LMFDB - Embedded newform 117.2.l.b.88.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(4,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("117.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			88.6
Character	$\chi$	$=$	117.88
Dual form			117.2.l.b.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.391710i q^{2} +(0.608332 + 1.62171i) q^{3} +1.84656 q^{4} +(-1.60580 + 0.927107i) q^{5} +(0.635238 - 0.238289i) q^{6} +(-0.0712374 + 0.0411289i) q^{7} -1.50674i q^{8} +(-2.25987 + 1.97307i) q^{9} +(0.363157 + 0.629006i) q^{10} -0.0536224i q^{11} +(1.12332 + 2.99458i) q^{12} +(1.83650 - 3.10278i) q^{13} +(0.0161106 + 0.0279044i) q^{14} +(-2.48035 - 2.04014i) q^{15} +3.10292 q^{16} +(2.16592 - 3.75149i) q^{17} +(0.772871 + 0.885211i) q^{18} +(-4.45806 - 2.57386i) q^{19} +(-2.96521 + 1.71196i) q^{20} +(-0.110035 - 0.0905061i) q^{21} -0.0210044 q^{22} +(-0.790827 + 1.36975i) q^{23} +(2.44348 - 0.916595i) q^{24} +(-0.780945 + 1.35264i) q^{25} +(-1.21539 - 0.719374i) q^{26} +(-4.57449 - 2.46456i) q^{27} +(-0.131544 + 0.0759472i) q^{28} -3.21440 q^{29} +(-0.799143 + 0.971578i) q^{30} +(-0.647844 + 0.374033i) q^{31} -4.22892i q^{32} +(0.0869598 - 0.0326202i) q^{33} +(-1.46949 - 0.848412i) q^{34} +(0.0762618 - 0.132089i) q^{35} +(-4.17298 + 3.64340i) q^{36} +(0.767413 - 0.443066i) q^{37} +(-1.00821 + 1.74626i) q^{38} +(6.14901 + 1.09074i) q^{39} +(1.39691 + 2.41951i) q^{40} +(-10.0995 - 5.83094i) q^{41} +(-0.0354521 + 0.0431018i) q^{42} +(2.89941 + 5.02193i) q^{43} -0.0990171i q^{44} +(1.79964 - 5.26349i) q^{45} +(0.536545 + 0.309774i) q^{46} +(8.48127 + 4.89667i) q^{47} +(1.88761 + 5.03203i) q^{48} +(-3.49662 + 6.05632i) q^{49} +(0.529841 + 0.305904i) q^{50} +(7.40141 + 1.23034i) q^{51} +(3.39121 - 5.72949i) q^{52} +12.5949 q^{53} +(-0.965390 + 1.79187i) q^{54} +(0.0497137 + 0.0861066i) q^{55} +(0.0619704 + 0.107336i) q^{56} +(1.46207 - 8.79543i) q^{57} +1.25911i q^{58} +6.02193i q^{59} +(-4.58013 - 3.76725i) q^{60} +(-5.44532 - 9.43157i) q^{61} +(0.146512 + 0.253767i) q^{62} +(0.0798366 - 0.233502i) q^{63} +4.54934 q^{64} +(-0.0724285 + 6.68507i) q^{65} +(-0.0127776 - 0.0340630i) q^{66} +(-3.76950 - 2.17632i) q^{67} +(3.99951 - 6.92736i) q^{68} +(-2.70242 - 0.449226i) q^{69} +(-0.0517407 - 0.0298725i) q^{70} +(11.1888 + 6.45987i) q^{71} +(2.97290 + 3.40502i) q^{72} +5.76996i q^{73} +(-0.173553 - 0.300603i) q^{74} +(-2.66865 - 0.443612i) q^{75} +(-8.23209 - 4.75280i) q^{76} +(0.00220543 + 0.00381992i) q^{77} +(0.427253 - 2.40862i) q^{78} +(-5.17653 + 8.96601i) q^{79} +(-4.98267 + 2.87674i) q^{80} +(1.21398 - 8.91775i) q^{81} +(-2.28403 + 3.95606i) q^{82} +(9.68239 + 5.59013i) q^{83} +(-0.203187 - 0.167125i) q^{84} +8.03216i q^{85} +(1.96714 - 1.13573i) q^{86} +(-1.95542 - 5.21281i) q^{87} -0.0807948 q^{88} +(-9.76265 + 5.63647i) q^{89} +(-2.06176 - 0.704934i) q^{90} +(-0.00321312 + 0.296568i) q^{91} +(-1.46031 + 2.52933i) q^{92} +(-1.00068 - 0.823076i) q^{93} +(1.91807 - 3.32220i) q^{94} +9.54498 q^{95} +(6.85806 - 2.57258i) q^{96} +(-9.66160 + 5.57813i) q^{97} +(2.37232 + 1.36966i) q^{98} +(0.105801 + 0.121179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) $ 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	0.391710i		−	0.276980i	−0.990364	−	0.138490i	$-0.955775\pi$
$2$		−	0.391710i		−	0.276980i	0.990364	−	0.138490i	$-0.0442250\pi$
$3$	0.608332	+	1.62171i	0.351220	+	0.936293i
$3$	0.608332	+	1.62171i	0.351220	+	0.936293i
$4$	1.84656			0.923282
$5$	−1.60580	+	0.927107i	−0.718134	+	0.414615i	−0.814066	−	0.580773i	$-0.802750\pi$
$5$	−1.60580	+	0.927107i	−0.718134	+	0.414615i	0.0959315	+	0.995388i	$0.469417\pi$
$6$	0.635238	−	0.238289i	0.259335	−	0.0972812i
$7$	−0.0712374	+	0.0411289i	−0.0269252	+	0.0155453i	−0.513402	−	0.858148i	$-0.671615\pi$
$7$	−0.0712374	+	0.0411289i	−0.0269252	+	0.0155453i	0.486477	+	0.873693i	$0.338282\pi$
$8$		−	1.50674i		−	0.532711i
$9$	−2.25987	+	1.97307i	−0.753288	+	0.657690i
$10$	0.363157	+	0.629006i	0.114840	+	0.198909i
$11$		−	0.0536224i		−	0.0161678i	−0.999967	−	0.00808388i	$-0.997427\pi$
$11$		−	0.0536224i		−	0.0161678i	0.999967	−	0.00808388i	$-0.00257321\pi$
$12$	1.12332	+	2.99458i	0.324275	+	0.864462i
$13$	1.83650	−	3.10278i	0.509353	−	0.860558i
$13$	1.83650	−	3.10278i	0.509353	−	0.860558i
$14$	0.0161106	+	0.0279044i	0.00430574	+	0.00745776i
$15$	−2.48035	−	2.04014i	−0.640424	−	0.526763i
$16$	3.10292			0.775731
$17$	2.16592	−	3.75149i	0.525313	−	0.909869i	−0.474252	−	0.880389i	$-0.657282\pi$
$17$	2.16592	−	3.75149i	0.525313	−	0.909869i	0.999565	−	0.0294799i	$-0.00938511\pi$
$18$	0.772871	+	0.885211i	0.182167	+	0.208646i
$19$	−4.45806	−	2.57386i	−1.02275	−	0.590484i	−0.107850	−	0.994167i	$-0.534397\pi$
$19$	−4.45806	−	2.57386i	−1.02275	−	0.590484i	−0.914899	+	0.403683i	$0.867730\pi$
$20$	−2.96521	+	1.71196i	−0.663040	+	0.382806i
$21$	−0.110035	−	0.0905061i	−0.0240116	−	0.0197501i
$22$	−0.0210044			−0.00447815
$23$	−0.790827	+	1.36975i	−0.164899	+	0.285613i	−0.936619	−	0.350349i	$-0.886063\pi$
$23$	−0.790827	+	1.36975i	−0.164899	+	0.285613i	0.771721	+	0.635962i	$0.219396\pi$
$24$	2.44348	−	0.916595i	0.498774	−	0.187099i
$25$	−0.780945	+	1.35264i	−0.156189	+	0.270527i
$26$	−1.21539	−	0.719374i	−0.238358	−	0.141081i
$27$	−4.57449	−	2.46456i	−0.880361	−	0.474304i
$28$	−0.131544	+	0.0759472i	−0.0248596	+	0.0143527i
$29$	−3.21440			−0.596899			−0.298449	−	0.954425i	$-0.596469\pi$
$29$	−3.21440			−0.596899			−0.298449	+	0.954425i	$0.596469\pi$
$30$	−0.799143	+	0.971578i	−0.145903	+	0.177385i
$31$	−0.647844	+	0.374033i	−0.116356	+	0.0671783i	−0.557049	−	0.830480i	$-0.688066\pi$
$31$	−0.647844	+	0.374033i	−0.116356	+	0.0671783i	0.440692	+	0.897658i	$0.354733\pi$
$32$		−	4.22892i		−	0.747574i
$33$	0.0869598	−	0.0326202i	0.0151378	−	0.00567845i
$34$	−1.46949	−	0.848412i	−0.252016	−	0.145501i
$35$	0.0762618	−	0.132089i	0.0128906	−	0.0223272i
$36$	−4.17298	+	3.64340i	−0.695497	+	0.607234i
$37$	0.767413	−	0.443066i	0.126162	−	0.0728396i	−0.435591	−	0.900145i	$-0.643461\pi$
$37$	0.767413	−	0.443066i	0.126162	−	0.0728396i	0.561753	+	0.827305i	$0.310127\pi$
$38$	−1.00821	+	1.74626i	−0.163553	+	0.283281i
$39$	6.14901	+	1.09074i	0.984629	+	0.174658i
$40$	1.39691	+	2.41951i	0.220870	+	0.382558i
$41$	−10.0995	−	5.83094i	−1.57727	−	0.910640i	−0.995238	−	0.0974774i	$-0.968923\pi$
$41$	−10.0995	−	5.83094i	−1.57727	−	0.910640i	−0.582037	−	0.813162i	$-0.697744\pi$
$42$	−0.0354521	+	0.0431018i	−0.00547038	+	0.00665075i
$43$	2.89941	+	5.02193i	0.442156	+	0.765837i	0.997849	−	0.0655507i	$-0.0208804\pi$
$43$	2.89941	+	5.02193i	0.442156	+	0.765837i	−0.555693	+	0.831387i	$0.687547\pi$
$44$		−	0.0990171i		−	0.0149274i
$45$	1.79964	−	5.26349i	0.268274	−	0.784634i
$46$	0.536545	+	0.309774i	0.0791092	+	0.0456737i
$47$	8.48127	+	4.89667i	1.23712	+	0.714252i	0.968505	−	0.248995i	$-0.0801003\pi$
$47$	8.48127	+	4.89667i	1.23712	+	0.714252i	0.268616	+	0.963247i	$0.413434\pi$
$48$	1.88761	+	5.03203i	0.272453	+	0.726311i
$49$	−3.49662	+	6.05632i	−0.499517	+	0.865188i
$50$	0.529841	+	0.305904i	0.0749308	+	0.0432613i
$51$	7.40141	+	1.23034i	1.03640	+	0.172282i
$52$	3.39121	−	5.72949i	0.470276	−	0.794537i
$53$	12.5949			1.73004			0.865019	−	0.501738i	$-0.167306\pi$
$53$	12.5949			1.73004			0.865019	+	0.501738i	$0.167306\pi$
$54$	−0.965390	+	1.79187i	−0.131373	+	0.243843i
$55$	0.0497137	+	0.0861066i	0.00670339	+	0.0116106i
$56$	0.0619704	+	0.107336i	0.00828115	+	0.0143434i
$57$	1.46207	−	8.79543i	0.193656	−	1.16498i
$58$			1.25911i			0.165329i
$59$			6.02193i			0.783988i	0.919968	+	0.391994i	$0.128215\pi$
$59$			6.02193i			0.783988i	−0.919968	+	0.391994i	$0.871785\pi$
$60$	−4.58013	−	3.76725i	−0.591292	−	0.486350i
$61$	−5.44532	−	9.43157i	−0.697202	−	1.20759i	−0.969433	−	0.245357i	$-0.921095\pi$
$61$	−5.44532	−	9.43157i	−0.697202	−	1.20759i	0.272231	−	0.962232i	$-0.412238\pi$
$62$	0.146512	+	0.253767i	0.0186071	+	0.0322284i
$63$	0.0798366	−	0.233502i	0.0100585	−	0.0294185i
$64$	4.54934			0.568668
$65$	−0.0724285	+	6.68507i	−0.00898365	+	0.829181i
$66$	−0.0127776	−	0.0340630i	−0.00157282	−	0.00419286i
$67$	−3.76950	−	2.17632i	−0.460518	−	0.265880i	0.251744	−	0.967794i	$-0.418996\pi$
$67$	−3.76950	−	2.17632i	−0.460518	−	0.265880i	−0.712262	+	0.701914i	$0.752329\pi$
$68$	3.99951	−	6.92736i	0.485012	−	0.840065i
$69$	−2.70242	−	0.449226i	−0.325333	−	0.0540804i
$70$	−0.0517407	−	0.0298725i	−0.00618419	−	0.00357045i
$71$	11.1888	+	6.45987i	1.32787	+	0.766646i	0.984970	−	0.172726i	$-0.0552576\pi$
$71$	11.1888	+	6.45987i	1.32787	+	0.766646i	0.342900	+	0.939372i	$0.388591\pi$
$72$	2.97290	+	3.40502i	0.350359	+	0.401285i
$73$			5.76996i			0.675323i	0.941268	+	0.337662i	$0.109636\pi$
$73$			5.76996i			0.675323i	−0.941268	+	0.337662i	$0.890364\pi$
$74$	−0.173553	−	0.300603i	−0.0201751	−	0.0349444i
$75$	−2.66865	−	0.443612i	−0.308150	−	0.0512239i
$76$	−8.23209	−	4.75280i	−0.944285	−	0.545183i
