LMFDB - Embedded newform 225.2.q.a.106.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,2,Mod(16,225)] 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("225.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.7
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39878 - 0.297321i) q^{2} +(-1.19801 - 1.25091i) q^{3} +(0.0411076 + 0.0183023i) q^{4} +(1.76390 - 1.37429i) q^{5} +(1.30384 + 2.10594i) q^{6} +(1.92019 - 3.32586i) q^{7} +(2.26178 + 1.64328i) q^{8} +(-0.129533 + 2.99720i) q^{9} +(-2.87591 + 1.39789i) q^{10} +(-5.11325 - 1.08686i) q^{11} +(-0.0263530 - 0.0733481i) q^{12} +(3.28926 - 0.699153i) q^{13} +(-3.67477 + 4.08125i) q^{14} +(-3.83228 - 0.560051i) q^{15} +(-2.73539 - 3.03795i) q^{16} +(-3.90998 - 2.84077i) q^{17} +(1.07232 - 4.15393i) q^{18} +(-1.90903 - 1.38699i) q^{19} +(0.0976621 - 0.0242104i) q^{20} +(-6.46075 + 1.58245i) q^{21} +(6.82920 + 3.04055i) q^{22} +(-3.12041 + 3.46556i) q^{23} +(-0.654054 - 4.79795i) q^{24} +(1.22265 - 4.84821i) q^{25} -4.80884 q^{26} +(3.90440 - 3.42865i) q^{27} +(0.139805 - 0.101574i) q^{28} +(0.768054 + 7.30754i) q^{29} +(5.19401 + 1.92281i) q^{30} +(-0.0679615 + 0.646611i) q^{31} +(0.127249 + 0.220402i) q^{32} +(4.76619 + 7.69827i) q^{33} +(4.62460 + 5.13614i) q^{34} +(-1.18369 - 8.50536i) q^{35} +(-0.0601804 + 0.120837i) q^{36} +(0.315262 - 0.970276i) q^{37} +(2.25794 + 2.50769i) q^{38} +(-4.81515 - 3.27696i) q^{39} +(6.24790 - 0.209769i) q^{40} +(3.66775 - 0.779604i) q^{41} +(9.50769 - 0.292591i) q^{42} +(-2.34851 + 4.06773i) q^{43} +(-0.190302 - 0.138262i) q^{44} +(3.89054 + 5.46477i) q^{45} +(5.39516 - 3.91981i) q^{46} +(-1.24854 - 11.8791i) q^{47} +(-0.523169 + 7.06122i) q^{48} +(-3.87423 - 6.71036i) q^{49} +(-3.15170 + 6.41808i) q^{50} +(1.13067 + 8.29429i) q^{51} +(0.148010 + 0.0314604i) q^{52} +(2.92011 - 2.12158i) q^{53} +(-6.48082 + 3.63509i) q^{54} +(-10.5129 + 5.10999i) q^{55} +(9.80838 - 4.36697i) q^{56} +(0.552044 + 4.04964i) q^{57} +(1.09834 - 10.4500i) q^{58} +(7.61268 - 1.61813i) q^{59} +(-0.147285 - 0.0931618i) q^{60} +(6.44432 + 1.36978i) q^{61} +(0.287314 - 0.884263i) q^{62} +(9.71955 + 6.18599i) q^{63} +(2.41404 + 7.42965i) q^{64} +(4.84107 - 5.75363i) q^{65} +(-4.37801 - 12.1853i) q^{66} +(0.106476 - 1.01305i) q^{67} +(-0.108737 - 0.188339i) q^{68} +(8.07338 - 0.248451i) q^{69} +(-0.873097 + 12.2491i) q^{70} +(-2.82082 + 2.04945i) q^{71} +(-5.21823 + 6.56617i) q^{72} +(-1.38140 - 4.25150i) q^{73} +(-0.729467 + 1.26347i) q^{74} +(-7.52941 + 4.27879i) q^{75} +(-0.0530904 - 0.0919553i) q^{76} +(-13.4331 + 14.9190i) q^{77} +(5.76105 + 6.01540i) q^{78} +(-0.171432 - 1.63107i) q^{79} +(-8.99997 - 1.59942i) q^{80} +(-8.96644 - 0.776471i) q^{81} -5.36219 q^{82} +(10.3261 - 4.59747i) q^{83} +(-0.294548 - 0.0531957i) q^{84} +(-10.8008 + 0.362630i) q^{85} +(4.49448 - 4.99162i) q^{86} +(8.22091 - 9.71529i) q^{87} +(-9.77907 - 10.8608i) q^{88} +(-0.935178 - 2.87818i) q^{89} +(-3.81724 - 8.80077i) q^{90} +(3.99070 - 12.2821i) q^{91} +(-0.191700 + 0.0853504i) q^{92} +(0.890268 - 0.689634i) q^{93} +(-1.78546 + 16.9875i) q^{94} +(-5.27345 + 0.177052i) q^{95} +(0.123256 - 0.423221i) q^{96} +(-1.69408 - 16.1181i) q^{97} +(3.42408 + 10.5382i) q^{98} +(3.91986 - 15.1847i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−1.39878	−	0.297321i	−0.989090	−	0.210238i	−0.315165	−	0.949037i	$-0.602060\pi$
$2$	−1.39878	−	0.297321i	−0.989090	−	0.210238i	−0.673925	+	0.738799i	$0.735393\pi$
$3$	−1.19801	−	1.25091i	−0.691673	−	0.722211i
$3$	−1.19801	−	1.25091i	−0.691673	−	0.722211i
$4$	0.0411076	+	0.0183023i	0.0205538	+	0.00915114i
$5$	1.76390	−	1.37429i	0.788838	−	0.614601i
$5$	1.76390	−	1.37429i	0.788838	−	0.614601i
$6$	1.30384	+	2.10594i	0.532291	+	0.859747i
$7$	1.92019	−	3.32586i	0.725762	−	1.25706i	−0.232897	−	0.972501i	$-0.574821\pi$
$7$	1.92019	−	3.32586i	0.725762	−	1.25706i	0.958660	−	0.284556i	$-0.0918460\pi$
$8$	2.26178	+	1.64328i	0.799662	+	0.580988i
$9$	−0.129533	+	2.99720i	−0.0431775	+	0.999067i
$10$	−2.87591	+	1.39789i	−0.909444	+	0.442052i
$11$	−5.11325	−	1.08686i	−1.54170	−	0.327699i	−0.642865	−	0.765979i	$-0.722255\pi$
$11$	−5.11325	−	1.08686i	−1.54170	−	0.327699i	−0.898839	+	0.438280i	$0.855588\pi$
$12$	−0.0263530	−	0.0733481i	−0.00760745	−	0.0211738i
$13$	3.28926	−	0.699153i	0.912276	−	0.193910i	0.272217	−	0.962236i	$-0.412243\pi$
$13$	3.28926	−	0.699153i	0.912276	−	0.193910i	0.640059	+	0.768326i	$0.278910\pi$
$14$	−3.67477	+	4.08125i	−0.982125	+	1.09076i
$15$	−3.83228	−	0.560051i	−0.989490	−	0.144605i
$16$	−2.73539	−	3.03795i	−0.683847	−	0.759489i
$17$	−3.90998	−	2.84077i	−0.948309	−	0.688987i	0.00209712	−	0.999998i	$-0.499332\pi$
$17$	−3.90998	−	2.84077i	−0.948309	−	0.688987i	−0.950406	+	0.311011i	$0.899332\pi$
$18$	1.07232	−	4.15393i	0.252748	−	0.979090i
$19$	−1.90903	−	1.38699i	−0.437961	−	0.318197i	0.346863	−	0.937916i	$-0.387247\pi$
$19$	−1.90903	−	1.38699i	−0.437961	−	0.318197i	−0.784824	+	0.619719i	$0.787247\pi$
$20$	0.0976621	−	0.0242104i	0.0218379	−	0.00541362i
$21$	−6.46075	+	1.58245i	−1.40985	+	0.345319i
$22$	6.82920	+	3.04055i	1.45599	+	0.648248i
$23$	−3.12041	+	3.46556i	−0.650650	+	0.722620i	−0.974724	−	0.223412i	$-0.928281\pi$
$23$	−3.12041	+	3.46556i	−0.650650	+	0.722620i	0.324074	+	0.946032i	$0.394947\pi$
$24$	−0.654054	−	4.79795i	−0.133508	−	0.979378i
$25$	1.22265	−	4.84821i	0.244531	−	0.969641i
$26$	−4.80884			−0.943090
$27$	3.90440	−	3.42865i	0.751402	−	0.659844i
$28$	0.139805	−	0.101574i	0.0264207	−	0.0191957i
$29$	0.768054	+	7.30754i	0.142624	+	1.35698i	0.798448	+	0.602063i	$0.205654\pi$
$29$	0.768054	+	7.30754i	0.142624	+	1.35698i	−0.655824	+	0.754913i	$0.727679\pi$
$30$	5.19401	+	1.92281i	0.948293	+	0.351055i
$31$	−0.0679615	+	0.646611i	−0.0122062	+	0.116135i	−0.998928	−	0.0462828i	$-0.985262\pi$
$31$	−0.0679615	+	0.646611i	−0.0122062	+	0.116135i	0.986722	+	0.162417i	$0.0519291\pi$
$32$	0.127249	+	0.220402i	0.0224947	+	0.0389619i
$33$	4.76619	+	7.69827i	0.829687	+	1.34010i
$34$	4.62460	+	5.13614i	0.793112	+	0.880840i
$35$	−1.18369	−	8.50536i	−0.200080	−	1.43767i
$36$	−0.0601804	+	0.120837i	−0.0100301	+	0.0201395i
$37$	0.315262	−	0.970276i	0.0518287	−	0.159512i	−0.921792	−	0.387685i	$-0.873275\pi$
$37$	0.315262	−	0.970276i	0.0518287	−	0.159512i	0.973621	+	0.228172i	$0.0732749\pi$
$38$	2.25794	+	2.50769i	0.366286	+	0.406801i
$39$	−4.81515	−	3.27696i	−0.771041	−	0.524733i
$40$	6.24790	−	0.209769i	0.987880	−	0.0331674i
$41$	3.66775	−	0.779604i	0.572806	−	0.121754i	0.0876036	−	0.996155i	$-0.472079\pi$
$41$	3.66775	−	0.779604i	0.572806	−	0.121754i	0.485203	+	0.874402i	$0.338746\pi$
$42$	9.50769	−	0.292591i	1.46707	−	0.0451477i
$43$	−2.34851	+	4.06773i	−0.358144	+	0.620324i	−0.987651	−	0.156671i	$-0.949924\pi$
$43$	−2.34851	+	4.06773i	−0.358144	+	0.620324i	0.629507	+	0.776995i	$0.283257\pi$
$44$	−0.190302	−	0.138262i	−0.0286890	−	0.0208438i
$45$	3.89054	+	5.46477i	0.579968	+	0.814639i
$46$	5.39516	−	3.91981i	0.795473	−	0.577945i
$47$	−1.24854	−	11.8791i	−0.182118	−	1.73274i	−0.579400	−	0.815044i	$-0.696713\pi$
$47$	−1.24854	−	11.8791i	−0.182118	−	1.73274i	0.397281	−	0.917697i	$-0.369954\pi$
$48$	−0.523169	+	7.06122i	−0.0755130	+	1.01920i
$49$	−3.87423	−	6.71036i	−0.553461	−	0.958623i
$50$	−3.15170	+	6.41808i	−0.445718	+	0.907653i
$51$	1.13067	+	8.29429i	0.158326	+	1.16143i
$52$	0.148010	+	0.0314604i	0.0205252	+	0.00436277i
$53$	2.92011	−	2.12158i	0.401108	−	0.291422i	−0.368884	−	0.929475i	$-0.620260\pi$
$53$	2.92011	−	2.12158i	0.401108	−	0.291422i	0.769992	+	0.638054i	$0.220260\pi$
$54$	−6.48082	+	3.63509i	−0.881929	+	0.494673i
$55$	−10.5129	+	5.10999i	−1.41756	+	0.689031i
$56$	9.80838	−	4.36697i	1.31070	−	0.583561i
$57$	0.552044	+	4.04964i	0.0731200	+	0.536388i
$58$	1.09834	−	10.4500i	0.144220	−	1.37216i
$59$	7.61268	−	1.61813i	0.991087	−	0.210662i	0.316288	−	0.948663i	$-0.397563\pi$
$59$	7.61268	−	1.61813i	0.991087	−	0.210662i	0.674799	+	0.738001i	$0.264230\pi$
$60$	−0.147285	−	0.0931618i	−0.0190145	−	0.0120271i
$61$	6.44432	+	1.36978i	0.825110	+	0.175383i	0.601069	−	0.799197i	$-0.294742\pi$
$61$	6.44432	+	1.36978i	0.825110	+	0.175383i	0.224041	+	0.974580i	$0.428075\pi$
$62$	0.287314	−	0.884263i	0.0364890	−	0.112301i
$63$	9.71955	+	6.18599i	1.22455	+	0.779362i
$64$	2.41404	+	7.42965i	0.301755	+	0.928707i
$65$	4.84107	−	5.75363i	0.600461	−	0.713650i
$66$	−4.37801	−	12.1853i	−0.538896	−	1.49991i
$67$	0.106476	−	1.01305i	0.0130081	−	0.123764i	−0.986091	−	0.166208i	$-0.946848\pi$
$67$	0.106476	−	1.01305i	0.0130081	−	0.123764i	0.999099	+	0.0424441i	$0.0135144\pi$
$68$	−0.108737	−	0.188339i	−0.0131863	−	0.0228394i
$69$	8.07338	−	0.248451i	0.971921	−	0.0299100i
$70$	−0.873097	+	12.2491i	−0.104355	+	1.46405i
$71$	−2.82082	+	2.04945i	−0.334770	+	0.243225i	−0.742452	−	0.669899i	$-0.766337\pi$
$71$	−2.82082	+	2.04945i	−0.334770	+	0.243225i	0.407682	+	0.913124i	$0.366337\pi$
$72$	−5.21823	+	6.56617i	−0.614974	+	0.773830i
$73$	−1.38140	−	4.25150i	−0.161680	−	0.497601i	0.837096	−	0.547056i	$-0.184252\pi$
$73$	−1.38140	−	4.25150i	−0.161680	−	0.497601i	−0.998776	+	0.0494551i	$0.984252\pi$
$74$	−0.729467	+	1.26347i	−0.0847988	+	0.146876i
$75$	−7.52941	+	4.27879i	−0.869421	+	0.494072i
$76$	−0.0530904	−	0.0919553i	−0.00608989	−	0.0105480i
$77$	−13.4331	+	14.9190i	−1.53085	+	1.70018i
$78$	5.76105	+	6.01540i	0.652310	+	0.681110i
