LMFDB - Embedded newform 117.2.f.a.61.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(61,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.61"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.12
Character	$\chi$	$=$	117.61
Dual form			117.2.f.a.94.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32814 + 2.30041i) q^{2} +(0.201038 - 1.72034i) q^{3} +(-2.52792 + 4.37849i) q^{4} +(0.324360 + 0.561808i) q^{5} +(4.22450 - 1.82239i) q^{6} +1.54792 q^{7} -8.11720 q^{8} +(-2.91917 - 0.691710i) q^{9} +(-0.861592 + 1.49232i) q^{10} +(-2.53504 - 4.39082i) q^{11} +(7.02430 + 5.22914i) q^{12} +(3.32120 + 1.40344i) q^{13} +(2.05585 + 3.56084i) q^{14} +(1.03171 - 0.445066i) q^{15} +(-5.72495 - 9.91590i) q^{16} +(-0.103828 - 0.179835i) q^{17} +(-2.28585 - 7.63397i) q^{18} +(-1.79488 - 3.10883i) q^{19} -3.27983 q^{20} +(0.311190 - 2.66295i) q^{21} +(6.73378 - 11.6633i) q^{22} -3.20273 q^{23} +(-1.63187 + 13.9644i) q^{24} +(2.28958 - 3.96567i) q^{25} +(1.18254 + 9.50408i) q^{26} +(-1.77684 + 4.88291i) q^{27} +(-3.91301 + 6.77754i) q^{28} +(3.41513 + 5.91518i) q^{29} +(2.39409 + 1.78225i) q^{30} +(1.58024 + 2.73705i) q^{31} +(7.08989 - 12.2800i) q^{32} +(-8.06335 + 3.47842i) q^{33} +(0.275796 - 0.477692i) q^{34} +(0.502082 + 0.869631i) q^{35} +(10.4081 - 11.0330i) q^{36} +(-4.71300 + 8.16316i) q^{37} +(4.76772 - 8.25793i) q^{38} +(3.08209 - 5.43146i) q^{39} +(-2.63289 - 4.56031i) q^{40} -8.60228 q^{41} +(6.53918 - 2.82091i) q^{42} +5.99857 q^{43} +25.6335 q^{44} +(-0.558253 - 1.86437i) q^{45} +(-4.25368 - 7.36759i) q^{46} +(-1.42859 + 2.47438i) q^{47} +(-18.2097 + 7.85540i) q^{48} -4.60396 q^{49} +12.1636 q^{50} +(-0.330251 + 0.142466i) q^{51} +(-14.5407 + 10.9940i) q^{52} -2.48667 q^{53} +(-13.5926 + 2.39773i) q^{54} +(1.64453 - 2.84841i) q^{55} -12.5647 q^{56} +(-5.70909 + 2.46282i) q^{57} +(-9.07155 + 15.7124i) q^{58} +(1.49201 - 2.58424i) q^{59} +(-0.659371 + 5.64243i) q^{60} +8.04476 q^{61} +(-4.19756 + 7.27038i) q^{62} +(-4.51863 - 1.07071i) q^{63} +14.7657 q^{64} +(0.288800 + 2.32109i) q^{65} +(-18.7111 - 13.9292i) q^{66} +4.94864 q^{67} +1.04987 q^{68} +(-0.643871 + 5.50980i) q^{69} +(-1.33367 + 2.30999i) q^{70} +(-0.787066 - 1.36324i) q^{71} +(23.6955 + 5.61475i) q^{72} +3.03817 q^{73} -25.0382 q^{74} +(-6.36203 - 4.73612i) q^{75} +18.1493 q^{76} +(-3.92403 - 6.79661i) q^{77} +(16.5880 - 0.123685i) q^{78} +(3.23418 - 5.60177i) q^{79} +(3.71389 - 6.43264i) q^{80} +(8.04308 + 4.03843i) q^{81} +(-11.4251 - 19.7888i) q^{82} +(1.24623 - 2.15854i) q^{83} +(10.8730 + 8.09427i) q^{84} +(0.0673550 - 0.116662i) q^{85} +(7.96696 + 13.7992i) q^{86} +(10.8627 - 4.68602i) q^{87} +(20.5774 + 35.6411i) q^{88} +(-1.76275 + 3.05317i) q^{89} +(3.54738 - 3.76036i) q^{90} +(5.14094 + 2.17241i) q^{91} +(8.09626 - 14.0231i) q^{92} +(5.02635 - 2.16830i) q^{93} -7.58946 q^{94} +(1.16438 - 2.01676i) q^{95} +(-19.7006 - 14.6658i) q^{96} -9.38650 q^{97} +(-6.11471 - 10.5910i) q^{98} +(4.36303 + 14.5710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) $ 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	1.32814	+	2.30041i	0.939138	+	1.62664i	0.767083	+	0.641548i	$0.221708\pi$
$2$	1.32814	+	2.30041i	0.939138	+	1.62664i	0.172056	+	0.985087i	$0.444959\pi$
$3$	0.201038	−	1.72034i	0.116069	−	0.993241i
$3$	0.201038	−	1.72034i	0.116069	−	0.993241i
$4$	−2.52792	+	4.37849i	−1.26396	+	2.18925i
$5$	0.324360	+	0.561808i	0.145058	+	0.251248i	0.929395	−	0.369088i	$-0.120330\pi$
$5$	0.324360	+	0.561808i	0.145058	+	0.251248i	−0.784336	+	0.620336i	$0.786996\pi$
$6$	4.22450	−	1.82239i	1.72465	−	0.743988i
$7$	1.54792			0.585057			0.292529	−	0.956257i	$-0.405503\pi$
$7$	1.54792			0.585057			0.292529	+	0.956257i	$0.405503\pi$
$8$	−8.11720			−2.86986
$9$	−2.91917	−	0.691710i	−0.973056	−	0.230570i
$10$	−0.861592	+	1.49232i	−0.272459	+	0.471913i
$11$	−2.53504	−	4.39082i	−0.764343	−	1.32388i	−0.940593	−	0.339535i	$-0.889730\pi$
$11$	−2.53504	−	4.39082i	−0.764343	−	1.32388i	0.176250	−	0.984345i	$-0.443603\pi$
$12$	7.02430	+	5.22914i	2.02774	+	1.50952i
$13$	3.32120	+	1.40344i	0.921135	+	0.389244i
$13$	3.32120	+	1.40344i	0.921135	+	0.389244i
$14$	2.05585	+	3.56084i	0.549450	+	0.951675i
$15$	1.03171	−	0.445066i	0.266387	−	0.114915i
$16$	−5.72495	−	9.91590i	−1.43124	−	2.47897i
$17$	−0.103828	−	0.179835i	−0.0251819	−	0.0436163i	0.853160	−	0.521650i	$-0.174683\pi$
$17$	−0.103828	−	0.179835i	−0.0251819	−	0.0436163i	−0.878342	+	0.478033i	$0.841350\pi$
$18$	−2.28585	−	7.63397i	−0.538781	−	1.79934i
$19$	−1.79488	−	3.10883i	−0.411774	−	0.713214i	0.583310	−	0.812250i	$-0.301757\pi$
$19$	−1.79488	−	3.10883i	−0.411774	−	0.713214i	−0.995084	+	0.0990360i	$0.968424\pi$
$20$	−3.27983			−0.733392
$21$	0.311190	−	2.66295i	0.0679073	−	0.581103i
$22$	6.73378	−	11.6633i	1.43565	−	2.48661i
$23$	−3.20273			−0.667815			−0.333908	−	0.942606i	$-0.608367\pi$
$23$	−3.20273			−0.667815			−0.333908	+	0.942606i	$0.608367\pi$
$24$	−1.63187	+	13.9644i	−0.333103	+	2.85047i
$25$	2.28958	−	3.96567i	0.457916	−	0.793134i
$26$	1.18254	+	9.50408i	0.231914	+	1.86390i
$27$	−1.77684	+	4.88291i	−0.341954	+	0.939717i
$28$	−3.91301	+	6.77754i	−0.739490	+	1.28083i
$29$	3.41513	+	5.91518i	0.634173	+	1.09842i	0.986690	+	0.162615i	$0.0519928\pi$
$29$	3.41513	+	5.91518i	0.634173	+	1.09842i	−0.352516	+	0.935806i	$0.614674\pi$
$30$	2.39409	+	1.78225i	0.437100	+	0.325393i
$31$	1.58024	+	2.73705i	0.283819	+	0.491589i	0.972322	−	0.233645i	$-0.0750653\pi$
$31$	1.58024	+	2.73705i	0.283819	+	0.491589i	−0.688503	+	0.725233i	$0.741732\pi$
$32$	7.08989	−	12.2800i	1.25333	−	2.17083i
$33$	−8.06335	+	3.47842i	−1.40365	+	0.605515i
$34$	0.275796	−	0.477692i	0.0472986	−	0.0819235i
$35$	0.502082	+	0.869631i	0.0848673	+	0.146995i
$36$	10.4081	−	11.0330i	1.73468	−	1.83883i
$37$	−4.71300	+	8.16316i	−0.774813	+	1.34202i	0.160087	+	0.987103i	$0.448823\pi$
$37$	−4.71300	+	8.16316i	−0.774813	+	1.34202i	−0.934900	+	0.354912i	$0.884511\pi$
$38$	4.76772	−	8.25793i	0.773426	−	1.33961i
$39$	3.08209	−	5.43146i	0.493529	−	0.869729i
$40$	−2.63289	−	4.56031i	−0.416297	−	0.721048i
$41$	−8.60228			−1.34345			−0.671725	−	0.740800i	$-0.734446\pi$
$41$	−8.60228			−1.34345			−0.671725	+	0.740800i	$0.734446\pi$
$42$	6.53918	−	2.82091i	1.00902	−	0.435276i
$43$	5.99857			0.914774			0.457387	−	0.889268i	$-0.348786\pi$
$43$	5.99857			0.914774			0.457387	+	0.889268i	$0.348786\pi$
$44$	25.6335			3.86440
$45$	−0.558253	−	1.86437i	−0.0832194	−	0.277924i
$46$	−4.25368	−	7.36759i	−0.627171	−	1.08629i
$47$	−1.42859	+	2.47438i	−0.208381	+	0.360926i	−0.951205	−	0.308561i	$-0.900153\pi$
$47$	−1.42859	+	2.47438i	−0.208381	+	0.360926i	0.742824	+	0.669487i	$0.233486\pi$
$48$	−18.2097	+	7.85540i	−2.62834	+	1.13383i
$49$	−4.60396			−0.657708
$50$	12.1636			1.72019
$51$	−0.330251	+	0.142466i	−0.0462444	+	0.0199492i
$52$	−14.5407	+	10.9940i	−2.01643	+	1.52460i
$53$	−2.48667			−0.341571			−0.170786	−	0.985308i	$-0.554631\pi$
$53$	−2.48667			−0.341571			−0.170786	+	0.985308i	$0.554631\pi$
$54$	−13.5926	+	2.39773i	−1.84972	+	0.326290i
$55$	1.64453	−	2.84841i	0.221748	−	0.384079i
$56$	−12.5647			−1.67903
$57$	−5.70909	+	2.46282i	−0.756188	+	0.326209i
$58$	−9.07155	+	15.7124i	−1.19115	+	2.06314i
$59$	1.49201	−	2.58424i	0.194244	−	0.336440i	−0.752409	−	0.658697i	$-0.771108\pi$
$59$	1.49201	−	2.58424i	0.194244	−	0.336440i	0.946652	+	0.322257i	$0.104441\pi$
$60$	−0.659371	+	5.64243i	−0.0851244	+	0.728435i
$61$	8.04476			1.03003			0.515013	−	0.857182i	$-0.327787\pi$
$61$	8.04476			1.03003			0.515013	+	0.857182i	$0.327787\pi$
$62$	−4.19756	+	7.27038i	−0.533090	+	0.923339i
$63$	−4.51863	−	1.07071i	−0.569293	−	0.134897i
$64$	14.7657			1.84572
$65$	0.288800	+	2.32109i	0.0358212	+	0.287896i
$66$	−18.7111	−	13.9292i	−2.30317	−	1.71456i
$67$	4.94864			0.604573			0.302286	−	0.953217i	$-0.402250\pi$
$67$	4.94864			0.604573			0.302286	+	0.953217i	$0.402250\pi$
$68$	1.04987			0.127316
$69$	−0.643871	+	5.50980i	−0.0775130	+	0.663302i
$70$	−1.33367	+	2.30999i	−0.159404	+	0.276096i
$71$	−0.787066	−	1.36324i	−0.0934076	−	0.161787i	0.815535	−	0.578707i	$-0.196443\pi$
$71$	−0.787066	−	1.36324i	−0.0934076	−	0.161787i	−0.908943	+	0.416921i	$0.863109\pi$
$72$	23.6955	+	5.61475i	2.79254	+	0.661704i
$73$	3.03817			0.355591			0.177796	−	0.984067i	$-0.443103\pi$
$73$	3.03817			0.355591			0.177796	+	0.984067i	$0.443103\pi$
$74$	−25.0382			−2.91063
$75$	−6.36203	−	4.73612i	−0.734623	−	0.546880i
$76$	18.1493			2.08187
$77$	−3.92403	−	6.79661i	−0.447184	−	0.774546i
$78$	16.5880	−	0.123685i	1.87822	−	0.0140046i
$79$	3.23418	−	5.60177i	0.363874	−	0.630248i	−0.624721	−	0.780848i	$-0.714787\pi$
