LMFDB - Embedded newform 133.2.g.a.102.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(30,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("133.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.g (of order $3$, 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			102.11
Character	$\chi$	$=$	133.102
Dual form			133.2.g.a.30.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14607 - 1.98506i) q^{2} +2.15251 q^{3} +(-1.62697 - 2.81799i) q^{4} +(-1.58716 + 2.74903i) q^{5} +(2.46693 - 4.27285i) q^{6} +(-2.63669 - 0.218793i) q^{7} -2.87420 q^{8} +1.63329 q^{9} +O(q^{10})$	\(q+(1.14607 - 1.98506i) q^{2} +2.15251 q^{3} +(-1.62697 - 2.81799i) q^{4} +(-1.58716 + 2.74903i) q^{5} +(2.46693 - 4.27285i) q^{6} +(-2.63669 - 0.218793i) q^{7} -2.87420 q^{8} +1.63329 q^{9} +(3.63799 + 6.30119i) q^{10} +(1.48277 - 2.56823i) q^{11} +(-3.50206 - 6.06575i) q^{12} +(-2.75648 + 4.77436i) q^{13} +(-3.45616 + 4.98323i) q^{14} +(-3.41637 + 5.91732i) q^{15} +(-0.0401130 + 0.0694778i) q^{16} -0.323213 q^{17} +(1.87187 - 3.24218i) q^{18} +(3.78911 - 2.15468i) q^{19} +10.3290 q^{20} +(-5.67550 - 0.470955i) q^{21} +(-3.39872 - 5.88676i) q^{22} -2.19712 q^{23} -6.18675 q^{24} +(-2.53813 - 4.39617i) q^{25} +(6.31825 + 10.9435i) q^{26} -2.94185 q^{27} +(3.67325 + 7.78614i) q^{28} +(0.399878 - 0.692609i) q^{29} +(7.83081 + 13.5634i) q^{30} +(4.58337 - 7.93862i) q^{31} +(-2.78226 - 4.81901i) q^{32} +(3.19167 - 5.52813i) q^{33} +(-0.370426 + 0.641597i) q^{34} +(4.78631 - 6.90109i) q^{35} +(-2.65732 - 4.60261i) q^{36} +(4.67774 + 8.10209i) q^{37} +(0.0654382 - 9.99102i) q^{38} +(-5.93334 + 10.2768i) q^{39} +(4.56181 - 7.90129i) q^{40} +(0.864608 + 1.49755i) q^{41} +(-7.43941 + 10.7264i) q^{42} +(1.27315 + 2.20517i) q^{43} -9.64966 q^{44} +(-2.59229 + 4.48998i) q^{45} +(-2.51806 + 4.36141i) q^{46} -3.05138 q^{47} +(-0.0863436 + 0.149552i) q^{48} +(6.90426 + 1.15378i) q^{49} -11.6355 q^{50} -0.695720 q^{51} +17.9388 q^{52} +(-2.50124 - 4.33228i) q^{53} +(-3.37157 + 5.83974i) q^{54} +(4.70677 + 8.15236i) q^{55} +(7.57838 + 0.628857i) q^{56} +(8.15609 - 4.63796i) q^{57} +(-0.916579 - 1.58756i) q^{58} -7.00305 q^{59} +22.2333 q^{60} +2.47204 q^{61} +(-10.5057 - 18.1965i) q^{62} +(-4.30649 - 0.357354i) q^{63} -12.9151 q^{64} +(-8.74992 - 15.1553i) q^{65} +(-7.31577 - 12.6713i) q^{66} +(3.75535 + 6.50446i) q^{67} +(0.525858 + 0.910813i) q^{68} -4.72932 q^{69} +(-8.21360 - 17.4102i) q^{70} +(-5.16665 - 8.94891i) q^{71} -4.69442 q^{72} -0.510005 q^{73} +21.4442 q^{74} +(-5.46334 - 9.46279i) q^{75} +(-12.2366 - 7.17209i) q^{76} +(-4.47151 + 6.44720i) q^{77} +(13.6001 + 23.5560i) q^{78} +(-2.77908 + 4.81351i) q^{79} +(-0.127331 - 0.220544i) q^{80} -11.2322 q^{81} +3.96362 q^{82} +9.91911 q^{83} +(7.90670 + 16.7597i) q^{84} +(0.512990 - 0.888525i) q^{85} +5.83651 q^{86} +(0.860741 - 1.49085i) q^{87} +(-4.26178 + 7.38161i) q^{88} -17.1173 q^{89} +(5.94191 + 10.2917i) q^{90} +(8.31257 - 11.9854i) q^{91} +(3.57465 + 6.19147i) q^{92} +(9.86573 - 17.0880i) q^{93} +(-3.49710 + 6.05716i) q^{94} +(-0.0906230 + 13.8362i) q^{95} +(-5.98884 - 10.3730i) q^{96} +(1.59017 + 2.75425i) q^{97} +(10.2031 - 12.3830i) q^{98} +(2.42179 - 4.19467i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.14607	−	1.98506i	0.810396	−	1.40365i	−0.102191	−	0.994765i	$-0.532585\pi$
$2$	1.14607	−	1.98506i	0.810396	−	1.40365i	0.912587	−	0.408883i	$-0.134081\pi$
$3$	2.15251			1.24275			0.621376	−	0.783513i	$-0.286574\pi$
$3$	2.15251			1.24275			0.621376	+	0.783513i	$0.286574\pi$
$4$	−1.62697	−	2.81799i	−0.813484	−	1.40900i
$5$	−1.58716	+	2.74903i	−0.709798	+	1.22941i	0.255134	+	0.966906i	$0.417880\pi$
$5$	−1.58716	+	2.74903i	−0.709798	+	1.22941i	−0.964932	+	0.262500i	$0.915453\pi$
$6$	2.46693	−	4.27285i	1.00712	−	1.74438i
$7$	−2.63669	−	0.218793i	−0.996575	−	0.0826961i
$7$	−2.63669	−	0.218793i	−0.996575	−	0.0826961i
$8$	−2.87420			−1.01618
$9$	1.63329			0.544431
$10$	3.63799	+	6.30119i	1.15043	+	1.99261i
$11$	1.48277	−	2.56823i	0.447071	−	0.774350i	−0.551123	−	0.834424i	$-0.685800\pi$
$11$	1.48277	−	2.56823i	0.447071	−	0.774350i	0.998194	+	0.0600742i	$0.0191337\pi$
$12$	−3.50206	−	6.06575i	−1.01096	−	1.75103i
$13$	−2.75648	+	4.77436i	−0.764509	+	1.32417i	0.175996	+	0.984391i	$0.443685\pi$
$13$	−2.75648	+	4.77436i	−0.764509	+	1.32417i	−0.940506	+	0.339778i	$0.889648\pi$
$14$	−3.45616	+	4.98323i	−0.923697	+	1.33182i
$15$	−3.41637	+	5.91732i	−0.882102	+	1.52785i
$16$	−0.0401130	+	0.0694778i	−0.0100283	+	0.0173694i
$17$	−0.323213			−0.0783908			−0.0391954	−	0.999232i	$-0.512479\pi$
$17$	−0.323213			−0.0783908			−0.0391954	+	0.999232i	$0.512479\pi$
$18$	1.87187	−	3.24218i	0.441205	−	0.764189i
$19$	3.78911	−	2.15468i	0.869282	−	0.494317i
$19$	3.78911	−	2.15468i	0.869282	−	0.494317i
$20$	10.3290			2.30964
$21$	−5.67550	−	0.470955i	−1.23849	−	0.102771i
$22$	−3.39872	−	5.88676i	−0.724609	−	1.25506i
$23$	−2.19712			−0.458132			−0.229066	−	0.973411i	$-0.573567\pi$
$23$	−2.19712			−0.458132			−0.229066	+	0.973411i	$0.573567\pi$
$24$	−6.18675			−1.26286
$25$	−2.53813	−	4.39617i	−0.507626	−	0.879233i
$26$	6.31825	+	10.9435i	1.23911	+	2.14620i
$27$	−2.94185			−0.566159
$28$	3.67325	+	7.78614i	0.694179	+	1.47144i
$29$	0.399878	−	0.692609i	0.0742555	−	0.128614i	−0.826507	−	0.562927i	$-0.809675\pi$
$29$	0.399878	−	0.692609i	0.0742555	−	0.128614i	0.900762	+	0.434313i	$0.143009\pi$
$30$	7.83081	+	13.5634i	1.42970	+	2.47632i
$31$	4.58337	−	7.93862i	0.823197	−	1.42582i	−0.0800931	−	0.996787i	$-0.525522\pi$
$31$	4.58337	−	7.93862i	0.823197	−	1.42582i	0.903290	−	0.429031i	$-0.141145\pi$
$32$	−2.78226	−	4.81901i	−0.491839	−	0.851889i
$33$	3.19167	−	5.52813i	0.555598	−	0.962324i
$34$	−0.370426	+	0.641597i	−0.0635276	+	0.110033i
$35$	4.78631	−	6.90109i	0.809034	−	1.16650i
$36$	−2.65732	−	4.60261i	−0.442886	−	0.767101i
$37$	4.67774	+	8.10209i	0.769017	+	1.33198i	0.938097	+	0.346373i	$0.112587\pi$
$37$	4.67774	+	8.10209i	0.769017	+	1.33198i	−0.169080	+	0.985602i	$0.554080\pi$
$38$	0.0654382	−	9.99102i	0.0106155	−	1.62076i
$39$	−5.93334	+	10.2768i	−0.950095	+	1.64561i
$40$	4.56181	−	7.90129i	0.721286	−	1.24930i
$41$	0.864608	+	1.49755i	0.135029	+	0.233877i	0.925609	−	0.378482i	$-0.123554\pi$
$41$	0.864608	+	1.49755i	0.135029	+	0.233877i	−0.790579	+	0.612359i	$0.790221\pi$
$42$	−7.43941	+	10.7264i	−1.14793	+	1.65512i
$43$	1.27315	+	2.20517i	0.194154	+	0.336285i	0.946623	−	0.322343i	$-0.104470\pi$
$43$	1.27315	+	2.20517i	0.194154	+	0.336285i	−0.752469	+	0.658628i	$0.771137\pi$
$44$	−9.64966			−1.45474
$45$	−2.59229	+	4.48998i	−0.386436	+	0.669327i
$46$	−2.51806	+	4.36141i	−0.371268	+	0.643055i
$47$	−3.05138			−0.445089			−0.222545	−	0.974923i	$-0.571436\pi$
$47$	−3.05138			−0.445089			−0.222545	+	0.974923i	$0.571436\pi$
$48$	−0.0863436	+	0.149552i	−0.0124626	+	0.0215859i
$49$	6.90426	+	1.15378i	0.986323	+	0.164826i
$50$	−11.6355			−1.64551
$51$	−0.695720			−0.0974203
$52$	17.9388			2.48766
$53$	−2.50124	−	4.33228i	−0.343572	−	0.595084i	0.641521	−	0.767105i	$-0.278304\pi$
$53$	−2.50124	−	4.33228i	−0.343572	−	0.595084i	−0.985093	+	0.172021i	$0.944970\pi$
$54$	−3.37157	+	5.83974i	−0.458813	+	0.794687i
$55$	4.70677	+	8.15236i	0.634660	+	1.09926i
$56$	7.57838	+	0.628857i	1.01270	+	0.0840345i
$57$	8.15609	−	4.63796i	1.08030	−	0.614313i
$58$	−0.916579	−	1.58756i	−0.120353	−	0.208457i
$59$	−7.00305			−0.911720			−0.455860	−	0.890052i	$-0.650668\pi$
$59$	−7.00305			−0.911720			−0.455860	+	0.890052i	$0.650668\pi$
$60$	22.2333			2.87030
$61$	2.47204			0.316512			0.158256	−	0.987398i	$-0.449413\pi$
$61$	2.47204			0.316512			0.158256	+	0.987398i	$0.449413\pi$
$62$	−10.5057	−	18.1965i	−1.33423	−	2.31096i
$63$	−4.30649	−	0.357354i	−0.542566	−	0.0450223i
$64$	−12.9151			−1.61439
$65$	−8.74992	−	15.1553i	−1.08529	−	1.87978i
$66$	−7.31577	−	12.6713i	−0.900509	−	1.55973i
$67$	3.75535	+	6.50446i	0.458789	+	0.794646i	0.998897	−	0.0469498i	$-0.0149501\pi$
$67$	3.75535	+	6.50446i	0.458789	+	0.794646i	−0.540108	+	0.841595i	$0.681617\pi$
$68$	0.525858	+	0.910813i	0.0637696	+	0.110452i
$69$	−4.72932			−0.569344
$70$	−8.21360	−	17.4102i	−0.981713	−	2.08092i
$71$	−5.16665	−	8.94891i	−0.613169	−	1.06204i	−0.990703	−	0.136044i	$-0.956561\pi$
$71$	−5.16665	−	8.94891i	−0.613169	−	1.06204i	0.377534	−	0.925996i	$-0.376772\pi$
$72$	−4.69442			−0.553243
$73$	−0.510005			−0.0596916			−0.0298458	−	0.999555i	$-0.509502\pi$
$73$	−0.510005			−0.0596916			−0.0298458	+	0.999555i	$0.509502\pi$
$74$	21.4442			2.49283
$75$	−5.46334	−	9.46279i	−0.630852	−	1.09267i
$76$	−12.2366	−	7.17209i	−1.40364	−	0.822695i
