LMFDB - Embedded newform 187.2.h.a.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(100,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("187.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.h (of order $8$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			100.3
Character	$\chi$	$=$	187.100
Dual form			187.2.h.a.144.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08694 - 1.08694i) q^{2} +(1.18631 + 2.86400i) q^{3} +0.362879i q^{4} +(3.41797 - 1.41577i) q^{5} +(1.82355 - 4.40244i) q^{6} +(0.0878391 + 0.0363841i) q^{7} +(-1.77945 + 1.77945i) q^{8} +(-4.67384 + 4.67384i) q^{9} +O(q^{10})$	\(q+(-1.08694 - 1.08694i) q^{2} +(1.18631 + 2.86400i) q^{3} +0.362879i q^{4} +(3.41797 - 1.41577i) q^{5} +(1.82355 - 4.40244i) q^{6} +(0.0878391 + 0.0363841i) q^{7} +(-1.77945 + 1.77945i) q^{8} +(-4.67384 + 4.67384i) q^{9} +(-5.25399 - 2.17627i) q^{10} +(0.382683 - 0.923880i) q^{11} +(-1.03929 + 0.430486i) q^{12} -0.896265i q^{13} +(-0.0559285 - 0.135023i) q^{14} +(8.10952 + 8.10952i) q^{15} +4.59408 q^{16} +(3.99044 + 1.03750i) q^{17} +10.1604 q^{18} +(-2.70730 - 2.70730i) q^{19} +(0.513753 + 1.24031i) q^{20} +0.294734i q^{21} +(-1.42016 + 0.588248i) q^{22} +(-1.50048 + 3.62249i) q^{23} +(-7.20733 - 2.98537i) q^{24} +(6.14258 - 6.14258i) q^{25} +(-0.974187 + 0.974187i) q^{26} +(-10.3385 - 4.28235i) q^{27} +(-0.0132031 + 0.0318750i) q^{28} +(-4.87355 + 2.01869i) q^{29} -17.6291i q^{30} +(1.63494 + 3.94708i) q^{31} +(-1.43458 - 1.43458i) q^{32} +3.09997 q^{33} +(-3.20967 - 5.46507i) q^{34} +0.351743 q^{35} +(-1.69604 - 1.69604i) q^{36} +(-4.05299 - 9.78477i) q^{37} +5.88536i q^{38} +(2.56690 - 1.06325i) q^{39} +(-3.56282 + 8.60141i) q^{40} +(-5.55416 - 2.30061i) q^{41} +(0.320358 - 0.320358i) q^{42} +(4.77077 - 4.77077i) q^{43} +(0.335257 + 0.138868i) q^{44} +(-9.35797 + 22.5921i) q^{45} +(5.56836 - 2.30649i) q^{46} +9.15596i q^{47} +(5.44999 + 13.1574i) q^{48} +(-4.94336 - 4.94336i) q^{49} -13.3532 q^{50} +(1.76249 + 12.6594i) q^{51} +0.325236 q^{52} +(-4.58457 - 4.58457i) q^{53} +(6.58268 + 15.8920i) q^{54} -3.69958i q^{55} +(-0.221049 + 0.0915617i) q^{56} +(4.54202 - 10.9654i) q^{57} +(7.49145 + 3.10306i) q^{58} +(-0.815936 + 0.815936i) q^{59} +(-2.94278 + 2.94278i) q^{60} +(-13.1652 - 5.45322i) q^{61} +(2.51317 - 6.06732i) q^{62} +(-0.580600 + 0.240492i) q^{63} -6.06954i q^{64} +(-1.26890 - 3.06341i) q^{65} +(-3.36948 - 3.36948i) q^{66} +2.79934 q^{67} +(-0.376487 + 1.44805i) q^{68} -12.1548 q^{69} +(-0.382324 - 0.382324i) q^{70} +(-2.14136 - 5.16970i) q^{71} -16.6338i q^{72} +(5.71097 - 2.36556i) q^{73} +(-6.23011 + 15.0408i) q^{74} +(24.8793 + 10.3053i) q^{75} +(0.982425 - 0.982425i) q^{76} +(0.0672291 - 0.0672291i) q^{77} +(-3.94575 - 1.63439i) q^{78} +(-1.90626 + 4.60211i) q^{79} +(15.7024 - 6.50415i) q^{80} -14.8602i q^{81} +(3.53642 + 8.53767i) q^{82} +(7.88398 + 7.88398i) q^{83} -0.106953 q^{84} +(15.1081 - 2.10340i) q^{85} -10.3711 q^{86} +(-11.5630 - 11.5630i) q^{87} +(0.963033 + 2.32497i) q^{88} +7.13000i q^{89} +(34.7279 - 14.3848i) q^{90} +(0.0326098 - 0.0787271i) q^{91} +(-1.31453 - 0.544494i) q^{92} +(-9.36491 + 9.36491i) q^{93} +(9.95198 - 9.95198i) q^{94} +(-13.0864 - 5.42056i) q^{95} +(2.40679 - 5.81050i) q^{96} +(2.41637 - 1.00089i) q^{97} +10.7463i q^{98} +(2.52947 + 6.10667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 16 q^{6}+O(q^{10}) $ 56 * q - 16 * q^6	$ 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) $ 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−1.08694	−	1.08694i	−0.768583	−	0.768583i	0.209274	−	0.977857i	$-0.432890\pi$
$2$	−1.08694	−	1.08694i	−0.768583	−	0.768583i	−0.977857	+	0.209274i	$0.932890\pi$
$3$	1.18631	+	2.86400i	0.684915	+	1.65353i	0.754783	+	0.655974i	$0.227742\pi$
$3$	1.18631	+	2.86400i	0.684915	+	1.65353i	−0.0698684	+	0.997556i	$0.522258\pi$
$4$			0.362879i			0.181440i
$5$	3.41797	−	1.41577i	1.52856	−	0.633151i	0.549278	−	0.835640i	$-0.314903\pi$
$5$	3.41797	−	1.41577i	1.52856	−	0.633151i	0.979285	+	0.202489i	$0.0649029\pi$
$6$	1.82355	−	4.40244i	0.744462	−	1.79729i
$7$	0.0878391	+	0.0363841i	0.0332001	+	0.0137519i	0.399222	−	0.916854i	$-0.369280\pi$
$7$	0.0878391	+	0.0363841i	0.0332001	+	0.0137519i	−0.366022	+	0.930606i	$0.619280\pi$
$8$	−1.77945	+	1.77945i	−0.629132	+	0.629132i
$9$	−4.67384	+	4.67384i	−1.55795	+	1.55795i
$10$	−5.25399	−	2.17627i	−1.66146	−	0.688198i
$11$	0.382683	−	0.923880i	0.115383	−	0.278560i
$11$	0.382683	−	0.923880i	0.115383	−	0.278560i
$12$	−1.03929	+	0.430486i	−0.300016	+	0.124271i
$13$		−	0.896265i		−	0.248579i	−0.992246	−	0.124290i	$-0.960335\pi$
$13$		−	0.896265i		−	0.248579i	0.992246	−	0.124290i	$-0.0396652\pi$
$14$	−0.0559285	−	0.135023i	−0.0149475	−	0.0360865i
$15$	8.10952	+	8.10952i	2.09387	+	2.09387i
$16$	4.59408			1.14852
$17$	3.99044	+	1.03750i	0.967823	+	0.251631i
$17$	3.99044	+	1.03750i	0.967823	+	0.251631i
$18$	10.1604			2.39483
$19$	−2.70730	−	2.70730i	−0.621098	−	0.621098i	0.324714	−	0.945812i	$-0.394732\pi$
$19$	−2.70730	−	2.70730i	−0.621098	−	0.621098i	−0.945812	+	0.324714i	$0.894732\pi$
$20$	0.513753	+	1.24031i	0.114879	+	0.277342i
$21$			0.294734i			0.0643162i
$22$	−1.42016	+	0.588248i	−0.302778	+	0.125415i
$23$	−1.50048	+	3.62249i	−0.312872	+	0.755341i	0.686724	+	0.726919i	$0.259048\pi$
$23$	−1.50048	+	3.62249i	−0.312872	+	0.755341i	−0.999596	+	0.0284222i	$0.990952\pi$
$24$	−7.20733	−	2.98537i	−1.47119	−	0.609387i
$25$	6.14258	−	6.14258i	1.22852	−	1.22852i
$26$	−0.974187	+	0.974187i	−0.191054	+	0.191054i
$27$	−10.3385	−	4.28235i	−1.98965	−	0.824139i
$28$	−0.0132031	+	0.0318750i	−0.00249514	+	0.00602381i
$29$	−4.87355	+	2.01869i	−0.904995	+	0.374861i	−0.786139	−	0.618050i	$-0.787923\pi$
$29$	−4.87355	+	2.01869i	−0.904995	+	0.374861i	−0.118856	+	0.992911i	$0.537923\pi$
$30$		−	17.6291i		−	3.21863i
$31$	1.63494	+	3.94708i	0.293643	+	0.708917i	0.999999	+	0.00106063i	$0.000337608\pi$
$31$	1.63494	+	3.94708i	0.293643	+	0.708917i	−0.706356	+	0.707856i	$0.749662\pi$
$32$	−1.43458	−	1.43458i	−0.253601	−	0.253601i
$33$	3.09997			0.539636
$34$	−3.20967	−	5.46507i	−0.550454	−	0.937252i
$35$	0.351743			0.0594554
$36$	−1.69604	−	1.69604i	−0.282674	−	0.282674i
$37$	−4.05299	−	9.78477i	−0.666307	−	1.60861i	−0.787741	−	0.616007i	$-0.788749\pi$
$37$	−4.05299	−	9.78477i	−0.666307	−	1.60861i	0.121434	−	0.992600i	$-0.461251\pi$
$38$			5.88536i			0.954731i
$39$	2.56690	−	1.06325i	0.411033	−	0.170256i
$40$	−3.56282	+	8.60141i	−0.563331	+	1.36000i
$41$	−5.55416	−	2.30061i	−0.867414	−	0.359295i	−0.0958114	−	0.995400i	$-0.530545\pi$
$41$	−5.55416	−	2.30061i	−0.867414	−	0.359295i	−0.771603	+	0.636105i	$0.780545\pi$
$42$	0.320358	−	0.320358i	0.0494323	−	0.0494323i
$43$	4.77077	−	4.77077i	0.727536	−	0.727536i	−0.242592	−	0.970128i	$-0.577998\pi$
$43$	4.77077	−	4.77077i	0.727536	−	0.727536i	0.970128	+	0.242592i	$0.0779976\pi$
$44$	0.335257	+	0.138868i	0.0505419	+	0.0209351i
$45$	−9.35797	+	22.5921i	−1.39500	+	3.36784i
$46$	5.56836	−	2.30649i	0.821010	−	0.340074i
$47$			9.15596i			1.33553i	0.744371	+	0.667767i	$0.232750\pi$
$47$			9.15596i			1.33553i	−0.744371	+	0.667767i	$0.767250\pi$
$48$	5.44999	+	13.1574i	0.786638	+	1.89911i
$49$	−4.94336	−	4.94336i	−0.706194	−	0.706194i
$50$	−13.3532			−1.88843
$51$	1.76249	+	12.6594i	0.246798	+	1.77267i
$52$	0.325236			0.0451021
$53$	−4.58457	−	4.58457i	−0.629739	−	0.629739i	0.318264	−	0.948002i	$-0.396900\pi$
$53$	−4.58457	−	4.58457i	−0.629739	−	0.629739i	−0.948002	+	0.318264i	$0.896900\pi$
$54$	6.58268	+	15.8920i	0.895790	+	2.16263i
$55$		−	3.69958i		−	0.498852i
$56$	−0.221049	+	0.0915617i	−0.0295390	+	0.0122354i
$57$	4.54202	−	10.9654i	0.601605	−	1.45240i
$58$	7.49145	+	3.10306i	0.983676	+	0.407452i
$59$	−0.815936	+	0.815936i	−0.106226	+	0.106226i	−0.758222	−	0.651996i	$-0.773932\pi$
$59$	−0.815936	+	0.815936i	−0.106226	+	0.106226i	0.651996	+	0.758222i	$0.273932\pi$
$60$	−2.94278	+	2.94278i	−0.379911	+	0.379911i
$61$	−13.1652	−	5.45322i	−1.68564	−	0.698214i	−0.686067	−	0.727538i	$-0.740664\pi$
$61$	−13.1652	−	5.45322i	−1.68564	−	0.698214i	−0.999570	+	0.0293246i	$0.990664\pi$
$62$	2.51317	−	6.06732i	0.319173	−	0.770551i
$63$	−0.580600	+	0.240492i	−0.0731487	+	0.0302992i
$64$		−	6.06954i		−	0.758693i
$65$	−1.26890	−	3.06341i	−0.157388	−	0.379969i
$66$	−3.36948	−	3.36948i	−0.414755	−	0.414755i
$67$	2.79934			0.341993			0.170997	−	0.985272i	$-0.445301\pi$
$67$	2.79934			0.341993			0.170997	+	0.985272i	$0.445301\pi$
$68$	−0.376487	+	1.44805i	−0.0456558	+	0.175602i
$69$	−12.1548			−1.46327
$70$	−0.382324	−	0.382324i	−0.0456964	−	0.0456964i
$71$	−2.14136	−	5.16970i	−0.254133	−	0.613531i	0.744397	−	0.667737i	$-0.232737\pi$
$71$	−2.14136	−	5.16970i	−0.254133	−	0.613531i	−0.998530	+	0.0542064i	$0.982737\pi$
$72$		−	16.6338i		−	1.96031i
