	+	22.6294i	0.979187	+	1.08750i	−0.0169648	+	0.999856i	$0.505400\pi$
$434$	7.08700	−	3.15533i	0.340187	−	0.151461i
$435$	−2.62328	−	8.07363i	−0.125777	−	0.387101i
$436$	1.61198	−	4.96117i	0.0772000	−	0.237597i
$437$	16.4679	−	18.2895i	0.787766	−	0.874903i
$438$	14.2602			0.681380
$439$	7.83504	−	8.70170i	0.373946	−	0.415309i	−0.526570	−	0.850132i	$-0.676522\pi$
$439$	7.83504	−	8.70170i	0.373946	−	0.415309i	0.900516	+	0.434822i	$0.143189\pi$
$440$	−0.892023	+	1.54503i	−0.0425256	+	0.0736564i
$441$	−2.85206	−	4.93991i	−0.135812	−	0.235234i
$442$	1.68449	+	0.358050i	0.0801233	+	0.0170307i
$443$	−26.1694	+	11.6513i	−1.24334	+	0.553572i	−0.919706	−	0.392609i	$-0.871573\pi$
$443$	−26.1694	+	11.6513i	−1.24334	+	0.553572i	−0.323638	+	0.946181i	$0.604906\pi$
$444$	8.27347	−	1.75858i	0.392642	−	0.0834586i
$445$	29.1659	+	6.19940i	1.38260	+	0.293880i
$446$	16.4387	+	7.31897i	0.778394	+	0.346563i
$447$	4.52721	+	3.28921i	0.214130	+	0.155574i
$448$	0.843753	−	1.46142i	0.0398636	−	0.0690457i
$449$	0.0162523	+	0.154630i	0.000766992	+	0.00729744i	0.994899	−	0.100879i	$-0.0321655\pi$
$449$	0.0162523	+	0.154630i	0.000766992	+	0.00729744i	−0.994132	+	0.108176i	$0.965499\pi$
$450$	0.0625741	−	0.192583i	0.00294977	−	0.00907847i
$451$	4.08770	+	2.96989i	0.192482	+	0.139847i
$452$	−1.85452	+	17.6446i	−0.0872293	+	0.829931i
$453$	11.9832	+	5.33527i	0.563020	+	0.250673i
$454$	−2.40359	−	7.39748i	−0.112806	−	0.347181i
$455$	−0.836737	+	0.607925i	−0.0392268	+	0.0285000i
$456$	2.55608	+	4.42726i	0.119699	+	0.207325i
$457$	1.88045	−	17.8912i	0.0879635	−	0.836917i	−0.858219	−	0.513284i	$-0.828429\pi$
$457$	1.88045	−	17.8912i	0.0879635	−	0.836917i	0.946183	−	0.323633i	$-0.104904\pi$
$458$	2.04439	−	19.4510i	0.0955279	−	0.908887i
$459$	−17.7784	−	30.7931i	−0.829824	−	1.43730i
$460$	−11.2687	+	8.18717i	−0.525405	+	0.381729i
$461$	1.75073	+	5.38818i	0.0815394	+	0.250953i	0.983513	−	0.180839i	$-0.0578814\pi$
$461$	1.75073	+	5.38818i	0.0815394	+	0.250953i	−0.901973	+	0.431792i	$0.857881\pi$
$462$	−1.54591	−	0.688286i	−0.0719225	−	0.0320219i
$463$	2.49001	−	23.6909i	0.115721	−	1.10101i	−0.770402	−	0.637559i	$-0.779944\pi$
$463$	2.49001	−	23.6909i	0.115721	−	1.10101i	0.886123	−	0.463451i	$-0.153389\pi$
$464$	2.37371	+	1.72460i	0.110197	+	0.0800627i
$465$	4.11019	−	12.6498i	0.190605	−	0.586623i
$466$	−2.31705	−	22.0452i	−0.107335	−	1.02123i
$467$	−16.8443	+	29.1753i	−0.779463	+	1.35007i	0.152788	+	0.988259i	$0.451175\pi$
$467$	−16.8443	+	29.1753i	−0.779463	+	1.35007i	−0.932251	+	0.361811i	$0.882159\pi$
$468$	−0.300225	−	0.218126i	−0.0138779	−	0.0100829i
$469$	−17.4933	−	7.78850i	−0.807763	−	0.359639i
$470$	17.3886	+	3.69607i	0.802078	+	0.170487i
$471$	26.3639	−	5.60382i	1.21478	−	0.258210i
$472$	4.32713	−	1.92656i	0.199172	−	0.0886772i
$473$	1.50535	+	0.319971i	0.0692159	+	0.0147123i
$474$	0.545397	+	0.944655i	0.0250509	+	0.0433895i
$475$	−0.295455	+	0.511743i	−0.0135564	+	0.0234804i
$476$	7.19829	−	7.99452i	0.329933	−	0.366428i
$477$	10.0184			0.458711
$478$	−7.42313	+	8.24422i	−0.339526	+	0.377082i
$479$	−1.20472	+	3.70774i	−0.0550449	+	0.169411i	−0.974799	−	0.223084i	$-0.928388\pi$
$479$	−1.20472	+	3.70774i	−0.0550449	+	0.169411i	0.919754	+	0.392494i	$0.128388\pi$
$480$	−0.894076	−	2.75168i	−0.0408088	−	0.125597i
$481$	1.63684	−	0.728770i	0.0746337	−	0.0332291i
$482$	−6.67620	−	7.41467i	−0.304093	−	0.337729i
$483$	−8.84047	−	9.81834i	−0.402255	−	0.446750i
$484$	10.1548	−	2.15847i	0.461582	−	0.0981122i
$485$	17.1123	−	12.4328i	0.777028	−	0.564544i
$486$	1.35026	+	12.8468i	0.0612489	+	0.582744i
$487$	−6.71260			−0.304177			−0.152089	−	0.988367i	$-0.548600\pi$
$487$	−6.71260			−0.304177			−0.152089	+	0.988367i	$0.548600\pi$
$488$	−7.80644	−	0.243906i	−0.353381	−	0.0110411i
$489$	−9.79723			−0.443046
$490$	−0.984737	−	9.36914i	−0.0444859	−	0.423255i
$491$	−25.2333	+	18.3330i	−1.13876	+	0.827359i	−0.986946	−	0.161050i	$-0.948512\pi$
$491$	−25.2333	+	18.3330i	−1.13876	+	0.827359i	−0.151815	+	0.988409i	$0.548512\pi$
$492$	−8.01516	+	1.70367i	−0.361351	+	0.0768075i
$493$	12.5157	+	13.9001i	0.563678	+	0.626028i
$494$	0.724618	+	0.804769i	0.0326021	+	0.0362083i
$495$	2.23890	−	0.996820i	0.100631	−	0.0448037i
$496$	1.42059	+	4.37213i	0.0637864	+	0.196314i
$497$	4.89934	−	15.0786i	0.219766	−	0.676369i
$498$	−10.4338	+	11.5879i	−0.467550	+	0.519267i
$499$	4.26352			0.190862			0.0954308	−	0.995436i	$-0.469577\pi$
$499$	4.26352			0.190862			0.0954308	+	0.995436i	$0.469577\pi$
$500$	−7.36680	+	8.18166i	−0.329453	+	0.365895i
$501$	9.50098	−	16.4562i	0.424473	−	0.735208i
$502$	7.15910	+	12.3999i	0.319526	+	0.553436i
$503$	−12.3021	−	2.61488i	−0.548522	−	0.116592i	−0.0746892	−	0.997207i	$-0.523796\pi$
$503$	−12.3021	−	2.61488i	−0.548522	−	0.116592i	−0.473833	+	0.880615i	$0.657130\pi$
$504$	−2.11774	+	0.942879i	−0.0943316	+	0.0419992i
$505$	−15.3575	+	3.26434i	−0.683401	+	0.145261i
$506$	−4.72213	−	1.00372i	−0.209924	−	0.0446207i
$507$	−15.0601	−	6.70517i	−0.668841	−	0.297787i
$508$	−6.27221	−	4.55702i	−0.278284	−	0.202185i
$509$	−12.8026	+	22.1748i	−0.567466	+	0.982880i	0.429350	+	0.903138i	$0.358743\pi$
$509$	−12.8026	+	22.1748i	−0.567466	+	0.982880i	−0.996816	+	0.0797414i	$0.974591\pi$
$510$	−1.92797	−	18.3434i	−0.0853720	−	0.812260i
$511$	5.83117	−	17.9465i	0.257956	−	0.793906i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	2.33717	−	22.2366i	0.103188	−	0.981772i