$79$	3.23418	−	5.60177i	0.363874	−	0.630248i	0.988595	+	0.150600i	$0.0481205\pi$
$80$	3.71389	−	6.43264i	0.415225	−	0.719191i
$81$	8.04308	+	4.03843i	0.893675	+	0.448715i
$82$	−11.4251	−	19.7888i	−1.26169	−	2.18530i
$83$	1.24623	−	2.15854i	0.136792	−	0.236931i	−0.789489	−	0.613765i	$-0.789654\pi$
$83$	1.24623	−	2.15854i	0.136792	−	0.236931i	0.926281	+	0.376835i	$0.122987\pi$
$84$	10.8730	+	8.09427i	1.18635	+	0.883158i
$85$	0.0673550	−	0.116662i	0.00730568	−	0.0126538i
$86$	7.96696	+	13.7992i	0.859099	+	1.48800i
$87$	10.8627	−	4.68602i	1.16460	−	0.502394i
$88$	20.5774	+	35.6411i	2.19356	+	3.79936i
$89$	−1.76275	+	3.05317i	−0.186851	+	0.323635i	−0.944199	−	0.329376i	$-0.893161\pi$
$89$	−1.76275	+	3.05317i	−0.186851	+	0.323635i	0.757348	+	0.653012i	$0.226495\pi$
$90$	3.54738	−	3.76036i	0.373927	−	0.396377i
$91$	5.14094	+	2.17241i	0.538916	+	0.227730i
$92$	8.09626	−	14.0231i	0.844093	−	1.46201i
$93$	5.02635	−	2.16830i	0.521209	−	0.224842i
$94$	−7.58946			−0.782793
$95$	1.16438	−	2.01676i	0.119462	−	0.206915i
$96$	−19.7006	−	14.6658i	−2.01068	−	1.49682i
$97$	−9.38650			−0.953054			−0.476527	−	0.879160i	$-0.658105\pi$
$97$	−9.38650			−0.953054			−0.476527	+	0.879160i	$0.658105\pi$
$98$	−6.11471	−	10.5910i	−0.617679	−	1.06985i
$99$	4.36303	+	14.5710i	0.438501	+	1.46444i
$100$	11.5758	+	20.0498i	1.15758	+	2.00498i
$101$	2.09361	+	3.62624i	0.208322	+	0.360825i	0.951186	−	0.308618i	$-0.0998664\pi$
$101$	2.09361	+	3.62624i	0.208322	+	0.360825i	−0.742864	+	0.669442i	$0.766533\pi$
$102$	−0.766349	−	0.570498i	−0.0758799	−	0.0564877i
$103$	2.03207	+	3.51965i	0.200226	+	0.346801i	0.948601	−	0.316474i	$-0.102499\pi$
$103$	2.03207	+	3.51965i	0.200226	+	0.346801i	−0.748375	+	0.663275i	$0.769166\pi$
$104$	−26.9588	−	11.3920i	−2.64353	−	1.11708i
$105$	1.59700	−	0.688924i	0.155852	−	0.0672321i
$106$	−3.30266	−	5.72037i	−0.320782	−	0.555612i
$107$	5.05806	−	8.76081i	0.488981	−	0.846940i	−0.510939	−	0.859617i	$-0.670702\pi$
$107$	5.05806	−	8.76081i	0.488981	−	0.846940i	0.999920	+	0.0126775i	$0.00403549\pi$
$108$	−16.8881	−	20.1235i	−1.62506	−	1.93639i
$109$	−4.37589			−0.419134			−0.209567	−	0.977794i	$-0.567205\pi$
$109$	−4.37589			−0.419134			−0.209567	+	0.977794i	$0.567205\pi$
$110$	8.73668			0.833010
$111$	13.0960	+	9.74909i	1.24301	+	0.925343i
$112$	−8.86174	−	15.3490i	−0.837355	−	1.45034i
$113$	6.70710	−	11.6170i	0.630951	−	1.09284i	−0.356407	−	0.934331i	$-0.615998\pi$
$113$	6.70710	−	11.6170i	0.630951	−	1.09284i	0.987358	−	0.158508i	$-0.0506684\pi$
$114$	−13.2480	−	9.86227i	−1.24079	−	0.923687i
$115$	−1.03884	−	1.79932i	−0.0968721	−	0.167787i
$116$	−34.5327			−3.20628
$117$	−8.72436	−	6.39418i	−0.806567	−	0.591142i
$118$	7.92642			0.729686
$119$	−0.160716	−	0.278369i	−0.0147329	−	0.0255180i
$120$	−8.37461	+	3.61269i	−0.764494	+	0.329792i
$121$	−7.35284	+	12.7355i	−0.668440	+	1.15777i
$122$	10.6846	+	18.5062i	0.967337	+	1.67548i
$123$	−1.72939	+	14.7989i	−0.155934	+	1.33437i
$124$	−15.9789			−1.43494
$125$	6.21419			0.555814
$126$	−3.53831	−	11.8167i	−0.315218	−	1.05272i
$127$	6.23233	−	10.7947i	0.553029	−	0.957875i	−0.445024	−	0.895518i	$-0.646805\pi$
$127$	6.23233	−	10.7947i	0.553029	−	0.957875i	0.998054	−	0.0623567i	$-0.0198617\pi$
$128$	5.43122	+	9.40715i	0.480056	+	0.831482i
$129$	1.20594	−	10.3196i	0.106177	−	0.908591i
$130$	−4.95590	+	3.74710i	−0.434661	+	0.328643i
$131$	9.84851	+	17.0581i	0.860468	+	1.49037i	0.871478	+	0.490435i	$0.163162\pi$
$131$	9.84851	+	17.0581i	0.860468	+	1.49037i	−0.0110094	+	0.999939i	$0.503504\pi$
$132$	5.15332	−	44.0985i	0.448539	−	3.83828i
$133$	−2.77833	−	4.81220i	−0.240911	−	0.417271i
$134$	6.57250	+	11.3839i	0.567777	+	0.983419i
$135$	−3.31959	+	0.585577i	−0.285705	+	0.0503984i
$136$	0.842789	+	1.45975i	0.0722686	+	0.125173i
$137$	14.1965			1.21289			0.606444	−	0.795126i	$-0.292595\pi$
$137$	14.1965			1.21289			0.606444	+	0.795126i	$0.292595\pi$
$138$	−13.5299	+	5.83663i	−1.15175	+	0.496847i
$139$	−1.74686	+	3.02564i	−0.148166	+	0.256632i	−0.930550	−	0.366165i	$-0.880670\pi$
$139$	−1.74686	+	3.02564i	−0.148166	+	0.256632i	0.782383	+	0.622797i	$0.214004\pi$
$140$	−5.07690			−0.429076
$141$	3.96959	+	2.95511i	0.334300	+	0.248865i
$142$	2.09067	−	3.62115i	0.175445	−	0.303880i
$143$	−2.25712	−	18.1405i	−0.188750	−	1.51699i
$144$	9.85315	+	32.9062i	0.821096	+	2.74218i
$145$	−2.21546	+	3.83729i	−0.183984	+	0.318670i
$146$	4.03513	+	6.98904i	0.333949	+	0.578417i
$147$	−0.925571	+	7.92039i	−0.0763398	+	0.653263i
$148$	−23.8282	−	41.2717i	−1.95867	−	3.39251i
$149$	6.18580	−	10.7141i	0.506761	−	0.877735i	−0.493209	−	0.869911i	$-0.664176\pi$
$149$	6.18580	−	10.7141i	0.506761	−	0.877735i	0.999969	−	0.00782426i	$-0.00249056\pi$
$150$	2.44534	−	20.9255i	0.199661	−	1.70856i
$151$	0.517479	−	0.896300i	0.0421118	−	0.0729398i	−0.844201	−	0.536026i	$-0.819925\pi$
$151$	0.517479	−	0.896300i	0.0421118	−	0.0729398i	0.886313	+	0.463087i	$0.153258\pi$
$152$	14.5694	+	25.2350i	1.18174	+	2.04683i
$153$	0.178697	+	0.596786i	0.0144468	+	0.0482473i
$154$	10.4233	−	18.0537i	0.839936	−	1.45481i
$155$	−1.02513	+	1.77558i	−0.0823405	+	0.142618i
$156$	15.9903	+	27.2252i	1.28025	+	2.17976i
$157$	0.504491	+	0.873804i	0.0402628	+	0.0697372i	0.885455	−	0.464726i	$-0.153847\pi$
$157$	0.504491	+	0.873804i	0.0402628	+	0.0697372i	−0.845192	+	0.534463i	$0.820514\pi$
$158$	17.1818			1.36691
$159$	−0.499917	+	4.27794i	−0.0396460	+	0.339262i
$160$	9.19870			0.727221
$161$	−4.95756			−0.390710
$162$	1.39230	+	23.8660i	0.109389	+	1.87509i
$163$	−3.52876	−	6.11200i	−0.276394	−	0.478728i	0.694092	−	0.719886i	$-0.255806\pi$
$163$	−3.52876	−	6.11200i	−0.276394	−	0.478728i	−0.970486	+	0.241158i	$0.922473\pi$
$164$	21.7459	−	37.6650i	1.69807	−	2.94114i
$165$	−4.56963	−	3.40180i	−0.355745	−	0.264829i
$166$	6.62071			0.513867
$167$	−18.4563			−1.42819			−0.714094	−	0.700050i	$-0.753161\pi$
$167$	−18.4563			−1.42819			−0.714094	+	0.700050i	$0.753161\pi$
$168$	−2.52599	+	21.6157i	−0.194885	+	1.66769i
$169$	9.06071	+	9.32220i	0.696978	+	0.717093i
$170$	0.357828			0.0274442
$171$	3.08916	+	10.3167i	0.236234	+	0.788940i
$172$	−15.1639	+	26.2647i	−1.15624	+	2.00266i
$173$	1.75966			0.133785			0.0668923	−	0.997760i	$-0.478692\pi$
$173$	1.75966			0.133785			0.0668923	+	0.997760i	$0.478692\pi$
$174$	25.2070	+	18.7650i	1.91094	+	1.42257i
$175$	3.54408	−	6.13853i	0.267907	−	0.464029i
$176$	−29.0259	+	50.2744i	−2.18791	+	3.78957i
$177$	−4.14583	−	3.08631i	−0.311620	−	0.231981i
$178$	−9.36472			−0.701915
$179$	−4.63867	+	8.03441i	−0.346711	+	0.600520i	−0.985663	−	0.168726i	$-0.946035\pi$
$179$	−4.63867	+	8.03441i	−0.346711	+	0.600520i	0.638952	+	0.769246i	$0.279368\pi$
$180$	9.57437	+	2.26869i	0.713631	+	0.169098i
$181$	−17.7014			−1.31574			−0.657868	−	0.753133i	$-0.728541\pi$
$181$	−17.7014			−1.31574			−0.657868	+	0.753133i	$0.728541\pi$
$182$	1.83047	+	14.7115i	0.135683	+	1.09049i
$183$	1.61730	−	13.8398i	0.119555	−	1.02306i
$184$	25.9972			1.91654
$185$	−6.11484			−0.449572
$186$	11.6637	+	8.68287i	0.855223	+	0.636659i
$187$	−0.526414	+	0.911776i	−0.0384952	+	0.0666757i
$188$	−7.22271	−	12.5101i	−0.526771	−	0.912393i
$189$	−2.75040	+	7.55834i	−0.200062	+	0.549788i
$190$	6.18583			0.448767
$191$	0.543687			0.0393398			0.0196699	−	0.999807i	$-0.493738\pi$
$191$	0.543687			0.0393398			0.0196699	+	0.999807i	$0.493738\pi$
$192$	2.96848	−	25.4021i	0.214231	−	1.83324i
$193$	−24.7026			−1.77813			−0.889065	−	0.457780i	$-0.848645\pi$
$193$	−24.7026			−1.77813			−0.889065	+	0.457780i	$0.848645\pi$
$194$	−12.4666	−	21.5928i	−0.895050	−	1.55027i
$195$	4.05114	−	0.0302065i	0.290108	−	0.00216313i
$196$	11.6384	−	20.1584i	0.831318	−	1.43988i
$197$	9.01337	−	15.6116i	0.642176	−	1.11228i	−0.342770	−	0.939419i	$-0.611365\pi$
$197$	9.01337	−	15.6116i	0.642176	−	1.11228i	0.984946	−	0.172863i	$-0.0553016\pi$
$198$	−27.7246	+	29.3892i	−1.97030	+	2.08860i
$199$	−8.59093	−	14.8799i	−0.608995	−	1.05481i	−0.991406	−	0.130818i	$-0.958240\pi$
$199$	−8.59093	−	14.8799i	−0.608995	−	1.05481i	0.382412	−	0.923992i	$-0.375094\pi$
$200$	−18.5850	+	32.1901i	−1.31416	+	2.27619i
$201$	0.994866	−	8.51336i	0.0701724	−	0.600486i
$202$	−5.56123	+	9.63233i	−0.391287	+	0.677728i
$203$	5.28633	+	9.15620i	0.371028	+	0.642639i
$204$	0.211065	−	1.80614i	0.0147775	−	0.126455i
$205$	−2.79024	−	4.83283i	−0.194878	−	0.337539i
$206$	−5.39775	+	9.34918i	−0.376079	+	0.651388i
$207$	9.34931	+	2.21536i	0.649822	+	0.153978i
$208$	−5.09731	−	40.9673i	−0.353435	−	2.84057i
$209$	−9.10019	+	15.7620i	−0.629473	+	1.09028i
$210$	3.70586	+	2.75877i	0.255728	+	0.190373i
$211$	2.70321			0.186097			0.0930483	−	0.995662i	$-0.470339\pi$