$73$	5.71097	−	2.36556i	0.668418	−	0.276868i	−0.0225580	−	0.999746i	$-0.507181\pi$
$73$	5.71097	−	2.36556i	0.668418	−	0.276868i	0.690976	+	0.722878i	$0.257181\pi$
$74$	−6.23011	+	15.0408i	−0.724236	+	1.74846i
$75$	24.8793	+	10.3053i	2.87282	+	1.18996i
$76$	0.982425	−	0.982425i	0.112692	−	0.112692i
$77$	0.0672291	−	0.0672291i	0.00766147	−	0.00766147i
$78$	−3.94575	−	1.63439i	−0.446769	−	0.185058i
$79$	−1.90626	+	4.60211i	−0.214471	+	0.517778i	−0.994101	−	0.108463i	$-0.965407\pi$
$79$	−1.90626	+	4.60211i	−0.214471	+	0.517778i	0.779630	+	0.626241i	$0.215407\pi$
$80$	15.7024	−	6.50415i	1.75558	−	0.727186i
$81$		−	14.8602i		−	1.65113i
$82$	3.53642	+	8.53767i	0.390532	+	0.942827i
$83$	7.88398	+	7.88398i	0.865379	+	0.865379i	0.991957	−	0.126578i	$-0.0403993\pi$
$83$	7.88398	+	7.88398i	0.865379	+	0.865379i	−0.126578	+	0.991957i	$0.540399\pi$
$84$	−0.106953			−0.0116695
$85$	15.1081	−	2.10340i	1.63870	−	0.228146i
$86$	−10.3711			−1.11834
$87$	−11.5630	−	11.5630i	−1.23969	−	1.23969i
$88$	0.963033	+	2.32497i	0.102660	+	0.247842i
$89$			7.13000i			0.755778i	0.925851	+	0.377889i	$0.123350\pi$
$89$			7.13000i			0.755778i	−0.925851	+	0.377889i	$0.876650\pi$
$90$	34.7279	−	14.3848i	3.66064	−	1.51629i
$91$	0.0326098	−	0.0787271i	0.00341844	−	0.00825284i
$92$	−1.31453	−	0.544494i	−0.137049	−	0.0567675i
$93$	−9.36491	+	9.36491i	−0.971095	+	0.971095i
$94$	9.95198	−	9.95198i	1.02647	−	1.02647i
$95$	−13.0864	−	5.42056i	−1.34264	−	0.556138i
$96$	2.40679	−	5.81050i	0.245642	−	0.593032i
$97$	2.41637	−	1.00089i	0.245345	−	0.101625i	−0.256622	−	0.966512i	$-0.582610\pi$
$97$	2.41637	−	1.00089i	0.245345	−	0.101625i	0.501968	+	0.864886i	$0.332610\pi$
$98$			10.7463i			1.08554i
$99$	2.52947	+	6.10667i	0.254221	+	0.613744i
$100$	2.22901	+	2.22901i	0.222901	+	0.222901i
$101$	0.0982066			0.00977192			0.00488596	−	0.999988i	$-0.498445\pi$
$101$	0.0982066			0.00977192			0.00488596	+	0.999988i	$0.498445\pi$
$102$	11.8443	−	15.6757i	1.17276	−	1.55213i
$103$	−9.63768			−0.949629			−0.474814	−	0.880086i	$-0.657485\pi$
$103$	−9.63768			−0.949629			−0.474814	+	0.880086i	$0.657485\pi$
$104$	1.59486	+	1.59486i	0.156389	+	0.156389i
$105$	0.417275	+	1.00739i	0.0407219	+	0.0983113i
$106$			9.96630i			0.968013i
$107$	−5.17740	+	2.14455i	−0.500518	+	0.207321i	−0.618635	−	0.785678i	$-0.712314\pi$
$107$	−5.17740	+	2.14455i	−0.500518	+	0.207321i	0.118117	+	0.993000i	$0.462314\pi$
$108$	1.55398	−	3.75163i	0.149531	−	0.361001i
$109$	16.3220	+	6.76079i	1.56336	+	0.647566i	0.985670	−	0.168687i	$-0.0539527\pi$
$109$	16.3220	+	6.76079i	1.56336	+	0.647566i	0.577694	+	0.816253i	$0.303953\pi$
$110$	−4.02123	+	4.02123i	−0.383409	+	0.383409i
$111$	23.2155	−	23.2155i	2.20352	−	2.20352i
$112$	0.403540	+	0.167152i	0.0381309	+	0.0157943i
$113$	5.48682	−	13.2464i	0.516157	−	1.24611i	−0.424090	−	0.905620i	$-0.639406\pi$
$113$	5.48682	−	13.2464i	0.516157	−	1.24611i	0.940247	−	0.340493i	$-0.110594\pi$
$114$	−16.8557	+	6.98184i	−1.57868	+	0.653909i
$115$			14.5059i			1.35268i
$116$	−0.732540	−	1.76851i	−0.0680147	−	0.164202i
$117$	4.18900	+	4.18900i	0.387274	+	0.387274i
$118$	1.77375			0.163287
$119$	0.312768	+	0.236322i	0.0286714	+	0.0216636i
$120$	−28.8610			−2.63464
$121$	−0.707107	−	0.707107i	−0.0642824	−	0.0642824i
$122$	8.38251	+	20.2372i	0.758917	+	1.83219i
$123$		−	18.6363i		−	1.68038i
$124$	−1.43231	+	0.593284i	−0.128626	+	0.0532785i
$125$	5.21982	−	12.6018i	0.466875	−	1.12714i
$126$	0.892479	+	0.369677i	0.0795083	+	0.0329334i
$127$	−1.37333	+	1.37333i	−0.121864	+	0.121864i	−0.765408	−	0.643545i	$-0.777463\pi$
$127$	−1.37333	+	1.37333i	−0.121864	+	0.121864i	0.643545	+	0.765408i	$0.277463\pi$
$128$	−9.46640	+	9.46640i	−0.836719	+	0.836719i
$129$	19.3231	+	8.00389i	1.70130	+	0.704703i
$130$	−1.95052	+	4.70896i	−0.171072	+	0.413003i
$131$	3.44619	−	1.42746i	0.301095	−	0.124718i	−0.227021	−	0.973890i	$-0.572899\pi$
$131$	3.44619	−	1.42746i	0.301095	−	0.124718i	0.528116	+	0.849172i	$0.322899\pi$
$132$			1.12492i			0.0979113i
$133$	−0.139304	−	0.336310i	−0.0120792	−	0.0291618i
$134$	−3.04271	−	3.04271i	−0.262850	−	0.262850i
$135$	−41.3995			−3.56310
$136$	−8.94698	+	5.25462i	−0.767197	+	0.450580i
$137$	10.3384			0.883273			0.441636	−	0.897194i	$-0.354398\pi$
$137$	10.3384			0.883273			0.441636	+	0.897194i	$0.354398\pi$
$138$	13.2116	+	13.2116i	1.12464	+	1.12464i
$139$	4.51381	+	10.8973i	0.382857	+	0.924298i	0.991411	+	0.130785i	$0.0417498\pi$
$139$	4.51381	+	10.8973i	0.382857	+	0.924298i	−0.608554	+	0.793512i	$0.708250\pi$
$140$			0.127640i			0.0107876i
$141$	−26.2226	+	10.8618i	−2.20835	+	0.914727i
$142$	−3.29163	+	7.94669i	−0.276227	+	0.666872i
$143$	−0.828041	−	0.342986i	−0.0692443	−	0.0286819i
$144$	−21.4720	+	21.4720i	−1.78933	+	1.78933i
$145$	−13.7996	+	13.7996i	−1.14600	+	1.14600i
$146$	−8.77870	−	3.63626i	−0.726531	−	0.300939i
$147$	8.29343	−	20.0221i	0.684030	−	1.65140i
$148$	3.55069	−	1.47074i	0.291865	−	0.120894i
$149$			10.0583i			0.824007i	0.911182	+	0.412003i	$0.135171\pi$
$149$			10.0583i			0.824007i	−0.911182	+	0.412003i	$0.864829\pi$
$150$	−15.8410	−	38.2436i	−1.29341	−	3.12258i
$151$	4.82850	+	4.82850i	0.392938	+	0.392938i	0.875733	−	0.482795i	$-0.160379\pi$
$151$	4.82850	+	4.82850i	0.392938	+	0.392938i	−0.482795	+	0.875733i	$0.660379\pi$
$152$	9.63504			0.781505
$153$	−23.4998	+	13.8016i	−1.89985	+	1.11579i
$154$	−0.146148			−0.0117770
$155$	11.1763	+	11.1763i	0.897703	+	0.897703i
$156$	0.385830	+	0.931476i	0.0308911	+	0.0745777i
$157$		−	13.5217i		−	1.07915i	−0.841938	−	0.539575i	$-0.818585\pi$
$157$		−	13.5217i		−	1.07915i	0.841938	−	0.539575i	$-0.181415\pi$
$158$	7.07421	−	2.93023i	0.562794	−	0.233117i
$159$	7.69149	−	18.5689i	0.609975	−	1.47261i
$160$	−6.93440	−	2.87232i	−0.548212	−	0.227077i
$161$	−0.263602	+	0.263602i	−0.0207748	+	0.0207748i
$162$	−16.1522	+	16.1522i	−1.26903	+	1.26903i
$163$	−7.02455	−	2.90966i	−0.550205	−	0.227902i	0.0902216	−	0.995922i	$-0.471242\pi$
$163$	−7.02455	−	2.90966i	−0.550205	−	0.227902i	−0.640427	+	0.768019i	$0.721242\pi$
$164$	0.834843	−	2.01549i	0.0651903	−	0.157383i
$165$	10.5956	−	4.38884i	0.824866	−	0.341671i
$166$		−	17.1388i		−	1.33023i
$167$	4.48758	+	10.8340i	0.347259	+	0.838358i	0.996941	+	0.0781523i	$0.0249021\pi$
$167$	4.48758	+	10.8340i	0.347259	+	0.838358i	−0.649682	+	0.760206i	$0.725098\pi$
$168$	−0.524465	−	0.524465i	−0.0404634	−	0.0404634i
$169$	12.1967			0.938208
$170$	−18.7078	−	14.1353i	−1.43482	−	1.08413i
$171$	25.3070			1.93528
$172$	1.73122	+	1.73122i	0.132004	+	0.132004i
$173$	6.57288	+	15.8683i	0.499727	+	1.20645i	0.949631	+	0.313370i	$0.101458\pi$
$173$	6.57288	+	15.8683i	0.499727	+	1.20645i	−0.449904	+	0.893077i	$0.648542\pi$
$174$			25.1367i			1.90561i
$175$	0.763051	−	0.316066i	0.0576812	−	0.0238923i
$176$	1.75808	−	4.24437i	0.132520	−	0.319932i
$177$	−3.30479	−	1.36889i	−0.248403	−	0.102892i
$178$	7.74988	−	7.74988i	0.580878	−	0.580878i
$179$	11.4597	−	11.4597i	0.856536	−	0.856536i	−0.134392	−	0.990928i	$-0.542908\pi$
$179$	11.4597	−	11.4597i	0.856536	−	0.856536i	0.990928	+	0.134392i	$0.0429083\pi$
$180$	−8.19822	−	3.39581i	−0.611059	−	0.253109i
$181$	−3.73347	+	9.01340i	−0.277507	+	0.669961i	−0.999765	−	0.0216623i	$-0.993104\pi$
$181$	−3.73347	+	9.01340i	−0.277507	+	0.669961i	0.722258	+	0.691623i	$0.243104\pi$
$182$	−0.121017	+	0.0501267i	−0.00897035	+	0.00371564i
$183$		−	44.1744i		−	3.26547i
$184$	−3.77601	−	9.11608i	−0.278371	−	0.672047i
$185$	−27.7060	−	27.7060i	−2.03698	−	2.03698i
$186$	20.3582			1.49273
$187$	2.48560	−	3.28965i	0.181765	−	0.240563i
$188$	−3.32251			−0.242319
$189$	−0.752315	−	0.752315i	−0.0547229	−	0.0547229i
$190$	8.33231	+	20.1160i	0.604489	+	1.45937i
$191$			6.79216i			0.491463i	0.969338	+	0.245732i	$0.0790282\pi$
$191$			6.79216i			0.491463i	−0.969338	+	0.245732i	$0.920972\pi$
$192$	17.3832	−	7.20034i	1.25452	−	0.519640i
$193$	−4.10227	+	9.90376i	−0.295288	+	0.712888i	0.704706	+	0.709499i	$0.251079\pi$
$193$	−4.10227	+	9.90376i	−0.295288	+	0.712888i	−0.999994	+	0.00338905i	$0.998921\pi$
$194$	−3.71437	−	1.53854i	−0.266676	−	0.110461i
$195$	7.26828	−	7.26828i	0.520492	−	0.520492i
$196$	1.79384	−	1.79384i	0.128132	−	0.128132i
$197$	16.3397	+	6.76813i	1.16416	+	0.482209i	0.879257	−	0.476348i	$-0.158040\pi$
$197$	16.3397	+	6.76813i	1.16416	+	0.482209i	0.284899	+	0.958557i	$0.408040\pi$
$198$	3.88821	−	9.38697i	0.276323	−	0.667103i
$199$	−21.5784	+	8.93809i	−1.52966	+	0.633604i	−0.979498	−	0.201456i	$-0.935433\pi$
$199$	−21.5784	+	8.93809i	−1.52966	+	0.633604i	−0.550158	+	0.835060i	$0.685433\pi$
$200$			21.8608i			1.54580i
$201$	3.32087	+	8.01730i	0.234236	+	0.565497i
$202$	−0.106745	−	0.106745i	−0.00751053	−	0.00751053i
$203$	−0.501536			−0.0352009
$204$	−4.59384	+	0.639571i	−0.321633	+	0.0447789i
$205$	−22.2411			−1.55338
