LMFDB - Embedded newform 158.2.e.a.21.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [158,2,Mod(21,158)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("158.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(158, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 158 = 2 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	158.e (of order $13$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.26163635194$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			21.3
Character	$\chi$	$=$	158.21
Dual form			158.2.e.a.143.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.748511 + 0.663123i) q^{2} +(0.298584 - 0.432573i) q^{3} +(0.120537 - 0.992709i) q^{4} +(-0.874632 + 0.215577i) q^{5} +(0.0633559 + 0.521783i) q^{6} +(2.93311 - 4.24935i) q^{7} +(0.568065 + 0.822984i) q^{8} +(0.965847 + 2.54673i) q^{9} +(0.511717 - 0.741350i) q^{10} +(1.81264 + 0.446777i) q^{11} +(-0.393429 - 0.348548i) q^{12} +(0.402979 - 3.31883i) q^{13} +(0.622372 + 5.12570i) q^{14} +(-0.167898 + 0.442710i) q^{15} +(-0.970942 - 0.239316i) q^{16} +(-0.154482 + 1.27227i) q^{17} +(-2.41174 - 1.26578i) q^{18} +(2.26187 + 1.18712i) q^{19} +(0.108580 + 0.894240i) q^{20} +(-0.962374 - 2.53757i) q^{21} +(-1.65305 + 0.867589i) q^{22} -0.623540 q^{23} +0.525615 q^{24} +(-3.70877 + 1.94651i) q^{25} +(1.89916 + 2.75140i) q^{26} +(2.92106 + 0.719976i) q^{27} +(-3.86482 - 3.42393i) q^{28} +(2.28396 - 6.02231i) q^{29} +(-0.167898 - 0.442710i) q^{30} +(-7.05544 + 6.25057i) q^{31} +(0.885456 - 0.464723i) q^{32} +(0.734490 - 0.650701i) q^{33} +(-0.728041 - 1.05475i) q^{34} +(-1.64933 + 4.34893i) q^{35} +(2.64458 - 0.651831i) q^{36} +(-1.71378 - 0.899462i) q^{37} +(-2.48024 + 0.611324i) q^{38} +(-1.31531 - 1.16527i) q^{39} +(-0.674264 - 0.597346i) q^{40} +(-9.75810 + 2.40515i) q^{41} +(2.40307 + 1.26123i) q^{42} +(1.22756 - 0.302567i) q^{43} +(0.662009 - 1.74558i) q^{44} +(-1.39378 - 2.01924i) q^{45} +(0.466726 - 0.413484i) q^{46} +(-6.10696 + 3.20518i) q^{47} +(-0.393429 + 0.348548i) q^{48} +(-6.97157 - 18.3825i) q^{49} +(1.48528 - 3.91636i) q^{50} +(0.504225 + 0.446704i) q^{51} +(-3.24606 - 0.800081i) q^{52} +(3.36640 + 4.87707i) q^{53} +(-2.66388 + 1.39811i) q^{54} -1.68171 q^{55} +5.16334 q^{56} +(1.18887 - 0.623968i) q^{57} +(2.28396 + 6.02231i) q^{58} +(0.809907 + 6.67018i) q^{59} +(0.419244 + 0.220036i) q^{60} +(4.24627 + 2.22862i) q^{61} +(1.13618 - 9.35724i) q^{62} +(13.6549 + 3.36563i) q^{63} +(-0.354605 + 0.935016i) q^{64} +(0.363006 + 2.98963i) q^{65} +(-0.118279 + 0.974113i) q^{66} +(8.50105 + 7.53127i) q^{67} +(1.24437 + 0.306711i) q^{68} +(-0.186179 + 0.269727i) q^{69} +(-1.64933 - 4.34893i) q^{70} +(3.35030 + 4.85375i) q^{71} +(-1.54725 + 2.24158i) q^{72} +(1.08735 + 8.95516i) q^{73} +(1.87924 - 0.463191i) q^{74} +(-0.265369 + 2.18551i) q^{75} +(1.45110 - 2.10228i) q^{76} +(7.21520 - 6.39211i) q^{77} +1.75724 q^{78} +(8.57570 - 2.33611i) q^{79} +0.900808 q^{80} +(-4.93260 + 4.36990i) q^{81} +(5.70913 - 8.27110i) q^{82} +(2.05051 - 16.8874i) q^{83} +(-2.63507 + 0.649487i) q^{84} +(-0.139158 - 1.14607i) q^{85} +(-0.718205 + 1.04050i) q^{86} +(-1.92314 - 2.78614i) q^{87} +(0.662009 + 1.74558i) q^{88} +(-2.37059 + 3.43440i) q^{89} +(2.38226 + 0.587174i) q^{90} +(-12.9209 - 11.4469i) q^{91} +(-0.0751594 + 0.618994i) q^{92} +(0.597191 + 4.91831i) q^{93} +(2.44570 - 6.44878i) q^{94} +(-2.23422 - 0.550685i) q^{95} +(0.0633559 - 0.521783i) q^{96} +(-4.91877 - 2.58157i) q^{97} +(17.4082 + 9.13651i) q^{98} +(0.612918 + 5.04784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 11 q^{5} - 2 q^{6} - 8 q^{7} - 4 q^{8} - 18 q^{9} - 2 q^{10} - 8 q^{11} - 2 q^{12} + 16 q^{13} + 5 q^{14} - 2 q^{15} - 4 q^{16} + 6 q^{17} - 18 q^{18} + 6 q^{19} - 2 q^{20}+ \cdots - 58 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 11 * q^5 - 2 * q^6 - 8 * q^7 - 4 * q^8 - 18 * q^9 - 2 * q^10 - 8 * q^11 - 2 * q^12 + 16 * q^13 + 5 * q^14 - 2 * q^15 - 4 * q^16 + 6 * q^17 - 18 * q^18 + 6 * q^19 - 2 * q^20 - 12 * q^21 + 5 * q^22 - 16 * q^23 + 24 * q^24 - 17 * q^25 + 3 * q^26 + 7 * q^27 - 8 * q^28 - 34 * q^29 - 2 * q^30 - 19 * q^31 - 4 * q^32 + 8 * q^33 - 20 * q^34 + 122 * q^35 - 18 * q^36 - 4 * q^37 - 20 * q^38 - 50 * q^39 - 2 * q^40 - 36 * q^41 + 14 * q^42 - 24 * q^43 + 18 * q^44 - 4 * q^45 + 10 * q^46 - 22 * q^47 - 2 * q^48 - 28 * q^49 - 4 * q^50 + 78 * q^51 - 10 * q^52 - 12 * q^53 + 7 * q^54 - 88 * q^55 + 18 * q^56 - 28 * q^57 - 34 * q^58 - 52 * q^59 + 11 * q^60 - 47 * q^61 + 20 * q^62 + 11 * q^63 - 4 * q^64 - 16 * q^65 + 8 * q^66 + 67 * q^67 - 7 * q^68 - 4 * q^69 + 122 * q^70 - 12 * q^71 - 18 * q^72 + 101 * q^73 - 4 * q^74 - 62 * q^75 + 32 * q^76 + 113 * q^77 - 50 * q^78 - 2 * q^80 + 36 * q^81 + 29 * q^82 + 91 * q^83 + 53 * q^84 - q^85 - 24 * q^86 + 210 * q^87 + 18 * q^88 + 4 * q^89 + 126 * q^90 - 33 * q^91 - 3 * q^92 - 3 * q^93 + 17 * q^94 - 42 * q^95 - 2 * q^96 - 32 * q^97 + 24 * q^98 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/158\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{13}\right)$

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 $

$2$	−0.748511	+	0.663123i	−0.529277	+	0.468899i
$2$	−0.748511	+	0.663123i	−0.529277	+	0.468899i
$3$	0.298584	−	0.432573i	0.172387	−	0.249746i	−0.727261	−	0.686361i	$-0.759207\pi$
$3$	0.298584	−	0.432573i	0.172387	−	0.249746i	0.899649	+	0.436614i	$0.143823\pi$
$4$	0.120537	−	0.992709i	0.0602683	−	0.496354i
$5$	−0.874632	+	0.215577i	−0.391147	+	0.0964092i	−0.429984	−	0.902836i	$-0.641481\pi$
$5$	−0.874632	+	0.215577i	−0.391147	+	0.0964092i	0.0388368	+	0.999246i	$0.487635\pi$
$6$	0.0633559	+	0.521783i	0.0258650	+	0.213017i
$7$	2.93311	−	4.24935i	1.10861	−	1.60610i	0.374275	−	0.927318i	$-0.377892\pi$
$7$	2.93311	−	4.24935i	1.10861	−	1.60610i	0.734337	−	0.678785i	$-0.237493\pi$
$8$	0.568065	+	0.822984i	0.200841	+	0.290969i
$9$	0.965847	+	2.54673i	0.321949	+	0.848910i
$10$	0.511717	−	0.741350i	0.161819	−	0.234436i
$11$	1.81264	+	0.446777i	0.546533	+	0.134708i	0.502908	−	0.864340i	$-0.332263\pi$
$11$	1.81264	+	0.446777i	0.546533	+	0.134708i	0.0436246	+	0.999048i	$0.486109\pi$
$12$	−0.393429	−	0.348548i	−0.113573	−	0.100617i
$13$	0.402979	−	3.31883i	0.111766	−	0.920477i	−0.823691	−	0.567038i	$-0.808089\pi$
$13$	0.402979	−	3.31883i	0.111766	−	0.920477i	0.935458	−	0.353439i	$-0.114988\pi$
$14$	0.622372	+	5.12570i	0.166336	+	1.36990i
$15$	−0.167898	+	0.442710i	−0.0433510	+	0.114307i
$16$	−0.970942	−	0.239316i	−0.242735	−	0.0598289i
$17$	−0.154482	+	1.27227i	−0.0374673	+	0.308571i	0.961912	+	0.273358i	$0.0881342\pi$
$17$	−0.154482	+	1.27227i	−0.0374673	+	0.308571i	−0.999380	+	0.0352136i	$0.988789\pi$
$18$	−2.41174	−	1.26578i	−0.568453	−	0.298347i
$19$	2.26187	+	1.18712i	0.518908	+	0.272344i	0.703779	−	0.710419i	$-0.251494\pi$
$19$	2.26187	+	1.18712i	0.518908	+	0.272344i	−0.184871	+	0.982763i	$0.559187\pi$
$20$	0.108580	+	0.894240i	0.0242793	+	0.199958i
$21$	−0.962374	−	2.53757i	−0.210007	−	0.553743i
$22$	−1.65305	+	0.867589i	−0.352432	+	0.184971i
$23$	−0.623540			−0.130017			−0.0650085	−	0.997885i	$-0.520707\pi$
$23$	−0.623540			−0.130017			−0.0650085	+	0.997885i	$0.520707\pi$
$24$	0.525615			0.107291
$25$	−3.70877	+	1.94651i	−0.741754	+	0.389303i
$26$	1.89916	+	2.75140i	0.372455	+	0.539594i
$27$	2.92106	+	0.719976i	0.562158	+	0.138560i
$28$	−3.86482	−	3.42393i	−0.730382	−	0.647062i
$29$	2.28396	−	6.02231i	0.424121	−	1.11832i	−0.537338	−	0.843367i	$-0.680570\pi$
$29$	2.28396	−	6.02231i	0.424121	−	1.11832i	0.961459	−	0.274948i	$-0.0886608\pi$
$30$	−0.167898	−	0.442710i	−0.0306538	−	0.0808275i
$31$	−7.05544	+	6.25057i	−1.26719	+	1.12264i	−0.280534	+	0.959844i	$0.590512\pi$
$31$	−7.05544	+	6.25057i	−1.26719	+	1.12264i	−0.986660	+	0.162792i	$0.947950\pi$
$32$	0.885456	−	0.464723i	0.156528	−	0.0821522i
$33$	0.734490	−	0.650701i	0.127858	−	0.113273i
$34$	−0.728041	−	1.05475i	−0.124858	−	0.180888i
$35$	−1.64933	+	4.34893i	−0.278788	+	0.735103i
$36$	2.64458	−	0.651831i	0.440764	−	0.108638i
$37$	−1.71378	−	0.899462i	−0.281744	−	0.147871i	0.317932	−	0.948113i	$-0.397012\pi$
$37$	−1.71378	−	0.899462i	−0.281744	−	0.147871i	−0.599676	+	0.800243i	$0.704704\pi$
$38$	−2.48024	+	0.611324i	−0.402348	+	0.0991698i
$39$	−1.31531	−	1.16527i	−0.210619	−	0.186592i
$40$	−0.674264	−	0.597346i	−0.106611	−	0.0944487i
$41$	−9.75810	+	2.40515i	−1.52396	+	0.375622i	−0.910300	−	0.413949i	$-0.864149\pi$
$41$	−9.75810	+	2.40515i	−1.52396	+	0.375622i	−0.613659	+	0.789571i	$0.710303\pi$
$42$	2.40307	+	1.26123i	0.370801	+	0.194612i
$43$	1.22756	−	0.302567i	0.187202	−	0.0461411i	−0.144600	−	0.989490i	$-0.546190\pi$
$43$	1.22756	−	0.302567i	0.187202	−	0.0461411i	0.331802	+	0.943349i	$0.392343\pi$
$44$	0.662009	−	1.74558i	0.0998017	−	0.263155i
$45$	−1.39378	−	2.01924i	−0.207772	−	0.301010i
$46$	0.466726	−	0.413484i	0.0688151	−	0.0609648i
$47$	−6.10696	+	3.20518i	−0.890792	+	0.467524i	−0.847046	−	0.531519i	$-0.821621\pi$
$47$	−6.10696	+	3.20518i	−0.890792	+	0.467524i	−0.0437456	+	0.999043i	$0.513929\pi$
$48$	−0.393429	+	0.348548i	−0.0567866	+	0.0503085i
$49$	−6.97157	−	18.3825i	−0.995939	−	2.62607i
$50$	1.48528	−	3.91636i	0.210050	−	0.553857i
$51$	0.504225	+	0.446704i	0.0706056	+	0.0625511i
$52$	−3.24606	−	0.800081i	−0.450147	−	0.110951i
$53$	3.36640	+	4.87707i	0.462410	+	0.669916i	0.982940	−	0.183927i	$-0.0588810\pi$
$53$	3.36640	+	4.87707i	0.462410	+	0.669916i	−0.520530	+	0.853843i	$0.674266\pi$
$54$	−2.66388	+	1.39811i	−0.362508	+	0.190259i
$55$	−1.68171			−0.226762
$56$	5.16334			0.689981
$57$	1.18887	−	0.623968i	0.157470	−	0.0826466i
$58$	2.28396	+	6.02231i	0.299899	+	0.790769i