$211$	2.70321			0.186097			0.0930483	+	0.995662i	$0.470339\pi$
$212$	6.28612	−	10.8879i	0.431733	−	0.747783i
$213$	−2.50347	+	1.07996i	−0.171535	+	0.0739978i
$214$	26.8713			1.83688
$215$	1.94570	+	3.37004i	0.132695	+	0.229835i
$216$	14.4230	−	39.6356i	0.981360	−	2.69686i
$217$	2.44607	+	4.23672i	0.166050	+	0.287607i
$218$	−5.81180	−	10.0663i	−0.393625	−	0.681778i
$219$	0.610789	−	5.22670i	0.0412733	−	0.353188i
$220$	8.31449	+	14.4011i	0.560563	+	0.970923i
$221$	−0.0924449	−	0.742982i	−0.00621851	−	0.0499784i
$222$	−5.03363	+	43.0742i	−0.337835	+	2.89095i
$223$	−2.61210	−	4.52428i	−0.174919	−	0.302968i	0.765214	−	0.643776i	$-0.222633\pi$
$223$	−2.61210	−	4.52428i	−0.174919	−	0.302968i	−0.940133	+	0.340807i	$0.889300\pi$
$224$	10.9746	−	19.0085i	0.733268	−	1.27006i
$225$	−9.42676	+	9.99273i	−0.628451	+	0.666182i
$226$	35.6319			2.37020
$227$	−5.57109			−0.369766			−0.184883	−	0.982761i	$-0.559191\pi$
$227$	−5.57109			−0.369766			−0.184883	+	0.982761i	$0.559191\pi$
$228$	3.64870	−	31.2230i	0.241641	−	2.06780i
$229$	11.4445	+	19.8225i	0.756276	+	1.30991i	0.944737	+	0.327828i	$0.106317\pi$
$229$	11.4445	+	19.8225i	0.756276	+	1.30991i	−0.188461	+	0.982081i	$0.560350\pi$
$230$	2.75945	−	4.77950i	0.181953	−	0.315151i
$231$	−12.4814	+	5.38430i	−0.821215	+	0.354261i
$232$	−27.7213	−	48.0147i	−1.81999	−	3.15232i
$233$	15.4122			1.00969			0.504844	−	0.863211i	$-0.331550\pi$
$233$	15.4122			1.00969			0.504844	+	0.863211i	$0.331550\pi$
$234$	3.12205	−	28.5620i	0.204095	−	1.86716i
$235$	−1.85350			−0.120909
$236$	7.54339	+	13.0655i	0.491033	+	0.850494i
$237$	−8.98678	−	6.69008i	−0.583754	−	0.434567i
$238$	0.426909	−	0.739427i	0.0276724	−	0.0479300i
$239$	−5.97112	−	10.3423i	−0.386240	−	0.668987i	0.605701	−	0.795693i	$-0.292893\pi$
$239$	−5.97112	−	10.3423i	−0.386240	−	0.668987i	−0.991940	+	0.126706i	$0.959560\pi$
$240$	−10.3197	−	7.68237i	−0.666135	−	0.495895i
$241$	−17.8263			−1.14829			−0.574146	−	0.818753i	$-0.694666\pi$
$241$	−17.8263			−1.14829			−0.574146	+	0.818753i	$0.694666\pi$
$242$	−39.0625			−2.51103
$243$	8.56446	−	13.0250i	0.549410	−	0.835553i
$244$	−20.3365	+	35.2239i	−1.30191	+	2.25498i
$245$	−1.49334	−	2.58654i	−0.0954059	−	0.165248i
$246$	−36.3404	+	15.6767i	−2.31698	+	0.999511i
$247$	−1.59811	−	12.8440i	−0.101685	−	0.817247i
$248$	−12.8271	−	22.2172i	−0.814521	−	1.41079i
$249$	−3.46289	−	2.57790i	−0.219452	−	0.163368i
$250$	8.25333	+	14.2952i	0.521987	+	0.904107i
$251$	0.779623	+	1.35035i	0.0492094	+	0.0852331i	0.889581	−	0.456778i	$-0.150997\pi$
$251$	0.779623	+	1.35035i	0.0492094	+	0.0852331i	−0.840372	+	0.542011i	$0.817663\pi$
$252$	16.1108	−	17.0781i	1.01489	−	1.07582i
$253$	8.11905	+	14.0626i	0.510440	+	0.884108i
$254$	33.1097			2.07748
$255$	−0.187158	−	0.139327i	−0.0117203	−	0.00872502i
$256$	0.338874	−	0.586947i	0.0211796	−	0.0366842i
$257$	19.8031			1.23528			0.617641	−	0.786460i	$-0.288088\pi$
$257$	19.8031			1.23528			0.617641	+	0.786460i	$0.288088\pi$
$258$	25.3410	−	10.9317i	1.57766	−	0.680581i
$259$	−7.29533	+	12.6359i	−0.453310	+	0.785156i
$260$	−10.8930	−	4.60304i	−0.675553	−	0.285469i
$261$	−5.87775	−	19.6297i	−0.363823	−	1.21505i
$262$	−26.1604	+	45.3112i	−1.61620	+	2.79934i
$263$	−8.16120	−	14.1356i	−0.503241	−	0.871640i	−0.999993	−	0.00374687i	$-0.998807\pi$
$263$	−8.16120	−	14.1356i	−0.503241	−	0.871640i	0.496752	−	0.867893i	$-0.334526\pi$
$264$	65.4518	−	28.2350i	4.02828	−	1.73774i
$265$	−0.806578	−	1.39703i	−0.0495477	−	0.0858191i
$266$	7.38003	−	12.7826i	0.452498	−	0.783750i
$267$	4.89812	+	3.64634i	0.299760	+	0.223152i
$268$	−12.5098	+	21.6676i	−0.764157	+	1.32356i
$269$	15.1854	+	26.3019i	0.925870	+	1.60365i	0.790156	+	0.612906i	$0.210000\pi$
$269$	15.1854	+	26.3019i	0.925870	+	1.60365i	0.135714	+	0.990748i	$0.456667\pi$
$270$	−5.75596	−	6.85870i	−0.350297	−	0.417407i
$271$	−11.5518	+	20.0082i	−0.701719	+	1.21541i	0.266143	+	0.963933i	$0.414251\pi$
$271$	−11.5518	+	20.0082i	−0.701719	+	1.21541i	−0.967863	+	0.251480i	$0.919083\pi$
$272$	−1.18882	+	2.05909i	−0.0720825	+	0.124851i
$273$	4.77081	−	8.40744i	0.288743	−	0.508841i
$274$	18.8550	+	32.6578i	1.13907	+	1.97293i
$275$	−23.2167			−1.40002
$276$	−22.4969	−	16.7475i	−1.35416	−	1.00808i
$277$	−13.6884			−0.822457			−0.411228	−	0.911532i	$-0.634900\pi$
$277$	−13.6884			−0.822457			−0.411228	+	0.911532i	$0.634900\pi$
$278$	−9.28030			−0.556595
$279$	−2.71973	−	9.08297i	−0.162826	−	0.543783i
$280$	−4.07550	−	7.05897i	−0.243558	−	0.421854i
$281$	−13.2269	+	22.9096i	−0.789049	+	1.36667i	0.137501	+	0.990502i	$0.456093\pi$
$281$	−13.2269	+	22.9096i	−0.789049	+	1.36667i	−0.926550	+	0.376171i	$0.877240\pi$
$282$	−1.52577	+	13.0565i	−0.0908584	+	0.777503i
$283$	6.60036			0.392351			0.196175	−	0.980569i	$-0.437148\pi$
$283$	6.60036			0.392351			0.196175	+	0.980569i	$0.437148\pi$
$284$	7.95857			0.472254
$285$	−3.23543	−	2.40857i	−0.191651	−	0.142671i
$286$	38.7329	−	29.2855i	2.29032	−	1.73169i
$287$	−13.3156			−0.785996
$288$	−29.1908	+	30.9434i	−1.72008	+	1.82336i
$289$	8.47844	−	14.6851i	0.498732	−	0.863829i
$290$	−11.7698			−0.691146
$291$	−1.88704	+	16.1480i	−0.110621	+	0.946613i
$292$	−7.68027	+	13.3026i	−0.449454	+	0.778477i
$293$	0.247450	−	0.428597i	0.0144562	−	0.0250389i	−0.858707	−	0.512467i	$-0.828732\pi$
$293$	0.247450	−	0.428597i	0.0144562	−	0.0250389i	0.873163	+	0.487428i	$0.162065\pi$
$294$	−19.4494	+	8.39021i	−1.13431	+	0.489327i
$295$	1.93580			0.112706
$296$	38.2564	−	66.2620i	2.22361	−	3.85140i
$297$	25.9443	−	4.57658i	1.50544	−	0.265560i
$298$	32.8625			1.90367
$299$	−10.6369	−	4.49484i	−0.615148	−	0.259943i
$300$	36.8198	−	15.8835i	2.12579	−	0.917036i
$301$	9.28528			0.535195
$302$	2.74914			0.158195
$303$	6.65928	−	2.87272i	0.382566	−	0.165033i
$304$	−20.5512	+	35.5957i	−1.17869	+	2.04156i
$305$	2.60940	+	4.51961i	0.149414	+	0.258792i
$306$	−1.13552	+	1.20369i	−0.0649132	+	0.0688105i
$307$	3.08744			0.176210			0.0881048	−	0.996111i	$-0.471919\pi$
$307$	3.08744			0.176210			0.0881048	+	0.996111i	$0.471919\pi$
$308$	39.6786			2.26090
$309$	6.46352	−	2.78827i	0.367697	−	0.158619i
$310$	−5.44608			−0.309316
$311$	4.13808	+	7.16736i	0.234649	+	0.406424i	0.959171	−	0.282828i	$-0.0912727\pi$
$311$	4.13808	+	7.16736i	0.234649	+	0.406424i	−0.724522	+	0.689252i	$0.757939\pi$
$312$	−25.0179	+	44.0882i	−1.41636	+	2.49600i
$313$	14.4586	−	25.0429i	0.817246	−	1.41551i	−0.0904586	−	0.995900i	$-0.528833\pi$
$313$	14.4586	−	25.0429i	0.817246	−	1.41551i	0.907704	−	0.419611i	$-0.137833\pi$
$314$	−1.34007	+	2.32107i	−0.0756246	+	0.130986i
$315$	−0.864129	−	2.88589i	−0.0486881	−	0.162602i
$316$	16.3515	+	28.3217i	0.919846	+	1.59322i
$317$	−1.41121	+	2.44429i	−0.0792615	+	0.137285i	−0.902932	−	0.429784i	$-0.858590\pi$
$317$	−1.41121	+	2.44429i	−0.0792615	+	0.137285i	0.823670	+	0.567069i	$0.191923\pi$
$318$	−10.5050	+	4.53169i	−0.589089	+	0.254125i
$319$	17.3150	−	29.9904i	0.969452	−	1.67914i
$320$	4.78941	+	8.29551i	0.267736	+	0.463733i
$321$	−14.0547	−	10.4629i	−0.784459	−	0.583980i
$322$	−6.58434	−	11.4044i	−0.366931	−	0.635543i
$323$	−0.372717	+	0.645564i	−0.0207385	+	0.0359202i
$324$	−38.0145	+	25.0077i	−2.11192	+	1.38932i
$325$	13.1697	−	9.95749i	0.730525	−	0.552342i
$326$	9.37340	−	16.2352i	0.519144	−	0.899185i
$327$	−0.879721	+	7.52803i	−0.0486487	+	0.416301i
$328$	69.8264			3.85552
$329$	−2.21133	+	3.83014i	−0.121915	+	0.211162i
$330$	1.75641	−	15.0301i	0.0966870	−	0.827379i
$331$	−12.1581			−0.668268			−0.334134	−	0.942526i	$-0.608444\pi$
$331$	−12.1581			−0.668268			−0.334134	+	0.942526i	$0.608444\pi$
$332$	6.30077	+	10.9133i	0.345800	+	0.598943i
$333$	19.4046	−	20.5696i	1.06336	−	1.12721i
$334$	−24.5125	−	42.4569i	−1.34127	−	2.32314i
$335$	1.60514	+	2.78018i	0.0876982	+	0.151898i
$336$	−28.1871	+	12.1595i	−1.53773	+	0.663355i
$337$	−10.2611	−	17.7727i	−0.558956	−	0.968139i	−0.997584	−	0.0694709i	$-0.977869\pi$
$337$	−10.2611	−	17.7727i	−0.558956	−	0.968139i	0.438628	−	0.898668i	$-0.355464\pi$
$338$	−9.41097	+	33.2246i	−0.511889	+	1.80718i
$339$	−18.6369	−	13.8740i	−1.01222	−	0.753532i
$340$	0.340537	+	0.589827i	0.0184682	+	0.0319879i
$341$	8.01192	−	13.8771i	0.433870	−	0.751484i
$342$	−19.6299	+	20.8084i	−1.06146	+	1.12519i
$343$	−17.9619			−0.969854
$344$	−48.6916			−2.62527
$345$	−3.30429	+	1.42543i	−0.177897	+	0.0767423i
$346$	2.33708	+	4.04794i	0.125642	+	0.217619i
$347$	−10.8479	+	18.7892i	−0.582348	+	1.00866i	0.412853	+	0.910798i	$0.364532\pi$
$347$	−10.8479	+	18.7892i	−0.582348	+	1.00866i	−0.995200	+	0.0978578i	$0.968801\pi$
$348$	−6.94240	+	59.4082i	−0.372152	+	3.18461i