$206$	10.4756	+	10.4756i	0.729868	+	0.729868i
$207$	−9.91792	−	23.9440i	−0.689343	−	1.66422i
$208$		−	4.11751i		−	0.285498i
$209$	−3.53726	+	1.46518i	−0.244678	+	0.101349i
$210$	0.641421	−	1.54853i	0.0442623	−	0.106859i
$211$	−23.1276	−	9.57975i	−1.59217	−	0.659497i	−0.601886	−	0.798582i	$-0.705584\pi$
$211$	−23.1276	−	9.57975i	−1.59217	−	0.659497i	−0.990280	+	0.139085i	$0.955584\pi$
$212$	1.66364	−	1.66364i	0.114260	−	0.114260i
$213$	12.2657	−	12.2657i	0.840433	−	0.840433i
$214$	7.95852	+	3.29653i	0.544033	+	0.225346i
$215$	9.55205	−	23.0607i	0.651444	−	1.57273i
$216$	26.0171	−	10.7766i	1.77024	−	0.733258i
$217$			0.406194i			0.0275742i
$218$	−10.3925	−	25.0896i	−0.703866	−	1.69928i
$219$	13.5499	+	13.5499i	0.915619	+	0.915619i
$220$	1.34250			0.0905115
$221$	0.929874	−	3.57649i	0.0625501	−	0.240581i
$222$	−50.4677			−3.38717
$223$	3.65038	+	3.65038i	0.244448	+	0.244448i	0.818687	−	0.574240i	$-0.194702\pi$
$223$	3.65038	+	3.65038i	0.244448	+	0.244448i	−0.574240	+	0.818687i	$0.694702\pi$
$224$	−0.0738164	−	0.178209i	−0.00493207	−	0.0119071i
$225$			57.4189i			3.82793i
$226$	−20.3619	+	8.43416i	−1.35445	+	0.561032i
$227$	5.58265	−	13.4777i	0.370534	−	0.894547i	−0.623126	−	0.782121i	$-0.714138\pi$
$227$	5.58265	−	13.4777i	0.370534	−	0.894547i	0.993660	−	0.112426i	$-0.0358622\pi$
$228$	3.97912	+	1.64821i	0.263524	+	0.109155i
$229$	−2.68349	+	2.68349i	−0.177330	+	0.177330i	−0.790191	−	0.612861i	$-0.790019\pi$
$229$	−2.68349	+	2.68349i	−0.177330	+	0.177330i	0.612861	+	0.790191i	$0.290019\pi$
$230$	15.7670	−	15.7670i	1.03965	−	1.03965i
$231$	0.272299	+	0.112790i	0.0179159	+	0.00742102i
$232$	5.08008	−	12.2644i	0.333524	−	0.805198i
$233$	6.55846	−	2.71660i	0.429659	−	0.177971i	−0.157364	−	0.987541i	$-0.550300\pi$
$233$	6.55846	−	2.71660i	0.429659	−	0.177971i	0.587023	+	0.809570i	$0.300300\pi$
$234$		−	9.10640i		−	0.595304i
$235$	12.9627	+	31.2948i	0.845595	+	2.04145i
$236$	−0.296086	−	0.296086i	−0.0192736	−	0.0192736i
$237$	−15.4419			−1.00306
$238$	−0.0830926	−	0.596828i	−0.00538609	−	0.0386866i
$239$	10.9616			0.709046			0.354523	−	0.935047i	$-0.384643\pi$
$239$	10.9616			0.709046			0.354523	+	0.935047i	$0.384643\pi$
$240$	37.2558	+	37.2558i	2.40485	+	2.40485i
$241$	2.58086	+	6.23075i	0.166248	+	0.401358i	0.984945	−	0.172868i	$-0.0553033\pi$
$241$	2.58086	+	6.23075i	0.166248	+	0.401358i	−0.818697	+	0.574225i	$0.805303\pi$
$242$			1.53717i			0.0988128i
$243$	11.5441	−	4.78172i	0.740554	−	0.306748i
$244$	1.97886	−	4.77740i	0.126684	−	0.305841i
$245$	−23.8949	−	9.89759i	−1.52659	−	0.632334i
$246$	−20.2566	+	20.2566i	−1.29151	+	1.29151i
$247$	−2.42646	+	2.42646i	−0.154392	+	0.154392i
$248$	−9.93294	−	4.11436i	−0.630742	−	0.261262i
$249$	−13.2269	+	31.9325i	−0.838220	+	2.02364i
$250$	−19.3710	+	8.02373i	−1.22513	+	0.507465i
$251$			17.1003i			1.07936i	0.841869	+	0.539682i	$0.181456\pi$
$251$			17.1003i			1.07936i	−0.841869	+	0.539682i	$0.818544\pi$
$252$	−0.0872697	−	0.210688i	−0.00549748	−	0.0132721i
$253$	2.77253	+	2.77253i	0.174308	+	0.174308i
$254$	2.98546			0.187325
$255$	23.9469	+	40.7742i	1.49961	+	2.55338i
$256$	8.43974			0.527484
$257$	−5.37665	−	5.37665i	−0.335386	−	0.335386i	0.519241	−	0.854628i	$-0.326215\pi$
$257$	−5.37665	−	5.37665i	−0.335386	−	0.335386i	−0.854628	+	0.519241i	$0.826215\pi$
$258$	−12.3033	−	29.7028i	−0.765970	−	1.84922i
$259$		−	1.00695i		−	0.0625688i
$260$	1.11165	−	0.460459i	0.0689414	−	0.0285565i
$261$	13.3432	−	32.2132i	0.825921	−	1.99395i
$262$	−5.29737	−	2.19424i	−0.327273	−	0.135561i
$263$	−2.74146	+	2.74146i	−0.169046	+	0.169046i	−0.786560	−	0.617514i	$-0.788140\pi$
$263$	−2.74146	+	2.74146i	−0.169046	+	0.169046i	0.617514	+	0.786560i	$0.288140\pi$
$264$	−5.51625	+	5.51625i	−0.339502	+	0.339502i
$265$	−22.1606	−	9.17922i	−1.36131	−	0.563875i
$266$	−0.214134	+	0.516964i	−0.0131294	+	0.0316971i
$267$	−20.4203	+	8.45837i	−1.24970	+	0.517644i
$268$			1.01582i			0.0620512i
$269$	−5.78979	−	13.9778i	−0.353009	−	0.852240i	−0.996246	−	0.0865724i	$-0.972409\pi$
$269$	−5.78979	−	13.9778i	−0.353009	−	0.852240i	0.643236	−	0.765668i	$-0.277591\pi$
$270$	44.9988	+	44.9988i	2.73854	+	2.73854i
$271$	5.54303			0.336715			0.168357	−	0.985726i	$-0.446154\pi$
$271$	5.54303			0.336715			0.168357	+	0.985726i	$0.446154\pi$
$272$	18.3324	+	4.76635i	1.11156	+	0.289003i
$273$	0.264160			0.0159877
$274$	−11.2373	−	11.2373i	−0.678869	−	0.678869i
$275$	−3.32434	−	8.02566i	−0.200465	−	0.483966i
$276$		−	4.41074i		−	0.265495i
$277$	16.5316	−	6.84760i	0.993285	−	0.411432i	0.173955	−	0.984754i	$-0.444345\pi$
$277$	16.5316	−	6.84760i	0.993285	−	0.411432i	0.819331	+	0.573321i	$0.194345\pi$
$278$	6.93848	−	16.7510i	0.416142	−	1.00466i
$279$	−26.0895	−	10.8066i	−1.56194	−	0.646975i
$280$	−0.625910	+	0.625910i	−0.0374053	+	0.0374053i
$281$	−3.00841	+	3.00841i	−0.179467	+	0.179467i	−0.791123	−	0.611657i	$-0.790503\pi$
$281$	−3.00841	+	3.00841i	−0.179467	+	0.179467i	0.611657	+	0.791123i	$0.290503\pi$
$282$	40.3086	+	16.6964i	2.40034	+	0.994253i
$283$	6.14797	−	14.8425i	0.365459	−	0.882296i	−0.629023	−	0.777387i	$-0.716545\pi$
$283$	6.14797	−	14.8425i	0.365459	−	0.882296i	0.994482	−	0.104909i	$-0.0334552\pi$
$284$	1.87598	−	0.777056i	0.111319	−	0.0461098i
$285$		−	43.9099i		−	2.60100i
$286$	0.527226	+	1.27284i	0.0311755	+	0.0752644i
$287$	−0.404167	−	0.404167i	−0.0238572	−	0.0238572i
$288$	13.4100			0.790194
$289$	14.8472	+	8.28015i	0.873364	+	0.487068i
$290$	29.9988			1.76159
$291$	5.73312	+	5.73312i	0.336082	+	0.336082i
$292$	0.858413	+	2.07239i	0.0502348	+	0.121278i
$293$		−	10.8283i		−	0.632596i	−0.948660	−	0.316298i	$-0.897560\pi$
$293$		−	10.8283i		−	0.632596i	0.948660	−	0.316298i	$-0.102440\pi$
$294$	−30.7773	+	12.7484i	−1.79497	+	0.743500i
$295$	−1.63367	+	3.94402i	−0.0951158	+	0.229630i
$296$	24.6236	+	10.1994i	1.43122	+	0.592831i
$297$	−7.91275	+	7.91275i	−0.459144	+	0.459144i
$298$	10.9328	−	10.9328i	0.633317	−	0.633317i
$299$	3.24671	+	1.34483i	0.187762	+	0.0777736i
$300$	−3.73960	+	9.02819i	−0.215906	+	0.521243i
$301$	0.592641	−	0.245480i	0.0341593	−	0.0141492i
$302$		−	10.4966i		−	0.604011i
$303$	0.116503	+	0.281264i	0.00669293	+	0.0161582i
$304$	−12.4376	−	12.4376i	−0.713343	−	0.713343i
$305$	−52.7189			−3.01868
$306$	40.5444	+	10.5414i	2.31777	+	0.602611i
$307$	2.87088			0.163850			0.0819250	−	0.996638i	$-0.473893\pi$
$307$	2.87088			0.163850			0.0819250	+	0.996638i	$0.473893\pi$
$308$	0.0243961	+	0.0243961i	0.00139009	+	0.00139009i
$309$	−11.4332	−	27.6023i	−0.650415	−	1.57024i
$310$		−	24.2960i		−	1.37992i
$311$	8.77149	−	3.63327i	0.497386	−	0.206024i	−0.119865	−	0.992790i	$-0.538246\pi$
$311$	8.77149	−	3.63327i	0.497386	−	0.206024i	0.617251	+	0.786766i	$0.288246\pi$
$312$	−2.67569	+	6.45968i	−0.151481	+	0.365707i
$313$	26.0317	+	10.7827i	1.47140	+	0.609473i	0.967177	−	0.254102i	$-0.0817800\pi$
$313$	26.0317	+	10.7827i	1.47140	+	0.609473i	0.504220	+	0.863575i	$0.331780\pi$
$314$	−14.6973	+	14.6973i	−0.829416	+	0.829416i
$315$	−1.64399	+	1.64399i	−0.0926284	+	0.0926284i
$316$	−1.67001	−	0.691741i	−0.0939455	−	0.0389135i
$317$	−7.82321	+	18.8869i	−0.439395	+	1.06079i	0.536763	+	0.843733i	$0.319647\pi$
$317$	−7.82321	+	18.8869i	−0.439395	+	1.06079i	−0.976158	+	0.217061i	$0.930353\pi$
$318$	−28.5435	+	11.8231i	−1.60064	+	0.663006i
$319$			5.27509i			0.295348i
$320$	−8.59307	−	20.7455i	−0.480367	−	1.15971i
$321$	−12.2840	−	12.2840i	−0.685624	−	0.685624i
$322$	0.573040			0.0319343
$323$	−7.99450	−	13.6122i	−0.444826	−	0.757400i
$324$	5.39246			0.299581
$325$	−5.50538	−	5.50538i	−0.305383	−	0.305383i
$326$	4.47264	+	10.7979i	0.247716	+	0.598040i
$327$			54.7666i			3.02860i
$328$	13.9772	−	5.78954i	0.771761	−	0.319674i
$329$	−0.333132	+	0.804251i	−0.0183661	+	0.0443398i
$330$	−16.2872	−	6.74638i	−0.896581	−	0.371376i
$331$	13.2236	−	13.2236i	0.726835	−	0.726835i	−0.243153	−	0.969988i	$-0.578182\pi$
$331$	13.2236	−	13.2236i	0.726835	−	0.726835i	0.969988	+	0.243153i	$0.0781817\pi$
$332$	−2.86093	+	2.86093i	−0.157014	+	0.157014i
$333$	64.6755	+	26.7895i	3.54420	+	1.46805i
$334$	6.89816	−	16.6536i	0.377450	−	0.911246i
$335$	9.56805	−	3.96321i	0.522758	−	0.216534i
$336$			1.35403i			0.0738684i
$337$	2.36607	+	5.71220i	0.128888	+	0.311163i	0.975129	−	0.221637i	$-0.0711399\pi$
$337$	2.36607	+	5.71220i	0.128888	+	0.311163i	−0.846241	+	0.532800i	$0.821140\pi$
$338$	−13.2571	−	13.2571i	−0.721091	−	0.721091i
$339$	44.4466			2.41401
$340$	0.763280	+	5.48240i	0.0413947	+	0.297325i
$341$	4.27229			0.231358
$342$	−27.5072	−	27.5072i	−1.48742	−	1.48742i
$343$	−0.509049	−	1.22895i	−0.0274861	−	0.0663572i
$344$			16.9787i			0.915432i
$345$	−41.5448	+	17.2084i	−2.23670	+	0.926471i
$346$	10.1036	−	24.3923i	0.543173	−	1.31134i
$347$	−17.2473	−	7.14405i	−0.925881	−	0.383513i	−0.131767	−	0.991281i	$-0.542065\pi$
