LMFDB - Embedded newform 117.2.l.b.4.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(4,117)] 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("117.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

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

Embedding invariants

Embedding label			4.10
Character	$\chi$	$=$	117.4
Dual form			117.2.l.b.88.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00617i q^{2} +(1.62924 - 0.587859i) q^{3} -2.02472 q^{4} +(0.778411 + 0.449416i) q^{5} +(1.17935 + 3.26853i) q^{6} +(-2.10878 - 1.21751i) q^{7} -0.0495935i q^{8} +(2.30884 - 1.91553i) q^{9} +(-0.901605 + 1.56163i) q^{10} +0.984566i q^{11} +(-3.29875 + 1.19025i) q^{12} +(-3.22430 - 1.61366i) q^{13} +(2.44253 - 4.23058i) q^{14} +(1.53241 + 0.274610i) q^{15} -3.94995 q^{16} +(-2.01368 - 3.48780i) q^{17} +(3.84288 + 4.63193i) q^{18} +(0.316846 - 0.182931i) q^{19} +(-1.57607 - 0.909942i) q^{20} +(-4.15144 - 0.743942i) q^{21} -1.97521 q^{22} +(2.55664 + 4.42823i) q^{23} +(-0.0291540 - 0.0807997i) q^{24} +(-2.09605 - 3.63047i) q^{25} +(3.23728 - 6.46849i) q^{26} +(2.63560 - 4.47813i) q^{27} +(4.26970 + 2.46511i) q^{28} +4.88611 q^{29} +(-0.550914 + 3.07428i) q^{30} +(5.63094 + 3.25102i) q^{31} -8.02346i q^{32} +(0.578786 + 1.60409i) q^{33} +(6.99712 - 4.03979i) q^{34} +(-1.09433 - 1.89544i) q^{35} +(-4.67476 + 3.87841i) q^{36} +(3.80542 + 2.19706i) q^{37} +(0.366991 + 0.635647i) q^{38} +(-6.20176 - 0.733609i) q^{39} +(0.0222881 - 0.0386041i) q^{40} +(-8.50437 + 4.91000i) q^{41} +(1.49247 - 8.32849i) q^{42} +(3.11849 - 5.40139i) q^{43} -1.99347i q^{44} +(2.65810 - 0.453438i) q^{45} +(-8.88379 + 5.12906i) q^{46} +(-8.09457 + 4.67340i) q^{47} +(-6.43541 + 2.32201i) q^{48} +(-0.535355 - 0.927262i) q^{49} +(7.28333 - 4.20504i) q^{50} +(-5.33111 - 4.49870i) q^{51} +(6.52830 + 3.26722i) q^{52} -1.76240 q^{53} +(8.98389 + 5.28746i) q^{54} +(-0.442480 + 0.766397i) q^{55} +(-0.0603804 + 0.104582i) q^{56} +(0.408680 - 0.484300i) q^{57} +9.80236i q^{58} +10.3175i q^{59} +(-3.10271 - 0.556008i) q^{60} +(-7.41941 + 12.8508i) q^{61} +(-6.52211 + 11.2966i) q^{62} +(-7.20102 + 1.22840i) q^{63} +8.19653 q^{64} +(-1.78462 - 2.70514i) q^{65} +(-3.21809 + 1.16114i) q^{66} +(3.95165 - 2.28149i) q^{67} +(4.07714 + 7.06182i) q^{68} +(6.76856 + 5.71171i) q^{69} +(3.80258 - 2.19542i) q^{70} +(3.72139 - 2.14855i) q^{71} +(-0.0949977 - 0.114504i) q^{72} -16.9408i q^{73} +(-4.40768 + 7.63433i) q^{74} +(-5.54917 - 4.68272i) q^{75} +(-0.641525 + 0.370384i) q^{76} +(1.19872 - 2.07624i) q^{77} +(1.47174 - 12.4418i) q^{78} +(5.57094 + 9.64914i) q^{79} +(-3.07468 - 1.77517i) q^{80} +(1.66151 - 8.84530i) q^{81} +(-9.85030 - 17.0612i) q^{82} +(-1.50053 + 0.866332i) q^{83} +(8.40550 + 1.50627i) q^{84} -3.61992i q^{85} +(10.8361 + 6.25623i) q^{86} +(7.96064 - 2.87234i) q^{87} +0.0488281 q^{88} +(4.61799 + 2.66620i) q^{89} +(0.909673 + 5.33260i) q^{90} +(4.83470 + 7.32847i) q^{91} +(-5.17648 - 8.96593i) q^{92} +(11.0853 + 1.98650i) q^{93} +(-9.37565 - 16.2391i) q^{94} +0.328849 q^{95} +(-4.71666 - 13.0721i) q^{96} +(-2.54546 - 1.46962i) q^{97} +(1.86025 - 1.07401i) q^{98} +(1.88596 + 2.27321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) $ 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.00617i			1.41858i	0.704918	+	0.709288i	$0.250984\pi$
$2$			2.00617i			1.41858i	−0.704918	+	0.709288i	$0.749016\pi$
$3$	1.62924	−	0.587859i	0.940642	−	0.339401i
$3$	1.62924	−	0.587859i	0.940642	−	0.339401i
$4$	−2.02472			−1.01236
$5$	0.778411	+	0.449416i	0.348116	+	0.200985i	0.663855	−	0.747861i	$-0.268919\pi$
$5$	0.778411	+	0.449416i	0.348116	+	0.200985i	−0.315739	+	0.948846i	$0.602252\pi$
$6$	1.17935	+	3.26853i	0.481466	+	1.33437i
$7$	−2.10878	−	1.21751i	−0.797045	−	0.460174i	0.0453917	−	0.998969i	$-0.485546\pi$
$7$	−2.10878	−	1.21751i	−0.797045	−	0.460174i	−0.842437	+	0.538795i	$0.818880\pi$
$8$		−	0.0495935i		−	0.0175339i
$9$	2.30884	−	1.91553i	0.769614	−	0.638509i
$10$	−0.901605	+	1.56163i	−0.285113	+	0.493829i
$11$			0.984566i			0.296858i	0.988923	+	0.148429i	$0.0474216\pi$
$11$			0.984566i			0.296858i	−0.988923	+	0.148429i	$0.952578\pi$
$12$	−3.29875	+	1.19025i	−0.952268	+	0.343596i
$13$	−3.22430	−	1.61366i	−0.894259	−	0.447549i
$13$	−3.22430	−	1.61366i	−0.894259	−	0.447549i
$14$	2.44253	−	4.23058i	0.652793	−	1.13067i
$15$	1.53241	+	0.274610i	0.395667	+	0.0709039i
$16$	−3.94995			−0.987487
$17$	−2.01368	−	3.48780i	−0.488390	−	0.845916i	0.511521	−	0.859271i	$-0.329082\pi$
$17$	−2.01368	−	3.48780i	−0.488390	−	0.845916i	−0.999911	+	0.0133549i	$0.995749\pi$
$18$	3.84288	+	4.63193i	0.905774	+	1.09176i
$19$	0.316846	−	0.182931i	0.0726895	−	0.0419673i	−0.463215	−	0.886246i	$-0.653304\pi$
$19$	0.316846	−	0.182931i	0.0726895	−	0.0419673i	0.535904	+	0.844279i	$0.319971\pi$
$20$	−1.57607	−	0.909942i	−0.352419	−	0.203469i
$21$	−4.15144	−	0.743942i	−0.905918	−	0.162341i
$22$	−1.97521			−0.421116
$23$	2.55664	+	4.42823i	0.533097	+	0.923350i	0.999253	+	0.0386480i	$0.0123051\pi$
$23$	2.55664	+	4.42823i	0.533097	+	0.923350i	−0.466156	+	0.884702i	$0.654362\pi$
$24$	−0.0291540	−	0.0807997i	−0.00595104	−	0.0164932i
$25$	−2.09605	−	3.63047i	−0.419210	−	0.726093i
$26$	3.23728	−	6.46849i	0.634883	−	1.26858i
$27$	2.63560	−	4.47813i	0.507221	−	0.861816i
$28$	4.26970	+	2.46511i	0.806897	+	0.465862i
$29$	4.88611			0.907327			0.453664	−	0.891173i	$-0.350117\pi$
$29$	4.88611			0.907327			0.453664	+	0.891173i	$0.350117\pi$
$30$	−0.550914	+	3.07428i	−0.100583	+	0.561284i
$31$	5.63094	+	3.25102i	1.01135	+	0.583901i	0.911586	−	0.411110i	$-0.134859\pi$
$31$	5.63094	+	3.25102i	1.01135	+	0.583901i	0.0997609	+	0.995011i	$0.468192\pi$
$32$		−	8.02346i		−	1.41836i
$33$	0.578786	+	1.60409i	0.100754	+	0.279237i
$34$	6.99712	−	4.03979i	1.20000	−	0.692818i
$35$	−1.09433	−	1.89544i	−0.184976	−	0.320388i
$36$	−4.67476	+	3.87841i	−0.779127	+	0.646401i
$37$	3.80542	+	2.19706i	0.625608	+	0.361195i	0.779049	−	0.626963i	$-0.215702\pi$
$37$	3.80542	+	2.19706i	0.625608	+	0.361195i	−0.153441	+	0.988158i	$0.549036\pi$
$38$	0.366991	+	0.635647i	0.0595338	+	0.103116i
$39$	−6.20176	−	0.733609i	−0.993076	−	0.117471i
$40$	0.0222881	−	0.0386041i	0.00352406	−	0.00610385i
$41$	−8.50437	+	4.91000i	−1.32816	+	0.766813i	−0.985015	−	0.172470i	$-0.944825\pi$
$41$	−8.50437	+	4.91000i	−1.32816	+	0.766813i	−0.343144	+	0.939283i	$0.611492\pi$
$42$	1.49247	−	8.32849i	0.230294	−	1.28511i
$43$	3.11849	−	5.40139i	0.475566	−	0.823704i	−0.524042	−	0.851692i	$-0.675577\pi$
$43$	3.11849	−	5.40139i	0.475566	−	0.823704i	0.999608	+	0.0279879i	$0.00891000\pi$
$44$		−	1.99347i		−	0.300527i
$45$	2.65810	−	0.453438i	0.396246	−	0.0675945i
$46$	−8.88379	+	5.12906i	−1.30984	+	0.756238i
$47$	−8.09457	+	4.67340i	−1.18071	+	0.681686i	−0.956180	−	0.292780i	$-0.905420\pi$
$47$	−8.09457	+	4.67340i	−1.18071	+	0.681686i	−0.224535	+	0.974466i	$0.572086\pi$
$48$	−6.43541	+	2.32201i	−0.928872	+	0.335154i
$49$	−0.535355	−	0.927262i	−0.0764793	−	0.132466i
$50$	7.28333	−	4.20504i	1.03002	−	0.594682i
$51$	−5.33111	−	4.49870i	−0.746504	−	0.629944i
$52$	6.52830	+	3.26722i	0.905312	+	0.453081i
$53$	−1.76240			−0.242084			−0.121042	−	0.992647i	$-0.538624\pi$
$53$	−1.76240			−0.242084			−0.121042	+	0.992647i	$0.538624\pi$
$54$	8.98389	+	5.28746i	1.22255	+	0.719532i
$55$	−0.442480	+	0.766397i	−0.0596639	+	0.103341i
$56$	−0.0603804	+	0.104582i	−0.00806867	+	0.0139753i
$57$	0.408680	−	0.484300i	0.0541310	−	0.0641471i
$58$			9.80236i			1.28711i
$59$			10.3175i			1.34322i	0.740906	+	0.671609i	$0.234396\pi$
$59$			10.3175i			1.34322i	−0.740906	+	0.671609i	$0.765604\pi$
$60$	−3.10271	−	0.556008i	−0.400558	−	0.0717803i
$61$	−7.41941	+	12.8508i	−0.949959	+	1.64538i	−0.204454	+	0.978876i	$0.565542\pi$
$61$	−7.41941	+	12.8508i	−0.949959	+	1.64538i	−0.745505	+	0.666501i	$0.767791\pi$
$62$	−6.52211	+	11.2966i	−0.828309	+	1.43467i
$63$	−7.20102	+	1.22840i	−0.907243	+	0.154764i
$64$	8.19653			1.02457
$65$	−1.78462	−	2.70514i	−0.221355	−	0.335532i
$66$	−3.21809	+	1.16114i	−0.396119	+	0.142927i
$67$	3.95165	−	2.28149i	0.482771	−	0.278728i	−0.238800	−	0.971069i	$-0.576754\pi$
$67$	3.95165	−	2.28149i	0.482771	−	0.278728i	0.721570	+	0.692341i	$0.243421\pi$
$68$	4.07714	+	7.06182i	0.494426	+	0.856371i
$69$	6.76856	+	5.71171i	0.814839	+	0.687609i
$70$	3.80258	−	2.19542i	0.454495	−	0.262403i
$71$	3.72139	−	2.14855i	0.441648	−	0.254985i	−0.262649	−	0.964892i	$-0.584596\pi$
$71$	3.72139	−	2.14855i	0.441648	−	0.254985i	0.704296	+	0.709906i	$0.251263\pi$
$72$	−0.0949977	−	0.114504i	−0.0111956	−	0.0134944i
$73$		−	16.9408i		−	1.98277i	−0.130969	−	0.991386i	$-0.541809\pi$
$73$		−	16.9408i		−	1.98277i	0.130969	−	0.991386i	$-0.458191\pi$
$74$	−4.40768	+	7.63433i	−0.512383	+	0.887473i
$75$	−5.54917	−	4.68272i	−0.640763	−	0.540713i
