LMFDB - Embedded newform 770.2.l.c.573.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(573,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2, 0]))

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

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

chi := DirichletCharacter("770.573");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.l (of order $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			573.1
Character	$\chi$	$=$	770.573
Dual form			770.2.l.c.727.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-2.03841 + 2.03841i) q^{3} -1.00000i q^{4} +(-2.07139 + 0.842227i) q^{5} -2.88275i q^{6} +(-2.55056 - 0.703324i) q^{7} +(0.707107 + 0.707107i) q^{8} -5.31025i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.03841 + 2.03841i) q^{3} -1.00000i q^{4} +(-2.07139 + 0.842227i) q^{5} -2.88275i q^{6} +(-2.55056 - 0.703324i) q^{7} +(0.707107 + 0.707107i) q^{8} -5.31025i q^{9} +(0.869149 - 2.06024i) q^{10} -1.00000 q^{11} +(2.03841 + 2.03841i) q^{12} +(-3.99211 + 3.99211i) q^{13} +(2.30084 - 1.30619i) q^{14} +(2.50554 - 5.93915i) q^{15} -1.00000 q^{16} +(-3.39509 - 3.39509i) q^{17} +(3.75491 + 3.75491i) q^{18} +4.95398 q^{19} +(0.842227 + 2.07139i) q^{20} +(6.63275 - 3.76542i) q^{21} +(0.707107 - 0.707107i) q^{22} +(-2.50907 - 2.50907i) q^{23} -2.88275 q^{24} +(3.58131 - 3.48916i) q^{25} -5.64570i q^{26} +(4.70924 + 4.70924i) q^{27} +(-0.703324 + 2.55056i) q^{28} +7.25017i q^{29} +(2.42793 + 5.97130i) q^{30} -3.87087i q^{31} +(0.707107 - 0.707107i) q^{32} +(2.03841 - 2.03841i) q^{33} +4.80139 q^{34} +(5.87555 - 0.691287i) q^{35} -5.31025 q^{36} +(-2.92514 + 2.92514i) q^{37} +(-3.50299 + 3.50299i) q^{38} -16.2751i q^{39} +(-2.06024 - 0.869149i) q^{40} +4.22571i q^{41} +(-2.02751 + 7.35261i) q^{42} +(1.04912 + 1.04912i) q^{43} +1.00000i q^{44} +(4.47243 + 10.9996i) q^{45} +3.54836 q^{46} +(6.21956 + 6.21956i) q^{47} +(2.03841 - 2.03841i) q^{48} +(6.01067 + 3.58774i) q^{49} +(-0.0651599 + 4.99958i) q^{50} +13.8412 q^{51} +(3.99211 + 3.99211i) q^{52} +(-0.793267 - 0.793267i) q^{53} -6.65986 q^{54} +(2.07139 - 0.842227i) q^{55} +(-1.30619 - 2.30084i) q^{56} +(-10.0982 + 10.0982i) q^{57} +(-5.12665 - 5.12665i) q^{58} -8.39914 q^{59} +(-5.93915 - 2.50554i) q^{60} +12.9348i q^{61} +(2.73712 + 2.73712i) q^{62} +(-3.73483 + 13.5441i) q^{63} +1.00000i q^{64} +(4.90696 - 11.6315i) q^{65} +2.88275i q^{66} +(3.04387 - 3.04387i) q^{67} +(-3.39509 + 3.39509i) q^{68} +10.2290 q^{69} +(-3.66583 + 4.64346i) q^{70} -9.47305 q^{71} +(3.75491 - 3.75491i) q^{72} +(8.93324 - 8.93324i) q^{73} -4.13677i q^{74} +(-0.187840 + 14.4125i) q^{75} -4.95398i q^{76} +(2.55056 + 0.703324i) q^{77} +(11.5083 + 11.5083i) q^{78} -4.65746i q^{79} +(2.07139 - 0.842227i) q^{80} -3.26798 q^{81} +(-2.98803 - 2.98803i) q^{82} +(10.6779 - 10.6779i) q^{83} +(-3.76542 - 6.63275i) q^{84} +(9.89200 + 4.17312i) q^{85} -1.48368 q^{86} +(-14.7788 - 14.7788i) q^{87} +(-0.707107 - 0.707107i) q^{88} -16.0121 q^{89} +(-10.9404 - 4.61540i) q^{90} +(12.9899 - 7.37436i) q^{91} +(-2.50907 + 2.50907i) q^{92} +(7.89044 + 7.89044i) q^{93} -8.79578 q^{94} +(-10.2616 + 4.17237i) q^{95} +2.88275i q^{96} +(5.64356 + 5.64356i) q^{97} +(-6.78710 + 1.71327i) q^{98} +5.31025i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) $ 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−2.03841	+	2.03841i	−1.17688	+	1.17688i	−0.196342	+	0.980535i	$0.562906\pi$
$3$	−2.03841	+	2.03841i	−1.17688	+	1.17688i	−0.980535	+	0.196342i	$0.937094\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−2.07139	+	0.842227i	−0.926354	+	0.376655i
$5$	−2.07139	+	0.842227i	−0.926354	+	0.376655i
$6$		−	2.88275i		−	1.17688i
$7$	−2.55056	−	0.703324i	−0.964019	−	0.265832i
$7$	−2.55056	−	0.703324i	−0.964019	−	0.265832i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	5.31025i		−	1.77008i
$10$	0.869149	−	2.06024i	0.274849	−	0.651504i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	2.03841	+	2.03841i	0.588439	+	0.588439i
$13$	−3.99211	+	3.99211i	−1.10721	+	1.10721i	−0.113697	+	0.993515i	$0.536269\pi$
$13$	−3.99211	+	3.99211i	−1.10721	+	1.10721i	−0.993515	+	0.113697i	$0.963731\pi$
$14$	2.30084	−	1.30619i	0.614926	−	0.349094i
$15$	2.50554	−	5.93915i	0.646928	−	1.53348i
$16$	−1.00000			−0.250000
$17$	−3.39509	−	3.39509i	−0.823431	−	0.823431i	0.163167	−	0.986598i	$-0.447829\pi$
$17$	−3.39509	−	3.39509i	−0.823431	−	0.823431i	−0.986598	+	0.163167i	$0.947829\pi$
$18$	3.75491	+	3.75491i	0.885041	+	0.885041i
$19$	4.95398			1.13652			0.568260	−	0.822849i	$-0.307617\pi$
$19$	4.95398			1.13652			0.568260	+	0.822849i	$0.307617\pi$
$20$	0.842227	+	2.07139i	0.188328	+	0.463177i
$21$	6.63275	−	3.76542i	1.44738	−	0.821682i
$22$	0.707107	−	0.707107i	0.150756	−	0.150756i
$23$	−2.50907	−	2.50907i	−0.523177	−	0.523177i	0.395353	−	0.918529i	$-0.370622\pi$
$23$	−2.50907	−	2.50907i	−0.523177	−	0.523177i	−0.918529	+	0.395353i	$0.870622\pi$
$24$	−2.88275			−0.588439
$25$	3.58131	−	3.48916i	0.716262	−	0.697832i
$26$		−	5.64570i		−	1.10721i
$27$	4.70924	+	4.70924i	0.906293	+	0.906293i
$28$	−0.703324	+	2.55056i	−0.132916	+	0.482010i
$29$			7.25017i			1.34632i	0.739495	+	0.673162i	$0.235064\pi$
$29$			7.25017i			1.34632i	−0.739495	+	0.673162i	$0.764936\pi$
$30$	2.42793	+	5.97130i	0.443277	+	1.09020i
$31$		−	3.87087i		−	0.695229i	−0.937637	−	0.347615i	$-0.886992\pi$
$31$		−	3.87087i		−	0.695229i	0.937637	−	0.347615i	$-0.113008\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.03841	−	2.03841i	0.354842	−	0.354842i
$34$	4.80139			0.823431
$35$	5.87555	−	0.691287i	0.993150	−	0.116849i
$36$	−5.31025			−0.885041
$37$	−2.92514	+	2.92514i	−0.480889	+	0.480889i	−0.905416	−	0.424526i	$-0.860441\pi$
$37$	−2.92514	+	2.92514i	−0.480889	+	0.480889i	0.424526	+	0.905416i	$0.360441\pi$
$38$	−3.50299	+	3.50299i	−0.568260	+	0.568260i
$39$		−	16.2751i		−	2.60611i
$40$	−2.06024	−	0.869149i	−0.325752	−	0.137425i
$41$			4.22571i			0.659945i	0.943990	+	0.329973i	$0.107040\pi$
$41$			4.22571i			0.659945i	−0.943990	+	0.329973i	$0.892960\pi$
$42$	−2.02751	+	7.35261i	−0.312851	+	1.13453i
$43$	1.04912	+	1.04912i	0.159989	+	0.159989i	0.782562	−	0.622573i	$-0.213912\pi$
$43$	1.04912	+	1.04912i	0.159989	+	0.159989i	−0.622573	+	0.782562i	$0.713912\pi$
$44$			1.00000i			0.150756i
$45$	4.47243	+	10.9996i	0.666711	+	1.63972i
$46$	3.54836			0.523177
$47$	6.21956	+	6.21956i	0.907216	+	0.907216i	0.996047	−	0.0888309i	$-0.0283131\pi$
$47$	6.21956	+	6.21956i	0.907216	+	0.907216i	−0.0888309	+	0.996047i	$0.528313\pi$
$48$	2.03841	−	2.03841i	0.294219	−	0.294219i
$49$	6.01067	+	3.58774i	0.858667	+	0.512534i
$50$	−0.0651599	+	4.99958i	−0.00921500	+	0.707047i
$51$	13.8412			1.93816
$52$	3.99211	+	3.99211i	0.553606	+	0.553606i
$53$	−0.793267	−	0.793267i	−0.108964	−	0.108964i	0.650523	−	0.759487i	$-0.274550\pi$
$53$	−0.793267	−	0.793267i	−0.108964	−	0.108964i	−0.759487	+	0.650523i	$0.774550\pi$
$54$	−6.65986			−0.906293
$55$	2.07139	−	0.842227i	0.279306	−	0.113566i
$56$	−1.30619	−	2.30084i	−0.174547	−	0.307463i
$57$	−10.0982	+	10.0982i	−1.33755	+	1.33755i
$58$	−5.12665	−	5.12665i	−0.673162	−	0.673162i
$59$	−8.39914			−1.09348			−0.546738	−	0.837304i	$-0.684130\pi$
$59$	−8.39914			−1.09348			−0.546738	+	0.837304i	$0.684130\pi$
$60$	−5.93915	−	2.50554i	−0.766741	−	0.323464i
$61$			12.9348i			1.65613i	0.560634	+	0.828063i	$0.310557\pi$
$61$			12.9348i			1.65613i	−0.560634	+	0.828063i	$0.689443\pi$
$62$	2.73712	+	2.73712i	0.347615	+	0.347615i
$63$	−3.73483	+	13.5441i	−0.470544	+	1.70639i
$64$			1.00000i			0.125000i
$65$	4.90696	−	11.6315i	0.608633	−	1.44271i
$66$			2.88275i			0.354842i
$67$	3.04387	−	3.04387i	0.371868	−	0.371868i	−0.496289	−	0.868157i	$-0.665304\pi$
$67$	3.04387	−	3.04387i	0.371868	−	0.371868i	0.868157	+	0.496289i	$0.165304\pi$
$68$	−3.39509	+	3.39509i	−0.411716	+	0.411716i
$69$	10.2290			1.23143
$70$	−3.66583	+	4.64346i	−0.438150	+	0.554999i
$71$	−9.47305			−1.12424			−0.562122	−	0.827054i	$-0.690015\pi$
$71$	−9.47305			−1.12424			−0.562122	+	0.827054i	$0.690015\pi$
$72$	3.75491	−	3.75491i	0.442521	−	0.442521i
$73$	8.93324	−	8.93324i	1.04556	−	1.04556i	0.0466449	−	0.998912i	$-0.485147\pi$
$73$	8.93324	−	8.93324i	1.04556	−	1.04556i	0.998912	−	0.0466449i	$-0.0148529\pi$
$74$		−	4.13677i		−	0.480889i