$77$	0.00220543	+	0.00381992i	0.000251332	+	0.000435320i
$78$	0.427253	−	2.40862i	0.0483769	−	0.272723i
$79$	−5.17653	+	8.96601i	−0.582405	+	1.00876i	0.412788	+	0.910827i	$0.364555\pi$
$79$	−5.17653	+	8.96601i	−0.582405	+	1.00876i	−0.995193	+	0.0979283i	$0.968778\pi$
$80$	−4.98267	+	2.87674i	−0.557079	+	0.321630i
$81$	1.21398	−	8.91775i	0.134887	−	0.990861i
$82$	−2.28403	+	3.95606i	−0.252229	+	0.436874i
$83$	9.68239	+	5.59013i	1.06278	+	0.613597i	0.926200	−	0.377032i	$-0.123055\pi$
$83$	9.68239	+	5.59013i	1.06278	+	0.613597i	0.136581	+	0.990629i	$0.456389\pi$
$84$	−0.203187	−	0.167125i	−0.0221695	−	0.0182349i
$85$			8.03216i			0.871210i
$86$	1.96714	−	1.13573i	0.212122	−	0.122469i
$87$	−1.95542	−	5.21281i	−0.209643	−	0.558872i
$88$	−0.0807948			−0.00861275
$89$	−9.76265	+	5.63647i	−1.03484	+	0.597465i	−0.918367	−	0.395729i	$-0.870492\pi$
$89$	−9.76265	+	5.63647i	−1.03484	+	0.597465i	−0.116472	+	0.993194i	$0.537158\pi$
$90$	−2.06176	−	0.704934i	−0.217328	−	0.0743066i
$91$	−0.00321312	+	0.296568i	−0.000336826	+	0.0310887i
$92$	−1.46031	+	2.52933i	−0.152248	+	0.263701i
$93$	−1.00068	−	0.823076i	−0.103765	−	0.0853490i
$94$	1.91807	−	3.32220i	0.197834	−	0.342658i
$95$	9.54498			0.979294
$96$	6.85806	−	2.57258i	0.699948	−	0.262563i
$97$	−9.66160	+	5.57813i	−0.980987	+	0.566373i	−0.902568	−	0.430547i	$-0.858321\pi$
$97$	−9.66160	+	5.57813i	−0.980987	+	0.566373i	−0.0784191	+	0.996920i	$0.524987\pi$
$98$	2.37232	+	1.36966i	0.239640	+	0.138356i
$99$	0.105801	+	0.121179i	0.0106334	+	0.0121790i
$100$	−1.44206	+	2.49773i	−0.144206	+	0.249773i
$101$	−3.34073			−0.332415			−0.166208	−	0.986091i	$-0.553152\pi$
$101$	−3.34073			−0.332415			−0.166208	+	0.986091i	$0.553152\pi$
$102$	0.481936	−	2.89920i	0.0477188	−	0.287064i
$103$	−2.79024	−	4.83284i	−0.274931	−	0.476194i	0.695187	−	0.718829i	$-0.255322\pi$
$103$	−2.79024	−	4.83284i	−0.274931	−	0.476194i	−0.970118	+	0.242635i	$0.921988\pi$
$104$	−4.67508	−	2.76712i	−0.458429	−	0.271338i
$105$	0.260603	+	0.0433202i	0.0254322	+	0.00422762i
$106$		−	4.93353i		−	0.479187i
$107$	−5.35564	−	9.27624i	−0.517749	−	0.896768i	−0.999787	−	0.0206179i	$-0.993437\pi$
$107$	−5.35564	−	9.27624i	−0.517749	−	0.896768i	0.482038	−	0.876150i	$-0.339897\pi$
$108$	−8.44709	−	4.55096i	−0.812821	−	0.437916i
$109$		−	14.3994i		−	1.37922i	−0.724183	−	0.689608i	$-0.757783\pi$
$109$		−	14.3994i		−	1.37922i	0.724183	−	0.689608i	$-0.242217\pi$
$110$	0.0337288	−	0.0194733i	0.00321591	−	0.00185671i
$111$	1.18536	+	0.974987i	0.112510	+	0.0925417i
$112$	−0.221044	+	0.127620i	−0.0208867	+	0.0120590i
$113$	−8.00154			−0.752721			−0.376361	−	0.926473i	$-0.622825\pi$
$113$	−8.00154			−0.752721			−0.376361	+	0.926473i	$0.622825\pi$
$114$	−3.44525	−	0.572707i	−0.322677	−	0.0536389i
$115$		−	2.93272i		−	0.273478i
$116$	−5.93559			−0.551106
$117$	1.97178	+	10.6354i	0.182291	+	0.983245i
$118$	2.35885			0.217149
$119$			0.356328i			0.0326645i
$120$	−3.07396	+	3.73724i	−0.280612	+	0.341161i
$121$	10.9971			0.999739
$122$	−3.69443	+	2.13298i	−0.334478	+	0.193111i
$123$	3.31224	−	19.9255i	0.298655	−	1.79663i
$124$	−1.19628	+	0.690675i	−0.107430	+	0.0620245i
$125$		−	12.1671i		−	1.08826i
$126$	−0.0914651	−	0.0312728i	−0.00814836	−	0.00278600i
$127$	5.09674	+	8.82782i	0.452263	+	0.783342i	0.998526	−	0.0542714i	$-0.0172836\pi$
$127$	5.09674	+	8.82782i	0.452263	+	0.783342i	−0.546264	+	0.837613i	$0.683950\pi$
$128$		−	10.2399i		−	0.905084i
$129$	−6.38029	+	7.75699i	−0.561753	+	0.682965i
$130$	2.61861	+	0.0283709i	0.229667	+	0.00248829i
$131$	1.08499	+	1.87925i	0.0947956	+	0.164191i	0.909523	−	0.415653i	$-0.136447\pi$
$131$	1.08499	+	1.87925i	0.0947956	+	0.164191i	−0.814728	+	0.579844i	$0.803114\pi$
$132$	0.160577	−	0.0602353i	0.0139764	−	0.00524281i
$133$	0.423441			0.0367170
$134$	−0.852486	+	1.47655i	−0.0736436	+	0.127554i
$135$	9.63061	−	0.283465i	0.828871	−	0.0243968i
$136$	−5.65250	−	3.26347i	−0.484698	−	0.279840i
$137$	8.11876	−	4.68737i	0.693633	−	0.400469i	−0.111339	−	0.993783i	$-0.535514\pi$
$137$	8.11876	−	4.68737i	0.693633	−	0.400469i	0.804972	+	0.593313i	$0.202181\pi$
$138$	−0.175966	+	1.05856i	−0.0149792	+	0.0901110i
$139$	−2.51329			−0.213174			−0.106587	−	0.994303i	$-0.533992\pi$
$139$	−2.51329			−0.213174			−0.106587	+	0.994303i	$0.533992\pi$
$140$	0.140822	−	0.243911i	0.0119017	−	0.0206143i
$141$	−2.78153	+	16.7329i	−0.234247	+	1.40917i
$142$	2.53039	−	4.38277i	0.212346	−	0.367794i
$143$	−0.166379	−	0.0984774i	−0.0139133	−	0.00823509i
$144$	−7.01219	+	6.12229i	−0.584349	+	0.510191i
$145$	5.16167	−	2.98009i	0.428653	−	0.247483i
$146$	2.26015			0.187051
$147$	−11.9487	−	1.98624i	−0.985510	−	0.163822i
$148$	1.41708	−	0.818150i	0.116483	−	0.0672515i
$149$			13.4418i			1.10120i	0.834770	+	0.550599i	$0.185601\pi$
$149$			13.4418i			1.10120i	−0.834770	+	0.550599i	$0.814399\pi$
$150$	−0.173767	+	1.04534i	−0.0141880	+	0.0853514i
$151$	18.3027	+	10.5671i	1.48946	+	0.859938i	0.999927	−	0.0120496i	$-0.00383560\pi$
$151$	18.3027	+	10.5671i	1.48946	+	0.859938i	0.489528	+	0.871987i	$0.337169\pi$
$152$	−3.87813	+	6.71712i	−0.314558	+	0.544830i
$153$	2.50726	+	12.7514i	0.202700	+	1.03089i
$154$	0.00149630		0.000863889i	0.000120575		6.96141e-5i
$155$	0.693537	−	1.20124i	0.0557062	−	0.0964860i
$156$	11.3545	+	2.01412i	0.909090	+	0.161259i
$157$	−3.29169	−	5.70137i	−0.262705	−	0.455019i	0.704255	−	0.709947i	$-0.251281\pi$
$157$	−3.29169	−	5.70137i	−0.262705	−	0.455019i	−0.966960	+	0.254929i	$0.917948\pi$
$158$	3.51207	+	2.02770i	0.279405	+	0.161315i
$159$	7.66186	+	20.4252i	0.607625	+	1.61982i
$160$	3.92066	+	6.79078i	0.309955	+	0.536858i
$161$		−	0.130103i		−	0.0102536i
$162$	−3.49317	−	0.475528i	−0.274449	−	0.0373610i
$163$	−9.89577	−	5.71333i	−0.775097	−	0.447502i	0.0595929	−	0.998223i	$-0.481020\pi$
$163$	−9.89577	−	5.71333i	−0.775097	−	0.447502i	−0.834690	+	0.550720i	$0.814353\pi$
$164$	−18.6493	−	10.7672i	−1.45627	−	0.840777i
$165$	−0.109397	+	0.133002i	−0.00851657	+	0.0103542i
$166$	2.18971	−	3.79269i	0.169954	−	0.294370i
$167$	9.54181	+	5.50897i	0.738368	+	0.426297i	0.821476	−	0.570244i	$-0.193151\pi$
$167$	9.54181	+	5.50897i	0.738368	+	0.426297i	−0.0831078	+	0.996541i	$0.526485\pi$
$168$	−0.136369	+	0.165794i	−0.0105211	+	0.0127913i
$169$	−6.25455	−	11.3965i	−0.481119	−	0.876655i
$170$	3.14627			0.241308
$171$	15.1530	−	2.97949i	1.15878	−	0.227847i
$172$	5.35395	+	9.27331i	0.408235	+	0.707083i
$173$	−11.1472	−	19.3075i	−0.847506	−	1.46792i	−0.883427	−	0.468569i	$-0.844770\pi$
$173$	−11.1472	−	19.3075i	−0.847506	−	1.46792i	0.0359213	−	0.999355i	$-0.488563\pi$
$174$	−2.04191	+	0.765957i	−0.154797	+	0.0580670i
$175$		−	0.128478i		−	0.00971200i
$176$		−	0.166386i		−	0.0125418i
$177$	−9.76580	+	3.66333i	−0.734043	+	0.275353i
$178$	2.20786	+	3.82412i	0.165486	+	0.286630i
$179$	−6.37162	−	11.0360i	−0.476237	−	0.824867i	0.523392	−	0.852092i	$-0.324666\pi$
$179$	−6.37162	−	11.0360i	−0.476237	−	0.824867i	−0.999629	+	0.0272247i	$0.991333\pi$
$180$	3.32314	−	9.71936i	0.247692	−	0.724439i
$181$	6.44837			0.479303			0.239652	−	0.970859i	$-0.422967\pi$
$181$	6.44837			0.479303			0.239652	+	0.970859i	$0.422967\pi$
$182$	0.116168	+	0.00125861i	0.00861097	+	9.32944e-5i
$183$	11.9827	−	14.5682i	0.885785	−	1.07691i
$184$	2.06385	+	1.19157i	0.152149	+	0.0878435i
$185$	−0.821539	+	1.42295i	−0.0604008	+	0.104617i
$186$	−0.322407	+	0.391974i	−0.0236400	+	0.0287409i
$187$	−0.201164	−	0.116142i	−0.0147105	−	0.00849313i
$188$	15.6612	+	9.04201i	1.14221	+	0.659456i
$189$	0.427239	−	0.0125752i	0.0310771	−	0.000914715i
$190$		−	3.73886i		−	0.271245i
$191$	−0.806042	−	1.39611i	−0.0583232	−	0.101019i	0.835390	−	0.549658i	$-0.185242\pi$
$191$	−0.806042	−	1.39611i	−0.0583232	−	0.101019i	−0.893713	+	0.448640i	$0.851909\pi$
$192$	2.76751	+	7.37770i	0.199728	+	0.532440i
$193$	8.74810	+	5.05072i	0.629702	+	0.363559i	0.780637	−	0.624985i	$-0.214895\pi$
$193$	8.74810	+	5.05072i	0.629702	+	0.363559i	−0.150935	+	0.988544i	$0.548228\pi$
$194$	2.18501	+	3.78454i	0.156874	+	0.271714i
$195$	−10.8853	+	3.94928i	−0.779512	+	0.282814i
$196$	−6.45673	+	11.1834i	−0.461195	+	0.798813i
$197$	−6.42161	+	3.70752i	−0.457521	+	0.264150i	−0.711001	−	0.703191i	$-0.751758\pi$
$197$	−6.42161	+	3.70752i	−0.457521	+	0.264150i	0.253481	+	0.967340i	$0.418425\pi$
$198$	0.0474671	−	0.0414432i	0.00337334	−	0.00294524i
$199$	−5.19588	+	8.99952i	−0.368326	+	0.637959i	−0.989304	−	0.145869i	$-0.953402\pi$
$199$	−5.19588	+	8.99952i	−0.368326	+	0.637959i	0.620978	+	0.783828i	$0.286736\pi$
$200$	2.03807	+	1.17668i	0.144113	+	0.0832037i
$201$	1.23625	−	7.43695i	0.0871983	−	0.524562i
$202$			1.30860i			0.0920725i
$203$	0.228985	−	0.132205i	0.0160716	−	0.00927896i
$204$	13.6672	+	2.27190i	0.956893	+	0.159065i
$205$	21.6236			1.51026
$206$	−1.89307	+	1.09296i	−0.131896	+	0.0761505i
$207$	−0.915456	−	4.65581i	−0.0636286	−	0.323601i
$208$	5.69852	−	9.62771i	0.395121	−	0.667561i