$347$	−17.2473	−	7.14405i	−0.925881	−	0.383513i	−0.794115	+	0.607768i	$0.792065\pi$
$348$	4.19599	−	4.19599i	0.224929	−	0.224929i
$349$	13.6872	−	13.6872i	0.732658	−	0.732658i	−0.238488	−	0.971146i	$-0.576652\pi$
$349$	13.6872	−	13.6872i	0.732658	−	0.732658i	0.971146	+	0.238488i	$0.0766517\pi$
$350$	−1.17294	−	0.485846i	−0.0626960	−	0.0259696i
$351$	−3.83812	+	9.26604i	−0.204864	+	0.494585i
$352$	−1.87437	+	0.776391i	−0.0999044	+	0.0413818i
$353$		−	1.92803i		−	0.102619i	−0.998683	−	0.0513093i	$-0.983661\pi$
$353$		−	1.92803i		−	0.102619i	0.998683	−	0.0513093i	$-0.0163394\pi$
$354$	2.10421	+	5.08001i	0.111838	+	0.270000i
$355$	−14.6382	−	14.6382i	−0.776916	−	0.776916i
$356$	−2.58733			−0.137128
$357$	−0.305786	+	1.17612i	−0.0161839	+	0.0622467i
$358$	−24.9120			−1.31664
$359$	−19.0672	−	19.0672i	−1.00633	−	1.00633i	−0.999980	−	0.00634597i	$-0.997980\pi$
$359$	−19.0672	−	19.0672i	−1.00633	−	1.00633i	−0.00634597	−	0.999980i	$-0.502020\pi$
$360$	−23.5496	−	56.8537i	−1.24117	−	2.99645i
$361$		−	4.34101i		−	0.228474i
$362$	13.8551	−	5.73897i	0.728208	−	0.301634i
$363$	1.18631	−	2.86400i	0.0622650	−	0.150321i
$364$	0.0285684	+	0.0118334i	0.00149739	+	0.000620241i
$365$	16.1708	−	16.1708i	0.846419	−	0.846419i
$366$	−48.0150	+	48.0150i	−2.50978	+	2.50978i
$367$	26.2616	+	10.8779i	1.37084	+	0.567822i	0.942017	−	0.335564i	$-0.108927\pi$
$367$	26.2616	+	10.8779i	1.37084	+	0.567822i	0.428827	+	0.903386i	$0.358927\pi$
$368$	−6.89334	+	16.6420i	−0.359340	+	0.867523i
$369$	36.7120	−	15.2066i	1.91115	−	0.791624i
$370$			60.2294i			3.13118i
$371$	−0.235899	−	0.569510i	−0.0122472	−	0.0295675i
$372$	−3.39833	−	3.39833i	−0.176195	−	0.176195i
$373$	−7.32105			−0.379069			−0.189535	−	0.981874i	$-0.560698\pi$
$373$	−7.32105			−0.379069			−0.189535	+	0.981874i	$0.560698\pi$
$374$	−6.27735	+	0.873956i	−0.324594	+	0.0451912i
$375$	42.2837			2.18352
$376$	−16.2926	−	16.2926i	−0.840226	−	0.840226i
$377$	1.80928	+	4.36799i	0.0931827	+	0.224963i
$378$			1.63544i			0.0841182i
$379$	−11.5009	+	4.76381i	−0.590759	+	0.244700i	−0.657977	−	0.753038i	$-0.728588\pi$
$379$	−11.5009	+	4.76381i	−0.590759	+	0.244700i	0.0672180	+	0.997738i	$0.478588\pi$
$380$	1.96701	−	4.74878i	0.100905	−	0.243607i
$381$	−5.56242	−	2.30403i	−0.284972	−	0.118039i
$382$	7.38267	−	7.38267i	0.377730	−	0.377730i
$383$	−6.80764	+	6.80764i	−0.347854	+	0.347854i	−0.859310	−	0.511456i	$-0.829106\pi$
$383$	−6.80764	+	6.80764i	−0.347854	+	0.347854i	0.511456	+	0.859310i	$0.329106\pi$
$384$	−38.3418	−	15.8817i	−1.95662	−	0.810459i
$385$	0.134606	−	0.324968i	0.00686017	−	0.0165619i
$386$	15.2237	−	6.30587i	0.774867	−	0.320960i
$387$			44.5957i			2.26693i
$388$	0.363204	+	0.876852i	0.0184389	+	0.0445154i
$389$	−0.624000	−	0.624000i	−0.0316381	−	0.0316381i	0.691111	−	0.722749i	$-0.257122\pi$
$389$	−0.624000	−	0.624000i	−0.0316381	−	0.0316381i	−0.722749	+	0.691111i	$0.757122\pi$
$390$	−15.8004			−0.800083
$391$	−9.74591	+	12.8986i	−0.492872	+	0.652308i
$392$	17.5929			0.888577
$393$	8.17649	+	8.17649i	0.412449	+	0.412449i
$394$	−10.4037	−	25.1168i	−0.524133	−	1.26537i
$395$			18.4287i			0.927248i
$396$	−2.21599	+	0.917891i	−0.111357	+	0.0461258i
$397$	−4.90503	+	11.8418i	−0.246176	+	0.594322i	−0.997873	−	0.0651867i	$-0.979236\pi$
$397$	−4.90503	+	11.8418i	−0.246176	+	0.594322i	0.751697	+	0.659509i	$0.229236\pi$
$398$	33.1697	+	13.7393i	1.66264	+	0.688690i
$399$	0.797934	−	0.797934i	0.0399467	−	0.0399467i
$400$	28.2195	−	28.2195i	1.41097	−	1.41097i
$401$	2.78807	+	1.15485i	0.139229	+	0.0576707i	0.451210	−	0.892418i	$-0.350992\pi$
$401$	2.78807	+	1.15485i	0.139229	+	0.0576707i	−0.311981	+	0.950088i	$0.600992\pi$
$402$	5.10473	−	12.3239i	0.254601	−	0.614661i
$403$	3.53763	−	1.46534i	0.176222	−	0.0729935i
$404$			0.0356371i			0.00177301i
$405$	−21.0386	−	50.7917i	−1.04542	−	2.52386i
$406$	0.545140	+	0.545140i	0.0270548	+	0.0270548i
$407$	−10.5910			−0.524974
$408$	−25.6631	−	19.3905i	−1.27051	−	0.959975i
$409$	−19.9156			−0.984761			−0.492381	−	0.870380i	$-0.663873\pi$
$409$	−19.9156			−0.984761			−0.492381	+	0.870380i	$0.663873\pi$
$410$	24.1747	+	24.1747i	1.19390	+	1.19390i
$411$	12.2646	+	29.6093i	0.604967	+	1.46052i
$412$		−	3.49731i		−	0.172300i
$413$	−0.101358	+	0.0419840i	−0.00498751	+	0.00206590i
$414$	−15.2455	+	36.8059i	−0.749275	+	1.80891i
$415$	38.1091	+	15.7853i	1.87070	+	0.774870i
$416$	−1.28577	+	1.28577i	−0.0630399	+	0.0630399i
$417$	−25.8551	+	25.8551i	−1.26613	+	1.26613i
$418$	5.43736	+	2.25223i	0.265950	+	0.110160i
$419$	−8.98292	+	21.6867i	−0.438844	+	1.05946i	0.537504	+	0.843261i	$0.319367\pi$
$419$	−8.98292	+	21.6867i	−0.438844	+	1.05946i	−0.976349	+	0.216203i	$0.930633\pi$
$420$	−0.365561	+	0.151421i	−0.0178376	+	0.00738856i
$421$		−	7.34280i		−	0.357866i	−0.983861	−	0.178933i	$-0.942735\pi$
$421$		−	7.34280i		−	0.357866i	0.983861	−	0.178933i	$-0.0572645\pi$
$422$	14.7257	+	35.5509i	0.716834	+	1.73059i
$423$	−42.7935	−	42.7935i	−2.08069	−	2.08069i
$424$	16.3160			0.792377
$425$	30.8845	−	18.1387i	1.49812	−	0.879854i
$426$	−26.6642			−1.29188
$427$	−0.958012	−	0.958012i	−0.0463615	−	0.0463615i
$428$	−0.778212	−	1.87877i	−0.0376163	−	0.0908138i
$429$		−	2.77839i		−	0.134142i
$430$	−35.4481	+	14.6831i	−1.70946	+	0.708081i
$431$	−5.57883	+	13.4685i	−0.268723	+	0.648754i	−0.999424	−	0.0339438i	$-0.989193\pi$
$431$	−5.57883	+	13.4685i	−0.268723	+	0.648754i	0.730701	+	0.682697i	$0.239193\pi$
$432$	−47.4959	−	19.6734i	−2.28515	−	0.946539i
$433$	−23.2926	+	23.2926i	−1.11937	+	1.11937i	−0.127536	+	0.991834i	$0.540707\pi$
$433$	−23.2926	+	23.2926i	−1.11937	+	1.11937i	−0.991834	+	0.127536i	$0.959293\pi$
$434$	0.441509	−	0.441509i	0.0211931	−	0.0211931i
$435$	−55.8927	−	23.1515i	−2.67985	−	1.11003i
$436$	−2.45335	+	5.92292i	−0.117494	+	0.283656i
$437$	13.8694	−	5.74491i	0.663465	−	0.274816i
$438$		−	29.4559i		−	1.40746i
$439$	−7.20487	−	17.3941i	−0.343870	−	0.830174i	−0.997317	−	0.0732027i	$-0.976678\pi$
$439$	−7.20487	−	17.3941i	−0.343870	−	0.830174i	0.653448	−	0.756972i	$-0.273322\pi$
$440$	6.58323	+	6.58323i	0.313843	+	0.313843i
$441$	46.2090			2.20043
$442$	−4.89815	+	2.87671i	−0.232981	+	0.136831i
$443$	0.537124			0.0255195			0.0127598	−	0.999919i	$-0.495938\pi$
$443$	0.537124			0.0255195			0.0127598	+	0.999919i	$0.495938\pi$
$444$	8.42442	+	8.42442i	0.399805	+	0.399805i
$445$	10.0944	+	24.3701i	0.478522	+	1.15525i
$446$		−	7.93549i		−	0.375756i
$447$	−28.8069	+	11.9322i	−1.36252	+	0.564374i
$448$	0.220835	−	0.533143i	0.0104335	−	0.0251886i
$449$	16.9681	+	7.02843i	0.800776	+	0.331692i	0.745267	−	0.666766i	$-0.232322\pi$
$449$	16.9681	+	7.02843i	0.800776	+	0.331692i	0.0555089	+	0.998458i	$0.482322\pi$
$450$	62.4109	−	62.4109i	2.94208	−	2.94208i
$451$	−4.25097	+	4.25097i	−0.200170	+	0.200170i
$452$	4.80683	+	1.99105i	0.226094	+	0.0936513i
$453$	−8.10073	+	19.5569i	−0.380606	+	0.918864i
$454$	−20.7175	+	8.58146i	−0.972320	+	0.402748i
$455$		−	0.315255i		−	0.0147794i
$456$	11.4301	+	27.5947i	0.535264	+	1.29224i
$457$	5.31322	+	5.31322i	0.248542	+	0.248542i	0.820372	−	0.571830i	$-0.193766\pi$
$457$	5.31322	+	5.31322i	0.248542	+	0.248542i	−0.571830	+	0.820372i	$0.693766\pi$
$458$	5.83360			0.272586
$459$	−36.8122	−	27.8146i	−1.71825	−	1.29828i
$460$	−5.26389			−0.245430
$461$	−10.8389	−	10.8389i	−0.504817	−	0.504817i	0.408114	−	0.912931i	$-0.366187\pi$
$461$	−10.8389	−	10.8389i	−0.504817	−	0.504817i	−0.912931	+	0.408114i	$0.866187\pi$
$462$	−0.173377	−	0.418568i	−0.00806621	−	0.0194736i
$463$		−	28.5118i		−	1.32505i	−0.749038	−	0.662527i	$-0.769484\pi$
$463$		−	28.5118i		−	1.32505i	0.749038	−	0.662527i	$-0.230516\pi$
$464$	−22.3894	+	9.27401i	−1.03940	+	0.430535i
$465$	−18.7504	+	45.2675i	−0.869530	+	2.09923i
$466$	−10.0814	−	4.17587i	−0.467014	−	0.193444i
$467$	11.2669	−	11.2669i	0.521370	−	0.521370i	−0.396615	−	0.917985i	$-0.629815\pi$
$467$	11.2669	−	11.2669i	0.521370	−	0.521370i	0.917985	+	0.396615i	$0.129815\pi$
$468$	−1.52010	+	1.52010i	−0.0702668	+	0.0702668i
$469$	0.245891	+	0.101851i	0.0113542	+	0.00470306i
$470$	19.9259	−	48.1053i	0.919111	−	2.21893i
$471$	38.7261	−	16.0409i	1.78441	−	0.739125i
$472$		−	2.90384i		−	0.133660i
$473$	−2.58192	−	6.23332i	−0.118717	−	0.286608i
$474$	16.7844	+	16.7844i	0.770932	+	0.770932i
$475$	−33.2596			−1.52606
$476$	−0.0857562	+	0.113497i	−0.00393063	+	0.00520213i
$477$	42.8551			1.96220
$478$	−11.9146	−	11.9146i	−0.544961	−	0.544961i
$479$	−4.90595	−	11.8440i	−0.224158	−	0.541166i	0.771288	−	0.636486i	$-0.219613\pi$
$479$	−4.90595	−	11.8440i	−0.224158	−	0.541166i	−0.995447	+	0.0953197i	$0.969613\pi$
$480$		−	23.2676i		−	1.06201i
$481$	−8.76975	+	3.63255i	−0.399866	+	0.165630i
$482$	3.96721	−	9.57770i	0.180702	−	0.436252i
$483$	−1.06767	−	0.442243i	−0.0485806	−	0.0201228i