$76$	−0.641525	+	0.370384i	−0.0735879	+	0.0424860i
$77$	1.19872	−	2.07624i	0.136606	−	0.236609i
$78$	1.47174	−	12.4418i	0.166642	−	1.40875i
$79$	5.57094	+	9.64914i	0.626779	+	1.08561i	0.988194	+	0.153208i	$0.0489606\pi$
$79$	5.57094	+	9.64914i	0.626779	+	1.08561i	−0.361415	+	0.932405i	$0.617706\pi$
$80$	−3.07468	−	1.77517i	−0.343760	−	0.198470i
$81$	1.66151	−	8.84530i	0.184612	−	0.982811i
$82$	−9.85030	−	17.0612i	−1.08778	−	1.88410i
$83$	−1.50053	+	0.866332i	−0.164705	+	0.0950923i	−0.580087	−	0.814555i	$-0.696981\pi$
$83$	−1.50053	+	0.866332i	−0.164705	+	0.0950923i	0.415382	+	0.909647i	$0.363648\pi$
$84$	8.40550	+	1.50627i	0.917115	+	0.164348i
$85$		−	3.61992i		−	0.392636i
$86$	10.8361	+	6.25623i	1.16849	+	0.674627i
$87$	7.96064	−	2.87234i	0.853470	−	0.307948i
$88$	0.0488281			0.00520509
$89$	4.61799	+	2.66620i	0.489506	+	0.282617i	0.724370	−	0.689412i	$-0.242131\pi$
$89$	4.61799	+	2.66620i	0.489506	+	0.282617i	−0.234863	+	0.972028i	$0.575464\pi$
$90$	0.909673	+	5.33260i	0.0958880	+	0.562105i
$91$	4.83470	+	7.32847i	0.506814	+	0.768232i
$92$	−5.17648	−	8.96593i	−0.539686	−	0.934763i
$93$	11.0853	+	1.98650i	1.14949	+	0.205990i
$94$	−9.37565	−	16.2391i	−0.967024	−	1.67493i
$95$	0.328849			0.0337392
$96$	−4.71666	−	13.0721i	−0.481393	−	1.33417i
$97$	−2.54546	−	1.46962i	−0.258452	−	0.149217i	0.365176	−	0.930938i	$-0.381009\pi$
$97$	−2.54546	−	1.46962i	−0.258452	−	0.149217i	−0.623628	+	0.781721i	$0.714342\pi$
$98$	1.86025	−	1.07401i	0.187913	−	0.108492i
$99$	1.88596	+	2.27321i	0.189546	+	0.228466i
$100$	4.24392	+	7.35068i	0.424392	+	0.735068i
$101$	−3.28913			−0.327281			−0.163640	−	0.986520i	$-0.552324\pi$
$101$	−3.28913			−0.327281			−0.163640	+	0.986520i	$0.552324\pi$
$102$	9.02516	−	10.6951i	0.893624	−	1.05897i
$103$	−2.77531	+	4.80698i	−0.273460	+	0.473646i	−0.969745	−	0.244119i	$-0.921501\pi$
$103$	−2.77531	+	4.80698i	−0.273460	+	0.473646i	0.696286	+	0.717765i	$0.254835\pi$
$104$	−0.0800271	+	0.159904i	−0.00784731	+	0.0156799i
$105$	−2.89719	−	2.44481i	−0.282736	−	0.238589i
$106$		−	3.53568i		−	0.343415i
$107$	−8.45290	+	14.6408i	−0.817172	+	1.41538i	0.0905854	+	0.995889i	$0.471126\pi$
$107$	−8.45290	+	14.6408i	−0.817172	+	1.41538i	−0.907758	+	0.419495i	$0.862207\pi$
$108$	−5.33635	+	9.06696i	−0.513490	+	0.872468i
$109$		−	4.94085i		−	0.473247i	−0.971601	−	0.236624i	$-0.923959\pi$
$109$		−	4.94085i		−	0.473247i	0.971601	−	0.236624i	$-0.0760408\pi$
$110$	−1.53752	−	0.887690i	−0.146597	−	0.0846379i
$111$	7.49151	+	1.34249i	0.711063	+	0.127423i
$112$	8.32958	+	4.80909i	0.787072	+	0.454416i
$113$	14.3748			1.35227			0.676134	−	0.736779i	$-0.263654\pi$
$113$	14.3748			1.35227			0.676134	+	0.736779i	$0.263654\pi$
$114$	0.971588	+	0.819882i	0.0909975	+	0.0767890i
$115$			4.59598i			0.428577i
$116$	−9.89300			−0.918542
$117$	−10.5354	+	2.45054i	−0.973999	+	0.226552i
$118$	−20.6986			−1.90546
$119$			9.80669i			0.898977i
$120$	0.0136189	−	0.0759977i	0.00124323	−	0.00693760i
$121$	10.0306			0.911875
$122$	−25.7809	−	14.8846i	−2.33409	−	1.34759i
$123$	−10.9693	+	12.9989i	−0.989065	+	1.17207i
$124$	−11.4011	−	6.58241i	−1.02385	−	0.591118i
$125$		−	8.26215i		−	0.738990i
$126$	−2.46438	−	14.4465i	−0.219545	−	1.28699i
$127$	−0.291856	+	0.505510i	−0.0258980	+	0.0448567i	−0.878684	−	0.477404i	$-0.841578\pi$
$127$	−0.291856	+	0.505510i	−0.0258980	+	0.0448567i	0.852786	+	0.522261i	$0.174911\pi$
$128$			0.396718i			0.0350652i
$129$	1.90552	−	10.6334i	0.167771	−	0.936218i
$130$	5.42698	−	3.58026i	0.475978	−	0.314010i
$131$	3.56421	−	6.17340i	0.311407	−	0.539372i	−0.667260	−	0.744825i	$-0.732533\pi$
$131$	3.56421	−	6.17340i	0.311407	−	0.539372i	0.978667	+	0.205452i	$0.0658665\pi$
$132$	−1.17188	−	3.24784i	−0.101999	−	0.282688i
$133$	−0.890880			−0.0772491
$134$	4.57705	+	7.92768i	0.395397	+	0.684847i
$135$	4.06412	−	2.30135i	0.349784	−	0.198068i
$136$	−0.172972	+	0.0998655i	−0.0148322	+	0.00856340i
$137$	−5.12701	−	2.96008i	−0.438030	−	0.252897i	0.264732	−	0.964322i	$-0.414717\pi$
$137$	−5.12701	−	2.96008i	−0.438030	−	0.252897i	−0.702762	+	0.711425i	$0.748050\pi$
$138$	−11.4587	+	13.5789i	−0.975426	+	1.15591i
$139$	18.0150			1.52802			0.764008	−	0.645207i	$-0.223229\pi$
$139$	18.0150			1.52802			0.764008	+	0.645207i	$0.223229\pi$
$140$	2.21572	+	3.83774i	0.187263	+	0.324348i
$141$	−10.4407	+	12.3726i	−0.879265	+	1.04196i
$142$	4.31035	+	7.46574i	0.361716	+	0.626511i
$143$	1.58876	−	3.17453i	0.132859	−	0.265468i
$144$	−9.11981	+	7.56623i	−0.759984	+	0.630520i
$145$	3.80340	+	2.19589i	0.315855	+	0.182359i
$146$	33.9862			2.81272
$147$	−1.41732	−	1.19602i	−0.116899	−	0.0986459i
$148$	−7.70492	−	4.44844i	−0.633340	−	0.365659i
$149$		−	21.6704i		−	1.77531i	−0.460509	−	0.887655i	$-0.652333\pi$
$149$		−	21.6704i		−	1.77531i	0.460509	−	0.887655i	$-0.347667\pi$
$150$	9.39433	−	11.1326i	0.767044	−	0.908972i
$151$	−6.14639	+	3.54862i	−0.500187	+	0.288783i	−0.728791	−	0.684737i	$-0.759917\pi$
$151$	−6.14639	+	3.54862i	−0.500187	+	0.288783i	0.228604	+	0.973519i	$0.426584\pi$
$152$	−0.00907220	−	0.0157135i	−0.000735852	−	0.00127453i
$153$	−11.3303	−	4.19552i	−0.915997	−	0.339187i
$154$	4.16528	+	2.40483i	0.335648	+	0.193787i
$155$	2.92212	+	5.06127i	0.234711	+	0.406531i
$156$	12.5568	+	1.48535i	1.00535	+	0.118923i
$157$	−2.51333	+	4.35322i	−0.200586	+	0.347425i	−0.948717	−	0.316126i	$-0.897618\pi$
$157$	−2.51333	+	4.35322i	−0.200586	+	0.347425i	0.748131	+	0.663550i	$0.230951\pi$
$158$	−19.3578	+	11.1762i	−1.54003	+	0.889135i
$159$	−2.87137	+	1.03604i	−0.227715	+	0.0821636i
$160$	3.60587	−	6.24555i	0.285069	−	0.493754i
$161$		−	12.4509i		−	0.981269i
$162$	17.7452	+	3.33327i	1.39419	+	0.261886i
$163$	2.07274	−	1.19670i	0.162349	−	0.0937325i	−0.416624	−	0.909079i	$-0.636787\pi$
$163$	2.07274	−	1.19670i	0.162349	−	0.0937325i	0.578973	+	0.815346i	$0.303453\pi$
$164$	17.2190	−	9.94138i	1.34458	−	0.776291i
$165$	−0.270371	+	1.50876i	−0.0210484	+	0.117457i
$166$	−1.73801	−	3.01032i	−0.134896	−	0.233646i
$167$	−11.4182	+	6.59232i	−0.883569	+	0.510129i	−0.871834	−	0.489802i	$-0.837069\pi$
$167$	−11.4182	+	6.59232i	−0.883569	+	0.510129i	−0.0117355	+	0.999931i	$0.503736\pi$
$168$	−0.0368947	+	0.205884i	−0.00284649	+	0.0158843i
$169$	7.79219	+	10.4059i	0.599399	+	0.800450i
$170$	7.26218			0.556984
$171$	0.381138	−	1.02929i	0.0291464	−	0.0787115i
$172$	−6.31408	+	10.9363i	−0.481444	+	0.833885i
$173$	7.40505	−	12.8259i	0.562995	−	0.975137i	−0.434238	−	0.900798i	$-0.642982\pi$
$173$	7.40505	−	12.8259i	0.562995	−	0.975137i	0.997233	−	0.0743384i	$-0.0236845\pi$
$174$	5.76241	+	15.9704i	0.436847	+	1.21071i
$175$			10.2078i			0.771639i
$176$		−	3.88898i		−	0.293143i
$177$	6.06521	+	16.8096i	0.455889	+	1.26349i
$178$	−5.34885	+	9.26448i	−0.400913	+	0.694402i
$179$	9.30352	−	16.1142i	0.695377	−	1.20443i	−0.274676	−	0.961537i	$-0.588571\pi$
$179$	9.30352	−	16.1142i	0.695377	−	1.20443i	0.970053	−	0.242892i	$-0.0780961\pi$
$180$	−5.38191	+	0.918085i	−0.401144	+	0.0684300i
$181$	−7.70819			−0.572945			−0.286473	−	0.958088i	$-0.592483\pi$
$181$	−7.70819			−0.572945			−0.286473	+	0.958088i	$0.592483\pi$
$182$	−14.7022	+	9.69923i	−1.08980	+	0.718955i
$183$	−4.53354	+	25.2986i	−0.335129	+	1.87013i
$184$	0.219612	−	0.126793i	0.0161900	−	0.00934729i
$185$	1.97479	+	3.42044i	0.145189	+	0.251475i
$186$	−3.98525	+	22.2390i	−0.292213	+	1.63064i
$187$	3.43397	−	1.98260i	0.251117	−	0.144982i
$188$	16.3892	−	9.46234i	1.19531	−	0.690112i
$189$	−11.0101	+	6.23455i	−0.800863	+	0.453497i
$190$			0.659727i			0.0478616i
$191$	2.37949	−	4.12140i	0.172174	−	0.298214i	−0.767006	−	0.641640i	$-0.778254\pi$
$191$	2.37949	−	4.12140i	0.172174	−	0.298214i	0.939180	+	0.343426i	$0.111588\pi$
$192$	13.3541	−	4.81841i	0.963749	−	0.347738i
$193$	−7.85345	+	4.53419i	−0.565304	+	0.326378i	−0.755271	−	0.655412i	$-0.772495\pi$
$193$	−7.85345	+	4.53419i	−0.565304	+	0.326378i	0.189968	+	0.981790i	$0.439162\pi$
$194$	2.94831	−	5.10662i	0.211676	−	0.366634i
$195$	−4.49782	−	3.35822i	−0.322096	−	0.240487i
$196$	1.08394	+	1.87745i	0.0774246	+	0.134103i
$197$	11.2703	+	6.50689i	0.802973	+	0.463597i	0.844510	−	0.535540i	$-0.179892\pi$
$197$	11.2703	+	6.50689i	0.802973	+	0.463597i	−0.0415366	+	0.999137i	$0.513225\pi$
$198$	−4.56044	+	3.78356i	−0.324097	+	0.268886i
$199$	1.09764	+	1.90117i	0.0778099	+	0.134771i	0.902305	−	0.431099i	$-0.141874\pi$
$199$	1.09764	+	1.90117i	0.0778099	+	0.134771i	−0.824495	+	0.565869i	$0.808541\pi$
$200$	−0.180047	+	0.103950i	−0.0127313	+	0.00735041i
$201$	5.09699	−	6.04010i	0.359514	−	0.426036i
$202$		−	6.59856i		−	0.464273i
$203$	−10.3037	−	5.94887i	−0.723181	−	0.417529i
$204$	10.7940	+	9.10861i	0.755731	+	0.637730i
$205$	−8.82653			−0.616471
$206$	−9.64363	−	5.56775i	−0.671903	−	0.387924i
$207$	14.3853	+	5.32677i	0.999846	+	0.370236i
$208$	12.7358	+	6.37388i	0.883069	+	0.441949i