$514$	27.6455	+	12.3086i	1.21939	+	0.542908i
$515$	−9.79083	−	30.1331i	−0.431436	−	1.32782i
$516$	−2.01918	+	1.46702i	−0.0888895	+	0.0645820i
$517$	3.08070	+	5.33592i	0.135489	+	0.234674i
$518$	1.16994	−	11.1313i	0.0514044	−	0.489080i
$519$	2.26975	−	21.5953i	0.0996312	−	0.947927i
$520$	−0.306447	−	0.530783i	−0.0134386	−	0.0232764i
$521$	1.37300	−	0.997546i	0.0601524	−	0.0437033i	−0.557303	−	0.830309i	$-0.688164\pi$
$521$	1.37300	−	0.997546i	0.0601524	−	0.0437033i	0.617455	+	0.786606i	$0.288164\pi$
$522$	−1.24552	−	3.83331i	−0.0545148	−	0.167779i
$523$	−4.90091	−	2.18203i	−0.214302	−	0.0954134i	0.296778	−	0.954946i	$-0.404088\pi$
$523$	−4.90091	−	2.18203i	−0.214302	−	0.0954134i	−0.511080	+	0.859533i	$0.670754\pi$
$524$	−0.0951048	+	0.904861i	−0.00415467	+	0.0395291i
$525$	0.256635	+	0.186456i	0.0112005	+	0.00813762i
$526$	−4.01211	+	12.3480i	−0.174936	+	0.538398i
$527$	3.06334	+	29.1457i	0.133441	+	1.26961i
$528$	0.501395	−	0.868442i	0.0218204	−	0.0377941i
$529$	−11.8856	−	8.63539i	−0.516765	−	0.375452i
$530$	15.1156	+	6.72990i	0.656580	+	0.292328i
$531$	−6.36460	−	1.35284i	−0.276200	−	0.0587082i
$532$	6.61692	−	1.40647i	0.286880	−	0.0609782i
$533$	−1.58574	+	0.706016i	−0.0686859	+	0.0305810i
$534$	−16.3938	−	3.48461i	−0.709428	−	0.150794i
$535$	20.6174	+	35.7103i	0.891367	+	1.54389i
$536$	5.67368	−	9.82711i	0.245066	−	0.424466i
$537$	−21.0813	+	23.4131i	−0.909725	+	1.01035i
$538$	16.4523			0.709310
$539$	2.18481	−	2.42648i	0.0941066	−	0.104516i
$540$	−3.91044	+	12.0351i	−0.168278	+	0.517908i
$541$	5.19122	+	15.9769i	0.223188	+	0.686902i	0.998470	+	0.0552871i	$0.0176074\pi$
$541$	5.19122	+	15.9769i	0.223188	+	0.686902i	−0.775283	+	0.631614i	$0.782393\pi$
$542$	12.0731	−	5.37527i	0.518582	−	0.230888i
$543$	2.98834	+	3.31889i	0.128242	+	0.142427i
$544$	4.26564	+	4.73748i	0.182888	+	0.203118i
$545$	−11.5765	+	2.46066i	−0.495882	+	0.105403i
$546$	0.470319	−	0.341707i	0.0201278	−	0.0146237i
$547$	−0.301218	−	2.86590i	−0.0128792	−	0.122537i	0.986193	−	0.165598i	$-0.0529556\pi$
$547$	−0.301218	−	2.86590i	−0.0128792	−	0.122537i	−0.999072	+	0.0430614i	$0.986289\pi$
$548$	7.40585			0.316362
$549$	8.47883	+	6.57438i	0.361868	+	0.280588i
$550$	0.115912			0.00494249
$551$	1.22945	+	11.6974i	0.0523763	+	0.498328i
$552$	6.33398	−	4.60191i	0.269592	−	0.195870i
$553$	1.41187	−	0.300102i	0.0600388	−	0.0127616i
$554$	−16.6123	−	18.4499i	−0.705791	−	0.783860i
$555$	−12.8407	−	14.2610i	−0.545057	−	0.605347i
$556$	−13.1992	+	5.87666i	−0.559771	+	0.249226i
$557$	−2.46700	−	7.59265i	−0.104530	−	0.321711i	0.885090	−	0.465420i	$-0.154097\pi$
$557$	−2.46700	−	7.59265i	−0.104530	−	0.321711i	−0.989620	+	0.143710i	$0.954097\pi$
$558$	1.95149	−	6.00607i	0.0826132	−	0.254257i
$559$	−0.353771	+	0.392903i	−0.0149629	+	0.0166180i
$560$	−3.82860			−0.161788
$561$	4.27754	−	4.75069i	0.180598	−	0.200574i
$562$	0.630863	−	1.09269i	0.0266113	−	0.0460922i
$563$	−6.62306	−	11.4715i	−0.279129	−	0.483465i	0.692040	−	0.721859i	$-0.256712\pi$
$563$	−6.62306	−	11.4715i	−0.279129	−	0.483465i	−0.971168	+	0.238394i	$0.923379\pi$
$564$	−9.77393	−	2.07751i	−0.411557	−	0.0874791i
$565$	36.7724	−	16.3721i	1.54702	−	0.688780i
$566$	−1.87680	+	0.398926i	−0.0788878	+	0.0167681i
$567$	−4.93827	−	1.04966i	−0.207388	−	0.0440817i
$568$	8.58303	+	3.82141i	0.360136	+	0.160343i
$569$	−36.5470	−	26.5530i	−1.53213	−	1.11316i	−0.955039	−	0.296480i	$-0.904187\pi$
$569$	−36.5470	−	26.5530i	−1.53213	−	1.11316i	−0.577092	−	0.816679i	$-0.695813\pi$
$570$	5.79920	−	10.0445i	0.242902	−	0.420718i
$571$	3.00488	+	28.5895i	0.125750	+	1.19643i	0.857363	+	0.514713i	$0.172101\pi$
$571$	3.00488	+	28.5895i	0.125750	+	1.19643i	−0.731612	+	0.681721i	$0.761232\pi$
$572$	0.0656427	−	0.202027i	0.00274466	−	0.00844719i
$573$	−2.32422	−	1.68865i	−0.0970959	−	0.0705443i
$574$	−1.13342	+	10.7837i	−0.0473079	+	0.450104i
$575$	0.826735	+	0.368086i	0.0344772	+	0.0153503i
$576$	−0.424502	−	1.30648i	−0.0176876	−	0.0544368i
$577$	24.5162	−	17.8121i	1.02062	−	0.741526i	0.0542128	−	0.998529i	$-0.482735\pi$
$577$	24.5162	−	17.8121i	1.02062	−	0.741526i	0.966411	+	0.257003i	$0.0827351\pi$
$578$	11.8197	+	20.4723i	0.491634	+	0.851535i
$579$	0.393599	−	3.74484i	0.0163574	−	0.155630i
$580$	0.695823	−	6.62032i	0.0288925	−	0.274894i
$581$	10.3169	+	17.8694i	0.428017	+	0.741347i
$582$	−9.61858	+	6.98831i	−0.398703	+	0.289675i
$583$	1.77213	+	5.45406i	0.0733941	+	0.225884i
$584$	10.2155	+	4.54822i	0.422719	+	0.188207i
$585$	−0.0880071	+	0.837332i	−0.00363865	+	0.0346194i
$586$	14.8073	+	10.7581i	0.611685	+	0.444415i
$587$	−1.93425	+	5.95300i	−0.0798350	+	0.245707i	−0.983006	−	0.183575i	$-0.941233\pi$
$587$	−1.93425	+	5.95300i	−0.0798350	+	0.245707i	0.903171	+	0.429281i	$0.141233\pi$
$588$	0.553508	+	5.26628i	0.0228263	+	0.217178i
$589$	−9.21431	+	15.9597i	−0.379669	+	0.657606i
$590$	−8.69404	−	6.31659i	−0.357928	−	0.260050i
$591$	−9.88515	−	4.40115i	−0.406621	−	0.181039i
$592$	6.48769	+	1.37900i	0.266642	+	0.0566766i
$593$	−0.995806	+	0.211665i	−0.0408928	+	0.00869204i	−0.228313	−	0.973588i	$-0.573321\pi$
$593$	−0.995806	+	0.211665i	−0.0408928	+	0.00869204i	0.187420	+	0.982280i	$0.439988\pi$
$594$	−4.00674	+	1.78391i	−0.164398	+	0.0731949i
$595$	−23.8736	−	5.07448i	−0.978721	−	0.208034i
$596$	2.19404	+	3.80019i	0.0898715	+	0.155662i
$597$	14.2776	−	24.7296i	0.584345	−	1.01212i