$77$	−4.47151	+	6.44720i	−0.509576	+	0.734727i
$78$	13.6001	+	23.5560i	1.53991	+	2.66720i
$79$	−2.77908	+	4.81351i	−0.312671	+	0.541562i	−0.978940	−	0.204150i	$-0.934557\pi$
$79$	−2.77908	+	4.81351i	−0.312671	+	0.541562i	0.666269	+	0.745712i	$0.267890\pi$
$80$	−0.127331	−	0.220544i	−0.0142361	−	0.0246576i
$81$	−11.2322			−1.24803
$82$	3.96362			0.437708
$83$	9.91911			1.08876			0.544382	−	0.838837i	$-0.316764\pi$
$83$	9.91911			1.08876			0.544382	+	0.838837i	$0.316764\pi$
$84$	7.90670	+	16.7597i	0.862692	+	1.82864i
$85$	0.512990	−	0.888525i	0.0556416	−	0.0963741i
$86$	5.83651			0.629367
$87$	0.860741	−	1.49085i	0.0922811	−	0.159836i
$88$	−4.26178	+	7.38161i	−0.454307	+	0.786883i
$89$	−17.1173			−1.81443			−0.907216	−	0.420664i	$-0.861797\pi$
$89$	−17.1173			−1.81443			−0.907216	+	0.420664i	$0.861797\pi$
$90$	5.94191	+	10.2917i	0.626333	+	1.08484i
$91$	8.31257	−	11.9854i	0.871394	−	1.25641i
$92$	3.57465	+	6.19147i	0.372683	+	0.645505i
$93$	9.86573	−	17.0880i	1.02303	−	1.77194i
$94$	−3.49710	+	6.05716i	−0.360699	+	0.624748i
$95$	−0.0906230	+	13.8362i	−0.00929772	+	1.41956i
$96$	−5.98884	−	10.3730i	−0.611233	−	1.05869i
$97$	1.59017	+	2.75425i	0.161457	+	0.279651i	0.935391	−	0.353614i	$-0.115047\pi$
$97$	1.59017	+	2.75425i	0.161457	+	0.279651i	−0.773935	+	0.633266i	$0.781714\pi$
$98$	10.2031	−	12.3830i	1.03067	−	1.25088i
$99$	2.42179	−	4.19467i	0.243399	−	0.421580i
$100$	−8.25891	+	14.3048i	−0.825891	+	1.43048i
$101$	0.872350	+	1.51095i	0.0868021	+	0.150346i	0.906158	−	0.422940i	$-0.139002\pi$
$101$	0.872350	+	1.51095i	0.0868021	+	0.150346i	−0.819356	+	0.573286i	$0.805669\pi$
$102$	−0.797346	+	1.38104i	−0.0789490	+	0.136744i
$103$	4.78400	+	8.28614i	0.471382	+	0.816457i	0.999464	−	0.0327358i	$-0.0104220\pi$
$103$	4.78400	+	8.28614i	0.471382	+	0.816457i	−0.528082	+	0.849193i	$0.677089\pi$
$104$	7.92268	−	13.7225i	0.776883	−	1.34560i
$105$	10.3026	−	14.8547i	1.00543	−	1.44967i
$106$	−11.4664			−1.11372
$107$	9.60828	+	16.6420i	0.928867	+	1.60885i	0.785220	+	0.619217i	$0.212550\pi$
$107$	9.60828	+	16.6420i	0.928867	+	1.60885i	0.143647	+	0.989629i	$0.454117\pi$
$108$	4.78629	+	8.29010i	0.460561	+	0.797715i
$109$	0.938593			0.0899009			0.0449505	−	0.998989i	$-0.485687\pi$
$109$	0.938593			0.0899009			0.0449505	+	0.998989i	$0.485687\pi$
$110$	21.5772			2.05730
$111$	10.0689	+	17.4398i	0.955696	+	1.65531i
$112$	0.120967	−	0.174415i	0.0114303	−	0.0164807i
$113$	−0.578380			−0.0544094			−0.0272047	−	0.999630i	$-0.508661\pi$
$113$	−0.578380			−0.0544094			−0.0272047	+	0.999630i	$0.508661\pi$
$114$	0.140856	−	21.5058i	0.0131924	−	2.01420i
$115$	3.48717	−	6.03996i	0.325181	−	0.563230i
$116$	−2.60235			−0.241622
$117$	−4.50214	+	7.79793i	−0.416223	+	0.720919i
$118$	−8.02601	+	13.9015i	−0.738854	+	1.27973i
$119$	0.852213	+	0.0707170i	0.0781223	+	0.00648261i
$120$	9.81934	−	17.0076i	0.896379	−	1.55257i
$121$	1.10280	+	1.91011i	0.100255	+	0.173646i
$122$	2.83314	−	4.90714i	0.256500	−	0.444271i
$123$	1.86108	+	3.22348i	0.167808	+	0.290651i
$124$	−29.8280			−2.67863
$125$	0.242061			0.0216506
$126$	−5.64492	+	8.13907i	−0.502889	+	0.725086i
$127$	7.18207	−	12.4397i	0.637306	−	1.10385i	−0.348716	−	0.937228i	$-0.613382\pi$
$127$	7.18207	−	12.4397i	0.637306	−	1.10385i	0.986022	−	0.166617i	$-0.0532845\pi$
$128$	−9.23718	+	15.9993i	−0.816459	+	1.41415i
$129$	2.74047	+	4.74664i	0.241285	+	0.417918i
$130$	−40.1122			−3.51807
$131$	−2.74847	+	4.76048i	−0.240135	+	0.415925i	−0.960752	−	0.277407i	$-0.910525\pi$
$131$	−2.74847	+	4.76048i	−0.240135	+	0.415925i	0.720618	+	0.693332i	$0.243858\pi$
$132$	−20.7710			−1.80788
$133$	−10.4621	+	4.85219i	−0.907182	+	0.420738i
$134$	17.2156			1.48720
$135$	4.66917	−	8.08724i	0.401858	−	0.696039i
$136$	0.928982			0.0796595
$137$	−7.03489	−	12.1848i	−0.601031	−	1.04102i	−0.992665	−	0.120896i	$-0.961423\pi$
$137$	−7.03489	−	12.1848i	−0.601031	−	1.04102i	0.391634	−	0.920121i	$-0.371910\pi$
$138$	−5.42015	+	9.38798i	−0.461394	+	0.799158i
$139$	−6.44723	+	11.1669i	−0.546847	+	0.947166i	0.451642	+	0.892199i	$0.350839\pi$
$139$	−6.44723	+	11.1669i	−0.546847	+	0.947166i	−0.998488	+	0.0549666i	$0.982495\pi$
$140$	−27.2344	−	2.25992i	−2.30173	−	0.190998i
$141$	−6.56812			−0.553135
$142$	−23.6855			−1.98764
$143$	8.17443	+	14.1585i	0.683580	+	1.18400i
$144$	−0.0655163	+	0.113478i	−0.00545969	+	0.00945647i
$145$	1.26934	+	2.19856i	0.105413	+	0.182580i
$146$	−0.584503	+	1.01239i	−0.0483738	+	0.0837859i
$147$	14.8615	+	2.48352i	1.22575	+	0.204837i
$148$	15.2211	−	26.3637i	1.25117	−	2.16708i
$149$	11.8964	−	20.6052i	0.974595	−	1.68805i	0.293329	−	0.956012i	$-0.405237\pi$
$149$	11.8964	−	20.6052i	0.974595	−	1.68805i	0.681266	−	0.732036i	$-0.261430\pi$
$150$	−25.0456			−2.04496
$151$	2.69615	−	4.66987i	0.219410	−	0.380029i	−0.735218	−	0.677831i	$-0.762920\pi$
$151$	2.69615	−	4.66987i	0.219410	−	0.380029i	0.954628	+	0.297802i	$0.0962535\pi$
$152$	−10.8907	+	6.19299i	−0.883351	+	0.502318i
$153$	−0.527902			−0.0426784
$154$	7.67338	+	16.2652i	0.618339	+	1.31068i
$155$	14.5490	+	25.1997i	1.16861	+	2.02409i
$156$	38.6134			3.09155
$157$	9.59213			0.765535			0.382768	−	0.923845i	$-0.374971\pi$
$157$	9.59213			0.765535			0.382768	+	0.923845i	$0.374971\pi$
$158$	6.37006	+	11.0333i	0.506775	+	0.877759i
$159$	−5.38395	−	9.32527i	−0.426975	−	0.739542i
$160$	17.6635			1.39642
$161$	5.79313	+	0.480716i	0.456562	+	0.0378857i
$162$	−12.8730	+	22.2966i	−1.01140	+	1.75179i
$163$	−5.65598	−	9.79645i	−0.443011	−	0.767317i	0.554901	−	0.831917i	$-0.312756\pi$
$163$	−5.65598	−	9.79645i	−0.443011	−	0.767317i	−0.997911	+	0.0645996i	$0.979423\pi$
$164$	2.81338	−	4.87292i	0.219688	−	0.380511i
$165$	10.1314	+	17.5480i	0.788725	+	1.36611i
$166$	11.3680	−	19.6900i	0.882330	−	1.52824i
$167$	−1.93218	+	3.34664i	−0.149517	+	0.258971i	−0.931049	−	0.364894i	$-0.881105\pi$
$167$	−1.93218	+	3.34664i	−0.149517	+	0.258971i	0.781532	+	0.623865i	$0.214438\pi$
$168$	16.3125	+	1.35362i	1.25854	+	0.104434i
$169$	−8.69634	−	15.0625i	−0.668949	−	1.15865i
$170$	−1.17585	−	2.03663i	−0.0901835	−	0.156202i
$171$	6.18873	−	3.51922i	0.473264	−	0.269122i
$172$	4.14276	−	7.17547i	0.315882	−	0.547124i
$173$	1.09977	−	1.90486i	0.0836141	−	0.144824i	−0.821186	−	0.570661i	$-0.806687\pi$
$173$	1.09977	−	1.90486i	0.0836141	−	0.144824i	0.904800	+	0.425837i	$0.140020\pi$
$174$	−1.97294	−	3.41724i	−0.149568	−	0.259060i
$175$	5.73040	+	12.1467i	0.433178	+	0.918200i
$176$	0.118957	+	0.206039i	0.00896669	+	0.0155308i
$177$	−15.0741			−1.13304
$178$	−19.6177	+	33.9789i	−1.47041	+	2.54682i
$179$	3.49326	−	6.05051i	0.261099	−	0.452236i	−0.705436	−	0.708774i	$-0.749249\pi$
$179$	3.49326	−	6.05051i	0.261099	−	0.452236i	0.966534	+	0.256538i	$0.0825819\pi$
$180$	16.8703			1.25744
$181$	1.24357	−	2.15393i	0.0924339	−	0.160100i	−0.816101	−	0.577910i	$-0.803869\pi$
$181$	1.24357	−	2.15393i	0.0924339	−	0.160100i	0.908535	+	0.417809i	$0.137202\pi$
$182$	−14.2649	−	30.2371i	−1.05738	−	2.24132i
$183$	5.32108			0.393346
$184$	6.31498			0.465546
$185$	−29.6972			−2.18338
$186$	−22.6137	−	39.1681i	−1.65812	−	2.87194i
$187$	−0.479250	+	0.830086i	−0.0350463	+	0.0607019i
$188$	4.96449	+	8.59875i	0.362073	+	0.627129i
$189$	7.75674	+	0.643657i	0.564220	+	0.0468191i
$190$	27.3618	+	16.0372i	1.98503	+	1.16346i
$191$	7.74869	+	13.4211i	0.560676	+	0.971119i	0.997438	+	0.0715417i	$0.0227919\pi$
$191$	7.74869	+	13.4211i	0.560676	+	0.971119i	−0.436762	+	0.899577i	$0.643875\pi$
$192$	−27.8000			−2.00629
$193$	10.2326			0.736558			0.368279	−	0.929715i	$-0.379947\pi$
$193$	10.2326			0.736558			0.368279	+	0.929715i	$0.379947\pi$
$194$	7.28978			0.523376
$195$	−18.8343	−	32.6219i	−1.34875	−	2.33610i
$196$	−7.98167	−	21.3333i	−0.570119	−	1.52381i
$197$	1.83450			0.130703			0.0653513	−	0.997862i	$-0.479183\pi$
$197$	1.83450			0.130703			0.0653513	+	0.997862i	$0.479183\pi$
$198$	−5.55111	−	9.61480i	−0.394500	−	0.683294i
$199$	1.66009	+	2.87537i	0.117681	+	0.203829i	0.918848	−	0.394611i	$-0.129121\pi$
$199$	1.66009	+	2.87537i	0.117681	+	0.203829i	−0.801167	+	0.598440i	$0.795787\pi$
$200$	7.29510	+	12.6355i	0.515841	+	0.893463i
$201$	8.08342	+	14.0009i	0.570161	+	0.987547i
$202$	3.99911			0.281376
$203$	−1.20589	+	1.73870i	−0.0846370	+	0.122033i
$204$	1.13191	+	1.96053i	0.0792498	+	0.137265i
$205$	−5.48907			−0.383374
$206$	21.9313			1.52802
$207$	−3.58854			−0.249421
$208$	−0.221141	−	0.383028i	−0.0153334	−	0.0265582i
$209$	0.0846626	−	12.9262i	0.00585624	−	0.894123i
$210$	−17.6798	−	37.4757i	−1.22003	−	2.58607i