$209$	0.180108	+	0.311956i	0.0124583	+	0.0215784i
$210$	4.90471	−	5.81225i	0.338457	−	0.401083i
$211$	−0.624793	−	1.08217i	−0.0430125	−	0.0744999i	0.843718	−	0.536787i	$-0.180362\pi$
$211$	−0.624793	−	1.08217i	−0.0430125	−	0.0744999i	−0.886730	+	0.462287i	$0.847029\pi$
$212$	3.56837			0.245077
$213$	4.79999	−	5.68815i	0.328890	−	0.389746i
$214$	−29.3720	−	16.9579i	−2.00783	−	1.15922i
$215$	4.85494	−	2.80300i	0.331104	−	0.191163i
$216$	−0.222086	−	0.130708i	−0.0151110	−	0.00889358i
$217$	−7.91629	−	13.7114i	−0.537393	−	0.930791i
$218$	9.91218			0.671337
$219$	−9.95882	−	27.6006i	−0.672955	−	1.86508i
$220$	0.895898	−	1.55174i	0.0604014	−	0.104618i
$221$	0.864579	+	14.4951i	0.0581579	+	0.975046i
$222$	−2.69326	+	15.0292i	−0.180760	+	1.00870i
$223$		−	27.4662i		−	1.83927i	−0.392774	−	0.919635i	$-0.628485\pi$
$223$		−	27.4662i		−	1.83927i	0.392774	−	0.919635i	$-0.371515\pi$
$224$	−9.76861	+	16.9197i	−0.652693	+	1.13050i
$225$	−11.7937	−	4.36713i	−0.786247	−	0.291142i
$226$			28.8383i			1.91830i
$227$	−17.0695	−	9.85509i	−1.13294	−	0.654105i	−0.188270	−	0.982117i	$-0.560288\pi$
$227$	−17.0695	−	9.85509i	−1.13294	−	0.654105i	−0.944674	+	0.328012i	$0.893621\pi$
$228$	−0.827463	+	0.980571i	−0.0548001	+	0.0649399i
$229$	−18.0911	−	10.4449i	−1.19549	−	0.690219i	−0.235947	−	0.971766i	$-0.575819\pi$
$229$	−18.0911	−	10.4449i	−1.19549	−	0.690219i	−0.959547	+	0.281547i	$0.909152\pi$
$230$	−9.22032			−0.607970
$231$	0.732460	−	4.08736i	0.0481923	−	0.268929i
$232$		−	0.242319i		−	0.0159090i
$233$	−8.26641			−0.541551			−0.270775	−	0.962643i	$-0.587280\pi$
$233$	−8.26641			−0.541551			−0.270775	+	0.962643i	$0.587280\pi$
$234$	−4.91620	−	21.1358i	−0.321382	−	1.38169i
$235$	−8.40121			−0.548034
$236$		−	20.8900i		−	1.35982i
$237$	14.7487	+	12.4458i	0.958033	+	0.808444i
$238$	−19.6739			−1.27527
$239$	0.510566	+	0.294776i	0.0330258	+	0.0190674i	0.516422	−	0.856334i	$-0.327264\pi$
$239$	0.510566	+	0.294776i	0.0330258	+	0.0190674i	−0.483396	+	0.875402i	$0.660597\pi$
$240$	−6.05295	−	1.08469i	−0.390716	−	0.0700167i
$241$	14.2757	+	8.24209i	0.919580	+	0.530920i	0.883501	−	0.468429i	$-0.155180\pi$
$241$	14.2757	+	8.24209i	0.919580	+	0.530920i	0.0360792	+	0.999349i	$0.488513\pi$
$242$			20.1232i			1.29357i
$243$	−2.49280	−	15.3879i	−0.159913	−	0.987131i
$244$	15.0222	−	26.0193i	0.961700	−	1.66571i
$245$		−	0.962388i		−	0.0614847i
$246$	−26.0781	−	22.0062i	−1.66268	−	1.40306i
$247$	−1.31680	+	0.0785419i	−0.0837857	+	0.00499750i
$248$	0.161230	−	0.279258i	0.0102381	−	0.0177329i
$249$	−1.93544	+	2.29356i	−0.122654	+	0.145349i
$250$	16.5753			1.04831
$251$	9.74072	+	16.8714i	0.614829	+	1.06492i	0.990414	+	0.138127i	$0.0441083\pi$
$251$	9.74072	+	16.8714i	0.614829	+	1.06492i	−0.375585	+	0.926788i	$0.622558\pi$
$252$	14.5800	−	2.48717i	0.918457	−	0.156677i
$253$	−4.35989	+	2.51718i	−0.274104	+	0.158254i
$254$	−1.01414	−	0.585513i	−0.0636327	−	0.0367384i
$255$	−2.12801	−	5.89772i	−0.133261	−	0.369330i
$256$	15.5972			0.974823
$257$	4.04729	+	7.01012i	0.252463	+	0.437279i	0.964203	−	0.265164i	$-0.0854260\pi$
$257$	4.04729	+	7.01012i	0.252463	+	0.437279i	−0.711740	+	0.702443i	$0.752093\pi$
$258$	21.3324	+	3.82279i	1.32810	+	0.237996i
$259$	−5.34988	−	9.26626i	−0.332425	−	0.575777i
$260$	3.61336	+	5.47716i	0.224091	+	0.339679i
$261$	11.2812	−	9.35947i	0.698292	−	0.579337i
$262$	12.3849	+	7.15042i	0.765141	+	0.441754i
$263$	−24.8705			−1.53358			−0.766792	−	0.641896i	$-0.778148\pi$
$263$	−24.8705			−1.53358			−0.766792	+	0.641896i	$0.778148\pi$
$264$	0.0795526	−	0.0287040i	0.00489612	−	0.00176661i
$265$	−1.37187	−	0.792051i	−0.0842735	−	0.0486553i
$266$		−	1.78726i		−	0.109584i
$267$	9.09117	+	1.62915i	0.556370	+	0.0997022i
$268$	−8.00099	+	4.61937i	−0.488738	+	0.282173i
$269$	−5.03220	−	8.71603i	−0.306819	−	0.531426i	0.670846	−	0.741597i	$-0.265931\pi$
$269$	−5.03220	−	8.71603i	−0.306819	−	0.531426i	−0.977665	+	0.210171i	$0.932598\pi$
$270$	4.61689	+	8.15332i	0.280975	+	0.496195i
$271$	3.72974	+	2.15337i	0.226566	+	0.130808i	0.608987	−	0.793180i	$-0.291576\pi$
$271$	3.72974	+	2.15337i	0.226566	+	0.130808i	−0.382421	+	0.923988i	$0.624910\pi$
$272$	7.95394	+	13.7766i	0.482278	+	0.835331i
$273$	12.1850	+	9.09770i	0.737469	+	0.550618i
$274$	5.93843	−	10.2857i	0.358754	−	0.621379i
$275$	3.57443	−	2.06370i	0.215546	−	0.124446i
$276$	−13.7044	−	11.5646i	−0.824910	−	0.696108i
$277$	5.28874	−	9.16037i	0.317770	−	0.550393i	−0.662253	−	0.749281i	$-0.730399\pi$
$277$	5.28874	−	9.16037i	0.317770	−	0.550393i	0.980022	+	0.198887i	$0.0637328\pi$
$278$			36.1413i			2.16761i
$279$	19.2284	−	3.28012i	1.15117	−	0.196375i
$280$	−0.0940016	+	0.0542718i	−0.00561767	+	0.00324336i
$281$	6.17654	−	3.56602i	0.368461	−	0.212731i	−0.304325	−	0.952568i	$-0.598431\pi$
$281$	6.17654	−	3.56602i	0.368461	−	0.212731i	0.672786	+	0.739837i	$0.265097\pi$
$282$	−24.8215	−	20.9458i	−1.47810	−	1.24730i
$283$	−8.73995	−	15.1380i	−0.519536	−	0.899863i	−0.999742	−	0.0227075i	$-0.992771\pi$
$283$	−8.73995	−	15.1380i	−0.519536	−	0.899863i	0.480206	−	0.877156i	$-0.340562\pi$
$284$	−7.53477	+	4.35020i	−0.447107	+	0.258137i
$285$	0.535773	−	0.193317i	0.0317365	−	0.0114511i
$286$	6.36866	+	3.18732i	0.376587	+	0.188470i
$287$	23.9118			1.41147
$288$	−15.3692	−	18.5249i	−0.905636	−	1.09159i
$289$	0.390167	−	0.675789i	0.0229510	−	0.0397523i
$290$	−4.40534	+	7.63027i	−0.258690	+	0.448065i
$291$	−5.01109	−	0.897992i	−0.293755	−	0.0526412i
$292$			34.3004i			2.00728i
$293$			2.57519i			0.150444i	0.997167	+	0.0752222i	$0.0239666\pi$
$293$			2.57519i			0.150444i	−0.997167	+	0.0752222i	$0.976033\pi$
$294$	2.39942	−	2.84339i	0.139937	−	0.165830i
$295$	−4.63683	+	8.03122i	−0.269967	+	0.467596i
$296$	0.108960	−	0.188724i	0.00633317	−	0.0109694i
$297$	4.40901	+	2.59492i	0.255837	+	0.150572i
$298$	43.4746			2.51841
$299$	−1.09770	−	18.4035i	−0.0634816	−	1.06430i
$300$	11.2355	+	9.48119i	0.648683	+	0.547397i
$301$	−13.1525	+	7.59357i	−0.758095	+	0.437686i
$302$	−7.11914	−	12.3307i	−0.409661	−	0.709553i
$303$	−5.35878	+	1.93355i	−0.307854	+	0.111079i
$304$	−1.25153	+	0.722569i	−0.0717799	+	0.0414422i
$305$	−11.5507	+	6.66881i	−0.661392	+	0.381855i
$306$	8.41692	−	22.7304i	0.481163	−	1.29941i
$307$		−	10.3955i		−	0.593300i	−0.954986	−	0.296650i	$-0.904130\pi$
$307$		−	10.3955i		−	0.593300i	0.954986	−	0.296650i	$-0.0958695\pi$
$308$	−2.42706	+	4.20380i	−0.138295	+	0.239534i
$309$	−1.69582	+	9.46322i	−0.0964717	+	0.538344i
$310$	−10.1538	+	5.86228i	−0.576695	+	0.332955i
$311$	−4.60323	+	7.97302i	−0.261025	+	0.452109i	−0.966515	−	0.256612i	$-0.917394\pi$
$311$	−4.60323	+	7.97302i	−0.261025	+	0.452109i	0.705490	+	0.708720i	$0.250727\pi$
$312$	−0.0363822	+	0.307567i	−0.00205974	+	0.0174125i
$313$	−9.77715	−	16.9345i	−0.552637	−	0.957195i	−0.998083	−	0.0618867i	$-0.980288\pi$
$313$	−9.77715	−	16.9345i	−0.552637	−	0.957195i	0.445446	−	0.895309i	$-0.353045\pi$
$314$	−8.73330	−	5.04218i	−0.492849	−	0.284546i
$315$	−6.15742	−	2.28005i	−0.346931	−	0.128466i
$316$	−11.2796	−	19.5368i	−0.634526	−	1.09903i
$317$	9.82909	−	5.67483i	0.552056	−	0.318730i	−0.197895	−	0.980223i	$-0.563410\pi$
$317$	9.82909	−	5.67483i	0.552056	−	0.318730i	0.749951	+	0.661493i	$0.230077\pi$
$318$	−2.07848	−	5.76046i	−0.116555	−	0.323031i
$319$			4.81069i			0.269347i
$320$	6.38027	+	3.68365i	0.356668	+	0.205922i
$321$	−5.16503	+	28.8226i	−0.288284	+	1.60872i
$322$	24.9787			1.39201
$323$	−1.27605	−	0.736731i	−0.0710016	−	0.0409928i
$324$	−3.36409	+	17.9093i	−0.186894	+	0.994959i
$325$	0.899944	+	15.0880i	0.0499199	+	0.836933i
$326$	2.40078	+	4.15827i	0.132967	+	0.230305i
$327$	−2.90452	−	8.04982i	−0.160620	−	0.445156i
$328$	0.243504	+	0.421761i	0.0134453	+	0.0232879i
$329$	22.7596			1.25478
$330$	−3.02683	−	0.542411i	−0.166622	−	0.0298588i
$331$	−3.09270	−	1.78557i	−0.169990	−	0.0981438i	0.412591	−	0.910916i	$-0.364624\pi$
$331$	−3.09270	−	1.78557i	−0.169990	−	0.0981438i	−0.582581	+	0.812773i	$0.697957\pi$
$332$	3.03816	−	1.75408i	0.166741	−	0.0962677i
$333$	12.9947	−	2.21672i	0.712103	−	0.121476i
$334$	−13.2253	−	22.9069i	−0.723657	−	1.25341i
$335$	4.10134			0.224080
$336$	16.3980	+	2.93853i	0.894582	+	0.160310i
$337$	−11.5647	+	20.0307i	−0.629970	+	1.09114i	0.357587	+	0.933880i	$0.383599\pi$
$337$	−11.5647	+	20.0307i	−0.629970	+	1.09114i	−0.987557	+	0.157260i	$0.949734\pi$
$338$	−20.8759	+	15.6325i	−1.13550	+	0.850294i
$339$	23.4200	−	8.45036i	1.27200	−	0.458961i
$340$			7.32933i			0.397489i
$341$	−3.20085	+	5.54403i	−0.173336	+	0.300226i
$342$	2.06492	+	0.764628i	0.111658	+	0.0413463i
$343$			19.6523i			1.06112i
$344$	−0.267874	−	0.154657i	−0.0144428	−	0.00833855i
$345$	2.70179	+	7.48795i	0.145460	+	0.403138i
$346$	25.7310	+	14.8558i	1.38331	+	0.798652i
$347$	−6.68932			−0.359101			−0.179551	−	0.983749i	$-0.557464\pi$