$598$	1.10975	−	1.23250i	0.0453809	−	0.0504006i
$599$	−42.4429			−1.73417			−0.867086	−	0.498159i	$-0.834009\pi$
$599$	−42.4429			−1.73417			−0.867086	+	0.498159i	$0.834009\pi$
$600$	−0.125784	+	0.139697i	−0.00513509	+	0.00570310i
$601$	−9.02714	+	27.7827i	−0.368225	+	1.13328i	0.579713	+	0.814821i	$0.303165\pi$
$601$	−9.02714	+	27.7827i	−0.368225	+	1.13328i	−0.947937	+	0.318458i	$0.896835\pi$
$602$	1.02058	+	3.14102i	0.0415958	+	0.128019i
$603$	−14.2404	+	6.34024i	−0.579914	+	0.258195i
$604$	6.88265	+	7.64396i	0.280051	+	0.311028i
$605$	−15.7606	−	17.5039i	−0.640759	−	0.711634i
$606$	8.63228	−	1.83485i	0.350662	−	0.0745356i
$607$	−26.8531	+	19.5099i	−1.08993	+	0.791882i	−0.979388	−	0.201989i	$-0.935259\pi$
$607$	−26.8531	+	19.5099i	−1.08993	+	0.791882i	−0.110544	+	0.993871i	$0.535259\pi$
$608$	0.419026	+	3.98676i	0.0169937	+	0.161685i
$609$	6.31413			0.255861
$610$	8.37635	+	15.6150i	0.339149	+	0.632233i
$611$	−2.11670			−0.0856324
$612$	−0.915388	−	8.70934i	−0.0370024	−	0.352054i
$613$	−34.9244	+	25.3741i	−1.41058	+	1.02485i	−0.417348	+	0.908747i	$0.637040\pi$
$613$	−34.9244	+	25.3741i	−1.41058	+	1.02485i	−0.993237	+	0.116103i	$0.962960\pi$
$614$	−22.8665	+	4.86043i	−0.922819	+	0.196151i
$615$	12.4398	+	13.8158i	0.501620	+	0.557106i
$616$	−0.887908	−	0.986122i	−0.0357749	−	0.0397320i
$617$	33.5848	−	14.9529i	1.35208	−	0.601983i	0.402471	−	0.915433i	$-0.368152\pi$
$617$	33.5848	−	14.9529i	1.35208	−	0.601983i	0.949605	+	0.313450i	$0.101485\pi$
$618$	5.50330	+	16.9374i	0.221375	+	0.681323i
$619$	−5.75430	+	17.7099i	−0.231285	+	0.711821i	0.766308	+	0.642474i	$0.222092\pi$
$619$	−5.75430	+	17.7099i	−0.231285	+	0.711821i	−0.997593	+	0.0693477i	$0.977908\pi$
$620$	6.97898	−	7.75094i	0.280283	−	0.311285i
$621$	−34.2428			−1.37412
$622$	−12.8487	+	14.2700i	−0.515188	+	0.572174i
$623$	−11.0890	+	19.2067i	−0.444271	+	0.769500i
$624$	0.172250	+	0.298346i	0.00689553	+	0.0119434i
$625$	25.1534	+	5.34651i	1.00613	+	0.213860i
$626$	7.13031	−	3.17462i	0.284984	−	0.126883i
$627$	3.93206	−	0.835786i	0.157032	−	0.0333781i
$628$	20.6734	+	4.39426i	0.824958	+	0.175350i
$629$	38.6268	+	17.1978i	1.54015	+	0.685720i
$630$	4.25495	+	3.09140i	0.169521	+	0.123164i
$631$	20.8774	−	36.1607i	0.831116	−	1.43954i	−0.0660377	−	0.997817i	$-0.521036\pi$
$631$	20.8774	−	36.1607i	0.831116	−	1.43954i	0.897154	−	0.441718i	$-0.145631\pi$
$632$	0.0894086	+	0.850666i	0.00355648	+	0.0338377i
$633$	−3.74277	+	11.5191i	−0.148762	+	0.457842i
$634$	−11.3904	−	8.27561i	−0.452371	−	0.328667i
$635$	−1.83862	+	17.4933i	−0.0729633	+	0.694200i
$636$	−8.49629	−	3.78279i	−0.336900	−	0.149997i
$637$	0.346629	+	1.06682i	0.0137340	+	0.0422688i
$638$	1.86655	−	1.35613i	0.0738975	−	0.0536897i
$639$	−6.45324	−	11.1773i	−0.255286	−	0.442168i
$640$	0.237153	−	2.25636i	0.00937430	−	0.0891905i
$641$	−2.66542	+	25.3598i	−0.105278	+	1.00165i	0.806575	+	0.591132i	$0.201319\pi$
$641$	−2.66542	+	25.3598i	−0.105278	+	1.00165i	−0.911852	+	0.410518i	$0.865348\pi$
$642$	−11.5888	−	20.0723i	−0.457372	−	0.792192i
$643$	17.6117	−	12.7956i	0.694538	−	0.504611i	−0.183611	−	0.982999i	$-0.558779\pi$
$643$	17.6117	−	12.7956i	0.694538	−	0.504611i	0.878149	+	0.478388i	$0.158779\pi$
$644$	−3.20146	−	9.85310i	−0.126155	−	0.388266i
$645$	5.17300	+	2.30317i	0.203687	+	0.0906871i
$646$	−2.67125	+	25.4152i	−0.105099	+	0.999949i
$647$	5.19388	+	3.77357i	0.204192	+	0.148354i	0.685182	−	0.728372i	$-0.259723\pi$
$647$	5.19388	+	3.77357i	0.204192	+	0.148354i	−0.480990	+	0.876726i	$0.659723\pi$
$648$	0.924502	−	2.84532i	0.0363179	−	0.111775i
$649$	−0.389328	−	3.70421i	−0.0152825	−	0.145403i
$650$	−0.0199103	+	0.0344856i	−0.000780945	+	0.00135264i
$651$	8.00364	+	5.81499i	0.313688	+	0.227907i
$652$	−7.01836	−	3.12477i	−0.274860	−	0.122376i
$653$	11.5032	+	2.44508i	0.450154	+	0.0956833i	0.427410	−	0.904058i	$-0.359426\pi$
$653$	11.5032	+	2.44508i	0.450154	+	0.0956833i	0.0227446	+	0.999741i	$0.492760\pi$
$654$	6.50700	−	1.38310i	0.254444	−	0.0540837i
$655$	1.88578	−	0.839605i	0.0736837	−	0.0328061i
$656$	−6.28512	−	1.33594i	−0.245393	−	0.0521599i
$657$	−7.68061	−	13.3032i	−0.299649	−	0.519007i
$658$	−6.61123	+	11.4510i	−0.257732	+	0.446406i
$659$	−7.03942	+	7.81807i	−0.274217	+	0.304549i	−0.864485	−	0.502659i	$-0.832355\pi$
$659$	−7.03942	+	7.81807i	−0.274217	+	0.304549i	0.590268	+	0.807207i	$0.299022\pi$
$660$	−2.27512			−0.0885589
$661$	10.3371	−	11.4805i	0.402067	−	0.446540i	−0.507779	−	0.861488i	$-0.669533\pi$
$661$	10.3371	−	11.4805i	0.402067	−	0.446540i	0.909846	+	0.414947i	$0.136200\pi$
$662$	−1.54509	+	4.75528i	−0.0600514	+	0.184819i
$663$	0.678650	+	2.08867i	0.0263566	+	0.0811172i
$664$	−11.1703	+	4.97333i	−0.433491	+	0.193002i
$665$	−10.2697	−	11.4056i	−0.398241	−	0.442291i
$666$	−6.09668	−	6.77105i	−0.236242	−	0.262373i
$667$	17.6196	−	3.74516i	0.682233	−	0.145013i
$668$	12.0547	−	8.75829i	0.466412	−	0.338868i
$669$	2.39866	+	22.8218i	0.0927377	+	0.882340i
$670$	−25.7448			−0.994608
$671$	−2.07932	+	5.77883i	−0.0802713	+	0.223089i
$672$	2.15201			0.0830154
$673$	2.11156	+	20.0902i	0.0813947	+	0.774419i	0.956745	+	0.290929i	$0.0939643\pi$
$673$	2.11156	+	20.0902i	0.0813947	+	0.774419i	−0.875350	+	0.483490i	$0.839369\pi$
$674$	−22.4877	+	16.3383i	−0.866196	+	0.629328i
$675$	0.804208	−	0.170940i	0.0309540	−	0.00657947i
$676$	−8.64987	−	9.60665i	−0.332687	−	0.369487i