$59$	0.809907	+	6.67018i	0.105441	+	0.868384i	0.945440	+	0.325796i	$0.105632\pi$
$59$	0.809907	+	6.67018i	0.105441	+	0.868384i	−0.839999	+	0.542588i	$0.817445\pi$
$60$	0.419244	+	0.220036i	0.0541242	+	0.0284066i
$61$	4.24627	+	2.22862i	0.543679	+	0.285345i	0.714120	−	0.700023i	$-0.246827\pi$
$61$	4.24627	+	2.22862i	0.543679	+	0.285345i	−0.170441	+	0.985368i	$0.554519\pi$
$62$	1.13618	−	9.35724i	0.144294	−	1.18837i
$63$	13.6549	+	3.36563i	1.72035	+	0.424029i
$64$	−0.354605	+	0.935016i	−0.0443256	+	0.116877i
$65$	0.363006	+	2.98963i	0.0450254	+	0.370817i
$66$	−0.118279	+	0.974113i	−0.0145591	+	0.119905i
$67$	8.50105	+	7.53127i	1.03857	+	0.920092i	0.996872	−	0.0790387i	$-0.0251851\pi$
$67$	8.50105	+	7.53127i	1.03857	+	0.920092i	0.0416972	+	0.999130i	$0.486724\pi$
$68$	1.24437	+	0.306711i	0.150903	+	0.0371942i
$69$	−0.186179	+	0.269727i	−0.0224133	+	0.0324713i
$70$	−1.64933	−	4.34893i	−0.197133	−	0.519796i
$71$	3.35030	+	4.85375i	0.397608	+	0.576035i	0.969744	−	0.244124i	$-0.0785005\pi$
$71$	3.35030	+	4.85375i	0.397608	+	0.576035i	−0.572136	+	0.820159i	$0.693885\pi$
$72$	−1.54725	+	2.24158i	−0.182346	+	0.264173i
$73$	1.08735	+	8.95516i	0.127265	+	1.04812i	0.906740	+	0.421689i	$0.138563\pi$
$73$	1.08735	+	8.95516i	0.127265	+	1.04812i	−0.779475	+	0.626433i	$0.784514\pi$
$74$	1.87924	−	0.463191i	0.218457	−	0.0538448i
$75$	−0.265369	+	2.18551i	−0.0306422	+	0.252361i
$76$	1.45110	−	2.10228i	0.166453	−	0.241149i
$77$	7.21520	−	6.39211i	0.822249	−	0.728449i
$78$	1.75724			0.198968
$79$	8.57570	−	2.33611i	0.964841	−	0.262833i
$79$	8.57570	−	2.33611i	0.964841	−	0.262833i
$80$	0.900808			0.100713
$81$	−4.93260	+	4.36990i	−0.548066	+	0.485544i
$82$	5.70913	−	8.27110i	0.630468	−	0.913390i
$83$	2.05051	−	16.8874i	0.225072	−	1.85364i	−0.243101	−	0.970001i	$-0.578165\pi$
$83$	2.05051	−	16.8874i	0.225072	−	1.85364i	0.468174	−	0.883637i	$-0.344912\pi$
$84$	−2.63507	+	0.649487i	−0.287510	+	0.0708648i
$85$	−0.139158	−	1.14607i	−0.0150939	−	0.124309i
$86$	−0.718205	+	1.04050i	−0.0774461	+	0.112200i
$87$	−1.92314	−	2.78614i	−0.206182	−	0.298706i
$88$	0.662009	+	1.74558i	0.0705704	+	0.186079i
$89$	−2.37059	+	3.43440i	−0.251282	+	0.364045i	−0.928243	−	0.371974i	$-0.878681\pi$
$89$	−2.37059	+	3.43440i	−0.251282	+	0.364045i	0.676961	+	0.736019i	$0.263297\pi$
$90$	2.38226	+	0.587174i	0.251112	+	0.0618936i
$91$	−12.9209	−	11.4469i	−1.35448	−	1.19996i
$92$	−0.0751594	+	0.618994i	−0.00783591	+	0.0645346i
$93$	0.597191	+	4.91831i	0.0619258	+	0.510005i
$94$	2.44570	−	6.44878i	0.252255	−	0.665141i
$95$	−2.23422	−	0.550685i	−0.229226	−	0.0564991i
$96$	0.0633559	−	0.521783i	0.00646624	−	0.0532543i
$97$	−4.91877	−	2.58157i	−0.499426	−	0.262119i	0.196147	−	0.980575i	$-0.437157\pi$
$97$	−4.91877	−	2.58157i	−0.499426	−	0.262119i	−0.695573	+	0.718456i	$0.744849\pi$
$98$	17.4082	+	9.13651i	1.75849	+	0.922927i
$99$	0.612918	+	5.04784i	0.0616006	+	0.507327i
$100$	1.48528	+	3.91636i	0.148528	+	0.391636i
$101$	−13.4488	+	7.05845i	−1.33820	+	0.702342i	−0.973480	−	0.228774i	$-0.926528\pi$
$101$	−13.4488	+	7.05845i	−1.33820	+	0.702342i	−0.364722	+	0.931117i	$0.618836\pi$
$102$	−0.673637			−0.0667000
$103$	5.45414			0.537412			0.268706	−	0.963222i	$-0.413404\pi$
$103$	5.45414			0.537412			0.268706	+	0.963222i	$0.413404\pi$
$104$	2.96026	−	1.55366i	0.290277	−	0.152349i
$105$	1.38877	+	2.01198i	0.135530	+	0.196349i
$106$	−5.75388	−	1.41820i	−0.558866	−	0.137748i
$107$	5.43470	+	4.81472i	0.525392	+	0.465457i	0.883638	−	0.468171i	$-0.155087\pi$
$107$	5.43470	+	4.81472i	0.525392	+	0.465457i	−0.358246	+	0.933627i	$0.616625\pi$
$108$	1.06682	−	2.81298i	0.102655	−	0.270679i
$109$	−4.69235	−	12.3727i	−0.449445	−	1.18509i	−0.948011	−	0.318238i	$-0.896909\pi$
$109$	−4.69235	−	12.3727i	−0.449445	−	1.18509i	0.498565	−	0.866852i	$-0.333860\pi$
$110$	1.25878	−	1.11518i	0.120020	−	0.106328i
$111$	−0.900790	+	0.472771i	−0.0854992	+	0.0448735i
$112$	−3.86482	+	3.42393i	−0.365191	+	0.323531i
$113$	3.97111	+	5.75314i	0.373570	+	0.541210i	0.964008	−	0.265873i	$-0.0856603\pi$
$113$	3.97111	+	5.75314i	0.373570	+	0.541210i	−0.590438	+	0.807083i	$0.701045\pi$
$114$	−0.476116	+	1.25542i	−0.0445924	+	0.117580i
$115$	0.545368	−	0.134421i	0.0508558	−	0.0125348i
$116$	−5.70310	−	2.99322i	−0.529520	−	0.277913i
$117$	8.84137	−	2.17920i	0.817385	−	0.201467i
$118$	−5.02937	−	4.45564i	−0.462991	−	0.410175i
$119$	4.95321	+	4.38816i	0.454060	+	0.402262i
$120$	−0.459720	+	0.113311i	−0.0419665	+	0.0103438i
$121$	−6.65394	−	3.49226i	−0.604904	−	0.317478i
$122$	−4.65623	+	1.14766i	−0.421555	+	0.103904i
$123$	−1.87320	+	4.93923i	−0.168901	+	0.445355i
$124$	5.35456	+	7.75742i	0.480854	+	0.696637i
$125$	6.19551	−	5.48874i	0.554143	−	0.490928i
$126$	−12.4526	+	6.53565i	−1.10937	+	0.582242i
$127$	−5.03636	+	4.46182i	−0.446904	+	0.395923i	−0.856337	−	0.516418i	$-0.827265\pi$
$127$	−5.03636	+	4.46182i	−0.446904	+	0.395923i	0.409432	+	0.912340i	$0.365727\pi$
$128$	−0.354605	−	0.935016i	−0.0313429	−	0.0826445i
$129$	0.235648	−	0.621352i	0.0207476	−	0.0547070i
$130$	−2.25420	−	1.99705i	−0.197707	−	0.175153i
$131$	−18.4693	−	4.55226i	−1.61367	−	0.397733i	−0.673702	−	0.739003i	$-0.735297\pi$
$131$	−18.4693	−	4.55226i	−1.61367	−	0.397733i	−0.939965	+	0.341270i	$0.889143\pi$
$132$	−0.557424	−	0.807568i	−0.0485175	−	0.0702897i
$133$	11.6788	−	6.12951i	1.01268	−	0.531496i
$134$	−11.3573			−0.981120
$135$	−2.71006			−0.233245
$136$	−1.13481	+	0.595597i	−0.0973096	+	0.0510720i
$137$	−7.25485	−	19.1295i	−0.619824	−	1.63434i	−0.764321	−	0.644836i	$-0.776926\pi$
$137$	−7.25485	−	19.1295i	−0.619824	−	1.63434i	0.144497	−	0.989505i	$-0.453843\pi$
$138$	−0.0395050	−	0.325353i	−0.00336289	−	0.0276959i
$139$	1.20674	+	0.633347i	0.102354	+	0.0537198i	0.515124	−	0.857116i	$-0.327746\pi$
$139$	1.20674	+	0.633347i	0.102354	+	0.0537198i	−0.412769	+	0.910836i	$0.635438\pi$
$140$	4.11842	+	2.16151i	0.348070	+	0.182681i
$141$	−0.436964	+	3.59872i	−0.0367990	+	0.303067i
$142$	−5.72637	−	1.41142i	−0.480547	−	0.118444i
$143$	2.21323	−	5.83581i	0.185080	−	0.488015i
$144$	−0.328309	−	2.70387i	−0.0273591	−	0.225322i
$145$	−0.699352	+	5.75968i	−0.0580780	+	0.478315i
$146$	−6.75227	−	5.98199i	−0.558822	−	0.495073i
$147$	−10.0334	−	2.47301i	−0.827539	−	0.203970i
$148$	−1.09948	+	1.59287i	−0.0903765	+	0.130933i
$149$	4.94510	+	13.0391i	0.405118	+	1.06821i	0.970015	+	0.243047i	$0.0781468\pi$
$149$	4.94510	+	13.0391i	0.405118	+	1.06821i	−0.564897	+	0.825162i	$0.691084\pi$
$150$	−1.25063	−	1.81185i	−0.102114	−	0.147937i
$151$	4.10148	−	5.94202i	0.333774	−	0.483555i	−0.619781	−	0.784775i	$-0.712779\pi$
$151$	4.10148	−	5.94202i	0.333774	−	0.483555i	0.953555	+	0.301220i	$0.0973939\pi$
$152$	0.307907	+	2.53584i	0.0249745	+	0.205684i
$153$	−3.38934	+	0.835397i	−0.274012	+	0.0675379i
$154$	−1.16190	+	9.56913i	−0.0936288	+	0.771102i
$155$	4.82343	−	6.98795i	0.387427	−	0.561285i
$156$	−1.31531	+	1.16527i	−0.105309	+	0.0932959i
$157$	10.5195			0.839549			0.419775	−	0.907628i	$-0.362109\pi$
$157$	10.5195			0.839549			0.419775	+	0.907628i	$0.362109\pi$
$158$	−4.86988	+	7.43534i	−0.387427	+	0.591524i
$159$	3.11484			0.247023
$160$	−0.674264	+	0.597346i	−0.0533053	+	0.0472244i
$161$	−1.82891	+	2.64964i	−0.144139	+	0.208821i
$162$	0.794322	−	6.54183i	0.0624079	−	0.513975i
$163$	−8.33705	+	2.05490i	−0.653008	+	0.160952i	−0.551883	−	0.833922i	$-0.686090\pi$
$163$	−8.33705	+	2.05490i	−0.653008	+	0.160952i	−0.101125	+	0.994874i	$0.532244\pi$
$164$	1.21141	+	9.97686i	0.0945952	+	0.779062i
$165$	−0.502132	+	0.727463i	−0.0390909	+	0.0566330i
$166$	9.66362	+	14.0002i	0.750042	+	1.08662i
$167$	−0.00494652	−	0.0130429i	−0.000382774	−	0.00100929i	0.934825	−	0.355109i	$-0.115556\pi$
$167$	−0.00494652	−	0.0130429i	−0.000382774	−	0.00100929i	−0.935207	+	0.354100i	$0.884787\pi$
$168$	1.54169	−	2.23352i	0.118944	−	0.172320i
$169$	1.77002	+	0.436271i	0.136156	+	0.0335593i
$170$	0.864148	+	0.765569i	0.0662772	+	0.0587164i
$171$	−0.838655	+	6.90694i	−0.0641335	+	0.528187i
$172$	−0.152395	−	1.25508i	−0.0116200	−	0.0956992i
$173$	0.328881	−	0.867187i	0.0250043	−	0.0659310i	−0.921933	−	0.387350i	$-0.873391\pi$
$173$	0.328881	−	0.867187i	0.0250043	−	0.0659310i	0.946937	+	0.321419i	$0.104160\pi$
$174$	3.28704	+	0.810184i	0.249190	+	0.0614199i
$175$	−2.60683	+	21.4692i	−0.197058	+	1.62292i
$176$	−1.65305	−	0.867589i	−0.124603	−	0.0653970i
$177$	3.12717	+	1.64126i	0.235052	+	0.123365i
$178$	−0.503012	−	4.14267i	−0.0377023	−	0.310507i
$179$	−3.04293	−	8.02354i	−0.227439	−	0.599707i	0.771912	−	0.635729i	$-0.219301\pi$
$179$	−3.04293	−	8.02354i	−0.227439	−	0.599707i	−0.999351	+	0.0360221i	$0.988531\pi$
$180$	−2.17252	+	1.14022i	−0.161930	+	0.0849873i
$181$	−7.45050			−0.553791			−0.276896	−	0.960900i	$-0.589306\pi$
$181$	−7.45050			−0.553791			−0.276896	+	0.960900i	$0.589306\pi$
$182$	17.2621			1.27955
$183$	2.23191	−	1.17139i	0.164987	−	0.0865920i
$184$	−0.354211	−	0.513163i	−0.0261128	−	0.0378309i
$185$	1.69283	+	0.417246i	0.124460	+	0.0306765i
$186$	−3.70845	−	3.28540i	−0.271917	−	0.240897i
$187$	−0.848442	+	2.23716i	−0.0620442	+	0.163597i
$188$	2.44570	+	6.44878i	0.178371	+	0.470325i
$189$	11.6272	−	10.3008i	0.845756	−	0.749275i
$190$	2.03751	−	1.06937i	0.147816	−	0.0775800i
$191$	3.67294	−	3.25394i	0.265765	−	0.235447i	−0.519707	−	0.854345i	$-0.673959\pi$
$191$	3.67294	−	3.25394i	0.265765	−	0.235447i	0.785472	+	0.618897i	$0.212420\pi$
$192$	0.298584	+	0.432573i	0.0215484	+	0.0312183i
$193$	2.32744	−	6.13695i	0.167533	−	0.441748i	−0.824787	−	0.565443i	$-0.808705\pi$
$193$	2.32744	−	6.13695i	0.167533	−	0.441748i	0.992320	+	0.123695i	$0.0394745\pi$
$194$	5.39365	−	1.32942i	0.387242	−	0.0954465i