$75$	−0.187840	+	14.4125i	−0.0216899	+	1.66422i
$76$		−	4.95398i		−	0.568260i
$77$	2.55056	+	0.703324i	0.290663	+	0.0801512i
$78$	11.5083	+	11.5083i	1.30305	+	1.30305i
$79$		−	4.65746i		−	0.524005i	−0.965067	−	0.262002i	$-0.915617\pi$
$79$		−	4.65746i		−	0.524005i	0.965067	−	0.262002i	$-0.0843829\pi$
$80$	2.07139	−	0.842227i	0.231588	−	0.0941638i
$81$	−3.26798			−0.363109
$82$	−2.98803	−	2.98803i	−0.329973	−	0.329973i
$83$	10.6779	−	10.6779i	1.17205	−	1.17205i	0.190326	−	0.981721i	$-0.439046\pi$
$83$	10.6779	−	10.6779i	1.17205	−	1.17205i	0.981721	−	0.190326i	$-0.0609544\pi$
$84$	−3.76542	−	6.63275i	−0.410841	−	0.723692i
$85$	9.89200	+	4.17312i	1.07294	+	0.452639i
$86$	−1.48368			−0.159989
$87$	−14.7788	−	14.7788i	−1.58446	−	1.58446i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	−16.0121			−1.69727			−0.848637	−	0.528975i	$-0.822576\pi$
$89$	−16.0121			−1.69727			−0.848637	+	0.528975i	$0.822576\pi$
$90$	−10.9404	−	4.61540i	−1.15322	−	0.486506i
$91$	12.9899	−	7.37436i	1.36171	−	0.773043i
$92$	−2.50907	+	2.50907i	−0.261588	+	0.261588i
$93$	7.89044	+	7.89044i	0.818200	+	0.818200i
$94$	−8.79578			−0.907216
$95$	−10.2616	+	4.17237i	−1.05282	+	0.428076i
$96$			2.88275i			0.294219i
$97$	5.64356	+	5.64356i	0.573017	+	0.573017i	0.932970	−	0.359954i	$-0.117208\pi$
$97$	5.64356	+	5.64356i	0.573017	+	0.573017i	−0.359954	+	0.932970i	$0.617208\pi$
$98$	−6.78710	+	1.71327i	−0.685600	+	0.173067i
$99$			5.31025i			0.533700i
$100$	−3.48916	−	3.58131i	−0.348916	−	0.358131i
$101$		−	11.6120i		−	1.15544i	−0.816236	−	0.577718i	$-0.803943\pi$
$101$		−	11.6120i		−	1.15544i	0.816236	−	0.577718i	$-0.196057\pi$
$102$	−9.78720	+	9.78720i	−0.969078	+	0.969078i
$103$	9.90062	−	9.90062i	0.975537	−	0.975537i	−0.0241711	−	0.999708i	$-0.507695\pi$
$103$	9.90062	−	9.90062i	0.975537	−	0.975537i	0.999708	+	0.0241711i	$0.00769465\pi$
$104$	−5.64570			−0.553606
$105$	−10.5677	+	13.3859i	−1.03130	+	1.30633i
$106$	1.12185			0.108964
$107$	−2.83307	+	2.83307i	−0.273884	+	0.273884i	−0.830661	−	0.556778i	$-0.812037\pi$
$107$	−2.83307	+	2.83307i	−0.273884	+	0.273884i	0.556778	+	0.830661i	$0.312037\pi$
$108$	4.70924	−	4.70924i	0.453146	−	0.453146i
$109$		−	9.33658i		−	0.894282i	−0.894463	−	0.447141i	$-0.852442\pi$
$109$		−	9.33658i		−	0.894282i	0.894463	−	0.447141i	$-0.147558\pi$
$110$	−0.869149	+	2.06024i	−0.0828701	+	0.196436i
$111$		−	11.9253i		−	1.13190i
$112$	2.55056	+	0.703324i	0.241005	+	0.0664579i
$113$	9.75494	+	9.75494i	0.917667	+	0.917667i	0.996859	−	0.0791920i	$-0.0252340\pi$
$113$	9.75494	+	9.75494i	0.917667	+	0.917667i	−0.0791920	+	0.996859i	$0.525234\pi$
$114$		−	14.2811i		−	1.33755i
$115$	7.31046	+	3.08405i	0.681704	+	0.287589i
$116$	7.25017			0.673162
$117$	21.1991	+	21.1991i	1.95986	+	1.95986i
$118$	5.93909	−	5.93909i	0.546738	−	0.546738i
$119$	6.27152	+	11.0472i	0.574910	+	1.01270i
$120$	5.97130	−	2.42793i	0.545102	−	0.221639i
$121$	1.00000			0.0909091
$122$	−9.14626	−	9.14626i	−0.828063	−	0.828063i
$123$	−8.61374	−	8.61374i	−0.776675	−	0.776675i
$124$	−3.87087			−0.347615
$125$	−4.47962	+	10.2437i	−0.400670	+	0.916223i
$126$	−6.93619	−	12.2180i	−0.617925	−	1.08847i
$127$	11.3283	−	11.3283i	1.00523	−	1.00523i	0.00524084	−	0.999986i	$-0.498332\pi$
$127$	11.3283	−	11.3283i	1.00523	−	1.00523i	0.999986	−	0.00524084i	$-0.00166822\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−4.27708			−0.376576
$130$	4.75496	+	11.6944i	0.417037	+	1.02567i
$131$		−	20.7934i		−	1.81673i	−0.418178	−	0.908365i	$-0.637331\pi$
$131$		−	20.7934i		−	1.81673i	0.418178	−	0.908365i	$-0.362669\pi$
$132$	−2.03841	−	2.03841i	−0.177421	−	0.177421i
$133$	−12.6354	−	3.48425i	−1.09563	−	0.302123i
$134$			4.30469i			0.371868i
$135$	−13.7209	−	5.78842i	−1.18091	−	0.498188i
$136$		−	4.80139i		−	0.411716i
$137$	−1.11354	+	1.11354i	−0.0951365	+	0.0951365i	−0.753073	−	0.657937i	$-0.771429\pi$
$137$	−1.11354	+	1.11354i	−0.0951365	+	0.0951365i	0.657937	+	0.753073i	$0.271429\pi$
$138$	−7.23301	+	7.23301i	−0.615715	+	0.615715i
$139$	3.80609			0.322828			0.161414	−	0.986887i	$-0.448395\pi$
$139$	3.80609			0.322828			0.161414	+	0.986887i	$0.448395\pi$
$140$	−0.691287	−	5.87555i	−0.0584244	−	0.496575i
$141$	−25.3560			−2.13536
$142$	6.69846	−	6.69846i	0.562122	−	0.562122i
$143$	3.99211	−	3.99211i	0.333837	−	0.333837i
$144$			5.31025i			0.442521i
$145$	−6.10629	−	15.0179i	−0.507100	−	1.24717i
$146$			12.6335i			1.04556i
$147$	−19.5655	+	4.93894i	−1.61374	+	0.407357i
$148$	2.92514	+	2.92514i	0.240445	+	0.240445i
$149$			3.56176i			0.291791i	0.989300	+	0.145895i	$0.0466063\pi$
$149$			3.56176i			0.291791i	−0.989300	+	0.145895i	$0.953394\pi$
$150$	−10.0584	−	10.3240i	−0.821263	−	0.842952i
$151$	8.31210			0.676429			0.338215	−	0.941069i	$-0.390177\pi$
$151$	8.31210			0.676429			0.338215	+	0.941069i	$0.390177\pi$
$152$	3.50299	+	3.50299i	0.284130	+	0.284130i
$153$	−18.0288	+	18.0288i	−1.45754	+	1.45754i
$154$	−2.30084	+	1.30619i	−0.185407	+	0.105256i
$155$	3.26015	+	8.01809i	0.261862	+	0.644028i
$156$	−16.2751			−1.30305
$157$	−2.81649	−	2.81649i	−0.224781	−	0.224781i	0.585727	−	0.810508i	$-0.300809\pi$
$157$	−2.81649	−	2.81649i	−0.224781	−	0.224781i	−0.810508	+	0.585727i	$0.800809\pi$
$158$	3.29332	+	3.29332i	0.262002	+	0.262002i
$159$	3.23401			0.256474
$160$	−0.869149	+	2.06024i	−0.0687123	+	0.162876i
$161$	4.63483	+	8.16420i	0.365276	+	0.643429i
$162$	2.31081	−	2.31081i	0.181555	−	0.181555i
$163$	−15.1063	−	15.1063i	−1.18322	−	1.18322i	−0.978905	−	0.204314i	$-0.934504\pi$
$163$	−15.1063	−	15.1063i	−1.18322	−	1.18322i	−0.204314	−	0.978905i	$-0.565496\pi$
$164$	4.22571			0.329973
$165$	−2.50554	+	5.93915i	−0.195056	+	0.462362i
$166$			15.1008i			1.17205i
$167$	−2.40075	−	2.40075i	−0.185776	−	0.185776i	0.608091	−	0.793867i	$-0.291935\pi$
$167$	−2.40075	−	2.40075i	−0.185776	−	0.185776i	−0.793867	+	0.608091i	$0.791935\pi$
$168$	7.35261	+	2.02751i	0.567267	+	0.156426i
$169$		−	18.8739i		−	1.45184i
$170$	−9.94554	+	4.04386i	−0.762788	+	0.310150i
$171$		−	26.3068i		−	2.01173i
$172$	1.04912	−	1.04912i	0.0799947	−	0.0799947i
$173$	4.15568	−	4.15568i	0.315950	−	0.315950i	−0.531259	−	0.847209i	$-0.678281\pi$
$173$	4.15568	−	4.15568i	0.315950	−	0.315950i	0.847209	+	0.531259i	$0.178281\pi$
$174$	20.9004			1.58446
$175$	−11.5883	+	6.38047i	−0.875996	+	0.482318i
$176$	1.00000			0.0753778
$177$	17.1209	−	17.1209i	1.28689	−	1.28689i
$178$	11.3222	−	11.3222i	0.848637	−	0.848637i
$179$			6.60014i			0.493318i	0.969102	+	0.246659i	$0.0793327\pi$
$179$			6.60014i			0.493318i	−0.969102	+	0.246659i	$0.920667\pi$
$180$	10.9996	−	4.47243i	0.819861	−	0.333355i
$181$		−	14.4577i		−	1.07463i	−0.843381	−	0.537315i	$-0.819438\pi$
$181$		−	14.4577i		−	1.07463i	0.843381	−	0.537315i	$-0.180562\pi$
$182$	−3.97076	+	14.3997i	−0.294332	+	1.06737i
$183$	−26.3664	−	26.3664i	−1.94906	−	1.94906i
$184$		−	3.54836i		−	0.261588i
$185$	3.59547	−	8.52272i	0.264344	−	0.626603i
$186$	−11.1588			−0.818200
$187$	3.39509	+	3.39509i	0.248274	+	0.248274i
$188$	6.21956	−	6.21956i	0.453608	−	0.453608i
$189$	−8.69905	−	15.3233i	−0.632763	−	1.11461i
$190$	4.30575	−	10.2064i	0.312372	−	0.740448i
$191$	−10.1657			−0.735567			−0.367783	−	0.929912i	$-0.619883\pi$
$191$	−10.1657			−0.735567			−0.367783	+	0.929912i	$0.619883\pi$
$192$	−2.03841	−	2.03841i	−0.147110	−	0.147110i
$193$	−7.16762	−	7.16762i	−0.515937	−	0.515937i	0.400403	−	0.916339i	$-0.368870\pi$
$193$	−7.16762	−	7.16762i	−0.515937	−	0.515937i	−0.916339	+	0.400403i	$0.868870\pi$
$194$	−7.98120			−0.573017
$195$	13.7074	+	33.7122i	0.981604	+	2.41418i
$196$	3.58774	−	6.01067i	0.256267	−	0.429334i
$197$	−12.8091	+	12.8091i	−0.912608	+	0.912608i	−0.996477	−	0.0838687i	$-0.973272\pi$
$197$	−12.8091	+	12.8091i	−0.912608	+	0.912608i	0.0838687	+	0.996477i	$0.473272\pi$
$198$	−3.75491	−	3.75491i	−0.266850	−	0.266850i
$199$	−10.6361			−0.753972			−0.376986	−	0.926219i	$-0.623039\pi$
$199$	−10.6361			−0.753972			−0.376986	+	0.926219i	$0.623039\pi$
$200$	4.99958	+	0.0651599i	0.353523	+	0.00460750i
$201$			12.4093i			0.875287i
$202$	8.21092	+	8.21092i	0.577718	+	0.577718i
$203$	5.09922	−	18.4920i	0.357895	−	1.29788i
$204$		−	13.8412i		−	0.969078i
$205$	−3.55901	−	8.75310i	−0.248572	−	0.611343i
$206$			14.0016i			0.975537i
$207$	−13.3238	+	13.3238i	−0.926066	+	0.926066i