$677$	5.51971	+	6.13026i	0.212140	+	0.235605i	0.839818	−	0.542868i	$-0.182661\pi$
$677$	5.51971	+	6.13026i	0.212140	+	0.235605i	−0.627679	+	0.778473i	$0.715995\pi$
$678$	−20.6693	+	9.20256i	−0.793799	+	0.353422i
$679$	4.86164	+	14.9626i	0.186573	+	0.574212i
$680$	4.46941	−	13.7554i	0.171394	−	0.527496i
$681$	6.63722	−	7.37138i	0.254339	−	0.282472i
$682$	3.61492			0.138422
$683$	22.4725	−	24.9583i	0.859887	−	0.955002i	−0.139492	−	0.990223i	$-0.544547\pi$
$683$	22.4725	−	24.9583i	0.859887	−	0.955002i	0.999380	+	0.0352214i	$0.0112136\pi$
$684$	2.75343	−	4.76907i	0.105280	−	0.182350i
$685$	−8.40115	−	14.5512i	−0.320992	−	0.555974i
$686$	18.4084	+	3.91282i	0.702834	+	0.149392i
$687$	22.7854	−	10.1447i	0.869317	−	0.387045i
$688$	−1.91436	+	0.406910i	−0.0729844	+	0.0155133i
$689$	−1.92707	−	0.409611i	−0.0734155	−	0.0156049i
$690$	−16.2272	−	7.22481i	−0.617759	−	0.275044i
$691$	−1.57719	−	1.14589i	−0.0599990	−	0.0435918i	0.557382	−	0.830257i	$-0.311806\pi$
$691$	−1.57719	−	1.14589i	−0.0599990	−	0.0435918i	−0.617380	+	0.786665i	$0.711806\pi$
$692$	8.51366	−	14.7461i	0.323641	−	0.560562i
$693$	0.190541	+	1.81288i	0.00723807	+	0.0688656i
$694$	6.56037	−	20.1907i	0.249028	−	0.766430i
$695$	26.5197	+	19.2677i	1.00595	+	0.730866i
$696$	−0.391114	+	3.72120i	−0.0148251	+	0.141052i
$697$	−37.4208	−	16.6608i	−1.41741	−	0.631073i
$698$	−6.62763	−	20.3977i	−0.250859	−	0.772066i
$699$	22.8695	−	16.6156i	0.865003	−	0.628461i
$700$	0.124374	+	0.215422i	0.00470090	+	0.00814220i
$701$	4.02614	−	38.3061i	0.152065	−	1.44680i	−0.606437	−	0.795132i	$-0.707402\pi$
$701$	4.02614	−	38.3061i	0.152065	−	1.44680i	0.758502	−	0.651671i	$-0.225932\pi$
$702$	0.157498	−	1.49849i	0.00594438	−	0.0565570i
$703$	13.2942	+	23.0262i	0.501399	+	0.868449i
$704$	0.636165	−	0.462201i	0.0239764	−	0.0174199i
$705$	7.00554	+	21.5608i	0.263844	+	0.812028i
$706$	2.19141	+	0.975680i	0.0824749	+	0.0367202i
$707$	1.22068	−	11.6140i	0.0459085	−	0.436790i
$708$	4.88681	+	3.55047i	0.183657	+	0.133435i
$709$	3.69867	−	11.3833i	0.138906	−	0.427510i	−0.857271	−	0.514866i	$-0.827842\pi$
$709$	3.69867	−	11.3833i	0.138906	−	0.427510i	0.996177	+	0.0873559i	$0.0278417\pi$
$710$	−2.22812	−	21.1992i	−0.0836199	−	0.795591i
$711$	0.587506	−	1.01759i	0.0220332	−	0.0381626i
$712$	−10.6325	−	7.72495i	−0.398469	−	0.289505i
$713$	25.7833	+	11.4795i	0.965591	+	0.429909i
$714$	13.4190	+	2.85230i	0.502195	+	0.106745i
$715$	−0.471414	+	0.100202i	−0.0176299	+	0.00374735i
$716$	−22.5693	+	10.0485i	−0.843455	+	0.375530i
$717$	−13.8382	−	2.94139i	−0.516796	−	0.109848i
$718$	−4.83442	−	8.37346i	−0.180419	−	0.312495i
$719$	12.5240	−	21.6922i	0.467067	−	0.808984i	−0.532225	−	0.846603i	$-0.678644\pi$
$719$	12.5240	−	21.6922i	0.467067	−	0.808984i	0.999292	+	0.0376189i	$0.0119773\pi$
$720$	−2.08546	+	2.31614i	−0.0777206	+	0.0863175i
$721$	23.5661			0.877649
$722$	1.96064	−	2.17751i	0.0729676	−	0.0810387i
$723$	3.93187	−	12.1010i	0.146228	−	0.450043i
$724$	1.08219	+	3.33064i	0.0402193	+	0.123782i
$725$	−0.395108	+	0.175913i	−0.0146739	+	0.00653326i
$726$	8.85882	+	9.83872i	0.328782	+	0.365149i
$727$	−23.7771	−	26.4071i	−0.881843	−	0.979386i	0.118064	−	0.993006i	$-0.462331\pi$
$727$	−23.7771	−	26.4071i	−0.881843	−	0.979386i	−0.999907	+	0.0136200i	$0.995664\pi$
$728$	0.445904	−	0.0947798i	0.0165263	−	0.00351277i
$729$	−20.5883	+	14.9583i	−0.762529	+	0.554010i
$730$	−2.65190	−	25.2311i	−0.0981512	−	0.933846i
$731$	−12.4765			−0.461461
$732$	−4.70824	−	8.77700i	−0.174022	−	0.324407i
$733$	9.61948			0.355303			0.177652	−	0.984093i	$-0.443150\pi$
$733$	9.61948			0.355303			0.177652	+	0.984093i	$0.443150\pi$
$734$	−0.630905	−	6.00266i	−0.0232871	−	0.221562i
$735$	9.71944	−	7.06159i	0.358507	−	0.260471i
$736$	6.00517	−	1.27644i	0.221354	−	0.0470502i
$737$	−5.97060	−	6.63103i	−0.219930	−	0.244257i
$738$	5.90633	+	6.55964i	0.217415	+	0.241464i
$739$	−30.0273	+	13.3690i	−1.10457	+	0.491787i	−0.876279	−	0.481805i	$-0.839981\pi$
$739$	−30.0273	+	13.3690i	−1.10457	+	0.491787i	−0.228294	+	0.973592i	$0.573315\pi$
$740$	−4.65010	−	14.3115i	−0.170941	−	0.526102i
$741$	−0.426755	+	1.31342i	−0.0156772	+	0.0482495i
$742$	−8.23488	+	9.14576i	−0.302312	+	0.335751i
$743$	26.3435			0.966448			0.483224	−	0.875497i	$-0.339466\pi$
$743$	26.3435			0.966448			0.483224	+	0.875497i	$0.339466\pi$
$744$	−3.92280	+	4.35671i	−0.143817	+	0.159725i
$745$	4.97782	−	8.62184i	0.182373	−	0.315880i
$746$	14.3752	+	24.8987i	0.526315	+	0.911605i
$747$	16.4299	+	3.49229i	0.601139	+	0.127776i
$748$	4.57948	−	2.03891i	0.167442	−	0.0745501i
$749$	−29.9998	+	6.37666i	−1.09617	+	0.232998i
$750$	−13.7332	−	2.91907i	−0.501464	−	0.106590i
$751$	46.5176	+	20.7110i	1.69745	+	0.755755i	0.999204	+	0.0399002i	$0.0127040\pi$
$751$	46.5176	+	20.7110i	1.69745	+	0.755755i	0.698249	+	0.715855i	$0.253963\pi$
$752$	−6.33905	−	4.60559i	−0.231161	−	0.167949i
$753$	−9.12970	+	15.8131i	−0.332705	+	0.576262i
$754$	0.0828508	+	0.788273i	0.00301725	+	0.0287072i
$755$	7.21143	−	22.1945i	0.262451	−	0.807741i
$756$	−7.61468	−	5.53239i	−0.276943	−	0.201211i
$757$	4.17625	−	39.7343i	0.151788	−	1.44417i	−0.607968	−	0.793961i	$-0.708015\pi$
$757$	4.17625	−	39.7343i	0.151788	−	1.44417i	0.759757	−	0.650208i	$-0.225318\pi$
$758$	−13.8657	−	6.17342i	−0.503626	−	0.224229i
$759$	−1.90245	−	5.85514i	−0.0690546	−	0.212528i
$760$	7.35797	−	5.34588i	0.266902	−	0.193915i