$195$	1.40162	+	0.735627i	0.100372	+	0.0526793i
$196$	−19.0888	+	4.70497i	−1.36349	+	0.336069i
$197$	−14.2650	−	12.6376i	−1.01634	−	0.900395i	−0.0212861	−	0.999773i	$-0.506776\pi$
$197$	−14.2650	−	12.6376i	−1.01634	−	0.900395i	−0.995050	+	0.0993785i	$0.968315\pi$
$198$	−3.80611	−	3.37192i	−0.270488	−	0.239632i
$199$	7.72101	−	1.90306i	0.547328	−	0.134904i	0.0440509	−	0.999029i	$-0.485974\pi$
$199$	7.72101	−	1.90306i	0.547328	−	0.134904i	0.503277	+	0.864125i	$0.332127\pi$
$200$	−3.70877	−	1.94651i	−0.262250	−	0.137639i
$201$	5.79610	−	1.42861i	0.408825	−	0.100766i
$202$	5.38592	−	14.2015i	0.378952	−	0.999214i
$203$	−18.8918	−	27.3695i	−1.32594	−	1.92096i
$204$	0.504225	−	0.446704i	0.0353028	−	0.0312756i
$205$	8.01625	−	4.20725i	0.559879	−	0.293847i
$206$	−4.08248	+	3.61676i	−0.284440	+	0.251992i
$207$	−0.602245	−	1.58799i	−0.0418589	−	0.110373i
$208$	−1.18552	+	3.12595i	−0.0822007	+	0.216746i
$209$	3.56958	+	3.16238i	0.246913	+	0.218746i
$210$	−2.37369	−	0.585063i	−0.163800	−	0.0403732i
$211$	15.7815	+	22.8635i	1.08644	+	1.57399i	0.783937	+	0.620840i	$0.213209\pi$
$211$	15.7815	+	22.8635i	1.08644	+	1.57399i	0.302508	+	0.953147i	$0.402176\pi$
$212$	5.24728	−	2.75399i	0.360385	−	0.189144i
$213$	3.09995			0.212405
$214$	−7.26068			−0.496330
$215$	−1.00844	+	0.529270i	−0.0687750	+	0.0360959i
$216$	1.06682	+	2.81298i	0.0725880	+	0.191399i
$217$	5.86646	+	48.3147i	0.398241	+	3.27981i
$218$	11.7169	+	6.14950i	0.793568	+	0.416497i
$219$	4.19843	+	2.20351i	0.283703	+	0.148899i
$220$	−0.202708	+	1.66945i	−0.0136666	+	0.112554i
$221$	4.16020	+	1.02540i	0.279845	+	0.0689756i
$222$	0.360746	−	0.951209i	0.0242117	−	0.0638410i
$223$	−2.15538	−	17.7512i	−0.144335	−	1.18871i	−0.867287	−	0.497808i	$-0.834138\pi$
$223$	−2.15538	−	17.7512i	−0.144335	−	1.18871i	0.722952	−	0.690898i	$-0.242785\pi$
$224$	0.622372	−	5.12570i	0.0415840	−	0.342475i
$225$	−8.53935	−	7.56521i	−0.569290	−	0.504347i
$226$	−6.78745	−	1.67296i	−0.451495	−	0.111283i
$227$	10.7292	−	15.5439i	0.712122	−	1.03169i	−0.285194	−	0.958470i	$-0.592058\pi$
$227$	10.7292	−	15.5439i	0.712122	−	1.03169i	0.997316	−	0.0732170i	$-0.0233266\pi$
$228$	−0.476116	−	1.25542i	−0.0315316	−	0.0831419i
$229$	−6.93900	−	10.0529i	−0.458542	−	0.664313i	0.523706	−	0.851899i	$-0.324549\pi$
$229$	−6.93900	−	10.0529i	−0.458542	−	0.664313i	−0.982248	+	0.187586i	$0.939934\pi$
$230$	−0.319076	+	0.462262i	−0.0210393	+	0.0304806i
$231$	−0.610714	−	5.02968i	−0.0401820	−	0.330929i
$232$	6.25371	−	1.54140i	0.410576	−	0.101198i
$233$	−1.95158	+	16.0727i	−0.127852	+	1.05296i	0.777674	+	0.628667i	$0.216399\pi$
$233$	−1.95158	+	16.0727i	−0.127852	+	1.05296i	−0.905526	+	0.424290i	$0.860524\pi$
$234$	−5.17278	+	7.49407i	−0.338155	+	0.489903i
$235$	4.65038	−	4.11988i	0.303357	−	0.268751i
$236$	6.71917			0.437381
$237$	1.55003	−	4.40714i	0.100685	−	0.286274i
$238$	−6.61742			−0.428944
$239$	9.35265	−	8.28573i	0.604973	−	0.535959i	−0.304077	−	0.952648i	$-0.598348\pi$
$239$	9.35265	−	8.28573i	0.604973	−	0.535959i	0.909049	+	0.416689i	$0.136809\pi$
$240$	0.268967	−	0.389665i	0.0173617	−	0.0251528i
$241$	−1.88733	+	15.5436i	−0.121574	+	1.00125i	0.796445	+	0.604711i	$0.206712\pi$
$241$	−1.88733	+	15.5436i	−0.121574	+	1.00125i	−0.918018	+	0.396538i	$0.870212\pi$
$242$	7.29635	−	1.79839i	0.469027	−	0.115605i
$243$	1.50540	+	12.3981i	0.0965718	+	0.795340i
$244$	2.72420	−	3.94668i	0.174399	−	0.252660i
$245$	10.0604	+	14.5750i	0.642736	+	0.931164i
$246$	−1.87320	−	4.93923i	−0.119431	−	0.314914i
$247$	4.85133	−	7.02836i	0.308683	−	0.447204i
$248$	−9.15207	−	2.25578i	−0.581157	−	0.143242i
$249$	−6.69280	−	5.92931i	−0.424139	−	0.375755i
$250$	−0.997696	+	8.21677i	−0.0630998	+	0.519674i
$251$	−2.47908	−	20.4170i	−0.156478	−	1.28871i	−0.833406	−	0.552662i	$-0.813612\pi$
$251$	−2.47908	−	20.4170i	−0.156478	−	1.28871i	0.676928	−	0.736049i	$-0.263311\pi$
$252$	4.98700	−	13.1496i	0.314152	−	0.828350i
$253$	−1.13026	−	0.278583i	−0.0710586	−	0.0175144i
$254$	0.811031	−	6.67944i	0.0508886	−	0.419106i
$255$	−0.537311	−	0.282002i	−0.0336477	−	0.0176597i
$256$	0.885456	+	0.464723i	0.0553410	+	0.0290452i
$257$	−0.860413	−	7.08614i	−0.0536711	−	0.442021i	−0.994630	−	0.103499i	$-0.966996\pi$
$257$	−0.860413	−	7.08614i	−0.0536711	−	0.442021i	0.940958	−	0.338522i	$-0.109927\pi$
$258$	0.235648	+	0.621352i	0.0146708	+	0.0386837i
$259$	−8.84884	+	4.64423i	−0.549840	+	0.288579i
$260$	3.01158			0.186771
$261$	17.5432			1.08589
$262$	16.8431	−	8.83997i	1.04057	−	0.546135i
$263$	−6.17875	−	8.95146i	−0.380998	−	0.551971i	0.584830	−	0.811156i	$-0.301161\pi$
$263$	−6.17875	−	8.95146i	−0.380998	−	0.551971i	−0.965828	+	0.259185i	$0.916546\pi$
$264$	0.952754	+	0.234833i	0.0586380	+	0.0144530i
$265$	−3.99574	−	3.53992i	−0.245457	−	0.217456i
$266$	−4.67709	+	12.3325i	−0.286771	+	0.756153i
$267$	0.777807	+	2.05091i	0.0476010	+	0.125514i
$268$	8.50105	−	7.53127i	0.519284	−	0.460046i
$269$	−11.8656	+	6.22752i	−0.723456	+	0.379699i	−0.785903	−	0.618349i	$-0.787802\pi$
$269$	−11.8656	+	6.22752i	−0.723456	+	0.379699i	0.0624477	+	0.998048i	$0.480109\pi$
$270$	2.02851	−	1.79710i	0.123451	−	0.109368i
$271$	−1.28445	−	1.86085i	−0.0780250	−	0.113039i	0.782028	−	0.623243i	$-0.214185\pi$
$271$	−1.28445	−	1.86085i	−0.0780250	−	0.113039i	−0.860053	+	0.510204i	$0.829570\pi$
$272$	0.454467	−	1.19833i	0.0275561	−	0.0726596i
$273$	−8.80958	+	2.17137i	−0.533180	+	0.131417i
$274$	18.1155	+	9.50776i	1.09440	+	0.574385i
$275$	−7.59234	+	1.87134i	−0.457836	+	0.112846i
$276$	0.245319	+	0.217333i	0.0147664	+	0.0130819i
$277$	21.4027	+	18.9611i	1.28596	+	1.13926i	0.982468	+	0.186430i	$0.0596916\pi$
$277$	21.4027	+	18.9611i	1.28596	+	1.13926i	0.303494	+	0.952833i	$0.401847\pi$
$278$	−1.32325	+	0.326151i	−0.0793630	+	0.0195612i
$279$	−22.7330	−	11.9312i	−1.36099	−	0.714302i
$280$	−4.51603	+	1.11310i	−0.269884	+	0.0665205i
$281$	−0.468150	+	1.23441i	−0.0279275	+	0.0736387i	−0.948255	−	0.317510i	$-0.897153\pi$
$281$	−0.468150	+	1.23441i	−0.0279275	+	0.0736387i	0.920327	+	0.391149i	$0.127922\pi$
$282$	−2.05932	−	2.98344i	−0.122631	−	0.177661i
$283$	4.80245	−	4.25460i	0.285476	−	0.252910i	−0.508216	−	0.861230i	$-0.669695\pi$
$283$	4.80245	−	4.25460i	0.285476	−	0.252910i	0.793692	+	0.608320i	$0.208156\pi$
$284$	5.22220	−	2.74082i	0.309880	−	0.162638i
$285$	−0.905313	+	0.802037i	−0.0536261	+	0.0475086i
$286$	2.21323	+	5.83581i	0.130871	+	0.345079i
$287$	−18.4013	+	48.5201i	−1.08619	+	2.86405i
$288$	2.03874	+	1.80617i	0.120134	+	0.106429i
$289$	14.9112	+	3.67528i	0.877129	+	0.216193i
$290$	−3.29590	−	4.77494i	−0.193542	−	0.280394i
$291$	−2.58538	+	1.35691i	−0.151558	+	0.0795437i
$292$	9.02094			0.527910
$293$	−16.5474			−0.966709			−0.483355	−	0.875425i	$-0.660582\pi$
$293$	−16.5474			−0.966709			−0.483355	+	0.875425i	$0.660582\pi$
$294$	9.15000	−	4.80229i	0.533639	−	0.280075i
$295$	−2.14631	−	5.65936i	−0.124963	−	0.329501i
$296$	−0.233296	−	1.92137i	−0.0135601	−	0.111677i
$297$	4.97317	+	2.61012i	0.288573	+	0.151455i
$298$	−12.3480	−	6.48074i	−0.715301	−	0.375419i
$299$	−0.251273	+	2.06942i	−0.0145315	+	0.119678i
$300$	2.13759	+	0.526869i	0.123414	+	0.0304188i
$301$	2.31487	−	6.10381i	0.133427	−	0.351818i
$302$	0.870286	+	7.16745i	0.0500793	+	0.412440i
$303$	−0.962282	+	7.92511i	−0.0552817	+	0.455286i
$304$	−1.91205	−	1.69392i	−0.109663	−	0.0971532i
$305$	−4.19437	−	1.03382i	−0.240169	−	0.0591963i
$306$	1.98299	−	2.87285i	0.113360	−	0.164230i
$307$	0.826990	+	2.18059i	0.0471988	+	0.124453i	0.956543	−	0.291592i	$-0.0941850\pi$
$307$	0.826990	+	2.18059i	0.0471988	+	0.124453i	−0.909344	+	0.416045i	$0.863416\pi$
$308$	−5.47581	−	7.93308i	−0.312013	−	0.452029i
$309$	1.62852	−	2.35931i	0.0926430	−	0.134217i
$310$	1.02348	+	8.42908i	0.0581295	+	0.478740i
$311$	27.7305	−	6.83496i	1.57245	−	0.387575i	0.645804	−	0.763503i	$-0.276522\pi$
$311$	27.7305	−	6.83496i	1.57245	−	0.387575i	0.926649	+	0.375928i	$0.122676\pi$
$312$	0.211812	−	1.74443i	0.0119915	−	0.0987587i
$313$	5.64909	−	8.18411i	0.319305	−	0.462594i	−0.630160	−	0.776465i	$-0.717011\pi$
$313$	5.64909	−	8.18411i	0.319305	−	0.462594i	0.949465	+	0.313872i	$0.101626\pi$
$314$	−7.87397	+	6.97573i	−0.444354	+	0.393663i
$315$	−12.6686			−0.713792
$316$	−1.28539	−	8.79476i	−0.0723088	−	0.494744i
$317$	2.78713			0.156541			0.0782704	−	0.996932i	$-0.475060\pi$
$317$	2.78713			0.156541			0.0782704	+	0.996932i	$0.475060\pi$
$318$	−2.33149	+	2.06552i	−0.130743	+	0.115829i
$319$	6.83064	−	9.89589i	0.382443	−	0.554064i
$320$	0.108580	−	0.894240i	0.00606983	−	0.0499895i
$321$	3.70543	−	0.913306i	0.206817	−	0.0509758i
$322$	−0.388074	−	3.19608i	−0.0216265	−	0.178110i
$323$	−1.85976	+	2.69432i	−0.103480	+	0.149916i
$324$	3.74348	+	5.42337i	0.207971	+	0.301298i
$325$	4.96559	+	13.0932i	0.275441	+	0.726279i
$326$	4.87772	−	7.06660i	0.270152	−	0.391383i
$327$	−6.75316	−	1.66450i	−0.373450	−	0.0920473i
$328$	−7.52263	−	6.66447i	−0.415368	−	0.367984i
$329$	−4.29248	+	35.3518i	−0.236652	+	1.94901i
$330$	−0.106546	−	0.877489i	−0.00586519	−	0.0483042i
$331$	−12.2598	+	32.3265i	−0.673861	+	1.77683i	−0.0454212	+	0.998968i	$0.514463\pi$
$331$	−12.2598	+	32.3265i	−0.673861	+	1.77683i	−0.628440	+	0.777858i	$0.716306\pi$
$332$	−16.5172	−	4.07111i	−0.906496	−	0.223431i
$333$	0.635436	−	5.23328i	0.0348217	−	0.286782i
$334$	0.0123516	+	0.00648261i	0.000675848	+	0.000354713i
$335$	−9.05887	−	4.75446i	−0.494939	−	0.259764i
$336$	0.327128	+	2.69415i	0.0178463	+	0.146978i
$337$	7.94042	+	20.9372i	0.432542	+	1.14052i	0.957256	+	0.289242i	$0.0934031\pi$
$337$	7.94042	+	20.9372i	0.432542	+	1.14052i	−0.524714	+	0.851279i	$0.675828\pi$
