LMFDB - Embedded newform 728.2.cz.a.309.40

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(309,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.309"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			309.40
Character	$\chi$	$=$	728.309
Dual form			728.2.cz.a.589.40

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.200580 + 1.39992i) q^{2} +(-1.59497 + 0.920859i) q^{3} +(-1.91954 - 0.561590i) q^{4} +4.03210 q^{5} +(-0.969207 - 2.41754i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(1.17120 - 2.57455i) q^{8} +(0.195963 - 0.339418i) q^{9} +(-0.808758 + 5.64461i) q^{10} +(-2.21196 - 3.83123i) q^{11} +(3.57876 - 0.871900i) q^{12} +(0.938451 + 3.48128i) q^{13} +(0.873666 - 1.11207i) q^{14} +(-6.43111 + 3.71300i) q^{15} +(3.36923 + 2.15598i) q^{16} +(-1.98699 + 3.44157i) q^{17} +(0.435851 + 0.342413i) q^{18} +(-2.45830 + 4.25790i) q^{19} +(-7.73977 - 2.26439i) q^{20} +1.84172 q^{21} +(5.80708 - 2.32810i) q^{22} +(4.19554 + 7.26688i) q^{23} +(0.502762 + 5.18485i) q^{24} +11.2579 q^{25} +(-5.06174 + 0.615479i) q^{26} -4.80334i q^{27} +(1.38157 + 1.44612i) q^{28} +(-3.84396 + 2.21931i) q^{29} +(-3.90794 - 9.74777i) q^{30} +9.30847i q^{31} +(-3.69400 + 4.28420i) q^{32} +(7.05605 + 4.07381i) q^{33} +(-4.41936 - 3.47193i) q^{34} +(-3.49191 - 2.01605i) q^{35} +(-0.566772 + 0.541474i) q^{36} +(-1.69763 - 2.94038i) q^{37} +(-5.46762 - 4.29546i) q^{38} +(-4.70257 - 4.68837i) q^{39} +(4.72240 - 10.3808i) q^{40} +(-5.81120 + 3.35510i) q^{41} +(-0.369411 + 2.57825i) q^{42} +(-2.86254 - 1.65269i) q^{43} +(2.09436 + 8.59640i) q^{44} +(0.790144 - 1.36857i) q^{45} +(-11.0146 + 4.41581i) q^{46} -1.69935i q^{47} +(-7.35920 - 0.336150i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-2.25810 + 15.7601i) q^{50} -7.31895i q^{51} +(0.153662 - 7.20947i) q^{52} -1.91459i q^{53} +(6.72427 + 0.963452i) q^{54} +(-8.91886 - 15.4479i) q^{55} +(-2.30156 + 1.64402i) q^{56} -9.05499i q^{57} +(-2.33583 - 5.82637i) q^{58} +(2.90950 - 5.03940i) q^{59} +(14.4299 - 3.51559i) q^{60} +(6.83979 + 3.94895i) q^{61} +(-13.0311 - 1.86709i) q^{62} +(-0.339418 + 0.195963i) q^{63} +(-5.25658 - 6.03061i) q^{64} +(3.78393 + 14.0369i) q^{65} +(-7.11830 + 9.06076i) q^{66} +(0.239464 + 0.414764i) q^{67} +(5.74685 - 5.49034i) q^{68} +(-13.3836 - 7.72700i) q^{69} +(3.52271 - 4.48400i) q^{70} +(5.62786 + 3.24925i) q^{71} +(-0.644336 - 0.902043i) q^{72} -3.66592i q^{73} +(4.45679 - 1.78676i) q^{74} +(-17.9560 + 10.3669i) q^{75} +(7.10999 - 6.79263i) q^{76} +4.42392i q^{77} +(7.50657 - 5.64282i) q^{78} -7.97702 q^{79} +(13.5851 + 8.69315i) q^{80} +(5.01109 + 8.67946i) q^{81} +(-3.53125 - 8.80817i) q^{82} +0.454650 q^{83} +(-3.53524 - 1.03429i) q^{84} +(-8.01175 + 13.8768i) q^{85} +(2.88780 - 3.67583i) q^{86} +(4.08735 - 7.07949i) q^{87} +(-12.4543 + 1.20767i) q^{88} +(-7.99925 + 4.61837i) q^{89} +(1.75740 + 1.38064i) q^{90} +(0.927918 - 3.48410i) q^{91} +(-3.97247 - 16.3052i) q^{92} +(-8.57179 - 14.8468i) q^{93} +(2.37894 + 0.340855i) q^{94} +(-9.91212 + 17.1683i) q^{95} +(1.94669 - 10.2348i) q^{96} +(10.3103 + 5.95267i) q^{97} +(-1.31265 + 0.526251i) q^{98} -1.73385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 18 q^{6} + 84 q^{9} - 8 q^{10} - 4 q^{12} + 8 q^{16} + 4 q^{17} - 18 q^{22} + 24 q^{23} + 48 q^{24} + 160 q^{25} - 30 q^{26} - 8 q^{30} + 22 q^{36} - 20 q^{38} - 48 q^{39} + 4 q^{40} + 12 q^{41}+ \cdots - 104 q^{95}+O(q^{100}) $ 168 * q - 18 * q^6 + 84 * q^9 - 8 * q^10 - 4 * q^12 + 8 * q^16 + 4 * q^17 - 18 * q^22 + 24 * q^23 + 48 * q^24 + 160 * q^25 - 30 * q^26 - 8 * q^30 + 22 * q^36 - 20 * q^38 - 48 * q^39 + 4 * q^40 + 12 * q^41 - 54 * q^48 + 84 * q^49 - 30 * q^50 - 58 * q^52 + 24 * q^54 - 32 * q^55 - 12 * q^58 + 28 * q^62 - 36 * q^64 + 12 * q^65 - 60 * q^66 - 64 * q^68 - 132 * q^72 + 62 * q^74 - 78 * q^76 + 30 * q^78 - 80 * q^79 + 48 * q^80 - 84 * q^81 - 18 * q^82 - 42 * q^84 - 24 * q^87 + 42 * q^88 + 40 * q^90 - 24 * q^92 + 12 * q^94 - 104 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.200580	+	1.39992i	−0.141831	+	0.989891i
$2$	−0.200580	+	1.39992i	−0.141831	+	0.989891i
$3$	−1.59497	+	0.920859i	−0.920859	+	0.531658i	−0.883909	−	0.467659i	$-0.845098\pi$
$3$	−1.59497	+	0.920859i	−0.920859	+	0.531658i	−0.0369501	+	0.999317i	$0.511764\pi$
$4$	−1.91954	−	0.561590i	−0.959768	−	0.280795i
$5$	4.03210			1.80321			0.901606	−	0.432558i	$-0.142389\pi$
$5$	4.03210			1.80321			0.901606	+	0.432558i	$0.142389\pi$
$6$	−0.969207	−	2.41754i	−0.395677	−	0.986956i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	1.17120	−	2.57455i	0.414081	−	0.910240i
$9$	0.195963	−	0.339418i	0.0653210	−	0.113139i
$10$	−0.808758	+	5.64461i	−0.255752	+	1.78498i
$11$	−2.21196	−	3.83123i	−0.666932	−	1.15516i	−0.978758	−	0.205020i	$-0.934274\pi$
$11$	−2.21196	−	3.83123i	−0.666932	−	1.15516i	0.311826	−	0.950139i	$-0.399059\pi$
$12$	3.57876	−	0.871900i	1.03310	−	0.251696i
$13$	0.938451	+	3.48128i	0.260279	+	0.965533i
$13$	0.938451	+	3.48128i	0.260279	+	0.965533i
$14$	0.873666	−	1.11207i	0.233497	−	0.297214i
$15$	−6.43111	+	3.71300i	−1.66050	+	0.958693i
$16$	3.36923	+	2.15598i	0.842308	+	0.538996i
$17$	−1.98699	+	3.44157i	−0.481916	+	0.834703i	−0.999785	−	0.0207574i	$-0.993392\pi$
$17$	−1.98699	+	3.44157i	−0.481916	+	0.834703i	0.517869	+	0.855460i	$0.326726\pi$
$18$	0.435851	+	0.342413i	0.102731	+	0.0807074i
$19$	−2.45830	+	4.25790i	−0.563972	+	0.976829i	0.433172	+	0.901311i	$0.357394\pi$
$19$	−2.45830	+	4.25790i	−0.563972	+	0.976829i	−0.997144	+	0.0755177i	$0.975939\pi$
$20$	−7.73977	−	2.26439i	−1.73066	−	0.506333i
$21$	1.84172			0.401896
$22$	5.80708	−	2.32810i	1.23807	−	0.496352i
$23$	4.19554	+	7.26688i	0.874830	+	1.51525i	0.856944	+	0.515410i	$0.172360\pi$
$23$	4.19554	+	7.26688i	0.874830	+	1.51525i	0.0178859	+	0.999840i	$0.494306\pi$
$24$	0.502762	+	5.18485i	0.102626	+	1.05835i
$25$	11.2579			2.25157
$26$	−5.06174	+	0.615479i	−0.992688	+	0.120705i
$27$		−	4.80334i		−	0.924403i
$28$	1.38157	+	1.44612i	0.261092	+	0.273291i
$29$	−3.84396	+	2.21931i	−0.713805	+	0.412116i	−0.812468	−	0.583005i	$-0.801877\pi$
$29$	−3.84396	+	2.21931i	−0.713805	+	0.412116i	0.0986631	+	0.995121i	$0.468543\pi$
$30$	−3.90794	−	9.74777i	−0.713490	−	1.77969i
$31$			9.30847i			1.67185i	0.548844	+	0.835925i	$0.315068\pi$
$31$			9.30847i			1.67185i	−0.548844	+	0.835925i	$0.684932\pi$
$32$	−3.69400	+	4.28420i	−0.653013	+	0.757347i
$33$	7.05605	+	4.07381i	1.22830	+	0.709159i
$34$	−4.41936	−	3.47193i	−0.757914	−	0.595431i
$35$	−3.49191	−	2.01605i	−0.590240	−	0.340775i
$36$	−0.566772	+	0.541474i	−0.0944620	+	0.0902457i
$37$	−1.69763	−	2.94038i	−0.279088	−	0.483395i	0.692070	−	0.721830i	$-0.256699\pi$
$37$	−1.69763	−	2.94038i	−0.279088	−	0.483395i	−0.971158	+	0.238435i	$0.923365\pi$
$38$	−5.46762	−	4.29546i	−0.886965	−	0.696816i
$39$	−4.70257	−	4.68837i	−0.753014	−	0.750741i
$40$	4.72240	−	10.3808i	0.746677	−	1.64136i
$41$	−5.81120	+	3.35510i	−0.907558	+	0.523979i	−0.879645	−	0.475632i	$-0.842220\pi$
$41$	−5.81120	+	3.35510i	−0.907558	+	0.523979i	−0.0279132	+	0.999610i	$0.508886\pi$
$42$	−0.369411	+	2.57825i	−0.0570014	+	0.397833i
$43$	−2.86254	−	1.65269i	−0.436534	−	0.252033i	0.265592	−	0.964085i	$-0.414432\pi$
$43$	−2.86254	−	1.65269i	−0.436534	−	0.252033i	−0.702126	+	0.712052i	$0.747766\pi$
$44$	2.09436	+	8.59640i	0.315736	+	1.29596i
$45$	0.790144	−	1.36857i	0.117788	−	0.204014i
$46$	−11.0146	+	4.41581i	−1.62401	+	0.651076i
$47$		−	1.69935i		−	0.247875i	−0.992290	−	0.123938i	$-0.960448\pi$
$47$		−	1.69935i		−	0.247875i	0.992290	−	0.123938i	$-0.0395523\pi$
$48$	−7.35920	−	0.336150i	−1.06221	−	0.0485191i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−2.25810	+	15.7601i	−0.319344	+	2.22881i
$51$		−	7.31895i		−	1.02486i
$52$	0.153662	−	7.20947i	0.0213091	−	0.999773i
$53$		−	1.91459i		−	0.262989i	−0.991317	−	0.131495i	$-0.958022\pi$
$53$		−	1.91459i		−	0.262989i	0.991317	−	0.131495i	$-0.0419776\pi$
$54$	6.72427	+	0.963452i	0.915058	+	0.131109i
$55$	−8.91886	−	15.4479i	−1.20262	−	2.08300i
$56$	−2.30156	+	1.64402i	−0.307559	+	0.219692i
$57$		−	9.05499i		−	1.19936i
$58$	−2.33583	−	5.82637i	−0.306710	−	0.765040i
$59$	2.90950	−	5.03940i	0.378785	−	0.656075i	−0.612101	−	0.790780i	$-0.709675\pi$
$59$	2.90950	−	5.03940i	0.378785	−	0.656075i	0.990886	+	0.134705i	$0.0430087\pi$
$60$	14.4299	−	3.51559i	1.86289	−	0.453861i
$61$	6.83979	+	3.94895i	0.875745	+	0.505612i	0.869253	−	0.494367i	$-0.164600\pi$
$61$	6.83979	+	3.94895i	0.875745	+	0.505612i	0.00649220	+	0.999979i	$0.497933\pi$
$62$	−13.0311	−	1.86709i	−1.65495	−	0.237121i
$63$	−0.339418	+	0.195963i	−0.0427627	+	0.0246890i
$64$	−5.25658	−	6.03061i	−0.657073	−	0.753827i
$65$	3.78393	+	14.0369i	0.469339	+	1.74106i
$66$	−7.11830	+	9.06076i	−0.876202	+	1.11530i
$67$	0.239464	+	0.414764i	0.0292552	+	0.0506715i	0.880282	−	0.474450i	$-0.157353\pi$
$67$	0.239464	+	0.414764i	0.0292552	+	0.0506715i	−0.851027	+	0.525122i	$0.824020\pi$
$68$	5.74685	−	5.49034i	0.696908	−	0.665801i
$69$	−13.3836	−	7.72700i	−1.61119	−	0.930221i