$209$	−0.138017	+	0.239052i	−0.00954681	+	0.0165356i
$210$	0.0169689	−	0.102081i	0.00117097	−	0.00704423i
$211$	−0.506925	+	0.878020i	−0.0348982	+	0.0604454i	−0.882947	−	0.469473i	$-0.844444\pi$
$211$	−0.506925	+	0.878020i	−0.0348982	+	0.0604454i	0.848049	+	0.529918i	$0.177777\pi$
$212$	23.2572			1.59731
$213$	−3.66950	+	22.0747i	−0.251430	+	1.51254i
$214$	−3.63359	+	2.09786i	−0.248387	+	0.143406i
$215$	−9.31173	−	5.37613i	−0.635055	−	0.366649i
$216$	−3.71344	+	6.89255i	−0.252667	+	0.468978i
$217$	0.0307671	−	0.0532902i	0.00208861	−	0.00361758i
$218$	−5.64040			−0.382016
$219$	−9.35719	+	3.51005i	−0.632300	+	0.237187i
$220$	0.0917995	+	0.159001i	0.00618912	+	0.0107199i
$221$	−7.66234	−	13.6100i	−0.515425	−	0.915507i
$222$	0.381912	−	0.464319i	0.0256322	−	0.0311630i
$223$		−	17.0633i		−	1.14264i	−0.820727	−	0.571321i	$-0.806431\pi$
$223$		−	17.0633i		−	1.14264i	0.820727	−	0.571321i	$-0.193569\pi$
$224$	0.173931	+	0.301257i	0.0116212	+	0.0201286i
$225$	−0.904017	−	4.59764i	−0.0602678	−	0.306509i
$226$			3.13428i			0.208489i
$227$	−4.61903	+	2.66680i	−0.306576	+	0.177001i	−0.645393	−	0.763851i	$-0.723306\pi$
$227$	−4.61903	+	2.66680i	−0.306576	+	0.177001i	0.338818	+	0.940852i	$0.389973\pi$
$228$	2.69981	−	16.2413i	0.178799	−	1.07561i
$229$	21.3778	−	12.3425i	1.41269	−	0.815615i	0.417046	−	0.908885i	$-0.363065\pi$
$229$	21.3778	−	12.3425i	1.41269	−	0.815615i	0.995641	+	0.0932703i	$0.0297321\pi$
$230$	−1.14878			−0.0757481
$231$	−0.00485316	+	0.00590034i	−0.000319314	+	0.000388214i
$232$			4.84325i			0.317975i
$233$	−14.2083			−0.930819			−0.465410	−	0.885095i	$-0.654093\pi$
$233$	−14.2083			−0.930819			−0.465410	+	0.885095i	$0.654093\pi$
$234$	4.16599	−	0.772364i	0.272340	−	0.0504910i
$235$	−18.1589			−1.18456
$236$			11.1199i			0.723842i
$237$	−17.6893	−	2.94050i	−1.14904	−	0.191006i
$238$	0.139577			0.00904744
$239$	−20.6178	+	11.9037i	−1.33365	+	0.769986i	−0.985858	−	0.167584i	$-0.946403\pi$
$239$	−20.6178	+	11.9037i	−1.33365	+	0.769986i	−0.347797	+	0.937570i	$0.613070\pi$
$240$	−7.69635	−	6.33041i	−0.496797	−	0.408626i
$241$	−0.895874	+	0.517233i	−0.0577083	+	0.0333179i	−0.528577	−	0.848886i	$-0.677274\pi$
$241$	−0.895874	+	0.517233i	−0.0577083	+	0.0333179i	0.470868	+	0.882204i	$0.343941\pi$
$242$		−	4.30768i		−	0.276908i
$243$	15.2005	−	3.45623i	0.975111	−	0.221717i
$244$	−10.0551	−	17.4160i	−0.643714	−	1.11494i
$245$		−	12.9670i		−	0.828428i
$246$	−7.80503	−	1.29744i	−0.497630	−	0.0827215i
$247$	−16.1734	+	9.10551i	−1.02909	+	0.579369i
$248$	0.563568	+	0.976129i	0.0357866	+	0.0619843i
$249$	−3.17545	+	19.1027i	−0.201236	+	1.21058i
$250$	−4.76599			−0.301428
$251$	0.598090	−	1.03592i	0.0377511	−	0.0653868i	−0.846533	−	0.532337i	$-0.821314\pi$
$251$	0.598090	−	1.03592i	0.0377511	−	0.0653868i	0.884284	+	0.466950i	$0.154647\pi$
$252$	0.147423	−	0.431177i	0.00928680	−	0.0271616i
$253$	0.0734494	+	0.0424060i	0.00461772	+	0.00266604i
$254$	3.45794	−	1.99644i	0.216970	−	0.125268i
$255$	−13.0258	+	4.88622i	−0.815708	+	0.305987i
$256$	5.08764			0.317977
$257$	11.4913	−	19.9035i	0.716807	−	1.24155i	−0.245451	−	0.969409i	$-0.578936\pi$
$257$	11.4913	−	19.9035i	0.716807	−	1.24155i	0.962258	−	0.272138i	$-0.0877307\pi$
$258$	3.03849	+	2.49922i	0.189168	+	0.155595i
$259$	−0.0364457	+	0.0631257i	−0.00226462	+	0.00392244i
$260$	−0.133744	+	12.3444i	−0.00829444	+	0.765568i
$261$	7.26411	−	6.34224i	0.449637	−	0.392575i
$262$	0.736120	−	0.424999i	0.0454777	−	0.0262565i
$263$	−5.72069			−0.352753			−0.176376	−	0.984323i	$-0.556438\pi$
$263$	−5.72069			−0.352753			−0.176376	+	0.984323i	$0.556438\pi$
$264$	−0.0491500	−	0.131025i	−0.00302497	−	0.00806406i
$265$	−20.2248	+	11.6768i	−1.24240	+	0.717300i
$266$		−	0.165866i		−	0.0101699i
$267$	−15.0796	−	12.4033i	−0.922858	−	0.759071i
$268$	−6.96062	−	4.01872i	−0.425188	−	0.245482i
$269$	−7.03822	+	12.1906i	−0.429128	+	0.743272i	−0.996796	−	0.0799859i	$-0.974512\pi$
$269$	−7.03822	+	12.1906i	−0.429128	+	0.743272i	0.567668	+	0.823258i	$0.307846\pi$
$270$	−0.111036	−	3.77240i	−0.00675743	−	0.229581i
$271$	17.2541	−	9.96164i	1.04811	−	0.605127i	0.125990	−	0.992031i	$-0.459789\pi$
$271$	17.2541	−	9.96164i	1.04811	−	0.605127i	0.922120	+	0.386905i	$0.126456\pi$
$272$	6.72069	−	11.6406i	0.407502	−	0.705814i
$273$	−0.482900	+	0.175201i	−0.0292265	+	0.0106036i
$274$	−1.83609	−	3.18020i	−0.110922	−	0.192123i
$275$	0.0725316	+	0.0418761i	0.00437382	+	0.00252523i
$276$	−4.99019	−	0.829524i	−0.300374	−	0.0499314i
$277$	3.73014	+	6.46079i	0.224122	+	0.388191i	0.956056	−	0.293185i	$-0.0947152\pi$
$277$	3.73014	+	6.46079i	0.224122	+	0.388191i	−0.731934	+	0.681376i	$0.761382\pi$
$278$			0.984479i			0.0590451i
$279$	0.726046	−	2.12350i	0.0434673	−	0.127131i
$280$	−0.199024	−	0.114906i	−0.0118939	−	0.00686697i
$281$	6.79878	+	3.92528i	0.405581	+	0.234163i	0.688889	−	0.724866i	$-0.258099\pi$
$281$	6.79878	+	3.92528i	0.405581	+	0.234163i	−0.283308	+	0.959029i	$0.591432\pi$
$282$	6.55445	+	1.08955i	0.390312	+	0.0648818i
$283$	8.80128	−	15.2443i	0.523182	−	0.906177i	−0.476454	−	0.879199i	$-0.658078\pi$
$283$	8.80128	−	15.2443i	0.523182	−	0.906177i	0.999636	−	0.0269779i	$-0.00858838\pi$
$284$	20.6609	+	11.9286i	1.22600	+	0.707830i
$285$	5.80651	+	15.4792i	0.343948	+	0.916906i
$286$	−0.0385745	+	0.0651721i	−0.00228096	+	0.00385371i
$287$	0.959281			0.0566246
$288$	8.34395	+	9.55678i	0.491672	+	0.563139i
$289$	−0.882429	−	1.52841i	−0.0519076	−	0.0899066i
$290$	−1.16733	−	2.02188i	−0.0685480	−	0.118729i
$291$	−14.9235	−	12.2749i	−0.874834	−	0.719569i
$292$			10.6546i			0.623514i
$293$		−	7.68929i		−	0.449213i	−0.974450	−	0.224606i	$-0.927890\pi$
$293$		−	7.68929i		−	0.449213i	0.974450	−	0.224606i	$-0.0721097\pi$
$294$	−0.778028	+	4.68041i	−0.0453755	+	0.272967i
$295$	−5.58297	−	9.66999i	−0.325053	−	0.563009i
$296$	−0.667583	−	1.15629i	−0.0388025	−	0.0672079i
$297$	−0.132155	+	0.245295i	−0.00766844	+	0.0142335i
$298$	5.26529			0.305010
$299$	2.79769	+	4.96931i	0.161795	+	0.287383i
$300$	−4.92784	−	0.819158i	−0.284509	−	0.0472941i
$301$	−0.413093	−	0.238499i	−0.0238103	−	0.0137469i
$302$	4.13923	−	7.16936i	0.238186	−	0.412550i
$303$	−2.03227	−	5.41769i	−0.116751	−	0.311238i
$304$	−13.8330	−	7.98650i	−0.793378	−	0.458057i
$305$	17.4881	+	10.0968i	1.00137	+	0.578140i
$306$	4.99483	−	0.982117i	0.285536	−	0.0561439i
$307$			30.5691i			1.74467i	0.488909	+	0.872335i	$0.337395\pi$
$307$			30.5691i			1.74467i	−0.488909	+	0.872335i	$0.662605\pi$
$308$	0.00407247	+	0.00705372i	0.000232050	+	0.000401923i
$309$	6.14006	−	7.46493i	0.349296	−	0.424665i
$310$	−0.470537	−	0.271665i	−0.0267247	−	0.0154295i
$311$	5.81691	+	10.0752i	0.329846	+	0.571311i	0.982481	−	0.186362i	$-0.0596697\pi$
$311$	5.81691	+	10.0752i	0.329846	+	0.571311i	−0.652635	+	0.757673i	$0.726336\pi$
$312$	1.64346	−	9.26493i	0.0930423	−	0.524523i
$313$	11.7304	−	20.3177i	0.663043	−	1.14842i	−0.316769	−	0.948503i	$-0.602598\pi$
$313$	11.7304	−	20.3177i	0.663043	−	1.14842i	0.979812	−	0.199921i	$-0.0640686\pi$
$314$	−2.23328	+	1.28939i	−0.126031	+	0.0727642i
$315$	0.0882803	+	0.448974i	0.00497403	+	0.0252968i
$316$	−9.55879	+	16.5563i	−0.537724	+	0.931365i
$317$	14.2780	+	8.24343i	0.801935	+	0.462997i	0.844147	−	0.536111i	$-0.180107\pi$
$317$	14.2780	+	8.24343i	0.801935	+	0.462997i	−0.0422125	+	0.999109i	$0.513441\pi$
$318$	8.00074	−	3.00122i	0.448659	−	0.168300i
$319$			0.172364i			0.00965051i
$320$	−7.30532	+	4.21773i	−0.408380	+	0.235778i
$321$	11.7853	−	14.3283i	0.657793	−	0.799728i
$322$	−0.0509628			−0.00284004
$323$	−19.3116	+	11.1496i	−1.07453	+	0.620378i
$324$	2.24169	−	16.4672i	0.124539	−	0.914844i
$325$	2.76274	+	4.90722i	0.153249	+	0.272204i
$326$	−2.23797	+	3.87627i	−0.123949	+	0.214687i
$327$	23.3517	−	8.75963i	1.29135	−	0.484409i
$328$	−8.78569	+	15.2173i	−0.485108	+	0.840232i
$329$	−0.805579			−0.0444130
$330$	0.0520983	+	0.0428520i	0.00286792	+	0.00235892i
$331$	−27.2064	+	15.7076i	−1.49540	+	0.863368i	−0.999986	−	0.00529152i	$-0.998316\pi$
$331$	−27.2064	+	15.7076i	−1.49540	+	0.863368i	−0.495410	+	0.868659i	$0.664982\pi$
$332$	17.8792	+	10.3225i	0.981246	+	0.566523i
$333$	−0.860049	+	2.51543i	−0.0471304	+	0.137845i
$334$	2.15792	−	3.73762i	0.118076	−	0.204513i
$335$	8.07073			0.440951
$336$	−0.341430	−	0.280834i	−0.0186266	−	0.0153207i
$337$	−1.32957	−	2.30288i	−0.0724261	−	0.125446i	0.827538	−	0.561410i	$-0.189741\pi$
$337$	−1.32957	−	2.30288i	−0.0724261	−	0.125446i	−0.899964	+	0.435964i	$0.856407\pi$
$338$	−4.46412	+	2.44997i	−0.242816	+	0.133261i
$339$	−4.86759	−	12.9761i	−0.264371	−	0.704767i
$340$			14.8319i			0.804373i
$341$	0.0200565	+	0.0347389i	0.00108612	+	0.00188122i
$342$	−1.16709	−	5.93558i	−0.0631092	−	0.320960i
$343$		−	1.15105i		−	0.0621510i
$344$	7.56672	−	4.36865i	0.407970	−	0.235542i
$345$	4.75602	−	1.78407i	0.256055	−	0.0960510i
$346$	−7.56294	+	4.36646i	−0.406586	+	0.234743i
$347$	32.3300			1.73557			0.867784	−	0.496942i	$-0.165544\pi$