$338$	−1.61418	+	0.847188i	−0.0877999	+	0.0460809i
$339$	3.67436			0.199564
$340$	−1.15449			−0.0626110
$341$	−15.5816	+	8.17786i	−0.843792	+	0.442856i
$342$	−3.95241	−	5.72605i	−0.213722	−	0.309629i
$343$	−63.4690	−	15.6437i	−3.42700	−	0.844680i
$344$	0.946343	+	0.838387i	0.0510234	+	0.0452028i
$345$	0.104691	−	0.276048i	0.00563638	−	0.0148619i
$346$	0.328881	+	0.867187i	0.0176807	+	0.0466202i
$347$	24.4255	−	21.6391i	1.31123	−	1.16165i	0.335651	−	0.941986i	$-0.391044\pi$
$347$	24.4255	−	21.6391i	1.31123	−	1.16165i	0.975576	−	0.219660i	$-0.0704949\pi$
$348$	−2.99764	+	1.57328i	−0.160690	+	0.0843368i
$349$	13.4575	−	11.9223i	0.720364	−	0.638187i	−0.221119	−	0.975247i	$-0.570971\pi$
$349$	13.4575	−	11.9223i	0.720364	−	0.638187i	0.941483	+	0.337060i	$0.109432\pi$
$350$	−12.2855	−	17.7986i	−0.656686	−	0.951374i
$351$	3.56660	−	9.40436i	0.190371	−	0.501967i
$352$	1.81264	−	0.446777i	0.0966143	−	0.0238133i
$353$	−4.69504	−	2.46415i	−0.249892	−	0.131153i	0.335127	−	0.942173i	$-0.391221\pi$
$353$	−4.69504	−	2.46415i	−0.249892	−	0.131153i	−0.585019	+	0.811019i	$0.698913\pi$
$354$	−3.42908	+	0.845192i	−0.182253	+	0.0449214i
$355$	−3.97664	−	3.52300i	−0.211058	−	0.186981i
$356$	3.12361	+	2.76728i	0.165551	+	0.146665i
$357$	3.37715	−	0.832393i	0.178738	−	0.0440549i
$358$	7.59825	+	3.98787i	0.401580	+	0.210766i
$359$	−29.7972	+	7.34435i	−1.57264	+	0.387620i	−0.926709	−	0.375780i	$-0.877375\pi$
$359$	−29.7972	+	7.34435i	−1.57264	+	0.387620i	−0.645926	+	0.763400i	$0.723529\pi$
$360$	0.870043	−	2.29412i	0.0458553	−	0.120910i
$361$	−7.08644	−	10.2665i	−0.372970	−	0.540341i
$362$	5.57678	−	4.94059i	0.293109	−	0.259672i
$363$	−3.49742	+	1.83559i	−0.183567	+	0.0963433i
$364$	−12.9209	+	11.4469i	−0.677238	+	0.599980i
$365$	−2.88157	−	7.59807i	−0.150828	−	0.397701i
$366$	−0.893827	+	2.35683i	−0.0467211	+	0.123193i
$367$	−7.76428	−	6.87855i	−0.405292	−	0.359057i	0.435712	−	0.900086i	$-0.356497\pi$
$367$	−7.76428	−	6.87855i	−0.405292	−	0.359057i	−0.841004	+	0.541029i	$0.818035\pi$
$368$	0.605421	+	0.149223i	0.0315598	+	0.00777878i
$369$	−15.5501	−	22.5282i	−0.809507	−	1.17277i
$370$	−1.54379	+	0.810243i	−0.0802578	+	0.0421225i
$371$	30.5984			1.58859
$372$	4.95444			0.256876
$373$	18.4921	−	9.70543i	0.957487	−	0.502528i	0.0878036	−	0.996138i	$-0.472015\pi$
$373$	18.4921	−	9.70543i	0.957487	−	0.502528i	0.869683	+	0.493610i	$0.164323\pi$
$374$	−0.848442	−	2.23716i	−0.0438719	−	0.115681i
$375$	−0.524404	−	4.31886i	−0.0270801	−	0.223025i
$376$	−6.10696	−	3.20518i	−0.314943	−	0.165295i
$377$	−19.0666	−	10.0069i	−0.981981	−	0.515384i
$378$	−1.87239	+	15.4206i	−0.0963056	+	0.793148i
$379$	−2.96757	−	0.731441i	−0.152434	−	0.0375716i	0.162360	−	0.986732i	$-0.448089\pi$
$379$	−2.96757	−	0.731441i	−0.152434	−	0.0375716i	−0.314794	+	0.949160i	$0.601935\pi$
$380$	−0.815976	+	2.15155i	−0.0418587	+	0.110372i
$381$	0.426291	+	3.51082i	0.0218395	+	0.179865i
$382$	−0.591474	+	4.87123i	−0.0302624	+	0.249234i
$383$	14.3028	+	12.6712i	0.730841	+	0.647468i	0.944150	−	0.329516i	$-0.106886\pi$
$383$	14.3028	+	12.6712i	0.730841	+	0.647468i	−0.213309	+	0.976985i	$0.568424\pi$
$384$	−0.510342	−	0.125788i	−0.0260433	−	0.00641909i
$385$	−4.93265	+	7.14618i	−0.251391	+	0.364203i
$386$	2.32744	+	6.13695i	0.118464	+	0.312363i
$387$	1.95620	+	2.83404i	0.0994390	+	0.144062i
$388$	−3.15564	+	4.57174i	−0.160203	+	0.232095i
$389$	−3.25393	−	26.7985i	−0.164981	−	1.35874i	−0.806319	−	0.591481i	$-0.798543\pi$
$389$	−3.25393	−	26.7985i	−0.164981	−	1.35874i	0.641338	−	0.767259i	$-0.278380\pi$
$390$	−1.53694	+	0.378821i	−0.0778259	+	0.0191824i
$391$	0.0963256	−	0.793313i	0.00487139	−	0.0401195i
$392$	11.1682	−	16.1800i	0.564080	−	0.817211i
$393$	−7.48381	+	6.63007i	−0.377508	+	0.334443i
$394$	19.0578			0.960117
$395$	−6.99697	+	3.89196i	−0.352056	+	0.195826i
$396$	5.08491			0.255526
$397$	−19.9654	+	17.6878i	−1.00204	+	0.887726i	−0.993681	−	0.112239i	$-0.964198\pi$
$397$	−19.9654	+	17.6878i	−1.00204	+	0.887726i	−0.00835422	+	0.999965i	$0.502659\pi$
$398$	−4.51730	+	6.54444i	−0.226432	+	0.328043i
$399$	0.835639	−	6.88210i	0.0418343	−	0.344536i
$400$	4.06683	−	1.00238i	0.203342	−	0.0501192i
$401$	3.94100	+	32.4571i	0.196804	+	1.62083i	0.671725	+	0.740800i	$0.265554\pi$
$401$	3.94100	+	32.4571i	0.196804	+	1.62083i	−0.474921	+	0.880028i	$0.657523\pi$
$402$	−3.39110	+	4.91286i	−0.169133	+	0.245031i
$403$	17.9014	+	25.9346i	0.891732	+	1.29190i
$404$	5.38592	+	14.2015i	0.267960	+	0.706551i
$405$	3.37216	−	4.88541i	0.167564	−	0.242758i
$406$	32.2900	+	7.95878i	1.60253	+	0.394987i
$407$	−2.70462	−	2.39608i	−0.134063	−	0.118769i
$408$	−0.0811980	+	0.668726i	−0.00401990	+	0.0331069i
$409$	−2.59966	−	21.4101i	−0.128545	−	1.05866i	−0.904082	−	0.427360i	$-0.859444\pi$
$409$	−2.59966	−	21.4101i	−0.128545	−	1.05866i	0.775537	−	0.631302i	$-0.217479\pi$
$410$	−3.21032	+	8.46493i	−0.158547	+	0.418053i
$411$	−10.4411	−	2.57349i	−0.515020	−	0.126941i
$412$	0.657423	−	5.41437i	0.0323889	−	0.266747i
$413$	30.7195	+	16.1228i	1.51161	+	0.793352i
$414$	1.50382	+	0.789264i	0.0739086	+	0.0387902i
$415$	1.84711	+	15.2123i	0.0906712	+	0.746744i
$416$	−1.18552	−	3.12595i	−0.0581247	−	0.153262i
$417$	0.634282	−	0.332897i	0.0310609	−	0.0163020i
$418$	−4.76892			−0.233255
$419$	32.1692			1.57157			0.785784	−	0.618501i	$-0.212260\pi$
$419$	32.1692			1.57157			0.785784	+	0.618501i	$0.212260\pi$
$420$	2.16470	−	1.13612i	0.105627	−	0.0554372i
$421$	−7.33110	−	10.6209i	−0.357296	−	0.517633i	0.602579	−	0.798059i	$-0.294140\pi$
$421$	−7.33110	−	10.6209i	−0.357296	−	0.517633i	−0.959876	+	0.280426i	$0.909524\pi$
$422$	−26.9739	−	6.64848i	−1.31307	−	0.323643i
$423$	−14.0611	−	12.4571i	−0.683675	−	0.605683i
$424$	−2.10142	+	5.54098i	−0.102054	+	0.269094i
$425$	−1.90356	−	5.01927i	−0.0923361	−	0.243470i
$426$	−2.32035	+	2.05565i	−0.112421	+	0.0995964i
$427$	21.9250	−	11.5071i	1.06102	−	0.556868i
$428$	5.43470	−	4.81472i	0.262696	−	0.232728i
$429$	−1.86358	−	2.69986i	−0.0899745	−	0.130351i
$430$	0.403857	−	1.06488i	0.0194757	−	0.0513532i
$431$	−1.60240	+	0.394957i	−0.0771850	+	0.0190244i	−0.277719	−	0.960662i	$-0.589578\pi$
$431$	−1.60240	+	0.394957i	−0.0771850	+	0.0190244i	0.200534	+	0.979687i	$0.435732\pi$
$432$	−2.66388	−	1.39811i	−0.128166	−	0.0672666i
$433$	−12.0372	+	2.96690i	−0.578470	+	0.142580i	−0.517686	−	0.855571i	$-0.673206\pi$
$433$	−12.0372	+	2.96690i	−0.578470	+	0.142580i	−0.0607845	+	0.998151i	$0.519360\pi$
$434$	−36.4297	−	32.2739i	−1.74868	−	1.54919i
$435$	2.28267	+	2.02227i	0.109446	+	0.0969603i
$436$	−12.8481	+	3.16677i	−0.615312	+	0.151661i
$437$	−1.41037	−	0.740217i	−0.0674669	−	0.0354094i
$438$	−4.60376	+	1.13473i	−0.219976	+	0.0542193i
$439$	−9.79704	+	25.8327i	−0.467587	+	1.23293i	0.469221	+	0.883081i	$0.344535\pi$
$439$	−9.79704	+	25.8327i	−0.467587	+	1.23293i	−0.936808	+	0.349845i	$0.886234\pi$
$440$	−0.955322	−	1.38402i	−0.0455432	−	0.0659807i
$441$	40.0818	−	35.5094i	1.90866	−	1.69092i
$442$	−3.79392	+	1.99120i	−0.180458	+	0.0947118i
$443$	16.7483	−	14.8377i	0.795736	−	0.704961i	−0.163816	−	0.986491i	$-0.552380\pi$
$443$	16.7483	−	14.8377i	0.795736	−	0.704961i	0.959552	+	0.281530i	$0.0908419\pi$
$444$	0.360746	+	0.951209i	0.0171202	+	0.0451424i
$445$	1.33302	−	3.51488i	0.0631911	−	0.166621i
$446$	13.3845	+	11.8577i	0.633776	+	0.561476i
$447$	7.11691	+	1.75416i	0.336618	+	0.0829689i
$448$	2.93311	+	4.24935i	0.138577	+	0.200763i
$449$	−14.6731	+	7.70106i	−0.692468	+	0.363435i	−0.773956	−	0.633239i	$-0.781725\pi$
$449$	−14.6731	+	7.70106i	−0.692468	+	0.363435i	0.0814881	+	0.996674i	$0.474033\pi$
$450$	11.4085			0.537800
$451$	−18.7625			−0.883493
$452$	6.18986	−	3.24869i	0.291146	−	0.152805i
$453$	−1.34572	−	3.54838i	−0.0632276	−	0.166717i
$454$	2.27661	+	18.7496i	0.106847	+	0.879961i
$455$	13.7687	+	7.22637i	0.645487	+	0.338777i
$456$	1.18887	+	0.623968i	0.0556741	+	0.0292200i
$457$	2.34636	−	19.3240i	0.109758	−	0.903940i	−0.828973	−	0.559289i	$-0.811074\pi$
$457$	2.34636	−	19.3240i	0.109758	−	0.903940i	0.938731	−	0.344651i	$-0.112003\pi$
$458$	11.8602	+	2.92328i	0.554191	+	0.136596i
$459$	−1.36726	+	3.60516i	−0.0638181	+	0.168274i
$460$	−0.0677042	−	0.557595i	−0.00315673	−	0.0259980i
$461$	2.43265	−	20.0347i	0.113300	−	0.933107i	−0.819591	−	0.572949i	$-0.805799\pi$
$461$	2.43265	−	20.0347i	0.113300	−	0.933107i	0.932891	−	0.360159i	$-0.117277\pi$
$462$	3.79242	+	3.35979i	0.176439	+	0.156312i
$463$	−0.165930	−	0.0408982i	−0.00771144	−	0.00190070i	0.235458	−	0.971885i	$-0.424341\pi$
$463$	−0.165930	−	0.0408982i	−0.00771144	−	0.00190070i	−0.243169	+	0.969984i	$0.578187\pi$
$464$	−3.65883	+	5.30073i	−0.169857	+	0.246080i
$465$	−1.58260	−	4.17297i	−0.0733913	−	0.193517i
$466$	−9.19739	−	13.3247i	−0.426061	−	0.617256i
$467$	−0.885273	+	1.28254i	−0.0409655	+	0.0593488i	−0.842931	−	0.538021i	$-0.819172\pi$
$467$	−0.885273	+	1.28254i	−0.0409655	+	0.0593488i	0.801966	+	0.597370i	$0.203788\pi$
$468$	−1.09760	−	9.03958i	−0.0507368	−	0.417855i
$469$	56.9375	−	14.0338i	2.62913	−	0.648023i
$470$	−0.748876	+	6.16755i	−0.0345431	+	0.284488i
$471$	3.14096	−	4.55046i	0.144728	−	0.209674i
$472$	−5.02937	+	4.45564i	−0.231496	+	0.205087i
$473$	2.36032			0.108527
$474$	1.76226	+	4.32665i	0.0809434	+	0.198730i
$475$	−10.6995			−0.490927
$476$	4.95321	−	4.38816i	0.227030	−	0.201131i
$477$	−9.16915	+	13.2838i	−0.419826	+	0.608224i
$478$	−1.50611	+	12.4039i	−0.0688877	+	0.567342i
$479$	32.2240	−	7.94250i	1.47235	−	0.362902i	0.580139	−	0.814518i	$-0.302998\pi$
$479$	32.2240	−	7.94250i	1.47235	−	0.362902i	0.892213	+	0.451616i	$0.149152\pi$
$480$	0.0570715	+	0.470026i	0.00260495	+	0.0214537i