$208$	3.99211	−	3.99211i	0.276803	−	0.276803i
$209$	−4.95398			−0.342674
$210$	−1.99281	−	16.9377i	−0.137517	−	1.16882i
$211$	17.8348			1.22780			0.613899	−	0.789385i	$-0.289600\pi$
$211$	17.8348			1.22780			0.613899	+	0.789385i	$0.289600\pi$
$212$	−0.793267	+	0.793267i	−0.0544818	+	0.0544818i
$213$	19.3100	−	19.3100i	1.32310	−	1.32310i
$214$		−	4.00657i		−	0.273884i
$215$	−3.05674	−	1.28954i	−0.208468	−	0.0879460i
$216$			6.65986i			0.453146i
$217$	−2.72248	+	9.87288i	−0.184814	+	0.670215i
$218$	6.60196	+	6.60196i	0.447141	+	0.447141i
$219$			36.4192i			2.46098i
$220$	−0.842227	−	2.07139i	−0.0567829	−	0.139653i
$221$	27.1072			1.82343
$222$	8.43243	+	8.43243i	0.565948	+	0.565948i
$223$	1.13707	−	1.13707i	0.0761441	−	0.0761441i	−0.668009	−	0.744153i	$-0.732853\pi$
$223$	1.13707	−	1.13707i	0.0761441	−	0.0761441i	0.744153	+	0.668009i	$0.232853\pi$
$224$	−2.30084	+	1.30619i	−0.153731	+	0.0872735i
$225$	−18.5283	−	19.0176i	−1.23522	−	1.26784i
$226$	−13.7956			−0.917667
$227$	0.774054	+	0.774054i	0.0513758	+	0.0513758i	0.732328	−	0.680952i	$-0.238434\pi$
$227$	0.774054	+	0.774054i	0.0513758	+	0.0513758i	−0.680952	+	0.732328i	$0.738434\pi$
$228$	10.0982	+	10.0982i	0.668773	+	0.668773i
$229$	3.16280			0.209004			0.104502	−	0.994525i	$-0.466675\pi$
$229$	3.16280			0.209004			0.104502	+	0.994525i	$0.466675\pi$
$230$	−7.35003	+	2.98852i	−0.484647	+	0.197057i
$231$	−6.63275	+	3.76542i	−0.436403	+	0.247746i
$232$	−5.12665	+	5.12665i	−0.336581	+	0.336581i
$233$	1.78200	+	1.78200i	0.116743	+	0.116743i	0.763065	−	0.646322i	$-0.223694\pi$
$233$	1.78200	+	1.78200i	0.116743	+	0.116743i	−0.646322	+	0.763065i	$0.723694\pi$
$234$	−29.9801			−1.95986
$235$	−18.1214	−	7.64485i	−1.18211	−	0.498695i
$236$			8.39914i			0.546738i
$237$	9.49382	+	9.49382i	0.616690	+	0.616690i
$238$	−12.2462	−	3.37693i	−0.793804	−	0.218894i
$239$			10.5851i			0.684692i	0.939574	+	0.342346i	$0.111221\pi$
$239$			10.5851i			0.684692i	−0.939574	+	0.342346i	$0.888779\pi$
$240$	−2.50554	+	5.93915i	−0.161732	+	0.383370i
$241$			16.7551i			1.07929i	0.841892	+	0.539646i	$0.181442\pi$
$241$			16.7551i			1.07929i	−0.841892	+	0.539646i	$0.818558\pi$
$242$	−0.707107	+	0.707107i	−0.0454545	+	0.0454545i
$243$	−7.46621	+	7.46621i	−0.478958	+	0.478958i
$244$	12.9348			0.828063
$245$	−15.4721	−	2.36925i	−0.988478	−	0.151366i
$246$	12.1817			0.776675
$247$	−19.7768	+	19.7768i	−1.25837	+	1.25837i
$248$	2.73712	−	2.73712i	0.173807	−	0.173807i
$249$			43.5317i			2.75871i
$250$	−4.07580	−	10.4109i	−0.257776	−	0.658446i
$251$		−	12.0951i		−	0.763438i	−0.924278	−	0.381719i	$-0.875332\pi$
$251$		−	12.0951i		−	0.763438i	0.924278	−	0.381719i	$-0.124668\pi$
$252$	13.5441	+	3.73483i	0.853197	+	0.235272i
$253$	2.50907	+	2.50907i	0.157744	+	0.157744i
$254$			16.0207i			1.00523i
$255$	−28.6705	+	11.6574i	−1.79542	+	0.730016i
$256$	1.00000			0.0625000
$257$	−5.75224	−	5.75224i	−0.358815	−	0.358815i	0.504561	−	0.863376i	$-0.331654\pi$
$257$	−5.75224	−	5.75224i	−0.358815	−	0.358815i	−0.863376	+	0.504561i	$0.831654\pi$
$258$	3.02435	−	3.02435i	0.188288	−	0.188288i
$259$	9.51804	−	5.40340i	0.591422	−	0.335751i
$260$	−11.6315	−	4.90696i	−0.721354	−	0.304317i
$261$	38.5002			2.38310
$262$	14.7032	+	14.7032i	0.908365	+	0.908365i
$263$	10.6818	+	10.6818i	0.658665	+	0.658665i	0.955064	−	0.296399i	$-0.0957858\pi$
$263$	10.6818	+	10.6818i	0.658665	+	0.658665i	−0.296399	+	0.955064i	$0.595786\pi$
$264$	2.88275			0.177421
$265$	2.31127	+	0.975054i	0.141980	+	0.0598971i
$266$	11.3983	−	6.47083i	0.698875	−	0.396752i
$267$	32.6392	−	32.6392i	1.99748	−	1.99748i
$268$	−3.04387	−	3.04387i	−0.185934	−	0.185934i
$269$	−6.24110			−0.380527			−0.190263	−	0.981733i	$-0.560934\pi$
$269$	−6.24110			−0.380527			−0.190263	+	0.981733i	$0.560934\pi$
$270$	13.7952	−	5.60912i	0.839548	−	0.341360i
$271$		−	19.1386i		−	1.16259i	−0.813693	−	0.581294i	$-0.802547\pi$
$271$		−	19.1386i		−	1.16259i	0.813693	−	0.581294i	$-0.197453\pi$
$272$	3.39509	+	3.39509i	0.205858	+	0.205858i
$273$	−11.4467	+	41.5107i	−0.692786	+	2.51234i
$274$		−	1.57479i		−	0.0951365i
$275$	−3.58131	+	3.48916i	−0.215961	+	0.210404i
$276$		−	10.2290i		−	0.615715i
$277$	−16.1046	+	16.1046i	−0.967629	+	0.967629i	−0.999492	−	0.0318632i	$-0.989856\pi$
$277$	−16.1046	+	16.1046i	−0.967629	+	0.967629i	0.0318632	+	0.999492i	$0.489856\pi$
$278$	−2.69131	+	2.69131i	−0.161414	+	0.161414i
$279$	−20.5553			−1.23061
$280$	4.64346	+	3.66583i	0.277500	+	0.219075i
$281$	1.15556			0.0689351			0.0344676	−	0.999406i	$-0.489026\pi$
$281$	1.15556			0.0689351			0.0344676	+	0.999406i	$0.489026\pi$
$282$	17.9294	−	17.9294i	1.06768	−	1.06768i
$283$	0.394143	−	0.394143i	0.0234294	−	0.0234294i	−0.695295	−	0.718724i	$-0.744726\pi$
$283$	0.394143	−	0.394143i	0.0234294	−	0.0234294i	0.718724	+	0.695295i	$0.244726\pi$
$284$			9.47305i			0.562122i
$285$	12.4124	−	29.4224i	0.735246	−	1.74283i
$286$			5.64570i			0.333837i
$287$	2.97205	−	10.7779i	0.175434	−	0.636200i
$288$	−3.75491	−	3.75491i	−0.221260	−	0.221260i
$289$			6.05332i			0.356077i
$290$	14.9371	+	6.30148i	0.877136	+	0.370036i
$291$	−23.0078			−1.34874
$292$	−8.93324	−	8.93324i	−0.522778	−	0.522778i
$293$	21.2666	−	21.2666i	1.24241	−	1.24241i	0.283413	−	0.958998i	$-0.408533\pi$
$293$	21.2666	−	21.2666i	1.24241	−	1.24241i	0.958998	−	0.283413i	$-0.0914666\pi$
$294$	10.3425	−	17.3273i	0.603189	−	1.01055i
$295$	17.3979	−	7.07398i	1.01294	−	0.411863i
$296$	−4.13677			−0.240445
$297$	−4.70924	−	4.70924i	−0.273258	−	0.273258i
$298$	−2.51854	−	2.51854i	−0.145895	−	0.145895i
$299$	20.0330			1.15854
$300$	14.4125	+	0.187840i	0.832108	+	0.0108449i
$301$	−1.93797	−	3.41371i	−0.111703	−	0.196763i
$302$	−5.87754	+	5.87754i	−0.338215	+	0.338215i
$303$	23.6700	+	23.6700i	1.35981	+	1.35981i
$304$	−4.95398			−0.284130
$305$	−10.8940	−	26.7929i	−0.623789	−	1.53416i
$306$		−	25.4966i		−	1.45754i
$307$	20.7732	+	20.7732i	1.18559	+	1.18559i	0.978274	+	0.207315i	$0.0664724\pi$
$307$	20.7732	+	20.7732i	1.18559	+	1.18559i	0.207315	+	0.978274i	$0.433528\pi$
$308$	0.703324	−	2.55056i	0.0400756	−	0.145331i
$309$			40.3631i			2.29617i
$310$	−7.97492	−	3.36437i	−0.452945	−	0.191083i
$311$			19.8702i			1.12673i	0.826207	+	0.563367i	$0.190494\pi$
$311$			19.8702i			1.12673i	−0.826207	+	0.563367i	$0.809506\pi$
$312$	11.5083	−	11.5083i	0.651527	−	0.651527i
$313$	−8.66468	+	8.66468i	−0.489757	+	0.489757i	−0.908229	−	0.418473i	$-0.862566\pi$
$313$	−8.66468	+	8.66468i	−0.489757	+	0.489757i	0.418473	+	0.908229i	$0.362566\pi$
$314$	3.98313			0.224781
$315$	−3.67091	−	31.2006i	−0.206832	−	1.75796i
$316$	−4.65746			−0.262002
$317$	7.80201	−	7.80201i	0.438205	−	0.438205i	−0.453203	−	0.891407i	$-0.649719\pi$
$317$	7.80201	−	7.80201i	0.438205	−	0.438205i	0.891407	+	0.453203i	$0.149719\pi$
$318$	−2.28679	+	2.28679i	−0.128237	+	0.128237i
$319$		−	7.25017i		−	0.405932i
$320$	−0.842227	−	2.07139i	−0.0470819	−	0.115794i
$321$		−	11.5499i		−	0.644655i
$322$	−9.05028	−	2.49565i	−0.504353	−	0.139077i
$323$	−16.8192	−	16.8192i	−0.935846	−	0.935846i
$324$			3.26798i			0.181555i
$325$	−0.367873	+	28.2261i	−0.0204059	+	1.56570i
$326$	21.3636			1.18322
$327$	19.0318	+	19.0318i	1.05246	+	1.05246i
$328$	−2.98803	+	2.98803i	−0.164986	+	0.164986i
$329$	−11.4890	−	20.2377i	−0.633407	−	1.11574i
$330$	−2.42793	−	5.97130i	−0.133653	−	0.328709i
$331$	3.80505			0.209145			0.104572	−	0.994517i	$-0.466653\pi$
$331$	3.80505			0.209145			0.104572	+	0.994517i	$0.466653\pi$
$332$	−10.6779	−	10.6779i	−0.586023	−	0.586023i
$333$	15.5332	+	15.5332i	0.851214	+	0.851214i
$334$	3.39518			0.185776
$335$	−3.74142	+	8.86868i	−0.204415	+	0.484548i
$336$	−6.63275	+	3.76542i	−0.361846	+	0.205420i
$337$	22.5106	−	22.5106i	1.22623	−	1.22623i	0.260853	−	0.965379i	$-0.415996\pi$
$337$	22.5106	−	22.5106i	1.22623	−	1.22623i	0.965379	−	0.260853i	$-0.0840037\pi$
$338$	13.3459	+	13.3459i	0.725920	+	0.725920i
$339$	−39.7692			−2.15996
$340$	4.17312	−	9.89200i	0.226319	−	0.536469i
$341$			3.87087i			0.209620i
$342$	18.6017	+	18.6017i	1.00587	+	1.00587i
$343$	−12.8072	−	13.3782i	−0.691524	−	0.722353i
$344$			1.48368i			0.0799947i
$345$	−21.1883	+	8.61516i	−1.14074	+	0.463825i
$346$			5.87702i			0.315950i
$347$	13.9134	−	13.9134i	0.746912	−	0.746912i	−0.226986	−	0.973898i	$-0.572887\pi$