$349$	17.2243	+	29.8333i	0.921995	+	1.59694i	0.796324	+	0.604871i	$0.206775\pi$
$349$	17.2243	+	29.8333i	0.921995	+	1.59694i	0.125671	+	0.992072i	$0.459891\pi$
$350$	18.8282			1.00641
$351$	−12.7541	+	13.7234i	−0.680765	+	0.732502i
$352$	−71.8926			−3.83189
$353$	0.713616	+	1.23602i	0.0379819	+	0.0657867i	0.884391	−	0.466746i	$-0.154574\pi$
$353$	0.713616	+	1.23602i	0.0379819	+	0.0657867i	−0.846410	+	0.532533i	$0.821240\pi$
$354$	1.59351	−	13.6362i	0.0846943	−	0.724754i
$355$	0.510585	−	0.884360i	0.0270991	−	0.0469370i
$356$	−8.91218	−	15.4364i	−0.472345	−	0.818125i
$357$	−0.511201	+	0.220525i	−0.0270556	+	0.0116714i
$358$	−24.6433			−1.30244
$359$	8.30365			0.438250			0.219125	−	0.975697i	$-0.429680\pi$
$359$	8.30365			0.438250			0.219125	+	0.975697i	$0.429680\pi$
$360$	4.53145	+	15.1335i	0.238828	+	0.797605i
$361$	3.05680	−	5.29453i	0.160884	−	0.278659i
$362$	−23.5100	−	40.7205i	−1.23566	−	2.14022i
$363$	20.4312	+	15.2097i	1.07236	+	0.798304i
$364$	−22.5078	+	17.0179i	−1.17973	+	0.891979i
$365$	0.985461	+	1.70687i	0.0515814	+	0.0893416i
$366$	33.9851	−	14.6607i	1.77643	−	0.766327i
$367$	15.4596	+	26.7768i	0.806984	+	1.39774i	0.914943	+	0.403582i	$0.132235\pi$
$367$	15.4596	+	26.7768i	0.806984	+	1.39774i	−0.107959	+	0.994155i	$0.534432\pi$
$368$	18.3355	+	31.7580i	0.955802	+	1.65550i
$369$	25.1115	+	5.95028i	1.30725	+	0.309759i
$370$	−8.12137	−	14.0666i	−0.422210	−	0.731289i
$371$	−3.84916			−0.199839
$372$	−3.21236	+	27.4891i	−0.166553	+	1.42525i
$373$	−7.12879	+	12.3474i	−0.369115	+	0.639326i	−0.989427	−	0.145029i	$-0.953672\pi$
$373$	−7.12879	+	12.3474i	−0.369115	+	0.639326i	0.620313	+	0.784355i	$0.287006\pi$
$374$	−2.79661			−0.144609
$375$	1.24929	−	10.6905i	0.0645131	−	0.552058i
$376$	11.5961	−	20.0851i	0.598024	−	1.03581i
$377$	3.04072	+	24.4384i	0.156605	+	1.25864i
$378$	−21.0402	+	3.71149i	−1.08219	+	0.190899i
$379$	3.17631	−	5.50154i	0.163156	−	0.282595i	−0.772843	−	0.634598i	$-0.781166\pi$
$379$	3.17631	−	5.50154i	0.163156	−	0.282595i	0.935999	+	0.352003i	$0.114499\pi$
$380$	5.88690	+	10.1964i	0.301992	+	0.523065i
$381$	−17.3177	−	12.8919i	−0.887211	−	0.660472i
$382$	0.722094	+	1.25070i	0.0369455	+	0.0639915i
$383$	−14.5580	+	25.2151i	−0.743877	+	1.28843i	0.206840	+	0.978375i	$0.433682\pi$
$383$	−14.5580	+	25.2151i	−0.743877	+	1.28843i	−0.950717	+	0.310059i	$0.899651\pi$
$384$	17.2754	−	7.45237i	0.881582	−	0.380302i
$385$	2.54559	−	4.40910i	0.129735	−	0.224708i
$386$	−32.8085	−	56.8261i	−1.66991	−	2.89237i
$387$	−17.5108	−	4.14927i	−0.890126	−	0.210919i
$388$	23.7283	−	41.0987i	1.20462	−	2.08647i
$389$	15.8354	−	27.4277i	0.802887	−	1.39064i	−0.114821	−	0.993386i	$-0.536629\pi$
$389$	15.8354	−	27.4277i	0.802887	−	1.39064i	0.917708	−	0.397255i	$-0.130037\pi$
$390$	5.44998	+	9.27917i	0.275970	+	0.469869i
$391$	0.332532	+	0.575962i	0.0168169	+	0.0291277i
$392$	37.3712			1.88753
$393$	31.3258	−	13.5135i	1.58018	−	0.681665i
$394$	47.8842			2.41237
$395$	4.19616			0.211132
$396$	−74.8286	−	17.7310i	−3.76028	−	0.891015i
$397$	7.89246	+	13.6701i	0.396111	+	0.686085i	0.993242	−	0.116059i	$-0.0370261\pi$
$397$	7.89246	+	13.6701i	0.396111	+	0.686085i	−0.597131	+	0.802144i	$0.703693\pi$
$398$	22.8199	−	39.5253i	1.14386	−	1.98122i
$399$	−8.83720	+	3.81224i	−0.442413	+	0.190851i
$400$	−52.4309			−2.62155
$401$	−0.758995			−0.0379024			−0.0189512	−	0.999820i	$-0.506033\pi$
$401$	−0.758995			−0.0379024			−0.0189512	+	0.999820i	$0.506033\pi$
$402$	20.9055	−	9.01836i	1.04267	−	0.449795i
$403$	1.40699	+	11.3080i	0.0700873	+	0.563294i
$404$	−21.1700			−1.05324
$405$	0.340028	+	5.82857i	0.0168961	+	0.289624i
$406$	−14.0420	+	24.3215i	−0.696893	+	1.20705i
$407$	47.7906			2.36889
$408$	2.68071	−	1.15642i	0.132715	−	0.0572514i
$409$	13.4857	−	23.3579i	0.666824	−	1.15497i	−0.311963	−	0.950094i	$-0.600986\pi$
$409$	13.4857	−	23.3579i	0.666824	−	1.15497i	0.978787	−	0.204879i	$-0.0656802\pi$
$410$	7.41166	−	12.8374i	0.366036	−	0.633992i
$411$	2.85404	−	24.4229i	0.140779	−	1.20469i
$412$	−20.5477			−1.01231
$413$	2.30951	−	4.00019i	0.113644	−	0.196836i
$414$	7.32097	+	24.4495i	0.359806	+	1.20163i
$415$	1.61691			0.0793712
$416$	40.7812	−	30.8342i	1.99946	−	1.51177i
$417$	4.85396	+	3.61346i	0.237700	+	0.176952i
$418$	−48.3454			−2.36465
$419$	10.6016			0.517921			0.258960	−	0.965888i	$-0.416620\pi$
$419$	10.6016			0.517921			0.258960	+	0.965888i	$0.416620\pi$
$420$	−1.02065	+	8.73401i	−0.0498026	+	0.426176i
$421$	−8.35573	+	14.4725i	−0.407233	+	0.705349i	−0.994579	−	0.103988i	$-0.966840\pi$
$421$	−8.35573	+	14.4725i	−0.407233	+	0.705349i	0.587345	+	0.809336i	$0.300173\pi$
$422$	3.59025	+	6.21849i	0.174771	+	0.302711i
$423$	5.88184	−	6.23497i	0.285985	−	0.303155i
$424$	20.1848			0.980262
$425$	−0.950887			−0.0461248
$426$	−5.80932	−	4.32466i	−0.281462	−	0.209531i
$427$	12.4526			0.602624
$428$	25.5728	+	44.2933i	1.23611	+	2.14100i
$429$	−31.6617	+	0.236080i	−1.52864	+	0.0113980i
$430$	−5.16832	+	8.95180i	−0.249239	+	0.431694i
$431$	−4.15171	+	7.19098i	−0.199981	+	0.346377i	−0.948522	−	0.316711i	$-0.897421\pi$
$431$	−4.15171	+	7.19098i	−0.199981	+	0.346377i	0.748541	+	0.663089i	$0.230755\pi$
$432$	58.5908	−	10.3354i	2.81895	−	0.497263i
$433$	0.0394092	+	0.0682587i	0.00189388	+	0.00328030i	0.866971	−	0.498359i	$-0.166064\pi$
$433$	0.0394092	+	0.0682587i	0.00189388	+	0.00328030i	−0.865077	+	0.501639i	$0.832730\pi$
$434$	−6.49746	+	11.2539i	−0.311888	+	0.540206i
$435$	6.15607	+	4.58280i	0.295161	+	0.219728i
$436$	11.0619	−	19.1598i	0.529769	−	0.917587i
$437$	5.74852	+	9.95673i	0.274989	+	0.476295i
$438$	12.8348	−	5.53674i	0.613269	−	0.264556i
$439$	−12.8710	−	22.2932i	−0.614298	−	1.06400i	−0.990507	−	0.137461i	$-0.956106\pi$
$439$	−12.8710	−	22.2932i	−0.614298	−	1.06400i	0.376209	−	0.926535i	$-0.377227\pi$
$440$	−13.3490	+	23.1211i	−0.636387	+	1.10226i
$441$	13.4397	+	3.18460i	0.639987	+	0.151648i
$442$	1.58638	−	1.19945i	0.0754566	−	0.0570519i
$443$	−14.1715	+	24.5458i	−0.673309	+	1.16621i	0.303651	+	0.952783i	$0.401794\pi$
$443$	−14.1715	+	24.5458i	−0.673309	+	1.16621i	−0.976960	+	0.213422i	$0.931539\pi$
$444$	−75.7919	+	32.6955i	−3.59692	+	1.55166i
$445$	−2.28706			−0.108417
$446$	6.93847	−	12.0178i	0.328546	−	0.569059i
$447$	−17.1884	−	12.7957i	−0.812983	−	0.605214i
$448$	22.8561			1.07985
$449$	2.18709	+	3.78815i	0.103215	+	0.178774i	0.913008	−	0.407943i	$-0.133754\pi$
$449$	2.18709	+	3.78815i	0.103215	+	0.178774i	−0.809792	+	0.586716i	$0.800420\pi$
$450$	−35.5075	−	8.41365i	−1.67384	−	0.396623i
$451$	21.8071	+	37.7710i	1.02686	+	1.77857i
$452$	33.9101	+	58.7340i	1.59500	+	2.76261i
$453$	−1.43791	−	1.07043i	−0.0675589	−	0.0502933i
$454$	−7.39920	−	12.8158i	−0.347262	−	0.601475i
$455$	0.447038	+	3.59286i	0.0209575	+	0.168436i
$456$	46.3418	−	19.9912i	2.17016	−	0.936174i
$457$	6.77841	+	11.7405i	0.317080	+	0.549199i	0.979878	−	0.199600i	$-0.0639641\pi$
$457$	6.77841	+	11.7405i	0.317080	+	0.549199i	−0.662797	+	0.748799i	$0.730631\pi$
$458$	−30.3999	+	52.6542i	−1.42050	+	2.46037i
$459$	1.06260	−	0.187443i	0.0495980	−	0.00874909i
$460$	10.5044			0.489770
$461$	2.00590			0.0934240			0.0467120	−	0.998908i	$-0.485126\pi$
$461$	2.00590			0.0934240			0.0467120	+	0.998908i	$0.485126\pi$
$462$	−28.9632	−	21.5612i	−1.34749	−	1.00312i
$463$	−20.7451	−	35.9315i	−0.964104	−	1.66988i	−0.712002	−	0.702177i	$-0.752211\pi$
$463$	−20.7451	−	35.9315i	−0.964104	−	1.66988i	−0.252102	−	0.967701i	$-0.581122\pi$
$464$	39.1029	−	67.7281i	1.81530	−	3.14420i
$465$	2.84851	+	2.12054i	0.132097	+	0.0983375i
$466$	20.4696	+	35.4544i	0.948237	+	1.64239i
$467$	−25.0664			−1.15993			−0.579967	−	0.814640i	$-0.696935\pi$
$467$	−25.0664			−1.15993			−0.579967	+	0.814640i	$0.696935\pi$
$468$	50.0514	−	22.0355i	2.31363	−	1.01859i
$469$	7.66008			0.353710
$470$	−2.46172	−	4.26382i	−0.113551	−	0.196675i
$471$	1.60467	−	0.692230i	0.0739391	−	0.0318963i
$472$	−12.1110	+	20.9768i	−0.557452	+	0.965536i
$473$	−15.2066	−	26.3386i	−0.699201	−	1.21105i
$474$	3.45420	−	29.5586i	0.158657	−	1.35767i
$475$	−16.4381			−0.754232
$476$	1.62512			0.0744870
$477$	7.25902	+	1.72006i	0.332368	+	0.0787560i
$478$	15.8610	−	27.4720i	0.725465	−	1.25654i
$479$	3.05611	+	5.29334i	0.139637	+	0.241859i	0.927359	−	0.374172i	$-0.122073\pi$
$479$	3.05611	+	5.29334i	0.139637	+	0.241859i	−0.787722	+	0.616031i	$0.788740\pi$
$480$	1.84929	−	15.8249i	0.0844082	−	0.722306i
$481$	−27.1093	+	20.4971i	−1.23608	+	0.934585i
$482$	−23.6759	−	41.0078i	−1.07841	−	1.86785i
$483$	−0.996659	+	8.52870i	−0.0453495	+	0.388070i
$484$	−37.1749	−	64.3887i	−1.68977	−	2.92676i
$485$	−3.04460	−	5.27341i	−0.138248	−	0.239453i