$70$	3.52271	−	4.48400i	0.421045	−	0.535940i
$71$	5.62786	+	3.24925i	0.667904	+	0.385615i	0.795282	−	0.606240i	$-0.207323\pi$
$71$	5.62786	+	3.24925i	0.667904	+	0.385615i	−0.127378	+	0.991854i	$0.540656\pi$
$72$	−0.644336	−	0.902043i	−0.0759357	−	0.106307i
$73$		−	3.66592i		−	0.429064i	−0.976717	−	0.214532i	$-0.931177\pi$
$73$		−	3.66592i		−	0.429064i	0.976717	−	0.214532i	$-0.0688226\pi$
$74$	4.45679	−	1.78676i	0.518092	−	0.207706i
$75$	−17.9560	+	10.3669i	−2.07338	+	1.19707i
$76$	7.10999	−	6.79263i	0.815571	−	0.779168i
$77$			4.42392i			0.504153i
$78$	7.50657	−	5.64282i	0.849952	−	0.638924i
$79$	−7.97702			−0.897485			−0.448743	−	0.893661i	$-0.648128\pi$
$79$	−7.97702			−0.897485			−0.448743	+	0.893661i	$0.648128\pi$
$80$	13.5851	+	8.69315i	1.51886	+	0.971924i
$81$	5.01109	+	8.67946i	0.556787	+	0.964384i
$82$	−3.53125	−	8.80817i	−0.389962	−	0.972700i
$83$	0.454650			0.0499043			0.0249522	−	0.999689i	$-0.492057\pi$
$83$	0.454650			0.0499043			0.0249522	+	0.999689i	$0.492057\pi$
$84$	−3.53524	−	1.03429i	−0.385727	−	0.112850i
$85$	−8.01175	+	13.8768i	−0.868996	+	1.50515i
$86$	2.88780	−	3.67583i	0.311399	−	0.396375i
$87$	4.08735	−	7.07949i	0.438209	−	0.759001i
$88$	−12.4543	+	1.20767i	−1.32764	+	0.128738i
$89$	−7.99925	+	4.61837i	−0.847919	+	0.489546i	−0.859948	−	0.510381i	$-0.829504\pi$
$89$	−7.99925	+	4.61837i	−0.847919	+	0.489546i	0.0120291	+	0.999928i	$0.496171\pi$
$90$	1.75740	+	1.38064i	0.185246	+	0.145533i
$91$	0.927918	−	3.48410i	0.0972722	−	0.365233i
$92$	−3.97247	−	16.3052i	−0.414159	−	1.69994i
$93$	−8.57179	−	14.8468i	−0.888853	−	1.53954i
$94$	2.37894	+	0.340855i	0.245369	+	0.0351565i
$95$	−9.91212	+	17.1683i	−1.01696	+	1.76143i
$96$	1.94669	−	10.2348i	0.198683	−	1.04459i
$97$	10.3103	+	5.95267i	1.04685	+	0.604402i	0.921767	−	0.387744i	$-0.126745\pi$
$97$	10.3103	+	5.95267i	1.04685	+	0.604402i	0.125088	+	0.992146i	$0.460079\pi$
$98$	−1.31265	+	0.526251i	−0.132598	+	0.0531594i
$99$	−1.73385			−0.174259
$100$	−21.6099	−	6.32231i	−2.16099	−	0.632231i
$101$	12.7874	−	7.38280i	1.27239	−	0.734616i	0.296955	−	0.954892i	$-0.404029\pi$
$101$	12.7874	−	7.38280i	1.27239	−	0.734616i	0.975438	+	0.220275i	$0.0706956\pi$
$102$	10.2459	+	1.46803i	1.01450	+	0.145357i
$103$	13.2606			1.30660			0.653302	−	0.757098i	$-0.273383\pi$
$103$	13.2606			1.30660			0.653302	+	0.757098i	$0.273383\pi$
$104$	10.0618	+	1.66119i	0.986644	+	0.162893i
$105$	7.42600			0.724704
$106$	2.68027	+	0.384028i	0.260331	+	0.0373001i
$107$	−6.73730	+	3.88978i	−0.651319	+	0.376039i	−0.788961	−	0.614443i	$-0.789381\pi$
$107$	−6.73730	+	3.88978i	−0.651319	+	0.376039i	0.137642	+	0.990482i	$0.456048\pi$
$108$	−2.69751	+	9.22018i	−0.259568	+	0.887212i
$109$	−7.01062			−0.671495			−0.335748	−	0.941952i	$-0.608989\pi$
$109$	−7.01062			−0.671495			−0.335748	+	0.941952i	$0.608989\pi$
$110$	23.4148	−	9.38713i	2.23251	−	0.895027i
$111$	5.41534	+	3.12655i	0.514002	+	0.296759i
$112$	−1.83985	−	3.55175i	−0.173849	−	0.335609i
$113$	2.37147	−	4.10751i	0.223089	−	0.386402i	−0.732655	−	0.680600i	$-0.761719\pi$
$113$	2.37147	−	4.10751i	0.223089	−	0.386402i	0.955744	+	0.294198i	$0.0950525\pi$
$114$	12.6762	+	1.81625i	1.18724	+	0.170107i
$115$	16.9168	+	29.3008i	1.57750	+	2.73232i
$116$	8.62496	−	2.10132i	0.800807	−	0.195102i
$117$	1.36551	+	0.363675i	0.126242	+	0.0336218i
$118$	6.47116	+	5.08386i	0.595719	+	0.468008i
$119$	3.44157	−	1.98699i	0.315488	−	0.182147i
$120$	2.02719	+	20.9058i	0.185056	+	1.90843i
$121$	−4.28555	+	7.42279i	−0.389595	+	0.674799i
$122$	−6.90013	+	8.78306i	−0.624709	+	0.795181i
$123$	6.17915	−	10.7026i	0.557155	−	0.965021i
$124$	5.22754	−	17.8679i	0.469447	−	1.60459i
$125$	25.2324			2.25685
$126$	−0.206252	−	0.514463i	−0.0183744	−	0.0458320i
$127$	−4.89957	−	8.48630i	−0.434766	−	0.753037i	0.562510	−	0.826790i	$-0.309836\pi$
$127$	−4.89957	−	8.48630i	−0.434766	−	0.753037i	−0.997277	+	0.0737530i	$0.976502\pi$
$128$	9.49673	−	6.14916i	0.839400	−	0.543514i
$129$	6.08758			0.535982
$130$	−20.4095	+	2.48168i	−1.79003	+	0.217657i
$131$			15.6494i			1.36730i	0.729812	+	0.683648i	$0.239607\pi$
$131$			15.6494i			1.36730i	−0.729812	+	0.683648i	$0.760393\pi$
$132$	−11.2565	−	11.7824i	−0.979754	−	1.02553i
$133$	4.25790	−	2.45830i	0.369207	−	0.213162i
$134$	−0.628667	+	0.252037i	−0.0543085	+	0.0217726i
$135$		−	19.3676i		−	1.66689i
$136$	6.53332	+	9.14636i	0.560227	+	0.784294i
$137$	−4.15939	−	2.40143i	−0.355361	−	0.205168i	0.311683	−	0.950186i	$-0.399107\pi$
$137$	−4.15939	−	2.40143i	−0.355361	−	0.205168i	−0.667044	+	0.745018i	$0.732441\pi$
$138$	13.5016	−	17.1860i	1.14933	−	1.46297i
$139$	4.84829	+	2.79916i	0.411227	+	0.237422i	0.691317	−	0.722552i	$-0.257031\pi$
$139$	4.84829	+	2.79916i	0.411227	+	0.237422i	−0.280090	+	0.959974i	$0.590364\pi$
$140$	5.57064	+	5.83090i	0.470805	+	0.492801i
$141$	1.56486	+	2.71042i	0.131785	+	0.228258i
$142$	−5.67751	+	7.22680i	−0.476446	+	0.606460i
$143$	11.2618	−	11.2959i	0.941756	−	0.944609i
$144$	1.39203	−	0.721086i	0.116002	−	0.0600905i
$145$	−15.4992	+	8.94849i	−1.28714	+	0.743132i
$146$	5.13199	+	0.735309i	0.424726	+	0.0608546i
$147$	−1.59497	−	0.920859i	−0.131551	−	0.0759512i
$148$	1.60737	+	6.59753i	0.132125	+	0.542313i
$149$	7.08729	−	12.2755i	0.580613	−	1.00565i	−0.414793	−	0.909916i	$-0.636146\pi$
$149$	7.08729	−	12.2755i	0.580613	−	1.00565i	0.995407	−	0.0957361i	$-0.0305205\pi$
$150$	−10.9112	−	27.2163i	−0.890896	−	2.22220i
$151$			12.2640i			0.998029i	0.866594	+	0.499015i	$0.166305\pi$
$151$			12.2640i			0.998029i	−0.866594	+	0.499015i	$0.833695\pi$
$152$	8.08300	+	11.3159i	0.655618	+	0.917837i
$153$	0.778754	+	1.34884i	0.0629585	+	0.109047i
$154$	−6.19313	−	0.887349i	−0.499056	−	0.0715046i
$155$			37.5327i			3.01470i
$156$	6.39381	+	11.6404i	0.511915	+	0.931979i
$157$		−	13.1023i		−	1.04567i	−0.852432	−	0.522837i	$-0.824873\pi$
$157$		−	13.1023i		−	1.04567i	0.852432	−	0.522837i	$-0.175127\pi$
$158$	1.60003	−	11.1672i	0.127291	−	0.888413i
$159$	1.76307	+	3.05373i	0.139821	+	0.242176i
$160$	−14.8946	+	17.2743i	−1.17752	+	1.36566i
$161$		−	8.39107i		−	0.661309i
$162$	−13.1556	+	5.27418i	−1.03360	+	0.414379i
$163$	−6.56679	+	11.3740i	−0.514351	+	0.890882i	0.485511	+	0.874231i	$0.338634\pi$
$163$	−6.56679	+	11.3740i	−0.514351	+	0.890882i	−0.999861	+	0.0166509i	$0.994700\pi$
$164$	13.0390	−	3.17672i	1.01818	−	0.248060i
$165$	28.4507	+	16.4260i	2.21489	+	1.27876i
$166$	−0.0911935	+	0.636472i	−0.00707799	+	0.0493998i
$167$	2.81113	−	1.62300i	0.217531	−	0.125592i	−0.387275	−	0.921964i	$-0.626584\pi$
$167$	2.81113	−	1.62300i	0.217531	−	0.125592i	0.604807	+	0.796372i	$0.293250\pi$
$168$	2.15702	−	4.74159i	0.166418	−	0.365822i
$169$	−11.2386	+	6.53402i	−0.864509	+	0.502617i
$170$	−17.8193	−	13.9992i	−1.36668	−	1.07369i
$171$	0.963472	+	1.66878i	0.0736785	+	0.127615i
$172$	4.56662	+	4.77998i	0.348202	+	0.364470i
$173$	−13.5554	−	7.82621i	−1.03060	−	0.595016i	−0.113442	−	0.993545i	$-0.536187\pi$
$173$	−13.5554	−	7.82621i	−1.03060	−	0.595016i	−0.917156	+	0.398529i	$0.869521\pi$
$174$	9.09086	+	7.14195i	0.689176	+	0.541430i
$175$	−9.74960	−	5.62893i	−0.737001	−	0.425507i
$176$	0.807454	−	17.6773i	0.0608641	−	1.33247i
$177$			10.7170i			0.805536i
$178$	−4.86085	−	12.1246i	−0.364336	−	0.908780i
$179$	15.3489	−	8.86168i	1.14723	−	0.662353i	0.199019	−	0.979996i	$-0.436225\pi$
$179$	15.3489	−	8.86168i	1.14723	−	0.662353i	0.948211	+	0.317643i	$0.102891\pi$
$180$	−2.28528	+	2.18328i	−0.170335	+	0.162732i
$181$		−	12.8464i		−	0.954868i	−0.878668	−	0.477434i	$-0.841567\pi$
$181$		−	12.8464i		−	0.954868i	0.878668	−	0.477434i	$-0.158433\pi$
$182$	4.69133	+	1.99785i	0.347745	+	0.148090i
$183$	−14.5457			−1.07525
$184$	23.6227	−	2.29064i	1.74149	−	0.168868i
$185$	−6.84501	−	11.8559i	−0.503255	−	0.871663i
$186$	22.5036	−	9.02183i	1.65004	−	0.661513i
$187$	17.5806			1.28562
$188$	−0.954336	+	3.26196i	−0.0696021	+	0.237903i
$189$	−2.40167	+	4.15981i	−0.174696	+	0.302582i
$190$	−22.0460	−	17.3198i	−1.59939	−	1.25651i
$191$	7.19438	−	12.4610i	0.520567	−	0.901649i	−0.479147	−	0.877735i	$-0.659054\pi$
$191$	7.19438	−	12.4610i	0.520567	−	0.901649i	0.999714	−	0.0239142i	$-0.00761286\pi$
$192$	13.9375	+	4.77810i	1.00585	+	0.344830i
$193$	−11.9296	+	6.88753i	−0.858708	+	0.495776i	−0.863580	−	0.504213i	$-0.831783\pi$
$193$	−11.9296	+	6.88753i	−0.858708	+	0.495776i	0.00487109	+	0.999988i	$0.498449\pi$
$194$	−10.4013	+	13.2396i	−0.746769	+	0.950549i
$195$	−18.9613	−	18.9040i	−1.35784	−	1.35374i
$196$	−0.473417	−	1.94316i	−0.0338155	−	0.138797i
$197$	10.1851	+	17.6411i	0.725658	+	1.25688i	0.958702	+	0.284411i	$0.0917980\pi$
$197$	10.1851	+	17.6411i	0.725658	+	1.25688i	−0.233044	+	0.972466i	$0.574869\pi$
$198$	0.347776	−	2.42725i	0.0247153	−	0.172497i
$199$	−4.92200	+	8.52515i	−0.348911	+	0.604332i	−0.986056	−	0.166412i	$-0.946782\pi$
$199$	−4.92200	+	8.52515i	−0.348911	+	0.604332i	0.637145	+	0.770744i	$0.280115\pi$
$200$	13.1852	−	28.9839i	0.932335	−	2.04947i
$201$	−0.763878	−	0.441025i	−0.0538798	−	0.0311075i