$484$	0.256594	−	0.256594i	0.0116634	−	0.0116634i
$485$	6.84205	−	6.84205i	0.310682	−	0.310682i
$486$	−17.7452	−	7.35030i	−0.804939	−	0.333416i
$487$	−3.45238	+	8.33479i	−0.156442	+	0.377685i	−0.982595	−	0.185761i	$-0.940525\pi$
$487$	−3.45238	+	8.33479i	−0.156442	+	0.377685i	0.826153	+	0.563447i	$0.190525\pi$
$488$	33.1307	−	13.7232i	1.49976	−	0.621219i
$489$		−	23.5701i		−	1.06587i
$490$	15.2142	+	36.7304i	0.687309	+	1.65931i
$491$	−30.6061	−	30.6061i	−1.38123	−	1.38123i	−0.842435	−	0.538799i	$-0.818878\pi$
$491$	−30.6061	−	30.6061i	−1.38123	−	1.38123i	−0.538799	−	0.842435i	$-0.681122\pi$
$492$	6.76274			0.304888
$493$	−21.5420	+	2.99915i	−0.970202	+	0.135075i
$494$	5.27484			0.237326
$495$	17.2913	+	17.2913i	0.777185	+	0.777185i
$496$	7.51102	+	18.1332i	0.337255	+	0.814205i
$497$		−	0.532014i		−	0.0238641i
$498$	49.0856	−	20.3319i	2.19958	−	0.911095i
$499$	4.68463	−	11.3097i	0.209713	−	0.506291i	−0.783665	−	0.621183i	$-0.786652\pi$
$499$	4.68463	−	11.3097i	0.209713	−	0.506291i	0.993378	+	0.114892i	$0.0366522\pi$
$500$	4.57292	+	1.89416i	0.204507	+	0.0847096i
$501$	−25.7049	+	25.7049i	−1.14841	+	1.14841i
$502$	18.5871	−	18.5871i	0.829581	−	0.829581i
$503$	−21.2706	−	8.81057i	−0.948409	−	0.392844i	−0.145776	−	0.989318i	$-0.546568\pi$
$503$	−21.2706	−	8.81057i	−0.948409	−	0.392844i	−0.802632	+	0.596474i	$0.796568\pi$
$504$	0.605206	−	1.46110i	0.0269580	−	0.0650824i
$505$	0.335667	−	0.139038i	0.0149370	−	0.00618710i
$506$		−	6.02715i		−	0.267940i
$507$	14.4690	+	34.9314i	0.642593	+	1.55136i
$508$	−0.498355	−	0.498355i	−0.0221109	−	0.0221109i
$509$	−0.912120			−0.0404290			−0.0202145	−	0.999796i	$-0.506435\pi$
$509$	−0.912120			−0.0404290			−0.0202145	+	0.999796i	$0.506435\pi$
$510$	18.2902	−	70.3480i	0.809904	−	3.11506i
$511$	0.587715			0.0259990
$512$	9.75930	+	9.75930i	0.431304	+	0.431304i
$513$	16.3959	+	39.5831i	0.723895	+	1.74764i
$514$			11.6882i			0.515544i
$515$	−32.9413	+	13.6447i	−1.45157	+	0.601259i
$516$	−2.90445	+	7.01195i	−0.127861	+	0.308684i
$517$	8.45900	+	3.50383i	0.372026	+	0.154098i
$518$	−1.09449	+	1.09449i	−0.0480893	+	0.0480893i
$519$	−37.6494	+	37.6494i	−1.65263	+	1.65263i
$520$	7.70914	+	3.19323i	0.338068	+	0.140032i
$521$	−11.3942	+	27.5082i	−0.499191	+	1.20515i	0.450729	+	0.892661i	$0.351164\pi$
$521$	−11.3942	+	27.5082i	−0.499191	+	1.20515i	−0.949920	+	0.312493i	$0.898836\pi$
$522$	−49.5171	+	20.5107i	−2.16730	+	0.897727i
$523$		−	1.69297i		−	0.0740283i	−0.999315	−	0.0370141i	$-0.988215\pi$
$523$		−	1.69297i		−	0.0740283i	0.999315	−	0.0370141i	$-0.0117847\pi$
$524$	0.517996	+	1.25055i	0.0226288	+	0.0546306i
$525$	1.81043	+	1.81043i	0.0790134	+	0.0790134i
$526$	5.95960			0.259851
$527$	2.42901	+	17.4468i	0.105809	+	0.759996i
$528$	14.2415			0.619782
$529$	5.39249	+	5.39249i	0.234456	+	0.234456i
$530$	14.1100	+	34.0645i	0.612899	+	1.47967i
$531$		−	7.62712i		−	0.330989i
$532$	0.122040	−	0.0505506i	0.00529110	−	0.00219165i
$533$	−2.06195	+	4.97800i	−0.0893132	+	0.215621i
$534$	31.3894	+	13.0019i	1.35835	+	0.562648i
$535$	−14.6600	+	14.6600i	−0.633807	+	0.633807i
$536$	−4.98129	+	4.98129i	−0.215159	+	0.215159i
$537$	46.4152	+	19.2258i	2.00296	+	0.829654i
$538$	−8.89986	+	21.4862i	−0.383700	+	0.926334i
$539$	−6.45881	+	2.67532i	−0.278200	+	0.115234i
$540$		−	15.0230i		−	0.646488i
$541$	−15.1790	−	36.6453i	−0.652595	−	1.57550i	−0.808999	−	0.587810i	$-0.799990\pi$
$541$	−15.1790	−	36.6453i	−0.652595	−	1.57550i	0.156404	−	0.987693i	$-0.450010\pi$
$542$	−6.02494	−	6.02494i	−0.258793	−	0.258793i
$543$	−30.2434			−1.29787
$544$	−4.23624	−	7.21299i	−0.181627	−	0.309255i
$545$	65.3598			2.79971
$546$	−0.287126	−	0.287126i	−0.0122879	−	0.0122879i
$547$	12.2891	+	29.6686i	0.525446	+	1.26854i	0.934479	+	0.356019i	$0.115866\pi$
$547$	12.2891	+	29.6686i	0.525446	+	1.26854i	−0.409033	+	0.912520i	$0.634134\pi$
$548$			3.75161i			0.160261i
$549$	87.0198	−	36.0448i	3.71392	−	1.53835i
$550$	−5.11006	+	12.3368i	−0.217894	+	0.526042i
$551$	18.6594	+	7.72897i	0.794916	+	0.329265i
$552$	21.6290	−	21.6290i	0.920589	−	0.920589i
$553$	−0.334888	+	0.334888i	−0.0142409	+	0.0142409i
$554$	−25.4118	−	10.5259i	−1.07964	−	0.447202i
$555$	46.4821	−	112.218i	1.97305	−	4.76337i
$556$	−3.95441	+	1.63797i	−0.167704	+	0.0694654i
$557$			30.9158i			1.30995i	0.755652	+	0.654973i	$0.227320\pi$
$557$			30.9158i			1.30995i	−0.755652	+	0.654973i	$0.772680\pi$
$558$	16.6116	+	40.1039i	0.703224	+	1.69773i
$559$	−4.27588	−	4.27588i	−0.180850	−	0.180850i
$560$	1.61593			0.0682857
$561$	12.3702	+	3.21622i	0.522272	+	0.135789i
$562$	6.53993			0.275870
$563$	12.4594	+	12.4594i	0.525102	+	0.525102i	0.919108	−	0.394006i	$-0.128911\pi$
$563$	12.4594	+	12.4594i	0.525102	+	0.525102i	−0.394006	+	0.919108i	$0.628911\pi$
$564$	−3.94151	−	9.51566i	−0.165968	−	0.400681i
$565$		−	53.0437i		−	2.23157i
$566$	−22.8154	+	9.45045i	−0.959003	+	0.397232i
$567$	0.540676	−	1.30531i	0.0227063	−	0.0548177i
$568$	13.0097	+	5.38879i	0.545875	+	0.226109i
$569$	26.8184	−	26.8184i	1.12429	−	1.12429i	0.133195	−	0.991090i	$-0.457476\pi$
$569$	26.8184	−	26.8184i	1.12429	−	1.12429i	0.991090	−	0.133195i	$-0.0425238\pi$
$570$	−47.7274	+	47.7274i	−1.99908	+	1.99908i
$571$	−16.3471	−	6.77118i	−0.684104	−	0.283365i	0.0134372	−	0.999910i	$-0.495723\pi$
$571$	−16.3471	−	6.77118i	−0.684104	−	0.283365i	−0.697541	+	0.716544i	$0.745723\pi$
$572$	0.124462	−	0.300479i	0.00520404	−	0.0125637i
$573$	−19.4527	+	8.05759i	−0.812650	+	0.336610i
$574$			0.878610i			0.0366725i
$575$	13.0346	+	31.4682i	0.543579	+	1.31232i
$576$	28.3681	+	28.3681i	1.18200	+	1.18200i
$577$	2.89617			0.120569			0.0602846	−	0.998181i	$-0.480799\pi$
$577$	2.89617			0.120569			0.0602846	+	0.998181i	$0.480799\pi$
$578$	−7.13798	−	25.1380i	−0.296901	−	1.04560i
$579$	−33.2309			−1.38103
$580$	−5.00760	−	5.00760i	−0.207929	−	0.207929i
$581$	0.405670	+	0.979373i	0.0168300	+	0.0406313i
$582$		−	12.4631i		−	0.516613i
$583$	−5.99003	+	2.48115i	−0.248082	+	0.102759i
$584$	−5.95299	+	14.3718i	−0.246337	+	0.594709i
$585$	20.2485	+	8.38722i	0.837174	+	0.346769i
$586$	−11.7697	+	11.7697i	−0.486203	+	0.486203i
$587$	−16.2904	+	16.2904i	−0.672375	+	0.672375i	−0.958263	−	0.285888i	$-0.907712\pi$
$587$	−16.2904	+	16.2904i	−0.672375	+	0.672375i	0.285888	+	0.958263i	$0.407712\pi$
$588$	7.26561	+	3.00951i	0.299629	+	0.124110i
$589$	6.25969	−	15.1122i	0.257926	−	0.622688i
$590$	6.06262	−	2.51122i	0.249594	−	0.103385i
$591$			54.8260i			2.25524i
$592$	−18.6197	−	44.9520i	−0.765266	−	1.84752i
$593$	−16.9991	−	16.9991i	−0.698070	−	0.698070i	0.265924	−	0.963994i	$-0.414323\pi$
$593$	−16.9991	−	16.9991i	−0.698070	−	0.698070i	−0.963994	+	0.265924i	$0.914323\pi$
$594$	17.2014			0.705781
$595$	1.40361	+	0.364933i	0.0575423	+	0.0149608i
$596$	−3.64994			−0.149507
$597$	−51.1973	−	51.1973i	−2.09537	−	2.09537i
$598$	−2.06723	−	4.99073i	−0.0845352	−	0.204086i
$599$		−	3.74151i		−	0.152874i	−0.997074	−	0.0764369i	$-0.975646\pi$
$599$		−	3.74151i		−	0.152874i	0.997074	−	0.0764369i	$-0.0243544\pi$
$600$	−62.6094	+	25.9337i	−2.55602	+	1.05874i
$601$	8.49447	−	20.5075i	0.346497	−	0.836517i	−0.650532	−	0.759479i	$-0.725454\pi$
$601$	8.49447	−	20.5075i	0.346497	−	0.836517i	0.997028	−	0.0770376i	$-0.0245461\pi$
$602$	−0.910988	−	0.377343i	−0.0371291	−	0.0153794i
$603$	−13.0837	+	13.0837i	−0.532808	+	0.532808i
$604$	−1.75216	+	1.75216i	−0.0712945	+	0.0712945i
$605$	−3.41797	−	1.41577i	−0.138960	−	0.0575592i
$606$	0.179085	−	0.432349i	0.00727482	−	0.0175630i
$607$	36.8894	−	15.2801i	1.49729	−	0.620199i	0.524403	−	0.851470i	$-0.324288\pi$
$607$	36.8894	−	15.2801i	1.49729	−	0.620199i	0.972889	+	0.231271i	$0.0742884\pi$
$608$			7.76770i			0.315022i
$609$	−0.594976	−	1.43640i	−0.0241096	−	0.0582058i
$610$	57.3023	+	57.3023i	2.32010	+	2.32010i
$611$	8.20616			0.331986
$612$	−5.00831	−	8.52759i	−0.202449	−	0.344707i
$613$	8.71507			0.351998			0.175999	−	0.984390i	$-0.443684\pi$
$613$	8.71507			0.351998			0.175999	+	0.984390i	$0.443684\pi$
$614$	−3.12048	−	3.12048i	−0.125932	−	0.125932i
$615$	−26.3847	−	63.6984i	−1.06394	−	2.56857i
$616$			0.239262i			0.00964015i
$617$	39.4784	−	16.3525i	1.58934	−	0.658326i	0.599481	−	0.800389i	$-0.295374\pi$
$617$	39.4784	−	16.3525i	1.58934	−	0.658326i	0.989858	+	0.142063i	$0.0453736\pi$
$618$	−17.5748	+	42.4293i	−0.706962	+	1.70676i
$619$	12.3704	+	5.12398i	0.497208	+	0.205950i	0.617172	−	0.786828i	$-0.288278\pi$
$619$	12.3704	+	5.12398i	0.497208	+	0.205950i	−0.119965	+	0.992778i	$0.538278\pi$
$620$	−4.05565	+	4.05565i	−0.162879	+	0.162879i
$621$	31.0255	−	31.0255i	1.24501	−	1.24501i
$622$	−13.4832	−	5.58494i	−0.540629	−	0.223936i
$623$	−0.259419	+	0.626293i	−0.0103934	+	0.0250919i
$624$	11.7925	−	4.88463i	0.472080	−	0.195542i
$625$		−	7.02791i		−	0.281117i