$486$	41.3376	+	2.40275i	1.87511	+	0.108991i
$487$	−5.55082	−	9.61430i	−0.251532	−	0.435666i	0.712416	−	0.701757i	$-0.247601\pi$
$487$	−5.55082	−	9.61430i	−0.251532	−	0.435666i	−0.963948	+	0.266092i	$0.914268\pi$
$488$	−65.3009			−2.95603
$489$	−11.2242	+	4.84194i	−0.507574	+	0.218960i
$490$	3.96673	−	6.87058i	0.179199	−	0.310381i
$491$	2.27715			0.102766			0.0513832	−	0.998679i	$-0.483637\pi$
$491$	2.27715			0.102766			0.0513832	+	0.998679i	$0.483637\pi$
$492$	−60.4250	−	44.9826i	−2.72417	−	2.02797i
$493$	0.709169	−	1.22832i	0.0319394	−	0.0553206i
$494$	27.4240	−	20.7350i	1.23387	−	0.932912i
$495$	−6.77093	+	7.17745i	−0.304331	+	0.322602i
$496$	18.0935	−	31.3389i	0.812424	−	1.40716i
$497$	−1.21831	−	2.11018i	−0.0546488	−	0.0946545i
$498$	1.33102	−	11.3899i	0.0596442	−	0.510393i
$499$	−5.67665	−	9.83225i	−0.254122	−	0.440152i	0.710535	−	0.703662i	$-0.248453\pi$
$499$	−5.67665	−	9.83225i	−0.254122	−	0.440152i	−0.964657	+	0.263510i	$0.915120\pi$
$500$	−15.7090	+	27.2088i	−0.702528	+	1.21681i
$501$	−3.71041	+	31.7511i	−0.165769	+	1.41853i
$502$	−2.07090	+	3.58690i	−0.0924288	+	0.160091i
$503$	−17.2266	−	29.8374i	−0.768097	−	1.33038i	−0.938594	−	0.345025i	$-0.887871\pi$
$503$	−17.2266	−	29.8374i	−0.768097	−	1.33038i	0.170497	−	0.985358i	$-0.445463\pi$
$504$	36.6786	+	8.69115i	1.63379	+	0.387135i
$505$	−1.35817	+	2.35241i	−0.0604377	+	0.104681i
$506$	−21.5665	+	37.3543i	−0.958748	+	1.66060i
$507$	17.8589	−	13.7134i	0.793144	−	0.609035i
$508$	31.5097	+	54.5764i	1.39802	+	2.42144i
$509$	1.36933			0.0606944			0.0303472	−	0.999539i	$-0.490339\pi$
$509$	1.36933			0.0606944			0.0303472	+	0.999539i	$0.490339\pi$
$510$	0.0719371	−	0.615588i	0.00318543	−	0.0272587i
$511$	4.70284			0.208041
$512$	23.5252			1.03968
$513$	18.3694	−	3.24035i	0.811027	−	0.143065i
$514$	26.3013	+	45.5552i	1.16010	+	2.00935i
$515$	−1.31824	+	2.28326i	−0.0580887	+	0.100613i
$516$	42.1358	+	31.3674i	1.85492	+	1.38087i
$517$	14.4861			0.637097
$518$	−38.7570			−1.70288
$519$	0.353759	−	3.02722i	0.0155283	−	0.132880i
$520$	−2.34425	−	18.8408i	−0.102802	−	0.826223i
$521$	−4.08021			−0.178757			−0.0893785	−	0.995998i	$-0.528488\pi$
$521$	−4.08021			−0.178757			−0.0893785	+	0.995998i	$0.528488\pi$
$522$	37.3498	−	39.5922i	1.63476	−	1.73290i
$523$	3.04053	−	5.26635i	0.132953	−	0.230281i	−0.791861	−	0.610702i	$-0.790887\pi$
$523$	3.04053	−	5.26635i	0.132953	−	0.230281i	0.924814	+	0.380420i	$0.124221\pi$
$524$	−99.5851			−4.35040
$525$	−9.84788	−	7.33111i	−0.429797	−	0.319956i
$526$	21.6785	−	37.5482i	0.945227	−	1.63718i
$527$	0.328144	−	0.568363i	0.0142942	−	0.0247583i
$528$	80.6539	+	60.0416i	3.51001	+	2.61298i
$529$	−12.7425			−0.554023
$530$	2.14250	−	3.71092i	0.0930642	−	0.161192i
$531$	−6.14298	+	6.51180i	−0.266583	+	0.282588i
$532$	28.0936			1.21801
$533$	−28.5699	−	12.0728i	−1.23750	−	0.522930i
$534$	−1.88267	+	16.1105i	−0.0814710	+	0.697171i
$535$	6.56252			0.283723
$536$	−40.1691			−1.73504
$537$	12.8894	+	9.59533i	0.556219	+	0.414069i
$538$	−40.3367	+	69.8653i	−1.73904	+	3.01211i
$539$	11.6712	+	20.2151i	0.502714	+	0.870727i
$540$	5.82774	−	16.0151i	0.250786	−	0.689181i
$541$	−25.5909			−1.10024			−0.550120	−	0.835086i	$-0.685418\pi$
$541$	−25.5909			−1.10024			−0.550120	+	0.835086i	$0.685418\pi$
$542$	−61.3695			−2.63605
$543$	−3.55866	+	30.4525i	−0.152717	+	1.30684i
$544$	−2.94451			−0.126245
$545$	−1.41936	−	2.45841i	−0.0607988	−	0.105307i
$546$	25.6769	−	0.191455i	1.09887	−	0.00819350i
$547$	−11.9024	+	20.6155i	−0.508909	+	0.881457i	0.491037	+	0.871139i	$0.336618\pi$
$547$	−11.9024	+	20.6155i	−0.508909	+	0.881457i	−0.999947	+	0.0103185i	$0.996715\pi$
$548$	−35.8876	+	62.1592i	−1.53304	+	2.65531i
$549$	−23.4840	−	5.56464i	−1.00227	−	0.237493i
$550$	−30.8351	−	53.4079i	−1.31481	−	2.27732i
$551$	12.2595	−	21.2341i	0.522272	−	0.904602i
$552$	5.22643	−	44.7241i	0.222452	−	1.90359i
$553$	5.00624	−	8.67107i	0.212887	−	0.368731i
$554$	−18.1802	−	31.4889i	−0.772401	−	1.33784i
$555$	−1.22932	+	10.5196i	−0.0521815	+	0.446533i
$556$	−8.83184	−	15.2972i	−0.374553	−	0.648746i
$557$	11.0730	−	19.1790i	0.469178	−	0.812639i	−0.530202	−	0.847872i	$-0.677884\pi$
$557$	11.0730	−	19.1790i	0.469178	−	0.812639i	0.999379	+	0.0352323i	$0.0112171\pi$
$558$	17.2824	−	18.3200i	0.731621	−	0.775546i
$559$	19.9224	+	8.41863i	0.842630	+	0.356070i
$560$	5.74878	−	9.95719i	0.242930	−	0.420768i
$561$	1.46274	+	1.08892i	0.0617569	+	0.0459740i
$562$	−70.2687			−2.96410
$563$	10.3612	−	17.9462i	0.436674	−	0.756341i	−0.560757	−	0.827980i	$-0.689490\pi$
$563$	10.3612	−	17.9462i	0.436674	−	0.756341i	0.997431	+	0.0716395i	$0.0228231\pi$
$564$	−22.9737	+	9.91054i	−0.967369	+	0.417309i
$565$	8.70206			0.366098
$566$	8.76621	+	15.1835i	0.368471	+	0.638211i
$567$	12.4500	+	6.25116i	0.522851	+	0.262524i
$568$	6.38877	+	11.0657i	0.268067	+	0.464306i
$569$	22.2713	+	38.5750i	0.933661	+	1.61715i	0.777005	+	0.629494i	$0.216738\pi$
$569$	22.2713	+	38.5750i	0.933661	+	1.61715i	0.156656	+	0.987653i	$0.449929\pi$
$570$	1.24359	−	10.6417i	0.0520881	−	0.445734i
$571$	16.8188	+	29.1310i	0.703845	+	1.21910i	0.967107	+	0.254371i	$0.0818685\pi$
$571$	16.8188	+	29.1310i	0.703845	+	1.21910i	−0.263261	+	0.964725i	$0.584798\pi$
$572$	85.1340	+	35.9751i	3.55963	+	1.50420i
$573$	0.109302	−	0.935329i	0.00456615	−	0.0390739i
$574$	−17.6850	−	30.6314i	−0.738159	−	1.27853i
$575$	−7.33291	+	12.7010i	−0.305804	+	0.529667i
$576$	−43.1037	−	10.2136i	−1.79599	−	0.425567i
$577$	30.4547			1.26784			0.633922	−	0.773397i	$-0.281444\pi$
$577$	30.4547			1.26784			0.633922	+	0.773397i	$0.281444\pi$
$578$	45.0423			1.87351
$579$	−4.96616	+	42.4969i	−0.206387	+	1.76611i
$580$	−11.2010	−	19.4008i	−0.465098	−	0.805573i
$581$	1.92907	−	3.34124i	0.0800312	−	0.138618i
$582$	−39.6533	+	17.1059i	−1.64368	+	0.709061i
$583$	6.30382	+	10.9185i	0.261077	+	0.452199i
$584$	−24.6615			−1.02050
$585$	0.762469	−	6.97543i	0.0315242	−	0.288399i
$586$	1.31460			0.0543055
$587$	−21.0143	−	36.3979i	−0.867354	−	1.50230i	−0.864690	−	0.502305i	$-0.832485\pi$
$587$	−21.0143	−	36.3979i	−0.867354	−	1.50230i	−0.00266391	−	0.999996i	$-0.500848\pi$
$588$	−32.3396	−	24.0747i	−1.33366	−	0.992826i
$589$	5.67267	−	9.82536i	0.233738	−	0.404847i
$590$	2.57101	+	4.45313i	0.105847	+	0.183332i
$591$	−25.0453	−	18.6446i	−1.03023	−	0.766938i
$592$	107.927			4.43576
$593$	−6.55587			−0.269217			−0.134609	−	0.990899i	$-0.542978\pi$
$593$	−6.55587			−0.269217			−0.134609	+	0.990899i	$0.542978\pi$
$594$	44.9858	+	53.6042i	1.84579	+	2.19941i
$595$	0.104260	−	0.180583i	0.00427424	−	0.00740320i
$596$	31.2745	+	54.1690i	1.28105	+	2.21885i
$597$	−27.3257	+	11.7879i	−1.11837	+	0.482447i
$598$	−3.78735	−	30.4390i	−0.154876	−	1.24474i
$599$	11.5220	+	19.9566i	0.470774	+	0.815405i	0.999441	−	0.0334242i	$-0.0106412\pi$
$599$	11.5220	+	19.9566i	0.470774	+	0.815405i	−0.528667	+	0.848829i	$0.677308\pi$
$600$	51.6418	+	38.4440i	2.10827	+	1.56947i
$601$	−2.90695	−	5.03498i	−0.118577	−	0.205381i	0.800627	−	0.599163i	$-0.204500\pi$
$601$	−2.90695	−	5.03498i	−0.118577	−	0.205381i	−0.919204	+	0.393782i	$0.871167\pi$
$602$	12.3322	+	21.3600i	0.502622	+	0.870567i
$603$	−14.4459	−	3.42302i	−0.588283	−	0.139396i
$604$	2.61629	+	4.53155i	0.106455	+	0.184386i
$605$	−9.53987			−0.387851
$606$	15.4529	+	11.5037i	0.627731	+	0.467306i
$607$	−16.4010	+	28.4074i	−0.665696	+	1.15302i	0.313400	+	0.949621i	$0.398532\pi$
$607$	−16.4010	+	28.4074i	−0.665696	+	1.15302i	−0.979096	+	0.203398i	$0.934801\pi$
$608$	−50.9021			−2.06435
$609$	16.8146	−	7.25356i	0.681360	−	0.293929i
$610$	−6.93130	+	12.0054i	−0.280640	+	0.486083i
$611$	−8.21727	+	6.21298i	−0.332435	+	0.251350i
$612$	−3.06476	−	0.726207i	−0.123885	−	0.0293552i
$613$	1.48010	−	2.56360i	0.0597805	−	0.103543i	−0.834586	−	0.550877i	$-0.814293\pi$
$613$	1.48010	−	2.56360i	0.0597805	−	0.103543i	0.894367	+	0.447334i	$0.147627\pi$
$614$	4.10056	+	7.10238i	0.165485	+	0.286629i
$615$	−8.87507	+	3.82858i	−0.357877	+	0.154383i
$616$	31.8521	+	55.1695i	1.28336	+	2.22284i
$617$	22.7498	−	39.4038i	0.915871	−	1.58634i	0.110251	−	0.993904i	$-0.464835\pi$
$617$	22.7498	−	39.4038i	0.915871	−	1.58634i	0.805620	−	0.592432i	$-0.201832\pi$
$618$	14.9987	+	11.1655i	0.603334	+	0.449144i
$619$	24.4251	−	42.3055i	0.981728	−	1.70040i	0.326069	−	0.945346i	$-0.394276\pi$
$619$	24.4251	−	42.3055i	0.981728	−	1.70040i	0.655659	−	0.755057i	$-0.272391\pi$
$620$	−5.18290	−	8.97705i	−0.208150	−	0.360527i
$621$	5.69075	−	15.6387i	0.228362	−	0.627557i
$622$	−10.9919	+	19.0385i	−0.440735	+	0.763376i
$623$	−2.72859	+	4.72605i	−0.109318	+	0.189345i
$624$	−71.5026	+	0.533145i	−2.86239	+	0.0213429i