$202$	7.77042	+	19.3821i	0.546725	+	1.36372i
$203$	4.43862			0.311530
$204$	−4.11025	+	14.0490i	−0.287775	+	0.983626i
$205$	−23.4314	+	13.5281i	−1.63652	+	0.944845i
$206$	−2.65980	+	18.5637i	−0.185317	+	1.29339i
$207$	3.28868			0.228579
$208$	−4.34372	+	13.7525i	−0.301183	+	0.953566i
$209$	21.7507			1.50452
$210$	−1.48951	+	10.3958i	−0.102786	+	0.717377i
$211$	3.86793	−	2.23315i	0.266279	−	0.153736i	−0.360916	−	0.932598i	$-0.617536\pi$
$211$	3.86793	−	2.23315i	0.266279	−	0.153736i	0.627196	+	0.778862i	$0.284203\pi$
$212$	−1.07522	+	3.67513i	−0.0738461	+	0.252409i
$213$	−11.9684			−0.820061
$214$	−4.09400	−	10.2119i	−0.279860	−	0.698069i
$215$	−11.5421	−	6.66382i	−0.787163	−	0.454469i
$216$	−12.3664	−	5.62566i	−0.841428	−	0.382778i
$217$	4.65423	−	8.06137i	0.315950	−	0.547241i
$218$	1.40619	−	9.81428i	0.0952390	−	0.664707i
$219$	3.37580	+	5.84705i	0.228115	+	0.395107i
$220$	8.44467	+	34.6616i	0.569340	+	2.33688i
$221$	−13.8458	−	3.68753i	−0.931366	−	0.248050i
$222$	−5.46312	+	6.95391i	−0.366661	+	0.466716i
$223$	6.72300	−	3.88152i	0.450205	−	0.259926i	−0.257712	−	0.966222i	$-0.582968\pi$
$223$	6.72300	−	3.88152i	0.450205	−	0.259926i	0.707917	+	0.706296i	$0.249635\pi$
$224$	5.34120	−	1.86323i	0.356874	−	0.124492i
$225$	2.20613	−	3.82112i	0.147075	−	0.254742i
$226$	5.27450	+	4.14375i	0.350855	+	0.275638i
$227$	−0.274173	+	0.474882i	−0.0181975	+	0.0315190i	−0.874981	−	0.484158i	$-0.839126\pi$
$227$	−0.274173	+	0.474882i	−0.0181975	+	0.0315190i	0.856783	+	0.515677i	$0.172459\pi$
$228$	−5.08519	+	17.3814i	−0.336775	+	1.15111i
$229$	−5.70242			−0.376827			−0.188413	−	0.982090i	$-0.560334\pi$
$229$	−5.70242			−0.376827			−0.188413	+	0.982090i	$0.560334\pi$
$230$	−44.4119	+	17.8050i	−2.92843	+	1.17403i
$231$	−4.07381	−	7.05605i	−0.268037	−	0.464254i
$232$	1.21168	+	12.4957i	0.0795506	+	0.820383i
$233$	10.5205			0.689220			0.344610	−	0.938746i	$-0.388011\pi$
$233$	10.5205			0.689220			0.344610	+	0.938746i	$0.388011\pi$
$234$	−0.783009	+	1.83866i	−0.0511869	+	0.120197i
$235$		−	6.85194i		−	0.446972i
$236$	−8.41497	+	8.03937i	−0.547768	+	0.523318i
$237$	12.7232	−	7.34572i	0.826458	−	0.477156i
$238$	2.09131	+	5.21646i	0.135560	+	0.338133i
$239$			21.2231i			1.37281i	0.727219	+	0.686405i	$0.240812\pi$
$239$			21.2231i			1.37281i	−0.727219	+	0.686405i	$0.759188\pi$
$240$	−29.6731	−	1.35539i	−1.91539	−	0.0874902i
$241$	5.22336	+	3.01571i	0.336466	+	0.194259i	0.658708	−	0.752399i	$-0.271103\pi$
$241$	5.22336	+	3.01571i	0.336466	+	0.194259i	−0.322242	+	0.946657i	$0.604437\pi$
$242$	−9.53169	−	7.48827i	−0.612720	−	0.481364i
$243$	−3.50568	−	2.02400i	−0.224889	−	0.129840i
$244$	−10.9115	−	11.4213i	−0.698539	−	0.731175i
$245$	2.01605	+	3.49191i	0.128801	+	0.223090i
$246$	13.7433	+	10.7970i	0.876244	+	0.688393i
$247$	−17.1299	−	4.56220i	−1.08995	−	0.290286i
$248$	23.9651	+	10.9021i	1.52178	+	0.692282i
$249$	−0.725155	+	0.418668i	−0.0459548	+	0.0265320i
$250$	−5.06111	+	35.3233i	−0.320092	+	2.23404i
$251$	11.7576	+	6.78825i	0.742132	+	0.428470i	0.822844	−	0.568267i	$-0.192386\pi$
$251$	11.7576	+	6.78825i	0.742132	+	0.428470i	−0.0807117	+	0.996737i	$0.525719\pi$
$252$	0.761576	−	0.185544i	0.0479748	−	0.0116882i
$253$	18.5607	−	32.1481i	1.16690	−	2.02114i
$254$	12.8629	−	5.15681i	0.807088	−	0.323567i
$255$		−	29.5108i		−	1.84804i
$256$	6.70347	+	14.5280i	0.418967	+	0.908002i
$257$	−13.2942	−	23.0263i	−0.829272	−	1.43634i	−0.898610	−	0.438748i	$-0.855422\pi$
$257$	−13.2942	−	23.0263i	−0.829272	−	1.43634i	0.0693380	−	0.997593i	$-0.477911\pi$
$258$	−1.22105	+	8.52211i	−0.0760190	+	0.530563i
$259$			3.39525i			0.210971i
$260$	0.619583	−	29.0693i	0.0384249	−	1.80280i
$261$			1.73961i			0.107679i
$262$	−21.9079	−	3.13895i	−1.35347	−	0.193925i
$263$	−10.3204	−	17.8754i	−0.636381	−	1.10224i	−0.986221	−	0.165435i	$-0.947097\pi$
$263$	−10.3204	−	17.8754i	−0.636381	−	1.10224i	0.349839	−	0.936810i	$-0.386236\pi$
$264$	18.7523	−	13.3949i	1.15412	−	0.824398i
$265$		−	7.71984i		−	0.474226i
$266$	2.58737	+	6.45379i	0.158642	+	0.395707i
$267$	8.50574	−	14.7324i	0.520543	−	0.901606i
$268$	−0.226733	−	0.930635i	−0.0138499	−	0.0568476i
$269$	−7.94661	−	4.58798i	−0.484513	−	0.279734i	0.237782	−	0.971319i	$-0.423580\pi$
$269$	−7.94661	−	4.58798i	−0.484513	−	0.279734i	−0.722295	+	0.691585i	$0.756913\pi$
$270$	27.1130	+	3.88474i	1.65004	+	0.236418i
$271$	−9.62861	+	5.55908i	−0.584896	+	0.337690i	−0.763077	−	0.646308i	$-0.776312\pi$
$271$	−9.62861	+	5.55908i	−0.584896	+	0.337690i	0.178181	+	0.983998i	$0.442979\pi$
$272$	−14.1146	+	7.31153i	−0.855823	+	0.443326i
$273$	1.72836	+	6.41154i	0.104605	+	0.388044i
$274$	4.19609	−	5.34113i	0.253495	−	0.322669i
$275$	−24.9020	−	43.1315i	−1.50165	−	2.60093i
$276$	21.3508	+	22.3483i	1.28517	+	1.34521i
$277$	10.6573	+	6.15298i	0.640334	+	0.369697i	0.784743	−	0.619821i	$-0.212795\pi$
$277$	10.6573	+	6.15298i	0.640334	+	0.369697i	−0.144409	+	0.989518i	$0.546128\pi$
$278$	−4.89107	+	6.22575i	−0.293347	+	0.373396i
$279$	3.15946	+	1.82412i	0.189152	+	0.109207i
$280$	−9.28014	+	6.62888i	−0.554594	+	0.396151i
$281$		−	15.1383i		−	0.903076i	−0.892252	−	0.451538i	$-0.850876\pi$
$281$		−	15.1383i		−	0.903076i	0.892252	−	0.451538i	$-0.149124\pi$
$282$	−4.10824	+	1.64702i	−0.244642	+	0.0980785i
$283$	22.5694	−	13.0304i	1.34161	−	0.774579i	0.354566	−	0.935031i	$-0.384628\pi$
$283$	22.5694	−	13.0304i	1.34161	−	0.774579i	0.987044	+	0.160452i	$0.0512951\pi$
$284$	−8.97813	−	9.39759i	−0.532754	−	0.557645i
$285$		−	36.5107i		−	2.16271i
$286$	13.5544	+	18.0313i	0.801489	+	1.06621i
$287$	6.71020			0.396091
$288$	0.730248	+	2.09336i	0.0430303	+	0.123352i
$289$	0.603742	+	1.04571i	0.0355143	+	0.0615125i
$290$	−9.41831	−	23.4925i	−0.553062	−	1.37953i
$291$	−21.9263			−1.28534
$292$	−2.05874	+	7.03687i	−0.120479	+	0.411801i
$293$	11.8132	−	20.4611i	0.690136	−	1.19535i	−0.281657	−	0.959515i	$-0.590884\pi$
$293$	11.8132	−	20.4611i	0.690136	−	1.19535i	0.971793	−	0.235835i	$-0.0757826\pi$
$294$	1.60905	−	2.04813i	0.0938415	−	0.119449i
$295$	11.7314	−	20.3194i	0.683029	−	1.18304i
$296$	−9.55839	+	0.926854i	−0.555570	+	0.0538723i
$297$	−18.4027	+	10.6248i	−1.06783	+	0.616513i
$298$	15.7632	+	12.3838i	0.913136	+	0.717377i
$299$	−21.3607	+	21.4254i	−1.23532	+	1.23907i
$300$	40.2892	−	9.81574i	2.32610	−	0.566712i
$301$	1.65269	+	2.86254i	0.0952595	+	0.164994i
$302$	−17.1686	−	2.45991i	−0.987940	−	0.141552i
$303$	−13.5970	+	23.5508i	−0.781130	+	1.35296i
$304$	−17.4625	+	9.04580i	−1.00155	+	0.518812i
$305$	27.5788	+	15.9226i	1.57915	+	0.911725i
$306$	−2.04447	+	0.819640i	−0.116874	+	0.0468557i
$307$	−13.3939			−0.764432			−0.382216	−	0.924073i	$-0.624839\pi$
$307$	−13.3939			−0.764432			−0.382216	+	0.924073i	$0.624839\pi$
$308$	2.48443	−	8.49188i	0.141564	−	0.483870i
$309$	−21.1503	+	12.2111i	−1.20320	+	0.694667i
$310$	−52.5427	−	7.52830i	−2.98422	−	0.427579i
$311$	25.0924			1.42286			0.711430	−	0.702757i	$-0.248048\pi$
$311$	25.0924			1.42286			0.711430	+	0.702757i	$0.248048\pi$
$312$	−17.5781	+	6.61598i	−0.995163	+	0.374556i
$313$	31.2014			1.76361			0.881804	−	0.471617i	$-0.156329\pi$
$313$	31.2014			1.76361			0.881804	+	0.471617i	$0.156329\pi$
$314$	18.3421	+	2.62805i	1.03510	+	0.148309i
$315$	−1.36857	+	0.790144i	−0.0771102	+	0.0445196i
$316$	15.3122	+	4.47982i	0.861378	+	0.252009i
$317$	1.26736			0.0711818			0.0355909	−	0.999366i	$-0.488669\pi$
$317$	1.26736			0.0711818			0.0355909	+	0.999366i	$0.488669\pi$
$318$	−4.62860	+	1.85564i	−0.259559	+	0.104059i
$319$	17.0054	+	9.81806i	0.952118	+	0.549706i
$320$	−21.1951	−	24.3161i	−1.18484	−	1.35931i
$321$	7.16388	−	12.4082i	0.399849	−	0.692558i
$322$	11.7468	+	1.68308i	0.654624	+	0.0937943i
$323$	−9.76923	−	16.9208i	−0.543575	−	0.941499i
$324$	−4.74466	−	19.4747i	−0.263592	−	1.08193i
$325$	10.5650	+	39.1918i	0.586038	+	2.17397i
$326$	−14.6055	−	11.4744i	−0.808925	−	0.635506i
$327$	11.1818	−	6.45579i	0.618352	−	0.357006i
$328$	1.83179	+	18.8907i	0.101143	+	1.04307i
$329$	−0.849673	+	1.47168i	−0.0468440	+	0.0811362i
$330$	−28.7017	+	36.5339i	−1.57998	+	2.01113i
$331$	−1.57404	+	2.72632i	−0.0865171	+	0.149852i	−0.906037	−	0.423199i	$-0.860907\pi$
$331$	−1.57404	+	2.72632i	−0.0865171	+	0.149852i	0.819520	+	0.573051i	$0.194240\pi$
$332$	−0.872716	−	0.255327i	−0.0478965	−	0.0140129i
$333$	−1.33069			−0.0729213
$334$	1.70822	+	4.26089i	0.0934695	+	0.233145i
$335$	0.965544	+	1.67237i	0.0527533	+	0.0913714i
$336$	6.20518	+	3.97071i	0.338520	+	0.216620i
$337$	5.72365			0.311787			0.155894	−	0.987774i	$-0.450174\pi$
$337$	5.72365			0.311787			0.155894	+	0.987774i	$0.450174\pi$
$338$	−6.89285	−	17.0437i	−0.374921	−	0.927057i
$339$			8.73517i			0.474429i
$340$	23.1719	−	22.1376i	1.25667	−	1.20058i
$341$	35.6629	−	20.5900i	1.93125	−	1.11501i
$342$	−2.52941	+	1.01406i	−0.136775	+	0.0548339i
$343$		−	1.00000i		−	0.0539949i
$344$	−7.60754	+	5.43413i	−0.410171	+	0.292988i
$345$	−53.9639	−	31.1561i	−2.90532	−	1.67739i
$346$	13.6750	−	17.4066i	0.735171	−	0.935787i
$347$	−3.78560	−	2.18562i	−0.203222	−	0.117330i	0.394936	−	0.918709i	$-0.370767\pi$