$481$	−3.67578	+	5.32528i	−0.167601	+	0.242812i
$482$	−8.89460	−	12.8861i	−0.405138	−	0.586944i
$483$	0.600079	+	1.58228i	0.0273045	+	0.0719961i
$484$	−4.26884	+	6.18448i	−0.194038	+	0.281113i
$485$	4.85865	+	1.19755i	0.220620	+	0.0543779i
$486$	−9.34829	−	8.28186i	−0.424047	−	0.375673i
$487$	1.67648	−	13.8070i	0.0759683	−	0.625656i	−0.904146	−	0.427223i	$-0.859492\pi$
$487$	1.67648	−	13.8070i	0.0759683	−	0.625656i	0.980115	−	0.198432i	$-0.0635851\pi$
$488$	0.578043	+	4.76061i	0.0261668	+	0.215503i
$489$	−1.60041	+	4.21994i	−0.0723732	+	0.190832i
$490$	−17.1954	−	4.23828i	−0.776807	−	0.191466i
$491$	−2.64882	+	21.8150i	−0.119539	+	0.984496i	0.802299	+	0.596922i	$0.203610\pi$
$491$	−2.64882	+	21.8150i	−0.119539	+	0.984496i	−0.921839	+	0.387574i	$0.873313\pi$
$492$	4.67743	+	2.45490i	0.210875	+	0.110676i
$493$	7.30919	+	3.83616i	0.329189	+	0.172772i
$494$	1.02940	+	8.47783i	0.0463147	+	0.381436i
$495$	−1.62428	−	4.28287i	−0.0730058	−	0.192501i
$496$	8.34628	−	4.38047i	0.374759	−	0.196689i
$497$	30.4521			1.36596
$498$	8.94149			0.400678
$499$	32.5612	−	17.0895i	1.45764	−	0.765029i	0.464907	−	0.885359i	$-0.346088\pi$
$499$	32.5612	−	17.0895i	1.45764	−	0.765029i	0.992734	+	0.120330i	$0.0383954\pi$
$500$	−4.70194	−	6.81193i	−0.210277	−	0.304639i
$501$	−0.00711896	−	0.00175467i	−0.000318052	−	7.83927e-5i
$502$	15.3946	+	13.6384i	0.687095	+	0.608713i
$503$	4.54326	−	11.9796i	0.202574	−	0.534144i	−0.794776	−	0.606903i	$-0.792411\pi$
$503$	4.54326	−	11.9796i	0.202574	−	0.534144i	0.997349	+	0.0727599i	$0.0231807\pi$
$504$	4.98700	+	13.1496i	0.222139	+	0.585732i
$505$	10.2411	−	9.07280i	0.455722	−	0.403734i
$506$	1.03074	−	0.540976i	0.0458222	−	0.0240493i
$507$	0.717219	−	0.635400i	0.0318528	−	0.0282191i
$508$	3.82223	+	5.53745i	0.169584	+	0.245685i
$509$	−3.78692	+	9.98530i	−0.167852	+	0.442591i	−0.992378	−	0.123235i	$-0.960673\pi$
$509$	−3.78692	+	9.98530i	−0.167852	+	0.442591i	0.824525	+	0.565825i	$0.191442\pi$
$510$	0.589185	−	0.145221i	0.0260895	−	0.00643050i
$511$	41.2429	+	21.6460i	1.82448	+	0.957561i
$512$	−0.970942	+	0.239316i	−0.0429100	+	0.0105764i
$513$	5.75235	+	5.09614i	0.253972	+	0.225000i
$514$	5.34301	+	4.73349i	0.235670	+	0.208785i
$515$	−4.77036	+	1.17579i	−0.210207	+	0.0518114i
$516$	−0.588418	−	0.308825i	−0.0259037	−	0.0135953i
$517$	−12.5018	+	3.08141i	−0.549827	+	0.135520i
$518$	3.54376	−	9.34413i	0.155704	−	0.410557i
$519$	−0.276923	−	0.401193i	−0.0121556	−	0.0176104i
$520$	−2.25420	+	1.99705i	−0.0988533	+	0.0875764i
$521$	−35.9437	+	18.8647i	−1.57472	+	0.826479i	−0.574757	+	0.818324i	$0.694903\pi$
$521$	−35.9437	+	18.8647i	−1.57472	+	0.826479i	−0.999967	+	0.00815426i	$0.997404\pi$
$522$	−13.1312	+	11.6333i	−0.574739	+	0.509174i
$523$	−4.98619	−	13.1475i	−0.218031	−	0.574900i	0.780719	−	0.624882i	$-0.214853\pi$
$523$	−4.98619	−	13.1475i	−0.218031	−	0.574900i	−0.998750	+	0.0499816i	$0.984084\pi$
$524$	−6.74530	+	17.7859i	−0.294670	+	0.776980i
$525$	8.50864	+	7.53800i	0.371348	+	0.328985i
$526$	10.5608	+	2.60300i	0.460472	+	0.113496i
$527$	−6.86249	−	9.94204i	−0.298935	−	0.433082i
$528$	−0.868870	+	0.456018i	−0.0378127	+	0.0198456i
$529$	−22.6112			−0.983096
$530$	5.33826			0.231879
$531$	−16.2049	+	8.50500i	−0.703233	+	0.369085i
$532$	−4.67709	−	12.3325i	−0.202778	−	0.534681i
$533$	4.04999	+	33.3547i	0.175425	+	1.44475i
$534$	−1.94220	−	1.01935i	−0.0840472	−	0.0441114i
$535$	−5.79131	−	3.03951i	−0.250380	−	0.131410i
$536$	−1.36897	+	11.2745i	−0.0591305	+	0.486983i
$537$	−4.37933	−	1.07941i	−0.188982	−	0.0465799i
$538$	4.75188	−	12.5297i	0.204868	−	0.540193i
$539$	−4.42410	−	36.4357i	−0.190559	−	1.56940i
$540$	−0.326662	+	2.69030i	−0.0140573	+	0.115772i
$541$	−21.9350	−	19.4328i	−0.943061	−	0.835479i	0.0434695	−	0.999055i	$-0.486159\pi$
$541$	−21.9350	−	19.4328i	−0.943061	−	0.835479i	−0.986531	+	0.163575i	$0.947697\pi$
$542$	2.19540	+	0.541118i	0.0943006	+	0.0232430i
$543$	−2.22460	+	3.22288i	−0.0954666	+	0.138307i
$544$	0.454467	+	1.19833i	0.0194851	+	0.0513781i
$545$	6.77136	+	9.81000i	0.290053	+	0.420214i
$546$	5.15418	−	7.46712i	0.220579	−	0.319563i
$547$	2.41853	+	19.9184i	0.103409	+	0.851649i	0.948445	+	0.316940i	$0.102656\pi$
$547$	2.41853	+	19.9184i	0.103409	+	0.851649i	−0.845037	+	0.534709i	$0.820421\pi$
$548$	−19.8645	+	4.89615i	−0.848568	+	0.209153i
$549$	−1.57443	+	12.9666i	−0.0671951	+	0.553402i
$550$	4.44202	−	6.43538i	0.189408	−	0.274405i
$551$	12.3152	−	10.9103i	0.524646	−	0.464796i
$552$	−0.327742			−0.0139496
$553$	15.2266	−	43.2932i	0.647499	−	1.84101i
$554$	−28.5937			−1.21483
$555$	0.685941	−	0.607691i	0.0291166	−	0.0257951i
$556$	0.774185	−	1.12160i	0.0328328	−	0.0475665i
$557$	−2.79515	+	23.0201i	−0.118434	+	0.975394i	0.805435	+	0.592685i	$0.201932\pi$
$557$	−2.79515	+	23.0201i	−0.118434	+	0.975394i	−0.923869	+	0.382709i	$0.874991\pi$
$558$	24.9278	−	6.14414i	1.05528	−	0.260102i
$559$	−0.509486	−	4.19600i	−0.0215490	−	0.177472i
$560$	2.64217	−	3.82785i	0.111652	−	0.161756i
$561$	0.714403	+	1.03499i	0.0301621	+	0.0436974i
$562$	−0.468150	−	1.23441i	−0.0197477	−	0.0520705i
$563$	−0.178213	+	0.258187i	−0.00751080	+	0.0108813i	−0.826721	−	0.562612i	$-0.809797\pi$
$563$	−0.178213	+	0.258187i	−0.00751080	+	0.0108813i	0.819210	+	0.573493i	$0.194412\pi$
$564$	3.51981	+	0.867556i	0.148211	+	0.0365307i
$565$	−4.71350	−	4.17580i	−0.198299	−	0.175677i
$566$	−0.773364	+	6.36923i	−0.0325069	+	0.267719i
$567$	4.10136	+	33.7777i	0.172241	+	1.41853i
$568$	−2.09137	+	5.51449i	−0.0877520	+	0.231383i
$569$	5.80574	+	1.43099i	0.243389	+	0.0599900i	0.359123	−	0.933290i	$-0.383076\pi$
$569$	5.80574	+	1.43099i	0.243389	+	0.0599900i	−0.115734	+	0.993280i	$0.536922\pi$
$570$	0.145787	−	1.20067i	0.00610636	−	0.0502904i
$571$	−22.9058	−	12.0219i	−0.958577	−	0.503100i	−0.0885323	−	0.996073i	$-0.528218\pi$
$571$	−22.9058	−	12.0219i	−0.958577	−	0.503100i	−0.870044	+	0.492974i	$0.835910\pi$
$572$	−5.52649	−	2.90052i	−0.231074	−	0.121277i
$573$	−0.310888	−	2.56039i	−0.0129875	−	0.106962i
$574$	−18.4013	−	48.5201i	−0.768054	−	2.02519i
$575$	2.31257	−	1.21373i	0.0964408	−	0.0506160i
$576$	−2.72373			−0.113489
$577$	−19.0451			−0.792857			−0.396428	−	0.918066i	$-0.629750\pi$
$577$	−19.0451			−0.792857			−0.396428	+	0.918066i	$0.629750\pi$
$578$	−13.5984	+	7.13697i	−0.565617	+	0.296859i
$579$	−1.95975	−	2.83918i	−0.0814443	−	0.117992i
$580$	5.63339	+	1.38851i	0.233914	+	0.0576546i
$581$	−65.7462	−	58.2461i	−2.72761	−	2.41645i
$582$	1.03539	−	2.73009i	0.0429182	−	0.113166i
$583$	3.92312	+	10.3444i	0.162479	+	0.428422i
$584$	−6.75227	+	5.98199i	−0.279411	+	0.247536i
$585$	−7.26316	+	3.81200i	−0.300295	+	0.157607i
$586$	12.3859	−	10.9730i	0.511657	−	0.453289i
$587$	−10.1555	−	14.7127i	−0.419161	−	0.607259i	0.555345	−	0.831620i	$-0.312586\pi$
$587$	−10.1555	−	14.7127i	−0.419161	−	0.607259i	−0.974506	+	0.224360i	$0.927971\pi$
$588$	−3.66436	+	9.66214i	−0.151116	+	0.398460i
$589$	−23.3787	+	5.76232i	−0.963301	+	0.237432i
$590$	5.35939	+	2.81282i	0.220643	+	0.115802i
$591$	−9.72599	+	2.39724i	−0.400074	+	0.0986093i
$592$	1.44873	+	1.28346i	0.0595423	+	0.0527499i
$593$	12.9977	+	11.5150i	0.533752	+	0.472863i	0.886418	−	0.462886i	$-0.153186\pi$
$593$	12.9977	+	11.5150i	0.533752	+	0.472863i	−0.352666	+	0.935749i	$0.614725\pi$
$594$	−5.45331	+	1.34412i	−0.223752	+	0.0551499i
$595$	−5.27823	−	2.77023i	−0.216386	−	0.113568i
$596$	13.5401	−	3.33735i	0.554626	−	0.136703i
$597$	1.48216	−	3.90812i	0.0606606	−	0.159949i
$598$	−1.18420	−	1.71561i	−0.0484255	−	0.0701565i
$599$	0.0227053	−	0.0201151i	0.000927714	−	0.000821883i	−0.662659	−	0.748922i	$-0.730572\pi$
$599$	0.0227053	−	0.0201151i	0.000927714	−	0.000821883i	0.663586	+	0.748100i	$0.269034\pi$
$600$	−1.94939	+	1.02312i	−0.0795834	+	0.0417686i
$601$	−6.34623	+	5.62227i	−0.258868	+	0.229337i	−0.782567	−	0.622566i	$-0.786090\pi$
$601$	−6.34623	+	5.62227i	−0.258868	+	0.229337i	0.523699	+	0.851903i	$0.324552\pi$
$602$	2.31487	+	6.10381i	0.0943470	+	0.248773i
$603$	−10.9694	+	28.9239i	−0.446709	+	1.17787i
$604$	−5.40432	−	4.78781i	−0.219899	−	0.194813i
$605$	6.57261	+	1.62000i	0.267214	+	0.0658624i
$606$	−4.53504	−	6.57014i	−0.184223	−	0.266894i
$607$	−16.1163	+	8.45850i	−0.654141	+	0.343320i	−0.758928	−	0.651175i	$-0.774276\pi$
$607$	−16.1163	+	8.45850i	−0.654141	+	0.343320i	0.104786	+	0.994495i	$0.466584\pi$
$608$	2.55447			0.103597
$609$	−17.4801			−0.708328
$610$	3.82508	−	2.00755i	0.154873	−	0.0812835i
$611$	8.17647	+	21.5596i	0.330784	+	0.872207i
$612$	0.420766	+	3.46532i	0.0170085	+	0.140077i
$613$	18.2170	+	9.56104i	0.735779	+	0.386167i	0.790603	−	0.612329i	$-0.209767\pi$
$613$	18.2170	+	9.56104i	0.735779	+	0.386167i	−0.0548235	+	0.998496i	$0.517460\pi$
$614$	−2.06501	−	1.08380i	−0.0833371	−	0.0437387i
$615$	0.573577	−	4.72383i	0.0231288	−	0.190483i
$616$	9.35931	+	2.30686i	0.377097	+	0.0929461i
$617$	13.1364	−	34.6377i	0.528850	−	1.39446i	−0.358571	−	0.933502i	$-0.616736\pi$
$617$	13.1364	−	34.6377i	0.528850	−	1.39446i	0.887421	−	0.460960i	$-0.152495\pi$
$618$	0.345552	+	2.84588i	0.0139001	+	0.114478i
$619$	−0.327895	+	2.70045i	−0.0131792	+	0.108540i	−0.997814	−	0.0660862i	$-0.978949\pi$
$619$	−0.327895	+	2.70045i	−0.0131792	+	0.108540i	0.984635	+	0.174627i	$0.0558718\pi$
$620$	−6.35560	−	5.63057i	−0.255247	−	0.226129i
$621$	−1.82140	−	0.448934i	−0.0730902	−	0.0180151i
$622$	−16.2242	+	23.5048i	−0.650530	+	0.942456i
$623$	7.64073	+	20.1469i	0.306119	+	0.807170i
$624$	0.998226	+	1.44618i	0.0399610	+	0.0578935i
$625$	7.66128	−	11.0993i	0.306451	−	0.443971i
$626$	1.19867	+	9.87194i	0.0479085	+	0.394562i