$347$	13.9134	−	13.9134i	0.746912	−	0.746912i	0.973898	+	0.226986i	$0.0728871\pi$
$348$	−14.7788	+	14.7788i	−0.792229	+	0.792229i
$349$	−1.48453			−0.0794652			−0.0397326	−	0.999210i	$-0.512651\pi$
$349$	−1.48453			−0.0794652			−0.0397326	+	0.999210i	$0.512651\pi$
$350$	3.68252	−	12.7059i	0.196839	−	0.679157i
$351$	−37.5996			−2.00692
$352$	−0.707107	+	0.707107i	−0.0376889	+	0.0376889i
$353$	−3.45605	+	3.45605i	−0.183947	+	0.183947i	−0.793073	−	0.609126i	$-0.791520\pi$
$353$	−3.45605	+	3.45605i	−0.183947	+	0.183947i	0.609126	+	0.793073i	$0.291520\pi$
$354$			24.2126i			1.28689i
$355$	19.6224	−	7.97846i	1.04145	−	0.423452i
$356$			16.0121i			0.848637i
$357$	−35.3027	−	9.73485i	−1.86842	−	0.515223i
$358$	−4.66701	−	4.66701i	−0.246659	−	0.246659i
$359$			16.7966i			0.886489i	0.896401	+	0.443244i	$0.146173\pi$
$359$			16.7966i			0.886489i	−0.896401	+	0.443244i	$0.853827\pi$
$360$	−4.61540	+	10.9404i	−0.243253	+	0.576608i
$361$	5.54188			0.291678
$362$	10.2231	+	10.2231i	0.537315	+	0.537315i
$363$	−2.03841	+	2.03841i	−0.106989	+	0.106989i
$364$	−7.37436	−	12.9899i	−0.386521	−	0.680853i
$365$	−10.9804	+	26.0280i	−0.574741	+	1.36237i
$366$	37.2877			1.94906
$367$	−6.67097	−	6.67097i	−0.348222	−	0.348222i	0.511225	−	0.859447i	$-0.329192\pi$
$367$	−6.67097	−	6.67097i	−0.348222	−	0.348222i	−0.859447	+	0.511225i	$0.829192\pi$
$368$	2.50907	+	2.50907i	0.130794	+	0.130794i
$369$	22.4396			1.16816
$370$	3.48409	+	8.56885i	0.181129	+	0.445474i
$371$	1.46535	+	2.58119i	0.0760770	+	0.134009i
$372$	7.89044	−	7.89044i	0.409100	−	0.409100i
$373$	−1.53906	−	1.53906i	−0.0796893	−	0.0796893i	0.666139	−	0.745828i	$-0.267946\pi$
$373$	−1.53906	−	1.53906i	−0.0796893	−	0.0796893i	−0.745828	+	0.666139i	$0.767946\pi$
$374$	−4.80139			−0.248274
$375$	−11.7495	−	30.0122i	−0.606743	−	1.54982i
$376$			8.79578i			0.453608i
$377$	−28.9435	−	28.9435i	−1.49067	−	1.49067i
$378$	16.9864	+	4.68404i	0.873684	+	0.240921i
$379$		−	15.4053i		−	0.791315i	−0.918398	−	0.395657i	$-0.870517\pi$
$379$		−	15.4053i		−	0.791315i	0.918398	−	0.395657i	$-0.129483\pi$
$380$	4.17237	+	10.2616i	0.214038	+	0.526410i
$381$			46.1836i			2.36606i
$382$	7.18826	−	7.18826i	0.367783	−	0.367783i
$383$	2.84084	−	2.84084i	0.145160	−	0.145160i	−0.630792	−	0.775952i	$-0.717270\pi$
$383$	2.84084	−	2.84084i	0.145160	−	0.145160i	0.775952	+	0.630792i	$0.217270\pi$
$384$	2.88275			0.147110
$385$	−5.87555	+	0.691287i	−0.299446	+	0.0352313i
$386$	10.1365			0.515937
$387$	5.57109	−	5.57109i	0.283195	−	0.283195i
$388$	5.64356	−	5.64356i	0.286508	−	0.286508i
$389$			14.6913i			0.744878i	0.928057	+	0.372439i	$0.121478\pi$
$389$			14.6913i			0.744878i	−0.928057	+	0.372439i	$0.878522\pi$
$390$	−33.5307	−	14.1455i	−1.69789	−	0.716287i
$391$			17.0370i			0.861600i
$392$	1.71327	+	6.78710i	0.0865334	+	0.342800i
$393$	42.3856	+	42.3856i	2.13807	+	2.13807i
$394$		−	18.1148i		−	0.912608i
$395$	3.92263	+	9.64741i	0.197369	+	0.485414i
$396$	5.31025			0.266850
$397$	6.91985	+	6.91985i	0.347297	+	0.347297i	0.859102	−	0.511805i	$-0.171023\pi$
$397$	6.91985	+	6.91985i	0.347297	+	0.347297i	−0.511805	+	0.859102i	$0.671023\pi$
$398$	7.52085	−	7.52085i	0.376986	−	0.376986i
$399$	32.8585	−	18.6538i	1.64498	−	0.933858i
$400$	−3.58131	+	3.48916i	−0.179065	+	0.174458i
$401$	30.3644			1.51633			0.758163	−	0.652065i	$-0.226097\pi$
$401$	30.3644			1.51633			0.758163	+	0.652065i	$0.226097\pi$
$402$	−8.77473	−	8.77473i	−0.437644	−	0.437644i
$403$	15.4530	+	15.4530i	0.769767	+	0.769767i
$404$	−11.6120			−0.577718
$405$	6.76927	−	2.75238i	0.336368	−	0.136767i
$406$	9.47010	+	16.6815i	0.469993	+	0.827889i
$407$	2.92514	−	2.92514i	0.144994	−	0.144994i
$408$	9.78720	+	9.78720i	0.484539	+	0.484539i
$409$	−5.57334			−0.275584			−0.137792	−	0.990461i	$-0.544001\pi$
$409$	−5.57334			−0.275584			−0.137792	+	0.990461i	$0.544001\pi$
$410$	8.70597	+	3.67277i	0.429957	+	0.181385i
$411$		−	4.53972i		−	0.223928i
$412$	−9.90062	−	9.90062i	−0.487768	−	0.487768i
$413$	21.4225	+	5.90732i	1.05413	+	0.290680i
$414$		−	18.8427i		−	0.926066i
$415$	−13.1248	+	31.1112i	−0.644272	+	1.52719i
$416$			5.64570i			0.276803i
$417$	−7.75838	+	7.75838i	−0.379929	+	0.379929i
$418$	3.50299	−	3.50299i	0.171337	−	0.171337i
$419$	−35.9081			−1.75422			−0.877112	−	0.480286i	$-0.840533\pi$
$419$	−35.9081			−1.75422			−0.877112	+	0.480286i	$0.840533\pi$
$420$	13.3859	+	10.5677i	0.653166	+	0.515649i
$421$	−7.31996			−0.356753			−0.178377	−	0.983962i	$-0.557085\pi$
$421$	−7.31996			−0.356753			−0.178377	+	0.983962i	$0.557085\pi$
$422$	−12.6111	+	12.6111i	−0.613899	+	0.613899i
$423$	33.0274	−	33.0274i	1.60585	−	1.60585i
$424$		−	1.12185i		−	0.0544818i
$425$	−24.0049	−	0.312858i	−1.16441	−	0.0151758i
$426$			27.3084i			1.32310i
$427$	9.09733	−	32.9908i	0.440251	−	1.59654i
$428$	2.83307	+	2.83307i	0.136942	+	0.136942i
$429$			16.2751i			0.785771i
$430$	3.07328	−	1.24960i	0.148207	−	0.0602609i
$431$	−15.5322			−0.748162			−0.374081	−	0.927396i	$-0.622042\pi$
$431$	−15.5322			−0.748162			−0.374081	+	0.927396i	$0.622042\pi$
$432$	−4.70924	−	4.70924i	−0.226573	−	0.226573i
$433$	−22.3747	+	22.3747i	−1.07526	+	1.07526i	−0.0783304	+	0.996927i	$0.524959\pi$
$433$	−22.3747	+	22.3747i	−1.07526	+	1.07526i	−0.996927	+	0.0783304i	$0.975041\pi$
$434$	−5.05610	−	8.90626i	−0.242700	−	0.427514i
$435$	43.0599	+	18.1656i	2.06456	+	0.870974i
$436$	−9.33658			−0.447141
$437$	−12.4299	−	12.4299i	−0.594601	−	0.594601i
$438$	−25.7523	−	25.7523i	−1.23049	−	1.23049i
$439$	37.7109			1.79984			0.899922	−	0.436052i	$-0.143624\pi$
$439$	37.7109			1.79984			0.899922	+	0.436052i	$0.143624\pi$
$440$	2.06024	+	0.869149i	0.0982180	+	0.0414351i
$441$	19.0518	−	31.9181i	0.907227	−	1.51991i
$442$	−19.1677	+	19.1677i	−0.911713	+	0.911713i
$443$	−27.1381	−	27.1381i	−1.28937	−	1.28937i	−0.935170	−	0.354198i	$-0.884754\pi$
$443$	−27.1381	−	27.1381i	−1.28937	−	1.28937i	−0.354198	−	0.935170i	$-0.615246\pi$
$444$	−11.9253			−0.565948
$445$	33.1672	−	13.4858i	1.57228	−	0.639287i
$446$			1.60807i			0.0761441i
$447$	−7.26033	−	7.26033i	−0.343402	−	0.343402i
$448$	0.703324	−	2.55056i	0.0332290	−	0.120502i
$449$		−	33.2293i		−	1.56819i	−0.620643	−	0.784093i	$-0.713128\pi$
$449$		−	33.2293i		−	1.56819i	0.620643	−	0.784093i	$-0.286872\pi$
$450$	26.5490	+	0.346015i	1.25153	+	0.0163113i
$451$		−	4.22571i		−	0.198981i
$452$	9.75494	−	9.75494i	0.458834	−	0.458834i
$453$	−16.9435	+	16.9435i	−0.796075	+	0.796075i
$454$	−1.09468			−0.0513758
$455$	−20.6962	+	26.2156i	−0.970251	+	1.22900i
$456$	−14.2811			−0.668773
$457$	−6.27630	+	6.27630i	−0.293593	+	0.293593i	−0.838498	−	0.544905i	$-0.816566\pi$
$457$	−6.27630	+	6.27630i	−0.293593	+	0.293593i	0.544905	+	0.838498i	$0.316566\pi$
$458$	−2.23644	+	2.23644i	−0.104502	+	0.104502i
$459$		−	31.9766i		−	1.49254i
$460$	3.08405	−	7.31046i	0.143795	−	0.340852i
$461$			19.2476i			0.896449i	0.893921	+	0.448225i	$0.147943\pi$
$461$			19.2476i			0.896449i	−0.893921	+	0.448225i	$0.852057\pi$
$462$	2.02751	−	7.35261i	0.0943282	−	0.342075i
$463$	−7.44058	−	7.44058i	−0.345793	−	0.345793i	0.512747	−	0.858540i	$-0.328628\pi$
$463$	−7.44058	−	7.44058i	−0.345793	−	0.345793i	−0.858540	+	0.512747i	$0.828628\pi$
$464$		−	7.25017i		−	0.336581i
$465$	−22.9897	−	9.69863i	−1.06612	−	0.449763i
$466$	−2.52013			−0.116743
$467$	1.72747	+	1.72747i	0.0799379	+	0.0799379i	0.745945	−	0.666007i	$-0.231998\pi$
$467$	1.72747	+	1.72747i	0.0799379	+	0.0799379i	−0.666007	+	0.745945i	$0.731998\pi$
$468$	21.1991	−	21.1991i	0.979929	−	0.979929i
$469$	−9.90440	+	5.62274i	−0.457343	+	0.259634i
$470$	18.2195	−	7.40804i	0.840403	−	0.341708i
$471$	11.4824			0.529079
$472$	−5.93909	−	5.93909i	−0.273369	−	0.273369i
$473$	−1.04912	−	1.04912i	−0.0482386	−	0.0482386i
$474$	−13.4263			−0.616690
$475$	17.7417	−	17.2852i	0.814046	−	0.793100i
$476$	11.0472	−	6.27152i	0.506349	−	0.287455i
$477$	−4.21244	+	4.21244i	−0.192874	+	0.192874i
$478$	−7.48478	−	7.48478i	−0.342346	−	0.342346i
$479$	3.14575			0.143733			0.0718664	−	0.997414i	$-0.477104\pi$
$479$	3.14575			0.143733			0.0718664	+	0.997414i	$0.477104\pi$
$480$	−2.42793	−	5.97130i	−0.110819	−	0.272551i
$481$		−	23.3549i		−	1.06489i
$482$	−11.8477	−	11.8477i	−0.539646	−	0.539646i
$483$	−26.0897	−	7.19432i	−1.18712	−	0.327353i
$484$		−	1.00000i		−	0.0454545i