$761$	−7.17185	−	12.4220i	−0.259980	−	0.450298i	0.706257	−	0.707956i	$-0.250382\pi$
$761$	−7.17185	−	12.4220i	−0.259980	−	0.450298i	−0.966236	+	0.257658i	$0.917049\pi$
$762$	1.03346	−	9.83275i	0.0374384	−	0.356203i
$763$	0.920148	−	8.75463i	0.0333116	−	0.316939i
$764$	−1.12640	−	1.95098i	−0.0407517	−	0.0705840i
$765$	−16.0740	+	11.6784i	−0.581155	+	0.422234i
$766$	−4.57190	−	14.0709i	−0.165190	−	0.508401i
$767$	1.16894	+	0.520445i	0.0422079	+	0.0187922i
$768$	−0.133301	+	1.26827i	−0.00481008	+	0.0457648i
$769$	−29.0002	−	21.0699i	−1.04577	−	0.759799i	−0.0743698	−	0.997231i	$-0.523695\pi$
$769$	−29.0002	−	21.0699i	−1.04577	−	0.759799i	−0.971404	+	0.237431i	$0.923695\pi$
$770$	−0.930323	+	2.86324i	−0.0335265	+	0.103184i
$771$	4.03392	+	38.3802i	0.145278	+	1.38223i
$772$	1.47636	−	2.55712i	0.0531352	−	0.0920329i
$773$	15.2246	+	11.0613i	0.547590	+	0.397847i	0.826896	−	0.562355i	$-0.190104\pi$
$773$	15.2246	+	11.0613i	0.547590	+	0.397847i	−0.279306	+	0.960202i	$0.590104\pi$
$774$	2.45611	+	1.09353i	0.0882829	+	0.0393061i
$775$	−0.662836	−	0.140890i	−0.0238098	−	0.00506093i
$776$	−9.11927	+	1.93836i	−0.327363	+	0.0695831i
$777$	13.0394	−	5.80553i	0.467787	−	0.208272i
$778$	−1.21103	−	0.257413i	−0.0434176	−	0.00922870i
$779$	−12.8791	−	22.3073i	−0.461442	−	0.799241i
$780$	0.390800	−	0.676885i	0.0139929	−	0.0242364i
$781$	4.94349	−	5.49030i	0.176892	−	0.196458i
$782$	39.1376			1.39956
$783$	10.9504	−	12.1616i	0.391335	−	0.434622i
$784$	−1.28314	+	3.94910i	−0.0458264	+	0.141039i
$785$	−14.8178	−	45.6045i	−0.528870	−	1.62770i
$786$	−1.05998	+	0.471932i	−0.0378081	+	0.0168332i
$787$	23.9093	+	26.5539i	0.852274	+	0.946546i	0.999091	−	0.0426179i	$-0.0135698\pi$
$787$	23.9093	+	26.5539i	0.852274	+	0.946546i	−0.146818	+	0.989164i	$0.546903\pi$
$788$	−5.67761	−	6.30563i	−0.202257	−	0.224629i
$789$	−16.1954	+	3.44245i	−0.576573	+	0.122554i
$790$	1.56999	−	1.14066i	0.0558577	−	0.0405830i
$791$	3.12951	+	29.7753i	0.111273	+	1.05869i
$792$	−1.08021			−0.0383837
$793$	−1.36213	−	1.61127i	−0.0483706	−	0.0572177i
$794$	−20.9892			−0.744879
$795$	2.20561	+	20.9849i	0.0782248	+	0.744259i
$796$	18.1153	−	13.1616i	0.642081	−	0.466499i
$797$	−2.05970	+	0.437803i	−0.0729583	+	0.0155078i	−0.244246	−	0.969713i	$-0.578541\pi$
$797$	−2.05970	+	0.437803i	−0.0729583	+	0.0155078i	0.171288	+	0.985221i	$0.445207\pi$
$798$	5.77245	+	6.41096i	0.204343	+	0.226945i
$799$	−33.4234	−	37.1205i	−1.18244	−	1.31323i
$800$	−0.134662	+	0.0599554i	−0.00476102	+	0.00211974i
$801$	5.57900	+	17.1704i	0.197124	+	0.606686i
$802$	−7.29281	+	22.4450i	−0.257518	+	0.792559i
$803$	5.88371	−	6.53452i	0.207632	−	0.230598i
$804$	14.4708			0.510347
$805$	−15.7279	+	17.4676i	−0.554337	+	0.615653i
$806$	−0.620939	+	1.07550i	−0.0218716	+	0.0378828i
$807$	10.4905	+	18.1701i	0.369283	+	0.639616i
$808$	6.76904	+	1.43880i	0.238134	+	0.0506170i
$809$	16.6463	−	7.41143i	0.585254	−	0.260572i	−0.0926785	−	0.995696i	$-0.529543\pi$
$809$	16.6463	−	7.41143i	0.585254	−	0.260572i	0.677932	+	0.735124i	$0.262876\pi$
$810$	−6.63933	+	1.41123i	−0.233282	+	0.0495856i
$811$	1.28384	+	0.272889i	0.0450817	+	0.00958241i	0.230397	−	0.973097i	$-0.425997\pi$
$811$	1.28384	+	0.272889i	0.0450817	+	0.00958241i	−0.185316	+	0.982679i	$0.559331\pi$
$812$	4.52320	+	2.01386i	0.158733	+	0.0706726i
$813$	13.6346	+	9.90612i	0.478187	+	0.347423i
$814$	2.60776	−	4.51677i	0.0914019	−	0.158313i
$815$	1.82194	+	17.3346i	0.0638198	+	0.607205i
$816$	−2.51220	+	7.73175i	−0.0879445	+	0.270665i
$817$	−6.34722	−	4.61152i	−0.222061	−	0.161337i
$818$	0.662960	−	6.30764i	0.0231798	−	0.220541i
$819$	−0.572090	−	0.254711i	−0.0199904	−	0.00890032i
$820$	4.50491	+	13.8647i	0.157318	+	0.484176i
$821$	−18.7984	+	13.6578i	−0.656069	+	0.476662i	−0.865333	−	0.501197i	$-0.832893\pi$
$821$	−18.7984	+	13.6578i	−0.656069	+	0.476662i	0.209264	+	0.977859i	$0.432893\pi$
$822$	4.72218	+	8.17906i	0.164705	+	0.285277i
$823$	−3.56917	+	33.9584i	−0.124414	+	1.18372i	0.737029	+	0.675861i	$0.236228\pi$
$823$	−3.56917	+	33.9584i	−0.124414	+	1.18372i	−0.861443	+	0.507855i	$0.830439\pi$
$824$	−1.45975	+	13.8886i	−0.0508527	+	0.483831i
$825$	0.0739086	+	0.128014i	0.00257317	+	0.00445686i
$826$	6.46655	−	4.69822i	0.225000	−	0.163472i
$827$	−4.98799	−	15.3515i	−0.173449	−	0.533822i	0.826110	−	0.563509i	$-0.190549\pi$
$827$	−4.98799	−	15.3515i	−0.173449	−	0.533822i	−0.999559	+	0.0296867i	$0.990549\pi$
$828$	−7.70457	−	3.43030i	−0.267752	−	0.119211i
$829$	−0.235490	+	2.24054i	−0.00817892	+	0.0778172i	−0.997850	−	0.0655398i	$-0.979123\pi$
$829$	−0.235490	+	2.24054i	−0.00817892	+	0.0778172i	0.989671	+	0.143357i	$0.0457897\pi$
$830$	22.4432	+	16.3060i	0.779016	+	0.565988i
$831$	9.78364	−	30.1109i	0.339391	−	1.04454i
$832$	0.0282375	+	0.268662i	0.000978959	+	0.00931418i
$833$	−13.2353	+	22.9243i	−0.458577	+	0.794279i
$834$	−14.9064	−	10.8301i	−0.516167	−	0.375017i
$835$	−30.8834	−	13.7502i	−1.06876	−	0.475844i
$836$	3.08335	+	0.655386i	0.106640	+	0.0226670i
$837$	25.0807	−	5.33107i	0.866916	−	0.184269i
$838$	22.2932	−	9.92556i	0.770105	−	0.342873i
$839$	38.0193	+	8.08126i	1.31257	+	0.278996i	0.810454	−	0.585802i	$-0.199220\pi$
$839$	38.0193	+	8.08126i	1.31257	+	0.278996i	0.502120	+	0.864798i	$0.332554\pi$
$840$	−2.44122	−	4.22832i	−0.0842302	−	0.145891i
$841$	10.1956	−	17.6593i	0.351573	−	0.608943i
$842$	−18.4630	+	20.5053i	−0.636278	+	0.706659i
$843$	1.60903			0.0554178