$347$	32.3300			1.73557			0.867784	+	0.496942i	$0.165544\pi$
$348$	−3.61081	−	9.62579i	−0.193560	−	0.515996i
$349$		−	2.79887i		−	0.149820i	−0.997190	−	0.0749099i	$-0.976133\pi$
$349$		−	2.79887i		−	0.149820i	0.997190	−	0.0749099i	$-0.0238669\pi$
$350$	−0.0503260			−0.00269004
$351$	−16.0480	+	9.66750i	−0.856581	+	0.516013i
$352$	−0.226765			−0.0120866
$353$			19.8717i			1.05766i	0.848726	+	0.528832i	$0.177370\pi$
$353$			19.8717i			1.05766i	−0.848726	+	0.528832i	$0.822630\pi$
$354$	1.43496	+	3.82536i	0.0762673	+	0.203315i
$355$	−23.9560			−1.27145
$356$	−18.0274	+	10.4081i	−0.955448	+	0.551628i
$357$	−0.577860	+	0.216766i	−0.0305836	+	0.0114725i
$358$	−4.32290	+	2.49582i	−0.228472	+	0.131908i
$359$		−	16.8556i		−	0.889602i	−0.895629	−	0.444801i	$-0.853274\pi$
$359$		−	16.8556i		−	0.889602i	0.895629	−	0.444801i	$-0.146726\pi$
$360$	−7.93068	−	2.71158i	−0.417984	−	0.142913i
$361$	3.74953	+	6.49437i	0.197343	+	0.341809i
$362$		−	2.52589i		−	0.132758i
$363$	6.68990	+	17.8341i	0.351129	+	0.936048i
$364$	−0.00593323	+	0.547631i	−0.000310986	+	0.0287037i
$365$	−5.34938	−	9.26539i	−0.279999	−	0.484973i
$366$	−5.70651	−	4.69373i	−0.298284	−	0.245345i
$367$	12.4865			0.651788			0.325894	−	0.945406i	$-0.394335\pi$
$367$	12.4865			0.651788			0.325894	+	0.945406i	$0.394335\pi$
$368$	−2.45388	+	4.25024i	−0.127917	+	0.221559i
$369$	34.3283	−	6.74986i	1.78706	−	0.351384i
$370$	0.557382	+	0.321805i	0.0289769	+	0.0167298i
$371$	−0.897226	+	0.518014i	−0.0465817	+	0.0268939i
$372$	−1.84781	−	1.51986i	−0.0958045	−	0.0788012i
$373$	12.1869			0.631012			0.315506	−	0.948924i	$-0.397826\pi$
$373$	12.1869			0.631012			0.315506	+	0.948924i	$0.397826\pi$
$374$	−0.0454939	+	0.0787977i	−0.00235243	+	0.00407453i
$375$	19.7315	−	7.40166i	1.01893	−	0.382220i
$376$	7.37798	−	12.7790i	0.380490	−	0.659029i
$377$	−5.90324	+	9.97359i	−0.304032	+	0.513666i
$378$	−0.00492584	−	0.167354i	−0.000253358	−	0.00860775i
$379$	13.3687	−	7.71841i	0.686703	−	0.396468i	−0.115673	−	0.993287i	$-0.536902\pi$
$379$	13.3687	−	7.71841i	0.686703	−	0.396468i	0.802376	+	0.596819i	$0.203569\pi$
$380$	17.6254			0.904165
$381$	−11.2156	+	13.6357i	−0.574594	+	0.698576i
$382$	−0.546868	+	0.315734i	−0.0279802	+	0.0161544i
$383$			6.13276i			0.313370i	0.987649	+	0.156685i	$0.0500807\pi$
$383$			6.13276i			0.313370i	−0.987649	+	0.156685i	$0.949919\pi$
$384$	16.6060	−	6.22923i	0.847423	−	0.317884i
$385$	−0.00708295	−	0.00408934i	−0.000360980	−	0.000208412i
$386$	1.97841	−	3.42671i	0.100699	−	0.174415i
$387$	−16.4609	−	5.62813i	−0.836754	−	0.286094i
$388$	−17.8408	+	10.3004i	−0.905728	+	0.522922i
$389$	10.2264	−	17.7127i	0.518502	−	0.898071i	−0.481267	−	0.876574i	$-0.659823\pi$
$389$	10.2264	−	17.7127i	0.518502	−	0.898071i	0.999769	−	0.0214972i	$-0.00684328\pi$
$390$	1.54697	+	4.26387i	0.0783340	+	0.215909i
$391$	3.42574	+	5.93355i	0.173247	+	0.300073i
$392$	9.12527	+	5.26848i	0.460896	+	0.266098i
$393$	−2.38756	+	2.90274i	−0.120437	+	0.146424i
$394$	1.45227	+	2.51540i	0.0731643	+	0.126724i
$395$		−	19.1968i		−	0.965895i
$396$	0.195368	+	0.223765i	0.00981760	+	0.0112446i
$397$	13.3751	+	7.72211i	0.671276	+	0.387561i	0.796560	−	0.604560i	$-0.206651\pi$
$397$	13.3751	+	7.72211i	0.671276	+	0.387561i	−0.125284	+	0.992121i	$0.539984\pi$
$398$	3.52520	+	2.03527i	0.176702	+	0.102019i
$399$	0.257592	+	0.686697i	0.0128957	+	0.0343778i
$400$	−2.42321	+	4.19713i	−0.121161	+	0.209856i
$401$	−16.1004	−	9.29556i	−0.804015	−	0.464198i	0.0408584	−	0.999165i	$-0.486991\pi$
$401$	−16.1004	−	9.29556i	−0.804015	−	0.464198i	−0.844873	+	0.534967i	$0.820324\pi$
$402$	−2.91312	−	0.484251i	−0.145293	−	0.0241522i
$403$	−0.0292206	+	2.69703i	−0.00145558	+	0.134349i
$404$	−6.16887			−0.306913
$405$	6.31830	+	15.4456i	0.313959	+	0.767497i
$406$	−0.0517859	−	0.0896958i	−0.00257009	−	0.00445153i
$407$	−0.0237583	−	0.0411505i	−0.00117765	−	0.00203975i
$408$	1.85380	−	11.1520i	0.0917767	−	0.552105i
$409$			4.43706i			0.219399i	0.993965	+	0.109699i	$0.0349888\pi$
$409$			4.43706i			0.219399i	−0.993965	+	0.109699i	$0.965011\pi$
$410$		−	8.47018i		−	0.418312i
$411$	12.5404	+	10.3148i	0.618574	+	0.508790i
$412$	−5.15236	−	8.92415i	−0.253839	−	0.439661i
$413$	−0.247676	−	0.428987i	−0.0121873	−	0.0211090i
$414$	−1.82373	+	0.358593i	−0.0896313	+	0.0176239i
$415$	−20.7306			−1.01763
$416$	−13.1214	−	7.76640i	−0.643330	−	0.380779i
$417$	−1.52891	−	4.07582i	−0.0748712	−	0.199594i
$418$	0.0936388	+	0.0540624i	0.00458003	+	0.00264428i
$419$	−17.7869	+	30.8078i	−0.868947	+	1.50506i	−0.00587248	+	0.999983i	$0.501869\pi$
$419$	−17.7869	+	30.8078i	−0.868947	+	1.50506i	−0.863074	+	0.505077i	$0.831464\pi$
$420$	0.481220	+	0.0799935i	0.0234811	+	0.00390328i
$421$	−1.01863	−	0.588105i	−0.0496449	−	0.0286625i	0.474972	−	0.880001i	$-0.342458\pi$
$421$	−1.01863	−	0.588105i	−0.0496449	−	0.0286625i	−0.524617	+	0.851338i	$0.675791\pi$
$422$	0.343929	+	0.198567i	0.0167422	+	0.00966611i
$423$	−28.8280	+	5.66835i	−1.40167	+	0.275605i
$424$		−	18.9771i		−	0.921612i
$425$	3.38293	+	5.85941i	0.164096	+	0.284223i
$426$	8.64689	+	1.43738i	0.418943	+	0.0696412i
$427$	0.775821	+	0.447920i	0.0375446	+	0.0216764i
$428$	−9.88953	−	17.1292i	−0.478029	−	0.827970i
$429$	0.0584880	−	0.329724i	0.00282383	−	0.0159192i
$430$	−2.10588	+	3.64749i	−0.101555	+	0.175898i
$431$	31.4949	−	18.1836i	1.51706	−	0.875873i	0.517258	−	0.855830i	$-0.326953\pi$
$431$	31.4949	−	18.1836i	1.51706	−	0.875873i	0.999799	−	0.0200434i	$-0.00638045\pi$
$432$	−14.1943	−	7.64733i	−0.682923	−	0.367933i
$433$	15.1235	−	26.1947i	0.726791	−	1.25884i	−0.231441	−	0.972849i	$-0.574344\pi$
$433$	15.1235	−	26.1947i	0.726791	−	1.25884i	0.958233	−	0.285990i	$-0.0923225\pi$
$434$	−0.0208743	−	0.0120518i	−0.00100200	−	0.000578504i
$435$	7.97284	+	6.55783i	0.382268	+	0.314424i
$436$		−	26.5895i		−	1.27341i
$437$	7.05110	−	4.07096i	0.337300	−	0.194740i
$438$	1.37492	+	3.66530i	0.0656963	+	0.175135i
$439$	2.82760			0.134954			0.0674770	−	0.997721i	$-0.478505\pi$
$439$	2.82760			0.134954			0.0674770	+	0.997721i	$0.478505\pi$
$440$	0.129740	−	0.0749054i	0.00618511	−	0.00357097i
$441$	−4.04766	−	20.5855i	−0.192746	−	0.980264i
$442$	−5.33116	+	3.00141i	−0.253577	+	0.142763i
$443$	−0.939708	+	1.62762i	−0.0446469	+	0.0773306i	−0.887485	−	0.460836i	$-0.847550\pi$
$443$	−0.939708	+	1.62762i	−0.0446469	+	0.0773306i	0.842838	+	0.538167i	$0.180883\pi$
$444$	2.18885	+	1.80038i	0.103878	+	0.0854421i
$445$	10.4512	−	18.1020i	0.495435	−	0.858119i
$446$	−6.68385			−0.316489
$447$	−21.7987	+	8.17709i	−1.03104	+	0.386763i
$448$	−0.324083	+	0.187110i	−0.0153115	+	0.00884010i
$449$	3.98506	+	2.30078i	0.188067	+	0.108580i	0.591077	−	0.806615i	$-0.298703\pi$
$449$	3.98506	+	2.30078i	0.188067	+	0.108580i	−0.403011	+	0.915195i	$0.632036\pi$
$450$	−1.80094	+	0.354112i	−0.0848970	+	0.0166930i
$451$	−0.312669	+	0.541558i	−0.0147230	+	0.0255010i
$452$	−14.7753			−0.694974
$453$	−6.00259	+	36.1100i	−0.282026	+	1.69659i
$454$	1.04461	+	1.80932i	0.0490259	+	0.0849154i
$455$	−0.269790	−	0.479206i	−0.0126480	−	0.0224655i
$456$	−13.2524	−	2.20295i	−0.620600	−	0.103163i
$457$			9.69251i			0.453396i	0.973965	+	0.226698i	$0.0727931\pi$
$457$			9.69251i			0.453396i	−0.973965	+	0.226698i	$0.927207\pi$
$458$	−4.83467	−	8.37390i	−0.225909	−	0.391287i
$459$	−19.1537	+	11.8231i	−0.894020	+	0.551855i
$460$		−	5.41546i		−	0.252497i
$461$	−24.0814	+	13.9034i	−1.12158	+	0.647546i	−0.941805	−	0.336161i	$-0.890871\pi$
$461$	−24.0814	+	13.9034i	−1.12158	+	0.647546i	−0.179778	+	0.983707i	$0.557538\pi$
$462$	0.00231122	+	0.00190103i	0.000107528	+	8.84438e-5i
$463$	−11.2964	+	6.52199i	−0.524989	+	0.303102i	−0.738973	−	0.673735i	$-0.764689\pi$
$463$	−11.2964	+	6.52199i	−0.524989	+	0.303102i	0.213985	+	0.976837i	$0.431356\pi$
$464$	−9.97404			−0.463033
$465$	2.36996	+	0.393960i	0.109904	+	0.0182695i
$466$			5.56554i			0.257819i
$467$	−40.5417			−1.87605			−0.938024	−	0.346570i	$-0.887346\pi$
$467$	−40.5417			−1.87605			−0.938024	+	0.346570i	$0.887346\pi$
$468$	3.64101	+	19.6390i	0.168306	+	0.907812i
$469$	0.358039			0.0165327
$470$			7.11303i			0.328099i
$471$	7.24351	−	8.80648i	0.333763	−	0.405781i
$472$	9.07346			0.417640
$473$	0.269288	−	0.155473i	0.0123819	−	0.00714867i
$474$	−1.15182	+	6.92906i	−0.0529050	+	0.318262i
$475$	6.96300	−	4.02009i	0.319484	−	0.184454i
$476$			0.657983i			0.0301586i
$477$	−28.4627	+	24.8506i	−1.30322	+	1.13783i
$478$	4.66279	+	8.07619i	0.213271	+	0.369396i
$479$		−	5.23554i		−	0.239218i	−0.992821	−	0.119609i	$-0.961836\pi$
$479$		−	5.23554i		−	0.239218i	0.992821	−	0.119609i	$-0.0381641\pi$
$480$	−8.62759	+	10.4892i	−0.393794	+	0.478764i
$481$	0.0346137	−	3.19481i	0.00157825	−	0.145671i
$482$	0.202605	+	0.350922i	0.00922841	+	0.0159841i
$483$	0.210990	−	0.0791460i	0.00960036	−	0.00360127i
$484$	20.3069			0.923040
$485$	10.3430	−	17.9147i	0.469653	−	0.813464i
$486$	−1.35384	−	5.95417i	−0.0614113	−	0.270087i