$347$	−3.78560	−	2.18562i	−0.203222	−	0.117330i	−0.598157	+	0.801379i	$0.704100\pi$
$348$	−11.8216	+	11.2939i	−0.633703	+	0.605418i
$349$	−11.8775	−	20.5724i	−0.635786	−	1.10121i	−0.986348	−	0.164674i	$-0.947343\pi$
$349$	−11.8775	−	20.5724i	−0.635786	−	1.10121i	0.350562	−	0.936539i	$-0.385990\pi$
$350$	9.83561	−	12.5196i	0.525736	−	0.669200i
$351$	16.7218	−	4.50769i	0.892542	−	0.240603i
$352$	24.5847	+	4.67607i	1.31037	+	0.249235i
$353$	18.9156	−	10.9209i	1.00678	−	0.581263i	0.0965311	−	0.995330i	$-0.469225\pi$
$353$	18.9156	−	10.9209i	1.00678	−	0.581263i	0.910247	+	0.414067i	$0.135892\pi$
$354$	−15.0029	−	2.14961i	−0.797393	−	0.114250i
$355$	22.6921	+	13.1013i	1.20437	+	0.695345i
$356$	17.9485	−	4.37283i	0.951267	−	0.231759i
$357$	−3.65948	+	6.33840i	−0.193680	+	0.335464i
$358$	9.32694	+	23.2646i	0.492944	+	1.22957i
$359$			7.58796i			0.400477i	0.979747	+	0.200239i	$0.0641718\pi$
$359$			7.58796i			0.400477i	−0.979747	+	0.200239i	$0.935828\pi$
$360$	−2.59803	−	3.63713i	−0.136928	−	0.191694i
$361$	−2.58647	−	4.47990i	−0.136130	−	0.235784i
$362$	17.9839	+	2.57674i	0.945215	+	0.135430i
$363$		−	15.7855i		−	0.828526i
$364$	−3.73781	+	6.16675i	−0.195914	+	0.323225i
$365$		−	14.7814i		−	0.773693i
$366$	2.91758	−	20.3628i	0.152504	−	1.06438i
$367$	−6.63128	−	11.4857i	−0.346150	−	0.599549i	0.639412	−	0.768864i	$-0.279178\pi$
$367$	−6.63128	−	11.4857i	−0.346150	−	0.599549i	−0.985562	+	0.169315i	$0.945845\pi$
$368$	−1.53154	+	33.5293i	−0.0798369	+	1.74784i
$369$			2.62990i			0.136907i
$370$	17.9703	−	7.20439i	0.934229	−	0.374538i
$371$	−0.957296	+	1.65809i	−0.0497003	+	0.0860835i
$372$	8.11605	+	33.3127i	0.420798	+	1.72718i
$373$	−11.3945	−	6.57860i	−0.589984	−	0.340627i	0.175107	−	0.984549i	$-0.443973\pi$
$373$	−11.3945	−	6.57860i	−0.589984	−	0.340627i	−0.765091	+	0.643922i	$0.777306\pi$
$374$	−3.52631	+	24.6114i	−0.182341	+	1.27262i
$375$	−40.2450	+	23.2355i	−2.07824	+	1.19987i
$376$	−4.37505	−	1.99027i	−0.225626	−	0.102641i
$377$	−11.3334	−	11.2992i	−0.583700	−	0.581938i
$378$	−5.34167	−	4.19651i	−0.274746	−	0.215845i
$379$	−13.2037	−	22.8695i	−0.678229	−	1.17473i	−0.975514	−	0.219938i	$-0.929414\pi$
$379$	−13.2037	−	22.8695i	−0.678229	−	1.17473i	0.297285	−	0.954789i	$-0.403919\pi$
$380$	28.6682	−	27.3886i	1.47065	−	1.40501i
$381$	15.6294	+	9.02362i	0.800717	+	0.462294i
$382$	16.0014	+	12.5710i	0.818701	+	0.643187i
$383$	21.5868	+	12.4631i	1.10303	+	0.636837i	0.937016	−	0.349286i	$-0.113576\pi$
$383$	21.5868	+	12.4631i	1.10303	+	0.636837i	0.166017	+	0.986123i	$0.446909\pi$
$384$	−9.48452	+	18.5529i	−0.484005	+	0.946774i
$385$			17.8377i			0.909095i
$386$	−7.24915	−	18.0819i	−0.368972	−	0.920344i
$387$	−1.12191	+	0.647733i	−0.0570297	+	0.0329261i
$388$	−16.4481	−	17.2165i	−0.835025	−	0.874037i
$389$			35.5001i			1.79993i	0.435965	+	0.899964i	$0.356407\pi$
$389$			35.5001i			1.79993i	−0.435965	+	0.899964i	$0.643593\pi$
$390$	30.2673	−	22.7524i	1.53264	−	1.15211i
$391$	−33.3460			−1.68638
$392$	2.81522	−	0.272985i	0.142190	−	0.0137878i
$393$	−14.4109	−	24.9604i	−0.726934	−	1.25909i
$394$	−26.7390	+	10.7198i	−1.34709	+	0.540058i
$395$	−32.1642			−1.61836
$396$	3.32819	+	0.973714i	0.167248	+	0.0489310i
$397$	−8.59288	+	14.8833i	−0.431264	+	0.746971i	−0.996982	−	0.0776272i	$-0.975266\pi$
$397$	−8.59288	+	14.8833i	−0.431264	+	0.746971i	0.565718	+	0.824599i	$0.308599\pi$
$398$	−10.9473	−	8.60036i	−0.548736	−	0.431097i
$399$	−4.52749	+	7.84185i	−0.226658	+	0.392584i
$400$	37.9304	+	24.2718i	1.89652	+	1.21359i
$401$	15.7456	−	9.09071i	0.786297	−	0.453969i	−0.0523605	−	0.998628i	$-0.516674\pi$
$401$	15.7456	−	9.09071i	0.786297	−	0.453969i	0.838657	+	0.544660i	$0.183341\pi$
$402$	0.770618	−	0.980906i	0.0384349	−	0.0489231i
$403$	−32.4054	+	8.73554i	−1.61423	+	0.435148i
$404$	−28.6920	+	6.99028i	−1.42748	+	0.347780i
$405$	20.2052	+	34.9965i	1.00401	+	1.73899i
$406$	−0.890297	+	6.21370i	−0.0441847	+	0.308381i
$407$	−7.51017	+	13.0080i	−0.372265	+	0.644782i
$408$	−18.8430	−	8.57195i	−0.932867	−	0.424375i
$409$	−2.23712	−	1.29160i	−0.110618	−	0.0638655i	0.443670	−	0.896190i	$-0.353676\pi$
$409$	−2.23712	−	1.29160i	−0.110618	−	0.0638655i	−0.554288	+	0.832325i	$0.687010\pi$
$410$	−14.2384	−	35.5155i	−0.703184	−	1.75398i
$411$	8.84551			0.436317
$412$	−25.4541	−	7.44701i	−1.25404	−	0.366888i
$413$	−5.03940	+	2.90950i	−0.247973	+	0.143167i
$414$	−0.659643	+	4.60388i	−0.0324197	+	0.226268i
$415$	1.83320			0.0899880
$416$	−18.3811	−	8.83933i	−0.901209	−	0.433384i
$417$	−10.3105			−0.504909
$418$	−4.36274	+	30.4491i	−0.213389	+	1.48931i
$419$	16.1478	−	9.32293i	0.788871	−	0.455455i	−0.0506936	−	0.998714i	$-0.516143\pi$
$419$	16.1478	−	9.32293i	0.788871	−	0.455455i	0.839565	+	0.543259i	$0.182810\pi$
$420$	−14.2545	−	4.17037i	−0.695547	−	0.203493i
$421$	−17.7843			−0.866755			−0.433377	−	0.901213i	$-0.642678\pi$
$421$	−17.7843			−0.866755			−0.433377	+	0.901213i	$0.642678\pi$
$422$	2.35040	+	5.86270i	0.114415	+	0.285392i
$423$	−0.576789	−	0.333009i	−0.0280444	−	0.0161915i
$424$	−4.92921	−	2.24237i	−0.239384	−	0.108899i
$425$	−22.3693	+	38.7447i	−1.08507	+	1.87939i
$426$	2.40062	−	16.7548i	0.116310	−	0.811771i
$427$	−3.94895	−	6.83979i	−0.191103	−	0.331001i
$428$	15.1169	−	3.68297i	0.730705	−	0.178023i
$429$	−7.56032	+	28.3871i	−0.365016	+	1.37054i
$430$	11.6439	−	14.8213i	0.561519	−	0.714748i
$431$	−0.590862	+	0.341134i	−0.0284608	+	0.0164319i	−0.514163	−	0.857693i	$-0.671897\pi$
$431$	−0.590862	+	0.341134i	−0.0284608	+	0.0164319i	0.485702	+	0.874124i	$0.338564\pi$
$432$	10.3559	−	16.1836i	0.498249	−	0.778632i
$433$	−4.33306	+	7.50509i	−0.208234	+	0.360671i	−0.951158	−	0.308704i	$-0.900105\pi$
$433$	−4.33306	+	7.50509i	−0.208234	+	0.360671i	0.742924	+	0.669375i	$0.233438\pi$
$434$	10.3517	+	8.13249i	0.496898	+	0.390372i
$435$	16.4806	−	28.5452i	0.790184	−	1.36864i
$436$	13.4571	+	3.93709i	0.644479	+	0.188552i
$437$	−41.2555			−1.97352
$438$	−8.86250	+	3.55304i	−0.423467	+	0.169771i
$439$	−6.57274	−	11.3843i	−0.313700	−	0.543344i	0.665460	−	0.746433i	$-0.268235\pi$
$439$	−6.57274	−	11.3843i	−0.313700	−	0.543344i	−0.979160	+	0.203089i	$0.934902\pi$
$440$	−50.2172	+	4.86943i	−2.39401	+	0.232141i
$441$	0.391926			0.0186632
$442$	7.93941	−	18.6433i	0.377639	−	0.886770i
$443$			21.8170i			1.03656i	0.855211	+	0.518279i	$0.173427\pi$
$443$			21.8170i			1.03656i	−0.855211	+	0.518279i	$0.826573\pi$
$444$	−8.63911	−	9.04273i	−0.409994	−	0.429149i
$445$	−32.2538	+	18.6218i	−1.52898	+	0.882756i
$446$	4.08532	+	10.1902i	0.193445	+	0.482520i
$447$			26.1056i			1.23475i
$448$	1.53703	+	7.85096i	0.0726178	+	0.370923i
$449$	−2.48898	−	1.43702i	−0.117462	−	0.0678170i	0.440118	−	0.897940i	$-0.354937\pi$
$449$	−2.48898	−	1.43702i	−0.117462	−	0.0678170i	−0.557580	+	0.830123i	$0.688270\pi$
$450$	4.90675	+	3.85484i	0.231307	+	0.181719i
$451$	25.7083	+	14.8427i	1.21056	+	0.698916i
$452$	−6.85886	+	6.55272i	−0.322614	+	0.308214i
$453$	−11.2934	−	19.5608i	−0.530610	−	0.919044i
$454$	−0.609802	−	0.479072i	−0.0286194	−	0.0224840i
$455$	3.74146	−	14.0483i	0.175402	−	0.658593i
$456$	−23.3125	−	10.6052i	−1.09171	−	0.496634i
$457$	−10.8689	+	6.27514i	−0.508424	+	0.293539i	−0.732186	−	0.681105i	$-0.761500\pi$
$457$	−10.8689	+	6.27514i	−0.508424	+	0.293539i	0.223761	+	0.974644i	$0.428166\pi$
$458$	1.14379	−	7.98292i	0.0534458	−	0.373017i
$459$	16.5310	+	9.54418i	0.771601	+	0.445484i
$460$	−16.0174	−	65.7443i	−0.746817	−	3.06534i
$461$	−19.2607	+	33.3606i	−0.897062	+	1.55376i	−0.0658309	+	0.997831i	$0.520970\pi$
$461$	−19.2607	+	33.3606i	−0.897062	+	1.55376i	−0.831231	+	0.555927i	$0.812364\pi$
$462$	10.6950	−	4.28770i	0.497577	−	0.199482i
$463$			2.76518i			0.128509i	0.997934	+	0.0642544i	$0.0204669\pi$
$463$			2.76518i			0.128509i	−0.997934	+	0.0642544i	$0.979533\pi$
$464$	−17.7360	−	0.810137i	−0.823373	−	0.0376097i
$465$	−34.5623	−	59.8637i	−1.60279	−	2.77611i
$466$	−2.11020	+	14.7278i	−0.0977529	+	0.682252i
$467$		−	10.9089i		−	0.504803i	−0.967623	−	0.252401i	$-0.918780\pi$
$467$		−	10.9089i		−	0.504803i	0.967623	−	0.252401i	$-0.0812204\pi$
$468$	−2.41691	−	1.46495i	−0.111722	−	0.0677171i
$469$		−	0.478928i		−	0.0221149i
$470$	9.59215	+	1.37436i	0.442453	+	0.0633946i
$471$	12.0653	+	20.8978i	0.555942	+	0.962919i
$472$	−9.56658	−	13.3928i	−0.440337	−	0.616453i
$473$			14.6228i			0.672355i
$474$	7.73139	+	19.2848i	0.355114	+	0.885778i
$475$	−27.6752	+	47.9349i	−1.26983	+	2.19940i
$476$	−7.72208	+	1.88135i	−0.353941	+	0.0862314i
$477$	−0.649847	−	0.375190i	−0.0297545	−	0.0171787i
$478$	−29.7106	−	4.25693i	−1.35893	−	0.194707i
$479$	19.8929	−	11.4852i	0.908928	−	0.524770i	0.0288422	−	0.999584i	$-0.490818\pi$
$479$	19.8929	−	11.4852i	0.908928	−	0.524770i	0.880086	+	0.474814i	$0.157485\pi$
$480$	7.84925	−	41.2680i	0.358268	−	1.88362i
$481$	8.64313	−	8.66931i	0.394093	−	0.395287i
$482$	−5.26944	+	6.70738i	−0.240016	+	0.305513i
$483$	7.72700	+	13.3836i	0.351591	+	0.608973i
$484$	12.3948	−	11.8416i	0.563401	−	0.538254i