$79$	−0.171432	−	1.63107i	−0.0192877	−	0.183510i	0.980636	−	0.195838i	$-0.0627425\pi$
$79$	−0.171432	−	1.63107i	−0.0192877	−	0.183510i	−0.999924	+	0.0123278i	$0.996076\pi$
$80$	−8.99997	−	1.59942i	−1.00623	−	0.178821i
$81$	−8.96644	−	0.776471i	−0.996271	−	0.0862745i
$82$	−5.36219			−0.592154
$83$	10.3261	−	4.59747i	1.13344	−	0.504638i	0.247704	−	0.968836i	$-0.420324\pi$
$83$	10.3261	−	4.59747i	1.13344	−	0.504638i	0.885731	+	0.464198i	$0.153657\pi$
$84$	−0.294548	−	0.0531957i	−0.0321378	−	0.00580413i
$85$	−10.8008	+	0.362630i	−1.17151	+	0.0393328i
$86$	4.49448	−	4.99162i	0.484652	−	0.538261i
$87$	8.22091	−	9.71529i	0.881374	−	1.04159i
$88$	−9.77907	−	10.8608i	−1.04245	−	1.15776i
$89$	−0.935178	−	2.87818i	−0.0991286	−	0.305087i	0.889179	−	0.457559i	$-0.151276\pi$
$89$	−0.935178	−	2.87818i	−0.0991286	−	0.305087i	−0.988308	+	0.152473i	$0.951276\pi$
$90$	−3.81724	−	8.80077i	−0.402373	−	0.927683i
$91$	3.99070	−	12.2821i	0.418339	−	1.28752i
$92$	−0.191700	+	0.0853504i	−0.0199861	+	0.00889839i
$93$	0.890268	−	0.689634i	0.0923165	−	0.0715117i
$94$	−1.78546	+	16.9875i	−0.184156	+	1.75212i
$95$	−5.27345	+	0.177052i	−0.541044	+	0.0181652i
$96$	0.123256	−	0.423221i	0.0125798	−	0.0431948i
$97$	−1.69408	−	16.1181i	−0.172008	−	1.63654i	−0.651251	−	0.758862i	$-0.725755\pi$
$97$	−1.69408	−	16.1181i	−0.172008	−	1.63654i	0.479243	−	0.877682i	$-0.340911\pi$
$98$	3.42408	+	10.5382i	0.345885	+	1.06452i
$99$	3.91986	−	15.1847i	0.393961	−	1.52612i
$100$	0.138994	−	0.176921i	0.0138994	−	0.0176921i
$101$	−2.79104	+	4.83422i	−0.277719	+	0.481023i	−0.970817	−	0.239820i	$-0.922912\pi$
$101$	−2.79104	+	4.83422i	−0.277719	+	0.481023i	0.693099	+	0.720843i	$0.256245\pi$
$102$	0.884499	−	11.9381i	0.0875785	−	1.18205i
$103$	0.569374	+	0.253501i	0.0561020	+	0.0249782i	0.434596	−	0.900626i	$-0.356891\pi$
$103$	0.569374	+	0.253501i	0.0561020	+	0.0249782i	−0.378494	+	0.925604i	$0.623558\pi$
$104$	8.58850	+	3.82385i	0.842172	+	0.374959i
$105$	−9.22134	+	11.6702i	−0.899910	+	1.13890i
$106$	−4.71539	+	2.09943i	−0.457999	+	0.203914i
$107$	8.51791			0.823458			0.411729	−	0.911306i	$-0.364925\pi$
$107$	8.51791			0.823458			0.411729	+	0.911306i	$0.364925\pi$
$108$	0.223253	−	0.0694842i	0.0214825	−	0.00668612i
$109$	−3.14970	+	9.69377i	−0.301686	+	0.928495i	0.679207	+	0.733947i	$0.262324\pi$
$109$	−3.14970	+	9.69377i	−0.301686	+	0.928495i	−0.980893	+	0.194548i	$0.937676\pi$
$110$	16.2246	−	4.02208i	1.54695	−	0.383490i
$111$	−1.59141	+	0.768040i	−0.151050	+	0.0728991i
$112$	−15.3563	+	3.26407i	−1.45103	+	0.308426i
$113$	6.20262	−	1.31841i	0.583494	−	0.124025i	0.0932987	−	0.995638i	$-0.470259\pi$
$113$	6.20262	−	1.31841i	0.583494	−	0.124025i	0.490195	+	0.871613i	$0.336926\pi$
$114$	0.431852	−	5.82871i	0.0404466	−	0.545909i
$115$	−0.741384	+	10.4012i	−0.0691344	+	0.969920i
$116$	−0.102172	+	0.314453i	−0.00948642	+	0.0291962i
$117$	1.66944	+	9.94913i	0.154340	+	0.919798i
$118$	−11.1296			−1.02456
$119$	−16.9559	+	7.54924i	−1.55434	+	0.692038i
$120$	−7.74746	−	7.56423i	−0.707243	−	0.690517i
$121$	14.9151	+	6.64063i	1.35592	+	0.603694i
$122$	−8.60695	−	3.83206i	−0.779236	−	0.346938i
$123$	−5.36922	−	3.65404i	−0.484127	−	0.329473i
$124$	−0.0146282	+	0.0253368i	−0.00131365	+	0.00227531i
$125$	−4.50621	−	10.2320i	−0.403047	−	0.915179i
$126$	−11.7563	−	11.5427i	−1.04734	−	1.02831i
$127$	4.60449	+	14.1712i	0.408583	+	1.25749i	0.917867	+	0.396889i	$0.129910\pi$
$127$	4.60449	+	14.1712i	0.408583	+	1.25749i	−0.509284	+	0.860599i	$0.670090\pi$
$128$	−1.22094	−	11.6164i	−0.107917	−	1.02676i
$129$	7.90189	−	1.93543i	0.695723	−	0.170405i
$130$	−8.48228	+	6.60873i	−0.743946	+	0.579624i
$131$	1.40768	−	13.3932i	0.122989	−	1.17017i	−0.742714	−	0.669609i	$-0.766462\pi$
$131$	1.40768	−	13.3932i	0.122989	−	1.17017i	0.865703	−	0.500558i	$-0.166872\pi$
$132$	0.0550306	+	0.403689i	0.00478980	+	0.0351366i
$133$	−8.27862	+	3.68588i	−0.717847	+	0.319606i
$134$	−0.450138	+	1.38538i	−0.0388860	+	0.119679i
$135$	2.17499	−	11.4136i	0.187194	−	0.982323i
$136$	−4.17535	−	12.8504i	−0.358033	−	1.10191i
$137$	6.11073	+	6.78665i	0.522075	+	0.579823i	0.945300	−	0.326201i	$-0.105769\pi$
$137$	6.11073	+	6.78665i	0.522075	+	0.579823i	−0.423225	+	0.906024i	$0.639102\pi$
$138$	−11.3668	−	2.05285i	−0.967606	−	0.174751i
$139$	7.85045	−	8.71881i	0.665866	−	0.739520i	−0.311692	−	0.950183i	$-0.600896\pi$
$139$	7.85045	−	8.71881i	0.665866	−	0.739520i	0.977559	+	0.210664i	$0.0675625\pi$
$140$	0.107009	−	0.371299i	0.00904391	−	0.0313805i
$141$	−13.3638	+	15.7931i	−1.12544	+	1.33002i
$142$	4.55506	−	2.02805i	0.382253	−	0.170190i
$143$	−17.5787			−1.47000
$144$	9.45969	−	7.80499i	0.788307	−	0.650416i
$145$	11.3974	+	11.8342i	0.946507	+	0.982778i
$146$	0.668217	+	6.35766i	0.0553020	+	0.526163i
$147$	−3.75266	+	12.8854i	−0.309514	+	1.06277i
$148$	0.0307179	−	0.0341157i	0.00252500	−	0.00280429i
$149$	−4.73317	−	8.19809i	−0.387756	−	0.671614i	0.604391	−	0.796688i	$-0.293416\pi$
$149$	−4.73317	−	8.19809i	−0.387756	−	0.671614i	−0.992147	+	0.125074i	$0.960083\pi$
$150$	11.8042	−	3.74645i	0.963808	−	0.305896i
$151$	7.67377	−	13.2914i	0.624482	−	1.08164i	−0.364158	−	0.931337i	$-0.618643\pi$
$151$	7.67377	−	13.2914i	0.624482	−	1.08164i	0.988641	−	0.150298i	$-0.0480234\pi$
$152$	−2.03859	−	6.27414i	−0.165352	−	0.508900i
$153$	9.02082	−	11.3510i	0.729290	−	0.917676i
$154$	23.2258	−	16.8745i	1.87159	−	1.35979i
$155$	0.768753	+	1.23395i	0.0617478	+	0.0991134i
$156$	−0.137963	−	0.222836i	−0.0110459	−	0.0178412i
$157$	10.9037	+	18.8858i	0.870210	+	1.50725i	0.861780	+	0.507283i	$0.169350\pi$
$157$	10.9037	+	18.8858i	0.870210	+	1.50725i	0.00843010	+	0.999964i	$0.497317\pi$
$158$	−0.245154	+	2.33249i	−0.0195034	+	0.185563i
$159$	−6.15222	−	1.11110i	−0.487903	−	0.0881158i
$160$	0.527351	+	0.213889i	0.0416907	+	0.0169094i
$161$	5.53422	+	17.0326i	0.436157	+	1.34235i
$162$	12.3113	+	3.75203i	0.967264	+	0.294787i
$163$	−3.56614	+	10.9754i	−0.279321	+	0.859663i	0.708722	+	0.705488i	$0.249272\pi$
$163$	−3.56614	+	10.9754i	−0.279321	+	0.859663i	−0.988044	+	0.154175i	$0.950728\pi$
$164$	0.165041	+	0.0350805i	0.0128875	+	0.00273933i
$165$	18.9867	+	7.02882i	1.47811	+	0.547193i
$166$	−15.8109	+	3.36071i	−1.22716	+	0.260842i
$167$	0.441309	−	4.19878i	0.0341495	−	0.324911i	−0.964089	−	0.265580i	$-0.914437\pi$
$167$	0.441309	−	4.19878i	0.0341495	−	0.324911i	0.998238	−	0.0593312i	$-0.0188968\pi$
$168$	−17.2132	−	7.03767i	−1.32803	−	0.542968i
$169$	−1.54569	+	0.688185i	−0.118899	+	0.0529373i
$170$	15.2159	+	2.70407i	1.16700	+	0.207393i
$171$	4.40437	−	5.54208i	0.336810	−	0.423813i
$172$	−0.170990	+	0.124232i	−0.0130379	+	0.00947258i
$173$	9.65824	+	2.05292i	0.734302	+	0.156081i	0.559861	−	0.828587i	$-0.310855\pi$
$173$	9.65824	+	2.05292i	0.734302	+	0.156081i	0.174441	+	0.984668i	$0.444188\pi$
$174$	−14.3878	+	11.1453i	−1.09074	+	0.844927i
$175$	−13.7767	−	13.3758i	−1.04142	−	1.01112i
$176$	10.6849	+	18.5068i	0.805405	+	1.39500i
$177$	−11.1442	−	7.58422i	−0.837650	−	0.570065i
$178$	0.452369	+	4.30400i	0.0339065	+	0.322599i
$179$	−2.85965	+	2.07766i	−0.213740	+	0.155292i	−0.689504	−	0.724281i	$-0.742172\pi$
$179$	−2.85965	+	2.07766i	−0.213740	+	0.155292i	0.475764	+	0.879573i	$0.342172\pi$
$180$	0.0599132	+	0.295849i	0.00446566	+	0.0220513i
$181$	12.3513	+	8.97372i	0.918062	+	0.667011i	0.943041	−	0.332677i	$-0.107952\pi$
$181$	12.3513	+	8.97372i	0.918062	+	0.667011i	−0.0249788	+	0.999688i	$0.507952\pi$
$182$	−9.23386	+	15.9935i	−0.684459	+	1.18552i
$183$	−6.00690	−	9.70225i	−0.444043	−	0.717211i
$184$	−12.7526	+	2.71065i	−0.940134	+	0.199832i
$185$	−0.777352	−	2.14473i	−0.0571520	−	0.157683i
$186$	−1.45034	+	0.699954i	−0.106344	+	0.0513231i
$187$	16.9052	+	18.7751i	1.23623	+	1.37297i
$188$	0.166090	−	0.511171i	0.0121133	−	0.0372810i
$189$	−3.90604	−	19.5691i	−0.284123	−	1.42345i
$190$	7.42906	+	1.32025i	0.538960	+	0.0957808i
$191$	12.4128	+	13.7858i	0.898157	+	0.997505i	0.999996	+	0.00270389i	$0.000860677\pi$
$191$	12.4128	+	13.7858i	0.898157	+	0.997505i	−0.101839	+	0.994801i	$0.532473\pi$
$192$	6.40175	−	11.9206i	0.462006	−	0.860292i
$193$	−5.82208	−	10.0841i	−0.419082	−	0.725872i	0.576765	−	0.816910i	$-0.304315\pi$
$193$	−5.82208	−	10.0841i	−0.419082	−	0.725872i	−0.995847	+	0.0910384i	$0.970981\pi$
$194$	−2.42259	+	23.0494i	−0.173932	+	1.65485i
$195$	−12.9969	+	0.837195i	−0.930728	+	0.0599528i
$196$	−0.0364453	−	0.346754i	−0.00260324	−	0.0247681i
$197$	6.93084	−	5.03555i	0.493802	−	0.358768i	−0.312843	−	0.949805i	$-0.601281\pi$
$197$	6.93084	−	5.03555i	0.493802	−	0.358768i	0.806645	+	0.591037i	$0.201281\pi$
$198$	−9.99776	+	20.0746i	−0.710510	+	1.42664i
$199$	17.3700			1.23133			0.615663	−	0.788010i	$-0.288888\pi$
$199$	17.3700			1.23133			0.615663	+	0.788010i	$0.288888\pi$
$200$	10.7324	−	8.95644i	0.758892	−	0.633316i
$201$	−1.39479	+	1.08045i	−0.0983809	+	0.0762094i
$202$	5.34137	−	5.93220i	0.375818	−	0.417388i
$203$	25.7787	+	11.4774i	1.80931	+	0.805556i
$204$	−0.105325	+	0.361652i	−0.00737424	+	0.0253207i
$205$	5.39813	−	6.41569i	0.377021	−	0.448091i
$206$	−0.721060	−	0.523881i	−0.0502386	−	0.0365005i
$207$	−9.98280	−	9.80140i	−0.693853	−	0.681244i
$208$	−11.1214	−	8.08016i	−0.771129	−	0.560258i
$209$	8.25388	+	9.16686i	0.570933	+	0.634085i
$210$	16.3685	−	13.5824i	1.12953	−	0.937276i
$211$	−3.14108	+	3.48852i	−0.216241	+	0.240160i	−0.841500	−	0.540258i	$-0.818327\pi$