$347$	−6.68932			−0.359101			−0.179551	+	0.983749i	$0.557464\pi$
$348$	−16.1181	+	5.81569i	−0.864019	+	0.311754i
$349$		−	13.7258i		−	0.734723i	−0.930078	−	0.367361i	$-0.880261\pi$
$349$		−	13.7258i		−	0.734723i	0.930078	−	0.367361i	$-0.119739\pi$
$350$	−20.4786			−1.09463
$351$	−15.7241	+	10.1859i	−0.839292	+	0.543681i
$352$	7.89962			0.421051
$353$		−	0.411261i		−	0.0218892i	−0.999940	−	0.0109446i	$-0.996516\pi$
$353$		−	0.411261i		−	0.0218892i	0.999940	−	0.0109446i	$-0.00348384\pi$
$354$	−33.7229	+	12.1679i	−1.79235	+	0.646714i
$355$	3.86236			0.204993
$356$	−9.35015	−	5.39831i	−0.495557	−	0.286110i
$357$	5.76495	+	15.9774i	0.305114	+	0.845616i
$358$	32.3278	+	18.6644i	1.70858	+	0.986446i
$359$			6.33956i			0.334589i	0.985907	+	0.167295i	$0.0535031\pi$
$359$			6.33956i			0.334589i	−0.985907	+	0.167295i	$0.946497\pi$
$360$	−0.0224876	−	0.131824i	−0.00118520	−	0.00694775i
$361$	−9.43307	+	16.3386i	−0.496477	+	0.859924i
$362$		−	15.4639i		−	0.812767i
$363$	16.3423	−	5.89660i	0.857748	−	0.309491i
$364$	−9.78892	−	14.8381i	−0.513079	−	0.777728i
$365$	7.61347	−	13.1869i	0.398507	−	0.690235i
$366$	−50.7533	−	9.09505i	−2.65292	−	0.475406i
$367$	28.1063			1.46714			0.733568	−	0.679616i	$-0.237854\pi$
$367$	28.1063			1.46714			0.733568	+	0.679616i	$0.237854\pi$
$368$	−10.0986	−	17.4913i	−0.526426	−	0.911796i
$369$	−10.2300	+	27.6268i	−0.532553	+	1.43819i
$370$	−6.86198	+	3.96176i	−0.356737	+	0.205962i
$371$	3.71652	+	2.14574i	0.192952	+	0.111401i
$372$	−22.4446	−	4.02210i	−1.16370	−	0.208536i
$373$	6.68700			0.346240			0.173120	−	0.984901i	$-0.444615\pi$
$373$	6.68700			0.346240			0.173120	+	0.984901i	$0.444615\pi$
$374$	3.97744	+	6.88913i	0.205669	+	0.356228i
$375$	−4.85699	−	13.4610i	−0.250814	−	0.695124i
$376$	0.231770	+	0.401438i	0.0119526	+	0.0207026i
$377$	−15.7543	−	7.88453i	−0.811386	−	0.406074i
$378$	−12.5076	−	22.0880i	−0.643320	−	1.13609i
$379$	0.841149	+	0.485637i	0.0432069	+	0.0249455i	0.521448	−	0.853283i	$-0.325392\pi$
$379$	0.841149	+	0.485637i	0.0432069	+	0.0249455i	−0.478241	+	0.878229i	$0.658725\pi$
$380$	−0.665827			−0.0341562
$381$	−0.178335	+	0.995167i	−0.00913637	+	0.0509839i
$382$	8.26823	+	4.77367i	0.423040	+	0.244242i
$383$			23.8103i			1.21665i	0.793687	+	0.608326i	$0.208159\pi$
$383$			23.8103i			1.21665i	−0.793687	+	0.608326i	$0.791841\pi$
$384$	0.233214	+	0.646348i	0.0119012	+	0.0329838i
$385$	1.86619	−	1.07744i	0.0951097	−	0.0549116i
$386$	−9.09636	−	15.7554i	−0.462993	−	0.801927i
$387$	−3.14640	−	18.4445i	−0.159941	−	0.937588i
$388$	5.15384	+	2.97557i	0.261647	+	0.151062i
$389$	18.5682	+	32.1610i	0.941443	+	1.63063i	0.762721	+	0.646727i	$0.223863\pi$
$389$	18.5682	+	32.1610i	0.941443	+	1.63063i	0.178721	+	0.983900i	$0.442804\pi$
$390$	6.73716	−	9.02340i	0.341149	−	0.456918i
$391$	10.2965	−	17.8341i	0.520718	−	0.901910i
$392$	−0.0459862	+	0.0265501i	−0.00232265	+	0.00134098i
$393$	2.17787	−	12.1532i	0.109859	−	0.613048i
$394$	−13.0539	+	22.6101i	−0.657648	+	1.13908i
$395$			10.0147i			0.503893i
$396$	−3.81855	−	4.60261i	−0.191889	−	0.231290i
$397$	−7.03686	+	4.06274i	−0.353170	+	0.203903i	−0.666081	−	0.745880i	$-0.732029\pi$
$397$	−7.03686	+	4.06274i	−0.353170	+	0.203903i	0.312911	+	0.949783i	$0.398696\pi$
$398$	−3.81408	+	2.20206i	−0.191182	+	0.110379i
$399$	−1.45146	+	0.523712i	−0.0726637	+	0.0262184i
$400$	8.27929	+	14.3402i	0.413965	+	0.717008i
$401$	9.15169	−	5.28373i	0.457014	−	0.263857i	−0.253774	−	0.967264i	$-0.581672\pi$
$401$	9.15169	−	5.28373i	0.457014	−	0.263857i	0.710788	+	0.703406i	$0.248339\pi$
$402$	12.1175	+	10.2254i	0.604365	+	0.509998i
$403$	−12.9098	−	19.5687i	−0.643081	−	0.974786i
$404$	6.65957			0.331326
$405$	5.26856	−	6.13858i	0.261797	−	0.305028i
$406$	11.9344	−	20.6711i	0.592296	−	1.02589i
$407$	−2.16315	+	3.74669i	−0.107223	+	0.185717i
$408$	−0.223106	+	0.264388i	−0.0110454	+	0.0130892i
$409$			8.38307i			0.414516i	0.978286	+	0.207258i	$0.0664540\pi$
$409$			8.38307i			0.414516i	−0.978286	+	0.207258i	$0.933546\pi$
$410$		−	17.7075i		−	0.874512i
$411$	−10.0932	−	1.80872i	−0.497863	−	0.0892176i
$412$	5.61923	−	9.73279i	0.276840	−	0.479500i
$413$	12.5616	−	21.7573i	0.618114	−	1.07061i
$414$	−10.6864	+	28.8593i	−0.525209	+	1.41836i
$415$	−1.55737			−0.0764485
$416$	−12.9471	+	25.8700i	−0.634786	+	1.26838i
$417$	29.3508	−	10.5903i	1.43732	−	0.518610i
$418$	−0.625837	+	0.361327i	−0.0306107	+	0.0176731i
$419$	−14.6417	−	25.3601i	−0.715292	−	1.23892i	−0.962847	−	0.270048i	$-0.912961\pi$
$419$	−14.6417	−	25.3601i	−0.715292	−	1.23892i	0.247555	−	0.968874i	$-0.420373\pi$
$420$	5.86599	+	4.95007i	0.286231	+	0.241538i
$421$	−27.8767	+	16.0946i	−1.35863	+	0.784404i	−0.989439	−	0.144951i	$-0.953698\pi$
$421$	−27.8767	+	16.0946i	−1.35863	+	0.784404i	−0.369188	+	0.929355i	$0.620364\pi$
$422$	2.17102	−	1.25344i	0.105684	−	0.0610166i
$423$	−9.73706	+	26.2955i	−0.473432	+	1.27853i
$424$			0.0874036i			0.00424470i
$425$	−8.44156	+	14.6212i	−0.409476	+	0.709233i
$426$	11.4114	+	9.62960i	0.552884	+	0.466556i
$427$	31.2919	−	18.0664i	1.51432	−	0.874293i
$428$	17.1147	−	29.6436i	0.827273	−	1.43288i
$429$	0.722286	−	6.10604i	0.0348723	−	0.294802i
$430$	5.62330	+	9.73984i	0.271180	+	0.469697i
$431$	2.03163	+	1.17296i	0.0978601	+	0.0564995i	0.548131	−	0.836392i	$-0.315339\pi$
$431$	2.03163	+	1.17296i	0.0978601	+	0.0564995i	−0.450271	+	0.892892i	$0.648673\pi$
$432$	−10.4105	+	17.6884i	−0.500874	+	0.851032i
$433$	7.44780	+	12.9000i	0.357918	+	0.619933i	0.987613	−	0.156910i	$-0.0501532\pi$
$433$	7.44780	+	12.9000i	0.357918	+	0.619933i	−0.629694	+	0.776843i	$0.716820\pi$
$434$	27.5074	−	15.8814i	1.32040	−	0.762333i
$435$	7.48753	+	1.34177i	0.358999	+	0.0643331i
$436$			10.0038i			0.479097i
$437$	1.62012	+	0.935379i	0.0775010	+	0.0447452i
$438$	55.3716	−	19.9791i	2.64576	−	0.954638i
$439$	27.4729			1.31121			0.655606	−	0.755103i	$-0.272413\pi$
$439$	27.4729			1.31121			0.655606	+	0.755103i	$0.272413\pi$
$440$	0.0380083	+	0.0219441i	0.00181198	+	0.00104614i
$441$	−3.01225	−	1.11541i	−0.143440	−	0.0531150i
$442$	−29.0797	+	1.73449i	−1.38318	+	0.0825014i
$443$	−3.91212	−	6.77599i	−0.185870	−	0.321937i	0.757999	−	0.652256i	$-0.226177\pi$
$443$	−3.91212	−	6.77599i	−0.185870	−	0.321937i	−0.943869	+	0.330319i	$0.892844\pi$
$444$	−15.1682	−	2.71816i	−0.719851	−	0.128998i
$445$	2.39647	+	4.15080i	0.113603	+	0.196767i
$446$	55.1018			2.60915
$447$	−12.7392	−	35.3063i	−0.602542	−	1.66993i
$448$	−17.2847	−	9.97933i	−0.816625	−	0.471479i
$449$	−10.0371	+	5.79492i	−0.473680	+	0.273479i	−0.717779	−	0.696271i	$-0.754841\pi$
$449$	−10.0371	+	5.79492i	−0.473680	+	0.273479i	0.244099	+	0.969750i	$0.421508\pi$
$450$	8.76121	−	23.6602i	0.413007	−	1.11535i
$451$	−4.83422	−	8.37311i	−0.227634	−	0.394274i
$452$	−29.1050			−1.36898
$453$	−7.92786	+	9.39477i	−0.372483	+	0.441405i
$454$	19.7710	−	34.2444i	0.927899	−	1.60717i
$455$	0.469855	+	7.87735i	0.0220271	+	0.369296i
$456$	−0.0240181	−	0.0202679i	−0.00112475	−	0.000949131i
$457$			23.8391i			1.11515i	0.830128	+	0.557573i	$0.188267\pi$
$457$			23.8391i			1.11515i	−0.830128	+	0.557573i	$0.811733\pi$
$458$	20.9543	−	36.2939i	0.979128	−	1.69590i
$459$	−20.9261	−	0.174905i	−0.976745	−	0.00816388i
$460$		−	9.30558i		−	0.433875i
$461$	−17.1647	−	9.91004i	−0.799439	−	0.461556i	0.0438358	−	0.999039i	$-0.486042\pi$
$461$	−17.1647	−	9.91004i	−0.799439	−	0.461556i	−0.843275	+	0.537482i	$0.819375\pi$
$462$	8.19995	+	1.46944i	0.381496	+	0.0683645i
$463$	−11.3204	−	6.53583i	−0.526103	−	0.303746i	0.213325	−	0.976981i	$-0.431571\pi$
$463$	−11.3204	−	6.53583i	−0.526103	−	0.303746i	−0.739428	+	0.673235i	$0.764904\pi$
$464$	−19.2999			−0.895974
$465$	7.73615	+	6.52822i	0.358756	+	0.302739i
$466$		−	16.5838i		−	0.768231i
$467$	7.50387			0.347237			0.173619	−	0.984813i	$-0.444454\pi$
$467$	7.50387			0.347237			0.173619	+	0.984813i	$0.444454\pi$
$468$	21.3313	−	4.96166i	0.986038	−	0.229353i
$469$	−11.1109			−0.513054
$470$		−	16.8543i		−	0.777429i
$471$	−1.53574	+	8.56993i	−0.0707631	+	0.394881i
$472$	0.511679			0.0235519
$473$	5.31802	+	3.07036i	0.244523	+	0.141175i
$474$	−24.9685	+	29.5885i	−1.14684	+	1.35904i
$475$	−1.32825	−	0.766866i	−0.0609443	−	0.0351862i
$476$		−	19.8558i		−	0.910089i
$477$	−4.06911	+	3.37593i	−0.186312	+	0.154573i
$478$	−0.591370	+	1.02428i	−0.0270486	+	0.0468496i
$479$			26.6603i			1.21814i	0.793116	+	0.609071i	$0.208458\pi$
$479$			26.6603i			1.21814i	−0.793116	+	0.609071i	$0.791542\pi$
$480$	2.20332	−	12.2952i	0.100567	−	0.561198i
$481$	−8.72450	−	13.2246i	−0.397803	−	0.602992i
$482$	−16.5350	+	28.6395i	−0.753151	+	1.30450i
$483$	−7.31939	−	20.2855i	−0.333044	−	0.923023i
$484$	−20.3092			−0.923146
$485$	−1.32094	−	2.28794i	−0.0599809	−	0.103890i
$486$	30.8707	−	5.00099i	1.40032	−	0.226849i