$485$	41.5723	+	24.0018i	1.88770	+	1.08987i
$486$	3.53661	−	4.50168i	0.160424	−	0.204201i
$487$	−6.40865	−	3.70004i	−0.290404	−	0.167665i	0.347720	−	0.937598i	$-0.386956\pi$
$487$	−6.40865	−	3.70004i	−0.290404	−	0.167665i	−0.638124	+	0.769934i	$0.720289\pi$
$488$	18.1775	−	12.9843i	0.822858	−	0.587774i
$489$		−	24.1884i		−	1.09384i
$490$	−5.29276	+	2.12190i	−0.239102	+	0.0958577i
$491$	24.4015	−	14.0882i	1.10123	−	0.635793i	0.164684	−	0.986346i	$-0.447340\pi$
$491$	24.4015	−	14.0882i	1.10123	−	0.635793i	0.936543	+	0.350553i	$0.114006\pi$
$492$	−17.8716	+	17.0739i	−0.805713	+	0.769750i
$493$		−	17.6390i		−	0.794420i
$494$	9.82262	−	23.0654i	0.441940	−	1.03776i
$495$	−6.99107			−0.314225
$496$	−20.0689	+	31.3624i	−0.901120	+	1.40821i
$497$	−3.24925	−	5.62786i	−0.145749	−	0.252444i
$498$	−0.440650	−	1.09913i	−0.0197460	−	0.0492533i
$499$	3.55263			0.159037			0.0795187	−	0.996833i	$-0.474662\pi$
$499$	3.55263			0.159037			0.0795187	+	0.996833i	$0.474662\pi$
$500$	−48.4345	−	14.1703i	−2.16606	−	0.633713i
$501$	−2.98912	+	5.17730i	−0.133544	+	0.231305i
$502$	−11.8613	+	15.0981i	−0.529396	+	0.673860i
$503$	18.6884	−	32.3692i	0.833273	−	1.44327i	−0.0621566	−	0.998066i	$-0.519798\pi$
$503$	18.6884	−	32.3692i	0.833273	−	1.44327i	0.895429	−	0.445204i	$-0.146869\pi$
$504$	0.106990	+	1.10336i	0.00476572	+	0.0491476i
$505$	51.5601	−	29.7682i	2.29439	−	1.32467i
$506$	41.2818	+	32.4317i	1.83520	+	1.44177i
$507$	11.9084	−	20.7708i	0.528871	−	0.922463i
$508$	4.63907	+	19.0413i	0.205826	+	0.844821i
$509$	17.1540	+	29.7116i	0.760337	+	1.31694i	0.942677	+	0.333707i	$0.108300\pi$
$509$	17.1540	+	29.7116i	0.760337	+	1.31694i	−0.182339	+	0.983236i	$0.558367\pi$
$510$	41.3126	+	5.91926i	1.82935	+	0.262109i
$511$	−1.83296	+	3.17478i	−0.0810854	+	0.140444i
$512$	−21.6826	+	6.47027i	−0.958245	+	0.285948i
$513$	20.4521	+	11.8080i	0.902983	+	0.521338i
$514$	34.9015	−	13.9922i	1.53944	−	0.617171i
$515$	53.4680			2.35608
$516$	−11.6853	−	3.41872i	−0.514418	−	0.150501i
$517$	−6.51059	+	3.75889i	−0.286335	+	0.165316i
$518$	−4.75307	−	0.681019i	−0.208838	−	0.0299223i
$519$	28.8273			1.26538
$520$	40.5704	+	6.69808i	1.77913	+	0.293730i
$521$	24.8533			1.08884			0.544421	−	0.838812i	$-0.316750\pi$
$521$	24.8533			1.08884			0.544421	+	0.838812i	$0.316750\pi$
$522$	−2.43531	−	0.348931i	−0.106591	−	0.0152723i
$523$	−15.8621	+	9.15799i	−0.693602	+	0.400451i	−0.804960	−	0.593329i	$-0.797813\pi$
$523$	−15.8621	+	9.15799i	−0.693602	+	0.400451i	0.111358	+	0.993780i	$0.464480\pi$
$524$	8.78855	−	30.0396i	0.383930	−	1.31229i
$525$	20.7338			0.904898
$526$	27.0941	−	10.8622i	1.18136	−	0.473615i
$527$	−32.0357	−	18.4958i	−1.39550	−	0.805691i
$528$	14.9904	+	28.9383i	0.652373	+	1.25938i
$529$	−23.7051	+	41.0584i	−1.03065	+	1.78515i
$530$	10.8071	+	1.54844i	0.469432	+	0.0672601i
$531$	−1.14031	−	1.97508i	−0.0494852	−	0.0857110i
$532$	−9.55374	+	2.32760i	−0.414207	+	0.100914i
$533$	−17.1336	−	17.0818i	−0.742137	−	0.739896i
$534$	18.9180	+	14.8623i	0.818663	+	0.643156i
$535$	−27.1655	+	15.6840i	−1.17447	+	0.678079i
$536$	1.34829	−	0.130740i	0.0582372	−	0.00564712i
$537$	−16.3207	+	28.2683i	−0.704291	+	1.21987i
$538$	8.01672	−	10.2043i	0.345625	−	0.439940i
$539$	2.21196	−	3.83123i	0.0952759	−	0.165023i
$540$	−10.8766	+	37.1767i	−0.468055	+	1.59983i
$541$	2.68331			0.115365			0.0576823	−	0.998335i	$-0.481629\pi$
$541$	2.68331			0.115365			0.0576823	+	0.998335i	$0.481629\pi$
$542$	−5.85095	−	14.5943i	−0.251320	−	0.626878i
$543$	11.8298	+	20.4897i	0.507664	+	0.879299i
$544$	−7.40443	−	21.2258i	−0.317462	−	0.910049i
$545$	−28.2675			−1.21085
$546$	−9.32229	+	1.13354i	−0.398957	+	0.0485110i
$547$			16.7970i			0.718186i	0.933302	+	0.359093i	$0.116914\pi$
$547$			16.7970i			0.718186i	−0.933302	+	0.359093i	$0.883086\pi$
$548$	6.63549	+	6.94550i	0.283454	+	0.296697i
$549$	2.68069	−	1.54770i	0.114409	−	0.0660542i
$550$	65.3753	−	26.2094i	2.78761	−	1.11757i
$551$		−	21.8229i		−	0.929688i
$552$	−35.5683	+	25.4067i	−1.51389	+	1.08138i
$553$	6.90831	+	3.98851i	0.293771	+	0.169609i
$554$	−10.7513	+	13.6851i	−0.456779	+	0.581426i
$555$	21.8352	+	12.6066i	0.926854	+	0.535119i
$556$	−7.73449	−	8.09585i	−0.328015	−	0.343340i
$557$	−20.2056	−	34.9971i	−0.856137	−	1.48287i	−0.875586	−	0.483062i	$-0.839525\pi$
$557$	−20.2056	−	34.9971i	−0.856137	−	1.48287i	0.0194492	−	0.999811i	$-0.493809\pi$
$558$	−3.18734	+	4.05710i	−0.134931	+	0.171751i
$559$	3.06712	−	11.5163i	0.129725	−	0.487087i
$560$	−7.41847	−	14.3210i	−0.313487	−	0.605174i
$561$	−28.0406	+	16.1892i	−1.18387	+	0.683510i
$562$	21.1924	+	3.03644i	0.893946	+	0.128084i
$563$	2.53321	+	1.46255i	0.106762	+	0.0616391i	0.552430	−	0.833559i	$-0.313701\pi$
$563$	2.53321	+	1.46255i	0.106762	+	0.0616391i	−0.445668	+	0.895198i	$0.647034\pi$
$564$	−1.48166	−	6.08155i	−0.0623892	−	0.256079i
$565$	9.56202	−	16.5619i	0.402277	−	0.696765i
$566$	13.7146	+	34.2089i	0.576466	+	1.43791i
$567$		−	10.0222i		−	0.420892i
$568$	14.9567	−	10.6837i	0.627569	−	0.448277i
$569$	23.3133	+	40.3798i	0.977345	+	1.69281i	0.671969	+	0.740579i	$0.265449\pi$
$569$	23.3133	+	40.3798i	0.977345	+	1.69281i	0.305376	+	0.952232i	$0.401218\pi$
$570$	51.1119	+	7.32330i	2.14084	+	0.306739i
$571$		−	12.4742i		−	0.522028i	−0.965335	−	0.261014i	$-0.915943\pi$
$571$		−	12.4742i		−	0.522028i	0.965335	−	0.261014i	$-0.0840569\pi$
$572$	−27.9610	+	15.3583i	−1.16911	+	0.642165i
$573$			26.5001i			1.10706i
$574$	−1.34593	+	9.39373i	−0.0561780	+	0.392087i
$575$	47.2328	+	81.8096i	1.96974	+	3.41170i
$576$	−3.07700	+	0.602402i	−0.128208	+	0.0251001i
$577$		−	15.0894i		−	0.628181i	−0.949393	−	0.314091i	$-0.898300\pi$
$577$		−	15.0894i		−	0.628181i	0.949393	−	0.314091i	$-0.101700\pi$
$578$	−1.58501	+	0.635441i	−0.0659277	+	0.0264308i
$579$	12.6849	−	21.9709i	0.527166	−	0.913079i
$580$	34.7767	−	8.47273i	1.44403	−	0.351811i
$581$	−0.393738	−	0.227325i	−0.0163350	−	0.00943103i
$582$	4.39797	−	30.6950i	0.182302	−	1.27235i
$583$	−7.33524	+	4.23500i	−0.303795	+	0.175396i
$584$	−9.43809	−	4.29352i	−0.390551	−	0.177667i
$585$	5.50588	+	1.46638i	0.227640	+	0.0606272i
$586$	26.2744	+	20.6416i	1.08538	+	0.852697i
$587$	2.35810	+	4.08435i	0.0973293	+	0.168579i	0.910578	−	0.413336i	$-0.135637\pi$
$587$	2.35810	+	4.08435i	0.0973293	+	0.168579i	−0.813249	+	0.581916i	$0.802303\pi$
$588$	2.54447	+	2.66334i	0.104932	+	0.109834i
$589$	−39.6345	−	22.8830i	−1.63311	−	0.942877i
$590$	26.0924	+	20.4987i	1.07421	+	0.843917i
$591$	−32.4900	−	18.7581i	−1.33646	−	0.771605i
$592$	0.619701	−	13.5669i	0.0254696	−	0.557595i
$593$			25.9946i			1.06747i	0.845651	+	0.533736i	$0.179212\pi$
$593$			25.9946i			1.06747i	−0.845651	+	0.533736i	$0.820788\pi$
$594$	−11.1826	−	27.8934i	−0.458829	−	1.14448i
$595$	13.8768	−	8.01175i	0.568892	−	0.328450i
$596$	−20.4981	+	19.5832i	−0.839636	+	0.802159i
$597$		−	18.1299i		−	0.742006i
$598$	−25.7093	−	34.2008i	−1.05133	−	1.39857i
$599$	−0.0131579			−0.000537619			−0.000268809	−	1.00000i	$-0.500086\pi$
$599$	−0.0131579			−0.000537619			−0.000268809		1.00000i	$0.500086\pi$
$600$	5.66003	+	58.3703i	0.231070	+	2.38296i
$601$	−4.71242	−	8.16215i	−0.192224	−	0.332941i	0.753763	−	0.657146i	$-0.228237\pi$
$601$	−4.71242	−	8.16215i	−0.192224	−	0.332941i	−0.945987	+	0.324205i	$0.894903\pi$
$602$	−4.33882	+	1.73946i	−0.176837	+	0.0708952i
$603$	0.187705			0.00764392
$604$	6.88733	−	23.5412i	0.280242	−	0.957876i
$605$	−17.2798	+	29.9295i	−0.702523	+	1.21681i
$606$	−30.2418	−	23.7585i	−1.22849	−	0.965125i
$607$	7.98474	−	13.8300i	0.324091	−	0.561342i	−0.657237	−	0.753684i	$-0.728275\pi$
$607$	7.98474	−	13.8300i	0.324091	−	0.561342i	0.981328	+	0.192342i	$0.0616084\pi$
$608$	−9.16074	−	26.2605i	−0.371517	−	1.06500i
$609$	−7.07949	+	4.08735i	−0.286875	+	0.165628i
$610$	−27.8221	+	35.4142i	−1.12648	+	1.43388i
$611$	5.91590	−	1.59475i	0.239332	−	0.0645168i
$612$	−0.737350	−	3.02649i	−0.0298056	−	0.122339i
$613$	−18.1185	−	31.3821i	−0.731798	−	1.26751i	−0.956114	−	0.292994i	$-0.905348\pi$
$613$	−18.1185	−	31.3821i	−0.731798	−	1.26751i	0.224316	−	0.974516i	$-0.427985\pi$
$614$	2.68655	−	18.7504i	0.108420	−	0.756704i
$615$	24.9150	−	43.1540i	1.00467	−	1.74014i
$616$	11.3896	+	5.18130i	0.458900	+	0.208760i
$617$	−8.83305	−	5.09976i	−0.355605	−	0.205309i	0.311546	−	0.950231i	$-0.399153\pi$
$617$	−8.83305	−	5.09976i	−0.355605	−	0.205309i	−0.667151	+	0.744922i	$0.732487\pi$
$618$	−12.8522	−	32.0579i	−0.516993	−	1.28956i
$619$	−13.4910			−0.542249			−0.271125	−	0.962544i	$-0.587396\pi$
$619$	−13.4910			−0.542249			−0.271125	+	0.962544i	$0.587396\pi$
$620$	21.0780	−	72.0454i	0.846512	−	2.89341i
$621$	34.9053	−	20.1526i	1.40070	−	0.808695i
$622$	−5.03303	+	35.1273i	−0.201806	+	1.40848i
$623$	9.23674			0.370062
$624$	−5.73601	−	25.9349i	−0.229624	−	1.03823i
$625$	45.4503			1.81801
$626$	−6.25837	+	43.6794i	−0.250135	+	1.74578i
$627$	−34.6917	+	20.0293i	−1.38545	+	0.799893i
$628$	−7.35810	+	25.1503i	−0.293620	+	1.00360i
$629$	13.4927			0.537988
$630$	−0.831629	−	2.07437i	−0.0331329	−	0.0826449i