$211$	1.61107	+	2.79046i	0.110911	+	0.192103i	0.916138	−	0.400864i	$-0.131290\pi$
$211$	1.61107	+	2.79046i	0.110911	+	0.192103i	−0.805227	+	0.592967i	$0.797957\pi$
$212$	−8.13888	+	14.0970i	−0.558981	+	0.968183i
$213$	−11.1213	−	19.2626i	−0.762017	−	1.31985i
$214$	44.0472			3.01100
$215$	−8.08277			−0.551241
$216$	8.45547			0.575322
$217$	−13.8218	+	19.9289i	−0.938287	+	1.35286i
$218$	1.07570	−	1.86316i	0.0728554	−	0.126189i
$219$	−1.09779			−0.0741818
$220$	15.3155	−	26.5272i	1.03257	−	1.78847i
$221$	0.890931	−	1.54314i	0.0599305	−	0.103803i
$222$	46.1587			3.09797
$223$	−13.9573	−	24.1748i	−0.934653	−	1.61887i	−0.775252	−	0.631652i	$-0.782377\pi$
$223$	−13.9573	−	24.1748i	−0.934653	−	1.61887i	−0.159400	−	0.987214i	$-0.550956\pi$
$224$	6.28158	+	13.3150i	0.419706	+	0.889645i
$225$	−4.14551	−	7.18023i	−0.276367	−	0.478682i
$226$	−0.662866	+	1.14812i	−0.0440932	+	0.0763716i
$227$	10.1380	−	17.5595i	0.672881	−	1.16546i	−0.304203	−	0.952607i	$-0.598390\pi$
$227$	10.1380	−	17.5595i	0.672881	−	1.16546i	0.977084	−	0.212856i	$-0.0682766\pi$
$228$	−26.3394	−	15.4380i	−1.74437	−	1.02241i
$229$	−8.06488	−	13.9688i	−0.532942	−	0.923083i	−0.999260	−	0.0384655i	$-0.987753\pi$
$229$	−8.06488	−	13.9688i	−0.532942	−	0.923083i	0.466318	−	0.884617i	$-0.345580\pi$
$230$	−7.99312	−	13.8445i	−0.527050	−	0.912878i
$231$	−9.62496	+	13.8777i	−0.633276	+	0.913083i
$232$	−1.14933	+	1.99070i	−0.0754573	+	0.130696i
$233$	1.19080	−	2.06252i	0.0780116	−	0.135120i	−0.824380	−	0.566036i	$-0.808476\pi$
$233$	1.19080	−	2.06252i	0.0780116	−	0.135120i	0.902392	+	0.430916i	$0.141810\pi$
$234$	10.3196	+	17.8740i	0.674611	+	1.16846i
$235$	4.84301	−	8.38834i	0.315923	−	0.547195i
$236$	11.3937	+	19.7345i	0.741669	+	1.28461i
$237$	−5.98199	+	10.3611i	−0.388572	+	0.673027i
$238$	1.11708	−	1.61065i	0.0724093	−	0.104403i
$239$	13.6506			0.882982			0.441491	−	0.897266i	$-0.354450\pi$
$239$	13.6506			0.882982			0.441491	+	0.897266i	$0.354450\pi$
$240$	−0.274082	−	0.474723i	−0.0176919	−	0.0306432i
$241$	11.6643	+	20.2032i	0.751365	+	1.30140i	0.947161	+	0.320757i	$0.103937\pi$
$241$	11.6643	+	20.2032i	0.751365	+	1.30140i	−0.195797	+	0.980645i	$0.562729\pi$
$242$	5.05557			0.324984
$243$	−15.3519			−0.984827
$244$	−4.02193	−	6.96618i	−0.257477	−	0.445964i
$245$	−14.1299	+	17.1488i	−0.902727	+	1.09560i
$246$	8.53172			0.543963
$247$	−0.157389	+	24.0299i	−0.0100144	+	1.52899i
$248$	−13.1735	+	22.8172i	−0.836520	+	1.44889i
$249$	21.3510			1.35306
$250$	0.277419	−	0.480504i	0.0175455	−	0.0303898i
$251$	−2.24314	+	3.88524i	−0.141586	+	0.245234i	−0.928094	−	0.372346i	$-0.878554\pi$
$251$	−2.24314	+	3.88524i	−0.141586	+	0.245234i	0.786508	+	0.617580i	$0.211887\pi$
$252$	5.99950	+	12.7170i	0.377933	+	0.801099i
$253$	−3.25782	+	5.64271i	−0.204817	+	0.354754i
$254$	−16.4624	−	28.5136i	−1.03294	−	1.78910i
$255$	1.10422	−	1.91256i	0.0691487	−	0.119769i
$256$	8.25783	+	14.3030i	0.516115	+	0.893937i
$257$	−5.31411			−0.331485			−0.165743	−	0.986169i	$-0.553002\pi$
$257$	−5.31411			−0.331485			−0.165743	+	0.986169i	$0.553002\pi$
$258$	12.5631			0.782147
$259$	−10.5611	−	22.3862i	−0.656233	−	1.39101i
$260$	−28.4717	+	49.3144i	−1.76574	+	3.05835i
$261$	0.653118	−	1.13123i	0.0404270	−	0.0700216i
$262$	6.29989	+	10.9117i	0.389208	+	0.674128i
$263$	−16.1182			−0.993890			−0.496945	−	0.867782i	$-0.665545\pi$
$263$	−16.1182			−0.993890			−0.496945	+	0.867782i	$0.665545\pi$
$264$	−9.17351	+	15.8890i	−0.564590	+	0.977899i
$265$	15.8794			0.975467
$266$	−2.35851	+	26.3289i	−0.144609	+	1.61433i
$267$	−36.8452			−2.25489
$268$	12.2197	−	21.1651i	0.746435	−	1.29286i
$269$	−13.6253			−0.830751			−0.415375	−	0.909650i	$-0.636350\pi$
$269$	−13.6253			−0.830751			−0.415375	+	0.909650i	$0.636350\pi$
$270$	−10.7024	−	18.5371i	−0.651329	−	1.12813i
$271$	−1.17953	+	2.04301i	−0.0716515	+	0.124104i	−0.899625	−	0.436663i	$-0.856160\pi$
$271$	−1.17953	+	2.04301i	−0.0716515	+	0.124104i	0.827974	+	0.560767i	$0.189494\pi$
$272$	0.0129651	−	0.0224562i	0.000786123	−	0.00136160i
$273$	17.8929	−	25.7987i	1.08293	−	1.56141i
$274$	−32.2500			−1.94829
$275$	−15.0538			−0.907779
$276$	7.69446	+	13.3272i	0.463152	+	0.802203i
$277$	−9.88193	+	17.1160i	−0.593748	+	1.02840i	0.399975	+	0.916526i	$0.369019\pi$
$277$	−9.88193	+	17.1160i	−0.593748	+	1.02840i	−0.993722	+	0.111875i	$0.964314\pi$
$278$	14.7780	+	25.5962i	0.886325	+	1.53516i
$279$	7.48598	−	12.9661i	0.448174	−	0.776260i
$280$	−13.7568	+	19.8351i	−0.822128	+	1.18538i
$281$	−4.04837	+	7.01198i	−0.241505	+	0.418300i	−0.961143	−	0.276050i	$-0.910974\pi$
$281$	−4.04837	+	7.01198i	−0.241505	+	0.418300i	0.719638	+	0.694350i	$0.244308\pi$
$282$	−7.52754	+	13.0381i	−0.448259	+	0.776407i
$283$	−10.9294			−0.649688			−0.324844	−	0.945768i	$-0.605312\pi$
$283$	−10.9294			−0.649688			−0.324844	+	0.945768i	$0.605312\pi$
$284$	−16.8120	+	29.1192i	−0.997606	+	1.72790i
$285$	−0.195067	+	29.7826i	−0.0115548	+	1.76417i
$286$	37.4740			2.21588
$287$	−1.95205	−	4.13773i	−0.115226	−	0.244243i
$288$	−4.54425	−	7.87087i	−0.267772	−	0.463795i
$289$	−16.8955			−0.993855
$290$	5.81901			0.341704
$291$	3.42284	+	5.92854i	0.200651	+	0.347537i
$292$	0.829762	+	1.43719i	0.0485581	+	0.0841051i
$293$	−16.5911			−0.969264			−0.484632	−	0.874718i	$-0.661046\pi$
$293$	−16.5911			−0.969264			−0.484632	+	0.874718i	$0.661046\pi$
$294$	21.9623	−	26.6546i	1.28087	−	1.55453i
$295$	11.1149	−	19.2516i	0.647137	−	1.12087i
$296$	−13.4448	−	23.2871i	−0.781463	−	1.35353i
$297$	−4.36208	+	7.55534i	−0.253113	+	0.438405i
$298$	−27.2684	−	47.2302i	−1.57962	−	2.73597i
$299$	6.05632	−	10.4898i	0.350246	−	0.606644i
$300$	−17.7774	+	30.7913i	−1.02638	+	1.77774i
$301$	−2.87443	−	6.09290i	−0.165680	−	0.351189i
$302$	−6.17998	−	10.7040i	−0.355618	−	0.615948i
$303$	1.87774	+	3.25234i	0.107873	+	0.186842i
$304$	−0.00229036	+	0.349690i	−0.000131361	+	0.0200561i
$305$	−3.92351	+	6.79572i	−0.224659	+	0.389122i
$306$	−0.605015	+	1.04792i	−0.0345864	+	0.0599054i
$307$	−6.31566	−	10.9390i	−0.360454	−	0.624324i	0.627582	−	0.778551i	$-0.284045\pi$
$307$	−6.31566	−	10.9390i	−0.360454	−	0.624324i	−0.988036	+	0.154226i	$0.950712\pi$
$308$	25.4431	+	2.11128i	1.44976	+	0.120301i
$309$	10.2976	+	17.8360i	0.585811	+	1.01465i
$310$	66.6970			3.78814
$311$	−8.01806	+	13.8877i	−0.454662	+	0.787498i	−0.998669	−	0.0515829i	$-0.983573\pi$
$311$	−8.01806	+	13.8877i	−0.454662	+	0.787498i	0.544006	+	0.839081i	$0.316907\pi$
$312$	17.0536	−	29.5378i	0.965472	−	1.67225i
$313$	17.5381			0.991312			0.495656	−	0.868519i	$-0.334928\pi$
$313$	17.5381			0.991312			0.495656	+	0.868519i	$0.334928\pi$
$314$	10.9933	−	19.0409i	0.620387	−	1.07454i
$315$	7.81744	−	11.2715i	0.440463	−	0.635077i
$316$	18.0859			1.01741
$317$	5.56774			0.312715			0.156358	−	0.987700i	$-0.450025\pi$
$317$	5.56774			0.312715			0.156358	+	0.987700i	$0.450025\pi$
$318$	−24.6816			−1.38407
$319$	−1.18585	−	2.05396i	−0.0663949	−	0.114999i
$320$	20.4983	−	35.5042i	1.14589	−	1.98474i
$321$	20.6819	+	35.8221i	1.15435	+	1.99940i
$322$	7.59360	−	10.9488i	0.423175	−	0.610150i
$323$	−1.22469	+	0.696421i	−0.0681437	+	0.0387499i
$324$	18.2745	+	31.6523i	1.01525	+	1.75846i
$325$	27.9852			1.55234
$326$	−25.9287			−1.43606
$327$	2.02033			0.111725
$328$	−2.48506	−	4.30425i	−0.137215	−	0.237663i
$329$	8.04553	+	0.667621i	0.443565	+	0.0368071i
$330$	46.4451			2.55672
$331$	−3.25456	−	5.63707i	−0.178887	−	0.309841i	0.762613	−	0.646856i	$-0.223916\pi$
$331$	−3.25456	−	5.63707i	−0.178887	−	0.309841i	−0.941500	+	0.337014i	$0.890583\pi$
$332$	−16.1381	−	27.9520i	−0.885692	−	1.53406i
$333$	7.64013	+	13.2331i	0.418677	+	0.725169i
$334$	4.42885	+	7.67099i	0.242336	+	0.419738i
$335$	−23.8413			−1.30259
$336$	0.260382	−	0.375429i	0.0142050	−	0.0204814i
$337$	13.3980	+	23.2059i	0.729833	+	1.26411i	0.956953	+	0.290241i	$0.0937356\pi$
$337$	13.3980	+	23.2059i	0.729833	+	1.26411i	−0.227120	+	0.973867i	$0.572931\pi$
$338$	−39.8666			−2.16845
$339$	−1.24497			−0.0676174
$340$	−3.33847			−0.181054
$341$	−13.5921	−	23.5423i	−0.736055	−	1.27488i
$342$	0.106880	−	16.3183i	0.00577939	−	0.882391i
$343$	−17.9519	−	4.55277i	−0.969314	−	0.245826i
$344$	−3.65930	−	6.33810i	−0.197296	−	0.341727i
$345$	7.50617	−	13.0011i	0.404119	−	0.699954i
$346$	−2.52084	−	4.36622i	−0.135521	−	0.234729i
$347$	−0.706517			−0.0379278			−0.0189639	−	0.999820i	$-0.506037\pi$
$347$	−0.706517			−0.0379278			−0.0189639	+	0.999820i	$0.506037\pi$
$348$	−5.60159			−0.300277
$349$	−2.68714			−0.143839			−0.0719196	−	0.997410i	$-0.522912\pi$
$349$	−2.68714			−0.143839			−0.0719196	+	0.997410i	$0.522912\pi$