$487$	−11.7307	−	6.77275i	−0.531571	−	0.306903i	0.210085	−	0.977683i	$-0.432626\pi$
$487$	−11.7307	−	6.77275i	−0.531571	−	0.306903i	−0.741656	+	0.670781i	$0.765959\pi$
$488$	−14.2109	+	8.20465i	−0.643296	+	0.371407i
$489$	3.24543	−	19.5236i	0.146763	−	0.882890i
$490$	−5.07928			−0.229458
$491$	7.14104	−	12.3686i	0.322270	−	0.558189i	−0.658686	−	0.752418i	$-0.728887\pi$
$491$	7.14104	−	12.3686i	0.322270	−	0.558189i	0.980956	+	0.194229i	$0.0622206\pi$
$492$	6.11626	−	36.7938i	0.275742	−	1.65879i
$493$	−6.96213	+	12.0588i	−0.313559	+	0.543100i
$494$	3.56671	+	6.33526i	0.160474	+	0.285037i
$495$	−0.282241	−	0.0965008i	−0.0126858	−	0.00433739i
$496$	−2.01021	+	1.16060i	−0.0902611	+	0.0521123i
$497$	−1.06275			−0.0476709
$498$	7.48269	+	1.24385i	0.335307	+	0.0557384i
$499$	27.1661	−	15.6843i	1.21612	−	0.702127i	0.252034	−	0.967718i	$-0.418901\pi$
$499$	27.1661	−	15.6843i	1.21612	−	0.702127i	0.964086	+	0.265591i	$0.0855672\pi$
$500$		−	22.4674i		−	1.00477i
$501$	−3.12934	+	18.8253i	−0.139809	+	0.841053i
$502$	−0.405780	−	0.234277i	−0.0181109	−	0.0104563i
$503$	−2.88310	+	4.99368i	−0.128551	+	0.222657i	−0.923116	−	0.384523i	$-0.874366\pi$
$503$	−2.88310	+	4.99368i	−0.128551	+	0.222657i	0.794564	+	0.607180i	$0.207699\pi$
$504$	−0.351826	−	0.120293i	−0.0156716	−	0.00535826i
$505$	5.36453	−	3.09722i	0.238719	−	0.137824i
$506$	0.0166108	−	0.0287708i	0.000738442	−	0.00127902i
$507$	14.6770	−	17.0759i	0.651827	−	0.758368i
$508$	9.41146	+	16.3011i	0.417566	+	0.723245i
$509$	−29.2359	−	16.8793i	−1.29586	−	0.748164i	−0.316171	−	0.948702i	$-0.602397\pi$
$509$	−29.2359	−	16.8793i	−1.29586	−	0.748164i	−0.979686	+	0.200539i	$0.935731\pi$
$510$	1.91398	+	5.10233i	0.0847524	+	0.225935i
$511$	−0.237313	−	0.411037i	−0.0104981	−	0.0181832i
$512$		−	22.4726i		−	0.993157i
$513$	14.0499	+	22.7612i	0.620319	+	1.00493i
$514$	−7.79640	−	4.50125i	−0.343884	−	0.198542i
$515$	8.96113	+	5.17371i	0.394874	+	0.227981i
$516$	−11.7816	+	14.3238i	−0.518656	+	0.630569i
$517$	0.262571	−	0.454786i	0.0115479	−	0.0200015i
$518$	0.0247270	+	0.0142761i	0.00108644	+	0.000627256i
$519$	24.5299	−	29.8229i	1.07674	−	1.30908i
$520$	10.0726	+	0.109131i	0.441714	+	0.00478569i
$521$	39.9945			1.75219			0.876094	−	0.482140i	$-0.160140\pi$
$521$	39.9945			1.75219			0.876094	+	0.482140i	$0.160140\pi$
$522$	−2.48431	−	2.84542i	−0.108735	−	0.124541i
$523$	−8.47279	−	14.6753i	−0.370489	−	0.641706i	0.619152	−	0.785272i	$-0.287477\pi$
$523$	−8.47279	−	14.6753i	−0.370489	−	0.641706i	−0.989641	+	0.143565i	$0.954143\pi$
$524$	2.00349	+	3.47016i	0.0875231	+	0.151594i
$525$	0.208353	−	0.0781571i	0.00909328	−	0.00341105i
$526$			2.24085i			0.0977056i
$527$			3.24050i			0.141158i
$528$	0.269830	−	0.101218i	0.0117428	−	0.00440495i
$529$	10.2492	+	17.7521i	0.445617	+	0.771831i
$530$	4.57391	+	7.92225i	0.198678	+	0.344120i
$531$	−11.8817	−	13.6087i	−0.515622	−	0.590569i
$532$	0.781910			0.0339001
$533$	−36.6398	+	20.6280i	−1.58705	+	0.893499i
$534$	−4.85850	+	5.90683i	−0.210248	+	0.255614i
$535$	17.2001	+	9.93050i	0.743627	+	0.429333i
$536$	−3.27914	+	5.67964i	−0.141637	+	0.245323i
$537$	14.0211	−	17.0464i	0.605053	−	0.735608i
$538$	4.77516	+	2.75694i	0.205872	+	0.118860i
$539$	0.324754	+	0.187497i	0.0139882	+	0.00807606i
$540$	17.7835	−	0.523436i	0.765281	−	0.0225251i
$541$		−	4.76584i		−	0.204899i	−0.994738	−	0.102450i	$-0.967332\pi$
$541$		−	4.76584i		−	0.204899i	0.994738	−	0.102450i	$-0.0326681\pi$
$542$	−3.90207	−	6.75858i	−0.167608	−	0.290306i
$543$	3.92274	+	10.4574i	0.168341	+	0.448768i
$544$	−15.8647	−	9.15950i	−0.680194	−	0.392710i
$545$	13.3498	+	23.1226i	0.571843	+	0.990462i
$546$	0.0686278	+	0.189157i	0.00293700	+	0.00809516i
$547$	−0.953108	+	1.65083i	−0.0407520	+	0.0705845i	−0.885682	−	0.464292i	$-0.846309\pi$
$547$	−0.953108	+	1.65083i	−0.0407520	+	0.0705845i	0.844930	+	0.534877i	$0.179642\pi$
$548$	14.9918	−	8.65553i	0.640419	−	0.369746i
$549$	30.9148	+	10.5701i	1.31941	+	0.451120i
$550$	0.0164033	−	0.0284113i	0.000699438	−	0.00121146i
$551$	14.3300	+	8.27342i	0.610478	+	0.352459i
$552$	−0.676864	+	4.07183i	−0.0288092	+	0.173309i
$553$		−	0.851621i		−	0.0362146i
$554$	2.53075	−	1.46113i	0.107521	−	0.0620775i
$555$	−2.80737	−	0.466672i	−0.119166	−	0.0198091i
$556$	−4.64095			−0.196820
$557$	13.6414	−	7.87589i	0.578006	−	0.333712i	−0.182334	−	0.983237i	$-0.558365\pi$
$557$	13.6414	−	7.87589i	0.578006	−	0.333712i	0.760341	+	0.649524i	$0.225032\pi$
$558$	−0.831797	−	0.284399i	−0.0352128	−	0.0120396i
$559$	20.9067	+	0.226511i	0.884260	+	0.00958039i
$560$	0.236635	−	0.409863i	0.00999964	−	0.0173199i
$561$	0.0659738	−	0.396881i	0.00278542	−	0.0167563i
$562$	1.53757	−	2.66315i	0.0648585	−	0.112338i
$563$	−10.9469			−0.461359			−0.230679	−	0.973030i	$-0.574095\pi$
$563$	−10.9469			−0.461359			−0.230679	+	0.973030i	$0.574095\pi$
$564$	−5.13627	+	30.8984i	−0.216276	+	1.30106i
$565$	12.8488	−	7.41828i	0.540555	−	0.312089i
$566$	−5.97132	−	3.44754i	−0.250993	−	0.144911i
$567$	0.280297	+	0.685207i	0.0117714	+	0.0287760i
$568$	9.73332	−	16.8586i	0.408401	−	0.707371i
$569$	−3.19831			−0.134080			−0.0670400	−	0.997750i	$-0.521356\pi$
$569$	−3.19831			−0.134080			−0.0670400	+	0.997750i	$0.521356\pi$
$570$	6.06333	−	2.27447i	0.253965	−	0.0952669i
$571$	−3.17090	−	5.49215i	−0.132698	−	0.229839i	0.792018	−	0.610498i	$-0.209031\pi$
$571$	−3.17090	−	5.49215i	−0.132698	−	0.229839i	−0.924716	+	0.380659i	$0.875697\pi$
$572$	−0.307229	−	0.181845i	−0.0128459	−	0.00760331i
$573$	1.77373	−	2.15646i	0.0740988	−	0.0900874i
$574$		−	0.375760i		−	0.0156839i
$575$	−1.23518	−	2.13940i	−0.0515108	−	0.0892192i
$576$	−10.2809	+	8.97618i	−0.428371	+	0.374007i
$577$			34.1519i			1.42176i	0.703313	+	0.710881i	$0.251703\pi$
$577$			34.1519i			1.42176i	−0.703313	+	0.710881i	$0.748297\pi$
$578$	−0.598694	+	0.345656i	−0.0249024	+	0.0143774i
$579$	−2.86904	+	17.2594i	−0.119233	+	0.717275i
$580$	9.53135	−	5.50293i	0.395768	−	0.228497i
$581$	−0.919665			−0.0381541
$582$	−4.80821	+	5.84570i	−0.199307	+	0.242312i
$583$		−	0.675367i		−	0.0279709i
$584$	8.69381			0.359752
$585$	−13.0264	−	15.2503i	−0.538577	−	0.630521i
$586$	−3.01197			−0.124423
$587$		−	25.4676i		−	1.05116i	−0.850744	−	0.525580i	$-0.823848\pi$
$587$		−	25.4676i		−	1.05116i	0.850744	−	0.525580i	$-0.176152\pi$
$588$	−22.0640	−	3.66771i	−0.909903	−	0.151254i
$589$	3.85083			0.158671
$590$	−3.78783	+	2.18690i	−0.155942	+	0.0900334i
$591$	−9.91897	−	8.15856i	−0.408012	−	0.335598i
$592$	2.38122	−	1.37480i	0.0978677	−	0.0565039i
$593$			16.5099i			0.677982i	0.940790	+	0.338991i	$0.110086\pi$
$593$			16.5099i			0.677982i	−0.940790	+	0.338991i	$0.889914\pi$
$594$	0.0960844	+	0.0517665i	0.00394239	+	0.00212401i
$595$	−0.330354	−	0.572190i	−0.0135432	−	0.0234575i
$596$			24.8212i			1.01672i
$597$	−17.7554	−	2.95149i	−0.726680	−	0.120797i
$598$	1.94653	−	1.09588i	0.0795994	−	0.0448140i
$599$	−7.18714	−	12.4485i	−0.293659	−	0.508632i	0.681013	−	0.732271i	$-0.261540\pi$
$599$	−7.18714	−	12.4485i	−0.293659	−	0.508632i	−0.974672	+	0.223639i	$0.928206\pi$
$600$	−0.668406	+	4.02096i	−0.0272876	+	0.164155i
$601$	−8.12688			−0.331502			−0.165751	−	0.986168i	$-0.553005\pi$
$601$	−8.12688			−0.331502			−0.165751	+	0.986168i	$0.553005\pi$
$602$	−0.0934225	+	0.161812i	−0.00380762	+	0.00659498i
$603$	12.8126	−	2.51930i	0.521769	−	0.102594i
$604$	33.7972	+	19.5128i	1.37519	+	0.793965i
$605$	−17.6591	+	10.1955i	−0.717946	+	0.414506i
$606$	−2.12216	+	0.796061i	−0.0862068	+	0.0323377i
$607$	−9.19452			−0.373194			−0.186597	−	0.982437i	$-0.559746\pi$
$607$	−9.19452			−0.373194			−0.186597	+	0.982437i	$0.559746\pi$
$608$	−10.8846	+	18.8528i	−0.441431	+	0.764580i
$609$	0.353696	+	0.290923i	0.0143325	+	0.0117888i
$610$	3.95501	−	6.85027i	0.160134	−	0.277359i
$611$	30.7691	−	17.3229i	1.24479	−	0.700808i
$612$	4.62981	+	23.5462i	0.187149	+	0.951799i
$613$	−16.5468	+	9.55328i	−0.668318	+	0.385853i	−0.795439	−	0.606034i	$-0.792760\pi$
$613$	−16.5468	+	9.55328i	−0.668318	+	0.385853i	0.127121	+	0.991887i	$0.459426\pi$
$614$	11.9742			0.483239
$615$	13.1543	+	35.0672i	0.530434	+	1.41404i
$616$	0.00575561	−	0.00332300i	0.000231900	−	0.000133888i
$617$		−	24.4607i		−	0.984751i	−0.870383	−	0.492376i	$-0.836129\pi$
$617$		−	24.4607i		−	0.984751i	0.870383	−	0.492376i	$-0.163871\pi$
$618$	−2.92408	−	2.40512i	−0.117624	−	0.0967481i
$619$	−27.6401	−	15.9580i	−1.11095	−	0.641406i	−0.171873	−	0.985119i	$-0.554982\pi$
$619$	−27.6401	−	15.9580i	−1.11095	−	0.641406i	−0.939075	+	0.343713i	$0.888315\pi$
$620$	1.28066	−	2.21817i	0.0514325	−	0.0890838i
$621$	6.99346	−	4.31688i	0.280638	−	0.173230i
$622$	3.94654	−	2.27854i	0.158242	−	0.0913610i
$623$	0.463644	−	0.803055i	0.0185755	−	0.0321737i
$624$	19.0799	+	3.38448i	0.763808	+	0.135488i
$625$	7.37552	+	12.7748i	0.295021	+	0.510991i
$626$	−7.95863	−	4.59492i	−0.318091	−	0.183650i
$627$	−0.471632	−	0.0783997i	−0.0188352	−	0.00313098i