$485$	−16.4432	−	6.93685i	−0.746646	−	0.314986i
$486$		−	10.5588i		−	0.478958i
$487$	10.6347	−	10.6347i	0.481903	−	0.481903i	−0.423836	−	0.905739i	$-0.639317\pi$
$487$	10.6347	−	10.6347i	0.481903	−	0.481903i	0.905739	+	0.423836i	$0.139317\pi$
$488$	−9.14626	+	9.14626i	−0.414032	+	0.414032i
$489$	61.5859			2.78501
$490$	12.6158	−	9.26513i	0.569922	−	0.418556i
$491$	10.7113			0.483395			0.241698	−	0.970352i	$-0.422296\pi$
$491$	10.7113			0.483395			0.241698	+	0.970352i	$0.422296\pi$
$492$	−8.61374	+	8.61374i	−0.388337	+	0.388337i
$493$	24.6150	−	24.6150i	1.10860	−	1.10860i
$494$		−	27.9687i		−	1.25837i
$495$	−4.47243	−	10.9996i	−0.201021	−	0.494395i
$496$			3.87087i			0.173807i
$497$	24.1615	+	6.66263i	1.08379	+	0.298860i
$498$	−30.7816	−	30.7816i	−1.37936	−	1.37936i
$499$			17.5095i			0.783835i	0.920000	+	0.391917i	$0.128188\pi$
$499$			17.5095i			0.783835i	−0.920000	+	0.391917i	$0.871812\pi$
$500$	10.2437	+	4.47962i	0.458111	+	0.200335i
$501$	9.78745			0.437271
$502$	8.55255	+	8.55255i	0.381719	+	0.381719i
$503$	−24.1937	+	24.1937i	−1.07874	+	1.07874i	−0.0821196	+	0.996622i	$0.526169\pi$
$503$	−24.1937	+	24.1937i	−1.07874	+	1.07874i	−0.996622	+	0.0821196i	$0.973831\pi$
$504$	−12.2180	+	6.93619i	−0.544234	+	0.308963i
$505$	9.77993	+	24.0530i	0.435201	+	1.07034i
$506$	−3.54836			−0.157744
$507$	38.4728	+	38.4728i	1.70864	+	1.70864i
$508$	−11.3283	−	11.3283i	−0.502614	−	0.502614i
$509$	36.3493			1.61116			0.805578	−	0.592490i	$-0.201855\pi$
$509$	36.3493			1.61116			0.805578	+	0.592490i	$0.201855\pi$
$510$	12.0301	−	28.5162i	0.532700	−	1.26272i
$511$	−29.0677	+	16.5018i	−1.28588	+	0.729995i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	23.3294	+	23.3294i	1.03002	+	1.03002i
$514$	8.13490			0.358815
$515$	−12.1695	+	28.8466i	−0.536251	+	1.27113i
$516$			4.27708i			0.188288i
$517$	−6.21956	−	6.21956i	−0.273536	−	0.273536i
$518$	−2.90949	+	10.5511i	−0.127836	+	0.463587i
$519$			16.9420i			0.743670i
$520$	11.6944	−	4.75496i	0.512835	−	0.208519i
$521$			5.91957i			0.259341i	0.991557	+	0.129671i	$0.0413920\pi$
$521$			5.91957i			0.259341i	−0.991557	+	0.129671i	$0.958608\pi$
$522$	−27.2238	+	27.2238i	−1.19155	+	1.19155i
$523$	−3.66023	+	3.66023i	−0.160051	+	0.160051i	−0.782589	−	0.622539i	$-0.786101\pi$
$523$	−3.66023	+	3.66023i	−0.160051	+	0.160051i	0.622539	+	0.782589i	$0.286101\pi$
$524$	−20.7934			−0.908365
$525$	10.6158	−	36.6278i	0.463310	−	1.59857i
$526$	−15.1063			−0.658665
$527$	−13.1420	+	13.1420i	−0.572474	+	0.572474i
$528$	−2.03841	+	2.03841i	−0.0887105	+	0.0887105i
$529$		−	10.4092i		−	0.452572i
$530$	−2.32378	+	0.944850i	−0.100939	+	0.0410417i
$531$			44.6015i			1.93554i
$532$	−3.48425	+	12.6354i	−0.151061	+	0.547814i
$533$	−16.8695	−	16.8695i	−0.730700	−	0.730700i
$534$			46.1587i			1.99748i
$535$	3.48231	−	8.25449i	0.150553	−	0.356873i
$536$	4.30469			0.185934
$537$	−13.4538	−	13.4538i	−0.580575	−	0.580575i
$538$	4.41312	−	4.41312i	0.190263	−	0.190263i
$539$	−6.01067	−	3.58774i	−0.258898	−	0.154535i
$540$	−5.78842	+	13.7209i	−0.249094	+	0.590454i
$541$	0.483794			0.0207999			0.0104000	−	0.999946i	$-0.496690\pi$
$541$	0.483794			0.0207999			0.0104000	+	0.999946i	$0.496690\pi$
$542$	13.5331	+	13.5331i	0.581294	+	0.581294i
$543$	29.4707	+	29.4707i	1.26471	+	1.26471i
$544$	−4.80139			−0.205858
$545$	7.86352	+	19.3397i	0.336836	+	0.828421i
$546$	−21.2584	−	37.4465i	−0.909777	−	1.60256i
$547$	−25.3812	+	25.3812i	−1.08522	+	1.08522i	−0.0892091	+	0.996013i	$0.528434\pi$
$547$	−25.3812	+	25.3812i	−1.08522	+	1.08522i	−0.996013	+	0.0892091i	$0.971566\pi$
$548$	1.11354	+	1.11354i	0.0475682	+	0.0475682i
$549$	68.6868			2.93148
$550$	0.0651599	−	4.99958i	0.00277843	−	0.213183i
$551$			35.9172i			1.53012i
$552$	7.23301	+	7.23301i	0.307858	+	0.307858i
$553$	−3.27570	+	11.8791i	−0.139297	+	0.505151i
$554$		−	22.7753i		−	0.967629i
$555$	10.0438	+	24.7019i	0.426334	+	1.04854i
$556$		−	3.80609i		−	0.161414i
$557$	4.55744	−	4.55744i	0.193105	−	0.193105i	−0.603931	−	0.797036i	$-0.706400\pi$
$557$	4.55744	−	4.55744i	0.193105	−	0.193105i	0.797036	+	0.603931i	$0.206400\pi$
$558$	14.5348	−	14.5348i	0.615307	−	0.615307i
$559$	−8.37642			−0.354285
$560$	−5.87555	+	0.691287i	−0.248287	+	0.0292122i
$561$	−13.8412			−0.584376
$562$	−0.817106	+	0.817106i	−0.0344676	+	0.0344676i
$563$	11.4679	−	11.4679i	0.483316	−	0.483316i	−0.422873	−	0.906189i	$-0.638978\pi$
$563$	11.4679	−	11.4679i	0.483316	−	0.483316i	0.906189	+	0.422873i	$0.138978\pi$
$564$			25.3560i			1.06768i
$565$	−28.4221	−	11.9904i	−1.19573	−	0.504440i
$566$			0.557403i			0.0234294i
$567$	8.33517	+	2.29845i	0.350044	+	0.0965259i
$568$	−6.69846	−	6.69846i	−0.281061	−	0.281061i
$569$		−	47.4536i		−	1.98936i	−0.103021	−	0.994679i	$-0.532851\pi$
$569$		−	47.4536i		−	1.98936i	0.103021	−	0.994679i	$-0.467149\pi$
$570$	12.0279	+	29.5817i	0.503793	+	1.23904i
$571$	−14.9321			−0.624890			−0.312445	−	0.949936i	$-0.601148\pi$
$571$	−14.9321			−0.624890			−0.312445	+	0.949936i	$0.601148\pi$
$572$	−3.99211	−	3.99211i	−0.166919	−	0.166919i
$573$	20.7220	−	20.7220i	0.865672	−	0.865672i
$574$	5.51958	+	9.72269i	0.230383	+	0.405817i
$575$	−17.7403	−	0.231211i	−0.739821	−	0.00964215i
$576$	5.31025			0.221260
$577$	−24.7173	−	24.7173i	−1.02900	−	1.02900i	−0.999567	−	0.0294289i	$-0.990631\pi$
$577$	−24.7173	−	24.7173i	−1.02900	−	1.02900i	−0.0294289	−	0.999567i	$-0.509369\pi$
$578$	−4.28034	−	4.28034i	−0.178039	−	0.178039i
$579$	29.2211			1.21439
$580$	−15.0179	+	6.10629i	−0.623586	+	0.253550i
$581$	−34.7445	+	19.7245i	−1.44144	+	0.818309i
$582$	16.2690	−	16.2690i	0.674370	−	0.674370i
$583$	0.793267	+	0.793267i	0.0328537	+	0.0328537i
$584$	12.6335			0.522778
$585$	−61.7660	−	26.0572i	−2.55371	−	1.07733i
$586$			30.0756i			1.24241i
$587$	17.4764	+	17.4764i	0.721328	+	0.721328i	0.968876	−	0.247548i	$-0.0796247\pi$
$587$	17.4764	+	17.4764i	0.721328	+	0.721328i	−0.247548	+	0.968876i	$0.579625\pi$
$588$	4.93894	+	19.5655i	0.203678	+	0.806868i
$589$		−	19.1762i		−	0.790142i
$590$	−7.30011	+	17.3042i	−0.300541	+	0.712404i
$591$		−	52.2203i		−	2.14806i
$592$	2.92514	−	2.92514i	0.120222	−	0.120222i
$593$	5.44521	−	5.44521i	0.223608	−	0.223608i	−0.586408	−	0.810016i	$-0.699458\pi$
$593$	5.44521	−	5.44521i	0.223608	−	0.223608i	0.810016	+	0.586408i	$0.199458\pi$
$594$	6.65986			0.273258
$595$	−22.2950	−	17.6011i	−0.914007	−	0.721573i
$596$	3.56176			0.145895
$597$	21.6807	−	21.6807i	0.887333	−	0.887333i
$598$	−14.1654	+	14.1654i	−0.579268	+	0.579268i
$599$			1.24075i			0.0506958i	0.999679	+	0.0253479i	$0.00806936\pi$
$599$			1.24075i			0.0506958i	−0.999679	+	0.0253479i	$0.991931\pi$
$600$	−10.3240	+	10.0584i	−0.421476	+	0.410631i
$601$			2.86931i			0.117042i	0.998286	+	0.0585208i	$0.0186384\pi$
$601$			2.86931i			0.117042i	−0.998286	+	0.0585208i	$0.981362\pi$
$602$	3.78421	+	1.04351i	0.154233	+	0.0425303i
$603$	−16.1637	−	16.1637i	−0.658238	−	0.658238i
$604$		−	8.31210i		−	0.338215i
$605$	−2.07139	+	0.842227i	−0.0842140	+	0.0342414i
$606$	−33.4745			−1.35981
$607$	7.78887	+	7.78887i	0.316141	+	0.316141i	0.847283	−	0.531142i	$-0.178237\pi$
$607$	7.78887	+	7.78887i	0.316141	+	0.316141i	−0.531142	+	0.847283i	$0.678237\pi$
$608$	3.50299	−	3.50299i	0.142065	−	0.142065i
$609$	27.2999	+	48.0886i	1.10625	+	1.94865i
$610$	26.6487	+	11.2422i	1.07897	+	0.455185i
$611$	−49.6584			−2.00896
$612$	18.0288	+	18.0288i	0.728770	+	0.728770i
$613$	0.261621	+	0.261621i	0.0105668	+	0.0105668i	0.712370	−	0.701804i	$-0.247622\pi$
$613$	0.261621	+	0.261621i	0.0105668	+	0.0105668i	−0.701804	+	0.712370i	$0.747622\pi$
$614$	−29.3777			−1.18559
$615$	25.0971	+	10.5877i	1.01201	+	0.426937i
$616$	1.30619	+	2.30084i	0.0526279	+	0.0927035i
$617$	−2.56934	+	2.56934i	−0.103438	+	0.103438i	−0.756932	−	0.653494i	$-0.773303\pi$
$617$	−2.56934	+	2.56934i	−0.103438	+	0.103438i	0.653494	+	0.756932i	$0.273303\pi$
$618$	−28.5410	−	28.5410i	−1.14809	−	1.14809i
$619$	10.5621			0.424528			0.212264	−	0.977212i	$-0.431916\pi$
$619$	10.5621			0.424528			0.212264	+	0.977212i	$0.431916\pi$
$620$	8.01809	−	3.26015i	0.322014	−	0.130931i
$621$		−	23.6316i		−	0.948303i
$622$	−14.0503	−	14.0503i	−0.563367	−	0.563367i
$623$	40.8396	+	11.2617i	1.63621	+	0.451189i
$624$			16.2751i			0.651527i
$625$	0.651544	−	24.9915i	0.0260618	−	0.999660i