$625$	−9.43227	−	16.3372i	−0.377291	−	0.653487i
$626$	76.8120			3.07003
$627$	25.2866	+	18.8242i	1.00985	+	0.751767i
$628$	−5.10126			−0.203562
$629$	1.95736			0.0780450
$630$	5.49105	−	5.82073i	0.218769	−	0.231903i
$631$	−10.2771	−	17.8004i	−0.409123	−	0.708622i	0.585669	−	0.810551i	$-0.300832\pi$
$631$	−10.2771	−	17.8004i	−0.409123	−	0.708622i	−0.994792	+	0.101929i	$0.967499\pi$
$632$	−26.2525	+	45.4707i	−1.04427	+	1.80873i
$633$	0.543449	−	4.65045i	0.0216001	−	0.184839i
$634$	−7.49716			−0.297750
$635$	8.08607			0.320886
$636$	−17.4672	−	13.0032i	−0.692618	−	0.515609i
$637$	−15.2906	−	6.46138i	−0.605838	−	0.256009i
$638$	91.9869			3.64180
$639$	1.35461	+	4.52394i	0.0535876	+	0.178964i
$640$	−3.52334	+	6.10260i	−0.139272	+	0.241227i
$641$	5.82969			0.230259			0.115129	−	0.993350i	$-0.463272\pi$
$641$	5.82969			0.230259			0.115129	+	0.993350i	$0.463272\pi$
$642$	5.40215	−	46.2278i	0.213206	−	1.82447i
$643$	−22.1314	+	38.3327i	−0.872777	+	1.51169i	−0.0136648	+	0.999907i	$0.504350\pi$
$643$	−22.1314	+	38.3327i	−0.872777	+	1.51169i	−0.859112	+	0.511787i	$0.828984\pi$
$644$	12.5323	−	21.7066i	0.493843	−	0.855361i
$645$	6.18879	−	2.66976i	0.243684	−	0.105122i
$646$	−1.98008			−0.0779053
$647$	8.63857	−	14.9624i	0.339617	−	0.588234i	−0.644744	−	0.764399i	$-0.723036\pi$
$647$	8.63857	−	14.9624i	0.339617	−	0.588234i	0.984361	+	0.176165i	$0.0563692\pi$
$648$	−65.2872	−	32.7808i	−2.56472	−	1.28775i
$649$	−15.1292			−0.593875
$650$	40.3976	+	17.0708i	1.58452	+	0.669573i
$651$	7.78037	−	3.35634i	0.304937	−	0.131545i
$652$	35.6818			1.39741
$653$	−6.95379			−0.272123			−0.136061	−	0.990700i	$-0.543444\pi$
$653$	−6.95379			−0.272123			−0.136061	+	0.990700i	$0.543444\pi$
$654$	−18.4860	+	7.97458i	−0.722858	+	0.311831i
$655$	−6.38892	+	11.0659i	−0.249636	+	0.432382i
$656$	49.2476	+	85.2994i	1.92280	+	3.33038i
$657$	−8.86893	−	2.10153i	−0.346010	−	0.0819886i
$658$	−11.7479			−0.457979
$659$	17.8455			0.695164			0.347582	−	0.937650i	$-0.387003\pi$
$659$	17.8455			0.695164			0.347582	+	0.937650i	$0.387003\pi$
$660$	26.4464	−	11.4086i	1.02943	−	0.444080i
$661$	−4.41391			−0.171681			−0.0858407	−	0.996309i	$-0.527358\pi$
$661$	−4.41391			−0.171681			−0.0858407	+	0.996309i	$0.527358\pi$
$662$	−16.1477	−	27.9686i	−0.627596	−	1.08703i
$663$	−1.29677	+	0.00966911i	−0.0503624	+	0.000375517i
$664$	−10.1159	+	17.5213i	−0.392574	+	0.679959i
$665$	1.80236	−	3.12177i	0.0698924	−	0.121057i
$666$	73.0906	+	17.3191i	2.83220	+	0.671103i
$667$	−10.9377	−	18.9447i	−0.423511	−	0.733542i
$668$	46.6560	−	80.8105i	1.80517	−	3.12665i
$669$	−8.30846	+	3.58415i	−0.321223	+	0.138571i
$670$	−4.26371	+	7.38496i	−0.164721	+	0.285306i
$671$	−20.3938	−	35.3231i	−0.787293	−	1.36363i
$672$	−30.4948	−	22.7014i	−1.17636	−	0.875727i
$673$	−14.1154	−	24.4486i	−0.544110	−	0.942426i	−0.998662	−	0.0517061i	$-0.983534\pi$
$673$	−14.1154	−	24.4486i	−0.544110	−	0.942426i	0.454552	−	0.890720i	$-0.349799\pi$
$674$	27.2563	−	47.2093i	1.04987	−	1.81843i
$675$	15.2958	+	18.2262i	0.588735	+	0.701527i
$676$	−63.7220	+	16.1064i	−2.45085	+	0.619478i
$677$	−6.30338	+	10.9178i	−0.242259	+	0.419604i	−0.961357	−	0.275304i	$-0.911222\pi$
$677$	−6.30338	+	10.9178i	−0.242259	+	0.419604i	0.719099	+	0.694908i	$0.244555\pi$
$678$	7.16338	−	61.2992i	0.275108	−	2.35418i
$679$	−14.5295			−0.557591
$680$	−0.546734	+	0.946971i	−0.0209663	+	0.0363147i
$681$	−1.12000	+	9.58419i	−0.0429186	+	0.367267i
$682$	42.5639			1.62985
$683$	−12.3897	−	21.4597i	−0.474081	−	0.821132i	0.525479	−	0.850807i	$-0.323886\pi$
$683$	−12.3897	−	21.4597i	−0.474081	−	0.821132i	−0.999560	+	0.0296749i	$0.990553\pi$
$684$	−52.9808	−	12.5540i	−2.02577	−	0.480016i
$685$	4.60477	+	7.97570i	0.175939	+	0.304736i
$686$	−23.8560	−	41.3198i	−0.910827	−	1.57760i
$687$	36.4023	−	15.7035i	1.38884	−	0.599124i
$688$	−34.3415	−	59.4812i	−1.30926	−	2.26770i
$689$	−8.25874	−	3.48990i	−0.314633	−	0.132955i
$690$	−7.66764	−	5.70806i	−0.291902	−	0.217302i
$691$	−8.40431	−	14.5567i	−0.319715	−	0.553762i	0.660714	−	0.750638i	$-0.270254\pi$
$691$	−8.40431	−	14.5567i	−0.319715	−	0.553762i	−0.980428	+	0.196876i	$0.936920\pi$
$692$	−4.44829	+	7.70466i	−0.169099	+	0.292887i
$693$	6.75361	+	22.5547i	0.256548	+	0.856784i
$694$	−57.6304			−2.18762
$695$	−2.26644			−0.0859710
$696$	−88.1748	+	38.0373i	−3.34226	+	1.44180i
$697$	0.893154	+	1.54699i	0.0338306	+	0.0585964i
$698$	−45.7526	+	79.2459i	−1.73176	+	2.99950i
$699$	3.09844	−	26.5143i	0.117194	−	1.00286i
$700$	17.9183	+	31.0354i	0.677249	+	1.17303i
$701$	11.1825			0.422358			0.211179	−	0.977447i	$-0.432270\pi$
$701$	11.1825			0.422358			0.211179	+	0.977447i	$0.432270\pi$
$702$	−48.5088	−	11.1130i	−1.83085	−	0.419435i
$703$	33.8371			1.27619
$704$	−37.4317	−	64.8336i	−1.41076	−	2.44351i
$705$	−0.372625	+	3.18867i	−0.0140339	+	0.120092i
$706$	−1.89557	+	3.28322i	−0.0713406	+	0.123566i
$707$	3.24073	+	5.61312i	0.121880	+	0.211103i
$708$	23.9937	−	10.3506i	0.901739	−	0.388998i
$709$	−26.3363			−0.989081			−0.494541	−	0.869154i	$-0.664664\pi$
$709$	−26.3363			−0.989081			−0.494541	+	0.869154i	$0.664664\pi$
$710$	2.71252			0.101799
$711$	−13.3159	+	14.1154i	−0.499386	+	0.529368i
$712$	14.3086	−	24.7832i	0.536237	−	0.928789i
$713$	−5.06107	−	8.76603i	−0.189539	−	0.328290i
$714$	−1.18624	−	0.883083i	−0.0443941	−	0.0330485i
$715$	9.45938	−	7.15213i	0.353761	−	0.267475i
$716$	−23.4524	−	40.6208i	−0.876458	−	1.51807i
$717$	−18.9927	+	8.19319i	−0.709296	+	0.305980i
$718$	11.0284	+	19.1018i	0.411577	+	0.712873i
$719$	−7.74314	−	13.4115i	−0.288770	−	0.500165i	0.684746	−	0.728782i	$-0.259913\pi$
$719$	−7.74314	−	13.4115i	−0.288770	−	0.500165i	−0.973516	+	0.228617i	$0.926580\pi$
$720$	−15.2910	+	16.2090i	−0.569861	+	0.604075i
$721$	3.14547	+	5.44812i	0.117143	+	0.202898i
$722$	16.2394			0.604369
$723$	−3.58377	+	30.6674i	−0.133282	+	1.14053i
$724$	44.7478	−	77.5055i	1.66304	−	2.88047i
$725$	31.2769			1.16159
$726$	−7.85305	+	67.2009i	−0.291454	+	2.49406i
$727$	11.8967	−	20.6057i	0.441225	−	0.764225i	−0.556555	−	0.830811i	$-0.687877\pi$
$727$	11.8967	−	20.6057i	0.441225	−	0.764225i	0.997781	+	0.0665857i	$0.0212106\pi$
$728$	−41.7300	−	17.6339i	−1.54662	−	0.653554i
$729$	−20.6857	−	17.3523i	−0.766135	−	0.642679i
$730$	−2.61767	+	4.53393i	−0.0968842	+	0.167808i
$731$	−0.622817	−	1.07875i	−0.0230357	−	0.0398991i
$732$	56.5088	+	42.0672i	2.08863	+	1.55485i
$733$	2.12642	+	3.68306i	0.0785410	+	0.136037i	0.902621	−	0.430437i	$-0.141641\pi$
$733$	2.12642	+	3.68306i	0.0785410	+	0.136037i	−0.824080	+	0.566474i	$0.808307\pi$
$734$	−41.0651	+	71.1268i	−1.51574	+	2.62534i
$735$	−4.74995	+	2.04906i	−0.175205	+	0.0755808i
$736$	−22.7070	+	39.3297i	−0.836991	+	1.44971i
$737$	−12.5450	−	21.7286i	−0.462101	−	0.800382i
$738$	19.6636	+	65.6696i	0.723825	+	2.41733i
$739$	−2.29397	+	3.97326i	−0.0843849	+	0.146159i	−0.905129	−	0.425137i	$-0.860226\pi$
$739$	−2.29397	+	3.97326i	−0.0843849	+	0.146159i	0.820744	+	0.571296i	$0.193559\pi$
$740$	15.4578	−	26.7738i	0.568241	−	0.984223i
$741$	−22.4174	+	0.167151i	−0.823526	+	0.00614045i
$742$	−5.11224	−	8.85465i	−0.187676	−	0.325065i
$743$	22.2171			0.815066			0.407533	−	0.913190i	$-0.366389\pi$
$743$	22.2171			0.815066			0.407533	+	0.913190i	$0.366389\pi$
$744$	−40.7999	+	17.6005i	−1.49580	+	0.645266i
$745$	8.02571			0.294039
$746$	−37.8722			−1.38660
$747$	−5.13105	+	5.43911i	−0.187735	+	0.199007i
$748$	−2.66147	−	4.60980i	−0.0973129	−	0.168551i
$749$	7.82945	−	13.5610i	0.286082	−	0.495508i
$750$	26.2519	−	11.3247i	0.958583	−	0.413519i
$751$	−9.66680			−0.352747			−0.176373	−	0.984323i	$-0.556437\pi$
$751$	−9.66680			−0.352747			−0.176373	+	0.984323i	$0.556437\pi$
$752$	32.7143			1.19297
$753$	2.47979	−	1.06975i	0.0903688	−	0.0389838i
$754$	−52.1798	+	39.4526i	−1.90028	+	1.43678i
$755$	0.671398			0.0244347
$756$	−26.1413	−	31.1495i	−0.950750	−	1.13290i
$757$	9.26864	−	16.0538i	0.336875	−	0.583484i	−0.646969	−	0.762517i	$-0.723964\pi$
$757$	9.26864	−	16.0538i	0.336875	−	0.583484i	0.983843	+	0.179033i	$0.0572968\pi$
$758$	16.8744			0.612905
$759$	25.8247	−	11.1404i	0.937379	−	0.404372i
$760$	−9.45147	+	16.3704i	−0.342841	+	0.593818i
$761$	−11.5733	+	20.0456i	−0.419533	+	0.726652i	−0.995892	−	0.0905442i	$-0.971139\pi$
$761$	−11.5733	+	20.0456i	−0.419533	+	0.726652i	0.576360	+	0.817196i	$0.304473\pi$
$762$	6.65631	−	56.9600i	0.241133	−	2.06344i
$763$	−6.77351			−0.245217
$764$	−1.37440	+	2.38053i	−0.0497240	+	0.0861245i
$765$	−0.277317	+	0.293967i	−0.0100264	+	0.0106284i
$766$	−77.3402			−2.79442
$767$	8.58210	−	6.48883i	0.309882	−	0.234298i
$768$	−0.941624	−	0.700979i	−0.0339779	−	0.0252944i