$844$	−6.35512	+	7.05808i	−0.218752	+	0.242949i
$845$	−9.06307	+	27.8932i	−0.311779	+	0.959557i
$846$	3.32618	+	10.2369i	0.114357	+	0.351953i
$847$	16.0045	−	7.12567i	0.549921	−	0.244841i
$848$	−4.87991	−	5.41969i	−0.167577	−	0.186113i
$849$	−1.63728	−	1.81838i	−0.0561912	−	0.0624067i
$850$	−0.919164	+	0.195374i	−0.0315271	+	0.00670128i
$851$	32.9431	−	23.9345i	1.12927	−	0.820466i
$852$	1.25240	+	11.9158i	0.0429065	+	0.408228i
$853$	2.63752			0.0903070			0.0451535	−	0.998980i	$-0.485622\pi$
$853$	2.63752			0.0903070			0.0451535	+	0.998980i	$0.485622\pi$
$854$	−12.9711	+	2.33631i	−0.443862	+	0.0799468i
$855$	−12.4939			−0.427282
$856$	−1.89978	−	18.0752i	−0.0649332	−	0.617798i
$857$	0.0897879	−	0.0652347i	0.00306709	−	0.00222837i	−0.586251	−	0.810130i	$-0.699397\pi$
$857$	0.0897879	−	0.0652347i	0.00306709	−	0.00222837i	0.589318	+	0.807901i	$0.299397\pi$
$858$	0.264976	−	0.0563224i	0.00904613	−	0.00192281i
$859$	−24.8799	−	27.6319i	−0.848891	−	0.942789i	0.150056	−	0.988678i	$-0.452055\pi$
$859$	−24.8799	−	27.6319i	−0.848891	−	0.942789i	−0.998947	+	0.0458888i	$0.985388\pi$
$860$	2.97115	+	3.29980i	0.101315	+	0.112522i
$861$	−12.6323	+	5.62427i	−0.430508	+	0.191675i
$862$	−11.2030	−	34.4792i	−0.381575	−	1.17437i
$863$	1.01108	−	3.11180i	0.0344177	−	0.105927i	−0.932372	−	0.361501i	$-0.882264\pi$
$863$	1.01108	−	3.11180i	0.0344177	−	0.105927i	0.966789	+	0.255574i	$0.0822645\pi$
$864$	3.73215	−	4.14498i	0.126970	−	0.141015i
$865$	−38.6314			−1.31351
$866$	−20.3756	+	22.6294i	−0.692390	+	0.768977i
$867$	−15.0731	+	26.1075i	−0.511911	+	0.886656i
$868$	3.87884	+	6.71835i	0.131656	+	0.228036i
$869$	0.657902	+	0.139841i	0.0223178	+	0.00474379i
$870$	7.75519	−	3.45284i	0.262926	−	0.117062i
$871$	2.99841	−	0.637332i	0.101597	−	0.0215952i
$872$	5.10249	+	1.08457i	0.172792	+	0.0367281i
$873$	11.6999	+	5.20914i	0.395982	+	0.176303i
$874$	19.9106	+	14.4659i	0.673487	+	0.489317i
$875$	−9.28931	+	16.0896i	−0.314036	+	0.543926i
$876$	1.49060	+	14.1821i	0.0503627	+	0.479169i
$877$	−15.9377	+	49.0512i	−0.538178	+	1.65634i	0.198501	+	0.980101i	$0.436393\pi$
$877$	−15.9377	+	49.0512i	−0.538178	+	1.65634i	−0.736680	+	0.676242i	$0.763607\pi$
$878$	9.47301	+	6.88255i	0.319699	+	0.232275i
$879$	−2.43978	+	23.2130i	−0.0822919	+	0.782955i
$880$	−1.62981	−	0.725637i	−0.0549408	−	0.0244612i
$881$	3.42462	+	10.5399i	0.115378	+	0.355098i	0.992026	−	0.126035i	$-0.0402252\pi$
$881$	3.42462	+	10.5399i	0.115378	+	0.355098i	−0.876647	+	0.481134i	$0.840225\pi$
$882$	4.61473	−	3.35280i	0.155386	−	0.112895i
$883$	−3.70734	−	6.42129i	−0.124762	−	0.216094i	0.796878	−	0.604140i	$-0.206483\pi$
$883$	−3.70734	−	6.42129i	−0.124762	−	0.216094i	−0.921640	+	0.388046i	$0.873150\pi$
$884$	−0.180011	+	1.71269i	−0.00605444	+	0.0576041i
$885$	1.43251	−	13.6294i	0.0481532	−	0.458147i
$886$	−14.3230	−	24.8081i	−0.481189	−	0.833444i
$887$	28.4228	−	20.6504i	0.954344	−	0.693371i	0.00251344	−	0.999997i	$-0.499200\pi$
$887$	28.4228	−	20.6504i	0.954344	−	0.693371i	0.951830	+	0.306626i	$0.0991999\pi$
$888$	2.61376	+	8.04433i	0.0877121	+	0.269950i
$889$	−11.9519	−	5.32134i	−0.400855	−	0.178472i
$890$	−3.11678	+	29.6541i	−0.104475	+	0.994009i
$891$	−1.90325	−	1.38279i	−0.0637612	−	0.0463252i
$892$	−5.56057	+	17.1137i	−0.186182	+	0.573008i
$893$	−3.28328	−	31.2383i	−0.109871	−	1.04535i
$894$	−2.79797	+	4.84623i	−0.0935782	+	0.162082i
$895$	45.3461	+	32.9459i	1.51575	+	1.10126i
$896$	1.54161	+	0.686370i	0.0515017	+	0.0229300i
$897$	2.06879	+	0.439734i	0.0690747	+	0.0146823i
$898$	−0.152084	+	0.0323265i	−0.00507511	+	0.00107875i
$899$	−12.3222	+	5.48618i	−0.410967	+	0.182974i
$900$	0.198069	+	0.0421009i	0.00660230	+	0.00140336i
$901$	−23.2458	−	40.2629i	−0.774430	−	1.34135i
$902$	−2.52634	+	4.37575i	−0.0841179	+	0.145696i
$903$	−2.81821	+	3.12994i	−0.0937843	+	0.104158i
$904$	−17.7418			−0.590083
$905$	5.31651	−	5.90458i	0.176727	−	0.196275i
$906$	−4.05346	+	12.4753i	−0.134667	+	0.414463i
$907$	1.66290	+	5.11789i	0.0552158	+	0.169937i	0.974861	−	0.222813i	$-0.0715239\pi$
$907$	1.66290	+	5.11789i	0.0552158	+	0.169937i	−0.919645	+	0.392750i	$0.871524\pi$
$908$	7.10571	−	3.16367i	0.235811	−	0.104990i
$909$	−6.36108	−	7.06470i	−0.210984	−	0.234321i
$910$	−0.692057	−	0.768608i	−0.0229415	−	0.0254791i
$911$	−28.5716	+	6.07308i	−0.946620	+	0.201210i	−0.655260	−	0.755403i	$-0.727441\pi$
$911$	−28.5716	+	6.07308i	−0.946620	+	0.201210i	−0.291360	+	0.956614i	$0.594108\pi$
$912$	−4.13582	+	3.00485i	−0.136951	+	0.0995005i
$913$	1.00503	+	9.56225i	0.0332617	+	0.316464i
$914$	17.9898			0.595049
$915$	−11.9043	+	19.2075i	−0.393544	+	0.634979i
$916$	19.5582			0.646220
$917$	0.160490	+	1.52696i	0.00529984	+	0.0504246i
$918$	28.7660	−	20.8997i	0.949420	−	0.689794i
$919$	15.7484	−	3.34742i	0.519491	−	0.110421i	0.0592985	−	0.998240i	$-0.481114\pi$
$919$	15.7484	−	3.34742i	0.519491	−	0.110421i	0.460193	+	0.887819i	$0.347780\pi$
$920$	−9.32022	−	10.3512i	−0.307279	−	0.341267i
$921$	−19.9483	−	22.1548i	−0.657318	−	0.730025i
$922$	−5.17566	+	2.30435i	−0.170451	+	0.0758898i
$923$	0.784304	+	2.41384i	0.0258157	+	0.0794525i
$924$	0.522923	−	1.60939i	0.0172029	−	0.0529451i
$925$	−0.654201	+	0.726564i	−0.0215100	+	0.0238893i
$926$	23.8214			0.782820
$927$	12.8366	−	14.2565i	0.421611	−	0.468246i
$928$	−1.46703	+	2.54098i	−0.0481578	+	0.0834117i
$929$	9.93382	+	17.2059i	0.325918	+	0.564507i	0.981698	−	0.190446i	$-0.0609933\pi$