$631$	−2.34707	−	1.35508i	−0.0934355	−	0.0539450i	0.452554	−	0.891737i	$-0.350513\pi$
$631$	−2.34707	−	1.35508i	−0.0934355	−	0.0539450i	−0.545990	+	0.837792i	$0.683846\pi$
$632$	−9.34268	+	20.5372i	−0.371632	+	0.816927i
$633$	−4.11283	+	7.12363i	−0.163470	+	0.283139i
$634$	−0.254206	+	1.77419i	−0.0100958	+	0.0704622i
$635$	−19.7556	−	34.2177i	−0.783976	−	1.35789i
$636$	−1.66933	−	6.85186i	−0.0661934	−	0.271694i
$637$	−2.54565	+	2.55336i	−0.100862	+	0.101168i
$638$	−17.1554	+	21.8368i	−0.679189	+	0.864528i
$639$	2.20571	−	1.27347i	0.0872564	−	0.0503775i
$640$	38.2918	−	24.7941i	1.51362	−	0.980072i
$641$	11.3343	−	19.6316i	0.447679	−	0.775403i	−0.550555	−	0.834799i	$-0.685584\pi$
$641$	11.3343	−	19.6316i	0.447679	−	0.775403i	0.998235	+	0.0593954i	$0.0189173\pi$
$642$	15.9335	+	12.5177i	0.628846	+	0.494033i
$643$	7.98286	−	13.8267i	0.314813	−	0.545272i	−0.664585	−	0.747213i	$-0.731391\pi$
$643$	7.98286	−	13.8267i	0.314813	−	0.545272i	0.979398	+	0.201941i	$0.0647248\pi$
$644$	−4.71234	+	16.1070i	−0.185692	+	0.634703i
$645$	24.5458			0.966489
$646$	25.6472	−	10.2821i	1.00908	−	0.404545i
$647$	15.1034	+	26.1599i	0.593776	+	1.02845i	0.993718	+	0.111910i	$0.0356967\pi$
$647$	15.1034	+	26.1599i	0.593776	+	1.02845i	−0.399943	+	0.916540i	$0.630970\pi$
$648$	28.2146	−	2.73591i	1.10838	−	0.107477i
$649$	−25.7428			−1.01049
$650$	−56.9844	+	6.92898i	−2.23511	+	0.271777i
$651$			17.1436i			0.671910i
$652$	18.9927	−	18.1450i	0.743812	−	0.710612i
$653$	24.6296	−	14.2199i	0.963832	−	0.556469i	0.0664816	−	0.997788i	$-0.478823\pi$
$653$	24.6296	−	14.2199i	0.963832	−	0.556469i	0.897350	+	0.441319i	$0.145489\pi$
$654$	6.79474	+	16.9484i	0.265695	+	0.662736i
$655$			63.1001i			2.46552i
$656$	−26.8128	−	1.22475i	−1.04687	−	0.0478183i
$657$	−1.24428	−	0.718385i	−0.0485440	−	0.0280269i
$658$	−1.88980	−	1.48466i	−0.0736720	−	0.0578781i
$659$	34.7249	+	20.0484i	1.35269	+	0.780976i	0.988625	−	0.150398i	$-0.0480556\pi$
$659$	34.7249	+	20.0484i	1.35269	+	0.780976i	0.364064	+	0.931374i	$0.381389\pi$
$660$	−45.3875	−	47.5080i	−1.76671	−	1.84925i
$661$	12.5211	+	21.6872i	0.487014	+	0.843533i	0.999889	−	0.0149305i	$-0.00475270\pi$
$661$	12.5211	+	21.6872i	0.487014	+	0.843533i	−0.512874	+	0.858464i	$0.671419\pi$
$662$	−3.50090	−	2.75037i	−0.136066	−	0.106896i
$663$	25.4793	−	6.86847i	0.989535	−	0.266749i
$664$	0.532486	−	1.17052i	0.0206644	−	0.0454249i
$665$	17.1683	−	9.91212i	0.665758	−	0.384376i
$666$	0.266909	−	1.86285i	0.0103425	−	0.0721841i
$667$	−32.2549	−	18.6224i	−1.24892	−	0.721062i
$668$	−6.30752	+	1.53671i	−0.244045	+	0.0594573i
$669$	−7.14868	+	12.3819i	−0.276384	+	0.478711i
$670$	−2.53485	+	1.01624i	−0.0979298	+	0.0392607i
$671$		−	34.9397i		−	1.34883i
$672$	−6.80330	+	7.89029i	−0.262443	+	0.304375i
$673$	−19.9373	−	34.5324i	−0.768526	−	1.33113i	−0.938362	−	0.345653i	$-0.887657\pi$
$673$	−19.9373	−	34.5324i	−0.768526	−	1.33113i	0.169837	−	0.985472i	$-0.445676\pi$
$674$	−1.14805	+	8.01264i	−0.0442212	+	0.308635i
$675$		−	54.0753i		−	2.08136i
$676$	25.2424	−	6.23079i	0.970860	−	0.239646i
$677$			23.9300i			0.919704i	0.887996	+	0.459852i	$0.152098\pi$
$677$			23.9300i			0.919704i	−0.887996	+	0.459852i	$0.847902\pi$
$678$	−12.2285	−	1.75210i	−0.469633	−	0.0672889i
$679$	−5.95267	−	10.3103i	−0.228442	−	0.395674i
$680$	26.3430	+	36.8791i	1.01021	+	1.41425i
$681$		−	1.00990i		−	0.0386995i
$682$	21.6710	+	54.0550i	0.829825	+	2.06987i
$683$	13.6088	−	23.5712i	0.520727	−	0.901925i	−0.478983	−	0.877824i	$-0.658994\pi$
$683$	13.6088	−	23.5712i	0.520727	−	0.901925i	0.999710	−	0.0241008i	$-0.00767227\pi$
$684$	−0.912247	−	3.74436i	−0.0348806	−	0.143169i
$685$	−16.7711	−	9.68281i	−0.640791	−	0.369961i
$686$	1.39992	+	0.200580i	0.0534491	+	0.00765817i
$687$	9.09522	−	5.25113i	0.347004	−	0.200343i
$688$	−6.08141	−	11.7399i	−0.231851	−	0.447580i
$689$	6.66523	−	1.79675i	0.253925	−	0.0684507i
$690$	54.4400	−	69.2957i	2.07249	−	2.63804i
$691$	−11.2061	−	19.4095i	−0.426299	−	0.738371i	0.570242	−	0.821477i	$-0.306849\pi$
$691$	−11.2061	−	19.4095i	−0.426299	−	0.738371i	−0.996541	+	0.0831059i	$0.973516\pi$
$692$	21.6249	+	22.6353i	0.822057	+	0.860463i
$693$	1.50156	+	0.866926i	0.0570395	+	0.0329318i
$694$	3.81900	−	4.86113i	0.144967	−	0.184526i
$695$	19.5488	+	11.2865i	0.741529	+	0.428122i
$696$	−13.4394	−	18.8146i	−0.509418	−	0.713164i
$697$		−	26.6662i		−	1.01005i
$698$	31.1820	−	12.5011i	1.18026	−	0.473172i
$699$	−16.7799	+	9.68788i	−0.634674	+	0.366429i
$700$	15.5536	+	16.2802i	0.587869	+	0.615334i
$701$		−	3.04835i		−	0.115135i	−0.998342	−	0.0575673i	$-0.981666\pi$
$701$		−	3.04835i		−	0.115135i	0.998342	−	0.0575673i	$-0.0183344\pi$
$702$	2.95635	+	24.3132i	0.111580	+	0.917644i
$703$	16.6931			0.629592
$704$	−11.4773	+	33.4787i	−0.432567	+	1.26178i
$705$	6.30968	+	10.9287i	0.237636	+	0.411598i
$706$	11.4943	+	28.6708i	0.432595	+	1.07904i
$707$	−14.7656			−0.555318
$708$	6.01854	−	20.5716i	0.226191	−	0.773128i
$709$	−6.37308	+	11.0385i	−0.239346	+	0.414559i	−0.960527	−	0.278187i	$-0.910266\pi$
$709$	−6.37308	+	11.0385i	−0.239346	+	0.414559i	0.721181	+	0.692747i	$0.243600\pi$
$710$	−22.8923	+	29.1392i	−0.859133	+	1.09358i
$711$	−1.56320	+	2.70755i	−0.0586247	+	0.101541i
$712$	2.52149	+	26.0035i	0.0944970	+	0.974522i
$713$	−67.6435	+	39.0540i	−2.53327	+	1.46258i
$714$	−8.13921	−	6.39432i	−0.304602	−	0.239301i
$715$	45.4086	−	45.5462i	1.69819	−	1.70333i
$716$	−34.4394	+	8.39053i	−1.28706	+	0.313569i
$717$	−19.5435	−	33.8504i	−0.729866	−	1.26416i
$718$	−10.6225	−	1.52199i	−0.396429	−	0.0568002i
$719$	4.23568	−	7.33641i	0.157964	−	0.273602i	−0.776170	−	0.630523i	$-0.782840\pi$
$719$	4.23568	−	7.33641i	0.157964	−	0.273602i	0.934134	+	0.356921i	$0.116174\pi$
$720$	5.61279	−	2.90749i	0.209176	−	0.108356i
$721$	−11.4840	−	6.63029i	−0.427686	−	0.246925i
$722$	6.79027	−	2.72227i	0.252708	−	0.101312i
$723$	−11.1082			−0.413117
$724$	−7.21443	+	24.6592i	−0.268122	+	0.916452i
$725$	−43.2748	+	24.9847i	−1.60719	+	0.927909i
$726$	22.0985	+	3.16626i	0.820151	+	0.117511i
$727$	−45.7119			−1.69536			−0.847680	−	0.530507i	$-0.822001\pi$
$727$	−45.7119			−1.69536			−0.847680	+	0.530507i	$0.822001\pi$
$728$	−7.88321	−	6.46955i	−0.292171	−	0.239777i
$729$	−22.6112			−0.837453
$730$	20.6927	+	2.96484i	0.765871	+	0.109734i
$731$	11.3757	−	6.56776i	0.420745	−	0.242917i
$732$	27.9210	+	8.16873i	1.03199	+	0.301925i
$733$	0.388585			0.0143527			0.00717635	−	0.999974i	$-0.497716\pi$
$733$	0.388585			0.0143527			0.00717635	+	0.999974i	$0.497716\pi$
$734$	17.4091	−	6.97944i	0.642583	−	0.257616i
$735$	−6.43111	−	3.71300i	−0.237215	−	0.136956i
$736$	−46.6311	−	8.86933i	−1.71884	−	0.326928i
$737$	1.05937	−	1.83488i	0.0390224	−	0.0675888i
$738$	−3.68165	−	0.527505i	−0.135523	−	0.0194177i
$739$	10.7434	+	18.6082i	0.395203	+	0.684512i	0.993127	−	0.117041i	$-0.0373408\pi$
$739$	10.7434	+	18.6082i	0.395203	+	0.684512i	−0.597924	+	0.801553i	$0.704008\pi$
$740$	6.48108	+	26.6019i	0.238249	+	0.977906i
$741$	31.5230	−	8.49766i	1.15802	−	0.312169i
$742$	−2.12917	−	1.67271i	−0.0781642	−	0.0614072i
$743$	0.874998	−	0.505180i	0.0321006	−	0.0185333i	−0.483864	−	0.875143i	$-0.660767\pi$
$743$	0.874998	−	0.505180i	0.0321006	−	0.0185333i	0.515964	+	0.856610i	$0.327434\pi$
$744$	−48.2630	+	4.67994i	−1.76941	+	0.171575i
$745$	28.5767	−	49.4963i	1.04697	−	1.81340i
$746$	11.4950	−	14.6318i	0.420862	−	0.535708i
$747$	0.0890946	−	0.154316i	0.00325980	−	0.00564614i
$748$	−33.7466	−	9.87308i	−1.23390	−	0.360995i
$749$	7.77956			0.284259
$750$	−24.4554	−	61.0003i	−0.892985	−	2.22741i
$751$	20.3707	+	35.2832i	0.743339	+	1.28750i	0.950967	+	0.309293i	$0.100092\pi$
$751$	20.3707	+	35.2832i	0.743339	+	1.28750i	−0.207628	+	0.978208i	$0.566574\pi$
$752$	3.66376	−	5.72550i	0.133604	−	0.208787i
$753$	−25.0041			−0.911199
$754$	18.0912	−	13.5994i	0.658842	−	0.495263i
$755$			49.4497i			1.79966i
$756$	6.94620	−	6.63615i	0.252631	−	0.241355i
$757$	−29.2679	+	16.8979i	−1.06376	+	0.614163i	−0.926470	−	0.376368i	$-0.877173\pi$
$757$	−29.2679	+	16.8979i	−1.06376	+	0.614163i	−0.137291	+	0.990531i	$0.543840\pi$
$758$	34.6638	−	13.8969i	1.25905	−	0.504760i
$759$			68.3673i			2.48157i
$760$	32.5915	+	45.6267i	1.18222	+	1.65505i
$761$	27.3786	+	15.8070i	0.992473	+	0.573005i	0.906013	−	0.423251i	$-0.139111\pi$
$761$	27.3786	+	15.8070i	0.992473	+	0.573005i	0.0864603	+	0.996255i	$0.472444\pi$
$762$	−15.7673	+	20.0699i	−0.571188	+	0.727055i
$763$	6.07137	+	3.50531i	0.219798	+	0.126901i
$764$	−20.8079	+	19.8791i	−0.752802	+	0.719201i
$765$	3.14002	+	5.43867i	0.113528	+	0.196635i
$766$	−21.7772	+	27.7199i	−0.786843	+	1.00156i
$767$	20.2740	+	5.39956i	0.732052	+	0.194967i
$768$	−24.0701	−	16.9989i	−0.868556	−	0.613394i
$769$	14.4740	−	8.35659i	0.521947	−	0.301347i	−0.215784	−	0.976441i	$-0.569231\pi$
$769$	14.4740	−	8.35659i	0.521947	−	0.301347i	0.737731	+	0.675095i	$0.235897\pi$
$770$	−24.9713	−	3.57789i	−0.899904	−	0.128938i
$771$	42.4080	+	24.4843i	1.52729	+	0.881779i