$769$	41.8358			1.50864			0.754318	−	0.656509i	$-0.227967\pi$
$769$	41.8358			1.50864			0.754318	+	0.656509i	$0.227967\pi$
$770$	13.5236			0.487358
$771$	3.98118	−	34.0681i	0.143379	−	1.22693i
$772$	62.4462	−	108.160i	2.24749	−	3.89277i
$773$	−8.76453	−	15.1806i	−0.315238	−	0.546009i	0.664250	−	0.747511i	$-0.268751\pi$
$773$	−8.76453	−	15.1806i	−0.315238	−	0.546009i	−0.979488	+	0.201502i	$0.935418\pi$
$774$	−13.7119	−	45.7929i	−0.492862	−	1.64599i
$775$	14.4723			0.519861
$776$	76.1921			2.73514
$777$	20.2714	+	15.0908i	0.727234	+	0.541379i
$778$	84.1267			3.01609
$779$	15.4401	+	26.7430i	0.553198	+	0.958168i
$780$	−10.1087	+	17.8142i	−0.361950	+	0.637852i
$781$	−3.99049	+	6.91173i	−0.142791	+	0.247321i
$782$	−0.883299	+	1.52992i	−0.0315867	+	0.0547098i
$783$	−34.9514	+	6.16543i	−1.24906	+	0.220335i
$784$	26.3574	+	45.6524i	0.941336	+	1.63044i
$785$	−0.327273	+	0.566854i	−0.0116809	+	0.0202319i
$786$	72.6916	+	54.1142i	2.59282	+	1.93019i
$787$	9.79754	−	16.9698i	0.349245	−	0.604909i	−0.636871	−	0.770970i	$-0.719772\pi$
$787$	9.79754	−	16.9698i	0.349245	−	0.604909i	0.986115	+	0.166061i	$0.0531049\pi$
$788$	45.5702	+	78.9300i	1.62337	+	2.81176i
$789$	−25.9588	+	11.1983i	−0.924159	+	0.398669i
$790$	5.57309	+	9.65288i	0.198282	+	0.343434i
$791$	10.3820	−	17.9822i	0.369142	−	0.639373i
$792$	−35.4156	−	118.276i	−1.25844	−	4.20275i
$793$	26.7182	+	11.2903i	0.948793	+	0.400932i
$794$	−20.9646	+	36.3118i	−0.744006	+	1.28866i
$795$	−2.56553	+	1.10673i	−0.0909900	+	0.0392518i
$796$	86.8688			3.07898
$797$	5.36406	−	9.29083i	0.190005	−	0.329098i	−0.755247	−	0.655441i	$-0.772483\pi$
$797$	5.36406	−	9.29083i	0.190005	−	0.329098i	0.945252	+	0.326343i	$0.105816\pi$
$798$	−20.5068	−	15.2660i	−0.725932	−	0.540410i
$799$	0.593307			0.0209897
$800$	−32.4658	−	56.2323i	−1.14784	−	1.98811i
$801$	7.25766	−	7.69340i	0.256437	−	0.271833i
$802$	−1.00805	−	1.74600i	−0.0355956	−	0.0616534i
$803$	−7.70189	−	13.3401i	−0.271794	−	0.470760i
$804$	34.7607	+	25.8771i	1.22592	+	0.912616i
$805$	−1.60803	−	2.78519i	−0.0566757	−	0.0981652i
$806$	−24.1445	+	18.2554i	−0.850452	+	0.643018i
$807$	48.3011	−	20.8364i	1.70028	−	0.733477i
$808$	−16.9943	−	29.4349i	−0.597856	−	1.03552i
$809$	−21.3013	+	36.8949i	−0.748914	+	1.29716i	0.199430	+	0.979912i	$0.436091\pi$
$809$	−21.3013	+	36.8949i	−0.748914	+	1.29716i	−0.948344	+	0.317245i	$0.897242\pi$
$810$	−12.9565	+	8.52337i	−0.455245	+	0.299481i
$811$	−12.5260			−0.439847			−0.219923	−	0.975517i	$-0.570581\pi$
$811$	−12.5260			−0.439847			−0.219923	+	0.975517i	$0.570581\pi$
$812$	−53.4538			−1.87586
$813$	32.0987	+	23.8954i	1.12575	+	0.838049i
$814$	63.4727	+	109.938i	2.22472	+	3.85332i
$815$	2.28918	−	3.96497i	0.0801864	−	0.138887i
$816$	3.30334	+	2.45913i	0.115640	+	0.0860866i
$817$	−10.7667	−	18.6485i	−0.376680	−	0.652429i
$818$	71.6436			2.50496
$819$	−13.5046	−	9.89766i	−0.471888	−	0.345852i
$820$	28.2140			0.985276
$821$	−19.4744	−	33.7306i	−0.679661	−	1.17721i	−0.975083	−	0.221840i	$-0.928794\pi$
$821$	−19.4744	−	33.7306i	−0.679661	−	1.17721i	0.295422	−	0.955367i	$-0.404540\pi$
$822$	59.9731	−	25.8716i	2.09180	−	0.902374i
$823$	−19.7923	+	34.2812i	−0.689916	+	1.19497i	0.281949	+	0.959429i	$0.409019\pi$
$823$	−19.7923	+	34.2812i	−0.689916	+	1.19497i	−0.971865	+	0.235540i	$0.924314\pi$
$824$	−16.4947	−	28.5697i	−0.574620	−	0.995271i
$825$	−4.66745	+	39.9407i	−0.162500	+	1.39056i
$826$	12.2694			0.426908
$827$	−19.0344			−0.661890			−0.330945	−	0.943650i	$-0.607367\pi$
$827$	−19.0344			−0.661890			−0.330945	+	0.943650i	$0.607367\pi$
$828$	−33.3343	+	35.3356i	−1.15845	+	1.22800i
$829$	−5.06015	+	8.76445i	−0.175746	+	0.304402i	−0.940419	−	0.340017i	$-0.889567\pi$
$829$	−5.06015	+	8.76445i	−0.175746	+	0.304402i	0.764673	+	0.644419i	$0.222901\pi$
$830$	2.14749	+	3.71957i	0.0745405	+	0.129108i
$831$	−2.75189	+	23.5488i	−0.0954621	+	0.816898i
$832$	49.0399	+	20.7228i	1.70015	+	0.718435i
$833$	0.478018	+	0.827951i	0.0165623	+	0.0286868i
$834$	−1.86569	+	15.9653i	−0.0646037	+	0.552833i
$835$	−5.98647	−	10.3689i	−0.207170	−	0.358829i
$836$	−46.0092	−	79.6902i	−1.59126	−	2.75614i
$837$	−16.1726	+	2.85285i	−0.559007	+	0.0986088i
$838$	14.0804	+	24.3880i	0.486399	+	0.842468i
$839$	27.2305			0.940100			0.470050	−	0.882640i	$-0.344236\pi$
$839$	27.2305			0.940100			0.470050	+	0.882640i	$0.344236\pi$
$840$	−12.9632	+	5.59214i	−0.447272	+	0.192947i
$841$	−8.82620	+	15.2874i	−0.304352	+	0.527153i
$842$	−44.3904			−1.52979
$843$	36.7533	+	27.3605i	1.26585	+	0.942345i
$844$	−6.83351	+	11.8360i	−0.235219	+	0.407411i
$845$	−2.29836	+	8.11413i	−0.0790658	+	0.279135i
$846$	22.1549	+	5.24971i	0.761702	+	0.180489i
$847$	−11.3816	+	19.7135i	−0.391076	+	0.677363i
$848$	14.2361	+	24.6576i	0.488869	+	0.846746i
$849$	1.32692	−	11.3549i	0.0455399	−	0.389699i
$850$	−1.26291	−	2.18743i	−0.0433176	−	0.0750282i
$851$	15.0945	−	26.1444i	0.517432	−	0.896218i
$852$	1.59998	−	13.6915i	0.0548143	−	0.469062i
$853$	−4.43767	+	7.68627i	−0.151943	+	0.263173i	−0.931942	−	0.362608i	$-0.881886\pi$
$853$	−4.43767	+	7.68627i	−0.151943	+	0.263173i	0.779999	+	0.625781i	$0.215220\pi$
$854$	16.5388	+	28.6461i	0.565948	+	0.980250i
$855$	−4.79402	+	5.08184i	−0.163952	+	0.173795i
$856$	−41.0572	+	71.1132i	−1.40331	+	2.43060i
$857$	−18.5179	+	32.0740i	−0.632560	+	1.09563i	0.354467	+	0.935069i	$0.384662\pi$
$857$	−18.5179	+	32.0740i	−0.632560	+	1.09563i	−0.987027	+	0.160557i	$0.948671\pi$
$858$	−42.5944	−	72.5214i	−1.45415	−	2.47584i
$859$	−23.2978	−	40.3530i	−0.794912	−	1.37683i	−0.922895	−	0.385052i	$-0.874184\pi$
$859$	−23.2978	−	40.3530i	−0.794912	−	1.37683i	0.127983	−	0.991776i	$-0.459150\pi$
$860$	−19.6743			−0.670887
$861$	−2.67695	+	22.9074i	−0.0912301	+	0.780683i
$862$	−22.0563			−0.751240
$863$	−38.8584			−1.32275			−0.661377	−	0.750053i	$-0.730028\pi$
$863$	−38.8584			−1.32275			−0.661377	+	0.750053i	$0.730028\pi$
$864$	47.3648	+	56.4390i	1.61138	+	1.92009i
$865$	0.570764	+	0.988591i	0.0194065	+	0.0336131i
$866$	−0.104682	+	0.181315i	−0.00355724	+	0.00616132i
$867$	−23.5589	−	17.5381i	−0.800103	−	0.595625i
$868$	−24.7339			−0.839525
$869$	−32.7951			−1.11250
$870$	−2.36618	+	20.2481i	−0.0802209	+	0.686475i
$871$	16.4354	+	6.94512i	0.556893	+	0.235326i
$872$	35.5199			1.20286
$873$	27.4008	+	6.49273i	0.927375	+	0.219746i
$874$	−15.2697	+	26.4479i	−0.516506	+	0.894614i
$875$	9.61905			0.325183
$876$	21.3410	+	15.8870i	0.721047	+	0.536773i
$877$	8.10630	−	14.0405i	0.273730	−	0.474115i	−0.696084	−	0.717961i	$-0.745076\pi$
$877$	8.10630	−	14.0405i	0.273730	−	0.474115i	0.969814	+	0.243846i	$0.0784091\pi$
$878$	34.1890	−	59.2170i	1.15382	−	1.99848i
$879$	−0.687586	−	0.511864i	−0.0231917	−	0.0172647i
$880$	−37.6594			−1.26950
$881$	−17.4979	+	30.3072i	−0.589518	+	1.02107i	0.404778	+	0.914415i	$0.367349\pi$
$881$	−17.4979	+	30.3072i	−0.589518	+	1.02107i	−0.994296	+	0.106660i	$0.965984\pi$
$882$	10.5240	+	35.1465i	0.354360	+	1.18344i
$883$	−22.3562			−0.752346			−0.376173	−	0.926549i	$-0.622760\pi$
$883$	−22.3562			−0.752346			−0.376173	+	0.926549i	$0.622760\pi$
$884$	3.48684	+	1.47343i	0.117275	+	0.0495569i
$885$	0.389169	−	3.33024i	0.0130818	−	0.111945i
$886$	−75.2871			−2.52932
$887$	−13.8753			−0.465886			−0.232943	−	0.972490i	$-0.574836\pi$
$887$	−13.8753			−0.465886			−0.232943	+	0.972490i	$0.574836\pi$
$888$	−106.302	−	79.1353i	−3.56728	−	2.65561i
$889$	9.64712	−	16.7093i	0.323554	−	0.560412i
$890$	−3.03754	−	5.26117i	−0.101819	−	0.176355i
$891$	−2.65749	−	45.5532i	−0.0890293	−	1.52609i
$892$	26.4127			0.884363
$893$	10.2566			0.343223
$894$	6.60662	−	56.5348i	0.220958	−	1.89081i
$895$	−6.01840			−0.201173
$896$	8.40707	+	14.5615i	0.280861	+	0.486465i
$897$	−9.87109	+	17.3955i	−0.329586	+	0.580819i
$898$	−5.80953	+	10.0624i	−0.193866	+	0.335787i
$899$	−10.7934	+	18.6947i	−0.359981	+	0.623505i
$900$	−19.9230	−	66.5359i	−0.664099	−	2.21786i
$901$	0.258185	+	0.447190i	0.00860141	+	0.0148981i
$902$	−57.9259	+	100.331i	−1.92872	+	3.34064i
$903$	1.86670	−	15.9739i	0.0621198	−	0.531578i
$904$	−54.4429	+	94.2978i	−1.81074	+	3.13630i
$905$	−5.74163	−	9.94479i	−0.190858	−	0.330576i
$906$	0.552683	−	4.72947i	0.0183617	−	0.157126i
$907$	23.5396	+	40.7718i	0.781621	+	1.35381i	0.930997	+	0.365026i	$0.118940\pi$
$907$	23.5396	+	40.7718i	0.781621	+	1.35381i	−0.149376	+	0.988780i	$0.547727\pi$
$908$	14.0833	−	24.3930i	0.467371	−	0.809509i
$909$	−3.60330	−	12.0338i	−0.119514	−	0.399135i
$910$	−7.67132	+	5.80020i	−0.254302	+	0.192275i
$911$	18.3507	−	31.7844i	0.607987	−	1.05306i	−0.383585	−	0.923505i	$-0.625311\pi$