$211$	−3.14108	+	3.48852i	−0.216241	+	0.240160i	0.625259	+	0.780418i	$0.284993\pi$
$212$	0.158868	−	0.0337685i	0.0109111	−	0.00231923i
$213$	5.94304	+	1.07332i	0.407211	+	0.0735427i
$214$	−11.9147	−	2.53255i	−0.814474	−	0.173122i
$215$	1.44772	+	10.4026i	0.0987340	+	0.709450i
$216$	14.4652	−	1.33884i	0.984229	−	0.0910965i
$217$	2.02004	+	1.46764i	0.137129	+	0.0996301i
$218$	7.28791	−	12.6230i	0.493599	−	0.854939i
$219$	−3.66330	+	6.82135i	−0.247543	+	0.460944i
$220$	−0.525684	+	0.0176495i	−0.0354416	+	0.00118993i
$221$	−14.8471	−	6.61034i	−0.998721	−	0.444659i
$222$	2.45440	−	0.601162i	0.164728	−	0.0403474i
$223$	−15.4209	−	3.27781i	−1.03266	−	0.219499i	−0.339745	−	0.940518i	$-0.610341\pi$
$223$	−15.4209	−	3.27781i	−1.03266	−	0.219499i	−0.692915	+	0.721019i	$0.743674\pi$
$224$	0.977368			0.0653032
$225$	14.3727	+	4.29254i	0.958179	+	0.286170i
$226$	−9.06813			−0.603203
$227$	−7.05368	−	1.49931i	−0.468169	−	0.0995124i	−0.0322143	−	0.999481i	$-0.510256\pi$
$227$	−7.05368	−	1.49931i	−0.468169	−	0.0995124i	−0.435955	+	0.899969i	$0.643589\pi$
$228$	−0.0514245	+	0.176575i	−0.00340567	+	0.0116939i
$229$	9.43095	+	4.19893i	0.623215	+	0.277473i	0.693951	−	0.720022i	$-0.255868\pi$
$229$	9.43095	+	4.19893i	0.623215	+	0.277473i	−0.0707365	+	0.997495i	$0.522535\pi$
$230$	4.12954	−	14.3287i	0.272294	−	0.944804i
$231$	34.7553	−	1.06956i	2.28673	−	0.0703722i
$232$	−10.2712	+	17.7902i	−0.674337	+	1.16799i
$233$	−10.0148	−	7.27620i	−0.656094	−	0.476680i	0.209248	−	0.977863i	$-0.432898\pi$
$233$	−10.0148	−	7.27620i	−0.656094	−	0.476680i	−0.865341	+	0.501183i	$0.832898\pi$
$234$	0.622901	−	14.4131i	0.0407203	−	0.942211i
$235$	−18.5276	−	19.2376i	−1.20861	−	1.25492i
$236$	0.342555	+	0.0728122i	0.0222984	+	0.00473967i
$237$	−1.83494	+	2.16849i	−0.119192	+	0.140858i
$238$	25.9622	−	5.51843i	1.68288	−	0.357707i
$239$	10.7186	−	11.9042i	0.693326	−	0.770016i	−0.288973	−	0.957337i	$-0.593314\pi$
$239$	10.7186	−	11.9042i	0.693326	−	0.770016i	0.982299	+	0.187321i	$0.0599804\pi$
$240$	8.78135	+	13.1742i	0.566833	+	0.850393i
$241$	−1.95862	−	2.17526i	−0.126166	−	0.140121i	0.676752	−	0.736211i	$-0.263387\pi$
$241$	−1.95862	−	2.17526i	−0.126166	−	0.140121i	−0.802918	+	0.596090i	$0.796720\pi$
$242$	−18.8886	−	13.7234i	−1.21421	−	0.882173i
$243$	9.77062	+	12.1464i	0.626785	+	0.779192i
$244$	0.239840	+	0.174254i	0.0153542	+	0.0111555i
$245$	−16.0557	−	6.51206i	−1.02576	−	0.416041i
$246$	6.42396	+	6.70759i	0.409577	+	0.427660i
$247$	−7.24900	−	3.22746i	−0.461243	−	0.205358i
$248$	−1.21628	+	1.35081i	−0.0772338	+	0.0857768i
$249$	−18.1218	−	7.40914i	−1.14842	−	0.469535i
$250$	3.26102	+	15.6522i	0.206245	+	0.989930i
$251$	−4.72015			−0.297933			−0.148967	−	0.988842i	$-0.547595\pi$
$251$	−4.72015			−0.297933			−0.148967	+	0.988842i	$0.547595\pi$
$252$	0.286329	+	0.432181i	0.0180371	+	0.0272249i
$253$	19.7220	−	14.3289i	1.23991	−	0.900849i
$254$	−2.22731	−	21.1914i	−0.139754	−	1.32967i
$255$	13.3931	+	13.0764i	0.838711	+	0.818875i
$256$	−0.112829	+	1.07349i	−0.00705179	+	0.0670933i
$257$	−10.6050	−	18.3684i	−0.661523	−	1.14579i	−0.980215	−	0.197934i	$-0.936577\pi$
$257$	−10.6050	−	18.3684i	−0.661523	−	1.14579i	0.318692	−	0.947858i	$-0.396756\pi$
$258$	−11.6285	+	0.357856i	−0.723958	+	0.0222792i
$259$	−2.62164	−	2.91163i	−0.162901	−	0.180920i
$260$	0.304309	−	0.147915i	0.0188725	−	0.00917331i
$261$	−22.0017	+	1.35545i	−1.36187	+	0.0839001i
$262$	−5.95111	+	18.3156i	−0.367661	+	1.13154i
$263$	−4.94948	−	5.49696i	−0.305198	−	0.338957i	0.570962	−	0.820976i	$-0.306570\pi$
$263$	−4.94948	−	5.49696i	−0.305198	−	0.338957i	−0.876161	+	0.482019i	$0.839904\pi$
$264$	−1.87034	+	25.2440i	−0.115112	+	1.55366i
$265$	2.23509	−	7.75532i	0.137301	−	0.476406i
$266$	12.6759	−	2.69434i	0.777209	−	0.165201i
$267$	−2.47998	+	4.61792i	−0.151772	+	0.282612i
$268$	0.0229181	−	0.0396953i	0.00139994	−	0.00242478i
$269$	22.6424	+	16.4507i	1.38053	+	1.00301i	0.996830	+	0.0795565i	$0.0253504\pi$
$269$	22.6424	+	16.4507i	1.38053	+	1.00301i	0.383700	+	0.923458i	$0.374650\pi$
$270$	−6.43584	+	15.3184i	−0.391672	+	0.932251i
$271$	−16.6545	+	12.1002i	−1.01169	+	0.735034i	−0.964562	−	0.263855i	$-0.915006\pi$
$271$	−16.6545	+	12.1002i	−1.01169	+	0.735034i	−0.0471255	+	0.998889i	$0.515006\pi$
$272$	2.06519	+	19.6489i	0.125220	+	1.19139i
$273$	−20.1447	+	9.72213i	−1.21921	+	0.588410i
$274$	−6.52978	−	11.3099i	−0.394479	−	0.683257i
$275$	−11.5210	+	23.4613i	−0.694745	+	1.41477i
$276$	0.336424	+	0.137548i	0.0202504	+	0.00827942i
$277$	2.66279	+	0.565994i	0.159992	+	0.0340073i	0.287211	−	0.957867i	$-0.407272\pi$
$277$	2.66279	+	0.565994i	0.159992	+	0.0340073i	−0.127219	+	0.991875i	$0.540605\pi$
$278$	−13.5734	+	9.86163i	−0.814077	+	0.591461i
$279$	−1.92922	−	0.287452i	−0.115499	−	0.0172093i
$280$	11.2995	−	21.1824i	0.675272	−	1.26589i
$281$	−21.9561	+	9.77547i	−1.30979	+	0.583156i	−0.938474	−	0.345351i	$-0.887760\pi$
$281$	−21.9561	+	9.77547i	−1.30979	+	0.583156i	−0.371316	+	0.928507i	$0.621093\pi$
$282$	23.3887	−	18.1178i	1.39278	−	1.07890i
$283$	−0.805482	+	7.66365i	−0.0478809	+	0.455557i	0.944146	+	0.329528i	$0.106890\pi$
$283$	−0.805482	+	7.66365i	−0.0478809	+	0.455557i	−0.992027	+	0.126028i	$0.959777\pi$
$284$	−0.153467	+	0.0326204i	−0.00910657	+	0.00193566i
$285$	6.53913	+	6.38448i	0.387345	+	0.378184i
$286$	24.5888	+	5.22651i	1.45397	+	0.309050i
$287$	4.44991	−	13.6954i	0.262670	−	0.808415i
$288$	−0.677072	+	0.352842i	−0.0398969	+	0.0207914i
$289$	1.96470	+	6.04671i	0.115570	+	0.355689i
$290$	−12.4240	−	19.9422i	−0.729563	−	1.17105i
$291$	−18.1327	+	21.4288i	−1.06296	+	1.25618i
$292$	0.0210263	−	0.200052i	0.00123047	−	0.0117071i
$293$	−13.7967	−	23.8965i	−0.806010	−	1.39605i	−0.915607	−	0.402074i	$-0.868289\pi$
$293$	−13.7967	−	23.8965i	−0.806010	−	1.39605i	0.109597	−	0.993976i	$-0.465044\pi$
$294$	9.08026	−	16.9081i	0.529571	−	0.986103i
$295$	11.2042	−	13.3162i	0.652334	−	0.775302i
$296$	2.30749	−	1.67649i	0.134120	−	0.0974441i
$297$	−23.6906	+	13.2880i	−1.37467	+	0.771051i
$298$	4.18322	+	12.8746i	0.242327	+	0.745807i
$299$	−7.84086	+	13.5808i	−0.453449	+	0.785397i
$300$	−0.387827	+	0.0380853i	−0.0223912	+	0.00219885i
$301$	9.01914	+	15.6216i	0.519855	+	0.900415i
$302$	−14.6857	+	16.3102i	−0.845070	+	0.938545i
$303$	9.39085	−	2.30013i	0.539490	−	0.132139i
$304$	1.00832	+	9.59348i	0.0578309	+	0.550224i
$305$	13.2496	−	6.44021i	0.758669	−	0.368765i
$306$	−15.9931	+	13.1956i	−0.914264	+	0.754340i
$307$	−29.8034			−1.70097			−0.850485	−	0.526000i	$-0.823691\pi$
$307$	−29.8034			−1.70097			−0.850485	+	0.526000i	$0.823691\pi$
$308$	−0.825255	+	0.367427i	−0.0470233	+	0.0209361i
$309$	−0.365010	−	1.01593i	−0.0207647	−	0.0577943i
$310$	−0.708441	−	1.95460i	−0.0402367	−	0.111014i
$311$	−3.70318	+	4.11280i	−0.209988	+	0.233215i	−0.838933	−	0.544234i	$-0.816820\pi$
$311$	−3.70318	+	4.11280i	−0.209988	+	0.233215i	0.628945	+	0.777450i	$0.283487\pi$
$312$	−5.50586	−	15.3244i	−0.311708	−	0.867575i
$313$	3.83120	+	4.25498i	0.216552	+	0.240506i	0.841627	−	0.540059i	$-0.181598\pi$
$313$	3.83120	+	4.25498i	0.216552	+	0.240506i	−0.625075	+	0.780565i	$0.714932\pi$
$314$	−9.63679	−	29.6590i	−0.543836	−	1.67375i
$315$	25.6456	−	2.44603i	1.44497	−	0.137818i
$316$	0.0228051	−	0.0701870i	0.00128289	−	0.00394833i
$317$	10.6366	−	4.73570i	0.597409	−	0.265984i	−0.0856755	−	0.996323i	$-0.527305\pi$
$317$	10.6366	−	4.73570i	0.597409	−	0.265984i	0.683084	+	0.730340i	$0.260638\pi$
$318$	8.27528	+	3.38337i	0.464055	+	0.189730i
$319$	4.01499	−	38.2001i	0.224796	−	2.13879i
$320$	14.4686	+	9.78754i	0.808820	+	0.547140i
$321$	−10.2046	−	10.6551i	−0.569563	−	0.594710i
$322$	−2.67704	−	25.4703i	−0.149186	−	1.41941i
$323$	3.52414	+	10.8462i	0.196089	+	0.603498i
$324$	−0.354378	−	0.196025i	−0.0196876	−	0.0108903i
$325$	0.631986	−	16.8018i	0.0350563	−	0.931998i
$326$	8.25148	−	14.2920i	0.457007	−	0.791560i
$327$	15.8994	−	7.67328i	0.879237	−	0.424334i
$328$	9.57677	+	4.26385i	0.528789	+	0.235432i
$329$	−41.9056	−	18.6576i	−2.31033	−	1.02862i
$330$	−24.4685	−	15.4769i	−1.34695	−	0.851978i
$331$	−18.2816	+	8.13951i	−1.00485	+	0.447388i	−0.842124	−	0.539284i	$-0.818695\pi$
$331$	−18.2816	+	8.13951i	−1.00485	+	0.447388i	−0.162725	+	0.986671i	$0.552028\pi$
$332$	0.508625			0.0279144
$333$	2.86728	+	1.07059i	0.157126	+	0.0586677i
$334$	−1.86568	+	5.74198i	−0.102086	+	0.314187i
$335$	−1.20441	−	1.93324i	−0.0658040	−	0.105624i
$336$	22.4800	+	15.2988i	1.22639	+	0.834620i
$337$	3.88794	−	0.826407i	0.211790	−	0.0450173i	−0.100795	−	0.994907i	$-0.532139\pi$
$337$	3.88794	−	0.826407i	0.211790	−	0.0450173i	0.312584	+	0.949890i	$0.398805\pi$
$338$	2.36670	−	0.503057i	0.128731	−	0.0273627i
$339$	−9.08003	−	6.17943i	−0.493159	−	0.335621i
$340$	−0.450633	−	0.182773i	−0.0244390	−	0.00991226i
$341$	1.05028	−	3.23242i	0.0568757	−	0.175045i
$342$	−7.80853	+	6.44266i	−0.422237	+	0.348379i
$343$	−2.87436			−0.155201
$344$	−11.9963	+	5.34108i	−0.646795	+	0.287972i
$345$	13.8992	−	11.5334i	0.748305	−	0.620938i
$346$	−12.8994	−	5.74319i	−0.693477	−	0.308756i
$347$	33.5579	+	14.9409i	1.80148	+	0.802072i	0.968601	+	0.248620i	$0.0799772\pi$
$347$	33.5579	+	14.9409i	1.80148	+	0.802072i	0.832882	+	0.553451i	$0.186689\pi$
$348$	0.515754	−	0.248911i	0.0276473	−	0.0133430i
$349$	5.56763	−	9.64341i	0.298028	−	0.516200i	−0.677657	−	0.735378i	$-0.737004\pi$