$350$	30.6793	+	2.54577i	1.63988	+	0.136077i
$351$	8.10914	−	14.0454i	0.432834	−	0.749690i
$352$	−16.5018			−0.879547
$353$	4.96782	−	8.60451i	0.264410	−	0.457972i	−0.702999	−	0.711191i	$-0.748156\pi$
$353$	4.96782	−	8.60451i	0.264410	−	0.457972i	0.967409	+	0.253219i	$0.0814894\pi$
$354$	−17.2761	+	29.9230i	−0.918212	+	1.59039i
$355$	32.8011			1.74090
$356$	27.8493	+	48.2365i	1.47601	+	2.55653i
$357$	1.83440	+	0.152219i	0.0970866	+	0.00805628i
$358$	−8.00707	−	13.8686i	−0.423187	−	0.732981i
$359$	−16.4577	+	28.5056i	−0.868605	+	1.50447i	−0.00518287	+	0.999987i	$0.501650\pi$
$359$	−16.4577	+	28.5056i	−0.868605	+	1.50447i	−0.863422	+	0.504482i	$0.831684\pi$
$360$	7.45078	−	12.9051i	0.392690	−	0.680160i
$361$	9.71472	−	16.3286i	0.511301	−	0.859402i
$362$	−2.85045	−	4.93712i	−0.149816	−	0.259489i
$363$	2.37379	+	4.11153i	0.124592	+	0.215799i
$364$	−47.2990	−	3.92489i	−2.47914	−	0.205720i
$365$	0.809457	−	1.40202i	0.0423689	−	0.0733852i
$366$	6.09835	−	10.5627i	0.318766	−	0.552119i
$367$	0.356039	+	0.616677i	0.0185851	+	0.0321903i	0.875168	−	0.483818i	$-0.160751\pi$
$367$	0.356039	+	0.616677i	0.0185851	+	0.0321903i	−0.856583	+	0.516009i	$0.827417\pi$
$368$	0.0881332	−	0.152651i	0.00459426	−	0.00795749i
$369$	1.41216	+	2.44593i	0.0735141	+	0.127330i
$370$	−34.0352	+	58.9507i	−1.76941	+	3.06470i
$371$	5.64712	+	11.9701i	0.293184	+	0.621458i
$372$	−64.2049			−3.32887
$373$	−0.751466	−	1.30158i	−0.0389094	−	0.0673931i	0.845915	−	0.533318i	$-0.179055\pi$
$373$	−0.751466	−	1.30158i	−0.0389094	−	0.0673931i	−0.884824	+	0.465925i	$0.845722\pi$
$374$	1.09851	+	1.90268i	0.0568027	+	0.0983852i
$375$	0.521038			0.0269063
$376$	8.77028			0.452293
$377$	2.20451	+	3.81832i	0.113538	+	0.196654i
$378$	10.1675	−	14.6599i	0.522959	−	0.754023i
$379$	−12.6890			−0.651790			−0.325895	−	0.945406i	$-0.605666\pi$
$379$	−12.6890			−0.651790			−0.325895	+	0.945406i	$0.605666\pi$
$380$	39.1377	−	22.2557i	2.00772	−	1.14169i
$381$	15.4595	−	26.7766i	0.792013	−	1.37181i
$382$	35.5223			1.81748
$383$	7.58043	−	13.1297i	0.387342	−	0.670895i	−0.604749	−	0.796416i	$-0.706727\pi$
$383$	7.58043	−	13.1297i	0.387342	−	0.670895i	0.992091	+	0.125520i	$0.0400601\pi$
$384$	−19.8831	+	34.4386i	−1.01466	+	1.75744i
$385$	−10.6266	−	22.5250i	−0.541581	−	1.14798i
$386$	11.7273	−	20.3123i	0.596904	−	1.03387i
$387$	2.07943	+	3.60168i	0.105704	+	0.183084i
$388$	5.17430	−	8.96214i	0.262685	−	0.454984i
$389$	−3.63812	−	6.30141i	−0.184460	−	0.319494i	0.758934	−	0.651167i	$-0.225720\pi$
$389$	−3.63812	−	6.30141i	−0.184460	−	0.319494i	−0.943394	+	0.331673i	$0.892387\pi$
$390$	−86.3418			−4.37209
$391$	0.710139			0.0359133
$392$	−19.8443	−	3.31620i	−1.00229	−	0.167493i
$393$	−5.91610	+	10.2470i	−0.298428	+	0.516892i
$394$	2.10247	−	3.64158i	0.105921	−	0.183460i
$395$	−8.82167	−	15.2796i	−0.443866	−	0.768799i
$396$	−15.7607			−0.792006
$397$	2.16355	−	3.74738i	0.108585	−	0.188075i	−0.806612	−	0.591081i	$-0.798701\pi$
$397$	2.16355	−	3.74738i	0.108585	−	0.188075i	0.915197	+	0.403006i	$0.132035\pi$
$398$	7.61036			0.381473
$399$	−22.5198	+	10.4444i	−1.12740	+	0.522873i
$400$	0.407248			0.0203624
$401$	12.7940	−	22.1599i	0.638904	−	1.10661i	−0.346770	−	0.937950i	$-0.612722\pi$
$401$	12.7940	−	22.1599i	0.638904	−	1.10661i	0.985674	−	0.168664i	$-0.0539452\pi$
$402$	37.0568			1.84822
$403$	25.2679	+	43.7653i	1.25868	+	2.18010i
$404$	2.83857	−	4.91655i	0.141224	−	0.244607i
$405$	17.8273	−	30.8778i	0.885846	−	1.53433i
$406$	2.06939	+	4.38645i	0.102702	+	0.217696i
$407$	27.7440			1.37522
$408$	1.99964			0.0989970
$409$	−12.8996	−	22.3427i	−0.637842	−	1.10478i	−0.985905	−	0.167304i	$-0.946494\pi$
$409$	−12.8996	−	22.3427i	−0.637842	−	1.10478i	0.348063	−	0.937471i	$-0.386840\pi$
$410$	−6.29088	+	10.8961i	−0.310684	+	0.538121i
$411$	−15.1427	−	26.2279i	−0.746933	−	1.29373i
$412$	15.5668	−	26.9626i	0.766923	−	1.32835i
$413$	18.4649	+	1.53222i	0.908597	+	0.0753957i
$414$	−4.11273	+	7.12347i	−0.202130	+	0.350099i
$415$	−15.7432	+	27.2680i	−0.772802	+	1.33853i
$416$	30.6769			1.50406
$417$	−13.8777	+	24.0369i	−0.679594	+	1.17709i
$418$	−25.5622	−	14.9824i	−1.25029	−	0.732814i
$419$	3.69187			0.180360			0.0901799	−	0.995925i	$-0.471256\pi$
$419$	3.69187			0.180360			0.0901799	+	0.995925i	$0.471256\pi$
$420$	−58.6222	−	4.86449i	−2.86047	−	0.237363i
$421$	−5.24839	−	9.09048i	−0.255791	−	0.443043i	0.709319	−	0.704887i	$-0.249003\pi$
$421$	−5.24839	−	9.09048i	−0.255791	−	0.443043i	−0.965110	+	0.261845i	$0.915669\pi$
$422$	7.38562			0.359526
$423$	−4.98379			−0.242320
$424$	7.18908	+	12.4519i	0.349133	+	0.604716i
$425$	0.820357	+	1.42090i	0.0397932	+	0.0689238i
$426$	−50.9831			−2.47014
$427$	−6.51799	−	0.540865i	−0.315428	−	0.0261743i
$428$	31.2647	−	54.1521i	1.51124	−	2.61754i
$429$	17.5955	+	30.4763i	0.849520	+	1.47141i
$430$	−9.26345	+	16.0448i	−0.446723	+	0.773747i
$431$	15.6059	+	27.0303i	0.751711	+	1.30200i	0.946993	+	0.321255i	$0.104105\pi$
$431$	15.6059	+	27.0303i	0.751711	+	1.30200i	−0.195282	+	0.980747i	$0.562562\pi$
$432$	0.118006	−	0.204393i	0.00567758	−	0.00983386i
$433$	−15.9357	+	27.6015i	−0.765822	+	1.32644i	0.173989	+	0.984748i	$0.444334\pi$
$433$	−15.9357	+	27.6015i	−0.765822	+	1.32644i	−0.939811	+	0.341694i	$0.888999\pi$
$434$	23.7191	+	50.2771i	1.13855	+	2.41338i
$435$	2.73226	+	4.73241i	0.131002	+	0.226902i
$436$	−1.52706	−	2.64495i	−0.0731330	−	0.126670i
$437$	−8.32514	+	4.73409i	−0.398245	+	0.226462i
$438$	−1.25815	+	2.17918i	−0.0601166	+	0.104125i
$439$	−10.6340	+	18.4187i	−0.507535	+	0.879076i	0.492427	+	0.870354i	$0.336110\pi$
$439$	−10.6340	+	18.4187i	−0.507535	+	0.879076i	−0.999962	+	0.00872250i	$0.997224\pi$
$440$	−13.5282	−	23.4315i	−0.644932	−	1.11705i
$441$	11.2767	+	1.88446i	0.536985	+	0.0897363i
$442$	−2.04214	−	3.53710i	−0.0971349	−	0.168243i
$443$	−31.7444			−1.50822			−0.754110	−	0.656748i	$-0.771932\pi$
$443$	−31.7444			−1.50822			−0.754110	+	0.656748i	$0.771932\pi$
$444$	32.7635	−	56.7481i	1.55489	−	2.69314i
$445$	27.1679	−	47.0561i	1.28788	−	2.23067i
$446$	−63.9845			−3.02976
$447$	25.6072	−	44.3530i	1.21118	−	2.09782i
$448$	34.0532	+	2.82575i	1.60886	+	0.133504i
$449$	21.0194			0.991965			0.495983	−	0.868332i	$-0.334808\pi$
$449$	21.0194			0.991965			0.495983	+	0.868332i	$0.334808\pi$
$450$	−19.0042			−0.895868
$451$	5.12805			0.241471
$452$	0.941005	+	1.62987i	0.0442612	+	0.0766626i
$453$	5.80349	−	10.0519i	0.272672	−	0.472282i
$454$	−23.2377	−	40.2489i	−1.09060	−	1.88897i
$455$	19.7549	+	41.8743i	0.926126	+	1.96310i
$456$	−23.4423	+	13.3305i	−1.09779	+	0.624256i
$457$	14.0877	+	24.4007i	0.658996	+	1.14142i	0.980876	+	0.194635i	$0.0623521\pi$
$457$	14.0877	+	24.4007i	0.658996	+	1.14142i	−0.321879	+	0.946781i	$0.604315\pi$
$458$	−36.9718			−1.72758
$459$	0.950845			0.0443816
$460$	−22.6941			−1.05812
$461$	11.7266	+	20.3111i	0.546162	+	0.945980i	0.998533	+	0.0541501i	$0.0172450\pi$
$461$	11.7266	+	20.3111i	0.546162	+	0.945980i	−0.452371	+	0.891830i	$0.649422\pi$
$462$	16.5170	+	35.0109i	0.768442	+	1.62885i
$463$	−21.0750			−0.979438			−0.489719	−	0.871880i	$-0.662901\pi$
$463$	−21.0750			−0.979438			−0.489719	+	0.871880i	$0.662901\pi$
$464$	0.0320806	+	0.0555653i	0.00148931	+	0.00257955i
$465$	31.3169	+	54.2425i	1.45229	+	2.51544i
$466$	−2.72948	−	4.72760i	−0.126441	−	0.219002i
$467$	0.537579	+	0.931115i	0.0248762	+	0.0430869i	0.878196	−	0.478302i	$-0.158748\pi$
$467$	0.537579	+	0.931115i	0.0248762	+	0.0430869i	−0.853319	+	0.521389i	$0.825414\pi$
$468$	29.2993			1.35436
$469$	−8.47856	−	17.9719i	−0.391503	−	0.829864i
$470$	−11.1009	−	19.2273i	−0.512046	−	0.886890i
$471$	20.6471			0.951370
$472$	20.1282			0.926476
$473$	7.55116			0.347203
$474$	13.7116	+	23.7492i	0.629795	+	1.09084i
$475$	−19.0896	−	11.1887i	−0.875890	−	0.513373i
$476$	−1.18724	−	2.51658i	−0.0544172	−	0.115347i
$477$	−4.08526	−	7.07588i	−0.187051	−	0.323982i
$478$	15.6445	−	27.0972i	0.715565	−	1.23939i
$479$	−6.19738	−	10.7342i	−0.283165	−	0.490457i	0.688997	−	0.724764i	$-0.258051\pi$
$479$	−6.19738	−	10.7342i	−0.283165	−	0.490457i	−0.972163	+	0.234307i	$0.924718\pi$
$480$	38.0209			1.73541
$481$	−51.5764			−2.35168
$482$	53.4727			2.43561
$483$	12.4698	+	1.03474i	0.567393	+	0.0470825i
$484$	3.58845	−	6.21538i	0.163111	−	0.282517i
$485$	−10.0954			−0.458407
$486$	−17.5944	+	30.4745i	−0.798100	+	1.38235i
$487$	17.9098	−	31.0207i	0.811570	−	1.40568i	−0.100195	−	0.994968i	$-0.531947\pi$
$487$	17.9098	−	31.0207i	0.811570	−	1.40568i	0.911765	−	0.410712i	$-0.134720\pi$
$488$	−7.10514			−0.321635
$489$	−12.1746	−	21.0869i	−0.550552	−	0.953584i