$627$	2.43378	−	0.599872i	0.0971957	−	0.0239566i
$628$	1.26799	−	10.4428i	0.0505982	−	0.416714i
$629$	1.40911	−	2.04145i	0.0561848	−	0.0813978i
$630$	9.48255	−	8.40080i	0.377794	−	0.334696i
$631$	15.7651			0.627599			0.313799	−	0.949489i	$-0.398398\pi$
$631$	15.7651			0.627599			0.313799	+	0.949489i	$0.398398\pi$
$632$	6.79413	+	5.73060i	0.270256	+	0.227951i
$633$	14.6022			0.580387
$634$	−2.08620	+	1.84821i	−0.0828534	+	0.0734017i
$635$	3.44309	−	4.98818i	0.136635	−	0.197950i
$636$	0.375452	−	3.09213i	0.0148876	−	0.122611i
$637$	−63.8178	+	15.7297i	−2.52855	+	0.623232i
$638$	1.44938	+	11.9367i	0.0573816	+	0.472580i
$639$	−9.12532	+	13.2203i	−0.360992	+	0.522987i
$640$	0.511717	+	0.741350i	0.0202274	+	0.0293045i
$641$	6.48269	+	17.0935i	0.256051	+	0.675151i	0.999976	+	0.00688827i	$0.00219262\pi$
$641$	6.48269	+	17.0935i	0.256051	+	0.675151i	−0.743925	+	0.668263i	$0.767038\pi$
$642$	−2.16792	+	3.14077i	−0.0855610	+	0.123956i
$643$	−14.7345	−	3.63172i	−0.581071	−	0.143221i	−0.0621850	−	0.998065i	$-0.519807\pi$
$643$	−14.7345	−	3.63172i	−0.581071	−	0.143221i	−0.518886	+	0.854844i	$0.673653\pi$
$644$	2.40987	+	2.13496i	0.0949621	+	0.0841291i
$645$	−0.0721556	+	0.594255i	−0.00284113	+	0.0233988i
$646$	−0.394619	−	3.24998i	−0.0155261	−	0.127869i
$647$	7.82689	−	20.6378i	0.307707	−	0.811356i	−0.688572	−	0.725168i	$-0.741762\pi$
$647$	7.82689	−	20.6378i	0.307707	−	0.811356i	0.996279	−	0.0861880i	$-0.0274686\pi$
$648$	−6.39839	−	1.57706i	−0.251353	−	0.0619528i
$649$	−1.51201	+	12.4525i	−0.0593516	+	0.488804i
$650$	−12.3992	−	6.50759i	−0.486336	−	0.255249i
$651$	22.6512	+	11.8883i	0.887772	+	0.465939i
$652$	1.03500	+	8.52396i	0.0405336	+	0.333824i
$653$	−2.08871	−	5.50748i	−0.0817376	−	0.215524i	0.887917	−	0.460004i	$-0.152152\pi$
$653$	−2.08871	−	5.50748i	−0.0817376	−	0.215524i	−0.969654	+	0.244480i	$0.921383\pi$
$654$	6.15858	−	3.23227i	0.240820	−	0.126392i
$655$	17.1352			0.669527
$656$	10.0501			0.392392
$657$	−21.7562	+	11.4185i	−0.848789	+	0.445479i
$658$	−20.2296	−	29.3076i	−0.788631	−	1.14253i
$659$	−2.83774	−	0.699440i	−0.110543	−	0.0272463i	0.183656	−	0.982991i	$-0.441207\pi$
$659$	−2.83774	−	0.699440i	−0.110543	−	0.0272463i	−0.294199	+	0.955744i	$0.595053\pi$
$660$	0.661634	+	0.586157i	0.0257541	+	0.0228161i
$661$	13.5811	−	35.8105i	0.528244	−	1.39287i	−0.359766	−	0.933043i	$-0.617143\pi$
$661$	13.5811	−	35.8105i	0.528244	−	1.39287i	0.888010	−	0.459823i	$-0.152087\pi$
$662$	−12.2598	−	32.3265i	−0.476492	−	1.25641i
$663$	1.68573	−	1.49342i	0.0654682	−	0.0579997i
$664$	15.0629	−	7.90563i	0.584554	−	0.306798i
$665$	−8.89327	+	7.87875i	−0.344866	+	0.305525i
$666$	2.99468	+	4.33854i	0.116041	+	0.168115i
$667$	−1.42414	+	3.75515i	−0.0551430	+	0.145400i
$668$	−0.0135441	+	0.00333831i	−0.000524035	+	0.000129163i
$669$	−8.32224	−	4.36785i	−0.321756	−	0.168871i
$670$	9.93345	−	2.44838i	0.383763	−	0.0945890i
$671$	6.70129	+	5.93682i	0.258700	+	0.229189i
$672$	−2.03141	−	1.79967i	−0.0783633	−	0.0694238i
$673$	−30.0580	+	7.40864i	−1.15865	+	0.285582i	−0.771375	−	0.636381i	$-0.780431\pi$
$673$	−30.0580	+	7.40864i	−1.15865	+	0.285582i	−0.387277	+	0.921963i	$0.626584\pi$
$674$	−19.8274	−	10.4062i	−0.763723	−	0.400833i
$675$	−12.2350	+	3.01565i	−0.470925	+	0.116073i
$676$	0.646443	−	1.70453i	0.0248632	−	0.0655588i
$677$	−2.37942	−	3.44718i	−0.0914484	−	0.132486i	0.774589	−	0.632464i	$-0.217957\pi$
$677$	−2.37942	−	3.44718i	−0.0914484	−	0.132486i	−0.866038	+	0.499979i	$0.833341\pi$
$678$	−2.75030	+	2.43655i	−0.105625	+	0.0935752i
$679$	−25.3973	+	13.3295i	−0.974659	+	0.511541i
$680$	0.864148	−	0.765569i	0.0331386	−	0.0293582i
$681$	−3.52032	−	9.28233i	−0.134899	−	0.355699i
$682$	6.24008	−	16.4537i	0.238945	−	0.630046i
$683$	−27.1611	−	24.0627i	−1.03929	−	0.920733i	−0.0423678	−	0.999102i	$-0.513490\pi$
$683$	−27.1611	−	24.0627i	−1.03929	−	0.920733i	−0.996924	+	0.0783696i	$0.975029\pi$
$684$	6.75550	+	1.66508i	0.258303	+	0.0636659i
$685$	10.4692	+	15.1673i	0.400008	+	0.579511i
$686$	57.8809	−	30.3782i	2.20990	−	1.15985i
$687$	−6.42047			−0.244956
$688$	−1.26430			−0.0482010
$689$	17.5427	−	9.20713i	0.668325	−	0.350764i
$690$	0.104691	+	0.276048i	0.00398552	+	0.0105090i
$691$	−1.61886	−	13.3325i	−0.0615842	−	0.507192i	−0.990563	−	0.137058i	$-0.956235\pi$
$691$	−1.61886	−	13.3325i	−0.0615842	−	0.507192i	0.928979	−	0.370133i	$-0.120688\pi$
$692$	−0.821222	−	0.431010i	−0.0312182	−	0.0163846i
$693$	23.2478	+	12.2014i	0.883110	+	0.463492i
$694$	−3.93336	+	32.3942i	−0.149308	+	1.22967i
$695$	−1.19199	−	0.293799i	−0.0452148	−	0.0111444i
$696$	1.20049	−	3.16542i	0.0455043	−	0.119985i
$697$	−1.55256	−	12.7865i	−0.0588075	−	0.484323i
$698$	−2.16714	+	17.8480i	−0.0820273	+	0.675555i
$699$	6.36991	+	5.64324i	0.240932	+	0.213447i
$700$	20.9985	+	5.17565i	0.793667	+	0.195621i
$701$	8.83338	−	12.7974i	0.333632	−	0.483350i	−0.619883	−	0.784694i	$-0.712820\pi$
$701$	8.83338	−	12.7974i	0.333632	−	0.483350i	0.953515	+	0.301345i	$0.0974354\pi$
$702$	3.56660	+	9.40436i	0.134613	+	0.354945i
$703$	−2.80858	−	4.06893i	−0.105928	−	0.153463i
$704$	−1.06052	+	1.53642i	−0.0399697	+	0.0579061i
$705$	−0.393621	−	3.24176i	−0.0148246	−	0.122092i
$706$	5.14832	−	1.26895i	0.193760	−	0.0477575i
$707$	−9.45291	+	77.8517i	−0.355513	+	2.92791i
$708$	2.00624	−	2.90653i	0.0753989	−	0.109234i
$709$	−28.6278	+	25.3621i	−1.07514	+	0.952492i	−0.999005	−	0.0446054i	$-0.985797\pi$
$709$	−28.6278	+	25.3621i	−1.07514	+	0.952492i	−0.0761365	+	0.997097i	$0.524258\pi$
$710$	5.31274			0.199384
$711$	14.2323	+	19.5837i	0.533751	+	0.734445i
$712$	−4.17310			−0.156394
$713$	4.39935	−	3.89748i	0.164757	−	0.145962i
$714$	−1.97585	+	2.86252i	−0.0739445	+	0.107127i
$715$	−0.677694	+	5.58131i	−0.0253443	+	0.208729i
$716$	−8.33182	+	2.05361i	−0.311375	+	0.0767470i
$717$	−0.791633	−	6.51969i	−0.0295641	−	0.243482i
$718$	17.4333	−	25.2565i	0.650605	−	0.942565i
$719$	13.4867	+	19.5389i	0.502969	+	0.728677i	0.989428	−	0.145027i	$-0.0463268\pi$
$719$	13.4867	+	19.5389i	0.502969	+	0.728677i	−0.486458	+	0.873704i	$0.661711\pi$
$720$	0.870043	+	2.29412i	0.0324246	+	0.0854966i
$721$	15.9976	−	23.1765i	0.595782	−	0.863139i
$722$	12.1122	+	2.98539i	0.450770	+	0.111105i
$723$	6.16020	+	5.45746i	0.229100	+	0.202965i
$724$	−0.898058	+	7.39618i	−0.0333761	+	0.274877i
$725$	3.25182	+	26.7812i	0.120770	+	0.994627i
$726$	1.40064	−	3.69317i	0.0519824	−	0.137066i
$727$	16.7745	+	4.13453i	0.622130	+	0.153341i	0.537767	−	0.843094i	$-0.319268\pi$
$727$	16.7745	+	4.13453i	0.622130	+	0.153341i	0.0843635	+	0.996435i	$0.473114\pi$
$728$	2.08072	−	17.1362i	0.0771165	−	0.635111i
$729$	−11.6926	−	6.13673i	−0.433058	−	0.227286i
$730$	7.19533	+	3.77640i	0.266311	+	0.139771i
$731$	0.195312	+	1.60854i	0.00722386	+	0.0594938i
$732$	−0.893827	−	2.35683i	−0.0330368	−	0.0871109i
$733$	−26.4861	+	13.9010i	−0.978286	+	0.513444i	−0.876521	−	0.481364i	$-0.840141\pi$
$733$	−26.4861	+	13.9010i	−0.978286	+	0.513444i	−0.101765	+	0.994808i	$0.532449\pi$
$734$	10.3730			0.382873
$735$	9.30864			0.343354
$736$	−0.552117	+	0.289774i	−0.0203513	+	0.0106812i
$737$	12.0446	+	17.4496i	0.443668	+	0.642764i
$738$	26.5784	+	6.55099i	0.978365	+	0.241145i
$739$	23.1015	+	20.4661i	0.849801	+	0.752858i	0.970824	−	0.239791i	$-0.0770790\pi$
$739$	23.1015	+	20.4661i	0.849801	+	0.752858i	−0.121023	+	0.992650i	$0.538618\pi$
$740$	0.618252	−	1.63020i	0.0227274	−	0.0599272i
$741$	−1.59175	−	4.19711i	−0.0584745	−	0.154185i
$742$	−22.9032	+	20.2905i	−0.840803	+	0.744887i
$743$	−5.79530	+	3.04161i	−0.212609	+	0.111586i	−0.567666	−	0.823259i	$-0.692154\pi$
$743$	−5.79530	+	3.04161i	−0.212609	+	0.111586i	0.355057	+	0.934844i	$0.384461\pi$
$744$	−3.70845	+	3.28540i	−0.135958	+	0.120449i
$745$	−7.13609	−	10.3384i	−0.261446	−	0.378770i
$746$	−7.40568	+	19.5272i	−0.271141	+	0.714941i
$747$	44.9882	−	11.0886i	1.64603	−	0.405711i
$748$	2.11858	+	1.11192i	0.0774629	+	0.0406557i
$749$	36.4000	−	8.97179i	1.33003	−	0.327822i
$750$	3.25646	+	2.88497i	0.118909	+	0.105344i
$751$	37.2133	+	32.9681i	1.35793	+	1.20302i	0.958100	+	0.286434i	$0.0924700\pi$
$751$	37.2133	+	32.9681i	1.35793	+	1.20302i	0.399832	+	0.916588i	$0.369068\pi$
$752$	6.69655	−	1.65055i	0.244198	−	0.0601895i
$753$	−9.57207	−	5.02381i	−0.348826	−	0.183078i
$754$	20.9074	−	5.15321i	0.761403	−	0.187669i
$755$	−2.30632	+	6.08127i	−0.0839356	+	0.221320i
$756$	−8.82421	−	12.7841i	−0.320933	−	0.464952i
$757$	19.0127	−	16.8438i	0.691029	−	0.612198i	−0.242733	−	0.970093i	$-0.578044\pi$
$757$	19.0127	−	16.8438i	0.691029	−	0.612198i	0.933762	+	0.357895i	$0.116506\pi$
$758$	2.70629	−	1.42037i	0.0982970	−	0.0515903i
$759$	−0.457984	+	0.405738i	−0.0166238	+	0.0147274i
$760$	−0.815976	−	2.15155i	−0.0295985	−	0.0780449i
$761$	9.64957	−	25.4438i	0.349797	−	0.922338i	−0.638476	−	0.769641i	$-0.720435\pi$
$761$	9.64957	−	25.4438i	0.349797	−	0.922338i	0.988273	−	0.152697i	$-0.0487958\pi$
$762$	−2.64719	−	2.34520i	−0.0958975	−	0.0849577i
$763$	−66.3391	−	16.3511i	−2.40164	−	0.591950i
$764$	−2.78750	−	4.03838i	−0.100848	−	0.146104i
$765$	2.78433	−	1.46133i	0.100668	−	0.0528345i
$766$	−19.1084			−0.690414
$767$	22.4636			0.811112
$768$	0.465409	−	0.244266i	0.0167940	−	0.00881418i
$769$	−5.61579	−	14.8076i	−0.202510	−	0.533976i	0.794832	−	0.606829i	$-0.207559\pi$
$769$	−5.61579	−	14.8076i	−0.202510	−	0.533976i	−0.997343	+	0.0728531i	$0.976790\pi$
$770$	−1.04665	−	8.61995i	−0.0377187	−	0.310641i
$771$	−3.32218	−	1.74361i	−0.119645	−	0.0627947i
$772$	−5.81167	−	3.05020i	−0.209166	−	0.109779i
$773$	5.51023	−	45.3808i	0.198189	−	1.63223i	−0.466081	−	0.884742i	$-0.654335\pi$
$773$	5.51023	−	45.3808i	0.198189	−	1.63223i	0.664271	−	0.747492i	$-0.268742\pi$