$349$	5.56763	−	9.64341i	0.298028	−	0.516200i	0.975685	+	0.219179i	$0.0703377\pi$
$350$	15.2938	+	22.8060i	0.817486	+	1.21903i
$351$	10.4454	−	14.0075i	0.557536	−	0.747665i
$352$	−0.411112	−	1.26527i	−0.0219124	−	0.0674393i
$353$	0.311118	+	2.96009i	0.0165592	+	0.157550i	0.999677	−	0.0254251i	$-0.00809395\pi$
$353$	0.311118	+	2.96009i	0.0165592	+	0.157550i	−0.983118	+	0.182975i	$0.941427\pi$
$354$	13.3334	+	13.9221i	0.708663	+	0.739951i
$355$	−2.15910	+	7.49164i	−0.114593	+	0.397615i
$356$	0.0142344	−	0.135431i	0.000754420	−	0.00717783i
$357$	29.7567	+	12.1661i	1.57489	+	0.643900i
$358$	4.61777	−	2.05596i	0.244057	−	0.108661i
$359$	0.714480	−	2.19894i	0.0377088	−	0.116056i	−0.930430	−	0.366469i	$-0.880567\pi$
$359$	0.714480	−	2.19894i	0.0377088	−	0.116056i	0.968139	+	0.250413i	$0.0805665\pi$
$360$	−0.180587	+	18.7534i	−0.00951776	+	0.988390i
$361$	−4.15068	−	12.7745i	−0.218457	−	0.672341i
$362$	−14.6087	−	16.2246i	−0.767815	−	0.852745i
$363$	−9.56167	−	26.6130i	−0.501858	−	1.39682i
$364$	0.388839	−	0.431849i	0.0203807	−	0.0226351i
$365$	−8.27944	−	5.60077i	−0.433366	−	0.293158i
$366$	5.51768	+	15.3573i	0.288414	+	0.802741i
$367$	−15.4758	+	6.89027i	−0.807830	+	0.359669i	−0.768736	−	0.639567i	$-0.779114\pi$
$367$	−15.4758	+	6.89027i	−0.807830	+	0.359669i	−0.0390939	+	0.999236i	$0.512447\pi$
$368$	19.0637			0.993766
$369$	1.86154	+	11.0940i	0.0969079	+	0.577529i
$370$	0.449676	+	3.23113i	0.0233775	+	0.167979i
$371$	−1.44894	−	13.7857i	−0.0752250	−	0.715718i
$372$	0.0492186	−	0.0120553i	0.00255187	−	0.000625036i
$373$	−16.8689	+	18.7348i	−0.873437	+	0.970050i	−0.999759	−	0.0219391i	$-0.993016\pi$
$373$	−16.8689	+	18.7348i	−0.873437	+	0.970050i	0.126322	+	0.991989i	$0.459683\pi$
$374$	−18.0645	−	31.2886i	−0.934094	−	1.61790i
$375$	−7.40080	+	17.8949i	−0.382175	+	0.924090i
$376$	16.6967	−	28.9196i	0.861069	−	1.49141i
$377$	7.63542	+	23.4994i	0.393244	+	1.21028i
$378$	−0.354602	+	28.5344i	−0.0182387	+	1.46765i
$379$	19.7932	−	14.3806i	1.01671	−	0.738681i	0.0511021	−	0.998693i	$-0.483727\pi$
$379$	19.7932	−	14.3806i	1.01671	−	0.738681i	0.965605	+	0.260012i	$0.0837266\pi$
$380$	−0.220019	−	0.0892379i	−0.0112867	−	0.00457781i
$381$	12.2106	−	22.7370i	0.625566	−	1.16485i
$382$	−13.2640	−	22.9739i	−0.678645	−	1.17545i
$383$	0.000525732	−	0.00500201i	2.68637e−5	−	0.000255591i	−0.994508	−	0.104656i	$-0.966626\pi$
$383$	0.000525732	−	0.00500201i	2.68637e−5	−	0.000255591i	0.994535	+	0.104401i	$0.0332924\pi$
$384$	−13.0684	+	15.4439i	−0.666893	+	0.788119i
$385$	−3.19160	+	44.7766i	−0.162659	+	2.28203i
$386$	5.14561	+	15.8365i	0.261904	+	0.806059i
$387$	−11.8876	−	7.56585i	−0.604281	−	0.384594i
$388$	0.225358	−	0.693582i	0.0114408	−	0.0352113i
$389$	−10.1990	−	2.16786i	−0.517109	−	0.109915i	−0.0580377	−	0.998314i	$-0.518484\pi$
$389$	−10.1990	−	2.16786i	−0.517109	−	0.109915i	−0.459071	+	0.888400i	$0.651818\pi$
$390$	18.4288	+	2.69320i	0.933178	+	0.136375i
$391$	22.0456	−	4.68593i	1.11489	−	0.236978i
$392$	2.26435	−	21.5439i	0.114367	−	1.08813i
$393$	−18.4400	+	14.2843i	−0.930176	+	0.720548i
$394$	−11.1919	+	4.98297i	−0.563841	+	0.251038i
$395$	−2.54395	−	2.64144i	−0.128000	−	0.132905i
$396$	0.439050	−	0.552463i	0.0220631	−	0.0277623i
$397$	−4.80180	+	3.48871i	−0.240996	+	0.175094i	−0.701727	−	0.712446i	$-0.747587\pi$
$397$	−4.80180	+	3.48871i	−0.240996	+	0.175094i	0.460731	+	0.887540i	$0.347587\pi$
$398$	−24.2969	−	5.16446i	−1.21789	−	0.258871i
$399$	14.5286	+	5.94004i	0.727338	+	0.297374i
$400$	−18.0731	+	9.54735i	−0.903653	+	0.477368i
$401$	9.95507	+	17.2427i	0.497133	+	0.861059i	0.999995	−	0.00330780i	$-0.00105291\pi$
$401$	9.95507	+	17.2427i	0.497133	+	0.861059i	−0.502862	+	0.864367i	$0.667720\pi$
$402$	2.27225	−	1.09662i	0.113330	−	0.0546946i
$403$	0.228537	+	2.17438i	0.0113842	+	0.108314i
$404$	−0.203210	+	0.147641i	−0.0101101	+	0.00734540i
$405$	−16.8830	+	10.9529i	−0.838921	+	0.544253i
$406$	−32.6463	−	23.7190i	−1.62021	−	1.17715i
$407$	−2.66656	+	4.61862i	−0.132177	+	0.228937i
$408$	−11.0725	+	20.6179i	−0.548172	+	1.02074i
$409$	4.78216	−	1.01648i	0.236463	−	0.0502617i	−0.0881559	−	0.996107i	$-0.528097\pi$
$409$	4.78216	−	1.01648i	0.236463	−	0.0502617i	0.324619	+	0.945845i	$0.394764\pi$
$410$	−9.45833	+	7.36920i	−0.467114	+	0.363939i
$411$	1.16874	−	15.7744i	0.0576495	−	0.778096i
$412$	0.0187659	+	0.0208417i	0.000924531	+	0.00102680i
$413$	9.23611	−	28.4258i	0.454479	−	1.39874i
$414$	11.0496	+	16.6781i	0.543060	+	0.819686i
$415$	11.8959	−	22.3005i	0.583946	−	1.09469i
$416$	0.572650	+	0.635993i	0.0280765	+	0.0311821i
$417$	−20.3113	+	0.625064i	−0.994651	+	0.0306095i
$418$	−8.81990	−	15.2765i	−0.431395	−	0.747199i
$419$	−1.33241	+	12.6770i	−0.0650923	+	0.619312i	0.912540	+	0.408988i	$0.134118\pi$
$419$	−1.33241	+	12.6770i	−0.0650923	+	0.619312i	−0.977632	+	0.210323i	$0.932548\pi$
$420$	−0.592658	+	0.310963i	−0.0289188	+	0.0151734i
$421$	1.83515	+	17.4603i	0.0894397	+	0.850962i	0.943630	+	0.331001i	$0.107387\pi$
$421$	1.83515	+	17.4603i	0.0894397	+	0.850962i	−0.854191	+	0.519960i	$0.825947\pi$
$422$	5.43091	−	3.94579i	0.264372	−	0.192078i
$423$	35.7657	−	2.20340i	1.73899	−	0.107133i
$424$	10.0910			0.490063
$425$	−18.5532	+	15.4831i	−0.899961	+	0.751041i
$426$	−7.99392	−	3.26833i	−0.387307	−	0.158351i
$427$	16.9300	−	18.8027i	0.819300	−	0.909925i
$428$	0.350151	+	0.155897i	0.0169252	+	0.00753558i
$429$	21.0595	+	21.9893i	1.01676	+	1.06165i
$430$	1.06785	−	14.9814i	0.0514964	−	0.722468i
$431$	23.8727	+	17.3445i	1.14991	+	0.835456i	0.988469	−	0.151427i	$-0.0483867\pi$
$431$	23.8727	+	17.3445i	1.14991	+	0.835456i	0.161438	+	0.986883i	$0.448387\pi$
$432$	−21.0961	−	2.48270i	−1.01499	−	0.119449i
$433$	15.9668	+	11.6006i	0.767316	+	0.557488i	0.901146	−	0.433517i	$-0.142727\pi$
$433$	15.9668	+	11.6006i	0.767316	+	0.557488i	−0.133830	+	0.991004i	$0.542727\pi$
$434$	−2.38924	−	2.65352i	−0.114687	−	0.127373i
$435$	1.14921	−	28.4347i	0.0551002	−	1.36334i
$436$	−0.306895	+	0.340841i	−0.0146976	+	0.0163233i
$437$	10.7636	−	2.28788i	0.514895	−	0.109444i
$438$	7.15230	−	8.45243i	0.341750	−	0.403873i
$439$	−12.0097	−	2.55274i	−0.573192	−	0.121836i	−0.0878087	−	0.996137i	$-0.527986\pi$
$439$	−12.0097	−	2.55274i	−0.573192	−	0.121836i	−0.485383	+	0.874302i	$0.661320\pi$
$440$	−32.1751	−	5.71796i	−1.53389	−	0.272593i
$441$	20.6142	−	10.7426i	0.981626	−	0.511554i
$442$	18.8024	+	13.6608i	0.894341	+	0.649777i
$443$	−11.4062	+	19.7562i	−0.541926	+	0.938643i	0.456868	+	0.889535i	$0.348971\pi$
$443$	−11.4062	+	19.7562i	−0.541926	+	0.938643i	−0.998793	+	0.0491085i	$0.984362\pi$
$444$	−0.0794760	+	0.00244580i	−0.00377176	+	0.000116073i
$445$	−5.60501	−	3.79161i	−0.265703	−	0.179739i
$446$	20.5960	+	9.16991i	0.975247	+	0.434208i
$447$	−4.58465	+	15.7422i	−0.216846	+	0.744579i
$448$	29.3454	+	6.23756i	1.38644	+	0.294697i
$449$	−4.10374			−0.193668			−0.0968338	−	0.995301i	$-0.530872\pi$
$449$	−4.10374			−0.193668			−0.0968338	+	0.995301i	$0.530872\pi$
$450$	−18.8280	−	10.2776i	−0.887562	−	0.484493i
$451$	−19.6015			−0.922997
$452$	0.279105	+	0.0593256i	0.0131280	+	0.00279044i
$453$	−25.8195	+	6.32405i	−1.21311	+	0.297130i
$454$	9.42080	+	4.19441i	0.442140	+	0.196853i
$455$	−9.84001	−	27.1487i	−0.461307	−	1.27275i
$456$	−5.40610	+	10.0666i	−0.253164	+	0.471411i
$457$	9.06472	−	15.7006i	0.424030	−	0.734441i	−0.572299	−	0.820045i	$-0.693948\pi$
$457$	9.06472	−	15.7006i	0.424030	−	0.734441i	0.996329	+	0.0856035i	$0.0272818\pi$
$458$	−11.9434	−	8.67742i	−0.558080	−	0.405469i
$459$	−25.0061	+	2.31447i	−1.16719	+	0.108030i
$460$	−0.220843	+	0.414001i	−0.0102968	+	0.0193029i
$461$	−23.0180	−	4.89262i	−1.07205	−	0.227872i	−0.362113	−	0.932134i	$-0.617945\pi$
$461$	−23.0180	−	4.89262i	−1.07205	−	0.227872i	−0.709940	+	0.704262i	$0.751278\pi$
$462$	−48.9332	−	8.83739i	−2.27658	−	0.411153i
$463$	3.50086	−	0.744131i	0.162699	−	0.0345827i	−0.125842	−	0.992050i	$-0.540163\pi$
$463$	3.50086	−	0.744131i	0.162699	−	0.0345827i	0.288541	+	0.957468i	$0.406830\pi$
$464$	20.0991	−	22.3223i	0.933075	−	1.03629i
$465$	0.622583	−	2.43993i	0.0288716	−	0.113149i
$466$	11.8452	+	13.1555i	0.548720	+	0.609415i
$467$	12.8399	+	9.32877i	0.594162	+	0.431684i	0.843802	−	0.536655i	$-0.180312\pi$
$467$	12.8399	+	9.32877i	0.594162	+	0.431684i	−0.249640	+	0.968339i	$0.580312\pi$
$468$	−0.113465	+	0.439539i	−0.00524493	+	0.0203177i
$469$	−3.16481	−	2.29937i	−0.146137	−	0.106175i
$470$	20.1964	+	32.4179i	0.931589	+	1.49532i
$471$	10.5615	−	36.2649i	0.486650	−	1.67100i
$472$	19.8773	+	8.84994i	0.914927	+	0.407352i
$473$	16.4296	−	18.2469i	0.755432	−	0.838992i
$474$	3.21142	−	2.48768i	0.147505	−	0.114263i
$475$	−9.05849	+	7.55955i	−0.415632	+	0.346856i
$476$	−0.835184			−0.0382806
$477$	5.98056	+	9.02696i	0.273831	+	0.413316i
$478$	−18.5323	+	13.4645i	−0.847648	+	0.615852i
$479$	1.76013	+	16.7466i	0.0804226	+	0.765170i	0.958200	+	0.286100i	$0.0923591\pi$
$479$	1.76013	+	16.7466i	0.0804226	+	0.765170i	−0.877777	+	0.479069i	$0.840974\pi$
$480$	−0.364218	−	0.915908i	−0.0166242	−	0.0418053i
$481$	0.358606	−	3.41191i	0.0163510	−	0.155569i
$482$	2.09293	+	3.62506i	0.0953304	+	0.165117i
$483$	14.6761	−	27.3280i	0.667785	−	1.24347i
$484$	0.491585	+	0.545961i	0.0223448	+	0.0248164i
$485$	−25.1391	−	26.1025i	−1.14151	−	1.18525i
$486$	−10.0556	−	19.8952i	−0.456132	−	0.902465i
$487$	−3.07445	+	9.46219i	−0.139317	+	0.428773i	−0.996236	−	0.0866771i	$-0.972375\pi$