$490$	17.8475	+	47.7025i	0.806266	+	2.15498i
$491$	−9.63680	−	16.6914i	−0.434903	−	0.753274i	0.562385	−	0.826876i	$-0.309884\pi$
$491$	−9.63680	−	16.6914i	−0.434903	−	0.753274i	−0.997288	+	0.0736018i	$0.976551\pi$
$492$	6.05583	−	10.4890i	0.273018	−	0.472880i
$493$	−0.129246	+	0.223860i	−0.00582094	+	0.0100822i
$494$	47.5203	+	27.8524i	2.13804	+	1.25314i
$495$	7.68753	+	13.3152i	0.345529	+	0.598473i
$496$	0.367705	+	0.636884i	0.0165104	+	0.0285969i
$497$	11.6649	+	24.7259i	0.523242	+	1.10911i
$498$	24.4698	−	42.3829i	1.09652	−	1.89922i
$499$	10.8969	−	18.8739i	0.487810	−	0.844913i	−0.512091	−	0.858931i	$-0.671129\pi$
$499$	10.8969	−	18.8739i	0.487810	−	0.844913i	0.999902	+	0.0140185i	$0.00446238\pi$
$500$	−0.393825	−	0.682125i	−0.0176124	−	0.0305056i
$501$	−4.15904	+	7.20367i	−0.185812	+	0.321836i
$502$	5.14161	+	8.90554i	0.229481	+	0.397474i
$503$	11.5263	−	19.9641i	0.513931	−	0.890154i	−0.485939	−	0.873993i	$-0.661522\pi$
$503$	11.5263	−	19.9641i	0.513931	−	0.890154i	0.999869	−	0.0161610i	$-0.00514444\pi$
$504$	12.3777	+	1.02711i	0.551348	+	0.0457510i
$505$	−5.53822			−0.246448
$506$	7.46740	+	12.9339i	0.331966	+	0.574983i
$507$	−18.7189	−	32.4222i	−0.831337	−	1.43992i
$508$	−46.7400			−2.07375
$509$	25.1446			1.11452			0.557258	−	0.830339i	$-0.311853\pi$
$509$	25.1446			1.11452			0.557258	+	0.830339i	$0.311853\pi$
$510$	−2.53102	−	4.38386i	−0.112076	−	0.194121i
$511$	1.34472	+	0.111586i	0.0594871	+	0.00493626i
$512$	0.907591			0.0401102
$513$	−11.1470	+	6.33874i	−0.492151	+	0.279862i
$514$	−6.09036	+	10.5488i	−0.268634	+	0.465288i
$515$	−30.3718			−1.33834
$516$	8.91733	−	15.4453i	0.392563	−	0.679940i
$517$	−4.52448	+	7.83663i	−0.198986	+	0.344655i
$518$	−56.5416	−	4.69184i	−2.48429	−	0.206148i
$519$	2.36727	−	4.10023i	0.103912	−	0.179980i
$520$	25.1491	+	43.5594i	1.10286	+	1.91021i
$521$	−5.72373	+	9.91379i	−0.250761	+	0.434331i	−0.963736	−	0.266859i	$-0.914014\pi$
$521$	−5.72373	+	9.91379i	−0.250761	+	0.434331i	0.712974	+	0.701190i	$0.247348\pi$
$522$	−1.49704	−	2.59295i	−0.0655237	−	0.113490i
$523$	30.7575			1.34493			0.672465	−	0.740129i	$-0.265236\pi$
$523$	30.7575			1.34493			0.672465	+	0.740129i	$0.265236\pi$
$524$	17.8867			0.781382
$525$	12.3347	+	26.1458i	0.538332	+	1.14109i
$526$	−18.4726	+	31.9955i	−0.805445	+	1.39507i
$527$	−1.48141	+	2.56587i	−0.0645310	+	0.111771i
$528$	0.256055	+	0.443500i	0.0111434	+	0.0193009i
$529$	−18.1727			−0.790116
$530$	18.1990	−	31.5216i	0.790514	−	1.36921i
$531$	−11.4380			−0.496369
$532$	30.6950	+	21.5879i	1.33080	+	0.935952i
$533$	−9.53309			−0.412924
$534$	−42.2273	+	73.1398i	−1.82735	+	3.16507i
$535$	−60.9994			−2.63723
$536$	−10.7936	−	18.6951i	−0.466214	−	0.807507i
$537$	7.51928	−	13.0238i	0.324481	−	0.562017i
$538$	−15.6156	+	27.0470i	−0.673237	+	1.16608i
$539$	13.2006	−	16.0209i	0.568589	−	0.690070i
$540$	−30.3864			−1.30762
$541$	21.5277			0.925548			0.462774	−	0.886476i	$-0.346854\pi$
$541$	21.5277			0.925548			0.462774	+	0.886476i	$0.346854\pi$
$542$	2.70366	+	4.68288i	0.116132	+	0.201147i
$543$	2.67680	−	4.63635i	0.114872	−	0.198965i
$544$	0.899264	+	1.55757i	0.0385556	+	0.0667803i
$545$	−1.48969	+	2.58023i	−0.0638115	+	0.110525i
$546$	−30.7053	−	65.0856i	−1.31407	−	2.78541i
$547$	4.85829	−	8.41481i	0.207726	−	0.359791i	−0.743272	−	0.668989i	$-0.766727\pi$
$547$	4.85829	−	8.41481i	0.207726	−	0.359791i	0.950998	+	0.309198i	$0.100061\pi$
$548$	−22.8911	+	39.6485i	−0.977859	+	1.69370i
$549$	4.03756			0.172319
$550$	−17.2528	+	29.8827i	−0.735661	+	1.27420i
$551$	0.0228321	−	3.48598i	0.000972681	−	0.148508i
$552$	13.5930			0.578558
$553$	8.38073	−	12.0837i	0.356385	−	0.513850i
$554$	22.6508	+	39.2324i	0.962342	+	1.66682i
$555$	−63.9236			−2.71340
$556$	41.9577			1.77940
$557$	7.37853	+	12.7800i	0.312638	+	0.541506i	0.978933	−	0.204183i	$-0.0654538\pi$
$557$	7.37853	+	12.7800i	0.312638	+	0.541506i	−0.666294	+	0.745689i	$0.732121\pi$
$558$	−17.1590	−	29.7202i	−0.726397	−	1.25816i
$559$	−14.0377			−0.593730
$560$	0.287479	+	0.609366i	0.0121482	+	0.0257504i
$561$	−1.03159	+	1.78677i	−0.0435538	+	0.0754374i
$562$	9.27945	+	16.0725i	0.391430	+	0.677977i
$563$	15.6881	−	27.1727i	0.661176	−	1.14519i	−0.319131	−	0.947711i	$-0.603391\pi$
$563$	15.6881	−	27.1727i	0.661176	−	1.14519i	0.980307	−	0.197480i	$-0.0632758\pi$
$564$	10.6861	+	18.5089i	0.449967	+	0.779365i
$565$	0.917979	−	1.58999i	0.0386197	−	0.0668912i
$566$	−12.5259	+	21.6956i	−0.526505	+	0.911933i
$567$	29.6159	+	2.45754i	1.24375	+	0.103207i
$568$	14.8500	+	25.7210i	0.623093	+	1.07923i
$569$	−14.9767	−	25.9405i	−0.627857	−	1.08748i	−0.987981	−	0.154576i	$-0.950599\pi$
$569$	−14.9767	−	25.9405i	−0.627857	−	1.08748i	0.360124	−	0.932905i	$-0.382734\pi$
$570$	58.8965	+	34.5202i	2.46690	+	1.44589i
$571$	10.9566	−	18.9773i	0.458518	−	0.794177i	−0.540364	−	0.841431i	$-0.681714\pi$
$571$	10.9566	−	18.9773i	0.458518	−	0.794177i	0.998883	+	0.0472538i	$0.0150470\pi$
$572$	26.5991	−	46.0709i	1.11216	−	1.92632i
$573$	16.6791	+	28.8891i	0.696781	+	1.20686i
$574$	−10.4508	−	0.867213i	−0.436209	−	0.0361968i
$575$	5.57658	+	9.65891i	0.232559	+	0.402805i
$576$	−21.0942			−0.878926
$577$	−17.0301	+	29.4970i	−0.708972	+	1.22798i	0.256267	+	0.966606i	$0.417507\pi$
$577$	−17.0301	+	29.4970i	−0.708972	+	1.22798i	−0.965239	+	0.261369i	$0.915826\pi$
$578$	−19.3635	+	33.5386i	−0.805416	+	1.39502i
$579$	22.0257			0.915359
$580$	4.13034	−	7.15396i	0.171503	−	0.297052i
$581$	−26.1536	−	2.17024i	−1.08503	−	0.0900366i
$582$	15.6913			0.650426
$583$	−14.8350			−0.614405
$584$	1.46586			0.0606577
$585$	−14.2912	−	24.7531i	−0.590868	−	1.02341i
$586$	−19.0146	+	32.9343i	−0.785488	+	1.36050i
$587$	−13.3678	−	23.1537i	−0.551747	−	0.955654i	−0.998149	−	0.0608214i	$-0.980628\pi$
$587$	−13.3678	−	23.1537i	−0.551747	−	0.955654i	0.446401	−	0.894833i	$-0.352705\pi$
$588$	−17.1806	−	45.9201i	−0.708516	−	1.89371i
$589$	0.261700	−	39.9560i	0.0107831	−	1.64636i
$590$	−25.4771	−	44.1276i	−1.04887	−	1.81670i
$591$	3.94877			0.162431
$592$	−0.750554			−0.0308476
$593$	5.95960			0.244732			0.122366	−	0.992485i	$-0.460952\pi$
$593$	5.95960			0.244732			0.122366	+	0.992485i	$0.460952\pi$
$594$	9.99852	+	17.3179i	0.410244	+	0.710564i
$595$	−1.54700	+	2.23053i	−0.0634208	+	0.0914426i
$596$	−77.4205			−3.17127
$597$	3.57337	+	6.18926i	0.146248	+	0.253309i
$598$	−13.8820	−	24.0443i	−0.567676	−	0.983243i
$599$	3.41276	+	5.91108i	0.139442	+	0.241520i	0.927285	−	0.374355i	$-0.122136\pi$
$599$	3.41276	+	5.91108i	0.139442	+	0.241520i	−0.787844	+	0.615875i	$0.788803\pi$
$600$	15.7028	+	27.1980i	0.641063	+	1.11035i
$601$	36.4128			1.48531			0.742655	−	0.669674i	$-0.233566\pi$
$601$	36.4128			1.48531			0.742655	+	0.669674i	$0.233566\pi$
$602$	−15.3891	−	1.27699i	−0.627211	−	0.0520462i
$603$	6.13359	+	10.6237i	0.249779	+	0.432630i
$604$	−17.5462			−0.713946
$605$	−7.00128			−0.284643
$606$	8.60811			0.349681
$607$	5.25346	+	9.09926i	0.213231	+	0.369328i	0.952724	−	0.303837i	$-0.0982678\pi$
$607$	5.25346	+	9.09926i	0.213231	+	0.369328i	−0.739493	+	0.673165i	$0.764934\pi$
$608$	−20.9257	−	12.2649i	−0.848650	−	0.497408i
$609$	−2.59569	+	3.74257i	−0.105183	+	0.151657i
$610$	8.99326	+	15.5768i	0.364126	+	0.630685i
$611$	8.41105	−	14.5684i	0.340275	−	0.589373i
$612$	0.858880	+	1.48762i	0.0347182	+	0.0601336i
$613$	−29.4204			−1.18828			−0.594138	−	0.804363i	$-0.702507\pi$
$613$	−29.4204			−1.18828			−0.594138	+	0.804363i	$0.702507\pi$
$614$	−28.9528			−1.16844
$615$	−11.8153			−0.476438
$616$	12.8520	−	18.5306i	0.517823	−	0.746618i
$617$	−16.4116	+	28.4258i	−0.660707	+	1.14438i	0.319723	+	0.947511i	$0.396410\pi$
$617$	−16.4116	+	28.4258i	−0.660707	+	1.14438i	−0.980430	+	0.196868i	$0.936923\pi$
$618$	47.2073			1.89895
$619$	−7.86775	+	13.6273i	−0.316232	+	0.547729i	−0.979699	−	0.200476i	$-0.935751\pi$
$619$	−7.86775	+	13.6273i	−0.316232	+	0.547729i	0.663467	+	0.748206i	$0.269084\pi$
$620$	47.3416	−	81.9981i	1.90128	−	3.29312i
$621$	6.46360			0.259375
$622$	18.3786	+	31.8326i	0.736913	+	1.27637i
$623$	45.1331	+	3.74516i	1.80822	+	0.150047i
$624$	−0.476008	−	0.824471i	−0.0190556	−	0.0330052i
$625$	12.3065	−	21.3154i	0.492258	−	0.852616i
$626$	20.0999	−	34.8141i	0.803355	−	1.39145i
$627$	0.182237	−	27.8237i	0.00727785	−	1.11117i
$628$	−15.6061	−	27.0305i	−0.622750	−	1.07864i
$629$	−1.51191	−	2.61871i	−0.0602838	−	0.104415i
$630$	−13.4152	−	28.4360i	−0.534475	−	1.13292i
$631$	−8.30928	+	14.3921i	−0.330787	+	0.572940i	−0.982666	−	0.185382i	$-0.940648\pi$
$631$	−8.30928	+	14.3921i	−0.330787	+	0.572940i	0.651879	+	0.758323i	$0.273981\pi$