$626$		−	12.2537i		−	0.489757i
$627$	10.0982	−	10.0982i	0.403285	−	0.403285i
$628$	−2.81649	+	2.81649i	−0.112390	+	0.112390i
$629$	19.8622			0.791958
$630$	24.6579	+	19.4665i	0.982394	+	0.775562i
$631$	−17.1559			−0.682967			−0.341483	−	0.939888i	$-0.610929\pi$
$631$	−17.1559			−0.682967			−0.341483	+	0.939888i	$0.610929\pi$
$632$	3.29332	−	3.29332i	0.131001	−	0.131001i
$633$	−36.3547	+	36.3547i	−1.44497	+	1.44497i
$634$			11.0337i			0.438205i
$635$	−13.9244	+	33.0064i	−0.552572	+	1.30982i
$636$		−	3.23401i		−	0.128237i
$637$	−38.3179	+	9.67262i	−1.51821	+	0.383243i
$638$	5.12665	+	5.12665i	0.202966	+	0.202966i
$639$			50.3042i			1.99001i
$640$	2.06024	+	0.869149i	0.0814380	+	0.0343561i
$641$	11.8476			0.467954			0.233977	−	0.972242i	$-0.424826\pi$
$641$	11.8476			0.467954			0.233977	+	0.972242i	$0.424826\pi$
$642$	8.16704	+	8.16704i	0.322328	+	0.322328i
$643$	−16.2690	+	16.2690i	−0.641586	+	0.641586i	−0.950945	−	0.309359i	$-0.899885\pi$
$643$	−16.2690	+	16.2690i	−0.641586	+	0.641586i	0.309359	+	0.950945i	$0.399885\pi$
$644$	8.16420	−	4.63483i	0.321715	−	0.182638i
$645$	8.85950	−	3.60227i	0.348843	−	0.141839i
$646$	23.7860			0.935846
$647$	−17.9057	−	17.9057i	−0.703945	−	0.703945i	0.261310	−	0.965255i	$-0.415846\pi$
$647$	−17.9057	−	17.9057i	−0.703945	−	0.703945i	−0.965255	+	0.261310i	$0.915846\pi$
$648$	−2.31081	−	2.31081i	−0.0907773	−	0.0907773i
$649$	8.39914			0.329695
$650$	−19.6987	−	20.2190i	−0.772648	−	0.793054i
$651$	−14.5755	−	25.6745i	−0.571257	−	1.00626i
$652$	−15.1063	+	15.1063i	−0.591610	+	0.591610i
$653$	−18.2688	−	18.2688i	−0.714915	−	0.714915i	0.252644	−	0.967559i	$-0.418700\pi$
$653$	−18.2688	−	18.2688i	−0.714915	−	0.714915i	−0.967559	+	0.252644i	$0.918700\pi$
$654$	−26.9150			−1.05246
$655$	17.5128	+	43.0713i	0.684281	+	1.68293i
$656$		−	4.22571i		−	0.164986i
$657$	−47.4377	−	47.4377i	−1.85072	−	1.85072i
$658$	22.4341	+	6.18629i	0.874574	+	0.241167i
$659$		−	29.9625i		−	1.16718i	−0.812050	−	0.583588i	$-0.801648\pi$
$659$		−	29.9625i		−	1.16718i	0.812050	−	0.583588i	$-0.198352\pi$
$660$	5.93915	+	2.50554i	0.231181	+	0.0975280i
$661$			36.3565i			1.41410i	0.707162	+	0.707051i	$0.249975\pi$
$661$			36.3565i			1.41410i	−0.707162	+	0.707051i	$0.750025\pi$
$662$	−2.69058	+	2.69058i	−0.104572	+	0.104572i
$663$	−55.2556	+	55.2556i	−2.14595	+	2.14595i
$664$	15.1008			0.586023
$665$	29.1073	−	3.42462i	1.12873	−	0.132801i
$666$	−21.9673			−0.851214
$667$	18.1912	−	18.1912i	0.704365	−	0.704365i
$668$	−2.40075	+	2.40075i	−0.0928879	+	0.0928879i
$669$			4.63565i			0.179225i
$670$	−3.62552	−	8.91669i	−0.140066	−	0.344482i
$671$		−	12.9348i		−	0.499341i
$672$	2.02751	−	7.35261i	0.0782128	−	0.283633i
$673$	10.7229	+	10.7229i	0.413336	+	0.413336i	0.882899	−	0.469563i	$-0.155589\pi$
$673$	10.7229	+	10.7229i	0.413336	+	0.413336i	−0.469563	+	0.882899i	$0.655589\pi$
$674$			31.8348i			1.22623i
$675$	33.2965	+	0.433956i	1.28158	+	0.0167030i
$676$	−18.8739			−0.725920
$677$	−0.526391	−	0.526391i	−0.0202308	−	0.0202308i	0.696919	−	0.717150i	$-0.254554\pi$
$677$	−0.526391	−	0.526391i	−0.0202308	−	0.0202308i	−0.717150	+	0.696919i	$0.754554\pi$
$678$	28.1210	−	28.1210i	1.07998	−	1.07998i
$679$	−10.4250	−	18.3635i	−0.400073	−	0.704725i
$680$	4.04386	+	9.94554i	0.155075	+	0.381394i
$681$	−3.15568			−0.120926
$682$	−2.73712	−	2.73712i	−0.104810	−	0.104810i
$683$	−26.5539	−	26.5539i	−1.01606	−	1.01606i	−0.999869	−	0.0161871i	$-0.994847\pi$
$683$	−26.5539	−	26.5539i	−1.01606	−	1.01606i	−0.0161871	−	0.999869i	$-0.505153\pi$
$684$	−26.3068			−1.00587
$685$	1.36873	−	3.24444i	0.0522964	−	0.123964i
$686$	18.5159	+	0.403733i	0.706939	+	0.0154146i
$687$	−6.44709	+	6.44709i	−0.245972	+	0.245972i
$688$	−1.04912	−	1.04912i	−0.0399974	−	0.0399974i
$689$	6.33362			0.241292
$690$	8.89055	−	21.0742i	0.338458	−	0.802282i
$691$		−	44.7424i		−	1.70208i	−0.525099	−	0.851041i	$-0.675972\pi$
$691$		−	44.7424i		−	1.70208i	0.525099	−	0.851041i	$-0.324028\pi$
$692$	−4.15568	−	4.15568i	−0.157975	−	0.157975i
$693$	3.73483	−	13.5441i	0.141874	−	0.514497i
$694$			19.6766i			0.746912i
$695$	−7.88389	+	3.20559i	−0.299053	+	0.121595i
$696$		−	20.9004i		−	0.792229i
$697$	14.3467	−	14.3467i	0.543419	−	0.543419i
$698$	1.04972	−	1.04972i	0.0397326	−	0.0397326i
$699$	−7.26492			−0.274784
$700$	6.38047	+	11.5883i	0.241159	+	0.437998i
$701$	25.7985			0.974394			0.487197	−	0.873292i	$-0.338019\pi$
$701$	25.7985			0.974394			0.487197	+	0.873292i	$0.338019\pi$
$702$	26.5869	−	26.5869i	1.00346	−	1.00346i
$703$	−14.4911	+	14.4911i	−0.546540	+	0.546540i
$704$		−	1.00000i		−	0.0376889i
$705$	52.5222	−	21.3555i	1.97810	−	0.804296i
$706$		−	4.88759i		−	0.183947i
$707$	−8.16700	+	29.6170i	−0.307152	+	1.11386i
$708$	−17.1209	−	17.1209i	−0.643443	−	0.643443i
$709$			1.81465i			0.0681505i	0.999419	+	0.0340752i	$0.0108486\pi$
$709$			1.81465i			0.0681505i	−0.999419	+	0.0340752i	$0.989151\pi$
$710$	−8.23350	+	19.5167i	−0.308998	+	0.732450i
$711$	−24.7322			−0.927532
$712$	−11.3222	−	11.3222i	−0.424319	−	0.424319i
$713$	−9.71228	+	9.71228i	−0.363728	+	0.363728i
$714$	31.8464	−	18.0792i	1.19182	−	0.676598i
$715$	−4.90696	+	11.6315i	−0.183510	+	0.434993i
$716$	6.60014			0.246659
$717$	−21.5767	−	21.5767i	−0.805798	−	0.805798i
$718$	−11.8770	−	11.8770i	−0.443244	−	0.443244i
$719$	8.10544			0.302282			0.151141	−	0.988512i	$-0.451705\pi$
$719$	8.10544			0.302282			0.151141	+	0.988512i	$0.451705\pi$
$720$	−4.47243	−	10.9996i	−0.166678	−	0.409931i
$721$	−32.2154	+	18.2887i	−1.19976	+	0.681108i
$722$	−3.91870	+	3.91870i	−0.145839	+	0.145839i
$723$	−34.1538	−	34.1538i	−1.27019	−	1.27019i
$724$	−14.4577			−0.537315
$725$	25.2970	+	25.9651i	0.939507	+	0.964320i
$726$		−	2.88275i		−	0.106989i
$727$	26.0738	+	26.0738i	0.967025	+	0.967025i	0.999473	−	0.0324487i	$-0.0103305\pi$
$727$	26.0738	+	26.0738i	0.967025	+	0.967025i	−0.0324487	+	0.999473i	$0.510331\pi$
$728$	14.3997	+	3.97076i	0.533687	+	0.147166i
$729$		−	40.2424i		−	1.49046i
$730$	−10.6403	−	26.1689i	−0.393814	−	0.968555i
$731$		−	7.12373i		−	0.263481i
$732$	−26.3664	+	26.3664i	−0.974529	+	0.974529i
$733$	−7.51195	+	7.51195i	−0.277460	+	0.277460i	−0.832094	−	0.554634i	$-0.812858\pi$
$733$	−7.51195	+	7.51195i	−0.277460	+	0.277460i	0.554634	+	0.832094i	$0.312858\pi$
$734$	9.43418			0.348222
$735$	36.3681	−	26.7091i	1.34146	−	0.985178i
$736$	−3.54836			−0.130794
$737$	−3.04387	+	3.04387i	−0.112123	+	0.112123i
$738$	−15.8672	+	15.8672i	−0.584079	+	0.584079i
$739$		−	24.9390i		−	0.917396i	−0.888592	−	0.458698i	$-0.848316\pi$
$739$		−	24.9390i		−	0.917396i	0.888592	−	0.458698i	$-0.151684\pi$
$740$	−8.52272	−	3.59547i	−0.313301	−	0.132172i
$741$		−	80.6267i		−	2.96189i
$742$	−2.86134	−	0.789023i	−0.105043	−	0.0289660i
$743$	−19.2817	−	19.2817i	−0.707377	−	0.707377i	0.258606	−	0.965983i	$-0.416737\pi$
$743$	−19.2817	−	19.2817i	−0.707377	−	0.707377i	−0.965983	+	0.258606i	$0.916737\pi$
$744$			11.1588i			0.409100i
$745$	−2.99981	−	7.37779i	−0.109904	−	0.270301i
$746$	2.17655			0.0796893
$747$	−56.7020	−	56.7020i	−2.07462	−	2.07462i
$748$	3.39509	−	3.39509i	0.124137	−	0.124137i
$749$	9.21848	−	5.23334i	0.336836	−	0.191222i
$750$	29.5300	+	12.9136i	1.07828	+	0.471539i
$751$	29.2201			1.06626			0.533129	−	0.846034i	$-0.321016\pi$
$751$	29.2201			1.06626			0.533129	+	0.846034i	$0.321016\pi$
$752$	−6.21956	−	6.21956i	−0.226804	−	0.226804i
$753$	24.6549	+	24.6549i	0.898473	+	0.898473i
$754$	40.9323			1.49067
$755$	−17.2176	+	7.00067i	−0.626613	+	0.254781i
$756$	−15.3233	+	8.69905i	−0.557303	+	0.316381i
$757$	23.4814	−	23.4814i	0.853445	−	0.853445i	−0.137111	−	0.990556i	$-0.543782\pi$
$757$	23.4814	−	23.4814i	0.853445	−	0.853445i	0.990556	+	0.137111i	$0.0437818\pi$
$758$	10.8932	+	10.8932i	0.395657	+	0.395657i
$759$	−10.2290			−0.371290
$760$	−10.2064	−	4.30575i	−0.370224	−	0.156186i
$761$		−	12.4697i		−	0.452027i	−0.974124	−	0.226013i	$-0.927431\pi$
$761$		−	12.4697i		−	0.452027i	0.974124	−	0.226013i	$-0.0725693\pi$
$762$	−32.6568	−	32.6568i	−1.18303	−	1.18303i
$763$	−6.56664	+	23.8135i	−0.237728	+	0.862105i
$764$			10.1657i			0.367783i
$765$	22.1603	−	52.5290i	0.801208	−	1.89919i
$766$			4.01756i			0.145160i
$767$	33.5303	−	33.5303i	1.21071	−	1.21071i
$768$	−2.03841	+	2.03841i	−0.0735549	+	0.0735549i