$487$	−3.07445	+	9.46219i	−0.139317	+	0.428773i	0.856920	+	0.515450i	$0.172375\pi$
$488$	12.3247	+	13.6880i	0.557914	+	0.619626i
$489$	18.0015	−	8.68781i	0.814057	−	0.392876i
$490$	20.5223	+	13.8827i	0.927104	+	0.627155i
$491$	−11.4989	+	2.44418i	−0.518940	+	0.110304i	−0.459933	−	0.887953i	$-0.652127\pi$
$491$	−11.4989	+	2.44418i	−0.518940	+	0.110304i	−0.0590068	+	0.998258i	$0.518793\pi$
$492$	−0.153839	−	0.248478i	−0.00693558	−	0.0112022i
$493$	17.7559	−	30.7542i	0.799688	−	1.38510i
$494$	9.18019	+	6.66980i	0.413036	+	0.300089i
$495$	−13.9539	−	32.1712i	−0.627182	−	1.44599i
$496$	2.15027	−	1.56227i	0.0965502	−	0.0701478i
$497$	1.39967	+	13.3170i	0.0627838	+	0.597348i
$498$	23.1456	+	15.7518i	1.03718	+	0.705854i
$499$	12.7440	+	22.0733i	0.570501	+	0.988137i	0.996514	+	0.0834204i	$0.0265844\pi$
$499$	12.7440	+	22.0733i	0.570501	+	0.988137i	−0.426013	+	0.904717i	$0.640082\pi$
$500$	0.00202981	−	0.503087i	9.07757e−5	−	0.0224987i
$501$	−5.78097	+	4.47815i	−0.258275	+	0.200069i
$502$	6.60247	+	1.40340i	0.294683	+	0.0626367i
$503$	−3.86329	+	2.80684i	−0.172256	+	0.125151i	−0.670573	−	0.741844i	$-0.733952\pi$
$503$	−3.86329	+	2.80684i	−0.172256	+	0.125151i	0.498317	+	0.866995i	$0.333952\pi$
$504$	11.8182	+	29.9634i	0.526424	+	1.33467i
$505$	1.72052	+	12.3628i	0.0765621	+	0.550135i
$506$	−31.8471	+	14.1792i	−1.41578	+	0.630344i
$507$	2.71261	+	1.10906i	0.120471	+	0.0492550i
$508$	−0.0700851	+	0.666815i	−0.00310952	+	0.0295851i
$509$	0.205186	−	0.0436136i	0.00909471	−	0.00193314i	−0.203362	−	0.979104i	$-0.565187\pi$
$509$	0.205186	−	0.0436136i	0.00909471	−	0.00193314i	0.212457	+	0.977170i	$0.431854\pi$
$510$	−14.8462	−	22.2731i	−0.657403	−	0.986270i
$511$	−16.7924	−	3.56935i	−0.742854	−	0.157899i
$512$	−6.74190	+	20.7494i	−0.297953	+	0.917005i
$513$	−12.2091	+	1.13003i	−0.539045	+	0.0498919i
$514$	9.37282	+	28.8466i	0.413417	+	1.27237i
$515$	1.35270	−	0.335334i	0.0596071	−	0.0147766i
$516$	0.360251	+	0.0650617i	0.0158591	+	0.00286418i
$517$	−6.52673	+	62.0977i	−0.287045	+	2.73105i
$518$	2.80142	+	4.85221i	0.123088	+	0.213194i
$519$	−9.00267	−	14.5410i	−0.395174	−	0.638278i
$520$	20.4043	−	5.05822i	0.894787	−	0.221818i
$521$	−10.5015	+	7.62978i	−0.460079	+	0.334267i	−0.793562	−	0.608489i	$-0.791776\pi$
$521$	−10.5015	+	7.62978i	−0.460079	+	0.334267i	0.333484	+	0.942756i	$0.391776\pi$
$522$	31.1786	+	4.64558i	1.36465	+	0.203331i
$523$	11.1175	+	34.2162i	0.486136	+	1.49617i	0.830329	+	0.557273i	$0.188152\pi$
$523$	11.1175	+	34.2162i	0.486136	+	1.49617i	−0.344194	+	0.938899i	$0.611848\pi$
$524$	0.302992	−	0.524797i	0.0132363	−	0.0229259i
$525$	−0.227220	+	33.2578i	−0.00991669	+	1.45149i
$526$	5.28890	+	9.16064i	0.230607	+	0.399423i
$527$	2.10260	−	2.33517i	0.0915906	−	0.101722i
$528$	10.3496	−	35.5372i	0.450409	−	1.54656i
$529$	0.130967	+	1.24606i	0.00569420	+	0.0541767i
$530$	−5.43223	+	10.1835i	−0.235961	+	0.442342i
$531$	3.86376	+	23.0264i	0.167673	+	0.999259i
$532$	−0.407774			−0.0176792
$533$	11.5191	−	5.12864i	0.498948	−	0.222146i
$534$	4.84196	−	5.72212i	0.209532	−	0.247620i
$535$	15.0247	−	11.7061i	0.649575	−	0.506098i
$536$	1.90555	−	2.11633i	0.0823073	−	0.0914116i
$537$	6.02486	+	1.08810i	0.259992	+	0.0469548i
$538$	−26.7807	−	29.7430i	−1.15460	−	1.28231i
$539$	12.5167	+	38.5225i	0.539133	+	1.65928i
$540$	0.298303	−	0.429377i	0.0128369	−	0.0184774i
$541$	5.95413	−	18.3249i	0.255988	−	0.787850i	−0.737646	−	0.675188i	$-0.764062\pi$
$541$	5.95413	−	18.3249i	0.255988	−	0.787850i	0.993633	−	0.112661i	$-0.0359376\pi$
$542$	26.8937	−	11.9738i	1.15518	−	0.514320i
$543$	−3.57169	−	26.2009i	−0.153276	−	1.12439i
$544$	0.128569	−	1.22325i	0.00551235	−	0.0524465i
$545$	7.76632	+	21.4274i	0.332672	+	0.917849i
$546$	31.0687	−	7.60974i	1.32962	−	0.325667i
$547$	−4.57078	−	43.4881i	−0.195433	−	1.85942i	−0.450868	−	0.892591i	$-0.648885\pi$
$547$	−4.57078	−	43.4881i	−0.195433	−	1.85942i	0.255435	−	0.966826i	$-0.417781\pi$
$548$	0.126986	+	0.390823i	0.00542458	+	0.0166951i
$549$	−4.94026	+	19.1375i	−0.210845	+	0.816768i
$550$	23.0910	−	29.3918i	0.984603	−	1.25327i
$551$	8.66924	−	15.0156i	0.369322	−	0.639685i
$552$	18.6685	+	12.7049i	0.794585	+	0.540757i
$553$	−5.75389	−	2.56180i	−0.244680	−	0.108939i
$554$	−3.55639	−	1.58341i	−0.151097	−	0.0672726i
$555$	−1.75158	+	3.54180i	−0.0743502	+	0.150341i
$556$	0.482287	−	0.214728i	0.0204535	−	0.00910650i
$557$	42.9035			1.81788			0.908939	−	0.416929i	$-0.136894\pi$
$557$	42.9035			1.81788			0.908939	+	0.416929i	$0.136894\pi$
$558$	2.61310	+	0.975680i	0.110621	+	0.0413038i
$559$	−4.88088	+	15.0218i	−0.206439	+	0.635354i
$560$	−22.6011	+	26.8614i	−0.955069	+	1.13510i
$561$	3.23329	−	43.6397i	0.136509	−	1.84247i
$562$	33.6183	−	7.14578i	1.41810	−	0.301427i
$563$	−15.5556	+	3.30645i	−0.655591	+	0.139350i	−0.523685	−	0.851912i	$-0.675443\pi$
$563$	−15.5556	+	3.30645i	−0.655591	+	0.139350i	−0.131906	+	0.991262i	$0.542110\pi$
$564$	−0.838404	+	0.404627i	−0.0353032	+	0.0170379i
$565$	9.12891	−	10.8497i	0.384056	−	0.456452i
$566$	3.40526	−	10.4803i	0.143134	−	0.440520i
$567$	−19.7997	+	28.3302i	−0.831508	+	1.18976i
$568$	−9.74791			−0.409013
$569$	21.5787	−	9.60744i	0.904624	−	0.402765i	0.0989287	−	0.995095i	$-0.468458\pi$
$569$	21.5787	−	9.60744i	0.904624	−	0.402765i	0.805696	+	0.592330i	$0.201792\pi$
$570$	−7.24860	−	10.8747i	−0.303610	−	0.455492i
$571$	−1.06659	−	0.474875i	−0.0446353	−	0.0198729i	0.384298	−	0.923209i	$-0.374444\pi$
$571$	−1.06659	−	0.474875i	−0.0446353	−	0.0198729i	−0.428933	+	0.903336i	$0.641110\pi$
$572$	−0.722618	−	0.321730i	−0.0302142	−	0.0134522i
$573$	2.37406	−	32.0428i	0.0991780	−	1.33861i
$574$	−10.2964	+	17.8339i	−0.429763	+	0.744372i
$575$	12.9866	+	19.3656i	0.541578	+	0.807600i
$576$	−22.5809	+	6.27299i	−0.940870	+	0.261374i
$577$	−10.2147	−	31.4377i	−0.425244	−	1.30877i	−0.902760	−	0.430144i	$-0.858463\pi$
$577$	−10.2147	−	31.4377i	−0.425244	−	1.30877i	0.477516	−	0.878623i	$-0.341537\pi$
$578$	−0.950373	−	9.04219i	−0.0395303	−	0.376106i
$579$	−5.63938	+	19.3638i	−0.234365	+	0.804731i
$580$	0.251929	+	0.695075i	0.0104608	+	0.0288614i
$581$	4.53747	−	43.1711i	0.188246	−	1.79104i
$582$	31.7350	−	24.5831i	1.31546	−	1.01900i
$583$	−17.2371	+	7.67445i	−0.713888	+	0.317843i
$584$	3.86200	−	11.8860i	0.159811	−	0.491847i
$585$	16.6177	+	15.2549i	0.687058	+	0.630714i
$586$	12.1936	+	37.5281i	0.503714	+	1.55027i
$587$	2.46506	+	2.73772i	0.101744	+	0.112998i	0.791866	−	0.610695i	$-0.209110\pi$
$587$	2.46506	+	2.73772i	0.101744	+	0.112998i	−0.690122	+	0.723693i	$0.742443\pi$
$588$	−0.390095	+	0.461005i	−0.0160872	+	0.0190115i
$589$	1.02658	−	1.14013i	0.0422996	−	0.0469784i
$590$	−19.6315	+	15.2953i	−0.808215	+	0.629698i
$591$	−14.6022	−	2.63718i	−0.600656	−	0.108479i
$592$	−3.81002	+	1.69633i	−0.156591	+	0.0697187i
$593$	18.3600			0.753956			0.376978	−	0.926222i	$-0.376963\pi$
$593$	18.3600			0.753956			0.376978	+	0.926222i	$0.376963\pi$
$594$	37.0889	−	11.5434i	1.52178	−	0.473631i
$595$	−19.5335	+	36.6184i	−0.800797	+	1.50121i
$596$	−0.0445255	−	0.423631i	−0.00182383	−	0.0173526i
$597$	−20.8095	−	21.7282i	−0.851674	−	0.889277i
$598$	15.0055	−	16.6653i	0.613622	−	0.681496i
$599$	21.7553	+	37.6813i	0.888897	+	1.53961i	0.841181	+	0.540754i	$0.181861\pi$
$599$	21.7553	+	37.6813i	0.888897	+	1.53961i	0.0477161	+	0.998861i	$0.484806\pi$
$600$	−24.0612	−	2.69525i	−0.982293	−	0.110033i
$601$	4.47712	−	7.75460i	0.182626	−	0.316317i	−0.760148	−	0.649750i	$-0.774874\pi$
$601$	4.47712	−	7.75460i	0.182626	−	0.316317i	0.942774	+	0.333433i	$0.108207\pi$
$602$	−7.97120	−	24.5328i	−0.324882	−	0.999884i
$603$	3.02252	+	0.450352i	0.123087	+	0.0183398i
$604$	0.558712	−	0.405928i	0.0227337	−	0.0165170i
$605$	35.4348	−	8.78430i	1.44063	−	0.357132i
$606$	−13.8197	+	0.425288i	−0.561385	+	0.0172761i
$607$	2.21210	+	3.83147i	0.0897864	+	0.155515i	0.907421	−	0.420223i	$-0.138048\pi$
$607$	2.21210	+	3.83147i	0.0897864	+	0.155515i	−0.817634	+	0.575738i	$0.804715\pi$
$608$	0.0627731	−	0.597246i	0.00254579	−	0.0242215i
$609$	−16.5260	−	45.9968i	−0.669668	−	1.86388i
$610$	−20.4481	+	5.06909i	−0.827920	+	0.205241i
$611$	−12.4121	−	38.2004i	−0.502138	−	1.54542i
$612$	0.578574	−	0.301512i	0.0233875	−	0.0121879i
$613$	−6.60377	+	20.3243i	−0.266724	+	0.820891i	0.724568	+	0.689204i	$0.242040\pi$
$613$	−6.60377	+	20.3243i	−0.266724	+	0.820891i	−0.991291	+	0.131687i	$0.957960\pi$
$614$	41.6885	+	8.86117i	1.68241	+	0.357608i
$615$	−14.4925	+	0.933531i	−0.584392	+	0.0376436i
$616$	−54.8990	+	11.6691i	−2.21194	+	0.470163i
$617$	3.36726	−	32.0374i	0.135561	−	1.28978i	−0.689315	−	0.724462i	$-0.742088\pi$
$617$	3.36726	−	32.0374i	0.135561	−	1.28978i	0.824876	−	0.565314i	$-0.191245\pi$
$618$	0.208513	+	1.52959i	0.00838763	+	0.0615293i
$619$	−36.7704	+	16.3712i	−1.47793	+	0.658015i	−0.978105	−	0.208113i	$-0.933268\pi$
$619$	−36.7704	+	16.3712i	−1.47793	+	0.658015i	−0.499822	+	0.866128i	$0.666601\pi$
$620$	0.00901746	+	0.0647948i	0.000362150	+	0.00260222i
$621$	−0.301107	+	24.2297i	−0.0120830	+	0.972306i
$622$	6.40277	−	4.65188i	0.256728	−	0.186524i
$623$	−11.3681	−	2.41637i	−0.455455	−	0.0968099i
$624$	3.21604	+	23.5919i	0.128745	+	0.944434i
$625$	−22.0102	−	11.8554i	−0.880409	−	0.474215i
$626$	−4.09393	−	7.09089i	−0.163626	−	0.283409i
$627$	1.57863	−	21.3068i	0.0630446	−	0.850913i
$628$	0.102572	+	0.975910i	0.00409308	+	0.0389431i