$929$	9.93382	+	17.2059i	0.325918	+	0.564507i	−0.655780	+	0.754952i	$0.727660\pi$
$930$	13.0102	+	2.76540i	0.426621	+	0.0906810i
$931$	−15.2064	+	6.77034i	−0.498371	+	0.221889i
$932$	21.6823	−	4.60871i	0.710226	−	0.150963i
$933$	−23.9526	−	5.09128i	−0.784172	−	0.166681i
$934$	−30.7761	−	13.7024i	−1.00703	−	0.448357i
$935$	−9.20105	−	6.68495i	−0.300907	−	0.218621i
$936$	0.185549	−	0.321381i	0.00606487	−	0.0105047i
$937$	−3.04807	−	29.0005i	−0.0995761	−	0.947404i	−0.924248	−	0.381792i	$-0.875307\pi$
$937$	−3.04807	−	29.0005i	−0.0995761	−	0.947404i	0.824672	−	0.565611i	$-0.191360\pi$
$938$	5.91729	−	18.2115i	0.193206	−	0.594628i
$939$	8.05256	+	5.85053i	0.262785	+	0.190925i
$940$	−1.85821	+	17.6797i	−0.0606082	+	0.576649i
$941$	13.9174	+	6.19644i	0.453696	+	0.201998i	0.620845	−	0.783933i	$-0.286790\pi$
$941$	13.9174	+	6.19644i	0.453696	+	0.201998i	−0.167149	+	0.985932i	$0.553456\pi$
$942$	8.32890	+	25.6337i	0.271370	+	0.835192i
$943$	−31.9145	+	23.1873i	−1.03928	+	0.755081i
$944$	2.36832	+	4.10204i	0.0770821	+	0.133510i
$945$	−2.23215	+	21.2375i	−0.0726117	+	0.690855i
$946$	−0.160867	+	1.53055i	−0.00523023	+	0.0497623i
$947$	−12.0881	−	20.9372i	−0.392810	−	0.680367i	0.600009	−	0.799993i	$-0.295164\pi$
$947$	−12.0881	−	20.9372i	−0.392810	−	0.680367i	−0.992819	+	0.119626i	$0.961830\pi$
$948$	−0.882471	+	0.641153i	−0.0286613	+	0.0208237i
$949$	0.933474	+	2.87294i	0.0303019	+	0.0932595i
$950$	−0.539823	−	0.240345i	−0.0175142	−	0.00779781i
$951$	1.87678	−	17.8564i	0.0608589	−	0.579033i
$952$	8.70315	+	6.32321i	0.282071	+	0.204936i
$953$	−8.54250	+	26.2911i	−0.276719	+	0.851653i	0.712041	+	0.702138i	$0.247771\pi$
$953$	−8.54250	+	26.2911i	−0.276719	+	0.851653i	−0.988760	+	0.149515i	$0.952229\pi$
$954$	1.04721	+	9.96352i	0.0339046	+	0.322581i
$955$	−2.55556	+	4.42637i	−0.0826961	+	0.143234i
$956$	−8.97498	−	6.52071i	−0.290272	−	0.210895i
$957$	2.68788	+	1.19672i	0.0868870	+	0.0386846i
$958$	−3.81335	−	0.810553i	−0.123204	−	0.0261878i
$959$	12.2243	−	2.59836i	0.394743	−	0.0839053i
$960$	2.64315	−	1.17681i	0.0853074	−	0.0379813i
$961$	9.65079	+	2.05134i	0.311316	+	0.0661722i
$962$	0.895875	+	1.55170i	0.0288842	+	0.0500288i
$963$	−12.4835	+	21.6221i	−0.402275	+	0.696761i
$964$	6.67620	−	7.41467i	0.215026	−	0.238810i
$965$	−6.69908			−0.215651
$966$	8.84047	−	9.81834i	0.284437	−	0.315900i
$967$	−10.7483	+	33.0800i	−0.345643	+	1.06378i	0.615596	+	0.788062i	$0.288915\pi$
$967$	−10.7483	+	33.0800i	−0.345643	+	1.06378i	−0.961239	+	0.275718i	$0.911085\pi$
$968$	3.20811	+	9.87355i	0.103113	+	0.317348i
$969$	−29.7720	+	13.2553i	−0.956414	+	0.425823i
$970$	14.1534	+	15.7189i	0.454438	+	0.504705i
$971$	−3.80645	−	4.22749i	−0.122155	−	0.135667i	0.678965	−	0.734171i	$-0.262429\pi$
$971$	−3.80645	−	4.22749i	−0.122155	−	0.135667i	−0.801120	+	0.598504i	$0.795762\pi$
$972$	−12.6353	+	2.68572i	−0.405278	+	0.0861445i
$973$	−19.7252	+	14.3312i	−0.632359	+	0.459436i
$974$	−0.701658	−	6.67583i	−0.0224826	−	0.213907i
$975$	−0.0507814			−0.00162631
$976$	−0.573425	−	7.78917i	−0.0183549	−	0.249325i
$977$	12.3728			0.395839			0.197920	−	0.980218i	$-0.436581\pi$
$977$	12.3728			0.395839			0.197920	+	0.980218i	$0.436581\pi$
$978$	−1.02409	−	9.74356i	−0.0327468	−	0.311565i
$979$	−8.36077	+	6.07446i	−0.267212	+	0.194141i
$980$	9.21488	−	1.95868i	0.294359	−	0.0625679i
$981$	−4.79497	−	5.32536i	−0.153092	−	0.170026i
$982$	−20.8702	−	23.1787i	−0.665995	−	0.739663i
$983$	−1.98446	+	0.883538i	−0.0632944	+	0.0281805i	−0.438140	−	0.898907i	$-0.644362\pi$
$983$	−1.98446	+	0.883538i	−0.0632944	+	0.0281805i	0.374845	+	0.927087i	$0.377696\pi$
$984$	−2.53215	−	7.79316i	−0.0807221	−	0.248437i
$985$	−5.94883	+	18.3086i	−0.189545	+	0.583361i
$986$	−12.5157	+	13.9001i	−0.398581	+	0.442669i
$987$	−16.8620			−0.536725
$988$	−0.724618	+	0.804769i	−0.0230532	+	0.0256031i
$989$	−6.00774	+	10.4057i	−0.191035	+	0.330882i
$990$	1.22539	+	2.12243i	0.0389454	+	0.0674554i
$991$	2.29035	+	0.486828i	0.0727552	+	0.0154646i	0.244145	−	0.969739i	$-0.421493\pi$
$991$	2.29035	+	0.486828i	0.0727552	+	0.0154646i	−0.171390	+	0.985203i	$0.554826\pi$
$992$	−4.19969	+	1.86982i	−0.133340	+	0.0593669i
$993$	−6.23695	+	1.32571i	−0.197924	+	0.0420700i
$994$	15.5081	+	3.29636i	0.491889	+	0.104554i
$995$	−46.4102	−	20.6631i	−1.47130	−	0.655065i
$996$	−12.6151	−	9.16538i	−0.399723	−	0.290416i
$997$	11.9642	−	20.7226i	0.378910	−	0.656291i	−0.611994	−	0.790862i	$-0.709632\pi$
$997$	11.9642	−	20.7226i	0.378910	−	0.656291i	0.990904	+	0.134571i	$0.0429657\pi$
$998$	0.445660	+	4.24017i	0.0141071	+	0.134220i
$999$	11.4318	−	35.1836i	0.361688	−	1.11316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.i.a.15.1	✓	16
4.3	odd	2		976.2.bw.a.625.2		16
61.22	even	15		7442.2.a.p.1.7		8
61.39	even	30		7442.2.a.r.1.7		8
61.57	even	15	inner	122.2.i.a.57.1	yes	16
244.179	odd	30		976.2.bw.a.545.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.i.a.15.1	✓	16	1.1	even	1	trivial
122.2.i.a.57.1	yes	16	61.57	even	15	inner
976.2.bw.a.545.2		16	244.179	odd	30
976.2.bw.a.625.2		16	4.3	odd	2
7442.2.a.p.1.7		8	61.22	even	15
7442.2.a.r.1.7		8	61.39	even	30