$628$	−6.07831	−	10.5279i	−0.242551	−	0.420111i
$629$		−	3.83858i		−	0.153054i
$630$	0.175867	−	0.0345802i	0.00700673	−	0.00137771i
$631$	−7.01719	−	4.05137i	−0.279350	−	0.161283i	0.353779	−	0.935329i	$-0.384896\pi$
$631$	−7.01719	−	4.05137i	−0.279350	−	0.161283i	−0.633129	+	0.774046i	$0.718230\pi$
$632$	13.5094	+	7.79966i	0.537375	+	0.310254i
$633$	−1.73227	−	0.287956i	−0.0688515	−	0.0114452i
$634$	3.22903	−	5.59284i	0.128241	−	0.222120i
$635$	−16.3687	−	9.45045i	−0.649570	−	0.375030i
$636$	14.1481	+	37.7164i	0.561009	+	1.49555i
$637$	12.3699	+	21.9717i	0.490114	+	0.870549i
$638$	0.0675165			0.00267300
$639$	−38.0310	+	7.47791i	−1.50448	+	0.295822i
$640$	9.49344	+	16.4431i	0.375261	+	0.649971i
$641$	1.37495	+	2.38149i	0.0543073	+	0.0940630i	0.891901	−	0.452231i	$-0.149372\pi$
$641$	1.37495	+	2.38149i	0.0543073	+	0.0940630i	−0.837594	+	0.546294i	$0.816038\pi$
$642$	−5.61254	−	4.61643i	−0.221509	−	0.182196i
$643$		−	37.5033i		−	1.47899i	−0.673163	−	0.739494i	$-0.735065\pi$
$643$		−	37.5033i		−	1.47899i	0.673163	−	0.739494i	$-0.264935\pi$
$644$		−	0.240244i		−	0.00946695i
$645$	3.05389	−	18.3714i	0.120247	−	0.723372i
$646$	4.36739	+	7.56454i	0.171833	+	0.297623i
$647$	24.1409	+	41.8133i	0.949078	+	1.64385i	0.747373	+	0.664405i	$0.231315\pi$
$647$	24.1409	+	41.8133i	0.949078	+	1.64385i	0.201705	+	0.979446i	$0.435352\pi$
$648$	−13.4367	−	1.82915i	−0.527843	−	0.0718558i
$649$	0.322910			0.0126753
$650$	1.92220	−	1.08219i	0.0753951	−	0.0424470i
$651$	0.105138	+	0.0174771i	0.00412067	+	0.000684983i
$652$	−18.2732	−	10.5500i	−0.715633	−	0.413171i
$653$	−10.4618	+	18.1203i	−0.409400	+	0.709102i	−0.994823	−	0.101626i	$-0.967595\pi$
$653$	−10.4618	+	18.1203i	−0.409400	+	0.709102i	0.585422	+	0.810728i	$0.300929\pi$
$654$	−3.43123	−	9.14707i	−0.134172	−	0.357679i
$655$	−3.48453	−	2.01180i	−0.136152	−	0.0786074i
$656$	−31.3379	−	18.0930i	−1.22354	−	0.706412i
$657$	−11.3846	−	13.0393i	−0.444154	−	0.508713i
$658$			0.315553i			0.0123015i
$659$	−16.0220	−	27.7510i	−0.624130	−	1.08102i	−0.988708	−	0.149852i	$-0.952120\pi$
$659$	−16.0220	−	27.7510i	−0.624130	−	1.08102i	0.364579	−	0.931173i	$-0.381213\pi$
$660$	−0.202009	+	0.245597i	−0.00786319	+	0.00955987i
$661$	19.2213	+	11.0974i	0.747623	+	0.431641i	0.824835	−	0.565374i	$-0.191268\pi$
$661$	19.2213	+	11.0974i	0.747623	+	0.431641i	−0.0772111	+	0.997015i	$0.524602\pi$
$662$	6.15281	+	10.6570i	0.239136	+	0.414196i
$663$	17.4102	−	20.7055i	0.676154	−	0.804133i
$664$	8.42285	−	14.5888i	0.326870	−	0.566156i
$665$	−0.679960	+	0.392575i	−0.0263677	+	0.0152234i
$666$	0.985318	+	0.336889i	0.0381803	+	0.0130542i
$667$	2.54203	−	4.40293i	0.0984279	−	0.170482i
$668$	17.6196	+	10.1727i	0.681722	+	0.393592i
$669$	27.6716	−	10.3801i	1.06985	−	0.401319i
$670$		−	3.16138i		−	0.122135i
$671$	−0.505743	+	0.291991i	−0.0195240	+	0.0112722i
$672$	−0.382743	+	0.465329i	−0.0147646	+	0.0179505i
$673$	−43.6116			−1.68110			−0.840551	−	0.541733i	$-0.817769\pi$
$673$	−43.6116			−1.68110			−0.840551	+	0.541733i	$0.817769\pi$
$674$	−0.902059	+	0.520804i	−0.0347460	+	0.0200606i
$675$	6.90608	−	4.26294i	0.265815	−	0.164081i
$676$	−11.5494	−	21.0444i	−0.444209	−	0.809400i
$677$	−6.92480	+	11.9941i	−0.266142	+	0.460971i	−0.967862	−	0.251481i	$-0.919082\pi$
$677$	−6.92480	+	11.9941i	−0.266142	+	0.460971i	0.701720	+	0.712453i	$0.252416\pi$
$678$	−5.08288	+	1.90668i	−0.195207	+	0.0732256i
$679$	0.458845	−	0.794743i	0.0176089	−	0.0304994i
$680$	12.1023			0.464104
$681$	−7.13466	−	5.86841i	−0.273401	−	0.224878i
$682$	0.0136076	−	0.00785633i	0.000521061	−	0.000300835i
$683$	5.13516	+	2.96479i	0.196491	+	0.113444i	0.595018	−	0.803712i	$-0.297145\pi$
$683$	5.13516	+	2.96479i	0.196491	+	0.113444i	−0.398526	+	0.917157i	$0.630478\pi$
$684$	27.9810	−	5.50181i	1.06988	−	0.210367i
$685$	−8.69139	+	15.0539i	−0.332081	+	0.575181i
$686$	−0.450879			−0.0172146
$687$	33.0207	+	27.1602i	1.25982	+	1.03623i
$688$	8.99665	+	15.5827i	0.342994	+	0.594083i
$689$	23.1305	−	39.0792i	0.881200	−	1.48880i
$690$	−0.698837	−	1.86298i	−0.0266043	−	0.0709224i
$691$		−	1.58516i		−	0.0603025i	−0.999545	−	0.0301512i	$-0.990401\pi$
$691$		−	1.58516i		−	0.0603025i	0.999545	−	0.0301512i	$-0.00959890\pi$
$692$	−20.5840	−	35.6526i	−0.782487	−	1.35531i
$693$	−0.0125210	−	0.00428103i	−0.000475632	−	0.000162623i
$694$		−	12.6640i		−	0.480718i
$695$	4.03583	−	2.33009i	0.153088	−	0.0883852i
$696$	−7.85433	+	2.94630i	−0.297718	+	0.111679i
$697$	−43.7494	+	25.2587i	−1.65713	+	0.956742i
$698$	−1.09634			−0.0414972
$699$	−8.64338	−	23.0418i	−0.326923	−	0.871519i
$700$		−	0.237242i		−	0.00896692i
$701$	2.31919			0.0875945			0.0437972	−	0.999040i	$-0.486054\pi$
$701$	2.31919			0.0875945			0.0437972	+	0.999040i	$0.486054\pi$
$702$	3.78685	+	6.28617i	0.142926	+	0.237256i
$703$	−4.56156			−0.172043
$704$		−	0.243947i		−	0.00919408i
$705$	−11.0467	−	29.4485i	−0.416041	−	1.10909i
$706$	7.78394			0.292952
$707$	0.237985	−	0.137401i	0.00895035	−	0.00516749i
$708$	−18.0332	+	6.76457i	−0.677728	+	0.254228i
$709$	−0.303872	+	0.175441i	−0.0114122	+	0.00658881i	−0.505695	−	0.862712i	$-0.668764\pi$
$709$	−0.303872	+	0.175441i	−0.0114122	+	0.00658881i	0.494283	+	0.869301i	$0.335431\pi$
$710$			9.38378i			0.352167i
$711$	−5.99232	−	30.4756i	−0.224730	−	1.14293i
$712$	8.49267	+	14.7097i	0.318276	+	0.551271i
$713$		−	1.18318i		−	0.0443105i
$714$	0.0849092	+	0.226353i	0.00317765	+	0.00847105i
$715$	0.358469	+	0.00388379i	0.0134060	+	0.000145245i
$716$	−11.7656	−	20.3786i	−0.439701	−	0.761585i
$717$	−31.8468	−	26.1946i	−1.18934	−	0.978256i
$718$	−6.60248			−0.246402
$719$	−24.0475	+	41.6515i	−0.896821	+	1.55334i	−0.0652858	+	0.997867i	$0.520796\pi$
$719$	−24.0475	+	41.6515i	−0.896821	+	1.55334i	−0.831535	+	0.555472i	$0.812537\pi$
$720$	5.58413	−	16.3322i	0.208108	−	0.608665i
$721$	0.397539	+	0.229519i	0.0148051	+	0.00854775i
$722$	2.54391	−	1.46872i	0.0946744	−	0.0546603i
$723$	−1.38379	−	1.13820i	−0.0514637	−	0.0423300i
$724$	11.9073			0.442532
$725$	2.51027	−	4.34791i	0.0932290	−	0.161477i
$726$	6.98579	−	2.62050i	0.259267	−	0.0972558i
$727$	−9.59899	+	16.6259i	−0.356007	+	0.616622i	−0.987290	−	0.158931i	$-0.949195\pi$
$727$	−9.59899	+	16.6259i	−0.356007	+	0.616622i	0.631283	+	0.775553i	$0.282529\pi$
$728$	0.446849	+	0.00484132i	0.0165613	+	0.000179431i
$729$	14.8519	+	22.5482i	0.550071	+	0.835118i
$730$	−3.62934	+	2.09540i	−0.134328	+	0.0775543i
$731$	25.1196			0.929081
$732$	22.1268	−	26.9012i	0.817829	−	0.994296i
$733$	−16.7960	+	9.69719i	−0.620376	+	0.358174i	−0.777015	−	0.629482i	$-0.783267\pi$
$733$	−16.7960	+	9.69719i	−0.620376	+	0.358174i	0.156640	+	0.987656i	$0.449934\pi$
$734$		−	4.89106i		−	0.180532i
$735$	21.0286	−	7.88821i	0.775651	−	0.290961i
$736$	5.79257	+	3.34434i	0.213517	+	0.123274i
$737$	−0.116700	+	0.202130i	−0.00429868	+	0.00744554i
$738$	−2.64398	−	13.4467i	−0.0973264	−	0.494981i
$739$	−18.6042	+	10.7411i	−0.684365	+	0.395118i	−0.801498	−	0.597998i	$-0.795963\pi$
$739$	−18.6042	+	10.7411i	−0.684365	+	0.395118i	0.117133	+	0.993116i	$0.462630\pi$
$740$	−1.51702	+	2.62756i	−0.0557669	+	0.0965912i
$741$	−24.6052	−	20.6893i	−0.903895	−	0.760039i
$742$	0.202911	+	0.351452i	0.00744909	+	0.0129022i
$743$	−2.74350	−	1.58396i	−0.100649	−	0.0581098i	0.448831	−	0.893617i	$-0.351841\pi$
$743$	−2.74350	−	1.58396i	−0.100649	−	0.0581098i	−0.549480	+	0.835507i	$0.685174\pi$
$744$	−1.24016	+	1.50775i	−0.0454664	+	0.0552769i
$745$	−12.4620	−	21.5848i	−0.456573	−	0.790808i
$746$		−	4.77371i		−	0.174778i
$747$	−32.9106	+	6.47110i	−1.20414	+	0.236765i
$748$	−0.371461	−	0.214463i	−0.0135820	−	0.00784156i
$749$	0.763044	+	0.440544i	0.0278810	+	0.0160971i
$750$	−2.89930	−	7.72903i	−0.105868	−	0.282224i
$751$	−20.0073	+	34.6536i	−0.730076	+	1.26453i	0.226774	+	0.973947i	$0.427182\pi$
$751$	−20.0073	+	34.6536i	−0.730076	+	1.26453i	−0.956850	+	0.290582i	$0.906151\pi$
$752$	26.3168	+	15.1940i	0.959673	+	0.554068i
$753$	2.04380	+	0.339742i	0.0744801	+	0.0123809i
$754$	3.90675	+	2.31235i	0.142275	+	0.0842110i
$755$	−39.1873			−1.42617
$756$	0.788925	−	0.0232210i	0.0286929	−	0.000844540i
$757$	−19.7335	−	34.1795i	−0.717227	−	1.24227i	−0.962094	−	0.272717i	$-0.912078\pi$
$757$	−19.7335	−	34.1795i	−0.717227	−	1.24227i	0.244867	−	0.969557i	$-0.421256\pi$
$758$	−3.02338	−	5.23664i	−0.109814	−	0.190203i
$759$	−0.0240885	+	0.144910i	−0.000874359	+	0.00525991i
$760$		−	14.3818i		−	0.521681i
$761$			3.38516i			0.122712i	0.998116	+	0.0613560i	$0.0195425\pi$
$761$			3.38516i			0.122712i	−0.998116	+	0.0613560i	$0.980458\pi$
$762$	5.34122	+	4.39326i	0.193492	+	0.159151i
$763$	0.592234	+	1.02578i	0.0214403	+	0.0371357i
$764$	−1.48841	−	2.57800i	−0.0538487	−	0.0932687i
$765$	−15.8480	−	18.1516i	−0.572987	−	0.656273i
$766$	2.40226			0.0867972
$767$	18.6848	+	11.0593i	0.674667	+	0.399327i
$768$	3.09497	+	8.25065i	0.111680	+	0.297720i
$769$	−32.9803	−	19.0412i	−1.18930	−	0.686642i	−0.231151	−	0.972918i	$-0.574249\pi$