$769$	−42.2430			−1.52332			−0.761661	−	0.647976i	$-0.775616\pi$
$769$	−42.2430			−1.52332			−0.761661	+	0.647976i	$0.775616\pi$
$770$	3.66583	−	4.64346i	0.132107	−	0.167339i
$771$	23.4509			0.844563
$772$	−7.16762	+	7.16762i	−0.257968	+	0.257968i
$773$	12.7135	−	12.7135i	0.457272	−	0.457272i	−0.440487	−	0.897759i	$-0.645194\pi$
$773$	12.7135	−	12.7135i	0.457272	−	0.457272i	0.897759	+	0.440487i	$0.145194\pi$
$774$			7.87872i			0.283195i
$775$	−13.5061	−	13.8628i	−0.485153	−	0.497966i
$776$			7.98120i			0.286508i
$777$	−8.38733	+	30.4160i	−0.300894	+	1.09117i
$778$	−10.3883	−	10.3883i	−0.372439	−	0.372439i
$779$			20.9341i			0.750041i
$780$	33.7122	−	13.7074i	1.20709	−	0.490802i
$781$	9.47305			0.338972
$782$	−12.0470	−	12.0470i	−0.430800	−	0.430800i
$783$	−34.1428	+	34.1428i	−1.22016	+	1.22016i
$784$	−6.01067	−	3.58774i	−0.214667	−	0.128133i
$785$	8.20619	+	3.46193i	0.292891	+	0.123562i
$786$	−59.9422			−2.13807
$787$	36.0382	+	36.0382i	1.28462	+	1.28462i	0.938008	+	0.346614i	$0.112669\pi$
$787$	36.0382	+	36.0382i	1.28462	+	1.28462i	0.346614	+	0.938008i	$0.387331\pi$
$788$	12.8091	+	12.8091i	0.456304	+	0.456304i
$789$	−43.5476			−1.55034
$790$	−9.59547	−	4.04803i	−0.341391	−	0.144022i
$791$	−18.0196	−	31.7414i	−0.640704	−	1.12859i
$792$	−3.75491	+	3.75491i	−0.133425	+	0.133425i
$793$	−51.6370	−	51.6370i	−1.83368	−	1.83368i
$794$	−9.78614			−0.347297
$795$	−6.69889	+	2.72377i	−0.237585	+	0.0966021i
$796$			10.6361i			0.376986i
$797$	−13.3328	−	13.3328i	−0.472274	−	0.472274i	0.430376	−	0.902650i	$-0.358381\pi$
$797$	−13.3328	−	13.3328i	−0.472274	−	0.472274i	−0.902650	+	0.430376i	$0.858381\pi$
$798$	−10.0442	+	36.4247i	−0.355562	+	1.28942i
$799$		−	42.2320i		−	1.49406i
$800$	0.0651599	−	4.99958i	0.00230375	−	0.176762i
$801$			85.0280i			3.00432i
$802$	−21.4709	+	21.4709i	−0.758163	+	0.758163i
$803$	−8.93324	+	8.93324i	−0.315247	+	0.315247i
$804$	12.4093			0.437644
$805$	−16.4766	−	13.0077i	−0.580725	−	0.458460i
$806$	−21.8538			−0.769767
$807$	12.7219	−	12.7219i	0.447833	−	0.447833i
$808$	8.21092	−	8.21092i	0.288859	−	0.288859i
$809$		−	53.6514i		−	1.88628i	−0.332394	−	0.943141i	$-0.607856\pi$
$809$		−	53.6514i		−	1.88628i	0.332394	−	0.943141i	$-0.392144\pi$
$810$	−2.84037	+	6.73282i	−0.0998003	+	0.236567i
$811$		−	6.67559i		−	0.234412i	−0.993108	−	0.117206i	$-0.962606\pi$
$811$		−	6.67559i		−	0.234412i	0.993108	−	0.117206i	$-0.0373937\pi$
$812$	−18.4920	−	5.09922i	−0.648941	−	0.178948i
$813$	39.0124	+	39.0124i	1.36822	+	1.36822i
$814$			4.13677i			0.144994i
$815$	44.0141	+	18.5681i	1.54174	+	0.650414i
$816$	−13.8412			−0.484539
$817$	5.19732	+	5.19732i	0.181831	+	0.181831i
$818$	3.94095	−	3.94095i	0.137792	−	0.137792i
$819$	−39.1597	−	68.9793i	−1.36835	−	2.41033i
$820$	−8.75310	+	3.55901i	−0.305671	+	0.124286i
$821$	4.69542			0.163871			0.0819357	−	0.996638i	$-0.473890\pi$
$821$	4.69542			0.163871			0.0819357	+	0.996638i	$0.473890\pi$
$822$	3.21007	+	3.21007i	0.111964	+	0.111964i
$823$	21.8412	+	21.8412i	0.761336	+	0.761336i	0.976564	−	0.215228i	$-0.0690495\pi$
$823$	21.8412	+	21.8412i	0.761336	+	0.761336i	−0.215228	+	0.976564i	$0.569050\pi$
$824$	14.0016			0.487768
$825$	0.187840	−	14.4125i	0.00653974	−	0.501780i
$826$	−19.3251	+	10.9709i	−0.672406	+	0.381726i
$827$	−4.03102	+	4.03102i	−0.140172	+	0.140172i	−0.773711	−	0.633539i	$-0.781602\pi$
$827$	−4.03102	+	4.03102i	−0.140172	+	0.140172i	0.633539	+	0.773711i	$0.281602\pi$
$828$	13.3238	+	13.3238i	0.463033	+	0.463033i
$829$	−33.3279			−1.15753			−0.578764	−	0.815495i	$-0.696465\pi$
$829$	−33.3279			−1.15753			−0.578764	+	0.815495i	$0.696465\pi$
$830$	−12.7183	−	31.2796i	−0.441458	−	1.08573i
$831$		−	65.6554i		−	2.27756i
$832$	−3.99211	−	3.99211i	−0.138402	−	0.138402i
$833$	−8.22609	−	32.5875i	−0.285017	−	1.12909i
$834$		−	10.9720i		−	0.379929i
$835$	6.99487	+	2.95092i	0.242068	+	0.102121i
$836$			4.95398i			0.171337i
$837$	18.2289	−	18.2289i	0.630081	−	0.630081i
$838$	25.3908	−	25.3908i	0.877112	−	0.877112i
$839$	−30.5646			−1.05521			−0.527604	−	0.849491i	$-0.676909\pi$
$839$	−30.5646			−1.05521			−0.527604	+	0.849491i	$0.676909\pi$
$840$	−16.9377	+	1.99281i	−0.584408	+	0.0687584i
$841$	−23.5650			−0.812587
$842$	5.17599	−	5.17599i	0.178377	−	0.178377i
$843$	−2.35551	+	2.35551i	−0.0811282	+	0.0811282i
$844$		−	17.8348i		−	0.613899i
$845$	15.8961	+	39.0952i	0.546843	+	1.34492i
$846$			46.7078i			1.60585i
$847$	−2.55056	−	0.703324i	−0.0876381	−	0.0241665i
$848$	0.793267	+	0.793267i	0.0272409	+	0.0272409i
$849$			1.60685i			0.0551471i
$850$	17.1952	−	16.7528i	0.589792	−	0.574616i
$851$	14.6787			0.503180
$852$	−19.3100	−	19.3100i	−0.661549	−	0.661549i
$853$	−15.3416	+	15.3416i	−0.525288	+	0.525288i	−0.919164	−	0.393876i	$-0.871134\pi$
$853$	−15.3416	+	15.3416i	−0.525288	+	0.525288i	0.393876	+	0.919164i	$0.371134\pi$
$854$	16.8953	+	29.7608i	0.578144	+	1.01839i
$855$	22.1563	+	54.4917i	0.757730	+	1.86358i
$856$	−4.00657			−0.136942
$857$	−31.7855	−	31.7855i	−1.08577	−	1.08577i	−0.995959	−	0.0898137i	$-0.971373\pi$
$857$	−31.7855	−	31.7855i	−1.08577	−	1.08577i	−0.0898137	−	0.995959i	$-0.528627\pi$
$858$	−11.5083	−	11.5083i	−0.392886	−	0.392886i
$859$	−7.02928			−0.239836			−0.119918	−	0.992784i	$-0.538263\pi$
$859$	−7.02928			−0.239836			−0.119918	+	0.992784i	$0.538263\pi$
$860$	−1.28954	+	3.05674i	−0.0439730	+	0.104234i
$861$	15.9116	+	28.0281i	0.542265	+	0.955195i
$862$	10.9830	−	10.9830i	0.374081	−	0.374081i
$863$	−3.04516	−	3.04516i	−0.103659	−	0.103659i	0.653375	−	0.757034i	$-0.273352\pi$
$863$	−3.04516	−	3.04516i	−0.103659	−	0.103659i	−0.757034	+	0.653375i	$0.773352\pi$
$864$	6.65986			0.226573
$865$	−5.10801	+	12.1081i	−0.173677	+	0.411686i
$866$		−	31.6426i		−	1.07526i
$867$	−12.3392	−	12.3392i	−0.419060	−	0.419060i
$868$	9.87288	+	2.72248i	0.335107	+	0.0924070i
$869$			4.65746i			0.157993i
$870$	−43.2929	+	17.6029i	−1.46777	+	0.596794i
$871$			24.3030i			0.823475i
$872$	6.60196	−	6.60196i	0.223571	−	0.223571i
$873$	29.9687	−	29.9687i	1.01429	−	1.01429i
$874$	17.5785			0.594601
$875$	18.6302	−	22.9764i	0.629814	−	0.776746i
$876$	36.4192			1.23049
$877$	−3.88099	+	3.88099i	−0.131052	+	0.131052i	−0.769590	−	0.638538i	$-0.779539\pi$
$877$	−3.88099	+	3.88099i	−0.131052	+	0.131052i	0.638538	+	0.769590i	$0.279539\pi$
$878$	−26.6656	+	26.6656i	−0.899922	+	0.899922i
$879$			86.7004i			2.92433i
$880$	−2.07139	+	0.842227i	−0.0698265	+	0.0283915i
$881$		−	14.1935i		−	0.478192i	−0.970996	−	0.239096i	$-0.923149\pi$
$881$		−	14.1935i		−	0.478192i	0.970996	−	0.239096i	$-0.0768510\pi$
$882$	9.09790	+	36.0412i	0.306342	+	1.21357i
$883$	30.1032	+	30.1032i	1.01305	+	1.01305i	0.999914	+	0.0131401i	$0.00418273\pi$
$883$	30.1032	+	30.1032i	1.01305	+	1.01305i	0.0131401	+	0.999914i	$0.495817\pi$
$884$		−	27.1072i		−	0.911713i
$885$	−21.0444	+	49.8838i	−0.707400	+	1.67682i
$886$	38.3790			1.28937
$887$	0.346940	+	0.346940i	0.0116491	+	0.0116491i	0.712907	−	0.701258i	$-0.247378\pi$
$887$	0.346940	+	0.346940i	0.0116491	+	0.0116491i	−0.701258	+	0.712907i	$0.747378\pi$
$888$	8.43243	−	8.43243i	0.282974	−	0.282974i
$889$	−36.8610	+	20.9261i	−1.23628	+	0.701837i
$890$	−13.9169	+	32.9886i	−0.466494	+	1.10578i
$891$	3.26798			0.109482
$892$	−1.13707	−	1.13707i	−0.0380721	−	0.0380721i
$893$	30.8115	+	30.8115i	1.03107	+	1.03107i
$894$	10.2677			0.343402
$895$	−5.55882	−	13.6715i	−0.185811	−	0.456987i
$896$	1.30619	+	2.30084i	0.0436367	+	0.0768657i
$897$	−40.8354	+	40.8354i	−1.36346	+	1.36346i
$898$	23.4966	+	23.4966i	0.784093	+	0.784093i
$899$	28.0645			0.936004
$900$	−19.0176	+	18.5283i	−0.633921	+	0.617610i
$901$			5.38643i			0.179448i
$902$	2.98803	+	2.98803i	0.0994905	+	0.0994905i
$903$	10.9089	+	3.00818i	0.363027	+	0.100106i
$904$			13.7956i			0.458834i
$905$	12.1766	+	29.9475i	0.404765	+	0.995488i
$906$		−	23.9617i		−	0.796075i
$907$	−0.417174	+	0.417174i	−0.0138520	+	0.0138520i	−0.713999	−	0.700147i	$-0.753118\pi$
$907$	−0.417174	+	0.417174i	−0.0138520	+	0.0138520i	0.700147	+	0.713999i	$0.253118\pi$
$908$	0.774054	−	0.774054i	0.0256879	−	0.0256879i
$909$	−61.6626			−2.04522
$910$	−3.90280	−	33.1716i	−0.129377	−	1.09963i
$911$	46.8741			1.55301			0.776504	−	0.630112i	$-0.216991\pi$
$911$	46.8741			1.55301			0.776504	+	0.630112i	$0.216991\pi$