$487$	3.32314	−	1.91861i	0.150586	−	0.0869407i	−0.422814	−	0.906217i	$-0.638958\pi$
$487$	3.32314	−	1.91861i	0.150586	−	0.0869407i	0.573400	+	0.819276i	$0.305624\pi$
$488$	0.637316	+	0.367955i	0.0288499	+	0.0166565i
$489$	2.67350	−	3.16818i	0.120900	−	0.143270i
$490$	1.93072			0.0872208
$491$	9.58845	+	16.6077i	0.432720	+	0.749494i	0.997107	−	0.0760171i	$-0.0242204\pi$
$491$	9.58845	+	16.6077i	0.432720	+	0.749494i	−0.564386	+	0.825511i	$0.690887\pi$
$492$	22.2097	−	26.3192i	1.00129	−	1.18656i
$493$	−9.83907	−	17.0418i	−0.443129	−	0.767522i
$494$	−0.157569	−	2.64172i	−0.00708934	−	0.118856i
$495$	0.446439	+	2.61707i	0.0200660	+	0.117629i
$496$	−22.2419	−	12.8414i	−0.998691	−	0.576595i
$497$	−10.4635			−0.469351
$498$	−4.60128	−	3.88283i	−0.206188	−	0.173994i
$499$	−13.6804	−	7.89837i	−0.612418	−	0.353579i	0.161493	−	0.986874i	$-0.448369\pi$
$499$	−13.6804	−	7.89837i	−0.612418	−	0.353579i	−0.773911	+	0.633294i	$0.781702\pi$
$500$			16.7286i			0.748124i
$501$	−14.7277	+	17.4528i	−0.657984	+	0.779733i
$502$	−33.8470	+	19.5416i	−1.51066	+	0.872182i
$503$	−0.153970	−	0.266683i	−0.00686517	−	0.0118908i	0.862572	−	0.505934i	$-0.168852\pi$
$503$	−0.153970	−	0.266683i	−0.00686517	−	0.0118908i	−0.869438	+	0.494043i	$0.835519\pi$
$504$	0.0609207	+	0.357124i	0.00271363	+	0.0159075i
$505$	−2.56030	−	1.47819i	−0.113932	−	0.0657785i
$506$	−5.04990	−	8.74668i	−0.224495	−	0.388837i
$507$	18.8125	+	12.3729i	0.835493	+	0.549501i
$508$	0.590927	−	1.02352i	0.0262181	−	0.0454112i
$509$	5.68251	−	3.28080i	0.251873	−	0.145419i	−0.368749	−	0.929529i	$-0.620214\pi$
$509$	5.68251	−	3.28080i	0.251873	−	0.145419i	0.620621	+	0.784110i	$0.286880\pi$
$510$	11.8318	−	4.26914i	0.523923	−	0.189041i
$511$	−20.6256	+	35.7245i	−0.912421	+	1.58036i
$512$			32.0840i			1.41793i
$513$	0.0158891	−	1.90101i	0.000701522	−	0.0839316i
$514$	−14.0635	+	8.11956i	−0.620314	+	0.358138i
$515$	−4.32067	+	2.49454i	−0.190391	+	0.109923i
$516$	−3.85814	+	21.5297i	−0.169845	+	0.947790i
$517$	−4.60127	−	7.96964i	−0.202364	−	0.350504i
$518$	18.5897	−	10.7328i	0.816784	−	0.471570i
$519$	4.52476	−	25.2496i	0.198615	−	1.10834i
$520$	−0.134158	+	0.0885057i	−0.00588320	+	0.00388123i
$521$	−29.1859			−1.27866			−0.639330	−	0.768933i	$-0.720788\pi$
$521$	−29.1859			−1.27866			−0.639330	+	0.768933i	$0.720788\pi$
$522$	18.7767	+	22.6321i	0.821834	+	0.990581i
$523$	0.274105	−	0.474764i	0.0119858	−	0.0207600i	−0.859970	−	0.510344i	$-0.829518\pi$
$523$	0.274105	−	0.474764i	0.0119858	−	0.0207600i	0.871956	+	0.489584i	$0.162851\pi$
$524$	−7.21654	+	12.4994i	−0.315256	+	0.546039i
$525$	6.00076	+	16.6310i	0.261895	+	0.725836i
$526$		−	49.8946i		−	2.17551i
$527$		−	26.1861i		−	1.14069i
$528$	−2.28618	−	6.33609i	−0.0994931	−	0.275743i
$529$	−1.57283	+	2.72422i	−0.0683839	+	0.118444i
$530$	1.58899	−	2.75221i	0.0690213	−	0.119548i
$531$	19.7634	+	23.8214i	0.857657	+	1.03376i
$532$	1.80378			0.0782039
$533$	35.3437	−	2.10812i	1.53091	−	0.0913128i
$534$	−3.26835	+	18.2384i	−0.141435	+	0.789254i
$535$	−13.1597	+	7.59773i	−0.568942	+	0.328479i
$536$	−0.113147	−	0.195976i	−0.00488720	−	0.00846488i
$537$	5.68479	−	31.7230i	0.245317	−	1.36895i
$538$	17.4858	−	10.0955i	0.753868	−	0.435246i
$539$	0.912951	−	0.527092i	0.0393236	−	0.0227035i
$540$	−8.22871	+	4.65958i	−0.354107	+	0.200517i
$541$		−	30.6605i		−	1.31820i	−0.752056	−	0.659099i	$-0.770938\pi$
$541$		−	30.6605i		−	1.31820i	0.752056	−	0.659099i	$-0.229062\pi$
$542$	−4.32002	+	7.48249i	−0.185561	+	0.321401i
$543$	−12.5585	+	4.53133i	−0.538936	+	0.194458i
$544$	−27.9842	+	16.1567i	−1.19981	+	0.692712i
$545$	2.22049	−	3.84601i	0.0951155	−	0.164745i
$546$	−18.2515	+	24.4452i	−0.781094	+	1.04616i
$547$	2.50752	+	4.34315i	0.107214	+	0.185700i	0.914641	−	0.404268i	$-0.132474\pi$
$547$	2.50752	+	4.34315i	0.107214	+	0.185700i	−0.807427	+	0.589968i	$0.799140\pi$
$548$	10.3808	+	5.99334i	0.443444	+	0.256023i
$549$	7.48581	+	43.8826i	0.319487	+	1.87286i
$550$	4.14013	+	7.17092i	0.176536	+	0.305769i
$551$	1.54814	−	0.893821i	0.0659531	−	0.0380781i
$552$	0.283263	−	0.335676i	0.0120565	−	0.0142873i
$553$		−	27.1306i		−	1.15371i
$554$	18.3773	+	10.6101i	0.780775	+	0.450781i
$555$	5.22814	+	4.41181i	0.221922	+	0.187271i
$556$	−36.4754			−1.54690
$557$	−8.78270	−	5.07069i	−0.372135	−	0.214852i	0.302256	−	0.953227i	$-0.402260\pi$
$557$	−8.78270	−	5.07069i	−0.372135	−	0.214852i	−0.674391	+	0.738375i	$0.735594\pi$
$558$	6.58047	+	38.5754i	0.278574	+	1.63303i
$559$	−18.7710	+	12.3835i	−0.793927	+	0.523766i
$560$	4.32256	+	7.48690i	0.182662	+	0.316379i
$561$	4.42927	−	5.24883i	0.187004	−	0.221606i
$562$	7.15405	+	12.3912i	0.301776	+	0.522691i
$563$	−22.5820			−0.951717			−0.475859	−	0.879522i	$-0.657863\pi$
$563$	−22.5820			−0.951717			−0.475859	+	0.879522i	$0.657863\pi$
$564$	21.1395	−	25.0510i	0.890133	−	1.05484i
$565$	11.1895	+	6.46027i	0.470746	+	0.271785i
$566$	30.3695	−	17.5338i	1.27653	−	0.737002i
$567$	−14.2730	+	16.6299i	−0.599409	+	0.698392i
$568$	−0.106554	−	0.184557i	−0.00447090	−	0.00774383i
$569$	−0.236522			−0.00991551			−0.00495776	−	0.999988i	$-0.501578\pi$
$569$	−0.236522			−0.00991551			−0.00495776	+	0.999988i	$0.501578\pi$
$570$	0.387827	+	1.07485i	0.0162443	+	0.0450206i
$571$	−18.7999	+	32.5624i	−0.786751	+	1.36269i	0.141196	+	0.989982i	$0.454905\pi$
$571$	−18.7999	+	32.5624i	−0.786751	+	1.36269i	−0.927947	+	0.372712i	$0.878428\pi$
$572$	−3.21679	+	6.42754i	−0.134501	+	0.268749i
$573$	1.45396	−	8.11355i	0.0607399	−	0.338949i
$574$			47.9712i			2.00228i
$575$	10.7177	−	18.5636i	0.446959	−	0.774156i
$576$	18.9245	−	15.7007i	0.788520	−	0.654195i
$577$		−	2.86303i		−	0.119189i	−0.998223	−	0.0595947i	$-0.981019\pi$
$577$		−	2.86303i		−	0.119189i	0.998223	−	0.0595947i	$-0.0189808\pi$
$578$	1.35575	+	0.782742i	0.0563917	+	0.0325578i
$579$	−10.1297	+	12.0040i	−0.420975	+	0.498869i
$580$	−7.70082	−	4.44607i	−0.319759	−	0.184613i
$581$	4.21906			0.175036
$582$	1.80153	−	10.0531i	0.0746757	−	0.416714i
$583$		−	1.73520i		−	0.0718646i
$584$	−0.840154			−0.0347658
$585$	−9.30219	−	2.82725i	−0.384598	−	0.116893i
$586$	−5.16628			−0.213417
$587$		−	27.2282i		−	1.12383i	−0.827196	−	0.561913i	$-0.810066\pi$
$587$		−	27.2282i		−	1.12383i	0.827196	−	0.561913i	$-0.189934\pi$
$588$	2.86968	+	2.42160i	0.118344	+	0.0998652i
$589$	2.37885			0.0980190
$590$	−16.1120	−	9.30227i	−0.663321	−	0.382968i
$591$	22.1871	+	3.97595i	0.912655	+	0.163549i
$592$	−15.0312	−	8.67828i	−0.617779	−	0.356675i
$593$			42.4254i			1.74220i	0.491102	+	0.871102i	$0.336594\pi$
$593$			42.4254i			1.74220i	−0.491102	+	0.871102i	$0.663406\pi$
$594$	−5.20585	+	8.84523i	−0.213599	+	0.362924i
$595$	−4.40728	+	7.63364i	−0.180681	+	0.312949i
$596$			43.8765i			1.79725i
$597$	2.90595	+	2.45221i	0.118932	+	0.100362i
$598$	36.9206	−	2.20217i	1.50979	−	0.0900536i
$599$	−13.2727	+	22.9890i	−0.542308	+	0.939305i	0.456463	+	0.889742i	$0.349116\pi$
$599$	−13.2727	+	22.9890i	−0.542308	+	0.939305i	−0.998771	+	0.0495624i	$0.984217\pi$
$600$	−0.232232	+	0.275203i	−0.00948084	+	0.0112351i
$601$	40.4721			1.65089			0.825446	−	0.564481i	$-0.190924\pi$
$601$	40.4721			1.65089			0.825446	+	0.564481i	$0.190924\pi$
$602$	−15.2340	−	26.3861i	−0.620892	−	1.07542i
$603$	4.75349	−	12.8371i	0.193577	−	0.522767i
$604$	12.4447	−	7.18497i	0.506369	−	0.292352i
$605$	7.80796	+	4.50793i	0.317439	+	0.183273i
$606$	−3.87902	−	10.7506i	−0.157575	−	0.436714i
$607$	6.94068			0.281714			0.140857	−	0.990030i	$-0.455014\pi$
$607$	6.94068			0.281714			0.140857	+	0.990030i	$0.455014\pi$
$608$	−1.46774	−	2.54220i	−0.0595247	−	0.103100i
$609$	−20.2844	−	3.63498i	−0.821964	−	0.147297i
$610$	−13.3788	−	23.1727i	−0.541690	−	0.938235i
$611$	33.6406	−	2.00654i	1.36095	−	0.0811758i
$612$	22.9406	+	8.49475i	0.927319	+	0.343380i
$613$	36.4418	+	21.0397i	1.47187	+	0.849784i	0.999500	−	0.0316168i	$-0.0100656\pi$
$613$	36.4418	+	21.0397i	1.47187	+	0.849784i	0.472369	+	0.881401i	$0.343399\pi$
$614$	20.8551			0.841642
$615$	−14.3805	+	5.18876i	−0.579879	+	0.209231i
$616$	−0.102968	−	0.0594485i	−0.00414869	−	0.00239525i
$617$			2.46826i			0.0993682i	0.998765	+	0.0496841i	$0.0158215\pi$
$617$			2.46826i			0.0993682i	−0.998765	+	0.0496841i	$0.984179\pi$
$618$	−18.9848	−	3.40210i	−0.763682	−	0.136853i
$619$	10.1895	−	5.88292i	0.409551	−	0.236454i	−0.281046	−	0.959694i	$-0.590681\pi$
$619$	10.1895	−	5.88292i	0.409551	−	0.236454i	0.690597	+	0.723240i	$0.257348\pi$
$620$	−5.91648	−	10.2477i	−0.237612	−	0.411556i
$621$	26.5685	+	0.222066i	1.06616	+	0.00891120i
$622$	−15.9952	−	9.23486i	−0.641351	−	0.370284i
$623$	−6.49223	−	11.2449i	−0.260106	−	0.450516i
$624$	24.4966	+	2.89772i	0.980650	+	0.116001i
$625$	−6.76711	+	11.7210i	−0.270684	+	0.468839i
$626$	33.9735	−	19.6146i	1.35786	−	0.783958i
$627$	0.476825	+	0.402373i	0.0190426	+	0.0160692i