$769$	−32.9803	−	19.0412i	−1.18930	−	0.686642i	−0.958147	+	0.286276i	$0.907583\pi$
$770$	−0.00160183	+	0.00277446i	−5.77261e−5	+	9.99845e-5i
$771$	39.2682	+	6.52758i	1.41421	+	0.235085i
$772$	16.1539	+	9.32647i	0.581392	+	0.335667i
$773$	−7.58226	−	4.37762i	−0.272715	−	0.157452i	0.357406	−	0.933949i	$-0.383661\pi$
$773$	−7.58226	−	4.37762i	−0.272715	−	0.157452i	−0.630121	+	0.776497i	$0.716995\pi$
$774$	−2.20459	+	6.44789i	−0.0792425	+	0.231765i
$775$		−	1.16840i		−	0.0419700i
$776$	8.40476	+	14.5575i	0.301713	+	0.522583i
$777$	−0.124542	−	0.0207028i	−0.00446794	−	0.000742708i
$778$	−6.93824	−	4.00580i	−0.248748	−	0.143615i
$779$	30.0161	+	51.9893i	1.07544	+	1.86271i
$780$	−20.1004	+	7.29260i	−0.719709	+	0.261117i
$781$	0.346394	−	0.599972i	0.0123949	−	0.0214687i
$782$	2.32423	−	1.34189i	0.0831142	−	0.0479860i
$783$	14.7042	+	7.92207i	0.525486	+	0.283112i
$784$	−10.8497	+	18.7923i	−0.387491	+	0.671154i
$785$	10.5716	+	6.10349i	0.377315	+	0.217843i
$786$	1.13703	+	0.935231i	0.0405565	+	0.0333586i
$787$			41.2919i			1.47190i	0.677038	+	0.735948i	$0.263263\pi$
$787$			41.2919i			1.47190i	−0.677038	+	0.735948i	$0.736737\pi$
$788$	−11.8579	+	6.84617i	−0.422420	+	0.243885i
$789$	−3.48007	−	9.27728i	−0.123894	−	0.330280i
$790$	−7.51957			−0.267534
$791$	0.570009	−	0.329095i	0.0202672	−	0.0117013i
$792$	0.182585	−	0.159414i	0.00648788	−	0.00566452i
$793$	−39.2644	−	0.425405i	−1.39432	−	0.0151066i
$794$	3.02482	−	5.23915i	0.107347	−	0.185930i
$795$	−31.2397	−	25.6953i	−1.10796	−	0.911320i
$796$	−9.59452	+	16.6182i	−0.340069	+	0.589016i
$797$	2.11338			0.0748597			0.0374298	−	0.999299i	$-0.488083\pi$
$797$	2.11338			0.0748597			0.0374298	+	0.999299i	$0.488083\pi$
$798$	0.268986	−	0.100901i	0.00952199	−	0.00357187i
$799$	36.7395	−	21.2116i	1.29975	−	0.750412i
$800$	5.72019	+	3.30255i	0.202239	+	0.116763i
$801$	10.9411	−	32.0001i	0.386586	−	1.13067i
$802$	−3.64116	+	6.30667i	−0.128574	+	0.222696i
$803$	0.309399			0.0109185
$804$	2.28281	−	13.7328i	0.0805086	−	0.484318i
$805$	0.120620	+	0.208920i	0.00425129	+	0.00736345i
$806$	1.05645	+	0.0114460i	0.0372119	+	0.000403168i
$807$	−24.0511	−	3.99803i	−0.846639	−	0.140737i
$808$			5.03360i			0.177081i
$809$	10.8893	+	18.8609i	0.382848	+	0.663113i	0.991468	−	0.130349i	$-0.0416099\pi$
$809$	10.8893	+	18.8609i	0.382848	+	0.663113i	−0.608620	+	0.793462i	$0.708277\pi$
$810$	6.05018	−	2.47494i	0.212582	−	0.0869605i
$811$			6.04752i			0.212357i	0.994347	+	0.106179i	$0.0338615\pi$
$811$			6.04752i			0.212357i	−0.994347	+	0.106179i	$0.966138\pi$
$812$	0.422836	−	0.244125i	0.0148386	−	0.00856709i
$813$	26.6511	+	21.9211i	0.934693	+	0.768805i
$814$	−0.0161190	+	0.00930634i	−0.000564972	+	0.000326187i
$815$	21.1875			0.742165
$816$	22.9660	+	3.81766i	0.803971	+	0.133645i
$817$		−	29.8507i		−	1.04434i
$818$	1.73804			0.0607691
$819$	−0.577888	−	0.676542i	−0.0201930	−	0.0236403i
$820$	39.9294			1.39439
$821$			18.9464i			0.661235i	0.943765	+	0.330618i	$0.107257\pi$
$821$			18.9464i			0.661235i	−0.943765	+	0.330618i	$0.892743\pi$
$822$	4.04040	−	4.91221i	0.140925	−	0.171333i
$823$	11.4297			0.398416			0.199208	−	0.979957i	$-0.436163\pi$
$823$	11.4297			0.398416			0.199208	+	0.979957i	$0.436163\pi$
$824$	−7.28182	+	4.20416i	−0.253674	+	0.146459i
$825$	−0.0237875	+	0.143100i	−0.000828176	+	0.00498209i
$826$	−0.168038	+	0.0970169i	−0.00584679	+	0.00337565i
$827$			29.0415i			1.00987i	0.863156	+	0.504937i	$0.168484\pi$
$827$			29.0415i			1.00987i	−0.863156	+	0.504937i	$0.831516\pi$
$828$	−1.69045	−	8.59725i	−0.0587471	−	0.298775i
$829$	−8.75841	−	15.1700i	−0.304192	−	0.526876i	0.672889	−	0.739744i	$-0.265053\pi$
$829$	−8.75841	−	15.1700i	−0.304192	−	0.526876i	−0.977081	+	0.212867i	$0.931720\pi$
$830$			8.12038i			0.281862i
$831$	−8.20834	+	9.97949i	−0.284744	+	0.346185i
$832$	8.35486	−	14.1156i	0.289653	−	0.489371i
$833$	15.1468	+	26.2350i	0.524805	+	0.908989i
$834$	−1.59654	+	0.598890i	−0.0552835	+	0.0207378i
$835$	−20.4296			−0.706996
$836$	−0.254856	+	0.441424i	−0.00881439	+	0.0152670i
$837$	3.88538	−	0.114361i	0.134298	−	0.00395290i
$838$	12.0677	+	6.96730i	0.416872	+	0.240681i
$839$	24.4025	−	14.0888i	0.842467	−	0.486398i	−0.0156353	−	0.999878i	$-0.504977\pi$
$839$	24.4025	−	14.0888i	0.842467	−	0.486398i	0.858102	+	0.513479i	$0.171644\pi$
$840$	0.0652721	−	0.392659i	0.00225210	−	0.0135480i
$841$	−18.6676			−0.643712
$842$	−0.230366	+	0.399006i	−0.00793895	+	0.0137507i
$843$	−2.22974	+	13.4135i	−0.0767962	+	0.461986i
$844$	−0.936069	+	1.62132i	−0.0322208	+	0.0558081i
$845$	20.6093	+	12.5019i	0.708982	+	0.430077i
$846$	2.22035	+	11.2922i	0.0763371	+	0.388234i
$847$	−0.783407	+	0.452300i	−0.0269182	+	0.0155412i
$848$	39.0809			1.34205
$849$	30.0758	+	4.99952i	1.03220	+	0.171583i
$850$	2.29519	−	1.32513i	0.0787242	−	0.0454515i
$851$			1.40155i			0.0480446i
$852$	−6.77597	+	40.7624i	−0.232141	+	1.39650i
$853$	14.5761	+	8.41549i	0.499075	+	0.288141i	0.728331	−	0.685225i	$-0.240296\pi$
$853$	14.5761	+	8.41549i	0.499075	+	0.288141i	−0.229257	+	0.973366i	$0.573630\pi$
$854$	0.175455	−	0.303896i	0.00600393	−	0.0103991i
$855$	−21.5704	+	18.8329i	−0.737691	+	0.644072i
$856$	−13.9768	+	8.06953i	−0.477719	+	0.275811i
$857$	22.9063	−	39.6748i	0.782463	−	1.35527i	−0.148040	−	0.988981i	$-0.547296\pi$
$857$	22.9063	−	39.6748i	0.782463	−	1.35527i	0.930503	−	0.366285i	$-0.119370\pi$
$858$	−0.129156	−	0.0229103i	−0.00440932	−	0.000782145i
$859$	4.40873	+	7.63614i	0.150424	+	0.260542i	0.931383	−	0.364040i	$-0.118603\pi$
$859$	4.40873	+	7.63614i	0.150424	+	0.260542i	−0.780959	+	0.624582i	$0.785269\pi$
$860$	−17.1947	−	9.92736i	−0.586334	−	0.338520i
$861$	0.583561	+	1.55567i	0.0198877	+	0.0530172i
$862$	−7.12269	−	12.3369i	−0.242600	−	0.420195i
$863$		−	47.6647i		−	1.62253i	−0.584682	−	0.811263i	$-0.698781\pi$
$863$		−	47.6647i		−	1.62253i	0.584682	−	0.811263i	$-0.301219\pi$
$864$	−10.4224	+	19.3451i	−0.354577	+	0.658135i
$865$	35.8003	+	20.6693i	1.21725	+	0.702777i
$866$	−10.2607	−	5.92404i	−0.348674	−	0.201307i
$867$	1.94183	−	2.36082i	0.0659479	−	0.0801777i
$868$	0.0568135	−	0.0984038i	0.00192837	−	0.00334004i
$869$	0.480779	+	0.277578i	0.0163093	+	0.00941618i
$870$	2.56876	−	3.12304i	0.0870893	−	0.105881i
$871$	−13.6753	+	7.69913i	−0.463371	+	0.260875i
$872$	−21.6961			−0.734724
$873$	10.8279	−	31.6688i	0.366468	−	1.07183i
$874$	−1.59463	−	2.76198i	−0.0539393	−	0.0934255i
$875$	0.500422	+	0.866756i	0.0169173	+	0.0293017i
$876$	−17.2786	+	6.48153i	−0.583791	+	0.218991i
$877$		−	4.32143i		−	0.145924i	−0.997335	−	0.0729621i	$-0.976755\pi$
$877$		−	4.32143i		−	0.145924i	0.997335	−	0.0729621i	$-0.0232452\pi$
$878$		−	1.10760i		−	0.0373796i
$879$	12.4698	−	4.67764i	0.420595	−	0.157773i
$880$	0.154258	+	0.267182i	0.00520003	+	0.00900672i
$881$	11.9001	+	20.6115i	0.400924	+	0.694420i	0.993838	−	0.110846i	$-0.0353559\pi$
$881$	11.9001	+	20.6115i	0.400924	+	0.694420i	−0.592914	+	0.805266i	$0.702023\pi$
$882$	−8.06355	+	1.58551i	−0.271514	+	0.0533868i
$883$	32.4747			1.09286			0.546430	−	0.837505i	$-0.315986\pi$
$883$	32.4747			1.09286			0.546430	+	0.837505i	$0.315986\pi$
$884$	−14.1490	−	25.1317i	−0.475882	−	0.845271i
$885$	12.2856	−	14.9365i	0.412976	−	0.502085i
$886$	0.637555	+	0.368092i	0.0214191	+	0.0123663i
$887$	−8.53136	+	14.7767i	−0.286455	+	0.496154i	−0.972961	−	0.230970i	$-0.925810\pi$
$887$	−8.53136	+	14.7767i	−0.286455	+	0.496154i	0.686506	+	0.727124i	$0.259144\pi$
$888$	1.46905	−	1.78603i	0.0492980	−	0.0599353i
$889$	−0.726157	−	0.419247i	−0.0243545	−	0.0140611i
$890$	−7.09074	−	4.09384i	−0.237682	−	0.137226i
$891$	−0.478191	−	0.0650966i	−0.0160200	−	0.00218082i
$892$		−	31.5084i		−	1.05498i
$893$	−25.2067	−	43.6592i	−0.843509	−	1.46100i
$894$	3.20304	+	8.53876i	0.107126	+	0.285579i
$895$	20.4631	+	11.8144i	0.684005	+	0.394910i
$896$	0.421154	+	0.729461i	0.0140698	+	0.0243696i
$897$	−6.35684	+	7.56003i	−0.212249	+	0.252422i
$898$	0.901236	−	1.56099i	0.0300746	−	0.0520908i
$899$	2.08243	−	1.20229i	0.0694528	−	0.0400986i
$900$	−1.66933	−	8.48983i	−0.0556442	−	0.282994i
$901$	27.2795	−	47.2495i	0.908812	−	1.57411i
$902$	0.212134	+	0.122475i	0.00706328	+	0.00407798i
$903$	0.135478	−	0.815002i	0.00450844	−	0.0271216i
$904$			12.0562i			0.400983i
$905$	−10.3548	+	5.97832i	−0.344204	+	0.198726i
$906$	14.1446	+	2.35127i	0.469924	+	0.0781157i
$907$	−1.28119			−0.0425413			−0.0212707	−	0.999774i	$-0.506771\pi$
$907$	−1.28119			−0.0425413			−0.0212707	+	0.999774i	$0.506771\pi$
$908$	−8.52933	+	4.92441i	−0.283056	+	0.163422i
$909$	7.54960	−	6.59150i	0.250405	−	0.218626i
$910$	−0.187710	+	0.105679i	−0.00622251	+	0.00350324i
$911$	−12.0142	+	20.8092i	−0.398047	+	0.689438i	−0.993485	−	0.113963i	$-0.963645\pi$
$911$	−12.0142	+	20.8092i	−0.398047	+	0.689438i	0.595438	+	0.803401i	$0.296979\pi$
$912$	4.53669	−	27.2915i	0.150225	−	0.903713i
$913$	0.299756	−	0.519193i	0.00992048	−	0.0171828i