$772$	26.7672	−	6.52135i	0.963372	−	0.234708i
$773$	−0.763518	+	1.32245i	−0.0274618	+	0.0475653i	−0.879430	−	0.476029i	$-0.842076\pi$
$773$	−0.763518	+	1.32245i	−0.0274618	+	0.0475653i	0.851968	+	0.523594i	$0.175409\pi$
$774$	−0.681741	−	1.70050i	−0.0245047	−	0.0611231i
$775$			104.793i			3.76429i
$776$	27.4009	−	19.5727i	0.983634	−	0.702617i
$777$	−3.12655	−	5.41534i	−0.112164	−	0.194274i
$778$	−49.6972	−	7.12060i	−1.78173	−	0.255286i
$779$		−	32.9914i		−	1.18204i
$780$	25.7805	+	46.9354i	0.923091	+	1.68056i
$781$		−	28.7488i		−	1.02871i
$782$	6.68852	−	46.6816i	0.239181	−	1.66933i
$783$	10.6601	+	18.4638i	0.380961	+	0.659843i
$784$	−0.182520	+	3.99583i	−0.00651857	+	0.142708i
$785$		−	52.8297i		−	1.88557i
$786$	37.8330	−	15.1675i	1.34946	−	0.541007i
$787$	−6.10234	+	10.5696i	−0.217525	+	0.376764i	−0.954051	−	0.299645i	$-0.903132\pi$
$787$	−6.10234	+	10.5696i	−0.217525	+	0.376764i	0.736526	+	0.676409i	$0.236465\pi$
$788$	−9.64359	−	39.5826i	−0.343539	−	1.41007i
$789$	32.9215	+	19.0072i	1.17204	+	0.676675i
$790$	6.45149	−	45.0272i	0.229534	−	1.60200i
$791$	−4.10751	+	2.37147i	−0.146046	+	0.0843198i
$792$	−2.03069	+	4.46388i	−0.0721573	+	0.158617i
$793$	−7.32861	+	27.5171i	−0.260247	+	0.977162i
$794$	−19.1118	−	15.0146i	−0.678253	−	0.532848i
$795$	7.10888	+	12.3129i	0.252126	+	0.436695i
$796$	14.2356	−	13.6002i	0.504567	−	0.482046i
$797$	−29.2764	−	16.9028i	−1.03702	−	0.598726i	−0.118035	−	0.993009i	$-0.537660\pi$
$797$	−29.2764	−	16.9028i	−1.03702	−	0.598726i	−0.918989	+	0.394283i	$0.870993\pi$
$798$	−10.0698	−	7.91103i	−0.356468	−	0.280048i
$799$	5.84842	+	3.37658i	0.206902	+	0.119455i
$800$	−41.5866	+	48.2310i	−1.47031	+	1.70522i
$801$			3.62012i			0.127911i
$802$	9.56800	+	23.8659i	0.337858	+	0.842735i
$803$	−14.0450	+	8.10888i	−0.495637	+	0.286156i
$804$	1.21862	+	1.27555i	0.0429773	+	0.0449852i
$805$		−	33.8337i		−	1.19248i
$806$	−5.72916	−	47.1170i	−0.201801	−	1.65963i
$807$	16.8995			0.594891
$808$	−4.03079	−	41.5685i	−0.141803	−	1.46237i
$809$	11.5204	+	19.9539i	0.405035	+	0.701541i	0.994326	−	0.106380i	$-0.0339260\pi$
$809$	11.5204	+	19.9539i	0.405035	+	0.701541i	−0.589291	+	0.807921i	$0.700593\pi$
$810$	−53.0449	+	21.2661i	−1.86381	+	0.747213i
$811$	−30.0247			−1.05431			−0.527155	−	0.849769i	$-0.676741\pi$
$811$	−30.0247			−1.05431			−0.527155	+	0.849769i	$0.676741\pi$
$812$	−8.52009	−	2.49269i	−0.298997	−	0.0874761i
$813$	10.2383	−	17.7332i	0.359071	−	0.621930i
$814$	−16.7037	−	13.1228i	−0.585465	−	0.459952i
$815$	−26.4780	+	45.8612i	−0.927484	+	1.60645i
$816$	15.7795	−	24.6593i	0.552394	−	0.863247i
$817$	14.0740	−	8.12562i	0.492386	−	0.284279i
$818$	2.25685	−	2.87271i	0.0789090	−	0.100442i
$819$	−1.00073	−	0.997708i	−0.0349683	−	0.0348627i
$820$	52.5746	−	12.8089i	1.83599	−	0.447305i
$821$	19.2533	+	33.3477i	0.671945	+	1.16384i	0.977352	+	0.211622i	$0.0678744\pi$
$821$	19.2533	+	33.3477i	0.671945	+	1.16384i	−0.305406	+	0.952222i	$0.598792\pi$
$822$	−1.77423	+	12.3830i	−0.0618833	+	0.431906i
$823$	22.9293	−	39.7147i	0.799265	−	1.38437i	−0.120831	−	0.992673i	$-0.538556\pi$
$823$	22.9293	−	39.7147i	0.799265	−	1.38437i	0.920096	−	0.391694i	$-0.128111\pi$
$824$	15.5308	−	34.1400i	0.541040	−	1.18932i
$825$	79.4361	+	45.8624i	2.76561	+	1.59672i
$826$	−3.06226	−	7.63834i	−0.106550	−	0.265772i
$827$	11.5441			0.401427			0.200714	−	0.979650i	$-0.435674\pi$
$827$	11.5441			0.401427			0.200714	+	0.979650i	$0.435674\pi$
$828$	−6.31274	−	1.84689i	−0.219383	−	0.0641839i
$829$	−4.20155	+	2.42576i	−0.145926	+	0.0842503i	−0.571185	−	0.820821i	$-0.693516\pi$
$829$	−4.20155	+	2.42576i	−0.145926	+	0.0842503i	0.425259	+	0.905072i	$0.360183\pi$
$830$	−0.367702	+	2.56632i	−0.0127631	+	0.0890783i
$831$	−22.6641			−0.786210
$832$	16.0612	−	23.9591i	0.556822	−	0.830632i
$833$	−3.97398			−0.137690
$834$	2.06809	−	14.4339i	0.0716120	−	0.499805i
$835$	11.3348	−	6.54412i	0.392255	−	0.226469i
$836$	−41.7512	−	12.2149i	−1.44399	−	0.422463i
$837$	44.7117			1.54546
$838$	9.81241	+	24.4756i	0.338964	+	0.845494i
$839$	−29.1095	−	16.8064i	−1.00497	−	0.580221i	−0.0952566	−	0.995453i	$-0.530367\pi$
$839$	−29.1095	−	16.8064i	−1.00497	−	0.580221i	−0.909716	+	0.415232i	$0.863700\pi$
$840$	8.69733	−	19.1186i	0.300086	−	0.659654i
$841$	−4.64932	+	8.05286i	−0.160321	+	0.277685i
$842$	3.56717	−	24.8966i	0.122933	−	0.857993i
$843$	13.9402	+	24.1452i	0.480128	+	0.831605i
$844$	−8.67874	+	2.11442i	−0.298734	+	0.0727813i
$845$	−45.3153	+	26.3459i	−1.55889	+	0.906325i
$846$	0.581878	−	0.740662i	0.0200054	−	0.0254645i
$847$	7.42279	−	4.28555i	0.255050	−	0.147253i
$848$	4.12783	−	6.45071i	0.141750	−	0.221518i
$849$	−23.9984	+	41.5664i	−0.823623	+	1.42656i
$850$	−49.7526	−	39.0865i	−1.70650	−	1.34066i
$851$	14.2449	−	24.6729i	0.488309	−	0.845776i
$852$	22.9738	+	6.72133i	0.787068	+	0.230269i
$853$	44.7052			1.53068			0.765338	−	0.643628i	$-0.222572\pi$
$853$	44.7052			1.53068			0.765338	+	0.643628i	$0.222572\pi$
$854$	10.3672	−	4.15629i	0.354759	−	0.142225i
$855$	3.88482	+	6.72871i	0.132858	+	0.230117i
$856$	2.12371	+	21.9012i	0.0725868	+	0.748567i
$857$	31.2352			1.06697			0.533487	−	0.845808i	$-0.320881\pi$
$857$	31.2352			1.06697			0.533487	+	0.845808i	$0.320881\pi$
$858$	−38.2232	−	16.2777i	−1.30492	−	0.555712i
$859$			15.8692i			0.541450i	0.962657	+	0.270725i	$0.0872634\pi$
$859$			15.8692i			0.541450i	−0.962657	+	0.270725i	$0.912737\pi$
$860$	18.4131	+	19.2734i	0.627881	+	0.657216i
$861$	−10.7026	+	6.17915i	−0.364744	+	0.210585i
$862$	−0.359045	−	0.895582i	−0.0122291	−	0.0305036i
$863$		−	52.2254i		−	1.77777i	−0.458126	−	0.888887i	$-0.651479\pi$
$863$		−	52.2254i		−	1.77777i	0.458126	−	0.888887i	$-0.348521\pi$
$864$	20.5785	+	17.7435i	0.700093	+	0.603647i
$865$	−54.6568	−	31.5561i	−1.85839	−	1.07294i
$866$	−9.63737	−	7.57130i	−0.327491	−	0.257283i
$867$	−1.92591	−	1.11192i	−0.0654073	−	0.0377629i
$868$	−13.4611	+	12.8603i	−0.456901	+	0.436507i
$869$	17.6449	+	30.5618i	0.598561	+	1.03674i
$870$	36.6553	+	28.7971i	1.24273	+	0.976312i
$871$	−1.21918	+	1.22288i	−0.0413105	+	0.0414356i
$872$	−8.21083	+	18.0492i	−0.278054	+	0.611222i
$873$	4.04089	−	2.33301i	0.136763	−	0.0789603i
$874$	8.27502	−	57.7543i	0.279907	−	1.95357i
$875$	−21.8519	−	12.6162i	−0.738729	−	0.426505i
$876$	−3.19632	−	13.1194i	−0.107994	−	0.443265i
$877$	15.4337	−	26.7320i	0.521160	−	0.902675i	−0.478538	−	0.878067i	$-0.658833\pi$
$877$	15.4337	−	26.7320i	0.521160	−	0.902675i	0.999697	−	0.0246079i	$-0.00783372\pi$
$878$	17.2555	−	6.91783i	0.582344	−	0.233465i
$879$			43.5133i			1.46767i
$880$	3.25574	−	71.2766i	0.109751	−	2.40273i
$881$	19.3392	+	33.4965i	0.651554	+	1.12852i	0.982746	+	0.184961i	$0.0592158\pi$
$881$	19.3392	+	33.4965i	0.651554	+	1.12852i	−0.331192	+	0.943563i	$0.607451\pi$
$882$	−0.0786125	+	0.548664i	−0.00264702	+	0.0184745i
$883$			20.1198i			0.677087i	0.940951	+	0.338543i	$0.109934\pi$
$883$			20.1198i			0.677087i	−0.940951	+	0.338543i	$0.890066\pi$
$884$	24.5065	+	14.8540i	0.824244	+	0.499593i
$885$			43.2119i			1.45255i
$886$	−30.5420	−	4.37605i	−1.02608	−	0.147016i
$887$	6.96785	+	12.0687i	0.233957	+	0.405226i	0.958969	−	0.283510i	$-0.0914990\pi$
$887$	6.96785	+	12.0687i	0.233957	+	0.405226i	−0.725012	+	0.688736i	$0.758166\pi$
$888$	14.3919	−	10.2802i	0.482960	−	0.344982i
$889$			9.79913i			0.328652i
$890$	−19.5994	−	48.8878i	−0.656975	−	1.63872i
$891$	22.1687	−	38.3972i	0.742678	−	1.28636i
$892$	−15.0849	+	3.67516i	−0.505078	+	0.123053i
$893$	7.23565	+	4.17750i	0.242132	+	0.139795i
$894$	−36.5456	−	5.23625i	−1.22227	−	0.175126i
$895$	61.8883	−	35.7312i	2.06870	−	1.19436i
$896$	−11.2990	+	0.576969i	−0.377473	+	0.0192752i
$897$	14.3400	−	53.8433i	0.478800	−	1.79778i
$898$	2.51094	−	3.19613i	0.0837912	−	0.106656i
$899$	−20.6584	−	35.7814i	−0.688995	−	1.19338i
$900$	−6.38065	+	6.09585i	−0.212688	+	0.203195i
$901$	6.58920	+	3.80428i	0.219518	+	0.126739i
$902$	−25.9351	+	33.0124i	−0.863545	+	1.09919i
$903$	−5.27200	−	3.04379i	−0.175441	−	0.101291i
$904$	−7.79751	−	10.9162i	−0.259341	−	0.363067i
$905$		−	51.7982i		−	1.72183i
$906$	29.6487	−	11.8863i	0.985011	−	0.394897i
$907$	−30.9183	+	17.8507i	−1.02663	+	0.592723i	−0.916017	−	0.401140i	$-0.868614\pi$
$907$	−30.9183	+	17.8507i	−1.02663	+	0.592723i	−0.110610	+	0.993864i	$0.535281\pi$
$908$	0.792975	−	0.757581i	0.0263158	−	0.0251412i
$909$		−	5.78703i		−	0.191944i
$910$	18.9159	+	8.05553i	0.627057	+	0.267038i
$911$	−20.7490			−0.687445			−0.343722	−	0.939071i	$-0.611688\pi$
$911$	−20.7490			−0.687445			−0.343722	+	0.939071i	$0.611688\pi$
$912$	19.5224	−	30.5084i	0.646452	−	1.01023i
$913$	−1.00567	−	1.74187i	−0.0332828	−	0.0576474i
$914$	−6.60461	−	16.4742i	−0.218461	−	0.544917i
$915$	−58.6499			−1.93891
$916$	10.9460	+	3.20242i	0.361666	+	0.105811i
$917$	7.82470	−	13.5528i	0.258395	−	0.447552i
$918$	−16.6768	+	21.2277i	−0.550418	+	0.700618i
$919$	14.0013	−	24.2510i	0.461860	−	0.799965i	−0.537194	−	0.843459i	$-0.680516\pi$
$919$	14.0013	−	24.2510i	0.461860	−	0.799965i	0.999054	+	0.0434938i	$0.0138489\pi$