$628$	5.08880	−	8.81406i	0.203065	−	0.351719i
$629$		−	17.6967i		−	0.705615i
$630$	4.57417	−	12.3528i	0.182239	−	0.492148i
$631$	32.1077	−	18.5374i	1.27819	−	0.737962i	0.301673	−	0.953411i	$-0.402455\pi$
$631$	32.1077	−	18.5374i	1.27819	−	0.737962i	0.976515	+	0.215449i	$0.0691216\pi$
$632$	0.478535	−	0.276282i	0.0190351	−	0.0109899i
$633$	−1.65410	−	1.39583i	−0.0657447	−	0.0554792i
$634$	11.3847	+	19.7188i	0.452143	+	0.783135i
$635$	−0.454368	+	0.262330i	−0.0180311	+	0.0104102i
$636$	5.81373	−	2.09770i	0.230529	−	0.0831792i
$637$	0.229856	+	3.85365i	0.00910722	+	0.152687i
$638$	−9.65107			−0.382090
$639$	4.47650	−	12.0891i	0.177088	−	0.478236i
$640$	−0.178291	+	0.308809i	−0.00704758	+	0.0122068i
$641$	−10.0513	+	17.4094i	−0.397002	+	0.687628i	−0.993355	−	0.115095i	$-0.963283\pi$
$641$	−10.0513	+	17.4094i	−0.397002	+	0.687628i	0.596352	+	0.802723i	$0.296616\pi$
$642$	−57.8230	−	10.3619i	−2.28209	−	0.408953i
$643$			10.3085i			0.406526i	0.979124	+	0.203263i	$0.0651547\pi$
$643$			10.3085i			0.406526i	−0.979124	+	0.203263i	$0.934845\pi$
$644$			25.2096i			0.993398i
$645$	6.26209	−	7.42078i	0.246570	−	0.292193i
$646$	1.47801	−	2.55998i	0.0581514	−	0.100721i
$647$	−4.08961	+	7.08342i	−0.160779	+	0.278478i	−0.935148	−	0.354256i	$-0.884734\pi$
$647$	−4.08961	+	7.08342i	−0.160779	+	0.278478i	0.774369	+	0.632734i	$0.218067\pi$
$648$	−0.438669	−	0.0824000i	−0.0172326	−	0.00323698i
$649$	−10.1582			−0.398745
$650$	−30.2691	+	1.80544i	−1.18725	+	0.0708152i
$651$	−20.9579	−	17.6855i	−0.821405	−	0.693150i
$652$	−4.19672	+	2.42298i	−0.164356	+	0.0948911i
$653$	−17.2882	−	29.9440i	−0.676538	−	1.17180i	−0.976017	−	0.217695i	$-0.930146\pi$
$653$	−17.2882	−	29.9440i	−0.676538	−	1.17180i	0.299479	−	0.954103i	$-0.403187\pi$
$654$	16.1493	−	5.82697i	0.631488	−	0.227852i
$655$	5.54885	−	3.20363i	0.216811	−	0.125176i
$656$	33.5918	−	19.3942i	1.31154	−	0.757218i
$657$	−32.4506	−	39.1137i	−1.26602	−	1.52597i
$658$			45.6596i			1.78000i
$659$	6.46188	−	11.1923i	0.251719	−	0.435990i	−0.712280	−	0.701895i	$-0.752337\pi$
$659$	6.46188	−	11.1923i	0.251719	−	0.435990i	0.963999	+	0.265905i	$0.0856708\pi$
$660$	0.547427	−	3.05482i	0.0213086	−	0.118909i
$661$	32.3898	−	18.7003i	1.25982	−	0.727357i	0.286780	−	0.957997i	$-0.407415\pi$
$661$	32.3898	−	18.7003i	1.25982	−	0.727357i	0.973039	+	0.230640i	$0.0740819\pi$
$662$	3.58216	−	6.20448i	0.139225	−	0.241144i
$663$	9.92969	+	23.1078i	0.385637	+	0.897431i
$664$	0.0429645	+	0.0744166i	0.00166734	+	0.00288792i
$665$	−0.693471	−	0.400376i	−0.0268916	−	0.0155259i
$666$	4.44712	+	26.0695i	0.172323	+	1.01017i
$667$	12.4920	+	21.6368i	0.483693	+	0.837781i
$668$	23.1187	−	13.3476i	0.894490	−	0.516434i
$669$	−16.1462	−	44.7489i	−0.624250	−	1.73009i
$670$			8.22800i			0.317875i
$671$	−12.6525	−	7.30490i	−0.488443	−	0.282003i
$672$	−5.96898	+	33.3089i	−0.230259	+	1.28492i
$673$	37.3610			1.44016			0.720081	−	0.693890i	$-0.244105\pi$
$673$	37.3610			1.44016			0.720081	+	0.693890i	$0.244105\pi$
$674$	−40.1849	−	23.2008i	−1.54787	−	0.893661i
$675$	−21.7820	−	0.182060i	−0.838391	−	0.00700748i
$676$	−15.7770	−	21.0689i	−0.606808	−	0.810344i
$677$	−8.76311	−	15.1781i	−0.336794	−	0.583344i	0.647034	−	0.762461i	$-0.276009\pi$
$677$	−8.76311	−	15.1781i	−0.336794	−	0.583344i	−0.983828	+	0.179117i	$0.942676\pi$
$678$	16.9529	+	46.9845i	0.651071	+	1.80443i
$679$	3.57855	+	6.19822i	0.137332	+	0.237866i
$680$	−0.179525			−0.00688446
$681$	−33.6037	−	6.02182i	−1.28770	−	0.230757i
$682$	−11.1223	−	6.42145i	−0.425894	−	0.245890i
$683$	1.64996	−	0.952607i	0.0631341	−	0.0364505i	−0.468101	−	0.883675i	$-0.655062\pi$
$683$	1.64996	−	0.952607i	0.0631341	−	0.0364505i	0.531235	+	0.847225i	$0.321728\pi$
$684$	−0.771698	+	2.08402i	−0.0295066	+	0.0796844i
$685$	−2.66062	−	4.60832i	−0.101657	−	0.176075i
$686$	−39.4258			−1.50529
$687$	−35.6149	−	6.38222i	−1.35879	−	0.243497i
$688$	−12.3179	+	21.3352i	−0.469615	+	0.813397i
$689$	5.68251	+	2.84392i	0.216486	+	0.108345i
$690$	−15.0221	+	5.42025i	−0.571882	+	0.206346i
$691$		−	22.9809i		−	0.874234i	−0.899405	−	0.437117i	$-0.856000\pi$
$691$		−	22.9809i		−	0.874234i	0.899405	−	0.437117i	$-0.144000\pi$
$692$	−14.9932	+	25.9689i	−0.569954	+	0.987190i
$693$	−1.20944	−	7.08988i	−0.0459429	−	0.269322i
$694$		−	13.4199i		−	0.509413i
$695$	14.0231	+	8.09625i	0.531927	+	0.307108i
$696$	−0.142450	−	0.394796i	−0.00539954	−	0.0149647i
$697$	34.2502	+	19.7744i	1.29732	+	0.749007i
$698$	27.5362			1.04226
$699$	−13.4680	+	4.85949i	−0.509405	+	0.183803i
$700$		−	20.6680i		−	0.781176i
$701$	−28.3145			−1.06942			−0.534711	−	0.845035i	$-0.679580\pi$
$701$	−28.3145			−1.06942			−0.534711	+	0.845035i	$0.679580\pi$
$702$	−20.4346	−	31.5453i	−0.771253	−	1.19060i
$703$	1.60764			0.0606335
$704$			8.07002i			0.304150i
$705$	−13.6876	+	4.93873i	−0.515504	+	0.186003i
$706$	0.825059			0.0310515
$707$	6.93606	+	4.00454i	0.260857	+	0.150606i
$708$	−12.2804	−	34.0347i	−0.461524	−	1.27910i
$709$	−18.9071	−	10.9160i	−0.710072	−	0.409960i	0.101016	−	0.994885i	$-0.467791\pi$
$709$	−18.9071	−	10.9160i	−0.710072	−	0.409960i	−0.811088	+	0.584925i	$0.801124\pi$
$710$			7.74856i			0.290798i
$711$	31.3456	+	11.6071i	1.17555	+	0.435299i
$712$	0.132226	−	0.229022i	0.00495538	−	0.00858298i
$713$			33.2468i			1.24510i
$714$	−32.0535	+	11.5655i	−1.19957	+	0.432827i
$715$	2.66339	−	1.75708i	0.0996052	−	0.0657111i
$716$	−18.8370	+	32.6267i	−0.703972	+	1.21932i
$717$	1.00512	+	0.180119i	0.0375369	+	0.00672666i
$718$	−12.7182			−0.474641
$719$	−9.12308	−	15.8016i	−0.340234	−	0.589302i	0.644242	−	0.764821i	$-0.277173\pi$
$719$	−9.12308	−	15.8016i	−0.340234	−	0.589302i	−0.984476	+	0.175520i	$0.943839\pi$
$720$	−10.4993	+	1.79106i	−0.391288	+	0.0667487i
$721$	11.7051	−	6.75792i	0.435919	−	0.251678i
$722$	−32.7779	−	18.9244i	−1.21987	−	0.704291i
$723$	28.1038	+	5.03622i	1.04519	+	0.187299i
$724$	15.6069			0.580027
$725$	−10.2415	−	17.7388i	−0.380361	−	0.658804i
$726$	11.8296	+	32.7854i	0.439037	+	1.21678i
$727$	11.1889	+	19.3797i	0.414973	+	0.718755i	0.995426	−	0.0955395i	$-0.0304576\pi$
$727$	11.1889	+	19.3797i	0.414973	+	0.718755i	−0.580452	+	0.814294i	$0.697124\pi$
$728$	0.363444	−	0.239770i	0.0134701	−	0.00888646i
$729$	−13.1073	−	23.6051i	−0.485454	−	0.874262i
$730$	26.4552	+	15.2739i	0.979152	+	0.565313i
$731$	−25.1186			−0.929046
$732$	9.17915	−	51.2226i	0.339271	−	1.89324i
$733$	−12.1370	−	7.00731i	−0.448291	−	0.258821i	0.258817	−	0.965926i	$-0.416667\pi$
$733$	−12.1370	−	7.00731i	−0.448291	−	0.258821i	−0.707108	+	0.707105i	$0.750001\pi$
$734$			56.3860i			2.08124i
$735$	−0.565749	−	1.56796i	−0.0208680	−	0.0578351i
$736$	35.5297	−	20.5131i	1.30964	−	0.756123i
$737$	2.24627	+	3.89066i	0.0827425	+	0.143314i
$738$	−55.4240	−	20.5231i	−2.04019	−	0.755467i
$739$	25.1799	+	14.5376i	0.926258	+	0.534775i	0.885626	−	0.464399i	$-0.153730\pi$
$739$	25.1799	+	14.5376i	0.926258	+	0.534775i	0.0406320	+	0.999174i	$0.487063\pi$
$740$	−3.99840	−	6.92543i	−0.146984	−	0.254584i
$741$	−2.09920	+	0.902054i	−0.0771162	+	0.0331378i
$742$	−4.30471	+	7.45598i	−0.158031	+	0.273718i
$743$	10.1598	−	5.86576i	0.372727	−	0.215194i	−0.301922	−	0.953333i	$-0.597628\pi$
$743$	10.1598	−	5.86576i	0.372727	−	0.215194i	0.674649	+	0.738139i	$0.264295\pi$
$744$	0.0985173	−	0.549758i	0.00361182	−	0.0201551i
$745$	9.73903	−	16.8685i	0.356811	−	0.618014i
$746$			13.4153i			0.491168i
$747$	−1.80501	+	4.87454i	−0.0660418	+	0.178350i
$748$	−6.95283	+	4.01422i	−0.254221	+	0.146774i
$749$	35.6506	−	20.5829i	1.30265	−	0.752083i
$750$	27.0051	−	9.74394i	0.986087	−	0.355798i
$751$	−18.1154	−	31.3767i	−0.661039	−	1.14495i	−0.980343	−	0.197301i	$-0.936783\pi$
$751$	−18.1154	−	31.3767i	−0.661039	−	1.14495i	0.319304	−	0.947652i	$-0.396551\pi$
$752$	31.9731	−	18.4597i	1.16594	−	0.673156i
$753$	25.7880	+	21.7614i	0.939767	+	0.793030i
$754$	15.8177	−	31.6057i	0.576047	−	1.15101i
$755$	−6.37923			−0.232164
$756$	22.2923	−	12.6232i	0.810762	−	0.459102i
$757$	−13.4651	+	23.3223i	−0.489399	+	0.847664i	−0.999926	−	0.0121978i	$-0.996117\pi$
$757$	−13.4651	+	23.3223i	−0.489399	+	0.847664i	0.510526	+	0.859862i	$0.329451\pi$
$758$	−0.974272	+	1.68749i	−0.0353871	+	0.0612923i
$759$	−5.62355	+	6.66409i	−0.204122	+	0.241891i
$760$		−	0.0163088i		−	0.000591581i
$761$		−	18.6146i		−	0.674780i	−0.941365	−	0.337390i	$-0.890456\pi$
$761$		−	18.6146i		−	0.674780i	0.941365	−	0.337390i	$-0.109544\pi$
$762$	−1.99647	−	0.357770i	−0.0723246	−	0.0129606i
$763$	−6.01551	+	10.4192i	−0.217776	+	0.377199i
$764$	−4.81780	+	8.34468i	−0.174302	+	0.301900i
$765$	−6.93406	−	8.35783i	−0.250702	−	0.302178i
$766$	−47.7676			−1.72591
$767$	16.6489	−	33.2665i	0.601156	−	1.20119i
$768$	25.4115	−	9.16894i	0.916959	−	0.330856i
$769$	−9.37090	+	5.41029i	−0.337923	+	0.195100i	−0.659353	−	0.751833i	$-0.729170\pi$