$629$	−3.98900	+	2.89817i	−0.159052	+	0.115558i
$630$	−36.5999	−	4.20351i	−1.45818	−	0.167472i
$631$	−0.646758	−	0.469897i	−0.0257470	−	0.0187063i	0.574837	−	0.818268i	$-0.305065\pi$
$631$	−0.646758	−	0.469897i	−0.0257470	−	0.0187063i	−0.600584	+	0.799561i	$0.705065\pi$
$632$	2.29257	−	3.97084i	0.0911934	−	0.157952i
$633$	8.12687	−	0.250097i	0.323014	−	0.00994047i
$634$	−16.2863	+	3.46176i	−0.646811	+	0.137484i
$635$	27.5971	+	18.6686i	1.09516	+	0.740839i
$636$	−0.232567	−	0.158274i	−0.00922190	−	0.00627598i
$637$	−17.4349	−	19.3634i	−0.690796	−	0.767207i
$638$	−16.9738	+	52.2399i	−0.671999	+	2.06820i
$639$	−5.77722	−	8.72004i	−0.228543	−	0.344960i
$640$	−18.1180	−	18.8123i	−0.716175	−	0.743620i
$641$	−19.2596	−	21.3900i	−0.760709	−	0.844853i	0.231054	−	0.972941i	$-0.425783\pi$
$641$	−19.2596	−	21.3900i	−0.760709	−	0.844853i	−0.991763	+	0.128088i	$0.959116\pi$
$642$	11.1060	+	17.9382i	0.438319	+	0.707966i
$643$	24.5329	+	42.4923i	0.967484	+	1.67573i	0.702789	+	0.711399i	$0.251938\pi$
$643$	24.5329	+	42.4923i	0.967484	+	1.67573i	0.264695	+	0.964332i	$0.414729\pi$
$644$	−0.0842365	+	0.801456i	−0.00331938	+	0.0315818i
$645$	11.2783	−	14.2734i	0.444081	−	0.562014i
$646$	−1.70472	−	16.2193i	−0.0670712	−	0.638139i
$647$	−11.9156	+	8.65721i	−0.468452	+	0.340350i	−0.796838	−	0.604194i	$-0.793495\pi$
$647$	−11.9156	+	8.65721i	−0.468452	+	0.340350i	0.328386	+	0.944544i	$0.393495\pi$
$648$	−19.0042	−	16.4906i	−0.746556	−	0.647812i
$649$	−40.6843			−1.59700
$650$	−5.87955	+	23.3142i	−0.230615	+	0.914460i
$651$	−0.584146	−	4.28513i	−0.0228945	−	0.167948i
$652$	−0.347471	+	0.385905i	−0.0136080	+	0.0151132i
$653$	−24.4047	−	10.8657i	−0.955030	−	0.425207i	−0.130766	−	0.991413i	$-0.541744\pi$
$653$	−24.4047	−	10.8657i	−0.955030	−	0.425207i	−0.824263	+	0.566207i	$0.808410\pi$
$654$	−24.5212	+	6.00605i	−0.958856	+	0.234855i
$655$	−15.9231	−	25.5587i	−0.622167	−	0.998661i
$656$	−12.4011	−	9.00994i	−0.484182	−	0.351779i
$657$	12.9216	−	3.58962i	0.504118	−	0.140044i
$658$	53.0696	+	38.5573i	2.06887	+	1.50312i
$659$	−3.60401	−	4.00266i	−0.140392	−	0.155922i	0.668848	−	0.743399i	$-0.266788\pi$
$659$	−3.60401	−	4.00266i	−0.140392	−	0.155922i	−0.809240	+	0.587478i	$0.800121\pi$
$660$	0.651854	+	0.636438i	0.0253734	+	0.0247733i
$661$	−16.2515	+	18.0492i	−0.632111	+	0.702031i	−0.971077	−	0.238768i	$-0.923256\pi$
$661$	−16.2515	+	18.0492i	−0.632111	+	0.702031i	0.338965	+	0.940799i	$0.389923\pi$
$662$	27.9921	−	5.94991i	1.08794	−	0.231250i
$663$	9.51805	+	26.4915i	0.369650	+	1.02885i
$664$	30.9103	+	6.57019i	1.19955	+	0.254973i
$665$	−9.53715	+	17.8787i	−0.369835	+	0.693307i
$666$	−3.69240	−	2.35002i	−0.143077	−	0.0910614i
$667$	−27.7214	−	20.1408i	−1.07338	−	0.779854i
$668$	0.0949884	−	0.164525i	0.00367521	−	0.00636565i
$669$	14.3742	+	23.2170i	0.555739	+	0.897620i
$670$	1.10992	+	3.06229i	0.0428799	+	0.118306i
$671$	−31.4627	−	14.0081i	−1.21460	−	0.540776i
$672$	−1.17090	−	1.22260i	−0.0451684	−	0.0471627i
$673$	−33.3569	−	7.09023i	−1.28581	−	0.273308i	−0.486213	−	0.873840i	$-0.661622\pi$
$673$	−33.3569	−	7.09023i	−1.28581	−	0.273308i	−0.799601	+	0.600532i	$0.794955\pi$
$674$	−5.68410			−0.218943
$675$	−11.8491	−	23.1214i	−0.456072	−	0.889943i
$676$	−0.0761349			−0.00292826
$677$	−4.88333	−	1.03798i	−0.187682	−	0.0398930i	0.113112	−	0.993582i	$-0.463918\pi$
$677$	−4.88333	−	1.03798i	−0.187682	−	0.0398930i	−0.300794	+	0.953689i	$0.597252\pi$
$678$	10.8637	+	11.3434i	0.417219	+	0.435640i
$679$	−56.8595	−	25.3155i	−2.18207	−	0.971519i
$680$	−25.0251	−	16.9286i	−0.959667	−	0.649183i
$681$	6.57490	+	10.6197i	0.251951	+	0.406947i
$682$	−2.43018	+	4.20919i	−0.0930563	+	0.161178i
$683$	6.26357	+	4.55075i	0.239669	+	0.174130i	0.701136	−	0.713028i	$-0.252677\pi$
$683$	6.26357	+	4.55075i	0.239669	+	0.174130i	−0.461467	+	0.887157i	$0.652677\pi$
$684$	0.282486	−	0.147211i	0.0108011	−	0.00562877i
$685$	20.1055	+	3.57303i	0.768192	+	0.136519i
$686$	4.02062	+	0.854608i	0.153508	+	0.0326291i
$687$	−6.04593	−	16.8276i	−0.230667	−	0.642013i
$688$	18.7817	−	3.99217i	0.716044	−	0.152200i
$689$	8.12167	−	9.02003i	0.309411	−	0.343636i
$690$	−22.8710	+	12.0002i	−0.870686	+	0.456842i
$691$	21.4759	+	23.8514i	0.816983	+	0.907351i	0.997085	−	0.0762967i	$-0.0243096\pi$
$691$	21.4759	+	23.8514i	0.816983	+	0.907351i	−0.180103	+	0.983648i	$0.557643\pi$
$692$	0.359454	+	0.261158i	0.0136644	+	0.00992775i
$693$	−42.9752	−	42.1943i	−1.63249	−	1.60283i
$694$	−42.4980	−	30.8766i	−1.61320	−	1.17206i
$695$	1.86520	−	26.1679i	0.0707512	−	0.992603i
$696$	34.5589	−	8.46461i	1.30995	−	0.320850i
$697$	−16.5555	−	7.37098i	−0.627084	−	0.279196i
$698$	−10.6551	+	11.8337i	−0.403301	+	0.447911i
$699$	2.89605	+	21.2446i	0.109539	+	0.803545i
$700$	−0.321520	−	0.801994i	−0.0121523	−	0.0303125i
$701$	−2.23365			−0.0843639			−0.0421819	−	0.999110i	$-0.513431\pi$
$701$	−2.23365			−0.0843639			−0.0421819	+	0.999110i	$0.513431\pi$
$702$	−18.7756	+	16.4878i	−0.708640	+	0.622293i
$703$	−1.94761	+	1.41502i	−0.0734553	+	0.0533684i
$704$	−4.26864	−	40.6134i	−0.160881	−	1.53068i
$705$	−1.86814	+	46.2231i	−0.0703581	+	1.74086i
$706$	0.444910	−	4.23303i	0.0167444	−	0.159312i
$707$	10.7186	+	18.5652i	0.403115	+	0.698216i
$708$	−0.319303	−	0.515733i	−0.0120002	−	0.0193825i
$709$	27.4071	+	30.4387i	1.02930	+	1.14315i	0.989587	+	0.143938i	$0.0459765\pi$
$709$	27.4071	+	30.4387i	1.02930	+	1.14315i	0.0397092	+	0.999211i	$0.487357\pi$
$710$	5.24754	−	9.83724i	0.196936	−	0.369185i
$711$	4.91085	−	0.302541i	0.184171	−	0.0113462i
$712$	2.61449	−	8.04659i	0.0979823	−	0.301559i
$713$	−2.02880	−	2.25321i	−0.0759793	−	0.0843835i
$714$	−38.0060	−	25.8651i	−1.42234	−	0.967977i
$715$	−31.0070	+	24.1582i	−1.15959	+	0.903466i
$716$	−0.155579	+	0.0330694i	−0.00581427	+	0.00123586i
$717$	−27.7320	+	0.853426i	−1.03567	+	0.0318718i
$718$	−1.65319	+	2.86342i	−0.0616967	+	0.106862i
$719$	11.5919	+	8.42199i	0.432304	+	0.314087i	0.782570	−	0.622563i	$-0.213909\pi$
$719$	11.5919	+	8.42199i	0.432304	+	0.314087i	−0.350265	+	0.936650i	$0.613909\pi$
$720$	5.95957	−	26.7675i	0.222100	−	0.997567i
$721$	1.93641	−	1.40689i	0.0721158	−	0.0523952i
$722$	2.00779	+	19.1028i	0.0747221	+	0.710934i
$723$	−0.374604	+	5.05604i	−0.0139317	+	0.188036i
$724$	0.343491	+	0.594944i	0.0127657	+	0.0221109i
$725$	36.3676	+	5.21092i	1.35066	+	0.193529i
$726$	5.46213	+	40.0687i	0.202719	+	1.48709i
$727$	33.4120	+	7.10195i	1.23918	+	0.263397i	0.780473	−	0.625189i	$-0.214978\pi$
$727$	33.4120	+	7.10195i	1.23918	+	0.263397i	0.458710	+	0.888586i	$0.348312\pi$
$728$	29.2091	−	21.2217i	1.08256	−	0.786527i
$729$	3.48869	−	26.7737i	0.129211	−	0.991617i
$730$	9.91593	+	10.2959i	0.367005	+	0.381069i
$731$	20.7381	−	9.23319i	0.767026	−	0.341502i
$732$	−0.0693560	−	0.508776i	−0.00256347	−	0.0188049i
$733$	4.64837	−	44.2263i	0.171691	−	1.63353i	−0.481574	−	0.876405i	$-0.659935\pi$
$733$	4.64837	−	44.2263i	0.171691	−	1.63353i	0.653266	−	0.757129i	$-0.273398\pi$
$734$	23.6959	−	5.03672i	0.874632	−	0.185909i
$735$	11.0890	+	27.8857i	0.409023	+	1.02858i
$736$	−1.16089	−	0.246754i	−0.0427908	−	0.00909548i
$737$	−1.64548	+	5.06426i	−0.0606119	+	0.186544i
$738$	0.694578	−	16.0716i	0.0255678	−	0.591602i
$739$	−6.83528	−	21.0368i	−0.251440	−	0.773852i	−0.994510	−	0.104639i	$-0.966631\pi$
$739$	−6.83528	−	21.0368i	−0.251440	−	0.773852i	0.743071	−	0.669213i	$-0.233369\pi$
$740$	0.00729833	−	0.102392i	0.000268292	−	0.00376400i
$741$	4.64714	+	12.9344i	0.170717	+	0.475155i
$742$	−2.07203	+	19.7140i	−0.0760665	+	0.723724i
$743$	5.42519	+	9.39670i	0.199031	+	0.344732i	0.948214	−	0.317631i	$-0.102887\pi$
$743$	5.42519	+	9.39670i	0.199031	+	0.344732i	−0.749184	+	0.662362i	$0.769554\pi$
$744$	3.14686	−	0.0968418i	0.115369	−	0.00355039i
$745$	−19.6154	−	7.95583i	−0.718651	−	0.291479i
$746$	29.1662	−	21.1905i	1.06785	−	0.775838i
$747$	12.4420	+	31.5449i	0.455228	+	1.15417i
$748$	0.351305	+	1.08120i	0.0128450	+	0.0395328i
$749$	16.3560	−	28.3294i	0.597635	−	1.03513i
$750$	15.6727	−	22.8307i	0.572284	−	0.833660i
$751$	7.68498	+	13.3108i	0.280429	+	0.485717i	0.971490	−	0.237079i	$-0.0761900\pi$
$751$	7.68498	+	13.3108i	0.280429	+	0.485717i	−0.691062	+	0.722796i	$0.742857\pi$
$752$	−32.6728	+	36.2869i	−1.19146	+	1.32325i
$753$	5.65479	+	5.90446i	0.206072	+	0.215171i
$754$	−3.69344	−	35.1408i	−0.134507	−	1.27975i
$755$	−4.73045	−	33.9905i	−0.172159	−	1.23704i
$756$	0.197592	−	0.875930i	0.00718635	−	0.0318573i
$757$	−32.9738			−1.19845			−0.599226	−	0.800580i	$-0.704525\pi$
$757$	−32.9738			−1.19845			−0.599226	+	0.800580i	$0.704525\pi$
$758$	−31.9620	+	14.2304i	−1.16091	+	0.516872i
$759$	−41.5513	−	7.50421i	−1.50822	−	0.272385i
$760$	−12.2184	−	8.26531i	−0.443206	−	0.299814i
$761$	−21.4690	+	23.8438i	−0.778251	+	0.864336i	−0.993688	−	0.112182i	$-0.964216\pi$
$761$	−21.4690	+	23.8438i	−0.778251	+	0.864336i	0.215436	+	0.976518i	$0.430883\pi$
$762$	−23.8401	+	28.1737i	−0.863637	+	1.02063i
$763$	26.1921	+	29.0893i	0.948219	+	1.05310i
$764$	0.257948	+	0.793883i	0.00933224	+	0.0287217i
$765$	0.312183	−	32.4192i	0.0112870	−	1.17212i
$766$	−0.00222259	+	0.00684042i	−8.03054e−5	+	0.000247155i
$767$	23.9088	−	10.6449i	0.863295	−	0.384364i
$768$	1.47801	−	1.14492i	0.0533331	−	0.0413137i
$769$	4.43746	−	42.2196i	0.160019	−	1.52248i	−0.559981	−	0.828505i	$-0.689192\pi$
$769$	4.43746	−	42.2196i	0.160019	−	1.52248i	0.720000	−	0.693974i	$-0.244142\pi$