$626$	−16.5748	−	40.0150i	−0.662461	−	1.59932i
$627$	−8.39256	−	8.39256i	−0.335167	−	0.335167i
$628$	4.90675			0.195801
$629$	−6.02149	−	43.2505i	−0.240093	−	1.72451i
$630$	3.57384			0.142385
$631$	−12.5317	−	12.5317i	−0.498877	−	0.498877i	0.412211	−	0.911088i	$-0.364757\pi$
$631$	−12.5317	−	12.5317i	−0.498877	−	0.498877i	−0.911088	+	0.412211i	$0.864757\pi$
$632$	−4.79715	−	11.5813i	−0.190820	−	0.460681i
$633$		−	77.6018i		−	3.08440i
$634$	29.0323	−	12.0256i	1.15302	−	0.477597i
$635$	−2.74969	+	6.63834i	−0.109118	+	0.263434i
$636$	6.73827	+	2.79108i	0.267190	+	0.110674i
$637$	−4.43056	+	4.43056i	−0.175545	+	0.175545i
$638$	5.73371	−	5.73371i	0.227000	−	0.227000i
$639$	34.1708	+	14.1540i	1.35178	+	0.559924i
$640$	−18.9536	+	45.7581i	−0.749208	+	1.80875i
$641$	−34.1347	+	14.1391i	−1.34824	+	0.558460i	−0.935802	−	0.352526i	$-0.885323\pi$
$641$	−34.1347	+	14.1391i	−1.34824	+	0.558460i	−0.412439	+	0.910985i	$0.635323\pi$
$642$			26.7039i			1.05392i
$643$	7.07562	+	17.0821i	0.279035	+	0.673651i	0.999809	−	0.0195191i	$-0.00621351\pi$
$643$	7.07562	+	17.0821i	0.279035	+	0.673651i	−0.720774	+	0.693170i	$0.756214\pi$
$644$	−0.0956558	−	0.0956558i	−0.00376937	−	0.00376937i
$645$	77.3774			3.04673
$646$	−6.10605	+	23.4851i	−0.240239	+	0.924011i
$647$	−19.8329			−0.779713			−0.389856	−	0.920876i	$-0.627475\pi$
$647$	−19.8329			−0.779713			−0.389856	+	0.920876i	$0.627475\pi$
$648$	26.4430	+	26.4430i	1.03878	+	1.03878i
$649$	0.441582	+	1.06607i	0.0173336	+	0.0418470i
$650$			11.9680i			0.469425i
$651$	−1.16334	+	0.481871i	−0.0455948	+	0.0188860i
$652$	1.05586	−	2.54906i	0.0413505	−	0.0998290i
$653$	−10.4727	−	4.33794i	−0.409829	−	0.169757i	0.168238	−	0.985746i	$-0.446192\pi$
$653$	−10.4727	−	4.33794i	−0.409829	−	0.169757i	−0.578066	+	0.815990i	$0.696192\pi$
$654$	59.5280	−	59.5280i	2.32773	−	2.32773i
$655$	9.75803	−	9.75803i	0.381278	−	0.381278i
$656$	−25.5162	−	10.5692i	−0.996242	−	0.412657i
$657$	−15.6359	+	37.7484i	−0.610015	+	1.47271i
$658$	1.23627	−	0.512079i	0.0481947	−	0.0199629i
$659$			30.7372i			1.19735i	0.800991	+	0.598676i	$0.204306\pi$
$659$			30.7372i			1.19735i	−0.800991	+	0.598676i	$0.795694\pi$
$660$	1.59262	+	3.84492i	0.0619926	+	0.149663i
$661$	8.18926	+	8.18926i	0.318525	+	0.318525i	0.848201	−	0.529675i	$-0.177686\pi$
$661$	8.18926	+	8.18926i	0.318525	+	0.318525i	−0.529675	+	0.848201i	$0.677686\pi$
$662$	−28.7465			−1.11727
$663$	11.3462	−	1.57966i	0.440649	−	0.0613488i
$664$	−28.0583			−1.08887
$665$	−0.952275	−	0.952275i	−0.0369276	−	0.0369276i
$666$	−41.1799	−	99.4170i	−1.59569	−	3.85233i
$667$		−	20.6834i		−	0.800863i
$668$	−3.93143	+	1.62845i	−0.152111	+	0.0630066i
$669$	−6.12421	+	14.7852i	−0.236776	+	0.571627i
$670$	−14.7077	−	6.09212i	−0.568207	−	0.235359i
$671$	−10.0762	+	10.0762i	−0.388989	+	0.388989i
$672$	0.422820	−	0.422820i	0.0163106	−	0.0163106i
$673$	23.0650	+	9.55384i	0.889091	+	0.368274i	0.780016	−	0.625760i	$-0.215211\pi$
$673$	23.0650	+	9.55384i	0.889091	+	0.368274i	0.109075	+	0.994033i	$0.465211\pi$
$674$	3.63704	−	8.78060i	0.140094	−	0.338216i
$675$	−89.8097	+	37.2004i	−3.45678	+	1.43184i
$676$			4.42593i			0.170228i
$677$	7.71750	+	18.6317i	0.296608	+	0.716074i	0.999986	+	0.00525867i	$0.00167390\pi$
$677$	7.71750	+	18.6317i	0.296608	+	0.716074i	−0.703379	+	0.710815i	$0.748326\pi$
$678$	−48.3108	−	48.3108i	−1.85537	−	1.85537i
$679$	0.248669			0.00954303
$680$	−23.1412	+	30.6270i	−0.887423	+	1.17449i
$681$	45.2229			1.73295
$682$	−4.64373	−	4.64373i	−0.177817	−	0.177817i
$683$	−2.00446	−	4.83921i	−0.0766987	−	0.185167i	0.880879	−	0.473341i	$-0.156952\pi$
$683$	−2.00446	−	4.83921i	−0.0766987	−	0.185167i	−0.957578	+	0.288174i	$0.906952\pi$
$684$			9.18340i			0.351136i
$685$	35.3365	−	14.6369i	1.35014	−	0.559245i
$686$	−0.782493	+	1.88911i	−0.0298757	+	0.0721264i
$687$	−10.8690	−	4.50208i	−0.414677	−	0.171765i
$688$	21.9173	−	21.9173i	0.835590	−	0.835590i
$689$	−4.10899	+	4.10899i	−0.156540	+	0.156540i
$690$	63.8613	+	26.4522i	2.43116	+	1.00702i
$691$	4.45613	−	10.7581i	0.169519	−	0.409256i	−0.816174	−	0.577807i	$-0.803909\pi$
$691$	4.45613	−	10.7581i	0.169519	−	0.409256i	0.985693	+	0.168551i	$0.0539087\pi$
$692$	−5.75829	+	2.38516i	−0.218897	+	0.0906702i
$693$			0.628437i			0.0238724i
$694$	10.9816	+	26.5119i	0.416855	+	1.00638i
$695$	30.8561	+	30.8561i	1.17044	+	1.17044i
$696$	41.1518			1.55985
$697$	−19.7767	−	14.9429i	−0.749094	−	0.566002i
$698$	−29.7543			−1.12622
$699$	15.5607	+	15.5607i	0.588560	+	0.588560i
$700$	0.114694	+	0.276895i	0.00433502	+	0.0104657i
$701$		−	36.0183i		−	1.36039i	−0.733030	−	0.680196i	$-0.761895\pi$
$701$		−	36.0183i		−	1.36039i	0.733030	−	0.680196i	$-0.238105\pi$
$702$	14.2434	−	5.89983i	0.537584	−	0.222675i
$703$	−15.5177	+	37.4630i	−0.585261	+	1.41294i
$704$	−5.60753	−	2.32271i	−0.211342	−	0.0875405i
$705$	−74.2504	+	74.2504i	−2.79643	+	2.79643i
$706$	−2.09565	+	2.09565i	−0.0788710	+	0.0788710i
$707$	0.00862638	+	0.00357316i	0.000324428	+	0.000134383i
$708$	0.496742	−	1.19924i	0.0186687	−	0.0450702i
$709$	−27.2097	+	11.2706i	−1.02188	+	0.423278i	−0.829776	−	0.558096i	$-0.811532\pi$
$709$	−27.2097	+	11.2706i	−1.02188	+	0.423278i	−0.192107	+	0.981374i	$0.561532\pi$
$710$			31.8217i			1.19425i
$711$	−12.6000	−	30.4191i	−0.472537	−	1.14081i
$712$	−12.6875	−	12.6875i	−0.475484	−	0.475484i
$713$	−16.7514			−0.627347
$714$	1.61074	−	0.945998i	0.0602805	−	0.0354031i
$715$	−3.31581			−0.124004
$716$	4.15848	+	4.15848i	0.155410	+	0.155410i
$717$	13.0038	+	31.3940i	0.485636	+	1.17243i
$718$			41.4497i			1.54689i
$719$	−11.3234	+	4.69029i	−0.422290	+	0.174918i	−0.583701	−	0.811969i	$-0.698396\pi$
$719$	−11.3234	+	4.69029i	−0.422290	+	0.174918i	0.161410	+	0.986887i	$0.448396\pi$
$720$	−42.9912	+	103.790i	−1.60219	+	3.86803i
$721$	−0.846565	−	0.350659i	−0.0315277	−	0.0130592i
$722$	−4.71842	+	4.71842i	−0.175602	+	0.175602i
$723$	−14.7832	+	14.7832i	−0.549792	+	0.549792i
$724$	−3.27078	−	1.35480i	−0.121557	−	0.0503508i
$725$	−17.5362	+	42.3361i	−0.651277	+	1.57232i
$726$	−4.40244	+	1.82355i	−0.163390	+	0.0676783i
$727$		−	19.3391i		−	0.717249i	−0.933482	−	0.358624i	$-0.883246\pi$
$727$		−	19.3391i		−	0.717249i	0.933482	−	0.358624i	$-0.116754\pi$
$728$	0.0820635	+	0.198119i	0.00304148	+	0.00734277i
$729$	−4.13356	−	4.13356i	−0.153095	−	0.153095i
$730$	−35.1534			−1.30109
$731$	23.9872	−	14.0878i	0.887197	−	0.521056i
$732$	16.0300			0.592486
$733$	7.22872	+	7.22872i	0.266999	+	0.266999i	0.827890	−	0.560891i	$-0.189541\pi$
$733$	7.22872	+	7.22872i	0.266999	+	0.266999i	−0.560891	+	0.827890i	$0.689541\pi$
$734$	−16.7212	−	40.3684i	−0.617189	−	1.49003i
$735$		−	80.1765i		−	2.95736i
$736$	7.34933	−	3.04419i	0.270900	−	0.112210i
$737$	1.07126	−	2.58625i	0.0394604	−	0.0952657i
$738$	−56.4324	−	23.3751i	−2.07730	−	0.860448i
$739$	33.8531	−	33.8531i	1.24531	−	1.24531i	0.287536	−	0.957770i	$-0.407164\pi$
$739$	33.8531	−	33.8531i	1.24531	−	1.24531i	0.957770	−	0.287536i	$-0.0928361\pi$
$740$	10.0539	−	10.0539i	0.369589	−	0.369589i
$741$	−9.82791	−	4.07085i	−0.361037	−	0.149547i
$742$	−0.362615	+	0.875431i	−0.0133120	+	0.0321381i
$743$	−42.0888	+	17.4337i	−1.54409	+	0.639582i	−0.982235	−	0.187656i	$-0.939911\pi$
$743$	−42.0888	+	17.4337i	−1.54409	+	0.639582i	−0.561852	+	0.827237i	$0.689911\pi$
$744$		−	33.3288i		−	1.22189i
$745$	14.2402	+	34.3789i	0.521721	+	1.25955i
$746$	7.95754	+	7.95754i	0.291346	+	0.291346i
$747$	−73.6970			−2.69643
$748$	1.19375	+	0.901972i	0.0436477	+	0.0329794i
$749$	−0.532806			−0.0194683
$750$	−45.9599	−	45.9599i	−1.67822	−	1.67822i
$751$	−10.2161	−	24.6638i	−0.372789	−	0.899993i	−0.993275	−	0.115776i	$-0.963065\pi$
$751$	−10.2161	−	24.6638i	−0.372789	−	0.899993i	0.620486	−	0.784218i	$-0.286935\pi$
$752$			42.0632i			1.53389i
$753$	−48.9754	+	20.2863i	−1.78476	+	0.739273i
$754$	2.78116	−	6.71432i	0.101284	−	0.244521i
$755$	23.3397	+	9.66762i	0.849419	+	0.351841i
$756$	0.273000	−	0.273000i	0.00992890	−	0.00992890i
$757$	10.6346	−	10.6346i	0.386521	−	0.386521i	−0.486924	−	0.873444i	$-0.661881\pi$
$757$	10.6346	−	10.6346i	0.386521	−	0.386521i	0.873444	+	0.486924i	$0.161881\pi$
$758$	17.6787	+	7.32277i	0.642120	+	0.265975i
$759$	−4.65145	+	11.2296i	−0.168837	+	0.407609i
$760$	32.9323	−	13.6410i	1.19458	−	0.494811i
$761$		−	54.9519i		−	1.99200i	−0.0893342	−	0.996002i	$-0.528474\pi$
$761$		−	54.9519i		−	1.99200i	0.0893342	−	0.996002i	$-0.471526\pi$
$762$	3.54168	+	8.55037i	0.128301	+	0.309747i
$763$	1.18772	+	1.18772i	0.0429985	+	0.0429985i
$764$	−2.46473			−0.0891709
$765$	−60.7817	+	80.4437i	−2.19757	+	2.90845i
$766$	14.7990			0.534709
$767$	0.731295	+	0.731295i	0.0264055	+	0.0264055i
$768$	10.0121	+	24.1714i	0.361281	+	0.872210i
$769$			16.8750i			0.608530i	0.952587	+	0.304265i	$0.0984108\pi$