$769$	−9.37090	+	5.41029i	−0.337923	+	0.195100i	0.321430	+	0.946933i	$0.395837\pi$
$770$	2.16154	+	3.74389i	0.0778964	+	0.134920i
$771$	10.7150	+	9.04192i	0.385890	+	0.325637i
$772$	15.9010	−	9.18047i	0.572291	−	0.330412i
$773$	5.30693	−	3.06396i	0.190877	−	0.110203i	−0.401516	−	0.915852i	$-0.631517\pi$
$773$	5.30693	−	3.06396i	0.190877	−	0.110203i	0.592393	+	0.805649i	$0.298183\pi$
$774$	37.0029	−	6.31222i	1.33004	−	0.226888i
$775$		−	27.2572i		−	0.979109i
$776$	−0.0728836	+	0.126238i	−0.00261637	+	0.00453168i
$777$	−14.1635	−	11.9520i	−0.508112	−	0.428775i
$778$	−64.5204	+	37.2509i	−2.31317	+	1.33551i
$779$	−1.79638	+	3.11143i	−0.0643621	+	0.111478i
$780$	9.10684	+	6.79945i	0.326077	+	0.243460i
$781$	2.11538	+	3.66395i	0.0756944	+	0.131107i
$782$	35.7783	+	20.6566i	1.27943	+	0.738678i
$783$	12.8778	−	21.8806i	0.460215	−	0.781949i
$784$	2.11462	+	3.66264i	0.0755223	+	0.130808i
$785$	−3.91281	+	2.25906i	−0.139654	+	0.0806295i
$786$	24.3814	+	4.36917i	0.869656	+	0.155843i
$787$			10.3544i			0.369093i	0.982824	+	0.184547i	$0.0590817\pi$
$787$			10.3544i			0.369093i	−0.982824	+	0.184547i	$0.940918\pi$
$788$	−22.8191	−	13.1746i	−0.812898	−	0.469327i
$789$	−40.5201	+	14.6204i	−1.44255	+	0.520500i
$790$	−20.0911			−0.714811
$791$	−30.3133	−	17.5014i	−1.07782	−	0.622279i
$792$	0.112736	−	0.0935315i	0.00400591	−	0.00332350i
$793$	44.6593	−	29.4624i	1.58590	−	1.04624i
$794$	−8.15054	−	14.1172i	−0.289252	−	0.500999i
$795$	−2.70072	−	0.483973i	−0.0957848	−	0.0171647i
$796$	−2.22242	−	3.84934i	−0.0787716	−	0.136436i
$797$	1.17869			0.0417513			0.0208756	−	0.999782i	$-0.493355\pi$
$797$	1.17869			0.0417513			0.0208756	+	0.999782i	$0.493355\pi$
$798$	−1.05066	−	2.91187i	−0.0371928	−	0.103079i
$799$	32.5998	+	18.8215i	1.15330	+	0.665857i
$800$	−29.1289	+	16.8176i	−1.02986	+	0.594591i
$801$	15.7694	−	2.69006i	0.557184	−	0.0950486i
$802$	10.6001	+	18.3599i	0.374302	+	0.648309i
$803$	16.6794			0.588602
$804$	−10.3200	+	12.2295i	−0.363958	+	0.431302i
$805$	5.59564	−	9.69193i	0.197220	−	0.341596i
$806$	39.2582	−	25.8992i	1.38281	−	0.912260i
$807$	−13.3225	−	11.2423i	−0.468973	−	0.395747i
$808$			0.163119i			0.00573852i
$809$	−1.35288	+	2.34325i	−0.0475646	+	0.0823843i	−0.888828	−	0.458242i	$-0.848479\pi$
$809$	−1.35288	+	2.34325i	−0.0475646	+	0.0823843i	0.841263	+	0.540626i	$0.181813\pi$
$810$	12.3150	+	10.5696i	0.432706	+	0.371379i
$811$		−	10.3761i		−	0.364353i	−0.983266	−	0.182176i	$-0.941686\pi$
$811$		−	10.3761i		−	0.364353i	0.983266	−	0.182176i	$-0.0583142\pi$
$812$	20.8622	+	12.0448i	0.732119	+	0.422689i
$813$	7.34252	+	1.31579i	0.257513	+	0.0461467i
$814$	−7.51650	−	4.33965i	−0.263453	−	0.152105i
$815$	2.15126			0.0753553
$816$	21.0576	+	17.7696i	0.737163	+	0.622061i
$817$		−	2.28188i		−	0.0798328i
$818$	−16.8179			−0.588023
$819$	25.2004	+	7.65928i	0.880575	+	0.267637i
$820$	17.8713			0.624091
$821$			44.2060i			1.54280i	0.636350	+	0.771401i	$0.280444\pi$
$821$			44.2060i			1.54280i	−0.636350	+	0.771401i	$0.719556\pi$
$822$	3.62860	−	20.2488i	0.126562	−	0.706257i
$823$	1.42911			0.0498158			0.0249079	−	0.999690i	$-0.492071\pi$
$823$	1.42911			0.0498158			0.0249079	+	0.999690i	$0.492071\pi$
$824$	0.238395	+	0.137637i	0.00830488	+	0.00479483i
$825$	4.61044	−	5.46353i	0.160515	−	0.190216i
$826$	43.6488	+	25.2006i	1.51874	+	0.876843i
$827$			3.66392i			0.127407i	0.997969	+	0.0637035i	$0.0202912\pi$
$827$			3.66392i			0.127407i	−0.997969	+	0.0637035i	$0.979709\pi$
$828$	−29.1262	−	10.7852i	−1.01220	−	0.374813i
$829$	−7.11625	+	12.3257i	−0.247157	+	0.428089i	−0.962736	−	0.270443i	$-0.912830\pi$
$829$	−7.11625	+	12.3257i	−0.247157	+	0.428089i	0.715579	+	0.698532i	$0.246163\pi$
$830$		−	3.12436i		−	0.108448i
$831$	3.23162	−	18.0335i	0.112104	−	0.625574i
$832$	−26.4280	−	13.2264i	−0.916227	−	0.458544i
$833$	−2.15607	+	3.73442i	−0.0747034	+	0.129390i
$834$	21.2460	+	58.8828i	0.735688	+	2.03894i
$835$	−11.8508			−0.410113
$836$	−0.364668	−	0.631623i	−0.0126123	−	0.0218452i
$837$	29.3994	−	16.6477i	1.01619	−	0.575428i
$838$	50.8767	−	29.3737i	1.75751	−	1.01470i
$839$	8.67180	+	5.00667i	0.299384	+	0.172849i	0.642166	−	0.766566i	$-0.278036\pi$
$839$	8.67180	+	5.00667i	0.299384	+	0.172849i	−0.342782	+	0.939415i	$0.611369\pi$
$840$	−0.121247	+	0.143682i	−0.00418341	+	0.00495748i
$841$	−5.12597			−0.176757
$842$	−32.2886	−	55.9254i	−1.11274	−	1.92732i
$843$	7.96673	−	9.44084i	0.274389	−	0.325160i
$844$	1.26503	+	2.19110i	0.0435442	+	0.0754207i
$845$	1.38897	+	11.6020i	0.0477820	+	0.399120i
$846$	−52.7533	−	19.5342i	−1.81370	−	0.671600i
$847$	−21.1524	−	12.2124i	−0.726806	−	0.419622i
$848$	6.96139			0.239055
$849$	−23.1385	−	19.5256i	−0.794112	−	0.670118i
$850$	−29.3326	−	16.9352i	−1.00610	−	0.580873i
$851$			22.4684i			0.770207i
$852$	−9.71864	+	11.5169i	−0.332955	+	0.394563i
$853$	−25.0077	+	14.4382i	−0.856248	+	0.494355i	−0.862754	−	0.505624i	$-0.831262\pi$
$853$	−25.0077	+	14.4382i	−0.856248	+	0.494355i	0.00650586	+	0.999979i	$0.497929\pi$
$854$	36.2442	+	62.7768i	1.24025	+	2.14818i
$855$	0.759260	−	0.629919i	0.0259661	−	0.0215428i
$856$	0.726091	+	0.419209i	0.0248173	+	0.0143283i
$857$	16.7420	+	28.9979i	0.571894	+	0.990550i	0.996371	+	0.0851112i	$0.0271246\pi$
$857$	16.7420	+	28.9979i	0.571894	+	0.990550i	−0.424477	+	0.905439i	$0.639542\pi$
$858$	12.2498	+	1.44903i	0.418200	+	0.0494690i
$859$	−23.8893	+	41.3775i	−0.815093	+	1.41178i	0.0941674	+	0.995556i	$0.469981\pi$
$859$	−23.8893	+	41.3775i	−0.815093	+	1.41178i	−0.909261	+	0.416227i	$0.863352\pi$
$860$	−9.82990	+	5.67530i	−0.335197	+	0.193526i
$861$	38.9581	−	14.0568i	1.32769	−	0.479054i
$862$	−2.35316	+	4.07579i	−0.0801489	+	0.138822i
$863$			35.0051i			1.19159i	0.803138	+	0.595793i	$0.203162\pi$
$863$			35.0051i			1.19159i	−0.803138	+	0.595793i	$0.796838\pi$
$864$	−35.9301	−	21.1466i	−1.22237	−	0.719422i
$865$	11.5283	−	6.65589i	0.391976	−	0.226307i
$866$	−25.8795	+	14.9416i	−0.879423	+	0.507735i
$867$	0.238407	−	1.33039i	0.00809671	−	0.0451823i
$868$	16.0283	+	27.7618i	0.544035	+	0.942296i
$869$	−9.50022	+	5.48495i	−0.322273	+	0.186064i
$870$	−2.69182	+	15.0213i	−0.0912614	+	0.509268i
$871$	−16.4228	+	0.979561i	−0.556467	+	0.0331912i
$872$	−0.245034			−0.00829789
$873$	−8.69216	+	1.48277i	−0.294185	+	0.0501842i
$874$	−1.87653	+	3.25024i	−0.0634746	+	0.109941i
$875$	−10.0592	+	17.4231i	−0.340064	+	0.589008i
$876$	20.1638	+	55.8836i	0.681273	+	1.88813i
$877$		−	29.9403i		−	1.01101i	−0.862823	−	0.505507i	$-0.831306\pi$
$877$		−	29.9403i		−	1.01101i	0.862823	−	0.505507i	$-0.168694\pi$
$878$			55.1154i			1.86006i
$879$	1.51385	+	4.19561i	0.0510609	+	0.141514i
$880$	1.74777	−	3.02723i	0.0589174	−	0.102048i
$881$	−24.6188	+	42.6410i	−0.829428	+	1.43661i	0.0690591	+	0.997613i	$0.478000\pi$
$881$	−24.6188	+	42.6410i	−0.829428	+	1.43661i	−0.898487	+	0.438999i	$0.855333\pi$
$882$	2.23771	−	6.04308i	0.0753477	−	0.203481i
$883$	−17.8905			−0.602062			−0.301031	−	0.953614i	$-0.597331\pi$
$883$	−17.8905			−0.602062			−0.301031	+	0.953614i	$0.597331\pi$
$884$	−1.75053	−	29.3485i	−0.0588767	−	0.987098i
$885$	−2.83327	+	15.8106i	−0.0952395	+	0.531467i
$886$	13.5938	−	7.84838i	0.456692	−	0.263671i
$887$	23.9868	+	41.5464i	0.805399	+	1.39499i	0.916021	+	0.401129i	$0.131382\pi$
$887$	23.9868	+	41.5464i	0.805399	+	1.39499i	−0.110623	+	0.993862i	$0.535284\pi$
$888$	0.0665786	−	0.371530i	0.00223423	−	0.0124677i
$889$	1.23092	−	0.710674i	0.0412838	−	0.0238352i
$890$	−8.32721	+	4.80772i	−0.279129	+	0.161155i
$891$	8.70879	+	1.63586i	0.291755	+	0.0548035i
$892$			55.6113i			1.86200i
$893$	−1.70982	+	2.96150i	−0.0572170	+	0.0991028i
$894$	70.8305	−	25.5569i	2.36893	−	0.854752i
$895$	14.4839	−	8.36230i	0.484144	−	0.279521i
$896$	0.483006	−	0.836592i	0.0161361	−	0.0279486i
$897$	−12.6071	−	29.3384i	−0.420938	−	0.979581i
$898$	−11.6256	−	20.1361i	−0.387951	−	0.671951i
$899$	27.5134	+	15.8848i	0.917622	+	0.529789i
$900$	23.8790	+	8.84222i	0.795965	+	0.294741i
$901$	3.54892	+	6.14690i	0.118232	+	0.204783i
$902$	16.7979	−	9.69827i	0.559309	−	0.322917i
$903$	−16.9645	+	20.1035i	−0.564545	+	0.669004i
$904$		−	0.712897i		−	0.0237106i
$905$	−6.00014	−	3.46418i	−0.199451	−	0.115153i
$906$	−18.8475	−	15.9046i	−0.626167	−	0.528396i
$907$	−49.5755			−1.64613			−0.823064	−	0.567949i	$-0.807737\pi$
$907$	−49.5755			−1.64613			−0.823064	+	0.567949i	$0.807737\pi$
$908$	34.5610	+	19.9538i	1.14695	+	0.662190i
$909$	−7.59408	+	6.30042i	−0.251880	+	0.208972i
$910$	−15.8033	+	0.942609i	−0.523875	+	0.0312472i
$911$	4.09220	+	7.08790i	0.135581	+	0.234833i	0.925819	−	0.377967i	$-0.123377\pi$
$911$	4.09220	+	7.08790i	0.135581	+	0.234833i	−0.790238	+	0.612799i	$0.790043\pi$
$912$	−1.61427	+	1.91296i	−0.0534537	+	0.0633444i
$913$	−0.852962	−	1.47737i	−0.0282289	−	0.0488939i
$914$	−47.8253			−1.58192