$774$	−3.34355	−	0.824111i	−0.120181	−	0.0296221i
$775$	14.0002	−	36.9155i	0.502902	−	1.32604i
$776$	−0.669590	−	5.51457i	−0.0240369	−	0.197962i
$777$	−0.633150	+	5.21446i	−0.0227141	+	0.187068i
$778$	20.2063	+	17.9012i	0.724432	+	0.641791i
$779$	−24.9267	−	6.14389i	−0.893093	−	0.220128i
$780$	0.899210	−	1.30273i	0.0321969	−	0.0466452i
$781$	3.90437	+	10.2950i	0.139709	+	0.368383i
$782$	0.453963	+	0.657679i	0.0162337	+	0.0235185i
$783$	11.0075	−	15.9471i	0.393376	−	0.569904i
$784$	2.36976	+	19.5168i	0.0846344	+	0.697027i
$785$	−9.20071	+	2.26777i	−0.328387	+	0.0809402i
$786$	1.20516	−	9.92536i	0.0429865	−	0.354026i
$787$	18.3248	−	26.5481i	0.653209	−	0.946336i	−0.346756	−	0.937955i	$-0.612717\pi$
$787$	18.3248	−	26.5481i	0.653209	−	0.946336i	0.999965	−	0.00838110i	$-0.00266782\pi$
$788$	−14.2650	+	12.6376i	−0.508168	+	0.450197i
$789$	−5.71704			−0.203532
$790$	2.65646	−	7.55302i	0.0945125	−	0.268725i
$791$	36.0948			1.28338
$792$	−3.80611	+	3.37192i	−0.135244	+	0.119816i
$793$	9.10755	−	13.1946i	0.323418	−	0.468553i
$794$	3.21514	−	26.4790i	0.114101	−	0.939706i
$795$	−2.72434	+	0.671489i	−0.0966223	+	0.0238153i
$796$	−0.958518	−	7.89411i	−0.0339738	−	0.279799i
$797$	−19.4518	+	28.1808i	−0.689019	+	0.998216i	0.309855	+	0.950784i	$0.399719\pi$
$797$	−19.4518	+	28.1808i	−0.689019	+	0.998216i	−0.998874	+	0.0474327i	$0.984896\pi$
$798$	3.93819	+	5.70546i	0.139411	+	0.201971i
$799$	−3.13445	−	8.26486i	−0.110889	−	0.292390i
$800$	−2.37936	+	3.44710i	−0.0841232	+	0.121874i
$801$	−11.0361	−	2.72016i	−0.389942	−	0.0961120i
$802$	−24.4729	−	21.6811i	−0.864168	−	0.765586i
$803$	−2.02997	+	16.7183i	−0.0716362	+	0.589977i
$804$	−0.719552	−	5.92604i	−0.0253766	−	0.208995i
$805$	1.02842	−	2.71173i	0.0362472	−	0.0955760i
$806$	−30.5972	−	7.54154i	−1.07774	−	0.265639i
$807$	−0.849001	+	6.99216i	−0.0298863	+	0.246136i
$808$	−13.4488	−	7.05845i	−0.473126	−	0.248315i
$809$	47.9834	+	25.1836i	1.68701	+	0.885409i	0.984855	+	0.173381i	$0.0554692\pi$
$809$	47.9834	+	25.1836i	1.68701	+	0.885409i	0.702151	+	0.712028i	$0.252223\pi$
$810$	0.715532	+	5.89294i	0.0251412	+	0.207057i
$811$	−1.11624	−	2.94329i	−0.0391966	−	0.103353i	0.913989	−	0.405739i	$-0.132986\pi$
$811$	−1.11624	−	2.94329i	−0.0391966	−	0.103353i	−0.953185	+	0.302386i	$0.902217\pi$
$812$	−29.4471	+	15.4550i	−1.03339	+	0.542365i
$813$	−1.18847			−0.0416815
$814$	3.61333			0.126647
$815$	6.84887	−	3.59456i	0.239905	−	0.125912i
$816$	−0.382670	−	0.554393i	−0.0133961	−	0.0194076i
$817$	3.13577	+	0.772898i	0.109707	+	0.0270403i
$818$	16.1434	+	14.3018i	0.564441	+	0.500051i
$819$	16.6726	−	43.9619i	0.582586	−	1.53615i
$820$	−3.21032	−	8.46493i	−0.112109	−	0.295608i
$821$	14.7103	−	13.0322i	0.513395	−	0.454828i	−0.366211	−	0.930532i	$-0.619345\pi$
$821$	14.7103	−	13.0322i	0.513395	−	0.454828i	0.879605	+	0.475704i	$0.157807\pi$
$822$	9.52180	−	4.99742i	0.332111	−	0.174305i
$823$	−24.3298	+	21.5543i	−0.848085	+	0.751337i	−0.970490	−	0.241143i	$-0.922478\pi$
$823$	−24.3298	+	21.5543i	−0.848085	+	0.751337i	0.122405	+	0.992480i	$0.460939\pi$
$824$	3.09830	+	4.48867i	0.107934	+	0.156370i
$825$	−1.45746	+	3.84300i	−0.0507421	+	0.133796i
$826$	−33.6853	+	8.30267i	−1.17206	+	0.288887i
$827$	−31.2526	−	16.4026i	−1.08676	−	0.570375i	−0.176452	−	0.984309i	$-0.556462\pi$
$827$	−31.2526	−	16.4026i	−1.08676	−	0.570375i	−0.910307	+	0.413934i	$0.864155\pi$
$828$	−1.64900	+	0.406443i	−0.0573068	+	0.0141249i
$829$	13.6323	+	12.0772i	0.473469	+	0.419457i	0.865818	−	0.500360i	$-0.166799\pi$
$829$	13.6323	+	12.0772i	0.473469	+	0.419457i	−0.392349	+	0.919817i	$0.628337\pi$
$830$	−11.4702	−	10.1617i	−0.398138	−	0.352719i
$831$	14.5926	−	3.59674i	0.506210	−	0.124770i
$832$	2.96026	+	1.55366i	0.102629	+	0.0538636i
$833$	24.4645	−	6.02997i	0.847646	−	0.208926i
$834$	−0.254015	+	0.669783i	−0.00879583	+	0.0231927i
$835$	0.00713815	+	0.0103414i	0.000247026	+	0.000357879i
$836$	3.56958	−	3.16238i	0.123457	−	0.109373i
$837$	−25.1096	+	13.1785i	−0.867916	+	0.455517i
$838$	−24.0790	+	21.3321i	−0.831795	+	0.736906i
$839$	−7.83291	−	20.6537i	−0.270422	−	0.713045i	−0.999588	−	0.0287075i	$-0.990861\pi$
$839$	−7.83291	−	20.6537i	−0.270422	−	0.713045i	0.729166	−	0.684337i	$-0.239908\pi$
$840$	−0.866914	+	2.28586i	−0.0299114	+	0.0788698i
$841$	−9.34497	−	8.27892i	−0.322240	−	0.285480i
$842$	12.5304	+	3.08847i	0.431826	+	0.106436i
$843$	0.394191	+	0.571084i	0.0135766	+	0.0196692i
$844$	24.5990	−	12.9106i	0.846734	−	0.444400i
$845$	−1.64217			−0.0564923
$846$	18.7855			0.645858
$847$	−34.3566	+	18.0317i	−1.18051	+	0.619578i
$848$	−2.10142	−	5.54098i	−0.0721629	−	0.190278i
$849$	−0.406492	−	3.34776i	−0.0139508	−	0.114895i
$850$	4.75322	+	2.49468i	0.163034	+	0.0855670i
$851$	1.06861	+	0.560851i	0.0366315	+	0.0192257i
$852$	0.373658	−	3.07735i	0.0128013	−	0.105428i
$853$	−36.4896	−	8.99387i	−1.24938	−	0.307944i	−0.441483	−	0.897270i	$-0.645548\pi$
$853$	−36.4896	−	8.99387i	−1.24938	−	0.307944i	−0.807896	+	0.589325i	$0.799394\pi$
$854$	−8.78044	+	23.1521i	−0.300461	+	0.792249i
$855$	−0.755467	−	6.22183i	−0.0258364	−	0.212782i
$856$	−0.875178	+	7.20774i	−0.0299130	+	0.246355i
$857$	23.6725	+	20.9720i	0.808638	+	0.716390i	0.962376	−	0.271721i	$-0.0875928\pi$
$857$	23.6725	+	20.9720i	0.808638	+	0.716390i	−0.153738	+	0.988112i	$0.549131\pi$
$858$	3.18525	+	0.785094i	0.108743	+	0.0268027i
$859$	−22.4498	+	32.5241i	−0.765977	+	1.10971i	0.224826	+	0.974399i	$0.427819\pi$
$859$	−22.4498	+	32.5241i	−0.765977	+	1.10971i	−0.990803	+	0.135310i	$0.956797\pi$
$860$	0.403857	+	1.06488i	0.0137714	+	0.0363122i
$861$	15.4942	+	22.4472i	0.528041	+	0.764999i
$862$	0.937511	−	1.35822i	0.0319317	−	0.0462611i
$863$	0.336282	+	2.76953i	0.0114472	+	0.0942759i	0.997313	−	0.0732628i	$-0.0233412\pi$
$863$	0.336282	+	2.76953i	0.0114472	+	0.0942759i	−0.985866	+	0.167539i	$0.946418\pi$
$864$	2.92106	−	0.719976i	0.0993765	−	0.0244941i
$865$	−0.100704	+	0.829369i	−0.00342402	+	0.0281994i
$866$	7.04255	−	10.2029i	0.239315	−	0.346708i
$867$	6.04207	−	5.35280i	0.205199	−	0.181791i
$868$	48.6695			1.65195
$869$	16.5884	−	0.403111i	0.562723	−	0.0136746i
$870$	−3.04961			−0.103392
$871$	28.4207	−	25.1786i	0.963000	−	0.853144i
$872$	7.51698	−	10.8902i	0.254557	−	0.368790i
$873$	1.82378	−	15.0202i	0.0617257	−	0.508357i
$874$	1.54653	−	0.381185i	0.0523121	−	0.0128938i
$875$	−5.15145	−	42.4260i	−0.174151	−	1.43426i
$876$	2.69350	−	3.90221i	0.0910051	−	0.131844i
$877$	−13.7369	−	19.9014i	−0.463863	−	0.672021i	0.519334	−	0.854572i	$-0.326180\pi$
$877$	−13.7369	−	19.9014i	−0.463863	−	0.672021i	−0.983197	+	0.182550i	$0.941565\pi$
$878$	−9.79704	−	25.8327i	−0.330634	−	0.871810i
$879$	−4.94078	+	7.15796i	−0.166648	+	0.241432i
$880$	1.63284	+	0.402460i	0.0550432	+	0.0135669i
$881$	36.4957	+	32.3324i	1.22957	+	1.08931i	0.993052	+	0.117679i	$0.0375455\pi$
$881$	36.4957	+	32.3324i	1.22957	+	1.08931i	0.236521	+	0.971626i	$0.423993\pi$
$882$	−6.45459	+	53.1584i	−0.217337	+	1.78994i
$883$	−1.01514	−	8.36041i	−0.0341621	−	0.281350i	−0.999772	−	0.0213549i	$-0.993202\pi$
$883$	−1.01514	−	8.36041i	−0.0341621	−	0.281350i	0.965610	−	0.259995i	$-0.0837211\pi$
$884$	1.51938	−	4.00627i	0.0511022	−	0.134745i
$885$	−3.08894	−	0.761355i	−0.103834	−	0.0255927i
$886$	−2.69707	+	22.2124i	−0.0906099	+	0.746239i
$887$	−47.4966	−	24.9281i	−1.59478	−	0.837005i	−0.999438	−	0.0335333i	$-0.989324\pi$
$887$	−47.4966	−	24.9281i	−1.59478	−	0.837005i	−0.595343	−	0.803472i	$-0.702984\pi$
$888$	−0.900790	−	0.472771i	−0.0302285	−	0.0158652i
$889$	4.18763	+	34.4883i	0.140449	+	1.15670i
$890$	1.33302	+	3.51488i	0.0446829	+	0.117819i
$891$	−10.8934	+	5.71731i	−0.364943	+	0.191537i
$892$	−17.8815			−0.598718
$893$	−17.6181			−0.589566
$894$	−6.49031	+	3.40638i	−0.217068	+	0.113926i
$895$	4.39114	+	6.36166i	0.146779	+	0.212647i
$896$	−5.01331	−	1.23567i	−0.167483	−	0.0412808i
$897$	0.820150	+	0.726589i	0.0273840	+	0.0242601i
$898$	5.87626	−	15.4944i	0.196093	−	0.517055i
$899$	21.5286	+	56.7662i	0.718018	+	1.89326i
$900$	−8.53935	+	7.56521i	−0.284645	+	0.252174i
$901$	−6.72500	+	3.52955i	−0.224042	+	0.117586i
$902$	14.0440	−	12.4419i	0.467613	−	0.414269i
$903$	−1.94916	−	2.82385i	−0.0648640	−	0.0939717i
$904$	−2.47890	+	6.53631i	−0.0824468	+	0.217394i
$905$	6.51645	−	1.60616i	0.216614	−	0.0533905i
$906$	3.36030	+	1.76362i	0.111638	+	0.0585924i
$907$	26.8433	−	6.61629i	0.891318	−	0.219690i	0.233042	−	0.972467i	$-0.425132\pi$
$907$	26.8433	−	6.61629i	0.891318	−	0.219690i	0.658276	+	0.752776i	$0.271286\pi$
$908$	−14.1373	−	12.5246i	−0.469164	−	0.415643i
$909$	−30.9654	−	27.4330i	−1.02706	−	0.909894i
$910$	−15.0980	+	3.72132i	−0.500493	+	0.123361i
$911$	15.8493	+	8.31836i	0.525111	+	0.275600i	0.706379	−	0.707834i	$-0.250328\pi$
$911$	15.8493	+	8.31836i	0.525111	+	0.275600i	−0.181267	+	0.983434i	$0.558020\pi$
$912$	−1.30365	+	0.321321i	−0.0431682	+	0.0106400i
$913$	11.2618	−	29.6948i	0.372710	−	0.982755i
$914$	11.0579	+	16.0202i	0.365764	+	0.529900i
$915$	−1.69957	+	1.50569i	−0.0561861	+	0.0497765i
$916$	−10.8160	+	5.67666i	−0.357370	+	0.187562i
$917$	−73.5166	+	65.1300i	−2.42773	+	2.15078i
$918$	−1.36726	−	3.60516i	−0.0451262	−	0.118988i
$919$	6.07406	−	16.0160i	0.200365	−	0.528319i	−0.796743	−	0.604318i	$-0.793446\pi$
$919$	6.07406	−	16.0160i	0.200365	−	0.528319i	0.997108	+	0.0759995i	$0.0242147\pi$
$920$	0.420431	+	0.372469i	0.0138612	+	0.0122799i
$921$	1.19019	+	0.293356i	0.0392181	+	0.00966641i
$922$	11.4646	+	16.6093i	0.377566	+	0.546998i
$923$	17.4589	−	9.16312i	0.574666	−	0.301608i
$924$	−5.06662			−0.166680
$925$	8.10684			0.266551