$770$	17.7774	−	61.6838i	0.640652	−	2.22293i
$771$	−10.2722	+	35.2715i	−0.369946	+	1.27027i
$772$	−0.0547689	−	0.521092i	−0.00197118	−	0.0187545i
$773$	0.355723	+	1.09480i	0.0127945	+	0.0393773i	0.957250	−	0.289262i	$-0.0934099\pi$
$773$	0.355723	+	1.09480i	0.0127945	+	0.0393773i	−0.944455	+	0.328639i	$0.893410\pi$
$774$	14.3787	+	14.1174i	0.516832	+	0.507441i
$775$	3.05181	+	1.12007i	0.109624	+	0.0402342i
$776$	22.6549	−	39.2395i	0.813265	−	1.40862i
$777$	−0.501414	+	6.76759i	−0.0179881	+	0.242786i
$778$	13.6216	+	6.06474i	0.488359	+	0.217431i
$779$	−8.08313	−	3.59884i	−0.289608	−	0.128942i
$780$	−0.549594	−	0.203458i	−0.0196786	−	0.00728496i
$781$	16.6510	−	7.41352i	0.595821	−	0.265276i
$782$	−32.2302			−1.15255
$783$	28.0538	+	25.8982i	1.00256	+	0.925526i
$784$	−9.78826	+	30.1252i	−0.349581	+	1.07590i
$785$	45.1875	+	18.3277i	1.61281	+	0.654142i
$786$	30.0406	−	14.4981i	1.07151	−	0.517129i
$787$	−10.0265	+	2.13121i	−0.357407	+	0.0759693i	−0.383116	−	0.923700i	$-0.625149\pi$
$787$	−10.0265	+	2.13121i	−0.357407	+	0.0759693i	0.0257087	+	0.999669i	$0.491816\pi$
$788$	0.377072	−	0.0801492i	0.0134326	−	0.00285520i
$789$	−0.946636	+	12.7768i	−0.0337011	+	0.454865i
$790$	2.77309	+	4.45118i	0.0986620	+	0.158366i
$791$	7.52535	−	23.1607i	0.267571	−	0.823498i
$792$	33.8186	−	27.9030i	1.20169	−	0.991491i
$793$	22.1547			0.786737
$794$	7.75396	−	3.45228i	0.275178	−	0.122517i
$795$	−12.3789	+	6.49508i	−0.439033	+	0.230357i
$796$	0.714038	+	0.317910i	0.0253084	+	0.0112680i
$797$	−44.1753	−	19.6681i	−1.56477	−	0.696680i	−0.572399	−	0.819975i	$-0.693987\pi$
$797$	−44.1753	−	19.6681i	−1.56477	−	0.696680i	−0.992370	+	0.123295i	$0.960654\pi$
$798$	−18.5562	−	12.6285i	−0.656884	−	0.447044i
$799$	−28.8639	+	49.9937i	−1.02113	+	1.76865i
$800$	1.22414	−	0.347455i	0.0432798	−	0.0122844i
$801$	8.74763	−	2.43010i	0.309082	−	0.0858633i
$802$	−8.79839	−	27.0787i	−0.310682	−	0.956181i
$803$	2.44266	+	23.2404i	0.0861998	+	0.820136i
$804$	−0.0771112	+	0.0188871i	−0.00271950	+	0.000666096i
$805$	33.1695	+	22.4380i	1.16907	+	0.790837i
$806$	0.326816	−	3.10944i	0.0115116	−	0.109526i
$807$	−6.54763	−	48.0316i	−0.230488	−	1.69079i
$808$	−14.2567	+	6.34750i	−0.501550	+	0.223304i
$809$	−4.53484	+	13.9568i	−0.159436	+	0.490695i	−0.998583	−	0.0532099i	$-0.983055\pi$
$809$	−4.53484	+	13.9568i	−0.159436	+	0.490695i	0.839147	+	0.543905i	$0.183055\pi$
$810$	26.8721	−	10.3011i	0.944191	−	0.361942i
$811$	8.81534	+	27.1308i	0.309549	+	0.952692i	0.977941	+	0.208883i	$0.0669829\pi$
$811$	8.81534	+	27.1308i	0.309549	+	0.952692i	−0.668392	+	0.743809i	$0.733017\pi$
$812$	0.849636	+	0.943617i	0.0298164	+	0.0331145i
$813$	35.0885	+	6.33702i	1.23061	+	0.222249i
$814$	5.10316	−	5.66764i	0.178866	−	0.198651i
$815$	8.79314	+	24.2604i	0.308010	+	0.849806i
$816$	22.1049	−	26.1230i	0.773825	−	0.914489i
$817$	10.1253	−	4.50806i	0.354238	−	0.157717i
$818$	−6.99144			−0.244450
$819$	36.2951	+	13.5519i	1.26825	+	0.473541i
$820$	0.339326	−	0.164936i	0.0118498	−	0.00575980i
$821$	5.60308	+	53.3098i	0.195549	+	1.86052i	0.449465	+	0.893298i	$0.351614\pi$
$821$	5.60308	+	53.3098i	0.195549	+	1.86052i	−0.253917	+	0.967226i	$0.581719\pi$
$822$	−6.32488	+	21.7176i	−0.220606	+	0.757487i
$823$	−1.36607	+	1.51717i	−0.0476181	+	0.0528852i	−0.766483	−	0.642264i	$-0.777995\pi$
$823$	−1.36607	+	1.51717i	−0.0476181	+	0.0528852i	0.718865	+	0.695149i	$0.244662\pi$
$824$	0.871226	+	1.50901i	0.0303506	+	0.0525688i
$825$	43.1502	−	13.6951i	1.50230	−	0.476804i
$826$	−21.3709	+	37.0155i	−0.743589	+	1.28793i
$827$	13.2520	+	40.7853i	0.460816	+	1.41824i	0.864170	+	0.503201i	$0.167844\pi$
$827$	13.2520	+	40.7853i	0.460816	+	1.41824i	−0.403354	+	0.915044i	$0.632156\pi$
$828$	−0.230981	−	0.585620i	−0.00802714	−	0.0203517i
$829$	30.3646	−	22.0611i	1.05460	−	0.766215i	0.0815222	−	0.996672i	$-0.474022\pi$
$829$	30.3646	−	22.0611i	1.05460	−	0.766215i	0.973083	+	0.230456i	$0.0740219\pi$
$830$	−23.2702	+	27.6567i	−0.807719	+	0.959978i
$831$	−2.48205	−	4.00897i	−0.0861015	−	0.139070i
$832$	13.1349	+	22.7503i	0.455370	+	0.788723i
$833$	−3.91441	+	37.2432i	−0.135626	+	1.29040i
$834$	28.5970	+	5.16466i	0.990235	+	0.178837i
$835$	−4.99192	−	8.01269i	−0.172752	−	0.277291i
$836$	0.171523	+	0.527892i	0.00593223	+	0.0182575i
$837$	1.95165	+	2.75764i	0.0674590	+	0.0953181i
$838$	5.63288	−	17.3362i	0.194585	−	0.598870i
$839$	0.761764	+	0.161918i	0.0262990	+	0.00559003i	0.221042	−	0.975264i	$-0.429054\pi$
$839$	0.761764	+	0.161918i	0.0262990	+	0.00559003i	−0.194743	+	0.980854i	$0.562387\pi$
$840$	−40.0341	+	11.2422i	−1.38131	+	0.387894i
$841$	−24.4440	+	5.19573i	−0.842897	+	0.179163i
$842$	2.62433	−	24.9688i	0.0904402	−	0.860481i
$843$	38.5318	+	15.7538i	1.32711	+	0.542591i
$844$	−0.192970	+	0.0859159i	−0.00664231	+	0.00295735i
$845$	−1.78067	+	3.33811i	−0.0612568	+	0.114834i
$846$	−50.6836	−	7.55180i	−1.74254	−	0.259636i
$847$	50.7256	−	36.8543i	1.74295	−	1.26633i
$848$	−14.4329	−	3.06781i	−0.495627	−	0.105349i
$849$	10.5515	−	8.17356i	0.362126	−	0.280516i
$850$	30.5554	−	16.1413i	1.04804	−	0.553642i
$851$	2.37881	+	4.12022i	0.0815445	+	0.141239i
$852$	0.224660	+	0.152893i	0.00769673	+	0.00523802i
$853$	0.221478	+	2.10722i	0.00758327	+	0.0721500i	0.997659	−	0.0683847i	$-0.0217845\pi$
$853$	0.221478	+	2.10722i	0.00758327	+	0.0721500i	−0.990076	+	0.140535i	$0.955118\pi$
$854$	−29.2718	+	21.2672i	−1.00166	+	0.727750i
$855$	0.152422	−	15.8285i	0.00521271	−	0.541324i
$856$	19.2657	+	13.9973i	0.658488	+	0.478419i
$857$	2.95942	−	5.12586i	0.101092	−	0.175096i	−0.811043	−	0.584987i	$-0.801100\pi$
$857$	2.95942	−	5.12586i	0.101092	−	0.175096i	0.912135	+	0.409890i	$0.134433\pi$
$858$	−22.9198	−	37.0197i	−0.782469	−	1.26383i
$859$	−30.2234	+	6.42418i	−1.03121	+	0.219190i	−0.692285	−	0.721624i	$-0.743396\pi$
$859$	−30.2234	+	6.42418i	−1.03121	+	0.219190i	−0.338923	+	0.940814i	$0.610063\pi$
$860$	−0.130879	+	0.454122i	−0.00446292	+	0.0154854i
$861$	−22.4627	+	10.8409i	−0.765527	+	0.369455i
$862$	−28.2359	−	31.3591i	−0.961717	−	1.06810i
$863$	9.30552	−	28.6394i	0.316764	−	0.974898i	−0.658259	−	0.752792i	$-0.728707\pi$
$863$	9.30552	−	28.6394i	0.316764	−	0.974898i	0.975022	−	0.222106i	$-0.0712933\pi$
$864$	1.25251	+	0.424245i	0.0426114	+	0.0144331i
$865$	19.8574	−	9.65208i	0.675173	−	0.328180i
$866$	−18.8850	−	20.9740i	−0.641740	−	0.712724i
$867$	5.21014	−	9.70169i	0.176946	−	0.329487i
$868$	0.0561777	+	0.0973026i	0.00190679	+	0.00330266i
$869$	−0.896161	+	8.52640i	−0.0304002	+	0.289238i
$870$	−10.0617	+	39.4323i	−0.341124	+	1.33688i
$871$	−0.358051	−	3.40662i	−0.0121321	−	0.115429i
$872$	−23.0535	+	16.7494i	−0.780692	+	0.567206i
$873$	48.5286	−	2.98968i	1.64245	−	0.101185i
$874$	−15.7362			−0.532286
$875$	−42.6830	−	4.66035i	−1.44295	−	0.157549i
$876$	−0.275436	+	0.213363i	−0.00930611	+	0.00720886i
$877$	28.3653	−	31.5028i	0.957828	−	1.06378i	−0.0400850	−	0.999196i	$-0.512763\pi$
$877$	28.3653	−	31.5028i	0.957828	−	1.06378i	0.997913	−	0.0645791i	$-0.0205705\pi$
$878$	16.0400	+	7.14147i	0.541324	+	0.241013i
$879$	−13.3637	+	45.8867i	−0.450748	+	1.54772i
$880$	44.2808	+	17.9599i	1.49270	+	0.605428i
$881$	0.943118	+	0.685215i	0.0317744	+	0.0230855i	0.603559	−	0.797318i	$-0.293749\pi$
$881$	0.943118	+	0.685215i	0.0317744	+	0.0230855i	−0.571785	+	0.820404i	$0.693749\pi$
$882$	−32.0288	+	8.89762i	−1.07846	+	0.299598i
$883$	−13.1391	−	9.54614i	−0.442167	−	0.321253i	0.344328	−	0.938849i	$-0.388107\pi$
$883$	−13.1391	−	9.54614i	−0.442167	−	0.321253i	−0.786495	+	0.617596i	$0.788107\pi$
$884$	−0.489343	−	0.543470i	−0.0164584	−	0.0182789i
$885$	−30.0801	+	1.93761i	−1.01113	+	0.0651321i
$886$	21.8288	−	24.2433i	0.733352	−	0.814469i
$887$	28.4517	−	6.04760i	0.955315	−	0.203058i	0.296221	−	0.955119i	$-0.404273\pi$
$887$	28.4517	−	6.04760i	0.955315	−	0.203058i	0.659094	+	0.752061i	$0.270940\pi$
$888$	−4.86154	−	0.877999i	−0.163143	−	0.0294637i
$889$	55.9728	+	11.8974i	1.87727	+	0.399026i
$890$	6.71288	+	6.97013i	0.225016	+	0.233639i
$891$	45.0038	+	13.7155i	1.50768	+	0.459487i
$892$	−0.573925	−	0.416981i	−0.0192164	−	0.0139615i
$893$	−14.0926	+	24.4092i	−0.471592	+	0.816822i
$894$	11.0934	−	20.6568i	0.371019	−	0.690866i
$895$	−2.18882	+	7.59476i	−0.0731643	+	0.253865i
$896$	−40.9791	−	18.2451i	−1.36901	−	0.609525i
$897$	26.3817	−	6.46175i	0.880860	−	0.215752i
$898$	5.74025	+	1.22013i	0.191555	+	0.0407162i
$899$	−4.77733			−0.159333
$900$	0.512263	+	0.439509i	0.0170754	+	0.0146503i
$901$	−17.4445			−0.581160
$902$	27.4182	+	5.82792i	0.912927	+	0.194049i
$903$	8.73613	−	29.9970i	0.290720	−	0.998237i
$904$	16.1955	+	7.21071i	0.538655	+	0.239825i
$905$	34.1188	−	1.14552i	1.13415	−	0.0380782i
$906$	37.9962	−	1.16930i	1.26234	−	0.0388474i
$907$	−2.44109	+	4.22810i	−0.0810552	+	0.140392i	−0.903703	−	0.428159i	$-0.859162\pi$
$907$	−2.44109	+	4.22810i	−0.0810552	+	0.140392i	0.822648	+	0.568551i	$0.192496\pi$
$908$	−0.262519	−	0.190731i	−0.00871200	−	0.00632964i
$909$	−14.1276	−	8.99149i	−0.468583	−	0.298229i
$910$	5.69216	+	40.9009i	0.188693	+	1.35585i
$911$	49.9896	+	10.6256i	1.65623	+	0.352042i	0.938766	−	0.344555i	$-0.111970\pi$
$911$	49.9896	+	10.6256i	1.65623	+	0.352042i	0.717462	+	0.696597i	$0.245304\pi$
$912$	10.7926	−	12.7544i	0.357378	−	0.422341i
$913$	−57.7967	+	12.2851i	−1.91279	+	0.406576i
$914$	−17.3477	+	19.2666i	−0.573811	+	0.637281i