$920$	95.2494	−	9.23610i	3.14028	−	0.304505i
$921$	21.3630	−	12.3339i	0.703934	−	0.406417i
$922$	−42.8387	−	33.6549i	−1.41082	−	1.10837i
$923$	−6.03007	+	22.6414i	−0.198482	+	0.745251i
$924$	3.85722	+	15.8321i	0.126893	+	0.520839i
$925$	−19.1117	−	33.1024i	−0.628388	−	1.08840i
$926$	−3.87102	−	0.554639i	−0.127210	−	0.0182266i
$927$	2.59858	−	4.50088i	0.0853487	−	0.147828i
$928$	4.69160	−	24.6664i	0.154009	−	0.809715i
$929$	−49.8775	−	28.7968i	−1.63643	−	0.944792i	−0.982049	−	0.188624i	$-0.939597\pi$
$929$	−49.8775	−	28.7968i	−1.63643	−	0.944792i	−0.654378	−	0.756167i	$-0.727070\pi$
$930$	90.7368	−	36.3770i	2.97538	−	1.19285i
$931$	−4.91660			−0.161135
$932$	−20.1944	−	5.90820i	−0.661491	−	0.193529i
$933$	−40.0218	+	23.1066i	−1.31025	+	0.756475i
$934$	15.2715	+	2.18810i	0.499700	+	0.0715968i
$935$	70.8868			2.31824
$936$	2.53559	−	3.08964i	0.0828782	−	0.100988i
$937$	13.5587			0.442944			0.221472	−	0.975167i	$-0.428914\pi$
$937$	13.5587			0.442944			0.221472	+	0.975167i	$0.428914\pi$
$938$	0.670460	+	0.0960633i	0.0218913	+	0.00313658i
$939$	−49.7654	+	28.7321i	−1.62403	+	0.937636i
$940$	−3.84798	+	13.1526i	−0.125507	+	0.428989i
$941$	−16.7377			−0.545634			−0.272817	−	0.962066i	$-0.587955\pi$
$941$	−16.7377			−0.545634			−0.272817	+	0.962066i	$0.587955\pi$
$942$	−31.6752	+	12.6988i	−1.03203	+	0.413749i
$943$	−48.7622	−	28.1529i	−1.58792	−	0.916784i
$944$	20.6677	−	10.7061i	0.672675	−	0.348454i
$945$	−9.68378	+	16.7728i	−0.315013	+	0.545619i
$946$	−20.4706	−	2.93303i	−0.665558	−	0.0953610i
$947$	19.3472	+	33.5103i	0.628698	+	1.08894i	0.987813	+	0.155644i	$0.0497453\pi$
$947$	19.3472	+	33.5103i	0.628698	+	1.08894i	−0.359115	+	0.933293i	$0.616921\pi$
$948$	−28.5478	+	6.95517i	−0.927190	+	0.225893i
$949$	12.7621	−	3.44029i	0.414275	−	0.111676i
$950$	−61.5538	−	48.3578i	−1.99707	−	1.56893i
$951$	−2.02140	+	1.16706i	−0.0655484	+	0.0378444i
$952$	−1.08484	−	11.1876i	−0.0351598	−	0.362593i
$953$	−19.9746	+	34.5969i	−0.647039	+	1.12070i	0.336787	+	0.941581i	$0.390660\pi$
$953$	−19.9746	+	34.5969i	−0.647039	+	1.12070i	−0.983826	+	0.179124i	$0.942674\pi$
$954$	0.655580	−	0.834477i	0.0212252	−	0.0270172i
$955$	29.0085	−	50.2442i	0.938693	−	1.62586i
$956$	11.9187	−	40.7386i	0.385478	−	1.31758i
$957$	−36.1642			−1.16902
$958$	12.0882	+	30.1521i	0.390551	+	0.974169i
$959$	2.40143	+	4.15939i	0.0775461	+	0.134314i
$960$	56.1973	+	19.2658i	1.81376	+	0.621802i
$961$	−55.6475			−1.79508
$962$	10.4027	+	13.8386i	0.335396	+	0.446173i
$963$			3.04901i			0.0982531i
$964$	−8.33283	−	8.72214i	−0.268382	−	0.280921i
$965$	−48.1012	+	27.7713i	−1.54843	+	0.893989i
$966$	−20.2857	+	8.13269i	−0.652683	+	0.261665i
$967$		−	37.2115i		−	1.19664i	−0.801256	−	0.598321i	$-0.795835\pi$
$967$		−	37.2115i		−	1.19664i	0.801256	−	0.598321i	$-0.204165\pi$
$968$	14.0911	+	19.7269i	0.452905	+	0.634047i
$969$	31.1634	+	17.9922i	1.00111	+	0.577992i
$970$	−41.9391	+	53.3835i	−1.34658	+	1.71404i
$971$	−7.76569	−	4.48353i	−0.249213	−	0.143883i	0.370191	−	0.928956i	$-0.379292\pi$
$971$	−7.76569	−	4.48353i	−0.249213	−	0.143883i	−0.619404	+	0.785073i	$0.712626\pi$
$972$	5.59261	+	5.85390i	0.179383	+	0.187764i
$973$	−2.79916	−	4.84829i	−0.0897371	−	0.155429i
$974$	6.46519	−	8.22943i	0.207158	−	0.263688i
$975$	−52.9410	−	52.7811i	−1.69547	−	1.69035i
$976$	14.5310	+	28.0514i	0.465125	+	0.897904i
$977$	−24.2582	+	14.0055i	−0.776089	+	0.448075i	−0.835042	−	0.550186i	$-0.814557\pi$
$977$	−24.2582	+	14.0055i	−0.776089	+	0.448075i	0.0589536	+	0.998261i	$0.481224\pi$
$978$	33.8617	+	4.85169i	1.08278	+	0.155140i
$979$	35.3881	+	20.4313i	1.13101	+	0.652988i
$980$	−1.90887	−	7.83503i	−0.0609765	−	0.250281i
$981$	−1.37382	+	2.37953i	−0.0438628	+	0.0759725i
$982$	14.8279	+	36.9860i	0.473178	+	1.18027i
$983$			1.37666i			0.0439086i	0.999759	+	0.0219543i	$0.00698883\pi$
$983$			1.37666i			0.0439086i	−0.999759	+	0.0219543i	$0.993011\pi$
$984$	−20.3173	−	28.4434i	−0.647693	−	0.906742i
$985$	41.0674	+	71.1308i	1.30852	+	2.26642i
$986$	24.6931	+	3.53802i	0.786389	+	0.112674i
$987$		−	3.12972i		−	0.0996200i
$988$	30.3194	+	18.3773i	0.964589	+	0.584660i
$989$		−	27.7357i		−	0.881944i
$990$	1.40227	−	9.78692i	0.0445670	−	0.311049i
$991$	−18.7644	−	32.5009i	−0.596070	−	1.03242i	−0.993395	−	0.114746i	$-0.963395\pi$
$991$	−18.7644	−	32.5009i	−0.596070	−	1.03242i	0.397325	−	0.917678i	$-0.369939\pi$
$992$	−39.8793	−	34.3855i	−1.26617	−	1.09174i
$993$		−	5.79788i		−	0.183990i
$994$	8.53027	−	3.41984i	0.270564	−	0.108471i
$995$	−19.8460	+	34.3743i	−0.629161	+	1.08974i
$996$	1.62708	−	0.396409i	0.0515560	−	0.0125607i
$997$	51.9089	+	29.9696i	1.64397	+	0.949147i	0.979402	+	0.201920i	$0.0647183\pi$
$997$	51.9089	+	29.9696i	1.64397	+	0.949147i	0.664569	+	0.747227i	$0.268615\pi$
$998$	−0.712585	+	4.97338i	−0.0225565	+	0.157430i
$999$	−14.1236	+	8.15427i	−0.446851	+	0.257990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.cz.a.309.40	yes	168
8.5	even	2	inner	728.2.cz.a.309.11	✓	168
13.4	even	6	inner	728.2.cz.a.589.11	yes	168
104.69	even	6	inner	728.2.cz.a.589.40	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.cz.a.309.11	✓	168	8.5	even	2	inner
728.2.cz.a.309.40	yes	168	1.1	even	1	trivial
728.2.cz.a.589.11	yes	168	13.4	even	6	inner
728.2.cz.a.589.40	yes	168	104.69	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.200580 + 1.39992i) q^{2} +(-1.59497 + 0.920859i) q^{3} +(-1.91954 - 0.561590i) q^{4} +4.03210 q^{5} +(-0.969207 - 2.41754i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(1.17120 - 2.57455i) q^{8} +(0.195963 - 0.339418i) q^{9} +(-0.808758 + 5.64461i) q^{10} +(-2.21196 - 3.83123i) q^{11} +(3.57876 - 0.871900i) q^{12} +(0.938451 + 3.48128i) q^{13} +(0.873666 - 1.11207i) q^{14} +(-6.43111 + 3.71300i) q^{15} +(3.36923 + 2.15598i) q^{16} +(-1.98699 + 3.44157i) q^{17} +(0.435851 + 0.342413i) q^{18} +(-2.45830 + 4.25790i) q^{19} +(-7.73977 - 2.26439i) q^{20} +1.84172 q^{21} +(5.80708 - 2.32810i) q^{22} +(4.19554 + 7.26688i) q^{23} +(0.502762 + 5.18485i) q^{24} +11.2579 q^{25} +(-5.06174 + 0.615479i) q^{26} -4.80334i q^{27} +(1.38157 + 1.44612i) q^{28} +(-3.84396 + 2.21931i) q^{29} +(-3.90794 - 9.74777i) q^{30} +9.30847i q^{31} +(-3.69400 + 4.28420i) q^{32} +(7.05605 + 4.07381i) q^{33} +(-4.41936 - 3.47193i) q^{34} +(-3.49191 - 2.01605i) q^{35} +(-0.566772 + 0.541474i) q^{36} +(-1.69763 - 2.94038i) q^{37} +(-5.46762 - 4.29546i) q^{38} +(-4.70257 - 4.68837i) q^{39} +(4.72240 - 10.3808i) q^{40} +(-5.81120 + 3.35510i) q^{41} +(-0.369411 + 2.57825i) q^{42} +(-2.86254 - 1.65269i) q^{43} +(2.09436 + 8.59640i) q^{44} +(0.790144 - 1.36857i) q^{45} +(-11.0146 + 4.41581i) q^{46} -1.69935i q^{47} +(-7.35920 - 0.336150i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-2.25810 + 15.7601i) q^{50} -7.31895i q^{51} +(0.153662 - 7.20947i) q^{52} -1.91459i q^{53} +(6.72427 + 0.963452i) q^{54} +(-8.91886 - 15.4479i) q^{55} +(-2.30156 + 1.64402i) q^{56} -9.05499i q^{57} +(-2.33583 - 5.82637i) q^{58} +(2.90950 - 5.03940i) q^{59} +(14.4299 - 3.51559i) q^{60} +(6.83979 + 3.94895i) q^{61} +(-13.0311 - 1.86709i) q^{62} +(-0.339418 + 0.195963i) q^{63} +(-5.25658 - 6.03061i) q^{64} +(3.78393 + 14.0369i) q^{65} +(-7.11830 + 9.06076i) q^{66} +(0.239464 + 0.414764i) q^{67} +(5.74685 - 5.49034i) q^{68} +(-13.3836 - 7.72700i) q^{69} +(3.52271 - 4.48400i) q^{70} +(5.62786 + 3.24925i) q^{71} +(-0.644336 - 0.902043i) q^{72} -3.66592i q^{73} +(4.45679 - 1.78676i) q^{74} +(-17.9560 + 10.3669i) q^{75} +(7.10999 - 6.79263i) q^{76} +4.42392i q^{77} +(7.50657 - 5.64282i) q^{78} -7.97702 q^{79} +(13.5851 + 8.69315i) q^{80} +(5.01109 + 8.67946i) q^{81} +(-3.53125 - 8.80817i) q^{82} +0.454650 q^{83} +(-3.53524 - 1.03429i) q^{84} +(-8.01175 + 13.8768i) q^{85} +(2.88780 - 3.67583i) q^{86} +(4.08735 - 7.07949i) q^{87} +(-12.4543 + 1.20767i) q^{88} +(-7.99925 + 4.61837i) q^{89} +(1.75740 + 1.38064i) q^{90} +(0.927918 - 3.48410i) q^{91} +(-3.97247 - 16.3052i) q^{92} +(-8.57179 - 14.8468i) q^{93} +(2.37894 + 0.340855i) q^{94} +(-9.91212 + 17.1683i) q^{95} +(1.94669 - 10.2348i) q^{96} +(10.3103 + 5.95267i) q^{97} +(-1.31265 + 0.526251i) q^{98} -1.73385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 18 q^{6} + 84 q^{9} - 8 q^{10} - 4 q^{12} + 8 q^{16} + 4 q^{17} - 18 q^{22} + 24 q^{23} + 48 q^{24} + 160 q^{25} - 30 q^{26} - 8 q^{30} + 22 q^{36} - 20 q^{38} - 48 q^{39} + 4 q^{40} + 12 q^{41}+ \cdots - 104 q^{95}+O(q^{100}) \) 168 * q - 18 * q^6 + 84 * q^9 - 8 * q^10 - 4 * q^12 + 8 * q^16 + 4 * q^17 - 18 * q^22 + 24 * q^23 + 48 * q^24 + 160 * q^25 - 30 * q^26 - 8 * q^30 + 22 * q^36 - 20 * q^38 - 48 * q^39 + 4 * q^40 + 12 * q^41 - 54 * q^48 + 84 * q^49 - 30 * q^50 - 58 * q^52 + 24 * q^54 - 32 * q^55 - 12 * q^58 + 28 * q^62 - 36 * q^64 + 12 * q^65 - 60 * q^66 - 64 * q^68 - 132 * q^72 + 62 * q^74 - 78 * q^76 + 30 * q^78 - 80 * q^79 + 48 * q^80 - 84 * q^81 - 18 * q^82 - 42 * q^84 - 24 * q^87 + 42 * q^88 + 40 * q^90 - 24 * q^92 + 12 * q^94 - 104 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more