$926$	0.151321	−	0.0794195i	0.00497272	−	0.00260989i
$927$	5.26786	+	13.8902i	0.173019	+	0.456214i
$928$	−0.776361	−	6.39390i	−0.0254853	−	0.209890i
$929$	−8.36330	−	4.38940i	−0.274391	−	0.144011i	0.321915	−	0.946768i	$-0.395673\pi$
$929$	−8.36330	−	4.38940i	−0.274391	−	0.144011i	−0.596306	+	0.802757i	$0.703366\pi$
$930$	3.95179	+	2.07406i	0.129584	+	0.0680110i
$931$	6.05348	−	49.8549i	0.198395	−	1.63393i
$932$	15.7203	+	3.87470i	0.514935	+	0.126920i
$933$	5.32326	−	14.0363i	0.174276	−	0.459527i
$934$	−0.187844	−	1.54704i	−0.00614646	−	0.0506206i
$935$	0.259794	−	2.13960i	0.00849617	−	0.0699723i
$936$	6.81592	+	6.03838i	0.222785	+	0.197371i
$937$	−11.4640	−	2.82563i	−0.374514	−	0.0923093i	0.0475660	−	0.998868i	$-0.484854\pi$
$937$	−11.4640	−	2.82563i	−0.374514	−	0.0923093i	−0.422080	+	0.906559i	$0.638700\pi$
$938$	−33.3122	+	48.2611i	−1.08768	+	1.57578i
$939$	−1.85350	−	4.88729i	−0.0604868	−	0.159491i
$940$	−3.52930	−	5.11307i	−0.115113	−	0.166770i
$941$	−25.6134	+	37.1074i	−0.834972	+	1.20967i	0.140617	+	0.990064i	$0.455091\pi$
$941$	−25.6134	+	37.1074i	−0.834972	+	1.20967i	−0.975590	+	0.219602i	$0.929524\pi$
$942$	0.666474	+	5.48891i	0.0217149	+	0.178838i
$943$	6.08456	−	1.49971i	0.198141	−	0.0488373i
$944$	0.809907	−	6.67018i	0.0263602	−	0.217096i
$945$	−7.94892	+	11.5160i	−0.258578	+	0.374616i
$946$	−1.76672	+	1.56518i	−0.0574411	+	0.0508884i
$947$	11.1644			0.362793			0.181397	−	0.983410i	$-0.441938\pi$
$947$	11.1644			0.362793			0.181397	+	0.983410i	$0.441938\pi$
$948$	−4.18817	−	2.06995i	−0.136025	−	0.0672287i
$949$	30.1588			0.978997
$950$	8.00869	−	7.09508i	0.259836	−	0.230195i
$951$	0.832191	−	1.20564i	0.0269856	−	0.0390955i
$952$	−0.797642	+	6.56918i	−0.0258517	+	0.212908i
$953$	32.1169	−	7.91610i	1.04037	−	0.256428i	0.318111	−	0.948053i	$-0.396951\pi$
$953$	32.1169	−	7.91610i	1.04037	−	0.256428i	0.722256	+	0.691626i	$0.243105\pi$
$954$	−1.94559	−	16.0233i	−0.0629907	−	0.518775i
$955$	−2.51100	+	3.63781i	−0.0812540	+	0.117717i
$956$	−7.09798	−	10.2832i	−0.229565	−	0.332582i
$957$	−2.24118	−	5.90950i	−0.0724470	−	0.191027i
$958$	−18.8531	+	27.3135i	−0.609118	+	0.882459i
$959$	−102.567	−	25.2805i	−3.31206	−	0.816350i
$960$	−0.354404	−	0.313974i	−0.0114383	−	0.0101335i
$961$	6.97292	−	57.4271i	0.224933	−	1.85249i
$962$	−0.779957	−	6.42352i	−0.0251468	−	0.207103i
$963$	−7.01271	+	18.4910i	−0.225981	+	0.595864i
$964$	15.2027	+	3.74714i	0.489647	+	0.120687i
$965$	−0.712665	+	5.86932i	−0.0229415	+	0.188940i
$966$	−1.49841	−	0.786426i	−0.0482105	−	0.0253028i
$967$	−17.3884	−	9.12615i	−0.559174	−	0.293477i	0.161361	−	0.986895i	$-0.448412\pi$
$967$	−17.3884	−	9.12615i	−0.559174	−	0.293477i	−0.720535	+	0.693418i	$0.756104\pi$
$968$	−0.905798	−	7.45992i	−0.0291135	−	0.239771i
$969$	0.610198	+	1.60896i	0.0196024	+	0.0516873i
$970$	−4.43087	+	2.32550i	−0.142267	+	0.0746673i
$971$	17.2928			0.554952			0.277476	−	0.960733i	$-0.410502\pi$
$971$	17.2928			0.554952			0.277476	+	0.960733i	$0.410502\pi$
$972$	12.4892			0.400591
$973$	6.23082	−	3.27019i	0.199751	−	0.104837i
$974$	7.90089	+	11.4464i	0.253161	+	0.366767i
$975$	7.14640	+	1.76143i	0.228868	+	0.0564109i
$976$	−3.58954	−	3.18006i	−0.114898	−	0.101791i
$977$	6.74126	−	17.7752i	0.215672	−	0.568681i	−0.782897	−	0.622151i	$-0.786259\pi$
$977$	6.74126	−	17.7752i	0.215672	−	0.568681i	0.998569	+	0.0534703i	$0.0170282\pi$
$978$	−1.60041	−	4.21994i	−0.0511756	−	0.134939i
$979$	−5.83145	+	5.16621i	−0.186374	+	0.165113i
$980$	15.6814	−	8.23024i	0.500924	−	0.262905i
$981$	26.9779	−	23.9003i	0.861337	−	0.763078i
$982$	−12.4833	−	18.0852i	−0.398359	−	0.577123i
$983$	−8.22766	+	21.6946i	−0.262422	+	0.691949i	0.737442	+	0.675411i	$0.236034\pi$
$983$	−8.22766	+	21.6946i	−0.262422	+	0.691949i	−0.999863	+	0.0165380i	$0.994736\pi$
$984$	−5.12901	+	1.26419i	−0.163507	+	0.0403008i
$985$	15.2010	+	7.97809i	0.484343	+	0.254203i
$986$	−8.01485	+	1.97548i	−0.255245	+	0.0629122i
$987$	14.0106	+	12.4123i	0.445961	+	0.395087i
$988$	−6.39236	−	5.66313i	−0.203368	−	0.180168i
$989$	−0.765435	+	0.188663i	−0.0243394	+	0.00599913i
$990$	4.05586	+	2.12868i	0.128904	+	0.0676538i
$991$	−3.53013	+	0.870100i	−0.112138	+	0.0276396i	−0.294986	−	0.955502i	$-0.595315\pi$
$991$	−3.53013	+	0.870100i	−0.112138	+	0.0276396i	0.182847	+	0.983141i	$0.441469\pi$
$992$	−3.34250	+	8.81344i	−0.106124	+	0.279827i
$993$	10.3230	+	14.9554i	0.327590	+	0.474597i
$994$	−22.7937	+	20.1935i	−0.722973	+	0.640498i
$995$	−6.34279	+	3.32895i	−0.201080	+	0.105535i
$996$	−6.69280	+	5.92931i	−0.212070	+	0.187877i
$997$	−14.3293	−	37.7833i	−0.453814	−	1.19661i	−0.945438	−	0.325802i	$-0.894366\pi$
$997$	−14.3293	−	37.7833i	−0.453814	−	1.19661i	0.491624	−	0.870808i	$-0.336404\pi$
$998$	−13.0400	+	34.3837i	−0.412775	+	1.08840i
$999$	−4.35847	−	3.86127i	−0.137896	−	0.122165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	158.2.e.a.21.3	✓	48
79.64	even	13	inner	158.2.e.a.143.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
158.2.e.a.21.3	✓	48	1.1	even	1	trivial
158.2.e.a.143.3	yes	48	79.64	even	13	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:	\( N \)	\(=\)	\( 158 = 2 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	158.e (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.748511 + 0.663123i) q^{2} +(0.298584 - 0.432573i) q^{3} +(0.120537 - 0.992709i) q^{4} +(-0.874632 + 0.215577i) q^{5} +(0.0633559 + 0.521783i) q^{6} +(2.93311 - 4.24935i) q^{7} +(0.568065 + 0.822984i) q^{8} +(0.965847 + 2.54673i) q^{9} +(0.511717 - 0.741350i) q^{10} +(1.81264 + 0.446777i) q^{11} +(-0.393429 - 0.348548i) q^{12} +(0.402979 - 3.31883i) q^{13} +(0.622372 + 5.12570i) q^{14} +(-0.167898 + 0.442710i) q^{15} +(-0.970942 - 0.239316i) q^{16} +(-0.154482 + 1.27227i) q^{17} +(-2.41174 - 1.26578i) q^{18} +(2.26187 + 1.18712i) q^{19} +(0.108580 + 0.894240i) q^{20} +(-0.962374 - 2.53757i) q^{21} +(-1.65305 + 0.867589i) q^{22} -0.623540 q^{23} +0.525615 q^{24} +(-3.70877 + 1.94651i) q^{25} +(1.89916 + 2.75140i) q^{26} +(2.92106 + 0.719976i) q^{27} +(-3.86482 - 3.42393i) q^{28} +(2.28396 - 6.02231i) q^{29} +(-0.167898 - 0.442710i) q^{30} +(-7.05544 + 6.25057i) q^{31} +(0.885456 - 0.464723i) q^{32} +(0.734490 - 0.650701i) q^{33} +(-0.728041 - 1.05475i) q^{34} +(-1.64933 + 4.34893i) q^{35} +(2.64458 - 0.651831i) q^{36} +(-1.71378 - 0.899462i) q^{37} +(-2.48024 + 0.611324i) q^{38} +(-1.31531 - 1.16527i) q^{39} +(-0.674264 - 0.597346i) q^{40} +(-9.75810 + 2.40515i) q^{41} +(2.40307 + 1.26123i) q^{42} +(1.22756 - 0.302567i) q^{43} +(0.662009 - 1.74558i) q^{44} +(-1.39378 - 2.01924i) q^{45} +(0.466726 - 0.413484i) q^{46} +(-6.10696 + 3.20518i) q^{47} +(-0.393429 + 0.348548i) q^{48} +(-6.97157 - 18.3825i) q^{49} +(1.48528 - 3.91636i) q^{50} +(0.504225 + 0.446704i) q^{51} +(-3.24606 - 0.800081i) q^{52} +(3.36640 + 4.87707i) q^{53} +(-2.66388 + 1.39811i) q^{54} -1.68171 q^{55} +5.16334 q^{56} +(1.18887 - 0.623968i) q^{57} +(2.28396 + 6.02231i) q^{58} +(0.809907 + 6.67018i) q^{59} +(0.419244 + 0.220036i) q^{60} +(4.24627 + 2.22862i) q^{61} +(1.13618 - 9.35724i) q^{62} +(13.6549 + 3.36563i) q^{63} +(-0.354605 + 0.935016i) q^{64} +(0.363006 + 2.98963i) q^{65} +(-0.118279 + 0.974113i) q^{66} +(8.50105 + 7.53127i) q^{67} +(1.24437 + 0.306711i) q^{68} +(-0.186179 + 0.269727i) q^{69} +(-1.64933 - 4.34893i) q^{70} +(3.35030 + 4.85375i) q^{71} +(-1.54725 + 2.24158i) q^{72} +(1.08735 + 8.95516i) q^{73} +(1.87924 - 0.463191i) q^{74} +(-0.265369 + 2.18551i) q^{75} +(1.45110 - 2.10228i) q^{76} +(7.21520 - 6.39211i) q^{77} +1.75724 q^{78} +(8.57570 - 2.33611i) q^{79} +0.900808 q^{80} +(-4.93260 + 4.36990i) q^{81} +(5.70913 - 8.27110i) q^{82} +(2.05051 - 16.8874i) q^{83} +(-2.63507 + 0.649487i) q^{84} +(-0.139158 - 1.14607i) q^{85} +(-0.718205 + 1.04050i) q^{86} +(-1.92314 - 2.78614i) q^{87} +(0.662009 + 1.74558i) q^{88} +(-2.37059 + 3.43440i) q^{89} +(2.38226 + 0.587174i) q^{90} +(-12.9209 - 11.4469i) q^{91} +(-0.0751594 + 0.618994i) q^{92} +(0.597191 + 4.91831i) q^{93} +(2.44570 - 6.44878i) q^{94} +(-2.23422 - 0.550685i) q^{95} +(0.0633559 - 0.521783i) q^{96} +(-4.91877 - 2.58157i) q^{97} +(17.4082 + 9.13651i) q^{98} +(0.612918 + 5.04784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 11 q^{5} - 2 q^{6} - 8 q^{7} - 4 q^{8} - 18 q^{9} - 2 q^{10} - 8 q^{11} - 2 q^{12} + 16 q^{13} + 5 q^{14} - 2 q^{15} - 4 q^{16} + 6 q^{17} - 18 q^{18} + 6 q^{19} - 2 q^{20}+ \cdots - 58 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 11 * q^5 - 2 * q^6 - 8 * q^7 - 4 * q^8 - 18 * q^9 - 2 * q^10 - 8 * q^11 - 2 * q^12 + 16 * q^13 + 5 * q^14 - 2 * q^15 - 4 * q^16 + 6 * q^17 - 18 * q^18 + 6 * q^19 - 2 * q^20 - 12 * q^21 + 5 * q^22 - 16 * q^23 + 24 * q^24 - 17 * q^25 + 3 * q^26 + 7 * q^27 - 8 * q^28 - 34 * q^29 - 2 * q^30 - 19 * q^31 - 4 * q^32 + 8 * q^33 - 20 * q^34 + 122 * q^35 - 18 * q^36 - 4 * q^37 - 20 * q^38 - 50 * q^39 - 2 * q^40 - 36 * q^41 + 14 * q^42 - 24 * q^43 + 18 * q^44 - 4 * q^45 + 10 * q^46 - 22 * q^47 - 2 * q^48 - 28 * q^49 - 4 * q^50 + 78 * q^51 - 10 * q^52 - 12 * q^53 + 7 * q^54 - 88 * q^55 + 18 * q^56 - 28 * q^57 - 34 * q^58 - 52 * q^59 + 11 * q^60 - 47 * q^61 + 20 * q^62 + 11 * q^63 - 4 * q^64 - 16 * q^65 + 8 * q^66 + 67 * q^67 - 7 * q^68 - 4 * q^69 + 122 * q^70 - 12 * q^71 - 18 * q^72 + 101 * q^73 - 4 * q^74 - 62 * q^75 + 32 * q^76 + 113 * q^77 - 50 * q^78 - 2 * q^80 + 36 * q^81 + 29 * q^82 + 91 * q^83 + 53 * q^84 - q^85 - 24 * q^86 + 210 * q^87 + 18 * q^88 + 4 * q^89 + 126 * q^90 - 33 * q^91 - 3 * q^92 - 3 * q^93 + 17 * q^94 - 42 * q^95 - 2 * q^96 - 32 * q^97 + 24 * q^98 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more