$915$	−23.9293	−	8.85853i	−0.791077	−	0.292854i
$916$	0.310834	+	0.345216i	0.0102702	+	0.0114063i
$917$	−41.8408	−	30.3991i	−1.38170	−	1.00387i
$918$	35.6663	+	4.19740i	1.17716	+	0.138535i
$919$	−14.6917	−	10.6741i	−0.484634	−	0.352107i	0.318483	−	0.947928i	$-0.396827\pi$
$919$	−14.6917	−	10.6741i	−0.484634	−	0.352107i	−0.803117	+	0.595822i	$0.796827\pi$
$920$	−18.7690	+	22.3071i	−0.618796	+	0.735442i
$921$	35.7048	+	37.2812i	1.17651	+	1.22846i
$922$	30.7425	+	13.6874i	1.01245	+	0.450772i
$923$	−7.84553	+	8.71335i	−0.258239	+	0.286803i
$924$	1.44828	+	0.592134i	0.0476450	+	0.0194798i
$925$	−4.31864	−	2.71477i	−0.141996	−	0.0892610i
$926$	−5.11819			−0.168194
$927$	−0.833548	+	1.67369i	−0.0273773	+	0.0549712i
$928$	−1.51286	+	1.09916i	−0.0496622	+	0.0360817i
$929$	−2.58266	−	24.5724i	−0.0847343	−	0.806193i	−0.951535	−	0.307539i	$-0.900494\pi$
$929$	−2.58266	−	24.5724i	−0.0847343	−	0.806193i	0.866801	−	0.498654i	$-0.166172\pi$
$930$	−1.59630	+	3.22783i	−0.0523448	+	0.105845i
$931$	−1.91119	+	18.1838i	−0.0626368	+	0.595949i
$932$	−0.278515	−	0.482401i	−0.00912305	−	0.0158016i
$933$	9.58118	−	0.294852i	0.313674	−	0.00965303i
$934$	−15.1867	−	16.8665i	−0.496923	−	0.551889i
$935$	55.6215	+	9.88472i	1.81902	+	0.323265i
$936$	−12.5733	+	25.2462i	−0.410972	+	0.825197i
$937$	−0.780220	+	2.40127i	−0.0254887	+	0.0784461i	−0.962992	−	0.269531i	$-0.913131\pi$
$937$	−0.780220	+	2.40127i	−0.0254887	+	0.0784461i	0.937503	+	0.347977i	$0.113131\pi$
$938$	3.74323	+	4.15728i	0.122221	+	0.135740i
$939$	0.732754	−	9.88999i	0.0239125	−	0.322748i
$940$	−0.409533	−	1.12991i	−0.0133575	−	0.0368535i
$941$	−4.08041	+	0.867319i	−0.133018	+	0.0282738i	−0.273939	−	0.961747i	$-0.588327\pi$
$941$	−4.08041	+	0.867319i	−0.133018	+	0.0282738i	0.140922	+	0.990021i	$0.454993\pi$
$942$	−25.5556	+	47.5866i	−0.832647	+	1.55045i
$943$	−8.74311	+	15.1435i	−0.284715	+	0.493140i
$944$	−25.7394	−	18.7008i	−0.837747	−	0.608659i
$945$	−33.7835	−	29.1499i	−1.09898	−	0.948246i
$946$	−28.4066	+	20.6386i	−0.923577	+	0.671018i
$947$	−5.72558	−	54.4752i	−0.186056	−	1.77021i	−0.546532	−	0.837438i	$-0.684052\pi$
$947$	−5.72558	−	54.4752i	−0.186056	−	1.77021i	0.360475	−	0.932769i	$-0.382614\pi$
$948$	−0.115118	+	0.0555578i	−0.00373886	+	0.00180443i
$949$	−7.51623	−	13.0185i	−0.243987	−	0.422598i
$950$	14.9185	−	7.88090i	0.484020	−	0.255690i
$951$	−18.6667	−	7.63191i	−0.605308	−	0.247482i
$952$	−50.7561	−	10.7885i	−1.64501	−	0.349659i
$953$	−6.88510	+	5.00232i	−0.223030	+	0.162041i	−0.693690	−	0.720274i	$-0.744016\pi$
$953$	−6.88510	+	5.00232i	−0.223030	+	0.162041i	0.470659	+	0.882315i	$0.344016\pi$
$954$	−5.68161	−	14.4049i	−0.183949	−	0.466377i
$955$	40.8405	+	7.25793i	1.32157	+	0.234861i
$956$	0.658487	−	0.293177i	0.0212970	−	0.00948204i
$957$	−52.5947	+	40.7418i	−1.70015	+	1.31700i
$958$	2.51705	−	23.9482i	0.0813223	−	0.773730i
$959$	34.3052	−	7.29180i	1.10777	−	0.235464i
$960$	−5.09028	−	29.8245i	−0.164288	−	0.962581i
$961$	29.9091	+	6.35737i	0.964809	+	0.205077i
$962$	−1.51604	+	4.66590i	−0.0488792	+	0.150435i
$963$	−1.10335	+	25.5299i	−0.0355549	+	0.822690i
$964$	−0.0407017	−	0.125267i	−0.00131091	−	0.00403458i
$965$	−24.1281	−	9.78613i	−0.776709	−	0.315027i
$966$	−28.6539	+	33.8625i	−0.921923	+	1.08951i
$967$	4.97753	−	47.3581i	0.160067	−	1.52293i	−0.559688	−	0.828704i	$-0.689079\pi$
$967$	4.97753	−	47.3581i	0.160067	−	1.52293i	0.719754	−	0.694229i	$-0.244254\pi$
$968$	22.8223	+	39.5294i	0.733537	+	1.27052i
$969$	9.34560	−	17.4022i	0.300224	−	0.559041i
$970$	27.4034	+	43.9861i	0.879870	+	1.41231i
$971$	4.89465	−	3.55617i	0.157077	−	0.114123i	−0.506471	−	0.862257i	$-0.669050\pi$
$971$	4.89465	−	3.55617i	0.157077	−	0.114123i	0.663547	+	0.748134i	$0.269050\pi$
$972$	0.179340	+	0.678134i	0.00575233	+	0.0217512i
$973$	−13.9232	−	42.8512i	−0.446358	−	1.37375i
$974$	7.11380	−	12.3215i	0.227941	−	0.394805i
$975$	−21.7746	+	19.3382i	−0.697346	+	0.619319i
$976$	−13.4664	−	23.3244i	−0.431048	−	0.746597i
$977$	−4.87939	+	5.41911i	−0.156105	+	0.173373i	−0.816124	−	0.577876i	$-0.803882\pi$
$977$	−4.87939	+	5.41911i	−0.156105	+	0.173373i	0.660019	+	0.751249i	$0.270548\pi$
$978$	−27.7633	+	6.80015i	−0.887773	+	0.217445i
$979$	1.65363	+	15.7333i	0.0528504	+	0.502838i
$980$	−0.540826	−	0.561552i	−0.0172761	−	0.0179381i
$981$	−28.6462	−	10.6959i	−0.914603	−	0.341495i
$982$	16.8113			0.536469
$983$	−22.0824	+	9.83170i	−0.704318	+	0.313582i	−0.727460	−	0.686150i	$-0.759299\pi$
$983$	−22.0824	+	9.83170i	−0.704318	+	0.313582i	0.0231427	+	0.999732i	$0.492633\pi$
$984$	−6.13941	−	17.0878i	−0.195717	−	0.544739i
$985$	5.30497	−	18.4072i	0.169030	−	0.586501i
$986$	−33.9806	+	37.7393i	−1.08216	+	1.20186i
$987$	26.8645	+	74.7719i	0.855107	+	2.38002i
$988$	−0.238919	−	0.265346i	−0.00760102	−	0.00844179i
$989$	−6.76869	−	20.8319i	−0.215232	−	0.662415i
$990$	9.95336	+	49.1494i	0.316339	+	1.56207i
$991$	15.5428	−	47.8359i	0.493734	−	1.51956i	−0.325186	−	0.945650i	$-0.605427\pi$
$991$	15.5428	−	47.8359i	0.493734	−	1.51956i	0.818920	−	0.573907i	$-0.194573\pi$
$992$	−0.151162	+	0.0673018i	−0.00479941	+	0.00213683i
$993$	32.0834	+	13.1174i	1.01814	+	0.416267i
$994$	2.00158	−	19.0437i	0.0634862	−	0.604030i
$995$	30.6388	−	23.8714i	0.971316	−	0.756774i
$996$	−0.609339	−	0.636242i	−0.0193076	−	0.0201601i
$997$	4.05546	+	38.5851i	0.128438	+	1.22200i	0.848917	+	0.528526i	$0.177255\pi$
$997$	4.05546	+	38.5851i	0.128438	+	1.22200i	−0.720479	+	0.693476i	$0.756078\pi$
$998$	−11.2633	−	34.6649i	−0.356534	−	1.09730i
$999$	−2.09583	−	4.86927i	−0.0663092	−	0.154057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.7	yes	224
3.2	odd	2		675.2.r.a.181.22		224
9.4	even	3	inner	225.2.q.a.31.22	✓	224
9.5	odd	6		675.2.r.a.631.7		224
25.21	even	5	inner	225.2.q.a.196.22	yes	224
75.71	odd	10		675.2.r.a.46.7		224
225.121	even	15	inner	225.2.q.a.121.7	yes	224
225.221	odd	30		675.2.r.a.496.22		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.22	✓	224	9.4	even	3	inner
225.2.q.a.106.7	yes	224	1.1	even	1	trivial
225.2.q.a.121.7	yes	224	225.121	even	15	inner
225.2.q.a.196.22	yes	224	25.21	even	5	inner
675.2.r.a.46.7		224	75.71	odd	10
675.2.r.a.181.22		224	3.2	odd	2
675.2.r.a.496.22		224	225.221	odd	30
675.2.r.a.631.7		224	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39878 - 0.297321i) q^{2} +(-1.19801 - 1.25091i) q^{3} +(0.0411076 + 0.0183023i) q^{4} +(1.76390 - 1.37429i) q^{5} +(1.30384 + 2.10594i) q^{6} +(1.92019 - 3.32586i) q^{7} +(2.26178 + 1.64328i) q^{8} +(-0.129533 + 2.99720i) q^{9} +(-2.87591 + 1.39789i) q^{10} +(-5.11325 - 1.08686i) q^{11} +(-0.0263530 - 0.0733481i) q^{12} +(3.28926 - 0.699153i) q^{13} +(-3.67477 + 4.08125i) q^{14} +(-3.83228 - 0.560051i) q^{15} +(-2.73539 - 3.03795i) q^{16} +(-3.90998 - 2.84077i) q^{17} +(1.07232 - 4.15393i) q^{18} +(-1.90903 - 1.38699i) q^{19} +(0.0976621 - 0.0242104i) q^{20} +(-6.46075 + 1.58245i) q^{21} +(6.82920 + 3.04055i) q^{22} +(-3.12041 + 3.46556i) q^{23} +(-0.654054 - 4.79795i) q^{24} +(1.22265 - 4.84821i) q^{25} -4.80884 q^{26} +(3.90440 - 3.42865i) q^{27} +(0.139805 - 0.101574i) q^{28} +(0.768054 + 7.30754i) q^{29} +(5.19401 + 1.92281i) q^{30} +(-0.0679615 + 0.646611i) q^{31} +(0.127249 + 0.220402i) q^{32} +(4.76619 + 7.69827i) q^{33} +(4.62460 + 5.13614i) q^{34} +(-1.18369 - 8.50536i) q^{35} +(-0.0601804 + 0.120837i) q^{36} +(0.315262 - 0.970276i) q^{37} +(2.25794 + 2.50769i) q^{38} +(-4.81515 - 3.27696i) q^{39} +(6.24790 - 0.209769i) q^{40} +(3.66775 - 0.779604i) q^{41} +(9.50769 - 0.292591i) q^{42} +(-2.34851 + 4.06773i) q^{43} +(-0.190302 - 0.138262i) q^{44} +(3.89054 + 5.46477i) q^{45} +(5.39516 - 3.91981i) q^{46} +(-1.24854 - 11.8791i) q^{47} +(-0.523169 + 7.06122i) q^{48} +(-3.87423 - 6.71036i) q^{49} +(-3.15170 + 6.41808i) q^{50} +(1.13067 + 8.29429i) q^{51} +(0.148010 + 0.0314604i) q^{52} +(2.92011 - 2.12158i) q^{53} +(-6.48082 + 3.63509i) q^{54} +(-10.5129 + 5.10999i) q^{55} +(9.80838 - 4.36697i) q^{56} +(0.552044 + 4.04964i) q^{57} +(1.09834 - 10.4500i) q^{58} +(7.61268 - 1.61813i) q^{59} +(-0.147285 - 0.0931618i) q^{60} +(6.44432 + 1.36978i) q^{61} +(0.287314 - 0.884263i) q^{62} +(9.71955 + 6.18599i) q^{63} +(2.41404 + 7.42965i) q^{64} +(4.84107 - 5.75363i) q^{65} +(-4.37801 - 12.1853i) q^{66} +(0.106476 - 1.01305i) q^{67} +(-0.108737 - 0.188339i) q^{68} +(8.07338 - 0.248451i) q^{69} +(-0.873097 + 12.2491i) q^{70} +(-2.82082 + 2.04945i) q^{71} +(-5.21823 + 6.56617i) q^{72} +(-1.38140 - 4.25150i) q^{73} +(-0.729467 + 1.26347i) q^{74} +(-7.52941 + 4.27879i) q^{75} +(-0.0530904 - 0.0919553i) q^{76} +(-13.4331 + 14.9190i) q^{77} +(5.76105 + 6.01540i) q^{78} +(-0.171432 - 1.63107i) q^{79} +(-8.99997 - 1.59942i) q^{80} +(-8.96644 - 0.776471i) q^{81} -5.36219 q^{82} +(10.3261 - 4.59747i) q^{83} +(-0.294548 - 0.0531957i) q^{84} +(-10.8008 + 0.362630i) q^{85} +(4.49448 - 4.99162i) q^{86} +(8.22091 - 9.71529i) q^{87} +(-9.77907 - 10.8608i) q^{88} +(-0.935178 - 2.87818i) q^{89} +(-3.81724 - 8.80077i) q^{90} +(3.99070 - 12.2821i) q^{91} +(-0.191700 + 0.0853504i) q^{92} +(0.890268 - 0.689634i) q^{93} +(-1.78546 + 16.9875i) q^{94} +(-5.27345 + 0.177052i) q^{95} +(0.123256 - 0.423221i) q^{96} +(-1.69408 - 16.1181i) q^{97} +(3.42408 + 10.5382i) q^{98} +(3.91986 - 15.1847i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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