$632$	7.98764	−	13.8350i	0.317731	−	0.550327i
$633$	3.46784	+	6.00648i	0.137834	+	0.238736i
$634$	6.38104	−	11.0523i	0.253423	−	0.438942i
$635$	22.7981	+	39.4875i	0.904716	+	1.56701i
$636$	−17.5190	+	30.3438i	−0.694674	+	1.20321i
$637$	−24.5400	+	29.7830i	−0.972310	+	1.18005i
$638$	−5.43629			−0.215225
$639$	−8.43866	−	14.6162i	−0.333828	−	0.578208i
$640$	−29.3217	−	50.7867i	−1.15904	−	2.00752i
$641$	−22.5774			−0.891755			−0.445878	−	0.895094i	$-0.647108\pi$
$641$	−22.5774			−0.891755			−0.445878	+	0.895094i	$0.647108\pi$
$642$	94.8119			3.74193
$643$	9.63253	+	16.6840i	0.379870	+	0.657954i	0.991043	−	0.133543i	$-0.0426355\pi$
$643$	9.63253	+	16.6840i	0.379870	+	0.657954i	−0.611173	+	0.791497i	$0.709302\pi$
$644$	−8.07058	−	17.1071i	−0.318025	−	0.674114i
$645$	−17.3982			−0.685055
$646$	−0.0211505	+	3.22923i	−0.000832155	+	0.127052i
$647$	−17.3266	+	30.0106i	−0.681179	+	1.17984i	0.293442	+	0.955977i	$0.405199\pi$
$647$	−17.3266	+	30.0106i	−0.681179	+	1.17984i	−0.974621	+	0.223860i	$0.928134\pi$
$648$	32.2837			1.26822
$649$	−10.3839	+	17.9854i	−0.407604	+	0.705990i
$650$	32.0731	−	55.5522i	1.25801	−	2.17894i
$651$	−29.7516	+	42.8971i	−1.16606	+	1.68127i
$652$	−18.4042	+	31.8770i	−0.720764	+	1.24840i
$653$	19.1148	+	33.1079i	0.748021	+	1.29561i	0.948770	+	0.315968i	$0.102329\pi$
$653$	19.1148	+	33.1079i	0.748021	+	1.29561i	−0.200748	+	0.979643i	$0.564337\pi$
$654$	2.31545	−	4.01047i	0.0905411	−	0.156822i
$655$	−8.72449	−	15.1113i	−0.340894	−	0.590446i
$656$	−0.138728			−0.00541643
$657$	−0.832988			−0.0324979
$658$	10.5460	−	15.2057i	0.411127	−	0.592780i
$659$	16.7820	−	29.0673i	0.653734	−	1.13230i	−0.328476	−	0.944512i	$-0.606535\pi$
$659$	16.7820	−	29.0673i	0.653734	−	1.13230i	0.982210	−	0.187788i	$-0.0601317\pi$
$660$	32.9668	−	57.1001i	1.28323	−	2.22262i
$661$	−4.73115	−	8.19460i	−0.184021	−	0.318733i	0.759225	−	0.650828i	$-0.225578\pi$
$661$	−4.73115	−	8.19460i	−0.184021	−	0.318733i	−0.943246	+	0.332095i	$0.892245\pi$
$662$	−14.9199			−0.579877
$663$	1.91774	−	3.32162i	0.0744787	−	0.129001i
$664$	−28.5096			−1.10639
$665$	3.26621	−	36.4620i	0.126658	−	1.41393i
$666$	35.0246			1.35718
$667$	−0.878580	+	1.52175i	−0.0340188	+	0.0589222i
$668$	12.5744			0.486518
$669$	−30.0433	−	52.0365i	−1.16154	−	2.01185i
$670$	−27.3239	+	47.3263i	−1.05561	+	1.82838i
$671$	3.66546	−	6.34876i	0.141503	−	0.245091i
$672$	13.5212	+	28.6606i	0.521590	+	1.10561i
$673$	−7.48268			−0.288436			−0.144218	−	0.989546i	$-0.546067\pi$
$673$	−7.48268			−0.288436			−0.144218	+	0.989546i	$0.546067\pi$
$674$	61.4202			2.36582
$675$	7.46679	+	12.9329i	0.287397	+	0.497786i
$676$	−28.2973	+	49.0124i	−1.08836	+	1.88509i
$677$	−8.07516	−	13.9866i	−0.310353	−	0.537548i	0.668085	−	0.744085i	$-0.267114\pi$
$677$	−8.07516	−	13.9866i	−0.310353	−	0.537548i	−0.978439	+	0.206537i	$0.933781\pi$
$678$	−1.42682	+	2.47133i	−0.0547969	+	0.0949109i
$679$	−3.59016	−	7.61001i	−0.137778	−	0.292045i
$680$	−1.47444	+	2.55380i	−0.0565421	+	0.0979339i
$681$	21.8221	−	37.7969i	0.836223	−	1.44838i
$682$	−62.3103			−2.38598
$683$	11.5814	−	20.0596i	0.443150	−	0.767559i	−0.554771	−	0.832003i	$-0.687194\pi$
$683$	11.5814	−	20.0596i	0.443150	−	0.767559i	0.997921	+	0.0644443i	$0.0205275\pi$
$684$	−19.9860	−	11.7141i	−0.764184	−	0.447901i
$685$	44.6619			1.70644
$686$	−29.6117	+	30.4178i	−1.13058	+	1.16136i
$687$	−17.3597	−	30.0679i	−0.662315	−	1.14716i
$688$	−0.204280			−0.00778811
$689$	27.5785			1.05066
$690$	−17.2052	−	29.8004i	−0.654993	−	1.13448i
$691$	1.26620	+	2.19313i	0.0481686	+	0.0834305i	0.889104	−	0.457704i	$-0.151328\pi$
$691$	1.26620	+	2.19313i	0.0481686	+	0.0834305i	−0.840936	+	0.541135i	$0.817995\pi$
$692$	−7.15717			−0.272075
$693$	−7.30328	+	10.5302i	−0.277429	+	0.400008i
$694$	−0.809720	+	1.40248i	−0.0307366	+	0.0532373i
$695$	−20.4655	−	35.4473i	−0.776301	−	1.34459i
$696$	−2.47394	+	4.28500i	−0.0937746	+	0.162422i
$697$	−0.279453	−	0.484027i	−0.0105850	−	0.0183338i
$698$	−3.07966	+	5.33412i	−0.116567	+	0.201899i
$699$	2.56320	−	4.43959i	0.0969491	−	0.167921i
$700$	24.9060	−	35.9104i	0.941357	−	1.35729i
$701$	−4.16789	−	7.21899i	−0.157419	−	0.272658i	0.776518	−	0.630095i	$-0.216984\pi$
$701$	−4.16789	−	7.21899i	−0.157419	−	0.272658i	−0.933937	+	0.357437i	$0.883651\pi$
$702$	−18.5873	−	32.1942i	−0.701534	−	1.21509i
$703$	35.1819	+	20.6207i	1.32691	+	0.777724i
$704$	−19.1502	+	33.1690i	−0.721749	+	1.25011i
$705$	10.4246	−	18.0560i	0.392614	−	0.680028i
$706$	−11.3870	−	19.7228i	−0.428554	−	0.742277i
$707$	−1.96953	−	4.17478i	−0.0740717	−	0.157009i
$708$	24.5251	+	42.4788i	0.921711	+	1.59645i
$709$	23.4320			0.880006			0.440003	−	0.897996i	$-0.354977\pi$
$709$	23.4320			0.880006			0.440003	+	0.897996i	$0.354977\pi$
$710$	37.5925	−	65.1121i	1.41082	−	2.44361i
$711$	−4.53905	+	7.86187i	−0.170228	+	0.294843i
$712$	49.1987			1.84380
$713$	−10.0702	+	17.4421i	−0.377132	+	0.653212i
$714$	2.40452	−	3.46693i	0.0899868	−	0.129747i
$715$	−51.8964			−1.94081
$716$	−22.7337			−0.849598
$717$	29.3830			1.09733
$718$	37.7235	+	65.3390i	1.40783	+	2.43843i
$719$	2.10950	−	3.65376i	0.0786710	−	0.136262i	−0.824006	−	0.566581i	$-0.808266\pi$
$719$	2.10950	−	3.65376i	0.0786710	−	0.136262i	0.902677	+	0.430319i	$0.141599\pi$
$720$	−0.207969	−	0.360213i	−0.00775056	−	0.0134244i
$721$	−10.8010	−	22.8947i	−0.402250	−	0.852642i
$722$	−21.2795	−	37.9981i	−0.791941	−	1.41414i
$723$	25.1075	+	43.4875i	0.933760	+	1.61732i
$724$	−8.09300			−0.300774
$725$	−4.05976			−0.150776
$726$	10.8822			0.403875
$727$	15.9598	+	27.6432i	0.591917	+	1.02523i	0.993974	+	0.109615i	$0.0349619\pi$
$727$	15.9598	+	27.6432i	0.591917	+	1.02523i	−0.402057	+	0.915614i	$0.631705\pi$
$728$	−23.8920	+	34.4485i	−0.885498	+	1.27675i
$729$	0.651524			0.0241305
$730$	−1.85540	−	3.21364i	−0.0686713	−	0.118942i
$731$	−0.411500	−	0.712740i	−0.0152199	−	0.0263616i
$732$	−8.65723	−	14.9948i	−0.319980	−	0.554222i
$733$	−7.60674	−	13.1753i	−0.280961	−	0.486640i	0.690660	−	0.723179i	$-0.257320\pi$
$733$	−7.60674	−	13.1753i	−0.280961	−	0.486640i	−0.971622	+	0.236540i	$0.923987\pi$
$734$	1.63219			0.0602451
$735$	−30.4148	+	36.9130i	−1.12187	+	1.36156i
$736$	6.11296	+	10.5880i	0.225327	+	0.390277i
$737$	22.2732			0.820445
$738$	6.47375			0.238302
$739$	21.9973			0.809185			0.404593	−	0.914497i	$-0.367413\pi$
$739$	21.9973			0.809185			0.404593	+	0.914497i	$0.367413\pi$
$740$	48.3165	+	83.6866i	1.77615	+	3.07638i
$741$	−0.338780	+	51.7246i	−0.0124454	+	1.90015i
$742$	30.2334	+	2.50878i	1.10990	+	0.0921001i
$743$	23.6548	+	40.9713i	0.867810	+	1.50309i	0.864230	+	0.503098i	$0.167806\pi$
$743$	23.6548	+	40.9713i	0.867810	+	1.50309i	0.00358041	+	0.999994i	$0.498860\pi$
$744$	−28.3561	+	49.1143i	−1.03959	+	1.80062i
$745$	37.7630	+	65.4075i	1.38353	+	2.39634i
$746$	−3.44494			−0.126128
$747$	16.2008			0.592757
$748$	3.11890			0.114038
$749$	−21.6929	−	45.9821i	−0.792641	−	1.68015i
$750$	0.597148	−	1.03429i	0.0218047	−	0.0377669i
$751$	41.5850			1.51746			0.758729	−	0.651407i	$-0.225821\pi$
$751$	41.5850			1.51746			0.758729	+	0.651407i	$0.225821\pi$
$752$	0.122400	−	0.212003i	0.00446347	−	0.00773095i
$753$	−4.82839	+	8.36301i	−0.175956	+	0.304765i
$754$	10.1061			0.368043
$755$	8.55843	+	14.8236i	0.311473	+	0.539487i
$756$	−10.8061	−	22.9056i	−0.393016	−	0.833070i
$757$	6.79436	+	11.7682i	0.246945	+	0.427722i	0.962677	−	0.270654i	$-0.0872398\pi$
$757$	6.79436	+	11.7682i	0.246945	+	0.427722i	−0.715731	+	0.698376i	$0.753907\pi$
$758$	−14.5425	+	25.1884i	−0.528209	+	0.914884i
$759$	−7.01249	+	12.1460i	−0.254537	+	0.440871i
$760$	0.260469	−	39.7681i	0.00944820	−	1.44254i
$761$	3.62246	+	6.27428i	0.131314	+	0.227443i	0.924183	−	0.381949i	$-0.124747\pi$
$761$	3.62246	+	6.27428i	0.131314	+	0.227443i	−0.792869	+	0.609392i	$0.791414\pi$
$762$	−35.4354	−	61.3759i	−1.28369	−	2.22341i
$763$	−2.47478	−	0.205358i	−0.0895930	−	0.00743446i
$764$	25.2137	−	43.6715i	0.912201	−	1.57998i
$765$	0.837863	−	1.45122i	0.0302930	−	0.0524690i
$766$	−17.3754	−	30.0952i	−0.627800	−	1.08738i
$767$	19.3038	−	33.4351i	0.697018	−	1.20727i
$768$	17.7751	+	30.7873i	0.641402	+	1.11094i
$769$	4.19229	−	7.26126i	0.151178	−	0.261848i	−0.780483	−	0.625177i	$-0.785027\pi$
$769$	4.19229	−	7.26126i	0.151178	−	0.261848i	0.931661	+	0.363329i	$0.118360\pi$
$770$	−56.8923	−	4.72095i	−2.05026	−	0.170131i
$771$	−11.4387			−0.411954
$772$	−16.6481	−	28.8354i	−0.599178	−	1.03781i
$773$	−21.8938	−	37.9212i	−0.787465	−	1.36393i	−0.927515	−	0.373785i	$-0.878060\pi$