$769$			16.8750i			0.608530i	−0.952587	+	0.304265i	$0.901589\pi$
$770$	−0.499530	+	0.206912i	−0.0180018	+	0.00745659i
$771$	9.02036	−	21.7771i	0.324860	−	0.784282i
$772$	−3.59387	−	1.48863i	−0.129346	−	0.0535769i
$773$	−17.6394	+	17.6394i	−0.634444	+	0.634444i	−0.949179	−	0.314735i	$-0.898084\pi$
$773$	−17.6394	+	17.6394i	−0.634444	+	0.634444i	0.314735	+	0.949179i	$0.398084\pi$
$774$	48.4729	−	48.4729i	1.74232	−	1.74232i
$775$	34.2880	+	14.2025i	1.23166	+	0.510170i
$776$	−2.51878	+	6.08087i	−0.0904188	+	0.218290i
$777$	2.88390	−	1.19455i	0.103459	−	0.0428543i
$778$			1.35650i			0.0486329i
$779$	8.80835	+	21.2652i	0.315592	+	0.761906i
$780$	2.63751	+	2.63751i	0.0944380	+	0.0944380i
$781$	−5.59565			−0.200228
$782$	24.6132	−	3.42674i	0.880166	−	0.122540i
$783$	59.0299			2.10956
$784$	−22.7102	−	22.7102i	−0.811077	−	0.811077i
$785$	−19.1436	−	46.2168i	−0.683265	−	1.64955i
$786$		−	17.7747i		−	0.634003i
$787$	−3.88673	+	1.60994i	−0.138547	+	0.0573880i	−0.450880	−	0.892585i	$-0.648890\pi$
$787$	−3.88673	+	1.60994i	−0.138547	+	0.0573880i	0.312333	+	0.949973i	$0.398890\pi$
$788$	−2.45601	+	5.92934i	−0.0874919	+	0.211224i
$789$	−11.1037	−	4.59932i	−0.395304	−	0.163740i
$790$	20.0309	−	20.0309i	0.712667	−	0.712667i
$791$	0.963915	−	0.963915i	0.0342729	−	0.0342729i
$792$	−15.3676	−	6.36547i	−0.546064	−	0.226187i
$793$	−4.88753	+	11.7995i	−0.173561	+	0.419014i
$794$	18.2028	−	7.53984i	0.645993	−	0.267579i
$795$		−	74.3573i		−	2.63718i
$796$	−3.24345	−	7.83037i	−0.114961	−	0.277540i
$797$	13.0345	+	13.0345i	0.461705	+	0.461705i	0.899214	−	0.437509i	$-0.144139\pi$
$797$	13.0345	+	13.0345i	0.461705	+	0.461705i	−0.437509	+	0.899214i	$0.644139\pi$
$798$	−1.73461			−0.0614047
$799$	−9.49930	+	36.5363i	−0.336061	+	1.29256i
$800$	−17.6241			−0.623105
$801$	−33.3245	−	33.3245i	−1.17746	−	1.17746i
$802$	−1.77520	−	4.28572i	−0.0626846	−	0.151334i
$803$		−	6.18150i		−	0.218141i
$804$	−2.90931	+	1.20508i	−0.102604	+	0.0424998i
$805$	−0.527784	+	1.27418i	−0.0186020	+	0.0449091i
$806$	−5.43793	−	2.25246i	−0.191543	−	0.0793396i
$807$	33.1639	−	33.1639i	1.16742	−	1.16742i
$808$	−0.174754	+	0.174754i	−0.00614782	+	0.00614782i
$809$	−7.50571	−	3.10897i	−0.263887	−	0.109306i	0.246817	−	0.969062i	$-0.420615\pi$
$809$	−7.50571	−	3.10897i	−0.263887	−	0.109306i	−0.510704	+	0.859757i	$0.670615\pi$
$810$	−32.3399	+	78.0753i	−1.13631	+	2.74329i
$811$	−10.6538	+	4.41293i	−0.374104	+	0.154959i	−0.561810	−	0.827266i	$-0.689895\pi$
$811$	−10.6538	+	4.41293i	−0.374104	+	0.154959i	0.187706	+	0.982225i	$0.439895\pi$
$812$		−	0.181997i		−	0.00638685i
$813$	6.57573	+	15.8752i	0.230621	+	0.556768i
$814$	11.5117	+	11.5117i	0.403486	+	0.403486i
$815$	−28.1291			−0.985319
$816$	8.09701	+	58.1583i	0.283452	+	2.03595i
$817$	−25.8319			−0.903743
$818$	21.6470	+	21.6470i	0.756871	+	0.756871i
$819$	0.215545	+	0.520372i	0.00753175	+	0.0181833i
$820$		−	8.07083i		−	0.281845i
$821$	17.8157	−	7.37950i	0.621772	−	0.257546i	−0.0494805	−	0.998775i	$-0.515757\pi$
$821$	17.8157	−	7.37950i	0.621772	−	0.257546i	0.671253	+	0.741229i	$0.265757\pi$
$822$	18.8527	−	45.5144i	0.657563	−	1.58750i
$823$	0.484723	+	0.200779i	0.0168964	+	0.00699871i	0.391116	−	0.920342i	$-0.372089\pi$
$823$	0.484723	+	0.200779i	0.0168964	+	0.00699871i	−0.374219	+	0.927340i	$0.622089\pi$
$824$	17.1498	−	17.1498i	0.597441	−	0.597441i
$825$	19.0418	−	19.0418i	0.662950	−	0.662950i
$826$	0.155804	+	0.0645363i	0.00542113	+	0.00224551i
$827$	4.40750	−	10.6406i	0.153264	−	0.370011i	−0.828535	−	0.559938i	$-0.810825\pi$
$827$	4.40750	−	10.6406i	0.153264	−	0.370011i	0.981798	+	0.189927i	$0.0608250\pi$
$828$	8.68877	−	3.59901i	0.301956	−	0.125074i
$829$		−	19.2228i		−	0.667634i	−0.942638	−	0.333817i	$-0.891663\pi$
$829$		−	19.2228i		−	0.667634i	0.942638	−	0.333817i	$-0.108337\pi$
$830$	−24.2646	−	58.5800i	−0.842238	−	2.03334i
$831$	39.2230	+	39.2230i	1.36063	+	1.36063i
$832$	−5.43992			−0.188595
$833$	−14.5974	−	24.8549i	−0.505771	−	0.861171i
$834$	56.2059			1.94625
$835$	30.6768	+	30.6768i	1.06162	+	1.06162i
$836$	−0.531684	−	1.28360i	−0.0183887	−	0.0443942i
$837$		−	47.8083i		−	1.65250i
$838$	33.3360	−	13.8082i	1.15157	−	0.476997i
$839$	−1.64758	+	3.97760i	−0.0568807	+	0.137322i	−0.949765	−	0.312964i	$-0.898678\pi$
$839$	−1.64758	+	3.97760i	−0.0568807	+	0.137322i	0.892884	+	0.450286i	$0.148678\pi$
$840$	−2.53513	−	1.05008i	−0.0874702	−	0.0362313i
$841$	−0.829749	+	0.829749i	−0.0286120	+	0.0286120i
$842$	−7.98118	+	7.98118i	−0.275050	+	0.275050i
$843$	−12.1850	−	5.04719i	−0.419674	−	0.173834i
$844$	3.47629	−	8.39251i	0.119659	−	0.288882i
$845$	41.6880	−	17.2677i	1.43411	−	0.594028i
$846$			93.0280i			3.19837i
$847$	−0.0363841	−	0.0878391i	−0.00125017	−	0.00301819i
$848$	−21.0619	−	21.0619i	−0.723267	−	0.723267i
$849$	49.8023			1.70921
$850$	−53.2852	−	13.8540i	−1.82767	−	0.475187i
$851$	41.5266			1.42352
$852$	4.45097	+	4.45097i	0.152488	+	0.152488i
$853$	9.87090	+	23.8305i	0.337973	+	0.815940i	0.997910	+	0.0646186i	$0.0205831\pi$
$853$	9.87090	+	23.8305i	0.337973	+	0.815940i	−0.659937	+	0.751321i	$0.729417\pi$
$854$			2.08261i			0.0712653i
$855$	86.4987	−	35.8289i	2.95819	−	1.22532i
$856$	5.39681	−	13.0291i	0.184459	−	0.445324i
$857$	−11.2121	−	4.64421i	−0.382999	−	0.158643i	0.182873	−	0.983137i	$-0.441460\pi$
$857$	−11.2121	−	4.64421i	−0.382999	−	0.158643i	−0.565872	+	0.824493i	$0.691460\pi$
$858$	−3.01995	+	3.01995i	−0.103099	+	0.103099i
$859$	4.50139	−	4.50139i	0.153586	−	0.153586i	−0.626132	−	0.779717i	$-0.715363\pi$
$859$	4.50139	−	4.50139i	0.153586	−	0.153586i	0.779717	+	0.626132i	$0.215363\pi$
$860$	8.36824	+	3.46624i	0.285355	+	0.118198i
$861$	0.678067	−	1.63700i	0.0231085	−	0.0557888i
$862$	20.7033	−	8.57558i	0.705157	−	0.292085i
$863$		−	14.6773i		−	0.499622i	−0.968295	−	0.249811i	$-0.919631\pi$
$863$		−	14.6773i		−	0.499622i	0.968295	−	0.249811i	$-0.0803686\pi$
$864$	8.68806	+	20.9748i	0.295574	+	0.713578i
$865$	44.9318	+	44.9318i	1.52773	+	1.52773i
$866$	50.6353			1.72066
$867$	−6.10102	+	52.3451i	−0.207201	+	1.77773i
$868$	−0.147399			−0.00500306
$869$	3.52230	+	3.52230i	0.119486	+	0.119486i
$870$	35.5877	+	85.9164i	1.20654	+	2.91284i
$871$		−	2.50895i		−	0.0850125i
$872$	−41.0747	+	17.0137i	−1.39097	+	0.576157i
$873$	−6.61573	+	15.9718i	−0.223908	+	0.540563i
$874$	−21.3196	−	8.83088i	−0.721147	−	0.298709i
$875$	0.917009	−	0.917009i	0.0310005	−	0.0310005i
$876$	−4.91699	+	4.91699i	−0.166130	+	0.166130i
$877$	−41.8080	−	17.3174i	−1.41175	−	0.584768i	−0.458980	−	0.888447i	$-0.651785\pi$
$877$	−41.8080	−	17.3174i	−1.41175	−	0.584768i	−0.952774	+	0.303679i	$0.901785\pi$
$878$	−11.0751	+	26.7376i	−0.373766	+	0.902350i
$879$	31.0122	−	12.8457i	1.04602	−	0.433274i
$880$		−	16.9962i		−	0.572941i
$881$	−12.3584	−	29.8359i	−0.416366	−	1.00520i	−0.983392	−	0.181496i	$-0.941906\pi$
$881$	−12.3584	−	29.8359i	−0.416366	−	1.00520i	0.567026	−	0.823700i	$-0.308094\pi$
$882$	−50.2264	−	50.2264i	−1.69121	−	1.69121i
$883$	43.2178			1.45439			0.727197	−	0.686429i	$-0.240823\pi$
$883$	43.2178			1.45439			0.727197	+	0.686429i	$0.240823\pi$
$884$	1.29783	+	0.337432i	0.0436509	+	0.0113491i
$885$	−13.2337			−0.444846
$886$	−0.583822	−	0.583822i	−0.0196139	−	0.0196139i
$887$	−6.61328	−	15.9659i	−0.222052	−	0.536082i	0.773116	−	0.634264i	$-0.218697\pi$
$887$	−6.61328	−	15.9659i	−0.222052	−	0.536082i	−0.995168	+	0.0981829i	$0.968697\pi$
$888$			82.6217i			2.77260i
$889$	−0.170600	+	0.0706648i	−0.00572174	+	0.00237002i
$890$	15.5168	−	37.4609i	0.520125	−	1.25569i
$891$	−13.7290	−	5.68676i	−0.459940	−	0.190513i
$892$	−1.32465	+	1.32465i	−0.0443525	+	0.0443525i
$893$	24.7880	−	24.7880i	0.829497	−	0.829497i
$894$	44.2810	+	18.3418i	1.48098	+	0.613441i
$895$	22.9445	−	55.3930i	0.766952	−	1.85158i
$896$	−1.17595	+	0.487093i	−0.0392856	+	0.0162726i
$897$			10.8940i			0.363738i
$898$	−10.8039	−	26.0829i	−0.360530	−	0.870396i
$899$	−15.9359	−	15.9359i	−0.531491	−	0.531491i
$900$	−20.8361			−0.694538
$901$	−13.5379	−	23.0509i	−0.451014	−	0.767937i
$902$	9.24110			0.307695
$903$	1.40611	+	1.40611i	0.0467924	+	0.0467924i
$904$	13.8077	+	33.3348i	0.459238	+	1.10870i
$905$			36.0933i			1.19978i
$906$	30.0622	−	12.4522i	0.998750	−	0.413696i
$907$	7.57407	−	18.2854i	0.251493	−	0.607157i	−0.746832	−	0.665012i	$-0.768426\pi$
$907$	7.57407	−	18.2854i	0.251493	−	0.607157i	0.998325	+	0.0578553i	$0.0184262\pi$
$908$	4.89078	+	2.02583i	0.162306	+	0.0672295i
$909$	−0.459002	+	0.459002i	−0.0152241	+	0.0152241i
$910$	−0.342663	+	0.342663i	−0.0113592	+	0.0113592i
$911$	−15.5437	−	6.43839i	−0.514984	−	0.213314i	0.110028	−	0.993929i	$-0.464906\pi$
$911$	−15.5437	−	6.43839i	−0.514984	−	0.213314i	−0.625012	+	0.780615i	$0.714906\pi$
$912$	20.8664	−	50.3759i	0.690955	−	1.66811i
$913$	10.3009	−	4.26678i	0.340911	−	0.141210i