$914$	3.79665			0.125582
$915$	−5.73543	+	34.5028i	−0.189608	+	1.14063i
$916$	39.4755	−	22.7912i	1.30431	−	0.753043i
$917$	−0.154583	−	0.0892486i	−0.00510478	−	0.00294725i
$918$	4.63122	+	7.50270i	0.152853	+	0.247626i
$919$	−9.37173	+	16.2323i	−0.309145	+	0.535455i	−0.978176	−	0.207780i	$-0.933376\pi$
$919$	−9.37173	+	16.2323i	−0.309145	+	0.535455i	0.669031	+	0.743235i	$0.266709\pi$
$920$	−4.41884			−0.145685
$921$	−49.5741	+	18.5961i	−1.63352	+	0.612764i
$922$	5.44610	+	9.43292i	0.179358	+	0.310657i
$923$	40.5919	−	22.8530i	1.33610	−	0.752215i
$924$	−0.00896166	+	0.0108954i	−0.000294817	+	0.000358431i
$925$			1.38404i			0.0455070i
$926$	2.55472	+	4.42491i	0.0839534	+	0.145412i
$927$	15.8411	+	5.41623i	0.520291	+	0.177892i
$928$			13.5934i			0.446226i
$929$	−2.46814	+	1.42498i	−0.0809769	+	0.0467520i	−0.539942	−	0.841702i	$-0.681554\pi$
$929$	−2.46814	+	1.42498i	−0.0809769	+	0.0467520i	0.458965	+	0.888454i	$0.348220\pi$
$930$	0.154318	−	0.928336i	0.00506029	−	0.0304413i
$931$	31.1762	−	17.9996i	1.02176	−	0.589914i
$932$	−26.2366			−0.859408
$933$	−12.8004	+	15.5624i	−0.419065	+	0.509489i
$934$			15.8806i			0.519629i
$935$	0.430704			0.0140855
$936$	16.0248	−	2.97095i	0.523786	−	0.0971084i
$937$	−28.1137			−0.918435			−0.459218	−	0.888324i	$-0.651870\pi$
$937$	−28.1137			−0.918435			−0.459218	+	0.888324i	$0.651870\pi$
$938$		−	0.140247i		−	0.00457924i
$939$	40.0853	+	6.66341i	1.30814	+	0.217452i
$940$	−33.5316			−1.09368
$941$	24.3302	−	14.0471i	0.793143	−	0.457921i	−0.0479252	−	0.998851i	$-0.515261\pi$
$941$	24.3302	−	14.0471i	0.793143	−	0.457921i	0.841068	+	0.540930i	$0.181928\pi$
$942$	−3.44958	−	2.83735i	−0.112393	−	0.0924459i
$943$	15.9739	−	9.22253i	0.520181	−	0.300327i
$944$			18.6856i			0.608164i
$945$	−0.674401	+	0.416290i	−0.0219383	+	0.0135419i
$946$	−0.0609004	−	0.105483i	−0.00198004	−	0.00342953i
$947$		−	32.0405i		−	1.04118i	−0.853808	−	0.520588i	$-0.825713\pi$
$947$		−	32.0405i		−	1.04118i	0.853808	−	0.520588i	$-0.174287\pi$
$948$	−32.6644	−	5.42983i	−1.06089	−	0.176353i
$949$	17.9030	+	10.5965i	0.581155	+	0.343978i
$950$	−1.57471	−	2.72747i	−0.0510902	−	0.0884909i
$951$	−4.68264	+	28.1695i	−0.151845	+	0.913460i
$952$	0.536892			0.0174008
$953$	−20.6503	+	35.7674i	−0.668929	+	1.15862i	0.309275	+	0.950973i	$0.399914\pi$
$953$	−20.6503	+	35.7674i	−0.668929	+	1.15862i	−0.978204	+	0.207647i	$0.933420\pi$
$954$	9.73421	+	11.1491i	0.315157	+	0.360966i
$955$	2.58868	+	1.49457i	0.0837677	+	0.0483633i
$956$	−38.0721	+	21.9809i	−1.23134	+	0.710914i
$957$	−0.279523	+	0.104854i	−0.00903571	+	0.00338946i
$958$	−2.05081			−0.0662586
$959$	−0.385573	+	0.667832i	−0.0124508	+	0.0215654i
$960$	−11.2840	−	9.28131i	−0.364189	−	0.299553i
$961$	−15.2202	+	26.3622i	−0.490974	+	0.850392i
$962$	−1.25144	−	0.0135585i	−0.0403479	−	0.000437144i
$963$	30.4057	+	10.3960i	0.979810	+	0.335006i
$964$	−1.65429	+	0.955104i	−0.0532811	+	0.0307618i
$965$	−18.7302			−0.602947
$966$	−0.0310023	−	0.0826466i	−0.000997481	−	0.00265911i
$967$	46.4255	−	26.8038i	1.49294	−	0.861951i	0.492976	−	0.870043i	$-0.335909\pi$
$967$	46.4255	−	26.8038i	1.49294	−	0.861951i	0.999967	+	0.00809154i	$0.00257564\pi$
$968$		−	16.5698i		−	0.532572i
$969$	−29.8292	−	24.5351i	−0.958251	−	0.788182i
$970$	−7.01735	−	4.05147i	−0.225314	−	0.130085i
$971$	−17.9918	+	31.1627i	−0.577384	+	1.00006i	0.418394	+	0.908265i	$0.362593\pi$
$971$	−17.9918	+	31.1627i	−0.577384	+	1.00006i	−0.995778	+	0.0917925i	$0.970740\pi$
$972$	28.0686	−	6.38214i	0.900302	−	0.204707i
$973$	0.179040	−	0.103369i	0.00573976	−	0.00331385i
$974$	−2.65295	+	4.59504i	−0.0850060	+	0.147235i
$975$	−6.27741	+	7.46556i	−0.201038	+	0.239089i
$976$	−16.8964	−	29.2654i	−0.540841	−	0.936764i
$977$	24.1659	+	13.9522i	0.773135	+	0.446370i	0.833992	−	0.551777i	$-0.186050\pi$
$977$	24.1659	+	13.9522i	0.773135	+	0.446370i	−0.0608570	+	0.998146i	$0.519383\pi$
$978$	−7.64760	−	1.27127i	−0.244543	−	0.0406506i
$979$	0.302241	+	0.523497i	0.00965966	+	0.0167310i
$980$		−	23.9443i		−	0.764873i
$981$	28.4111	+	32.5408i	0.907097	+	1.03895i
$982$	−4.84491	−	2.79721i	−0.154607	−	0.0892626i
$983$	−20.2268	−	11.6779i	−0.645135	−	0.372469i	0.141455	−	0.989945i	$-0.454822\pi$
$983$	−20.2268	−	11.6779i	−0.645135	−	0.372469i	−0.786590	+	0.617476i	$0.788155\pi$
$984$	−30.0225	−	4.99067i	−0.957083	−	0.159097i
$985$	6.87453	−	11.9070i	0.219041	−	0.379390i
$986$	4.72353	+	2.72713i	0.150428	+	0.0868496i
$987$	−0.490059	−	1.30641i	−0.0155987	−	0.0415836i
$988$	−29.8651	+	16.8139i	−0.950136	+	0.534921i
$989$	−9.17173			−0.291644
$990$	−0.0378003	+	0.110556i	−0.00120137	+	0.00351371i
$991$	2.01905	+	3.49710i	0.0641373	+	0.111089i	0.896311	−	0.443426i	$-0.146237\pi$
$991$	2.01905	+	3.49710i	0.0641373	+	0.111089i	−0.832174	+	0.554515i	$0.812904\pi$
$992$	1.58175	+	2.73968i	0.0502207	+	0.0869848i
$993$	−42.0236	−	34.5653i	−1.33358	−	1.09690i
$994$			0.416290i			0.0132039i
$995$		−	19.2685i		−	0.610854i
$996$	−5.86367	+	35.2743i	−0.185797	+	1.11771i
$997$	22.4700	+	38.9191i	0.711631	+	1.23258i	0.964245	+	0.265014i	$0.0853765\pi$
$997$	22.4700	+	38.9191i	0.711631	+	1.23258i	−0.252614	+	0.967567i	$0.581290\pi$
$998$	−6.14370	−	10.6412i	−0.194475	−	0.336841i
$999$	−4.60248	+	0.135468i	−0.145616	+	0.00428603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.l.b.88.6	yes	22
3.2	odd	2		351.2.l.b.127.6		22
9.4	even	3		117.2.r.b.49.6	yes	22
9.5	odd	6		351.2.r.b.10.6		22
13.4	even	6		117.2.r.b.43.6	yes	22
39.17	odd	6		351.2.r.b.316.6		22
117.4	even	6	inner	117.2.l.b.4.6	✓	22
117.95	odd	6		351.2.l.b.199.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.6	✓	22	117.4	even	6	inner
117.2.l.b.88.6	yes	22	1.1	even	1	trivial
117.2.r.b.43.6	yes	22	13.4	even	6
117.2.r.b.49.6	yes	22	9.4	even	3
351.2.l.b.127.6		22	3.2	odd	2
351.2.l.b.199.6		22	117.95	odd	6
351.2.r.b.10.6		22	9.5	odd	6
351.2.r.b.316.6		22	39.17	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.391710i q^{2} +(0.608332 + 1.62171i) q^{3} +1.84656 q^{4} +(-1.60580 + 0.927107i) q^{5} +(0.635238 - 0.238289i) q^{6} +(-0.0712374 + 0.0411289i) q^{7} -1.50674i q^{8} +(-2.25987 + 1.97307i) q^{9} +(0.363157 + 0.629006i) q^{10} -0.0536224i q^{11} +(1.12332 + 2.99458i) q^{12} +(1.83650 - 3.10278i) q^{13} +(0.0161106 + 0.0279044i) q^{14} +(-2.48035 - 2.04014i) q^{15} +3.10292 q^{16} +(2.16592 - 3.75149i) q^{17} +(0.772871 + 0.885211i) q^{18} +(-4.45806 - 2.57386i) q^{19} +(-2.96521 + 1.71196i) q^{20} +(-0.110035 - 0.0905061i) q^{21} -0.0210044 q^{22} +(-0.790827 + 1.36975i) q^{23} +(2.44348 - 0.916595i) q^{24} +(-0.780945 + 1.35264i) q^{25} +(-1.21539 - 0.719374i) q^{26} +(-4.57449 - 2.46456i) q^{27} +(-0.131544 + 0.0759472i) q^{28} -3.21440 q^{29} +(-0.799143 + 0.971578i) q^{30} +(-0.647844 + 0.374033i) q^{31} -4.22892i q^{32} +(0.0869598 - 0.0326202i) q^{33} +(-1.46949 - 0.848412i) q^{34} +(0.0762618 - 0.132089i) q^{35} +(-4.17298 + 3.64340i) q^{36} +(0.767413 - 0.443066i) q^{37} +(-1.00821 + 1.74626i) q^{38} +(6.14901 + 1.09074i) q^{39} +(1.39691 + 2.41951i) q^{40} +(-10.0995 - 5.83094i) q^{41} +(-0.0354521 + 0.0431018i) q^{42} +(2.89941 + 5.02193i) q^{43} -0.0990171i q^{44} +(1.79964 - 5.26349i) q^{45} +(0.536545 + 0.309774i) q^{46} +(8.48127 + 4.89667i) q^{47} +(1.88761 + 5.03203i) q^{48} +(-3.49662 + 6.05632i) q^{49} +(0.529841 + 0.305904i) q^{50} +(7.40141 + 1.23034i) q^{51} +(3.39121 - 5.72949i) q^{52} +12.5949 q^{53} +(-0.965390 + 1.79187i) q^{54} +(0.0497137 + 0.0861066i) q^{55} +(0.0619704 + 0.107336i) q^{56} +(1.46207 - 8.79543i) q^{57} +1.25911i q^{58} +6.02193i q^{59} +(-4.58013 - 3.76725i) q^{60} +(-5.44532 - 9.43157i) q^{61} +(0.146512 + 0.253767i) q^{62} +(0.0798366 - 0.233502i) q^{63} +4.54934 q^{64} +(-0.0724285 + 6.68507i) q^{65} +(-0.0127776 - 0.0340630i) q^{66} +(-3.76950 - 2.17632i) q^{67} +(3.99951 - 6.92736i) q^{68} +(-2.70242 - 0.449226i) q^{69} +(-0.0517407 - 0.0298725i) q^{70} +(11.1888 + 6.45987i) q^{71} +(2.97290 + 3.40502i) q^{72} +5.76996i q^{73} +(-0.173553 - 0.300603i) q^{74} +(-2.66865 - 0.443612i) q^{75} +(-8.23209 - 4.75280i) q^{76} +(0.00220543 + 0.00381992i) q^{77} +(0.427253 - 2.40862i) q^{78} +(-5.17653 + 8.96601i) q^{79} +(-4.98267 + 2.87674i) q^{80} +(1.21398 - 8.91775i) q^{81} +(-2.28403 + 3.95606i) q^{82} +(9.68239 + 5.59013i) q^{83} +(-0.203187 - 0.167125i) q^{84} +8.03216i q^{85} +(1.96714 - 1.13573i) q^{86} +(-1.95542 - 5.21281i) q^{87} -0.0807948 q^{88} +(-9.76265 + 5.63647i) q^{89} +(-2.06176 - 0.704934i) q^{90} +(-0.00321312 + 0.296568i) q^{91} +(-1.46031 + 2.52933i) q^{92} +(-1.00068 - 0.823076i) q^{93} +(1.91807 - 3.32220i) q^{94} +9.54498 q^{95} +(6.85806 - 2.57258i) q^{96} +(-9.66160 + 5.57813i) q^{97} +(2.37232 + 1.36966i) q^{98} +(0.105801 + 0.121179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) \) 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

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