$773$	−21.8938	−	37.9212i	−0.787465	−	1.36393i	0.140050	−	0.990144i	$-0.455274\pi$
$774$	9.53273			0.342647
$775$	−46.5327			−1.67150
$776$	−4.57046	−	7.91627i	−0.164070	−	0.284177i
$777$	−22.7328	−	48.1864i	−0.815535	−	1.72868i
$778$	−16.6782			−0.597942
$779$	6.50283	+	3.81141i	0.232988	+	0.136558i
$780$	−61.2855	+	106.150i	−2.19437	+	3.80077i
$781$	−30.6438			−1.09652
$782$	0.813872	−	1.40967i	0.0291040	−	0.0504096i
$783$	−1.17638	+	2.03755i	−0.0420404	+	0.0728161i
$784$	−0.357113	+	0.433411i	−0.0127540	+	0.0154790i
$785$	−15.2242	+	26.3691i	−0.543375	+	0.941153i
$786$	13.5606	+	23.4876i	0.483689	+	0.837774i
$787$	15.8396	−	27.4350i	0.564621	−	0.977953i	−0.432464	−	0.901651i	$-0.642356\pi$
$787$	15.8396	−	27.4350i	0.564621	−	0.977953i	0.997085	−	0.0763012i	$-0.0243111\pi$
$788$	−2.98467	−	5.16960i	−0.106324	−	0.184159i
$789$	−34.6946			−1.23516
$790$	−40.4411			−1.43883
$791$	1.52501	+	0.126546i	0.0542230	+	0.00449945i
$792$	−6.96073	+	12.0563i	−0.247339	+	0.428403i
$793$	−6.81412	+	11.8024i	−0.241976	+	0.419115i
$794$	−4.95917	−	8.58954i	−0.175994	−	0.304831i
$795$	34.1806			1.21226
$796$	5.40184	−	9.35626i	0.191463	−	0.331624i
$797$	7.19512			0.254864			0.127432	−	0.991847i	$-0.459327\pi$
$797$	7.19512			0.254864			0.127432	+	0.991847i	$0.459327\pi$
$798$	−5.07671	+	56.6732i	−0.179714	+	2.00621i
$799$	0.986246			0.0348909
$800$	−14.1235	+	24.4626i	−0.499340	+	0.864882i
$801$	−27.9576			−0.987834
$802$	−29.3258	−	50.7938i	−1.03553	−	1.79359i
$803$	−0.756219	+	1.30981i	−0.0266864	+	0.0462222i
$804$	26.3029	−	45.5580i	0.927633	−	1.60671i
$805$	−10.5161	+	15.1625i	−0.370644	+	0.534409i
$806$	115.835			4.08013
$807$	−29.3286			−1.03242
$808$	−2.50731	−	4.34279i	−0.0882069	−	0.152779i
$809$	−24.3770	+	42.2222i	−0.857049	+	1.48445i	0.0176812	+	0.999844i	$0.494372\pi$
$809$	−24.3770	+	42.2222i	−0.857049	+	1.48445i	−0.874731	+	0.484609i	$0.838962\pi$
$810$	−40.8628	−	70.7764i	−1.43577	−	2.48683i
$811$	2.50985	−	4.34718i	0.0881327	−	0.152650i	−0.818589	−	0.574379i	$-0.805243\pi$
$811$	2.50985	−	4.34718i	0.0881327	−	0.152650i	0.906722	+	0.421729i	$0.138577\pi$
$812$	6.86160	+	0.569378i	0.240795	+	0.0199812i
$813$	−2.53895	+	4.39760i	−0.0890450	+	0.154230i
$814$	31.7967	−	55.0735i	1.11447	−	1.93032i
$815$	35.9077			1.25779
$816$	0.0279074	−	0.0483371i	0.000976955	−	0.00169214i
$817$	9.57555	+	5.61238i	0.335006	+	0.196352i
$818$	−59.1354			−2.06762
$819$	13.5769	−	19.5757i	0.474414	−	0.684030i
$820$	8.93055	+	15.4682i	0.311868	+	0.540172i
$821$	−5.05070			−0.176271			−0.0881353	−	0.996109i	$-0.528091\pi$
$821$	−5.05070			−0.176271			−0.0881353	+	0.996109i	$0.528091\pi$
$822$	−69.4184			−2.42125
$823$	1.29591	+	2.24458i	0.0451725	+	0.0782410i	0.887728	−	0.460369i	$-0.152283\pi$
$823$	1.29591	+	2.24458i	0.0451725	+	0.0782410i	−0.842555	+	0.538610i	$0.818950\pi$
$824$	−13.7502	−	23.8161i	−0.479011	−	0.829672i
$825$	−32.4035			−1.12814
$826$	24.2036	−	34.8978i	0.842152	−	1.21425i
$827$	−6.37399	+	11.0401i	−0.221645	+	0.383901i	−0.955308	−	0.295613i	$-0.904476\pi$
$827$	−6.37399	+	11.0401i	−0.221645	+	0.383901i	0.733662	+	0.679514i	$0.237809\pi$
$828$	5.83845	+	10.1125i	0.202900	+	0.351433i
$829$	6.82147	−	11.8151i	0.236919	−	0.410356i	−0.722909	−	0.690943i	$-0.757196\pi$
$829$	6.82147	−	11.8151i	0.236919	−	0.410356i	0.959829	+	0.280586i	$0.0905289\pi$
$830$	36.0857	+	62.5022i	1.25255	+	2.16948i
$831$	−21.2709	+	36.8423i	−0.737881	+	1.27805i
$832$	35.6003	−	61.6615i	1.23422	−	2.13773i
$833$	−2.23155	−	0.372917i	−0.0773186	−	0.0129208i
$834$	31.8097	+	55.0961i	1.10148	+	1.90782i
$835$	−6.13335	−	10.6233i	−0.212253	−	0.367634i
$836$	−36.5636	+	20.7919i	−1.26458	+	0.719103i
$837$	−13.4836	+	23.3542i	−0.466060	+	0.807240i
$838$	4.23116	−	7.32858i	0.146163	−	0.253162i
$839$	−9.62739	−	16.6751i	−0.332374	−	0.575689i	0.650603	−	0.759418i	$-0.274516\pi$
$839$	−9.62739	−	16.6751i	−0.332374	−	0.575689i	−0.982977	+	0.183729i	$0.941183\pi$
$840$	−29.6117	+	42.6953i	−1.02170	+	1.47313i
$841$	14.1802	+	24.5608i	0.488972	+	0.846925i
$842$	−24.0602			−0.829168
$843$	−8.71415	+	15.0933i	−0.300131	+	0.519842i
$844$	5.24232	−	9.07997i	0.180448	−	0.312545i
$845$	55.2098			1.89927
$846$	−5.71179	+	9.89312i	−0.196376	+	0.340132i
$847$	−2.48983	−	5.27765i	−0.0855515	−	0.181342i
$848$	0.401329			0.0137817
$849$	−23.5257			−0.807401
$850$	3.76076			0.128993
$851$	−10.2776	−	17.8013i	−0.352311	−	0.610220i
$852$	−36.1879	+	62.6792i	−1.23978	+	2.14736i
$853$	−2.47229	−	4.28213i	−0.0846496	−	0.146617i	0.820592	−	0.571514i	$-0.193644\pi$
$853$	−2.47229	−	4.28213i	−0.0846496	−	0.146617i	−0.905242	+	0.424897i	$0.860310\pi$
$854$	−8.54375	+	12.3187i	−0.292361	+	0.421538i
$855$	−0.148014	+	22.5986i	−0.00506197	+	0.772855i
$856$	−27.6162	−	47.8326i	−0.943901	−	1.63488i
$857$	14.1853			0.484560			0.242280	−	0.970206i	$-0.422105\pi$
$857$	14.1853			0.484560			0.242280	+	0.970206i	$0.422105\pi$
$858$	80.6631			2.75379
$859$	44.6382			1.52304			0.761519	−	0.648143i	$-0.224454\pi$
$859$	44.6382			1.52304			0.761519	+	0.648143i	$0.224454\pi$
$860$	13.1504	+	22.7772i	0.448425	+	0.776695i
$861$	−4.20181	−	8.90651i	−0.143197	−	0.303533i
$862$	71.5422			2.43674
$863$	8.16022	+	14.1339i	0.277777	+	0.481124i	0.970832	−	0.239761i	$-0.0770690\pi$
$863$	8.16022	+	14.1339i	0.277777	+	0.481124i	−0.693055	+	0.720885i	$0.743736\pi$
$864$	8.18498	+	14.1768i	0.278459	+	0.482305i
$865$	3.49102	+	6.04662i	0.118698	+	0.205591i
$866$	36.5270	+	63.2666i	1.24124	+	2.14989i
$867$	−36.3678			−1.23511
$868$	78.6470	+	6.52616i	2.66945	+	0.221512i
$869$	8.24146	+	14.2746i	0.279572	+	0.484233i
$870$	12.5255			0.424653
$871$	−41.4061			−1.40299
$872$	−2.69771			−0.0913560
$873$	2.59721	+	4.49849i	0.0879021	+	0.152251i
$874$	−0.143776	+	21.9515i	−0.00486328	+	0.742520i
$875$	−0.638239	−	0.0529613i	−0.0215764	−	0.00179042i
$876$	1.78607	+	3.09356i	0.0603457	+	0.104522i
$877$	5.87471	−	10.1753i	0.198375	−	0.343595i	−0.749627	−	0.661861i	$-0.769767\pi$
$877$	5.87471	−	10.1753i	0.198375	−	0.343595i	0.948002	+	0.318266i	$0.103100\pi$
$878$	24.3748	+	42.2183i	0.822609	+	1.42480i
$879$	−35.7125			−1.20455
$880$	−0.755210			−0.0254581
$881$	−15.2523			−0.513864			−0.256932	−	0.966429i	$-0.582712\pi$
$881$	−15.2523			−0.513864			−0.256932	+	0.966429i	$0.582712\pi$
$882$	16.6647	−	20.2251i	0.561129	−	0.681015i
$883$	−9.72161	+	16.8383i	−0.327158	+	0.566655i	−0.981947	−	0.189157i	$-0.939424\pi$
$883$	−9.72161	+	16.8383i	−0.327158	+	0.566655i	0.654789	+	0.755812i	$0.272758\pi$
$884$	−5.79806			−0.195010
$885$	23.9250	−	41.4393i	0.804230	−	1.39297i
$886$	−36.3814	+	63.0144i	−1.22226	+	2.11701i
$887$	−30.8341			−1.03531			−0.517653	−	0.855590i	$-0.673194\pi$
$887$	−30.8341			−1.03531			−0.517653	+	0.855590i	$0.673194\pi$
$888$	−28.9400	−	50.1256i	−0.971164	−	1.68211i
$889$	−21.6586	+	31.2283i	−0.726407	+	1.04736i
$890$	−62.2727	−	107.860i	−2.08739	−	3.61546i
$891$	−16.6548	+	28.8469i	−0.557956	+	0.966409i
$892$	−45.4163	+	78.6633i	−1.52065	+	2.63384i
$893$	−11.5620	+	6.57474i	−0.386908	+	0.220015i
$894$	−58.6955	−	101.664i	−1.96307	−	3.40014i
$895$	11.0887	+	19.2062i	0.370654	+	0.641992i
$896$	27.8561	−	40.1641i	0.930607	−	1.34179i
$897$	13.0363	−	22.5795i	0.435268	−	0.753907i
$898$	24.0897	−	41.7246i	0.803885	−	1.39237i
$899$	−3.66557	−	6.34896i	−0.122254	−	0.211750i
$900$	−13.4892	+	23.3640i	−0.449641	+	0.778800i
$901$	0.808435	+	1.40025i	0.0269329	+	0.0466491i
$902$	5.87712	−	10.1795i	0.195687	−	0.338939i
$903$	−6.18724	−	13.1150i	−0.205899	−	0.436440i
$904$	1.66238			0.0552900
$905$	3.94748	+	6.83724i	0.131219	+	0.227278i
$906$	−13.3025	−	23.0405i	−0.441945	−	0.765470i
$907$	20.0832			0.666853			0.333427	−	0.942776i	$-0.391795\pi$
$907$	20.0832			0.666853			0.333427	+	0.942776i	$0.391795\pi$
$908$	−65.9766			−2.18951
$909$	1.42480	+	2.46783i	0.0472577	+	0.0818528i
$910$	105.763	+	8.77628i	3.50602	+	0.290931i
$911$	18.2981			0.606242			0.303121	−	0.952952i	$-0.401971\pi$
$911$	18.2981			0.606242			0.303121	+	0.952952i	$0.401971\pi$
$912$	−0.00493002	+	0.752710i	−0.000163249	+	0.0249247i
$913$	14.7077	−	25.4745i	0.486755	−	0.843084i
$914$	64.5823			2.13619
$915$	−8.44539	+	14.6278i	−0.279196	+	0.483581i
$916$	−26.2426	+	45.4535i	−0.867080	+	1.50183i
$917$	8.28841	−	11.9506i	0.273707	−	0.394642i
$918$	1.08974	−	1.88748i	0.0359667	−	0.0622962i
$919$	−11.7585	−	20.3663i	−0.387877	−	0.671823i	0.604287	−	0.796767i	$-0.293458\pi$
$919$	−11.7585	−	20.3663i	−0.387877	−	0.671823i	−0.992164	+	0.124944i	$0.960125\pi$
$920$	−10.0229	+	17.3601i	−0.330444	+	0.572345i