$914$		−	11.5503i		−	0.382050i
$915$	−62.5408	−	150.987i	−2.06754	−	4.99147i
$916$	−0.973785	−	0.973785i	−0.0321748	−	0.0321748i
$917$	0.354648			0.0117115
$918$	9.77985	+	70.2456i	0.322783	+	2.31845i
$919$	−51.6707			−1.70446			−0.852230	−	0.523167i	$-0.824750\pi$
$919$	−51.6707			−1.70446			−0.852230	+	0.523167i	$0.824750\pi$
$920$	−25.8125	−	25.8125i	−0.851014	−	0.851014i
$921$	3.40575	+	8.22221i	0.112223	+	0.270931i
$922$			23.5624i			0.775988i
$923$	−4.63343	+	1.91923i	−0.152511	+	0.0631721i
$924$	−0.0409291	+	0.0988115i	−0.00134647	+	0.00325066i
$925$	−84.9995	−	35.2079i	−2.79477	−	1.15763i
$926$	−30.9906	+	30.9906i	−1.01841	+	1.01841i
$927$	45.0450	−	45.0450i	1.47947	−	1.47947i
$928$	9.88748	+	4.09553i	0.324573	+	0.134442i
$929$	−15.7682	+	38.0677i	−0.517336	+	1.24896i	0.422197	+	0.906504i	$0.361259\pi$
$929$	−15.7682	+	38.0677i	−0.517336	+	1.24896i	−0.939534	+	0.342457i	$0.888741\pi$
$930$	69.5837	−	28.8225i	2.28174	−	0.945127i
$931$			26.7663i			0.877231i
$932$	0.985800	+	2.37993i	0.0322909	+	0.0779572i
$933$	20.8114	+	20.8114i	0.681334	+	0.681334i
$934$	−24.4929			−0.801432
$935$	3.83831	−	14.7630i	0.125526	−	0.482800i
$936$	−14.9083			−0.487292
$937$	26.7259	+	26.7259i	0.873098	+	0.873098i	0.992809	−	0.119711i	$-0.0381967\pi$
$937$	26.7259	+	26.7259i	0.873098	+	0.873098i	−0.119711	+	0.992809i	$0.538197\pi$
$938$	−0.156563	−	0.377976i	−0.00511195	−	0.0123413i
$939$			87.3463i			2.85044i
$940$	−11.3562	+	4.70390i	−0.370399	+	0.153424i
$941$	8.77513	−	21.1850i	0.286061	−	0.690612i	−0.713893	−	0.700255i	$-0.753070\pi$
$941$	8.77513	−	21.1850i	0.286061	−	0.690612i	0.999954	+	0.00964307i	$0.00306953\pi$
$942$	−59.5285	−	24.6575i	−1.93954	−	0.803385i
$943$	16.6678	−	16.6678i	0.542780	−	0.542780i
$944$	−3.74847	+	3.74847i	−0.122002	+	0.122002i
$945$	−3.63650	−	1.50629i	−0.118295	−	0.0489995i
$946$	−3.96885	+	9.58164i	−0.129038	+	0.311526i
$947$	−27.4425	+	11.3670i	−0.891761	+	0.369379i	−0.781047	−	0.624473i	$-0.785314\pi$
$947$	−27.4425	+	11.3670i	−0.891761	+	0.369379i	−0.110714	+	0.993852i	$0.535314\pi$
$948$		−	5.60353i		−	0.181994i
$949$	−2.12017	−	5.11854i	−0.0688236	−	0.166155i
$950$	36.1512	+	36.1512i	1.17290	+	1.17290i
$951$	−63.3728			−2.05500
$952$	−0.977079	+	0.136033i	−0.0316673	+	0.00440884i
$953$	−47.5888			−1.54155			−0.770776	−	0.637106i	$-0.780131\pi$
$953$	−47.5888			−1.54155			−0.770776	+	0.637106i	$0.780131\pi$
$954$	−46.5810	−	46.5810i	−1.50811	−	1.50811i
$955$	9.61613	+	23.2154i	0.311171	+	0.751232i
$956$			3.97773i			0.128649i
$957$	−15.1078	+	6.25788i	−0.488367	+	0.202288i
$958$	−7.54125	+	18.2062i	−0.243647	+	0.588216i
$959$	0.908120	+	0.376155i	0.0293247	+	0.0121467i
$960$	49.2211	−	49.2211i	1.58860	−	1.58860i
$961$	9.01386	−	9.01386i	0.290770	−	0.290770i
$962$	13.4806	+	5.58383i	0.434631	+	0.180030i
$963$	14.1751	−	34.2216i	0.456785	−	1.10278i
$964$	−2.26101	+	0.936541i	−0.0728222	+	0.0301640i
$965$			39.6586i			1.27666i
$966$	0.679801	+	1.64119i	0.0218722	+	0.0528043i
$967$	26.8630	+	26.8630i	0.863857	+	0.863857i	0.991784	−	0.127927i	$-0.0408323\pi$
$967$	26.8630	+	26.8630i	0.863857	+	0.863857i	−0.127927	+	0.991784i	$0.540832\pi$
$968$	2.51653			0.0808842
$969$	29.5013	−	39.0444i	0.947717	−	1.25429i
$970$	−14.8738			−0.477569
$971$	−9.21003	−	9.21003i	−0.295564	−	0.295564i	0.543710	−	0.839273i	$-0.317019\pi$
$971$	−9.21003	−	9.21003i	−0.295564	−	0.295564i	−0.839273	+	0.543710i	$0.817019\pi$
$972$	1.73519	+	4.18912i	0.0556562	+	0.134366i
$973$			1.12144i			0.0359517i
$974$	12.8120	−	5.30689i	0.410522	−	0.170044i
$975$	9.23632	−	22.2985i	0.295799	−	0.714122i
$976$	−60.4822	−	25.0525i	−1.93599	−	0.801912i
$977$	25.9890	−	25.9890i	0.831463	−	0.831463i	−0.156254	−	0.987717i	$-0.549942\pi$
$977$	25.9890	−	25.9890i	0.831463	−	0.831463i	0.987717	+	0.156254i	$0.0499418\pi$
$978$	−25.6192	+	25.6192i	−0.819213	+	0.819213i
$979$	6.58726	+	2.72853i	0.210530	+	0.0872043i
$980$	3.59163	−	8.67096i	0.114730	−	0.276984i
$981$	−107.885	+	44.6876i	−3.44452	+	1.42676i
$982$			66.5340i			2.12318i
$983$	13.4691	+	32.5173i	0.429597	+	1.03714i	0.979415	+	0.201855i	$0.0646970\pi$
$983$	13.4691	+	32.5173i	0.429597	+	1.03714i	−0.549818	+	0.835284i	$0.685303\pi$
$984$	33.1625	+	33.1625i	1.05718	+	1.05718i
$985$	65.4307			2.08480
$986$	26.6747	+	20.1549i	0.849497	+	0.641864i
$987$	−2.69857			−0.0858964
$988$	−0.880513	−	0.880513i	−0.0280128	−	0.0280128i
$989$	10.1236	+	24.4405i	0.321912	+	0.777164i
$990$		−	37.5892i		−	1.19466i
$991$	−19.3826	+	8.02854i	−0.615709	+	0.255035i	−0.668667	−	0.743562i	$-0.733135\pi$
$991$	−19.3826	+	8.02854i	−0.615709	+	0.255035i	0.0529582	+	0.998597i	$0.483135\pi$
$992$	3.31697	−	8.00787i	0.105314	−	0.254250i
$993$	53.5596	+	22.1851i	1.69966	+	0.704024i
$994$	−0.578267	+	0.578267i	−0.0183415	+	0.0183415i
$995$	−61.1002	+	61.1002i	−1.93701	+	1.93701i
$996$	−11.5877	−	4.79976i	−0.367169	−	0.152086i
$997$	−5.08072	+	12.2659i	−0.160908	+	0.388466i	−0.983685	−	0.179897i	$-0.942423\pi$
$997$	−5.08072	+	12.2659i	−0.160908	+	0.388466i	0.822777	+	0.568364i	$0.192423\pi$
$998$	−17.3849	+	7.20105i	−0.550309	+	0.227945i
$999$			118.516i			3.74969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.100.3	✓	56
17.5	odd	16		3179.2.a.bh.1.22		28
17.8	even	8	inner	187.2.h.a.144.3	yes	56
17.12	odd	16		3179.2.a.bi.1.22		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.100.3	✓	56	1.1	even	1	trivial
187.2.h.a.144.3	yes	56	17.8	even	8	inner
3179.2.a.bh.1.22		28	17.5	odd	16
3179.2.a.bi.1.22		28	17.12	odd	16

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08694 - 1.08694i) q^{2} +(1.18631 + 2.86400i) q^{3} +0.362879i q^{4} +(3.41797 - 1.41577i) q^{5} +(1.82355 - 4.40244i) q^{6} +(0.0878391 + 0.0363841i) q^{7} +(-1.77945 + 1.77945i) q^{8} +(-4.67384 + 4.67384i) q^{9} +O(q^{10})\)	\(q+(-1.08694 - 1.08694i) q^{2} +(1.18631 + 2.86400i) q^{3} +0.362879i q^{4} +(3.41797 - 1.41577i) q^{5} +(1.82355 - 4.40244i) q^{6} +(0.0878391 + 0.0363841i) q^{7} +(-1.77945 + 1.77945i) q^{8} +(-4.67384 + 4.67384i) q^{9} +(-5.25399 - 2.17627i) q^{10} +(0.382683 - 0.923880i) q^{11} +(-1.03929 + 0.430486i) q^{12} -0.896265i q^{13} +(-0.0559285 - 0.135023i) q^{14} +(8.10952 + 8.10952i) q^{15} +4.59408 q^{16} +(3.99044 + 1.03750i) q^{17} +10.1604 q^{18} +(-2.70730 - 2.70730i) q^{19} +(0.513753 + 1.24031i) q^{20} +0.294734i q^{21} +(-1.42016 + 0.588248i) q^{22} +(-1.50048 + 3.62249i) q^{23} +(-7.20733 - 2.98537i) q^{24} +(6.14258 - 6.14258i) q^{25} +(-0.974187 + 0.974187i) q^{26} +(-10.3385 - 4.28235i) q^{27} +(-0.0132031 + 0.0318750i) q^{28} +(-4.87355 + 2.01869i) q^{29} -17.6291i q^{30} +(1.63494 + 3.94708i) q^{31} +(-1.43458 - 1.43458i) q^{32} +3.09997 q^{33} +(-3.20967 - 5.46507i) q^{34} +0.351743 q^{35} +(-1.69604 - 1.69604i) q^{36} +(-4.05299 - 9.78477i) q^{37} +5.88536i q^{38} +(2.56690 - 1.06325i) q^{39} +(-3.56282 + 8.60141i) q^{40} +(-5.55416 - 2.30061i) q^{41} +(0.320358 - 0.320358i) q^{42} +(4.77077 - 4.77077i) q^{43} +(0.335257 + 0.138868i) q^{44} +(-9.35797 + 22.5921i) q^{45} +(5.56836 - 2.30649i) q^{46} +9.15596i q^{47} +(5.44999 + 13.1574i) q^{48} +(-4.94336 - 4.94336i) q^{49} -13.3532 q^{50} +(1.76249 + 12.6594i) q^{51} +0.325236 q^{52} +(-4.58457 - 4.58457i) q^{53} +(6.58268 + 15.8920i) q^{54} -3.69958i q^{55} +(-0.221049 + 0.0915617i) q^{56} +(4.54202 - 10.9654i) q^{57} +(7.49145 + 3.10306i) q^{58} +(-0.815936 + 0.815936i) q^{59} +(-2.94278 + 2.94278i) q^{60} +(-13.1652 - 5.45322i) q^{61} +(2.51317 - 6.06732i) q^{62} +(-0.580600 + 0.240492i) q^{63} -6.06954i q^{64} +(-1.26890 - 3.06341i) q^{65} +(-3.36948 - 3.36948i) q^{66} +2.79934 q^{67} +(-0.376487 + 1.44805i) q^{68} -12.1548 q^{69} +(-0.382324 - 0.382324i) q^{70} +(-2.14136 - 5.16970i) q^{71} -16.6338i q^{72} +(5.71097 - 2.36556i) q^{73} +(-6.23011 + 15.0408i) q^{74} +(24.8793 + 10.3053i) q^{75} +(0.982425 - 0.982425i) q^{76} +(0.0672291 - 0.0672291i) q^{77} +(-3.94575 - 1.63439i) q^{78} +(-1.90626 + 4.60211i) q^{79} +(15.7024 - 6.50415i) q^{80} -14.8602i q^{81} +(3.53642 + 8.53767i) q^{82} +(7.88398 + 7.88398i) q^{83} -0.106953 q^{84} +(15.1081 - 2.10340i) q^{85} -10.3711 q^{86} +(-11.5630 - 11.5630i) q^{87} +(0.963033 + 2.32497i) q^{88} +7.13000i q^{89} +(34.7279 - 14.3848i) q^{90} +(0.0326098 - 0.0787271i) q^{91} +(-1.31453 - 0.544494i) q^{92} +(-9.36491 + 9.36491i) q^{93} +(9.95198 - 9.95198i) q^{94} +(-13.0864 - 5.42056i) q^{95} +(2.40679 - 5.81050i) q^{96} +(2.41637 - 1.00089i) q^{97} +10.7463i q^{98} +(2.52947 + 6.10667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 16 q^{6}+O(q^{10}) \) 56 * q - 16 * q^6	\( 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) \) 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

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