$915$	−14.8986	+	17.6553i	−0.492531	+	0.583666i
$916$	36.6294	+	21.1480i	1.21027	+	0.698750i
$917$	−15.0323	+	8.67891i	−0.496411	+	0.286603i
$918$	0.350890	−	41.9813i	0.0115811	−	1.38559i
$919$	0.684534	+	1.18565i	0.0225807	+	0.0391109i	0.877095	−	0.480317i	$-0.159478\pi$
$919$	0.684534	+	1.18565i	0.0225807	+	0.0391109i	−0.854514	+	0.519428i	$0.826145\pi$
$920$	0.227931			0.00751466
$921$	−6.11107	−	16.9367i	−0.201367	−	0.558083i
$922$	19.8812	−	34.4353i	0.654753	−	1.13407i
$923$	−15.4659	+	0.922483i	−0.509066	+	0.0303639i
$924$	−1.48303	+	8.27577i	−0.0487880	+	0.272253i
$925$		−	18.4206i		−	0.605666i
$926$	13.1120	−	22.7106i	0.430887	−	0.746318i
$927$	2.80015	+	16.4148i	0.0919689	+	0.539131i
$928$		−	39.2035i		−	1.28692i
$929$	−39.2535	−	22.6630i	−1.28787	−	0.743550i	−0.309594	−	0.950869i	$-0.600193\pi$
$929$	−39.2535	−	22.6630i	−1.28787	−	0.743550i	−0.978273	+	0.207319i	$0.933526\pi$
$930$	−13.0967	+	15.5200i	−0.429458	+	0.508922i
$931$	−0.339250	−	0.195866i	−0.0111185	−	0.00641926i
$932$	16.7372			0.548244
$933$	−2.81274	+	15.6960i	−0.0920850	+	0.513864i
$934$			15.0540i			0.492583i
$935$	3.56405			0.116557
$936$	0.121531	+	0.522488i	0.00397236	+	0.0170780i
$937$	27.3417			0.893213			0.446607	−	0.894730i	$-0.352632\pi$
$937$	27.3417			0.893213			0.446607	+	0.894730i	$0.352632\pi$
$938$		−	22.2904i		−	0.727806i
$939$	−25.8844	−	21.8428i	−0.844706	−	0.712813i
$940$	17.0101			0.554808
$941$	−38.2649	−	22.0923i	−1.24740	−	0.720187i	−0.276811	−	0.960924i	$-0.589278\pi$
$941$	−38.2649	−	22.0923i	−1.24740	−	0.720187i	−0.970590	+	0.240737i	$0.922611\pi$
$942$	−17.1927	−	3.08096i	−0.560170	−	0.100383i
$943$	−43.4852	−	25.1062i	−1.41607	−	0.817571i
$944$		−	40.7534i		−	1.32641i
$945$	−11.3723	−	0.0950521i	−0.369939	−	0.00309205i
$946$	−6.15967	+	10.6689i	−0.200268	+	0.346875i
$947$		−	38.8062i		−	1.26103i	−0.776176	−	0.630516i	$-0.782843\pi$
$947$		−	38.8062i		−	1.26103i	0.776176	−	0.630516i	$-0.217157\pi$
$948$	−29.8621	−	25.1993i	−0.969875	−	0.818437i
$949$	−27.3368	+	54.6222i	−0.887389	+	1.77311i
$950$	1.53846	−	2.66470i	0.0499144	−	0.0864542i
$951$	12.6779	−	15.0238i	0.411110	−	0.487179i
$952$	0.486348			0.0157626
$953$	−4.35281	−	7.53929i	−0.141001	−	0.244222i	0.786873	−	0.617115i	$-0.211699\pi$
$953$	−4.35281	−	7.53929i	−0.141001	−	0.244222i	−0.927874	+	0.372894i	$0.878366\pi$
$954$	−6.77269	−	8.16332i	−0.219274	−	0.264297i
$955$	3.70445	−	2.13876i	0.119873	−	0.0692087i
$956$	−1.03375	−	0.596838i	−0.0334340	−	0.0193031i
$957$	2.82801	+	7.83777i	0.0914166	+	0.253359i
$958$	−53.4852			−1.72803
$959$	7.20784	+	12.4843i	0.232753	+	0.403140i
$960$	12.5605	+	2.25085i	0.405387	+	0.0726458i
$961$	5.63831	+	9.76585i	0.181881	+	0.315027i
$962$	26.5309	−	17.5028i	0.855391	−	0.564314i
$963$	8.52854	+	49.9952i	0.274828	+	1.61107i
$964$	−28.9044	−	16.6879i	−0.930947	−	0.537482i
$965$	−8.15095			−0.262388
$966$	40.6962	−	14.6839i	1.30938	−	0.472448i
$967$	26.0040	+	15.0134i	0.836234	+	0.482800i	0.855982	−	0.517005i	$-0.172953\pi$
$967$	26.0040	+	15.0134i	0.836234	+	0.482800i	−0.0197486	+	0.999805i	$0.506287\pi$
$968$		−	0.497454i		−	0.0159888i
$969$	−2.51209	−	0.450170i	−0.0807000	−	0.0144615i
$970$	4.58999	−	2.65003i	0.147376	−	0.0850875i
$971$	−16.7536	−	29.0182i	−0.537650	−	0.931237i	−0.999030	−	0.0440347i	$-0.985979\pi$
$971$	−16.7536	−	29.0182i	−0.537650	−	0.931237i	0.461380	−	0.887203i	$-0.347355\pi$
$972$	5.04723	+	31.1561i	0.161890	+	0.999332i
$973$	−37.9898	−	21.9334i	−1.21790	−	0.703154i
$974$	3.84907	+	6.66678i	0.123332	+	0.213617i
$975$	10.3359	+	24.0530i	0.331012	+	0.770311i
$976$	29.3063	−	50.7600i	0.938072	−	1.62479i
$977$	−42.6985	+	24.6520i	−1.36604	+	0.788686i	−0.990420	−	0.138086i	$-0.955905\pi$
$977$	−42.6985	+	24.6520i	−1.36604	+	0.788686i	−0.375624	+	0.926772i	$0.622572\pi$
$978$	6.35592	+	5.36349i	0.203240	+	0.171506i
$979$	−2.62505	+	4.54672i	−0.0838969	+	0.145314i
$980$			1.94857i			0.0622447i
$981$	−9.46433	−	11.4076i	−0.302173	−	0.364218i
$982$	−33.3178	+	19.2361i	−1.06321	+	0.613847i
$983$	−0.601713	+	0.347399i	−0.0191917	+	0.0110803i	−0.509565	−	0.860432i	$-0.670194\pi$
$983$	−0.601713	+	0.347399i	−0.0191917	+	0.0110803i	0.490373	+	0.871512i	$0.336860\pi$
$984$	0.644663	+	0.544004i	0.0205511	+	0.0173422i
$985$	5.84860	+	10.1301i	0.186352	+	0.322771i
$986$	34.1887	−	19.7388i	1.08879	−	0.628613i
$987$	37.0808	−	13.3794i	1.18030	−	0.425873i
$988$	2.66614	−	0.159025i	0.0848213	−	0.00505927i
$989$	31.8915			1.01409
$990$	−5.25029	+	0.895633i	−0.166865	+	0.0284651i
$991$	3.63758	−	6.30047i	0.115551	−	0.200141i	−0.802449	−	0.596721i	$-0.796470\pi$
$991$	3.63758	−	6.30047i	0.115551	−	0.200141i	0.918000	+	0.396580i	$0.129803\pi$
$992$	26.0844	−	45.1796i	0.828182	−	1.43445i
$993$	−6.08841	−	1.09105i	−0.193210	−	0.0346234i
$994$		−	20.9915i		−	0.665810i
$995$			1.97319i			0.0625544i
$996$	3.91873	−	4.64383i	0.124170	−	0.147145i
$997$	2.03187	−	3.51930i	0.0643499	−	0.111457i	−0.832056	−	0.554692i	$-0.812836\pi$
$997$	2.03187	−	3.51930i	0.0643499	−	0.111457i	0.896405	+	0.443235i	$0.146169\pi$
$998$	15.8455	−	27.4452i	0.501580	−	0.868761i
$999$	19.8683	−	11.2506i	0.628605	−	0.355953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.l.b.4.10	✓	22
3.2	odd	2		351.2.l.b.199.2		22
9.2	odd	6		351.2.r.b.316.2		22
9.7	even	3		117.2.r.b.43.10	yes	22
13.10	even	6		117.2.r.b.49.10	yes	22
39.23	odd	6		351.2.r.b.10.2		22
117.88	even	6	inner	117.2.l.b.88.2	yes	22
117.101	odd	6		351.2.l.b.127.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.10	✓	22	1.1	even	1	trivial
117.2.l.b.88.2	yes	22	117.88	even	6	inner
117.2.r.b.43.10	yes	22	9.7	even	3
117.2.r.b.49.10	yes	22	13.10	even	6
351.2.l.b.127.10		22	117.101	odd	6
351.2.l.b.199.2		22	3.2	odd	2
351.2.r.b.10.2		22	39.23	odd	6
351.2.r.b.316.2		22	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.00617i q^{2} +(1.62924 - 0.587859i) q^{3} -2.02472 q^{4} +(0.778411 + 0.449416i) q^{5} +(1.17935 + 3.26853i) q^{6} +(-2.10878 - 1.21751i) q^{7} -0.0495935i q^{8} +(2.30884 - 1.91553i) q^{9} +(-0.901605 + 1.56163i) q^{10} +0.984566i q^{11} +(-3.29875 + 1.19025i) q^{12} +(-3.22430 - 1.61366i) q^{13} +(2.44253 - 4.23058i) q^{14} +(1.53241 + 0.274610i) q^{15} -3.94995 q^{16} +(-2.01368 - 3.48780i) q^{17} +(3.84288 + 4.63193i) q^{18} +(0.316846 - 0.182931i) q^{19} +(-1.57607 - 0.909942i) q^{20} +(-4.15144 - 0.743942i) q^{21} -1.97521 q^{22} +(2.55664 + 4.42823i) q^{23} +(-0.0291540 - 0.0807997i) q^{24} +(-2.09605 - 3.63047i) q^{25} +(3.23728 - 6.46849i) q^{26} +(2.63560 - 4.47813i) q^{27} +(4.26970 + 2.46511i) q^{28} +4.88611 q^{29} +(-0.550914 + 3.07428i) q^{30} +(5.63094 + 3.25102i) q^{31} -8.02346i q^{32} +(0.578786 + 1.60409i) q^{33} +(6.99712 - 4.03979i) q^{34} +(-1.09433 - 1.89544i) q^{35} +(-4.67476 + 3.87841i) q^{36} +(3.80542 + 2.19706i) q^{37} +(0.366991 + 0.635647i) q^{38} +(-6.20176 - 0.733609i) q^{39} +(0.0222881 - 0.0386041i) q^{40} +(-8.50437 + 4.91000i) q^{41} +(1.49247 - 8.32849i) q^{42} +(3.11849 - 5.40139i) q^{43} -1.99347i q^{44} +(2.65810 - 0.453438i) q^{45} +(-8.88379 + 5.12906i) q^{46} +(-8.09457 + 4.67340i) q^{47} +(-6.43541 + 2.32201i) q^{48} +(-0.535355 - 0.927262i) q^{49} +(7.28333 - 4.20504i) q^{50} +(-5.33111 - 4.49870i) q^{51} +(6.52830 + 3.26722i) q^{52} -1.76240 q^{53} +(8.98389 + 5.28746i) q^{54} +(-0.442480 + 0.766397i) q^{55} +(-0.0603804 + 0.104582i) q^{56} +(0.408680 - 0.484300i) q^{57} +9.80236i q^{58} +10.3175i q^{59} +(-3.10271 - 0.556008i) q^{60} +(-7.41941 + 12.8508i) q^{61} +(-6.52211 + 11.2966i) q^{62} +(-7.20102 + 1.22840i) q^{63} +8.19653 q^{64} +(-1.78462 - 2.70514i) q^{65} +(-3.21809 + 1.16114i) q^{66} +(3.95165 - 2.28149i) q^{67} +(4.07714 + 7.06182i) q^{68} +(6.76856 + 5.71171i) q^{69} +(3.80258 - 2.19542i) q^{70} +(3.72139 - 2.14855i) q^{71} +(-0.0949977 - 0.114504i) q^{72} -16.9408i q^{73} +(-4.40768 + 7.63433i) q^{74} +(-5.54917 - 4.68272i) q^{75} +(-0.641525 + 0.370384i) q^{76} +(1.19872 - 2.07624i) q^{77} +(1.47174 - 12.4418i) q^{78} +(5.57094 + 9.64914i) q^{79} +(-3.07468 - 1.77517i) q^{80} +(1.66151 - 8.84530i) q^{81} +(-9.85030 - 17.0612i) q^{82} +(-1.50053 + 0.866332i) q^{83} +(8.40550 + 1.50627i) q^{84} -3.61992i q^{85} +(10.8361 + 6.25623i) q^{86} +(7.96064 - 2.87234i) q^{87} +0.0488281 q^{88} +(4.61799 + 2.66620i) q^{89} +(0.909673 + 5.33260i) q^{90} +(4.83470 + 7.32847i) q^{91} +(-5.17648 - 8.96593i) q^{92} +(11.0853 + 1.98650i) q^{93} +(-9.37565 - 16.2391i) q^{94} +0.328849 q^{95} +(-4.71666 - 13.0721i) q^{96} +(-2.54546 - 1.46962i) q^{97} +(1.86025 - 1.07401i) q^{98} +(1.88596 + 2.27321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) \) 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Introduction

L-functions

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