$921$	−13.5945	−	23.5464i	−0.447955	−	0.775880i
$922$	53.7581			1.77043
$923$	56.9670			1.87509
$924$	54.7666	+	4.54455i	1.80169	+	0.149505i
$925$	23.7454	−	41.1283i	0.780745	−	1.35229i
$926$	−24.1535	+	41.8351i	−0.793733	+	1.37479i
$927$	7.81368	+	13.5337i	0.256635	+	0.444505i
$928$	−4.45026			−0.146087
$929$	−13.9986	+	24.2462i	−0.459278	+	0.795493i	−0.998923	−	0.0464000i	$-0.985225\pi$
$929$	−13.9986	+	24.2462i	−0.459278	+	0.795493i	0.539645	+	0.841893i	$0.318558\pi$
$930$	143.566			4.70771
$931$	28.6470	−	10.5047i	0.938868	−	0.344276i
$932$	−7.74955			−0.253845
$933$	−17.2589	+	29.8934i	−0.565032	+	0.978665i
$934$	2.46442			0.0806383
$935$	−1.52129	−	2.63495i	−0.0497515	−	0.0861721i
$936$	12.9401	−	22.4128i	0.422959	−	0.732587i
$937$	26.0860	−	45.1823i	0.852193	−	1.47604i	−0.0270322	−	0.999635i	$-0.508606\pi$
$937$	26.0860	−	45.1823i	0.852193	−	1.47604i	0.879225	−	0.476407i	$-0.158061\pi$
$938$	−45.3922	−	3.76666i	−1.48211	−	0.122986i
$939$	37.7509			1.23195
$940$	−31.5177			−1.02799
$941$	5.96083	+	10.3245i	0.194318	+	0.336568i	0.946677	−	0.322185i	$-0.104417\pi$
$941$	5.96083	+	10.3245i	0.194318	+	0.336568i	−0.752359	+	0.658753i	$0.771084\pi$
$942$	23.6631	−	40.9857i	0.770986	−	1.33539i
$943$	−1.89965	−	3.29029i	−0.0618611	−	0.107147i
$944$	0.280913	−	0.486556i	0.00914296	−	0.0158361i
$945$	−14.0806	+	20.3020i	−0.458042	+	0.660423i
$946$	8.65418	−	14.9895i	0.281372	−	0.487350i
$947$	1.63747	−	2.83618i	0.0532106	−	0.0921634i	−0.838193	−	0.545373i	$-0.816388\pi$
$947$	1.63747	−	2.83618i	0.0532106	−	0.0921634i	0.891404	+	0.453210i	$0.149721\pi$
$948$	38.9300			1.26439
$949$	1.40582	−	2.43495i	0.0456348	−	0.0790417i
$950$	−44.0883	+	25.0708i	−1.43041	+	0.813405i
$951$	11.9846			0.388628
$952$	−2.44944	−	0.203255i	−0.0793867	−	0.00658753i
$953$	−3.49589	−	6.05506i	−0.113243	−	0.196142i	0.803833	−	0.594855i	$-0.202790\pi$
$953$	−3.49589	−	6.05506i	−0.113243	−	0.196142i	−0.917076	+	0.398712i	$0.869457\pi$
$954$	−18.7280			−0.606343
$955$	−49.1935			−1.59187
$956$	−22.2090	−	38.4672i	−0.718291	−	1.24412i
$957$	−2.55256	−	4.42116i	−0.0825124	−	0.142916i
$958$	−28.4106			−0.917905
$959$	15.8829	+	33.6667i	0.512885	+	1.08715i
$960$	44.1229	−	76.4231i	1.42406	−	2.46654i
$961$	−26.5145	−	45.9244i	−0.855306	−	1.48143i
$962$	−59.1103	+	102.382i	−1.90579	+	3.30093i
$963$	15.6931	+	27.1813i	0.505704	+	0.875906i
$964$	37.9549	−	65.7399i	1.22245	−	2.11734i
$965$	−16.2407	+	28.1298i	−0.522807	+	0.905529i
$966$	16.3453	−	23.5673i	0.525901	−	0.758265i
$967$	−14.7256	−	25.5055i	−0.473544	−	0.820202i	0.525998	−	0.850486i	$-0.323692\pi$
$967$	−14.7256	−	25.5055i	−0.473544	−	0.820202i	−0.999541	+	0.0302843i	$0.990359\pi$
$968$	−3.16968	−	5.49005i	−0.101877	−	0.176457i
$969$	−2.63616	+	1.49905i	−0.0846856	+	0.0481565i
$970$	−11.5700	+	20.0399i	−0.371491	+	0.643441i
$971$	20.4467	−	35.4148i	0.656167	−	1.13651i	−0.325433	−	0.945565i	$-0.605510\pi$
$971$	20.4467	−	35.4148i	0.656167	−	1.13651i	0.981600	−	0.190949i	$-0.0611565\pi$
$972$	24.9771	+	43.2616i	0.801141	+	1.38762i
$973$	19.4426	−	28.0331i	0.623300	−	0.898700i
$974$	−41.0518	−	71.1039i	−1.31539	−	2.27832i
$975$	60.2383			1.92917
$976$	−0.0991609	+	0.171752i	−0.00317406	+	0.00549764i
$977$	−7.05764	+	12.2242i	−0.225794	+	0.391087i	−0.956557	−	0.291544i	$-0.905831\pi$
$977$	−7.05764	+	12.2242i	−0.225794	+	0.391087i	0.730763	+	0.682631i	$0.239164\pi$
$978$	−55.8117			−1.78466
$979$	−25.3810	+	43.9612i	−0.811181	+	1.40501i
$980$	71.3141	+	11.9174i	2.27805	+	0.380687i
$981$	1.53300			0.0489449
$982$	−44.1779			−1.40977
$983$	24.2293			0.772795			0.386397	−	0.922332i	$-0.373719\pi$
$983$	24.2293			0.772795			0.386397	+	0.922332i	$0.373719\pi$
$984$	−5.34912	−	9.26494i	−0.170524	−	0.295356i
$985$	−2.91163	+	5.04310i	−0.0927723	+	0.160686i
$986$	0.296251	+	0.513121i	0.00943454	+	0.0163411i
$987$	17.3181	+	1.43706i	0.551241	+	0.0457421i
$988$	67.9721	−	38.6524i	2.16248	−	1.22970i
$989$	−2.79727	−	4.84502i	−0.0889481	−	0.154063i
$990$	35.2419			1.12006
$991$	−29.2105			−0.927901			−0.463950	−	0.885861i	$-0.653568\pi$
$991$	−29.2105			−0.927901			−0.463950	+	0.885861i	$0.653568\pi$
$992$	−51.0084			−1.61952
$993$	−7.00548	−	12.1338i	−0.222312	−	0.385056i
$994$	62.4512	+	5.18222i	1.98083	+	0.164370i
$995$	−10.5393			−0.334119
$996$	−34.7374	−	60.1669i	−1.10070	−	1.90646i
$997$	−19.3465	−	33.5091i	−0.612710	−	1.06124i	−0.990782	−	0.135468i	$-0.956746\pi$
$997$	−19.3465	−	33.5091i	−0.612710	−	1.06124i	0.378072	−	0.925776i	$-0.376587\pi$
$998$	−24.9772	−	43.2618i	−0.790639	−	1.36943i
$999$	−13.7612	−	23.8351i	−0.435386	−	0.754110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.g.a.102.11	yes	24
7.2	even	3		133.2.h.a.121.2	yes	24
7.3	odd	6		931.2.e.e.197.11		24
7.4	even	3		931.2.e.f.197.11		24
7.5	odd	6		931.2.h.h.520.2		24
7.6	odd	2		931.2.g.h.900.11		24
19.11	even	3		133.2.h.a.11.2	yes	24
133.11	even	3		931.2.e.f.638.11		24
133.30	even	3	inner	133.2.g.a.30.11	✓	24
133.68	odd	6		931.2.g.h.30.11		24
133.87	odd	6		931.2.e.e.638.11		24
133.125	odd	6		931.2.h.h.410.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.g.a.30.11	✓	24	133.30	even	3	inner
133.2.g.a.102.11	yes	24	1.1	even	1	trivial
133.2.h.a.11.2	yes	24	19.11	even	3
133.2.h.a.121.2	yes	24	7.2	even	3
931.2.e.e.197.11		24	7.3	odd	6
931.2.e.e.638.11		24	133.87	odd	6
931.2.e.f.197.11		24	7.4	even	3
931.2.e.f.638.11		24	133.11	even	3
931.2.g.h.30.11		24	133.68	odd	6
931.2.g.h.900.11		24	7.6	odd	2
931.2.h.h.410.2		24	133.125	odd	6
931.2.h.h.520.2		24	7.5	odd	6

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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14607 - 1.98506i) q^{2} +2.15251 q^{3} +(-1.62697 - 2.81799i) q^{4} +(-1.58716 + 2.74903i) q^{5} +(2.46693 - 4.27285i) q^{6} +(-2.63669 - 0.218793i) q^{7} -2.87420 q^{8} +1.63329 q^{9} +O(q^{10})\)	\(q+(1.14607 - 1.98506i) q^{2} +2.15251 q^{3} +(-1.62697 - 2.81799i) q^{4} +(-1.58716 + 2.74903i) q^{5} +(2.46693 - 4.27285i) q^{6} +(-2.63669 - 0.218793i) q^{7} -2.87420 q^{8} +1.63329 q^{9} +(3.63799 + 6.30119i) q^{10} +(1.48277 - 2.56823i) q^{11} +(-3.50206 - 6.06575i) q^{12} +(-2.75648 + 4.77436i) q^{13} +(-3.45616 + 4.98323i) q^{14} +(-3.41637 + 5.91732i) q^{15} +(-0.0401130 + 0.0694778i) q^{16} -0.323213 q^{17} +(1.87187 - 3.24218i) q^{18} +(3.78911 - 2.15468i) q^{19} +10.3290 q^{20} +(-5.67550 - 0.470955i) q^{21} +(-3.39872 - 5.88676i) q^{22} -2.19712 q^{23} -6.18675 q^{24} +(-2.53813 - 4.39617i) q^{25} +(6.31825 + 10.9435i) q^{26} -2.94185 q^{27} +(3.67325 + 7.78614i) q^{28} +(0.399878 - 0.692609i) q^{29} +(7.83081 + 13.5634i) q^{30} +(4.58337 - 7.93862i) q^{31} +(-2.78226 - 4.81901i) q^{32} +(3.19167 - 5.52813i) q^{33} +(-0.370426 + 0.641597i) q^{34} +(4.78631 - 6.90109i) q^{35} +(-2.65732 - 4.60261i) q^{36} +(4.67774 + 8.10209i) q^{37} +(0.0654382 - 9.99102i) q^{38} +(-5.93334 + 10.2768i) q^{39} +(4.56181 - 7.90129i) q^{40} +(0.864608 + 1.49755i) q^{41} +(-7.43941 + 10.7264i) q^{42} +(1.27315 + 2.20517i) q^{43} -9.64966 q^{44} +(-2.59229 + 4.48998i) q^{45} +(-2.51806 + 4.36141i) q^{46} -3.05138 q^{47} +(-0.0863436 + 0.149552i) q^{48} +(6.90426 + 1.15378i) q^{49} -11.6355 q^{50} -0.695720 q^{51} +17.9388 q^{52} +(-2.50124 - 4.33228i) q^{53} +(-3.37157 + 5.83974i) q^{54} +(4.70677 + 8.15236i) q^{55} +(7.57838 + 0.628857i) q^{56} +(8.15609 - 4.63796i) q^{57} +(-0.916579 - 1.58756i) q^{58} -7.00305 q^{59} +22.2333 q^{60} +2.47204 q^{61} +(-10.5057 - 18.1965i) q^{62} +(-4.30649 - 0.357354i) q^{63} -12.9151 q^{64} +(-8.74992 - 15.1553i) q^{65} +(-7.31577 - 12.6713i) q^{66} +(3.75535 + 6.50446i) q^{67} +(0.525858 + 0.910813i) q^{68} -4.72932 q^{69} +(-8.21360 - 17.4102i) q^{70} +(-5.16665 - 8.94891i) q^{71} -4.69442 q^{72} -0.510005 q^{73} +21.4442 q^{74} +(-5.46334 - 9.46279i) q^{75} +(-12.2366 - 7.17209i) q^{76} +(-4.47151 + 6.44720i) q^{77} +(13.6001 + 23.5560i) q^{78} +(-2.77908 + 4.81351i) q^{79} +(-0.127331 - 0.220544i) q^{80} -11.2322 q^{81} +3.96362 q^{82} +9.91911 q^{83} +(7.90670 + 16.7597i) q^{84} +(0.512990 - 0.888525i) q^{85} +5.83651 q^{86} +(0.860741 - 1.49085i) q^{87} +(-4.26178 + 7.38161i) q^{88} -17.1173 q^{89} +(5.94191 + 10.2917i) q^{90} +(8.31257 - 11.9854i) q^{91} +(3.57465 + 6.19147i) q^{92} +(9.86573 - 17.0880i) q^{93} +(-3.49710 + 6.05716i) q^{94} +(-0.0906230 + 13.8362i) q^{95} +(-5.98884 - 10.3730i) q^{96} +(1.59017 + 2.75425i) q^{97} +(10.2031 - 12.3830i) q^{98} +(2.42179 - 4.19467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

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