$912$	10.0982	−	10.0982i	0.334386	−	0.334386i
$913$	−10.6779	+	10.6779i	−0.353385	+	0.353385i
$914$		−	8.87603i		−	0.293593i
$915$	76.8215	+	32.4086i	2.53964	+	1.07139i
$916$		−	3.16280i		−	0.104502i
$917$	−14.6245	+	53.0348i	−0.482944	+	1.75136i
$918$	22.6109	+	22.6109i	0.746270	+	0.746270i
$919$		−	41.8925i		−	1.38190i	−0.722900	−	0.690952i	$-0.757191\pi$
$919$		−	41.8925i		−	1.38190i	0.722900	−	0.690952i	$-0.242809\pi$
$920$	2.98852	+	7.35003i	0.0985286	+	0.242323i
$921$	−84.6887			−2.79059
$922$	−13.6101	−	13.6101i	−0.448225	−	0.448225i
$923$	37.8175	−	37.8175i	1.24478	−	1.24478i
$924$	3.76542	+	6.63275i	0.123873	+	0.218201i
$925$	−0.269551	+	20.6821i	−0.00886279	+	0.680022i
$926$	10.5226			0.345793
$927$	−52.5747	−	52.5747i	−1.72678	−	1.72678i
$928$	5.12665	+	5.12665i	0.168290	+	0.168290i
$929$	27.7966			0.911977			0.455988	−	0.889986i	$-0.349286\pi$
$929$	27.7966			0.911977			0.455988	+	0.889986i	$0.349286\pi$
$930$	23.1141	−	9.39821i	0.757943	−	0.308179i
$931$	29.7767	+	17.7736i	0.975892	+	0.582505i
$932$	1.78200	−	1.78200i	0.0583715	−	0.0583715i
$933$	−40.5036	−	40.5036i	−1.32603	−	1.32603i
$934$	−2.44301			−0.0799379
$935$	−9.89200	−	4.17312i	−0.323503	−	0.136476i
$936$			29.9801i			0.979929i
$937$	35.1304	+	35.1304i	1.14766	+	1.14766i	0.987011	+	0.160650i	$0.0513590\pi$
$937$	35.1304	+	35.1304i	1.14766	+	1.14766i	0.160650	+	0.987011i	$0.448641\pi$
$938$	3.02759	−	10.9793i	0.0988544	−	0.358488i
$939$		−	35.3244i		−	1.15277i
$940$	−7.64485	+	18.1214i	−0.249348	+	0.591055i
$941$			29.0178i			0.945952i	0.881075	+	0.472976i	$0.156820\pi$
$941$			29.0178i			0.945952i	−0.881075	+	0.472976i	$0.843180\pi$
$942$	−8.11925	+	8.11925i	−0.264539	+	0.264539i
$943$	10.6026	−	10.6026i	0.345268	−	0.345268i
$944$	8.39914			0.273369
$945$	30.9248	+	24.4139i	1.00598	+	0.794185i
$946$	1.48368			0.0482386
$947$	−8.51386	+	8.51386i	−0.276663	+	0.276663i	−0.831775	−	0.555112i	$-0.812675\pi$
$947$	−8.51386	+	8.51386i	−0.276663	+	0.276663i	0.555112	+	0.831775i	$0.312675\pi$
$948$	9.49382	−	9.49382i	0.308345	−	0.308345i
$949$			71.3250i			2.31531i
$950$	−0.322801	+	24.7678i	−0.0104730	+	0.803573i
$951$			31.8074i			1.03143i
$952$	−3.37693	+	12.2462i	−0.109447	+	0.396902i
$953$	0.0324873	+	0.0324873i	0.00105237	+	0.00105237i	0.707633	−	0.706580i	$-0.249763\pi$
$953$	0.0324873	+	0.0324873i	0.00105237	+	0.00105237i	−0.706580	+	0.707633i	$0.749763\pi$
$954$		−	5.95729i		−	0.192874i
$955$	21.0572	−	8.56185i	0.681395	−	0.277055i
$956$	10.5851			0.342346
$957$	14.7788	+	14.7788i	0.477732	+	0.477732i
$958$	−2.22438	+	2.22438i	−0.0718664	+	0.0718664i
$959$	3.62334	−	2.05697i	0.117004	−	0.0664231i
$960$	5.93915	+	2.50554i	0.191685	+	0.0808660i
$961$	16.0163			0.516656
$962$	16.5144	+	16.5144i	0.532447	+	0.532447i
$963$	15.0443	+	15.0443i	0.484797	+	0.484797i
$964$	16.7551			0.539646
$965$	20.8837	+	8.81017i	0.672270	+	0.283610i
$966$	23.5354	−	13.3611i	0.757238	−	0.429885i
$967$	13.0637	−	13.0637i	0.420099	−	0.420099i	−0.465139	−	0.885238i	$-0.653995\pi$
$967$	13.0637	−	13.0637i	0.420099	−	0.420099i	0.885238	+	0.465139i	$0.153995\pi$
$968$	0.707107	+	0.707107i	0.0227273	+	0.0227273i
$969$	68.5690			2.20275
$970$	16.5322	−	6.72198i	0.530816	−	0.215830i
$971$			26.9200i			0.863905i	0.901896	+	0.431952i	$0.142175\pi$
$971$			26.9200i			0.863905i	−0.901896	+	0.431952i	$0.857825\pi$
$972$	7.46621	+	7.46621i	0.239479	+	0.239479i
$973$	−9.70764	−	2.67692i	−0.311213	−	0.0858180i
$974$			15.0397i			0.481903i
$975$	−56.7865	−	58.2863i	−1.81862	−	1.86666i
$976$		−	12.9348i		−	0.414032i
$977$	−36.5953	+	36.5953i	−1.17079	+	1.17079i	−0.188765	+	0.982022i	$0.560448\pi$
$977$	−36.5953	+	36.5953i	−1.17079	+	1.17079i	−0.982022	+	0.188765i	$0.939552\pi$
$978$	−43.5478	+	43.5478i	−1.39250	+	1.39250i
$979$	16.0121			0.511747
$980$	−2.36925	+	15.4721i	−0.0756830	+	0.494239i
$981$	−49.5795			−1.58295
$982$	−7.57405	+	7.57405i	−0.241698	+	0.241698i
$983$	−7.49060	+	7.49060i	−0.238913	+	0.238913i	−0.816400	−	0.577487i	$-0.804033\pi$
$983$	−7.49060	+	7.49060i	−0.238913	+	0.238913i	0.577487	+	0.816400i	$0.304033\pi$
$984$		−	12.1817i		−	0.388337i
$985$	15.7444	−	37.3207i	0.501659	−	1.18914i
$986$			34.8109i			1.10860i
$987$	64.6720	+	17.8335i	2.05853	+	0.567647i
$988$	19.7768	+	19.7768i	0.629185	+	0.629185i
$989$		−	5.26463i		−	0.167406i
$990$	10.9404	+	4.61540i	0.347708	+	0.146687i
$991$	44.1927			1.40383			0.701914	−	0.712262i	$-0.252329\pi$
$991$	44.1927			1.40383			0.701914	+	0.712262i	$0.252329\pi$
$992$	−2.73712	−	2.73712i	−0.0869037	−	0.0869037i
$993$	−7.75627	+	7.75627i	−0.246138	+	0.246138i
$994$	−21.7960	+	12.3736i	−0.691327	+	0.392467i
$995$	22.0315	−	8.95799i	0.698444	−	0.283987i
$996$	43.5317			1.37936
$997$	13.0234	+	13.0234i	0.412454	+	0.412454i	0.882593	−	0.470138i	$-0.155796\pi$
$997$	13.0234	+	13.0234i	0.412454	+	0.412454i	−0.470138	+	0.882593i	$0.655796\pi$
$998$	−12.3811	−	12.3811i	−0.391917	−	0.391917i
$999$	−27.5503			−0.871653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.l.c.573.1	✓	40
5.2	odd	4	inner	770.2.l.c.727.10	yes	40
7.6	odd	2	inner	770.2.l.c.573.10	yes	40
35.27	even	4	inner	770.2.l.c.727.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.l.c.573.1	✓	40	1.1	even	1	trivial
770.2.l.c.573.10	yes	40	7.6	odd	2	inner
770.2.l.c.727.1	yes	40	35.27	even	4	inner
770.2.l.c.727.10	yes	40	5.2	odd	4	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.03841 + 2.03841i) q^{3} -1.00000i q^{4} +(-2.07139 + 0.842227i) q^{5} -2.88275i q^{6} +(-2.55056 - 0.703324i) q^{7} +(0.707107 + 0.707107i) q^{8} -5.31025i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.03841 + 2.03841i) q^{3} -1.00000i q^{4} +(-2.07139 + 0.842227i) q^{5} -2.88275i q^{6} +(-2.55056 - 0.703324i) q^{7} +(0.707107 + 0.707107i) q^{8} -5.31025i q^{9} +(0.869149 - 2.06024i) q^{10} -1.00000 q^{11} +(2.03841 + 2.03841i) q^{12} +(-3.99211 + 3.99211i) q^{13} +(2.30084 - 1.30619i) q^{14} +(2.50554 - 5.93915i) q^{15} -1.00000 q^{16} +(-3.39509 - 3.39509i) q^{17} +(3.75491 + 3.75491i) q^{18} +4.95398 q^{19} +(0.842227 + 2.07139i) q^{20} +(6.63275 - 3.76542i) q^{21} +(0.707107 - 0.707107i) q^{22} +(-2.50907 - 2.50907i) q^{23} -2.88275 q^{24} +(3.58131 - 3.48916i) q^{25} -5.64570i q^{26} +(4.70924 + 4.70924i) q^{27} +(-0.703324 + 2.55056i) q^{28} +7.25017i q^{29} +(2.42793 + 5.97130i) q^{30} -3.87087i q^{31} +(0.707107 - 0.707107i) q^{32} +(2.03841 - 2.03841i) q^{33} +4.80139 q^{34} +(5.87555 - 0.691287i) q^{35} -5.31025 q^{36} +(-2.92514 + 2.92514i) q^{37} +(-3.50299 + 3.50299i) q^{38} -16.2751i q^{39} +(-2.06024 - 0.869149i) q^{40} +4.22571i q^{41} +(-2.02751 + 7.35261i) q^{42} +(1.04912 + 1.04912i) q^{43} +1.00000i q^{44} +(4.47243 + 10.9996i) q^{45} +3.54836 q^{46} +(6.21956 + 6.21956i) q^{47} +(2.03841 - 2.03841i) q^{48} +(6.01067 + 3.58774i) q^{49} +(-0.0651599 + 4.99958i) q^{50} +13.8412 q^{51} +(3.99211 + 3.99211i) q^{52} +(-0.793267 - 0.793267i) q^{53} -6.65986 q^{54} +(2.07139 - 0.842227i) q^{55} +(-1.30619 - 2.30084i) q^{56} +(-10.0982 + 10.0982i) q^{57} +(-5.12665 - 5.12665i) q^{58} -8.39914 q^{59} +(-5.93915 - 2.50554i) q^{60} +12.9348i q^{61} +(2.73712 + 2.73712i) q^{62} +(-3.73483 + 13.5441i) q^{63} +1.00000i q^{64} +(4.90696 - 11.6315i) q^{65} +2.88275i q^{66} +(3.04387 - 3.04387i) q^{67} +(-3.39509 + 3.39509i) q^{68} +10.2290 q^{69} +(-3.66583 + 4.64346i) q^{70} -9.47305 q^{71} +(3.75491 - 3.75491i) q^{72} +(8.93324 - 8.93324i) q^{73} -4.13677i q^{74} +(-0.187840 + 14.4125i) q^{75} -4.95398i q^{76} +(2.55056 + 0.703324i) q^{77} +(11.5083 + 11.5083i) q^{78} -4.65746i q^{79} +(2.07139 - 0.842227i) q^{80} -3.26798 q^{81} +(-2.98803 - 2.98803i) q^{82} +(10.6779 - 10.6779i) q^{83} +(-3.76542 - 6.63275i) q^{84} +(9.89200 + 4.17312i) q^{85} -1.48368 q^{86} +(-14.7788 - 14.7788i) q^{87} +(-0.707107 - 0.707107i) q^{88} -16.0121 q^{89} +(-10.9404 - 4.61540i) q^{90} +(12.9899 - 7.37436i) q^{91} +(-2.50907 + 2.50907i) q^{92} +(7.89044 + 7.89044i) q^{93} -8.79578 q^{94} +(-10.2616 + 4.17237i) q^{95} +2.88275i q^{96} +(5.64356 + 5.64356i) q^{97} +(-6.78710 + 1.71327i) q^{98} +5.31025i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) \) 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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