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 + 0.994522i) q^{2} +(-1.03171 + 0.749578i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.51812 + 1.68604i) q^{5} +(-0.853314 - 0.947701i) q^{6} +(-1.54161 + 0.686370i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.424502 + 1.30648i) q^{9} +O(q^{10})\)	\(q+(0.104528 + 0.994522i) q^{2} +(-1.03171 + 0.749578i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.51812 + 1.68604i) q^{5} +(-0.853314 - 0.947701i) q^{6} +(-1.54161 + 0.686370i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.424502 + 1.30648i) q^{9} +(-1.51812 + 1.68604i) q^{10} -0.786343 q^{11} +(0.853314 - 0.947701i) q^{12} +(0.135071 - 0.233950i) q^{13} +(-0.843753 - 1.46142i) q^{14} +(-2.83007 - 0.601549i) q^{15} +(0.913545 - 0.406737i) q^{16} +(6.23559 - 1.32542i) q^{17} +(-1.34370 - 0.285612i) q^{18} +(3.66215 + 1.63049i) q^{19} +(-1.83549 - 1.33356i) q^{20} +(1.07600 - 1.86369i) q^{21} +(-0.0821952 - 0.782035i) q^{22} +(1.89716 - 5.83885i) q^{23} +(1.03171 + 0.749578i) q^{24} +(-0.0154081 + 0.146598i) q^{25} +(0.246787 + 0.109877i) q^{26} +(-1.72358 - 5.30463i) q^{27} +(1.36522 - 0.991891i) q^{28} +(1.46703 + 2.54098i) q^{29} +(0.302431 - 2.87744i) q^{30} +(-0.480531 + 4.57195i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.811274 - 0.589425i) q^{33} +(1.96995 + 6.06289i) q^{34} +(-3.49760 - 1.55723i) q^{35} +(0.143593 - 1.36619i) q^{36} +(5.36591 + 3.89856i) q^{37} +(-1.23876 + 3.81252i) q^{38} +(0.0360101 + 0.342613i) q^{39} +(1.13439 - 1.96483i) q^{40} +(-5.19837 - 3.77684i) q^{41} +(1.96595 + 0.875299i) q^{42} +(-1.91436 - 0.406910i) q^{43} +(0.769160 - 0.163490i) q^{44} +(-2.84722 + 1.26767i) q^{45} +(6.00517 + 1.27644i) q^{46} +(-3.91775 - 6.78574i) q^{47} +(-0.637629 + 1.10441i) q^{48} +(-2.77845 + 3.08578i) q^{49} -0.147406 q^{50} +(-5.43979 + 6.04150i) q^{51} +(-0.0834784 + 0.256920i) q^{52} +(-2.25363 - 6.93597i) q^{53} +(5.09541 - 2.26862i) q^{54} +(-1.19376 - 1.32581i) q^{55} +(1.12916 + 1.25406i) q^{56} +(-5.00044 + 1.06288i) q^{57} +(-2.37371 + 1.72460i) q^{58} +(0.495113 + 4.71068i) q^{59} +2.89329 q^{60} +(2.64429 - 7.34899i) q^{61} -4.59713 q^{62} +(-0.242313 - 2.30546i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.599502 - 0.127428i) q^{65} +(0.670998 + 0.745218i) q^{66} +(7.59287 + 8.43274i) q^{67} +(-5.82376 + 2.59291i) q^{68} +(2.41937 + 7.44604i) q^{69} +(1.18310 - 3.64121i) q^{70} +(-6.28668 + 6.98206i) q^{71} +1.37372 q^{72} +(-7.48237 + 8.31001i) q^{73} +(-3.31631 + 5.74402i) q^{74} +(-0.0939903 - 0.162796i) q^{75} +(-3.92112 - 0.833461i) q^{76} +(1.21224 - 0.539723i) q^{77} +(-0.336972 + 0.0716257i) q^{78} +(-0.836660 - 0.177838i) q^{79} +(2.07264 + 0.922800i) q^{80} +(2.42038 + 1.75851i) q^{81} +(3.21277 - 5.56468i) q^{82} +(-1.27811 - 12.1604i) q^{83} +(-0.665006 + 2.04668i) q^{84} +(11.7011 + 8.50132i) q^{85} +(0.204576 - 1.94641i) q^{86} +(-3.41821 - 1.52188i) q^{87} +(0.242993 + 0.747857i) q^{88} +(10.6325 - 7.72495i) q^{89} +(-1.55834 - 2.69912i) q^{90} +(-0.0476510 + 0.453369i) q^{91} +(-0.641735 + 6.10570i) q^{92} +(-2.93126 - 5.07710i) q^{93} +(6.33905 - 4.60559i) q^{94} +(2.81049 + 8.64981i) q^{95} +(-1.16501 - 0.518694i) q^{96} +(0.974518 - 9.27192i) q^{97} +(-3.35930 - 2.44068i) q^{98} +(0.333804 - 1.02734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{11} + q^{12} - 9 q^{13} - 10 q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 24 q^{18} + 10 q^{19} - 7 q^{20} - 6 q^{21} - 11 q^{22} - 11 q^{23} - 3 q^{24} - 28 q^{25} + 4 q^{26} - 33 q^{27} + 5 q^{28} + 15 q^{29} - 12 q^{30} - 12 q^{31} + 8 q^{32} + 15 q^{33} - 11 q^{34} + 19 q^{35} + q^{36} + 16 q^{37} - 10 q^{38} + 24 q^{39} + 4 q^{40} - 20 q^{41} - 19 q^{42} - 21 q^{43} - 4 q^{44} + 17 q^{45} + 2 q^{46} - 11 q^{47} + q^{48} - 10 q^{49} + 4 q^{50} - 56 q^{51} - 2 q^{52} - 8 q^{53} + 41 q^{54} + 35 q^{55} + 10 q^{56} + 49 q^{57} - 10 q^{58} + 35 q^{59} + 6 q^{60} + 15 q^{61} + 16 q^{62} - 26 q^{63} - 4 q^{64} + 24 q^{65} + 10 q^{66} + 22 q^{67} + 12 q^{68} + 46 q^{69} + 28 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 7 q^{74} - 15 q^{75} - 20 q^{76} + 2 q^{77} + 11 q^{78} + 10 q^{79} - 4 q^{80} - 27 q^{81} + 15 q^{82} - 45 q^{83} + 17 q^{84} + 2 q^{85} + 11 q^{86} - 9 q^{87} - 8 q^{88} - 26 q^{89} + 8 q^{90} - 84 q^{91} - 47 q^{92} - 33 q^{93} - 2 q^{94} + 37 q^{95} + 9 q^{96} - 41 q^{97} - 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9 - 6 * q^10 - 2 * q^11 + q^12 - 9 * q^13 - 10 * q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 24 * q^18 + 10 * q^19 - 7 * q^20 - 6 * q^21 - 11 * q^22 - 11 * q^23 - 3 * q^24 - 28 * q^25 + 4 * q^26 - 33 * q^27 + 5 * q^28 + 15 * q^29 - 12 * q^30 - 12 * q^31 + 8 * q^32 + 15 * q^33 - 11 * q^34 + 19 * q^35 + q^36 + 16 * q^37 - 10 * q^38 + 24 * q^39 + 4 * q^40 - 20 * q^41 - 19 * q^42 - 21 * q^43 - 4 * q^44 + 17 * q^45 + 2 * q^46 - 11 * q^47 + q^48 - 10 * q^49 + 4 * q^50 - 56 * q^51 - 2 * q^52 - 8 * q^53 + 41 * q^54 + 35 * q^55 + 10 * q^56 + 49 * q^57 - 10 * q^58 + 35 * q^59 + 6 * q^60 + 15 * q^61 + 16 * q^62 - 26 * q^63 - 4 * q^64 + 24 * q^65 + 10 * q^66 + 22 * q^67 + 12 * q^68 + 46 * q^69 + 28 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 7 * q^74 - 15 * q^75 - 20 * q^76 + 2 * q^77 + 11 * q^78 + 10 * q^79 - 4 * q^80 - 27 * q^81 + 15 * q^82 - 45 * q^83 + 17 * q^84 + 2 * q^85 + 11 * q^86 - 9 * q^87 - 8 * q^88 - 26 * q^89 + 8 * q^90 - 84 * q^91 - 47 * q^92 - 33 * q^93 - 2 * q^94 + 37 * q^95 + 9 * q^96 - 41 * q^97 - 5 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

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