$911$	18.3507	−	31.7844i	0.607987	−	1.05306i	0.991572	−	0.129558i	$-0.0413559\pi$
$912$	57.1053	+	42.5113i	1.89095	+	1.40769i
$913$	−12.6370			−0.418224
$914$	−18.0054	+	31.1862i	−0.595565	+	1.03155i
$915$	8.29987	−	3.58045i	0.274385	−	0.118366i
$916$	−115.724			−3.82362
$917$	15.2447	+	26.4045i	0.503423	+	0.871955i
$918$	1.84248	+	2.19547i	0.0608110	+	0.0724613i
$919$	−3.87476	−	6.71128i	−0.127817	−	0.221385i	0.795014	−	0.606591i	$-0.207464\pi$
$919$	−3.87476	−	6.71128i	−0.127817	−	0.221385i	−0.922830	+	0.385206i	$0.874130\pi$
$920$	8.43245	+	14.6054i	0.278010	+	0.481527i
$921$	0.620694	−	5.31146i	0.0204526	−	0.175019i
$922$	2.66412	+	4.61439i	0.0877381	+	0.151967i
$923$	−0.700779	−	5.63219i	−0.0230664	−	0.185386i
$924$	7.97691	−	68.2608i	0.262421	−	2.24561i
$925$	21.5816	+	37.3804i	0.709599	+	1.22906i
$926$	55.1048	−	95.4443i	1.81085	−	3.13649i
$927$	−3.49737	−	11.6800i	−0.114869	−	0.383623i
$928$	96.8515			3.17931
$929$	−19.0269			−0.624253			−0.312127	−	0.950040i	$-0.601041\pi$
$929$	−19.0269			−0.624253			−0.312127	+	0.950040i	$0.601041\pi$
$930$	−1.09487	+	9.36912i	−0.0359022	+	0.307226i
$931$	8.26356	+	14.3129i	0.270827	+	0.469086i
$932$	−38.9609	+	67.4823i	−1.27621	+	2.21045i
$933$	13.1622	−	5.67800i	0.430912	−	0.185889i
$934$	−33.2917	−	57.6630i	−1.08934	−	1.88679i
$935$	−0.682990			−0.0223362
$936$	70.8174	+	51.9028i	2.31474	+	1.69650i
$937$	−19.2901			−0.630179			−0.315090	−	0.949062i	$-0.602035\pi$
$937$	−19.2901			−0.630179			−0.315090	+	0.949062i	$0.602035\pi$
$938$	10.1737	+	17.6213i	0.332182	+	0.575357i
$939$	−40.1758	−	29.9083i	−1.31109	−	0.976019i
$940$	4.68552	−	8.11555i	0.152825	−	0.264700i
$941$	19.9180	+	34.4989i	0.649307	+	1.12463i	0.983289	+	0.182053i	$0.0582744\pi$
$941$	19.9180	+	34.4989i	0.649307	+	1.12463i	−0.333981	+	0.942580i	$0.608392\pi$
$942$	3.72364	+	2.77201i	0.121323	+	0.0903169i
$943$	27.5508			0.897177
$944$	−34.1668			−1.11203
$945$	−5.13845	+	0.906423i	−0.167154	+	0.0294860i
$946$	40.3931	−	69.9629i	1.31329	−	2.27469i
$947$	8.11418	+	14.0542i	0.263675	+	0.456699i	0.967216	−	0.253956i	$-0.0817319\pi$
$947$	8.11418	+	14.0542i	0.263675	+	0.456699i	−0.703540	+	0.710655i	$0.748399\pi$
$948$	52.0103	−	22.4365i	1.68922	−	0.728704i
$949$	10.0904	+	4.26389i	0.327547	+	0.138412i
$950$	−21.8322	−	37.8144i	−0.708329	−	1.22686i
$951$	3.92131	+	2.91916i	0.127157	+	0.0946604i
$952$	1.30457	+	2.25958i	0.0422813	+	0.0732333i
$953$	4.95942	+	8.58997i	0.160651	+	0.278256i	0.935102	−	0.354377i	$-0.115307\pi$
$953$	4.95942	+	8.58997i	0.160651	+	0.278256i	−0.774451	+	0.632634i	$0.781974\pi$
$954$	5.68417	+	18.9832i	0.184032	+	0.614604i
$955$	0.176350	+	0.305448i	0.00570656	+	0.00988405i
$956$	60.3781			1.95277
$957$	−48.1128	−	35.8169i	−1.55527	−	1.15780i
$958$	−8.11789	+	14.0606i	−0.262277	+	0.454278i
$959$	21.9750			0.709609
$960$	15.2340	−	6.57172i	0.491675	−	0.212101i
$961$	10.5057	−	18.1964i	0.338894	−	0.586981i
$962$	−83.1567	−	35.1395i	−2.68108	−	1.13294i
$963$	−20.8253	+	22.0756i	−0.671084	+	0.711375i
$964$	45.0635	−	78.0523i	1.45140	−	2.51389i
$965$	−8.01253	−	13.8781i	−0.257932	−	0.446752i
$966$	−20.9432	+	9.03461i	−0.673837	+	0.290684i
$967$	17.1795	+	29.7558i	0.552456	+	0.956882i	0.998097	+	0.0616702i	$0.0196427\pi$
$967$	17.1795	+	29.7558i	0.552456	+	0.956882i	−0.445640	+	0.895212i	$0.647024\pi$
$968$	59.6845	−	103.377i	1.91833	−	3.32265i
$969$	1.03566	+	0.770984i	0.0332703	+	0.0247676i
$970$	8.08733	−	14.0077i	0.259669	−	0.449759i
$971$	28.7211	+	49.7464i	0.921705	+	1.59644i	0.796777	+	0.604273i	$0.206537\pi$
$971$	28.7211	+	49.7464i	0.921705	+	1.59644i	0.124928	+	0.992166i	$0.460130\pi$
$972$	35.3795	+	70.4256i	1.13480	+	2.25890i
$973$	−2.70399	+	4.68344i	−0.0866859	+	0.150144i
$974$	14.7446	−	25.5383i	0.472446	−	0.818300i
$975$	−14.4827	−	24.6583i	−0.463817	−	0.789698i
$976$	−46.0558	−	79.7711i	−1.47421	−	2.55341i
$977$	−17.1534			−0.548787			−0.274394	−	0.961617i	$-0.588477\pi$
$977$	−17.1534			−0.548787			−0.274394	+	0.961617i	$0.588477\pi$
$978$	−26.0457	−	19.3894i	−0.832850	−	0.620003i
$979$	17.8745			0.571273
$980$	15.1002			0.482358
$981$	12.7739	+	3.02684i	0.407841	+	0.0966397i
$982$	3.02438	+	5.23839i	0.0965119	+	0.167164i
$983$	−30.5798	+	52.9658i	−0.975346	+	1.68935i	−0.296556	+	0.955016i	$0.595838\pi$
$983$	−30.5798	+	52.9658i	−0.975346	+	1.68935i	−0.678790	+	0.734333i	$0.737495\pi$
$984$	14.0378	−	120.125i	0.447508	−	3.82946i
$985$	11.6943			0.372612
$986$	3.76751			0.119982
$987$	6.14459	+	4.57426i	0.195585	+	0.145600i
$988$	60.2774	+	25.4714i	1.91768	+	0.810355i
$989$	−19.2118			−0.610900
$990$	−25.5038	−	6.04325i	−0.810565	−	0.192067i
$991$	11.0154	−	19.0792i	0.349915	−	0.606071i	−0.636319	−	0.771426i	$-0.719544\pi$
$991$	11.0154	−	19.0792i	0.349915	−	0.606071i	0.986234	+	0.165355i	$0.0528770\pi$
$992$	44.8148			1.42287
$993$	−2.44424	+	20.9161i	−0.0775656	+	0.663752i
$994$	3.23618	−	5.60524i	0.102646	−	0.177787i
$995$	5.57310	−	9.65290i	0.176679	−	0.306018i
$996$	20.0413	−	8.64551i	0.635031	−	0.273944i
$997$	32.8900			1.04164			0.520818	−	0.853668i	$-0.325627\pi$
$997$	32.8900			1.04164			0.520818	+	0.853668i	$0.325627\pi$
$998$	15.0788	−	26.1173i	0.477311	−	0.826727i
$999$	−31.4857	−	37.5178i	−0.996164	−	1.18701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.f.a.61.12	✓	24
3.2	odd	2		351.2.f.a.100.1		24
9.4	even	3		117.2.h.a.22.1	yes	24
9.5	odd	6		351.2.h.a.334.12		24
13.3	even	3		117.2.h.a.16.1	yes	24
39.29	odd	6		351.2.h.a.289.12		24
117.68	odd	6		351.2.f.a.172.1		24
117.94	even	3	inner	117.2.f.a.94.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.12	✓	24	1.1	even	1	trivial
117.2.f.a.94.12	yes	24	117.94	even	3	inner
117.2.h.a.16.1	yes	24	13.3	even	3
117.2.h.a.22.1	yes	24	9.4	even	3
351.2.f.a.100.1		24	3.2	odd	2
351.2.f.a.172.1		24	117.68	odd	6
351.2.h.a.289.12		24	39.29	odd	6
351.2.h.a.334.12		24	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32814 + 2.30041i) q^{2} +(0.201038 - 1.72034i) q^{3} +(-2.52792 + 4.37849i) q^{4} +(0.324360 + 0.561808i) q^{5} +(4.22450 - 1.82239i) q^{6} +1.54792 q^{7} -8.11720 q^{8} +(-2.91917 - 0.691710i) q^{9} +(-0.861592 + 1.49232i) q^{10} +(-2.53504 - 4.39082i) q^{11} +(7.02430 + 5.22914i) q^{12} +(3.32120 + 1.40344i) q^{13} +(2.05585 + 3.56084i) q^{14} +(1.03171 - 0.445066i) q^{15} +(-5.72495 - 9.91590i) q^{16} +(-0.103828 - 0.179835i) q^{17} +(-2.28585 - 7.63397i) q^{18} +(-1.79488 - 3.10883i) q^{19} -3.27983 q^{20} +(0.311190 - 2.66295i) q^{21} +(6.73378 - 11.6633i) q^{22} -3.20273 q^{23} +(-1.63187 + 13.9644i) q^{24} +(2.28958 - 3.96567i) q^{25} +(1.18254 + 9.50408i) q^{26} +(-1.77684 + 4.88291i) q^{27} +(-3.91301 + 6.77754i) q^{28} +(3.41513 + 5.91518i) q^{29} +(2.39409 + 1.78225i) q^{30} +(1.58024 + 2.73705i) q^{31} +(7.08989 - 12.2800i) q^{32} +(-8.06335 + 3.47842i) q^{33} +(0.275796 - 0.477692i) q^{34} +(0.502082 + 0.869631i) q^{35} +(10.4081 - 11.0330i) q^{36} +(-4.71300 + 8.16316i) q^{37} +(4.76772 - 8.25793i) q^{38} +(3.08209 - 5.43146i) q^{39} +(-2.63289 - 4.56031i) q^{40} -8.60228 q^{41} +(6.53918 - 2.82091i) q^{42} +5.99857 q^{43} +25.6335 q^{44} +(-0.558253 - 1.86437i) q^{45} +(-4.25368 - 7.36759i) q^{46} +(-1.42859 + 2.47438i) q^{47} +(-18.2097 + 7.85540i) q^{48} -4.60396 q^{49} +12.1636 q^{50} +(-0.330251 + 0.142466i) q^{51} +(-14.5407 + 10.9940i) q^{52} -2.48667 q^{53} +(-13.5926 + 2.39773i) q^{54} +(1.64453 - 2.84841i) q^{55} -12.5647 q^{56} +(-5.70909 + 2.46282i) q^{57} +(-9.07155 + 15.7124i) q^{58} +(1.49201 - 2.58424i) q^{59} +(-0.659371 + 5.64243i) q^{60} +8.04476 q^{61} +(-4.19756 + 7.27038i) q^{62} +(-4.51863 - 1.07071i) q^{63} +14.7657 q^{64} +(0.288800 + 2.32109i) q^{65} +(-18.7111 - 13.9292i) q^{66} +4.94864 q^{67} +1.04987 q^{68} +(-0.643871 + 5.50980i) q^{69} +(-1.33367 + 2.30999i) q^{70} +(-0.787066 - 1.36324i) q^{71} +(23.6955 + 5.61475i) q^{72} +3.03817 q^{73} -25.0382 q^{74} +(-6.36203 - 4.73612i) q^{75} +18.1493 q^{76} +(-3.92403 - 6.79661i) q^{77} +(16.5880 - 0.123685i) q^{78} +(3.23418 - 5.60177i) q^{79} +(3.71389 - 6.43264i) q^{80} +(8.04308 + 4.03843i) q^{81} +(-11.4251 - 19.7888i) q^{82} +(1.24623 - 2.15854i) q^{83} +(10.8730 + 8.09427i) q^{84} +(0.0673550 - 0.116662i) q^{85} +(7.96696 + 13.7992i) q^{86} +(10.8627 - 4.68602i) q^{87} +(20.5774 + 35.6411i) q^{88} +(-1.76275 + 3.05317i) q^{89} +(3.54738 - 3.76036i) q^{90} +(5.14094 + 2.17241i) q^{91} +(8.09626 - 14.0231i) q^{92} +(5.02635 - 2.16830i) q^{93} -7.58946 q^{94} +(1.16438 - 2.01676i) q^{95} +(-19.7006 - 14.6658i) q^{96} -9.38650 q^{97} +(-6.11471 - 10.5910i) q^{98} +(4.36303 + 14.5710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more